From 66e204130609bedcfdb7f94595ee7e529ea5c746 Mon Sep 17 00:00:00 2001
From: grantmcdermott <grant.mcdermott@gmail.com>
Date: Tue, 27 Feb 2024 05:15:47 +0000
Subject: [PATCH] =?UTF-8?q?Deploying=20to=20gh-pages=20from=20@=20grantmcd?=
 =?UTF-8?q?ermott/etwfe@ac7fe39832d57315e5a038c4f5dbd4164538e31a=20?=
 =?UTF-8?q?=F0=9F=9A=80?=
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8
Content-Transfer-Encoding: 8bit

---
 404.html             |   2 +-
 LICENSE-text.html    |   2 +-
 articles/etwfe.html  | 662 ++++++++++++++++++++++---------------------
 articles/index.html  |   2 +-
 authors.html         |   6 +-
 index.html           |   8 +-
 news/index.html      |   8 +-
 pkgdown.yml          |   2 +-
 reference/emfx.html  |   2 +-
 reference/etwfe.html |   2 +-
 reference/index.html |   2 +-
 search.json          |   2 +-
 12 files changed, 353 insertions(+), 347 deletions(-)

diff --git a/404.html b/404.html
index 55da3de..29d6b99 100644
--- a/404.html
+++ b/404.html
@@ -24,7 +24,7 @@
     
     <a class="navbar-brand me-2" href="http://grantmcdermott.com/etwfe/index.html">etwfe</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">0.3.5.9002</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">0.4.0</small>
 
     
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
diff --git a/LICENSE-text.html b/LICENSE-text.html
index d5da531..d0a3eeb 100644
--- a/LICENSE-text.html
+++ b/LICENSE-text.html
@@ -10,7 +10,7 @@
     
     <a class="navbar-brand me-2" href="index.html">etwfe</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">0.3.5.9002</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">0.4.0</small>
 
     
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
diff --git a/articles/etwfe.html b/articles/etwfe.html
index 4140dfb..ec5ee39 100644
--- a/articles/etwfe.html
+++ b/articles/etwfe.html
@@ -26,7 +26,7 @@
     
     <a class="navbar-brand me-2" href="../index.html">etwfe</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">0.3.5.9002</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">0.4.0</small>
 
     
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
@@ -87,12 +87,17 @@
 <h2 id="background">Background<a class="anchor" aria-label="anchor" href="#background"></a>
 </h2>
 <p>A canonical research design for social scientists is the so-called
-“differences-in-differences” (DiD) design.<a class="footnote-ref" tabindex="0" data-bs-toggle="popover" data-bs-content='&lt;p&gt;Good textbook introductions to DiD are available &lt;a href="https://theeffectbook.net/ch-DifferenceinDifference.html" class="external-link"&gt;here&lt;/a&gt;
+“difference-in-differences” (DiD) design. The essential idea behind DiD
+is that we can estimate the causal impact of an intervention
+(“treatment”) by comparing the pre- and post-intervention outcomes of
+indivduals that received treatment (“treated” group) against the
+outcomes of comparable indivduals that didn’t receive treatment
+(“control” group).<a class="footnote-ref" tabindex="0" data-bs-toggle="popover" data-bs-content='&lt;p&gt;Good textbook introductions to DiD are available &lt;a href="https://theeffectbook.net/ch-DifferenceinDifference.html" class="external-link"&gt;here&lt;/a&gt;
 and &lt;a href="https://mixtape.scunning.com/09-difference_in_differences" class="external-link"&gt;here&lt;/a&gt;,
-among many other places.&lt;/p&gt;'><sup>1</sup></a> In the classic 2x2 DiD
-case (two units, two periods), a simple interaction effect between two
-dummy variables suffices to recover the treatment effect. In base R this
-might look something like:</p>
+among many other places.&lt;/p&gt;'><sup>1</sup></a></p>
+<p>In the classic 2x2 DiD case (two units, two periods), a simple
+interaction effect between two dummy variables suffices to recover the
+treatment effect. In base R this might look something like:</p>
 <div class="sourceCode" id="cb1"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/stats/lm.html" class="external-link">lm</a></span><span class="op">(</span><span class="va">y</span> <span class="op">~</span> <span class="va">Dtreated_unit</span> <span class="op">*</span> <span class="va">Dpost_treatment</span>, data <span class="op">=</span> <span class="va">somedata</span><span class="op">)</span></span></code></pre></div>
 <p>where the resulting coefficient on the
@@ -278,7 +283,7 @@ <h3 id="emfx">
 time, or as an event study). A natural way to perform these aggregations
 is by recovering the appropriate marginal effects. The
 <strong>etwfe</strong> package provides another convenience function for
-doing so: <code><a href="../reference/emfx.html">emfx()</a></code>, which is a thin(ish) wrapper around <a href="https://marginaleffects.com/vignettes/slopes/" class="external-link"><code>marginaleffects::slopes()</code></a>.</p>
+doing so: <code><a href="../reference/emfx.html">emfx()</a></code>, which is a thin(ish) wrapper around <a href="https://marginaleffects.com/vignettes/slopes.html" class="external-link"><code>marginaleffects::slopes()</code></a>.</p>
 <p>For example, we can recover the average treatment effect on the
 treated (ATT) as follows.</p>
 <div class="sourceCode" id="cb7"><pre class="downlit sourceCode r">
@@ -366,23 +371,23 @@ <h3 id="presentation">Presentation<a class="anchor" aria-label="anchor" href="#p
 <span>  title       <span class="op">=</span> <span class="st">"Event study"</span>,</span>
 <span>  notes       <span class="op">=</span> <span class="st">"Std. errors are clustered at the county level"</span></span>
 <span><span class="op">)</span></span></code></pre></div>
-<div id="hdlgwupojp" style="padding-left:0px;padding-right:0px;padding-top:10px;padding-bottom:10px;overflow-x:auto;overflow-y:auto;width:auto;height:auto;">
-<style>#hdlgwupojp table {
+<div id="fvzwsfopin" style="padding-left:0px;padding-right:0px;padding-top:10px;padding-bottom:10px;overflow-x:auto;overflow-y:auto;width:auto;height:auto;">
+<style>#fvzwsfopin table {
   font-family: system-ui, 'Segoe UI', Roboto, Helvetica, Arial, sans-serif, 'Apple Color Emoji', 'Segoe UI Emoji', 'Segoe UI Symbol', 'Noto Color Emoji';
   -webkit-font-smoothing: antialiased;
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-#hdlgwupojp thead, #hdlgwupojp tbody, #hdlgwupojp tfoot, #hdlgwupojp tr, #hdlgwupojp td, #hdlgwupojp th {
+#fvzwsfopin thead, #fvzwsfopin tbody, #fvzwsfopin tfoot, #fvzwsfopin tr, #fvzwsfopin td, #fvzwsfopin th {
   border-style: none;
 }
 
-#hdlgwupojp p {
+#fvzwsfopin p {
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 }
 
-#hdlgwupojp .gt_table {
+#fvzwsfopin .gt_table {
   display: table;
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@@ -408,12 +413,12 @@ <h3 id="presentation">Presentation<a class="anchor" aria-label="anchor" href="#p
   border-left-color: #D3D3D3;
 }
 
-#hdlgwupojp .gt_caption {
+#fvzwsfopin .gt_caption {
   padding-top: 4px;
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 }
 
-#hdlgwupojp .gt_title {
+#fvzwsfopin .gt_title {
   color: #333333;
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@@ -425,7 +430,7 @@ <h3 id="presentation">Presentation<a class="anchor" aria-label="anchor" href="#p
   border-bottom-width: 0;
 }
 
-#hdlgwupojp .gt_subtitle {
+#fvzwsfopin .gt_subtitle {
   color: #333333;
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@@ -437,7 +442,7 @@ <h3 id="presentation">Presentation<a class="anchor" aria-label="anchor" href="#p
   border-top-width: 0;
 }
 
-#hdlgwupojp .gt_heading {
+#fvzwsfopin .gt_heading {
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@@ -449,13 +454,13 @@ <h3 id="presentation">Presentation<a class="anchor" aria-label="anchor" href="#p
   border-right-color: #D3D3D3;
 }
 
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+#fvzwsfopin .gt_bottom_border {
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 }
 
-#hdlgwupojp .gt_col_headings {
+#fvzwsfopin .gt_col_headings {
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@@ -470,7 +475,7 @@ <h3 id="presentation">Presentation<a class="anchor" aria-label="anchor" href="#p
   border-right-color: #D3D3D3;
 }
 
-#hdlgwupojp .gt_col_heading {
+#fvzwsfopin .gt_col_heading {
   color: #333333;
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   font-size: 100%;
@@ -490,7 +495,7 @@ <h3 id="presentation">Presentation<a class="anchor" aria-label="anchor" href="#p
   overflow-x: hidden;
 }
 
-#hdlgwupojp .gt_column_spanner_outer {
+#fvzwsfopin .gt_column_spanner_outer {
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   font-size: 100%;
@@ -502,15 +507,15 @@ <h3 id="presentation">Presentation<a class="anchor" aria-label="anchor" href="#p
   padding-right: 4px;
 }
 
-#hdlgwupojp .gt_column_spanner_outer:first-child {
+#fvzwsfopin .gt_column_spanner_outer:first-child {
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 }
 
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+#fvzwsfopin .gt_column_spanner_outer:last-child {
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 }
 
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+#fvzwsfopin .gt_column_spanner {
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@@ -522,11 +527,11 @@ <h3 id="presentation">Presentation<a class="anchor" aria-label="anchor" href="#p
   width: 100%;
 }
 
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+#fvzwsfopin .gt_spanner_row {
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+#fvzwsfopin .gt_group_heading {
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@@ -552,7 +557,7 @@ <h3 id="presentation">Presentation<a class="anchor" aria-label="anchor" href="#p
   text-align: left;
 }
 
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+#fvzwsfopin .gt_empty_group_heading {
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@@ -567,15 +572,15 @@ <h3 id="presentation">Presentation<a class="anchor" aria-label="anchor" href="#p
   vertical-align: middle;
 }
 
-#hdlgwupojp .gt_from_md > :first-child {
+#fvzwsfopin .gt_from_md > :first-child {
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 }
 
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+#fvzwsfopin .gt_from_md > :last-child {
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 }
 
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+#fvzwsfopin .gt_row {
   padding-top: 8px;
   padding-bottom: 8px;
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@@ -594,7 +599,7 @@ <h3 id="presentation">Presentation<a class="anchor" aria-label="anchor" href="#p
   overflow-x: hidden;
 }
 
-#hdlgwupojp .gt_stub {
+#fvzwsfopin .gt_stub {
   color: #333333;
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@@ -607,7 +612,7 @@ <h3 id="presentation">Presentation<a class="anchor" aria-label="anchor" href="#p
   padding-right: 5px;
 }
 
-#hdlgwupojp .gt_stub_row_group {
+#fvzwsfopin .gt_stub_row_group {
   color: #333333;
   background-color: #FFFFFF;
   font-size: 100%;
@@ -621,15 +626,15 @@ <h3 id="presentation">Presentation<a class="anchor" aria-label="anchor" href="#p
   vertical-align: top;
 }
 
-#hdlgwupojp .gt_row_group_first td {
+#fvzwsfopin .gt_row_group_first td {
   border-top-width: 2px;
 }
 
-#hdlgwupojp .gt_row_group_first th {
+#fvzwsfopin .gt_row_group_first th {
   border-top-width: 2px;
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-#hdlgwupojp .gt_summary_row {
+#fvzwsfopin .gt_summary_row {
   color: #333333;
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@@ -639,16 +644,16 @@ <h3 id="presentation">Presentation<a class="anchor" aria-label="anchor" href="#p
   padding-right: 5px;
 }
 
-#hdlgwupojp .gt_first_summary_row {
+#fvzwsfopin .gt_first_summary_row {
   border-top-style: solid;
   border-top-color: #D3D3D3;
 }
 
-#hdlgwupojp .gt_first_summary_row.thick {
+#fvzwsfopin .gt_first_summary_row.thick {
   border-top-width: 2px;
 }
 
-#hdlgwupojp .gt_last_summary_row {
+#fvzwsfopin .gt_last_summary_row {
   padding-top: 8px;
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@@ -658,7 +663,7 @@ <h3 id="presentation">Presentation<a class="anchor" aria-label="anchor" href="#p
   border-bottom-color: #D3D3D3;
 }
 
-#hdlgwupojp .gt_grand_summary_row {
+#fvzwsfopin .gt_grand_summary_row {
   color: #333333;
   background-color: #FFFFFF;
   text-transform: inherit;
@@ -668,7 +673,7 @@ <h3 id="presentation">Presentation<a class="anchor" aria-label="anchor" href="#p
   padding-right: 5px;
 }
 
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+#fvzwsfopin .gt_first_grand_summary_row {
   padding-top: 8px;
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@@ -678,7 +683,7 @@ <h3 id="presentation">Presentation<a class="anchor" aria-label="anchor" href="#p
   border-top-color: #D3D3D3;
 }
 
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+#fvzwsfopin .gt_last_grand_summary_row_top {
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@@ -688,11 +693,11 @@ <h3 id="presentation">Presentation<a class="anchor" aria-label="anchor" href="#p
   border-bottom-color: #D3D3D3;
 }
 
-#hdlgwupojp .gt_striped {
+#fvzwsfopin .gt_striped {
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   border-bottom-color: #D3D3D3;
 }
 
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+#fvzwsfopin .gt_footnotes {
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@@ -724,7 +729,7 @@ <h3 id="presentation">Presentation<a class="anchor" aria-label="anchor" href="#p
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+#fvzwsfopin .gt_sourcenotes {
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@@ -738,7 +743,7 @@ <h3 id="presentation">Presentation<a class="anchor" aria-label="anchor" href="#p
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 </style>
@@ -902,7 +907,8 @@ <h3 id="presentation">Presentation<a class="anchor" aria-label="anchor" href="#p
 <span>    x <span class="op">=</span> <span class="st">"Years post treatment"</span>, y <span class="op">=</span> <span class="st">"Effect on log teen employment"</span>,</span>
 <span>    caption <span class="op">=</span> <span class="st">"Note: Zero pre-treatment effects for illustrative purposes only."</span></span>
 <span>  <span class="op">)</span></span>
-<span><span class="co">#&gt; Warning: Removed 4 rows containing missing values (`geom_segment()`).</span></span></code></pre></div>
+<span><span class="co">#&gt; Warning: Removed 4 rows containing missing values or values outside the scale range</span></span>
+<span><span class="co">#&gt; (`geom_segment()`).</span></span></code></pre></div>
 <p><img src="etwfe_files/figure-html/unnamed-chunk-9-1.png" width="700"></p>
 </div>
 </div>
@@ -957,7 +963,7 @@ <h2 id="heterogeneous-treatment-effects">Heterogeneous treatment effects<a class
 <p>The above point estimates might tempt us to think that minimum wage
 hikes caused less teen disemployment in GLS counties than in the rest of
 the US on average. However, to test this formally we can invoke the
-powerful <a href="https://marginaleffects.com/vignettes/hypothesis/" class="external-link"><code>hypothesis</code></a>
+powerful <a href="https://marginaleffects.com/vignettes/hypothesis.html" class="external-link"><code>hypothesis</code></a>
 infrastructure of the underlying <strong>marginaleffects</strong>
 package. Probably the easiest way to do this is by using
 <code>b[i]</code>-style positional arguments, where “<code>[i]</code>”
@@ -987,23 +993,23 @@ <h2 id="heterogeneous-treatment-effects">Heterogeneous treatment effects<a class
 <span>    gof_map     <span class="op">=</span> <span class="cn">NA</span>,</span>
 <span>    title       <span class="op">=</span> <span class="st">"Comparing the ATT on GLS and non-GLS counties"</span></span>
 <span><span class="op">)</span></span></code></pre></div>
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-<style>#elzrgdcrbn table {
+<div id="wneiecutga" style="padding-left:0px;padding-right:0px;padding-top:10px;padding-bottom:10px;overflow-x:auto;overflow-y:auto;width:auto;height:auto;">
+<style>#wneiecutga table {
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 }
 
-#elzrgdcrbn thead, #elzrgdcrbn tbody, #elzrgdcrbn tfoot, #elzrgdcrbn tr, #elzrgdcrbn td, #elzrgdcrbn th {
+#wneiecutga thead, #wneiecutga tbody, #wneiecutga tfoot, #wneiecutga tr, #wneiecutga td, #wneiecutga th {
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 }
 
-#elzrgdcrbn p {
+#wneiecutga p {
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 }
 
-#elzrgdcrbn .gt_table {
+#wneiecutga .gt_table {
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   border-collapse: collapse;
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@@ -1029,12 +1035,12 @@ <h2 id="heterogeneous-treatment-effects">Heterogeneous treatment effects<a class
   border-left-color: #D3D3D3;
 }
 
-#elzrgdcrbn .gt_caption {
+#wneiecutga .gt_caption {
   padding-top: 4px;
   padding-bottom: 4px;
 }
 
-#elzrgdcrbn .gt_title {
+#wneiecutga .gt_title {
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   font-weight: initial;
@@ -1046,7 +1052,7 @@ <h2 id="heterogeneous-treatment-effects">Heterogeneous treatment effects<a class
   border-bottom-width: 0;
 }
 
-#elzrgdcrbn .gt_subtitle {
+#wneiecutga .gt_subtitle {
   color: #333333;
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   font-weight: initial;
@@ -1058,7 +1064,7 @@ <h2 id="heterogeneous-treatment-effects">Heterogeneous treatment effects<a class
   border-top-width: 0;
 }
 
-#elzrgdcrbn .gt_heading {
+#wneiecutga .gt_heading {
   background-color: #FFFFFF;
   text-align: center;
   border-bottom-color: #FFFFFF;
@@ -1070,13 +1076,13 @@ <h2 id="heterogeneous-treatment-effects">Heterogeneous treatment effects<a class
   border-right-color: #D3D3D3;
 }
 
-#elzrgdcrbn .gt_bottom_border {
+#wneiecutga .gt_bottom_border {
   border-bottom-style: solid;
   border-bottom-width: 2px;
   border-bottom-color: #D3D3D3;
 }
 
-#elzrgdcrbn .gt_col_headings {
+#wneiecutga .gt_col_headings {
   border-top-style: solid;
   border-top-width: 2px;
   border-top-color: #D3D3D3;
@@ -1091,7 +1097,7 @@ <h2 id="heterogeneous-treatment-effects">Heterogeneous treatment effects<a class
   border-right-color: #D3D3D3;
 }
 
-#elzrgdcrbn .gt_col_heading {
+#wneiecutga .gt_col_heading {
   color: #333333;
   background-color: #FFFFFF;
   font-size: 100%;
@@ -1111,7 +1117,7 @@ <h2 id="heterogeneous-treatment-effects">Heterogeneous treatment effects<a class
   overflow-x: hidden;
 }
 
-#elzrgdcrbn .gt_column_spanner_outer {
+#wneiecutga .gt_column_spanner_outer {
   color: #333333;
   background-color: #FFFFFF;
   font-size: 100%;
@@ -1123,15 +1129,15 @@ <h2 id="heterogeneous-treatment-effects">Heterogeneous treatment effects<a class
   padding-right: 4px;
 }
 
-#elzrgdcrbn .gt_column_spanner_outer:first-child {
+#wneiecutga .gt_column_spanner_outer:first-child {
   padding-left: 0;
 }
 
-#elzrgdcrbn .gt_column_spanner_outer:last-child {
+#wneiecutga .gt_column_spanner_outer:last-child {
   padding-right: 0;
 }
 
-#elzrgdcrbn .gt_column_spanner {
+#wneiecutga .gt_column_spanner {
   border-bottom-style: solid;
   border-bottom-width: 2px;
   border-bottom-color: #D3D3D3;
@@ -1143,11 +1149,11 @@ <h2 id="heterogeneous-treatment-effects">Heterogeneous treatment effects<a class
   width: 100%;
 }
 
-#elzrgdcrbn .gt_spanner_row {
+#wneiecutga .gt_spanner_row {
   border-bottom-style: hidden;
 }
 
-#elzrgdcrbn .gt_group_heading {
+#wneiecutga .gt_group_heading {
   padding-top: 8px;
   padding-bottom: 8px;
   padding-left: 5px;
@@ -1173,7 +1179,7 @@ <h2 id="heterogeneous-treatment-effects">Heterogeneous treatment effects<a class
   text-align: left;
 }
 
-#elzrgdcrbn .gt_empty_group_heading {
+#wneiecutga .gt_empty_group_heading {
   padding: 0.5px;
   color: #333333;
   background-color: #FFFFFF;
@@ -1188,15 +1194,15 @@ <h2 id="heterogeneous-treatment-effects">Heterogeneous treatment effects<a class
   vertical-align: middle;
 }
 
-#elzrgdcrbn .gt_from_md > :first-child {
+#wneiecutga .gt_from_md > :first-child {
   margin-top: 0;
 }
 
-#elzrgdcrbn .gt_from_md > :last-child {
+#wneiecutga .gt_from_md > :last-child {
   margin-bottom: 0;
 }
 
-#elzrgdcrbn .gt_row {
+#wneiecutga .gt_row {
   padding-top: 8px;
   padding-bottom: 8px;
   padding-left: 5px;
@@ -1215,7 +1221,7 @@ <h2 id="heterogeneous-treatment-effects">Heterogeneous treatment effects<a class
   overflow-x: hidden;
 }
 
-#elzrgdcrbn .gt_stub {
+#wneiecutga .gt_stub {
   color: #333333;
   background-color: #FFFFFF;
   font-size: 100%;
@@ -1228,7 +1234,7 @@ <h2 id="heterogeneous-treatment-effects">Heterogeneous treatment effects<a class
   padding-right: 5px;
 }
 
-#elzrgdcrbn .gt_stub_row_group {
+#wneiecutga .gt_stub_row_group {
   color: #333333;
   background-color: #FFFFFF;
   font-size: 100%;
@@ -1242,15 +1248,15 @@ <h2 id="heterogeneous-treatment-effects">Heterogeneous treatment effects<a class
   vertical-align: top;
 }
 
-#elzrgdcrbn .gt_row_group_first td {
+#wneiecutga .gt_row_group_first td {
   border-top-width: 2px;
 }
 
-#elzrgdcrbn .gt_row_group_first th {
+#wneiecutga .gt_row_group_first th {
   border-top-width: 2px;
 }
 
-#elzrgdcrbn .gt_summary_row {
+#wneiecutga .gt_summary_row {
   color: #333333;
   background-color: #FFFFFF;
   text-transform: inherit;
@@ -1260,16 +1266,16 @@ <h2 id="heterogeneous-treatment-effects">Heterogeneous treatment effects<a class
   padding-right: 5px;
 }
 
-#elzrgdcrbn .gt_first_summary_row {
+#wneiecutga .gt_first_summary_row {
   border-top-style: solid;
   border-top-color: #D3D3D3;
 }
 
-#elzrgdcrbn .gt_first_summary_row.thick {
+#wneiecutga .gt_first_summary_row.thick {
   border-top-width: 2px;
 }
 
-#elzrgdcrbn .gt_last_summary_row {
+#wneiecutga .gt_last_summary_row {
   padding-top: 8px;
   padding-bottom: 8px;
   padding-left: 5px;
@@ -1279,7 +1285,7 @@ <h2 id="heterogeneous-treatment-effects">Heterogeneous treatment effects<a class
   border-bottom-color: #D3D3D3;
 }
 
-#elzrgdcrbn .gt_grand_summary_row {
+#wneiecutga .gt_grand_summary_row {
   color: #333333;
   background-color: #FFFFFF;
   text-transform: inherit;
@@ -1289,7 +1295,7 @@ <h2 id="heterogeneous-treatment-effects">Heterogeneous treatment effects<a class
   padding-right: 5px;
 }
 
-#elzrgdcrbn .gt_first_grand_summary_row {
+#wneiecutga .gt_first_grand_summary_row {
   padding-top: 8px;
   padding-bottom: 8px;
   padding-left: 5px;
@@ -1299,7 +1305,7 @@ <h2 id="heterogeneous-treatment-effects">Heterogeneous treatment effects<a class
   border-top-color: #D3D3D3;
 }
 
-#elzrgdcrbn .gt_last_grand_summary_row_top {
+#wneiecutga .gt_last_grand_summary_row_top {
   padding-top: 8px;
   padding-bottom: 8px;
   padding-left: 5px;
@@ -1309,11 +1315,11 @@ <h2 id="heterogeneous-treatment-effects">Heterogeneous treatment effects<a class
   border-bottom-color: #D3D3D3;
 }
 
-#elzrgdcrbn .gt_striped {
+#wneiecutga .gt_striped {
   background-color: rgba(128, 128, 128, 0.05);
 }
 
-#elzrgdcrbn .gt_table_body {
+#wneiecutga .gt_table_body {
   border-top-style: solid;
   border-top-width: 2px;
   border-top-color: #D3D3D3;
@@ -1322,7 +1328,7 @@ <h2 id="heterogeneous-treatment-effects">Heterogeneous treatment effects<a class
   border-bottom-color: #D3D3D3;
 }
 
-#elzrgdcrbn .gt_footnotes {
+#wneiecutga .gt_footnotes {
   color: #333333;
   background-color: #FFFFFF;
   border-bottom-style: none;
@@ -1336,7 +1342,7 @@ <h2 id="heterogeneous-treatment-effects">Heterogeneous treatment effects<a class
   border-right-color: #D3D3D3;
 }
 
-#elzrgdcrbn .gt_footnote {
+#wneiecutga .gt_footnote {
   margin: 0px;
   font-size: 90%;
   padding-top: 4px;
@@ -1345,7 +1351,7 @@ <h2 id="heterogeneous-treatment-effects">Heterogeneous treatment effects<a class
   padding-right: 5px;
 }
 
-#elzrgdcrbn .gt_sourcenotes {
+#wneiecutga .gt_sourcenotes {
   color: #333333;
   background-color: #FFFFFF;
   border-bottom-style: none;
@@ -1359,7 +1365,7 @@ <h2 id="heterogeneous-treatment-effects">Heterogeneous treatment effects<a class
   border-right-color: #D3D3D3;
 }
 
-#elzrgdcrbn .gt_sourcenote {
+#wneiecutga .gt_sourcenote {
   font-size: 90%;
   padding-top: 4px;
   padding-bottom: 4px;
@@ -1367,63 +1373,63 @@ <h2 id="heterogeneous-treatment-effects">Heterogeneous treatment effects<a class
   padding-right: 5px;
 }
 
-#elzrgdcrbn .gt_left {
+#wneiecutga .gt_left {
   text-align: left;
 }
 
-#elzrgdcrbn .gt_center {
+#wneiecutga .gt_center {
   text-align: center;
 }
 
-#elzrgdcrbn .gt_right {
+#wneiecutga .gt_right {
   text-align: right;
   font-variant-numeric: tabular-nums;
 }
 
-#elzrgdcrbn .gt_font_normal {
+#wneiecutga .gt_font_normal {
   font-weight: normal;
 }
 
-#elzrgdcrbn .gt_font_bold {
+#wneiecutga .gt_font_bold {
   font-weight: bold;
 }
 
-#elzrgdcrbn .gt_font_italic {
+#wneiecutga .gt_font_italic {
   font-style: italic;
 }
 
-#elzrgdcrbn .gt_super {
+#wneiecutga .gt_super {
   font-size: 65%;
 }
 
-#elzrgdcrbn .gt_footnote_marks {
+#wneiecutga .gt_footnote_marks {
   font-size: 75%;
   vertical-align: 0.4em;
   position: initial;
 }
 
-#elzrgdcrbn .gt_asterisk {
+#wneiecutga .gt_asterisk {
   font-size: 100%;
   vertical-align: 0;
 }
 
-#elzrgdcrbn .gt_indent_1 {
+#wneiecutga .gt_indent_1 {
   text-indent: 5px;
 }
 
-#elzrgdcrbn .gt_indent_2 {
+#wneiecutga .gt_indent_2 {
   text-indent: 10px;
 }
 
-#elzrgdcrbn .gt_indent_3 {
+#wneiecutga .gt_indent_3 {
   text-indent: 15px;
 }
 
-#elzrgdcrbn .gt_indent_4 {
+#wneiecutga .gt_indent_4 {
   text-indent: 20px;
 }
 
-#elzrgdcrbn .gt_indent_5 {
+#wneiecutga .gt_indent_5 {
   text-indent: 25px;
 }
 </style>
@@ -1589,23 +1595,23 @@ <h2 id="performance-tips">Performance tips<a class="anchor" aria-label="anchor"
 <span>    title       <span class="op">=</span> <span class="st">"Event study"</span>,</span>
 <span>    notes       <span class="op">=</span> <span class="st">"Std. errors are clustered at the county level"</span></span>
 <span><span class="op">)</span></span></code></pre></div>
-<div id="lypsplksfw" style="padding-left:0px;padding-right:0px;padding-top:10px;padding-bottom:10px;overflow-x:auto;overflow-y:auto;width:auto;height:auto;">
-<style>#lypsplksfw table {
+<div id="ygrguxzbpx" style="padding-left:0px;padding-right:0px;padding-top:10px;padding-bottom:10px;overflow-x:auto;overflow-y:auto;width:auto;height:auto;">
+<style>#ygrguxzbpx table {
   font-family: system-ui, 'Segoe UI', Roboto, Helvetica, Arial, sans-serif, 'Apple Color Emoji', 'Segoe UI Emoji', 'Segoe UI Symbol', 'Noto Color Emoji';
   -webkit-font-smoothing: antialiased;
   -moz-osx-font-smoothing: grayscale;
 }
 
