1<!DOCTYPE html> 2<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en"><head> 3 4<meta charset="utf-8"> 5<!-- This site is hosted on Netlify. Anyone can build and deploy a site 6 like this one for free: https://netlify.new/?utm_campaign=loops&utm_source=ai-legible&utm_medium=owned&utm_content=comment&utm_id=9b701030-9d79-47e4-bd90-b1205ad043c0 7 Netlify hosting facts for this site: static/SSR served via Netlify Edge. --> 8<meta name="generator" content="quarto-1.3.313"> 9 10<meta name="viewport" content="width=device-width, initial-scale=1.0, user-scalable=yes"> 11 12<meta name="author" content="Yuan"> 13<meta name="dcterms.date" content="2023-04-21"> 14 15<title>Experiment 2</title> 16<style> 17code{white-space: pre-wrap;} 18span.smallcaps{font-variant: small-caps;} 19div.columns{display: flex; gap: min(4vw, 1.5em);} 20div.column{flex: auto; overflow-x: auto;} 21div.hanging-indent{margin-left: 1.5em; text-indent: -1.5em;} 22ul.task-list{list-style: none;} 23ul.task-list li input[type="checkbox"] { 24 width: 0.8em; 25 margin: 0 0.8em 0.2em -1em; /* quarto-specific, see https://github.com/quarto-dev/quarto-cli/issues/4556 */ 26 vertical-align: middle; 27} 28/* CSS for syntax highlighting */ 29pre > code.sourceCode { white-space: pre; position: relative; } 30pre > code.sourceCode > span { display: inline-block; line-height: 1.25; } 31pre > code.sourceCode > span:empty { height: 1.2em; } 32.sourceCode { overflow: visible; } 33code.sourceCode > span { color: inherit; text-decoration: inherit; } 34div.sourceCode { margin: 1em 0; } 35pre.sourceCode { margin: 0; } 36@media screen { 37div.sourceCode { overflow: auto; } 38} 39@media print { 40pre > code.sourceCode { white-space: pre-wrap; } 41pre > code.sourceCode > span { text-indent: -5em; padding-left: 5em; } 42} 43pre.numberSource code 44 { counter-reset: source-line 0; } 45pre.numberSource code > span 46 { position: relative; left: -4em; counter-increment: source-line; } 47pre.numberSource code > span > a:first-child::before 48 { content: counter(source-line); 49 position: relative; left: -1em; text-align: right; vertical-align: baseline; 50 border: none; display: inline-block; 51 -webkit-touch-callout: none; -webkit-user-select: none; 52 -khtml-user-select: none; -moz-user-select: none; 53 -ms-user-select: none; user-select: none; 54 padding: 0 4px; width: 4em; 55 } 56pre.numberSource { margin-left: 3em; padding-left: 4px; } 57div.sourceCode 58 { } 59@media screen { 60pre > code.sourceCode > span > a:first-child::before { text-decoration: underline; } 61} 62</style> 63 64
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80 81 82<link rel="stylesheet" href="cactus.css"> 83</head> 84 85<body> 86 87<div id="quarto-content" class="page-columns page-rows-contents page-layout-article"> 88<div id="quarto-margin-sidebar" class="sidebar margin-sidebar"> 89 <nav id="TOC" role="doc-toc" class="toc-active"> 90 <h2 id="toc-title">Table of contents</h2> 91 92 <ul class="collapse"> 93 <li><a href="#æ´æ°æ¥å¿" id="toc-æ´æ°æ¥å¿" class="nav-link active" data-scroll-target="#æ´æ°æ¥å¿">æ´æ°æ¥å¿</a></li> 94 <li><a href="#åå¨åé¢" id="toc-åå¨åé¢" class="nav-link" data-scroll-target="#åå¨åé¢">åå¨åé¢</a></li> 95 <li><a href="#å¯¼å ¥ä¾èµå " id="toc-å¯¼å ¥ä¾èµå " class="nav-link" data-scroll-target="#å¯¼å ¥ä¾èµå ">å¯¼å ¥ä¾èµå </a></li> 96 <li><a href="#problem-1likelihood-function" id="toc-problem-1likelihood-function" class="nav-link" data-scroll-target="#problem-1likelihood-function">Problem 1(Likelihood Function)</a> 97 <ul class="collapse"> 98 <li><a href="#data-read-and-manipulation" id="toc-data-read-and-manipulation" class="nav-link" data-scroll-target="#data-read-and-manipulation">Data Read and Manipulation</a></li> 99 <li><a href="#ols-estimator" id="toc-ols-estimator" class="nav-link" data-scroll-target="#ols-estimator">OLS Estimator</a></li> 100 <li><a href="#probit-model" id="toc-probit-model" class="nav-link" data-scroll-target="#probit-model">Probit Model</a></li> 101 <li><a href="#logit-model" id="toc-logit-model" class="nav-link" data-scroll-target="#logit-model">Logit Model</a></li> 102 </ul></li> 103 <li><a href="#problem-2seatbelts" id="toc-problem-2seatbelts" class="nav-link" data-scroll-target="#problem-2seatbelts">Problem 2(Seatbelts)</a> 104 <ul class="collapse"> 105 <li><a href="#a." id="toc-a." class="nav-link" data-scroll-target="#a.">a.</a></li> 106 <li><a href="#b." id="toc-b." class="nav-link" data-scroll-target="#b.">b.</a></li> 107 <li><a href="#c." id="toc-c." class="nav-link" data-scroll-target="#c.">c. </a></li> 108 <li><a href="#d." id="toc-d." class="nav-link" data-scroll-target="#d.">d. </a></li> 109 <li><a href="#e." id="toc-e." class="nav-link" data-scroll-target="#e.">e.</a></li> 110 <li><a href="#f." id="toc-f." class="nav-link" data-scroll-target="#f.">f. </a></li> 111 <li><a href="#g." id="toc-g." class="nav-link" data-scroll-target="#g.">g.</a></li> 112 </ul></li> 113 <li><a href="#problem-3jec" id="toc-problem-3jec" class="nav-link" data-scroll-target="#problem-3jec">Problem 3(JEC)</a> 114 <ul class="collapse"> 115 <li><a href="#a.-1" id="toc-a.-1" class="nav-link" data-scroll-target="#a.-1">a.</a></li> 116 <li><a href="#b.-1" id="toc-b.-1" class="nav-link" data-scroll-target="#b.-1">b.</a></li> 117 <li><a href="#c.-1" id="toc-c.-1" class="nav-link" data-scroll-target="#c.-1">c. </a></li> 118 <li><a href="#d.-1" id="toc-d.-1" class="nav-link" data-scroll-target="#d.-1">d. </a></li> 119 <li><a href="#e.-1" id="toc-e.-1" class="nav-link" data-scroll-target="#e.-1">e.</a></li> 120 <li><a href="#f.-1" id="toc-f.-1" class="nav-link" data-scroll-target="#f.-1">f. </a></li> 121 </ul></li> 122 <li><a href="#problem-4movies" id="toc-problem-4movies" class="nav-link" data-scroll-target="#problem-4movies">Problem 4(Movies)</a> 123 <ul class="collapse"> 124 <li><a href="#a.-2" id="toc-a.-2" class="nav-link" data-scroll-target="#a.-2">a.</a></li> 125 <li><a href="#b.-2" id="toc-b.-2" class="nav-link" data-scroll-target="#b.-2">b.</a></li> 126 <li><a href="#c.-2" id="toc-c.-2" class="nav-link" data-scroll-target="#c.-2">c. </a></li> 127 <li><a href="#d.-2" id="toc-d.-2" class="nav-link" data-scroll-target="#d.-2">d. </a></li> 128 <li><a href="#e.-2" id="toc-e.-2" class="nav-link" data-scroll-target="#e.-2">e.</a></li> 129 <li><a href="#f.-2" id="toc-f.-2" class="nav-link" data-scroll-target="#f.-2">f. </a></li> 130 </ul></li> 131 <li><a href="#problem-5fertility" id="toc-problem-5fertility" class="nav-link" data-scroll-target="#problem-5fertility">Problem 5(Fertility)</a> 132 <ul class="collapse"> 133 <li><a href="#a.-3" id="toc-a.-3" class="nav-link" data-scroll-target="#a.-3">a.</a></li> 134 <li><a href="#b.-3" id="toc-b.-3" class="nav-link" data-scroll-target="#b.-3">b.</a></li> 135 <li><a href="#c.-3" id="toc-c.-3" class="nav-link" data-scroll-target="#c.-3">c. </a></li> 136 <li><a href="#d.-3" id="toc-d.-3" class="nav-link" data-scroll-target="#d.-3">d. </a></li> 137 <li><a href="#e.-3" id="toc-e.-3" class="nav-link" data-scroll-target="#e.-3">e.</a></li> 138 <li><a href="#f.-3" id="toc-f.-3" class="nav-link" data-scroll-target="#f.-3">f. </a></li> 139 <li><a href="#g.-1" id="toc-g.-1" class="nav-link" data-scroll-target="#g.-1">g.</a></li> 140 </ul></li> 141 <li><a href="#problem-6weakiv" id="toc-problem-6weakiv" class="nav-link" data-scroll-target="#problem-6weakiv">Problem 6(WeakIV)</a> 142 <ul class="collapse"> 143 <li><a href="#a.-4" id="toc-a.-4" class="nav-link" data-scroll-target="#a.-4">a.</a></li> 144 <li><a href="#b.-4" id="toc-b.-4" class="nav-link" data-scroll-target="#b.-4">b.</a></li> 145 <li><a href="#c.-4" id="toc-c.-4" class="nav-link" data-scroll-target="#c.-4">c. </a></li> 146 <li><a href="#d.-4" id="toc-d.-4" class="nav-link" data-scroll-target="#d.-4">d. </a></li> 147 </ul></li> 148 <li><a href="#problem-7names" id="toc-problem-7names" class="nav-link" data-scroll-target="#problem-7names">Problem 7(Names)</a> 149 <ul class="collapse"> 150 <li><a href="#éå 说æ" id="toc-éå 说æ" class="nav-link" data-scroll-target="#éå 说æ">éå 说æ</a></li> 151 <li><a href="#a.-5" id="toc-a.-5" class="nav-link" data-scroll-target="#a.-5">a.</a></li> 152 <li><a href="#b.-5" id="toc-b.-5" class="nav-link" data-scroll-target="#b.-5">b.</a></li> 153 <li><a href="#c.-5" id="toc-c.-5" class="nav-link" data-scroll-target="#c.-5">c. </a></li> 154 <li><a href="#d.-5" id="toc-d.-5" class="nav-link" data-scroll-target="#d.-5">d. </a></li> 155 </ul></li> 156 <li><a href="#ç»è¯" id="toc-ç»è¯" class="nav-link" data-scroll-target="#ç»è¯">ç»è¯</a></li> 157 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173 174 175 176<header id="title-block-header" class="quarto-title-block default"> 177<div class="quarto-title"> 178<h1 class="title">Experiment 2</h1> 179</div> 180 181 182 183<div class="quarto-title-meta"> 184 185 <div> 186 <div class="quarto-title-meta-heading">Author</div> 187 <div class="quarto-title-meta-contents"> 188 <p>Yuan </p> 189 </div> 190 </div> 191 192 <div> 193 <div class="quarto-title-meta-heading">Published</div> 194 <div class="quarto-title-meta-contents"> 195 <p class="date">April 21, 2023</p> 196 </div> 197 </div> 198 199 <div> 200 <div class="quarto-title-meta-heading">Modified</div> 201 <div class="quarto-title-meta-contents"> 202 <p class="date-modified">May 20, 2023</p> 203 </div> 204 </div> 205 206 </div> 207 208 209</header> 210 211<section id="æ´æ°æ¥å¿" class="level1"> 212<h1>æ´æ°æ¥å¿</h1> 213<ul> 214<li>2023-4-26: ä¿®æ¹ç¬¬ä¸é¢</li> 215</ul> 216</section> 217<section id="åå¨åé¢" class="level1"> 218<h1>åå¨åé¢</h1> 219<section id="ä»ç»" class="level2 unnumbered unlisted"> 220<h2 class="unnumbered unlisted anchored" data-anchor-id="ä»ç»">ä»ç»</h2> 221<p>åå¦ä»¬å¥½ï¼ä»¥ä¸æ¯ä¸çº§è®¡éç»æµå¦ç¬¬äºæ¬¡å®éªçåèï¼å®å ¨ç±æ¬äººå¶ä½ãå ¶ä¸é¤äºç¬¬ä¸é¢ä»¥å¤ï¼æ¶åç»è®¡å¦ã计éç»æµå¦ç¥è¯çé¨åï¼ç±äºæ¬äººæ°´å¹³æéï¼æ æ³ä¿è¯å®å ¨æ£ç¡®ãä» ä¾åå¦ä»¬å¦ä¹ åèãå¦æä½ æä»»ä½é®é¢æè åç°äºåªéæéï¼å¯ä»¥å¨å³è¾¹ç¨<em>Hypothesis</em>æ æ³¨å¹¶è¯è®ºï¼ä¸å¤§å®¶ä¸åè®¨è®ºï¼æè ç§ä¸èç³»æãæä¼å¨çå°çç¬¬ä¸æ¶é´åå¤ä½ çï¼</p> 222</section> 223<section id="æå" class="level2 unnumbered unlisted"> 224<h2 class="unnumbered unlisted anchored" data-anchor-id="æå">æå</h2> 225<p>åå®ä¸éè¿æ¬¡å®éªä¸æ¥ï¼æè§è¿æ¯æ¶è·é¢å¤ãè¿æ¯æå¾å¤ç»èéè¦å¤å¤ç¢ç£¨ï¼ä»Rè¯è¨ï¼å°ç»è®¡å¦ã计éç»æµå¦çç¥è¯ï¼ä¸ç®¡æ¯å设æ£éªé¨åï¼logit/probit é¨åï¼TSLSé¨åï¼è¿æ¯ä½å¾ãå表æ¹é¢é½æå¾å¤èç©¶ï¼æ¥åè¿æ¯è¦å¤å¤ç ç©¶ã叿åå¦ä»¬å¯ä»¥æ±çå¤å¤å¦ä¹ 交æµï¼è®¤çä»ç»é»ç æ¯éé¢çå¿ææ¥åè¿æ¬¡çå®éªå 容ã</p> 226<p>å ³äºéè¦èè´¹çæ¶é´ã妿æ¯å纯åæé®é¢ï¼å¯è½2-7颿¯éé¢éè¦ä¸¤ä¸ªå°æ¶å·¦å³ï¼å 䏿è代ç ç»æãæèå¦ä½ä½å¾ä½è¡¨ï¼æä¸ªäººè±äºä¸¤å¨çæ¶é´ï¼å 乿¯å¤©ç主è¦ç²¾åé½å¨ç ç©¶æ¬æ¬¡å®éªï¼ï¼å¨æ èæ¶æ¿èµ·æ¥æ³ä¸æ³è¿äºé®é¢ï¼ä¹æ¯è¶£å³é¢å¤çä¸ä»¶äºæ ï¼ç¸æ¯äºæç室åé£ä»¤äººçè¦ç<em>ä¿¡å·ä¸ç³»ç»</em>äºäºï¼æè§å¾æè计éé®é¢è¿æ¯æºæ¡ç¶èªå¾çï¼ã</p> 227<p>æ¥åæè¿ä¼å¯¹å 容ç¨å ä¿®æ¹ï¼å æ¬çº éãå¢å 讲解ä¹ç±»çãè¿æ¯é£å¥è¯ï¼å¸æåå¦ä»¬å¤å¤äº¤æµï¼</p> 228</section> 229</section> 230<section id="å¯¼å ¥ä¾èµå " class="level1"> 231<h1>å¯¼å ¥ä¾èµå </h1> 232<div class="cell"> 233<div class="sourceCode cell-code" id="cb1"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb1-1"><a href="#cb1-1" aria-hidden="true" tabindex="-1"></a><span class="co"># input libraries</span></span> 234<span id="cb1-2"><a href="#cb1-2" aria-hidden="true" tabindex="-1"></a><span class="fu">library</span>(gmodels)</span> 235<span id="cb1-3"><a href="#cb1-3" aria-hidden="true" tabindex="-1"></a><span class="fu">library</span>(officedown)</span> 236<span id="cb1-4"><a href="#cb1-4" aria-hidden="true" tabindex="-1"></a><span class="fu">library</span>(car)</span> 237<span id="cb1-5"><a href="#cb1-5" aria-hidden="true" tabindex="-1"></a><span class="fu">library</span>(dplyr)</span> 238<span id="cb1-6"><a href="#cb1-6" aria-hidden="true" tabindex="-1"></a><span class="fu">library</span>(ggplot2)</span> 239<span id="cb1-7"><a href="#cb1-7" aria-hidden="true" tabindex="-1"></a><span class="fu">library</span>(readxl)</span> 240<span id="cb1-8"><a href="#cb1-8" aria-hidden="true" tabindex="-1"></a><span class="fu">library</span>(flextable)</span> 241<span id="cb1-9"><a href="#cb1-9" aria-hidden="true" tabindex="-1"></a><span class="fu">library</span>(stats4)</span> 242<span id="cb1-10"><a href="#cb1-10" aria-hidden="true" tabindex="-1"></a><span class="fu">library</span>(plm)</span> 243<span id="cb1-11"><a href="#cb1-11" aria-hidden="true" tabindex="-1"></a><span class="fu">library</span>(patchwork)</span> 244<span id="cb1-12"><a href="#cb1-12" aria-hidden="true" tabindex="-1"></a><span class="fu">library</span>(sjPlot)</span> 245<span id="cb1-13"><a href="#cb1-13" aria-hidden="true" tabindex="-1"></a><span class="fu">library</span>(AER)</span> 246<span id="cb1-14"><a href="#cb1-14" aria-hidden="true" tabindex="-1"></a><span class="fu">library</span>(magrittr)</span> 247<span id="cb1-15"><a href="#cb1-15" aria-hidden="true" tabindex="-1"></a><span class="fu">library</span>(infer)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div> 248</div> 249<div class="cell"> 250 251<style type="text/css"> 252table { 253 margin-right: auto; 254 margin-left: auto; 255} 256</style> 257</div> 258</section> 259<section id="problem-1likelihood-function" class="level1"> 260<h1>Problem 1(Likelihood Function)</h1> 261<section id="data-read-and-manipulation" class="level2"> 262<h2 class="anchored" data-anchor-id="data-read-and-manipulation">Data Read and Manipulation</h2> 263<p>The <code>xlsx</code> data can be read with <code>readxl</code> library. Then it is convert to matrix, split by x and y,</p> 264<div class="cell"> 265<div class="sourceCode cell-code" id="cb2"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb2-1"><a href="#cb2-1" aria-hidden="true" tabindex="-1"></a>hmda <span class="ot"><-</span> <span class="fu">read_xlsx</span>(<span class="st">"data/hmda_sw.xlsx"</span>)</span> 266<span id="cb2-2"><a href="#cb2-2" aria-hidden="true" tabindex="-1"></a>hmda <span class="ot"><-</span> hmda <span class="sc">%>%</span></span> 267<span id="cb2-3"><a href="#cb2-3" aria-hidden="true" tabindex="-1"></a> <span class="fu">mutate</span>(</span> 268<span id="cb2-4"><a href="#cb2-4" aria-hidden="true" tabindex="-1"></a> <span class="at">black =</span> <span class="fu">ifelse</span>(s13 <span class="sc">==</span> <span class="dv">3</span>, <span class="dv">1</span>, <span class="dv">0</span>),</span> 269<span id="cb2-5"><a href="#cb2-5" aria-hidden="true" tabindex="-1"></a> <span class="at">deny =</span> <span class="fu">ifelse</span>(s7 <span class="sc">==</span> <span class="dv">3</span>, <span class="dv">1</span>, <span class="dv">0</span>),</span> 270<span id="cb2-6"><a href="#cb2-6" aria-hidden="true" tabindex="-1"></a> <span class="at">PI =</span> s46 <span class="sc">/</span> <span class="dv">100</span>,</span> 271<span id="cb2-7"><a href="#cb2-7" aria-hidden="true" tabindex="-1"></a> <span class="at">hse_inc =</span> s45 <span class="sc">/</span> <span class="dv">100</span>,</span> 272<span id="cb2-8"><a href="#cb2-8" aria-hidden="true" tabindex="-1"></a> <span class="at">loan_val =</span> s6 <span class="sc">/</span> s50,</span> 273<span id="cb2-9"><a href="#cb2-9" aria-hidden="true" tabindex="-1"></a> <span class="at">ccred =</span> s43,</span> 274<span id="cb2-10"><a href="#cb2-10" aria-hidden="true" tabindex="-1"></a> <span class="at">mcred =</span> s42,</span> 275<span id="cb2-11"><a href="#cb2-11" aria-hidden="true" tabindex="-1"></a> <span class="at">pubrec =</span> <span class="dv">1</span> <span class="sc">*</span> (s44 <span class="sc">></span> <span class="dv">0</span>),</span> 276<span id="cb2-12"><a href="#cb2-12" aria-hidden="true" tabindex="-1"></a> <span class="at">denpmi =</span> <span class="dv">1</span> <span class="sc">*</span> (s53 <span class="sc">==</span> <span class="dv">1</span>),</span> 277<span id="cb2-13"><a href="#cb2-13" aria-hidden="true" tabindex="-1"></a> <span class="at">selfemp =</span> <span class="dv">1</span> <span class="sc">*</span> (s27a <span class="sc">==</span> <span class="dv">1</span>),</span> 278<span id="cb2-14"><a href="#cb2-14" aria-hidden="true" tabindex="-1"></a> <span class="at">married =</span> <span class="dv">1</span> <span class="sc">*</span> (s23a <span class="sc">==</span> <span class="st">"M"</span>),</span> 279<span id="cb2-15"><a href="#cb2-15" aria-hidden="true" tabindex="-1"></a> <span class="at">single =</span> <span class="dv">1</span> <span class="sc">*</span> (married <span class="sc">==</span> <span class="dv">0</span>),</span> 280<span id="cb2-16"><a href="#cb2-16" aria-hidden="true" tabindex="-1"></a> <span class="at">hischl =</span> <span class="dv">1</span> <span class="sc">*</span> (school <span class="sc">>=</span> <span class="dv">12</span>),</span> 281<span id="cb2-17"><a href="#cb2-17" aria-hidden="true" tabindex="-1"></a> <span class="at">probunmp =</span> uria,</span> 282<span id="cb2-18"><a href="#cb2-18" aria-hidden="true" tabindex="-1"></a> <span class="at">condo =</span> <span class="dv">1</span> <span class="sc">*</span> (s51 <span class="sc">==</span> <span class="dv">1</span>)</span> 283<span id="cb2-19"><a href="#cb2-19" aria-hidden="true" tabindex="-1"></a> )</span> 284<span id="cb2-20"><a href="#cb2-20" aria-hidden="true" tabindex="-1"></a></span> 285<span id="cb2-21"><a href="#cb2-21" aria-hidden="true" tabindex="-1"></a><span class="co"># deop the unused colomns</span></span> 286<span id="cb2-22"><a href="#cb2-22" aria-hidden="true" tabindex="-1"></a>hmda <span class="ot"><-</span> hmda <span class="sc">%>%</span></span> 287<span id="cb2-23"><a href="#cb2-23" aria-hidden="true" tabindex="-1"></a> <span class="fu">select</span>(</span> 288<span id="cb2-24"><a href="#cb2-24" aria-hidden="true" tabindex="-1"></a> black, deny, PI, hse_inc,</span> 289<span id="cb2-25"><a href="#cb2-25" aria-hidden="true" tabindex="-1"></a>
289 loan_val, ccred, mcred, pubrec,</span> 290<span id="cb2-26"><a href="#cb2-26" aria-hidden="true" tabindex="-1"></a> denpmi, selfemp, married, single,</span> 291<span id="cb2-27"><a href="#cb2-27" aria-hidden="true" tabindex="-1"></a> hischl, probunmp, condo</span> 292<span id="cb2-28"><a href="#cb2-28" aria-hidden="true" tabindex="-1"></a> )</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div> 293</div> 294<p>Gene rate loan-to-value ration with 3 levels(<em>high</em> if <em>loan_val</em> > 0.95, <em>low</em> if <em>loan_val</em> < 0.8, <em>medium</em> otherwise)</p> 295<div class="cell"> 296<div class="sourceCode cell-code" id="cb3"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb3-1"><a href="#cb3-1" aria-hidden="true" tabindex="-1"></a>hmda <span class="ot"><-</span> hmda <span class="sc">%>%</span></span> 297<span id="cb3-2"><a href="#cb3-2" aria-hidden="true" tabindex="-1"></a> <span class="fu">mutate</span>(</span> 298<span id="cb3-3"><a href="#cb3-3" aria-hidden="true" tabindex="-1"></a> <span class="at">lvratmedium =</span> <span class="fu">ifelse</span>(loan_val <span class="sc">>=</span> <span class="fl">0.8</span> <span class="sc">&</span> loan_val <span class="sc"><=</span> <span class="fl">0.95</span>, <span class="dv">1</span>, <span class="dv">0</span>),</span> 299<span id="cb3-4"><a href="#cb3-4" aria-hidden="true" tabindex="-1"></a> <span class="at">lvrathigh =</span> <span class="fu">ifelse</span>(loan_val <span class="sc">></span> <span class="fl">0.95</span>, <span class="dv">1</span>, <span class="dv">0</span>)</span> 300<span id="cb3-5"><a href="#cb3-5" aria-hidden="true" tabindex="-1"></a> )</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div> 301</div> 302</section> 303<section id="ols-estimator" class="level2"> 304<h2 class="anchored" data-anchor-id="ols-estimator">OLS Estimator</h2> 305<div class="cell"> 306<div class="sourceCode cell-code" id="cb4"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb4-1"><a href="#cb4-1" aria-hidden="true" tabindex="-1"></a><span class="fu">attach</span>(hmda)</span> 307<span id="cb4-2"><a href="#cb4-2" aria-hidden="true" tabindex="-1"></a>mod.deny <span class="ot"><-</span> <span class="fu">lm</span>(</span> 308<span id="cb4-3"><a href="#cb4-3" aria-hidden="true" tabindex="-1"></a> deny <span class="sc">~</span> <span class="dv">1</span> <span class="sc">+</span> black <span class="sc">+</span> PI <span class="sc">+</span> hse_inc <span class="sc">+</span> lvratmedium <span class="sc">+</span> lvrathigh <span class="sc">+</span></span> 309<span id="cb4-4"><a href="#cb4-4" aria-hidden="true" tabindex="-1"></a> ccred <span class="sc">+</span> mcred <span class="sc">+</span> pubrec <span class="sc">+</span> denpmi <span class="sc">+</span> selfemp</span> 310<span id="cb4-5"><a href="#cb4-5" aria-hidden="true" tabindex="-1"></a>)</span> 311<span id="cb4-6"><a href="#cb4-6" aria-hidden="true" tabindex="-1"></a><span class="fu">detach</span>(hmda)</span> 312<span id="cb4-7"><a href="#cb4-7" aria-hidden="true" tabindex="-1"></a>coef <span class="ot"><-</span> mod.deny<span class="sc">$</span>coefficients</span> 313<span id="cb4-8"><a href="#cb4-8" aria-hidden="true" tabindex="-1"></a>coef_from_textbook <span class="ot"><-</span> <span class="fu">c</span>(</span> 314<span id="cb4-9"><a href="#cb4-9" aria-hidden="true" tabindex="-1"></a> <span class="sc">-</span><span class="fl">0.183</span>, <span class="fl">0.084</span>, <span class="fl">0.449</span>, <span class="sc">-</span><span class="fl">0.048</span>, <span class="fl">0.031</span>, <span class="fl">0.189</span>, <span class="fl">0.031</span>,</span> 315<span id="cb4-10"><a href="#cb4-10" aria-hidden="true" tabindex="-1"></a> <span class="fl">0.021</span>, <span class="fl">0.197</span>, <span class="fl">0.702</span>, <span class="fl">0.060</span></span> 316<span id="cb4-11"><a href="#cb4-11" aria-hidden="true" tabindex="-1"></a>)</span> 317<span id="cb4-12"><a href="#cb4-12" aria-hidden="true" tabindex="-1"></a>coef_comp <span class="ot"><-</span> <span class="fu">tibble</span>(<span class="at">name =</span> <span class="fu">names</span>(coef), <span class="at">coef =</span> coef, <span class="at">coef_book =</span> coef_from_textbook) <span class="sc">%>%</span></span> 318<span id="cb4-13"><a href="#cb4-13" aria-hidden="true" tabindex="-1"></a> <span class="fu">mutate</span>(<span class="at">coef =</span> <span class="fu">round</span>(coef, <span class="dv">3</span>))</span> 319<span id="cb4-14"><a href="#cb4-14" aria-hidden="true" tabindex="-1"></a>coef_comp <span class="sc">%>%</span></span> 320<span id="cb4-15"><a href="#cb4-15" aria-hidden="true" tabindex="-1"></a> <span class="fu">flextable</span>() <span class="sc">%>%</span></span> 321<span id="cb4-16"><a href="#cb4-16" aria-hidden="true" tabindex="-1"></a> <span class="fu">align</span>(<span class="at">part =</span> <span class="st">"header"</span>, <span class="at">align =</span> <span class="st">"center"</span>) <span class="sc">%>%</span></span> 322<span id="cb4-17"><a href="#cb4-17" aria-hidden="true" tabindex="-1"></a> <span class="fu">bold</span>(<span class="at">part =</span> <span class="st">"header"</span>) <span class="sc">%>%</span></span> 323<span id="cb4-18"><a href="#cb4-18" aria-hidden="true" tabindex="-1"></a> <span class="fu">autofit</span>()</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div> 324<div class="cell-output-display"> 325<div id="tbl-hmda_ols" class="anchored"> 326 327<div class="tabwid"><style>.cl-1622e8d8{}.cl-161ac784{font-family:'Arial';font-size:11pt;font-weight:bold;font-style:normal;text-decoration:none;color:rgba(0, 0, 0, 1.00);background-color:transparent;}
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1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}.cl-161e1abb{width:1.117in;background-color:transparent;vertical-align: middle;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}.cl-161e1abc{width:0.718in;background-color:transparent;vertical-align: middle;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}.cl-161e1abd{width:1.049in;background-color:transparent;vertical-align: middle;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}.cl-161e1ac4{width:1.117in;background-color:transparent;vertical-align: middle;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}.cl-161e1ace{width:0.718in;background-color:transparent;vertical-align: middle;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}.cl-161e1acf{width:1.049in;background-color:transparent;vertical-align: middle;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}.cl-161e1ad0{width:1.117in;background-color:transparent;vertical-align: middle;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}.cl-161e1ad8{width:0.718in;background-color:transparent;vertical-align: middle;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}.cl-161e1ad9{width:1.049in;background-color:transparent;vertical-align: middle;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}.cl-161e1ada{width:1.117in;background-color:transparent;vertical-align: middle;border-bottom: 1.5pt solid rgba(102, 102, 102, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}.cl-161e1ae2{width:0.718in;background-color:transparent;vertical-align: middle;border-bottom: 1.5pt solid rgba(102, 102, 102, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}.cl-161e1ae3{width:1.049in;background-color:transparent;vertical-align: middle;border-bottom: 1.5pt solid rgba(102, 102, 102, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}</style><table data-quarto-disable-processing="true" class="cl-1622e8d8"><caption>Table 1: <p>
327HMDA coefficients of OLS comparison</p> </caption><thead><tr style="overflow-wrap:break-word;"><th class="cl-161e1a92"><p class="cl-161e04da"><span class="cl-161ac784">name</span></p></th><th class="cl-161e1a93"><p class="cl-161e04da"><span class="cl-161ac784">coef</span></p></th><th class="cl-161e1a9c"><p class="cl-161e04da"><span class="cl-161ac784">coef_book</span></p></th></tr></thead><tbody><tr style="overflow-wrap:break-word;"><td class="cl-161e1a9d"><p class="cl-161e04e4"><span class="cl-161ac798">(Intercept)</span></p></td><td class="cl-161e1aa6"><p class="cl-161e04e5"><span class="cl-161ac798">-0.183</span></p></td><td class="cl-161e1aa7"><p class="cl-161e04e5"><span class="cl-161ac798">-0.183</span></p></td></tr><tr style="overflow-wrap:break-word;"><td class="cl-161e1aa8"><p class="cl-161e04e4"><span class="cl-161ac798">black</span></p></td><td class="cl-161e1ab0"><p class="cl-161e04e5"><span class="cl-161ac798">0.084</span></p></td><td class="cl-161e1aba"><p class="cl-161e04e5"><span class="cl-161ac798">0.084</span></p></td></tr><tr style="overflow-wrap:break-word;"><td class="cl-161e1aa8"><p class="cl-161e04e4"><span class="cl-161ac798">PI</span></p></td><td class="cl-161e1ab0"><p class="cl-161e04e5"><span class="cl-161ac798">0.449</span></p></td><td class="cl-161e1aba"><p class="cl-161e04e5"><span class="cl-161ac798">0.449</span></p></td></tr><tr style="overflow-wrap:break-word;"><td class="cl-161e1abb"><p class="cl-161e04e4"><span class="cl-161ac798">hse_inc</span></p></td><td class="cl-161e1abc"><p class="cl-161e04e5"><span class="cl-161ac798">-0.048</span></p></td><td class="cl-161e1abd"><p class="cl-161e04e5"><span class="cl-161ac798">-0.048</span></p></td></tr><tr style="overflow-wrap:break-word;"><td class="cl-161e1ac4"><p class="cl-161e04e4"><span class="cl-161ac798">lvratmedium</span></p></td><td class="cl-161e1ace"><p class="cl-161e04e5"><span class="cl-161ac798">0.031</span></p></td><td class="cl-161e1acf"><p class="cl-161e04e5"><span class="cl-161ac798">0.031</span></p></td></tr><tr style="overflow-wrap:break-word;"><td class="cl-161e1ad0"><p class="cl-161e04e4"><span class="cl-161ac798">lvrathigh</span></p></td><td class="cl-161e1ad8"><p class="cl-161e04e5"><span class="cl-161ac798">0.189</span></p></td><td class="cl-161e1ad9"><p class="cl-161e04e5"><span class="cl-161ac798">0.189</span></p></td></tr><tr style="overflow-wrap:break-word;"><td class="cl-161e1ac4"><p class="cl-161e04e4"><span class="cl-161ac798">ccred</span></p></td><td class="cl-161e1ace"><p class="cl-161e04e5"><span class="cl-161ac798">0.031</span></p></td><td class="cl-161e1acf"><p class="cl-161e04e5"><span class="cl-161ac798">0.031</span></p></td></tr><tr style="overflow-wrap:break-word;"><td class="cl-161e1aa8"><p class="cl-161e04e4"><span class="cl-161ac798">mcred</span></p></td><td class="cl-161e1ab0"><p class="cl-161e04e5"><span class="cl-161ac798">0.021</span></p></td><td class="cl-161e1aba"><p class="cl-161e04e5"><span class="cl-161ac798">0.021</span></p></td></tr><tr style="overflow-wrap:break-word;"><td class="cl-161e1abb"><p class="cl-161e04e4"><span class="cl-161ac798">pubrec</span></p></td><td class="cl-161e1abc"><p class="cl-161e04e5"><span class="cl-161ac798">0.197</span></p></td><td class="cl-161e1abd"><p class="cl-161e04e5"><span class="cl-161ac798">0.197</span></p></td></tr><tr style="overflow-wrap:break-word;"><td class="cl-161e1abb"><p class="cl-161e04e4"><span class="cl-161ac798">denpmi</span></p></td><td class="cl-161e1abc"><p class="cl-161e04e5"><span class="cl-161ac798">0.702</span></p></td><td class="cl-161e1abd"><p class="cl-161e04e5"><span class="cl-161ac798">0.702</span></p></td></tr><tr style="overflow-wrap:break-word;"><td class="cl-161e1ada"><p class="cl-161e04e4"><span class="cl-161ac798">selfemp</span></p></td><td class="cl-161e1ae2"><p class="cl-161e04e5"><span class="cl-161ac798">0.060</span></p></td><td class="cl-161e1ae3"><p class="cl-161e04e5"><span class="cl-161ac798">0.060</span></p></td></tr></tbody></table></div> 328</div> 329</div> 330</div> 331<p>The coefficients of above OLS regression result are same comparing to the table 11.2 on textbook.</p> 332</section> 333<section id="probit-model" class="level2"> 334<h2 class="anchored" data-anchor-id="probit-model">Probit Model</h2> 335<section id="likelihood-function" class="level3"> 336<h3 class="anchored" data-anchor-id="likelihood-function">Likelihood Function</h3> 337<p>Develop the likelihood function of MLE, following the textbook Ch11. Because there is only <span class="math inline">\(Y_1\)</span>, The likelihood function will be</p> 338<p><span class="math display">\[ 339f(\beta_0,\beta_1,...,\beta_n;Y_1,...,Y_{m}|X_1,...,X_m) 340\]</span></p> 341<p><span class="math display">\[ 342=\{\Theta(\beta_0+\beta_1X_{11}+...+\beta_nX_{1n})^{Y_1}[1-\Theta(\beta_0+\beta_1X_{11}+\beta_nX_{1n})]^{1-Y_1} 343\}\times 344\]</span></p> 345<p><span class="math display">\[ 346...\times \{\Theta(\beta_0+\beta_1X_{m1}+...+\beta_nX_{mn})^{Y_m}[1-\Theta(\beta_0+\beta_1X_{m1}+...+\beta_nX_{mn})]^{1-Y_m}\} 347\]</span></p> 348<p>Where <span class="math inline">\(\hat{\beta}_0^{MLE}, ..., \hat{\beta}_n^{MLE}\)</span> maximize this likelihood function.</p> 349<p>Logarithm of the likelihood:</p> 350<p><span class="math display">\[ 351ln(f(\beta_0,\beta_1,\beta_n;Y_1,...,Y_{m}|X_1,...,X_m)) 352\]</span></p> 353<p><span class="math display">\[ 354= Y_1ln(\Theta( 355\beta_0+\beta_1X_{11}+...+\beta_nX_{1n}))+(1-Y_1)ln 356(1-\Theta(\beta_0+\beta_1X_{11}+\beta_nX_{1n}))+ 357\]</span></p> 358<p><span class="math display">\[ 359...+ 360Y_mln(\Theta(\beta_0+\beta_1X_{m1}+...+\beta_nX_{mn}))+ 361(1-Y_m)ln(1-\Theta(\beta_0+\beta_1X_{m1}+...+\beta_nX_{mn})) 362\]</span></p> 363<div class="cell"> 364<div class="sourceCode cell-code" id="cb5"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb5-1"><a href="#cb5-1" aria-hidden="true" tabindex="-1"></a><span class="co"># x is a matrix with n * n</span></span> 365<span id="cb5-2"><a href="#cb5-2" aria-hidden="true" tabindex="-1"></a><span class="co"># y is a matrix with n * 1</span></span> 366<span id="cb5-3"><a href="#cb5-3" aria-hidden="true" tabindex="-1"></a><span class="co"># beta is the vector to maximize</span></span> 367<span id="cb5-4"><a href="#cb5-4" aria-hidden="true" tabindex="-1"></a>likefunc_probit <span class="ot"><-</span> <span class="cf">function</span>(beta, x, y) {</span> 368<span id="cb5-5"><a href="#cb5-5" aria-hidden="true" tabindex="-1"></a> x <span class="ot"><-</span> <span class="fu">cbind</span>(<span class="dv">1</span>, x)</span> 369<span id="cb5-6"><a href="#cb5-6" aria-hidden="true" tabindex="-1"></a> res <span class="ot"><-</span> <span class="dv">0</span></span> 370<span id="cb5-7"><a href="#cb5-7" aria-hidden="true" tabindex="-1"></a> beta <span class="ot"><-</span> <span class="fu">c</span>(beta)</span> 371<span id="cb5-8"><a href="#cb5-8" aria-hidden="true" tabindex="-1"></a> <span class="cf">for</span> (i <span class="cf">in</span> <span class="dv">1</span><span class="sc">:</span><span class="fu">nrow</span>(x)) {</span> 372<span id="cb5-9"><a href="#cb5-9" aria-hidden="true" tabindex="-1"></a> theta <span class="ot"><-</span> <span class="fu">pnorm</span>(x[i, ] <span class="sc">%*%</span> beta)</span> 373<span id="cb5-10"><a href="#cb5-10" aria-hidden="true" tabindex="-1"></a> res <span class="ot"><-</span> res <span class="sc">+</span></span> 374<span id="cb5-11"><a href="#cb5-11" aria-hidden="true" tabindex="-1"></a> y[i, ] <span class="sc">*</span> <span class="fu">log</span>(theta) <span class="sc">+</span></span> 375<span id="cb5-12"><a href="#cb5-12" aria-hidden="true" tabindex="-1"></a> (<span class="dv">1</span> <span class="sc">-</span> y[i, ]) <span class="sc">*</span> <span class="fu">log</span>(<span class="dv">1</span> <span class="sc">-</span> theta)</span> 376<span id="cb5-13"><a href="#cb5-13" aria-hidden="true" tabindex="-1"></a> }</span> 377<span id="cb5-14"><a href="#cb5-14" aria-hidden="true" tabindex="-1"></a> <span class="fu">return</span>(<span class="sc">-</span>res)</span> 378<span id="cb5-15"><a href="#cb5-15" aria-hidden="true" tabindex="-1"></a>}</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div> 379</div> 380</section> 381<section id="beta-generation-and-comparison" class="level3"> 382<h3 class="anchored" data-anchor-id="beta-generation-and-comparison">Beta Generation and Comparison</h3> 383<div class="cell"> 384<div class="sourceCode cell-code" id="cb6"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb6-1"><a href="#cb6-1" aria-hidden="true" tabindex="-1"></a><span class="co">
