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<meta name="author" content="by Tomasz Woźniak">
<title>Bayesian Forecasting of Labour Market Indicators using the R package bvarPANELs</title>
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<div class="slides">
<section id="title-slide" data-background-color="#1614B1" class="quarto-title-block center">
<h1 class="title"><span style="color: #1A003F;">Bayesian Forecasting of Labour Market Indicators using the R package <a href="https://github.com/bsvars/bvarPANELs">bvarPANELs</a></span></h1>
<div class="quarto-title-authors">
<div class="quarto-title-author">
<div class="quarto-title-author-name">
by Tomasz Woźniak
</div>
</div>
</div>
</section>
<section id="section" class="slide level2" data-background-color="#1614B1">
<h2></h2>
<img data-src="bvarPANELs.png" class="r-stretch quarto-figure-center"></section>
<section id="coming-up-next" class="slide level2" data-background-color="#1614B1">
<h2>Coming up next</h2>
<p><span class="math display">\[ \]</span></p>
<h3 style="color:#1A003F;" id="modelling-and-forecasting-framework">modelling and forecasting framework</h3>
<h3 style="color:#1A003F;" id="the-r-package-bvarpanels">the R package <a href="https://github.com/bsvars/bvarPANELs">bvarPANELs</a></h3>
<!-- ### roadmap {style="color:#1A003F;"} -->
</section>
<section id="materials" class="slide level2" data-background-color="#1614B1">
<h2>Materials</h2>
<p><span class="math display">\[ \]</span></p>
<h3 style="color:#1A003F;" id="lecture-slides-as-a-website">Lecture Slides <a href="https://bsvars.org/2025-03-bvarPANELs-ilo/">as a website</a></h3>
<h3 style="color:#1A003F;" id="r-script-for-the-easy-results-reproduction"><a href="https://github.com/bsvars/2025-03-bvarPANELs-ilo/blob/master/bvarPANELs-ilo.R">R script</a> for the easy results reproduction</h3>
<h3 style="color:#1A003F;" id="github-repo-to-reproduce-the-slides-and-results">GitHub <a href="https://github.com/bsvars/2025-03-bvarPANELs-ilo">repo</a> to reproduce the slides and results</h3>
<h3 id="bvarpanels-package-repo"><a href="https://github.com/bsvars/bvarPANELs">bvarPANELs package repo</a></h3>
<h3 style="color:#1A003F;" id="bvarpanels-package-website"><a href="https://github.com/bsvars/bvarPANELs">bvarPANELs</a> package <a href="https://bsvars.org/bvarPANELs/">website</a></h3>
</section>
<section id="modelling-and-forecasting-framework-1" class="slide level2" data-background-color="#1614B1">
<h2>modelling and forecasting framework</h2>
</section>
<section id="modelling-and-forecasting-framework-2" class="slide level2">
<h2>modelling and forecasting framework</h2>
<h3 style="color:#1A003F;" id="characterisation">characterisation</h3>
<ul>
<li>contemporary Bayesian modelling and institutional setup</li>
<li>incorporates best knowledge and practices</li>
<li>a balance between model size, flexibility, and its capacity to extract signal from data</li>
<li>highly computational, application-specific modelling</li>
<li>inspirations: UN, IPCC, ECB, FED, Christopher Sims</li>
</ul>
<div class="footer">
<p><a href="https://bsvars.org/2025-03-bvarPANELs-ilo/">Forecasting with Bayesian Panel VARs</a></p>
</div>
</section>
<section id="modelling-and-forecasting-framework-3" class="slide level2">
<h2>modelling and forecasting framework</h2>
<h3 style="color:#1A003F;" id="modelling-features">modelling features</h3>
<ul>
<li>Bayesian nonstationary variables handling</li>
<li>system modelling</li>
<li>dynamic approach</li>
<li>global–to–local formulation</li>
<li>embedded flexibility</li>
<li>parameter estimation risk accountability</li>
</ul>
<div class="footer">
<p><a href="https://bsvars.org/2025-03-bvarPANELs-ilo/">Forecasting with Bayesian Panel VARs</a></p>
</div>
</section>