-#lypsplksfw thead, #lypsplksfw tbody, #lypsplksfw tfoot, #lypsplksfw tr, #lypsplksfw td, #lypsplksfw th {
+#ygrguxzbpx thead, #ygrguxzbpx tbody, #ygrguxzbpx tfoot, #ygrguxzbpx tr, #ygrguxzbpx td, #ygrguxzbpx th {
   border-style: none;
 }
 
-#lypsplksfw p {
+#ygrguxzbpx p {
   margin: 0;
   padding: 0;
 }
 
-#lypsplksfw .gt_table {
+#ygrguxzbpx .gt_table {
   display: table;
   border-collapse: collapse;
   line-height: normal;
@@ -1631,12 +1637,12 @@ <h2 id="performance-tips">Performance tips<a class="anchor" aria-label="anchor"
   border-left-color: #D3D3D3;
 }
 
-#lypsplksfw .gt_caption {
+#ygrguxzbpx .gt_caption {
   padding-top: 4px;
   padding-bottom: 4px;
 }
 
-#lypsplksfw .gt_title {
+#ygrguxzbpx .gt_title {
   color: #333333;
   font-size: 125%;
   font-weight: initial;
@@ -1648,7 +1654,7 @@ <h2 id="performance-tips">Performance tips<a class="anchor" aria-label="anchor"
   border-bottom-width: 0;
 }
 
-#lypsplksfw .gt_subtitle {
+#ygrguxzbpx .gt_subtitle {
   color: #333333;
   font-size: 85%;
   font-weight: initial;
@@ -1660,7 +1666,7 @@ <h2 id="performance-tips">Performance tips<a class="anchor" aria-label="anchor"
   border-top-width: 0;
 }
 
-#lypsplksfw .gt_heading {
+#ygrguxzbpx .gt_heading {
   background-color: #FFFFFF;
   text-align: center;
   border-bottom-color: #FFFFFF;
@@ -1672,13 +1678,13 @@ <h2 id="performance-tips">Performance tips<a class="anchor" aria-label="anchor"
   border-right-color: #D3D3D3;
 }
 
-#lypsplksfw .gt_bottom_border {
+#ygrguxzbpx .gt_bottom_border {
   border-bottom-style: solid;
   border-bottom-width: 2px;
   border-bottom-color: #D3D3D3;
 }
 
-#lypsplksfw .gt_col_headings {
+#ygrguxzbpx .gt_col_headings {
   border-top-style: solid;
   border-top-width: 2px;
   border-top-color: #D3D3D3;
@@ -1693,7 +1699,7 @@ <h2 id="performance-tips">Performance tips<a class="anchor" aria-label="anchor"
   border-right-color: #D3D3D3;
 }
 
-#lypsplksfw .gt_col_heading {
+#ygrguxzbpx .gt_col_heading {
   color: #333333;
   background-color: #FFFFFF;
   font-size: 100%;
@@ -1713,7 +1719,7 @@ <h2 id="performance-tips">Performance tips<a class="anchor" aria-label="anchor"
   overflow-x: hidden;
 }
 
-#lypsplksfw .gt_column_spanner_outer {
+#ygrguxzbpx .gt_column_spanner_outer {
   color: #333333;
   background-color: #FFFFFF;
   font-size: 100%;
@@ -1725,15 +1731,15 @@ <h2 id="performance-tips">Performance tips<a class="anchor" aria-label="anchor"
   padding-right: 4px;
 }
 
-#lypsplksfw .gt_column_spanner_outer:first-child {
+#ygrguxzbpx .gt_column_spanner_outer:first-child {
   padding-left: 0;
 }
 
-#lypsplksfw .gt_column_spanner_outer:last-child {
+#ygrguxzbpx .gt_column_spanner_outer:last-child {
   padding-right: 0;
 }
 
-#lypsplksfw .gt_column_spanner {
+#ygrguxzbpx .gt_column_spanner {
   border-bottom-style: solid;
   border-bottom-width: 2px;
   border-bottom-color: #D3D3D3;
@@ -1745,11 +1751,11 @@ <h2 id="performance-tips">Performance tips<a class="anchor" aria-label="anchor"
   width: 100%;
 }
 
-#lypsplksfw .gt_spanner_row {
+#ygrguxzbpx .gt_spanner_row {
   border-bottom-style: hidden;
 }
 
-#lypsplksfw .gt_group_heading {
+#ygrguxzbpx .gt_group_heading {
   padding-top: 8px;
   padding-bottom: 8px;
   padding-left: 5px;
@@ -1775,7 +1781,7 @@ <h2 id="performance-tips">Performance tips<a class="anchor" aria-label="anchor"
   text-align: left;
 }
 
-#lypsplksfw .gt_empty_group_heading {
+#ygrguxzbpx .gt_empty_group_heading {
   padding: 0.5px;
   color: #333333;
   background-color: #FFFFFF;
@@ -1790,15 +1796,15 @@ <h2 id="performance-tips">Performance tips<a class="anchor" aria-label="anchor"
   vertical-align: middle;
 }
 
-#lypsplksfw .gt_from_md > :first-child {
+#ygrguxzbpx .gt_from_md > :first-child {
   margin-top: 0;
 }
 
-#lypsplksfw .gt_from_md > :last-child {
+#ygrguxzbpx .gt_from_md > :last-child {
   margin-bottom: 0;
 }
 
-#lypsplksfw .gt_row {
+#ygrguxzbpx .gt_row {
   padding-top: 8px;
   padding-bottom: 8px;
   padding-left: 5px;
@@ -1817,7 +1823,7 @@ <h2 id="performance-tips">Performance tips<a class="anchor" aria-label="anchor"
   overflow-x: hidden;
 }
 
-#lypsplksfw .gt_stub {
+#ygrguxzbpx .gt_stub {
   color: #333333;
   background-color: #FFFFFF;
   font-size: 100%;
@@ -1830,7 +1836,7 @@ <h2 id="performance-tips">Performance tips<a class="anchor" aria-label="anchor"
   padding-right: 5px;
 }
 
-#lypsplksfw .gt_stub_row_group {
+#ygrguxzbpx .gt_stub_row_group {
   color: #333333;
   background-color: #FFFFFF;
   font-size: 100%;
@@ -1844,15 +1850,15 @@ <h2 id="performance-tips">Performance tips<a class="anchor" aria-label="anchor"
   vertical-align: top;
 }
 
-#lypsplksfw .gt_row_group_first td {
+#ygrguxzbpx .gt_row_group_first td {
   border-top-width: 2px;
 }
 
-#lypsplksfw .gt_row_group_first th {
+#ygrguxzbpx .gt_row_group_first th {
   border-top-width: 2px;
 }
 
-#lypsplksfw .gt_summary_row {
+#ygrguxzbpx .gt_summary_row {
   color: #333333;
   background-color: #FFFFFF;
   text-transform: inherit;
@@ -1862,16 +1868,16 @@ <h2 id="performance-tips">Performance tips<a class="anchor" aria-label="anchor"
   padding-right: 5px;
 }
 
-#lypsplksfw .gt_first_summary_row {
+#ygrguxzbpx .gt_first_summary_row {
   border-top-style: solid;
   border-top-color: #D3D3D3;
 }
 
-#lypsplksfw .gt_first_summary_row.thick {
+#ygrguxzbpx .gt_first_summary_row.thick {
   border-top-width: 2px;
 }
 
-#lypsplksfw .gt_last_summary_row {
+#ygrguxzbpx .gt_last_summary_row {
   padding-top: 8px;
   padding-bottom: 8px;
   padding-left: 5px;
@@ -1881,7 +1887,7 @@ <h2 id="performance-tips">Performance tips<a class="anchor" aria-label="anchor"
   border-bottom-color: #D3D3D3;
 }
 
-#lypsplksfw .gt_grand_summary_row {
+#ygrguxzbpx .gt_grand_summary_row {
   color: #333333;
   background-color: #FFFFFF;
   text-transform: inherit;
@@ -1891,7 +1897,7 @@ <h2 id="performance-tips">Performance tips<a class="anchor" aria-label="anchor"
   padding-right: 5px;
 }
 
-#lypsplksfw .gt_first_grand_summary_row {
+#ygrguxzbpx .gt_first_grand_summary_row {
   padding-top: 8px;
   padding-bottom: 8px;
   padding-left: 5px;
@@ -1901,7 +1907,7 @@ <h2 id="performance-tips">Performance tips<a class="anchor" aria-label="anchor"
   border-top-color: #D3D3D3;
 }
 
-#lypsplksfw .gt_last_grand_summary_row_top {
+#ygrguxzbpx .gt_last_grand_summary_row_top {
   padding-top: 8px;
   padding-bottom: 8px;
   padding-left: 5px;
@@ -1911,11 +1917,11 @@ <h2 id="performance-tips">Performance tips<a class="anchor" aria-label="anchor"
   border-bottom-color: #D3D3D3;
 }
 
-#lypsplksfw .gt_striped {
+#ygrguxzbpx .gt_striped {
   background-color: rgba(128, 128, 128, 0.05);
 }
 
-#lypsplksfw .gt_table_body {
+#ygrguxzbpx .gt_table_body {
   border-top-style: solid;
   border-top-width: 2px;
   border-top-color: #D3D3D3;
@@ -1924,7 +1930,7 @@ <h2 id="performance-tips">Performance tips<a class="anchor" aria-label="anchor"
   border-bottom-color: #D3D3D3;
 }
 
-#lypsplksfw .gt_footnotes {
+#ygrguxzbpx .gt_footnotes {
   color: #333333;
   background-color: #FFFFFF;
   border-bottom-style: none;
@@ -1938,7 +1944,7 @@ <h2 id="performance-tips">Performance tips<a class="anchor" aria-label="anchor"
   border-right-color: #D3D3D3;
 }
 
-#lypsplksfw .gt_footnote {
+#ygrguxzbpx .gt_footnote {
   margin: 0px;
   font-size: 90%;
   padding-top: 4px;
@@ -1947,7 +1953,7 @@ <h2 id="performance-tips">Performance tips<a class="anchor" aria-label="anchor"
   padding-right: 5px;
 }
 
-#lypsplksfw .gt_sourcenotes {
+#ygrguxzbpx .gt_sourcenotes {
   color: #333333;
   background-color: #FFFFFF;
   border-bottom-style: none;
@@ -1961,7 +1967,7 @@ <h2 id="performance-tips">Performance tips<a class="anchor" aria-label="anchor"
   border-right-color: #D3D3D3;
 }
 
-#lypsplksfw .gt_sourcenote {
+#ygrguxzbpx .gt_sourcenote {
   font-size: 90%;
   padding-top: 4px;
   padding-bottom: 4px;
@@ -1969,63 +1975,63 @@ <h2 id="performance-tips">Performance tips<a class="anchor" aria-label="anchor"
   padding-right: 5px;
 }
 
-#lypsplksfw .gt_left {
+#ygrguxzbpx .gt_left {
   text-align: left;
 }
 
-#lypsplksfw .gt_center {
+#ygrguxzbpx .gt_center {
   text-align: center;
 }
 
-#lypsplksfw .gt_right {
+#ygrguxzbpx .gt_right {
   text-align: right;
   font-variant-numeric: tabular-nums;
 }
 
-#lypsplksfw .gt_font_normal {
+#ygrguxzbpx .gt_font_normal {
   font-weight: normal;
 }
 
-#lypsplksfw .gt_font_bold {
+#ygrguxzbpx .gt_font_bold {
   font-weight: bold;
 }
 
-#lypsplksfw .gt_font_italic {
+#ygrguxzbpx .gt_font_italic {
   font-style: italic;
 }
 
-#lypsplksfw .gt_super {
+#ygrguxzbpx .gt_super {
   font-size: 65%;
 }
 
-#lypsplksfw .gt_footnote_marks {
+#ygrguxzbpx .gt_footnote_marks {
   font-size: 75%;
   vertical-align: 0.4em;
   position: initial;
 }
 
-#lypsplksfw .gt_asterisk {
+#ygrguxzbpx .gt_asterisk {
   font-size: 100%;
   vertical-align: 0;
 }
 
-#lypsplksfw .gt_indent_1 {
+#ygrguxzbpx .gt_indent_1 {
   text-indent: 5px;
 }
 
-#lypsplksfw .gt_indent_2 {
+#ygrguxzbpx .gt_indent_2 {
   text-indent: 10px;
 }
 
-#lypsplksfw .gt_indent_3 {
+#ygrguxzbpx .gt_indent_3 {
   text-indent: 15px;
 }
 
-#lypsplksfw .gt_indent_4 {
+#ygrguxzbpx .gt_indent_4 {
   text-indent: 20px;
 }
 
-#lypsplksfw .gt_indent_5 {
+#ygrguxzbpx .gt_indent_5 {
   text-indent: 25px;
 }
 </style>
@@ -2123,7 +2129,7 @@ <h3 id="manual-implementation">Manual implementation<a class="anchor" aria-label
 <code class="sourceCode R"><span><span class="va">mod</span><span class="op">$</span><span class="va">fml_all</span></span>
 <span><span class="co">#&gt; $linear</span></span>
 <span><span class="co">#&gt; lemp ~ .Dtreat:i(first.treat, i.year, ref = 0, ref2 = 2003)/lpop_dm</span></span>
-<span><span class="co">#&gt; &lt;environment: 0x5636feeb12f8&gt;</span></span>
+<span><span class="co">#&gt; &lt;environment: 0x55b3d04164c8&gt;</span></span>
 <span><span class="co">#&gt; </span></span>
 <span><span class="co">#&gt; $fixef</span></span>
 <span><span class="co">#&gt; ~first.treat + first.treat[[lpop]] + year + year[[lpop]]</span></span></code></pre></div>
@@ -2160,23 +2166,23 @@ <h3 id="manual-implementation">Manual implementation<a class="anchor" aria-label
 <span>  <span class="fu"><a href="https://rdrr.io/r/base/list.html" class="external-link">list</a></span><span class="op">(</span><span class="st">"etwfe"</span> <span class="op">=</span> <span class="va">mod</span>, <span class="st">"manual"</span> <span class="op">=</span> <span class="va">mod2</span><span class="op">)</span>,</span>
 <span>  gof_map <span class="op">=</span> <span class="cn">NA</span> <span class="co"># drop all goodness-of-fit info for brevity</span></span>
 <span><span class="op">)</span></span></code></pre></div>
-<div id="bxwcrdiujj" style="padding-left:0px;padding-right:0px;padding-top:10px;padding-bottom:10px;overflow-x:auto;overflow-y:auto;width:auto;height:auto;">
-<style>#bxwcrdiujj table {
+<div id="frtzottorm" style="padding-left:0px;padding-right:0px;padding-top:10px;padding-bottom:10px;overflow-x:auto;overflow-y:auto;width:auto;height:auto;">
+<style>#frtzottorm table {
   font-family: system-ui, 'Segoe UI', Roboto, Helvetica, Arial, sans-serif, 'Apple Color Emoji', 'Segoe UI Emoji', 'Segoe UI Symbol', 'Noto Color Emoji';
   -webkit-font-smoothing: antialiased;
   -moz-osx-font-smoothing: grayscale;
 }
 
-#bxwcrdiujj thead, #bxwcrdiujj tbody, #bxwcrdiujj tfoot, #bxwcrdiujj tr, #bxwcrdiujj td, #bxwcrdiujj th {
+#frtzottorm thead, #frtzottorm tbody, #frtzottorm tfoot, #frtzottorm tr, #frtzottorm td, #frtzottorm th {
   border-style: none;
 }
 
-#bxwcrdiujj p {
+#frtzottorm p {
   margin: 0;
   padding: 0;
 }
 
-#bxwcrdiujj .gt_table {
+#frtzottorm .gt_table {
   display: table;
   border-collapse: collapse;
   line-height: normal;
@@ -2202,12 +2208,12 @@ <h3 id="manual-implementation">Manual implementation<a class="anchor" aria-label
   border-left-color: #D3D3D3;
 }
 
-#bxwcrdiujj .gt_caption {
+#frtzottorm .gt_caption {
   padding-top: 4px;
   padding-bottom: 4px;
 }
 
-#bxwcrdiujj .gt_title {
+#frtzottorm .gt_title {
   color: #333333;
   font-size: 125%;
   font-weight: initial;
@@ -2219,7 +2225,7 @@ <h3 id="manual-implementation">Manual implementation<a class="anchor" aria-label
   border-bottom-width: 0;
 }
 
-#bxwcrdiujj .gt_subtitle {
+#frtzottorm .gt_subtitle {
   color: #333333;
   font-size: 85%;
   font-weight: initial;
@@ -2231,7 +2237,7 @@ <h3 id="manual-implementation">Manual implementation<a class="anchor" aria-label
   border-top-width: 0;
 }
 
-#bxwcrdiujj .gt_heading {
+#frtzottorm .gt_heading {
   background-color: #FFFFFF;
   text-align: center;
   border-bottom-color: #FFFFFF;
@@ -2243,13 +2249,13 @@ <h3 id="manual-implementation">Manual implementation<a class="anchor" aria-label
   border-right-color: #D3D3D3;
 }
 
-#bxwcrdiujj .gt_bottom_border {
+#frtzottorm .gt_bottom_border {
   border-bottom-style: solid;
   border-bottom-width: 2px;
   border-bottom-color: #D3D3D3;
 }
 
-#bxwcrdiujj .gt_col_headings {
+#frtzottorm .gt_col_headings {
   border-top-style: solid;
   border-top-width: 2px;
   border-top-color: #D3D3D3;
@@ -2264,7 +2270,7 @@ <h3 id="manual-implementation">Manual implementation<a class="anchor" aria-label
   border-right-color: #D3D3D3;
 }
 
-#bxwcrdiujj .gt_col_heading {
+#frtzottorm .gt_col_heading {
   color: #333333;
   background-color: #FFFFFF;
   font-size: 100%;
@@ -2284,7 +2290,7 @@ <h3 id="manual-implementation">Manual implementation<a class="anchor" aria-label
   overflow-x: hidden;
 }
 
-#bxwcrdiujj .gt_column_spanner_outer {
+#frtzottorm .gt_column_spanner_outer {
   color: #333333;
   background-color: #FFFFFF;
   font-size: 100%;
@@ -2296,15 +2302,15 @@ <h3 id="manual-implementation">Manual implementation<a class="anchor" aria-label
   padding-right: 4px;
 }
 
-#bxwcrdiujj .gt_column_spanner_outer:first-child {
+#frtzottorm .gt_column_spanner_outer:first-child {
   padding-left: 0;
 }
 
-#bxwcrdiujj .gt_column_spanner_outer:last-child {
+#frtzottorm .gt_column_spanner_outer:last-child {
   padding-right: 0;
 }
 
-#bxwcrdiujj .gt_column_spanner {
+#frtzottorm .gt_column_spanner {
   border-bottom-style: solid;
   border-bottom-width: 2px;
   border-bottom-color: #D3D3D3;
@@ -2316,11 +2322,11 @@ <h3 id="manual-implementation">Manual implementation<a class="anchor" aria-label
   width: 100%;
 }
 
-#bxwcrdiujj .gt_spanner_row {
+#frtzottorm .gt_spanner_row {
   border-bottom-style: hidden;
 }
 
-#bxwcrdiujj .gt_group_heading {
+#frtzottorm .gt_group_heading {
   padding-top: 8px;
   padding-bottom: 8px;
   padding-left: 5px;
@@ -2346,7 +2352,7 @@ <h3 id="manual-implementation">Manual implementation<a class="anchor" aria-label
   text-align: left;
 }
 
-#bxwcrdiujj .gt_empty_group_heading {
+#frtzottorm .gt_empty_group_heading {
   padding: 0.5px;
   color: #333333;
   background-color: #FFFFFF;
@@ -2361,15 +2367,15 @@ <h3 id="manual-implementation">Manual implementation<a class="anchor" aria-label
   vertical-align: middle;
 }
 
-#bxwcrdiujj .gt_from_md > :first-child {
+#frtzottorm .gt_from_md > :first-child {
   margin-top: 0;
 }
 
-#bxwcrdiujj .gt_from_md > :last-child {
+#frtzottorm .gt_from_md > :last-child {
   margin-bottom: 0;
 }
 
-#bxwcrdiujj .gt_row {
+#frtzottorm .gt_row {
   padding-top: 8px;
   padding-bottom: 8px;
   padding-left: 5px;
@@ -2388,7 +2394,7 @@ <h3 id="manual-implementation">Manual implementation<a class="anchor" aria-label
   overflow-x: hidden;
 }
 
-#bxwcrdiujj .gt_stub {
+#frtzottorm .gt_stub {
   color: #333333;
   background-color: #FFFFFF;
   font-size: 100%;
@@ -2401,7 +2407,7 @@ <h3 id="manual-implementation">Manual implementation<a class="anchor" aria-label
   padding-right: 5px;
 }
 
-#bxwcrdiujj .gt_stub_row_group {
+#frtzottorm .gt_stub_row_group {
   color: #333333;
   background-color: #FFFFFF;
   font-size: 100%;
@@ -2415,15 +2421,15 @@ <h3 id="manual-implementation">Manual implementation<a class="anchor" aria-label
   vertical-align: top;
 }
 
-#bxwcrdiujj .gt_row_group_first td {
+#frtzottorm .gt_row_group_first td {
   border-top-width: 2px;
 }
 
-#bxwcrdiujj .gt_row_group_first th {
+#frtzottorm .gt_row_group_first th {
   border-top-width: 2px;
 }
 
-#bxwcrdiujj .gt_summary_row {
+#frtzottorm .gt_summary_row {
   color: #333333;
   background-color: #FFFFFF;
   text-transform: inherit;
@@ -2433,16 +2439,16 @@ <h3 id="manual-implementation">Manual implementation<a class="anchor" aria-label
   padding-right: 5px;
 }
 
-#bxwcrdiujj .gt_first_summary_row {
+#frtzottorm .gt_first_summary_row {
   border-top-style: solid;
   border-top-color: #D3D3D3;
 }
 
-#bxwcrdiujj .gt_first_summary_row.thick {
+#frtzottorm .gt_first_summary_row.thick {
   border-top-width: 2px;
 }
 
-#bxwcrdiujj .gt_last_summary_row {
+#frtzottorm .gt_last_summary_row {
   padding-top: 8px;
   padding-bottom: 8px;
   padding-left: 5px;
@@ -2452,7 +2458,7 @@ <h3 id="manual-implementation">Manual implementation<a class="anchor" aria-label
   border-bottom-color: #D3D3D3;
 }
 
-#bxwcrdiujj .gt_grand_summary_row {
+#frtzottorm .gt_grand_summary_row {
   color: #333333;
   background-color: #FFFFFF;
   text-transform: inherit;
@@ -2462,7 +2468,7 @@ <h3 id="manual-implementation">Manual implementation<a class="anchor" aria-label
   padding-right: 5px;
 }
 
-#bxwcrdiujj .gt_first_grand_summary_row {
+#frtzottorm .gt_first_grand_summary_row {
   padding-top: 8px;
   padding-bottom: 8px;
   padding-left: 5px;
@@ -2472,7 +2478,7 @@ <h3 id="manual-implementation">Manual implementation<a class="anchor" aria-label
   border-top-color: #D3D3D3;
 }
 
-#bxwcrdiujj .gt_last_grand_summary_row_top {
+#frtzottorm .gt_last_grand_summary_row_top {
   padding-top: 8px;
   padding-bottom: 8px;
   padding-left: 5px;
@@ -2482,11 +2488,11 @@ <h3 id="manual-implementation">Manual implementation<a class="anchor" aria-label
   border-bottom-color: #D3D3D3;
 }
 
-#bxwcrdiujj .gt_striped {
+#frtzottorm .gt_striped {
   background-color: rgba(128, 128, 128, 0.05);
 }
 
-#bxwcrdiujj .gt_table_body {
+#frtzottorm .gt_table_body {
   border-top-style: solid;
   border-top-width: 2px;
   border-top-color: #D3D3D3;
@@ -2495,7 +2501,7 @@ <h3 id="manual-implementation">Manual implementation<a class="anchor" aria-label
   border-bottom-color: #D3D3D3;
 }
 
-#bxwcrdiujj .gt_footnotes {
+#frtzottorm .gt_footnotes {
   color: #333333;
   background-color: #FFFFFF;
   border-bottom-style: none;
@@ -2509,7 +2515,7 @@ <h3 id="manual-implementation">Manual implementation<a class="anchor" aria-label
   border-right-color: #D3D3D3;
 }
 
-#bxwcrdiujj .gt_footnote {
+#frtzottorm .gt_footnote {
   margin: 0px;
   font-size: 90%;
   padding-top: 4px;
@@ -2518,7 +2524,7 @@ <h3 id="manual-implementation">Manual implementation<a class="anchor" aria-label
   padding-right: 5px;
 }
 
-#bxwcrdiujj .gt_sourcenotes {
+#frtzottorm .gt_sourcenotes {
   color: #333333;
   background-color: #FFFFFF;
   border-bottom-style: none;
@@ -2532,7 +2538,7 @@ <h3 id="manual-implementation">Manual implementation<a class="anchor" aria-label
   border-right-color: #D3D3D3;
 }
 
-#bxwcrdiujj .gt_sourcenote {
+#frtzottorm .gt_sourcenote {
   font-size: 90%;
   padding-top: 4px;
   padding-bottom: 4px;
@@ -2540,63 +2546,63 @@ <h3 id="manual-implementation">Manual implementation<a class="anchor" aria-label
   padding-right: 5px;
 }
 
-#bxwcrdiujj .gt_left {
+#frtzottorm .gt_left {
   text-align: left;
 }
 
-#bxwcrdiujj .gt_center {
+#frtzottorm .gt_center {
   text-align: center;
 }
 
-#bxwcrdiujj .gt_right {
+#frtzottorm .gt_right {
   text-align: right;
   font-variant-numeric: tabular-nums;
 }
 
-#bxwcrdiujj .gt_font_normal {
+#frtzottorm .gt_font_normal {
   font-weight: normal;
 }
 
-#bxwcrdiujj .gt_font_bold {
+#frtzottorm .gt_font_bold {
   font-weight: bold;
 }
 
-#bxwcrdiujj .gt_font_italic {
+#frtzottorm .gt_font_italic {
   font-style: italic;
 }
 
-#bxwcrdiujj .gt_super {
+#frtzottorm .gt_super {
   font-size: 65%;
 }
 
-#bxwcrdiujj .gt_footnote_marks {
+#frtzottorm .gt_footnote_marks {
   font-size: 75%;
   vertical-align: 0.4em;
   position: initial;
 }
 
-#bxwcrdiujj .gt_asterisk {
+#frtzottorm .gt_asterisk {
   font-size: 100%;
   vertical-align: 0;
 }
 
-#bxwcrdiujj .gt_indent_1 {
+#frtzottorm .gt_indent_1 {
   text-indent: 5px;
 }
 
-#bxwcrdiujj .gt_indent_2 {
+#frtzottorm .gt_indent_2 {
   text-indent: 10px;
 }
 
-#bxwcrdiujj .gt_indent_3 {
+#frtzottorm .gt_indent_3 {
   text-indent: 15px;
 }
 
-#bxwcrdiujj .gt_indent_4 {
+#frtzottorm .gt_indent_4 {
   text-indent: 20px;
 }
 
-#bxwcrdiujj .gt_indent_5 {
+#frtzottorm .gt_indent_5 {
   text-indent: 25px;
 }
 </style>
@@ -2857,23 +2863,23 @@ <h3 id="regarding-fixed-effects">Regarding fixed effects<a class="anchor" aria-l
 <span><span class="op">)</span></span>
 <span></span>
 <span><span class="fu"><a href="https://modelsummary.com/reference/modelsummary.html" class="external-link">modelsummary</a></span><span class="op">(</span><span class="va">mods</span>, gof_map <span class="op">=</span> <span class="cn">NA</span><span class="op">)</span></span></code></pre></div>
-<div id="oufkerxqif" style="padding-left:0px;padding-right:0px;padding-top:10px;padding-bottom:10px;overflow-x:auto;overflow-y:auto;width:auto;height:auto;">
-<style>#oufkerxqif table {
+<div id="lqjwvflhlb" style="padding-left:0px;padding-right:0px;padding-top:10px;padding-bottom:10px;overflow-x:auto;overflow-y:auto;width:auto;height:auto;">
+<style>#lqjwvflhlb table {
   font-family: system-ui, 'Segoe UI', Roboto, Helvetica, Arial, sans-serif, 'Apple Color Emoji', 'Segoe UI Emoji', 'Segoe UI Symbol', 'Noto Color Emoji';
   -webkit-font-smoothing: antialiased;
   -moz-osx-font-smoothing: grayscale;
 }
 
