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<!doctype html>
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<title>Essays on the World Food Crisis: An Assessment of Policy Options</title>
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<meta name="author" content="Randall Romero-Aguilar">
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<div class="slides">
<section id="Title page">
<section data-background="figures/Library.jpg" class="essay-title">
<h1 style="color: lightblue">Essays on the World Food Crisis:</h1>
<h3 style="color: white">An Assessment of Policy Options</h3>
<p style="text-align: right; padding-right: 1em"> By <a href="http://randall-romero.com" style="color: white">Randall S. Romero-Aguilar</a></p>
<p style="text-align: right; padding-right: 1em"><small>July 15, 2015</small></p>
</section>
<section>
<h2 class="subtitle">Table of Contents</h2>
<nav id="presentable-toc" class="revealjs"></nav>
</section>
</section>
<!----------------------------------------------------------------------------------------------------------
INTRODUCTION
----------------------------------------------------------------------------------------------------------->
<section id="cover-essay0">
<section>
<h2>The World Food Crisis</h2>
<p>Despite rising production, food prices are higher and increasingly volatile</p>
<figure>
<img width="80%" data-src="figures/FAO-cereals-price.svg">
<figcaption class="small">Source: FAO's cereal price index</figcaption>
</figure>
<aside class="notes">
*** 2006-2008: maize 180%, rice 220%, wheat 170%
*** 2005-2015 inflation: 20%
*** Index: 10 wheat, 1 maize, 16 raize variaties. IGC
</aside>
</section>
<section>
<h3>Undernourished people in the world</h3>
<figure>
<img width="80%" data-src="figures/fig-hunger-estimates.svg" alt="FIGURE PENDING">
<figcaption class="small">Source: The Economist, Oct 10th 2012, based on FAO's SOFI reports.</figcaption>
</figure>
</section>
<section>
<h3>Revolts when food is expensive</h3>
<figure>
<img width="60%" data-src="figures/fig-Lagi-et-al-food-riots.svg">
<figcaption class="small">Source: Lagi, Bertrand, and Bar-Yam 2011</figcaption>
</figure>
<figure>
<img width="30%" data-src="figures/pic-food-riots.jpg">
<img width="30%" data-src="figures/pic-haiti-riots.jpg">
<figcaption class="small">Food riots</figcaption>
</figure>
</section>
<section>
<h3>Possible cause of the crisis</h3>
<div style="float: left; width: 48%">
<p class="label">Affecting supply:</p>
<ul>
<li>rising oil prices;</li>
<li>declining stocks and reserves;</li>
<li>regional catastrophic weather;</li>
<li>export restrictions;</li>
<li>decline in productivity and R&D in agriculture.</li>
</ul>
</div>
<div style="float: right; width: 48%">
<p class="label">Affecting demand:</p>
<ul>
<li>strong income growth in China and India;</li>
<li>biofuel production in the USA and Europe;</li>
<li>preventive imports surges;</li>
<li>speculation in financial markets.</li>
</ul>
</div>
</section>
</section>
<!--=========================================================================================================-->
<section id="The essays">
<section>
<h2>The essays:</h2>
<ul>
<li>To what extend do food security policies cause price spikes?</li>
<li>Food reserves to cope with the crisis?
<ul>
<li>In a poor developing country?</li>
<li>In a multilateral agreement?</li>
</ul>
</li>
</ul>
<aside class="notes">
***
</aside>
</section>
<section>
<h3>Drivers of the World Grain Price Crisis in the Short- and Long-Run: A Spatial-Temporal Rational Expectations Equilibrium Approach</h3>
<div style="width: 60%; float: left">
<ul>
<li style="color: darkred">Can food security policies worsen a food crisis?</li>
<li>Three policies
<ul>
<li>export restrictions</li>
<li>public buffer stock</li>
<li>ethanol production mandate</li>
</ul>
</li>
<li>long term price affected by ethanol mandate.</li>
<li>short term crisis worsened by export restrictions</li>
</ul>
</div>
<img width="35%" data-src="figures/essay2cover.jpg">
</section>
<section>
<h3>Food Security for Whom? The Effectiveness of Food Reserves in Poor Developing Countries</h3>
<div style="width: 60%; float: left">
<ul>
<li style="color: darkred">Can a food reserve help a poor country to deal with volatile prices?</li>
