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index.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="Tomasz Woźniak">
<title>index</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;
}
/* CSS for syntax highlighting */
pre > code.sourceCode { white-space: pre; position: relative; }
pre > code.sourceCode > span { display: inline-block; line-height: 1.25; }
pre > code.sourceCode > span:empty { height: 1.2em; }
.sourceCode { overflow: visible; }
code.sourceCode > span { color: inherit; text-decoration: inherit; }
div.sourceCode { margin: 1em 0; }
pre.sourceCode { margin: 0; }
@media screen {
div.sourceCode { overflow: auto; }
}
@media print {
pre > code.sourceCode { white-space: pre-wrap; }
pre > code.sourceCode > span { text-indent: -5em; padding-left: 5em; }
}
pre.numberSource code
{ counter-reset: source-line 0; }
pre.numberSource code > span
{ position: relative; left: -4em; counter-increment: source-line; }
pre.numberSource code > span > a:first-child::before
{ content: counter(source-line);
position: relative; left: -1em; text-align: right; vertical-align: baseline;
border: none; display: inline-block;
-webkit-touch-callout: none; -webkit-user-select: none;
-khtml-user-select: none; -moz-user-select: none;
-ms-user-select: none; user-select: none;
padding: 0 4px; width: 4em;
color: #aaaaaa;
}
pre.numberSource { margin-left: 3em; border-left: 1px solid #aaaaaa; padding-left: 4px; }
div.sourceCode
{ color: #003b4f; background-color: #f1f3f5; }
@media screen {
pre > code.sourceCode > span > a:first-child::before { text-decoration: underline; }
}
code span { color: #003b4f; } /* Normal */
code span.al { color: #ad0000; } /* Alert */
code span.an { color: #5e5e5e; } /* Annotation */
code span.at { color: #657422; } /* Attribute */
code span.bn { color: #ad0000; } /* BaseN */
code span.bu { } /* BuiltIn */
code span.cf { color: #003b4f; } /* ControlFlow */
code span.ch { color: #20794d; } /* Char */
code span.cn { color: #8f5902; } /* Constant */
code span.co { color: #5e5e5e; } /* Comment */
code span.cv { color: #5e5e5e; font-style: italic; } /* CommentVar */
code span.do { color: #5e5e5e; font-style: italic; } /* Documentation */
code span.dt { color: #ad0000; } /* DataType */
code span.dv { color: #ad0000; } /* DecVal */
code span.er { color: #ad0000; } /* Error */
code span.ex { } /* Extension */
code span.fl { color: #ad0000; } /* Float */
code span.fu { color: #4758ab; } /* Function */
code span.im { color: #00769e; } /* Import */
code span.in { color: #5e5e5e; } /* Information */
code span.kw { color: #003b4f; } /* Keyword */
code span.op { color: #5e5e5e; } /* Operator */
code span.ot { color: #003b4f; } /* Other */
code span.pp { color: #ad0000; } /* Preprocessor */
code span.sc { color: #5e5e5e; } /* SpecialChar */
code span.ss { color: #20794d; } /* SpecialString */
code span.st { color: #20794d; } /* String */
code span.va { color: #111111; } /* Variable */
code span.vs { color: #20794d; } /* VerbatimString */
code span.wa { color: #5e5e5e; font-style: italic; } /* Warning */
</style>
<link rel="stylesheet" href="index_files/libs/revealjs/dist/theme/quarto.css">
<link href="index_files/libs/revealjs/plugin/quarto-line-highlight/line-highlight.css" rel="stylesheet">
<link href="index_files/libs/revealjs/plugin/reveal-menu/menu.css" rel="stylesheet">
<link href="index_files/libs/revealjs/plugin/reveal-menu/quarto-menu.css" rel="stylesheet">
<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;
}
.callout .callout-body-container {
flex-grow: 1;
}
.callout.callout-style-simple .callout-body {
font-size: 1rem;
font-weight: 400;
}
.callout.callout-style-default .callout-body {
font-size: 0.9rem;
font-weight: 400;
}
.callout.callout-titled.callout-style-simple .callout-body {
margin-top: 0.2em;
}
.callout:not(.callout-titled) .callout-body {
display: flex;
}
.callout:not(.no-icon).callout-titled.callout-style-simple .callout-content {
padding-left: 1.6em;
}
.callout.callout-titled .callout-header {
padding-top: 0.2em;
margin-bottom: -0.2em;
}
.callout.callout-titled .callout-title p {
margin-top: 0.5em;
margin-bottom: 0.5em;
}
.callout.callout-titled.callout-style-simple .callout-content p {
margin-top: 0;
}
.callout.callout-titled.callout-style-default .callout-content p {
margin-top: 0.7em;
}
.callout.callout-style-simple div.callout-title {
border-bottom: none;
font-size: .9rem;
font-weight: 600;
opacity: 75%;
}
.callout.callout-style-default div.callout-title {
border-bottom: none;
font-weight: 600;
opacity: 85%;
font-size: 0.9rem;
padding-left: 0.5em;
padding-right: 0.5em;
}
.callout.callout-style-default div.callout-content {
padding-left: 0.5em;
padding-right: 0.5em;
}
.callout.callout-style-simple .callout-icon::before {
height: 1rem;
width: 1rem;
display: inline-block;
content: "";
background-repeat: no-repeat;
background-size: 1rem 1rem;
}
.callout.callout-style-default .callout-icon::before {
height: 0.9rem;
width: 0.9rem;
display: inline-block;
content: "";
background-repeat: no-repeat;
background-size: 0.9rem 0.9rem;
}
.callout-title {
display: flex
}
.callout-icon::before {
margin-top: 1rem;
padding-right: .5rem;
}
.callout.no-icon::before {
display: none !important;
}
.callout.callout-titled .callout-body > .callout-content > :last-child {
margin-bottom: 0.5rem;
}
.callout.callout-titled .callout-icon::before {
margin-top: .5rem;
padding-right: .5rem;
}
.callout:not(.callout-titled) .callout-icon::before {
margin-top: 1rem;
padding-right: .5rem;
}
/* Callout Types */
div.callout-note {
border-left-color: #4582ec !important;
}
div.callout-note .callout-icon::before {