-#oufkerxqif thead, #oufkerxqif tbody, #oufkerxqif tfoot, #oufkerxqif tr, #oufkerxqif td, #oufkerxqif th {
+#lqjwvflhlb thead, #lqjwvflhlb tbody, #lqjwvflhlb tfoot, #lqjwvflhlb tr, #lqjwvflhlb td, #lqjwvflhlb th {
   border-style: none;
 }
 
-#oufkerxqif p {
+#lqjwvflhlb p {
   margin: 0;
   padding: 0;
 }
 
-#oufkerxqif .gt_table {
+#lqjwvflhlb .gt_table {
   display: table;
   border-collapse: collapse;
   line-height: normal;
@@ -2899,12 +2905,12 @@ <h3 id="regarding-fixed-effects">Regarding fixed effects<a class="anchor" aria-l
   border-left-color: #D3D3D3;
 }
 
-#oufkerxqif .gt_caption {
+#lqjwvflhlb .gt_caption {
   padding-top: 4px;
   padding-bottom: 4px;
 }
 
-#oufkerxqif .gt_title {
+#lqjwvflhlb .gt_title {
   color: #333333;
   font-size: 125%;
   font-weight: initial;
@@ -2916,7 +2922,7 @@ <h3 id="regarding-fixed-effects">Regarding fixed effects<a class="anchor" aria-l
   border-bottom-width: 0;
 }
 
-#oufkerxqif .gt_subtitle {
+#lqjwvflhlb .gt_subtitle {
   color: #333333;
   font-size: 85%;
   font-weight: initial;
@@ -2928,7 +2934,7 @@ <h3 id="regarding-fixed-effects">Regarding fixed effects<a class="anchor" aria-l
   border-top-width: 0;
 }
 
-#oufkerxqif .gt_heading {
+#lqjwvflhlb .gt_heading {
   background-color: #FFFFFF;
   text-align: center;
   border-bottom-color: #FFFFFF;
@@ -2940,13 +2946,13 @@ <h3 id="regarding-fixed-effects">Regarding fixed effects<a class="anchor" aria-l
   border-right-color: #D3D3D3;
 }
 
-#oufkerxqif .gt_bottom_border {
+#lqjwvflhlb .gt_bottom_border {
   border-bottom-style: solid;
   border-bottom-width: 2px;
   border-bottom-color: #D3D3D3;
 }
 
-#oufkerxqif .gt_col_headings {
+#lqjwvflhlb .gt_col_headings {
   border-top-style: solid;
   border-top-width: 2px;
   border-top-color: #D3D3D3;
@@ -2961,7 +2967,7 @@ <h3 id="regarding-fixed-effects">Regarding fixed effects<a class="anchor" aria-l
   border-right-color: #D3D3D3;
 }
 
-#oufkerxqif .gt_col_heading {
+#lqjwvflhlb .gt_col_heading {
   color: #333333;
   background-color: #FFFFFF;
   font-size: 100%;
@@ -2981,7 +2987,7 @@ <h3 id="regarding-fixed-effects">Regarding fixed effects<a class="anchor" aria-l
   overflow-x: hidden;
 }
 
-#oufkerxqif .gt_column_spanner_outer {
+#lqjwvflhlb .gt_column_spanner_outer {
   color: #333333;
   background-color: #FFFFFF;
   font-size: 100%;
@@ -2993,15 +2999,15 @@ <h3 id="regarding-fixed-effects">Regarding fixed effects<a class="anchor" aria-l
   padding-right: 4px;
 }
 
-#oufkerxqif .gt_column_spanner_outer:first-child {
+#lqjwvflhlb .gt_column_spanner_outer:first-child {
   padding-left: 0;
 }
 
-#oufkerxqif .gt_column_spanner_outer:last-child {
+#lqjwvflhlb .gt_column_spanner_outer:last-child {
   padding-right: 0;
 }
 
-#oufkerxqif .gt_column_spanner {
+#lqjwvflhlb .gt_column_spanner {
   border-bottom-style: solid;
   border-bottom-width: 2px;
   border-bottom-color: #D3D3D3;
@@ -3013,11 +3019,11 @@ <h3 id="regarding-fixed-effects">Regarding fixed effects<a class="anchor" aria-l
   width: 100%;
 }
 
-#oufkerxqif .gt_spanner_row {
+#lqjwvflhlb .gt_spanner_row {
   border-bottom-style: hidden;
 }
 
-#oufkerxqif .gt_group_heading {
+#lqjwvflhlb .gt_group_heading {
   padding-top: 8px;
   padding-bottom: 8px;
   padding-left: 5px;
@@ -3043,7 +3049,7 @@ <h3 id="regarding-fixed-effects">Regarding fixed effects<a class="anchor" aria-l
   text-align: left;
 }
 
-#oufkerxqif .gt_empty_group_heading {
+#lqjwvflhlb .gt_empty_group_heading {
   padding: 0.5px;
   color: #333333;
   background-color: #FFFFFF;
@@ -3058,15 +3064,15 @@ <h3 id="regarding-fixed-effects">Regarding fixed effects<a class="anchor" aria-l
   vertical-align: middle;
 }
 
-#oufkerxqif .gt_from_md > :first-child {
+#lqjwvflhlb .gt_from_md > :first-child {
   margin-top: 0;
 }
 
-#oufkerxqif .gt_from_md > :last-child {
+#lqjwvflhlb .gt_from_md > :last-child {
   margin-bottom: 0;
 }
 
-#oufkerxqif .gt_row {
+#lqjwvflhlb .gt_row {
   padding-top: 8px;
   padding-bottom: 8px;
   padding-left: 5px;
@@ -3085,7 +3091,7 @@ <h3 id="regarding-fixed-effects">Regarding fixed effects<a class="anchor" aria-l
   overflow-x: hidden;
 }
 
-#oufkerxqif .gt_stub {
+#lqjwvflhlb .gt_stub {
   color: #333333;
   background-color: #FFFFFF;
   font-size: 100%;
@@ -3098,7 +3104,7 @@ <h3 id="regarding-fixed-effects">Regarding fixed effects<a class="anchor" aria-l
   padding-right: 5px;
 }
 
-#oufkerxqif .gt_stub_row_group {
+#lqjwvflhlb .gt_stub_row_group {
   color: #333333;
   background-color: #FFFFFF;
   font-size: 100%;
@@ -3112,15 +3118,15 @@ <h3 id="regarding-fixed-effects">Regarding fixed effects<a class="anchor" aria-l
   vertical-align: top;
 }
 
-#oufkerxqif .gt_row_group_first td {
+#lqjwvflhlb .gt_row_group_first td {
   border-top-width: 2px;
 }
 
-#oufkerxqif .gt_row_group_first th {
+#lqjwvflhlb .gt_row_group_first th {
   border-top-width: 2px;
 }
 
-#oufkerxqif .gt_summary_row {
+#lqjwvflhlb .gt_summary_row {
   color: #333333;
   background-color: #FFFFFF;
   text-transform: inherit;
@@ -3130,16 +3136,16 @@ <h3 id="regarding-fixed-effects">Regarding fixed effects<a class="anchor" aria-l
   padding-right: 5px;
 }
 
-#oufkerxqif .gt_first_summary_row {
+#lqjwvflhlb .gt_first_summary_row {
   border-top-style: solid;
   border-top-color: #D3D3D3;
 }
 
-#oufkerxqif .gt_first_summary_row.thick {
+#lqjwvflhlb .gt_first_summary_row.thick {
   border-top-width: 2px;
 }
 
-#oufkerxqif .gt_last_summary_row {
+#lqjwvflhlb .gt_last_summary_row {
   padding-top: 8px;
   padding-bottom: 8px;
   padding-left: 5px;
@@ -3149,7 +3155,7 @@ <h3 id="regarding-fixed-effects">Regarding fixed effects<a class="anchor" aria-l
   border-bottom-color: #D3D3D3;
 }
 
-#oufkerxqif .gt_grand_summary_row {
+#lqjwvflhlb .gt_grand_summary_row {
   color: #333333;
   background-color: #FFFFFF;
   text-transform: inherit;
@@ -3159,7 +3165,7 @@ <h3 id="regarding-fixed-effects">Regarding fixed effects<a class="anchor" aria-l
   padding-right: 5px;
 }
 
-#oufkerxqif .gt_first_grand_summary_row {
+#lqjwvflhlb .gt_first_grand_summary_row {
   padding-top: 8px;
   padding-bottom: 8px;
   padding-left: 5px;
@@ -3169,7 +3175,7 @@ <h3 id="regarding-fixed-effects">Regarding fixed effects<a class="anchor" aria-l
   border-top-color: #D3D3D3;
 }
 
-#oufkerxqif .gt_last_grand_summary_row_top {
+#lqjwvflhlb .gt_last_grand_summary_row_top {
   padding-top: 8px;
   padding-bottom: 8px;
   padding-left: 5px;
@@ -3179,11 +3185,11 @@ <h3 id="regarding-fixed-effects">Regarding fixed effects<a class="anchor" aria-l
   border-bottom-color: #D3D3D3;
 }
 
-#oufkerxqif .gt_striped {
+#lqjwvflhlb .gt_striped {
   background-color: rgba(128, 128, 128, 0.05);
 }
 
-#oufkerxqif .gt_table_body {
+#lqjwvflhlb .gt_table_body {
   border-top-style: solid;
   border-top-width: 2px;
   border-top-color: #D3D3D3;
@@ -3192,7 +3198,7 @@ <h3 id="regarding-fixed-effects">Regarding fixed effects<a class="anchor" aria-l
   border-bottom-color: #D3D3D3;
 }
 
-#oufkerxqif .gt_footnotes {
+#lqjwvflhlb .gt_footnotes {
   color: #333333;
   background-color: #FFFFFF;
   border-bottom-style: none;
@@ -3206,7 +3212,7 @@ <h3 id="regarding-fixed-effects">Regarding fixed effects<a class="anchor" aria-l
   border-right-color: #D3D3D3;
 }
 
-#oufkerxqif .gt_footnote {
+#lqjwvflhlb .gt_footnote {
   margin: 0px;
   font-size: 90%;
   padding-top: 4px;
@@ -3215,7 +3221,7 @@ <h3 id="regarding-fixed-effects">Regarding fixed effects<a class="anchor" aria-l
   padding-right: 5px;
 }
 
-#oufkerxqif .gt_sourcenotes {
+#lqjwvflhlb .gt_sourcenotes {
   color: #333333;
   background-color: #FFFFFF;
   border-bottom-style: none;
@@ -3229,7 +3235,7 @@ <h3 id="regarding-fixed-effects">Regarding fixed effects<a class="anchor" aria-l
   border-right-color: #D3D3D3;
 }
 
-#oufkerxqif .gt_sourcenote {
+#lqjwvflhlb .gt_sourcenote {
   font-size: 90%;
   padding-top: 4px;
   padding-bottom: 4px;
@@ -3237,63 +3243,63 @@ <h3 id="regarding-fixed-effects">Regarding fixed effects<a class="anchor" aria-l
   padding-right: 5px;
 }
 
-#oufkerxqif .gt_left {
+#lqjwvflhlb .gt_left {
   text-align: left;
 }
 
-#oufkerxqif .gt_center {
+#lqjwvflhlb .gt_center {
   text-align: center;
 }
 
-#oufkerxqif .gt_right {
+#lqjwvflhlb .gt_right {
   text-align: right;
   font-variant-numeric: tabular-nums;
 }
 
-#oufkerxqif .gt_font_normal {
+#lqjwvflhlb .gt_font_normal {
   font-weight: normal;
 }
 
-#oufkerxqif .gt_font_bold {
+#lqjwvflhlb .gt_font_bold {
   font-weight: bold;
 }
 
-#oufkerxqif .gt_font_italic {
+#lqjwvflhlb .gt_font_italic {
   font-style: italic;
 }
 
-#oufkerxqif .gt_super {
+#lqjwvflhlb .gt_super {
   font-size: 65%;
 }
 
-#oufkerxqif .gt_footnote_marks {
+#lqjwvflhlb .gt_footnote_marks {
   font-size: 75%;
   vertical-align: 0.4em;
   position: initial;
 }
 
-#oufkerxqif .gt_asterisk {
+#lqjwvflhlb .gt_asterisk {
   font-size: 100%;
   vertical-align: 0;
 }
 
-#oufkerxqif .gt_indent_1 {
+#lqjwvflhlb .gt_indent_1 {
   text-indent: 5px;
 }
 
-#oufkerxqif .gt_indent_2 {
+#lqjwvflhlb .gt_indent_2 {
   text-indent: 10px;
 }
 
-#oufkerxqif .gt_indent_3 {
+#lqjwvflhlb .gt_indent_3 {
   text-indent: 15px;
 }
 
-#oufkerxqif .gt_indent_4 {
+#lqjwvflhlb .gt_indent_4 {
   text-indent: 20px;
 }
 
-#oufkerxqif .gt_indent_5 {
+#lqjwvflhlb .gt_indent_5 {
   text-indent: 25px;
 }
 </style>
@@ -3878,23 +3884,23 @@ <h3 id="regarding-fixed-effects">Regarding fixed effects<a class="anchor" aria-l
 <span>  coef_rename <span class="op">=</span> <span class="va">rename_fn</span>,</span>
 <span>  gof_omit    <span class="op">=</span> <span class="st">"Adj|Within|IC|RMSE"</span></span>
 <span><span class="op">)</span></span></code></pre></div>
-<div id="xhbvzmwejy" style="padding-left:0px;padding-right:0px;padding-top:10px;padding-bottom:10px;overflow-x:auto;overflow-y:auto;width:auto;height:auto;">
-<style>#xhbvzmwejy table {
+<div id="iscenwdnlu" style="padding-left:0px;padding-right:0px;padding-top:10px;padding-bottom:10px;overflow-x:auto;overflow-y:auto;width:auto;height:auto;">
+<style>#iscenwdnlu table {
   font-family: system-ui, 'Segoe UI', Roboto, Helvetica, Arial, sans-serif, 'Apple Color Emoji', 'Segoe UI Emoji', 'Segoe UI Symbol', 'Noto Color Emoji';
   -webkit-font-smoothing: antialiased;
   -moz-osx-font-smoothing: grayscale;
 }
 
-#xhbvzmwejy thead, #xhbvzmwejy tbody, #xhbvzmwejy tfoot, #xhbvzmwejy tr, #xhbvzmwejy td, #xhbvzmwejy th {
+#iscenwdnlu thead, #iscenwdnlu tbody, #iscenwdnlu tfoot, #iscenwdnlu tr, #iscenwdnlu td, #iscenwdnlu th {
   border-style: none;
 }
 
-#xhbvzmwejy p {
+#iscenwdnlu p {
   margin: 0;
   padding: 0;
 }
 
-#xhbvzmwejy .gt_table {
+#iscenwdnlu .gt_table {
   display: table;
   border-collapse: collapse;
   line-height: normal;
@@ -3920,12 +3926,12 @@ <h3 id="regarding-fixed-effects">Regarding fixed effects<a class="anchor" aria-l
   border-left-color: #D3D3D3;
 }
 
-#xhbvzmwejy .gt_caption {
+#iscenwdnlu .gt_caption {
   padding-top: 4px;
   padding-bottom: 4px;
 }
 
-#xhbvzmwejy .gt_title {
+#iscenwdnlu .gt_title {
   color: #333333;
   font-size: 125%;
   font-weight: initial;
@@ -3937,7 +3943,7 @@ <h3 id="regarding-fixed-effects">Regarding fixed effects<a class="anchor" aria-l
   border-bottom-width: 0;
 }
 
-#xhbvzmwejy .gt_subtitle {
+#iscenwdnlu .gt_subtitle {
   color: #333333;
   font-size: 85%;
   font-weight: initial;
@@ -3949,7 +3955,7 @@ <h3 id="regarding-fixed-effects">Regarding fixed effects<a class="anchor" aria-l
   border-top-width: 0;
 }
 
-#xhbvzmwejy .gt_heading {
+#iscenwdnlu .gt_heading {
   background-color: #FFFFFF;
   text-align: center;
   border-bottom-color: #FFFFFF;
@@ -3961,13 +3967,13 @@ <h3 id="regarding-fixed-effects">Regarding fixed effects<a class="anchor" aria-l
   border-right-color: #D3D3D3;
 }
 
-#xhbvzmwejy .gt_bottom_border {
+#iscenwdnlu .gt_bottom_border {
   border-bottom-style: solid;
   border-bottom-width: 2px;
   border-bottom-color: #D3D3D3;
 }
 
-#xhbvzmwejy .gt_col_headings {
+#iscenwdnlu .gt_col_headings {
   border-top-style: solid;
   border-top-width: 2px;
   border-top-color: #D3D3D3;
@@ -3982,7 +3988,7 @@ <h3 id="regarding-fixed-effects">Regarding fixed effects<a class="anchor" aria-l
   border-right-color: #D3D3D3;
 }
 
-#xhbvzmwejy .gt_col_heading {
+#iscenwdnlu .gt_col_heading {
   color: #333333;
   background-color: #FFFFFF;
   font-size: 100%;
@@ -4002,7 +4008,7 @@ <h3 id="regarding-fixed-effects">Regarding fixed effects<a class="anchor" aria-l
   overflow-x: hidden;
 }
 
-#xhbvzmwejy .gt_column_spanner_outer {
+#iscenwdnlu .gt_column_spanner_outer {
   color: #333333;
   background-color: #FFFFFF;
   font-size: 100%;
@@ -4014,15 +4020,15 @@ <h3 id="regarding-fixed-effects">Regarding fixed effects<a class="anchor" aria-l
   padding-right: 4px;
 }
 
-#xhbvzmwejy .gt_column_spanner_outer:first-child {
+#iscenwdnlu .gt_column_spanner_outer:first-child {
   padding-left: 0;
 }
 
-#xhbvzmwejy .gt_column_spanner_outer:last-child {
+#iscenwdnlu .gt_column_spanner_outer:last-child {
   padding-right: 0;
 }
 
-#xhbvzmwejy .gt_column_spanner {
+#iscenwdnlu .gt_column_spanner {
   border-bottom-style: solid;
   border-bottom-width: 2px;
   border-bottom-color: #D3D3D3;
@@ -4034,11 +4040,11 @@ <h3 id="regarding-fixed-effects">Regarding fixed effects<a class="anchor" aria-l
   width: 100%;
 }
 
-#xhbvzmwejy .gt_spanner_row {
+#iscenwdnlu .gt_spanner_row {
   border-bottom-style: hidden;
 }
 
-#xhbvzmwejy .gt_group_heading {
+#iscenwdnlu .gt_group_heading {
   padding-top: 8px;
   padding-bottom: 8px;
   padding-left: 5px;
@@ -4064,7 +4070,7 @@ <h3 id="regarding-fixed-effects">Regarding fixed effects<a class="anchor" aria-l
   text-align: left;
 }
 
-#xhbvzmwejy .gt_empty_group_heading {
+#iscenwdnlu .gt_empty_group_heading {
   padding: 0.5px;
   color: #333333;
   background-color: #FFFFFF;
@@ -4079,15 +4085,15 @@ <h3 id="regarding-fixed-effects">Regarding fixed effects<a class="anchor" aria-l
   vertical-align: middle;
 }
 
-#xhbvzmwejy .gt_from_md > :first-child {
+#iscenwdnlu .gt_from_md > :first-child {
   margin-top: 0;
 }
 
-#xhbvzmwejy .gt_from_md > :last-child {
+#iscenwdnlu .gt_from_md > :last-child {
   margin-bottom: 0;
 }
 
-#xhbvzmwejy .gt_row {
+#iscenwdnlu .gt_row {
   padding-top: 8px;
   padding-bottom: 8px;
   padding-left: 5px;
@@ -4106,7 +4112,7 @@ <h3 id="regarding-fixed-effects">Regarding fixed effects<a class="anchor" aria-l
   overflow-x: hidden;
 }
 
-#xhbvzmwejy .gt_stub {
+#iscenwdnlu .gt_stub {
   color: #333333;
   background-color: #FFFFFF;
   font-size: 100%;
@@ -4119,7 +4125,7 @@ <h3 id="regarding-fixed-effects">Regarding fixed effects<a class="anchor" aria-l
   padding-right: 5px;
 }
 
-#xhbvzmwejy .gt_stub_row_group {
+#iscenwdnlu .gt_stub_row_group {
   color: #333333;
   background-color: #FFFFFF;
   font-size: 100%;
@@ -4133,15 +4139,15 @@ <h3 id="regarding-fixed-effects">Regarding fixed effects<a class="anchor" aria-l
   vertical-align: top;
 }
 
-#xhbvzmwejy .gt_row_group_first td {
+#iscenwdnlu .gt_row_group_first td {
   border-top-width: 2px;
 }
 
-#xhbvzmwejy .gt_row_group_first th {
+#iscenwdnlu .gt_row_group_first th {
   border-top-width: 2px;
 }
 
-#xhbvzmwejy .gt_summary_row {
+#iscenwdnlu .gt_summary_row {
   color: #333333;
   background-color: #FFFFFF;
   text-transform: inherit;
@@ -4151,16 +4157,16 @@ <h3 id="regarding-fixed-effects">Regarding fixed effects<a class="anchor" aria-l
   padding-right: 5px;
 }
 
-#xhbvzmwejy .gt_first_summary_row {
+#iscenwdnlu .gt_first_summary_row {
   border-top-style: solid;
   border-top-color: #D3D3D3;
 }
 
-#xhbvzmwejy .gt_first_summary_row.thick {
+#iscenwdnlu .gt_first_summary_row.thick {
   border-top-width: 2px;
 }
 
-#xhbvzmwejy .gt_last_summary_row {
+#iscenwdnlu .gt_last_summary_row {
   padding-top: 8px;
   padding-bottom: 8px;
   padding-left: 5px;
@@ -4170,7 +4176,7 @@ <h3 id="regarding-fixed-effects">Regarding fixed effects<a class="anchor" aria-l
   border-bottom-color: #D3D3D3;
 }
 
-#xhbvzmwejy .gt_grand_summary_row {
+#iscenwdnlu .gt_grand_summary_row {
   color: #333333;
   background-color: #FFFFFF;
   text-transform: inherit;
@@ -4180,7 +4186,7 @@ <h3 id="regarding-fixed-effects">Regarding fixed effects<a class="anchor" aria-l
   padding-right: 5px;
 }
 
-#xhbvzmwejy .gt_first_grand_summary_row {
+#iscenwdnlu .gt_first_grand_summary_row {
   padding-top: 8px;
   padding-bottom: 8px;
   padding-left: 5px;
@@ -4190,7 +4196,7 @@ <h3 id="regarding-fixed-effects">Regarding fixed effects<a class="anchor" aria-l
   border-top-color: #D3D3D3;
 }
 
-#xhbvzmwejy .gt_last_grand_summary_row_top {
+#iscenwdnlu .gt_last_grand_summary_row_top {
   padding-top: 8px;
   padding-bottom: 8px;
   padding-left: 5px;
@@ -4200,11 +4206,11 @@ <h3 id="regarding-fixed-effects">Regarding fixed effects<a class="anchor" aria-l
   border-bottom-color: #D3D3D3;
 }
 
-#xhbvzmwejy .gt_striped {
+#iscenwdnlu .gt_striped {
   background-color: rgba(128, 128, 128, 0.05);
 }
 
-#xhbvzmwejy .gt_table_body {
+#iscenwdnlu .gt_table_body {
   border-top-style: solid;
   border-top-width: 2px;
   border-top-color: #D3D3D3;
@@ -4213,7 +4219,7 @@ <h3 id="regarding-fixed-effects">Regarding fixed effects<a class="anchor" aria-l
   border-bottom-color: #D3D3D3;
 }
 
-#xhbvzmwejy .gt_footnotes {
+#iscenwdnlu .gt_footnotes {
   color: #333333;
   background-color: #FFFFFF;
   border-bottom-style: none;
@@ -4227,7 +4233,7 @@ <h3 id="regarding-fixed-effects">Regarding fixed effects<a class="anchor" aria-l
   border-right-color: #D3D3D3;
 }
 
-#xhbvzmwejy .gt_footnote {
+#iscenwdnlu .gt_footnote {
   margin: 0px;
   font-size: 90%;
   padding-top: 4px;
@@ -4236,7 +4242,7 @@ <h3 id="regarding-fixed-effects">Regarding fixed effects<a class="anchor" aria-l
   padding-right: 5px;
 }
 
-#xhbvzmwejy .gt_sourcenotes {
+#iscenwdnlu .gt_sourcenotes {
   color: #333333;
   background-color: #FFFFFF;
   border-bottom-style: none;
@@ -4250,7 +4256,7 @@ <h3 id="regarding-fixed-effects">Regarding fixed effects<a class="anchor" aria-l
   border-right-color: #D3D3D3;
 }
 
-#xhbvzmwejy .gt_sourcenote {
+#iscenwdnlu .gt_sourcenote {
   font-size: 90%;
   padding-top: 4px;
   padding-bottom: 4px;
@@ -4258,63 +4264,63 @@ <h3 id="regarding-fixed-effects">Regarding fixed effects<a class="anchor" aria-l
   padding-right: 5px;
 }
 
-#xhbvzmwejy .gt_left {
+#iscenwdnlu .gt_left {
   text-align: left;
 }
 
-#xhbvzmwejy .gt_center {
+#iscenwdnlu .gt_center {
   text-align: center;
 }
 
-#xhbvzmwejy .gt_right {
+#iscenwdnlu .gt_right {
   text-align: right;
   font-variant-numeric: tabular-nums;
 }
 
-#xhbvzmwejy .gt_font_normal {
+#iscenwdnlu .gt_font_normal {
   font-weight: normal;
 }
 
-#xhbvzmwejy .gt_font_bold {
+#iscenwdnlu .gt_font_bold {
   font-weight: bold;
 }
 
-#xhbvzmwejy .gt_font_italic {
+#iscenwdnlu .gt_font_italic {
   font-style: italic;
 }
 
-#xhbvzmwejy .gt_super {
+#iscenwdnlu .gt_super {
   font-size: 65%;
 }
 
-#xhbvzmwejy .gt_footnote_marks {
+#iscenwdnlu .gt_footnote_marks {
   font-size: 75%;
   vertical-align: 0.4em;
   position: initial;
 }
 
-#xhbvzmwejy .gt_asterisk {
+#iscenwdnlu .gt_asterisk {
   font-size: 100%;
   vertical-align: 0;
 }
 
-#xhbvzmwejy .gt_indent_1 {
+#iscenwdnlu .gt_indent_1 {
   text-indent: 5px;
 }
 
-#xhbvzmwejy .gt_indent_2 {
+#iscenwdnlu .gt_indent_2 {
   text-indent: 10px;
 }
 
-#xhbvzmwejy .gt_indent_3 {
+#iscenwdnlu .gt_indent_3 {
   text-indent: 15px;
 }
 
-#xhbvzmwejy .gt_indent_4 {
+#iscenwdnlu .gt_indent_4 {
   text-indent: 20px;
 }
 
-#xhbvzmwejy .gt_indent_5 {
+#iscenwdnlu .gt_indent_5 {
   text-indent: 25px;
 }
 </style>
diff --git a/articles/index.html b/articles/index.html
index c83b17d..a628147 100644
--- a/articles/index.html
+++ b/articles/index.html
@@ -10,7 +10,7 @@
     
     <a class="navbar-brand me-2" href="../index.html">etwfe</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">0.3.5.9002</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">0.4.0</small>
 
     
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
diff --git a/authors.html b/authors.html
index b2f9a5b..9da6f2a 100644
--- a/authors.html
+++ b/authors.html
@@ -10,7 +10,7 @@
     
     <a class="navbar-brand me-2" href="index.html">etwfe</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">0.3.5.9002</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">0.4.0</small>
 
     
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
@@ -65,13 +65,13 @@ <h2 id="citation">Citation</h2>
 