<li>A buffer stock relieves future hunger, but what about today's poor?</li>
<li>For Haiti, a buffer stock offers little protection; income transfers may be more effective. </li>
</ul>
</div>
<img width="35%" data-src="figures/essay1cover.jpg">
</section>
<section>
<h3>Sustainability of Regional Food Reserves When Default Is Possible</h3>
<div style="width: 60%; float: left">
<ul>
<li style="color: darkred">Can countries benefit from pooling their reserves?</li>
<li>Two reserve options
<ul>
<li>credit union</li>
<li>insurance union</li>
</ul>
</li>
<li>Risk sharing is more effective when production shocks are negatively correlated, but joint reserve is more stable if correlation is positive</li>
</ul>
</div>
<img width="35%" data-src="figures/essay3cover.jpg">
</section>
</section>
<!-----------------------------------------------------------------------------------------------------------
ESSAY 1: DRIVERS OF THE WORLD GRAIN PRICE CRISIS
------------------------------------------------------------------------------------------------------------>
<section data-background="figures/wheat-fields.jpg" class="essay-title" id="cover-essay1">
<h2>Drivers of the World Grain Price Crisis in the Short- and Long-Run:</h2>
<h3>A Spatial-Temporal Rational Expectations Equilibrium Approach</h3>
</section>
<!--=========================================================================================================-->
<section>
<section>
<h2>Introduction</h2>
<p>Build a model to examine some proposed drivers of the World Food Price Crisis:</p>
<ul>
<li>low grain stock levels;</li>
<li>trade restrictions by wheat exporters;</li>
<li>public storage by wheat importers; and</li>
<li>diversion of corn production to biofuels.</li>
</ul>
</section>
<section>
<h2>Share of corn used in ethanol production</h2>
<img width="60%" data-src="figures/ethanol_share.png" alt="Ethanol share">
</section>
</section>
<!--=========================================================================================================-->
<section>
<section>
<h2>The Model</h2>
<div style="float: left; width: 45%">
<ul>
<li>Trade: arbitrage</li>
<li>One fixed input: land</li>
</ul>
</div>
<div style="float: right; width: 55%">
<ul>
<li>Production: rational expectations</li>
<li>Storage: rational expectations</li>
</ul>
</div>
<img data-src="figures/trade-regions-2grains.svg" width="90%">
</section>
<section>
<h3>Supply, demand, production, consumption</h3>
<p>Supply and demand:</p>
\( \newcommand{\DEF}[2]{\underset{\scriptsize\color{grey}{\text{#1}}}{#2}}\)
\[
\DEF{production}{\tilde{Q}_i} + \DEF{past storage}{Z_{i,-1}} \equiv \DEF{availability}{A_i} = \DEF{consumption}{C_i} + \DEF{storage}{Z_i} + \DEF{net exports}{Y_i} \]
<br>
<p>Production</p>
\[\DEF{production}{\tilde{Q}_i} = \DEF{acreage}{q_{i,-1}} \times \DEF{yield}{\tilde{\epsilon}_i}\]
<br>
<p>Consumption demand</p>
\[\DEF{consumption}{C_i} = \alpha_i \DEF{price}{P_i}^{-\beta_i}\]
</section>
<section>
<h3>Trade and private storage</h3>
<p>Trade:</p>
\begin{equation}
0 \leq \DEF{exports}{y_{jk}} \leq \DEF{capacity}{\bar{y}_{jk}} \qquad\perp\qquad
\begin{cases}
P_k - \DEF{shipping}{\tau_{jk}} - P_j & \text{unrestricted} \\
\\
\min [P_k - \tau_{jk},\DEF{ceiling}{\bar{P}_j}] - P_j & \text{restricted}
\end{cases}
\end{equation}
<br>
<p>Private storage</p>
\begin{equation}
0 \leq Z_i \leq \DEF{capacity}{\bar{Z}_{i}} \qquad\perp\qquad
\delta \; \DEF{expected}{E P'_i} - P_i - \DEF{cost}{K}
\end{equation}
</section>
<section>
<h3>Public storage</h3>
<p>Public storage</p>
<br>
\[ 0 \leq Z_{i} \leq \DEF{capacity}{\bar{Z}_{i}} \qquad\perp\qquad \DEF{strike price}{\bar{P}_i} - P_i \]
<br>
<div style="float: left; width: 50%">
<p>alternatively</p>
<br>
\[ Z_i = \bar{Z}_i\;\frac{1+\exp\left[-s\bar{P}_i\right]}{1+\exp\left[-s(\bar{P}_i - P_i)\right]} \]
</div>
<img data-src="figures/storage-logistic.svg" width="45%">
</section>
<section>
<h3>Acreage</h3>
<p>Share of land cultivated with wheat</p>
<br>
\[ \lambda_\min \leq \DEF{wheat share}{\lambda} \leq \lambda_\max \qquad\perp\qquad E P'_{\text{wheat}} - \phi E P'_{\text{corn}} \]
<br>
<div style="float: left; width: 50%">
<br>
<p>Acreage:</p>
\begin{align}
q_\text{corn} &= (1-\lambda)\DEF{land}{L} \\