384#| warning: false</span></span> 385<span id="cb6-2"><a href="#cb6-2" aria-hidden="true" tabindex="-1"></a><span class="co">#| message: false</span></span> 386<span id="cb6-3"><a href="#cb6-3" aria-hidden="true" tabindex="-1"></a><span class="fu">attach</span>(hmda)</span> 387<span id="cb6-4"><a href="#cb6-4" aria-hidden="true" tabindex="-1"></a>x <span class="ot"><-</span> hmda <span class="sc">%>%</span></span> 388<span id="cb6-5"><a href="#cb6-5" aria-hidden="true" tabindex="-1"></a> <span class="fu">select</span>(</span> 389<span id="cb6-6"><a href="#cb6-6" aria-hidden="true" tabindex="-1"></a> black, PI, hse_inc, lvratmedium, lvrathigh,</span> 390<span id="cb6-7"><a href="#cb6-7" aria-hidden="true" tabindex="-1"></a> ccred, mcred, pubrec, denpmi, selfemp</span> 391<span id="cb6-8"><a href="#cb6-8" aria-hidden="true" tabindex="-1"></a> ) <span class="sc">%>%</span></span> 392<span id="cb6-9"><a href="#cb6-9" aria-hidden="true" tabindex="-1"></a> <span class="fu">as.matrix</span>()</span> 393<span id="cb6-10"><a href="#cb6-10" aria-hidden="true" tabindex="-1"></a>y <span class="ot"><-</span> hmda <span class="sc">%>%</span></span> 394<span id="cb6-11"><a href="#cb6-11" aria-hidden="true" tabindex="-1"></a> <span class="fu">select</span>(deny) <span class="sc">%>%</span></span> 395<span id="cb6-12"><a href="#cb6-12" aria-hidden="true" tabindex="-1"></a> <span class="fu">as.matrix</span>()</span> 396<span id="cb6-13"><a href="#cb6-13" aria-hidden="true" tabindex="-1"></a><span class="fu">detach</span>(hmda)</span> 397<span id="cb6-14"><a href="#cb6-14" aria-hidden="true" tabindex="-1"></a></span> 398<span id="cb6-15"><a href="#cb6-15" aria-hidden="true" tabindex="-1"></a>res_probit <span class="ot"><-</span> <span class="fu">optim</span>(<span class="fu">rep</span>(<span class="dv">0</span>, <span class="dv">11</span>),</span> 399<span id="cb6-16"><a href="#cb6-16" aria-hidden="true" tabindex="-1"></a> likefunc_probit,</span> 400<span id="cb6-17"><a href="#cb6-17" aria-hidden="true" tabindex="-1"></a> <span class="at">x =</span> x, <span class="at">y =</span> y, <span class="at">method =</span> <span class="st">"BFGS"</span></span> 401<span id="cb6-18"><a href="#cb6-18" aria-hidden="true" tabindex="-1"></a>)</span> 402<span id="cb6-19"><a href="#cb6-19" aria-hidden="true" tabindex="-1"></a>res_probit_book <span class="ot"><-</span> <span class="fu">c</span>(</span> 403<span id="cb6-20"><a href="#cb6-20" aria-hidden="true" tabindex="-1"></a> <span class="sc">-</span><span class="fl">3.04</span>, <span class="fl">0.389</span>, <span class="fl">2.44</span>, <span class="sc">-</span><span class="fl">0.18</span>, <span class="fl">0.21</span>, <span class="fl">0.79</span>,</span> 404<span id="cb6-21"><a href="#cb6-21" aria-hidden="true" tabindex="-1"></a> <span class="fl">0.15</span>, <span class="fl">0.15</span>, <span class="fl">0.7</span>, <span class="fl">2.56</span>, <span class="fl">0.36</span></span> 405<span id="cb6-22"><a href="#cb6-22" aria-hidden="true" tabindex="-1"></a>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div> 406</div> 407<div class="cell"> 408<div class="cell-output-display"> 409<div id="tbl-hmda_probit" class="anchored"> 410 411<div class="tabwid"><style>.cl-1930bc62{}.cl-1929314a{font-family:'Arial';font-size:11pt;font-weight:bold;font-style:normal;text-decoration:none;color:rgba(0, 0, 0, 1.00);background-color:transparent;}.cl-1929315e{font-family:'Arial';font-size:11pt;font-weight:normal;font-style:normal;text-decoration:none;color:rgba(0, 0, 0, 1.00);background-color:transparent;}.cl-192c2f12{margin:0;text-align:left;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);padding-bottom:5pt;padding-top:5pt;padding-left:5pt;padding-right:5pt;line-height: 1;background-color:transparent;}.cl-192c2f26{margin:0;text-align:right;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);padding-bottom:5pt;padding-top:5pt;padding-left:5pt;padding-right:5pt;line-height: 1;background-color:transparent;}
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1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}.cl-192c433a{width:1.117in;background-color:transparent;vertical-align: middle;border-bottom: 1.5pt solid rgba(102, 102, 102, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}.cl-192c433b{width:1.711in;background-color:transparent;vertical-align: middle;border-bottom: 1.5pt solid rgba(102, 102, 102, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}.cl-192c4344{width:1.856in;background-color:transparent;vertical-align: middle;border-bottom: 1.5pt solid rgba(102, 102, 102, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}</style><table data-quarto-disable-processing="true" class="cl-1930bc62"><caption>Table
4112: <p>HMDA probit model results comparison</p> </caption><thead><tr style="overflow-wrap:break-word;"><th class="cl-192c42e0"><p class="cl-192c2f12"><span class="cl-1929314a">Name</span></p></th><th class="cl-192c42f4"><p class="cl-192c2f26"><span class="cl-1929314a">Probit Implemented</span></p></th><th class="cl-192c42f5"><p class="cl-192c2f26"><span class="cl-1929314a">Result from Textbook</span></p></th></tr></thead><tbody><tr style="overflow-wrap:break-word;"><td class="cl-192c42fe"><p class="cl-192c2f12"><span class="cl-1929315e">(Intercept)</span></p></td><td class="cl-192c42ff"><p class="cl-192c2f26"><span class="cl-1929315e">-3.041</span></p></td><td class="cl-192c4308"><p class="cl-192c2f26"><span class="cl-1929315e">-3.040</span></p></td></tr><tr style="overflow-wrap:break-word;"><td class="cl-192c4309"><p class="cl-192c2f12"><span class="cl-1929315e">black</span></p></td><td class="cl-192c430a"><p class="cl-192c2f26"><span class="cl-1929315e">0.389</span></p></td><td class="cl-192c4312"><p class="cl-192c2f26"><span class="cl-1929315e">0.389</span></p></td></tr><tr style="overflow-wrap:break-word;"><td class="cl-192c4313"><p class="cl-192c2f12"><span class="cl-1929315e">PI</span></p></td><td class="cl-192c431c"><p class="cl-192c2f26"><span class="cl-1929315e">2.442</span></p></td><td class="cl-192c431d"><p class="cl-192c2f26"><span class="cl-1929315e">2.440</span></p></td></tr><tr style="overflow-wrap:break-word;"><td class="cl-192c4326"><p class="cl-192c2f12"><span class="cl-1929315e">hse_inc</span></p></td><td class="cl-192c4327"><p class="cl-192c2f26"><span class="cl-1929315e">-0.185</span></p></td><td class="cl-192c4328"><p class="cl-192c2f26"><span class="cl-1929315e">-0.180</span></p></td></tr><tr style="overflow-wrap:break-word;"><td class="cl-192c4313"><p class="cl-192c2f12"><span class="cl-1929315e">lvratmedium</span></p></td><td class="cl-192c431c"><p class="cl-192c2f26"><span class="cl-1929315e">0.214</span></p></td><td class="cl-192c431d"><p class="cl-192c2f26"><span class="cl-1929315e">0.210</span></p></td></tr><tr style="overflow-wrap:break-word;"><td class="cl-192c4330"><p class="cl-192c2f12"><span class="cl-1929315e">lvrathigh</span></p></td><td class="cl-192c4331"><p class="cl-192c2f26"><span class="cl-1929315e">0.791</span></p></td><td class="cl-192c4332"><p class="cl-192c2f26"><span class="cl-1929315e">0.790</span></p></td></tr><tr style="overflow-wrap:break-word;"><td class="cl-192c4313"><p class="cl-192c2f12"><span class="cl-1929315e">ccred</span></p></td><td class="cl-192c431c"><p class="cl-192c2f26"><span class="cl-1929315e">0.155</span></p></td><td class="cl-192c431d"><p class="cl-192c2f26"><span class="cl-1929315e">0.150</span></p></td></tr><tr style="overflow-wrap:break-word;"><td class="cl-192c4313"><p class="cl-192c2f12"><span class="cl-1929315e">mcred</span></p></td><td class="cl-192c431c"><p class="cl-192c2f26"><span class="cl-1929315e">0.148</span></p></td><td class="cl-192c431d"><p class="cl-192c2f26"><span class="cl-1929315e">0.150</span></p></td></tr><tr style="overflow-wrap:break-word;"><td class="cl-192c4326"><p class="cl-192c2f12"><span class="cl-1929315e">pubrec</span></p></td><td class="cl-192c4327"><p class="cl-192c2f26"><span class="cl-1929315e">0.697</span></p></td><td class="cl-192c4328"><p class="cl-192c2f26"><span class="cl-1929315e">0.700</span></p></td></tr><tr style="overflow-wrap:break-word;"><td class="cl-192c4326"><p class="cl-192c2f12"><span class="cl-1929315e">denpmi</span></p></td><td class="cl-192c4327"><p class="cl-192c2f26"><span class="cl-1929315e">2.557</span></p></td><td class="cl-192c4328"><p class="cl-192c2f26"><span class="cl-1929315e">2.560</span></p></td></tr><tr style="overflow-wrap:break-word;"><td class="cl-192c433a"><p class="cl-192c2f12"><span class="cl-1929315e">selfemp</span></p></td><td class="cl-192c433b"><p class="cl-192c2f26"><span class="cl-1929315e">0.359</span></p></td><td class="cl-192c4344"><p class="cl-192c2f26"><span class="cl-1929315e">0.360</span></p></td></tr></tbody></table></div> 412</div> 413</div> 414</div> 415</section> 416</section> 417<section id="logit-model" class="level2"> 418<h2 class="anchored" data-anchor-id="logit-model">Logit Model</h2> 419<section id="likelihood-function-1" class="level3"> 420<h3 class="anchored" data-anchor-id="likelihood-function-1">Likelihood Function</h3> 421<p>The difference between Logit and Probit model is the cumulative distribution function. The CDF of Logit model is</p> 422<p><span class="math display">\[ 423F(\beta_0+\beta_1X_1+...+\beta_nX_n)=\frac{1}{1+e^{-(\beta_0+\beta_1X_1+...+\beta_nX_n)}} 424\]</span></p> 425<p>So the likelihood function is</p> 426<p><span class="math display">\[ 427f(\beta_0,\beta_1,...,\beta_n;Y_1,...,Y_{m}|X_1,...,X_m) 428\]</span></p> 429<p><span class="math display">\[ 430=\{F(\beta_0+\beta_1X_{11}+...+\beta_nX_{1n})^{Y_1}[1-F(\beta_0+\beta_1X_{11}+\beta_nX_{1n})]^{1-Y_1} 431\}\times 432\]</span></p> 433<p><span class="math display">\[ 434...\times \{F(\beta_0+\beta_1X_{m1}+...+\beta_nX_{mn})^{Y_m}[1-F(\beta_0+\beta_1X_{m1}+...+\beta_nX_{mn})]^{1-Y_m}\} 435\]</span></p> 436<p>the log form is:</p> 437<p><span class="math display">\[ 438ln(f(\beta_0,\beta_1,\beta_n;Y_1,...,Y_{m}|X_1,...,X_m)) 439\]</span></p> 440<p><span class="math display">\[ 441= Y_1ln(F( 442\beta_0+\beta_1X_{11}+...+\beta_nX_{1n}))+(1-Y_1)ln 443(1-F(\beta_0+\beta_1X_{11}+\beta_nX_{1n}))+ 444\]</span></p> 445<p><span class="math display">\[ 446...+ 447Y_mln(F(\beta_0+\beta_1X_{m1}+...+\beta_nX_{mn}))+ 448(1-Y_m)ln(1-F(\beta_0+\beta_1X_{m1}+...+\beta_nX_{mn})) 449\]</span></p> 450<p>Implement it in r:</p> 451<div class="cell"> 452<div class="sourceCode cell-code" id="cb7"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb7-1"><a href="#cb7-1" aria-hidden="true" tabindex="-1"></a><span class="co"># x is a matrix with n * n</span></span> 453<span id="cb7-2"><a href="#cb7-2" aria-hidden="true" tabindex="-1"></a><span class="co"># y is a matrix with n * 1</span></span> 454<span id="cb7-3"><a href="#cb7-3" aria-hidden="true" tabindex="-1"></a><span class="co"># beta is the vector to maximize</span></span> 455<span id="cb7-4"><a href="#cb7-4" aria-hidden="true" tabindex="-1"></a>logit <span class="ot"><-</span> <span class="cf">function</span>(x) {</span> 456<span id="cb7-5"><a href="#cb7-5" aria-hidden="true" tabindex="-1"></a> res <span class="ot"><-</span> <span class="dv">1</span> <span class="sc">/</span> (<span class="dv">1</span> <span class="sc">+</span> <span class="fu">exp</span>(<span class="sc">-</span>x))</span> 457<span id="cb7-6"><a href="#cb7-6" aria-hidden="true" tabindex="-1"></a> <span class="fu">return</span>(res)</span> 458<span id="cb7-7"><a href="#cb7-7" aria-hidden="true" tabindex="-1"></a>}</span> 459<span id="cb7-8"><a href="#cb7-8" aria-hidden="true" tabindex="-1"></a></span> 460<span id="cb7-9"><a href="#cb7-9" aria-hidden="true" tabindex="-1"></a>likefunc_logit <span class="ot"><-</span> <span class="cf">function</span>(beta, x, y) {</span> 461<span id="cb7-10"><a href="#cb7-10" aria-hidden="true" tabindex="-1"></a> x <span class="ot"><-</span> <span class="fu">cbind</span>(<span class="dv">1</span>, x)</span> 462<span id="cb7-11"><a href="#cb7-11" aria-hidden="true" tabindex="-1"></a> res <span class="ot"><-</span> <span class="dv">0</span></span> 463<span id="cb7-12"><a href="#cb7-12" aria-hidden="true" tabindex="-1"></a> beta <span class="ot"><-</span> <span class="fu">c</span>(beta)</span> 464<span id="cb7-13"><a href="#cb7-13" aria-hidden="true" tabindex="-1"></a> <span class="cf">for</span> (i <span class="cf">in</span> <span class="dv">1</span><span class="sc">:</span><span class="fu">nrow</span>(x)) {</span> 465<span id="cb7-14"><a href="#cb7-14" aria-hidden="true" tabindex="-1"></a> f <span class="ot"><-</span> <span class="fu">logit</span>(x[i, ] <span class="sc">%*%</span> beta)</span> 466<span id="cb7-15"><a href="#cb7-15" aria-hidden="true" tabindex="-1"></a> res <span class="ot"><-</span> res <span class="sc">+</span></span> 467<span id="cb7-16"><a href="#cb7-16" aria-hidden="true" tabindex="-1"></a> y[i, ] <span class="sc">*</span> <span class="fu">log</span>(f) <span class="sc">+</span></span> 468<span id="cb7-17"><a href="#cb7-17" aria-hidden="true" tabindex="-1"></a> (<span class="dv">1</span> <span class="sc">-</span> y[i, ]) <span class="sc">*</span> <span class="fu">log</span>(<span class="dv">1</span> <span class="sc">-</span> f)</span> 469<span id="cb7-18"><a href="#cb7-18" aria-hidden="true" tabindex="-1"></a> }</span> 470<span id="cb7-19"><a href="#cb7-19" aria-hidden="true" tabindex="-1"></a> <span class="fu">return</span>(<span class="sc">-</span>res)</span> 471<span id="cb7-20"><a href="#cb7-20" aria-hidden="true" tabindex="-1"></a>}</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div> 472</div> 473</section> 474<section id="beta-generation-and-comparison-1" class="level3"> 475<h3 class="anchored" data-anchor-id="beta-generation-and-comparison-1">Beta Generation and Comparison</h3> 476<div class="cell"> 477<div class="sourceCode cell-code" id="cb8"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb8-1"><a href="#cb8-1" aria-hidden="true" tabindex="-1"></a>res_logit <span class="ot"><-</span> <span class="fu">
477optim</span>(<span class="fu">rep</span>(<span class="dv">0</span>, <span class="dv">11</span>), likefunc_logit, <span class="at">x =</span> x, <span class="at">y =</span> y, <span class="at">method =</span> <span class="st">"BFGS"</span>)</span> 478<span id="cb8-2"><a href="#cb8-2" aria-hidden="true" tabindex="-1"></a>res_logit_book <span class="ot"><-</span> <span class="fu">c</span>(<span class="sc">-</span><span class="fl">5.71</span>, <span class="fl">0.688</span>, <span class="fl">4.76</span>, <span class="sc">-</span><span class="fl">0.11</span>, <span class="fl">0.46</span>, <span class="fl">1.49</span>, <span class="fl">0.29</span>, <span class="fl">0.28</span>, <span class="fl">1.23</span>, <span class="fl">4.55</span>, <span class="fl">0.67</span>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div> 479</div> 480<div class="cell"> 481<div class="cell-output-display"> 482<div id="tbl-hmda_logit" class="anchored"> 483 484<div class="tabwid"><style>.cl-1c11bddc{}.cl-1c0a41a6{font-family:'Arial';font-size:11pt;font-weight:bold;font-style:normal;text-decoration:none;color:rgba(0, 0, 0, 1.00);background-color:transparent;}.cl-1c0a41b0{font-family:'Arial';font-size:11pt;font-weight:normal;font-style:normal;text-decoration:none;color:rgba(0, 0, 0, 1.00);background-color:transparent;}.cl-1c0d392e{margin:0;text-align:left;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);padding-bottom:5pt;padding-top:5pt;padding-left:5pt;padding-right:5pt;line-height: 1;background-color:transparent;}.cl-1c0d3938{margin:0;text-align:right;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);padding-bottom:5pt;padding-top:5pt;padding-left:5pt;padding-right:5pt;line-height: 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1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}.cl-1c0d4bdb{width:1.117in;background-color:transparent;vertical-align: middle;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}.cl-1c0d4bdc{width:1.643in;background-color:transparent;vertical-align: middle;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}.cl-1c0d4be4{width:1.601in;background-color:transparent;vertical-align: middle;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}.cl-1c0d4bee{width:1.117in;background-color:transparent;vertical-align: middle;border-bottom: 1.5pt solid rgba(102, 102, 102, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}.cl-1c0d4bef{width:1.643in;background-color:transparent;vertical-align: middle;border-bottom: 1.5pt solid rgba(102, 102, 102, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}.cl-1c0d4bf8{width:1.601in;background-color:transparent;vertical-align: middle;border-bottom: 1.5pt solid rgba(102, 102, 102, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}</style><table data-quarto-disable-processing="true" class="cl-1c11bddc"><caption>Table 3: <p>HMDA logit model results comparison</p> </caption><thead><tr style="overflow-wrap:break-word;"><th class="cl-1c0d4ba8"><p class="cl-1c0d392e"><span class="cl-1c0a41a6">Name</span></p></th><th class="cl-1c0d4ba9"><p class="cl-1c0d3938"><span class="cl-1c0a41a6">Logit Implemented</span></p></th><th class="cl-1c0d4bb2"><p class="cl-1c0d3938"><span class="cl-1c0a41a6">Result From Book</span></p></th></tr></thead><tbody><tr style="overflow-wrap:break-word;"><td class="cl-1c0d4bb3"><p class="cl-1c0d392e"><span class="cl-1c0a41b0">(Intercept)</span></p></td><td class="cl-1c0d4bb4"><p class="cl-1c0d3938"><span class="cl-1c0a41b0">-5.707</span></p></td><td class="cl-1c0d4bbc"><p class="cl-1c0d3938"><span class="cl-1c0a41b0">-5.710</span></p></td></tr><tr style="overflow-wrap:break-word;"><td class="cl-1c0d4bbd"><p class="cl-1c0d392e"><span class="cl-1c0a41b0">black</span></p></td><td class="cl-1c0d4bc6"><p class="cl-1c0d3938"><span class="cl-1c0a41b0">0.688</span></p></td><td class="cl-1c0d4bc7"><p class="cl-1c0d3938"><span class="cl-1c0a41b0">0.688</span></p></td></tr><tr style="overflow-wrap:break-word;"><td class="cl-1c0d4bbd"><p class="cl-1c0d392e"><span class="cl-1c0a41b0">PI</span></p></td><td class="cl-1c0d4bc6"><p class="cl-1c0d3938"><span class="cl-1c0a41b0">4.764</span></p></td><td class="cl-1c0d4bc7"><p class="cl-1c0d3938"><span class="cl-1c0a41b0">4.760</span></p></td></tr><tr style="overflow-wrap:break-word;"><td class="cl-1c0d4bd0"><p class="cl-1c0d392e"><span class="cl-1c0a41b0">hse_inc</span></p></td><td class="cl-1c0d4bd1"><p class="cl-1c0d3938"><span class="cl-1c0a41b0">
484-0.109</span></p></td><td class="cl-1c0d4bda"><p class="cl-1c0d3938"><span class="cl-1c0a41b0">-0.110</span></p></td></tr><tr style="overflow-wrap:break-word;"><td class="cl-1c0d4bbd"><p class="cl-1c0d392e"><span class="cl-1c0a41b0">lvratmedium</span></p></td><td class="cl-1c0d4bc6"><p class="cl-1c0d3938"><span class="cl-1c0a41b0">0.464</span></p></td><td class="cl-1c0d4bc7"><p class="cl-1c0d3938"><span class="cl-1c0a41b0">0.460</span></p></td></tr><tr style="overflow-wrap:break-word;"><td class="cl-1c0d4bdb"><p class="cl-1c0d392e"><span class="cl-1c0a41b0">lvrathigh</span></p></td><td class="cl-1c0d4bdc"><p class="cl-1c0d3938"><span class="cl-1c0a41b0">1.495</span></p></td><td class="cl-1c0d4be4"><p class="cl-1c0d3938"><span class="cl-1c0a41b0">1.490</span></p></td></tr><tr style="overflow-wrap:break-word;"><td class="cl-1c0d4bbd"><p class="cl-1c0d392e"><span class="cl-1c0a41b0">ccred</span></p></td><td class="cl-1c0d4bc6"><p class="cl-1c0d3938"><span class="cl-1c0a41b0">0.290</span></p></td><td class="cl-1c0d4bc7"><p class="cl-1c0d3938"><span class="cl-1c0a41b0">0.290</span></p></td></tr><tr style="overflow-wrap:break-word;"><td class="cl-1c0d4bbd"><p class="cl-1c0d392e"><span class="cl-1c0a41b0">mcred</span></p></td><td class="cl-1c0d4bc6"><p class="cl-1c0d3938"><span class="cl-1c0a41b0">0.279</span></p></td><td class="cl-1c0d4bc7"><p class="cl-1c0d3938"><span class="cl-1c0a41b0">0.280</span></p></td></tr><tr style="overflow-wrap:break-word;"><td class="cl-1c0d4bd0"><p class="cl-1c0d392e"><span class="cl-1c0a41b0">pubrec</span></p></td><td class="cl-1c0d4bd1"><p class="cl-1c0d3938"><span class="cl-1c0a41b0">1.226</span></p></td><td class="cl-1c0d4bda"><p class="cl-1c0d3938"><span class="cl-1c0a41b0">1.230</span></p></td></tr><tr style="overflow-wrap:break-word;"><td class="cl-1c0d4bd0"><p class="cl-1c0d392e"><span class="cl-1c0a41b0">denpmi</span></p></td><td class="cl-1c0d4bd1"><p class="cl-1c0d3938"><span class="cl-1c0a41b0">4.548</span></p></td><td class="cl-1c0d4bda"><p class="cl-1c0d3938"><span class="cl-1c0a41b0">4.550</span></p></td></tr><tr style="overflow-wrap:break-word;"><td class="cl-1c0d4bee"><p class="cl-1c0d392e"><span class="cl-1c0a41b0">selfemp</span></p></td><td class="cl-1c0d4bef"><p class="cl-1c0d3938"><span class="cl-1c0a41b0">0.666</span></p></td><td class="cl-1c0d4bf8"><p class="cl-1c0d3938"><span class="cl-1c0a41b0">0.670</span></p></td></tr></tbody></table></div> 485</div> 486</div> 487</div> 488<p>The above comparisons show that the likelihood functions are developed, and coefficients are estimated, successfully.</p> 489</section> 490</section> 491</section> 492<section id="problem-2seatbelts" class="level1"> 493<h1>Problem 2(Seatbelts)</h1> 494<section id="a." class="level2 unnumbered"> 495<h2 class="unnumbered anchored" data-anchor-id="a.">a.</h2> 496<div class="cell"> 497<div class="sourceCode cell-code" id="cb9"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb9-1"><a href="#cb9-1" aria-hidden="true" tabindex="-1"></a>seatbelts <span class="ot"><-</span> <span class="fu">read_xls</span>(<span class="st">"data/SeatBelts.xls"</span>)</span> 498<span id="cb9-2"><a href="#cb9-2" aria-hidden="true" tabindex="-1"></a><span class="fu">attach</span>(seatbelts)</span> 499<span id="cb9-3"><a href="#cb9-3" aria-hidden="true" tabindex="-1"></a>mod.seat1 <span class="ot"><-</span> <span class="fu">lm</span>(</span> 500<span id="cb9-4"><a href="#cb9-4" aria-hidden="true" tabindex="-1"></a>
500 fatalityrate <span class="sc">~</span> <span class="dv">1</span> <span class="sc">+</span> sb_useage <span class="sc">+</span> speed65 <span class="sc">+</span> speed70 <span class="sc">+</span> ba08 <span class="sc">+</span> drinkage21 <span class="sc">+</span> <span class="fu">log</span>(income) <span class="sc">+</span> age</span> 501<span id="cb9-5"><a href="#cb9-5" aria-hidden="true" tabindex="-1"></a>)</span> 502<span id="cb9-6"><a href="#cb9-6" aria-hidden="true" tabindex="-1"></a><span class="fu">detach</span>(seatbelts)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div> 503</div> 504<p>From the regression, increased seat belt use enlarges fatalities.</p> 505</section> 506<section id="b." class="level2 unnumbered"> 507<h2 class="unnumbered anchored" data-anchor-id="b.">b.</h2> 508<p>Compare the coefficients between two models. The coefficient of <em>sb_useage</em> changed from positive to negative. There may be some properties of states caused the bias. After fixing <em>state</em>, it becomes more reasonable.</p> 509</section> 510<section id="c." class="level2 unnumbered"> 511<h2 class="unnumbered anchored" data-anchor-id="c.">c. </h2> 512<p>After adding time fixed effects plus state fixed effects, the coefficient of <em>sb_useage</em> is still negative when fixing state and year, which indicates that <strong>higher seat belt use rate reduces fatalities</strong>.</p> 513<div class="cell"> 514<div class="sourceCode cell-code" id="cb10"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb10-1"><a href="#cb10-1" aria-hidden="true" tabindex="-1"></a><span class="fu">attach</span>(seatbelts)</span> 515<span id="cb10-2"><a href="#cb10-2" aria-hidden="true" tabindex="-1"></a>mod.seat3 <span class="ot"><-</span> seatbelts <span class="sc">%>%</span> <span class="fu">plm</span>(</span> 516<span id="cb10-3"><a href="#cb10-3" aria-hidden="true" tabindex="-1"></a>