<section id="modelling-and-forecasting-framework-4" class="slide level2">
<h2>modelling and forecasting framework</h2>
<h3 style="color:#1A003F;" id="forecasting-features">forecasting features</h3>
<ul>
<li>original non-stationary variables</li>
<li>density forecasting</li>
<li>conditional forecasting given <span class="math inline">\(gdp\)</span> projections</li>
<li>forecasting for models with exogenous variables</li>
<li>restricted forecasting of rates</li>
</ul>
<div class="footer">
<p><a href="https://bsvars.org/2025-03-bvarPANELs-ilo/">Forecasting with Bayesian Panel VARs</a></p>
</div>
</section>
<section id="the-model" class="slide level2">
<h2>the model</h2>
<h3 style="color:#1A003F;" id="bayesian-hierarchical-panel-var">Bayesian hierarchical panel VAR</h3>
<ul>
<li>country-specific vector autoregression</li>
<li>panel modelling: global model for prior mean</li>
<li>flexible 3-level hierarchical prior structure</li>
<li>density forecasting</li>
</ul>
<div class="footer">
<p><a href="https://bsvars.org/2025-03-bvarPANELs-ilo/">Forecasting with Bayesian Panel VARs</a></p>
</div>
</section>
<section id="the-model-1" class="slide level2">
<h2>the model</h2>
<h3 style="color:#1A003F;" id="country-specific-vector-autoregression">country-specific vector autoregression</h3>
<p><span class="math display">\[\begin{align}
&\\
\mathbf{y}_{c.t} &= \begin{bmatrix} gdp_{c.t} & UR_{c.t} & EPR_{c.t} & LFPR_{c.t} \end{bmatrix}'\\[3ex]
\mathbf{y}_{c.t} &= \mathbf{A}_{c.1} \mathbf{y}_{c.t-1} + \mathbf{A}_{d.c}\mathbf{x}_{c.t} + \boldsymbol\epsilon_{c.t}\\[1ex]
\boldsymbol\epsilon_{c.t}\mid \mathbf{y}_{c.t-1} & \sim N_4\left(\mathbf{0}_4, \boldsymbol\Sigma_c\right)\\[2ex]
\end{align}\]</span></p>
<ul>
<li>subscript <span class="math inline">\(c\)</span> is for country, and <span class="math inline">\(t\)</span> is for time</li>
</ul>
<div class="footer">
<p><a href="https://bsvars.org/2025-03-bvarPANELs-ilo/">Forecasting with Bayesian Panel VARs</a></p>
</div>
</section>
<section id="the-model-2" class="slide level2">
<h2>the model</h2>
<h3 style="color:#1A003F;" id="global-model-for-the-prior-mean">global model for the prior mean</h3>
<p><span class="math display">\[\begin{align}
&\\
E_\pi\left[\mathbf{A}_{c}\right] &= \mathbf{A}, \qquad \mathbf{A}_{c} = \begin{bmatrix} \mathbf{A}_{c.1} & \mathbf{A}_{d.c} \end{bmatrix}'\\[1ex]
E_\pi\left[\boldsymbol\Sigma_c\right] &= \boldsymbol\Sigma\\[3ex]
\mathbf{y}_{c.t} &= \mathbf{A}_{1} \mathbf{y}_{c.t-1} + \mathbf{A}_{d}\mathbf{x}_{c.t} + \boldsymbol\epsilon_{c.t}\\[1ex]
\boldsymbol\epsilon_{c.t}\mid \mathbf{y}_{c.t-1} & \sim N_4\left(\mathbf{0}_4, \boldsymbol\Sigma\right)
\end{align}\]</span></p>
<div class="footer">
<p><a href="https://bsvars.org/2025-03-bvarPANELs-ilo/">Forecasting with Bayesian Panel VARs</a></p>
</div>
</section>
<section id="the-model-3" class="slide level2">
<h2>the model</h2>
<h3 style="color:#1A003F;" id="flexible-3-level-hierarchical-prior-structure">flexible 3-level hierarchical prior structure</h3>
<ul>
<li>estimate country-specific parameters: <span class="math inline">\(\mathbf{A}_c\)</span> and <span class="math inline">\(\mathbf{\Sigma}_c\)</span></li>
<li>estimate global parameters: <span class="math inline">\(\mathbf{A}\)</span> and <span class="math inline">\(\mathbf{\Sigma}\)</span></li>
<li>estimate other prior means and shrinkage levels</li>
</ul>
<h3 style="color:#1A003F;" id="advantages">advantages</h3>
<ul>
<li>flexible modelling for various types of data</li>
<li>improved forecasting performance</li>
<li>robustness to different prior specifications</li>
<li>convenient estimation using the Gibbs sampler</li>
</ul>
<div class="footer">
<p><a href="https://bsvars.org/2025-03-bvarPANELs-ilo/">Forecasting with Bayesian Panel VARs</a></p>
</div>
