metadata: authors: 0: author: Do, Quy-Toan
1: author: Levchenko, Andrei A.
2: author: Ravallion, Martin
count: World
docna: 0: docna: Trade insulation as social protection
docty: Policy Research Working Paper
subtopic: Primary Metals,Social Protections & Assistance,Social Development & Poverty,International Trade and Trade Rules,Macroeconomic Management
teratopic: Agriculture,Private Sector Development,Macroeconomics and Economic Growth,Industry
abstracts: cdata!: In a world with volatile food prices,
            countries have an incentive to shelter their populations
            from induced real income shocks. When some agents are net
            food producers while others are net consumers, there is
            scope for insurance between the two groups. A domestic
            social protection scheme would therefore transfer resources
            away from the former group to the latter in times of high
            food prices, and do the reverse otherwise. This paper shows
            that in the presence of consumer preference heterogeneity,
            implementing the optimal social protection policy can
            potentially induce higher food price volatility. Such policy
            indeed generates a counter-cyclical demand shock that
            amplifies the effects of the underlying food shortage. The
            results call for a reassessment of food stabilization
            policies. In particular, the authors urge caution against
            the systematic condemnation of trade insulation practices.
repnme: repnme: Trade insulation as social protection
display_title: Trade insulation as social protection
listing_relative_url: /research/2013/05/17721206/trade-insulation-social-protection
topicv3: Price Volatility m1326059 1150,Trade m1326924 698,Social Insurance m1326950 751,Social Protection and Labor m1327194 697,Gold m1503518 2936
publishtoextweb_dt: 2013-05-01T00:00:00Z
historic_topic: Agriculture,Private Sector Development,Macroeconomics and Economic Growth,Industry
no_of_pages: 26
model_extractions: WPS6448 Policy Research Working Paper 6448

# Trade Insulation as Social Protection

_Quy-Toan Do Andrei A. Levchenko Martin Ravallion_ The World Bank Development Research Group Poverty and Inequality Team May 2013
Policy Research Working Paper 6448

# **Abstract**

In a world with volatile food prices, countries have an incentive to shelter their populations from induced real income shocks. When some agents are net food producers while others are net consumers, there is scope for insurance between the two groups. A domestic social protection scheme would therefore transfer resources away from the former group to the latter in times of high food prices, and do the reverse otherwise. This paper shows that in the presence of consumer preference heterogeneity, implementing the optimal social protection policy can potentially induce higher food price volatility. Such policy indeed generates a counter-cyclical demand shock that amplifies the effects of the underlying food shortage. The results call for a reassessment of food stabilization policies. In particular, the authors urge caution against the systematic condemnation of trade insulation practices.

This paper is a product of the Poverty and Inequality Team, Development Research Group. It is part of a larger effort by the World Bank to provide open access to its research and make a contribution to development policy discussions around the world. Policy Research Working Papers are also posted on the Web at http://econ.worldbank.org. The authors may be contacted at pflewitt@worldbank.org.

_The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those of the authors. They do not necessarily represent the views of the International Bank for Reconstruction and Development/World Bank and its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent._ Produced by the Research Support Team
# Trade Insulation as Social Protection<sup>_∗_</sup>

Quy-Toan Do, Andrei A. Levchenko, and Martin Ravallion<sup>_†_</sup> Keywords: food prices, trade insulation, social protection, beggar thy neighbor JEL Codes: Q17, O24 Sector Board: POV

> _∗_ We are grateful to Jishnu Das, Alan Deardor, Shantayanan Devarajan, Francisco Ferreira, Will Martin, Claudio Raddatz, Ron Trostle, an anonymous referee, Jean-Paul Chavas, David Hummels, and Brian Wright, editors of the present volume, and participants at the 2012 NBER conference on the Economics of Food Price Volatility for very helpful discussions. The ndings, interpretations, and conclusions expressed in this paper are entirely those of the authors. They do not necessarily reect the views of the World Bank, its Executive Directors, or the countries they represent.

> _†_ World Bank Research Department, University of Michigan Economics Department and NBER, and Georgetown University Economics Department, respectively.