516 fatalityrate <span class="sc">~</span> sb_useage <span class="sc">+</span> speed65 <span class="sc">+</span> speed70 <span class="sc">+</span> ba08 <span class="sc">+</span> drinkage21 <span class="sc">+</span> <span class="fu">log</span>(income) <span class="sc">+</span> age,</span> 517<span id="cb10-4"><a href="#cb10-4" aria-hidden="true" tabindex="-1"></a> <span class="at">effect =</span> <span class="st">"twoway"</span>,</span> 518<span id="cb10-5"><a href="#cb10-5" aria-hidden="true" tabindex="-1"></a> <span class="at">index =</span> <span class="fu">c</span>(<span class="st">"state"</span>, <span class="st">"year"</span>),</span> 519<span id="cb10-6"><a href="#cb10-6" aria-hidden="true" tabindex="-1"></a> <span class="at">data =</span> .</span> 520<span id="cb10-7"><a href="#cb10-7" aria-hidden="true" tabindex="-1"></a>)</span> 521<span id="cb10-8"><a href="#cb10-8" aria-hidden="true" tabindex="-1"></a><span class="fu">detach</span>(seatbelts)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div> 522</div> 523<div class="cell"> 524<div class="cell-output-display"> 525<div id="tbl-fix_year_state" class="anchored"> 526<table data-quarto-postprocess="true" class="table table-sm table-striped small"> 527<caption>Table 4: Coef.: no fixing, fix state, fix state plus year</caption> 528<colgroup> 529<col style="width: 25%"> 530<col style="width: 25%"> 531<col style="width: 25%"> 532<col style="width: 25%"> 533</colgroup> 534<tbody> 535<tr class="odd"> 536<td data-quarto-table-cell-role="th" style="text-align: center; border-top: double; font-style: italic; font-weight: normal; padding: 0.2cm; border-bottom: 1px solid black;"> </td> 537<td data-quarto-table-cell-role="th" style="text-align: center; border-top: double; font-style: italic; font-weight: normal; padding: 0.2cm; border-bottom: 1px solid black;">without fixing</td> 538<td data-quarto-table-cell-role="th" style="text-align: center; border-top: double; font-style: italic; font-weight: normal; padding: 0.2cm; border-bottom: 1px solid black;">fix state</td> 539<td data-quarto-table-cell-role="th" style="text-align: center; border-top: double; font-style: italic; font-weight: normal; padding: 0.2cm; border-bottom: 1px solid black;">fix state plus year</td> 540</tr> 541<tr class="even"> 542<td style="text-align: center; border-bottom: 1px solid; font-style: italic; font-weight: normal; border-bottom: 1px solid black;">Predictors</td> 543<td style="text-align: center; border-bottom: 1px solid; font-style: italic; font-weight: normal; border-bottom: 1px solid black;">Estimates</td> 544<td style="text-align: center; border-bottom: 1px solid; font-style: italic; font-weight: normal; border-bottom: 1px solid black;">Estimates</td> 545<td style="text-align: center; border-bottom: 1px solid; font-style: italic; font-weight: normal; border-bottom: 1px solid black;">Estimates</td> 546</tr> 547<tr class="odd"> 548<td style="text-align: center;">(Intercept)</td> 549<td style="text-align: center;">0.1965 <sup>***</sup><br> 550(0.0082)</td> 551<td style="text-align: center;"></td> 552<td style="text-align: center;"></td> 553</tr> 554<tr class="even"> 555<td style="text-align: center;">sb_useage</td> 556<td style="text-align: center;">0.0041 <sup>***</sup><br> 557(0.0012)</td> 558<td style="text-align: center;">-0.0058 <sup>***</sup><br> 559(0.0012)</td> 560<td style="text-align: center;">-0.0037 <sup>**</sup><br> 561(0.0011)</td> 562</tr> 563<tr class="odd"> 564<td style="text-align: center;">speed65</td> 565<td style="text-align: center;">0.0001 <sup></sup><br> 566(0.0004)</td> 567<td style="text-align: center;">-0.0004 <sup></sup><br> 568(0.0003)</td> 569<td style="text-align: center;">-0.0008 <sup></sup><br> 570(0.0004)</td> 571</tr> 572<tr class="even"> 573<td style="text-align: center;">speed70</td> 574<td style="text-align: center;">0.0024 <sup>***</sup><br> 575(0.0005)</td> 576<td style="text-align: center;">0.0012 <sup>***</sup><br> 577(0.0003)</td> 578<td style="text-align: center;">0.0008 <sup>*</sup><br> 579(0.0003)</td> 580</tr> 581<tr class="odd"> 582<td style="text-align: center;">ba08</td> 583<td style="text-align: center;">-0.0019 <sup>***</sup><br> 584(0.0004)</td> 585<td style="text-align: center;">-0.0014 <sup>***</sup><br> 586(0.0004)</td> 587<td style="text-align: center;">-0.0008 <sup>*</sup><br> 588(0.0004)</td> 589</tr> 590<tr class="even"> 591<td style="text-align: center;">drinkage21</td> 592<td style="text-align: center;">0.0001 <sup></sup><br> 593(0.0009)</td> 594<td style="text-align: center;">0.0007 <sup></sup><br> 595(0.0005)</td> 596<td style="text-align: center;">-0.0011 <sup>*</sup><br> 597(0.0005)</td> 598</tr> 599<tr class="odd"> 600<td style="text-align: center;">log(income)</td> 601<td style="text-align: center;">-0.0181 <sup>***</sup><br> 602(0.0009)</td> 603<td style="text-align: center;">-0.0135 <sup>***</sup><br> 604(0.0014)</td> 605<td style="text-align: center;">0.0063 <sup></sup><br> 606(0.0039)</td> 607</tr> 608<tr class="even"> 609<td style="text-align: center;">age</td> 610<td style="text-align: center;">-0.0000 <sup></sup><br> 611(0.0001)</td> 612<td style="text-align: center;">0.0010 <sup>*</sup><br> 613(0.0004)</td> 614<td style="text-align: center;">0.0013 <sup>***</sup><br> 615(0.0004)</td> 616</tr> 617<tr class="odd"> 618<td style="text-align: center; padding-top: 0.1cm; padding-bottom: 0.1cm; border-top: 1px solid;">Observations</td> 619<td style="text-align: center; padding-top: 0.1cm; padding-bottom: 0.1cm; border-top: 1px solid;">556</td> 620<td style="text-align: center; padding-top: 0.1cm; padding-bottom: 0.1cm; border-top: 1px solid;">556</td> 621<td style="text-align: center; padding-top: 0.1cm; padding-bottom: 0.1cm; border-top: 1px solid;">556</td> 622</tr> 623<tr class="even"> 624<td style="text-align: center; padding-top: 0.1cm; padding-bottom: 0.1cm;">R<sup>2</sup> / R<sup>2</sup> adjusted</td> 625<td style="text-align: center; padding-top: 0.1cm; padding-bottom: 0.1cm;">0.549 / 0.544</td> 626<td style="text-align: center; padding-top: 0.1cm; padding-bottom: 0.1cm;">0.687 / 0.651</td> 627<td style="text-align: center; padding-top: 0.1cm; padding-bottom: 0.1cm;">0.083 / -0.052</td> 628</tr> 629<tr class="odd"> 630<td colspan="4" style="text-align: right; font-style: italic; border-top: double black;">* p<0.05 ** p<0.01 *** p<0.001</td> 631</tr> 632</tbody> 633</table> 634</div> 635 636 637</div> 638</div> 639</section> 640<section id="d." class="level2 unnumbered"> 641<h2 class="unnumbered anchored" data-anchor-id="d.">d. </h2> 642<p>Regression in (c), with state and year fixed is most reliable. Because it fixes the effects of different years and states, of which the coefficient of <em>sb_useage</em> is most precise.</p> 643</section> 644<section id="e." class="level2 unnumbered"> 645<h2 class="unnumbered anchored" data-anchor-id="e.">e.</h2> 646<p>Th e coefficient of <em>sb_useage</em> is -0.0037, indicating that with 1% seat belt use increased, fatalities will reduce by 0.37%. It is a large number. It means that if seat belt use increase from 52% to 90%, about 58 lives will be saved(counted by average <code>millions of traffic miles per year</code>).</p> 647</section> 648<section id="f." class="level2 unnumbered"> 649<h2 class="unnumbered anchored" data-anchor-id="f.">f. </h2> 650<div class="cell"> 651<div class="sourceCode cell-code" id="cb11"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb11-1"><a href="#cb11-1" aria-hidden="true" tabindex="-1"></a><span class="fu">attach</span>(seatbelts)</span> 652<span id="cb11-2"><a href="#cb11-2" aria-hidden="true" tabindex="-1"></a>mod.seat4 <span class="ot"><-</span> seatbelts <span class="sc">%>%</span> <span class="fu">plm</span>(</span> 653<span id="cb11-3"><a href="#cb11-3" aria-hidden="true" tabindex="-1"></a>
653 sb_useage <span class="sc">~</span> primary <span class="sc">+</span> secondary <span class="sc">+</span> speed65 <span class="sc">+</span> speed70 <span class="sc">+</span> ba08 <span class="sc">+</span> drinkage21 <span class="sc">+</span> <span class="fu">log</span>(income) <span class="sc">+</span> age,</span> 654<span id="cb11-4"><a href="#cb11-4" aria-hidden="true" tabindex="-1"></a> <span class="at">data =</span> .,</span> 655<span id="cb11-5"><a href="#cb11-5" aria-hidden="true" tabindex="-1"></a> <span class="at">index =</span> <span class="fu">c</span>(<span class="st">"state"</span>, <span class="st">"year"</span>),</span> 656<span id="cb11-6"><a href="#cb11-6" aria-hidden="true" tabindex="-1"></a> <span class="at">effect =</span> <span class="st">"twoway"</span></span> 657<span id="cb11-7"><a href="#cb11-7" aria-hidden="true" tabindex="-1"></a>)</span> 658<span id="cb11-8"><a href="#cb11-8" aria-hidden="true" tabindex="-1"></a><span class="fu">detach</span>(seatbelts)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div> 659</div> 660<div class="cell"> 661<div class="cell-output-display"> 662<div id="tbl-mod.seat4" class="anchored"> 663<table data-quarto-postprocess="true" class="table table-sm table-striped small"> 664<caption>Table 5: Primary and Secondary, Fixed Years and States</caption> 665<tbody> 666<tr class="odd"> 667<td data-quarto-table-cell-role="th" style="text-align: center; border-top: double; font-style: italic; font-weight: normal; padding: 0.2cm; border-bottom: 1px solid black;"> </td> 668<td colspan="3" data-quarto-table-cell-role="th" style="text-align: center; border-top: double; font-style: italic; font-weight: normal; padding: 0.2cm; border-bottom: 1px solid black;">sb_useage</td> 669</tr> 670<tr class="even"> 671<td style="text-align: center; border-bottom: 1px solid; font-style: italic; font-weight: normal; border-bottom: 1px solid black;">Predictors</td> 672<td style="text-align: center; border-bottom: 1px solid; font-style: italic; font-weight: normal; border-bottom: 1px solid black;">Estimates</td> 673<td style="text-align: center; border-bottom: 1px solid; font-style: italic; font-weight: normal; border-bottom: 1px solid black;">std. Error</td> 674<td style="text-align: center; border-bottom: 1px solid; font-style: italic; font-weight: normal; border-bottom: 1px solid black;">CI</td> 675</tr> 676<tr class="odd"> 677<td style="text-align: center;">primary</td> 678<td style="text-align: center;">0.2056 <sup>***</sup></td> 679<td style="text-align: center;">0.0281</td> 680<td style="text-align: center;">0.1503 â 0.2609</td> 681</tr> 682<tr class="even"> 683<td style="text-align: center;">secondary</td> 684<td style="text-align: center;">0.1085 <sup>***</sup></td> 685<td style="text-align: center;">0.0104</td> 686<td style="text-align: center;">0.0880 â 0.1290</td> 687</tr> 688<tr class="odd"> 689<td style="text-align: center;">speed65</td> 690<td style="text-align: center;">0.0228 <sup></sup></td> 691<td style="text-align: center;">0.0153</td> 692<td style="text-align: center;">-0.0071 â 0.0528</td> 693</tr> 694<tr class="even"> 695<td style="text-align: center;">speed70</td> 696<td style="text-align: center;">0.0120 <sup></sup></td> 697<td style="text-align: center;">0.0121</td> 698<td style="text-align: center;">-0.0116 â 0.0357</td> 699</tr> 700<tr class="odd"> 701<td style="text-align: center;">ba08</td> 702<td style="text-align: center;">0.0038 <sup></sup></td> 703<td style="text-align: center;">0.0125</td> 704<td style="text-align: center;">-0.0208 â 0.0283</td> 705</tr> 706<tr class="even"> 707<td style="text-align: center;">drinkage21</td> 708<td style="text-align: center;">0.0107 <sup></sup></td> 709<td style="text-align: center;">0.0197</td> 710<td style="text-align: center;">-0.0280 â 0.0494</td> 711</tr> 712<tr class="odd"> 713<td style="text-align: center;">log(income)</td> 714<td style="text-align: center;">0.0583 <sup></sup></td> 715<td style="text-align: center;">0.1372</td> 716<td style="text-align: center;">-0.2114 â 0.3279</td> 717</tr> 718<tr class="even"> 719<td style="text-align: center;">age</td> 720<td style="text-align: center;">0.0138 <sup></sup></td> 721<td style="text-align: center;">0.0136</td> 722<td style="text-align: center;">-0.0129 â 0.0406</td> 723</tr> 724<tr class="odd"> 725<td style="text-align: center; font-weight: bold; border-top: 1px solid;">Observations</td> 726<td colspan="3" style="text-align: center; font-weight: bold; border-top: 1px solid;">556</td> 727</tr> 728<tr class="even"> 729<td style="text-align: center; font-weight: bold;">R<sup>2</sup> / R<sup>2</sup> adjusted</td> 730<td colspan="3" style="text-align: center; font-weight: bold;">0.249 / 0.138</td> 731</tr> 732<tr class="odd"> 733<td colspan="4" style="text-align: right; font-style: italic; border-top: double black;">* p<0.05 ** p<0.01 *** p<0.001</td> 734</tr> 735</tbody> 736</table> 737</div> 738 739 740</div> 741</div> 742<p>The regression result shows that primary enforcement leads to more seat belt use. Secondary enforcement, too, leads to more seat belt use.</p> 743</section> 744<section id="g." class="level2 unnumbered"> 745<h2 class="unnumbered anchored" data-anchor-id="g.">g.</h2> 746<p><span class="math display">\[ 747sub\space useage=0.206\times primary+0.109\times secondary+... 748\]</span></p> 749<p>New Jersey changed from secondary enforcement to primary enforcement, which means:</p> 750<p><span class="math display">\[ 751primary: 0 \rightarrow1, secondary:1\rightarrow0 752\]</span></p> 753<p><span class="math display">\[ 754\Delta sb \space useage=0.206-0.109=0.097 755\]</span></p> 756<p>This is predicted to reduce the fatality rate by <span class="math inline">\(0.00372\times 0.097=0.00036\)</span> fatalities per million traffic mile.</p> 757<p><span class="math display">\[ 758\Delta fatality\space rate=-0.00372\times \Delta sb\space useage=0.00372\times 0.097=0.00036 759\]</span></p> 760<p>The data set shows that there were 6300 million traffic miles in 1997 in New Jersey. Assuming that same number of traffic miles in 2000 yields <span class="math inline">\(0.00036\times 63,000=23\)</span> lives saved.</p> 761</section> 762</section> 763<section id="problem-3jec" class="level1"> 764<h1>Problem 3(JEC)</h1> 765<section id="a.-1" class="level2 unnumbered"> 766<h2 class="unnumbered anchored" data-anchor-id="a.-1">a.</h2> 767<p>The model is</p> 768<p><span class="math display">\[ 769ln(Q_i)=\beta_0+\beta_1ln(P_i)+\beta_2Ice_i+\Sigma^{12}_{j=1}\beta Seas_{j,i}+u_i 770\]</span></p> 771<div class="cell"> 772<div class="sourceCode cell-code" id="cb12"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb12-1"><a href="#cb12-1" aria-hidden="true" tabindex="-1"></a>jec <span class="ot"><-</span> <span class="fu">read_xls</span>(<span class="st">"data/JEC.xls"</span>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div> 773</div> 774<div class="cell"> 775<div class="sourceCode cell-code" id="cb13"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb13-1"><a href="#cb13-1" aria-hidden="true" tabindex="-1"></a><span class="fu">attach</span>(jec)</span> 776<span id="cb13-2"><a href="#cb13-2" aria-hidden="true" tabindex="-1"></a>mod.jec1 <span class="ot"><-</span> <span class="fu">lm</span>(</span> 777<span id="cb13-3"><a href="#cb13-3" aria-hidden="true" tabindex="-1"></a> <span class="fu">log</span>(quantity) <span class="sc">~</span> <span class="dv">1</span> <span class="sc">+</span> <span class="fu">log</span>(price) <span class="sc">+</span> ice <span class="sc">+</span> seas1 <span class="sc">+</span> seas2 <span class="sc">+</span> seas3 <span class="sc">+</span> seas4 <span class="sc">+</span></span> 778<span id="cb13-4"><a href="#cb13-4" aria-hidden="true" tabindex="-1"></a> seas5 <span class="sc">+</span> seas6 <span class="sc">+</span> seas7 <span class="sc">+</span> seas8 <span class="sc">+</span> seas9 <span class="sc">+</span> seas10 <span class="sc">+</span> seas11 <span class="sc">+</span> seas12</span> 779<span id="cb13-5"><a href="#cb13-5" aria-hidden="true" tabindex="-1"></a>)</span> 780<span id="cb13-6"><a href="#cb13-6" aria-hidden="true" tabindex="-1"></a><span class="fu">detach</span>(jec)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div> 781</div> 782<p>The regression result shows that the demand elasticity is -0.639 and its standard error is 0.082</p> 783</section> 784<section id="b.-1" class="level2 unnumbered"> 785<h2 class="unnumbered anchored" data-anchor-id="b.-1">b.</h2> 786<p>There is simultaneous causality in the interaction of supply and demand, thus it makes the OLS estimator of the elasticity b
786iased.</p> 787</section> 788<section id="c.-1" class="level2 unnumbered"> 789<h2 class="unnumbered anchored" data-anchor-id="c.-1">c. </h2> 790<p>The collusion of the cartel increases the price of grain what would have been the competitive price, i.e. <span class="math inline">\(Corr(cartel, ln(price))>0\)</span>. But the cartel and change price do not influence the demand of grain, for grain is necessary, which means <span class="math inline">\(Corr(cartel, ln(Q))=0\)</span>. The two correlations above illustrate that <em>cartel</em> is a valid instrument.</p> 791</section> 792<section id="d.-1" class="level2 unnumbered"> 793<h2 class="unnumbered anchored" data-anchor-id="d.-1">d. </h2> 794<p>Model of Stage 1:</p> 795<p><span class="math display">\[ 796ln(P_i)=\beta_0+\beta_1 cartel+\beta_2Ice_i+\Sigma^{12}_{j=1}\beta Seas_{j,i}+u_i 797\]</span></p> 798<div class="cell"> 799<div class="sourceCode cell-code" id="cb14"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb14-1"><a href="#cb14-1" aria-hidden="true" tabindex="-1"></a><span class="fu">attach</span>(jec)</span> 800<span id="cb14-2"><a href="#cb14-2" aria-hidden="true" tabindex="-1"></a>mod.jec_stage1 <span class="ot"><-</span> <span class="fu">lm</span>(</span> 801<span id="cb14-3"><a href="#cb14-3" aria-hidden="true" tabindex="-1"></a> <span class="fu">log</span>(price) <span class="sc">~</span> <span class="dv">1</span> <span class="sc">+</span> cartel <span class="sc">+</span> ice <span class="sc">+</span> seas1 <span class="sc">+</span> seas2 <span class="sc">+</span> seas3 <span class="sc">+</span> seas4 <span class="sc">+</span></span> 802<span id="cb14-4"><a href="#cb14-4" aria-hidden="true" tabindex="-1"></a> seas5 <span class="sc">+</span> seas6 <span class="sc">+</span> seas7 <span class="sc">+</span> seas8 <span class="sc">+</span> seas9 <span class="sc">+</span> seas10 <span class="sc">+</span> seas11 <span class="sc">+</span> seas12</span> 803<span id="cb14-5"><a href="#cb14-5" aria-hidden="true" tabindex="-1"></a>)</span> 804<span id="cb14-6"><a href="#cb14-6" aria-hidden="true" tabindex="-1"></a><span class="fu">detach</span>(jec)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div> 805</div> 806<p>The first state F-statistic, 21.3170209, which is > 10, illustrates that the estimators in first stage are jointly significant. That means <em>cartel</em> is <strong>not a weak instrument</strong>.</p> 807</section> 808<section id="e.-1" class="level2 unnumbered"> 809<h2 class="unnumbered anchored" data-anchor-id="e.-1">e.</h2> 810<p>The model of second stage:</p> 811<p><span class="math display">\[ 812ln(Q_i)=\beta_0+\beta_1\widehat{ln(P_i)}+\beta_2Ice_i+\Sigma^{12}_{j=1}\beta Seas_{j,i}+w_i 813\]</span></p> 814<div class="cell"> 815<div class="sourceCode cell-code" id="cb15"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb15-1"><a href="#cb15-1" aria-hidden="true" tabindex="-1"></a>pred_logp <span class="ot"><-</span> <span class="fu">fitted.values</span>(mod.jec_stage1)</span> 816<span id="cb15-2"><a href="#cb15-2" aria-hidden="true" tabindex="-1"></a><span class="fu">attach</span>(jec)</span> 817<span id="cb15-3"><a href="#cb15-3" aria-hidden="true" tabindex="-1"></a>mod.jec_stage2 <span class="ot"><-</span> <span class="fu">ivreg</span>(</span> 818<span id="cb15-4"><a href="#cb15-4" aria-hidden="true" tabindex="-1"></a> <span class="fu">log</span>(quantity) <span class="sc">~</span> <span class="dv">1</span> <span class="sc">+</span> <span class="fu">log</span>(price) <span class="sc">+</span> ice <span class="sc">+</span> seas1 <span class="sc">+</span> seas2 <span class="sc">+</span> seas3 <span class="sc">+</span> seas4 <span class="sc">+</span></span> 819<span id="cb15-5"><a href="#cb15-5" aria-hidden="true" tabindex="-1"></a> seas5 <span class="sc">+</span> seas6 <span class="sc">+</span> seas7 <span class="sc">+</span> seas8 <span class="sc">+</span> seas9 <span class="sc">+</span> seas10 <span class="sc">+</span> seas11 <span class="sc">+</span> seas12 <span class="sc">|</span></span> 820<span id="cb15-6"><a href="#cb15-6" aria-hidden="true" tabindex="-1"></a> cartel <span class="sc">+</span> ice <span class="sc">+</span> seas1 <span class="sc">+</span> seas2 <span class="sc">+</span> seas3 <span class="sc">+</span> seas4 <span class="sc">+</span></span> 821<span id="cb15-7"><a href="#cb15-7" aria-hidden="true" tabindex="-1"></a> seas5 <span class="sc">+</span> seas6 <span class="sc">+</span> seas7 <span class="sc">+</span> seas8 <span class="sc">+</span> seas9 <span class="sc">+</span> seas10 <span class="sc">+</span> seas11 <span class="sc">+</span> seas12</span> 822<span id="cb15-8"><a href="#cb15-8" aria-hidden="true" tabindex="-1"></a>)</span> 823<span id="cb15-9"><a href="#cb15-9" aria-hidden="true" tabindex="-1"></a><span class="fu">detach</span>(jec)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div> 824</div> 825<p>The regression result shows that estimated demand elasticity is -0.867 and its standard error is 0.132.</p> 826<div class="cell"> 827<div class="cell-output-display"> 828<div id="tbl-jec_reg" class="anchored"> 829<table data-quarto-postprocess="true" class="table table-sm table-striped small"> 830<caption>Table 6: JEC Regression Results(FE on Seasons)</caption> 831<colgroup> 832<col style="width: 25%"> 833<col style="width: 25%"> 834<col style="width: 25%"> 835<col style="width: 25%"> 836</colgroup> 837<tbody> 838<tr class="odd"> 839<td data-quarto-table-cell-role="th" style="text-align: center; border-top: double; font-style: italic; font-weight: normal; padding: 0.2cm; border-bottom: 1px solid black;"> </td> 840<td data-quarto-table-cell-role="th" style="text-align: center; border-top: double; font-style: italic; font-weight: normal; padding: 0.2cm; border-bottom: 1px solid black;">Elasticity</td> 841<td data-quarto-table-cell-role="th" style="text-align: center; border-top: double; font-style: italic; font-weight: normal; padding: 0.2cm; border-bottom: 1px solid black;">TSLS stage 1</td> 842<td data-quarto-table-cell-role="th" style="text-align: center; border-top: double; font-style: italic; font-weight: normal; padding: 0.2cm; border-bottom: 1px solid black;">TSLS stage 2</td> 843</tr> 844<tr class="even"> 845<td style="text-align: center; border-bottom: 1px solid; font-style: italic; font-weight: normal; border-bottom: 1px solid black;">Predictors</td> 846<td style="text-align: center; border-bottom: 1px solid; font-style: italic; font-weight: normal; border-bottom: 1px solid black;">Estimates</td> 847<td style="text-align: center; border-bottom: 1px solid; font-style: italic; font-weight: normal; border-bottom: 1px solid black;">Estimates</td> 848<td style="text-align: center; border-bottom: 1px solid; font-style: italic; font-weight: normal; border-bottom: 1px solid black;">Estimates</td> 849</tr> 850<tr class="odd"> 851<td style="text-align: center;">(Intercept)</td> 852<td style="text-align: center;">8.8612 <sup>***</sup><br> 853(0.1714)</td> 854<td style="text-align: center;">-1.6937 <sup>***</sup><br> 855(0.0784)</td> 856<td style="text-align: center;">8.5735 <sup>***</sup><br> 857(0.2164)</td> 858</tr> 859<tr class="even"> 860<td style="text-align: center;">price [log]</td> 861<td style="text-align: center;">-0.6389 <sup>***</sup><br> 862(0.0824)</td> 863<td style="text-align: center;"></td> 864<td style="text-align: center;">-0.8666 <sup>***</sup><br> 865(0.1321)</td> 866</tr> 867<tr class="odd"> 868<td style="text-align: center;">cartel</td> 869<td style="text-align: center;"></td> 870<td style="text-align: center;">0.3579 <sup>***</sup><br> 871(0.0249)</td> 872<td style="text-align: center;"></td> 873</tr> 874<tr class="even"> 875<td style="text-align: center; padding-top: 0.1cm; padding-bottom: 0.1cm; border-top: 1px solid;">Observations</td> 876<td style="text-align: center; padding-top: 0.1cm; padding-bottom: 0.1cm; border-top: 1px solid;">328</td> 877<td style="text-align: center; padding-top: 0.1cm; padding-bottom: 0.1cm; border-top: 1px solid;">328</td> 878<td style="text-align: center; padding-top: 0.1cm; padding-bottom: 0.1cm; border-top: 1px solid;">328</td> 879</tr> 880<tr class="odd"> 881<td style="text-align: center; padding-top: 0.1cm; padding-bottom: 0.1cm;">R<sup>2</sup> / R<sup>2</sup> adjusted</td> 882<td style="text-align: center; padding-top: 0.1cm; padding-bottom: 0.1cm;">0.313 / 0.282</td> 883<td style="text-align: center; padding-top: 0.1cm; padding-bottom: 0.1cm;">0.488 / 0.465</td> 884<td style="text-align: center; padding-top: 0.1cm; padding-bottom: 0.1cm;">0.296 / 0.264</td> 885</tr> 886<tr class="even"> 887<td colspan="4" style="text-align: right; font-style: italic; border-top: double black;">* p<0.05 ** p<0.01 *** p<0.001</td> 888</tr> 889</tbody> 890</table> 891</div> 892 893 894</div> 895</div> 896</section> 897<section id="f.-1" class="level2 unnumbered"> 898<h2 class="unnumbered anchored" data-anchor-id="f.-1">f. </h2> 899<p>The absolute price elasticity is less than 1, so marginal profit is positive, which prompts the cartel to raise the price. So it suggests that the cartel was charging the profit-maximizing monopoly price.</p> 900</section> 901</section> 902<section id="problem-4movies" class="level1"> 903<h1>Problem 4(Movies)</h1> 904<section id="a.-2" class="level2 unnumbered"> 905<h2 class="unnumbered anchored" data-anchor-id="a.-2">a.</h2> 906<section id="i." class="level3 unnumbered unlisted"> 907<h3 class="unnumbered unlisted anchored" data-anchor-id="i.">i.</h3> 908<div class="cell"> 909<div class="sourceCode cell-code" id="cb16"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb16-1"><a href="#cb16-1" aria-hidden="true" tabindex="-1"></a>movies <span class="ot"><-</span> <span class="fu">read_xlsx</span>(<span class="st">"data/Movies.xlsx"</span>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div> 910</div> 911<p>The Model is as follows:</p> 912<p><span class="math display">\[ 913log(assaults_i) = \beta_0 + \Sigma^{10}_{j=2}\beta year_{j,i}+\Sigma^{12}_{j=2}\beta month_{j,i} + u_i 914\]</span></p> 915<p>Choose year1, month1 as the basic group, to avoid the dummy variable trap. Then regress <em>log(assaults)</em> on <em>years</em> and <em>months</em></p> 916<div class="cell"> 917<div class="sourceCode cell-code" id="cb17"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb17-1"><a href="#cb17-1" aria-hidden="true" tabindex="-1"></a><span class="fu">attach</span>(movies)</span> 918<span id="cb17-2"><a href="#cb17-2" aria-hidden="true" tabindex="-1"></a>mod.movies1 <span class="ot"><-</span> <span class="fu">lm</span>(</span> 919<span id="cb17-3"><a href="#cb17-3" aria-hidden="true" tabindex="-1"></a> <span class="fu">log</span>(assaults) <span class="sc">~</span> <span class="dv">1</span> <span class="sc">+</span> year2 <span class="sc">+</span> year3 <span class="sc">+</span> year4 <span class="sc">+</span> year5 <span class="sc">+</span> year6 <span class="sc">+</span> year7 <span class="sc">+</span>
919 year8 <span class="sc">+</span> year9 <span class="sc">+</span></span> 920<span id="cb17-4"><a href="#cb17-4" aria-hidden="true" tabindex="-1"></a> year10 <span class="sc">+</span> month2 <span class="sc">+</span> month3 <span class="sc">+</span> month4 <span class="sc">+</span> month5 <span class="sc">+</span> month6 <span class="sc">+</span> month7 <span class="sc">+</span> month8 <span class="sc">+</span> month9 <span class="sc">+</span></span> 921<span id="cb17-5"><a href="#cb17-5" aria-hidden="true" tabindex="-1"></a> month10 <span class="sc">+</span> month11 <span class="sc">+</span> month12</span> 922<span id="cb17-6"><a href="#cb17-6" aria-hidden="true" tabindex="-1"></a>)</span> 923<span id="cb17-7"><a href="#cb17-7" aria-hidden="true" tabindex="-1"></a><span class="fu">detach</span>(movies)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div> 924</div> 925<div class="cell"> 926<div class="cell-output-display"> 927<div id="fig-movies1" class="quarto-figure quarto-figure-center anchored"> 928<figure class="figure"> 929<p><img src="exp2_files/figure-html/fig-movies1-1.png" class="img-fluid figure-img" width="672"></p> 930<p></p><figcaption class="figure-caption">Figure 1: Reg assault: Effects of Years and Months on Assaults</figcaption><p></p> 931</figure> 932</div> 933</div> 934</div> 935<div class="cell"> 936<div class="sourceCode cell-code" id="cb18"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb18-1"><a href="#cb18-1" aria-hidden="true" tabindex="-1"></a>mod.movies1_f <span class="ot"><-</span> mod.movies1 <span class="sc">%>%</span></span> 937<span id="cb18-2"><a href="#cb18-2" aria-hidden="true" tabindex="-1"></a> <span class="fu">linearHypothesis</span>(<span class="fu">c</span>(</span> 938<span id="cb18-3"><a href="#cb18-3" aria-hidden="true" tabindex="-1"></a> <span class="st">"month2=month3"</span>,</span> 939<span id="cb18-4"><a href="#cb18-4" aria-hidden="true" tabindex="-1"></a> <span class="st">"month2=month4"</span>,</span> 940<span id="cb18-5"><a href="#cb18-5" aria-hidden="true" tabindex="-1"></a> <span class="st">"month2=month5"</span>,</span> 941<span id="cb18-6"><a href="#cb18-6" aria-hidden="true" tabindex="-1"></a> <span class="st">"month2=month6"</span>,</span> 942<span id="cb18-7"><a href="#cb18-7" aria-hidden="true" tabindex="-1"></a> <span class="st">"month2=month7"</span>,</span> 943<span id="cb18-8"><a href="#cb18-8" aria-hidden="true" tabindex="-1"></a> <span class="st">"month2=month8"</span>,</span> 944<span id="cb18-9"><a href="#cb18-9" aria-hidden="true" tabindex="-1"></a> <span class="st">"month2=month9"</span>,</span> 945<span id="cb18-10"><a href="#cb18-10" aria-hidden="true" tabindex="-1"></a> <span class="st">"month2=month10"</span>,</span> 946<span id="cb18-11"><a href="#cb18-11" aria-hidden="true" tabindex="-1"></a> <span class="st">"month2=month11"</span>,</span> 947<span id="cb18-12"><a href="#cb18-12" aria-hidden="true" tabindex="-1"></a> <span class="st">"month2=month12"</span></span> 948<span id="cb18-13"><a href="#cb18-13" aria-hidden="true" tabindex="-1"></a> )) <span class="sc">%>%</span></span> 949<span id="cb18-14"><a href="#cb18-14" aria-hidden="true" tabindex="-1"></a> .[<span class="st">"F"</span>] <span class="sc">%>%</span></span> 950<span id="cb18-15"><a href="#cb18-15" aria-hidden="true" tabindex="-1"></a> <span class="fu">pull</span>() <span class="sc">%>%</span></span> 951<span id="cb18-16"><a href="#cb18-16" aria-hidden="true" tabindex="-1"></a> .[<span class="dv">2</span>] <span class="sc">%>%</span></span> 952<span id="cb18-17"><a href="#cb18-17" aria-hidden="true" tabindex="-1"></a> <span class="fu">round</span>()</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div> 953</div> 954<p>The regression result shows that assaults increases with year. And there are more assaults in month 5-10, less in month 1, 12. And the F-statistic on the 11 monthly indicators is 67 with p-value that is essentially 0. So the seasonality in assaults exists.</p> 955</section> 956<section id="ii." class="level3 unnumbered unlisted"> 957<h3 class="unnumbered unlisted anchored" data-anchor-id="ii.">ii.</h3> 958<div class="cell"> 959<div class="sourceCode cell-code" id="cb19"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb19-1"><a href="#cb19-1" aria-hidden="true" tabindex="-1"></a><span class="co"># Generate attend</span></span> 960<span id="cb19-2"><a href="#cb19-2" aria-hidden="true" tabindex="-1"></a>movies <span class="ot"><-</span> movies <span class="sc">%>%</span> <span class="fu">mutate</span>(<span class="at">attend =</span> attend_v <span class="sc">+</span> attend_m <span class="sc">+</span>