</section>
<section id="the-model-4" class="slide level2">
<h2>the model</h2>
<h3 style="color:#1A003F;" id="the-local-global-prior">the local-global prior</h3>
<p><span class="math display">\[\begin{align}
&\\
\mathbf{A}_c, \boldsymbol\Sigma_c | \mathbf{A}, \mathbf{V}, \mathbf{\Sigma}, \nu &\sim MNIW_{K\times N}\left(\mathbf{A}, \mathbf{V}, (N - \nu - 1)\mathbf{\Sigma}, \nu\right)\\[2ex]
\mathbf{A}', \mathbf{V} \mid m, w, s &\sim MNIW_{N\times K}\left(m\underline{\mathbf{M}}', w\underline{\mathbf{W}}, s\underline{\mathbf{S}}, \underline{\eta}\right)\label{eq:pgA}\\[2ex]
\mathbf{\Sigma}\mid s &\sim W_{N}\left(s\underline{\mathbf{S}}_\Sigma,\underline{\mu}_\Sigma\right)\\[3ex]
\end{align}\]</span></p>
<ul>
<li><span class="math inline">\(MNIW\)</span> is the matrix normal-inverse Wishart distribution (see <a href="https://doi.org/10.1111/1467-8462.12179">Woźniak (2016)</a>)</li>
<li><span class="math inline">\(W\)</span> is the Wishart distribution</li>
</ul>
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<p><a href="https://bsvars.org/2025-03-bvarPANELs-ilo/">Forecasting with Bayesian Panel VARs</a></p>
</div>
</section>
<section id="the-model-5" class="slide level2">
<h2>the model</h2>
<h3 style="color:#1A003F;" id="hierarchical-prior">hierarchical prior</h3>
<p><span class="math display">\[\begin{align}
&\\
\nu &\sim\exp\left(\underline\lambda\right)\\[1ex]
m &\sim N\left(\underline{\mu}_m, \underline{\sigma}_m^2\right)\\[1ex]
w &\sim G\left(\underline{s}_w, \underline{a}_w\right)\\[1ex]
s &\sim IG2\left(\underline{s}_s, \underline{\nu}_s\right)\\[3ex]
\end{align}\]</span></p>
<ul>
<li><span class="math inline">\(IG2\)</span> is the inverted gamma 2 distribution</li>
</ul>
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<p><a href="https://bsvars.org/2025-03-bvarPANELs-ilo/">Forecasting with Bayesian Panel VARs</a></p>
</div>
</section>
<section id="forecasting" class="slide level2">
<h2>forecasting</h2>
<h3 style="color:#1A003F;" id="one-period-ahead-predictive-density">one-period-ahead predictive density</h3>
<p><span class="math display">\[\begin{align}
&\\
{\color{lig}p\left(\mathbf{y}_{c.t+1}\mid \mathbf{y}_{c.t},\mathbf{A}_{c},\boldsymbol\Sigma_c\right)} & = N_4\left(\mathbf{A}_{c.1} \mathbf{y}_{c.t} + \mathbf{A}_{d.c}\mathbf{x}_{c.t+1}, \boldsymbol\Sigma_c\right)\\[5ex]
\end{align}\]</span></p>
<ul>
<li>is implied by the model</li>
<li>is the same as frequentist predictive density</li>
</ul>
<div class="footer">
<p><a href="https://bsvars.org/2025-03-bvarPANELs-ilo/">Forecasting with Bayesian Panel VARs</a></p>
</div>
</section>
<section id="forecasting-1" class="slide level2">
<h2>forecasting</h2>
<h3 style="color:#1A003F;" id="predictive-density">predictive density</h3>
<p><span class="math display">\[\begin{align}
p\left(\mathbf{y}_{c.t+h},\dots,\mathbf{y}_{c.t+1}\mid \mathbf{Y}_{c.t}\right)
&= \int p\left(\mathbf{y}_{c.t+h},\dots,\mathbf{y}_{c.t+1},\mathbf{A}_{c},\boldsymbol\Sigma_c\mid \mathbf{Y}_{c.t}\right)d\left(\mathbf{A}_{c},\boldsymbol\Sigma_c\right)\\[1ex]
&= \int{\color{lig} p\left(\mathbf{y}_{c.t+h}\mid \mathbf{y}_{c.t+h-1},\mathbf{A}_{c},\boldsymbol\Sigma_c\right)}\\[1ex]
&\qquad\times\dots\\[1ex]
&\qquad\times {\color{lig}p\left(\mathbf{y}_{c.t+1}\mid \mathbf{y}_{c.t},\mathbf{A}_{c},\boldsymbol\Sigma_c\right)}\\[1ex]
&\qquad\times p\left(\mathbf{A}_{c},\boldsymbol\Sigma_c\mid \mathbf{Y}_{c.t}\right)d\left(\mathbf{A}_{c},\boldsymbol\Sigma_c\right)
\end{align}\]</span></p>
<ul>
<li>conditional density structure determines the sampling algorithm</li>
</ul>
<div class="footer">
<p><a href="https://bsvars.org/2025-03-bvarPANELs-ilo/">Forecasting with Bayesian Panel VARs</a></p>
</div>
</section>
<section id="the-r-package-bvarpanels-1" class="slide level2" data-background-color="#1614B1">