1
# 1 Introduction

Over the last two centuries, there has been much debate about the role of trade policy in food crises. Governments of food-exporting but famine-aected areas have often been called upon by their citizens, and have often implemented, food export bans in the hope of protecting vulnerable people. Classical economists were inuential in arguing against such policies in favor of free trade. For example, Aykroyd (1974) describes how the Governor of Bombay in the early nineteenth century quoted Adam Smith's The Wealth of Nations in defending his policy stance against any form of trade intervention during the famines that aicted the region. Various Famine Commissions set up by the British Raj argued against the trade interventions that were being called upon to help protect vulnerable populations. Similarly, Woodham-Smith (1962) describes the inuence that Smith and other classical economists had on British policy responses to the severe famines in Ireland in the mid-nineteenth century. In modern time, free trade has been advocated as a means of stabilizing domestic food consumption in the presence of output shocks (World Bank, 1986). Others have been less supportive. Sen (1981) and Ravallion (1987) pointed to the possibility that real income declines in the famine aected areas can generate food export while people starved.<sup>1</sup> Regulated trade through taxes or even export bans may then be a defensible policy response in helping vulnerable groups relative to feasible alternatives (Ravallion, 1997).

This debate re-surfaced during the latest food price crises. Between 2007 and 2011 an estimated 33 countries resorted to restrictions on exports of grains and other food commodities (Sharma, 2011). The international policy community mobilized itself against these practices. Then World Bank president Robert Zoellick, at the 2008 High-Level Conference on World Food Security, advocated for an international call to remove export bans and restrictions. These controls encourage hoarding, drive up prices, and hurt the poorest people around the world who are struggling to feed themselves.<sup>2</sup> U.S. Secretary of State Hillary Clinton echoes the same concerns in a 2011 speech on global food security: We also saw how unwise policy also had an impact. Some policies that countries enacted with the hope of mitigating the crisis, such as export bans on rice, only made matters worse. (...) And that sounder approach includes (...) abstaining from export bans no matter how attractive they may appear to be, using export quotas and taxes sparingly if at all (...).<sup>3</sup> This paper revisits these claims and argues that trade policies are not necessarily the fundamental source of the macroeconomic amplication decried above. Rather, we show that an

> 1Though in Ravallion (1987), the analysis of the time series data for famines in British India indicated that the aggregate income eects were not strong enough to undermine the consumption-stabilizing eects of unrestricted trade in that specic period.

> 2http://go.worldbank.org/BUEP7C3NC0

> 3http://www.state.gov/secretary/rm/2011/05/162795.htm

2
optimal domestic social protection scheme would also take the shape of a beggar-thy-neighbor policy when beneciaries of social transfers have a higher propensity to spend on food. Trade insulation policies are then mere second-best instruments available to policy makers that ought to be evaluated against policy alternatives. We therefore encourage a reassessment of food price policy responses that would not single out trade-based instruments but rather consider these together with the wide range of second-best options available to policy makers and evaluate the distortions specic to each of them (as suggested earlier by Meade, 1955).

To develop our argument, we analyze a two-country two-sector endowment economy in which food price volatility is generated by endowment shocks. The endowment prole is such that some agents are net food sellers while others are net food buyers. Thus, there is some scope for insurance between the two types of agents: when food prices are high, net food sellers have a positive income shock, while it is negative for net food buyers, vice and versa. In an optimal social protection policy, the former would therefore transfer resources to the latter in times of food crisis, while the opposite would hold otherwise. Such domestic policy does not necessarily have any international implication unless agents also have heterogeneous preferences over items in their consumption baskets. In particular, when social protection payments during a crisis are being made to agents with a higher propensity to consume food, this will result in an increase in aggregate domestic consumption of food, with the associated implications for world food supply and therefore prices. Domestic social protection policies when agents have heterogeneous preferences therefore result in an amplication of supply shocks. Indeed, the insurance motive constitutes a counter-cyclical demand shock that exacerbates the eect of the output shock, thereby increasing overall food price volatility. When several countries engage in similar practices, policies are strategic complements, increasing the demand for insurance and resulting in even larger price increases.

