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<!DOCTYPE html>
<html lang="en"><head><meta charset="UTF-8"/><meta name="viewport" content="width=device-width, initial-scale=1.0"/><title>IV/2SLS examples · WildBootTests.jl</title><script data-outdated-warner src="../assets/warner.js"></script><link href="https://cdnjs.cloudflare.com/ajax/libs/lato-font/3.0.0/css/lato-font.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/juliamono/0.045/juliamono.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.15.4/css/fontawesome.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.15.4/css/solid.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.15.4/css/brands.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.13.24/katex.min.css" rel="stylesheet" type="text/css"/><script>documenterBaseURL=".."</script><script src="https://cdnjs.cloudflare.com/ajax/libs/require.js/2.3.6/require.min.js" data-main="../assets/documenter.js"></script><script src="../siteinfo.js"></script><script src="../../versions.js"></script><link class="docs-theme-link" rel="stylesheet" type="text/css" href="../assets/themes/documenter-dark.css" data-theme-name="documenter-dark" data-theme-primary-dark/><link class="docs-theme-link" rel="stylesheet" type="text/css" href="../assets/themes/documenter-light.css" data-theme-name="documenter-light" data-theme-primary/><script src="../assets/themeswap.js"></script></head><body><div id="documenter"><nav class="docs-sidebar"><div class="docs-package-name"><span class="docs-autofit"><a href="../">WildBootTests.jl</a></span></div><form class="docs-search" action="../search/"><input class="docs-search-query" id="documenter-search-query" name="q" type="text" placeholder="Search docs"/></form><ul class="docs-menu"><li><a class="tocitem" href="../">Overview</a></li><li><a class="tocitem" href="../OLSexamples/">OLS examples</a></li><li class="is-active"><a class="tocitem" href>IV/2SLS examples</a></li><li><a class="tocitem" href="../exported/">Public functions and types</a></li></ul><div class="docs-version-selector field has-addons"><div class="control"><span class="docs-label button is-static is-size-7">Version</span></div><div class="docs-selector control is-expanded"><div class="select is-fullwidth is-size-7"><select id="documenter-version-selector"></select></div></div></div></nav><div class="docs-main"><header class="docs-navbar"><nav class="breadcrumb"><ul class="is-hidden-mobile"><li class="is-active"><a href>IV/2SLS examples</a></li></ul><ul class="is-hidden-tablet"><li class="is-active"><a href>IV/2SLS examples</a></li></ul></nav><div class="docs-right"><a class="docs-edit-link" href="https://github.com/droodman/WildBootTests.jl/blob/master/docs/src/IVexamples.md" title="Edit on GitHub"><span class="docs-icon fab"></span><span class="docs-label is-hidden-touch">Edit on GitHub</span></a><a class="docs-settings-button fas fa-cog" id="documenter-settings-button" href="#" title="Settings"></a><a class="docs-sidebar-button fa fa-bars is-hidden-desktop" id="documenter-sidebar-button" href="#"></a></div></header><article class="content" id="documenter-page"><pre><code class="nohighlight hljs">using WildBootTests, CSV, DataFrames, StatsModels, GLM, Plots

# specify exactly identified model: regress wage on on tenure, instrumented by union,
# controlling for ttl_exp and collgrad
d = download(&quot;http://www.stata-press.com/data/r8/nlsw88.dta&quot;, tempname() * &quot;.dta&quot;)
df = DataFrame(load(d))[:, [:wage; :tenure; :ttl_exp; :collgrad; :industry; :union]]
dropmissing!(df)
f = @formula(wage ~ 1 + ttl_exp + collgrad)
f = apply_schema(f, schema(f, df))
resp, predexog = modelcols(f, df)
ivf = @formula(tenure ~ union)
ivf = apply_schema(ivf, schema(ivf, df))
predendog, inst = modelcols(ivf, df)

# test that coefficient on tenure = 0, clustering errors by industry
R = [0 0 0 1]; r = [0]
wildboottest(R, r; resp, predexog, predendog, inst, clustid=df.industry)

# use equal-tailed instead of symmetric p value
wildboottest(R, r; resp, predexog, predendog, inst, clustid=df.industry, ptype=:equaltail)

# perform bootstrap-c instead of bootstrap-t, as advocated by Young (2019)
wildboottest(R, r; resp, predexog, predendog, inst, clustid=df.industry, bootstrapc=true)

# Rao/score test without bootstrap
wildboottest(R, r; resp, predexog, predendog, inst, clustid=df.industry, reps=0)

# Wald test without bootstrap
wildboottest(R, r; resp, predexog, predendog, inst, clustid=df.industry, reps=0, imposenull=false)