<h2>the R package <a href="https://github.com/bsvars/bvarPANELs">bvarPANELs</a></h2>
</section>
<section id="the-r-package-bvarpanels-2" class="slide level2">
<h2>the R package <a href="https://github.com/bsvars/bvarPANELs">bvarPANELs</a></h2>
<h3 style="color:#1A003F;" id="features">features</h3>
<ul>
<li>precise estimation and forecasting</li>
<li>simple workflows in <strong>R</strong></li>
<li>excellent computational speed
<ul>
<li>frontier econometric and numerical techniques</li>
<li>algorithms written in <strong>C++</strong></li>
</ul></li>
<li>extensive documentation</li>
<li>up-to standards: ready for publication</li>
<li>install the package from the <a href="https://github.com/bsvars/bvarPANELs">GitHub repo</a></li>
</ul>
<pre><code>devtools::install_github("bsvars/bvarPANELs")</code></pre>
<div class="footer">
<p><a href="https://bsvars.org/2025-03-bvarPANELs-ilo/">Forecasting with Bayesian Panel VARs</a></p>
</div>
</section>
<section id="the-r-package-bvarpanels-3" class="slide level2">
<h2>the R package <a href="https://github.com/bsvars/bvarPANELs">bvarPANELs</a></h2>
<p><img data-src="grph_package.png" class="absolute" style="top: 100px; right: 250px; width: 600px; "></p>
<div class="footer">
<p><a href="https://bsvars.org/2025-03-bvarPANELs-ilo/">Forecasting with Bayesian Panel VARs</a></p>
</div>
</section>
<section id="the-r-package-bvarpanels-4" class="slide level2">
<h2>the R package <a href="https://github.com/bsvars/bvarPANELs">bvarPANELs</a></h2>
<p><img data-src="grph_paper.png" class="absolute" style="top: 100px; right: 250px; width: 600px; "></p>
<div class="footer">
<p><a href="https://bsvars.org/2025-03-bvarPANELs-ilo/">Forecasting with Bayesian Panel VARs</a></p>
</div>
</section>
<section id="the-r-package-bvarpanels-5" class="slide level2">
<h2>the R package <a href="https://github.com/bsvars/bvarPANELs">bvarPANELs</a></h2>
<h3 style="color:#1A003F;" id="load-data">load data</h3>
<div class="cell" data-hash="index_cache/revealjs/data_59ca3ffe8d8c537f3d881190d847f9bc">
<div class="sourceCode cell-code" id="cb2"><pre class="sourceCode numberSource r number-lines code-with-copy"><code class="sourceCode r"><span id="cb2-1"><a href="#cb2-1"></a><span class="fu">library</span>(bvarPANELs) <span class="co"># load the package</span></span>
<span id="cb2-2"><a href="#cb2-2"></a><span class="fu">data</span>(ilo_dynamic_panel) <span class="co"># load the data</span></span>
<span id="cb2-3"><a href="#cb2-3"></a>ilo_dynamic_panel<span class="sc">$</span>COL <span class="co"># show the data for Colombia</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>Time Series:
Start = 1991
End = 2023
Frequency = 1
gdp UR EPR LFPR
1991 25.53464 10.120000 59.96793 66.71999
1992 25.57429 9.440000 60.61868 66.93758
1993 25.62675 7.800000 62.04586 67.29486
1994 25.68326 8.250000 62.11328 67.69840
1995 25.73398 8.720000 62.11020 68.04361
1996 25.75433 11.810000 60.03138 68.07051
1997 25.78805 12.139999 59.96012 68.24507
1998 25.79374 15.000000 57.90753 68.12650
1999 25.75079 20.059999 53.95368 67.49272
2000 25.77962 20.520000 53.75205 67.62965
2001 25.79626 15.040001 57.46694 67.64000
2002 25.82099 14.481000 56.95565 66.60000
2003 25.85942 13.220999 58.52376 67.44000
2004 25.91138 13.717001 57.54213 66.69000
2005 25.95854 11.061999 58.11209 65.34000
2006 26.02355 11.091076 57.45149 64.61836
2007 26.08876 11.204000 56.73176 63.89000
2008 26.12106 11.273000 56.92724 64.16000
2009 26.13240 12.066000 58.87181 66.95000
2010 26.17636 11.153000 59.59857 67.08000
2011 26.24353 10.288000 60.56457 67.51000
2012 26.28191 9.959000 61.29091 68.07000
2013 26.33198 9.246000 61.05022 67.27000
2014 26.37599 8.799000 61.09555 66.99000
2015 26.40512 8.572000 61.27505 67.02000
2016 26.42578 8.922000 60.49401 66.42000