It is in this context that we analyze trade insulation policies. In a world with limited commitment, the aforementioned social protection contract may not be feasible if one party can renege on her commitment and either sell to (resp. buy from) the international consumer (resp. producer). Trade insulation is then a government intervention to enforce an implicit social protection contract in times of high food prices. Agricultural subsidies on the other hand could then be viewed as compensations when food prices are low. While we have argued that trade-based instruments are not necessarily at the root of the amplication phenomenon described above, they admittedly distort consumption patterns across countries and result in additional upward pressure on food prices. Such distortion nevertheless decreases with the extent of preference heterogeneity among agents and eventually vanishes in the degenerate case.

This paper builds on the literature that analyzes the interactions of international trade and 3
domestic risk-sharing. In a pioneering contribution, Newbery and Stiglitz (1984) showed that trade opening can reduce the de facto domestic risk sharing by making goods prices (and hence real incomes) less sensitive to supply shocks. Our paper is closest to Eaton and Grossman (1985), who argue that when domestic insurance markets are incomplete, trade restrictions may improve welfare.<sup>4</sup> Unlike these contributions, we analyze the global implications of trade restrictions on the volatility of food prices. Our main argument is not so much that some trade restrictions are preferable to none. Rather, our point is that the optimal domestic policy would result in similar international outcomes as would export restrictions. Our paper therefore relates to the literature on (ex-post) food price stabilization policies (von Braun et al., 2008; Wright, 2009; Gouel and Jean, 2012) and departs from Martin and Anderson (2012) and Anderson (2012) in that we view trade restrictions as second-best implementation tools of a domestic social protection scheme. We therefore argue that international eorts to restrict trade-based instruments would make vulnerable populations at risk without necessarily mitigating food price volatility. More broadly, our paper relates to the literature on the interplay between domestic and international risk-sharing in the presence of domestic asset market frictions (Levchenko, 2005; Leblebicioglu, 2009; Broner and Ventura, 2011). A repeated nding in this literature is that an increase in international risk-sharing can lead domestic risksharing to break down. In our model, it is greater domestic risk-sharing that leads to increased volatility internationally.

The rest of the paper is organized as follows. Section 2 lays out the foundation of the model and section 3 studies the optimal social protection policy. In section 4, we analyze trade insulation policies as government interventions to enforce an implicit social protection contract. Section 5 concludes. All the proofs are gathered in the Appendix.

# 2 Setting the Stage

We consider a two-country two-sector endowment economy. The two countries are labeled _D_ and _F_ for _Domestic_ and _Foreign_ , respectively. Agents have endowments of food and gold. There are are two types of domestic agents: a representative net food seller _s_ with an endowment (Φ _s,_ 0) of food and gold, respectively, and a representative net food buyer _b_ with endowment vector (0 _,_ Γ _b_ ) _._ On the other hand, the foreign country _F_ is populated with one representative agent _i_ with stochastic endowment ̃Φ _i,_ ̃Γ _i_ = (Φ _iε,_ ̃ Γ _i_ ) , such that _ε_ ̃ = _ε_<sup>_h_</sup> with � � ̃ probability _π_ and _ε_ = _ε_<sup>_l_</sup> with probability 1 _− π_ , where _πε_<sup>_h_</sup> + (1 _− π_ ) _ε_<sup>_l_</sup> = 1 _._ For the purpose

> 4Dixit (1987, 1989) challenges the view that trade may reduce welfare, or that trade restrictions may increase welfare when domestic asset markets are incomplete, by modeling explicitly the sources of domestic market incompleteness through moral hazard and adverse selection.

4
of the illustration, one can assume that _π_ is large and _ε_<sup>_h_</sup> is not much greater than 1, while _ε_<sup>_l_</sup> is small and implies a large negative aggregate shock on food availability, hence triggering a food price crisis.

Timing and Uncertainty The economy consists of one single time period. At the beginning of the period, consumers and producers have the ability to sign contracts. Uncertainty about _Foreign_ endowments is realized, and at the end of the period, payments if any are made, consumption takes place and agents die.