# Anderson-Rubin test that hypothesis holds and instrument is valid
wildboottest(R, r; resp, predexog, predendog, inst, clustid=df.industry, arubin=true)

# modify model to drop controls and make ttl_exp an instrument
f = @formula(wage ~ 1)
f = apply_schema(f, schema(f, df))
resp, predexog = modelcols(f, df)
ivf = @formula(tenure ~ collgrad + ttl_exp)
ivf = apply_schema(ivf, schema(ivf, df))
predendog, inst = modelcols(ivf, df)

# test same hypothesis in context of LIML regression
R = [0 1]; r = [0]
wildboottest(R, r; resp, predexog, predendog, inst, liml=true, clustid=df.industry)</code></pre></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../OLSexamples/">« OLS examples</a><a class="docs-footer-nextpage" href="../exported/">Public functions and types »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 0.27.25 on <span class="colophon-date" title="Wednesday 17 April 2024 22:06">Wednesday 17 April 2024</span>. Using Julia version 1.8.5.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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<!DOCTYPE html>
<html lang="en"><head><meta charset="UTF-8"/><meta name="viewport" content="width=device-width, initial-scale=1.0"/><title>OLS examples · WildBootTests.jl</title><script data-outdated-warner src="../assets/warner.js"></script><link href="https://cdnjs.cloudflare.com/ajax/libs/lato-font/3.0.0/css/lato-font.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/juliamono/0.045/juliamono.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.15.4/css/fontawesome.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.15.4/css/solid.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.15.4/css/brands.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.13.24/katex.min.css" rel="stylesheet" type="text/css"/><script>documenterBaseURL=".."</script><script src="https://cdnjs.cloudflare.com/ajax/libs/require.js/2.3.6/require.min.js" data-main="../assets/documenter.js"></script><script src="../siteinfo.js"></script><script src="../../versions.js"></script><link class="docs-theme-link" rel="stylesheet" type="text/css" href="../assets/themes/documenter-dark.css" data-theme-name="documenter-dark" data-theme-primary-dark/><link class="docs-theme-link" rel="stylesheet" type="text/css" href="../assets/themes/documenter-light.css" data-theme-name="documenter-light" data-theme-primary/><script src="../assets/themeswap.js"></script></head><body><div id="documenter"><nav class="docs-sidebar"><div class="docs-package-name"><span class="docs-autofit"><a href="../">WildBootTests.jl</a></span></div><form class="docs-search" action="../search/"><input class="docs-search-query" id="documenter-search-query" name="q" type="text" placeholder="Search docs"/></form><ul class="docs-menu"><li><a class="tocitem" href="../">Overview</a></li><li class="is-active"><a class="tocitem" href>OLS examples</a><ul class="internal"><li><a class="tocitem" href="#Basic-OLS-example"><span>Basic OLS example</span></a></li><li><a class="tocitem" href="#Further-examples"><span>Further examples</span></a></li></ul></li><li><a class="tocitem" href="../IVexamples/">IV/2SLS examples</a></li><li><a class="tocitem" href="../exported/">Public functions and types</a></li></ul><div class="docs-version-selector field has-addons"><div class="control"><span class="docs-label button is-static is-size-7">Version</span></div><div class="docs-selector control is-expanded"><div class="select is-fullwidth is-size-7"><select id="documenter-version-selector"></select></div></div></div></nav><div class="docs-main"><header class="docs-navbar"><nav class="breadcrumb"><ul class="is-hidden-mobile"><li class="is-active"><a href>OLS examples</a></li></ul><ul class="is-hidden-tablet"><li class="is-active"><a href>OLS examples</a></li></ul></nav><div class="docs-right"><a class="docs-edit-link" href="https://github.com/droodman/WildBootTests.jl/blob/master/docs/src/OLSexamples.md" title="Edit on GitHub"><span class="docs-icon fab"></span><span class="docs-label is-hidden-touch">Edit on GitHub</span></a><a class="docs-settings-button fas fa-cog" id="documenter-settings-button" href="#" title="Settings"></a><a class="docs-sidebar-button fa fa-bars is-hidden-desktop" id="documenter-sidebar-button" href="#"></a></div></header><article class="content" id="documenter-page"><h2 id="Basic-OLS-example"><a class="docs-heading-anchor" href="#Basic-OLS-example">Basic OLS example</a><a id="Basic-OLS-example-1"></a><a class="docs-heading-anchor-permalink" href="#Basic-OLS-example" title="Permalink"></a></h2><pre><code class="nohighlight hljs">julia&gt; using WildBootTests, CSV, DataFrames, StatsModels, GLM, Plots

julia&gt; d = download(&quot;https://raw.github.com/vincentarelbundock/Rdatasets/master/csv/sandwich/PetersenCL.csv&quot;);