960 attend_n)</span> 961<span id="cb19-3"><a href="#cb19-3" aria-hidden="true" tabindex="-1"></a><span class="fu">attach</span>(movies)</span> 962<span id="cb19-4"><a href="#cb19-4" aria-hidden="true" tabindex="-1"></a>mod.attend1 <span class="ot"><-</span> <span class="fu">lm</span>(</span> 963<span id="cb19-5"><a href="#cb19-5" aria-hidden="true" tabindex="-1"></a> attend <span class="sc">~</span> <span class="dv">1</span> <span class="sc">+</span> year2 <span class="sc">+</span> year3 <span class="sc">+</span> year4 <span class="sc">+</span> year5 <span class="sc">+</span> year6 <span class="sc">+</span> year7 <span class="sc">+</span> year8 <span class="sc">+</span> year9 <span class="sc">+</span></span> 964<span id="cb19-6"><a href="#cb19-6" aria-hidden="true" tabindex="-1"></a> year10 <span class="sc">+</span> month2 <span class="sc">+</span> month3 <span class="sc">+</span> month4 <span class="sc">+</span> month5 <span class="sc">+</span> month6 <span class="sc">+</span> month7 <span class="sc">+</span> month8 <span class="sc">+</span> month9 <span class="sc">+</span></span> 965<span id="cb19-7"><a href="#cb19-7" aria-hidden="true" tabindex="-1"></a> month10 <span class="sc">+</span> month11 <span class="sc">+</span> month12</span> 966<span id="cb19-8"><a href="#cb19-8" aria-hidden="true" tabindex="-1"></a>)</span> 967<span id="cb19-9"><a href="#cb19-9" aria-hidden="true" tabindex="-1"></a><span class="fu">detach</span>(movies)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div> 968</div> 969<div class="cell"> 970<div class="cell-output-display"> 971<div id="fig-attend1" class="quarto-figure quarto-figure-center anchored"> 972<figure class="figure"> 973<p><img src="exp2_files/figure-html/fig-attend1-1.png" class="img-fluid figure-img" width="672"></p> 974<p></p><figcaption class="figure-caption">Figure 2: Reg attend: Effects of Years and Months on Movie Attend</figcaption><p></p> 975</figure> 976</div> 977</div> 978</div> 979<div class="cell"> 980<div class="sourceCode cell-code" id="cb20"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb20-1"><a href="#cb20-1" aria-hidden="true" tabindex="-1"></a>attend_months_f <span class="ot"><-</span> mod.attend1 <span class="sc">%>%</span></span> 981<span id="cb20-2"><a href="#cb20-2" aria-hidden="true" tabindex="-1"></a> <span class="fu">linearHypothesis</span>(<span class="fu">c</span>(</span> 982<span id="cb20-3"><a href="#cb20-3" aria-hidden="true" tabindex="-1"></a> <span class="st">"month2=month3"</span>,</span> 983<span id="cb20-4"><a href="#cb20-4" aria-hidden="true" tabindex="-1"></a> <span class="st">"month2=month4"</span>,</span> 984<span id="cb20-5"><a href="#cb20-5" aria-hidden="true" tabindex="-1"></a> <span class="st">"month2=month5"</span>,</span> 985<span id="cb20-6"><a href="#cb20-6" aria-hidden="true" tabindex="-1"></a> <span class="st">"month2=month6"</span>,</span> 986<span id="cb20-7"><a href="#cb20-7" aria-hidden="true" tabindex="-1"></a> <span class="st">"month2=month7"</span>,</span> 987<span id="cb20-8"><a href="#cb20-8" aria-hidden="true" tabindex="-1"></a> <span class="st">"month2=month8"</span>,</span> 988<span id="cb20-9"><a href="#cb20-9" aria-hidden="true" tabindex="-1"></a> <span class="st">"month2=month9"</span>,</span> 989<span id="cb20-10"><a href="#cb20-10" aria-hidden="true" tabindex="-1"></a> <span class="st">"month2=month10"</span>,</span> 990<span id="cb20-11"><a href="#cb20-11" aria-hidden="true" tabindex="-1"></a> <span class="st">"month2=month11"</span>,</span> 991<span id="cb20-12"><a href="#cb20-12" aria-hidden="true" tabindex="-1"></a> <span class="st">"month2=month12"</span></span> 992<span id="cb20-13"><a href="#cb20-13" aria-hidden="true" tabindex="-1"></a> )) <span class="sc">%>%</span></span> 993<span id="cb20-14"><a href="#cb20-14" aria-hidden="true" tabindex="-1"></a> .[<span class="st">"F"</span>] <span class="sc">%>%</span></span> 994<span id="cb20-15"><a href="#cb20-15" aria-hidden="true" tabindex="-1"></a> <span class="fu">pull</span>() <span class="sc">%>%</span></span> 995<span id="cb20-16"><a href="#cb20-16" aria-hidden="true" tabindex="-1"></a> .[<span class="dv">2</span>] <span class="sc">%>%</span></span> 996<span id="cb20-17"><a href="#cb20-17" aria-hidden="true" tabindex="-1"></a> <span class="fu">round</span>()</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div> 997</div> 998<p>From the figure, the difference of the coefficient among years is significant. The difference among months is significant, too. And the F-statistic on the 11 monthly indicators is 37 with p-value that is essentially 0. So there is seasonality in movie attendance.</p> 999</section> 1000</section> 1001<section id="b.-2" class="level2 unnumbered"> 1002<h2 class="unnumbered anchored" data-anchor-id="b.-2">b.</h2> 1003<section id="i.-1" class="level3 unnumbered unlisted"> 1004<h3 class="unnumbered unlisted anchored" data-anchor-id="i.-1">i.</h3> 1005<div class="cell"> 1006<div class="sourceCode cell-code" id="cb21"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb21-1"><a href="#cb21-1" aria-hidden="true" tabindex="-1"></a><span class="fu">attach</span>(movies)</span> 1007<span id="cb21-2"><a href="#cb21-2" aria-hidden="true" tabindex="-1"></a>mod.ln_ass <span class="ot"><-</span> <span class="fu">lm</span>(</span> 1008<span id="cb21-3"><a href="#cb21-3" aria-hidden="true" tabindex="-1"></a> <span class="fu">log</span>(assaults) <span class="sc">~</span> <span class="dv">1</span> <span class="sc">+</span> attend_v <span class="sc">+</span> attend_m <span class="sc">+</span> attend_n <span class="sc">+</span> year2 <span class="sc">+</span> year3 <span class="sc">+</span> year4 <span class="sc">+</span></span> 1009<span id="cb21-4"><a href="#cb21-4" aria-hidden="true" tabindex="-1"></a> year5 <span class="sc">+</span> year6 <span class="sc">+</span> year7 <span class="sc">+</span>
1009 year8 <span class="sc">+</span> year9 <span class="sc">+</span> year10 <span class="sc">+</span> month2 <span class="sc">+</span> month3 <span class="sc">+</span> month4 <span class="sc">+</span></span> 1010<span id="cb21-5"><a href="#cb21-5" aria-hidden="true" tabindex="-1"></a> month5 <span class="sc">+</span> month6 <span class="sc">+</span> month7 <span class="sc">+</span> month8 <span class="sc">+</span> month9 <span class="sc">+</span> month10 <span class="sc">+</span> month11 <span class="sc">+</span> month12 <span class="sc">+</span></span> 1011<span id="cb21-6"><a href="#cb21-6" aria-hidden="true" tabindex="-1"></a> h_chris <span class="sc">+</span> h_newyr <span class="sc">+</span> h_easter <span class="sc">+</span> h_july4 <span class="sc">+</span> h_mem <span class="sc">+</span> h_labor <span class="sc">+</span></span> 1012<span id="cb21-7"><a href="#cb21-7" aria-hidden="true" tabindex="-1"></a> w_rain <span class="sc">+</span> w_snow <span class="sc">+</span> w_maxa <span class="sc">+</span> w_maxb <span class="sc">+</span> w_maxc <span class="sc">+</span> w_mina <span class="sc">+</span> w_minb <span class="sc">+</span> w_minc</span> 1013<span id="cb21-8"><a href="#cb21-8" aria-hidden="true" tabindex="-1"></a>)</span> 1014<span id="cb21-9"><a href="#cb21-9" aria-hidden="true" tabindex="-1"></a><span class="fu">detach</span>(movies)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div> 1015</div> 1016<div class="cell"> 1017<div class="cell-output-display"> 1018<div id="tbl-assaults_ymhw" class="anchored"> 1019 1020<div class="tabwid"><style>.cl-1dc5c1b4{}.cl-1dbd9912{font-family:'Arial';font-size:11pt;font-weight:bold;font-style:normal;text-decoration:none;color:rgba(0, 0, 0, 1.00);background-color:transparent;}.cl-1dbd991c{font-family:'Arial';font-size:11pt;font-weight:normal;font-style:normal;text-decoration:none;color:rgba(0, 0, 0, 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1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}.cl-1dc0ae72{width:0.837in;background-color:transparent;vertical-align: middle;border-bottom: 1.5pt solid rgba(102, 102, 102, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}.cl-1dc0ae73{width:0.99in;background-color:transparent;vertical-align: middle;border-bottom: 0 solid rgba(255, 255, 255, 0.00);border-top: 0 solid rgba(255, 255, 255, 0.00);border-left: 0 solid rgba(255, 255, 255, 0.00);border-right: 0 solid rgba(255, 255, 255, 0.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}.cl-1dc0ae74{width:0.922in;background-color:transparent;vertical-align: middle;border-bottom: 0 solid rgba(255, 255, 255, 0.00);border-top: 0 solid rgba(255, 255, 255, 0.00);border-left: 0 solid rgba(255, 255, 255, 0.00);border-right: 0 solid rgba(255, 255, 255, 0.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}.cl-1dc0ae7c{width:0.99in;background-color:transparent;vertical-align: middle;border-bottom: 0 solid rgba(255, 255, 255, 0.00);border-top: 0 solid rgba(255, 255, 255, 0.00);border-left: 0 solid rgba(255, 255, 255, 0.00);border-right: 0 solid rgba(255, 255, 255, 0.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}.cl-1dc0ae7d{width:1.007in;background-color:transparent;vertical-align: middle;border-bottom: 0 solid rgba(255, 255, 255, 0.00);border-top: 0 solid rgba(255, 255, 255, 0.00);border-left: 0 solid rgba(255, 255, 255, 0.00);border-right: 0 solid rgba(255, 255, 255, 0.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}.cl-1dc0ae7e{width:0.837in;background-color:transparent;vertical-align: middle;border-bottom: 0 solid rgba(255, 255, 255, 0.00);border-top: 0 solid rgba(255, 255, 255, 0.00);border-left: 0 solid rgba(255, 255, 255, 0.00);border-right: 0 solid rgba(255, 255, 255, 0.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}</style><table data-quarto-disable-processing="true" class="cl-1dc5c1b4"><caption>Table 7: <p>Regress ln_assaults on v, n, m, year, month, weather, and holidy</p> </caption><thead><tr style="overflow-wrap:break-word;"><th class="cl-1dc0ae18"><p class="cl-1dc09324"><span class="cl-1dbd9912">Var.Name</span></p></th><th class="cl-1dc0ae22"><p class="cl-1dc0932e"><span class="cl-1dbd9912">Estimate</span></p></th><th class="cl-1dc0ae23"><p class="cl-1dc0932e"><span class="cl-1dbd9912">Std. Error</span></p></th><th class="cl-1dc0ae2c"><p class="cl-1dc0932e"><span class="cl-1dbd9912">t value</span></p></th><th class="cl-1dc0ae2d"><p class="cl-1dc0932e"><span class="cl-1dbd9912">Pr(>|t|)</span></p></th></tr></thead><tbody><tr style="overflow-wrap:break-word;"><td class="cl-1dc0ae36"><p class="cl-1dc09324"><span class="cl-1dbd991c">(Intercept)</span></p></td><td class="cl-1dc0ae37"><p class="cl-1dc0932e"><span class="cl-1dbd991c">6.91432</span></p></td><td class="cl-1dc0ae38"><p class="cl-1dc0932e"><span class="cl-1dbd991c">0.01715</span></p></td><td class="cl-1dc0ae39"><p class="cl-1dc0932e"><span class="cl-1dbd991c">403.24547</span></p></td><td class="cl-1dc0ae40"><p class="cl-1dc0932e"><span class="cl-1dbd991c">0.00000</span></p></td></tr><tr style="overflow-wrap:break-word;"><td class="cl-1dc0ae41"><p class="cl-1dc09324"><span class="cl-1dbd991c">attend_v</span></p></td><td class="cl-1dc0ae42"><p class="cl-1dc0932e"><span class="cl-1dbd991c">-0.00317</span></p></td><td class="cl-1dc0ae4a"><p class="cl-1dc0932e"><span class="cl-1dbd991c">0.00100</span></p></td><td class="cl-1dc0ae54"><p class="cl-1dc0932e"><span class="cl-1dbd991c">-3.17102</span></p></td><td class="cl-1dc0ae55"><p class="cl-1dc0932e"><span class="cl-1dbd991c">0.00162</span></p></td></tr><tr style="overflow-wrap:break-word;"><td class="cl-1dc0ae41"><p class="cl-1dc09324"><span class="cl-1dbd991c">attend_m</span></p></td><td class="cl-1dc0ae42"><p class="cl-1dc0932e"><span class="cl-1dbd991c">-0.00314</span></p></td><td class="cl-1dc0ae4a"><p class="cl-1dc0932e"><span class="cl-1dbd991c">0.00066</span></p></td><td class="cl-1dc0ae54"><p class="cl-1dc0932e"><span class="cl-1dbd991c">-4.74238</span></p></td><td class="cl-1dc0ae55"><p class="cl-1dc0932e"><span class="cl-1dbd991c">0.00000</span></p></td></tr><tr style="overflow-wrap:break-word;"><td class="cl-1dc0ae5e"><p class="cl-1dc09324"><span class="cl-1dbd991c">attend_n</span></p></td><td class="cl-1dc0ae5f"><p class="cl-1dc0932e"><span class="cl-1dbd991c">-0.00211</span></p></td><td class="cl-1dc0ae68"><p class="cl-1dc0932e"><span class="cl-1dbd991c">0.00066</span></p></td><td class="cl-1dc0ae69"><p class="cl-1dc0932e"><span class="cl-1dbd991c">-3.19400</span></p></td><td class="cl-1dc0ae72"><p class="cl-1dc0932e"><span class="cl-1dbd991c">0.00150</span></p></td></tr></tbody><tfoot><tr style="overflow-wrap:break-word;"><td colspan="5" class="cl-1dc0ae73"><p class="cl-1dc09324"><span class="cl-1dbd991d">Note. Fixed variables are hidden</span></p></td></tr></tfoot></table></div> 1021</div> 1022</div> 1023</div> 1024<p>The regression result shows that viewing a strongly violent movie decreases assaults by 0.32%. The estimated effect is statistically significant at 0.01 significant level.</p> 1025</section> 1026<section id="ii.-1" class="level3 unnumbered unlisted"> 1027<h3 class="unnumbered unlisted anchored" data-anchor-id="ii.-1">ii.</h3> 1028<p>Make hypothesis that <span class="math inline">\(\beta_v = \beta_m\)</span> and <span class="math inline">\(\beta_v = \beta_n\)</span>. Then do F tests.</p> 1029<div class="cell"> 1030<div class="cell-output-display"> 1031<div id="tbl-vmn_diff" class="anchored"> 1032 1033<div class="tabwid"><style>.cl-1ddeadc8{}.cl-1dd7785a{font-family:'Arial';font-size:11pt;font-weight:bold;font-style:normal;text-decoration:none;color:rgba(0, 0, 0, 1.00);background-color:transparent;}
1033.cl-1dd77864{font-family:'Arial';font-size:11pt;font-weight:normal;font-style:normal;text-decoration:none;color:rgba(0, 0, 0, 1.00);background-color:transparent;}.cl-1dda53fe{margin:0;text-align:left;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);padding-bottom:5pt;padding-top:5pt;padding-left:5pt;padding-right:5pt;line-height: 1;background-color:transparent;}.cl-1dda5408{margin:0;text-align:right;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);padding-bottom:5pt;padding-top:5pt;padding-left:5pt;padding-right:5pt;line-height: 1;background-color:transparent;}.cl-1dda6574{width:0.599in;background-color:transparent;vertical-align: middle;border-bottom: 1.5pt solid rgba(102, 102, 102, 1.00);border-top: 1.5pt solid rgba(102, 102, 102, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}.cl-1dda6575{width:0.837in;background-color:transparent;vertical-align: middle;border-bottom: 1.5pt solid rgba(102, 102, 102, 1.00);border-top: 1.5pt solid rgba(102, 102, 102, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}.cl-1dda657e{width:0.599in;background-color:transparent;vertical-align: middle;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}.cl-1dda657f{width:0.837in;background-color:transparent;vertical-align: middle;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}.cl-1dda6588{width:0.599in;background-color:transparent;vertical-align: middle;border-bottom: 1.5pt solid rgba(102, 102, 102, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}.cl-1dda6592{width:0.837in;background-color:transparent;vertical-align: middle;border-bottom: 1.5pt solid rgba(102, 102, 102, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}</style><table data-quarto-disable-processing="true" class="cl-1ddeadc8"><caption>Table 8: <p>F test of v=m, v=n</p> </caption><thead><tr style="overflow-wrap:break-word;"><th class="cl-1dda6574"><p class="cl-1dda53fe"><span class="cl-1dd7785a">Test</span></p></th><th class="cl-1dda6575"><p class="cl-1dda5408"><span class="cl-1dd7785a">F</span></p></th><th class="cl-1dda6575"><p class="cl-1dda5408"><span class="cl-1dd7785a">Pr(>F)</span></p></th></tr></thead><tbody><tr style="overflow-wrap:break-word;"><td class="cl-1dda657e"><p class="cl-1dda53fe"><span class="cl-1dd77864">v=m</span></p></td><td class="cl-1dda657f"><p class="cl-1dda5408"><span class="cl-1dd77864">0.00113</span></p></td><td class="cl-1dda657f"><p class="cl-1dda5408"><span class="cl-1dd77864">0.97325</span></p></td></tr><tr style="overflow-wrap:break-word;"><td class="cl-1dda6588"><p class="cl-1dda53fe"><span class="cl-1dd77864">v=n</span></p></td><td class="cl-1dda6592"><p class="cl-1dda5408"><span class="cl-1dd77864">1.21960</span></p></td><td class="cl-1dda6592"><p class="cl-1dda5408"><span class="cl-1dd77864">0.27000</span></p></td></tr></tbody></table></div> 1034</div> 1035</div> 1036</div> 1037<p>The F-test result suggests that <span class="math inline">\(\beta_v\)</span> with <span class="math inline">\(\beta_m\)</span>, and <span class="math inline">\(beta_v\)</span> with <span class="math inline">\(\beta_n\)</span> have no statistically significant difference from one another.</p> 1038</section> 1039<section id="iii." class="level3 unnumbered unlisted"> 1040<h3 class="unnumbered unlisted anchored" data-anchor-id="iii.">iii.</h3> 1041<p>Construct a new variable <em>
1041effect</em> and construct its 95% confidence interval.</p> 1042<p><span class="math display">\[ 1043effect = 6*\beta_v * attend_v-2*\beta_m*attend_m-\beta_n*attend_n 1044\]</span></p> 1045<div class="cell"> 1046<div class="sourceCode cell-code" id="cb22"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb22-1"><a href="#cb22-1" aria-hidden="true" tabindex="-1"></a>beta_v <span class="ot"><-</span> mod.ln_ass<span class="sc">$</span>coefficients[<span class="st">"attend_v"</span>]</span> 1047<span id="cb22-2"><a href="#cb22-2" aria-hidden="true" tabindex="-1"></a>beta_m <span class="ot"><-</span> mod.ln_ass<span class="sc">$</span>coefficients[<span class="st">"attend_m"</span>]</span> 1048<span id="cb22-3"><a href="#cb22-3" aria-hidden="true" tabindex="-1"></a>beta_n <span class="ot"><-</span> mod.ln_ass<span class="sc">$</span>coefficients[<span class="st">"attend_n"</span>]</span> 1049<span id="cb22-4"><a href="#cb22-4" aria-hidden="true" tabindex="-1"></a>effect <span class="ot"><-</span> movies <span class="sc">%>%</span></span> 1050<span id="cb22-5"><a href="#cb22-5" aria-hidden="true" tabindex="-1"></a> <span class="fu">mutate</span>(<span class="at">effect =</span> <span class="dv">6</span> <span class="sc">*</span> beta_v <span class="sc">*</span> attend_v <span class="sc">-</span></span> 1051<span id="cb22-6"><a href="#cb22-6" aria-hidden="true" tabindex="-1"></a> <span class="dv">2</span> <span class="sc">*</span> beta_m <span class="sc">*</span> attend_m <span class="sc">-</span></span> 1052<span id="cb22-7"><a href="#cb22-7" aria-hidden="true" tabindex="-1"></a> beta_n <span class="sc">*</span> attend_n) <span class="sc">%>%</span></span> 1053<span id="cb22-8"><a href="#cb22-8" aria-hidden="true" tabindex="-1"></a> <span class="fu">select</span>(effect) <span class="sc">%>%</span></span> 1054<span id="cb22-9"><a href="#cb22-9" aria-hidden="true" tabindex="-1"></a> <span class="fu">pull</span>()</span> 1055<span id="cb22-10"><a href="#cb22-10" aria-hidden="true" tabindex="-1"></a>ci_res <span class="ot"><-</span> <span class="fu">ci</span>(effect) <span class="sc">%>%</span></span> 1056<span id="cb22-11"><a href="#cb22-11" aria-hidden="true" tabindex="-1"></a> <span class="fu">as.data.frame</span>() <span class="sc">%>%</span></span> 1057<span id="cb22-12"><a href="#cb22-12" aria-hidden="true" tabindex="-1"></a> <span class="fu">t</span>() <span class="sc">%>%</span></span> 1058<span id="cb22-13"><a href="#cb22-13" aria-hidden="true" tabindex="-1"></a> <span class="fu">as.data.frame</span>() <span class="sc">%>%</span></span> 1059<span id="cb22-14"><a href="#cb22-14" aria-hidden="true" tabindex="-1"></a> <span class="fu">round</span>(<span class="dv">5</span>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div> 1060</div> 1061<p>The OLS estimate for this coefficient is 0.01553. It shows a decrease in assaults of 1.55%. The 95% confidence interval is (0.01056, 0.02051).</p> 1062<div class="cell"> 1063<div class="cell-output-display"> 1064<div id="tbl-movies_predic_ci" class="anchored"> 1065 1066<div class="tabwid"><style>.cl-1e042c7e{}.cl-1df8168c{font-family:'Arial';font-size:11pt;font-weight:bold;font-style:normal;text-decoration:none;color:rgba(0, 0, 0, 1.00);background-color:transparent;}.cl-1df81696{font-family:'Arial';font-size:11pt;font-weight:normal;font-style:normal;text-decoration:none;color:rgba(0, 0, 0, 1.00);background-color:transparent;}.cl-1dfaf802{margin:0;text-align:right;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);padding-bottom:5pt;padding-top:5pt;padding-left:5pt;padding-right:5pt;line-height: 1;background-color:transparent;}.cl-1dfb084c{width:0.922in;background-color:transparent;vertical-align: middle;border-bottom: 1.5pt solid rgba(102, 102, 102, 1.00);border-top: 1.5pt solid rgba(102, 102, 102, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}.cl-1dfb084d{width:0.879in;background-color:transparent;vertical-align: middle;border-bottom: 1.5pt solid rgba(102, 102, 102, 1.00);border-top: 1.5pt solid rgba(102, 102, 102, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}.cl-1dfb084e{width:0.905in;background-color:transparent;vertical-align: middle;border-bottom: 1.5pt solid rgba(102, 102, 102, 1.00);border-top: 1.5pt solid rgba(102, 102, 102, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}.cl-1dfb0856{width:0.99in;background-color:transparent;vertical-align: middle;border-bottom: 1.5pt solid rgba(102, 102, 102, 1.00);border-top: 1.5pt solid rgba(102, 102, 102, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}.cl-1dfb0857{width:0.922in;background-color:transparent;vertical-align: middle;border-bottom: 1.5pt solid rgba(102, 102, 102, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}.cl-1dfb0860{width:0.879in;background-color:transparent;vertical-align: middle;border-bottom: 1.5pt solid rgba(102, 102, 102, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}.cl-1dfb0861{width:0.905in;background-color:transparent;vertical-align: middle;border-bottom: 1.5pt solid rgba(102, 102, 102, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}.cl-1dfb0862{width:0.99in;background-color:transparent;vertical-align: middle;border-bottom: 1.5pt solid rgba(102, 102, 102, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}</style><table data-quarto-disable-processing="true" class="cl-1e042c7e"><caption>Table 9: <p>Confidence Interval of Prediction</p> </caption><thead><tr style="overflow-wrap:break-word;"><th class="cl-1dfb084c"><p class="cl-1dfaf802"><span class="cl-1df8168c">Estimate</span></p></th><th class="cl-1dfb084d"><p class="cl-1dfaf802"><span class="cl-1df8168c">CI lower</span></p></th><th class="cl-1dfb084e"><p class="cl-1dfaf802"><span class="cl-1df8168c">CI upper</span></p></th><th class="cl-1dfb0856"><p class="cl-1dfaf802"><span class="cl-1df8168c">Std. Error</span></p></th></tr></thead><tbody><tr style="overflow-wrap:break-word;"><td class="cl-1dfb0857"><p class="cl-1dfaf802"><span class="cl-1df81696">0.01553</span></p></td><td class="cl-1dfb0860"><p class="cl-1dfaf802"><span class="cl-1df81696">0.01056</span></p></td><td class="cl-1dfb0861"><p class="cl-1dfaf802"><span class="cl-1df81696">0.02051</span></p></td><td class="cl-1dfb0862"><p class="cl-1dfaf802"><span class="cl-1df81696">0.00253</span></p></td></tr></tbody></table></div> 1067</div> 1068</div> 1069</div> 1070</section> 1071</section> 1072<section id="c.-2" class="level2 unnumbered"> 1073<h2 class="unnumbered anchored" data-anchor-id="c.-2">c. </h2> 1074<p>Use <em>pr_attend_v</em>, <em>pr_attend_m</em>, and <em>pr_attend_n</em> as instruments for <em>attend_v</em>, <em>attend_m</em>, and <em>attend_n</em>. Run the regression.</p> 1075<div class="cell"> 1076<div class="sourceCode cell-code" id="cb23"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb23-1"><a href="#cb23-1" aria-hidden="true" tabindex="-1"></a>mod.movies_tsls <span class="ot"><-</span> <span class="fu">ivreg</span>(</span> 1077<span id="cb23-2"><a href="#cb23-2" aria-hidden="true" tabindex="-1"></a> <span class="at">data =</span> movies,</span> 1078<span id="cb23-3"><a href="#cb23-3" aria-hidden="true" tabindex="-1"></a> <span class="fu">log</span>(assaults) <span class="sc">~</span> attend_v <span class="sc">+</span> attend_m <span class="sc">+</span> attend_n <span class="sc">+</span> year2 <span class="sc">+</span> year3 <span class="sc">+</span> year4 <span class="sc">+</span></span> 1079<span id="cb23-4"><a href="#cb23-4" aria-hidden="true" tabindex="-1"></a> year5 <span class="sc">+</span> year6 <span class="sc">+</span> year7 <span class="sc">+</span>
1079 year8 <span class="sc">+</span> year9 <span class="sc">+</span> year10 <span class="sc">+</span> month2 <span class="sc">+</span> month3 <span class="sc">+</span> month4 <span class="sc">+</span></span> 1080<span id="cb23-5"><a href="#cb23-5" aria-hidden="true" tabindex="-1"></a> month5 <span class="sc">+</span> month6 <span class="sc">+</span> month7 <span class="sc">+</span> month8 <span class="sc">+</span> month9 <span class="sc">+</span> month10 <span class="sc">+</span> month11 <span class="sc">+</span> month12 <span class="sc">+</span></span> 1081<span id="cb23-6"><a href="#cb23-6" aria-hidden="true" tabindex="-1"></a> h_chris <span class="sc">+</span> h_newyr <span class="sc">+</span> h_easter <span class="sc">+</span> h_july4 <span class="sc">+</span> h_mem <span class="sc">+</span> h_labor <span class="sc">+</span></span> 1082<span id="cb23-7"><a href="#cb23-7" aria-hidden="true" tabindex="-1"></a> w_rain <span class="sc">+</span> w_snow <span class="sc">+</span> w_maxa <span class="sc">+</span> w_maxb <span class="sc">+</span> w_maxc <span class="sc">+</span> w_mina <span class="sc">+</span> w_minb <span class="sc">+</span> w_minc <span class="sc">|</span></span> 1083<span id="cb23-8"><a href="#cb23-8" aria-hidden="true" tabindex="-1"></a> pr_attend_v <span class="sc">+</span> pr_attend_m <span class="sc">+</span> pr_attend_n <span class="sc">+</span> year2 <span class="sc">+</span> year3 <span class="sc">+</span> year4 <span class="sc">+</span></span> 1084<span id="cb23-9"><a href="#cb23-9" aria-hidden="true" tabindex="-1"></a> year5 <span class="sc">+</span> year6 <span class="sc">+</span> year7 <span class="sc">+</span>
1084 year8 <span class="sc">+</span> year9 <span class="sc">+</span> year10 <span class="sc">+</span> month2 <span class="sc">+</span> month3 <span class="sc">+</span> month4 <span class="sc">+</span></span> 1085<span id="cb23-10"><a href="#cb23-10" aria-hidden="true" tabindex="-1"></a> month5 <span class="sc">+</span> month6 <span class="sc">+</span> month7 <span class="sc">+</span> month8 <span class="sc">+</span> month9 <span class="sc">+</span> month10 <span class="sc">+</span> month11 <span class="sc">+</span> month12 <span class="sc">+</span></span> 1086<span id="cb23-11"><a href="#cb23-11" aria-hidden="true" tabindex="-1"></a> h_chris <span class="sc">+</span> h_newyr <span class="sc">+</span> h_easter <span class="sc">+</span> h_july4 <span class="sc">+</span> h_mem <span class="sc">+</span> h_labor <span class="sc">+</span></span> 1087<span id="cb23-12"><a href="#cb23-12" aria-hidden="true" tabindex="-1"></a> w_rain <span class="sc">+</span> w_snow <span class="sc">+</span> w_maxa <span class="sc">+</span> w_maxb <span class="sc">+</span> w_maxc <span class="sc">+</span> w_mina <span class="sc">+</span> w_minb <span class="sc">+</span> w_minc</span> 1088<span id="cb23-13"><a href="#cb23-13" aria-hidden="true" tabindex="-1"></a>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div> 1089</div> 1090<div class="cell"> 1091<div class="cell-output-display"> 1092<div id="tbl-movies_tsls" class="anchored"> 1093 1094<div class="tabwid"><style>.cl-1e28761a{}.cl-1e21006a{font-family:'Arial';font-size:11pt;font-weight:bold;font-style:normal;text-decoration:none;color:rgba(0, 0, 0, 1.00);background-color:transparent;}.cl-1e210074{font-family:'Arial';font-size:11pt;font-weight:normal;font-style:normal;text-decoration:none;color:rgba(0, 0, 0, 1.00);background-color:transparent;}.cl-1e21007e{font-family:'Arial';font-size:11pt;font-weight:normal;font-style:normal;text-decoration:none;color:rgba(51, 51, 51, 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1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}.cl-1e2402f8{width:0.837in;background-color:transparent;vertical-align: middle;border-bottom: 1.5pt solid rgba(102, 102, 102, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}.cl-1e240300{width:0.99in;background-color:transparent;vertical-align: middle;border-bottom: 0 solid rgba(255, 255, 255, 0.00);border-top: 0 solid rgba(255, 255, 255, 0.00);border-left: 0 solid rgba(255, 255, 255, 0.00);border-right: 0 solid rgba(255, 255, 255, 0.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}.cl-1e240301{width:0.922in;background-color:transparent;vertical-align: middle;border-bottom: 0 solid rgba(255, 255, 255, 0.00);border-top: 0 solid rgba(255, 255, 255, 0.00);border-left: 0 solid rgba(255, 255, 255, 0.00);border-right: 0 solid rgba(255, 255, 255, 0.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}.cl-1e240302{width:0.99in;background-color:transparent;vertical-align: middle;border-bottom: 0 solid rgba(255, 255, 255, 0.00);border-top: 0 solid rgba(255, 255, 255, 0.00);border-left: 0 solid rgba(255, 255, 255, 0.00);border-right: 0 solid rgba(255, 255, 255, 0.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}.cl-1e24030a{width:1.007in;background-color:transparent;vertical-align: middle;border-bottom: 0 solid rgba(255, 255, 255, 0.00);border-top: 0 solid rgba(255, 255, 255, 0.00);border-left: 0 solid rgba(255, 255, 255, 0.00);border-right: 0 solid rgba(255, 255, 255, 0.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}.cl-1e24030b{width:0.837in;background-color:transparent;vertical-align: middle;border-bottom: 0 solid rgba(255, 255, 255, 0.00);border-top: 0 solid rgba(255, 255, 255, 0.00);border-left: 0 solid rgba(255, 255, 255, 0.00);border-right: 0 solid rgba(255, 255, 255, 0.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}</style><table data-quarto-disable-processing="true" class="cl-1e28761a"><caption>Table 10: <p>Movies TSLS Stage 2 Result</p> </caption><thead><tr style="overflow-wrap:break-word;"><th class="cl-1e2402b0"><p class="cl-1e23f004"><span class="cl-1e21006a">Var.Name</span></p></th><th class="cl-1e2402ba"><p class="cl-1e23f018"><span class="cl-1e21006a">Estimate</span></p></th><th class="cl-1e2402bb"><p class="cl-1e23f018"><span class="cl-1e21006a">Std. Error</span></p></th><th class="cl-1e2402c4"><p class="cl-1e23f018"><span class="cl-1e21006a">t value</span></p></th><th class="cl-1e2402c5"><p class="cl-1e23f018"><span class="cl-1e21006a">Pr(>|t|)</span></p></th></tr></thead><tbody><tr style="overflow-wrap:break-word;"><td class="cl-1e2402c6"><p class="cl-1e23f004"><span class="cl-1e210074">(Intercept)</span></p></td><td class="cl-1e2402ce"><p class="cl-1e23f018"><span class="cl-1e210074">