2017 26.43928 9.086000 60.01233 66.01000
2018 26.46460 9.360000 59.13354 65.24000
2019 26.49597 10.280000 57.70790 64.32000
2020 26.42140 15.983000 53.28358 63.42000
2021 26.52396 13.897999 55.38942 64.33000
2022 26.59432 10.547000 56.49851 63.16000
2023 26.60042 9.565347 57.65713 63.75558</code></pre>
</div>
</div>
<div class="footer">
<p><a href="https://bsvars.org/2025-03-bvarPANELs-ilo/">Forecasting with Bayesian Panel VARs</a></p>
</div>
</section>
<section id="the-r-package-bvarpanels-6" class="slide level2">
<h2>the R package <a href="https://github.com/bsvars/bvarPANELs">bvarPANELs</a></h2>
<h3 style="color:#1A003F;" id="specify-and-estimate-the-model">specify and estimate the model</h3>
<div class="cell" data-hash="index_cache/revealjs/spec_f706070f1741f422ad188c8ea6a84f45">
<div class="sourceCode cell-code" id="cb4"><pre class="sourceCode numberSource r number-lines code-with-copy"><code class="sourceCode r"><span id="cb4-1"><a href="#cb4-1"></a>spec <span class="ot">=</span> specify_bvarPANEL<span class="sc">$</span><span class="fu">new</span>( <span class="co"># specify the model</span></span>
<span id="cb4-2"><a href="#cb4-2"></a> ilo_dynamic_panel, <span class="co"># data</span></span>
<span id="cb4-3"><a href="#cb4-3"></a> <span class="at">exogenous =</span> ilo_exogenous_variables, <span class="co"># exogenous variables</span></span>
<span id="cb4-4"><a href="#cb4-4"></a> <span class="at">stationary =</span> <span class="fu">c</span>(<span class="cn">FALSE</span>, <span class="cn">FALSE</span>, <span class="cn">FALSE</span>, <span class="cn">TRUE</span>), <span class="co"># stationarity (determines prior mean)</span></span>
<span id="cb4-5"><a href="#cb4-5"></a> <span class="at">type =</span> <span class="fu">c</span>(<span class="st">"real"</span>, <span class="st">"rate"</span>, <span class="st">"rate"</span>, <span class="st">"rate"</span>) <span class="co"># variable types</span></span>
<span id="cb4-6"><a href="#cb4-6"></a>)</span>
<span id="cb4-7"><a href="#cb4-7"></a></span>
<span id="cb4-8"><a href="#cb4-8"></a>burn <span class="ot">=</span> <span class="fu">estimate</span>(spec, <span class="at">S =</span> <span class="dv">10000</span>, <span class="at">show_progress =</span> <span class="cn">FALSE</span>) <span class="co"># run the burn-in</span></span>
<span id="cb4-9"><a href="#cb4-9"></a>post <span class="ot">=</span> <span class="fu">estimate</span>(burn, <span class="at">S =</span> <span class="dv">10000</span>) <span class="co"># estimate the model</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>**************************************************|
bvarPANELs: Forecasting with Bayesian Hierarchical|
Panel Vector Autoregressions |
**************************************************|
Progress of the MCMC simulation for 10000 draws
Every draw is saved via MCMC thinning
Press Esc to interrupt the computations
**************************************************|</code></pre>
</div>
</div>
<div class="footer">
<p><a href="https://bsvars.org/2025-03-bvarPANELs-ilo/">Forecasting with Bayesian Panel VARs</a></p>
</div>
</section>
<section id="the-r-package-bvarpanels-7" class="slide level2">
<h2>the R package <a href="https://github.com/bsvars/bvarPANELs">bvarPANELs</a></h2>
<h3 style="color:#1A003F;" id="forecast-labour-market-outcomes">forecast labour market outcomes</h3>
<div class="cell" data-hash="index_cache/revealjs/for_73d1d1b189a7d4e6ffad9311a50355fc">
<div class="sourceCode cell-code" id="cb6"><pre class="sourceCode numberSource r number-lines code-with-copy"><code class="sourceCode r"><span id="cb6-1"><a href="#cb6-1"></a>fore <span class="ot">=</span> <span class="fu">forecast</span>( <span class="co"># forecast the model </span></span>