background-image: url('data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACAAAAAgCAYAAABzenr0AAAAAXNSR0IArs4c6QAAAERlWElmTU0AKgAAAAgAAYdpAAQAAAABAAAAGgAAAAAAA6ABAAMAAAABAAEAAKACAAQAAAABAAAAIKADAAQAAAABAAAAIAAAAACshmLzAAAEU0lEQVRYCcVXTWhcVRQ+586kSUMMxkyaElstCto2SIhitS5Ek8xUKV2poatCcVHtUlFQk8mbaaziwpWgglJwVaquitBOfhQXFlqlzSJpFSpIYyXNjBNiTCck7x2/8/LeNDOZxDuEkgOXe++553zfefee+/OYLOXFk3+1LLrRdiO81yNqZ6K9cG0P3MeFaMIQjXssE8Z1JzLO9ls20MBZX7oG8w9GxB0goaPrW5aNMp1yOZIa7Wv6o2ykpLtmAPs/vrG14Z+6d4jpbSKuhdcSyq9wGMPXjonwmESXrriLzFGOdDBLB8Y6MNYBu0dRokSygMA/mrun8MGFN3behm6VVAwg4WR3i6FvYK1T7MHo9BK7ydH+1uurECoouk5MPRyVSBrBHMYwVobG2aOXM07sWrn5qgB60rc6mcwIDJtQrnrEr44kmy+UO9r0u9O5/YbkS9juQckLed3DyW2XV/qWBBB3ptvI8EUY3I9p/67OW+g967TNr3Sotn3IuVlfMLVnsBwH4fsnebJvyGm5GeIUA3jljERmrv49SizPYuq+z7c2H/jlGC+Ghhupn/hcapqmcudB9jwJ/3jvnvu6vu5lVzF1fXyZuZZ7U8nRmVzytvT+H3kilYvH09mLWrQdwFSsFEsxFVs5fK7A0g8gMZjbif4ACpKbjv7gNGaD8bUrlk8x+KRflttr22JEMRUbTUwwDQScyzPgedQHZT0xnx7ujw2jfVfExwYHwOsDTjLdJ2ebmeQIlJ7neo41s/DrsL3kl+W2lWvAga0tR3zueGr6GL78M3ifH0rGXrBC2aAR8uYcIA5gwV8zIE8onoh8u0Fca/ciF7j1uOzEnqcIm59sEXoGc0+z6+H45V1CvAvHcD7THztu669cnp+L0okAeIc6zjbM/24LgGM1gZk7jnRu1aQWoU9sfUOuhrmtaPIO3YY1KLLWZaEO5TKUbMY5zx8W9UJ6elpLwKXbsaZ4EFl7B4bMtDv0iRipKoDQT2sNQI9b1utXFdYisi+wzZ/ri/1m7QfDgEuvgUUEIJPq3DhX/5DWNqIXDOweC2wvIR90Oq3lDpdMIgD2r0dXvGdsEW5H6x6HLRJYU7C69VefO1x8Gde1ZFSJLfWS1jbCnhtOPxmpfv2LXOA2Xk2tvnwKKPFuZ/oRmwBwqRQDcKNeVQkYcOjtWVBuM/JuYw5b6isojIkYxyYAFn5K7ZBF10fea52y8QltAg6jnMqNHFBmGkQ1j+U43HMi2xMar1Nv0zGsf1s8nUsmUtPOOrbFIR8bHFDMB5zL13Gmr/kGlCkUzedTzzmzsaJXhYawnA3UmARpiYj5ooJZiUoxFRtK3X6pgNPv+IZVPcnwbOl6f+aBaO1CNvPW9n9LmCp01nuSaTRF2YxHqZ8DYQT6WsXT+RD6eUztwYLZ8rM+rcPxamv1VQzFUkzFXvkiVrySGQgJNvXHJAxiU3/NwiC03rSf05VBaPtu/Z7/B8Yn/w7eguloAAAAAElFTkSuQmCC');
}
div.callout-note.callout-style-default .callout-title {
background-color: #dae6fb
}
div.callout-important {
border-left-color: #d9534f !important;
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<body class="quarto-light">
<div class="reveal">
<div class="slides">
<section id="section" class="slide level2" data-background-color="#00bf63">
<h2></h2>
<p><img data-src="bsvars.png" class="absolute" style="top: 40px; right: 540px; width: 500px; "> <img data-src="bsvarSIGNs.png" class="absolute" style="top: 40px; right: 10px; width: 500px; "></p>
</section>
<section id="section-1" class="slide level2" data-background-color="#00bf63">
<h2></h2>
<p><span class="math display">\[ \]</span></p>
<h3 style="color:#8c52ff;" id="this-presentation">This presentation</h3>
<h4 style="color:white;" id="slides-as-a-website">Slides as a <a href="https://bsvars.github.io/2024-08-bsvars-monash/" style="color:#8c52ff;">Website</a></h4>
<h4 style="color:white;" id="github-repo-to-reproduce-the-slides-and-results">GitHub <a href="https://github.com/bsvars/2024-08-bsvars-monash" style="color:#8c52ff;">repo</a> to reproduce the slides and results</h4>
<p><span class="math display">\[ \]</span></p>
<h3 style="color:#8c52ff;" id="resources">Resources</h3>
<h4 style="color:white;" id="bsvars.github.io"><a href="https://bsvars.github.io" style="color:#8c52ff;">bsvars.github.io</a></h4>
<h4 style="color:white;" id="bsvars-on-cran"><a href="https://cran.r-project.org/package=bsvars" style="color:#8c52ff;">bsvars</a> on CRAN</h4>
<h4 style="color:white;" id="bsvarsigns-on-cran"><a href="https://cran.r-project.org/package=bsvarSIGNs" style="color:#8c52ff;">bsvarSIGNs</a> on CRAN</h4>
</section>
<section id="section-2" class="slide level2" data-background-color="#00bf63">
<h2></h2>
<p><img data-src="[email protected]" class="absolute" style="width: 735px; "></p>
</section>
<section id="section-3" class="slide level2" data-background-color="#00bf63">
<h2></h2>
<p><span class="math display">\[ \]</span></p>
<p><span class="math display">\[ \]</span></p>
<h3 id="bsvars-features"><a href="https://bsvars.github.io" style="color:#8c52ff;">bsvars</a> features</h3>
<h3 style="color:white;" id="bsvars-models-and-identification"><a href="https://bsvars.github.io" style="color:#8c52ff;">bsvars</a> models and identification</h3>
<h3 style="color:white;" id="bsvars-modeling-of-monetary-policy"><a href="https://bsvars.github.io" style="color:#8c52ff;">bsvars</a> modeling of monetary policy</h3>
</section>
<section id="bsvars-features-1" class="slide level2" data-background-color="#00bf63">
<h2><a href="https://bsvars.github.io" style="color:#8c52ff;">bsvars</a> features</h2>
</section>
<section id="section-4" class="slide level2">
<h2></h2>
<div class="columns">
<div class="column" style="width:50%;">
<p><img data-src="bsvars-cran.png" class="absolute" style="top: 10px; width: 530px; "></p>
</div><div class="column" style="width:50%;">
<p><img data-src="bsvarSIGNs-cran.png" class="absolute" style="top: 10px; width: 530px; "></p>
</div>
</div>
</section>
<section id="bsvars-features-2" class="slide level2" data-background-color="#00bf63">
<h2><a href="https://bsvars.github.io" style="color:#8c52ff;">bsvars</a> features</h2>
<p><span class="math display">\[ \]</span></p>
<ul>
<li>Bayesian estimation of Structural VARs</li>
<li>coherent code structure, workflows, and objects</li>
<li>excellent computational speed</li>
<li>frontier econometric techniques</li>
<li>efficient and fast Gibbs samplers</li>
<li>compiled code using <span style="color:#8c52ff;">cpp</span> via <a href="https://cran.r-project.org/package=Rcpp" style="color:#8c52ff;">Rcpp</a> and <a href="https://cran.r-project.org/package=RcppArmadillo" style="color:#8c52ff;">RcppArmadillo</a></li>
<li>data analysis in <a href="https://cran.r-project.org/" style="color:#8c52ff;">R</a></li>
</ul>
</section>
<section id="section-5" class="slide level2" data-background-color="#00bf63">
<h2></h2>
<div class="columns">
<div class="column" style="width:50%;">
<p><img data-src="bsvars.png" width="150"></p>
<ul>
<li>5 volatility & 3 non-normal models</li>
<li>identification using
<ul>
<li>exclusion restrictions</li>
<li>heteroskedasticity, and</li>
<li>non-normality</li>
</ul></li>
<li>Priors: 3-level eq-specific local-global shrinkage</li>
</ul>
</div><div class="column" style="width:50%;">
<p><img data-src="bsvarSIGNs.png" width="150"></p>
<ul>
<li>flexible Bayesian VAR</li>
<li>identification using
<ul>
<li>sign restrictions</li>
<li>sign & zero restrictions</li>
<li>narrative restrictions</li>
</ul></li>
<li>Priors: Minnesota with dummy observation and estimated shrinkage</li>
</ul>
</div>
</div>
</section>
<section id="section-6" class="slide level2" data-background-color="#00bf63">
<h2></h2>
<div class="columns">
<div class="column" style="width:50%;">
<p><img data-src="bsvars.png" width="150"></p>
<ul>
<li>package and data loading</li>
</ul>