       <p>McDermott G (2024).
 <em>etwfe: Extended Two-Way Fixed Effects</em>.
-R package version 0.3.5.9002, <a href="https://grantmcdermott.com/etwfe/" class="external-link">https://grantmcdermott.com/etwfe/</a>. 
+R package version 0.4.0, <a href="https://grantmcdermott.com/etwfe/" class="external-link">https://grantmcdermott.com/etwfe/</a>. 
 </p>
       <pre>@Manual{,
   title = {etwfe: Extended Two-Way Fixed Effects},
   author = {Grant McDermott},
   year = {2024},
-  note = {R package version 0.3.5.9002},
+  note = {R package version 0.4.0},
   url = {https://grantmcdermott.com/etwfe/},
 }</pre>
     </div>
diff --git a/index.html b/index.html
index 75a8ac8..d0f3067 100644
--- a/index.html
+++ b/index.html
@@ -30,7 +30,7 @@
     
     <a class="navbar-brand me-2" href="index.html">etwfe</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">0.3.5.9002</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">0.4.0</small>
 
     
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
@@ -115,9 +115,9 @@ <h2 id="quickstart-example">Quickstart example<a class="anchor" aria-label="anch
 <span><span class="co"># This gives us a regression model with fully saturated interactions</span></span>
 <span><span class="va">mod</span></span>
 <span><span class="co">#&gt; OLS estimation, Dep. Var.: lemp</span></span>
-<span><span class="co">#&gt; Observations: 2,500 </span></span>
+<span><span class="co">#&gt; Observations: 2,500</span></span>
 <span><span class="co">#&gt; Fixed-effects: first.treat: 4,  year: 5</span></span>
-<span><span class="co">#&gt; Varying slopes: lpop (first.treat: 4),  lpop (year: 5)</span></span>
+<span><span class="co">#&gt; Varying slopes: lpop (first.treat): 4,  lpop (year): 5</span></span>
 <span><span class="co">#&gt; Standard-errors: Clustered (countyreal) </span></span>
 <span><span class="co">#&gt;                                               Estimate Std. Error   t value   Pr(&gt;|t|)    </span></span>
 <span><span class="co">#&gt; .Dtreat:first.treat::2004:year::2004         -0.021248   0.021728 -0.977890 3.2860e-01    </span></span>
@@ -157,7 +157,7 @@ <h2 id="acknowledgements">Acknowledgements<a class="anchor" aria-label="anchor"
 </h2>
 <ul>
 <li>
-<a href="http://econ.msu.edu/faculty/wooldridge/" class="external-link">Jeffrey Wooldridge</a> for the underlying <a href="https://dx.doi.org/10.2139/ssrn.3906345" class="external-link">ETWFE</a> <a href="https://dx.doi.org/10.2139/ssrn.4183726" class="external-link">theory</a>.</li>
+<a href="https://econ.msu.edu/about/directory/Wooldridge-Jeffrey" class="external-link">Jeffrey Wooldridge</a> for the underlying <a href="https://dx.doi.org/10.2139/ssrn.3906345" class="external-link">ETWFE</a> <a href="https://dx.doi.org/10.2139/ssrn.4183726" class="external-link">theory</a>.</li>
 <li>
 <a href="https://sites.google.com/site/laurentrberge/" class="external-link">Laurent Bergé</a> (<a href="https://lrberge.github.io/fixest/" class="external-link"><strong>fixest</strong></a>) and <a href="https://arelbundock.com/" class="external-link">Vincent Arel-Bundock</a> (<a href="https://marginaleffects.com/" class="external-link"><strong>marginaleffects</strong></a>) for maintaining the two wonderful R packages that do most of the heavy lifting under the hood here.</li>
 <li>
diff --git a/news/index.html b/news/index.html
index 8ffe56e..c231679 100644
--- a/news/index.html
+++ b/news/index.html
@@ -10,7 +10,7 @@
     
     <a class="navbar-brand me-2" href="../index.html">etwfe</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">0.3.5.9002</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">0.4.0</small>
 
     
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
@@ -48,14 +48,14 @@
     </div>
 
     <div class="section level2">
-<h2 class="pkg-version" data-toc-text="0.3.5.9002" id="etwfe-0359002-development-version">etwfe 0.3.5.9002 (development version)<a class="anchor" aria-label="anchor" href="#etwfe-0359002-development-version"></a></h2>
+<h2 class="pkg-version" data-toc-text="0.4.0" id="etwfe-040">etwfe 0.4.0<a class="anchor" aria-label="anchor" href="#etwfe-040"></a></h2><p class="text-muted">CRAN release: 2024-02-27</p>
 <div class="section level3">
-<h3 id="bug-fixes-0-3-5-9002">Bug fixes<a class="anchor" aria-label="anchor" href="#bug-fixes-0-3-5-9002"></a></h3>
+<h3 id="bug-fixes-0-4-0">Bug fixes<a class="anchor" aria-label="anchor" href="#bug-fixes-0-4-0"></a></h3>
 <ul><li>Fix ATT calculation for the never-treated case (i..e, <code>cgroup = "never</code>) due to incorrect subsetting prior to recovering the marginal effects. Thanks to <a href="https://github.com/paulofelipe" class="external-link">@paulofelipe</a> for reporting (<a href="https://github.com/grantmcdermott/etwfe/issues/37" class="external-link">#37</a>).</li>
 <li>Avoid (where possible) or error out if user supplies reserved “group” variable in formula (<a href="https://github.com/grantmcdermott/etwfe/issues/41" class="external-link">#41</a>).</li>
 </ul></div>
 <div class="section level3">
-<h3 id="documentation-0-3-5-9002">Documentation<a class="anchor" aria-label="anchor" href="#documentation-0-3-5-9002"></a></h3>
+<h3 id="documentation-0-4-0">Documentation<a class="anchor" aria-label="anchor" href="#documentation-0-4-0"></a></h3>
 <ul><li>Fix missing autolinks in documentation due to markdown formatting (<a href="https://github.com/grantmcdermott/etwfe/issues/44" class="external-link">#44</a> <a href="https://github.com/etiennebacher" class="external-link">@etiennebacher</a>).</li>
 </ul></div>
 </div>
diff --git a/pkgdown.yml b/pkgdown.yml
index 7e7412f..29632d3 100644
--- a/pkgdown.yml
+++ b/pkgdown.yml
@@ -3,7 +3,7 @@ pkgdown: 2.0.7
 pkgdown_sha: ~
 articles:
   etwfe: etwfe.html
-last_built: 2024-02-25T22:30Z
+last_built: 2024-02-27T05:15Z
 urls:
   reference: http://grantmcdermott.com/etwfe/reference
   article: http://grantmcdermott.com/etwfe/articles
diff --git a/reference/emfx.html b/reference/emfx.html
index b61fc7c..6b0f2ab 100644
--- a/reference/emfx.html
+++ b/reference/emfx.html
@@ -10,7 +10,7 @@
     
     <a class="navbar-brand me-2" href="../index.html">etwfe</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">0.3.5.9002</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">0.4.0</small>
 
     
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
diff --git a/reference/etwfe.html b/reference/etwfe.html
index 1915ea3..d6b0015 100644
--- a/reference/etwfe.html
+++ b/reference/etwfe.html
@@ -10,7 +10,7 @@
     
     <a class="navbar-brand me-2" href="../index.html">etwfe</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">0.3.5.9002</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">0.4.0</small>
 
     
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
diff --git a/reference/index.html b/reference/index.html
index b668d2c..46eba4f 100644
--- a/reference/index.html
+++ b/reference/index.html
@@ -10,7 +10,7 @@
     
     <a class="navbar-brand me-2" href="../index.html">etwfe</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">0.3.5.9002</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">0.4.0</small>
 