\\
q_\text{wheat} &=\lambda \DEF{land}{L}
\end{align}
</div>
<img data-src="figures/production-frontier-2grains.svg" width="40%">
</section>
<section>
<h3>Dealing with the "curse of dimensionality"</h3>
<br>
<div style="float: left; width: 50%">
<ul>
<li>Collocation with Chebyshev polynomials, 9 nodes per dimension.</li>
<li><span style="color: steelblue">$A$</span> has 6 dimensions $\Rightarrow$ $9^6= 531\,441$ nodes and basis functions if using tensor product.</li>
<li>Use Smolyak's method to choose nodes and bases.</li>
<li>Result: only 1409 nodes and 389 polynomials.</li>
</ul>
</div>
<img data-src="figures/Smolyak-nodes2D9nodes.svg" width="45%">
</section>
</section>
<!--=========================================================================================================-->
<section>
<h2>Data Sources and regions</h2>
<p>Most parameters calibrated with historical data from PSD database (USDA)</p>
<table style="font-size: 70%; color: white;" >
<tr style="color: black;">
<td></td>
<td style="text-align: center">World</td>
<td style="text-align: center">Exporters</td>
<td style="text-align: center">Importers</td>
</tr>
<tr style=" border: solid #F0F1EB 10px;">
<td style="color: black; vertical-align: middle">Corn</td>
<td style="background-color: #1a54a1; border: solid #F0F1EB 10px;">
<ul><li>North America</li></ul>
</td>
<td style="background-color: darkred; border: solid #F0F1EB 10px;">
<ul>
<li>Former Soviet Union</li>
<li>South America</li>
</ul>
</td>
<td style="background-color: #374e0c; border: solid #F0F1EB 10px;">
<ul>
<li>East Asia</li>
<li>Southeast Asia</li>
<li>Middle East</li>
<li>Norht Africa</li>
<li>European Union</li>
</ul>
</td>
</tr>
<tr>
<td style="color: black; vertical-align: middle">Wheat</td>
<td style="background-color: #2a76dd; border: solid #F0F1EB 10px;">
<ul><li>North America</li></ul></td>
<td style="background-color: #aa2233; border: solid #F0F1EB 10px;">
<ul>
<li>Former Soviet Union</li>
<li>Oceania</li>
<li>European Union</li>
</ul>
</td><td style="background-color: #5E740B; border: solid #F0F1EB 10px;">
<ul>
<li>East Asia</li>
<li>Southeast Asia</li>
<li>Middle East</li>
<li>Norht Africa</li>
<li>Sub-Saharan Africa</li>
</ul>
</td>
</tr>
</table>
</section>
<section>
<h2>Numerical solution strategy</h2>
<ul>
<li>Dynamic model, with state variable <span style="color: steelblue">$A$</span></li>
<li>Given $A_i$, model can be reduced to a mixed-complementarity problem with unknowns <span style="color: steelblue">$P,\;Z,\;\lambda,\;y\;$</span> $\Rightarrow$ 17 or 18 variables.</li>
<li>$E P'_i$ is unknown $\Rightarrow$ collocation methods: $p_i\approx \hat{p}_i = \sum_h{c_h \phi_h(A)}$</li>
<li>Inner loop iteration to solve MCP, using <span style="color: steelblue">$A$</span> and numerical integration to evaluate
\begin{equation}
E P'_i \approx E\sum_{h=1}^H{c_h \phi_h(A')} \approx \sum_j\omega_j\sum_h{c_h \phi_h(Z + q\epsilon'_j)}
\end{equation}</li>
<li>Outer loop iteration to solve for collocation coeffs <span style="color: steelblue">$c_h$</span></li>
</ul>
</section>
<!--=========================================================================================================-->
<section>
<h2>Policy Scenarios</h2>
<p> </p>
<table style="font-size: 80%; " >
<tr style=" border: solid #F0F1EB 10px; color: white">
<td style="background-color: #1a54a1; border: solid #F0F1EB 10px; text-align: center">
Policy Scenarios
</td>
<td style="background-color: darkred; border: solid #F0F1EB 10px; text-align: center;">
Policy Shocks
</td>
</tr>
<tr style=" border: solid #F0F1EB 10px;">
<td style="background-color: #bee4fd; border: solid #F0F1EB 10px;">
<ol start="0">
<li style="margin-bottom: 14px">baseline</li>
<li style="margin-bottom: 14px">wheat exporters set price ceiling at baseline average</li>
<li style="margin-bottom: 14px">wheat importers set public storage, price around baseline average</li>
<li style="margin-bottom: 14px">wheat exporters and importers apply policies simultaneously</li>
<li style="margin-bottom: 14px">ethanol production increases corn demand by 20%</li>
</ol>
</td>
<td style="background-color: #ffcaca; border: solid #F0F1EB 10px;">
<ol>
<li style="margin-bottom: 24px">change of policy regime;</li>
