Optimal Food Price Stabilization in a Small Open Developing Country1 ´ bastien Jean Christophe Gouel and Se This paper analyzes the use of storage and trade policies to achieve food price stabiliza- tion in a small open developing country. Optimal stabilization policies are identified using a rational expectations storage model with risk-averse consumers and incomplete markets. Without public intervention, price dynamics are driven by domestic productive shocks and international prices. On its own, an optimal storage policy is found to be detrimental to consumers because its stabilizing benefits leak to the world market. In contrast, an optimal combination of storage and trade policies results in a powerful sta- bilization of domestic food prices. However, such an optimal combination is shown to entail two serious drawbacks: its distributive impacts are large compared to its efficiency benefits, and by distorting excess supply curves, it may aggravate high world price epi- sodes. JEL codes: D52, F13, Q11, Q17, Q18 In developing countries, staple foods frequently account for a significant share of poor households’ budgets. Many poor people have a limited ability to insure against adverse price shocks. Price spikes are problematic for poor households that are not self-sufficient, and these spikes often jeopardize these households’ ability to feed themselves. One important response by developing country gov- ernments to this concern is the implementation of food price stabilization poli- cies. However, the study of these policies has primarily been confined to closed economy contexts with an emphasis on the role of storage (see Wright 2001, for a survey). From a theoretical standpoint, little is known about the role of trade policy in price stabilization programs, despite the widespread use of these poli- cies. Recourse to trade policy to counter price volatility has been common in most Asian countries, where stabilizing the domestic price of rice is a central ob- jective (Dorosh 2008; Islam and Thomas 1996; Timmer 1989). Trade policies are also used in Middle Eastern and African countries in the case of wheat and, 1. Christophe Gouel (corresponding author) is junior researcher at INRA, E ´ conomie Publique, and ´ bastien Jean is director of CEPII research associate at CEPII; his email address is cgouel@grignon.inra.fr. Se and senior scientist at INRA, E ´ conomie Publique; his email address is sebastien.jean@cepii.fr. We would like to thank Jean-Marc Bourgeon, E ´ douard Challe, Christopher Gilbert, Michel Juillard, Will Martin and Brian Wright for helpful comments. A supplemental appendix to this article is available at http:// wber.oxfordjournals.org/. THE WORLD BANK ECONOMIC REVIEW, VOL. 29, NO. 1, pp. 72– 101 doi:10.1093/wber/lht018 Advance Access Publication July 8, 2013 # The Author 2013. Published by Oxford University Press on behalf of the International Bank for Reconstruction and Development / THE WORLD BANK. All rights reserved. For permissions, please e- mail: journals.permissions@oup.com 72 Gouel and Jean 73 to a lesser extent, maize and rice (Dorosh 2009; Wright and Cafiero 2011). The problem may be less acute in Latin America, where most countries are net ex- porters of grains, but it is not irrelevant, as evidenced by Chile’s use of a price- band system for wheat and other food products (Bagwell and Sykes 2004). More generally, based on a large-scale database of agricultural price distortions, Anderson and Nelgen (2012) show that countries tend to vary their nominal rates of assistance to agriculture to limit the effects of variations in the world prices on the domestic prices. Trade and trade policies are key aspects that must be considered when examin- ing food security and price stabilization in developing countries. These policies raise numerous questions, the most important of which may be how storage and trade policies should be combined to achieve price stabilization. Increased reli- ance on national buffer stocks is frequently suggested as a remedy for developing countries faced with significant volatility in world prices. Are buffer stocks a con- sistent policy per se, independent of trade policy interventions? Dorosh (2008) suggests that greater reliance on the world market allowed much more cost- effective price stabilization in Bangladesh than in India; the latter relied almost exclusively on huge public stocks and severe restrictions on imports. Can it be assumed that greater trade openness, or a more reactive trade policy, will reduce the level of stocks needed to achieve a given stabilization target, and to what extent can this be expected to occur? Export restrictions raise a number of additional questions. Most analysts of the 2007–08 food crisis agree that trade policies played a significant role in fueling the international price spikes (Braun 2008; Headey 2011; Mitra and Josling 2009). In particular, the export bans enforced by several rice exporters appear to have contributed greatly to the astonishing price levels that were reached (Slayton 2009). Noting the similar situation in the 1973–74 crisis, Martin and Anderson (2012) emphasize the collective action problem created by export restrictions: the use of these restrictions by some countries to provide shelter from price spikes aggravated the problem for others (see also Boue ¨ t and Laborde Debucquet 2012). The restrictions imposed by Russia on cereal exports following a drought in 2010 only add to this concern. A first step toward manag- ing this problem is to achieve a better understanding of the motivations and con- sequences of export restrictions. Based on a Marshallian surplus analysis, many authors conclude that such policies are harmful to the countries that enact them. Do these policies really cause harm, or do export restrictions make economic sense for a small