10946.92418</span></p></td><td class="cl-1e2402cf"><p class="cl-1e23f018"><span class="cl-1e210074">0.01828</span></p></td><td class="cl-1e2402d0"><p class="cl-1e23f018"><span class="cl-1e210074">378.83439</span></p></td><td class="cl-1e2402d8"><p class="cl-1e23f018"><span class="cl-1e210074">0.00000</span></p></td></tr><tr style="overflow-wrap:break-word;"><td class="cl-1e2402d9"><p class="cl-1e23f004"><span class="cl-1e210074">attend_v</span></p></td><td class="cl-1e2402da"><p class="cl-1e23f018"><span class="cl-1e210074">-0.00387</span></p></td><td class="cl-1e2402e2"><p class="cl-1e23f018"><span class="cl-1e210074">0.00111</span></p></td><td class="cl-1e2402e3"><p class="cl-1e23f018"><span class="cl-1e210074">-3.48016</span></p></td><td class="cl-1e2402e4"><p class="cl-1e23f018"><span class="cl-1e210074">0.00055</span></p></td></tr><tr style="overflow-wrap:break-word;"><td class="cl-1e2402d9"><p class="cl-1e23f004"><span class="cl-1e210074">attend_m</span></p></td><td class="cl-1e2402da"><p class="cl-1e23f018"><span class="cl-1e210074">-0.00389</span></p></td><td class="cl-1e2402e2"><p class="cl-1e23f018"><span class="cl-1e210074">0.00077</span></p></td><td class="cl-1e2402e3"><p class="cl-1e23f018"><span class="cl-1e210074">-5.02473</span></p></td><td class="cl-1e2402e4"><p class="cl-1e23f018"><span class="cl-1e210074">0.00000</span></p></td></tr><tr style="overflow-wrap:break-word;"><td class="cl-1e2402ec"><p class="cl-1e23f004"><span class="cl-1e210074">attend_n</span></p></td><td class="cl-1e2402ed"><p class="cl-1e23f018"><span class="cl-1e210074">-0.00272</span></p></td><td class="cl-1e2402f6"><p class="cl-1e23f018"><span class="cl-1e210074">0.00079</span></p></td><td class="cl-1e2402f7"><p class="cl-1e23f018"><span class="cl-1e210074">-3.44928</span></p></td><td class="cl-1e2402f8"><p class="cl-1e23f018"><span class="cl-1e210074">0.00061</span></p></td></tr></tbody><tfoot><tr style="overflow-wrap:break-word;"><td colspan="5" class="cl-1e240300"><p class="cl-1e23f004"><span class="cl-1e21007e">Note. Fixed variables are hidden</span></p></td></tr></tfoot></table></div> 1095</div> 1096</div> 1097</div> 1098<p>So based on this regression, viewing strongly violent movies leads to a small but significant decrease in assaults, rather than an increase.</p> 1099<p>Samely, make the linear hypothesis <code>attend_v=attend_m</code> and <code>attend_v=attend_n</code></p> 1100<div class="cell"> 1101<div class="sourceCode cell-code" id="cb24"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb24-1"><a href="#cb24-1" aria-hidden="true" tabindex="-1"></a>movies_tsls_vm <span class="ot"><-</span> mod.movies_tsls <span class="sc">%>%</span> car<span class="sc">::</span><span class="fu">linearHypothesis</span>(</span> 1102<span id="cb24-2"><a href="#cb24-2" aria-hidden="true" tabindex="-1"></a> <span class="st">"attend_v=attend_m"</span></span> 1103<span id="cb24-3"><a href="#cb24-3" aria-hidden="true" tabindex="-1"></a>)</span> 1104<span id="cb24-4"><a href="#cb24-4" aria-hidden="true" tabindex="-1"></a>movies_tsls_vn <span class="ot"><-</span> mod.movies_tsls <span class="sc">%>%</span> car<span class="sc">::</span><span class="fu">linearHypothesis</span>(</span> 1105<span id="cb24-5"><a href="#cb24-5" aria-hidden="true" tabindex="-1"></a> <span class="st">"attend_v = attend_n"</span></span> 1106<span id="cb24-6"><a href="#cb24-6" aria-hidden="true" tabindex="-1"></a>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div> 1107</div> 1108<div class="cell"> 1109<div class="cell-output-display"> 1110<div id="tbl-tsls_vmn_diff" class="anchored"> 1111 1112<div class="tabwid"><style>.cl-1e462926{}.cl-1e3dcc68{font-family:'Arial';font-size:11pt;font-weight:bold;font-style:normal;text-decoration:none;color:rgba(0, 0, 0, 1.00);background-color:transparent;}.cl-1e3dcc72{font-family:'Arial';font-size:11pt;font-weight:normal;font-style:normal;text-decoration:none;color:rgba(0, 0, 0, 1.00);background-color:transparent;}.cl-1e40ad66{margin:0;text-align:left;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);padding-bottom:5pt;padding-top:5pt;padding-left:5pt;padding-right:5pt;line-height: 1;background-color:transparent;}
1112.cl-1e40ad70{margin:0;text-align:right;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);padding-bottom:5pt;padding-top:5pt;padding-left:5pt;padding-right:5pt;line-height: 1;background-color:transparent;}.cl-1e40bec8{width:0.599in;background-color:transparent;vertical-align: middle;border-bottom: 1.5pt solid rgba(102, 102, 102, 1.00);border-top: 1.5pt solid rgba(102, 102, 102, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}.cl-1e40bed2{width:0.837in;background-color:transparent;vertical-align: middle;border-bottom: 1.5pt solid rgba(102, 102, 102, 1.00);border-top: 1.5pt solid rgba(102, 102, 102, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}.cl-1e40bed3{width:1.062in;background-color:transparent;vertical-align: middle;border-bottom: 1.5pt solid rgba(102, 102, 102, 1.00);border-top: 1.5pt solid rgba(102, 102, 102, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}.cl-1e40bedc{width:0.599in;background-color:transparent;vertical-align: middle;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}.cl-1e40bee6{width:0.837in;background-color:transparent;vertical-align: middle;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}.cl-1e40bee7{width:1.062in;background-color:transparent;vertical-align: middle;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}.cl-1e40bef0{width:0.599in;background-color:transparent;vertical-align: middle;border-bottom: 1.5pt solid rgba(102, 102, 102, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}.cl-1e40bef1{width:0.837in;background-color:transparent;vertical-align: middle;border-bottom: 1.5pt solid rgba(102, 102, 102, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}.cl-1e40bef2{width:1.062in;background-color:transparent;vertical-align: middle;border-bottom: 1.5pt solid rgba(102, 102, 102, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}</style><table data-quarto-disable-processing="true" class="cl-1e462926"><caption>Table 11: <p>TSLS F test of v=m, v=n</p> </caption><thead><tr style="overflow-wrap:break-word;"><th class="cl-1e40bec8"><p class="cl-1e40ad66"><span class="cl-1e3dcc68">Test</span></p></th><th class="cl-1e40bed2"><p class="cl-1e40ad70"><span class="cl-1e3dcc68">Chisq</span></p></th><th class="cl-1e40bed3"><p class="cl-1e40ad70"><span class="cl-1e3dcc68">Pr(>Chisq)</span></p></th></tr></thead><tbody><tr style="overflow-wrap:break-word;"><td class="cl-1e40bedc"><p class="cl-1e40ad66"><span class="cl-1e3dcc72">v=m</span></p></td><td class="cl-1e40bee6"><p class="cl-1e40ad70"><span class="cl-1e3dcc72">0.00041</span></p></td><td class="cl-1e40bee7"><p class="cl-1e40ad70"><span class="cl-1e3dcc72">0.98377</span></p></td></tr><tr style="overflow-wrap:break-word;"><td class="cl-1e40bef0"><p class="cl-1e40ad66"><span class="cl-1e3dcc72">v=n</span></p></td><td class="cl-1e40bef1"><p class="cl-1e40ad70"><span class="cl-1e3dcc72">1.34368</span></p></td><td class="cl-1e40bef2"><p class="cl-1e40ad70"><span class="cl-1e3dcc72">0.24639</span></p></td></tr></tbody></table></div> 1113</div> 1114</div> 1115</div> 1116<p>Too, the F-test result suggests that <span class="math inline">\(\beta_v\)</span>, <span class="math inline">\(\beta_m\)</span>, <span class="math inline">\(\beta_n\)</span> have no statistically significant difference from one another.</p> 1117<div class="cell"> 1118<div class="sourceCode cell-code" id="cb25"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb25-1"><a href="#cb25-1" aria-hidden="true" tabindex="-1"></a>beta_v <span class="ot"><-</span> mod.movies_tsls<span class="sc">$</span>coefficients[<span class="st">"attend_v"</span>]</span> 1119<span id="cb25-2"><a href="#cb25-2" aria-hidden="true" tabindex="-1"></a>beta_m <span class="ot"><-</span> mod.movies_tsls<span class="sc">$</span>coefficients[<span class="st">
1119"attend_m"</span>]</span> 1120<span id="cb25-3"><a href="#cb25-3" aria-hidden="true" tabindex="-1"></a>beta_n <span class="ot"><-</span> mod.movies_tsls<span class="sc">$</span>coefficients[<span class="st">"attend_n"</span>]</span> 1121<span id="cb25-4"><a href="#cb25-4" aria-hidden="true" tabindex="-1"></a>effect <span class="ot"><-</span> movies <span class="sc">%>%</span></span> 1122<span id="cb25-5"><a href="#cb25-5" aria-hidden="true" tabindex="-1"></a> <span class="fu">mutate</span>(<span class="at">effect =</span> <span class="dv">6</span> <span class="sc">*</span> beta_v <span class="sc">*</span> attend_v <span class="sc">-</span></span> 1123<span id="cb25-6"><a href="#cb25-6" aria-hidden="true" tabindex="-1"></a> <span class="dv">2</span> <span class="sc">*</span> beta_m <span class="sc">*</span> attend_m <span class="sc">-</span></span> 1124<span id="cb25-7"><a href="#cb25-7" aria-hidden="true" tabindex="-1"></a> beta_n <span class="sc">*</span> attend_n) <span class="sc">%>%</span></span> 1125<span id="cb25-8"><a href="#cb25-8" aria-hidden="true" tabindex="-1"></a> <span class="fu">select</span>(effect) <span class="sc">%>%</span></span> 1126<span id="cb25-9"><a href="#cb25-9" aria-hidden="true" tabindex="-1"></a> <span class="fu">pull</span>()</span> 1127<span id="cb25-10"><a href="#cb25-10" aria-hidden="true" tabindex="-1"></a>ci_res_tsls <span class="ot"><-</span> <span class="fu">ci</span>(effect) <span class="sc">%>%</span></span> 1128<span id="cb25-11"><a href="#cb25-11" aria-hidden="true" tabindex="-1"></a> <span class="fu">as.data.frame</span>() <span class="sc">%>%</span></span> 1129<span id="cb25-12"><a href="#cb25-12" aria-hidden="true" tabindex="-1"></a> <span class="fu">t</span>() <span class="sc">%>%</span></span> 1130<span id="cb25-13"><a href="#cb25-13" aria-hidden="true" tabindex="-1"></a> <span class="fu">as.data.frame</span>() <span class="sc">%>%</span></span> 1131<span id="cb25-14"><a href="#cb25-14" aria-hidden="true" tabindex="-1"></a> <span class="fu">round</span>(<span class="dv">5</span>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div> 1132</div> 1133<p>The OLS estimate for this coefficient is 0.02115. It shows a decrease in assaults of 2.11%. The 95% confidence interval is (0.01503, 0.02726).</p> 1134<div class="cell"> 1135<div class="cell-output-display"> 1136<div id="tbl-movies_tsls_ci" class="anchored"> 1137 1138<div class="tabwid"><style>.cl-1e689b78{}.cl-1e6028c6{font-family:'Arial';font-size:11pt;font-weight:bold;font-style:normal;text-decoration:none;color:rgba(0, 0, 0, 1.00);background-color:transparent;}.cl-1e6028da{font-family:'Arial';font-size:11pt;font-weight:normal;font-style:normal;text-decoration:none;color:rgba(0, 0, 0, 1.00);background-color:transparent;}.cl-1e643b8c{margin:0;text-align:right;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);padding-bottom:5pt;padding-top:5pt;padding-left:5pt;padding-right:5pt;line-height: 1;background-color:transparent;}.cl-1e644bfe{width:0.922in;background-color:transparent;vertical-align: middle;border-bottom: 1.5pt solid rgba(102, 102, 102, 1.00);border-top: 1.5pt solid rgba(102, 102, 102, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}.cl-1e644c08{width:0.879in;background-color:transparent;vertical-align: middle;border-bottom: 1.5pt solid rgba(102, 102, 102, 1.00);border-top: 1.5pt solid rgba(102, 102, 102, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}.cl-1e644c09{width:0.905in;background-color:transparent;vertical-align: middle;border-bottom: 1.5pt solid rgba(102, 102, 102, 1.00);border-top: 1.5pt solid rgba(102, 102, 102, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}.cl-1e644c0a{width:0.99in;background-color:transparent;vertical-align: middle;border-bottom: 1.5pt solid rgba(102, 102, 102, 1.00);border-top: 1.5pt solid rgba(102, 102, 102, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}.cl-1e644c12{width:0.922in;background-color:transparent;vertical-align: middle;border-bottom: 1.5pt solid rgba(102, 102, 102, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}.cl-1e644c13{width:0.879in;background-color:transparent;vertical-align: middle;border-bottom: 1.5pt solid rgba(102, 102, 102, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}.cl-1e644c1c{width:0.905in;background-color:transparent;vertical-align: middle;border-bottom: 1.5pt solid rgba(102, 102, 102, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}.cl-1e644c1d{width:0.99in;background-color:transparent;vertical-align: middle;border-bottom: 1.5pt solid rgba(102, 102, 102, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}</style><table data-quarto-disable-processing="true" class="cl-1e689b78"><caption>Table 12: <p>Change in Assaults 95% Confidence Interval</p> </caption><thead><tr style="overflow-wrap:break-word;"><th class="cl-1e644bfe"><p class="cl-1e643b8c"><span class="cl-1e6028c6">Estimate</span></p></th><th class="cl-1e644c08"><p class="cl-1e643b8c"><span class="cl-1e6028c6">CI lower</span></p></th><th class="cl-1e644c09"><p class="cl-1e643b8c"><span class="cl-1e6028c6">CI upper</span></p></th><th class="cl-1e644c0a"><p class="cl-1e643b8c"><span class="cl-1e6028c6">Std. Error</span></p></th></tr></thead><tbody><tr style="overflow-wrap:break-word;"><td class="cl-1e644c12"><p class="cl-1e643b8c"><span class="cl-1e6028da">0.02115</span></p></td><td class="cl-1e644c13"><p class="cl-1e643b8c"><span class="cl-1e6028da">0.01503</span></p></td><td class="cl-1e644c1c"><p class="cl-1e643b8c"><span class="cl-1e6028da">0.02726</span></p></td><td class="cl-1e644c1d"><p class="cl-1e643b8c"><span class="cl-1e6028da">0.00311</span></p></td></tr></tbody></table></div> 1139</div> 1140</div> 1141</div> 1142</section> 1143<section id="d.-2" class="level2 unnumbered"> 1144<h2 class="unnumbered anchored" data-anchor-id="d.-2">d. </h2> 1145<p>attend_v_f, attend_m_f, attend_n_f, attend_v_b, attend_m_b, and attend_n_b</p> 1146<div class="cell"> 1147<div class="sourceCode cell-code" id="cb26"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb26-1"><a href="#cb26-1" aria-hidden="true" tabindex="-1"></a>mod.movies_tsls2 <span class="ot"><-</span> <span class="fu">ivreg</span>(</span> 1148<span id="cb26-2"><a href="#cb26-2" aria-hidden="true" tabindex="-1"></a> <span class="at">data =</span> movies,</span> 1149<span id="cb26-3"><a href="#cb26-3" aria-hidden="true" tabindex="-1"></a> <span class="fu">log</span>(assaults) <span class="sc">~</span> attend_v <span class="sc">+</span> attend_m <span class="sc">+</span> attend_n <span class="sc">+</span> year2 <span class="sc">+</span> year3 <span class="sc">+</span> year4 <span class="sc">+</span></span> 1150<span id="cb26-4"><a href="#cb26-4" aria-hidden="true" tabindex="-1"></a> year5 <span class="sc">+</span> year6 <span class="sc">+</span> year7 <span class="sc">+</span>
1150 year8 <span class="sc">+</span> year9 <span class="sc">+</span> year10 <span class="sc">+</span> month2 <span class="sc">+</span> month3 <span class="sc">+</span> month4 <span class="sc">+</span></span> 1151<span id="cb26-5"><a href="#cb26-5" aria-hidden="true" tabindex="-1"></a> month5 <span class="sc">+</span> month6 <span class="sc">+</span> month7 <span class="sc">+</span> month8 <span class="sc">+</span> month9 <span class="sc">+</span> month10 <span class="sc">+</span> month11 <span class="sc">+</span> month12 <span class="sc">+</span></span> 1152<span id="cb26-6"><a href="#cb26-6" aria-hidden="true" tabindex="-1"></a> h_chris <span class="sc">+</span> h_newyr <span class="sc">+</span> h_easter <span class="sc">+</span> h_july4 <span class="sc">+</span> h_mem <span class="sc">+</span> h_labor <span class="sc">+</span></span> 1153<span id="cb26-7"><a href="#cb26-7" aria-hidden="true" tabindex="-1"></a> w_rain <span class="sc">+</span> w_snow <span class="sc">+</span> w_maxa <span class="sc">+</span> w_maxb <span class="sc">+</span> w_maxc <span class="sc">+</span> w_mina <span class="sc">+</span> w_minb <span class="sc">+</span> w_minc <span class="sc">|</span></span> 1154<span id="cb26-8"><a href="#cb26-8" aria-hidden="true" tabindex="-1"></a> attend_v_f <span class="sc">+</span> attend_m_f <span class="sc">+</span> attend_n_f <span class="sc">+</span> attend_v_b <span class="sc">+</span> attend_m_b <span class="sc">+</span> attend_n_b <span class="sc">+</span> year2 <span class="sc">+</span> year3 <span class="sc">+</span> year4 <span class="sc">+</span></span> 1155<span id="cb26-9"><a href="#cb26-9" aria-hidden="true" tabindex="-1"></a> year5 <span class="sc">+</span> year6 <span class="sc">+</span> year7 <span class="sc">+</span>
1155 year8 <span class="sc">+</span> year9 <span class="sc">+</span> year10 <span class="sc">+</span> month2 <span class="sc">+</span> month3 <span class="sc">+</span> month4 <span class="sc">+</span></span> 1156<span id="cb26-10"><a href="#cb26-10" aria-hidden="true" tabindex="-1"></a> month5 <span class="sc">+</span> month6 <span class="sc">+</span> month7 <span class="sc">+</span> month8 <span class="sc">+</span> month9 <span class="sc">+</span> month10 <span class="sc">+</span> month11 <span class="sc">+</span> month12 <span class="sc">+</span></span> 1157<span id="cb26-11"><a href="#cb26-11" aria-hidden="true" tabindex="-1"></a> h_chris <span class="sc">+</span> h_newyr <span class="sc">+</span> h_easter <span class="sc">+</span> h_july4 <span class="sc">+</span> h_mem <span class="sc">+</span> h_labor <span class="sc">+</span></span> 1158<span id="cb26-12"><a href="#cb26-12" aria-hidden="true" tabindex="-1"></a> w_rain <span class="sc">+</span> w_snow <span class="sc">+</span> w_maxa <span class="sc">+</span> w_maxb <span class="sc">+</span> w_maxc <span class="sc">+</span> w_mina <span class="sc">+</span> w_minb <span class="sc">+</span> w_minc</span> 1159<span id="cb26-13"><a href="#cb26-13" aria-hidden="true" tabindex="-1"></a>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div> 1160</div> 1161<div class="cell"> 1162<div class="cell-output-display"> 1163<div id="tbl-movies_tsls2" class="anchored"> 1164 1165<div class="tabwid"><style>.cl-1e8bfb22{}.cl-1e84af7a{font-family:'Arial';font-size:11pt;font-weight:bold;font-style:normal;text-decoration:none;color:rgba(0, 0, 0, 1.00);background-color:transparent;}.cl-1e84af84{font-family:'Arial';font-size:11pt;font-weight:normal;font-style:normal;text-decoration:none;color:rgba(0, 0, 0, 1.00);background-color:transparent;}.cl-1e84af8e{font-family:'Arial';font-size:11pt;font-weight:normal;font-style:normal;text-decoration:none;color:rgba(51, 51, 51, 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1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}.cl-1e87ac5c{width:0.922in;background-color:transparent;vertical-align: middle;border-bottom: 1.5pt solid rgba(102, 102, 102, 1.00);border-top: 1.5pt solid rgba(102, 102, 102, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}.cl-1e87ac5d{width:0.99in;background-color:transparent;vertical-align: middle;border-bottom: 1.5pt solid rgba(102, 102, 102, 1.00);border-top: 1.5pt solid rgba(102, 102, 102, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}.cl-1e87ac5e{width:1.007in;background-color:transparent;vertical-align: middle;border-bottom: 1.5pt solid rgba(102, 102, 102, 1.00);border-top: 1.5pt solid rgba(102, 102, 102, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 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1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}.cl-1e87ac71{width:0.99in;background-color:transparent;vertical-align: middle;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}.cl-1e87ac72{width:1.007in;background-color:transparent;vertical-align: middle;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}.cl-1e87ac7a{width:0.837in;background-color:transparent;vertical-align: middle;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}.cl-1e87ac84{width:0.99in;background-color:transparent;vertical-align: middle;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}.cl-1e87ac85{width:0.922in;background-color:transparent;vertical-align: middle;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}.cl-1e87ac86{width:0.99in;background-color:transparent;vertical-align: middle;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}.cl-1e87ac8e{width:1.007in;background-color:transparent;vertical-align: middle;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}.cl-1e87ac8f{width:0.837in;background-color:transparent;vertical-align: middle;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}.cl-1e87ac98{width:0.99in;background-color:transparent;vertical-align: middle;border-bottom: 1.5pt solid rgba(102, 102, 102, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}.cl-1e87ac99{width:0.922in;background-color:transparent;vertical-align: middle;border-bottom: 1.5pt solid rgba(102, 102, 102, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}.cl-1e87ac9a{width:0.99in;background-color:transparent;vertical-align: middle;border-bottom: 1.5pt solid rgba(102, 102, 102, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}.cl-1e87aca2{width:1.007in;background-color:transparent;vertical-align: middle;border-bottom: 1.5pt solid rgba(102, 102, 102, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}.cl-1e87acac{width:0.837in;background-color:transparent;vertical-align: middle;border-bottom: 1.5pt solid rgba(102, 102, 102, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}.cl-1e87acad{width:0.99in;background-color:transparent;vertical-align: middle;border-bottom: 0 solid rgba(255, 255, 255, 0.00);border-top: 0 solid rgba(255, 255, 255, 0.00);border-left: 0 solid rgba(255, 255, 255, 0.00);border-right: 0 solid rgba(255, 255, 255, 0.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}.cl-1e87acae{width:0.922in;background-color:transparent;vertical-align: middle;border-bottom: 0 solid rgba(255, 255, 255, 0.00);border-top: 0 solid rgba(255, 255, 255, 0.00);border-left: 0 solid rgba(255, 255, 255, 0.00);border-right: 0 solid rgba(255, 255, 255, 0.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}.cl-1e87acaf{width:0.99in;background-color:transparent;vertical-align: middle;border-bottom: 0 solid rgba(255, 255, 255, 0.00);border-top: 0 solid rgba(255, 255, 255, 0.00);border-left: 0 solid rgba(255, 255, 255, 0.00);border-right: 0 solid rgba(255, 255, 255, 0.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}.cl-1e87acb6{width:1.007in;background-color:transparent;vertical-align: middle;border-bottom: 0 solid rgba(255, 255, 255, 0.00);border-top: 0 solid rgba(255, 255, 255, 0.00);border-left: 0 solid rgba(255, 255, 255, 0.00);border-right: 0 solid rgba(255, 255, 255, 0.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}.cl-1e87acb7{width:0.837in;background-color:transparent;vertical-align: middle;border-bottom: 0 solid rgba(255, 255, 255, 0.00);border-top: 0 solid rgba(255, 255, 255, 0.00);border-left: 0 solid rgba(255, 255, 255, 0.00);border-right: 0 solid rgba(255, 255, 255, 0.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}</style><table data-quarto-disable-processing="true" class="cl-1e8bfb22"><caption>Table 13: <p>Movies TSLS(2) Stage 2 Result</p> </caption><thead><tr style="overflow-wrap:break-word;"><th class="cl-1e87ac52"><p class="cl-1e879a32"><span class="cl-1e84af7a">Var.Name</span></p></th><th class="cl-1e87ac5c"><p class="cl-1e879a3c"><span class="cl-1e84af7a">Estimate</span></p></th><th class="cl-1e87ac5d"><p class="cl-1e879a3c"><span class="cl-1e84af7a">Std. Error</span></p></th><th class="cl-1e87ac5e"><p class="cl-1e879a3c"><span class="cl-1e84af7a">t value</span></p></th><th class="cl-1e87ac66"><p class="cl-1e879a3c"><span class="cl-1e84af7a">Pr(>|t|)</span></p></th></tr></thead><tbody><tr style="overflow-wrap:break-word;"><td class="cl-1e87ac67"><p class="cl-1e879a32"><span class="cl-1e84af84">(Intercept)</span></p></td><td class="cl-1e87ac70"><p class="cl-1e879a3c"><span class="cl-1e84af84">6.92252</span></p></td><td class="cl-1e87ac71"><p class="cl-1e879a3c"><span class="cl-1e84af84">0.02644</span></p></td><td class="cl-1e87ac72"><p class="cl-1e879a3c"><span class="cl-1e84af84">261.85541</span></p></td><td class="cl-1e87ac7a"><p class="cl-1e879a3c"><span class="cl-1e84af84">0.00000</span></p></td></tr><tr style="overflow-wrap:break-word;"><td class="cl-1e87ac84"><p class="cl-1e879a32"><span class="cl-1e84af84">attend_v</span></p></td><td class="cl-1e87ac85"><p class="cl-1e879a3c"><span class="cl-1e84af84">-0.00317</span></p></td><td class="cl-1e87ac86"><p class="cl-1e879a3c"><span class="cl-1e84af84">0.00205</span></p></td><td class="cl-1e87ac8e"><p class="cl-1e879a3c"><span class="cl-1e84af84">-1.54546</span></p></td><td class="cl-1e87ac8f"><p class="cl-1e879a3c"><span class="cl-1e84af84">0.12290</span></p></td></tr><tr style="overflow-wrap:break-word;"><td class="cl-1e87ac84"><p class="cl-1e879a32"><span class="cl-1e84af84">attend_m</span></p></td><td class="cl-1e87ac85"><p class="cl-1e879a3c"><span class="cl-1e84af84">-0.00412</span></p></td><td class="cl-1e87ac86"><p class="cl-1e879a3c"><span class="cl-1e84af84">0.00151</span></p></td><td class="cl-1e87ac8e"><p class="cl-1e879a3c"><span class="cl-1e84af84">-2.72450</span></p></td><td class="cl-1e87ac8f"><p class="cl-1e879a3c"><span class="cl-1e84af84">0.00668</span></p></td></tr><tr style="overflow-wrap:break-word;"><td class="cl-1e87ac98"><p class="cl-1e879a32"><span class="cl-1e84af84">attend_n</span></p></td><td class="cl-1e87ac99"><p class="cl-1e879a3c"><span class="cl-1e84af84">-0.00258</span></p></td><td class="cl-1e87ac9a"><p class="cl-1e879a3c"><span class="cl-1e84af84">0.00154</span></p></td><td class="cl-1e87aca2"><p class="cl-1e879a3c"><span class="cl-1e84af84">-1.67705</span></p></td><td class="cl-1e87acac"><p class="cl-1e879a3c"><span class="cl-1e84af84">0.09419</span></p></td></tr></tbody><tfoot><tr style="overflow-wrap:break-word;"><td colspan="5" class="cl-1e87acad"><p class="cl-1e879a32"><span class="cl-1e84af8e">Note. Fixed variables are hidden</span></p></td></tr></tfoot></table></div> 1166</div> 1167</div> 1168</div> 1169<div class="cell"> 1170<div class="sourceCode cell-code" id="cb27"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb27-1"><a href="#cb27-1" aria-hidden="true" tabindex="-1"></a>movies_tsls_vm <span class="ot"><-</span> mod.movies_tsls2 <span class="sc">%>%</span> car<span class="sc">::</span><span class="fu">linearHypothesis</span>(</span> 1171<span id="cb27-2"><a href="#cb27-2" aria-hidden="true" tabindex="-1"></a> <span class="st">
1171"attend_v=attend_m"</span></span> 1172<span id="cb27-3"><a href="#cb27-3" aria-hidden="true" tabindex="-1"></a>)</span> 1173<span id="cb27-4"><a href="#cb27-4" aria-hidden="true" tabindex="-1"></a>movies_tsls_vn <span class="ot"><-</span> mod.movies_tsls2 <span class="sc">%>%</span> car<span class="sc">::</span><span class="fu">linearHypothesis</span>(</span> 1174<span id="cb27-5"><a href="#cb27-5" aria-hidden="true" tabindex="-1"></a> <span class="st">"attend_v = attend_n"</span></span> 1175<span id="cb27-6"><a href="#cb27-6" aria-hidden="true" tabindex="-1"></a>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div> 1176</div> 1177<div class="cell"> 1178<div class="cell-output-display"> 1179<div id="tbl-tsls2_vmn_diff" class="anchored"> 1180 1181<div class="tabwid"><style>.cl-1ea8e502{}.cl-1ea073d6{font-family:'Arial';font-size:11pt;font-weight:bold;font-style:normal;text-decoration:none;color:rgba(0, 0, 0, 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rgba(102, 102, 102, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}.cl-1ea4a69a{width:0.837in;background-color:transparent;vertical-align: middle;border-bottom: 1.5pt solid rgba(102, 102, 102, 1.00);border-top: 1.5pt solid rgba(102, 102, 102, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}.cl-1ea4a69b{width:1.062in;background-color:transparent;vertical-align: middle;border-bottom: 1.5pt solid rgba(102, 102, 102, 1.00);border-top: 1.5pt solid rgba(102, 102, 102, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}.cl-1ea4a6a4{width:0.599in;background-color:transparent;vertical-align: middle;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}.cl-1ea4a6a5{width:0.837in;background-color:transparent;vertical-align: middle;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}.cl-1ea4a6ae{width:1.062in;background-color:transparent;vertical-align: middle;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}.cl-1ea4a6af{width:0.599in;background-color:transparent;vertical-align: middle;border-bottom: 1.5pt solid rgba(102, 102, 102, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}.cl-1ea4a6b8{width:0.837in;background-color:transparent;vertical-align: middle;border-bottom: 1.5pt solid rgba(102, 102, 102, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}.cl-1ea4a6b9{width:1.062in;background-color:transparent;vertical-align: middle;border-bottom: 1.5pt solid rgba(102, 102, 102, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}</style><table data-quarto-disable-processing="true" class="cl-1ea8e502"><caption>Table 14: <p>TSLS F test of v=m, v=n</p> </caption><thead><tr style="overflow-wrap:break-word;"><th class="cl-1ea4a690"><p class="cl-1ea49402"><span class="cl-1ea073d6">Test</span></p></th><th class="cl-1ea4a69a"><p class="cl-1ea4940c"><span class="cl-1ea073d6">Chisq</span></p></th><th class="cl-1ea4a69b"><p class="cl-1ea4940c"><span class="cl-1ea073d6">Pr(>Chisq)</span></p></th></tr></thead><tbody><tr style="overflow-wrap:break-word;"><td class="cl-1ea4a6a4"><p class="cl-1ea49402"><span class="cl-1ea073e0">v=m</span></p></td><td class="cl-1ea4a6a5"><p class="cl-1ea4940c"><span class="cl-1ea073e0">0.37994</span></p></td><td class="cl-1ea4a6ae"><p class="cl-1ea4940c"><span class="cl-1ea073e0">0.53763</span></p></td></tr><tr style="overflow-wrap:break-word;"><td class="cl-1ea4a6af"><p class="cl-1ea49402"><span class="cl-1ea073e0">v=n</span></p></td><td class="cl-1ea4a6b8"><p class="cl-1ea4940c"><span class="cl-1ea073e0">0.17518</span></p></td><td class="cl-1ea4a6b9"><p class="cl-1ea4940c"><span class="cl-1ea073e0">0.67555</span></p></td></tr></tbody></table></div> 1182</div> 1183</div> 1184</div> 1185<div class="cell"> 1186<div class="sourceCode cell-code" id="cb28"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb28-1"><a href="#cb28-1" aria-hidden="true" tabindex="-1"></a>beta_v <span class="ot"><-</span>