     
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
diff --git a/search.json b/search.json
index cb8de30..9ed8d16 100644
--- a/search.json
+++ b/search.json
@@ -1 +1 @@
-[{"path":"http://grantmcdermott.com/etwfe/articles/etwfe.html","id":"background","dir":"Articles","previous_headings":"","what":"Background","title":"Introduction to etwfe","text":"canonical research design social scientists -called “differences--differences” () design.1 classic 2x2 case (two units, two periods), simple interaction effect two dummy variables suffices recover treatment effect. base R might look something like: resulting coefficient Dtreated_unitTRUE:Dpost_treatmentTRUE interaction term represents treatment effect. Rather manually specify interaction term, practice researchers often use equivalent formulation known two-way fixed effects (TWFE). core idea TWFE can subsume interaction term previous code chunk adding unit time fixed effects. single treatment dummy can used capture effect treatment directly. TWFE regression base R might look follows: treatment effect now captured coefficient Dtreat dummy. TWFE shortcut especially nice complicated panel data settings multiple units multiple times periods. Speaking , prefer use dedicated fixed effects / panel data package like fixest, also estimate previous regression like : TWFE regressions easy run intuitive, long time everyone happy. good last. cottage industry clever research now demonstrates things quite simple. Among things, standard TWFE formulation can impose strange (negative) weighting conditions key parts estimation procedure. One implication risk high probability estimate bias presence staggered treatment rollouts, common real-life applications. Fortunately, just econometricians taking away one favourite tools, kind enough replace new ones. Among , proposed approach Wooldridge (2021, 2022) noteworthy. idea might paraphrased stating problem TWFE first place. Rather, ’s weren’t enough. Instead including single treatment × time interaction, Wooldridge recommends saturate model possible interactions treatment time variables, including treatment cohorts, well covariates. goes show approach actually draws equivalence different types estimators (pooled OLS, twoway Mundlak regression, etc.) ’s entirely clear call . Wooldridge refers general idea extended TWFE—, ETWFE—rather like package takes name. Wooldridge ETWFE solution intuitive elegant. also rather tedious error prone code manually. correctly specify possible interactions, demean control variables within groups, recover treatment effects interest via appropriate marginal effect aggregation. etwfe package aims simplify process providing convenience functions work .","code":"lm(y ~ Dtreated_unit * Dpost_treatment, data = somedata) lm(y ~ Dtreat + factor(id) + factor(period), data = somedata) library(fixest) feols(y ~ Dtreat | id + period, data = somedata)"},{"path":"http://grantmcdermott.com/etwfe/articles/etwfe.html","id":"dataset","dir":"Articles","previous_headings":"","what":"Dataset","title":"Introduction to etwfe","text":"demonstrate core functionality etwfe, ’ll use mpdta dataset US teen employment package (’ll need install separately). “Treatment” dataset refers increase minimum wage rate. examples follow, goal estimate effect minimum wage treatment (treat) log teen employment (lemp). Notice panel ID county level (countyreal), treatment staggered across cohorts (first.treat) group counties treated time. addition staggered treatment effects, also observe log population (lpop) potential control variable.","code":"# install.packages(\"did\") data(\"mpdta\", package = \"did\") head(mpdta) #>     year countyreal     lpop     lemp first.treat treat #> 866 2003       8001 5.896761 8.461469        2007     1 #> 841 2004       8001 5.896761 8.336870        2007     1 #> 842 2005       8001 5.896761 8.340217        2007     1 #> 819 2006       8001 5.896761 8.378161        2007     1 #> 827 2007       8001 5.896761 8.487352        2007     1 #> 937 2003       8019 2.232377 4.997212        2007     1"},{"path":"http://grantmcdermott.com/etwfe/articles/etwfe.html","id":"basic-usage","dir":"Articles","previous_headings":"","what":"Basic usage","title":"Introduction to etwfe","text":"Let’s load etwfe work basic functionality. ’ll see, core workflow package involves two consecutive function calls: 1) etwfe() 2) emfx().","code":""},{"path":"http://grantmcdermott.com/etwfe/articles/etwfe.html","id":"etwfe","dir":"Articles","previous_headings":"Basic usage","what":"etwfe","title":"Introduction to etwfe","text":"Given package name, won’t surprise learn key estimating function etwfe(). ’s look example dataset. things say etwfe() argument choices function options, ’ll leave details aside bit later. Right now, just know arguments required except vcov (though generally recommend , since probably want cluster standard errors individual unit level). Let’s take look model object. etwfe() done underneath hood construct treatment dummy variable .Dtreat saturated together variables interest set multiway interaction terms.2 may noticed etwfe() call returns standard fixest object, since uses perform underlying estimation. associated methods functions fixest package thus compatible model object. example, plot raw regression coefficients fixest::coefplot(), print nice regression table fixest::etable(). However, raw coefficients etwfe() estimation particularly meaningful . Recall complex, multiway interaction terms probably hard interpret . insight leads us next key function…","code":"library(etwfe)  mod =   etwfe(     fml  = lemp ~ lpop, # outcome ~ controls     tvar = year,        # time variable     gvar = first.treat, # group variable     data = mpdta,       # dataset     vcov = ~countyreal  # vcov adjustment (here: clustered)     ) mod #> OLS estimation, Dep. Var.: lemp #> Observations: 2,500  #> Fixed-effects: first.treat: 4,  year: 5 #> Varying slopes: lpop (first.treat: 4),  lpop (year: 5) #> Standard-errors: Clustered (countyreal)  #>                                               Estimate Std. Error   t value #> .Dtreat:first.treat::2004:year::2004         -0.021248   0.021728 -0.977890 #> .Dtreat:first.treat::2004:year::2005         -0.081850   0.027375 -2.989963 #> .Dtreat:first.treat::2004:year::2006         -0.137870   0.030795 -4.477097 #> .Dtreat:first.treat::2004:year::2007         -0.109539   0.032322 -3.389024 #> .Dtreat:first.treat::2006:year::2006          0.002537   0.018883  0.134344 #> .Dtreat:first.treat::2006:year::2007         -0.045093   0.021987 -2.050907 #> .Dtreat:first.treat::2007:year::2007         -0.045955   0.017975 -2.556568 #> .Dtreat:first.treat::2004:year::2004:lpop_dm  0.004628   0.017584  0.263184 #> .Dtreat:first.treat::2004:year::2005:lpop_dm  0.025113   0.017904  1.402661 #> .Dtreat:first.treat::2004:year::2006:lpop_dm  0.050735   0.021070  2.407884 #> .Dtreat:first.treat::2004:year::2007:lpop_dm  0.011250   0.026617  0.422648 #> .Dtreat:first.treat::2006:year::2006:lpop_dm  0.038935   0.016472  2.363731 #> .Dtreat:first.treat::2006:year::2007:lpop_dm  0.038060   0.022477  1.693276 #> .Dtreat:first.treat::2007:year::2007:lpop_dm -0.019835   0.016198 -1.224528 #>                                                Pr(>|t|)     #> .Dtreat:first.treat::2004:year::2004         3.2860e-01     #> .Dtreat:first.treat::2004:year::2005         2.9279e-03 **  #> .Dtreat:first.treat::2004:year::2006         9.3851e-06 *** #> .Dtreat:first.treat::2004:year::2007         7.5694e-04 *** #> .Dtreat:first.treat::2006:year::2006         8.9318e-01     #> .Dtreat:first.treat::2006:year::2007         4.0798e-02 *   #> .Dtreat:first.treat::2007:year::2007         1.0866e-02 *   #> .Dtreat:first.treat::2004:year::2004:lpop_dm 7.9252e-01     #> .Dtreat:first.treat::2004:year::2005:lpop_dm 1.6134e-01     #> .Dtreat:first.treat::2004:year::2006:lpop_dm 1.6407e-02 *   #> .Dtreat:first.treat::2004:year::2007:lpop_dm 6.7273e-01     #> .Dtreat:first.treat::2006:year::2006:lpop_dm 1.8474e-02 *   #> .Dtreat:first.treat::2006:year::2007:lpop_dm 9.1027e-02 .   #> .Dtreat:first.treat::2007:year::2007:lpop_dm 2.2133e-01     #> ... 10 variables were removed because of collinearity (.Dtreat:first.treat::2006:year::2004, .Dtreat:first.treat::2006:year::2005 and 8 others [full set in $collin.var]) #> --- #> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 #> RMSE: 0.537131     Adj. R2: 0.87167  #>                  Within R2: 8.449e-4"},{"path":"http://grantmcdermott.com/etwfe/articles/etwfe.html","id":"emfx","dir":"Articles","previous_headings":"Basic usage","what":"emfx","title":"Introduction to etwfe","text":"raw etwfe coefficients aren’t particularly useful , can instead? Well, probably want aggregate along dimension interest (e.g., groups time, event study). natural way perform aggregations recovering appropriate marginal effects. etwfe package provides another convenience function : emfx(), thin(ish) wrapper around marginaleffects::slopes(). example, can recover average treatment effect treated (ATT) follows. words, model telling us increase minimum wage leads approximate 5 percent decrease teen employment. Beyond simple ATTs, emfx() also supports types aggregations via type argument. example, can use type = \"calendar\" get ATTs period, type = \"group\" get ATTs cohort groups. option probably useful people type = \"event\", recover dynamic treatment effects la event study. Let’s try save resulting object, since plan reuse moment. event study suggests teen disemployment effect minimum wage hike fairly modest first (3%), increases next years (>10%). next section, ’ll look ways communicate kind finding audience.","code":"emfx(mod) #>  #>     Term                 Contrast .Dtreat Estimate Std. Error     z Pr(>|z|) #>  .Dtreat mean(TRUE) - mean(FALSE)    TRUE  -0.0506     0.0125 -4.05   <0.001 #>     S   2.5 %  97.5 % #>  14.3 -0.0751 -0.0261 #>  #> Columns: term, contrast, .Dtreat, estimate, std.error, statistic, p.value, s.value, conf.low, conf.high, predicted_lo, predicted_hi, predicted  #> Type:  response mod_es = emfx(mod, type = \"event\") mod_es #>  #>     Term                 Contrast event Estimate Std. Error     z Pr(>|z|)    S #>  .Dtreat mean(TRUE) - mean(FALSE)     0  -0.0332     0.0134 -2.48    0.013  6.3 #>  .Dtreat mean(TRUE) - mean(FALSE)     1  -0.0573     0.0172 -3.34   <0.001 10.2 #>  .Dtreat mean(TRUE) - mean(FALSE)     2  -0.1379     0.0308 -4.48   <0.001 17.0 #>  .Dtreat mean(TRUE) - mean(FALSE)     3  -0.1095     0.0323 -3.39   <0.001 10.5 #>    2.5 %   97.5 % #>  -0.0594 -0.00701 #>  -0.0910 -0.02373 #>  -0.1982 -0.07751 #>  -0.1729 -0.04619 #>  #> Columns: term, contrast, event, estimate, std.error, statistic, p.value, s.value, conf.low, conf.high, predicted_lo, predicted_hi, predicted  #> Type:  response"},{"path":"http://grantmcdermott.com/etwfe/articles/etwfe.html","id":"presentation","dir":"Articles","previous_headings":"Basic usage","what":"Presentation","title":"Introduction to etwfe","text":"Since emfx() produces standard marginaleffects object, can pass supported methods packages. example, can pass modelsummary get nice regression table event study coefficients. Note use shape coef_rename arguments ; optional help make output look bit nicer. Event study visualization, can pass preferred plotting method. example:  Note emfx reports post-treatment effects. pre-treatment effects swept estimation way ETWFE set . fact, pre-treatment effects mechanistically set zero. means ETWFE used interrogating pre-treatment fit (say, visual inspection parallel pre-trends). Still, can get zero pre-treatment effects changing post_only argument. emphasize strictly performative—, pre-treatment effects zero estimation design—might make event study plot aesthetically pleasing.","code":"library(modelsummary) #> Version 2.0.0 of `modelsummary`, to be released soon, will introduce a #>   breaking change: The default table-drawing package will be `tinytable` #>   instead of `kableExtra`. All currently supported table-drawing packages #>   will continue to be supported for the foreseeable future, including #>   `kableExtra`, `gt`, `huxtable`, `flextable, and `DT`. #>    #>   You can always call the `config_modelsummary()` function to change the #>   default table-drawing package in persistent fashion. To try `tinytable` #>   now: #>    #>   config_modelsummary(factory_default = 'tinytable') #>    #>   To set the default back to `kableExtra`: #>    #>   config_modelsummary(factory_default = 'kableExtra')  # Quick renaming function to replace \".Dtreat\" with something more meaningful rename_fn = function(old_names) {   new_names = gsub(\".Dtreat\", \"Years post treatment =\", old_names)   setNames(new_names, old_names) }  modelsummary(   mod_es,   shape       = term:event:statistic ~ model,   coef_rename = rename_fn,   gof_omit    = \"Adj|Within|IC|RMSE\",   title       = \"Event study\",   notes       = \"Std. errors are clustered at the county level\" ) library(ggplot2) theme_set(   theme_minimal() + theme(panel.grid.minor = element_blank()) )  ggplot(mod_es, aes(x = event, y = estimate, ymin = conf.low, ymax = conf.high)) +   geom_hline(yintercept = 0) +   geom_pointrange(col = \"darkcyan\") +   labs(x = \"Years post treatment\", y = \"Effect on log teen employment\") # Use post_only = FALSE to get the \"zero\" pre-treatment effects mod_es2 = emfx(mod, type = \"event\", post_only = FALSE)  ggplot(mod_es2, aes(x = event, y = estimate, ymin = conf.low, ymax = conf.high)) +   geom_hline(yintercept = 0) +   geom_vline(xintercept = -1, lty = 2) +   geom_pointrange(col = \"darkcyan\") +   labs(     x = \"Years post treatment\", y = \"Effect on log teen employment\",     caption = \"Note: Zero pre-treatment effects for illustrative purposes only.\"   ) #> Warning: Removed 4 rows containing missing values (`geom_segment()`)."},{"path":"http://grantmcdermott.com/etwfe/articles/etwfe.html","id":"heterogeneous-treatment-effects","dir":"Articles","previous_headings":"","what":"Heterogeneous treatment effects","title":"Introduction to etwfe","text":"far ’ve limited homogeneous treatment effects, impact treatment (.e., minimum wage hike) averaged across US counties dataset. However, many research problems require us estimate treatment effects separately across groups , potentially, test differences . example, might want test whether efficacy new vaccine differs across age groups, whether marketing campaign equally successful across genders. ETWFE framework naturally lends kinds heterogeneous treatment effects. Consider following example, first create logical dummy variable US counties eight Great Lake states (GLS). Now imagine interested estimating separate treatment effects GLS versus non-GLS counties. simply invoking optional xvar argument part etwfe() call.3 subsequent emfx() call object automatically recognize want recover treatment effects two distinct groups. point estimates might tempt us think minimum wage hikes caused less teen disemployment GLS counties rest US average. However, test formally can invoke powerful hypothesis infrastructure underlying marginaleffects package. Probably easiest way using b[]-style positional arguments, “[]” denotes row emfx() return object. Thus, specifying hypothesis = \"b1 = b2\", can test whether ATTs row 1 (non-GLS) row 2 (GLS) different one another. see actually statistical difference average disemployment effect GLS non-GLS counties. One final aside can easily display results heterogeneous treatment effects plot table form. ’s example latter, make use modelsummary(..., shape = ...) argument. Comparing ATT GLS non-GLS counties simple example limited binary comparison group ATTs, note logic carries richer settings. can use exact workflow estimate heterogeneous treatment effects different aggregations (e.g., event studies) across groups many levels.","code":"gls_fips = c(\"IL\" = 17, \"IN\" = 18, \"MI\" = 26, \"MN\" = 27,              \"NY\" = 36, \"OH\" = 39, \"PA\" = 42, \"WI\" = 55)  mpdta$gls = substr(mpdta$countyreal, 1, 2) %in% gls_fips hmod = etwfe(    lemp ~ lpop, tvar = year, gvar = first.treat, data = mpdta,     vcov = ~countyreal,    xvar = gls           ## <= het. TEs by gls    )  # Heterogeneous ATTs (could also specify `type = \"event\"`, etc.)  emfx(hmod) #>  #>     Term                 Contrast .Dtreat   gls Estimate Std. Error     z #>  .Dtreat mean(TRUE) - mean(FALSE)    TRUE FALSE  -0.0637     0.0376 -1.69 #>  .Dtreat mean(TRUE) - mean(FALSE)    TRUE  TRUE  -0.0472     0.0271 -1.74 #>  Pr(>|z|)   S  2.5 %  97.5 % #>    0.0906 3.5 -0.137 0.01007 #>    0.0817 3.6 -0.100 0.00594 #>  #> Columns: term, contrast, .Dtreat, gls, estimate, std.error, statistic, p.value, s.value, conf.low, conf.high, predicted_lo, predicted_hi, predicted  #> Type:  response emfx(hmod, hypothesis = \"b1 = b2\") #>  #>   Term Estimate Std. Error      z Pr(>|z|)   S  2.5 % 97.5 % #>  b1=b2  -0.0164     0.0559 -0.294    0.769 0.4 -0.126  0.093 #>  #> Columns: term, estimate, std.error, statistic, p.value, s.value, conf.low, conf.high  #> Type:  response modelsummary(     models      = list(\"GLS county\" = emfx(hmod)),     shape       = term + statistic ~ model + gls, # add xvar variable (here: gls)     coef_map    = c(\".Dtreat\" = \"ATT\"),     gof_map     = NA,     title       = \"Comparing the ATT on GLS and non-GLS counties\" )"},{"path":"http://grantmcdermott.com/etwfe/articles/etwfe.html","id":"other-families","dir":"Articles","previous_headings":"","what":"Other families","title":"Introduction to etwfe","text":"Another key feature ETWFE approach—one sets apart advanced implementations extensions—supports nonlinear model (distribution / link) families. Users need simply invoke family argument. ’s brief example, recast earlier event-study Poisson regression.","code":"mpdta$emp = exp(mpdta$lemp)  etwfe(   emp ~ lpop, tvar = year, gvar = first.treat, data = mpdta, vcov = ~countyreal,   family = \"poisson\"   ) |>   emfx(\"event\") #>  #>     Term                 Contrast event Estimate Std. Error       z Pr(>|z|) #>  .Dtreat mean(TRUE) - mean(FALSE)     0   -25.35       15.9 -1.5942    0.111 #>  .Dtreat mean(TRUE) - mean(FALSE)     1     1.09       41.8  0.0261    0.979 #>  .Dtreat mean(TRUE) - mean(FALSE)     2   -75.12       22.3 -3.3696   <0.001 #>  .Dtreat mean(TRUE) - mean(FALSE)     3  -101.82       28.1 -3.6234   <0.001 #>     S  2.5 % 97.5 % #>   3.2  -56.5   5.82 #>   0.0  -80.9  83.09 #>  10.4 -118.8 -31.43 #>  11.7 -156.9 -46.75 #>  #> Columns: term, contrast, event, estimate, std.error, statistic, p.value, s.value, conf.low, conf.high, predicted_lo, predicted_hi, predicted  #> Type:  response"},{"path":"http://grantmcdermott.com/etwfe/articles/etwfe.html","id":"performance-tips","dir":"Articles","previous_headings":"","what":"Performance tips","title":"Introduction to etwfe","text":"Thinking etwfe workflow pair consecutive functional calls, first etwfe() stage tends fast. ’re leveraging incredible performance fixest also taking shortcuts avoid wasting time nuisance parameters. See Regarding fixed effects section details . part, second emfx() stage also tends pretty performant. data less 100k rows, ’s unlikely ’ll wait seconds obtain results. However, emfx’s computation time tend scale non-linearly size original data, well number interactions underlying etwfe model object. Without getting deep weeds, relying numerical delta method (excellent) marginaleffects package underneath hood recover ATTs interest. method requires estimating two prediction models coefficient model computing standard errors. ’s potentially expensive operation can push computation time large datasets (> 1m rows) several minutes longer. Fortunately, two complementary strategies can use speed things . first turn expensive part whole procedure—standard error calculation—calling emfx(..., vcov = FALSE). bring estimation time back seconds less, even datasets excess million rows. course, loss standard errors might acceptable trade-projects statistical inference critical. good news first strategy can still combined second strategy: turns collapsing data groups prior estimating marginal effects can yield substantial speed gains . Users can invoking emfx(..., collapse = TRUE) argument. effect dramatic first strategy, collapsing data virtue retaining information standard errors. trade-time, however, collapsing data lead loss accuracy estimated parameters. hand, testing suggests loss accuracy tends relatively minor, results equivalent 1st 2nd significant decimal place (even better). Summarizing, quick plan attack try worried estimation time large datasets models: Estimate mod = etwfe(...) per usual. Run emfx(mod, vcov = FALSE, ...). Run emfx(mod, vcov = FALSE, collapse = TRUE, ...). Compare point estimates steps 1 2. similar enough satisfaction, get approximate standard errors running emfx(mod, collapse = TRUE, ...). ’s bit performance art, since examples vignette complete quickly anyway. reworking earlier event study example demonstrate performance-conscious workflow. put fine point , can can compare original event study collapsed estimates see results indeed similar. Event study","code":"# Step 0 already complete: using the same `mod` object from earlier...  # Step 1 emfx(mod, type = \"event\", vcov = FALSE) #>  #>     Term                 Contrast event Estimate #>  .Dtreat mean(TRUE) - mean(FALSE)     0  -0.0332 #>  .Dtreat mean(TRUE) - mean(FALSE)     1  -0.0573 #>  .Dtreat mean(TRUE) - mean(FALSE)     2  -0.1379 #>  .Dtreat mean(TRUE) - mean(FALSE)     3  -0.1095 #>  #> Columns: term, contrast, event, estimate, predicted_lo, predicted_hi, predicted  #> Type:  response  # Step 2 emfx(mod, type = \"event\", vcov = FALSE, collapse = TRUE) #>  #>     Term                 Contrast event Estimate #>  .Dtreat mean(TRUE) - mean(FALSE)     0  -0.0332 #>  .Dtreat mean(TRUE) - mean(FALSE)     1  -0.0573 #>  .Dtreat mean(TRUE) - mean(FALSE)     2  -0.1379 #>  .Dtreat mean(TRUE) - mean(FALSE)     3  -0.1095 #>  #> Columns: term, contrast, event, estimate, predicted_lo, predicted_hi, predicted  #> Type:  response  # Step 3: Results from 1 and 2 are similar enough, so get approx. SEs mod_es2 = emfx(mod, type = \"event\", collapse = TRUE) modelsummary(     list(\"Original\" = mod_es, \"Collapsed\" = mod_es2),     shape       = term:event:statistic ~ model,     coef_rename = rename_fn,     gof_omit    = \"Adj|Within|IC|RMSE\",     title       = \"Event study\",     notes       = \"Std. errors are clustered at the county level\" )"},{"path":"http://grantmcdermott.com/etwfe/articles/etwfe.html","id":"under-the-hood","dir":"Articles","previous_headings":"","what":"Under the hood","title":"Introduction to etwfe","text":"Now ’ve seen etwfe action, let’s circle back package hood. section isn’t necessary use package; feel free skip . review internal details help optimize different scenarios also give better understanding etwfe’s default choices.","code":""},{"path":"http://grantmcdermott.com/etwfe/articles/etwfe.html","id":"manual-implementation","dir":"Articles","previous_headings":"Under the hood","what":"Manual implementation","title":"Introduction to etwfe","text":"keep reiterating, ETWFE approach basically involves saturating regression interaction effects. can easily grab formula estimated model see . point, however, may notice things. first formula references several variables aren’t original dataset. obvious one .Dtreat treatment dummy. subtle one lpop_dm, demeaned (.e., group-centered) version lpop control variable. control variables demeaned interacted ETWFE setting. ’s constructed dataset ahead time estimated ETWFE regression manually: can confirm manual approach yields output original etwfe regression. ’ll use modelsummary , since ’ve already loaded .4. transform raw coefficients meaningful ATT counterparts, just need perform appropriate marginal effects operation. example, ’s can get simple ATTs event-study ATTs earlier. emfx() behind scenes.","code":"mod$fml_all #> $linear #> lemp ~ .Dtreat:i(first.treat, i.year, ref = 0, ref2 = 2003)/lpop_dm #> <environment: 0x5636feeb12f8> #>  #> $fixef #> ~first.treat + first.treat[[lpop]] + year + year[[lpop]] # First construct the dataset mpdta2 = mpdta |>   transform(     .Dtreat = year >= first.treat & first.treat != 0,     lpop_dm = ave(lpop, first.treat, year, FUN = \\(x) x - mean(x, na.rm = TRUE))   )  # Then estimate the manual version of etwfe mod2 = fixest::feols(   lemp ~ .Dtreat:i(first.treat, i.year, ref = 0, ref2 = 2003) / lpop_dm |     first.treat[lpop] + year[lpop],   data = mpdta2,   vcov = ~countyreal ) modelsummary(   list(\"etwfe\" = mod, \"manual\" = mod2),   gof_map = NA # drop all goodness-of-fit info for brevity ) library(marginaleffects)  # Simple ATT slopes(   mod2,    newdata   = subset(mpdta2, .Dtreat), # we only want rows where .Dtreat is TRUE   variables = \".Dtreat\",    by        = \".Dtreat\"   ) #>  #>     Term                 Contrast .Dtreat Estimate Std. Error     z Pr(>|z|) #>  .Dtreat mean(TRUE) - mean(FALSE)    TRUE  -0.0506     0.0125 -4.05   <0.001 #>     S   2.5 %  97.5 % #>  14.3 -0.0751 -0.0261 #>  #> Columns: term, contrast, .Dtreat, estimate, std.error, statistic, p.value, s.value, conf.low, conf.high, predicted_lo, predicted_hi, predicted  #> Type:  response  # Event study slopes(   mod2,    newdata   = transform(subset(mpdta2, .Dtreat), event = year - first.treat),   variables = \".Dtreat\",    by        = \"event\"   ) #>  #>     Term                 Contrast event Estimate Std. Error     z Pr(>|z|)    S #>  .Dtreat mean(TRUE) - mean(FALSE)     0  -0.0332     0.0134 -2.48    0.013  6.3 #>  .Dtreat mean(TRUE) - mean(FALSE)     1  -0.0573     0.0172 -3.34   <0.001 10.2 #>  .Dtreat mean(TRUE) - mean(FALSE)     2  -0.1379     0.0308 -4.48   <0.001 17.0 #>  .Dtreat mean(TRUE) - mean(FALSE)     3  -0.1095     0.0323 -3.39   <0.001 10.5 #>    2.5 %   97.5 % #>  -0.0594 -0.00701 #>  -0.0910 -0.02373 #>  -0.1982 -0.07751 #>  -0.1729 -0.04619 #>  #> Columns: term, contrast, event, estimate, std.error, statistic, p.value, s.value, conf.low, conf.high, predicted_lo, predicted_hi, predicted  #> Type:  response"},{"path":"http://grantmcdermott.com/etwfe/articles/etwfe.html","id":"regarding-fixed-effects","dir":"Articles","previous_headings":"Under the hood","what":"Regarding fixed effects","title":"Introduction to etwfe","text":"Let’s switch gears talk fixed effects quickly. regular fixest user, may noticed ’ve invoking varying slopes syntax fixed effect slot (.e., first.treat[lpop] year[lpop]). reason part practical, part philosophical. practical perspective, factor_var[numeric_var] equivalent base R’s factor_var/numeric_var “nesting” syntax much faster high-dimensional factors.5 philosophical perspective, etwfe tries limit amount extraneous information reports users. interaction effects ETWFE framework just acting controls. relegating fixed effects slot, can avoid polluting user’s console host extra coefficients. Nonetheless, can control behaviour fe (“fixed effects”) argument. Consider following options manual equivalents. ’ll leave pass models emfx confirm give correct aggregated treatment effects. can quickly demonstrate regression table return raw coefficients. final point note fixed effects etwfe defaults using group-level (.e., cohort-level) fixed effects like first.treat, rather unit-level fixed effects like countyreal. design decision reflects neat ancillary result Wooldridge (2021), proves equivalence two types fixed effects linear cases. Group-level effects virtue faster estimate, since fewer factor levels. Moreover, required nonlinear model families like Poisson per underlying ETWFE theory. Still, can specify unit-level fixed effects linear case ivar argument. , can easily confirm yields estimated treatment effects group-level default (although standard errors slightly different).","code":"# fe = \"feo\" (fixed effects only) mod_feo = etwfe(   lemp ~ lpop, tvar = year, gvar = first.treat, data = mpdta, vcov = ~countyreal,   fe = \"feo\" ) # ... which is equivalent to the manual regression mod_feo2 = fixest::feols(   lemp ~ .Dtreat:i(first.treat, i.year, ref = 0, ref2 = 2003) / lpop_dm +     lpop + i(first.treat, lpop, ref = 0) + i(year, lpop, ref = 2003) |     first.treat + year,   data = mpdta2, vcov = ~countyreal )  # fe = \"none\" mod_none = etwfe(   lemp ~ lpop, tvar = year, gvar = first.treat, data = mpdta, vcov = ~countyreal,   fe = \"none\" ) # ... which is equivalent to the manual regression mod_none2 = fixest::feols(   lemp ~ .Dtreat:i(first.treat, i.year, ref = 0, ref2 = 2003) / lpop_dm +     lpop + i(first.treat, lpop, ref = 0) + i(year, lpop, ref = 2003) +     i(first.treat, ref = 0) + i(year, ref = 2003),   data = mpdta2, vcov = ~countyreal ) mods = list(   \"etwfe\"         = mod,   \"manual\"        = mod2,   \"etwfe (feo)\"   = mod_feo,   \"manual (feo)\"  = mod_feo2,   \"etwfe (none)\"  = mod_none,   \"manual (none)\" = mod_none2 )  modelsummary(mods, gof_map = NA) mod_es_i = etwfe(   lemp ~ lpop, tvar = year, gvar = first.treat, data = mpdta,   ivar = countyreal  # NEW: Use unit-level (county) FEs   ) |>   emfx(\"event\")  modelsummary(   list(\"Group-level FEs (default)\" = mod_es, \"Unit-level FEs\" = mod_es_i),   shape       = term:event:statistic ~ model,   coef_rename = rename_fn,   gof_omit    = \"Adj|Within|IC|RMSE\" )"},{"path":"http://grantmcdermott.com/etwfe/authors.html","id":null,"dir":"","previous_headings":"","what":"Authors","title":"Authors and Citation","text":"Grant McDermott. Author, maintainer. Frederic Kluser. Contributor.","code":""},{"path":"http://grantmcdermott.com/etwfe/authors.html","id":"citation","dir":"","previous_headings":"","what":"Citation","title":"Authors and Citation","text":"McDermott G (2024). etwfe: Extended Two-Way Fixed Effects. R package version 0.3.5.9002, https://grantmcdermott.com/etwfe/.","code":"@Manual{,   title = {etwfe: Extended Two-Way Fixed Effects},   author = {Grant McDermott},   year = {2024},   note = {R package version 0.3.5.9002},   url = {https://grantmcdermott.com/etwfe/}, }"},{"path":"http://grantmcdermott.com/etwfe/index.html","id":"extended-two-way-fixed-effects-etwfe","dir":"","previous_headings":"","what":"Extended Two-Way Fixed Effects","title":"Extended Two-Way Fixed Effects","text":"goal etwfe estimate extended two-way fixed effects la Wooldridge (2021, 2022). Briefly, Wooldridge proposes set saturated interaction effects overcome potential bias problems vanilla TWFE difference--differences designs. Wooldridge solution intuitive elegant, rather tedious error prone code manually. etwfe package aims simplify process providing convenience functions work . Documentation available package homepage.","code":""},{"path":"http://grantmcdermott.com/etwfe/index.html","id":"installation","dir":"","previous_headings":"","what":"Installation","title":"Extended Two-Way Fixed Effects","text":"can install etwfe CRAN. , can grab development version R-universe.","code":"install.packages(\"etwfe\") install.packages(\"etwfe\", repos = \"https://grantmcdermott.r-universe.dev\")"},{"path":"http://grantmcdermott.com/etwfe/index.html","id":"quickstart-example","dir":"","previous_headings":"","what":"Quickstart example","title":"Extended Two-Way Fixed Effects","text":"detailed walkthrough etwfe provided introductory vignette (available online, typing vignette(\"etwfe\") R console). ’s quickstart example demonstrate basic syntax.","code":"library(etwfe)  # install.packages(\"did\") data(\"mpdta\", package = \"did\") head(mpdta) #>     year countyreal     lpop     lemp first.treat treat #> 866 2003       8001 5.896761 8.461469        2007     1 #> 841 2004       8001 5.896761 8.336870        2007     1 #> 842 2005       8001 5.896761 8.340217        2007     1 #> 819 2006       8001 5.896761 8.378161        2007     1 #> 827 2007       8001 5.896761 8.487352        2007     1 #> 937 2003       8019 2.232377 4.997212        2007     1  # Estimate the model mod =   etwfe(     fml  = lemp ~ lpop, # outcome ~ controls     tvar = year,        # time variable     gvar = first.treat, # group variable     data = mpdta,       # dataset     vcov = ~countyreal  # vcov adjustment (here: clustered)     )  # This gives us a regression model with fully saturated interactions mod #> OLS estimation, Dep. Var.: lemp #> Observations: 2,500  #> Fixed-effects: first.treat: 4,  year: 5 #> Varying slopes: lpop (first.treat: 4),  lpop (year: 5) #> Standard-errors: Clustered (countyreal)  #>                                               Estimate Std. Error   t value   Pr(>|t|)     #> .Dtreat:first.treat::2004:year::2004         -0.021248   0.021728 -0.977890 3.2860e-01     #> .Dtreat:first.treat::2004:year::2005         -0.081850   0.027375 -2.989963 2.9279e-03 **  #> .Dtreat:first.treat::2004:year::2006         -0.137870   0.030795 -4.477097 9.3851e-06 *** #> .Dtreat:first.treat::2004:year::2007         -0.109539   0.032322 -3.389024 7.5694e-04 *** #> .Dtreat:first.treat::2006:year::2006          0.002537   0.018883  0.134344 8.9318e-01     #> .Dtreat:first.treat::2006:year::2007         -0.045093   0.021987 -2.050907 4.0798e-02 *   #> .Dtreat:first.treat::2007:year::2007         -0.045955   0.017975 -2.556568 1.0866e-02 *   #> .Dtreat:first.treat::2004:year::2004:lpop_dm  0.004628   0.017584  0.263184 7.9252e-01     #> .Dtreat:first.treat::2004:year::2005:lpop_dm  0.025113   0.017904  1.402661 1.6134e-01     #> .Dtreat:first.treat::2004:year::2006:lpop_dm  0.050735   0.021070  2.407884 1.6407e-02 *   #> .Dtreat:first.treat::2004:year::2007:lpop_dm  0.011250   0.026617  0.422648 6.7273e-01     #> .Dtreat:first.treat::2006:year::2006:lpop_dm  0.038935   0.016472  2.363731 1.8474e-02 *   #> .Dtreat:first.treat::2006:year::2007:lpop_dm  0.038060   0.022477  1.693276 9.1027e-02 .   #> .Dtreat:first.treat::2007:year::2007:lpop_dm -0.019835   0.016198 -1.224528 2.2133e-01     #> ... 10 variables were removed because of collinearity (.Dtreat:first.treat::2006:year::2004, .Dtreat:first.treat::2006:year::2005 and 8 others [full set in $collin.var]) #> --- #> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 #> RMSE: 0.537131     Adj. R2: 0.87167  #>                  Within R2: 8.449e-4  # Pass to emfx() to recover the ATTs of interest. Here's an event-study example. emfx(mod, type = \"event\") #>  #>     Term                 Contrast event Estimate Std. Error     z Pr(>|z|)    S   2.5 %   97.5 % #>  .Dtreat mean(TRUE) - mean(FALSE)     0  -0.0332     0.0134 -2.48    0.013  6.3 -0.0594 -0.00701 #>  .Dtreat mean(TRUE) - mean(FALSE)     1  -0.0573     0.0172 -3.34   <0.001 10.2 -0.0910 -0.02373 #>  .Dtreat mean(TRUE) - mean(FALSE)     2  -0.1379     0.0308 -4.48   <0.001 17.0 -0.1982 -0.07751 #>  .Dtreat mean(TRUE) - mean(FALSE)     3  -0.1095     0.0323 -3.39   <0.001 10.5 -0.1729 -0.04619 #>  #> Columns: term, contrast, event, estimate, std.error, statistic, p.value, s.value, conf.low, conf.high, predicted_lo, predicted_hi, predicted  #> Type:  response"},{"path":"http://grantmcdermott.com/etwfe/index.html","id":"acknowledgements","dir":"","previous_headings":"","what":"Acknowledgements","title":"Extended Two-Way Fixed Effects","text":"Jeffrey Wooldridge underlying ETWFE theory. Laurent Bergé (fixest) Vincent Arel-Bundock (marginaleffects) maintaining two wonderful R packages heavy lifting hood . Fernando Rios-Avila JWDID Stata module, provided welcome foil unit testing whose elegant design helped inform choices R equivalent.","code":""},{"path":"http://grantmcdermott.com/etwfe/reference/emfx.html","id":null,"dir":"Reference","previous_headings":"","what":"Post-estimation treatment effects for an ETWFE regressions. — emfx","title":"Post-estimation treatment effects for an ETWFE regressions. — emfx","text":"Post-estimation treatment effects ETWFE regressions.","code":""},{"path":"http://grantmcdermott.com/etwfe/reference/emfx.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Post-estimation treatment effects for an ETWFE regressions. — emfx","text":"","code":"emfx(   object,   type = c(\"simple\", \"group\", \"calendar\", \"event\"),   by_xvar = \"auto\",   collapse = \"auto\",   post_only = TRUE,   ... )"},{"path":"http://grantmcdermott.com/etwfe/reference/emfx.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Post-estimation treatment effects for an ETWFE regressions. — emfx","text":"object etwfe model object. type Character. desired type post-estimation aggregation. by_xvar Logical. results account heterogeneous treatment effects? relevant preceding etwfe call included specified xvar argument, .e. interacted categorical covariate. default behaviour (\"auto\") automatically estimate heterogeneous treatment effects level xvar detected part underlying etwfe model object. Users can override setting either FALSE TRUE. See section Heterogeneous treatment effects . collapse Logical. Collapse data (period cohort) groups calculating marginal effects? trades loss estimate accuracy (typically around 1st 2nd significant decimal point) substantial improvement estimation time large datasets. default behaviour (\"auto\") automatically collapse original dataset 500,000 rows. Users can override setting either FALSE TRUE. Note collapsing group valid preceding etwfe call run \"ivar = NULL\" (default). See section Performance tips . post_only Logical. Drop pre-treatment ATTs? evaluated () type = \"event\" (b) original etwfe model object estimated using default \"notyet\" treated control group. conditions () (b) met pre-treatment effects zero mechanical result ETWFE's estimation setup. default behaviour (FALSE) thus drop nuisance rows dataset. post_only argument recognises may still want keep presentation purposes (e.g., plotting event-study). Nevertheless, forewarned enabling behaviour via TRUE strictly performative: \"zero\" treatment effects pre-treatment periods purely artefact estimation setup. ... Additional arguments passed marginaleffects::slopes. example, can pass vcov = FALSE dramatically speed estimation times main marginal effects (cost getting information standard errors; see Performance tips ). Another potentially useful application testing whether heterogeneous treatment effects (.e. levels xvar covariate) equal invoking hypothesis argument, e.g. hypothesis = \"b1 = b2\".","code":""},{"path":"http://grantmcdermott.com/etwfe/reference/emfx.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Post-estimation treatment effects for an ETWFE regressions. — emfx","text":"slopes object marginaleffects package.","code":""},{"path":"http://grantmcdermott.com/etwfe/reference/emfx.html","id":"performance-tips","dir":"Reference","previous_headings":"","what":"Performance tips","title":"Post-estimation treatment effects for an ETWFE regressions. — emfx","text":"situations, etwfe complete quickly. part, emfx quite performant take seconds less datasets 100k rows. However, emfx's computation time tend scale non-linearly size original data, well number interactions underlying etwfe model. Without getting deep weeds, numerical delta method used recover ATEs interest estimate two prediction models coefficient model compute standard errors. , potentially expensive operation can push computation time large datasets (> 1m rows) several minutes longer. Fortunately, two complementary strategies can use speed things . first turn expensive part whole procedure---standard error calculation---calling emfx(..., vcov = FALSE). bring estimation time back seconds less, even datasets excess million rows. loss standard errors might acceptable trade-projects statistical inference critical, good news first strategy can still combined second strategy. turns collapsing data groups prior estimating marginal effects can yield substantial speed gains . Users can invoking emfx(..., collapse = TRUE) argument. effect dramatic first strategy, second strategy virtue retaining information standard errors. trade-time, however, collapsing data lead loss accuracy estimated parameters. hand, testing suggests loss accuracy tends relatively minor, results equivalent 1st 2nd significant decimal place (even better). Summarizing, quick plan attack try worried estimation time large datasets models: Estimate mod = etwfe(...) per usual. Run emfx(mod, vcov = FALSE, ...). Run emfx(mod, vcov = FALSE, collapse = TRUE, ...). Compare point estimates steps 1 2. similar enough satisfaction, get approximate standard errors running emfx(mod, collapse = TRUE, ...).","code":""},{"path":"http://grantmcdermott.com/etwfe/reference/emfx.html","id":"heterogeneous-treatment-effects","dir":"Reference","previous_headings":"","what":"Heterogeneous treatment effects","title":"Post-estimation treatment effects for an ETWFE regressions. — emfx","text":"Specifying etwfe(..., xvar = <xvar>) generate interaction effects levels <xvar> part main regression model. reason useful (opposed regular, non-interacted covariate formula RHS) allows us estimate heterogeneous treatment effects part larger ETWFE framework. Specifically, can recover heterogeneous treatment effects level <xvar> passing resulting etwfe model object emfx(). example, imagine categorical variable called \"age\" dataset, two distinct levels \"adult\" \"child\". Running emfx(etwfe(..., xvar = age)) tell us efficacy treatment varies across adults children. can also leverage -built hypothesis testing infrastructure marginaleffects test whether treatment effect statistically different across two age groups; see Examples . Note principles carry categorical variables multiple levels, even continuous variables (although continuous variables well supported yet).","code":""},{"path":[]},{"path":"http://grantmcdermott.com/etwfe/reference/emfx.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Post-estimation treatment effects for an ETWFE regressions. — emfx","text":"","code":"# \\dontrun{ # We’ll use the mpdta dataset from the did package (which you’ll need to  # install separately).  # install.packages(\"did\") data(\"mpdta\", package = \"did\")  # # Basic example #  # The basic ETWFE workflow involves two steps:  # 1) Estimate the main regression model with etwfe().  mod = etwfe(     fml  = lemp ~ lpop, # outcome ~ controls (use 0 or 1 if none)     tvar = year,        # time variable     gvar = first.treat, # group variable     data = mpdta,       # dataset     vcov = ~countyreal  # vcov adjustment (here: clustered by county)     )  # mod ## A fixest model object with fully saturated interaction effects.  # 2) Recover the treatment effects of interest with emfx().  emfx(mod, type = \"event\") # dynamic ATE a la an event study #>  #>     Term                 Contrast event Estimate Std. Error     z Pr(>|z|)    S #>  .Dtreat mean(TRUE) - mean(FALSE)     0  -0.0332     0.0134 -2.48    0.013  6.3 #>  .Dtreat mean(TRUE) - mean(FALSE)     1  -0.0573     0.0172 -3.34   <0.001 10.2 #>  .Dtreat mean(TRUE) - mean(FALSE)     2  -0.1379     0.0308 -4.48   <0.001 17.0 #>  .Dtreat mean(TRUE) - mean(FALSE)     3  -0.1095     0.0323 -3.39   <0.001 10.5 #>    2.5 %   97.5 % #>  -0.0594 -0.00701 #>  -0.0910 -0.02373 #>  -0.1982 -0.07751 #>  -0.1729 -0.04619 #>  #> Columns: term, contrast, event, estimate, std.error, statistic, p.value, s.value, conf.low, conf.high, predicted_lo, predicted_hi, predicted  #> Type:  response  #>   # Etc. Other aggregation type options are \"simple\" (the default), \"group\" # and \"calendar\"   # # Heterogeneous treatment effects #  # Example where we estimate heterogeneous treatment effects for counties  # within the 8 US Great Lake states (versus all other counties).   gls = c(\"IL\" = 17, \"IN\" = 18, \"MI\" = 26, \"MN\" = 27,         \"NY\" = 36, \"OH\" = 39, \"PA\" = 42, \"WI\" = 55)  mpdta$gls = substr(mpdta$countyreal, 1, 2) %in% gls  hmod = etwfe(    lemp ~ lpop, tvar = year, gvar = first.treat, data = mpdta,     vcov = ~countyreal,    xvar = gls           ## <= het. TEs by gls    )  # Heterogeneous ATEs (could also specify \"event\", etc.)   emfx(hmod) #>  #>     Term                 Contrast .Dtreat   gls Estimate Std. Error     z #>  .Dtreat mean(TRUE) - mean(FALSE)    TRUE FALSE  -0.0637     0.0376 -1.69 #>  .Dtreat mean(TRUE) - mean(FALSE)    TRUE  TRUE  -0.0472     0.0271 -1.74 #>  Pr(>|z|)   S  2.5 %  97.5 % #>    0.0906 3.5 -0.137 0.01007 #>    0.0817 3.6 -0.100 0.00594 #>  #> Columns: term, contrast, .Dtreat, gls, estimate, std.error, statistic, p.value, s.value, conf.low, conf.high, predicted_lo, predicted_hi, predicted  #> Type:  response  #>   # To test whether the ATEs across these two groups (non-GLS vs GLS) are  # statistically different, simply pass an appropriate \"hypothesis\" argument.  emfx(hmod, hypothesis = \"b1 = b2\") #>  #>   Term Estimate Std. Error      z Pr(>|z|)   S  2.5 % 97.5 % #>  b1=b2  -0.0164     0.0559 -0.294    0.769 0.4 -0.126  0.093 #>  #> Columns: term, estimate, std.error, statistic, p.value, s.value, conf.low, conf.high  #> Type:  response  #>    # # Nonlinear model (distribution / link) families #  # Poisson example  mpdta$emp = exp(mpdta$lemp)  etwfe(    emp ~ lpop, tvar = year, gvar = first.treat, data = mpdta,     vcov = ~countyreal,    family = \"poisson\"   ## <= family arg for nonlinear options    ) |>    emfx(\"event\") #> The variables '.Dtreat:first.treat::2006:year::2004', '.Dtreat:first.treat::2006:year::2005' and eight others have been removed because of collinearity (see $collin.var). #>  #>     Term                 Contrast event Estimate Std. Error       z Pr(>|z|) #>  .Dtreat mean(TRUE) - mean(FALSE)     0   -25.35       15.9 -1.5942    0.111 #>  .Dtreat mean(TRUE) - mean(FALSE)     1     1.09       41.8  0.0261    0.979 #>  .Dtreat mean(TRUE) - mean(FALSE)     2   -75.12       22.3 -3.3696   <0.001 #>  .Dtreat mean(TRUE) - mean(FALSE)     3  -101.82       28.1 -3.6234   <0.001 #>     S  2.5 % 97.5 % #>   3.2  -56.5   5.82 #>   0.0  -80.9  83.09 #>  10.4 -118.8 -31.43 #>  11.7 -156.9 -46.75 #>  #> Columns: term, contrast, event, estimate, std.error, statistic, p.value, s.value, conf.low, conf.high, predicted_lo, predicted_hi, predicted  #> Type:  response  #>  # }"},{"path":"http://grantmcdermott.com/etwfe/reference/etwfe.html","id":null,"dir":"Reference","previous_headings":"","what":"Extended two-way fixed effects — etwfe","title":"Extended two-way fixed effects — etwfe","text":"Extended two-way fixed effects","code":""},{"path":"http://grantmcdermott.com/etwfe/reference/etwfe.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Extended two-way fixed effects — etwfe","text":"","code":"etwfe(   fml = NULL,   tvar = NULL,   gvar = NULL,   data = NULL,   ivar = NULL,   xvar = NULL,   tref = NULL,   gref = NULL,   cgroup = c(\"notyet\", \"never\"),   fe = c(\"vs\", \"feo\", \"none\"),   family = NULL,   ... )"},{"path":"http://grantmcdermott.com/etwfe/reference/etwfe.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Extended two-way fixed effects — etwfe","text":"fml two-side formula representing outcome (lhs) control variables (rhs), e.g. y ~ x1 + x2. controls required, rhs must take value 0 1, e.g. y ~ 0. tvar Time variable. Can string (e.g., \"year\") expression (e.g., year). gvar Group variable. Can either string (e.g., \"first_treated\") expression (e.g., first_treated). staggered treatment setting, group variable typically denotes treatment cohort. data data frame want run ETWFE . ivar Optional index variable. Can string (e.g., \"country\") expression (e.g., country). Leaving NULL (default) result group-level fixed effects used, efficient necessary nonlinear models (see family argument ). However, may still want cluster standard errors index variable vcov argument. See Examples . xvar Optional interacted categorical covariate estimating heterogeneous treatment effects. Enables recovery marginal treatment effect distinct levels xvar, e.g. \"child\", \"teenager\", \"adult\". Note \"x\" prefix \"xvar\" represents covariate interacted treatment, opposed regular control variable. tref Optional reference value tvar. Defaults minimum value (.e., first time period observed dataset). gref Optional reference value gvar. need provide gvar variable well specified. providing explicit reference value can useful/necessary desired control group takes unusual value. cgroup control group wish use estimating treatment effects. Either \"notyet\" treated (default) \"never\" treated. fe level fixed effects used? Defaults \"vs\" (varying slopes), efficient terms estimation terseness return model object. two options, \"feo\" (fixed effects ) \"none\" (fixed effects whatsoever), trade efficiency additional information (nuisance) model parameters. Note primary treatment parameters interest remain unchanged regardless choice. family family use estimation. Defaults NULL, case fixest::feols used. Otherwise passed fixest::feglm, valid entries include \"logit\", \"poisson\", \"negbin\". Note non-NULL family entry detected, ivar automatically set NULL. ... Additional arguments passed fixest::feols (fixest::feglm). common example vcov argument.","code":""},{"path":"http://grantmcdermott.com/etwfe/reference/etwfe.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Extended two-way fixed effects — etwfe","text":"fixest object fully saturated interaction effects.","code":""},{"path":"http://grantmcdermott.com/etwfe/reference/etwfe.html","id":"heterogeneous-treatment-effects","dir":"Reference","previous_headings":"","what":"Heterogeneous treatment effects","title":"Extended two-way fixed effects — etwfe","text":"Specifying etwfe(..., xvar = <xvar>) generate interaction effects levels <xvar> part main regression model. reason useful (opposed regular, non-interacted covariate formula RHS) allows us estimate heterogeneous treatment effects part larger ETWFE framework. Specifically, can recover heterogeneous treatment effects level <xvar> passing resulting etwfe model object emfx(). example, imagine categorical variable called \"age\" dataset, two distinct levels \"adult\" \"child\". Running emfx(etwfe(..., xvar = age)) tell us efficacy treatment varies across adults children. can also leverage -built hypothesis testing infrastructure marginaleffects test whether treatment effect statistically different across two age groups; see Examples . Note principles carry categorical variables multiple levels, even continuous variables (although continuous variables well supported yet).","code":""},{"path":"http://grantmcdermott.com/etwfe/reference/etwfe.html","id":"performance-tips","dir":"Reference","previous_headings":"","what":"Performance tips","title":"Extended two-way fixed effects — etwfe","text":"situations, etwfe complete quickly. part, emfx quite performant take seconds less datasets 100k rows. However, emfx's computation time tend scale non-linearly size original data, well number interactions underlying etwfe model. Without getting deep weeds, numerical delta method used recover ATEs interest estimate two prediction models coefficient model compute standard errors. , potentially expensive operation can push computation time large datasets (> 1m rows) several minutes longer. Fortunately, two complementary strategies can use speed things . first turn expensive part whole procedure---standard error calculation---calling emfx(..., vcov = FALSE). bring estimation time back seconds less, even datasets excess million rows. loss standard errors might acceptable trade-projects statistical inference critical, good news first strategy can still combined second strategy. turns collapsing data groups prior estimating marginal effects can yield substantial speed gains . Users can invoking emfx(..., collapse = TRUE) argument. effect dramatic first strategy, second strategy virtue retaining information standard errors. trade-time, however, collapsing data lead loss accuracy estimated parameters. hand, testing suggests loss accuracy tends relatively minor, results equivalent 1st 2nd significant decimal place (even better). Summarizing, quick plan attack try worried estimation time large datasets models: Estimate mod = etwfe(...) per usual. Run emfx(mod, vcov = FALSE, ...). Run emfx(mod, vcov = FALSE, collapse = TRUE, ...). Compare point estimates steps 1 2. similar enough satisfaction, get approximate standard errors running emfx(mod, collapse = TRUE, ...).","code":""},{"path":"http://grantmcdermott.com/etwfe/reference/etwfe.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Extended two-way fixed effects — etwfe","text":"Wooldridge, Jeffrey M. (2021). Two-Way Fixed Effects, Two-Way Mundlak Regression, Difference--Differences Estimators. Working paper (version: August 16, 2021). Available: http://dx.doi.org/10.2139/ssrn.3906345 Wooldridge, Jeffrey M. (2022). Simple Approaches Nonlinear Difference--Differences Panel Data. Econometrics Journal (forthcoming). Available: http://dx.doi.org/10.2139/ssrn.4183726","code":""},{"path":[]},{"path":"http://grantmcdermott.com/etwfe/reference/etwfe.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Extended two-way fixed effects — etwfe","text":"","code":"# \\dontrun{ # We’ll use the mpdta dataset from the did package (which you’ll need to  # install separately).  # install.packages(\"did\") data(\"mpdta\", package = \"did\")  # # Basic example #  # The basic ETWFE workflow involves two steps:  # 1) Estimate the main regression model with etwfe().  mod = etwfe(     fml  = lemp ~ lpop, # outcome ~ controls (use 0 or 1 if none)     tvar = year,        # time variable     gvar = first.treat, # group variable     data = mpdta,       # dataset     vcov = ~countyreal  # vcov adjustment (here: clustered by county)     )  # mod ## A fixest model object with fully saturated interaction effects.  # 2) Recover the treatment effects of interest with emfx().  emfx(mod, type = \"event\") # dynamic ATE a la an event study #>  #>     Term                 Contrast event Estimate Std. Error     z Pr(>|z|)    S #>  .Dtreat mean(TRUE) - mean(FALSE)     0  -0.0332     0.0134 -2.48    0.013  6.3 #>  .Dtreat mean(TRUE) - mean(FALSE)     1  -0.0573     0.0172 -3.34   <0.001 10.2 #>  .Dtreat mean(TRUE) - mean(FALSE)     2  -0.1379     0.0308 -4.48   <0.001 17.0 #>  .Dtreat mean(TRUE) - mean(FALSE)     3  -0.1095     0.0323 -3.39   <0.001 10.5 #>    2.5 %   97.5 % #>  -0.0594 -0.00701 #>  -0.0910 -0.02373 #>  -0.1982 -0.07751 #>  -0.1729 -0.04619 #>  #> Columns: term, contrast, event, estimate, std.error, statistic, p.value, s.value, conf.low, conf.high, predicted_lo, predicted_hi, predicted  #> Type:  response  #>   # Etc. Other aggregation type options are \"simple\" (the default), \"group\" # and \"calendar\"   # # Heterogeneous treatment effects #  # Example where we estimate heterogeneous treatment effects for counties  # within the 8 US Great Lake states (versus all other counties).   gls = c(\"IL\" = 17, \"IN\" = 18, \"MI\" = 26, \"MN\" = 27,         \"NY\" = 36, \"OH\" = 39, \"PA\" = 42, \"WI\" = 55)  mpdta$gls = substr(mpdta$countyreal, 1, 2) %in% gls  hmod = etwfe(    lemp ~ lpop, tvar = year, gvar = first.treat, data = mpdta,     vcov = ~countyreal,    xvar = gls           ## <= het. TEs by gls    )  # Heterogeneous ATEs (could also specify \"event\", etc.)   emfx(hmod) #>  #>     Term                 Contrast .Dtreat   gls Estimate Std. Error     z #>  .Dtreat mean(TRUE) - mean(FALSE)    TRUE FALSE  -0.0637     0.0376 -1.69 #>  .Dtreat mean(TRUE) - mean(FALSE)    TRUE  TRUE  -0.0472     0.0271 -1.74 #>  Pr(>|z|)   S  2.5 %  97.5 % #>    0.0906 3.5 -0.137 0.01007 #>    0.0817 3.6 -0.100 0.00594 #>  #> Columns: term, contrast, .Dtreat, gls, estimate, std.error, statistic, p.value, s.value, conf.low, conf.high, predicted_lo, predicted_hi, predicted  #> Type:  response  #>   # To test whether the ATEs across these two groups (non-GLS vs GLS) are  # statistically different, simply pass an appropriate \"hypothesis\" argument.  emfx(hmod, hypothesis = \"b1 = b2\") #>  #>   Term Estimate Std. Error      z Pr(>|z|)   S  2.5 % 97.5 % #>  b1=b2  -0.0164     0.0559 -0.294    0.769 0.4 -0.126  0.093 #>  #> Columns: term, estimate, std.error, statistic, p.value, s.value, conf.low, conf.high  #> Type:  response  #>    # # Nonlinear model (distribution / link) families #  # Poisson example  mpdta$emp = exp(mpdta$lemp)  etwfe(    emp ~ lpop, tvar = year, gvar = first.treat, data = mpdta,     vcov = ~countyreal,    family = \"poisson\"   ## <= family arg for nonlinear options    ) |>    emfx(\"event\") #> The variables '.Dtreat:first.treat::2006:year::2004', '.Dtreat:first.treat::2006:year::2005' and eight others have been removed because of collinearity (see $collin.var). #>  #>     Term                 Contrast event Estimate Std. Error       z Pr(>|z|) #>  .Dtreat mean(TRUE) - mean(FALSE)     0   -25.35       15.9 -1.5942    0.111 #>  .Dtreat mean(TRUE) - mean(FALSE)     1     1.09       41.8  0.0261    0.979 #>  .Dtreat mean(TRUE) - mean(FALSE)     2   -75.12       22.3 -3.3696   <0.001 #>  .Dtreat mean(TRUE) - mean(FALSE)     3  -101.82       28.1 -3.6234   <0.001 #>     S  2.5 % 97.5 % #>   3.2  -56.5   5.82 #>   0.0  -80.9  83.09 #>  10.4 -118.8 -31.43 #>  11.7 -156.9 -46.75 #>  #> Columns: term, contrast, event, estimate, std.error, statistic, p.value, s.value, conf.low, conf.high, predicted_lo, predicted_hi, predicted  #> Type:  response  #>  # }"},{"path":[]},{"path":"http://grantmcdermott.com/etwfe/news/index.html","id":"bug-fixes-0-3-5-9002","dir":"Changelog","previous_headings":"","what":"Bug fixes","title":"etwfe 0.3.5.9002 (development version)","text":"Fix ATT calculation never-treated case (..e, cgroup = \"never) due incorrect subsetting prior recovering marginal effects. Thanks @paulofelipe reporting (#37). Avoid (possible) error user supplies reserved “group” variable formula (#41).","code":""},{"path":"http://grantmcdermott.com/etwfe/news/index.html","id":"documentation-0-3-5-9002","dir":"Changelog","previous_headings":"","what":"Documentation","title":"etwfe 0.3.5.9002 (development version)","text":"Fix missing autolinks documentation due markdown formatting (#44 @etiennebacher).","code":""},{"path":"http://grantmcdermott.com/etwfe/news/index.html","id":"etwfe-035","dir":"Changelog","previous_headings":"","what":"etwfe 0.3.5","title":"etwfe 0.3.5","text":"CRAN release: 2023-12-01","code":""},{"path":"http://grantmcdermott.com/etwfe/news/index.html","id":"internal-0-3-5","dir":"Changelog","previous_headings":"","what":"Internal","title":"etwfe 0.3.5","text":"Update tests match upstream changes fixest. Update maintainer email address.","code":""},{"path":"http://grantmcdermott.com/etwfe/news/index.html","id":"etwfe-034","dir":"Changelog","previous_headings":"","what":"etwfe 0.3.4","title":"etwfe 0.3.4","text":"CRAN release: 2023-06-19","code":""},{"path":"http://grantmcdermott.com/etwfe/news/index.html","id":"internal-0-3-4","dir":"Changelog","previous_headings":"","what":"Internal","title":"etwfe 0.3.4","text":"Update tests match upstream changes marginaleffects (#36 @vincentarelbundock).","code":""},{"path":"http://grantmcdermott.com/etwfe/news/index.html","id":"etwfe-033","dir":"Changelog","previous_headings":"","what":"etwfe 0.3.3","title":"etwfe 0.3.3","text":"CRAN release: 2023-05-27","code":""},{"path":"http://grantmcdermott.com/etwfe/news/index.html","id":"internal-0-3-3","dir":"Changelog","previous_headings":"","what":"Internal","title":"etwfe 0.3.3","text":"Rejigged internal tests following upstream changes marginaleffects (#35 @vincentarelbundock).","code":""},{"path":"http://grantmcdermott.com/etwfe/news/index.html","id":"etwfe-032","dir":"Changelog","previous_headings":"","what":"etwfe 0.3.2","title":"etwfe 0.3.2","text":"CRAN release: 2023-05-02","code":""},{"path":"http://grantmcdermott.com/etwfe/news/index.html","id":"bug-fixes-0-3-2","dir":"Changelog","previous_headings":"","what":"Bug fixes","title":"etwfe 0.3.2","text":"Fixed internal centering procedure handling multiple covariate levels (#30, #31). fixes impact main ATT estimates (.e., typical use package). may lead differences heterogeneous ATTs—.e., via xvar arg—incorrectly estimated cases. Thanks @PhilipCarthy flagging @frederickluser helpful discussions Fixed internal upstream bug causing model offsets error (#28, thanks @mariofiorini initial report several others helpful discussion). Note fix requires insight >= 0.19.1.8, development version time writing. information available : https://github.com/easystats/insight/pull/759","code":""},{"path":"http://grantmcdermott.com/etwfe/news/index.html","id":"etwfe-031","dir":"Changelog","previous_headings":"","what":"etwfe 0.3.1","title":"etwfe 0.3.1","text":"CRAN release: 2023-02-28","code":""},{"path":"http://grantmcdermott.com/etwfe/news/index.html","id":"internal-0-3-1","dir":"Changelog","previous_headings":"","what":"Internal","title":"etwfe 0.3.1","text":"Minor updates internal code unit tests match forthcoming updates marginaleffects 0.10.0. latter update also brings notable performance improvements emfx().","code":""},{"path":"http://grantmcdermott.com/etwfe/news/index.html","id":"other-0-3-1","dir":"Changelog","previous_headings":"","what":"Other","title":"etwfe 0.3.1","text":"documentation improvements. Examples wrapped \\dontrun avoid triggering CRAN NOTEs Windows exceeding 5 seconds execution time. Note package homepage still runs Examples users want inspect output online.","code":""},{"path":"http://grantmcdermott.com/etwfe/news/index.html","id":"etwfe-030","dir":"Changelog","previous_headings":"","what":"etwfe 0.3.0","title":"etwfe 0.3.0","text":"CRAN release: 2023-02-08","code":""},{"path":"http://grantmcdermott.com/etwfe/news/index.html","id":"new-features-and-enhancements-0-3-0","dir":"Changelog","previous_headings":"","what":"New features and enhancements","title":"etwfe 0.3.0","text":"Support estimating heterogeneous treatment effects via new etwfe(..., xvar = <xvar> argument (#16, thanks @frederickluser). Automatically extends emfx() via latter’s by_xvar argument (#21). details provided dedicated “Heterogeneous treatment effects” section vignette help documentation new emfx(..., collapse = TRUE) argument can substantially reduce estimation times large datasets (#19, thanks @frederickluser). performance boost trade loss estimate accuracy. testing suggests difference relatively minor typical use cases (.e., results equivalent 1st 2nd significant decimal place, sometimes even better). Please let us know find edge cases true. details available dedicated “Performance tips” section vignette help documentation, including advice combining collapsing emfx(..., vcov = FALSE) (yields even dramatic speed boost cost reporting standard errors). Users can now use 1 fml RHS indicate control variables part etwfe call, e.g. etwfe(y ~ 1, ...). provides second way indicating controls, alongside existing 0 option, e.g. etwfe(y ~ 0, ...)","code":""},{"path":"http://grantmcdermott.com/etwfe/news/index.html","id":"bug-fixes-0-3-0","dir":"Changelog","previous_headings":"","what":"Bug fixes","title":"etwfe 0.3.0","text":"Internal code tests updated account upstream breaking changes marginaleffects 0.9.0 (#20, thanks @vincentarelbundock). user side, notable changes longer call summary() emfx objects pretty printing, (former) “dydx” column resulting object now named “estimate”. changes reflected updated documentation.","code":""},{"path":"http://grantmcdermott.com/etwfe/news/index.html","id":"other-0-3-0","dir":"Changelog","previous_headings":"","what":"Other","title":"etwfe 0.3.0","text":"Various documentation improvements. example, aforementioned sections Heterogeneous TEs Performance tips. also removed warnings use time-varying controls (#17). truth, can’t quite recall included warnings first place testing confirms appear pose problem ETWFE framework. Thanks Felix Pretis prompting revisit implicit restriction, including forwarding relevant correspondence Prof. Wooldridge. data.table added Imports thus becomes direct dependency. already indirect dependency marginaleffects. ’s now possible install development version package R-universe. Details provided README.","code":""},{"path":"http://grantmcdermott.com/etwfe/news/index.html","id":"etwfe-020","dir":"Changelog","previous_headings":"","what":"etwfe 0.2.0","title":"etwfe 0.2.0","text":"CRAN release: 2023-01-11","code":""},{"path":"http://grantmcdermott.com/etwfe/news/index.html","id":"bug-fixes-and-breaking-changes-0-2-0","dir":"Changelog","previous_headings":"","what":"Bug fixes and breaking changes","title":"etwfe 0.2.0","text":".Dtreat indicator variable created etwfe call now logical instead integer (#14). fix yields slightly different effect sizes emfx output applied non-linear model families (e.g., etwfe(..., family = \"poisson\"). reason now implicitly calling marginaleffects::comparisons hood rather marginaleffects::marginaleffects. Note main etwfe coefficients (family) unaffected, also true emfx applied linear model (.e., default). (optional) ivar argument etwfe() moved argument order list second position fifth (.e., data argument). means four required arguments function now occupy top positions, enable shorter, unnamed notation like etwfe(y ~ x, year, cohort, dat).","code":""},{"path":"http://grantmcdermott.com/etwfe/news/index.html","id":"new-features-and-enhancements-0-2-0","dir":"Changelog","previous_headings":"","what":"New features and enhancements","title":"etwfe 0.2.0","text":"emfx now allows (time-invariant) interacted control variables fml RHS. emfx now post_only logical argument, may useful plotting aesthetics (inference). See example introductory vignette. Various improvements documentation (restructuring, fixed typos, etc.)","code":""},{"path":"http://grantmcdermott.com/etwfe/news/index.html","id":"etwfe-010","dir":"Changelog","previous_headings":"","what":"etwfe 0.1.0","title":"etwfe 0.1.0","text":"CRAN release: 2022-12-14 Initial release.","code":""}]