<div class="cell">
<div class="sourceCode cell-code" id="cb1"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb1-1"><a href="#cb1-1" aria-hidden="true" tabindex="-1"></a><span class="fu">library</span>(bsvars)</span>
<span id="cb1-2"><a href="#cb1-2" aria-hidden="true" tabindex="-1"></a><span class="fu">data</span>(us_fiscal_lsuw)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</div>
<ul>
<li>simple model setup</li>
</ul>
<div class="cell">
<div class="sourceCode cell-code" id="cb2"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb2-1"><a href="#cb2-1" aria-hidden="true" tabindex="-1"></a>spec <span class="ot">=</span> specify_bsvar<span class="sc">$</span><span class="fu">new</span>(us_fiscal_lsuw)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</div>
<ul>
<li>simple estimation</li>
</ul>
<div class="cell">
<div class="sourceCode cell-code" id="cb3"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb3-1"><a href="#cb3-1" aria-hidden="true" tabindex="-1"></a>burn <span class="ot">=</span> <span class="fu">estimate</span>(spec, <span class="at">S =</span> <span class="dv">1000</span>)</span>
<span id="cb3-2"><a href="#cb3-2" aria-hidden="true" tabindex="-1"></a>post <span class="ot">=</span> <span class="fu">estimate</span>(burn, <span class="at">S =</span> <span class="dv">10000</span>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</div>
</div><div class="column" style="width:50%;">
<p><img data-src="bsvarSIGNs.png" width="150"></p>
<ul>
<li>package and data loading</li>
</ul>
<div class="cell">
<div class="sourceCode cell-code" id="cb4"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb4-1"><a href="#cb4-1" aria-hidden="true" tabindex="-1"></a><span class="fu">library</span>(bsvarSIGNs)</span>
<span id="cb4-2"><a href="#cb4-2" aria-hidden="true" tabindex="-1"></a><span class="fu">data</span>(optimism)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</div>
<ul>
<li>simple model setup</li>
</ul>
<div class="cell">
<div class="sourceCode cell-code" id="cb5"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb5-1"><a href="#cb5-1" aria-hidden="true" tabindex="-1"></a>spec <span class="ot">=</span> specify_bsvarSIGN<span class="sc">$</span><span class="fu">new</span>(optimism)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</div>
<ul>
<li>simple estimation</li>
</ul>
<div class="cell">
<div class="sourceCode cell-code" id="cb6"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb6-1"><a href="#cb6-1" aria-hidden="true" tabindex="-1"></a>post <span class="ot">=</span> <span class="fu">estimate</span>(spec, <span class="at">S =</span> <span class="dv">10000</span>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</div>
</div>
</div>
</section>
<section id="section-7" class="slide level2" data-background-color="#00bf63">
<h2></h2>
<div class="columns">
<div class="column" style="width:50%;">
<p><img data-src="bsvars.png" width="150"></p>
<ul>
<li>structural analyses</li>
</ul>
<div class="cell">
<div class="sourceCode cell-code" id="cb7"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb7-1"><a href="#cb7-1" aria-hidden="true" tabindex="-1"></a>irfs <span class="ot">=</span> <span class="fu">compute_impulse_responses</span>(post , <span class="at">horizon =</span> <span class="dv">12</span>)</span>
<span id="cb7-2"><a href="#cb7-2" aria-hidden="true" tabindex="-1"></a>fevd <span class="ot">=</span> <span class="fu">compute_variance_decompositions</span>(post, <span class="at">horizon =</span> <span class="dv">12</span>)</span>
<span id="cb7-3"><a href="#cb7-3" aria-hidden="true" tabindex="-1"></a>hds <span class="ot">=</span> <span class="fu">compute_historical_decompositions</span>(post)</span>
<span id="cb7-4"><a href="#cb7-4" aria-hidden="true" tabindex="-1"></a>ss <span class="ot">=</span> <span class="fu">compute_structural_shocks</span>(post)</span>
<span id="cb7-5"><a href="#cb7-5" aria-hidden="true" tabindex="-1"></a>csds <span class="ot">=</span> <span class="fu">compute_conditional_sd</span>(post)</span>
<span id="cb7-6"><a href="#cb7-6" aria-hidden="true" tabindex="-1"></a>sddr <span class="ot">=</span> <span class="fu">verify_identification</span>(post)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</div>
<ul>
<li>predictive analyses</li>
</ul>
<div class="cell">
<div class="sourceCode cell-code" id="cb8"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb8-1"><a href="#cb8-1" aria-hidden="true" tabindex="-1"></a>fvs <span class="ot">=</span> <span class="fu">compute_fitted_values</span>(post)</span>
<span id="cb8-2"><a href="#cb8-2" aria-hidden="true" tabindex="-1"></a>fore <span class="ot">=</span> <span class="fu">forecast</span>(post, <span class="at">horizon =</span> <span class="dv">12</span>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</div>
<ul>
<li>plots and summaries</li>
</ul>
<div class="cell">
<div class="sourceCode cell-code" id="cb9"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb9-1"><a href="#cb9-1" aria-hidden="true" tabindex="-1"></a><span class="fu">plot</span>(irfs)</span>
<span id="cb9-2"><a href="#cb9-2" aria-hidden="true" tabindex="-1"></a><span class="fu">summary</span>(irfs)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</div>
</div><div class="column" style="width:50%;">
<p><img data-src="bsvarSIGNs.png" width="150"></p>
<ul>
<li>structural analyses</li>
</ul>
<div class="cell">
<div class="sourceCode cell-code" id="cb10"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb10-1"><a href="#cb10-1" aria-hidden="true" tabindex="-1"></a>irfs <span class="ot">=</span> <span class="fu">compute_impulse_responses</span>(post , <span class="at">horizon =</span> <span class="dv">12</span>)</span>
<span id="cb10-2"><a href="#cb10-2" aria-hidden="true" tabindex="-1"></a>fevd <span class="ot">=</span> <span class="fu">compute_variance_decompositions</span>(post, <span class="at">horizon =</span> <span class="dv">12</span>)</span>
<span id="cb10-3"><a href="#cb10-3" aria-hidden="true" tabindex="-1"></a>hds <span class="ot">=</span> <span class="fu">compute_historical_decompositions</span>(post)</span>