Preferences For a given consumption bundle ( _fk, gk_ ) of food and gold, respectively, agent _k ∈{s, b, i}_ derives utility i.e. agent _k_ has log-linear preferences over composite good _fk_<sup>_αkg_</sup> _k_<sup>1</sup><sup>_−αk_</sup> ; preferences for food relative to gold are therefore allowed to vary from one individual to the other. Composite good _f_<sup>_αi_</sup> _g_<sup>1</sup><sup>_−αi_</sup> will henceforth be the numeraire. In the rest of the paper, we will assume that _αb ≥ αs_ to capture the idea that net food buyers are also putting a higher weight on food in their consumption basket. Thus, the two building assumptions of this paper correspond to the case where (i) the poor consume a larger fraction of their income on food, and (ii) they are net food buyers on average. The former assumption is Engel's law and has ample empirical support (see e.g. Houthakker, 1957) while there is mounting evidence supporting the latter; Ivanic et al. (2011) for example nd that the 2010-2011 surge in food prices has induced an increase in extreme poverty across the world. Thus, the dierence _αb − αs_ that measures preference heterogeneity between net food buyers and net food sellers could be interpreted as the extent of inequality in the country; Engel's law implies that a larger wealth gap between the rich and the poor will translate into a larger gap in the share of food in their respective consumption baskets. We will henceforth refer to food consumers (resp. food producers) and the poor (resp. the rich) interchangeably.

Individual Consumption, Market Clearing and Prices As a benchmark case, agents are not allowed to contract at the beginning of the period; procurement of gold and food takes place on the international spot market at the end of the period. Prices for food and gold are ̃ denoted ( ̄ _p_<sup>_σ_</sup> _,_ ̄ _q_<sup>_σ_</sup> ) when _ε_ = _ε_<sup>_σ_</sup> with _σ ∈{l, h} ._ Agent _k_ dedicates a fraction _αk_ of her income to food consumption and the remaining to gold consumption. Since food consumption and 5
food production equalize in equilibrium, the relative price of food to gold is therefore Trade and Welfare Net food producing households therefore have welfare while consumers' is equal to Turning to the foreign representative agent, his utility is simply _V_<sup> ̄</sup> _i_<sup>_σ_</sup> = ln ( ̄ _p_<sup>_σ_</sup> Φ _iε_<sup>_σ_</sup> + ̄ _q_<sup>_σ_</sup> Γ _i_ ) . Subtracting total domestic consumption from total domestic food endowment (i.e. Φ _s_ ) gives a net export level equal to:

# 3 Social Protection

Focusing on domestic agents, we note that net food sellers and buyers face income uncertainty and since a positive shock for one is a negative shock for the other, there is scope for mutual insurance. We will refer to the domestic insurance scheme as social protection. Although social protection programs often have a redistribution component built-in so that payments are not necessarily state-dependent, we restrict to the insurance part of these policies. Food voucher programs that are being implemented in times of crisis or the equivalent cash transfer programs, workfare programs in that they are being taken up when market wages drop below the program's proposed wage, would therefore fall into the category of schemes being considered in this analysis.

## 3.1 Arrow-Debreu Securities

We view a social protection program as the implementation of the allocation of resources that domestic agents would achieve if they were given the opportunity to purchase Arrow-Debreu securities at the beginning of the period. The price of an Arrow-Debreu security that pays out 6
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respective budget constraints (3), (4) and (6). Furthermore, trade balance condition (5) holds and food and gold markets clear.

We now turn to the characterization of the equilibrium of the economy. For expositional simplicity, we can rewrite food sellers' budget constraint as a within-state-of-the-world budget constraint with a between-state-of-the-world budget constraint that _φ_<sup>_σ_</sup> _s_<sup>mustsatisfy,i.e.</sup> Similarly for net food buyers, their budget constraint can be rewritten as where _γb_<sup>_σ_veries</sup> Transfers _φ_<sup>_σ_</sup> _s_<sup>and</sup><sup>_γ_</sup> _b_<sup>_σ_couldbeinterpretedasinsurancepaymentsmadetoorfromagentsin</sup> state of the world _σ._ For simplicity and without loss of generality, we henceforth assume that food sellers have insurance payments made in food, while food buyers have insurance payments made in gold. When conditions (8) and (10) are binding, insurance policies are actuarially fair.