<li style="margin-bottom: 24px">change of regime while 20% drop in Exporter wheat production; and</li>
<li style="margin-bottom: 24px">change of regime, production shock, when initial wheat stocks are low.</li>
</ol>
</td>
</tr>
</table>
</section>
<!--=========================================================================================================-->
<section>
<section>
<h2>Long-term prices</h2>
<ul>
<li>Ethanol mandate:
<ul>
<li>only policy with large effect on long-term price (both grains)</li>
<li>greatly increases price volatility of both grains, in all regions</li>
</ul>
</li>
<li>Wheat Exporter price ceiling increases wheat price volatility in other regions</li>
<li>Public storage in Wheat Importer, despite displacing private storage, reduces wheat price volatility in all regions</li>
</ul>
</section>
<section>
<h3>Long-term prices: mean and standard deviation</h3>
<p> </p>
<table align="center" border="1" cellpadding="1" cellspacing="1" style="width: 100%; font-size:60%">
<thead>
<tr>
<th> </th>
<th colspan="3" style="text-align: center">CORN</th>
<th colspan="3" style="text-align: center">WHEAT</th>
</tr>
</thead>
<tbody>
<tr style="background-color: lightgrey">
<th> </th>
<td>World</td><td>Exporter</td><td>Importer</td><td>World</td><td>Exporter</td><td>Importer</td>
</tr>
<tr><td style="color: firebrick; text-align: left" colspan="7">MEAN</td></tr>
<tr>
<th>0: Baseline</th>
<td>100.00</td><td>100.00</td><td>108.91</td><td>100.00</td><td>100.05</td><td>112.22</td>
</tr>
<tr>
<th>1: Price ceiling</th>
<td>101.68</td><td>101.68</td><td>110.50</td><td>102.45</td><td>93.80</td><td>114.66</td>
</tr>
<tr>
<th>2: Public storage</th>
<td>101.63</td><td>101.63</td><td>110.41</td><td>98.28</td><td>98.34</td><td>110.51</td>
</tr>
<tr>
<th>3: Ceiling + storage</th>
<td>103.22</td><td>103.22</td><td>111.87</td><td>99.17</td><td>94.69</td><td>111.43</td>
</tr>
<tr>
<th>4: High demand</th>
<td>118.18</td><td>118.18</td><td>126.2</td><td>115.19</td><td>115.23</td><td>127.41</td>
</tr> <tr><td style="color: firebrick; text-align: left" colspan="7">STANDARD DEVIATION</td></tr>
<tr>
<th>0: Baseline</th>
<td>14.72</td><td>14.72</td><td>13.98</td><td>18.02</td><td>18.08</td><td>18.02</td>
</tr>
<tr>
<th>1: Price ceiling</th>
<td>16.07</td><td>16.07</td><td>14.93</td><td>24.54</td><td>6.92</td><td>24.54</td>
</tr>
<tr>
<th>2: Public storage</th>
<td>17.23</td><td>17.23</td><td>16.11</td><td>11.45</td><td>11.54</td><td>11.44</td>
</tr>
<tr>
<th>3: Ceiling + storage</th>
<td>19.26</td><td>19.26</td><td>17.50</td><td>14.64</td><td>4.73</td><td>14.53</td>
</tr>
<tr>
<th>4: High demand</th>
<td>21.31</td><td>21.31</td><td>16.88</td><td>18.09</td><td>18.13</td><td>18.09</td>
</tr>
<tr><td style="color: firebrick;" colspan="7"> </td></tr>
</tbody>
</table>
</section>
<section>
<h3>Long-term World prices: conditional on initial stock</h3>
<img data-src="figures/Price-vs-Stock-level-baseline.svg" width="90%">
</section>
<section>
<h3>Probability of crisis: conditional on initial stock</h3>
<img data-src="figures/Crisis-Stock-scenarios.svg" width="90%">
</section>
</section>
<!--=========================================================================================================-->
<section>
<section>
<h2>Short-term prices</h2>
<ul>
<li>By itself, introducing price ceiling or public storage have small impact in short-term prices</li>
<li>Initial grain storage is a key determinant of likelihood of severe price spikes</li>
<li>An export price ceiling can heighten a price surge originated in production shock & low stocks</li>
</ul>
</section>
<section>
<h3>Short-term adjustment</h3>
<img data-src="figures/Price_IRF.svg" width="90%">
</section>
</section>
<!------------------------------------------------------------------------------------------------
ESSAY 2: A COUNTRY RESERVE
------------------------------------------------------------------------------------------------->
<section data-background="figures/pic-silos1.jpg" class="essay-title" id="cover-essay2">
<h2>Food Security for Whom?</h2>
<h3>The Effectiveness of Food Reserves in Poor Developing Countries</h3>
</section>
<!--=========================================================================================================-->