<span id="cb10-4"><a href="#cb10-4" aria-hidden="true" tabindex="-1"></a>ss <span class="ot">=</span> <span class="fu">compute_structural_shocks</span>(post)</span>
<span id="cb10-5"><a href="#cb10-5" aria-hidden="true" tabindex="-1"></a>csds <span class="ot">=</span> <span class="fu">compute_conditional_sd</span>(post)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</div>
<ul>
<li>predictive analyses</li>
</ul>
<div class="cell">
<div class="sourceCode cell-code" id="cb11"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb11-1"><a href="#cb11-1" aria-hidden="true" tabindex="-1"></a>fvs <span class="ot">=</span> <span class="fu">compute_fitted_values</span>(post)</span>
<span id="cb11-2"><a href="#cb11-2" aria-hidden="true" tabindex="-1"></a>fore <span class="ot">=</span> <span class="fu">forecast</span>(post, <span class="at">horizon =</span> <span class="dv">12</span>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</div>
<ul>
<li>plots and summaries</li>
</ul>
<div class="cell">
<div class="sourceCode cell-code" id="cb12"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb12-1"><a href="#cb12-1" aria-hidden="true" tabindex="-1"></a><span class="fu">plot</span>(irfs)</span>
<span id="cb12-2"><a href="#cb12-2" aria-hidden="true" tabindex="-1"></a><span class="fu">summary</span>(irfs)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</div>
</div>
</div>
</section>
<section id="section-8" class="slide level2" data-background-color="#00bf63">
<h2></h2>
<div class="columns">
<div class="column" style="width:50%;">
<p><img data-src="bsvars.png" width="150"></p>
<ul>
<li>workflow with the pipe</li>
</ul>
<div class="cell">
<div class="sourceCode cell-code" id="cb13"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb13-1"><a href="#cb13-1" aria-hidden="true" tabindex="-1"></a><span class="fu">library</span>(bsvars)</span>
<span id="cb13-2"><a href="#cb13-2" aria-hidden="true" tabindex="-1"></a><span class="fu">data</span>(us_fiscal_lsuw)</span>
<span id="cb13-3"><a href="#cb13-3" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb13-4"><a href="#cb13-4" aria-hidden="true" tabindex="-1"></a>us_fiscal_lsuw <span class="sc">|></span> </span>
<span id="cb13-5"><a href="#cb13-5" aria-hidden="true" tabindex="-1"></a> specify_bsvar<span class="sc">$</span><span class="fu">new</span>() <span class="sc">|></span> </span>
<span id="cb13-6"><a href="#cb13-6" aria-hidden="true" tabindex="-1"></a> <span class="fu">estimate</span>(<span class="at">S =</span> <span class="dv">1000</span>) <span class="sc">|></span> </span>
<span id="cb13-7"><a href="#cb13-7" aria-hidden="true" tabindex="-1"></a> <span class="fu">estimate</span>(<span class="at">S =</span> <span class="dv">10000</span>) <span class="ot">-></span> post</span>
<span id="cb13-8"><a href="#cb13-8" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb13-9"><a href="#cb13-9" aria-hidden="true" tabindex="-1"></a>post <span class="sc">|></span> <span class="fu">compute_impulse_responses</span>(<span class="at">horizon =</span> <span class="dv">12</span>) <span class="sc">|></span> <span class="fu">plot</span>()</span>
<span id="cb13-10"><a href="#cb13-10" aria-hidden="true" tabindex="-1"></a>post <span class="sc">|></span> <span class="fu">compute_variance_decompositions</span>(<span class="at">horizon =</span> <span class="dv">12</span>) <span class="sc">|></span> <span class="fu">plot</span>()</span>
<span id="cb13-11"><a href="#cb13-11" aria-hidden="true" tabindex="-1"></a>post <span class="sc">|></span> <span class="fu">compute_historical_decompositions</span>() <span class="sc">|></span> <span class="fu">plot</span>()</span>
<span id="cb13-12"><a href="#cb13-12" aria-hidden="true" tabindex="-1"></a>post <span class="sc">|></span> <span class="fu">compute_structural_shocks</span>() <span class="sc">|></span> <span class="fu">plot</span>()</span>
<span id="cb13-13"><a href="#cb13-13" aria-hidden="true" tabindex="-1"></a>post <span class="sc">|></span> <span class="fu">compute_conditional_sd</span>() <span class="sc">|></span> <span class="fu">plot</span>()</span>
<span id="cb13-14"><a href="#cb13-14" aria-hidden="true" tabindex="-1"></a>post <span class="sc">|></span> <span class="fu">forecast</span>(<span class="at">horizon =</span> <span class="dv">12</span>) <span class="sc">|></span> <span class="fu">plot</span>()</span>
<span id="cb13-15"><a href="#cb13-15" aria-hidden="true" tabindex="-1"></a>post <span class="sc">|></span> <span class="fu">verify_identification</span>() <span class="sc">|></span> <span class="fu">summary</span>()</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</div>
</div><div class="column" style="width:50%;">
<p><img data-src="bsvarSIGNs.png" width="150"></p>
<ul>
<li>workflow with the pipe</li>
</ul>
<div class="cell">
<div class="sourceCode cell-code" id="cb14"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb14-1"><a href="#cb14-1" aria-hidden="true" tabindex="-1"></a><span class="fu">library</span>(bsvarSIGNs)</span>
<span id="cb14-2"><a href="#cb14-2" aria-hidden="true" tabindex="-1"></a><span class="fu">data</span>(optimism)</span>
<span id="cb14-3"><a href="#cb14-3" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb14-4"><a href="#cb14-4" aria-hidden="true" tabindex="-1"></a>optimism <span class="sc">|></span> </span>
<span id="cb14-5"><a href="#cb14-5" aria-hidden="true" tabindex="-1"></a> specify_bsvarSIGN<span class="sc">$</span><span class="fu">new</span>() <span class="sc">|></span> </span>
<span id="cb14-6"><a href="#cb14-6" aria-hidden="true" tabindex="-1"></a> <span class="fu">estimate</span>(<span class="at">S =</span> <span class="dv">10000</span>) <span class="ot">-></span> post</span>
<span id="cb14-7"><a href="#cb14-7" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb14-8"><a href="#cb14-8" aria-hidden="true" tabindex="-1"></a>post <span class="sc">|></span> <span class="fu">compute_impulse_responses</span>(<span class="at">horizon =</span> <span class="dv">12</span>) <span class="sc">|></span> <span class="fu">plot</span>()</span>