The budget constraints then pin down to for _σ_ = _h, l._ Consumer optimization and the demand for insurance _{_ (ˆ _p_<sup>_σ_</sup> _,_ ˆ _q_<sup>_σ_</sup> ) _}σ∈{h,l}_ refers to the equilibrium price vector. Consumer _k_ spends a share _αk_ of her state-contingent post-transfer income on food, and the remaining 1 _− αk_ on gold, so that her budget constraint is binding. Furthermore, since insurance contracts are actuarially fair in equilibrium, for every equilibrium ˆ insurance policy schedule _φ_<sup>_σ_</sup> _s_<sup>_,_ˆ</sup><sup>_γ_</sup> _b_<sup>_σ_</sup> , we denote _φ_<sup>ˆ</sup> = _−φ_<sup>ˆ</sup><sup>_l_</sup> _s_<sup>thepremiumpaidbyfoodsellersin</sup> � � ˆ ˆ times of a food crisis, and _γ_ = _−γb_<sup>_h_,thepremiumpaidbyfoodbuyersinnormaltimes,so</sup> that _φ_<sup>ˆ</sup><sup>_h_</sup> _s_<sup>=</sup><sup><u>1</u></sup><sup>_−_</sup> _π_<sup>_<u>π</u>_</sup> _p_ ˆ _<u>p</u>_ ˆ<sup>_hlφ,_ˆand</sup><sup>_γ_ˆ</sup> _b_<sup>_l_=</sup> 1 _−ππ_ _<u>q</u>_ ˆ _q_ ˆ<sup>_hlγ._ˆDomesticagents'indirectutilitiesarethereforegiven</sup> 8
by _W_<sup>ˆ</sup> _s φ_ ˆ and _W_<sup>ˆ</sup> _b_ (ˆ _γ_ ) _,_ respectively, with � � for net food sellers, and for net food buyers, we have Domestic agents choose their insurance policies to equalize their marginal utilities of consumption across states of the world, dening demand for insurance curves: As expected, the demand for insurance increases with the price dierence between the two states of the world.

Market clearing, trade balance and equilibrium insurance and price levels Food market clearing implies that world food consumption and world food endowment equalize, i.e.

and given the trade balance condition, _p_<sup>_<u>q</u>_ˆ</sup> ˆ<sup>_σσγ_ˆ</sup> _b_<sup>_σ_=</sup><sup>_−φ_ˆ</sup> _s_<sup>_σ,_relativepricesarethus</sup> When _σ_ = _l,_ the world economy experiences an aggregate food shortage pushing food prices up. By shifting wealth from individuals who value food less to individuals who value food more, domestic insurance policies induce aggregate demand for food to increase, inducing an additional upward pressure on food prices as captured in (13). The general equilibrium eect is stronger when preference heterogeneity is more pronounced. For the rest of the paper, we assume that _αb > αs,_ so that net food buyers are also those who put a higher weight on food in their consumption basket. Alternatively, interpreting ( _αb − αs_ ) as the extent of wealth inequality implies that the general equilibrium eect is stronger when wealth inequality is greater; a wealth transfer from the rich lowers their food consumption by less than it increases the poor's, and even more so when wealth dierences are starker. To fully characterize the 9
equilibrium of the economy, we need to solve for prices and insurance policies. To do so, we have the demand functions dened in (12), the market clearing and trade balance conditions. The following proposition characterizes the equilibrium of the economy.

