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index-speaker.html
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<!DOCTYPE html>
<html lang="en"><head>
<script src="index_files/libs/clipboard/clipboard.min.js"></script>
<script src="index_files/libs/quarto-html/tabby.min.js"></script>
<script src="index_files/libs/quarto-html/popper.min.js"></script>
<script src="index_files/libs/quarto-html/tippy.umd.min.js"></script>
<link href="index_files/libs/quarto-html/tippy.css" rel="stylesheet">
<link href="index_files/libs/quarto-html/light-border.css" rel="stylesheet">
<link href="index_files/libs/quarto-html/quarto-html.min.css" rel="stylesheet" data-mode="light">
<link href="index_files/libs/quarto-html/quarto-syntax-highlighting.css" rel="stylesheet" id="quarto-text-highlighting-styles"><meta charset="utf-8">
<meta name="generator" content="quarto-1.3.361">
<meta name="author" content="by Tomasz Woźniak">
<title>Bayesian Structural Vector Autoregressions</title>
<meta name="apple-mobile-web-app-capable" content="yes">
<meta name="apple-mobile-web-app-status-bar-style" content="black-translucent">
<meta name="viewport" content="width=device-width, initial-scale=1.0, maximum-scale=1.0, user-scalable=no, minimal-ui">
<link rel="stylesheet" href="index_files/libs/revealjs/dist/reset.css">
<link rel="stylesheet" href="index_files/libs/revealjs/dist/reveal.css">
<style>
code{white-space: pre-wrap;}
span.smallcaps{font-variant: small-caps;}
div.columns{display: flex; gap: min(4vw, 1.5em);}
div.column{flex: auto; overflow-x: auto;}
div.hanging-indent{margin-left: 1.5em; text-indent: -1.5em;}
ul.task-list{list-style: none;}
ul.task-list li input[type="checkbox"] {
width: 0.8em;
margin: 0 0.8em 0.2em -1em; /* quarto-specific, see https://github.com/quarto-dev/quarto-cli/issues/4556 */
vertical-align: middle;
}
</style>
<link rel="stylesheet" href="index_files/libs/revealjs/dist/theme/quarto.css">
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<link href="index_files/libs/revealjs/plugin/quarto-support/footer.css" rel="stylesheet">
<style type="text/css">
.callout {
margin-top: 1em;
margin-bottom: 1em;
border-radius: .25rem;
}
.callout.callout-style-simple {
padding: 0em 0.5em;
border-left: solid #acacac .3rem;
border-right: solid 1px silver;
border-top: solid 1px silver;
border-bottom: solid 1px silver;
display: flex;
}
.callout.callout-style-default {
border-left: solid #acacac .3rem;
border-right: solid 1px silver;
border-top: solid 1px silver;
border-bottom: solid 1px silver;
}
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flex-grow: 1;
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font-size: 1rem;
font-weight: 400;
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font-size: 0.9rem;
font-weight: 400;
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margin-top: 0;
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margin-top: 0.7em;
}
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border-bottom: none;
font-size: .9rem;
font-weight: 600;
opacity: 75%;
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<div class="slides">
<section id="title-slide" data-background-color="#ff69b4" class="quarto-title-block center">
<h1 class="title"><span style="color: #ffd700;">Bayesian Structural Vector Autoregressions</span></h1>
<div class="quarto-title-authors">
<div class="quarto-title-author">
<div class="quarto-title-author-name">
<span style="color: #ffd700;">by Tomasz Woźniak</span>
</div>
</div>
</div>
</section>
<section id="section" class="slide level2" data-background-color="#ff69b4">
<h2></h2>
<p><span class="math display">\[ \]</span></p>
<h3 style="color:#ffd700;" id="structural-vector-autoregressions">Structural Vector Autoregressions</h3>
<h3 style="color:#ffd700;" id="identification-of-structural-vars">Identification of Structural VARs</h3>
<h3 style="color:#ffd700;" id="dynamic-causal-effects">Dynamic Causal Effects</h3>
<h3 style="color:#ffd700;" id="bayesian-estimation">Bayesian Estimation</h3>
<h3 style="color:#ffd700;" id="monetary-policy-analysis-using-the-bsvars-package">Monetary Policy Analysis Using the <a href="https://cran.r-project.org/package=bsvars">bsvars</a> Package</h3>
</section>