<span id="cb14-9"><a href="#cb14-9" aria-hidden="true" tabindex="-1"></a>post <span class="sc">|></span> <span class="fu">compute_variance_decompositions</span>(<span class="at">horizon =</span> <span class="dv">12</span>) <span class="sc">|></span> <span class="fu">plot</span>()</span>
<span id="cb14-10"><a href="#cb14-10" aria-hidden="true" tabindex="-1"></a>post <span class="sc">|></span> <span class="fu">compute_historical_decompositions</span>() <span class="sc">|></span> <span class="fu">plot</span>()</span>
<span id="cb14-11"><a href="#cb14-11" aria-hidden="true" tabindex="-1"></a>post <span class="sc">|></span> <span class="fu">compute_structural_shocks</span>() <span class="sc">|></span> <span class="fu">plot</span>()</span>
<span id="cb14-12"><a href="#cb14-12" aria-hidden="true" tabindex="-1"></a>post <span class="sc">|></span> <span class="fu">compute_conditional_sd</span>() <span class="sc">|></span> <span class="fu">plot</span>()</span>
<span id="cb14-13"><a href="#cb14-13" aria-hidden="true" tabindex="-1"></a>post <span class="sc">|></span> <span class="fu">forecast</span>(<span class="at">horizon =</span> <span class="dv">12</span>) <span class="sc">|></span> <span class="fu">plot</span>()</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</div>
</div>
</div>
</section>
<section id="section-9" class="slide level2" data-background-color="#00bf63">
<h2></h2>
<div class="columns">
<div class="column" style="width:50%;">
<p><img data-src="bsvars.png" width="150"></p>
<ul>
<li>progress bar</li>
</ul>
<p><img data-src="bsvars_progress.png" width="500"></p>
</div><div class="column" style="width:50%;">
<p><img data-src="bsvarSIGNs.png" width="150"></p>
<ul>
<li>progress bar</li>
</ul>
<p><img data-src="bsvarSIGNs_progress.png" width="500"></p>
</div>
</div>
</section>
<section id="bsvars-models-and-identification-1" class="slide level2" data-background-color="#00bf63">
<h2><a href="https://bsvars.github.io" style="color:#8c52ff;">bsvars</a> models and identification</h2>
</section>
<section id="section-10" class="slide level2">
<h2></h2>
<p><img data-src="bsvars.png" class="absolute" style="right: 10px; width: 120px; "></p>
<p><span class="math display">\[ \]</span></p>
<h3 id="structural-var">Structural VAR</h3>
<p><span class="math display">\[\begin{align}
\text{reduced form:}&&\mathbf{y}_t &= \mathbf{A}\mathbf{x}_t + \boldsymbol{\varepsilon}_t \\
\text{structural form:}&&\mathbf{B}_0\boldsymbol{\varepsilon}_t &= \mathbf{u}_t \\
\text{structural shocks:}&&\mathbf{u}_t\mid\mathbf{x}_t &\sim N\left( \mathbf{0}_N, \text{diag}\left(\boldsymbol{\sigma}_t^2\right) \right)
\end{align}\]</span></p>
<ul>
<li>interpretable structural specification</li>
<li>identification through
<ul>
<li>exclusion restrictions</li>
<li>heteroskedasticity</li>
<li>non-normality</li>
</ul></li>
<li>facilitates application of frontier numerical techniques</li>
<li>features 3-level equation-specific local-global prior shrinkage</li>
</ul>
</section>
<section id="section-11" class="slide level2">
<h2></h2>
<p><img data-src="bsvarSIGNs.png" class="absolute" style="right: 10px; width: 120px; "></p>
<p><span class="math display">\[ \]</span></p>
<h3 id="structural-var-1">Structural VAR</h3>
<p><span class="math display">\[\begin{align}
\text{reduced form:}&&\mathbf{y}_t &= \mathbf{A}\mathbf{x}_t + \boldsymbol{\varepsilon}_t \\
\text{error term:}&&\boldsymbol{\varepsilon}_t\mid\mathbf{x}_t &\sim N\left( \mathbf{0}_N, \boldsymbol{\Sigma} \right)\\
\text{rotation:}&&\mathbf{Q} &\sim Haar \\
\text{structural form:}&&\left(\mathbf{A}, \boldsymbol{\Sigma}, \mathbf{Q}\right) &\rightarrow\left(\mathbf{A}, \mathbf{B}_0\right)
\end{align}\]</span></p>
<ul>
<li>identification through
<ul>
<li>sign & zero restrictions on structural matrix or impulse responses</li>
<li>narrative restrictions on shocks</li>
<li>all at once!</li>
</ul></li>
<li>facilitates independent sampling & application of frontier numerical techniques</li>
<li>features Minnesota and dummy observation priors with estimated shrinkage</li>
</ul>
</section>
<section id="section-12" class="slide level2">
<h2></h2>
<p><img data-src="bsvars.png" class="absolute" style="right: 10px; width: 120px; "></p>
<p><span class="math display">\[ \]</span></p>
<h3 id="non-centred-stochastic-volatility">Non-centred Stochastic Volatility</h3>
<p><span class="math display">\[\begin{align}
\text{conditional variance:}&&\sigma_{n.t}^2 &= \exp\left\{\omega_n h_{n.t}\right\}\\
\text{log-volatility:}&&h_{n.t} &= \rho_n h_{n.t-1} + v_{n.t}\\
\text{volatility innovation:}&&v_{n.t}&\sim N\left(0,1\right)\\
\end{align}\]</span></p>
<ul>
<li>excellent volatility forecasting performance</li>
<li>standardization around <span class="math inline">\(\sigma_{n.t}^2 = 1\)</span></li>
<li><code>verify_identification()</code> by checking <span class="math inline">\(H_0:\quad\omega_n = 0\)</span></li>
</ul>
</section>
<section id="section-13" class="slide level2">
<h2></h2>
<p><img data-src="bsvars.png" class="absolute" style="right: 10px; width: 120px; "></p>
<h3 id="stochastic-volatility-conditional-variances">Stochastic Volatility: conditional variances</h3>
<div class="cell">
<div class="cell-output-display">
<p><img data-src="index_files/figure-revealjs/plot_cv_prior-1.png" width="960"></p>
</div>
</div>
</section>
<section id="section-14" class="slide level2">
<h2></h2>
<p><img data-src="bsvars.png" class="absolute" style="right: 10px; width: 120px; "></p>
<p><span class="math display">\[ \]</span></p>
<h3 id="markov-switching-and-mixture-models.">Markov-switching and mixture models.</h3>
<p><span class="math display">\[\begin{align}
\text{structural shocks:}&&\mathbf{u}_t\mid s_t &\sim N\left( \mathbf{0}_N, \text{diag}\left(\boldsymbol{\sigma}_{s_t}^2\right) \right)\\
\text{prior & standardisation:}&& M^{-1}\left(\boldsymbol{\sigma}_{1}^2, \dots, \boldsymbol{\sigma}_{M}^2\right) &\sim Dirichlet(\underline{a}\boldsymbol\imath')\\
\text{latent process:}&& s_t&\sim \text{Markov or independent}
\end{align}\]</span></p>
<ul>
<li>modeling Markov-switching or mixture models</li>
<li>non-normality provides identification information</li>
<li>potential gains in forecasting precision</li>