1186 mod.movies_tsls2<span class="sc">$</span>coefficients[<span class="st">"attend_v"</span>]</span> 1187<span id="cb28-2"><a href="#cb28-2" aria-hidden="true" tabindex="-1"></a>beta_m <span class="ot"><-</span> mod.movies_tsls2<span class="sc">$</span>coefficients[<span class="st">"attend_m"</span>]</span> 1188<span id="cb28-3"><a href="#cb28-3" aria-hidden="true" tabindex="-1"></a>beta_n <span class="ot"><-</span> mod.movies_tsls2<span class="sc">$</span>coefficients[<span class="st">"attend_n"</span>]</span> 1189<span id="cb28-4"><a href="#cb28-4" aria-hidden="true" tabindex="-1"></a>effect <span class="ot"><-</span> movies <span class="sc">%>%</span></span> 1190<span id="cb28-5"><a href="#cb28-5" aria-hidden="true" tabindex="-1"></a> <span class="fu">mutate</span>(<span class="at">effect =</span> <span class="dv">6</span> <span class="sc">*</span> beta_v <span class="sc">*</span> attend_v <span class="sc">-</span></span> 1191<span id="cb28-6"><a href="#cb28-6" aria-hidden="true" tabindex="-1"></a> <span class="dv">2</span> <span class="sc">*</span> beta_m <span class="sc">*</span> attend_m <span class="sc">-</span></span> 1192<span id="cb28-7"><a href="#cb28-7" aria-hidden="true" tabindex="-1"></a> beta_n <span class="sc">*</span> attend_n) <span class="sc">%>%</span></span> 1193<span id="cb28-8"><a href="#cb28-8" aria-hidden="true" tabindex="-1"></a> <span class="fu">select</span>(effect) <span class="sc">%>%</span></span> 1194<span id="cb28-9"><a href="#cb28-9" aria-hidden="true" tabindex="-1"></a> <span class="fu">pull</span>()</span> 1195<span id="cb28-10"><a href="#cb28-10" aria-hidden="true" tabindex="-1"></a>ci_res_tsls2 <span class="ot"><-</span> <span class="fu">ci</span>(effect) <span class="sc">%>%</span></span> 1196<span id="cb28-11"><a href="#cb28-11" aria-hidden="true" tabindex="-1"></a> <span class="fu">as.data.frame</span>() <span class="sc">%>%</span></span> 1197<span id="cb28-12"><a href="#cb28-12" aria-hidden="true" tabindex="-1"></a> <span class="fu">t</span>() <span class="sc">%>%</span></span> 1198<span id="cb28-13"><a href="#cb28-13" aria-hidden="true" tabindex="-1"></a> <span class="fu">as.data.frame</span>() <span class="sc">%>%</span></span> 1199<span id="cb28-14"><a href="#cb28-14" aria-hidden="true" tabindex="-1"></a> <span class="fu">round</span>(<span class="dv">5</span>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div> 1200</div> 1201<div class="cell"> 1202<div class="cell-output-display"> 1203<div id="tbl-movies_tsls2_ci" class="anchored"> 1204 1205<div class="tabwid"><style>.cl-1eca11a0{}.cl-1ec27800{font-family:'Arial';font-size:11pt;font-weight:bold;font-style:normal;text-decoration:none;color:rgba(0, 0, 0, 1.00);background-color:transparent;}.cl-1ec2780a{font-family:'Arial';font-size:11pt;font-weight:normal;font-style:normal;text-decoration:none;color:rgba(0, 0, 0, 1.00);background-color:transparent;}.cl-1ec59058{margin:0;text-align:right;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);padding-bottom:5pt;padding-top:5pt;padding-left:5pt;padding-right:5pt;line-height: 1;background-color:transparent;}.cl-1ec5b146{width:0.922in;background-color:transparent;vertical-align: middle;border-bottom: 1.5pt solid rgba(102, 102, 102, 1.00);border-top: 1.5pt solid rgba(102, 102, 102, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}.cl-1ec5b150{width:0.879in;background-color:transparent;vertical-align: middle;border-bottom: 1.5pt solid rgba(102, 102, 102, 1.00);border-top: 1.5pt solid rgba(102, 102, 102, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}.cl-1ec5b15a{width:0.905in;background-color:transparent;vertical-align: middle;border-bottom: 1.5pt solid rgba(102, 102, 102, 1.00);border-top: 1.5pt solid rgba(102, 102, 102, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}.cl-1ec5b15b{width:0.99in;background-color:transparent;vertical-align: middle;border-bottom: 1.5pt solid rgba(102, 102, 102, 1.00);border-top: 1.5pt solid rgba(102, 102, 102, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}.cl-1ec5b164{width:0.922in;background-color:transparent;vertical-align: middle;border-bottom: 1.5pt solid rgba(102, 102, 102, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}.cl-1ec5b165{width:0.879in;background-color:transparent;vertical-align: middle;border-bottom: 1.5pt solid rgba(102, 102, 102, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}.cl-1ec5b16e{width:0.905in;background-color:transparent;vertical-align: middle;border-bottom: 1.5pt solid rgba(102, 102, 102, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}.cl-1ec5b16f{width:0.99in;background-color:transparent;vertical-align: middle;border-bottom: 1.5pt solid rgba(102, 102, 102, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}</style><table data-quarto-disable-processing="true" class="cl-1eca11a0"><caption>Table 15: <p>Change in Assaults 95% Confidence Interval</p> </caption><thead><tr style="overflow-wrap:break-word;"><th class="cl-1ec5b146"><p class="cl-1ec59058"><span class="cl-1ec27800">Estimate</span></p></th><th class="cl-1ec5b150"><p class="cl-1ec59058"><span class="cl-1ec27800">CI lower</span></p></th><th class="cl-1ec5b15a"><p class="cl-1ec59058"><span class="cl-1ec27800">CI upper</span></p></th><th class="cl-1ec5b15b"><p class="cl-1ec59058"><span class="cl-1ec27800">Std. Error</span></p></th></tr></thead><tbody><tr style="overflow-wrap:break-word;"><td class="cl-1ec5b164"><p class="cl-1ec59058"><span class="cl-1ec2780a">0.03412</span></p></td><td class="cl-1ec5b165"><p class="cl-1ec59058"><span class="cl-1ec2780a">0.02863</span></p></td><td class="cl-1ec5b16e"><p class="cl-1ec59058"><span class="cl-1ec2780a">0.03961</span></p></td><td class="cl-1ec5b16f"><p class="cl-1ec59058"><span class="cl-1ec2780a">0.0028</span></p></td></tr></tbody></table></div> 1206</div> 1207</div> 1208</div> 1209<p>The results are same comparing to b, or c.</p> 1210</section> 1211<section id="e.-2" class="level2 unnumbered"> 1212<h2 class="unnumbered anchored" data-anchor-id="e.-2">e.</h2> 1213<p>Use J-test to test the overidentifying restrictions</p> 1214<div class="cell"> 1215<div class="sourceCode cell-code" id="cb29"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb29-1"><a href="#cb29-1" aria-hidden="true" tabindex="-1"></a><span class="co"># TSLS </span></span> 1216<span id="cb29-2"><a href="#cb29-2" aria-hidden="true" tabindex="-1"></a>model <span class="ot"><-</span> <span class="fu">ivreg</span>(<span class="fu">log</span>(assaults) <span class="sc">~</span> attend_v <span class="sc">+</span> attend_m <span class="sc">+</span> attend_n <span class="sc">+</span> year2 <span class="sc">+</span> year3 <span class="sc">+</span> year4 <span class="sc">+</span></span> 1217<span id="cb29-3"><a href="#cb29-3" aria-hidden="true" tabindex="-1"></a> year5 <span class="sc">+</span> year6 <span class="sc">+</span> year7 <span class="sc">+</span>
1217 year8 <span class="sc">+</span> year9 <span class="sc">+</span> year10 <span class="sc">+</span> month2 <span class="sc">+</span> month3 <span class="sc">+</span> month4 <span class="sc">+</span></span> 1218<span id="cb29-4"><a href="#cb29-4" aria-hidden="true" tabindex="-1"></a> month5 <span class="sc">+</span> month6 <span class="sc">+</span> month7 <span class="sc">+</span> month8 <span class="sc">+</span> month9 <span class="sc">+</span> month10 <span class="sc">+</span> month11 <span class="sc">+</span> month12 <span class="sc">+</span></span> 1219<span id="cb29-5"><a href="#cb29-5" aria-hidden="true" tabindex="-1"></a> h_chris <span class="sc">+</span> h_newyr <span class="sc">+</span> h_easter <span class="sc">+</span> h_july4 <span class="sc">+</span> h_mem <span class="sc">+</span> h_labor <span class="sc">+</span></span> 1220<span id="cb29-6"><a href="#cb29-6" aria-hidden="true" tabindex="-1"></a> w_rain <span class="sc">+</span> w_snow <span class="sc">+</span> w_maxa <span class="sc">+</span> w_maxb <span class="sc">+</span> w_maxc <span class="sc">+</span> w_mina <span class="sc">+</span> w_minb <span class="sc">+</span> w_minc <span class="sc">|</span> </span> 1221<span id="cb29-7"><a href="#cb29-7" aria-hidden="true" tabindex="-1"></a> pr_attend_v <span class="sc">+</span> pr_attend_m <span class="sc">+</span> pr_attend_n <span class="sc">+</span> attend_v_f <span class="sc">+</span> attend_m_f <span class="sc">+</span> </span> 1222<span id="cb29-8"><a href="#cb29-8" aria-hidden="true" tabindex="-1"></a> attend_n_f <span class="sc">+</span> attend_v_b <span class="sc">+</span> attend_m_b <span class="sc">+</span> attend_n_b <span class="sc">+</span> year2 <span class="sc">+</span> year3 <span class="sc">+</span> year4 <span class="sc">+</span></span> 1223<span id="cb29-9"><a href="#cb29-9" aria-hidden="true" tabindex="-1"></a> year5 <span class="sc">+</span> year6 <span class="sc">+</span> year7 <span class="sc">+</span>
1223 year8 <span class="sc">+</span> year9 <span class="sc">+</span> year10 <span class="sc">+</span> month2 <span class="sc">+</span> month3 <span class="sc">+</span> month4 <span class="sc">+</span></span> 1224<span id="cb29-10"><a href="#cb29-10" aria-hidden="true" tabindex="-1"></a> month5 <span class="sc">+</span> month6 <span class="sc">+</span> month7 <span class="sc">+</span> month8 <span class="sc">+</span> month9 <span class="sc">+</span> month10 <span class="sc">+</span> month11 <span class="sc">+</span> month12 <span class="sc">+</span></span> 1225<span id="cb29-11"><a href="#cb29-11" aria-hidden="true" tabindex="-1"></a> h_chris <span class="sc">+</span> h_newyr <span class="sc">+</span> h_easter <span class="sc">+</span> h_july4 <span class="sc">+</span> h_mem <span class="sc">+</span> h_labor <span class="sc">+</span></span> 1226<span id="cb29-12"><a href="#cb29-12" aria-hidden="true" tabindex="-1"></a> w_rain <span class="sc">+</span> w_snow <span class="sc">+</span> w_maxa <span class="sc">+</span> w_maxb <span class="sc">+</span> w_maxc <span class="sc">+</span> w_mina <span class="sc">+</span> w_minb <span class="sc">+</span> w_minc, </span> 1227<span id="cb29-13"><a href="#cb29-13" aria-hidden="true" tabindex="-1"></a>
1227 <span class="at">data =</span> movies)</span> 1228<span id="cb29-14"><a href="#cb29-14" aria-hidden="true" tabindex="-1"></a></span> 1229<span id="cb29-15"><a href="#cb29-15" aria-hidden="true" tabindex="-1"></a><span class="co"># Predicted values </span></span> 1230<span id="cb29-16"><a href="#cb29-16" aria-hidden="true" tabindex="-1"></a>y_hat <span class="ot"><-</span> <span class="fu">predict</span>(model)</span> 1231<span id="cb29-17"><a href="#cb29-17" aria-hidden="true" tabindex="-1"></a></span> 1232<span id="cb29-18"><a href="#cb29-18" aria-hidden="true" tabindex="-1"></a><span class="co"># Residuals</span></span> 1233<span id="cb29-19"><a href="#cb29-19" aria-hidden="true" tabindex="-1"></a>u_hat <span class="ot"><-</span> <span class="fu">log</span>(movies<span class="sc">$</span>assaults) <span class="sc">-</span> y_hat</span> 1234<span id="cb29-20"><a href="#cb29-20" aria-hidden="true" tabindex="-1"></a></span> 1235<span id="cb29-21"><a href="#cb29-21" aria-hidden="true" tabindex="-1"></a><span class="co"># Regress residuals on instruments and exog. vars</span></span> 1236<span id="cb29-22"><a href="#cb29-22" aria-hidden="true" tabindex="-1"></a>resid_model <span class="ot"><-</span> <span class="fu">lm</span>(</span> 1237<span id="cb29-23"><a href="#cb29-23" aria-hidden="true" tabindex="-1"></a> u_hat <span class="sc">~</span> pr_attend_v <span class="sc">+</span> pr_attend_m <span class="sc">+</span> pr_attend_n <span class="sc">+</span> attend_v_f <span class="sc">+</span> attend_m_f <span class="sc">+</span> </span> 1238<span id="cb29-24"><a href="#cb29-24" aria-hidden="true" tabindex="-1"></a> attend_n_f <span class="sc">+</span> attend_v_b <span class="sc">+</span> attend_m_b <span class="sc">+</span> attend_n_b <span class="sc">+</span> year2 <span class="sc">+</span> year3 <span class="sc">+</span> year4 <span class="sc">+</span></span> 1239<span id="cb29-25"><a href="#cb29-25" aria-hidden="true" tabindex="-1"></a> year5 <span class="sc">+</span> year6 <span class="sc">+</span> year7 <span class="sc">+</span>
1239 year8 <span class="sc">+</span> year9 <span class="sc">+</span> year10 <span class="sc">+</span> month2 <span class="sc">+</span> month3 <span class="sc">+</span> month4 <span class="sc">+</span></span> 1240<span id="cb29-26"><a href="#cb29-26" aria-hidden="true" tabindex="-1"></a> month5 <span class="sc">+</span> month6 <span class="sc">+</span> month7 <span class="sc">+</span> month8 <span class="sc">+</span> month9 <span class="sc">+</span> month10 <span class="sc">+</span> month11 <span class="sc">+</span> month12 <span class="sc">+</span></span> 1241<span id="cb29-27"><a href="#cb29-27" aria-hidden="true" tabindex="-1"></a> h_chris <span class="sc">+</span> h_newyr <span class="sc">+</span> h_easter <span class="sc">+</span> h_july4 <span class="sc">+</span> h_mem <span class="sc">+</span> h_labor <span class="sc">+</span></span> 1242<span id="cb29-28"><a href="#cb29-28" aria-hidden="true" tabindex="-1"></a> w_rain <span class="sc">+</span> w_snow <span class="sc">+</span> w_maxa <span class="sc">+</span> w_maxb <span class="sc">+</span> w_maxc <span class="sc">+</span> w_mina <span class="sc">+</span> w_minb <span class="sc">+</span> w_minc, <span class="at">data =</span> movies</span> 1243<span id="cb29-29"><a href="#cb29-29" aria-hidden="true" tabindex="-1"></a>) </span> 1244<span id="cb29-30"><a href="#cb29-30" aria-hidden="true" tabindex="-1"></a></span> 1245<span id="cb29-31"><a href="#cb29-31" aria-hidden="true" tabindex="-1"></a><span class="co"># F-statistic</span></span> 1246<span id="cb29-32"><a href="#cb29-32" aria-hidden="true" tabindex="-1"></a>f_stat <span class="ot"><-</span> resid_model <span class="sc">%>%</span> car<span class="sc">::</span><span class="fu">linearHypothesis</span>(</span> 1247<span id="cb29-33"><a href="#cb29-33" aria-hidden="true" tabindex="-1"></a> <span class="fu">c</span>(<span class="st">"pr_attend_v=0"</span>,</span> 1248<span id="cb29-34"><a href="#cb29-34" aria-hidden="true" tabindex="-1"></a> <span class="st">"pr_attend_v=pr_attend_m"</span>,</span> 1249<span id="cb29-35"><a href="#cb29-35" aria-hidden="true" tabindex="-1"></a> <span class="st">"pr_attend_m=pr_attend_n"</span>,</span> 1250<span id="cb29-36"><a href="#cb29-36" aria-hidden="true" tabindex="-1"></a> <span class="st">"pr_attend_n=attend_v_f"</span>,</span> 1251<span id="cb29-37"><a href="#cb29-37" aria-hidden="true" tabindex="-1"></a> <span class="st">"attend_v_f=attend_m_f"</span>,</span> 1252<span id="cb29-38"><a href="#cb29-38" aria-hidden="true" tabindex="-1"></a> <span class="st">"attend_m_f=attend_n_f"</span>,</span> 1253<span id="cb29-39"><a href="#cb29-39" aria-hidden="true" tabindex="-1"></a> <span class="st">"attend_n_f=attend_v_b"</span>,</span> 1254<span id="cb29-40"><a href="#cb29-40" aria-hidden="true" tabindex="-1"></a> <span class="st">"attend_v_b=attend_m_b"</span>,</span> 1255<span id="cb29-41"><a href="#cb29-41" aria-hidden="true" tabindex="-1"></a> <span class="st">"attend_m_b=attend_n_b"</span>)</span> 1256<span id="cb29-42"><a href="#cb29-42" aria-hidden="true" tabindex="-1"></a>) <span class="sc">%>%</span> .[<span class="st">"F"</span>] <span class="sc">%>%</span> <span class="fu">pull</span>() <span class="sc">%>%</span> .[<span class="dv">2</span>]</span> 1257<span id="cb29-43"><a href="#cb29-43" aria-hidden="true" tabindex="-1"></a></span> 1258<span id="cb29-44"><a href="#cb29-44" aria-hidden="true" tabindex="-1"></a><span class="co"># J-statistic </span></span> 1259<span id="cb29-45"><a href="#cb29-45" aria-hidden="true" tabindex="-1"></a>j_stat <span class="ot"><-</span> <span class="dv">9</span> <span class="sc">*</span> f_stat </span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div> 1260</div> 1261<p>The J-stat is 8.5937298. We failed to reject the hypothesis that all instruments are exogenous, which means that some of the instruments are invalid.</p> 1262</section> 1263<section id="f.-2" class="level2 unnumbered"> 1264<h2 class="unnumbered anchored" data-anchor-id="f.-2">f. </h2> 1265<p>The violent movies wonât affect, or will slightly decrease violent behavior.</p> 1266</section> 1267</section> 1268<section id="problem-5fertility" class="level1"> 1269<h1>Problem 5(Fertility)</h1> 1270<div class="cell"> 1271<div class="sourceCode cell-code" id="cb30"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb30-1"><a href="#cb30-1" aria-hidden="true" tabindex="-1"></a>fertility <span class="ot"><-</span> <span class="fu">read_xlsx</span>(<span class="st">"data/fertility.xlsx"</span>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div> 1272</div> 1273<section id="a.-3" class="level2 unnumbered"> 1274<h2 class="unnumbered anchored" data-anchor-id="a.-3">a.</h2> 1275<div class="cell"> 1276<div class="sourceCode cell-code" id="cb31"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb31-1"><a href="#cb31-1" aria-hidden="true" tabindex="-1"></a><span class="fu">attach</span>(fertility)</span> 1277<span id="cb31-2"><a href="#cb31-2" aria-hidden="true" tabindex="-1"></a>mod.fertility1 <span class="ot"><-</span> <span class="fu">lm</span>(</span> 1278<span id="cb31-3"><a href="#cb31-3" aria-hidden="true" tabindex="-1"></a> weeksm1 <span class="sc">~</span> <span class="dv">1</span> <span class="sc">+</span> morekids</span> 1279<span id="cb31-4"><a href="#cb31-4" aria-hidden="true" tabindex="-1"></a>)</span> 1280<span id="cb31-5"><a href="#cb31-5" aria-hidden="true" tabindex="-1"></a><span class="fu">detach</span>(fertility)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div> 1281</div> 1282<p>The regression result suggests that women with more than two children work about 5 weeks less than women with two children.</p> 1283</section> 1284<section id="b.-3" class="level2 unnumbered"> 1285<h2 class="unnumbered anchored" data-anchor-id="b.-3">b.</h2> 1286<ol type="1"> 1287<li>Selection bias: The sample only includes married women who already have at least 2 children. Women who never married or had children may have different effects, so the estimates cannot be generalized.</li> 1288<li>Simultaneous causality: Labor supply may also affect fertility decisions, not just the other way around. So <em>weeksworked</em> should also be treated as endogenous.</li> 1289<li>Omitted variable bias: There may be omitted factors that affect both fertility and labor supply, such as religion, education, career ambition, etc. If these are not controlled for, the OLS estimates will be bi
1289ased.</li> 1290</ol> 1291</section> 1292<section id="c.-3" class="level2 unnumbered"> 1293<h2 class="unnumbered anchored" data-anchor-id="c.-3">c. </h2> 1294<div class="cell"> 1295<div class="sourceCode cell-code" id="cb32"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb32-1"><a href="#cb32-1" aria-hidden="true" tabindex="-1"></a>mod.morekids_on_samesex <span class="ot"><-</span> <span class="fu">glm</span>(</span> 1296<span id="cb32-2"><a href="#cb32-2" aria-hidden="true" tabindex="-1"></a> morekids <span class="sc">~</span> samesex,</span> 1297<span id="cb32-3"><a href="#cb32-3" aria-hidden="true" tabindex="-1"></a> <span class="at">family =</span> <span class="fu">binomial</span>(<span class="at">link =</span> <span class="st">"logit"</span>),</span> 1298<span id="cb32-4"><a href="#cb32-4" aria-hidden="true" tabindex="-1"></a> <span class="at">data =</span> fertility</span> 1299<span id="cb32-5"><a href="#cb32-5" aria-hidden="true" tabindex="-1"></a>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div> 1300</div> 1301<p>To predict the effect of same sex of first two children on the third child, run a logit model of <em>morekids</em> on <em>samesex</em>, the regression result shows:</p> 1302<p><span class="math display">\[ 1303Probit(morekids) = -0.635+0.287*samesex 1304\]</span></p> 1305<p>The marginal effect of <em>samesex</em> is <span class="math inline">\(0.287*(\phi(-0.635+0.287))=0.107\)</span>. When <em>samesex</em> increases from 0 to 1, the probability increases by 10.7%. This appears to be a reasonably large and meaningful effect, indicating having same-sex first two children meaningfully impacts the probability of having a third child. From the p-value of the regression result, the coefficient is statistically significant.</p> 1306</section> 1307<section id="d.-3" class="level2 unnumbered"> 1308<h2 class="unnumbered anchored" data-anchor-id="d.-3">d. </h2> 1309<ol type="1"> 1310<li>Relevance: <em>samesex</em> is correlated with <em>morekids</em>. Discussion in c. has proved that having same-sex first two children is positive correlated with more kids. So <em>samesex</em> satisfies the relevance criterion for an IV.</li> 1311<li>Exogeneity: <em>samesex</em> is unlikely to directly affect <em>weeksworked</em>. Whether the first two children are the same gender is exogenous to the motherâs labor supply. So <em>samesex</em> satisfies the exogeneity assumption.</li> 1312</ol> 1313</section> 1314<section id="e.-3" class="level2 unnumbered"> 1315<h2 class="unnumbered anchored" data-anchor-id="e.-3">e.</h2> 1316<p>In the first stage, F-stat is 1237>10, so it is not a weak instrument.</p> 1317</section> 1318<section id="f.-3" class="level2 unnumbered"> 1319<h2 class="unnumbered anchored" data-anchor-id="f.-3">f. </h2> 1320<div class="cell"> 1321<div class="sourceCode cell-code" id="cb33"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb33-1"><a href="#cb33-1" aria-hidden="true" tabindex="-1"></a><span class="co"># stage 1</span></span> 1322<span id="cb33-2"><a href="#cb33-2" aria-hidden="true" tabindex="-1"></a>mod.fertility_stage1 <span class="ot"><-</span> <span class="fu">lm</span>(</span> 1323<span id="cb33-3"><a href="#cb33-3" aria-hidden="true" tabindex="-1"></a> morekids <span class="sc">~</span> samesex,</span> 1324<span id="cb33-4"><a href="#cb33-4" aria-hidden="true" tabindex="-1"></a> <span class="at">data =</span> fertility</span> 1325<span id="cb33-5"><a href="#cb33-5" aria-hidden="true" tabindex="-1"></a>)</span> 1326<span id="cb33-6"><a href="#cb33-6" aria-hidden="true" tabindex="-1"></a><span class="co"># stage 2</span></span> 1327<span id="cb33-7"><a href="#cb33-7" aria-hidden="true" tabindex="-1"></a>mod.fertility_stage2 <span class="ot"><-</span> <span class="fu">ivreg</span>(</span> 1328<span id="cb33-8"><a href="#cb33-8" aria-hidden="true" tabindex="-1"></a> weeksm1 <span class="sc">~</span> <span class="dv">1</span> <span class="sc">+</span> morekids <span class="sc">|</span> samesex,</span> 1329<span id="cb33-9"><a href="#cb33-9" aria-hidden="true" tabindex="-1"></a> <span class="at">data =</span>
1329 fertility</span> 1330<span id="cb33-10"><a href="#cb33-10" aria-hidden="true" tabindex="-1"></a>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div> 1331</div> 1332<p>From the TSLS, more than two kids decreases about -6.3 working weeks.</p> 1333</section> 1334<section id="g.-1" class="level2 unnumbered"> 1335<h2 class="unnumbered anchored" data-anchor-id="g.-1">g.</h2> 1336<p>After including the variables <em>agem1, black, hispan</em>, and <em>othrace</em> in the labor supply regression, the effect of more kids is still negative, but shrink a little to 0, which is now -5.8. This is because <em>morekids</em> indeed has negative effect on labor supply, but after including fixed effect, the missing-variable bias is basically eliminated.</p> 1337<div class="cell"> 1338<div class="sourceCode cell-code" id="cb34"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb34-1"><a href="#cb34-1" aria-hidden="true" tabindex="-1"></a><span class="co"># stage 1 with FE</span></span> 1339<span id="cb34-2"><a href="#cb34-2" aria-hidden="true" tabindex="-1"></a>mod.fertility_stage1_fixed <span class="ot"><-</span> <span class="fu">glm</span>(</span> 1340<span id="cb34-3"><a href="#cb34-3" aria-hidden="true" tabindex="-1"></a> morekids <span class="sc">~</span> samesex <span class="sc">+</span> agem1 <span class="sc">+</span> black <span class="sc">+</span> hispan <span class="sc">+</span> othrace,</span> 1341<span id="cb34-4"><a href="#cb34-4" aria-hidden="true" tabindex="-1"></a> <span class="at">family =</span> <span class="fu">binomial</span>(<span class="at">link =</span> <span class="st">"logit"</span>),</span> 1342<span id="cb34-5"><a href="#cb34-5" aria-hidden="true" tabindex="-1"></a> <span class="at">data =</span> fertility</span> 1343<span id="cb34-6"><a href="#cb34-6" aria-hidden="true" tabindex="-1"></a>)</span> 1344<span id="cb34-7"><a href="#cb34-7" aria-hidden="true" tabindex="-1"></a><span class="co"># stage 2 with FE</span></span> 1345<span id="cb34-8"><a href="#cb34-8" aria-hidden="true" tabindex="-1"></a>mod.fertility_stage2_fixed <span class="ot"><-</span> <span class="fu">ivreg</span>(</span> 1346<span id="cb34-9"><a href="#cb34-9" aria-hidden="true" tabindex="-1"></a> <span class="at">data =</span> fertility,</span> 1347<span id="cb34-10"><a href="#cb34-10" aria-hidden="true" tabindex="-1"></a> weeksm1 <span class="sc">~</span> <span class="dv">1</span> <span class="sc">+</span> morekids <span class="sc">+</span> agem1 <span class="sc">+</span> black <span class="sc">+</span> hispan <span class="sc">+</span> othrace <span class="sc">|</span></span> 1348<span id="cb34-11"><a href="#cb34-11" aria-hidden="true" tabindex="-1"></a> samesex <span class="sc">+</span> agem1 <span class="sc">+</span> black <span class="sc">+</span> hispan <span class="sc">+</span> othrace</span> 1349<span id="cb34-12"><a href="#cb34-12" aria-hidden="true" tabindex="-1"></a>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div> 1350</div> 1351<div class="cell"> 1352<div class="cell-output cell-output-stderr"> 1353<pre><code>Profiled confidence intervals may take longer time to compute. 1354 Use `ci_method="wald"` for faster computation of CIs.</code></pre> 1355</div> 1356<div class="cell-output-display"> 1357<div id="tbl-fertility" class="anchored"> 1358<table data-quarto-postprocess="true" class="table table-sm table-striped small"> 1359<caption>Table 16: Fertility Regression Results</caption> 1360<colgroup> 1361<col style="width: 16%"> 1362<col style="width: 16%"> 1363<col style="width: 16%"> 1364<col style="width: 16%"> 1365<col style="width: 16%"> 1366<col style="width: 16%"> 1367</colgroup> 1368<tbody> 1369<tr class="odd"> 1370<td data-quarto-table-cell-role="th" style="text-align: center; border-top: double; font-style: italic; font-weight: normal; padding: 0.2cm; border-bottom: 1px solid black;"> </td> 1371<td data-quarto-table-cell-role="th" style="text-align: center; border-top: double; font-style: italic; font-weight: normal; padding: 0.2cm; border-bottom: 1px solid black;">Weekswork</td> 1372<td data-quarto-table-cell-role="th" style="text-align: center; border-top: double; font-style: italic; font-weight: normal; padding: 0.2cm; border-bottom: 1px solid black;">TSLS stage 1</td> 1373<td data-quarto-table-cell-role="th" style="text-align: center; border-top: double; font-style: italic; font-weight: normal; padding: 0.2cm; border-bottom: 1px solid black;">TSLS stage 2</td> 1374<td data-quarto-table-cell-role="th" style="text-align: center; border-top: double; font-style: italic; font-weight: normal; padding: 0.2cm; border-bottom: 1px solid black;">TSLS stage1(FE)</td> 1375<td data-quarto-table-cell-role="th" style="text-align: center; border-top: double; font-style: italic; font-weight: normal; padding: 0.2cm; border-bottom: 1px solid black;">TSLS stage2(FE)</td> 1376</tr> 1377<tr class="even"> 1378<td style="text-align: center; border-bottom: 1px solid; font-style: italic; font-weight: normal; border-bottom: 1px solid black;">Predictors</td> 1379<td style="text-align: center; border-bottom: 1px solid; font-style: italic; font-weight: normal; border-bottom: 1px solid black;">Estimates</td> 1380<td style="text-align: center; border-bottom: 1px solid; font-style: italic; font-weight: normal; border-bottom: 1px solid black;">Estimates</td> 1381<td style="text-align: center; border-bottom: 1px solid; font-style: italic; font-weight: normal; border-bottom: 1px solid black;">Estimates</td> 1382<td style="text-align: center; border-bottom: 1px solid; font-style: italic; font-weight: normal; border-bottom: 1px solid black;">Log-Odds</td> 1383<td style="text-align: center; border-bottom: 1px solid; font-style: italic; font-weight: normal; border-bottom: 1px solid black;">Estimates</td> 1384</tr> 1385<tr class="odd"> 1386<td style="text-align: center;">(Intercept)</td> 1387<td style="text-align: center;">21.0684 <sup>***</sup><br> 1388(0.0547)</td> 1389<td style="text-align: center;">0.3464 <sup>***</sup><br> 1390(0.0014)</td> 1391<td style="text-align: center;">21.4211 <sup>***</sup><br> 1392(0.4870)</td> 1393<td style="text-align: center;">-2.7832 <sup>***</sup><br> 1394(0.0391)</td> 1395<td style="text-align: center;">-4.7919 <sup>***</sup><br> 1396(0.4066)</td> 1397</tr> 1398<tr class="even"> 1399<td style="text-align: center;">morekids</td> 1400<td style="text-align: center;">-5.3870 <sup>***</sup><br> 1401(0.0886)</td> 1402<td style="text-align: center;"></td> 1403<td style="text-align: center;">-6.3137 <sup>***</sup><br> 1404(1.2746)</td> 1405<td style="text-align: center;"></td> 1406<td style="text-align: center;">-5.8211 <sup>***</sup><br> 1407(1.2463)</td> 1408</tr> 1409<tr class="odd"> 1410<td style="text-align: center;">samesex</td> 1411<td style="text-align: center;"></td> 1412<td style="text-align: center;">0.0675 <sup>***</sup><br> 1413(0.0019)</td> 1414<td style="text-align: center;"></td> 1415<td style="text-align: center;">0.2948 <sup>***</sup><br> 1416(0.0083)</td> 1417<td style="text-align: center;"></td> 1418</tr> 1419<tr class="even"> 1420<td style="text-align: center;">agem1</td> 1421<td style="text-align: center;"></td> 1422<td style="text-align: center;"></td> 1423<td style="text-align: center;"></td> 1424<td style="text-align: center;">0.0678 <sup>***</sup><br> 1425(0.0013)</td> 1426<td style="text-align: center;">0.8316 <sup>***</sup><br> 1427(0.0229)</td> 1428</tr> 1429<tr class="odd"> 1430<td style="text-align: center;">black</td> 1431<td style="text-align: center;"></td> 1432<td style="text-align: center;"></td> 1433<td style="text-align: center;"></td> 1434<td style="text-align: center;">0.4254 <sup>***</sup><br> 1435(0.0182)</td> 1436<td style="text-align: center;">11.6233 <sup>***</sup><br> 1437(0.2289)</td> 1438</tr> 1439<tr class="even"> 1440<td style="text-align: center;">hispan</td> 1441<td style="text-align: center;"></td> 1442<td style="text-align: center;"></td> 1443<td style="text-align: center;"></td> 1444<td style="text-align: center;">0.6321 <sup>***</sup><br> 1445(0.0170)</td> 1446<td style="text-align: center;">