Proposition 1: Optimal Social Protection The unique equilibrium of the economy is characterized by the following social protection policy: In times of food crises (i.e. _ε_ ̃ = _ε_<sup>_l_</sup> ), net food producers transfer an amount of food to net food consumers, and in normal times (i.e. _ε_ ̃ = _ε_<sup>_h_</sup> ), therefore receive in return, where relative prices _<u>q</u>_ ̄ ̄<sup>_σ_denedin(1).</sup> Equilibrium prices adjust � _p_<sup>_<u>σ</u>_</sup> � _σ∈{h,l}_<sup>are</sup> according to (13). ■ The optimal social protection scheme is the intersection of a demand for insurance curve and a food supply curve. The higher the price dierence between the two states of the world, the larger the insurance motive. On the other hand, as agents insure themselves against food price shocks, the supply shock is exacerbated since Domestic demand is higher subsequently to a wealth redistribution from food producers (the rich) who value food relatively less to food consumers (the poor) who value food relatively more. Such additional eect further increases the optimal level of social protection as indicated in (14).

# 3.3 The _n_ Country Case

We extend the analysis to the case of _n_ identical exporting countries to a large foreign market, the size of which is also assumed to grow linearly with _n_ . Among these _n_ countries, we denote by _m ≤ n_ , the number of countries that actually implement a social protection policy as described above and we denote _θ_ =<sup>_<u>m</u>_</sup> _n_<sup>thefractionofcountriesthatimplementasocial</sup> protection scheme. Since agents are price takers, the demand for insurance remains identical and determined by (12). Relative prices are however changed and for expositional simplicity, we focus on prices in times of food crisis, i.e. _σ_ = _l,_ and denote by _φ_<sup>ˆ</sup> _θ_ the optimal insurance 10
policy when _θn_ countries decide to implement a social protection scheme. Recall that _φ_<sup>ˆ</sup> _θ_ is the transfer made from net food producers in a given country to net food consumers of that same country and that transfers in other states of the world are dened by conditions (7) to (11) being binding. Prices are now equal to How will agents in each country choose their social protection levels? As pointed out in Proposition 1, optimal insurance schemes depend on price levels that in turn depend on equilibrium levels of contingent transfers.

Proposition 2: Optimal Social Protection with Multiple Countries The optimal social protection policy _φ_<sup>ˆ</sup> _θ_ is given by

# ■

As the number of countries implementing social protection policies increases, the upward pressure applied on prices further increases the scope for insuring food consumers more. This pecuniary externality exacerbates the eect of social protection on food prices that increase more than linearly as the number of participating countries increases. To look at the welfare implications for domestic consumers of a given country as _θ_ grows closer to 1, we assume that shocks are small enough so that second order eects are negligible. Formally, we notice that ˆ _φθ_ converges to zero as the magnitude of the output shock goes to zero (i.e. _ε_<sup>_l_</sup> gets arbitrarily close to 1), uniformly with respect to _θ._ Net food consumers' welfare levels can be written as

> _o_ <u>(1</u> _−ε_<sup>_l_</sup> <u>)</u> where _o_ �1 _− ε_<sup>_l_�</sup> is a continuous function of 1 _− ε_<sup>_l_</sup> , such that lim _εl→_ 1 1 _−ε_<sup>_l_</sup> = 0 _._ As _θ_ grows, net food consumers receive an increasing social protection payment _φ_<sup>ˆ</sup> _θ_ , the welfare benet of which is mitigated (or oset) by higher prices. The rst term in (16) is the baseline welfare

11
level, while the second term captures the income net of substitution eect. The following proposition establishes the conditions under which one eect dominates the other: Proposition 3: Social Protection and Welfare As the number of countries _θ_ implementing optimal social protection schemes increases, welfare of net food consumers in state of the world _σ_ = _l_ increases if and only if Domestic is a net food exporter, i.e.

## ■

For food exporting (resp. importing) countries, as _θ_ goes up, so does the price of food, inducing a positive (resp. negative) wealth eect. Thus, aggregate income increases in exporting countries, while it decreases in importing countries; for the poor in food exporting countries, the welfare gain from increased social protection transfers ends up exceeding the loss due to higher food prices. The opposite holds for the poor in food importing countries.

# 3.4 Discussion

Aggregate price volatility creates demand for insurance for domestic consumers. In the optimal social protection contract, wealth is transferred from net food producers to net food consumers in times of high food prices. However, such transfer might not be neutral in terms of aggregate consumption when agents have heterogeneous preferences over consumption goods. In particular, when resources are transferred to individuals with a higher propensity to spend on food, it results in an increase in aggregate food consumption, with the associated price implications.