open economy? In the latter case, is refraining from imposing export restrictions an important sacrifice for the country concerned? Would spe- cific flanking policies be preferable? Many studies have examined how uncertainty affects trade theory results, as discussed in the next section. However, a characteristic of staple food products is that they are storable, which is not considered in most of these works. Storage and its consequences are the subject of a separate strand of the literature, which includes some analyses of the relationships among storage, trade, and trade 74 THE WORLD BANK ECONOMIC REVIEW policy. Although several cases have been studied, these studies do not identify the optimal policies. In contrast, the present paper proposes an optimal stabilization policy design for a small open economy within a rational expectations storage model using tools developed for the analysis of optimal dynamic policies. The focus is on food security concerns in developing countries, assuming that con- sumers are risk averse with no insurance possibilities and assuming a country that is self-sufficient, on average. This policy design is challenging because the combination of rational expecta- tions and non-negative storage and trade constraints renders the model (which does not admit closed-form solutions) problematic to solve and even more diffi- cult to optimize along a dynamic path. Achieving model tractability and identify- ing stylized results requires some simplifications. For this reason, we focus on consumers’ risk aversion, which is linked most directly to food security concerns, and overlook producers’ risk aversion. A significant proportion of poor farmers in developing countries are actually net buyers of food (World Bank 2007), and therefore, their aversion is more akin to consumers’ than producers’ risk aver- sion. We also disregard supply reaction, which is a potentially important mecha- nism but is usually of limited quantitative importance over the time frame of a price surge. Furthermore, in the interest of simplicity, we work with a single- country model. To obtain initial insights into the export restrictions issue, we assess the consequences for developing countries of refraining from imposing such restrictions. For the sake of brevity, the paper focuses exclusively on storage and trade policies, although social assistance programs are also key policy instru- ments for addressing the consequences of food price volatility. However, we leave their analysis in a comparable framework for future work (see Larson, Lampietti, Gouel, Cafiero, and Roberts 2012, for a comparison of a storage policy with safety nets). I . T R A D E , U N C E R TA I N T Y, AND S TO R A G E : R E L AT E D L I T E R AT U R E Uncertainty is widely understood to potentially affect the main conclusions of trade theory. David Ricardo (1821, Ch. 19) concluded that temporary tariffs on cereals might be justified to avoid large losses to farmers who after increasing their production, and, thus, the required capital, to face a sudden change in trade, such as wars, would suffer greatly from an immediate return to the situa- tion prevailing before the crisis. The first formalization of this issue was achieved by Brainard and Cooper (1968). Based on a portfolio approach, these authors show that diversification in a primary producing country decreases fluctuations in national income, which increases national welfare if the country is risk averse. Based on a comparable framework that includes risk aversion in a context in which productive choices are made before uncertainty is resolved, several other papers challenge the idea of the optimality of free trade under uncertainty (Anderson and Riley 1976; Batra and Russell 1974; Turnovsky 1974). Gouel and Jean 75 Helpman and Razin (1978) point out that this result hinges crucially on the as- sumption of incomplete risk-sharing markets. These authors show that the main results of the Ricardian and Heckscher-Ohlin theories of international trade, in- cluding the optimality of free trade, carry over to uncertain environments if the risk can be shared appropriately. In their model, risk is shared because the stock market allows households to diversify their capital, and the cross-border trade in financial assets opens the possibility for international risk-sharing arrangements. Helpman and Razin’s seminal contributions clarify the conditions underlying the potential deviations from standard results and pave the way for insightful elaborations. Yet, there are many reasons why the conditions required for their results might not hold. For instance, households may need to invest their capital in a particular activity without any possibility to diversify, to insure against, or to trade the corresponding risk. In this context, which is particularly plausible for rural households in developing countries, Eaton and Grossman (1985) show that the optimal trade policy for a small open economy is not free trade. On average, the optimal policy entails an anti-trade bias. Similar conclusions emerge if market incompleteness is the result of a lack of international trade in financial assets (Feenstra 1987). In a specific-factor model with risk-averse factor owners, Cassing, Hillman, and Long (1986) show that a state-contingent tariff policy can increase the expected utility of all agents. Newbery and Stiglitz (1984) provide another illustration of the potential insurance role of trade restrictions, extending the analysis to a two-country model. Without insurance markets, Newbery and Stiglitz show that free trade may be Pareto inferior to no trade. Indeed, autarky directly links domestic prices to domestic output, thus providing perfect income insurance for farmers for a unitary price elasticity of demand. These cases show that a departure from free trade