<section>
<h2>Food reserve to cope with volatile prices?</h2>
<p>If a poor grain-importing country decides to operate a grain reserve to stabilize prices...</p>
<div style="width: 65%; float: left">
<ul>
<li>what is the ultimate target: welfare vs. hunger</li>
<li>what is the optimal size of the food reserve?</li>
<li>is it better to use a financial reserve to buy grain when needed?</li>
<li style="color: darkred">how is the country's hunger rate affected by its operations?</li>
</ul>
</div>
<img width="30%" data-src="figures/pic-silos2.jpg">
</section>
<!--=========================================================================================================-->
<!-- THIS SLIDE SEEMS REDUNDANT
<section id="motivation-is-grain-storage-a-good-idea">
<h2>Motivation: Is grain storage a good idea?</h2>
<div style="padding-bottom: 1.5em">
<ul>
<li>The logic behind grain storage is simple:
<ul style="padding-left: 1em">
<li>Seven years of abundance followed by seven years of famine…</li>
<li>What if country never has years of abundance?</li>
<li>Opportunity cost of storing grain is very high!</li>
</ul>
</li>
</ul>
</div>
<div class="fragment">
<ul>
<li>To answer this, a model should quantify
<ul>
<li>the increase on national hunger induced by an international crisis;</li>
<li>to what extent a reserve alleviates this increase, and at <span style="color: darkred">what cost</span>.</li>
</ul>
</li>
</ul>
</div>
</section>
-->
<!--=========================================================================================================-->
<section>
<section>
<h2>Key features of the model</h2>
<br>
<img data-src="figures/fig-Food-Distribution.svg" align="right">
<ul style="font-size: 90%">
<li>Nested utility: two goods, two food ingredients</li>
<li>Constant demand elasticities</li>
<li>Substitution between ingredients</li>
<li>Intertemporal, two grain prices</li>
<li>Heterogeneous households: log-logistic income distribution</li>
<li>Government objective: to prevent extreme hunger</li>
</ul>
</section>
<section>
<h3>Government problem: objectives and tools</h3>
<p>Government runs a grain stockpile to deal with price fluctuations.</p>
<ul>
<li>Objective</li>
\[ V_{p_g^*}\left(s\right) = \max_{\DEF{tariff}{\tau}} \left\{\tfrac{1}{1-\rho}\left[1-\Gamma(\tau, \DEF{intn'l price}{p_g^*})\right]^{1-\rho} + \delta E V_{{p_g^*}'}\left(s'\right) \right\} \]
<li>Stock accumulation</li>
\[ \DEF{stock}{s'} = (1-\DEF{cost}{\phi})\left[s +\tfrac{1}{p_g^*} \DEF{revenue}{\Upsilon}\left(\tau, p_g^*\right) \right] \geq 0 \]
<li>External shocks</li>
\[ \pi_{ij} = Pr\left({p_{g}^*}'= p_j\quad | \quad p_{g}^* = p_i\right)\]
</ul>
</section>
<section>
<h3>Reward function $r(\tau,P)$, by objective</h3>
<br>
<table cellspacing="2" cellpadding="1" border="1" width="95%" align="center">
<thead>
<tr>
<th>Objective, $V$</th>
<th>Reward function, $r(\tau,p_g^*)$</th>
</tr>
</thead>
<tbody>
<tr>
<th style="padding: 2ex">Hunger, $\Gamma$</th>
<td>$\frac{1}{1-\rho}\left[1-\Gamma(\tau,p_g^*)\right]^{1-\rho} $</td>
</tr>
<tr>
<th style="padding: 2ex">Welfare,$\int_y v_i$</th>
<td>$\frac{1}{1-\rho}\int_y\left[v(\tau,p_g^*)\right]^{1-\rho}$</td>
</tr>
</tbody>
</table>
<p>Hunger rate depends on price level, income per capita and income inequality</p>
$\DEF{hunger rate}{\Gamma(P)} =
\left[1+\left(\frac{c\DEF{price}{P^\alpha} (\DEF{Gini}{G}\pi)^\eta}
{\zeta \DEF{income}{Y^\eta}\sin^\eta(G\pi)}\right)^{1/{G\eta}}\right]^{-1}$
</section>
</section>
<!--=========================================================================================================-->
<section>
<section>
<h2>Food reserve in Haiti</h2>
<figure>
<img data-src="figures/Haiti_building_reserve.png" width="70%">
<figcaption class="small">Jul2013: gov't begins construction of reserve, 35.000 tonnes</figcaption>
</figure>
<div class="fragment">
<blockquote style="position: relative; top: -12em; width: 60%; background: rgba(0, 0, 0, .5); color: yellow ">
“The construction of this strategic reserve reflects the desire of my Government to promote national agricultural production, stabilize the market price of commodities and combat food insecurity. Indeed, the fight against hunger and extreme poverty constitutes the main pillars of government action.”