<li><code>verify_identification()</code> by checking <span class="math inline">\(H_0:\quad\boldsymbol{\sigma}_{1}^2, \dots, \boldsymbol{\sigma}_{M}^2 = 1\)</span></li>
</ul>
</section>
<section id="section-15" class="slide level2">
<h2></h2>
<p><img data-src="bsvars.png" class="absolute" style="right: 10px; width: 120px; "></p>
<p><span class="math display">\[ \]</span></p>
<h3 id="student-t-shocks.">Student-t shocks.</h3>
<p><span class="math display">\[\begin{align}
\text{structural shocks:}&&\mathbf{u}_t\mid\mathbf{x}_t &\sim t\left( \mathbf{0}_N, \mathbf{I}_N, \nu \right)
\end{align}\]</span></p>
<ul>
<li><span class="math inline">\(\nu\)</span> - the degrees of freedom parameter is estimated</li>
<li>fat tails provide identification information</li>
<li>potential gains in forecasting precision</li>
<li>robustness to outliers</li>
<li><code>verify_identification()</code> by checking <span class="math inline">\(H_0:\quad\nu \rightarrow\infty\)</span></li>
</ul>
</section>
<section id="section-16" class="slide level2" data-background-color="#00bf63">
<h2></h2>
<p><img data-src="bsvars.png" class="absolute" style="right: 10px; width: 120px; "></p>
<h3 style="color:#FFFFFF;" id="student-t-shocks.-1">Student-t shocks.</h3>
<div class="cell">
<div class="cell-output-display">
<p><img data-src="index_files/figure-revealjs/unnamed-chunk-16-1.png" width="960"></p>
</div>
</div>
</section>
<section id="section-17" class="slide level2">
<h2></h2>
<p><img data-src="bsvars.png" class="absolute" style="right: 10px; width: 120px; "></p>
<p><span class="math display">\[ \]</span></p>
<h3 id="identification-verification-via-sddr.">Identification verification via SDDR.</h3>
<p>Verify the restriction through the posterior odds ratio using the SDDR: <span class="math display">\[
SDDR = \frac{\Pr[H_0 | data]}{\Pr[H_1 | data]}= \frac{p(H_0 | data)}{p(H_0 )}
\]</span></p>
<ul>
<li>suitable to verify sharp restrictions on parameters</li>
<li>is interpreted as posterior odds ratio</li>
<li>values greater than 1 provide evidence in favour of the restriction</li>
<li>simple to compute given the unrestricted model estimation output</li>
<li>see methods <code>verify_identification()</code> and <code>verify_autoregression()</code></li>
</ul>
</section>
<section id="bsvars-modeling-of-monetary-policy-1" class="slide level2" data-background-color="#00bf63">
<h2><a href="https://bsvars.github.io" style="color:#8c52ff;">bsvars</a> modeling of monetary policy</h2>
</section>
<section id="bsvars-modeling-of-monetary-policy-2" class="slide level2">
<h2><a href="https://bsvars.github.io" style="color:#8c52ff;">bsvars</a> modeling of monetary policy</h2>
<h3 id="australian-domestic-sector.">Australian domestic sector.</h3>
<p>Consider a system of five domestic variables:</p>
<p><span class="math display">\[\begin{align}
y_t = \begin{bmatrix} rgdp_t & cpi_t & CR_t & EX_t & aord_t \end{bmatrix}'
\end{align}\]</span></p>
<ul>
<li><p><span class="math inline">\(rgdp_t\)</span> - log real Gross Domestic Product</p></li>
<li><p><span class="math inline">\(cpi_t\)</span> - log Consumer Price Index</p></li>
<li><p><span class="math inline">\(CR_t\)</span> - Cash Rate Target - Australian nominal interest rate</p></li>
<li><p><span class="math inline">\(EX_t\)</span> - USD/AUD exchange rate</p></li>
<li><p><span class="math inline">\(aord_t\)</span> - log All Ordinaries Index</p></li>
<li><p>monthly data from August 1990 to March 2024</p></li>
<li><p>quarterly variables interpolated to monthly frequency</p></li>
</ul>
</section>
<section id="bsvars-modeling-of-monetary-policy-3" class="slide level2">
<h2><a href="https://bsvars.github.io" style="color:#8c52ff;">bsvars</a> modeling of monetary policy</h2>
<h3 id="foreign-sector.">Foreign sector.</h3>
<p>The foreign sector includes three US variables:</p>
<ul>
<li><span class="math inline">\(rgdp_t^{(US)}\)</span> - log real Gross Domestic Product</li>
<li><span class="math inline">\(cpi_t^{(US)}\)</span> - log Consumer Price Index</li>
<li><span class="math inline">\(FFR_t\)</span> - Cash Rate Target - Australian nominal interest rate</li>
<li>monthly data from August 1990 to March 2024</li>
<li>quarterly variables interpolated to monthly frequency</li>
<li>contemporaneous and four lagged values are included in the model as exogenous variables</li>
</ul>
</section>
<section id="section-18" class="slide level2">
<h2></h2>
<p><img data-src="bsvars.png" class="absolute" style="right: 10px; width: 120px; "></p>
<p><span class="math display">\[ \]</span></p>
<h3 id="zero-restriction-identified-system.">Zero-restriction-identified system.</h3>
<p><span class="math display">\[\begin{align}
\begin{bmatrix}
B_{0.11}&0&0&0&0\\
B_{0.21}&B_{0.22}&0&0&0\\
B_{0.31}&B_{0.32}&B_{0.33}&0&0\\
B_{0.41}&B_{0.42}&B_{0.43}&B_{0.44}&0\\
B_{0.51}&B_{0.52}&B_{0.53}&B_{0.54}&B_{0.55}
\end{bmatrix}
\begin{bmatrix}rgdp_t \\ cpi_t \\ CR_t \\ EX_t\\ aord_t \end{bmatrix} &= \dots +
\begin{bmatrix} u_t^{ad} \\ u_t^{as} \\ u_t^{mps} \\ u_t^{ex} \\ u_t^{aord} \end{bmatrix}
\end{align}\]</span></p>
<h3 id="identified-shocks.">Identified shocks.</h3>
<ul>
<li><span class="math inline">\(u_t^{mps}\)</span> - identified via Taylor’s Rule extended by exchange rate</li>
<li><span class="math inline">\(u_t^{ex}\)</span> - currency shock indistinguishable from the monetary policy shock</li>
</ul>
</section>
<section id="section-19" class="slide level2">
<h2></h2>
<p><img data-src="bsvars.png" class="absolute" style="right: 10px; width: 120px; "></p>
<p><span class="math display">\[ \]</span></p>
<h3 id="specify-and-estimate-the-svar-sv.">Specify and estimate the SVAR-SV.</h3>
<div class="cell">
<div class="sourceCode cell-code" id="cb15"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb15-1"><a href="#cb15-1" aria-hidden="true" tabindex="-1"></a><span class="fu">library</span>(bsvars)</span>
<span id="cb15-2"><a href="#cb15-2" aria-hidden="true" tabindex="-1"></a><span class="fu">load</span>(<span class="st">"soe.rda"</span>)</span>
<span id="cb15-3"><a href="#cb15-3" aria-hidden="true" tabindex="-1"></a>soe <span class="ot">=</span> <span class="fu">as.matrix</span>(soe)</span>