<span id="cb6-2"><a href="#cb6-2"></a> post, <span class="co"># estimation output</span></span>
<span id="cb6-3"><a href="#cb6-3"></a> <span class="at">horizon =</span> <span class="dv">6</span>, <span class="co"># forecast horizon</span></span>
<span id="cb6-4"><a href="#cb6-4"></a> <span class="at">exogenous_forecast =</span> ilo_exogenous_forecasts, <span class="co"># forecasts for exogenous variables</span></span>
<span id="cb6-5"><a href="#cb6-5"></a> <span class="at">conditional_forecast =</span> ilo_conditional_forecasts <span class="co"># gdp projections</span></span>
<span id="cb6-6"><a href="#cb6-6"></a>)</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>**************************************************|
bvarPANELs: Forecasting with Bayesian Hierarchical|
Panel Vector Autoregressions |
**************************************************|
Progress of sampling 10000 draws from
the predictive density for 189 countries
Press Esc to interrupt the computations
**************************************************|</code></pre>
</div>
</div>
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<p><a href="https://bsvars.org/2025-03-bvarPANELs-ilo/">Forecasting with Bayesian Panel VARs</a></p>
</div>
</section>
<section id="the-r-package-bvarpanels-8" class="slide level2">
<h2>the R package <a href="https://github.com/bsvars/bvarPANELs">bvarPANELs</a></h2>
<h3 style="color:#1A003F;" id="forecast-labour-market-outcomes-1">forecast labour market outcomes</h3>
<div class="cell" data-hash="index_cache/revealjs/fore_plot_ad50257bcbbf8eecca393949849a69dd">
<div class="sourceCode cell-code" id="cb8"><pre class="sourceCode numberSource r number-lines code-with-copy"><code class="sourceCode r"><span id="cb8-1"><a href="#cb8-1"></a><span class="fu">plot</span>(fore, <span class="st">"COL"</span>, <span class="at">main =</span> <span class="st">"Forecasts for Colombia"</span>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</div>
<img data-src="index_files/figure-revealjs/fore_plot-1.png" width="960" class="r-stretch"><div class="footer">
<p><a href="https://bsvars.org/2025-03-bvarPANELs-ilo/">Forecasting with Bayesian Panel VARs</a></p>
</div>
</section>
<section id="the-r-package-bvarpanels-9" class="slide level2">
<h2>the R package <a href="https://github.com/bsvars/bvarPANELs">bvarPANELs</a></h2>
<h3 style="color:#1A003F;" id="forecast-labour-market-outcomes-2">forecast labour market outcomes</h3>
<div class="cell" data-hash="index_cache/revealjs/fore_summary_65ce9a74c48cb5a9edd3ae0bbf76442b">
<div class="sourceCode cell-code" id="cb9"><pre class="sourceCode numberSource r number-lines code-with-copy"><code class="sourceCode r"><span id="cb9-1"><a href="#cb9-1"></a><span class="fu">summary</span>(fore, <span class="st">"COL"</span>)<span class="sc">$</span>variable2</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|
**************************************************|
Posterior summary of forecasts |
**************************************************|</code></pre>
</div>
<div class="cell-output cell-output-stdout">
<pre><code> mean sd 5% quantile 95% quantile
1 10.294857 1.476505 7.872032 12.70846
2 9.841204 1.955355 6.707715 13.01481
3 9.270488 2.261769 5.611791 12.99134
4 8.846041 2.524810 4.745539 13.01309
5 8.492730 2.729845 4.030065 12.93011
6 8.222295 2.887869 3.420855 12.95301</code></pre>
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<p><a href="https://bsvars.org/2025-03-bvarPANELs-ilo/">Forecasting with Bayesian Panel VARs</a></p>
</div>
</section>
<section id="the-r-package-bvarpanels-10" class="slide level2">
<h2>the R package <a href="https://github.com/bsvars/bvarPANELs">bvarPANELs</a></h2>
<h3 style="color:#1A003F;" id="forecast-error-variance-decomposition">forecast error variance decomposition</h3>