<span style="font-size: 70%">Prime Minister, Laurent Lamothe</span>
</blockquote>
</div>
</section>
<section>
<h3> Solving the model: The food crisis in Haiti</h3>
<div style="width: 80%">
<p>Food Crisis in Haiti:</p>
<ul>
<li>Dec2007-Mar2008: rice price doubles</li>
<li>Early April 2008: violent protests in Port-au-Prince</li>
<li>April 12: Prime Minister Jacques Adouard Alexis ousted</li>
</ul>
</div>
<div style="width: 45%; float: left">
<figure>
<img data-src="figures/pic-haiti-riots.jpg" width="100%">
<figcaption class="small">Residents protest on the streets in Port-au-Prince. Photograph: Eduardo Munoz/Reuters</figcaption>
</figure>
</div>
<div class="fragment" style="width: 50%; float: right">
<p>Calibration of parameters: Haiti</p>
<ul>
<li>$\Gamma_{2011}=44.5\%$</li>
<li>Imports $\approx 70\%$ of cereals consumed</li>
<li>$p_g^*$ increased 85% during crisis</li>
</ul>
</div>
</section>
<section>
<h3>Solving the model: Numerical methods</h3>
<ul>
<li>Numerical solution:
<ul>
<li>Collocation method (<span style="font-style: italic">dpsolve</span> solver in <span style="color: #00008B">CompEcon</span>)</li>
<li>Chebyshev polynomials with 12 nodes for continuous state $s_t$</li>
<li>One discrete variable, price, with values 1.0 and 1.85</li>
</ul>
</li>
<li>Once solved, run Monte Carlo simulations to assess performance of the policy</li>
</ul>
</section>
<section>
<table align="center" border="1" cellpadding="1" cellspacing="1" style="width: 75%; font-size:60%;">
<thead>
<tr>
<th>Parameter</th>
<th>Description</th>
<th>Value</th>
</tr>
</thead>
<tbody>
<tr><th> α </th><th> price elasticity food demand </th><td> 0.788 </td></tr>
<tr><th> η </th><th> income elasticity food demand</th><td> 0.814 </td></tr>
<tr><th> σ </th><th> elasticity of substitution</th><td> 0.500 </td></tr>
<tr><th> θ </th><th> share of grain in food budget</th><td> 0.333 </td></tr>
<tr><th> c </th><th> hunger threshold</th><td> 30.258 </td></tr>
<tr><th> ζ </th><th> food demand scale</th><td> 1.208 </td></tr>
<tr><th> Y </th><th> income per capita</th><td> 114.925 </td></tr>
<tr><th> G </th><th> Gini coefficient</th><td> 0.590 </td></tr>
<tr><th> pL </th><th> price of grain when low</th><td> 1.000 </td></tr>
<tr><th> pH </th><th> price of grain when high</th><td> 1.850 </td></tr>
<tr><th> pv </th><th> price of vegetable</th><td> 1.000 </td></tr>
<tr><th> γ </th><th> proportion of years in crisis</th><td> 0.200 </td></tr>
<tr><th> ψ </th><th> expected duration of food crisis</th><td> 3.000 </td></tr>
<tr><th> δ </th><th> government discount factor</th><td> 0.970 </td></tr>
<tr><th> ρ </th><th> government relative risk aversion</th><td> 2.500 </td></tr>
<tr><th> φ </th><th> marginal cost of storage</th><td> 0.025 </td></tr>
<tr><th> r </th><th> interest rate</th><td> 0.010 </td></tr>
</tbody>
</table>
</section>
</section>
<!--=========================================================================================================-->
<section>
<section>
<h2>Main results</h2>
<p>The optimal grain storage policy will...</p>
<ul>
<li>not fully stabilize food prices.</li>
<li>not prevent extreme hunger, yet it would reduce its frequency.</li>
<li>be very sensitive to key parameters (price process, storage costs)</li>
<li>often be outperformed by policies that attack poverty directly.</li>
<li>not offer a clear advantage over accumulating financial assets.</li>
</ul>
</section>
<section>
<h3>The effect of crisis, without policy</h3>
<p> </p>
<table align="center" border="1" cellpadding="1" cellspacing="1" style="width: 85%;">
<thead>
<tr><th>Variable<br></th><th>tranquil<br></th><th>crisis</th><th>% change</th></tr>
</thead>
<tr><th>Price of grain<br></th><td>1.0</td><td>1.85</td><td>85.0</td></tr>