<span id="cb15-4"><a href="#cb15-4" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb15-5"><a href="#cb15-5" aria-hidden="true" tabindex="-1"></a>TT <span class="ot">=</span> <span class="fu">nrow</span>(soe)</span>
<span id="cb15-6"><a href="#cb15-6" aria-hidden="true" tabindex="-1"></a>lag_order <span class="ot">=</span> <span class="dv">8</span></span>
<span id="cb15-7"><a href="#cb15-7" aria-hidden="true" tabindex="-1"></a>lag_exogenous <span class="ot">=</span> <span class="dv">4</span></span>
<span id="cb15-8"><a href="#cb15-8" aria-hidden="true" tabindex="-1"></a>T <span class="ot">=</span> TT <span class="sc">-</span> <span class="fu">max</span>(lag_order, lag_exogenous)</span>
<span id="cb15-9"><a href="#cb15-9" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb15-10"><a href="#cb15-10" aria-hidden="true" tabindex="-1"></a>exogenous <span class="ot">=</span> <span class="fu">matrix</span>(<span class="cn">NA</span>, TT <span class="sc">-</span> lag_exogenous, <span class="dv">0</span>)</span>
<span id="cb15-11"><a href="#cb15-11" aria-hidden="true" tabindex="-1"></a><span class="cf">for</span> (i <span class="cf">in</span> <span class="dv">0</span><span class="sc">:</span>lag_exogenous) {</span>
<span id="cb15-12"><a href="#cb15-12" aria-hidden="true" tabindex="-1"></a> exogenous <span class="ot">=</span> <span class="fu">cbind</span>(exogenous, <span class="fu">as.matrix</span>(soe[(lag_exogenous <span class="sc">-</span> i <span class="sc">+</span> <span class="dv">1</span>)<span class="sc">:</span>(TT <span class="sc">-</span> i), <span class="dv">6</span><span class="sc">:</span><span class="dv">8</span>]))</span>
<span id="cb15-13"><a href="#cb15-13" aria-hidden="true" tabindex="-1"></a>}</span>
<span id="cb15-14"><a href="#cb15-14" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb15-15"><a href="#cb15-15" aria-hidden="true" tabindex="-1"></a><span class="fu">set.seed</span>(<span class="dv">1234</span>)</span>
<span id="cb15-16"><a href="#cb15-16" aria-hidden="true" tabindex="-1"></a>spec <span class="ot">=</span> specify_bsvar_sv<span class="sc">$</span><span class="fu">new</span>(</span>
<span id="cb15-17"><a href="#cb15-17" aria-hidden="true" tabindex="-1"></a> <span class="at">data =</span> <span class="fu">tail</span>(soe[,<span class="dv">1</span><span class="sc">:</span><span class="dv">5</span>], T),</span>
<span id="cb15-18"><a href="#cb15-18" aria-hidden="true" tabindex="-1"></a> <span class="at">p =</span> lag_order,</span>
<span id="cb15-19"><a href="#cb15-19" aria-hidden="true" tabindex="-1"></a> <span class="at">exogenous =</span> <span class="fu">tail</span>(exogenous, T)</span>
<span id="cb15-20"><a href="#cb15-20" aria-hidden="true" tabindex="-1"></a>)</span>
<span id="cb15-21"><a href="#cb15-21" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb15-22"><a href="#cb15-22" aria-hidden="true" tabindex="-1"></a>burn <span class="ot">=</span> <span class="fu">estimate</span>(spec, <span class="fl">1e4</span>)</span>
<span id="cb15-23"><a href="#cb15-23" aria-hidden="true" tabindex="-1"></a>post <span class="ot">=</span> <span class="fu">estimate</span>(burn, <span class="fl">1e4</span>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</div>
</section>
<section id="section-20" class="slide level2">
<h2></h2>
<p><img data-src="bsvars.png" class="absolute" style="right: 10px; width: 120px; "></p>
<p><span class="math display">\[ \]</span></p>
<h3 id="svar-sv-compute-and-plot-impulse-responses.">SVAR-SV: Compute and plot impulse responses.</h3>
<div class="cell" data-hash="index_cache/revealjs/bs00_dae4b9e6ef127effe1a2fdf3934196a1">
<div class="sourceCode cell-code" id="cb16"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb16-1"><a href="#cb16-1" aria-hidden="true" tabindex="-1"></a>post <span class="sc">|></span> <span class="fu">compute_impulse_responses</span>(<span class="at">horizon =</span> <span class="dv">60</span>) <span class="sc">|></span> <span class="fu">plot</span>(<span class="at">probability =</span> <span class="fl">0.68</span>, <span class="at">col =</span> <span class="st">"#00bf63"</span>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
<div class="cell-output-display">
<p><img data-src="index_files/figure-revealjs/bs00-1.png" width="960"></p>
</div>
</div>
</section>
<section id="section-21" class="slide level2">
<h2></h2>
<p><img data-src="bsvars.png" class="absolute" style="right: 10px; width: 120px; "></p>
<p><span class="math display">\[ \]</span></p>
<h3 id="svar-sv-forecast-error-variance-decompositions.">SVAR-SV: Forecast error variance decompositions.</h3>
<div class="cell" data-hash="index_cache/revealjs/bs00fevd_8b2d7a64456475aaf38dcff434a63b68">
<div class="sourceCode cell-code" id="cb17"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb17-1"><a href="#cb17-1" aria-hidden="true" tabindex="-1"></a>post <span class="sc">|></span> <span class="fu">compute_variance_decompositions</span>(<span class="at">horizon =</span> <span class="dv">60</span>) <span class="sc">|></span> <span class="fu">plot</span>(<span class="at">col =</span> bsvars_grad)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
<div class="cell-output-display">
<p><img data-src="index_files/figure-revealjs/bs00fevd-1.png" width="960"></p>
</div>
</div>
</section>
<section id="section-22" class="slide level2">
<h2></h2>
<p><img data-src="bsvars.png" class="absolute" style="right: 10px; width: 120px; "></p>
<p><span class="math display">\[ \]</span></p>
<h3 id="svar-sv-structural-shocks.">SVAR-SV: Structural shocks.</h3>
<div class="cell" data-hash="index_cache/revealjs/bs00sss_19b96e0d36388fafef5e0e961044977e">
<div class="sourceCode cell-code" id="cb18"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb18-1"><a href="#cb18-1" aria-hidden="true" tabindex="-1"></a>post <span class="sc">|></span> <span class="fu">compute_structural_shocks</span>() <span class="sc">|></span> <span class="fu">plot</span>(<span class="at">col =</span> <span class="st">"#00bf63"</span>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
<div class="cell-output-display">
<p><img data-src="index_files/figure-revealjs/bs00sss-1.png" width="960"></p>