<div class="cell" data-hash="index_cache/revealjs/fevd_cf822ba2d57f63b51bdc22db63f53f29">
<div class="sourceCode cell-code" id="cb12"><pre class="sourceCode numberSource r number-lines code-with-copy"><code class="sourceCode r"><span id="cb12-1"><a href="#cb12-1"></a>post <span class="sc">|></span> <span class="co"># estimation output</span></span>
<span id="cb12-2"><a href="#cb12-2"></a> <span class="fu">compute_variance_decompositions</span>(<span class="at">horizon =</span> <span class="dv">6</span>) <span class="sc">|></span> <span class="co"># compute variance decompositions</span></span>
<span id="cb12-3"><a href="#cb12-3"></a> <span class="fu">plot</span>(<span class="at">which_c =</span> <span class="st">"COL"</span>) <span class="co"># plot variance decompositions</span></span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
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<p><a href="https://bsvars.org/2025-03-bvarPANELs-ilo/">Forecasting with Bayesian Panel VARs</a></p>
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</section>
<section id="section-1" class="slide level2" data-background-color="#1614B1">
<h2></h2>
<p><img data-src="social_ilo.png" class="absolute" style="top: 80px; right: 50px; width: 900px; "></p>
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// Flags if it should be possible to pause the presentation (blackout)
pause: true,
// Flags if speaker notes should be visible to all viewers
showNotes: false,
// Global override for autoplaying embedded media (null/true/false)
autoPlayMedia: null,
// Global override for preloading lazy-loaded iframes (null/true/false)
preloadIframes: null,
// Number of milliseconds between automatically proceeding to the
// next slide, disabled when set to 0, this value can be overwritten
// by using a data-autoslide attribute on your slides
autoSlide: 0,
// Stop auto-sliding after user input
autoSlideStoppable: true,
// Use this method for navigation when auto-sliding
autoSlideMethod: null,
// Specify the average time in seconds that you think you will spend
// presenting each slide. This is used to show a pacing timer in the
// speaker view
defaultTiming: null,
// Enable slide navigation via mouse wheel
mouseWheel: false,
// The display mode that will be used to show slides
display: 'block',
// Hide cursor if inactive
hideInactiveCursor: true,
// Time before the cursor is hidden (in ms)
hideCursorTime: 5000,
// Opens links in an iframe preview overlay
previewLinks: false,
// Transition style (none/fade/slide/convex/concave/zoom)
transition: 'concave',
// Transition speed (default/fast/slow)
transitionSpeed: 'default',
// Transition style for full page slide backgrounds
// (none/fade/slide/convex/concave/zoom)
backgroundTransition: 'none',
// Number of slides away from the current that are visible
viewDistance: 3,
// Number of slides away from the current that are visible on mobile
// devices. It is advisable to set this to a lower number than
// viewDistance in order to save resources.
mobileViewDistance: 2,
// The "normal" size of the presentation, aspect ratio will be preserved
// when the presentation is scaled to fit different resolutions. Can be
// specified using percentage units.
width: 1050,
height: 700,
// Factor of the display size that should remain empty around the content
margin: 0.1,
math: {
mathjax: 'https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.0/MathJax.js',
config: 'TeX-AMS_HTML-full',
tex2jax: {
inlineMath: [['\\(','\\)']],
displayMath: [['\\[','\\]']],
balanceBraces: true,
processEscapes: false,
processRefs: true,
processEnvironments: true,
preview: 'TeX',
skipTags: ['script','noscript','style','textarea','pre','code'],
ignoreClass: 'tex2jax_ignore',
processClass: 'tex2jax_process'
},
},