<tr><th>Price of food<br></th><td>1.0</td><td>1.25</td><td>25.5</td></tr>
<tr><th>Food consumption<br></th><td>50.8</td><td>42.5</td><td>-16.4</td></tr>
<tr><th>Grain consumption<br></th><td>16.9</td><td>11.7</td><td>-31.1</td></tr>
<tr><th>Vegetable consumption<br></th><td>33.9</td><td>31.8</td><td>-6.3</td></tr>
<tr style="color: #710909">
<th>Hunger rate (%)<br></th><td>44.5</td><td>53.8</td><td>20.8</td>
</tr>
</table>
</section>
<section>
<h3>Government's policy</h3>
<table width="90%">
<tr >
<td style="border-color: transparent"><p style="color: darkgreen; margin: 0;">Storage</p><img data-src="figures/Storage-policy.svg"></td>
<td style="border-color: transparent"><p style="color: darkgreen; margin: 0;">Tariff</p><img data-src="figures/Tax-policy.svg"></td>
</tr>
<tr >
<td style="vertical-align: top"><p style="color: darkgreen; margin-right: -60px; text-align: right">Hunger</p></td>
<td><img data-src="figures/Hunger-policy.svg"></td>
</tr>
</table>
</section>
<section>
<h3>Long-term distribution of grain reserve</h3>
<p>In half of the crisis, the reserve would be empty!</p>
<img data-src="figures/Storage-cdf.svg" width="90%" align="middle">
</section>
<section>
<h3>Long-term distribution of hunger</h3>
<p>The reserve would fail at preventing extreme hunger.</p>
<img data-src="figures/Hunger-histogram.svg" width="90%" align="middle">
</section>
<section>
<h3>Cash vs. grain reserve?</h3>
<p style="font-size: 90%">In this scenario, a grain reserve outperforms a cash reserve, but difference is small.</p>
<img data-src="figures/Value-function-facet-baseline.svg" width="90%" align="middle">
</section>
<section>
<h3>Food storage vs. fighting poverty</h3>
<p>Resources used for grain reserve might be better spent at promoting growth.</p>
<img data-src="figures/fig-Effect-Income.svg" width="90%" align="middle">
</section>
<section>
<h3>Price stabilization vs. safety net?</h3>
<p>Income redistribution, targeting the poor, may have a better outcome.</p>
<img data-src="figures/fig-Effect-Inequality.svg" width="90%" align="middle">
</section>
</section>
<!-----------------------------------------------------------------------------------------
ESSAY 3: A JOINT RESERVE
------------------------------------------------------------------------------------------->
<section data-background="figures/pic-silos3.jpg" class="essay-title" id="cover-essay3">
<h2>Sustainability of Regional Food Reserves When Default Is Possible</h2>
</section>
<!--=========================================================================================================-->
<section>
<h2>The case for joint reserves</h2>
<p> </p>
<table style="font-size: 80%; " >
<tr style=" border: solid #F0F1EB 10px; color: white">
<td style="background-color: #1a54a1; border: solid #F0F1EB 10px; text-align: center; width: 50%">
The promises
</td>
<td style="background-color: darkred; border: solid #F0F1EB 10px; text-align: center; width: 50%;">
The challenges
</td>
</tr>
<tr style=" border: solid #F0F1EB 10px;">
<td style="background-color: #bee4fd; border: solid #F0F1EB 10px;">
<ul>
<li style="margin-bottom: 14px">risk diversification</li>
<li style="margin-bottom: 14px">economies of scale</li>
<li style="margin-bottom: 14px">independent management, free of political influence</li>
<li style="margin-bottom: 14px">provision of forum for collective agreements</li>
</ul>
</td>
<td style="background-color: #ffcaca; border: solid #F0F1EB 10px;">
<ul>
<li style="margin-bottom: 24px">implementation procedures</li>
<li style="margin-bottom: 24px">financial sustainability</li>
<li style="margin-bottom: 24px">implications for free trade</li>
<li style="margin-bottom: 24px">commitment of member countries</li>
</ul>
</td>
</tr>
</table>
</section>