</div>
</div>
</section>
<section id="section-23" class="slide level2">
<h2></h2>
<p><img data-src="bsvars.png" class="absolute" style="right: 10px; width: 120px; "></p>
<p><span class="math display">\[ \]</span></p>
<h3 id="svar-sv-shocks-conditional-standard-deviations.">SVAR-SV: Shocks’ conditional standard deviations.</h3>
<div class="cell" data-hash="index_cache/revealjs/bs00csd_c60d72ed544bdfa18bd03a3775ed4779">
<div class="sourceCode cell-code" id="cb19"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb19-1"><a href="#cb19-1" aria-hidden="true" tabindex="-1"></a>post <span class="sc">|></span> <span class="fu">compute_conditional_sd</span>() <span class="sc">|></span> <span class="fu">plot</span>(<span class="at">col =</span> <span class="st">"#00bf63"</span>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
<div class="cell-output-display">
<p><img data-src="index_files/figure-revealjs/bs00csd-1.png" width="960"></p>
</div>
</div>
</section>
<section id="section-24" class="slide level2">
<h2></h2>
<p><img data-src="bsvars.png" class="absolute" style="right: 10px; width: 120px; "></p>
<p><span class="math display">\[ \]</span></p>
<h3 id="svar-sv-identification-verification.">SVAR-SV: identification verification.</h3>
<div class="cell" data-hash="index_cache/revealjs/bs00vv_2b77c9d824d6435bd83b4b20236dfea9">
<div class="sourceCode cell-code" id="cb20"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb20-1"><a href="#cb20-1" aria-hidden="true" tabindex="-1"></a>post <span class="sc">|></span> <span class="fu">verify_identification</span>() <span class="sc">|></span> <span class="fu">summary</span>()</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
<div class="cell-output cell-output-stdout">
<pre><code> **************************************************|
bsvars: Bayesian Structural Vector Autoregressions|
**************************************************|
Summary of identification verification |
H0: omega_n = 0 [homoskedasticity] |
H1: omega_n != 0 [heteroskedasticity] |
**************************************************|</code></pre>
</div>
<div class="cell-output cell-output-stdout">
<pre><code> log(SDDR) NSE Pr[H0|data] Pr[H1|data]
shock 1 -139.2079238 56.216891 3.489529e-61 1.0000000
shock 2 -77.3369956 60.430724 2.588031e-34 1.0000000
shock 3 -20.9795368 20.576286 7.739322e-10 1.0000000
shock 4 -0.2618337 0.524091 4.349130e-01 0.5650870
shock 5 -2.5202529 1.911860 7.445051e-02 0.9255495</code></pre>
</div>
</div>
</section>
<section id="section-25" class="slide level2">
<h2></h2>
<p><img data-src="bsvars.png" class="absolute" style="right: 10px; width: 120px; "></p>
<p><span class="math display">\[ \]</span></p>
<h3 id="svar-sv-fitted-values.">SVAR-SV: Fitted Values.</h3>
<div class="cell" data-hash="index_cache/revealjs/bs00fit_c85a897e55cf4083266069293ea40735">
<div class="sourceCode cell-code" id="cb23"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb23-1"><a href="#cb23-1" aria-hidden="true" tabindex="-1"></a>post <span class="sc">|></span> <span class="fu">compute_fitted_values</span>() <span class="sc">|></span> <span class="fu">plot</span>(<span class="at">col =</span> <span class="st">"#00bf63"</span>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
<div class="cell-output-display">
<p><img data-src="index_files/figure-revealjs/bs00fit-1.png" width="960"></p>
</div>
</div>
</section>
<section id="section-26" class="slide level2">
<h2></h2>
<p><img data-src="bsvars.png" class="absolute" style="right: 10px; width: 120px; "></p>
<p><span class="math display">\[ \]</span></p>
<h3 id="svar-sv-does-foreign-sector-matter">SVAR-SV: Does foreign sector matter?</h3>
<div class="cell" data-hash="index_cache/revealjs/bs00va_ef229dd988ef25ed74f8b522fc74e427">
<div class="sourceCode cell-code" id="cb24"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb24-1"><a href="#cb24-1" aria-hidden="true" tabindex="-1"></a>A0 <span class="ot">=</span> <span class="fu">matrix</span>(<span class="cn">NA</span>, <span class="dv">5</span>, <span class="dv">56</span>)</span>
<span id="cb24-2"><a href="#cb24-2" aria-hidden="true" tabindex="-1"></a>A0[,<span class="dv">45</span><span class="sc">:</span><span class="dv">56</span>] <span class="ot">=</span> <span class="dv">0</span></span>
<span id="cb24-3"><a href="#cb24-3" aria-hidden="true" tabindex="-1"></a>post <span class="sc">|></span> <span class="fu">verify_autoregression</span>(<span class="at">hypothesis =</span> A0) <span class="sc">|></span> <span class="fu">summary</span>()</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
<div class="cell-output cell-output-stdout">
<pre><code> **************************************************|
bsvars: Bayesian Structural Vector Autoregressions|
**************************************************|
Summary of hypothesis verification |
for autoregressive parameters |
**************************************************|</code></pre>
</div>
<div class="cell-output cell-output-stdout">
<pre><code> log(SDDR) NSE Pr[H0|data] Pr[H1|data]
156.8253 4.668342 1 7.791643e-69</code></pre>
</div>
</div>
</section>
<section id="section-27" class="slide level2">
<h2></h2>
<p><img data-src="bsvarSIGNs.png" class="absolute" style="right: 10px; width: 120px; "></p>
<p><span class="math display">\[ \]</span></p>
<h3 id="sign-restricted-system.">Sign-restricted system.</h3>
<p><span class="math display">\[\begin{align}
\begin{bmatrix}rgdp_t \\ cpi_t \\ CR_t \\ EX_t\\ aord_t \end{bmatrix} &= \dots +
\begin{bmatrix}
-&*&*&*&*\\
-&*&*&*&*\\
+&*&*&*&*\\
*&*&*&*&*\\
*&*&*&*&*\\
\end{bmatrix}\begin{bmatrix} u_t^{ad} \\ u_t^{as} \\ u_t^{mps} \\ u_t^{ex} \\ u_t^{aord} \end{bmatrix}
\end{align}\]</span></p>
<h3 id="identified-shocks.-1">Identified shocks.</h3>
<ul>
<li><span class="math inline">\(u_t^{mps}\)</span> - identified via Taylor’s Rule extended by exchange rate</li>
<li><span class="math inline">\(u_t^{ex}\)</span> - currency shock indistinguishable from the monetary policy shock</li>
<li>identification through heteroskedasticity helps identifying the shocks</li>
</ul>
</section>
<section id="section-28" class="slide level2">