The model therefore produces a counter-cyclical demand shock stemming from agents' insurance motive: the consequences of an aggregate supply shock are exacerbated by a concomitant demand shock due to the implementation of social protection policies that end up increasing the share of food in national consumption. Thus, under some parameter congurations namely _αb > αs_ an optimal domestic social protection policy would qualify as a beggarthy-neighbor policy in that it further reduces the quantity of food available on international markets. As expected, the amplication of price shocks is further enhanced as more countries engage in similar social protection policies. Finally, such counter-cyclical demand shock further results in an overall increased food price volatility, since in normal times ( _σ_ = _h_ ), the aggregate demand for food also drops, driving food prices further down.

12
# 4 Trade Insulation

The previous section characterized the optimal insurance contract that domestic agents are willing to sign in a world with perfect commitment and no transaction costs. If insurance contracts cannot be enforced, then one party has an incentive to renege depending on the realization of the output shock. The insurance market therefore collapses. Trade insulation can then be considered as a government-provided alternative enforcement of a social protection ̃ in states of the world where countries face a food crisis, i.e. _ε_ = _ε_<sup>_l_</sup> _._ Admittedly, such an instrument will come with distortions that are the focus of the analysis in this section. When ̃ on the other hand _ε_ = _ε_<sup>_h_</sup> _,_ governments can resort to various forms of agricultural subsidies (input subsidies, credit...) as the medium through which agricultural households, i.e. net food sellers, receive compensations within the context of a broader social protection contract.

Note however that we are not arguing that trade insulation is a second best policy since we are not considering the whole range of possible interventions. Rather, we study trade insulation in isolation, and compare it with the rst-best benchmark which is the optimal social protection scheme described in section 3.

## 4.1 Export Restrictions and Equilibrium Prices

We restrict ourselves to the case of food exporting countries and dene _X_ , the quota on exports from Domestic to Foreign. Alternatively, the analysis applies to importing countries too and the results are unchanged whether quantity or price restrictions are being put into place. There are now two sets of prices; international prices (prices paid by foreign consumers) � _p_ ̈<sup>_l_</sup> _,_ ̈ _q_<sup>_l_�</sup> _,_ while domestic prices are denoted � _p_ ̇<sup>_l_</sup> _, q_ ̇<sup>_l_�</sup> .

Looking at the foreign country, the trade balance and food market clearing conditions pin _<u>q</u>_ ̈<sup>_l_</sup> down the international price ratio, i.e. _p_ ̈<sup>_l_=</sup><sup><u>(1</u></sup><sup>_−αi_</sup> _α_<sup><u>)</u></sup> _i_<sup>Φ</sup> Γ<sup>_<u>i</u>_</sup> _i_<sup>_εl_</sup><sup><u>+</u></sup><sup>_X_</sup> _,_ that we can rewrite The quantitative food export restriction aects the relative price of food in two ways: it both decreases the international supply of food, and at the same time, since trade should balance in equilibrium, it increases the international supply of gold, making food even more expensive relative to gold.

On the other hand, for a given export quota _X,_ domestic food sellers have income _p_ ̇<sup>_l_</sup> (Φ _s − X_ )+ 13
_p_ ̈<sup>_l_</sup> _X_ . The domestic food market clearing condition can therefore be expressed as and since the prices of gold equalize across markets, the above condition pins down to with the price ratio<sup>_<u>p</u>_ ̈</sup> ̈<sup>_l_denedin(17).</sup> _q_<sup>_l_</sup>

# 4.2 Trade Insulation as Social Protection

To evaluate the ability of trade policy to act as a substitute for social insurance, let's consider the optimal social insurance policy _φ,_<sup>ˆ</sup> and choose a level of export quota _X_<sup> ̇</sup> that keeps domestic food buyers at identical welfare level.