<!--=========================================================================================================-->
<section>
<section>
<h2>The Model</h2>
<ul>
<li>Two countries</li>
<li>No trade</li>
<li>One grain</li>
<li>Countries share a fraction of their grain</li>
<li>Objective: maximize lifetime utility of representative agent</li>
<li>Dynamic game with limited commitment</li>
<li>Nash-Markov sub-game perfect equilibria</li>
</ul>
</section>
<section>
<h3>A country in autarky</h3>
<p>Availability</p>
\[\DEF{production}{\tilde{q}_i} + (1-\phi)\DEF{past storage}{s_{i,-1}} \equiv \DEF{availability}{a_i} = \DEF{consumption}{c_i} + \DEF{storage}{s_i} \]
<br>
<p>Bellman equation</p>
\[ V\left(a\right) = \max_{s\in [0,a]} \left\{u(a-s) + \delta E V\left(a'\right)\right\} \]
<p>subject to</p>
\[a' = (1-\phi)s + \tilde{q}'\]
</section>
<section>
<h3>A joint reserve</h3>
<p>Redistributing availabilities: country $B$ transfers $l = \psi(a_B - a_A)$ units of grain to country $A$</p>
<table style="font-size: 80%; " >
<tr style=" border: solid #F0F1EB 10px; color: white">
<td style="background-color: #1a54a1; border: solid #F0F1EB 10px; text-align: center; width: 50%">
Insurance contract
</td>
<td style="background-color: darkgreen; border: solid #F0F1EB 10px; text-align: center; width: 50%;">
Credit contract
</td>
</tr>
<tr style=" border: solid #F0F1EB 10px;">
<td style="background-color: #bee4fd; border: solid #F0F1EB 10px;">
\[\hat{a}_A = (1-\psi)a_A + \psi a_B\]
<br>
\[\hat{a}_B = \psi a_A + (1-\psi)a_B\]
</td>
<td style="background-color: #caffca; border: solid #F0F1EB 10px;">
\[\hat{a}_A = (1-\psi)a_A + \psi a_B - l_{-1}\]
<br>
\[\hat{a}_B = \psi a_A + (1-\psi)a_B + l_{-1}\]
</td>
</tr>
</table>
<div class="fragment">
<p>If any country defaults, they remain in autarky forever </p>
<table style="font-size: 80%; " >
<tr style=" border: solid #F0F1EB 10px; color: white">
<td style="background-color: darkred; border: solid #F0F1EB 10px; text-align: center; width: 50%;">
Default
</td>
</tr>
<tr style=" border: solid #F0F1EB 10px;">
<td style="background-color: #ffcaca; border: solid #F0F1EB 10px;">
\[\hat{a}_A = a_A\]
<br>
\[\hat{a}_B = a_B\]
</td>
</tr>
</table>
</div>
</section>
<section>
<h3>A game of default</h3>
<br>
<table width="90%" class="game">
<tr>
<th colspan="2" rowspan="2" style="text-align: center; border-color: transparent">Insurance / <span style="color: red">Credit</span> game</th><th colspan="2" class="player">Country B</th>
</tr>
<tr><th class="strategy">Cooperate</th><th class="strategy">Default</th></tr>
<tr>
<th rowspan="2" class="player">Country A</th>
<th class="strategy-row">Cooperate</th>
<td class="payoff">$W^A(a_A,a_B\color{red}{, l}),W^B(a_A,a_B\color{red}{, l}) $</td>
<td class="payoff">$V^A(a_A), V^B(a_B) - \DEF{stigma}{\sigma}$</td>
</tr>
<tr>
<th class="strategy-row">Default</th>
<td class="payoff">$V^A(a_A) - \sigma, V^B(a_B)$</td>
<td class="payoff">$V^A(a_A) - \sigma, V^B(a_B) - \sigma$</td>
</tr>
</table>
<p>where</p>
\[\DEF{value of cooperating}{W(a_A,a_B\color{red}{, l})} =
\max_{s\in [0,\hat{a}]} \left\{u(\hat{a}-s) +
\delta E \DEF{game payoff}{U\left(a'_A,a'_B\color{red}{, l}\right)}\right\}\]
</section>
<section>
<h3>Solving the game</h3>
<p>Numerical solution builds on CompEcon's <i>gamesolve</i>:</p>
<ul>
<li>to allow discrete states</li>
<li>to allow discrete actions</li>
</ul>
<p>Approximation algorithm</p>
<ol start="0">
<li>Discretize the production shocks</li>
<li>Compute the value of autarky $V$</li>
<li>Guess $W^A$ and $W^B$, using Chebyshev polynomials</li>
<li>Get the payoffs $U^A$ and $U^B$ by solving the discrete game</li>
<li>Update $W^A$ and $W^B$ </li>
<li>Iterate steps 3 and 4 until convergence</li>
</ol>
</section>