julia&gt; df = CSV.read(d, DataFrame);

julia&gt; f = @formula(y ~ 1 + x); # state OLS model

julia&gt; f = apply_schema(f, schema(f, df)); # link model to data

julia&gt; lm(f, df) # run OLS for illustration; not needed for following lines
StatsModels.TableRegressionModel{LinearModel{GLM.LmResp{Vector{Float64}}, GLM.DensePredChol{Float64, LinearAlgebra.CholeskyPivoted{Float64, Matrix{Float64}}}}, Matrix{Float64}}

y ~ 1 + x

Coefficients:
─────────────────────────────────────────────────────────────────────────
Coef. Std. Error t Pr(&gt;|t|) Lower 95% Upper 95%
─────────────────────────────────────────────────────────────────────────
(Intercept) 0.0296797 0.0283593 1.05 0.2954 -0.025917 0.0852764
x 1.03483 0.0285833 36.20 &lt;1e-99 0.978798 1.09087
─────────────────────────────────────────────────────────────────────────

julia&gt; resp, predexog = modelcols(f, df); # extract response &amp; (exogenous) predictor variables

julia&gt; clustid = df.firm; # extract clustering variable

julia&gt; R = [0 1]; r = [1]; # put null that coefficient on x = 1 in Rβ̂ = r form, where β̂ is parameter vector

julia&gt; test = wildboottest(R, r; resp=resp, predexog=predexog, clustid=clustid)
WildBootTests.BootTestResult{Float32}

p = 0.492
ci = Float32[0.93461335 1.1347668]

julia&gt; test = wildboottest(R, r; resp, predexog, clustid); # same, using Julia syntactic sugar

julia&gt; p(test) # programmatically extract p value
0.49459493f0

julia&gt; ci(test) # programmatically extract confidence interval
1×2 Matrix{Float32}:
0.934961 1.13469

julia&gt; plot(plotpoints(test)...) # plot confidence curve</code></pre><h2 id="Further-examples"><a class="docs-heading-anchor" href="#Further-examples">Further examples</a><a id="Further-examples-1"></a><a class="docs-heading-anchor-permalink" href="#Further-examples" title="Permalink"></a></h2><pre><code class="nohighlight hljs">using WildBootTests, CSV, DataFrames, StatsModels, GLM, Plots

# use Webb instead of Rademacher weights, 99,999 bootstrap replications instead of 999
wildboottest(R, r; resp, predexog, clustid, reps=99999, auxwttype=:webb)

# jackknife the bootstrap data-generating process to reduce distortion from outliers
wildboottest(Float64, R, r; resp, predexog, clustid, jk=true)

# use guaranteed-stable random number generator for exact replicability
using StableRNGs
wildboottest(R, r; resp, predexog, clustid, rng=StableRNG(23948572))

# test that coefficient on intercept = 0 and coefficient on x = 1; plot confidence surface
test = wildboottest([1 0; 0 1], [0;1]; resp, predexog, clustid, reps=9999)
plot(plotpoints(test).X..., plotpoints(test).p, st=:contourf)

# multiway-cluster errors by firm and year; bootstrap by firm
wildboottest(R, r; resp, predexog, clustid=Matrix(df[:,[:firm, :year]]), nerrclustvar=2, nbootclustvar=1)

# same but bootstrap by year
wildboottest(R, r; resp, predexog, clustid=Matrix(df[:,[:year, :firm]]), nerrclustvar=2, nbootclustvar=1)

# same but bootstrap by year-firm pair
wildboottest(R, r; resp, predexog, clustid=Matrix(df[:,[:year, :firm]]), nerrclustvar=2, nbootclustvar=2)

# Rao/score test with multiway clustering of errors but no bootstrap
wildboottest(R, r; resp, predexog, predendog, inst, Matrix(df[:,[:year, :firm]]), reps=0)

# Same but Wald test: i.e., conventional, multiway clustered errors
wildboottest(R, r; resp, predexog, predendog, inst, clustid=Matrix(df[:,[:year, :firm]]), reps=0, imposenull=false)

# add year fixed effects to model; cluster by firm
wildboottest(R, r; resp, predexog, feid=df.year, clustid=df.firm)

# test hypotheses, while imposing model constraint that constant term = 0.2
R1 = [1 0]; r1 = [.2]
wildboottest(R, r; R1, r1, resp, predexog, clustid=df.firm)</code></pre></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../">« Overview</a><a class="docs-footer-nextpage" href="../IVexamples/">IV/2SLS examples »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 0.27.25 on <span class="colophon-date" title="Wednesday 17 April 2024 22:06">Wednesday 17 April 2024</span>. Using Julia version 1.8.5.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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