Trade insulation as social protection Recall that under a social insurance contract, net food buyers have welfare in times of high food prices. Considering small aggregate food shocks, i.e. ��1 _− εl_ �� _≪_ 1 _,_ we can rewrite food buyers' welfare as where As we saw previously, any income transfer to a net food buyer translates into a commensurate <u>1</u> welfare increase<sup>_<u>p</u>_</sup> ̄<sup> ̄</sup><sup>_l_</sup> _q_<sup>_l_</sup> _αb_ Γ _b_<sup>_,_but given general equilibrium implications, welfare is however reduced</sup> by higher food prices since _αb > αs_ .

On the other hand, for a given export quota _X,_ net food buyers have welfare level 14
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which, after plugging in the values of _η_ ˆ and _η_ ̇ and rearranging, pins down to This leads us to the following proposition: Proposition 4: Welfare loss from trade insulation Comparing with an economy where Domestic implements an optimal social protection policy, the enforcement of export quota _X_<sup> ̇</sup><sup>_l_</sup> as dened by (21) comes at a welfare loss to international consumers.

Furthermore, ∆ _Vi_<sup>_l_goes to zero as preference heterogeneity(</sup><sup>_αb −αs_)becomes arbitrarily close</sup> to 1. ■ Trade insulation as a substitute for the optimal social protection scheme comes with a price distortion since Domestic and Foreign prices now diverge. This induces Domestic agents to over-consume food while Foreign agents under-consume. However, as preference heterogeneity increases, the relative loss to international consumers decreases and eventually vanishes in the extreme case where food buyers (the poor) only value food, and food sellers (the rich) only value gold; in such degenerate case, the ineciency disappears since there is no longer scope for the substitution eect to operate.

This last result carries an implication for the long-standing debate on trade and famines discussed in the introduction. People at the brink of starvation will spend everything they have on food. While saving lives will surely become the over-riding policy goal, it is notable that in this extreme case the ineciencies of trade intervention vanish. The intuition is as follows: the richer the rich are, the weaker the price eect stemming from trade insulation will be. Thus, their food consumption will be less distorted by the price subsidy, and so will aggregate domestic consumption. In other words, the greater the wealth inequality, the more attractive trade insulation is as a self-targeted social protection program.

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# 5 Concluding Remarks

Critics of trade intervention for the purpose of protection from external price shocks have correctly pointed out that such a policy can exacerbate the problem of price volatility. However, in the absence of better options for aggregate inter-temporal smoothing, the optimal non-trade social protection policy would entail transfers between net food producers and net consumers, to co-insure, and this too would exacerbate the volatility. Given the symmetry between these policies, one cannot argue that the external trade intervention is necessarily an inferior form of social protection. We indeed argued above that trade insulation policies are not necessary to exacerbate food price shocks. Instead, trade policies are viewed as a mere instrument used to implement an underlying optimal social protection scheme. Such use of trade policy comes with some price distortions that need to be evaluated against distortions generated by alternative schemes. However, a priori there are no theoretical grounds for trade-based instruments to be systematically dominated by free trade alternatives from either domestic or international perspectives. Moreover, throughout the paper, we have maintained the constraint that countries were not allowed to run a trade decit, hence ruling out inter-temporal smoothing. Relaxing such constraint would allow agents to diversify across states of the world instead. Eciency gains could therefore be realized if countries were instead able to conduct countercyclical scal policies.

# References

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- Aykroyd, Wallace R., The Conquest of Famine, Chatto & Windus, 1974.

- Broner, Fernando and Jaume Ventura, Globalization and Risk Sharing, Review of Economic Studies, 2011, 78 (1), 4982.

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- Gouel, Christophe and Sébastien Jean, Optimal Food Price Stabilization in a Small Open Developing Country, Working Papers 2012-01, CEPII research center January 2012.

- Houthakker, H. S., An International Comparison of Household Expenditure Patterns, Commemorating the Centenary of Engel's Law, Econometrica, 1957, 25 (4), pp. 532551.

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- Ravallion, Martin, Trade and stabilization: Another look at British India's controversial foodgrain exports, Explorations in Economic History, October 1987, 24 (4), 354370. , Famines and Economics, Journal of Economic Literature, September 1997, 35 (3), 1205 1242.

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