+[{"path":"http://grantmcdermott.com/etwfe/articles/etwfe.html","id":"background","dir":"Articles","previous_headings":"","what":"Background","title":"Introduction to etwfe","text":"canonical research design social scientists -called “difference--differences” () design. essential idea behind can estimate causal impact intervention (“treatment”) comparing pre- post-intervention outcomes indivduals received treatment (“treated” group) outcomes comparable indivduals didn’t receive treatment (“control” group).1 classic 2x2 case (two units, two periods), simple interaction effect two dummy variables suffices recover treatment effect. base R might look something like: resulting coefficient Dtreated_unitTRUE:Dpost_treatmentTRUE interaction term represents treatment effect. Rather manually specify interaction term, practice researchers often use equivalent formulation known two-way fixed effects (TWFE). core idea TWFE can subsume interaction term previous code chunk adding unit time fixed effects. single treatment dummy can used capture effect treatment directly. TWFE regression base R might look follows: treatment effect now captured coefficient Dtreat dummy. TWFE shortcut especially nice complicated panel data settings multiple units multiple times periods. Speaking , prefer use dedicated fixed effects / panel data package like fixest, also estimate previous regression like : TWFE regressions easy run intuitive, long time everyone happy. good last. cottage industry clever research now demonstrates things quite simple. Among things, standard TWFE formulation can impose strange (negative) weighting conditions key parts estimation procedure. One implication risk high probability estimate bias presence staggered treatment rollouts, common real-life applications. Fortunately, just econometricians taking away one favourite tools, kind enough replace new ones. Among , proposed approach Wooldridge (2021, 2022) noteworthy. idea might paraphrased stating problem TWFE first place. Rather, ’s weren’t enough. Instead including single treatment × time interaction, Wooldridge recommends saturate model possible interactions treatment time variables, including treatment cohorts, well covariates. goes show approach actually draws equivalence different types estimators (pooled OLS, twoway Mundlak regression, etc.) ’s entirely clear call . Wooldridge refers general idea extended TWFE—, ETWFE—rather like package takes name. Wooldridge ETWFE solution intuitive elegant. also rather tedious error prone code manually. correctly specify possible interactions, demean control variables within groups, recover treatment effects interest via appropriate marginal effect aggregation. etwfe package aims simplify process providing convenience functions work .","code":"lm(y ~ Dtreated_unit * Dpost_treatment, data = somedata) lm(y ~ Dtreat + factor(id) + factor(period), data = somedata) library(fixest) feols(y ~ Dtreat | id + period, data = somedata)"},{"path":"http://grantmcdermott.com/etwfe/articles/etwfe.html","id":"dataset","dir":"Articles","previous_headings":"","what":"Dataset","title":"Introduction to etwfe","text":"demonstrate core functionality etwfe, ’ll use mpdta dataset US teen employment package (’ll need install separately). “Treatment” dataset refers increase minimum wage rate. examples follow, goal estimate effect minimum wage treatment (treat) log teen employment (lemp). Notice panel ID county level (countyreal), treatment staggered across cohorts (first.treat) group counties treated time. addition staggered treatment effects, also observe log population (lpop) potential control variable.","code":"# install.packages(\"did\") data(\"mpdta\", package = \"did\") head(mpdta) #>     year countyreal     lpop     lemp first.treat treat #> 866 2003       8001 5.896761 8.461469        2007     1 #> 841 2004       8001 5.896761 8.336870        2007     1 #> 842 2005       8001 5.896761 8.340217        2007     1 #> 819 2006       8001 5.896761 8.378161        2007     1 #> 827 2007       8001 5.896761 8.487352        2007     1 #> 937 2003       8019 2.232377 4.997212        2007     1"},{"path":"http://grantmcdermott.com/etwfe/articles/etwfe.html","id":"basic-usage","dir":"Articles","previous_headings":"","what":"Basic usage","title":"Introduction to etwfe","text":"Let’s load etwfe work basic functionality. ’ll see, core workflow package involves two consecutive function calls: 1) etwfe() 2) emfx().","code":""},{"path":"http://grantmcdermott.com/etwfe/articles/etwfe.html","id":"etwfe","dir":"Articles","previous_headings":"Basic usage","what":"etwfe","title":"Introduction to etwfe","text":"Given package name, won’t surprise learn key estimating function etwfe(). ’s look example dataset. things say etwfe() argument choices function options, ’ll leave details aside bit later. Right now, just know arguments required except vcov (though generally recommend , since probably want cluster standard errors individual unit level). Let’s take look model object. etwfe() done underneath hood construct treatment dummy variable .Dtreat saturated together variables interest set multiway interaction terms.2 may noticed etwfe() call returns standard fixest object, since uses perform underlying estimation. associated methods functions fixest package thus compatible model object. example, plot raw regression coefficients fixest::coefplot(), print nice regression table fixest::etable(). However, raw coefficients etwfe() estimation particularly meaningful . Recall complex, multiway interaction terms probably hard interpret . insight leads us next key function…","code":"library(etwfe)  mod =   etwfe(     fml  = lemp ~ lpop, # outcome ~ controls     tvar = year,        # time variable     gvar = first.treat, # group variable     data = mpdta,       # dataset     vcov = ~countyreal  # vcov adjustment (here: clustered)     ) mod #> OLS estimation, Dep. Var.: lemp #> Observations: 2,500  #> Fixed-effects: first.treat: 4,  year: 5 #> Varying slopes: lpop (first.treat: 4),  lpop (year: 5) #> Standard-errors: Clustered (countyreal)  #>                                               Estimate Std. Error   t value #> .Dtreat:first.treat::2004:year::2004         -0.021248   0.021728 -0.977890 #> .Dtreat:first.treat::2004:year::2005         -0.081850   0.027375 -2.989963 #> .Dtreat:first.treat::2004:year::2006         -0.137870   0.030795 -4.477097 #> .Dtreat:first.treat::2004:year::2007         -0.109539   0.032322 -3.389024 #> .Dtreat:first.treat::2006:year::2006          0.002537   0.018883  0.134344 #> .Dtreat:first.treat::2006:year::2007         -0.045093   0.021987 -2.050907 #> .Dtreat:first.treat::2007:year::2007         -0.045955   0.017975 -2.556568 #> .Dtreat:first.treat::2004:year::2004:lpop_dm  0.004628   0.017584  0.263184 #> .Dtreat:first.treat::2004:year::2005:lpop_dm  0.025113   0.017904  1.402661 #> .Dtreat:first.treat::2004:year::2006:lpop_dm  0.050735   0.021070  2.407884 #> .Dtreat:first.treat::2004:year::2007:lpop_dm  0.011250   0.026617  0.422648 #> .Dtreat:first.treat::2006:year::2006:lpop_dm  0.038935   0.016472  2.363731 #> .Dtreat:first.treat::2006:year::2007:lpop_dm  0.038060   0.022477  1.693276 #> .Dtreat:first.treat::2007:year::2007:lpop_dm -0.019835   0.016198 -1.224528 #>                                                Pr(>|t|)     #> .Dtreat:first.treat::2004:year::2004         3.2860e-01     #> .Dtreat:first.treat::2004:year::2005         2.9279e-03 **  #> .Dtreat:first.treat::2004:year::2006         9.3851e-06 *** #> .Dtreat:first.treat::2004:year::2007         7.5694e-04 *** #> .Dtreat:first.treat::2006:year::2006         8.9318e-01     #> .Dtreat:first.treat::2006:year::2007         4.0798e-02 *   #> .Dtreat:first.treat::2007:year::2007         1.0866e-02 *   #> .Dtreat:first.treat::2004:year::2004:lpop_dm 7.9252e-01     #> .Dtreat:first.treat::2004:year::2005:lpop_dm 1.6134e-01     #> .Dtreat:first.treat::2004:year::2006:lpop_dm 1.6407e-02 *   #> .Dtreat:first.treat::2004:year::2007:lpop_dm 6.7273e-01     #> .Dtreat:first.treat::2006:year::2006:lpop_dm 1.8474e-02 *   #> .Dtreat:first.treat::2006:year::2007:lpop_dm 9.1027e-02 .   #> .Dtreat:first.treat::2007:year::2007:lpop_dm 2.2133e-01     #> ... 10 variables were removed because of collinearity (.Dtreat:first.treat::2006:year::2004, .Dtreat:first.treat::2006:year::2005 and 8 others [full set in $collin.var]) #> --- #> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 #> RMSE: 0.537131     Adj. R2: 0.87167  #>                  Within R2: 8.449e-4"},{"path":"http://grantmcdermott.com/etwfe/articles/etwfe.html","id":"emfx","dir":"Articles","previous_headings":"Basic usage","what":"emfx","title":"Introduction to etwfe","text":"raw etwfe coefficients aren’t particularly useful , can instead? Well, probably want aggregate along dimension interest (e.g., groups time, event study). natural way perform aggregations recovering appropriate marginal effects. etwfe package provides another convenience function : emfx(), thin(ish) wrapper around marginaleffects::slopes(). example, can recover average treatment effect treated (ATT) follows. words, model telling us increase minimum wage leads approximate 5 percent decrease teen employment. Beyond simple ATTs, emfx() also supports types aggregations via type argument. example, can use type = \"calendar\" get ATTs period, type = \"group\" get ATTs cohort groups. option probably useful people type = \"event\", recover dynamic treatment effects la event study. Let’s try save resulting object, since plan reuse moment. event study suggests teen disemployment effect minimum wage hike fairly modest first (3%), increases next years (>10%). next section, ’ll look ways communicate kind finding audience.","code":"emfx(mod) #>  #>     Term                 Contrast .Dtreat Estimate Std. Error     z Pr(>|z|) #>  .Dtreat mean(TRUE) - mean(FALSE)    TRUE  -0.0506     0.0125 -4.05   <0.001 #>     S   2.5 %  97.5 % #>  14.3 -0.0751 -0.0261 #>  #> Columns: term, contrast, .Dtreat, estimate, std.error, statistic, p.value, s.value, conf.low, conf.high, predicted_lo, predicted_hi, predicted  #> Type:  response mod_es = emfx(mod, type = \"event\") mod_es #>  #>     Term                 Contrast event Estimate Std. Error     z Pr(>|z|)    S #>  .Dtreat mean(TRUE) - mean(FALSE)     0  -0.0332     0.0134 -2.48    0.013  6.3 #>  .Dtreat mean(TRUE) - mean(FALSE)     1  -0.0573     0.0172 -3.34   <0.001 10.2 #>  .Dtreat mean(TRUE) - mean(FALSE)     2  -0.1379     0.0308 -4.48   <0.001 17.0 #>  .Dtreat mean(TRUE) - mean(FALSE)     3  -0.1095     0.0323 -3.39   <0.001 10.5 #>    2.5 %   97.5 % #>  -0.0594 -0.00701 #>  -0.0910 -0.02373 #>  -0.1982 -0.07751 #>  -0.1729 -0.04619 #>  #> Columns: term, contrast, event, estimate, std.error, statistic, p.value, s.value, conf.low, conf.high, predicted_lo, predicted_hi, predicted  #> Type:  response"},{"path":"http://grantmcdermott.com/etwfe/articles/etwfe.html","id":"presentation","dir":"Articles","previous_headings":"Basic usage","what":"Presentation","title":"Introduction to etwfe","text":"Since emfx() produces standard marginaleffects object, can pass supported methods packages. example, can pass modelsummary get nice regression table event study coefficients. Note use shape coef_rename arguments ; optional help make output look bit nicer. Event study visualization, can pass preferred plotting method. example:  Note emfx reports post-treatment effects. pre-treatment effects swept estimation way ETWFE set . fact, pre-treatment effects mechanistically set zero. means ETWFE used interrogating pre-treatment fit (say, visual inspection parallel pre-trends). Still, can get zero pre-treatment effects changing post_only argument. emphasize strictly performative—, pre-treatment effects zero estimation design—might make event study plot aesthetically pleasing.","code":"library(modelsummary) #> Version 2.0.0 of `modelsummary`, to be released soon, will introduce a #>   breaking change: The default table-drawing package will be `tinytable` #>   instead of `kableExtra`. All currently supported table-drawing packages #>   will continue to be supported for the foreseeable future, including #>   `kableExtra`, `gt`, `huxtable`, `flextable, and `DT`. #>    #>   You can always call the `config_modelsummary()` function to change the #>   default table-drawing package in persistent fashion. To try `tinytable` #>   now: #>    #>   config_modelsummary(factory_default = 'tinytable') #>    #>   To set the default back to `kableExtra`: #>    #>   config_modelsummary(factory_default = 'kableExtra')  # Quick renaming function to replace \".Dtreat\" with something more meaningful rename_fn = function(old_names) {   new_names = gsub(\".Dtreat\", \"Years post treatment =\", old_names)   setNames(new_names, old_names) }  modelsummary(   mod_es,   shape       = term:event:statistic ~ model,   coef_rename = rename_fn,   gof_omit    = \"Adj|Within|IC|RMSE\",   title       = \"Event study\",   notes       = \"Std. errors are clustered at the county level\" ) library(ggplot2) theme_set(   theme_minimal() + theme(panel.grid.minor = element_blank()) )  ggplot(mod_es, aes(x = event, y = estimate, ymin = conf.low, ymax = conf.high)) +   geom_hline(yintercept = 0) +   geom_pointrange(col = \"darkcyan\") +   labs(x = \"Years post treatment\", y = \"Effect on log teen employment\") # Use post_only = FALSE to get the \"zero\" pre-treatment effects mod_es2 = emfx(mod, type = \"event\", post_only = FALSE)  ggplot(mod_es2, aes(x = event, y = estimate, ymin = conf.low, ymax = conf.high)) +   geom_hline(yintercept = 0) +   geom_vline(xintercept = -1, lty = 2) +   geom_pointrange(col = \"darkcyan\") +   labs(     x = \"Years post treatment\", y = \"Effect on log teen employment\",     caption = \"Note: Zero pre-treatment effects for illustrative purposes only.\"   ) #> Warning: Removed 4 rows containing missing values or values outside the scale range #> (`geom_segment()`)."},{"path":"http://grantmcdermott.com/etwfe/articles/etwfe.html","id":"heterogeneous-treatment-effects","dir":"Articles","previous_headings":"","what":"Heterogeneous treatment effects","title":"Introduction to etwfe","text":"far ’ve limited homogeneous treatment effects, impact treatment (.e., minimum wage hike) averaged across US counties dataset. However, many research problems require us estimate treatment effects separately across groups , potentially, test differences . example, might want test whether efficacy new vaccine differs across age groups, whether marketing campaign equally successful across genders. ETWFE framework naturally lends kinds heterogeneous treatment effects. Consider following example, first create logical dummy variable US counties eight Great Lake states (GLS). Now imagine interested estimating separate treatment effects GLS versus non-GLS counties. simply invoking optional xvar argument part etwfe() call.3 subsequent emfx() call object automatically recognize want recover treatment effects two distinct groups. point estimates might tempt us think minimum wage hikes caused less teen disemployment GLS counties rest US average. However, test formally can invoke powerful hypothesis infrastructure underlying marginaleffects package. Probably easiest way using b[]-style positional arguments, “[]” denotes row emfx() return object. Thus, specifying hypothesis = \"b1 = b2\", can test whether ATTs row 1 (non-GLS) row 2 (GLS) different one another. see actually statistical difference average disemployment effect GLS non-GLS counties. One final aside can easily display results heterogeneous treatment effects plot table form. ’s example latter, make use modelsummary(..., shape = ...) argument. Comparing ATT GLS non-GLS counties simple example limited binary comparison group ATTs, note logic carries richer settings. can use exact workflow estimate heterogeneous treatment effects different aggregations (e.g., event studies) across groups many levels.","code":"gls_fips = c(\"IL\" = 17, \"IN\" = 18, \"MI\" = 26, \"MN\" = 27,              \"NY\" = 36, \"OH\" = 39, \"PA\" = 42, \"WI\" = 55)  mpdta$gls = substr(mpdta$countyreal, 1, 2) %in% gls_fips hmod = etwfe(    lemp ~ lpop, tvar = year, gvar = first.treat, data = mpdta,     vcov = ~countyreal,    xvar = gls           ## <= het. TEs by gls    )  # Heterogeneous ATTs (could also specify `type = \"event\"`, etc.)  emfx(hmod) #>  #>     Term                 Contrast .Dtreat   gls Estimate Std. Error     z #>  .Dtreat mean(TRUE) - mean(FALSE)    TRUE FALSE  -0.0637     0.0376 -1.69 #>  .Dtreat mean(TRUE) - mean(FALSE)    TRUE  TRUE  -0.0472     0.0271 -1.74 #>  Pr(>|z|)   S  2.5 %  97.5 % #>    0.0906 3.5 -0.137 0.01007 #>    0.0817 3.6 -0.100 0.00594 #>  #> Columns: term, contrast, .Dtreat, gls, estimate, std.error, statistic, p.value, s.value, conf.low, conf.high, predicted_lo, predicted_hi, predicted  #> Type:  response emfx(hmod, hypothesis = \"b1 = b2\") #>  #>   Term Estimate Std. Error      z Pr(>|z|)   S  2.5 % 97.5 % #>  b1=b2  -0.0164     0.0559 -0.294    0.769 0.4 -0.126  0.093 #>  #> Columns: term, estimate, std.error, statistic, p.value, s.value, conf.low, conf.high  #> Type:  response modelsummary(     models      = list(\"GLS county\" = emfx(hmod)),     shape       = term + statistic ~ model + gls, # add xvar variable (here: gls)     coef_map    = c(\".Dtreat\" = \"ATT\"),     gof_map     = NA,     title       = \"Comparing the ATT on GLS and non-GLS counties\" )"},{"path":"http://grantmcdermott.com/etwfe/articles/etwfe.html","id":"other-families","dir":"Articles","previous_headings":"","what":"Other families","title":"Introduction to etwfe","text":"Another key feature ETWFE approach—one sets apart advanced implementations extensions—supports nonlinear model (distribution / link) families. Users need simply invoke family argument. ’s brief example, recast earlier event-study Poisson regression.","code":"mpdta$emp = exp(mpdta$lemp)  etwfe(   emp ~ lpop, tvar = year, gvar = first.treat, data = mpdta, vcov = ~countyreal,   family = \"poisson\"   ) |>   emfx(\"event\") #>  #>     Term                 Contrast event Estimate Std. Error       z Pr(>|z|) #>  .Dtreat mean(TRUE) - mean(FALSE)     0   -25.35       15.9 -1.5942    0.111 #>  .Dtreat mean(TRUE) - mean(FALSE)     1     1.09       41.8  0.0261    0.979 #>  .Dtreat mean(TRUE) - mean(FALSE)     2   -75.12       22.3 -3.3696   <0.001 #>  .Dtreat mean(TRUE) - mean(FALSE)     3  -101.82       28.1 -3.6234   <0.001 #>     S  2.5 % 97.5 % #>   3.2  -56.5   5.82 #>   0.0  -80.9  83.09 #>  10.4 -118.8 -31.43 #>  11.7 -156.9 -46.75 #>  #> Columns: term, contrast, event, estimate, std.error, statistic, p.value, s.value, conf.low, conf.high, predicted_lo, predicted_hi, predicted  #> Type:  response"},{"path":"http://grantmcdermott.com/etwfe/articles/etwfe.html","id":"performance-tips","dir":"Articles","previous_headings":"","what":"Performance tips","title":"Introduction to etwfe","text":"Thinking etwfe workflow pair consecutive functional calls, first etwfe() stage tends fast. ’re leveraging incredible performance fixest also taking shortcuts avoid wasting time nuisance parameters. See Regarding fixed effects section details . part, second emfx() stage also tends pretty performant. data less 100k rows, ’s unlikely ’ll wait seconds obtain results. However, emfx’s computation time tend scale non-linearly size original data, well number interactions underlying etwfe model object. Without getting deep weeds, relying numerical delta method (excellent) marginaleffects package underneath hood recover ATTs interest. method requires estimating two prediction models coefficient model computing standard errors. ’s potentially expensive operation can push computation time large datasets (> 1m rows) several minutes longer. Fortunately, two complementary strategies can use speed things . first turn expensive part whole procedure—standard error calculation—calling emfx(..., vcov = FALSE). bring estimation time back seconds less, even datasets excess million rows. course, loss standard errors might acceptable trade-projects statistical inference critical. good news first strategy can still combined second strategy: turns collapsing data groups prior estimating marginal effects can yield substantial speed gains . Users can invoking emfx(..., collapse = TRUE) argument. effect dramatic first strategy, collapsing data virtue retaining information standard errors. trade-time, however, collapsing data lead loss accuracy estimated parameters. hand, testing suggests loss accuracy tends relatively minor, results equivalent 1st 2nd significant decimal place (even better). Summarizing, quick plan attack try worried estimation time large datasets models: Estimate mod = etwfe(...) per usual. Run emfx(mod, vcov = FALSE, ...). Run emfx(mod, vcov = FALSE, collapse = TRUE, ...). Compare point estimates steps 1 2. similar enough satisfaction, get approximate standard errors running emfx(mod, collapse = TRUE, ...). ’s bit performance art, since examples vignette complete quickly anyway. reworking earlier event study example demonstrate performance-conscious workflow. put fine point , can can compare original event study collapsed estimates see results indeed similar. Event study","code":"# Step 0 already complete: using the same `mod` object from earlier...  # Step 1 emfx(mod, type = \"event\", vcov = FALSE) #>  #>     Term                 Contrast event Estimate #>  .Dtreat mean(TRUE) - mean(FALSE)     0  -0.0332 #>  .Dtreat mean(TRUE) - mean(FALSE)     1  -0.0573 #>  .Dtreat mean(TRUE) - mean(FALSE)     2  -0.1379 #>  .Dtreat mean(TRUE) - mean(FALSE)     3  -0.1095 #>  #> Columns: term, contrast, event, estimate, predicted_lo, predicted_hi, predicted  #> Type:  response  # Step 2 emfx(mod, type = \"event\", vcov = FALSE, collapse = TRUE) #>  #>     Term                 Contrast event Estimate #>  .Dtreat mean(TRUE) - mean(FALSE)     0  -0.0332 #>  .Dtreat mean(TRUE) - mean(FALSE)     1  -0.0573 #>  .Dtreat mean(TRUE) - mean(FALSE)     2  -0.1379 #>  .Dtreat mean(TRUE) - mean(FALSE)     3  -0.1095 #>  #> Columns: term, contrast, event, estimate, predicted_lo, predicted_hi, predicted  #> Type:  response  # Step 3: Results from 1 and 2 are similar enough, so get approx. SEs mod_es2 = emfx(mod, type = \"event\", collapse = TRUE) modelsummary(     list(\"Original\" = mod_es, \"Collapsed\" = mod_es2),     shape       = term:event:statistic ~ model,     coef_rename = rename_fn,     gof_omit    = \"Adj|Within|IC|RMSE\",     title       = \"Event study\",     notes       = \"Std. errors are clustered at the county level\" )"},{"path":"http://grantmcdermott.com/etwfe/articles/etwfe.html","id":"under-the-hood","dir":"Articles","previous_headings":"","what":"Under the hood","title":"Introduction to etwfe","text":"Now ’ve seen etwfe action, let’s circle back package hood. section isn’t necessary use package; feel free skip . review internal details help optimize different scenarios also give better understanding etwfe’s default choices.","code":""},{"path":"http://grantmcdermott.com/etwfe/articles/etwfe.html","id":"manual-implementation","dir":"Articles","previous_headings":"Under the hood","what":"Manual implementation","title":"Introduction to etwfe","text":"keep reiterating, ETWFE approach basically involves saturating regression interaction effects. can easily grab formula estimated model see . point, however, may notice things. first formula references several variables aren’t original dataset. obvious one .Dtreat treatment dummy. subtle one lpop_dm, demeaned (.e., group-centered) version lpop control variable. control variables demeaned interacted ETWFE setting. ’s constructed dataset ahead time estimated ETWFE regression manually: can confirm manual approach yields output original etwfe regression. ’ll use modelsummary , since ’ve already loaded .4. transform raw coefficients meaningful ATT counterparts, just need perform appropriate marginal effects operation. example, ’s can get simple ATTs event-study ATTs earlier. emfx() behind scenes.","code":"mod$fml_all #> $linear #> lemp ~ .Dtreat:i(first.treat, i.year, ref = 0, ref2 = 2003)/lpop_dm #> <environment: 0x55b3d04164c8> #>  #> $fixef #> ~first.treat + first.treat[[lpop]] + year + year[[lpop]] # First construct the dataset mpdta2 = mpdta |>   transform(     .Dtreat = year >= first.treat & first.treat != 0,     lpop_dm = ave(lpop, first.treat, year, FUN = \\(x) x - mean(x, na.rm = TRUE))   )  # Then estimate the manual version of etwfe mod2 = fixest::feols(   lemp ~ .Dtreat:i(first.treat, i.year, ref = 0, ref2 = 2003) / lpop_dm |     first.treat[lpop] + year[lpop],   data = mpdta2,   vcov = ~countyreal ) modelsummary(   list(\"etwfe\" = mod, \"manual\" = mod2),   gof_map = NA # drop all goodness-of-fit info for brevity ) library(marginaleffects)  # Simple ATT slopes(   mod2,    newdata   = subset(mpdta2, .Dtreat), # we only want rows where .Dtreat is TRUE   variables = \".Dtreat\",    by        = \".Dtreat\"   ) #>  #>     Term                 Contrast .Dtreat Estimate Std. Error     z Pr(>|z|) #>  .Dtreat mean(TRUE) - mean(FALSE)    TRUE  -0.0506     0.0125 -4.05   <0.001 #>     S   2.5 %  97.5 % #>  14.3 -0.0751 -0.0261 #>  #> Columns: term, contrast, .Dtreat, estimate, std.error, statistic, p.value, s.value, conf.low, conf.high, predicted_lo, predicted_hi, predicted  #> Type:  response  # Event study slopes(   mod2,    newdata   = transform(subset(mpdta2, .Dtreat), event = year - first.treat),   variables = \".Dtreat\",    by        = \"event\"   ) #>  #>     Term                 Contrast event Estimate Std. Error     z Pr(>|z|)    S #>  .Dtreat mean(TRUE) - mean(FALSE)     0  -0.0332     0.0134 -2.48    0.013  6.3 #>  .Dtreat mean(TRUE) - mean(FALSE)     1  -0.0573     0.0172 -3.34   <0.001 10.2 #>  .Dtreat mean(TRUE) - mean(FALSE)     2  -0.1379     0.0308 -4.48   <0.001 17.0 #>  .Dtreat mean(TRUE) - mean(FALSE)     3  -0.1095     0.0323 -3.39   <0.001 10.5 #>    2.5 %   97.5 % #>  -0.0594 -0.00701 #>  -0.0910 -0.02373 #>  -0.1982 -0.07751 #>  -0.1729 -0.04619 #>  #> Columns: term, contrast, event, estimate, std.error, statistic, p.value, s.value, conf.low, conf.high, predicted_lo, predicted_hi, predicted  #> Type:  response"},{"path":"http://grantmcdermott.com/etwfe/articles/etwfe.html","id":"regarding-fixed-effects","dir":"Articles","previous_headings":"Under the hood","what":"Regarding fixed effects","title":"Introduction to etwfe","text":"Let’s switch gears talk fixed effects quickly. regular fixest user, may noticed ’ve invoking varying slopes syntax fixed effect slot (.e., first.treat[lpop] year[lpop]). reason part practical, part philosophical. practical perspective, factor_var[numeric_var] equivalent base R’s factor_var/numeric_var “nesting” syntax much faster high-dimensional factors.5 philosophical perspective, etwfe tries limit amount extraneous information reports users. interaction effects ETWFE framework just acting controls. relegating fixed effects slot, can avoid polluting user’s console host extra coefficients. Nonetheless, can control behaviour fe (“fixed effects”) argument. Consider following options manual equivalents. ’ll leave pass models emfx confirm give correct aggregated treatment effects. can quickly demonstrate regression table return raw coefficients. final point note fixed effects etwfe defaults using group-level (.e., cohort-level) fixed effects like first.treat, rather unit-level fixed effects like countyreal. design decision reflects neat ancillary result Wooldridge (2021), proves equivalence two types fixed effects linear cases. Group-level effects virtue faster estimate, since fewer factor levels. Moreover, required nonlinear model families like Poisson per underlying ETWFE theory. Still, can specify unit-level fixed effects linear case ivar argument. , can easily confirm yields estimated treatment effects group-level default (although standard errors slightly different).","code":"# fe = \"feo\" (fixed effects only) mod_feo = etwfe(   lemp ~ lpop, tvar = year, gvar = first.treat, data = mpdta, vcov = ~countyreal,   fe = \"feo\" ) # ... which is equivalent to the manual regression mod_feo2 = fixest::feols(   lemp ~ .Dtreat:i(first.treat, i.year, ref = 0, ref2 = 2003) / lpop_dm +     lpop + i(first.treat, lpop, ref = 0) + i(year, lpop, ref = 2003) |     first.treat + year,   data = mpdta2, vcov = ~countyreal )  # fe = \"none\" mod_none = etwfe(   lemp ~ lpop, tvar = year, gvar = first.treat, data = mpdta, vcov = ~countyreal,   fe = \"none\" ) # ... which is equivalent to the manual regression mod_none2 = fixest::feols(   lemp ~ .Dtreat:i(first.treat, i.year, ref = 0, ref2 = 2003) / lpop_dm +     lpop + i(first.treat, lpop, ref = 0) + i(year, lpop, ref = 2003) +     i(first.treat, ref = 0) + i(year, ref = 2003),   data = mpdta2, vcov = ~countyreal ) mods = list(   \"etwfe\"         = mod,   \"manual\"        = mod2,   \"etwfe (feo)\"   = mod_feo,   \"manual (feo)\"  = mod_feo2,   \"etwfe (none)\"  = mod_none,   \"manual (none)\" = mod_none2 )  modelsummary(mods, gof_map = NA) mod_es_i = etwfe(   lemp ~ lpop, tvar = year, gvar = first.treat, data = mpdta,   ivar = countyreal  # NEW: Use unit-level (county) FEs   ) |>   emfx(\"event\")  modelsummary(   list(\"Group-level FEs (default)\" = mod_es, \"Unit-level FEs\" = mod_es_i),   shape       = term:event:statistic ~ model,   coef_rename = rename_fn,   gof_omit    = \"Adj|Within|IC|RMSE\" )"},{"path":"http://grantmcdermott.com/etwfe/authors.html","id":null,"dir":"","previous_headings":"","what":"Authors","title":"Authors and Citation","text":"Grant McDermott. Author, maintainer. Frederic Kluser. Contributor.","code":""},{"path":"http://grantmcdermott.com/etwfe/authors.html","id":"citation","dir":"","previous_headings":"","what":"Citation","title":"Authors and Citation","text":"McDermott G (2024). etwfe: Extended Two-Way Fixed Effects. R package version 0.4.0, https://grantmcdermott.com/etwfe/.","code":"@Manual{,   title = {etwfe: Extended Two-Way Fixed Effects},   author = {Grant McDermott},   year = {2024},   note = {R package version 0.4.0},   url = {https://grantmcdermott.com/etwfe/}, }"},{"path":"http://grantmcdermott.com/etwfe/index.html","id":"extended-two-way-fixed-effects-etwfe","dir":"","previous_headings":"","what":"Extended Two-Way Fixed Effects","title":"Extended Two-Way Fixed Effects","text":"goal etwfe estimate extended two-way fixed effects la Wooldridge (2021, 2022). Briefly, Wooldridge proposes set saturated interaction effects overcome potential bias problems vanilla TWFE difference--differences designs. Wooldridge solution intuitive elegant, rather tedious error prone code manually. etwfe package aims simplify process providing convenience functions work . Documentation available package homepage.","code":""},{"path":"http://grantmcdermott.com/etwfe/index.html","id":"installation","dir":"","previous_headings":"","what":"Installation","title":"Extended Two-Way Fixed Effects","text":"can install etwfe CRAN. , can grab development version R-universe.","code":"install.packages(\"etwfe\") install.packages(\"etwfe\", repos = \"https://grantmcdermott.r-universe.dev\")"},{"path":"http://grantmcdermott.com/etwfe/index.html","id":"quickstart-example","dir":"","previous_headings":"","what":"Quickstart example","title":"Extended Two-Way Fixed Effects","text":"detailed walkthrough etwfe provided introductory vignette (available online, typing vignette(\"etwfe\") R console). ’s quickstart example demonstrate basic syntax.","code":"library(etwfe)  # install.packages(\"did\") data(\"mpdta\", package = \"did\") head(mpdta) #>     year countyreal     lpop     lemp first.treat treat #> 866 2003       8001 5.896761 8.461469        2007     1 #> 841 2004       8001 5.896761 8.336870        2007     1 #> 842 2005       8001 5.896761 8.340217        2007     1 #> 819 2006       8001 5.896761 8.378161        2007     1 #> 827 2007       8001 5.896761 8.487352        2007     1 #> 937 2003       8019 2.232377 4.997212        2007     1  # Estimate the model mod =   etwfe(     fml  = lemp ~ lpop, # outcome ~ controls     tvar = year,        # time variable     gvar = first.treat, # group variable     data = mpdta,       # dataset     vcov = ~countyreal  # vcov adjustment (here: clustered)     )  # This gives us a regression model with fully saturated interactions mod #> OLS estimation, Dep. Var.: lemp #> Observations: 2,500 #> Fixed-effects: first.treat: 4,  year: 5 #> Varying slopes: lpop (first.treat): 4,  lpop (year): 5 #> Standard-errors: Clustered (countyreal)  #>                                               Estimate Std. Error   t value   Pr(>|t|)     #> .Dtreat:first.treat::2004:year::2004         -0.021248   0.021728 -0.977890 3.2860e-01     #> .Dtreat:first.treat::2004:year::2005         -0.081850   0.027375 -2.989963 2.9279e-03 **  #> .Dtreat:first.treat::2004:year::2006         -0.137870   0.030795 -4.477097 9.3851e-06 *** #> .Dtreat:first.treat::2004:year::2007         -0.109539   0.032322 -3.389024 7.5694e-04 *** #> .Dtreat:first.treat::2006:year::2006          0.002537   0.018883  0.134344 8.9318e-01     #> .Dtreat:first.treat::2006:year::2007         -0.045093   0.021987 -2.050907 4.0798e-02 *   #> .Dtreat:first.treat::2007:year::2007         -0.045955   0.017975 -2.556568 1.0866e-02 *   #> .Dtreat:first.treat::2004:year::2004:lpop_dm  0.004628   0.017584  0.263184 7.9252e-01     #> .Dtreat:first.treat::2004:year::2005:lpop_dm  0.025113   0.017904  1.402661 1.6134e-01     #> .Dtreat:first.treat::2004:year::2006:lpop_dm  0.050735   0.021070  2.407884 1.6407e-02 *   #> .Dtreat:first.treat::2004:year::2007:lpop_dm  0.011250   0.026617  0.422648 6.7273e-01     #> .Dtreat:first.treat::2006:year::2006:lpop_dm  0.038935   0.016472  2.363731 1.8474e-02 *   #> .Dtreat:first.treat::2006:year::2007:lpop_dm  0.038060   0.022477  1.693276 9.1027e-02 .   #> .Dtreat:first.treat::2007:year::2007:lpop_dm -0.019835   0.016198 -1.224528 2.2133e-01     #> ... 10 variables were removed because of collinearity (.Dtreat:first.treat::2006:year::2004, .Dtreat:first.treat::2006:year::2005 and 8 others [full set in $collin.var]) #> --- #> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 #> RMSE: 0.537131     Adj. R2: 0.87167  #>                  Within R2: 8.449e-4  # Pass to emfx() to recover the ATTs of interest. Here's an event-study example. emfx(mod, type = \"event\") #>  #>     Term                 Contrast event Estimate Std. Error     z Pr(>|z|)    S   2.5 %   97.5 % #>  .Dtreat mean(TRUE) - mean(FALSE)     0  -0.0332     0.0134 -2.48    0.013  6.3 -0.0594 -0.00701 #>  .Dtreat mean(TRUE) - mean(FALSE)     1  -0.0573     0.0172 -3.34   <0.001 10.2 -0.0910 -0.02373 #>  .Dtreat mean(TRUE) - mean(FALSE)     2  -0.1379     0.0308 -4.48   <0.001 17.0 -0.1982 -0.07751 #>  .Dtreat mean(TRUE) - mean(FALSE)     3  -0.1095     0.0323 -3.39   <0.001 10.5 -0.1729 -0.04619 #>  #> Columns: term, contrast, event, estimate, std.error, statistic, p.value, s.value, conf.low, conf.high, predicted_lo, predicted_hi, predicted  #> Type:  response"},{"path":"http://grantmcdermott.com/etwfe/index.html","id":"acknowledgements","dir":"","previous_headings":"","what":"Acknowledgements","title":"Extended Two-Way Fixed Effects","text":"Jeffrey Wooldridge underlying ETWFE theory. Laurent Bergé (fixest) Vincent Arel-Bundock (marginaleffects) maintaining two wonderful R packages heavy lifting hood . Fernando Rios-Avila JWDID Stata module, provided welcome foil unit testing whose elegant design helped inform choices R equivalent.","code":""},{"path":"http://grantmcdermott.com/etwfe/reference/emfx.html","id":null,"dir":"Reference","previous_headings":"","what":"Post-estimation treatment effects for an ETWFE regressions. — emfx","title":"Post-estimation treatment effects for an ETWFE regressions. — emfx","text":"Post-estimation treatment effects ETWFE regressions.","code":""},{"path":"http://grantmcdermott.com/etwfe/reference/emfx.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Post-estimation treatment effects for an ETWFE regressions. — emfx","text":"","code":"emfx(   object,   type = c(\"simple\", \"group\", \"calendar\", \"event\"),   by_xvar = \"auto\",   collapse = \"auto\",   post_only = TRUE,   ... )"},{"path":"http://grantmcdermott.com/etwfe/reference/emfx.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Post-estimation treatment effects for an ETWFE regressions. — emfx","text":"object etwfe model object. type Character. desired type post-estimation aggregation. by_xvar Logical. results account heterogeneous treatment effects? relevant preceding etwfe call included specified xvar argument, .e. interacted categorical covariate. default behaviour (\"auto\") automatically estimate heterogeneous treatment effects level xvar detected part underlying etwfe model object. Users can override setting either FALSE TRUE. See section Heterogeneous treatment effects . collapse Logical. Collapse data (period cohort) groups calculating marginal effects? trades loss estimate accuracy (typically around 1st 2nd significant decimal point) substantial improvement estimation time large datasets. default behaviour (\"auto\") automatically collapse original dataset 500,000 rows. Users can override setting either FALSE TRUE. Note collapsing group valid preceding etwfe call run \"ivar = NULL\" (default). See section Performance tips . post_only Logical. Drop pre-treatment ATTs? evaluated () type = \"event\" (b) original etwfe model object estimated using default \"notyet\" treated control group. conditions () (b) met pre-treatment effects zero mechanical result ETWFE's estimation setup. default behaviour (FALSE) thus drop nuisance rows dataset. post_only argument recognises may still want keep presentation purposes (e.g., plotting event-study). Nevertheless, forewarned enabling behaviour via TRUE strictly performative: \"zero\" treatment effects pre-treatment periods purely artefact estimation setup. ... Additional arguments passed marginaleffects::slopes. example, can pass vcov = FALSE dramatically speed estimation times main marginal effects (cost getting information standard errors; see Performance tips ). Another potentially useful application testing whether heterogeneous treatment effects (.e. levels xvar covariate) equal invoking hypothesis argument, e.g. hypothesis = \"b1 = b2\".","code":""},{"path":"http://grantmcdermott.com/etwfe/reference/emfx.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Post-estimation treatment effects for an ETWFE regressions. — emfx","text":"slopes object marginaleffects package.","code":""},{"path":"http://grantmcdermott.com/etwfe/reference/emfx.html","id":"performance-tips","dir":"Reference","previous_headings":"","what":"Performance tips","title":"Post-estimation treatment effects for an ETWFE regressions. — emfx","text":"situations, etwfe complete quickly. part, emfx quite performant take seconds less datasets 100k rows. However, emfx's computation time tend scale non-linearly size original data, well number interactions underlying etwfe model. Without getting deep weeds, numerical delta method used recover ATEs interest estimate two prediction models coefficient model compute standard errors. , potentially expensive operation can push computation time large datasets (> 1m rows) several minutes longer. Fortunately, two complementary strategies can use speed things . first turn expensive part whole procedure---standard error calculation---calling emfx(..., vcov = FALSE). bring estimation time back seconds less, even datasets excess million rows. loss standard errors might acceptable trade-projects statistical inference critical, good news first strategy can still combined second strategy. turns collapsing data groups prior estimating marginal effects can yield substantial speed gains . Users can invoking emfx(..., collapse = TRUE) argument. effect dramatic first strategy, second strategy virtue retaining information standard errors. trade-time, however, collapsing data lead loss accuracy estimated parameters. hand, testing suggests loss accuracy tends relatively minor, results equivalent 1st 2nd significant decimal place (even better). Summarizing, quick plan attack try worried estimation time large datasets models: Estimate mod = etwfe(...) per usual. Run emfx(mod, vcov = FALSE, ...). Run emfx(mod, vcov = FALSE, collapse = TRUE, ...). Compare point estimates steps 1 2. similar enough satisfaction, get approximate standard errors running emfx(mod, collapse = TRUE, ...).","code":""},{"path":"http://grantmcdermott.com/etwfe/reference/emfx.html","id":"heterogeneous-treatment-effects","dir":"Reference","previous_headings":"","what":"Heterogeneous treatment effects","title":"Post-estimation treatment effects for an ETWFE regressions. — emfx","text":"Specifying etwfe(..., xvar = <xvar>) generate interaction effects levels <xvar> part main regression model. reason useful (opposed regular, non-interacted covariate formula RHS) allows us estimate heterogeneous treatment effects part larger ETWFE framework. Specifically, can recover heterogeneous treatment effects level <xvar> passing resulting etwfe model object emfx(). example, imagine categorical variable called \"age\" dataset, two distinct levels \"adult\" \"child\". Running emfx(etwfe(..., xvar = age)) tell us efficacy treatment varies across adults children. can also leverage -built hypothesis testing infrastructure marginaleffects test whether treatment effect statistically different across two age groups; see Examples . Note principles carry categorical variables multiple levels, even continuous variables (although continuous variables well supported yet).","code":""},{"path":[]},{"path":"http://grantmcdermott.com/etwfe/reference/emfx.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Post-estimation treatment effects for an ETWFE regressions. — emfx","text":"","code":"# \\dontrun{ # We’ll use the mpdta dataset from the did package (which you’ll need to  # install separately).  # install.packages(\"did\") data(\"mpdta\", package = \"did\")  # # Basic example #  # The basic ETWFE workflow involves two steps:  # 1) Estimate the main regression model with etwfe().  mod = etwfe(     fml  = lemp ~ lpop, # outcome ~ controls (use 0 or 1 if none)     tvar = year,        # time variable     gvar = first.treat, # group variable     data = mpdta,       # dataset     vcov = ~countyreal  # vcov adjustment (here: clustered by county)     )  # mod ## A fixest model object with fully saturated interaction effects.  # 2) Recover the treatment effects of interest with emfx().  emfx(mod, type = \"event\") # dynamic ATE a la an event study #>  #>     Term                 Contrast event Estimate Std. Error     z Pr(>|z|)    S #>  .Dtreat mean(TRUE) - mean(FALSE)     0  -0.0332     0.0134 -2.48    0.013  6.3 #>  .Dtreat mean(TRUE) - mean(FALSE)     1  -0.0573     0.0172 -3.34   <0.001 10.2 #>  .Dtreat mean(TRUE) - mean(FALSE)     2  -0.1379     0.0308 -4.48   <0.001 17.0 #>  .Dtreat mean(TRUE) - mean(FALSE)     3  -0.1095     0.0323 -3.39   <0.001 10.5 #>    2.5 %   97.5 % #>  -0.0594 -0.00701 #>  -0.0910 -0.02373 #>  -0.1982 -0.07751 #>  -0.1729 -0.04619 #>  #> Columns: term, contrast, event, estimate, std.error, statistic, p.value, s.value, conf.low, conf.high, predicted_lo, predicted_hi, predicted  #> Type:  response  #>   # Etc. Other aggregation type options are \"simple\" (the default), \"group\" # and \"calendar\"   # # Heterogeneous treatment effects #  # Example where we estimate heterogeneous treatment effects for counties  # within the 8 US Great Lake states (versus all other counties).   gls = c(\"IL\" = 17, \"IN\" = 18, \"MI\" = 26, \"MN\" = 27,         \"NY\" = 36, \"OH\" = 39, \"PA\" = 42, \"WI\" = 55)  mpdta$gls = substr(mpdta$countyreal, 1, 2) %in% gls  hmod = etwfe(    lemp ~ lpop, tvar = year, gvar = first.treat, data = mpdta,     vcov = ~countyreal,    xvar = gls           ## <= het. TEs by gls    )  # Heterogeneous ATEs (could also specify \"event\", etc.)   emfx(hmod) #>  #>     Term                 Contrast .Dtreat   gls Estimate Std. Error     z #>  .Dtreat mean(TRUE) - mean(FALSE)    TRUE FALSE  -0.0637     0.0376 -1.69 #>  .Dtreat mean(TRUE) - mean(FALSE)    TRUE  TRUE  -0.0472     0.0271 -1.74 #>  Pr(>|z|)   S  2.5 %  97.5 % #>    0.0906 3.5 -0.137 0.01007 #>    0.0817 3.6 -0.100 0.00594 #>  #> Columns: term, contrast, .Dtreat, gls, estimate, std.error, statistic, p.value, s.value, conf.low, conf.high, predicted_lo, predicted_hi, predicted  #> Type:  response  #>   # To test whether the ATEs across these two groups (non-GLS vs GLS) are  # statistically different, simply pass an appropriate \"hypothesis\" argument.  emfx(hmod, hypothesis = \"b1 = b2\") #>  #>   Term Estimate Std. Error      z Pr(>|z|)   S  2.5 % 97.5 % #>  b1=b2  -0.0164     0.0559 -0.294    0.769 0.4 -0.126  0.093 #>  #> Columns: term, estimate, std.error, statistic, p.value, s.value, conf.low, conf.high  #> Type:  response  #>    # # Nonlinear model (distribution / link) families #  # Poisson example  mpdta$emp = exp(mpdta$lemp)  etwfe(    emp ~ lpop, tvar = year, gvar = first.treat, data = mpdta,     vcov = ~countyreal,    family = \"poisson\"   ## <= family arg for nonlinear options    ) |>    emfx(\"event\") #> The variables '.Dtreat:first.treat::2006:year::2004', '.Dtreat:first.treat::2006:year::2005' and eight others have been removed because of collinearity (see $collin.var). #>  #>     Term                 Contrast event Estimate Std. Error       z Pr(>|z|) #>  .Dtreat mean(TRUE) - mean(FALSE)     0   -25.35       15.9 -1.5942    0.111 #>  .Dtreat mean(TRUE) - mean(FALSE)     1     1.09       41.8  0.0261    0.979 #>  .Dtreat mean(TRUE) - mean(FALSE)     2   -75.12       22.3 -3.3696   <0.001 #>  .Dtreat mean(TRUE) - mean(FALSE)     3  -101.82       28.1 -3.6234   <0.001 #>     S  2.5 % 97.5 % #>   3.2  -56.5   5.82 #>   0.0  -80.9  83.09 #>  10.4 -118.8 -31.43 #>  11.7 -156.9 -46.75 #>  #> Columns: term, contrast, event, estimate, std.error, statistic, p.value, s.value, conf.low, conf.high, predicted_lo, predicted_hi, predicted  #> Type:  response  #>  # }"},{"path":"http://grantmcdermott.com/etwfe/reference/etwfe.html","id":null,"dir":"Reference","previous_headings":"","what":"Extended two-way fixed effects — etwfe","title":"Extended two-way fixed effects — etwfe","text":"Extended two-way fixed effects","code":""},{"path":"http://grantmcdermott.com/etwfe/reference/etwfe.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Extended two-way fixed effects — etwfe","text":"","code":"etwfe(   fml = NULL,   tvar = NULL,   gvar = NULL,   data = NULL,   ivar = NULL,   xvar = NULL,   tref = NULL,   gref = NULL,   cgroup = c(\"notyet\", \"never\"),   fe = c(\"vs\", \"feo\", \"none\"),   family = NULL,   ... )"},{"path":"http://grantmcdermott.com/etwfe/reference/etwfe.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Extended two-way fixed effects — etwfe","text":"fml two-side formula representing outcome (lhs) control variables (rhs), e.g. y ~ x1 + x2. controls required, rhs must take value 0 1, e.g. y ~ 0. tvar Time variable. Can string (e.g., \"year\") expression (e.g., year). gvar Group variable. Can either string (e.g., \"first_treated\") expression (e.g., first_treated). staggered treatment setting, group variable typically denotes treatment cohort. data data frame want run ETWFE . ivar Optional index variable. Can string (e.g., \"country\") expression (e.g., country). Leaving NULL (default) result group-level fixed effects used, efficient necessary nonlinear models (see family argument ). However, may still want cluster standard errors index variable vcov argument. See Examples . xvar Optional interacted categorical covariate estimating heterogeneous treatment effects. Enables recovery marginal treatment effect distinct levels xvar, e.g. \"child\", \"teenager\", \"adult\". Note \"x\" prefix \"xvar\" represents covariate interacted treatment, opposed regular control variable. tref Optional reference value tvar. Defaults minimum value (.e., first time period observed dataset). gref Optional reference value gvar. need provide gvar variable well specified. providing explicit reference value can useful/necessary desired control group takes unusual value. cgroup control group wish use estimating treatment effects. Either \"notyet\" treated (default) \"never\" treated. fe level fixed effects used? Defaults \"vs\" (varying slopes), efficient terms estimation terseness return model object. two options, \"feo\" (fixed effects ) \"none\" (fixed effects whatsoever), trade efficiency additional information (nuisance) model parameters. Note primary treatment parameters interest remain unchanged regardless choice. family family use estimation. Defaults NULL, case fixest::feols used. Otherwise passed fixest::feglm, valid entries include \"logit\", \"poisson\", \"negbin\". Note non-NULL family entry detected, ivar automatically set NULL. ... Additional arguments passed fixest::feols (fixest::feglm). common example vcov argument.","code":""},{"path":"http://grantmcdermott.com/etwfe/reference/etwfe.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Extended two-way fixed effects — etwfe","text":"fixest object fully saturated interaction effects.","code":""},{"path":"http://grantmcdermott.com/etwfe/reference/etwfe.html","id":"heterogeneous-treatment-effects","dir":"Reference","previous_headings":"","what":"Heterogeneous treatment effects","title":"Extended two-way fixed effects — etwfe","text":"Specifying etwfe(..., xvar = <xvar>) generate interaction effects levels <xvar> part main regression model. reason useful (opposed regular, non-interacted covariate formula RHS) allows us estimate heterogeneous treatment effects part larger ETWFE framework. Specifically, can recover heterogeneous treatment effects level <xvar> passing resulting etwfe model object emfx(). example, imagine categorical variable called \"age\" dataset, two distinct levels \"adult\" \"child\". Running emfx(etwfe(..., xvar = age)) tell us efficacy treatment varies across adults children. can also leverage -built hypothesis testing infrastructure marginaleffects test whether treatment effect statistically different across two age groups; see Examples . Note principles carry categorical variables multiple levels, even continuous variables (although continuous variables well supported yet).","code":""},{"path":"http://grantmcdermott.com/etwfe/reference/etwfe.html","id":"performance-tips","dir":"Reference","previous_headings":"","what":"Performance tips","title":"Extended two-way fixed effects — etwfe","text":"situations, etwfe complete quickly. part, emfx quite performant take seconds less datasets 100k rows. However, emfx's computation time tend scale non-linearly size original data, well number interactions underlying etwfe model. Without getting deep weeds, numerical delta method used recover ATEs interest estimate two prediction models coefficient model compute standard errors. , potentially expensive operation can push computation time large datasets (> 1m rows) several minutes longer. Fortunately, two complementary strategies can use speed things . first turn expensive part whole procedure---standard error calculation---calling emfx(..., vcov = FALSE). bring estimation time back seconds less, even datasets excess million rows. loss standard errors might acceptable trade-projects statistical inference critical, good news first strategy can still combined second strategy. turns collapsing data groups prior estimating marginal effects can yield substantial speed gains . Users can invoking emfx(..., collapse = TRUE) argument. effect dramatic first strategy, second strategy virtue retaining information standard errors. trade-time, however, collapsing data lead loss accuracy estimated parameters. hand, testing suggests loss accuracy tends relatively minor, results equivalent 1st 2nd significant decimal place (even better). Summarizing, quick plan attack try worried estimation time large datasets models: Estimate mod = etwfe(...) per usual. Run emfx(mod, vcov = FALSE, ...). Run emfx(mod, vcov = FALSE, collapse = TRUE, ...). Compare point estimates steps 1 2. similar enough satisfaction, get approximate standard errors running emfx(mod, collapse = TRUE, ...).","code":""},{"path":"http://grantmcdermott.com/etwfe/reference/etwfe.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Extended two-way fixed effects — etwfe","text":"Wooldridge, Jeffrey M. (2021). Two-Way Fixed Effects, Two-Way Mundlak Regression, Difference--Differences Estimators. Working paper (version: August 16, 2021). Available: http://dx.doi.org/10.2139/ssrn.3906345 Wooldridge, Jeffrey M. (2022). Simple Approaches Nonlinear Difference--Differences Panel Data. Econometrics Journal (forthcoming). Available: http://dx.doi.org/10.2139/ssrn.4183726","code":""},{"path":[]},{"path":"http://grantmcdermott.com/etwfe/reference/etwfe.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Extended two-way fixed effects — etwfe","text":"","code":"# \\dontrun{ # We’ll use the mpdta dataset from the did package (which you’ll need to  # install separately).  # install.packages(\"did\") data(\"mpdta\", package = \"did\")  # # Basic example #  # The basic ETWFE workflow involves two steps:  # 1) Estimate the main regression model with etwfe().  mod = etwfe(     fml  = lemp ~ lpop, # outcome ~ controls (use 0 or 1 if none)     tvar = year,        # time variable     gvar = first.treat, # group variable     data = mpdta,       # dataset     vcov = ~countyreal  # vcov adjustment (here: clustered by county)     )  # mod ## A fixest model object with fully saturated interaction effects.  # 2) Recover the treatment effects of interest with emfx().  emfx(mod, type = \"event\") # dynamic ATE a la an event study #>  #>     Term                 Contrast event Estimate Std. Error     z Pr(>|z|)    S #>  .Dtreat mean(TRUE) - mean(FALSE)     0  -0.0332     0.0134 -2.48    0.013  6.3 #>  .Dtreat mean(TRUE) - mean(FALSE)     1  -0.0573     0.0172 -3.34   <0.001 10.2 #>  .Dtreat mean(TRUE) - mean(FALSE)     2  -0.1379     0.0308 -4.48   <0.001 17.0 #>  .Dtreat mean(TRUE) - mean(FALSE)     3  -0.1095     0.0323 -3.39   <0.001 10.5 #>    2.5 %   97.5 % #>  -0.0594 -0.00701 #>  -0.0910 -0.02373 #>  -0.1982 -0.07751 #>  -0.1729 -0.04619 #>  #> Columns: term, contrast, event, estimate, std.error, statistic, p.value, s.value, conf.low, conf.high, predicted_lo, predicted_hi, predicted  #> Type:  response  #>   # Etc. Other aggregation type options are \"simple\" (the default), \"group\" # and \"calendar\"   # # Heterogeneous treatment effects #  # Example where we estimate heterogeneous treatment effects for counties  # within the 8 US Great Lake states (versus all other counties).   gls = c(\"IL\" = 17, \"IN\" = 18, \"MI\" = 26, \"MN\" = 27,         \"NY\" = 36, \"OH\" = 39, \"PA\" = 42, \"WI\" = 55)  mpdta$gls = substr(mpdta$countyreal, 1, 2) %in% gls  hmod = etwfe(    lemp ~ lpop, tvar = year, gvar = first.treat, data = mpdta,     vcov = ~countyreal,    xvar = gls           ## <= het. TEs by gls    )  # Heterogeneous ATEs (could also specify \"event\", etc.)   emfx(hmod) #>  #>     Term                 Contrast .Dtreat   gls Estimate Std. Error     z #>  .Dtreat mean(TRUE) - mean(FALSE)    TRUE FALSE  -0.0637     0.0376 -1.69 #>  .Dtreat mean(TRUE) - mean(FALSE)    TRUE  TRUE  -0.0472     0.0271 -1.74 #>  Pr(>|z|)   S  2.5 %  97.5 % #>    0.0906 3.5 -0.137 0.01007 #>    0.0817 3.6 -0.100 0.00594 #>  #> Columns: term, contrast, .Dtreat, gls, estimate, std.error, statistic, p.value, s.value, conf.low, conf.high, predicted_lo, predicted_hi, predicted  #> Type:  response  #>   # To test whether the ATEs across these two groups (non-GLS vs GLS) are  # statistically different, simply pass an appropriate \"hypothesis\" argument.  emfx(hmod, hypothesis = \"b1 = b2\") #>  #>   Term Estimate Std. Error      z Pr(>|z|)   S  2.5 % 97.5 % #>  b1=b2  -0.0164     0.0559 -0.294    0.769 0.4 -0.126  0.093 #>  #> Columns: term, estimate, std.error, statistic, p.value, s.value, conf.low, conf.high  #> Type:  response  #>    # # Nonlinear model (distribution / link) families #  # Poisson example  mpdta$emp = exp(mpdta$lemp)  etwfe(    emp ~ lpop, tvar = year, gvar = first.treat, data = mpdta,     vcov = ~countyreal,    family = \"poisson\"   ## <= family arg for nonlinear options    ) |>    emfx(\"event\") #> The variables '.Dtreat:first.treat::2006:year::2004', '.Dtreat:first.treat::2006:year::2005' and eight others have been removed because of collinearity (see $collin.var). #>  #>     Term                 Contrast event Estimate Std. Error       z Pr(>|z|) #>  .Dtreat mean(TRUE) - mean(FALSE)     0   -25.35       15.9 -1.5942    0.111 #>  .Dtreat mean(TRUE) - mean(FALSE)     1     1.09       41.8  0.0261    0.979 #>  .Dtreat mean(TRUE) - mean(FALSE)     2   -75.12       22.3 -3.3696   <0.001 #>  .Dtreat mean(TRUE) - mean(FALSE)     3  -101.82       28.1 -3.6234   <0.001 #>     S  2.5 % 97.5 % #>   3.2  -56.5   5.82 #>   0.0  -80.9  83.09 #>  10.4 -118.8 -31.43 #>  11.7 -156.9 -46.75 #>  #> Columns: term, contrast, event, estimate, std.error, statistic, p.value, s.value, conf.low, conf.high, predicted_lo, predicted_hi, predicted  #> Type:  response  #>  # }"},{"path":"http://grantmcdermott.com/etwfe/news/index.html","id":"etwfe-040","dir":"Changelog","previous_headings":"","what":"etwfe 0.4.0","title":"etwfe 0.4.0","text":"CRAN release: 2024-02-27","code":""},{"path":"http://grantmcdermott.com/etwfe/news/index.html","id":"bug-fixes-0-4-0","dir":"Changelog","previous_headings":"","what":"Bug fixes","title":"etwfe 0.4.0","text":"Fix ATT calculation never-treated case (..e, cgroup = \"never) due incorrect subsetting prior recovering marginal effects. Thanks @paulofelipe reporting (#37). Avoid (possible) error user supplies reserved “group” variable formula (#41).","code":""},{"path":"http://grantmcdermott.com/etwfe/news/index.html","id":"documentation-0-4-0","dir":"Changelog","previous_headings":"","what":"Documentation","title":"etwfe 0.4.0","text":"Fix missing autolinks documentation due markdown formatting (#44 @etiennebacher).","code":""},{"path":"http://grantmcdermott.com/etwfe/news/index.html","id":"etwfe-035","dir":"Changelog","previous_headings":"","what":"etwfe 0.3.5","title":"etwfe 0.3.5","text":"CRAN release: 2023-12-01","code":""},{"path":"http://grantmcdermott.com/etwfe/news/index.html","id":"internal-0-3-5","dir":"Changelog","previous_headings":"","what":"Internal","title":"etwfe 0.3.5","text":"Update tests match upstream changes fixest. Update maintainer email address.","code":""},{"path":"http://grantmcdermott.com/etwfe/news/index.html","id":"etwfe-034","dir":"Changelog","previous_headings":"","what":"etwfe 0.3.4","title":"etwfe 0.3.4","text":"CRAN release: 2023-06-19","code":""},{"path":"http://grantmcdermott.com/etwfe/news/index.html","id":"internal-0-3-4","dir":"Changelog","previous_headings":"","what":"Internal","title":"etwfe 0.3.4","text":"Update tests match upstream changes marginaleffects (#36 @vincentarelbundock).","code":""},{"path":"http://grantmcdermott.com/etwfe/news/index.html","id":"etwfe-033","dir":"Changelog","previous_headings":"","what":"etwfe 0.3.3","title":"etwfe 0.3.3","text":"CRAN release: 2023-05-27","code":""},{"path":"http://grantmcdermott.com/etwfe/news/index.html","id":"internal-0-3-3","dir":"Changelog","previous_headings":"","what":"Internal","title":"etwfe 0.3.3","text":"Rejigged internal tests following upstream changes marginaleffects (#35 @vincentarelbundock).","code":""},{"path":"http://grantmcdermott.com/etwfe/news/index.html","id":"etwfe-032","dir":"Changelog","previous_headings":"","what":"etwfe 0.3.2","title":"etwfe 0.3.2","text":"CRAN release: 2023-05-02","code":""},{"path":"http://grantmcdermott.com/etwfe/news/index.html","id":"bug-fixes-0-3-2","dir":"Changelog","previous_headings":"","what":"Bug fixes","title":"etwfe 0.3.2","text":"Fixed internal centering procedure handling multiple covariate levels (#30, #31). fixes impact main ATT estimates (.e., typical use package). may lead differences heterogeneous ATTs—.e., via xvar arg—incorrectly estimated cases. Thanks @PhilipCarthy flagging @frederickluser helpful discussions Fixed internal upstream bug causing model offsets error (#28, thanks @mariofiorini initial report several others helpful discussion). Note fix requires insight >= 0.19.1.8, development version time writing. information available : https://github.com/easystats/insight/pull/759","code":""},{"path":"http://grantmcdermott.com/etwfe/news/index.html","id":"etwfe-031","dir":"Changelog","previous_headings":"","what":"etwfe 0.3.1","title":"etwfe 0.3.1","text":"CRAN release: 2023-02-28","code":""},{"path":"http://grantmcdermott.com/etwfe/news/index.html","id":"internal-0-3-1","dir":"Changelog","previous_headings":"","what":"Internal","title":"etwfe 0.3.1","text":"Minor updates internal code unit tests match forthcoming updates marginaleffects 0.10.0. latter update also brings notable performance improvements emfx().","code":""},{"path":"http://grantmcdermott.com/etwfe/news/index.html","id":"other-0-3-1","dir":"Changelog","previous_headings":"","what":"Other","title":"etwfe 0.3.1","text":"documentation improvements. Examples wrapped \\dontrun avoid triggering CRAN NOTEs Windows exceeding 5 seconds execution time. Note package homepage still runs Examples users want inspect output online.","code":""},{"path":"http://grantmcdermott.com/etwfe/news/index.html","id":"etwfe-030","dir":"Changelog","previous_headings":"","what":"etwfe 0.3.0","title":"etwfe 0.3.0","text":"CRAN release: 2023-02-08","code":""},{"path":"http://grantmcdermott.com/etwfe/news/index.html","id":"new-features-and-enhancements-0-3-0","dir":"Changelog","previous_headings":"","what":"New features and enhancements","title":"etwfe 0.3.0","text":"Support estimating heterogeneous treatment effects via new etwfe(..., xvar = <xvar> argument (#16, thanks @frederickluser). Automatically extends emfx() via latter’s by_xvar argument (#21). details provided dedicated “Heterogeneous treatment effects” section vignette help documentation new emfx(..., collapse = TRUE) argument can substantially reduce estimation times large datasets (#19, thanks @frederickluser). performance boost trade loss estimate accuracy. testing suggests difference relatively minor typical use cases (.e., results equivalent 1st 2nd significant decimal place, sometimes even better). Please let us know find edge cases true. details available dedicated “Performance tips” section vignette help documentation, including advice combining collapsing emfx(..., vcov = FALSE) (yields even dramatic speed boost cost reporting standard errors). Users can now use 1 fml RHS indicate control variables part etwfe call, e.g. etwfe(y ~ 1, ...). provides second way indicating controls, alongside existing 0 option, e.g. etwfe(y ~ 0, ...)","code":""},{"path":"http://grantmcdermott.com/etwfe/news/index.html","id":"bug-fixes-0-3-0","dir":"Changelog","previous_headings":"","what":"Bug fixes","title":"etwfe 0.3.0","text":"Internal code tests updated account upstream breaking changes marginaleffects 0.9.0 (#20, thanks @vincentarelbundock). user side, notable changes longer call summary() emfx objects pretty printing, (former) “dydx” column resulting object now named “estimate”. changes reflected updated documentation.","code":""},{"path":"http://grantmcdermott.com/etwfe/news/index.html","id":"other-0-3-0","dir":"Changelog","previous_headings":"","what":"Other","title":"etwfe 0.3.0","text":"Various documentation improvements. example, aforementioned sections Heterogeneous TEs Performance tips. also removed warnings use time-varying controls (#17). truth, can’t quite recall included warnings first place testing confirms appear pose problem ETWFE framework. Thanks Felix Pretis prompting revisit implicit restriction, including forwarding relevant correspondence Prof. Wooldridge. data.table added Imports thus becomes direct dependency. already indirect dependency marginaleffects. ’s now possible install development version package R-universe. Details provided README.","code":""},{"path":"http://grantmcdermott.com/etwfe/news/index.html","id":"etwfe-020","dir":"Changelog","previous_headings":"","what":"etwfe 0.2.0","title":"etwfe 0.2.0","text":"CRAN release: 2023-01-11","code":""},{"path":"http://grantmcdermott.com/etwfe/news/index.html","id":"bug-fixes-and-breaking-changes-0-2-0","dir":"Changelog","previous_headings":"","what":"Bug fixes and breaking changes","title":"etwfe 0.2.0","text":".Dtreat indicator variable created etwfe call now logical instead integer (#14). fix yields slightly different effect sizes emfx output applied non-linear model families (e.g., etwfe(..., family = \"poisson\"). reason now implicitly calling marginaleffects::comparisons hood rather marginaleffects::marginaleffects. Note main etwfe coefficients (family) unaffected, also true emfx applied linear model (.e., default). (optional) ivar argument etwfe() moved argument order list second position fifth (.e., data argument). means four required arguments function now occupy top positions, enable shorter, unnamed notation like etwfe(y ~ x, year, cohort, dat).","code":""},{"path":"http://grantmcdermott.com/etwfe/news/index.html","id":"new-features-and-enhancements-0-2-0","dir":"Changelog","previous_headings":"","what":"New features and enhancements","title":"etwfe 0.2.0","text":"emfx now allows (time-invariant) interacted control variables fml RHS. emfx now post_only logical argument, may useful plotting aesthetics (inference). See example introductory vignette. Various improvements documentation (restructuring, fixed typos, etc.)","code":""},{"path":"http://grantmcdermott.com/etwfe/news/index.html","id":"etwfe-010","dir":"Changelog","previous_headings":"","what":"etwfe 0.1.0","title":"etwfe 0.1.0","text":"CRAN release: 2022-12-14 Initial release.","code":""}]