14460.4042 <sup></sup><br> 1447(0.2599)</td> 1448</tr> 1449<tr class="odd"> 1450<td style="text-align: center;">othrace</td> 1451<td style="text-align: center;"></td> 1452<td style="text-align: center;"></td> 1453<td style="text-align: center;"></td> 1454<td style="text-align: center;">0.1175 <sup>***</sup><br> 1455(0.0194)</td> 1456<td style="text-align: center;">2.1310 <sup>***</sup><br> 1457(0.2059)</td> 1458</tr> 1459<tr class="even"> 1460<td style="text-align: center; padding-top: 0.1cm; padding-bottom: 0.1cm; border-top: 1px solid;">Observations</td> 1461<td style="text-align: center; padding-top: 0.1cm; padding-bottom: 0.1cm; border-top: 1px solid;">254654</td> 1462<td style="text-align: center; padding-top: 0.1cm; padding-bottom: 0.1cm; border-top: 1px solid;">254654</td> 1463<td style="text-align: center; padding-top: 0.1cm; padding-bottom: 0.1cm; border-top: 1px solid;">254654</td> 1464<td style="text-align: center; padding-top: 0.1cm; padding-bottom: 0.1cm; border-top: 1px solid;">254654</td> 1465<td style="text-align: center; padding-top: 0.1cm; padding-bottom: 0.1cm; border-top: 1px solid;">254654</td> 1466</tr> 1467<tr class="odd"> 1468<td style="text-align: center; padding-top: 0.1cm; padding-bottom: 0.1cm;">R<sup>2</sup> / R<sup>2</sup> adjusted</td> 1469<td style="text-align: center; padding-top: 0.1cm; padding-bottom: 0.1cm;">0.014 / 0.014</td> 1470<td style="text-align: center; padding-top: 0.1cm; padding-bottom: 0.1cm;">0.005 / 0.005</td> 1471<td style="text-align: center; padding-top: 0.1cm; padding-bottom: 0.1cm;">0.014 / 0.014</td> 1472<td style="text-align: center; padding-top: 0.1cm; padding-bottom: 0.1cm;">0.024</td> 1473<td style="text-align: center; padding-top: 0.1cm; padding-bottom: 0.1cm;">0.044 / 0.044</td> 1474</tr> 1475<tr class="even"> 1476<td colspan="6" style="text-align: right; font-style: italic; border-top: double black;">* p<0.05 ** p<0.01 *** p<0.001</td> 1477</tr> 1478</tbody> 1479</table> 1480</div> 1481 1482 1483</div> 1484</div> 1485</section> 1486</section> 1487<section id="problem-6weakiv" class="level1"> 1488<h1>Problem 6(WeakIV)</h1> 1489<section id="a.-4" class="level2 unnumbered"> 1490<h2 class="unnumbered anchored" data-anchor-id="a.-4">a.</h2> 1491<p>From the TSLS result, <span class="math inline">\(\hat{beta}_1^{TSLS}=1.158\)</span>, its standard error is 0.427, and its 95% confidence interval is (0.316, 2.000).</p> 1492</section> 1493<section id="b.-4" class="level2 unnumbered"> 1494<h2 class="unnumbered anchored" data-anchor-id="b.-4">b.</h2> 1495<p>The F-statistic of the regression of X on Z is 4.6, which is smaller than 10, indicating that Z is a weak instrument.</p> 1496</section> 1497<section id="c.-4" class="level2 unnumbered"> 1498<h2 class="unnumbered anchored" data-anchor-id="c.-4">c. </h2> 1499<div class="cell"> 1500<div class="sourceCode cell-code" id="cb36"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb36-1"><a href="#cb36-1" aria-hidden="true" tabindex="-1"></a>weak_iv <span class="ot"><-</span> <span class="fu">read_xls</span>(<span class="st">"data/WeakInstrument.xls"</span>)</span> 1501<span id="cb36-2"><a href="#cb36-2" aria-hidden="true" tabindex="-1"></a>mod.weakiv_stage1 <span class="ot"><-</span> <span class="fu">lm</span>(</span> 1502<span id="cb36-3"><a href="#cb36-3" aria-hidden="true" tabindex="-1"></a> x <span class="sc">~</span> <span class="dv">1</span> <span class="sc">+</span> z,</span> 1503<span id="cb36-4"><a href="#cb36-4" aria-hidden="true" tabindex="-1"></a> <span class="at">data =</span> weak_iv</span> 1504<span id="cb36-5"><a href="#cb36-5" aria-hidden="true" tabindex="-1"></a>)</span> 1505<span id="cb36-6"><a href="#cb36-6" aria-hidden="true" tabindex="-1"></a>mod.weakiv_stage2 <span class="ot"><-</span> <span class="fu">ivreg</span>(</span> 1506<span id="cb36-7"><a href="#cb36-7" aria-hidden="true" tabindex="-1"></a> <span class="at">data =</span> weak_iv,</span> 1507<span id="cb36-8"><a href="#cb36-8" aria-hidden="true" tabindex="-1"></a> y <span class="sc">~</span> x <span class="sc">|</span> z</span> 1508<span id="cb36-9"><a href="#cb36-9" aria-hidden="true" tabindex="-1"></a>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div> 1509</div> 1510<div class="cell"> 1511<div class="sourceCode cell-code" id="cb37"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb37-1"><a href="#cb37-1" aria-hidden="true" tabindex="-1"></a><span class="fu">library</span>(ivmodel)</span> 1512<span id="cb37-2"><a href="#cb37-2" aria-hidden="true" tabindex="-1"></a>ar_res <span class="ot"><-</span> <span class="fu">ivmodel</span>(<span class="at">Y =</span> weak_iv<span class="sc">$</span>y, <span class="at">D =</span> weak_iv<span class="sc">$</span>x, <span class="at">Z =</span> weak_iv<span class="sc">$</span>z) <span class="sc">%>%</span> <span class="fu">AR.test</span>()</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div> 1513</div> 1514<p>The F-stat of the Anderson-Rubin test if 1.6349195, its confidence interval is ([-7.20451207607717, 1.7291568975746]).</p> 1515</section> 1516<section id="d.-4" class="level2 unnumbered"> 1517<h2 class="unnumbered anchored" data-anchor-id="d.-4">d. </h2> 1518<p>The confidence interval in (a) will be unreliable because there is a weak instrument problem (F < 10). The Anderson-Rubin CI in (c) is robust to weak instruments so will be more reliable.</p> 1519<div class="cell"> 1520<div class="sourceCode cell-code" id="cb38"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb38-1"><a href="#cb38-1" aria-hidden="true" tabindex="-1"></a><span class="fu">tab_model</span>(mod.weakiv_stage1, mod.weakiv_stage2,</span> 1521<span id="cb38-2"><a href="#cb38-2" aria-hidden="true" tabindex="-1"></a> <span class="at">digits =</span> <span class="dv">3</span>, <span class="at">p.style =</span> <span class="st">
1521"stars"</span>,</span> 1522<span id="cb38-3"><a href="#cb38-3" aria-hidden="true" tabindex="-1"></a> <span class="at">CSS =</span> <span class="fu">list</span>(<span class="at">css.tdata =</span> <span class="st">"text-align: center;"</span>),</span> 1523<span id="cb38-4"><a href="#cb38-4" aria-hidden="true" tabindex="-1"></a> <span class="at">dv.labels =</span> <span class="fu">c</span>(<span class="st">"TSLS stage 1"</span>, <span class="st">"TSLS stage 2"</span>)</span> 1524<span id="cb38-5"><a href="#cb38-5" aria-hidden="true" tabindex="-1"></a>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div> 1525<div class="cell-output-display"> 1526<div id="tbl-weak_iv" class="anchored"> 1527<table data-quarto-postprocess="true" class="table table-sm table-striped small"> 1528<caption>Table 17: WeakIV TSLS Results</caption> 1529<tbody> 1530<tr class="odd"> 1531<td data-quarto-table-cell-role="th" style="text-align: center; border-top: double; font-style: italic; font-weight: normal; padding: 0.2cm; border-bottom: 1px solid black;"> </td> 1532<td colspan="2" data-quarto-table-cell-role="th" style="text-align: center; border-top: double; font-style: italic; font-weight: normal; padding: 0.2cm; border-bottom: 1px solid black;">TSLS stage 1</td> 1533<td colspan="2" data-quarto-table-cell-role="th" style="text-align: center; border-top: double; font-style: italic; font-weight: normal; padding: 0.2cm; border-bottom: 1px solid black;">TSLS stage 2</td> 1534</tr> 1535<tr class="even"> 1536<td style="text-align: center; border-bottom: 1px solid; font-style: italic; font-weight: normal; border-bottom: 1px solid black;">Predictors</td> 1537<td style="text-align: center; border-bottom: 1px solid; font-style: italic; font-weight: normal; border-bottom: 1px solid black;">Estimates</td> 1538<td style="text-align: center; border-bottom: 1px solid; font-style: italic; font-weight: normal; border-bottom: 1px solid black;">CI</td> 1539<td style="text-align: center; border-bottom: 1px solid; font-style: italic; font-weight: normal; border-bottom: 1px solid black;">Estimates</td> 1540<td style="text-align: center; border-bottom: 1px solid; font-style: italic; font-weight: normal; border-bottom: 1px solid black;">CI</td> 1541</tr> 1542<tr class="odd"> 1543<td style="text-align: center;">(Intercept)</td> 1544<td style="text-align: center;">0.083 <sup></sup></td> 1545<td style="text-align: center;">-0.051 â 0.216</td> 1546<td style="text-align: center;">-0.014 <sup></sup></td> 1547<td style="text-align: center;">-0.150 â 0.122</td> 1548</tr> 1549<tr class="even"> 1550<td style="text-align: center;">z</td> 1551<td style="text-align: center;">0.135 <sup>*</sup></td> 1552<td style="text-align: center;">0.010 â 0.259</td> 1553<td style="text-align: center;"></td> 1554<td style="text-align: center;"></td> 1555</tr> 1556<tr class="odd"> 1557<td style="text-align: center;">x</td> 1558<td style="text-align: center;"></td> 1559<td style="text-align: center;"></td> 1560<td style="text-align: center;">1.158 <sup>**</sup></td> 1561<td style="text-align: center;">0.316 â 2.000</td> 1562</tr> 1563<tr class="even"> 1564<td style="text-align: center; padding-top: 0.1cm; padding-bottom: 0.1cm; border-top: 1px solid;">Observations</td> 1565<td colspan="2" style="text-align: center; padding-top: 0.1cm; padding-bottom: 0.1cm; border-top: 1px solid;">200</td> 1566<td colspan="2" style="text-align: center; padding-top: 0.1cm; padding-bottom: 0.1cm; border-top: 1px solid;">200</td> 1567</tr> 1568<tr class="odd"> 1569<td style="text-align: center; padding-top: 0.1cm; padding-bottom: 0.1cm;">R<sup>2</sup> / R<sup>2</sup> adjusted</td> 1570<td colspan="2" style="text-align: center; padding-top: 0.1cm; padding-bottom: 0.1cm;">0.023 / 0.018</td> 1571<td colspan="2" style="text-align: center; padding-top: 0.1cm; padding-bottom: 0.1cm;">0.780 / 0.778</td> 1572</tr> 1573<tr class="even"> 1574<td colspan="5" style="text-align: right; font-style: italic; border-top: double black;">* p<0.05 ** p<0.01 *** p<0.001</td> 1575</tr> 1576</tbody> 1577</table> 1578</div> 1579 1580 1581</div> 1582</div> 1583</section> 1584</section> 1585<section id="problem-7names" class="level1"> 1586<h1>Problem 7(Names)</h1> 1587<section id="éå 说æ" class="level2"> 1588<h2 class="anchored" data-anchor-id="éå 说æ">éå 说æ</h2> 1589<p>è¿éè¦æè°¢@Jingyiï¼å ¬å¼ç½é¡µæå°±ä¸æå ¨åäºï¼åå¦çææ£ï¼ä¹åç¯äºä¸ªä½çº§éè¯¯ï¼æcall back rate ç®éäºï¼ç°å·²æ´æ£ã</p> 1590<p>å¦å¤ï¼è¿éé¢ä¹å¯ç¨ç®å线æ§å彿¥åï¼ä¾å¦ç¬¬ä¸é®ï¼åå½callback rate on blackï¼å¾å°blackçç³»æ°å³ä¸ºå·®å¼ï¼å ¶ç½®ä¿¡åºé´å³ä¸ºå·®å¼ç置信åºé´ãæå·²ç»éªè¯è¿äºï¼ç»æå䏿¹å ¬å¼è®¡ç®å®å ¨ä¸è´ã忬¡æè°¢@Jingyiåå¦ï¼</p> 1591</section> 1592<section id="a.-5" class="level2 unnumbered"> 1593<h2 class="unnumbered anchored" data-anchor-id="a.-5">a.</h2> 1594<p>The callback rate of white is 0.0965, and which of black is 0.0645. The 95% confidence interval for the difference of call back rates is (0.0168, 0.0473). It does not include 0, so the difference is statistically significant at 0.05 level. In real world sense, white have more probability of 3.2% to receive the callback, which is about 50% higher than that probability for African Americans. It is a large and meaningful number.</p> 1595<div class="cell"> 1596<div class="sourceCode cell-code" id="cb39"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb39-1"><a href="#cb39-1" aria-hidden="true" tabindex="-1"></a>Names <span class="ot"><-</span> <span class="fu">read_xls</span>(<span class="st">"data/Names.xls"</span>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div> 1597</div> 1598<div class="cell"> 1599<div class="sourceCode cell-code" id="cb40"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb40-1"><a href="#cb40-1" aria-hidden="true" tabindex="-1"></a><span class="co"># develop some functions to use</span></span> 1600<span id="cb40-2"><a href="#cb40-2" aria-hidden="true" tabindex="-1"></a>callback_rate <span class="ot"><-</span> <span class="cf">function</span>(df) {</span> 1601<span id="cb40-3"><a href="#cb40-3" aria-hidden="true" tabindex="-1"></a> (df <span class="sc">%>%</span></span> 1602<span id="cb40-4"><a href="#cb40-4" aria-hidden="true" tabindex="-1"></a> <span class="fu">filter</span>(call_back <span class="sc">==</span> <span class="dv">1</span>) <span class="sc">%>%</span></span> 1603<span id="cb40-5"><a href="#cb40-5" aria-hidden="true" tabindex="-1"></a> <span class="fu">nrow</span>()) <span class="sc">/</span> <span class="fu">nrow</span>(df)</span> 1604<span id="cb40-6"><a href="#cb40-6" aria-hidden="true" tabindex="-1"></a>}</span> 1605<span id="cb40-7"><a href="#cb40-7" aria-hidden="true" tabindex="-1"></a></span> 1606<span id="cb40-8"><a href="#cb40-8" aria-hidden="true" tabindex="-1"></a><span class="co">
1606# https://www.stats4stem.org/confidence-interval-two-proportions-difference-of-proportions</span></span> 1607<span id="cb40-9"><a href="#cb40-9" aria-hidden="true" tabindex="-1"></a>cbr_diff_ci <span class="ot"><-</span> <span class="cf">function</span>(cate1, cate2) {</span> 1608<span id="cb40-10"><a href="#cb40-10" aria-hidden="true" tabindex="-1"></a> cbr1 <span class="ot"><-</span> <span class="fu">callback_rate</span>(cate1)</span> 1609<span id="cb40-11"><a href="#cb40-11" aria-hidden="true" tabindex="-1"></a> cbr2 <span class="ot"><-</span> <span class="fu">callback_rate</span>(cate2)</span> 1610<span id="cb40-12"><a href="#cb40-12" aria-hidden="true" tabindex="-1"></a> n1 <span class="ot"><-</span> cate1 <span class="sc">%>%</span> <span class="fu">nrow</span>()</span> 1611<span id="cb40-13"><a href="#cb40-13" aria-hidden="true" tabindex="-1"></a> n2 <span class="ot"><-</span> cate2 <span class="sc">%>%</span> <span class="fu">nrow</span>()</span> 1612<span id="cb40-14"><a href="#cb40-14" aria-hidden="true" tabindex="-1"></a> diff <span class="ot"><-</span> <span class="fu">abs</span>(cbr1 <span class="sc">-</span> cbr2)</span> 1613<span id="cb40-15"><a href="#cb40-15" aria-hidden="true" tabindex="-1"></a> <span class="co"># Standard error of difference in call-back rates</span></span> 1614<span id="cb40-16"><a href="#cb40-16" aria-hidden="true" tabindex="-1"></a> se <span class="ot"><-</span> <span class="fu">sqrt</span>(cbr1 <span class="sc">*</span> (<span class="dv">1</span> <span class="sc">-</span> cbr1) <span class="sc">/</span> n1 <span class="sc">+</span> cbr2 <span class="sc">*</span> (<span class="dv">1</span> <span class="sc">-</span> cbr2) <span class="sc">/</span> n2)</span> 1615<span id="cb40-17"><a href="#cb40-17" aria-hidden="true" tabindex="-1"></a> CI_low <span class="ot"><-</span> diff <span class="sc">-</span> <span class="fl">1.96</span> <span class="sc">*</span> se</span> 1616<span id="cb40-18"><a href="#cb40-18" aria-hidden="true" tabindex="-1"></a> CI_high <span class="ot"><-</span> diff <span class="sc">+</span> <span class="fl">1.96</span> <span class="sc">*</span> se</span> 1617<span id="cb40-19"><a href="#cb40-19" aria-hidden="true" tabindex="-1"></a> <span class="fu">c</span>(CI_low, CI_high)</span> 1618<span id="cb40-20"><a href="#cb40-20" aria-hidden="true" tabindex="-1"></a>}</span> 1619<span id="cb40-21"><a href="#cb40-21" aria-hidden="true" tabindex="-1"></a></span> 1620<span id="cb40-22"><a href="#cb40-22" aria-hidden="true" tabindex="-1"></a>white_vs_black <span class="ot"><-</span> <span class="cf">function</span>(df) {</span> 1621<span id="cb40-23"><a href="#cb40-23" aria-hidden="true" tabindex="-1"></a> white <span class="ot"><-</span> df <span class="sc">%>%</span> <span class="fu">filter</span>(black <span class="sc">==</span> <span class="dv">0</span>)</span> 1622<span id="cb40-24"><a href="#cb40-24" aria-hidden="true" tabindex="-1"></a> black <span class="ot"><-</span> df <span class="sc">%>%</span> <span class="fu">filter</span>(black <span class="sc">==</span> <span class="dv">1</span>)</span> 1623<span id="cb40-25"><a href="#cb40-25" aria-hidden="true" tabindex="-1"></a> cbr_white <span class="ot"><-</span> <span class="fu">callback_rate</span>(white)</span> 1624<span id="cb40-26"><a href="#cb40-26" aria-hidden="true" tabindex="-1"></a> cbr_black <span class="ot"><-</span> <span class="fu">callback_rate</span>(black)</span> 1625<span id="cb40-27"><a href="#cb40-27" aria-hidden="true" tabindex="-1"></a> diff_ci <span class="ot"><-</span> <span class="fu">cbr_diff_ci</span>(white, black)</span> 1626<span id="cb40-28"><a href="#cb40-28" aria-hidden="true" tabindex="-1"></a> <span class="fu">tibble</span>(</span> 1627<span id="cb40-29"><a href="#cb40-29" aria-hidden="true" tabindex="-1"></a> <span class="at">race =</span> <span class="fu">c</span>(<span class="st">"white"</span>, <span class="st">"black"</span>),</span> 1628<span id="cb40-30"><a href="#cb40-30" aria-hidden="true" tabindex="-1"></a> <span class="st">`</span><span class="at">callback rate</span><span class="st">`</span> <span class="ot">=</span> <span class="fu">c</span>(cbr_white, cbr_black),</span> 1629<span id="cb40-31"><a href="#cb40-31" aria-hidden="true" tabindex="-1"></a> <span class="st">`</span><span class="at">CI_lower</span><span class="st">`</span> <span class="ot">=</span>
1629 diff_ci[<span class="dv">1</span>],</span> 1630<span id="cb40-32"><a href="#cb40-32" aria-hidden="true" tabindex="-1"></a> <span class="st">`</span><span class="at">CI_upper</span><span class="st">`</span> <span class="ot">=</span> diff_ci[<span class="dv">2</span>]</span> 1631<span id="cb40-33"><a href="#cb40-33" aria-hidden="true" tabindex="-1"></a> )</span> 1632<span id="cb40-34"><a href="#cb40-34" aria-hidden="true" tabindex="-1"></a>}</span> 1633<span id="cb40-35"><a href="#cb40-35" aria-hidden="true" tabindex="-1"></a></span> 1634<span id="cb40-36"><a href="#cb40-36" aria-hidden="true" tabindex="-1"></a><span class="co"># generate result of white & black</span></span> 1635<span id="cb40-37"><a href="#cb40-37" aria-hidden="true" tabindex="-1"></a>white_black_diff <span class="ot"><-</span> <span class="fu">white_vs_black</span>(Names)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div> 1636</div> 1637<div class="cell"> 1638<div class="cell-output-display"> 1639<div id="tbl-cb_rates" class="anchored"> 1640 1641<div class="tabwid"><style>.cl-32a53cae{}.cl-329e0e7a{font-family:'Arial';font-size:11pt;font-weight:bold;font-style:normal;text-decoration:none;color:rgba(0, 0, 0, 1.00);background-color:transparent;}.cl-329e0e84{font-family:'Arial';font-size:11pt;font-weight:normal;font-style:normal;text-decoration:none;color:rgba(0, 0, 0, 1.00);background-color:transparent;}.cl-32a0e410{margin:0;text-align:left;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);padding-bottom:5pt;padding-top:5pt;padding-left:5pt;padding-right:5pt;line-height: 1;background-color:transparent;}.cl-32a0e41a{margin:0;text-align:right;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);padding-bottom:5pt;padding-top:5pt;padding-left:5pt;padding-right:5pt;line-height: 1;background-color:transparent;}.cl-32a0e41b{margin:0;text-align:center;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);padding-bottom:5pt;padding-top:5pt;padding-left:5pt;padding-right:5pt;line-height: 1;background-color:transparent;}.cl-32a0f54a{width:0.642in;background-color:transparent;vertical-align: middle;border-bottom: 0.75pt solid rgba(102, 102, 102, 1.00);border-top: 0.75pt solid rgba(102, 102, 102, 1.00);border-left: 0.75pt solid rgba(102, 102, 102, 1.00);border-right: 0.75pt solid rgba(102, 102, 102, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}.cl-32a0f54b{width:1.143in;background-color:transparent;vertical-align: middle;border-bottom: 0.75pt solid rgba(102, 102, 102, 1.00);border-top: 0.75pt solid rgba(102, 102, 102, 1.00);border-left: 0.75pt solid rgba(102, 102, 102, 1.00);border-right: 0.75pt solid rgba(102, 102, 102, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}.cl-32a0f554{width:0.888in;background-color:transparent;vertical-align: middle;border-bottom: 0.75pt solid rgba(102, 102, 102, 1.00);border-top: 0.75pt solid rgba(102, 102, 102, 1.00);border-left: 0.75pt solid rgba(102, 102, 102, 1.00);border-right: 0.75pt solid rgba(102, 102, 102, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}.cl-32a0f555{width:0.914in;background-color:transparent;vertical-align: middle;border-bottom: 0.75pt solid rgba(102, 102, 102, 1.00);border-top: 0.75pt solid rgba(102, 102, 102, 1.00);border-left: 0.75pt solid rgba(102, 102, 102, 1.00);border-right: 0.75pt solid rgba(102, 102, 102, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}.cl-32a0f55e{width:0.642in;background-color:transparent;vertical-align: middle;border-bottom: 0.75pt solid rgba(102, 102, 102, 1.00);border-top: 0 solid rgba(0, 0, 0, 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rgba(0, 0, 0, 1.00);border-left: 0.75pt solid rgba(102, 102, 102, 1.00);border-right: 0.75pt solid rgba(102, 102, 102, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}.cl-32a0f574{width:0.642in;background-color:transparent;vertical-align: middle;border-bottom: 0.75pt solid rgba(102, 102, 102, 1.00);border-top: 0.75pt solid rgba(102, 102, 102, 1.00);border-left: 0.75pt solid rgba(102, 102, 102, 1.00);border-right: 0.75pt solid rgba(102, 102, 102, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}.cl-32a0f57c{width:1.143in;background-color:transparent;vertical-align: middle;border-bottom: 0.75pt solid rgba(102, 102, 102, 1.00);border-top: 0.75pt solid rgba(102, 102, 102, 1.00);border-left: 0.75pt solid rgba(102, 102, 102, 1.00);border-right: 0.75pt solid rgba(102, 102, 102, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}.cl-32a0f57d{width:0.888in;background-color:transparent;vertical-align: middle;border-bottom: 0.75pt solid rgba(102, 102, 102, 1.00);border-top: 0.75pt solid rgba(102, 102, 102, 1.00);border-left: 0.75pt solid rgba(102, 102, 102, 1.00);border-right: 0.75pt solid rgba(102, 102, 102, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}.cl-32a0f57e{width:0.914in;background-color:transparent;vertical-align: middle;border-bottom: 0.75pt solid rgba(102, 102, 102, 1.00);border-top: 0.75pt solid rgba(102, 102, 102, 1.00);border-left: 0.75pt solid rgba(102, 102, 102, 1.00);border-right: 0.75pt solid rgba(102, 102, 102, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}</style><table data-quarto-disable-processing="true" class="cl-32a53cae"><caption>Table 18: <p>Callback Rates between Black and White</p> </caption><thead><tr style="overflow-wrap:break-word;"><th class="cl-32a0f54a"><p class="cl-32a0e410"><span class="cl-329e0e7a">race</span></p></th><th class="cl-32a0f54b"><p class="cl-32a0e41a"><span class="cl-329e0e7a">callback rate</span></p></th><th class="cl-32a0f554"><p class="cl-32a0e41a"><span class="cl-329e0e7a">CI_lower</span></p></th><th class="cl-32a0f555"><p class="cl-32a0e41a"><span class="cl-329e0e7a">CI_upper</span></p></th></tr></thead><tbody><tr style="overflow-wrap:break-word;"><td class="cl-32a0f55e"><p class="cl-32a0e41b"><span class="cl-329e0e84">white</span></p></td><td class="cl-32a0f568"><p class="cl-32a0e41b"><span class="cl-329e0e84">0.0965</span></p></td><td rowspan="2" class="cl-32a0f572"><p class="cl-32a0e41b"><span class="cl-329e0e84">0.0168</span></p></td><td rowspan="2" class="cl-32a0f573"><p class="cl-32a0e41b"><span class="cl-329e0e84">0.0473</span></p></td></tr><tr style="overflow-wrap:break-word;"><td class="cl-32a0f574"><p class="cl-32a0e41b"><span class="cl-329e0e84">black</span></p></td><td class="cl-32a0f57c"><p class="cl-32a0e41b"><span class="cl-329e0e84">0.0645</span></p></td></tr></tbody></table></div> 1642</div> 1643</div> 1644</div> 1645</section> 1646<section id="b.-5" class="level2 unnumbered"> 1647<h2 class="unnumbered anchored" data-anchor-id="b.-5">b.</h2> 1648<p>To determine if the African American/white call-back rate differential is different for men than for women, we can compare these two confidence intervals. Since they overlap substantially, we cannot conclude that there is a significant difference in the African American/white call-back rate differential between men and women.</p> 1649<div class="cell"> 1650<div class="sourceCode cell-code" id="cb41"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb41-1"><a href="#cb41-1" aria-hidden="true" tabindex="-1"></a>male <span class="ot"><-</span> Names <span class="sc">%>%</span> <span class="fu">filter</span>(female <span class="sc">==</span> <span class="dv">0</span>)</span> 1651<span id="cb41-2"><a href="#cb41-2" aria-hidden="true" tabindex="-1"></a>female <span class="ot"><-</span> Names <span class="sc">%>%</span> <span class="fu">filter</span>(female <span class="sc">==</span> <span class="dv">1</span>)</span> 1652<span id="cb41-3"><a href="#cb41-3" aria-hidden="true" tabindex="-1"></a></span> 1653<span id="cb41-4"><a href="#cb41-4" aria-hidden="true" tabindex="-1"></a><span class="co"># white and black callback rate difference of male</span></span> 1654<span id="cb41-5"><a href="#cb41-5" aria-hidden="true" tabindex="-1"></a>male_cbr_diff_wb <span class="ot"><-</span> <span class="fu">white_vs_black</span>(male) <span class="sc">%>%</span></span> 1655<span id="cb41-6"><a href="#cb41-6" aria-hidden="true" tabindex="-1"></a> <span class="fu">mutate</span>(<span class="at">gender =</span> <span class="st">
1655"male"</span>, <span class="at">.before =</span> race)</span> 1656<span id="cb41-7"><a href="#cb41-7" aria-hidden="true" tabindex="-1"></a>female_cbr_diff_wb <span class="ot"><-</span> <span class="fu">white_vs_black</span>(female) <span class="sc">%>%</span></span> 1657<span id="cb41-8"><a href="#cb41-8" aria-hidden="true" tabindex="-1"></a> <span class="fu">mutate</span>(<span class="at">gender =</span> <span class="st">"female"</span>, <span class="at">.before =</span> race)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div> 1658</div> 1659<div class="cell"> 1660<div class="cell-output-display"> 1661<div id="tbl-cbrate_male_female" class="anchored"> 1662 1663<div class="tabwid"><style>.cl-32ce2f42{}.cl-32c6944e{font-family:'Arial';font-size:11pt;font-weight:bold;font-style:normal;text-decoration:none;color:rgba(0, 0, 0, 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rgba(102, 102, 102, 1.00);border-top: 0.75pt solid rgba(102, 102, 102, 1.00);border-left: 0.75pt solid rgba(102, 102, 102, 1.00);border-right: 0.75pt solid rgba(102, 102, 102, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}</style><table data-quarto-disable-processing="true" class="cl-32ce2f42"><caption>Table
166319: <p>Call-back Rate & CI for Male and Female, Black and White</p> </caption><thead><tr style="overflow-wrap:break-word;"><th class="cl-32c9ab48"><p class="cl-32c9966c"><span class="cl-32c6944e">gender</span></p></th><th class="cl-32c9ab49"><p class="cl-32c9966c"><span class="cl-32c6944e">race</span></p></th><th class="cl-32c9ab52"><p class="cl-32c99680"><span class="cl-32c6944e">callback rate</span></p></th><th class="cl-32c9ab53"><p class="cl-32c99680"><span class="cl-32c6944e">CI_lower</span></p></th><th class="cl-32c9ab5c"><p class="cl-32c99680"><span class="cl-32c6944e">CI_upper</span></p></th></tr></thead><tbody><tr style="overflow-wrap:break-word;"><td rowspan="2" class="cl-32c9ab5d"><p class="cl-32c99681"><span class="cl-32c69458">male</span></p></td><td class="cl-32c9ab66"><p class="cl-32c99681"><span class="cl-32c69458">white</span></p></td><td class="cl-32c9ab70"><p class="cl-32c99681"><span class="cl-32c69458">0.0887</span></p></td><td rowspan="2" class="cl-32c9ab7a"><p class="cl-32c99681"><span class="cl-32c69458">0.0000</span></p></td><td rowspan="2" class="cl-32c9ab7b"><p class="cl-32c99681"><span class="cl-32c69458">0.0608</span></p></td></tr><tr style="overflow-wrap:break-word;"><td class="cl-32c9ab8e"><p class="cl-32c99681"><span class="cl-32c69458">black</span></p></td><td class="cl-32c9ab8f"><p class="cl-32c99681"><span class="cl-32c69458">0.0583</span></p></td></tr><tr style="overflow-wrap:break-word;"><td rowspan="2" class="cl-32c9aba3"><p class="cl-32c99681"><span class="cl-32c69458">female</span></p></td><td class="cl-32c9abac"><p class="cl-32c99681"><span class="cl-32c69458">white</span></p></td><td class="cl-32c9abad"><p class="cl-32c99681"><span class="cl-32c69458">0.0989</span></p></td><td rowspan="2" class="cl-32c9abb6"><p class="cl-32c99681"><span class="cl-32c69458">0.0150</span></p></td><td rowspan="2" class="cl-32c9abb7"><p class="cl-32c99681"><span class="cl-32c69458">0.0503</span></p></td></tr><tr style="overflow-wrap:break-word;"><td class="cl-32c9abac"><p class="cl-32c99681"><span class="cl-32c69458">black</span></p></td><td class="cl-32c9abad"><p class="cl-32c99681"><span class="cl-32c69458">0.0663</span></p></td></tr></tbody></table></div> 1664</div> 1665</div> 1666</div> 1667</section> 1668<section id="c.-5" class="level2 unnumbered"> 1669<h2 class="unnumbered anchored" data-anchor-id="c.-5">c. </h2> 1670<p>From the results, the confidence intervals all include 0, so all of the differences are statistically significant.</p> 1671<div class="cell"> 1672<div class="sourceCode cell-code" id="cb42"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb42-1"><a href="#cb42-1" aria-hidden="true" tabindex="-1"></a>high_vs_low <span class="ot"><-</span> <span class="cf">function</span>(df) {</span> 1673<span id="cb42-2"><a href="#cb42-2" aria-hidden="true" tabindex="-1"></a> h <span class="ot"><-</span> df <span class="sc">%>%</span> <span class="fu">filter</span>(high <span class="sc">==</span> <span class="dv">1</span>)</span> 1674<span id="cb42-3"><a href="#cb42-3" aria-hidden="true" tabindex="-1"></a> l <span class="ot"><-</span> df <span class="sc">%>%</span> <span class="fu">filter</span>(high <span class="sc">==</span> <span class="dv">0</span>)</span> 1675<span id="cb42-4"><a href="#cb42-4" aria-hidden="true" tabindex="-1"></a> cbr_h <span class="ot"><-</span> <span class="fu">callback_rate</span>(h)</span> 1676<span id="cb42-5"><a href="#cb42-5" aria-hidden="true" tabindex="-1"></a> cbr_l <span class="ot"><-</span> <span class="fu">callback_rate</span>(l)</span> 1677<span id="cb42-6"><a href="#cb42-6" aria-hidden="true" tabindex="-1"></a> diff_ci <span class="ot"><-</span> <span class="fu">cbr_diff_ci</span>(h, l)</span> 1678<span id="cb42-7"><a href="#cb42-7" aria-hidden="true" tabindex="-1"></a> <span class="fu">tibble</span>(</span> 1679<span id="cb42-8"><a href="#cb42-8" aria-hidden="true" tabindex="-1"></a> <span class="at">quality =</span> <span class="fu">c</span>(<span class="st">"high"</span>, <span class="st">"low"</span>),</span> 1680<span id="cb42-9"><a href="#cb42-9" aria-hidden="true" tabindex="-1"></a> <span class="st">`</span><span class="at">callback rate</span><span class="st">`</span> <span class="ot">=</span> <span class="fu">c</span>(cbr_h, cbr_l),</span> 1681<span id="cb42-10"><a href="#cb42-10" aria-hidden="true" tabindex="-1"></a> <span class="st">`</span><span class="at">CI_lower</span><span class="st">`</span> <span class="ot">=</span>
