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11 | 11 | <meta name="generator" content="quarto-1.5.57"> |
12 | 12 |
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13 | 13 | <meta name="author" content="Paul Schrimpf"> |
14 | | - <meta name="dcterms.date" content="2024-09-18"> |
| 14 | + <meta name="dcterms.date" content="2024-09-23"> |
15 | 15 | <title>ECON 626 – Identification</title> |
16 | 16 | <meta name="apple-mobile-web-app-capable" content="yes"> |
17 | 17 | <meta name="apple-mobile-web-app-status-bar-style" content="black-translucent"> |
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31 | 31 | vertical-align: middle; |
32 | 32 | } |
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| 35 | + pre > code.sourceCode > span { line-height: 1.25; } |
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| 59 | + padding: 0 4px; width: 4em; |
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| 61 | + pre.numberSource { margin-left: 3em; padding-left: 4px; } |
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33 | 98 | /* CSS for citations */ |
34 | 99 | div.csl-bib-body { } |
35 | 100 | div.csl-entry { |
@@ -363,7 +428,7 @@ <h1 class="title">Identification</h1> |
363 | 428 | </div> |
364 | 429 | </div> |
365 | 430 |
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366 | | - <p class="date">2024-09-18</p> |
| 431 | + <p class="date">2024-09-23</p> |
367 | 432 | </section> |
368 | 433 | <section id="reading" class="slide level2"> |
369 | 434 | <h2>Reading</h2> |
@@ -748,6 +813,22 @@ <h2>Example: Regression</h2> |
748 | 813 | \]</span></li> |
749 | 814 | </ul> |
750 | 815 | </section> |
| 816 | +<section id="caution" class="slide level2"> |
| 817 | +<h2>Caution</h2> |
| 818 | +<ul> |
| 819 | +<li><p>Regression being a linear approximation to <span class="math inline">\(\Er[Y|X]\)</span> does not mean <span class="math inline">\(\beta = \Er[X X']^{-1} \Er[X Y]\)</span> necessarily has the sign you want</p></li> |
| 820 | +<li><p>In example below, <span class="math inline">\(\Er[Y|x_1=1, x_2] > \Er[Y|x_1=9,x_2]\)</span>, but <span class="math inline">\(\beta_1 < 0\)</span></p></li> |
| 821 | +</ul> |
| 822 | +<div class="sourceCode" id="cb1"><pre class="sourceCode numberSource {julia} number-lines code-with-copy"><code class="sourceCode"><span id="cb1-1"><a></a>using LinearAlgebra</span> |
| 823 | +<span id="cb1-2"><a></a>n = 10_000</span> |
| 824 | +<span id="cb1-3"><a></a>EYX(x) = x[2]>0 ? -1.0 + 1.0*x[1] : (1.0 + 0.1*x[1])</span> |
| 825 | +<span id="cb1-4"><a></a>x2 = randn(n)</span> |
| 826 | +<span id="cb1-5"><a></a>x1 = (x2*3 + randn(n) .> 0)</span> |
| 827 | +<span id="cb1-6"><a></a>X = hcat(x1,x2)</span> |
| 828 | +<span id="cb1-7"><a></a>y = EYX.(eachrow(X)) + randn(n)</span> |
| 829 | +<span id="cb1-8"><a></a>X = hcat(ones(n), X)</span> |
| 830 | +<span id="cb1-9"><a></a>β = (X'*X) \ (X'*y)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div> |
| 831 | +</section> |
751 | 832 | <section id="example-potential-outcomes-3" class="slide level2"> |
752 | 833 | <h2>Example: Potential Outcomes</h2> |
753 | 834 | <ul> |
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