<section id="section-1" class="slide level2" data-background-color="#ff69b4">
<h2></h2>
<p><img data-src="bsvars.png" class="absolute" style="top: 30px; right: 275px; width: 500px; "></p>
</section>
<section id="materials" class="slide level2" data-background-color="#ff69b4">
<h2><span style="color: #ffd700;">Materials</span></h2>
<p><span class="math display">\[ \]</span></p>
<h3 style="color:#ffd700;" id="lecture-slides-as-a-website">Lecture Slides <a href="https://bsvars.github.io/2024-10-be24-bsvars">as a Website</a></h3>
<h3 style="color:#ffd700;" id="r-script-for-your-own-australian-monetary-policy-analysis"><a href="https://github.com/bsvars/2024-10-be24-bsvars/blob/main/be24-bsvars.R">R script</a> for your own Australian monetary policy analysis</h3>
<h3 style="color:#ffd700;" id="github-repo-to-reproduce-the-slides-and-results">GitHub <a href="https://github.com/bsvars/2024-10-be24-bsvars">repo</a> to reproduce the slides and results</h3>
<h3 style="color:#ffd700;" id="tasks">Tasks</h3>
</section>
<section id="structural-vector-autoregressions-1" class="slide level2" data-background-color="#ff69b4">
<h2><span style="color: #ffd700;">Structural Vector Autoregressions</span></h2>
</section>
<section id="structural-vector-autoregressions-2" class="slide level2">
<h2>Structural Vector Autoregressions</h2>
<ul>
<li>go-to models for the analysis of policy effects</li>
</ul>
<div>
<ul>
<li class="fragment">facilitate the analysis of <strong>dynamic causal effects</strong> of a well-isolated cause</li>
<li class="fragment">extensively used for: <em>monetary</em> and <em>fiscal</em> policy, <em>financial</em> markets, …</li>
<li class="fragment">relatively simple to work with data and provide <em>empirical evidence on the propagation of shocks</em> through economies and markets</li>
<li class="fragment">provide data-driven stylised facts to be incorporated in theoretical model</li>
<li class="fragment">require identification of the cause of the dynamic effects</li>
<li class="fragment">extendible: <em>featuring many variations in specification</em>
<ul>
<li class="fragment">non-normality</li>
<li class="fragment">heteroskedasticity</li>
<li class="fragment">time-varying parameters</li>
<li class="fragment">Bayesian</li>
</ul></li>
<li class="fragment">Proposed by <a href="https://doi.org/10.2307/1912017">Sims (1980)</a></li>
</ul>
</div>
<div class="footer">
<p><a href="https://bsvars.github.io/2024-10-be24-bsvars">Bayesian Structural VARs</a></p>
</div>
</section>
<section id="structural-vector-autoregressions-3" class="slide level2">
<h2>Structural Vector Autoregressions</h2>
<div class="footer">
<p><a href="https://bsvars.github.io/2024-10-be24-bsvars">Bayesian Structural VARs</a></p>
</div>
<h3 id="the-model.">The model.</h3>
<p><span class="math display">\[\begin{align}
\text{VAR equation: }&& y_t &= \mathbf{A}_1 y_{t-1} + \dots + \mathbf{A}_p y_{t-p} + \boldsymbol\mu_0 + \epsilon_t\\[1ex]
\text{structural equation: }&& \mathbf{B}\epsilon_t &= u_t\\[1ex]
\text{structural shocks: }&& u_t |Y_{t-1} &\sim N_N\left(\mathbf{0}_N,\mathbf{I}_N\right)
\end{align}\]</span></p>
<div class="fragment">
<!-- -->
<h3 id="notation.">Notation.</h3>
<ul>
<li><p><span class="math inline">\(\mathbf{B}\)</span> - <span class="math inline">\(N\times N\)</span> structural matrix of contemporaneous relationships</p></li>
<li><p><span class="math inline">\(u_t\)</span> - <span class="math inline">\(N\)</span>-vector of structural shocks at time <span class="math inline">\(t\)</span></p>
<p>Isolating these shocks allows us to <em>identify dynamic effects of uncorrelated shocks</em> on variables <span class="math inline">\(y_t\)</span></p></li>
<li><p><span class="math inline">\(\epsilon_t\)</span> - <span class="math inline">\(N\)</span>-vector with error terms at time <span class="math inline">\(t\)</span></p></li>
<li><p>the rest as in the lecture on <a href="https://bsvars.github.io/2024-10-be24-bsvarSIGNs/#/varp-model">Bayesian VARs</a></p></li>
</ul>
</div>
</section>
<section id="section-2" class="slide level2" data-background-color="#ff69b4">
<h2></h2>
<p><img data-src="social.png" class="absolute" style="top: 30px; right: 200px; width: 800px; "></p>
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