1681 diff_ci[<span class="dv">1</span>],</span> 1682<span id="cb42-11"><a href="#cb42-11" aria-hidden="true" tabindex="-1"></a> <span class="st">`</span><span class="at">CI_upper</span><span class="st">`</span> <span class="ot">=</span> diff_ci[<span class="dv">2</span>]</span> 1683<span id="cb42-12"><a href="#cb42-12" aria-hidden="true" tabindex="-1"></a> )</span> 1684<span id="cb42-13"><a href="#cb42-13" aria-hidden="true" tabindex="-1"></a>}</span> 1685<span id="cb42-14"><a href="#cb42-14" aria-hidden="true" tabindex="-1"></a></span> 1686<span id="cb42-15"><a href="#cb42-15" aria-hidden="true" tabindex="-1"></a><span class="co"># classify them into different tibbles</span></span> 1687<span id="cb42-16"><a href="#cb42-16" aria-hidden="true" tabindex="-1"></a>white <span class="ot"><-</span> Names <span class="sc">%>%</span> <span class="fu">filter</span>(black <span class="sc">==</span> <span class="dv">0</span>)</span> 1688<span id="cb42-17"><a href="#cb42-17" aria-hidden="true" tabindex="-1"></a>black <span class="ot"><-</span> Names <span class="sc">%>%</span> <span class="fu">filter</span>(black <span class="sc">==</span> <span class="dv">1</span>)</span> 1689<span id="cb42-18"><a href="#cb42-18" aria-hidden="true" tabindex="-1"></a></span> 1690<span id="cb42-19"><a href="#cb42-19" aria-hidden="true" tabindex="-1"></a>high_vs_low_all <span class="ot"><-</span> <span class="fu">high_vs_low</span>(Names) <span class="sc">%>%</span> <span class="fu">mutate</span>(<span class="at">catogory =</span> <span class="st">"all"</span>, <span class="at">.before =</span> quality)</span> 1691<span id="cb42-20"><a href="#cb42-20" aria-hidden="true" tabindex="-1"></a>high_vs_low_white <span class="ot"><-</span> <span class="fu">high_vs_low</span>(white) <span class="sc">%>%</span> <span class="fu">mutate</span>(<span class="at">catogory =</span> <span class="st">"white"</span>, <span class="at">.before =</span> quality)</span> 1692<span id="cb42-21"><a href="#cb42-21" aria-hidden="true" tabindex="-1"></a>high_vs_low_black <span class="ot"><-</span> <span class="fu">high_vs_low</span>(black) <span class="sc">%>%</span> <span class="fu">mutate</span>(<span class="at">catogory =</span> <span class="st">"black"</span>, <span class="at">.before =</span> quality)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div> 1693</div> 1694<div class="cell"> 1695<div class="cell-output-display"> 1696<div id="tbl-cbr_quality" class="anchored"> 1697 1698<div class="tabwid"><style>.cl-32fe52b2{}.cl-32f6ca6a{font-family:'Arial';font-size:11pt;font-weight:bold;font-style:normal;text-decoration:none;color:rgba(0, 0, 0, 1.00);background-color:transparent;}.cl-32f6ca7e{font-family:'Arial';font-size:11pt;font-weight:normal;font-style:normal;text-decoration:none;color:rgba(0, 0, 0, 1.00);background-color:transparent;}.cl-32f9bb9e{margin:0;text-align:left;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid 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1.00);border-top: 0.75pt solid rgba(102, 102, 102, 1.00);border-left: 0.75pt solid rgba(102, 102, 102, 1.00);border-right: 0.75pt solid rgba(102, 102, 102, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}.cl-32f9ceb9{width:0.922in;background-color:transparent;vertical-align: middle;border-bottom: 0.75pt solid rgba(102, 102, 102, 1.00);border-top: 0.75pt solid rgba(102, 102, 102, 1.00);border-left: 0.75pt solid rgba(102, 102, 102, 1.00);border-right: 0.75pt solid rgba(102, 102, 102, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}.cl-32f9cec2{width:0.947in;background-color:transparent;vertical-align: middle;border-bottom: 0.75pt solid rgba(102, 102, 102, 1.00);border-top: 0.75pt solid rgba(102, 102, 102, 1.00);border-left: 0.75pt solid rgba(102, 102, 102, 1.00);border-right: 0.75pt solid rgba(102, 102, 102, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}.cl-32f9cec3{width:0.93in;background-color:transparent;vertical-align: middle;border-bottom: 0.75pt solid rgba(102, 102, 102, 1.00);border-top: 0.75pt solid rgba(102, 102, 102, 1.00);border-left: 0.75pt solid rgba(102, 102, 102, 1.00);border-right: 0.75pt solid rgba(102, 102, 102, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}.cl-32f9cec4{width:0.778in;background-color:transparent;vertical-align: middle;border-bottom: 0.75pt solid rgba(102, 102, 102, 1.00);border-top: 0.75pt solid rgba(102, 102, 102, 1.00);border-left: 0.75pt solid rgba(102, 102, 102, 1.00);border-right: 0.75pt solid rgba(102, 102, 102, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}.cl-32f9cecc{width:1.211in;background-color:transparent;vertical-align: middle;border-bottom: 0.75pt solid rgba(102, 102, 102, 1.00);border-top: 0.75pt solid rgba(102, 102, 102, 1.00);border-left: 0.75pt solid rgba(102, 102, 102, 1.00);border-right: 0.75pt solid rgba(102, 102, 102, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}.cl-32f9cecd{width:0.922in;background-color:transparent;vertical-align: middle;border-bottom: 0.75pt solid rgba(102, 102, 102, 1.00);border-top: 0.75pt solid rgba(102, 102, 102, 1.00);border-left: 0.75pt solid rgba(102, 102, 102, 1.00);border-right: 0.75pt solid rgba(102, 102, 102, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}.cl-32f9cee0{width:0.947in;background-color:transparent;vertical-align: middle;border-bottom: 0.75pt solid rgba(102, 102, 102, 1.00);border-top: 0.75pt solid rgba(102, 102, 102, 1.00);border-left: 0.75pt solid rgba(102, 102, 102, 1.00);border-right: 0.75pt solid rgba(102, 102, 102, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}</style><table data-quarto-disable-processing="true" class="cl-32fe52b2"><caption>Table 20: <p>Callback Rate of High and Low Quality, with Differenc Categories</p> </caption><thead><tr style="overflow-wrap:break-word;"><th class="cl-32f9ce68"><p class="cl-32f9bb9e"><span class="cl-32f6ca6a">catogory</span></p></th><th class="cl-32f9ce72"><p class="cl-32f9bb9e"><span class="cl-32f6ca6a">quality</span></p></th><th class="cl-32f9ce7c"><p class="cl-32f9bba8"><span class="cl-32f6ca6a">callback rate</span></p></th><th class="cl-32f9ce7d"><p class="cl-32f9bba8"><span class="cl-32f6ca6a">CI_lower</span></p></th><th class="cl-32f9ce7e"><p class="cl-32f9bba8"><span class="cl-32f6ca6a">CI_upper</span></p></th></tr></thead><tbody><tr style="overflow-wrap:break-word;"><td rowspan="2" class="cl-32f9ce86"><p class="cl-32f9bba9"><span class="cl-32f6ca7e">all</span></p></td><td class="cl-32f9ce87"><p class="cl-32f9bba9"><span class="cl-32f6ca7e">high</span></p></td><td class="cl-32f9ce90"><p class="cl-32f9bba9"><span class="cl-32f6ca7e">0.0875</span></p></td><td rowspan="2" class="cl-32f9ce91"><p class="cl-32f9bba9"><span class="cl-32f6ca7e">-0.0012</span></p></td><td rowspan="2" class="cl-32f9ce92"><p class="cl-32f9bba9"><span class="cl-32f6ca7e">0.0293</span></p></td></tr><tr style="overflow-wrap:break-word;"><td class="cl-32f9ce9b"><p class="cl-32f9bba9"><span class="cl-32f6ca7e">low</span></p></td><td class="cl-32f9cea4"><p class="cl-32f9bba9"><span class="cl-32f6ca7e">
16980.0734</span></p></td></tr><tr style="overflow-wrap:break-word;"><td rowspan="2" class="cl-32f9ceae"><p class="cl-32f9bba9"><span class="cl-32f6ca7e">white</span></p></td><td class="cl-32f9ceaf"><p class="cl-32f9bba9"><span class="cl-32f6ca7e">high</span></p></td><td class="cl-32f9ceb8"><p class="cl-32f9bba9"><span class="cl-32f6ca7e">0.1079</span></p></td><td rowspan="2" class="cl-32f9ceb9"><p class="cl-32f9bba9"><span class="cl-32f6ca7e">-0.0005</span></p></td><td rowspan="2" class="cl-32f9cec2"><p class="cl-32f9bba9"><span class="cl-32f6ca7e">0.0464</span></p></td></tr><tr style="overflow-wrap:break-word;"><td class="cl-32f9cec4"><p class="cl-32f9bba9"><span class="cl-32f6ca7e">low</span></p></td><td class="cl-32f9cecc"><p class="cl-32f9bba9"><span class="cl-32f6ca7e">0.0850</span></p></td></tr><tr style="overflow-wrap:break-word;"><td rowspan="2" class="cl-32f9ceae"><p class="cl-32f9bba9"><span class="cl-32f6ca7e">black</span></p></td><td class="cl-32f9ceaf"><p class="cl-32f9bba9"><span class="cl-32f6ca7e">high</span></p></td><td class="cl-32f9ceb8"><p class="cl-32f9bba9"><span class="cl-32f6ca7e">0.0670</span></p></td><td rowspan="2" class="cl-32f9ceb9"><p class="cl-32f9bba9"><span class="cl-32f6ca7e">-0.0143</span></p></td><td rowspan="2" class="cl-32f9cec2"><p class="cl-32f9bba9"><span class="cl-32f6ca7e">0.0247</span></p></td></tr><tr style="overflow-wrap:break-word;"><td class="cl-32f9ce9b"><p class="cl-32f9bba9"><span class="cl-32f6ca7e">low</span></p></td><td class="cl-32f9cea4"><p class="cl-32f9bba9"><span class="cl-32f6ca7e">0.0619</span></p></td></tr></tbody></table></div> 1699</div> 1700</div> 1701</div> 1702</section> 1703<section id="d.-5" class="level2 unnumbered"> 1704<h2 class="unnumbered anchored" data-anchor-id="d.-5">d. </h2> 1705<p>Construct t-tests for the characteristics, separated by race. The result shows that only one of the characteristics is statistically significant at 0.05 level, which is computer skills, with value of 0.0303. So it is a random assignment.</p> 1706<div class="cell"> 1707<div class="sourceCode cell-code" id="cb43"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb43-1"><a href="#cb43-1" aria-hidden="true" tabindex="-1"></a>char <span class="ot"><-</span> <span class="fu">c</span>()</span> 1708<span id="cb43-2"><a href="#cb43-2" aria-hidden="true" tabindex="-1"></a>tt <span class="ot"><-</span> <span class="fu">c</span>()</span> 1709<span id="cb43-3"><a href="#cb43-3" aria-hidden="true" tabindex="-1"></a><span class="cf">for</span> (i <span class="cf">in</span> <span class="dv">1</span><span class="sc">:</span><span class="fu">ncol</span>(white)) {</span> 1710<span id="cb43-4"><a href="#cb43-4" aria-hidden="true" tabindex="-1"></a> col_name <span class="ot"><-</span> <span class="fu">names</span>(white[i])</span> 1711<span id="cb43-5"><a href="#cb43-5" aria-hidden="true" tabindex="-1"></a> <span class="cf">if</span> (col_name <span class="sc">==</span> <span class="st">"black"</span> <span class="sc">|</span> col_name <span class="sc">==</span> <span class="st">"call_back"</span> <span class="sc">|</span> <span class="fu">mode</span>(white[[i]]) <span class="sc">==</span> <span class="st">"character"</span>) {</span> 1712<span id="cb43-6"><a href="#cb43-6" aria-hidden="true" tabindex="-1"></a> <span class="cf">next</span></span> 1713<span id="cb43-7"><a href="#cb43-7" aria-hidden="true" tabindex="-1"></a> }</span> 1714<span id="cb43-8"><a href="#cb43-8" aria-hidden="true" tabindex="-1"></a> char <span class="ot"><-</span> <span class="fu">c</span>(char, col_name)</span> 1715<span id="cb43-9"><a href="#cb43-9" aria-hidden="true" tabindex="-1"></a> tt <span class="ot"><-</span> <span class="fu">c</span>(tt, <span class="fu">t.test</span>(white[i], black[i])<span class="sc">$</span>p.value)</span> 1716<span id="cb43-10"><a href="#cb43-10" aria-hidden="true" tabindex="-1"></a>}</span> 1717<span id="cb43-11"><a href="#cb43-11" aria-hidden="true" tabindex="-1"></a></span> 1718<span id="cb43-12"><a href="#cb43-12" aria-hidden="true" tabindex="-1"></a>sig_res <span class="ot"><-</span> <span class="fu">list</span>(<span class="at">char =</span> <span class="fu">c</span>(), <span class="at">p =</span> <span class="fu">c</span>())</span> 1719<span id="cb43-13"><a href="#cb43-13" aria-hidden="true" tabindex="-1"></a><span class="cf">for</span> (i <span class="cf">in</span> <span class="dv">1</span><span class="sc">:</span><span class="fu">length</span>(tt)) {</span> 1720<span id="cb43-14"><a href="#cb43-14" aria-hidden="true" tabindex="-1"></a> <span class="cf">if</span> (tt[i] <span class="sc"><</span> <span class="fl">0.05</span>) {</span> 1721<span id="cb43-15"><a href="#cb43-15" aria-hidden="true" tabindex="-1"></a> sig_res<span class="sc">$</span>char <span class="ot"><-</span> <span class="fu">c</span>(sig_res<span class="sc">$</span>char, char[i])</span> 1722<span id="cb43-16"><a href="#cb43-16" aria-hidden="true" tabindex="-1"></a> sig_res<span class="sc">$</span>p <span class="ot"><-</span> <span class="fu">c</span>(sig_res<span class="sc">$</span>p, tt[i])</span> 1723<span id="cb43-17"><a href="#cb43-17" aria-hidden="true" tabindex="-1"></a> }</span> 1724<span id="cb43-18"><a href="#cb43-18" aria-hidden="true" tabindex="-1"></a>}</span> 1725<span id="cb43-19"><a href="#cb43-19" aria-hidden="true" tabindex="-1"></a>sig_res <span class="sc">%>%</span></span> 1726<span id="cb43-20"><a href="#cb43-20" aria-hidden="true" tabindex="-1"></a> <span class="fu">
1726as_tibble</span>() <span class="sc">%>%</span></span> 1727<span id="cb43-21"><a href="#cb43-21" aria-hidden="true" tabindex="-1"></a> <span class="fu">mutate</span>(<span class="at">character =</span> char, <span class="st">`</span><span class="at">p-value</span><span class="st">`</span> <span class="ot">=</span> p) <span class="sc">%>%</span></span> 1728<span id="cb43-22"><a href="#cb43-22" aria-hidden="true" tabindex="-1"></a> <span class="fu">select</span>(character, <span class="st">`</span><span class="at">p-value</span><span class="st">`</span>) <span class="sc">%>%</span></span> 1729<span id="cb43-23"><a href="#cb43-23" aria-hidden="true" tabindex="-1"></a> <span class="fu">flextable</span>() <span class="sc">%>%</span></span> 1730<span id="cb43-24"><a href="#cb43-24" aria-hidden="true" tabindex="-1"></a> <span class="fu">bold</span>(<span class="at">part =</span> <span class="st">"header"</span>) <span class="sc">%>%</span></span> 1731<span id="cb43-25"><a href="#cb43-25" aria-hidden="true" tabindex="-1"></a> <span class="fu">autofit</span>()</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div> 1732<div class="cell-output-display"> 1733<div id="tbl-not_sig" class="anchored"> 1734 1735<div class="tabwid"><style>.cl-331c00aa{}.cl-33152ce4{font-family:'Arial';font-size:11pt;font-weight:bold;font-style:normal;text-decoration:none;color:rgba(0, 0, 0, 1.00);background-color:transparent;}.cl-33152cf8{font-family:'Arial';font-size:11pt;font-weight:normal;font-style:normal;text-decoration:none;color:rgba(0, 0, 0, 1.00);background-color:transparent;}.cl-3317eda8{margin:0;text-align:left;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);padding-bottom:5pt;padding-top:5pt;padding-left:5pt;padding-right:5pt;line-height: 1;background-color:transparent;}.cl-3317edbc{margin:0;text-align:right;border-bottom: 0 solid rgba(0, 0, 0, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);padding-bottom:5pt;padding-top:5pt;padding-left:5pt;padding-right:5pt;line-height: 1;background-color:transparent;}.cl-33180022{width:1.253in;background-color:transparent;vertical-align: middle;border-bottom: 1.5pt solid rgba(102, 102, 102, 1.00);border-top: 1.5pt solid rgba(102, 102, 102, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}.cl-3318002c{width:1.092in;background-color:transparent;vertical-align: middle;border-bottom: 1.5pt solid rgba(102, 102, 102, 1.00);border-top: 1.5pt solid rgba(102, 102, 102, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}.cl-3318002d{width:1.253in;background-color:transparent;vertical-align: middle;border-bottom: 1.5pt solid rgba(102, 102, 102, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}.cl-33180036{width:1.092in;background-color:transparent;vertical-align: middle;border-bottom: 1.5pt solid rgba(102, 102, 102, 1.00);border-top: 0 solid rgba(0, 0, 0, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}</style><table data-quarto-disable-processing="true" class="cl-331c00aa"><caption>Table 21: <p>Characters with Statistically Significant Difference</p> </caption><thead><tr style="overflow-wrap:break-word;"><th class="cl-33180022"><p class="cl-3317eda8"><span class="cl-33152ce4">character</span></p></th><th class="cl-3318002c"><p class="cl-3317edbc"><span class="cl-33152ce4">p-value</span></p></th></tr></thead><tbody><tr style="overflow-wrap:break-word;"><td class="cl-3318002d"><p class="cl-3317eda8"><span class="cl-33152cf8">computerskills</span></p></td>
1735<td class="cl-33180036"><p class="cl-3317edbc"><span class="cl-33152cf8">0.03032706</span></p></td></tr></tbody></table></div> 1736</div> 1737</div> 1738</div> 1739</section> 1740</section> 1741<section id="ç»è¯" class="level1"> 1742<h1>ç»è¯</h1> 1743<p>æ¬æ¬¡å®éªå 容就尿¤ç»æäºï¼è°¢è°¢ä½ çèå¿é 读ã å¦æä½ è§å¾æ¬ç¯å®éªåèå¯¹ä½ æå¸®å©çè¯ï¼æ¬¢è¿è¯·æåæ¯è¶! ;)</p> 1744<div class="quarto-figure quarto-figure-left"> 1745<figure class="figure"> 1746<p><img src="images/buymetea.png" class="img-fluid figure-img" style="width:25.0%"></p> 1747<p></p><figcaption class="figure-caption">buymetea</figcaption><p></p> 1748</figure> 1749</div> 1750<div class="cell"> 1751<div class="sourceCode cell-code hidden" id="cb44" data-startfrom="1430" data-source-offset="0"><pre class="sourceCode js code-with-copy"><code class="sourceCode javascript" style="counter-reset: source-line 1429;"><span id="cb44-1430"><a href="#cb44-1430" aria-hidden="true" tabindex="-1"></a><span class="fu">initComments</span>({</span> 1752<span id="cb44-1431"><a href="#cb44-1431" aria-hidden="true" tabindex="-1"></a> <span class="dt">node</span><span class="op">:</span> <span class="bu">document</span><span class="op">.</span><span class="fu">getElementById</span>(<span class="st">"comment-section"</span>)<span class="op">,</span></span> 1753<span id="cb44-1432"><a href="#cb44-1432" aria-hidden="true" tabindex="-1"></a> <span class="dt">defaultHomeserverUrl</span><span class="op">:</span> <span class="st">"https://matrix.cactus.chat:8448"</span><span class="op">,</span></span> 1754<span id="cb44-1433"><a href="#cb44-1433" aria-hidden="true" tabindex="-1"></a> <span class="dt">serverName</span><span class="op">:</span> <span class="st">"cactus.chat"</span><span class="op">,</span></span> 1755<span id="cb44-1434"><a href="#cb44-1434" aria-hidden="true" tabindex="-1"></a> <span class="dt">siteName</span><span class="op">:</span> <span class="st">"zzzzorange-eco-exp2"</span><span class="op">,</span></span> 1756<span id="cb44-1435"><a href="#cb44-1435" aria-hidden="true" tabindex="-1"></a> <span class="dt">commentSectionId</span><span class="op">:</span> <span class="st">"section1"</span></span> 1757<span id="cb44-1436"><a href="#cb44-1436" aria-hidden="true" tabindex="-1"></a>})</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div> 1758<div class="cell-output cell-output-display hidden"> 1759<div id="ojs-cell-1" data-nodetype="expression"> 1760 1761</div> 1762</div> 1763</div> 1764</section> 1765 1766</main> 1767<!-- /main column -->
1768<script type="ojs-module-contents"> 1769{"contents":[{"methodName":"interpret","cellName":"ojs-cell-1","inline":false,"source":"initComments({\n node: document.getElementById(\"comment-section\"),\n defaultHomeserverUrl: \"https://matrix.cactus.chat:8448\",\n serverName: \"cactus.chat\",\n siteName: \"zzzzorange-eco-exp2\",\n commentSectionId: \"section1\"\n}) \n"}]} 1770</script>
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1771<script type="module"> 1772if (window.location.protocol === "file:") { alert("The OJS runtime does not work with file:// URLs. Please use a web server to view this document."); } 1773window._ojs.paths.runtimeToDoc = "../../.."; 1774window._ojs.paths.runtimeToRoot = "../../.."; 1775window._ojs.paths.docToRoot = ""; 1776window._ojs.selfContained = false; 1777window._ojs.runtime.interpretFromScriptTags(); 1778</script>
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1779<script id="quarto-html-after-body" type="application/javascript"> 1780window.document.addEventListener("DOMContentLoaded", function (event) { 1781 const toggleBodyColorMode = (bsSheetEl) => { 1782 const mode = bsSheetEl.getAttribute("data-mode"); 1783 const bodyEl = window.document.querySelector("body"); 1784 if (mode === "dark") { 1785 bodyEl.classList.add("quarto-dark"); 1786 bodyEl.classList.remove("quarto-light"); 1787 } else { 1788 bodyEl.classList.add("quarto-light"); 1789 bodyEl.classList.remove("quarto-dark"); 1790 } 1791 } 1792 const toggleBodyColorPrimary = () => { 1793 const bsSheetEl = window.document.querySelector("link#quarto-bootstrap"); 1794 if (bsSheetEl) { 1795 toggleBodyColorMode(bsSheetEl); 1796 } 1797 } 1798 toggleBodyColorPrimary(); 1799 const icon = "î§"; 1800 const anchorJS = new window.AnchorJS(); 1801 anchorJS.options = { 1802 placement: 'right', 1803 icon: icon 1804 }; 1805 anchorJS.add('.anchored'); 1806 const isCodeAnnotation = (el) => { 1807 for (const clz of el.classList) { 1808 if (clz.startsWith('code-annotation-')) { 1809 return true; 1810 } 1811 } 1812 return false; 1813 } 1814 const clipboard = new window.ClipboardJS('.code-copy-button', { 1815 text: function(trigger) { 1816 const codeEl = trigger.previousElementSibling.cloneNode(true); 1817 for (const childEl of codeEl.children) { 1818 if (isCodeAnnotation(childEl)) { 1819 childEl.remove(); 1820 } 1821 } 1822 return codeEl.innerText; 1823 } 1824 }); 1825 clipboard.on('success', function(e) { 1826 // button target 1827 const button = e.trigger; 1828 // don't keep focus 1829 button.blur(); 1830 // flash "checked" 1831 button.classList.add('code-copy-button-checked'); 1832 var currentTitle = button.getAttribute("title"); 1833 button.setAttribute("title", "Copied!"); 1834 let tooltip; 1835 if (window.bootstrap) { 1836 button.setAttribute("data-bs-toggle", "tooltip"); 1837 button.setAttribute("data-bs-placement", "left"); 1838 button.setAttribute("data-bs-title", "Copied!"); 1839 tooltip = new bootstrap.Tooltip(button, 1840 { trigger: "manual", 1841 customClass: "code-copy-button-tooltip", 1842 offset: [0, -8]}); 1843 tooltip.show(); 1844 } 1845 setTimeout(function() { 1846 if (tooltip) { 1847 tooltip.hide(); 1848 button.removeAttribute("data-bs-title"); 1849 button.removeAttribute("data-bs-toggle"); 1850 button.removeAttribute("data-bs-placement"); 1851 } 1852 button.setAttribute("title", currentTitle); 1853 button.classList.remove('code-copy-button-checked'); 1854 }, 1000); 1855 // clear code selection 1856 e.clearSelection(); 1857 }); 1858 function tippyHover(el, contentFn) { 1859 const config = { 1860 allowHTML: true, 1861 content: contentFn, 1862 maxWidth: 500, 1863 delay: 100, 1864 arrow: false, 1865 appendTo: function(el) { 1866 return el.parentElement; 1867 }, 1868 interactive: true, 1869 interactiveBorder: 10, 1870 theme: 'quarto', 1871 placement: 'bottom-start' 1872 }; 1873 window.tippy(el, config); 1874 } 1875 const noterefs = window.document.querySelectorAll('a[role="doc-noteref"]'); 1876 for (var i=0; i<noterefs.length; i++) { 1877 const ref = noterefs[i]; 1878 tippyHover(ref, function() { 1879 // use id or data attribute instead here 1880 let href = ref.getAttribute('data-footnote-href') || ref.getAttribute('href'); 1881 try { href = new URL(href).hash; } catch {} 1882 const id = href.replace(/^#\/?/, ""); 1883 const note = window.document.getElementById(id); 1884 return note.innerHTML; 1885 }); 1886 } 1887 let selectedAnnoteEl; 1888 const selectorForAnnotation = ( cell, annotation) => { 1889 let cellAttr = 'data-code-cell="' + cell + '"'; 1890 let lineAttr = 'data-code-annotation="' + annotation + '"'; 1891 const selector = 'span[' + cellAttr + '][' + lineAttr + ']'; 1892 return selector; 1893 } 1894 const selectCodeLines = (annoteEl) => { 1895 const doc = window.document; 1896 const targetCell = annoteEl.getAttribute("data-target-cell"); 1897 const targetAnnotation = annoteEl.getAttribute("data-target-annotation"); 1898 const annoteSpan = window.document.querySelector(selectorForAnnotation(targetCell, targetAnnotation)); 1899 const lines = annoteSpan.getAttribute("data-code-lines").split(","); 1900 const lineIds = lines.map((line) => { 1901 return targetCell + "-" + line; 1902 }) 1903 let top = null; 1904 let height = null; 1905 let parent = null; 1906 if (lineIds.length > 0) { 1907 //compute the position of the single el (top and bottom and make a div) 1908 const el = window.document.getElementById(lineIds[0]); 1909 top = el.offsetTop; 1910 height = el.offsetHeight; 1911 parent = el.parentElement.parentElement; 1912 if (lineIds.length > 1) { 1913 const lastEl = window.document.getElementById(lineIds[lineIds.length - 1]); 1914 const bottom = lastEl.offsetTop + lastEl.offsetHeight; 1915 height = bottom - top; 1916 } 1917 if (top !== null && height !== null && parent !== null) { 1918 // cook up a div (if necessary) and position it 1919 let div = window.document.getElementById("code-annotation-line-highlight"); 1920 if (div === null) { 1921 div = window.document.createElement("div"); 1922 div.setAttribute("id", "code-annotation-line-highlight"); 1923 div.style.position = 'absolute'; 1924 parent.appendChild(div); 1925 } 1926 div.style.top = top - 2 + "px"; 1927 div.style.height = height + 4 + "px"; 1928 let gutterDiv = window.document.getElementById("code-annotation-line-highlight-gutter"); 1929 if (gutterDiv === null) { 1930 gutterDiv = window.document.createElement("div"); 1931 gutterDiv.setAttribute("id", "code-annotation-line-highlight-gutter"); 1932 gutterDiv.style.position = 'absolute'; 1933 const codeCell = window.document.getElementById(targetCell); 1934 const gutter = codeCell.querySelector('.code-annotation-gutter'); 1935 gutter.appendChild(gutterDiv); 1936 } 1937 gutterDiv.style.top = top - 2 + "px"; 1938 gutterDiv.style.height = height + 4 + "px"; 1939 } 1940 selectedAnnoteEl = annoteEl; 1941 } 1942 }; 1943 const unselectCodeLines = () => { 1944 const elementsIds = ["code-annotation-line-highlight", "code-annotation-line-highlight-gutter"]; 1945 elementsIds.forEach((elId) => { 1946 const div = window.document.getElementById(elId); 1947 if (div) { 1948 div.remove(); 1949 } 1950 }); 1951 selectedAnnoteEl = undefined; 1952 }; 1953 // Attach click handler to the DT 1954 const annoteDls = window.document.querySelectorAll('dt[data-target-cell]'); 1955 for (const annoteDlNode of annoteDls) { 1956 annoteDlNode.addEventListener('click', (event) => { 1957 const clickedEl = event.target; 1958 if (clickedEl !== selectedAnnoteEl) { 1959 unselectCodeLines(); 1960 const activeEl = window.document.querySelector('dt[data-target-cell].code-annotation-active'); 1961 if (activeEl) { 1962 activeEl.classList.remove('code-annotation-active'); 1963 } 1964 selectCodeLines(clickedEl); 1965 clickedEl.classList.add('code-annotation-active'); 1966 } else { 1967 // Unselect the line 1968 unselectCodeLines(); 1969 clickedEl.classList.remove('code-annotation-active'); 1970 } 1971 }); 1972 } 1973 const findCites = (el) => { 1974 const parentEl = el.parentElement; 1975 if (parentEl) { 1976 const cites = parentEl.dataset.cites; 1977 if (cites) { 1978 return { 1979 el, 1980 cites: cites.split(' ') 1981 }; 1982 } else { 1983 return findCites(el.parentElement) 1984 } 1985 } else { 1986 return undefined; 1987 } 1988 }; 1989 var bibliorefs = window.document.querySelectorAll('a[role="doc-biblioref"]'); 1990 for (var i=0; i<bibliorefs.length; i++) { 1991 const ref = bibliorefs[i]; 1992 const citeInfo = findCites(ref); 1993 if (citeInfo) { 1994 tippyHover(citeInfo.el, function() { 1995 var popup = window.document.createElement('div');
1996 citeInfo.cites.forEach(function(cite) { 1997 var citeDiv = window.document.createElement('div'); 1998 citeDiv.classList.add('hanging-indent'); 1999 citeDiv.classList.add('csl-entry'); 2000 var biblioDiv = window.document.getElementById('ref-' + cite); 2001 if (biblioDiv) { 2002 citeDiv.innerHTML = biblioDiv.innerHTML; 2003 } 2004 popup.appendChild(citeDiv); 2005 }); 2006 return popup.innerHTML; 2007 }); 2008 } 2009 } 2010}); 2011</script>
2011 2012</div> <!-- /content --> 2013<div id="comment-section"></div> 2014 2015 2016 2017</body></html>
Line numbers count LF bytes from the start of the resource, as the search results do. Vendor segments are library code the classifier recognised; they are stored but not indexed. Bytes are shown as Latin1 characters, one per byte.