may be motivated by risk- sharing objectives when other arrangements are not available.2 When addressing food security in developing countries, it appears to be reasonable to assume in- complete insurance markets. Poor households have little opportunity to insure against the real income risk associated with variable food prices, and poor farmers (as well as many other poor workers) cannot diversify their income source, at least in the short run. Because we focus on food security in a develop- ing country, we adopt this assumption of market incompleteness and assume that consumers are risk averse, with no insurance schemes available. Addressing food security requires accounting for the fact that staple food products are storable. Storability is especially important because storage is a central feature of these markets and can be considered an intertemporal risk- sharing arrangement. Studies of food security have long regarded storage as a key feature. Early analyses of storage-trade interactions relied upon idealized or arbitrary storage technologies (Bigman and Reutlinger 1979; Feder, Just, and Schmitz 1977; Pelcovits 1979; Reutlinger and Knapp 1980). Although these are 2. It is worth noting that Dixit (1987, 1989) criticizes the idea that the absence of insurance markets provides a rationale for trade policy when incomplete markets result from informational problems. 76 THE WORLD BANK ECONOMIC REVIEW useful to ensure tractability, such simplified representations that are not rooted in a consistent description of agent behavior do not accurately reflect the risk- sharing properties of storage. These representations are also vulnerable to the Lucas critique, to the extent that the consequences of policies on agents’ expecta- tions are not taken into account. Hence the interest in a rational expectations, infinite-horizon framework. In addition to specific analyses of oil-related problems, in which world prices are the primary source of uncertainty (Teisberg 1981; Wright and Williams 1982b), storage-trade interactions were first studied in a rational expectations, infinite-horizon framework by Williams and Wright (1991, Ch. 9), who consider a small open market to be the extreme case in a two-country model.3 Srinivasan and Jha (2001) model Indian agricultural markets in relation to the world. They consider the rice market, for which India is a large country, and the wheat market, for which India is a small country. In both markets, there are competitive private storers. World prices are randomly generated without accounting for serial correlation. The authors find that international trade is stabilizing even when the international price is more volatile than the domestic price. Brennan (2003) considers the Bangladesh rice market and shows that opening the market to trade is as stabilizing as some public policies (such as subsidies to private storage or a price ceiling) and has no fiscal cost. In all of these studies, welfare is measured by changes in surpluses. In contrast to the theoretical analyses of trade under uncertainty mentioned previously, these storage-trade models focus on the assessment of given exogenous policies. The models provide no hints of what the optimal policy might be. The present paper extends the normative analyses of trade theory in an uncertain environment to an intertemporal framework with storage under rational expectations. Because it is very difficult to design optimal policies in a dynamic setting, we consider a single-country model. We follow Williams and Wright’s insight and represent the world price as generated by a storage model, and we consider it to be exogenous to the country.4 II. THE MODEL We consider the market for a storable commodity in a small open economy. The world price is taken as given, and the per-unit transport cost is constant. Consumers are risk averse, and domestic food price volatility is driven by random output and a stochastic world price. Production is defined by exogenous 3. Miranda and Glauber (1995) confirm Williams and Wright’s results and propose an improved numerical method. Makki, Tweeten, and Miranda (1996, 2001) present a policy application of this model. Based on a three-country model that includes the EU, the US, and the rest of the world, they analyze the effects of removing current policy distortions such as export subsidies. Coleman (2009) extends Williams and Wright’s work by considering that trade takes time; the time to ship provides a new motive for stockpiling. 4. Country-level policies of price insulation might influence the formation of world prices (Martin and Anderson 2012), but this is difficult to account for in the present framework. Gouel and Jean 77 stochastic shocks, so producers are not represented explicitly but are introduced later, when we account for the effect of the policies on their welfare. Consumers The economy is populated with risk-averse consumers whose final demand for food has an isoelastic specification: D(Pt) ¼ dPt a Y h, where d . 0 is a parameter of normalization; Pt is the period t price; and a, with a , 0 and a = 2 1, and h = 1 are the price and income elasticities, respectively. Income, Y, is assumed to be constant over time, which limits the number of state variables and allows a diagrammatic exposition of the results. Assuming that there are only two goods and that the second good is the numeraire, the integration of this demand function provides the following instantaneous indirect utility function (Hausman 1981): Y 1Àh P1þa vðPt ; Y Þ ¼ ^ Àd t : ð1Þ 1Àh 1þa This utility function has a relative risk aversion equal to the income elasticity of demand. To distinguish income elasticity from risk aversion, we follow Helms (1985a); we assume v ˆ (Pt, Y) to be positive and apply a monotone transformation to the indirect utility function: vðPt ; Y ފ1þu ½^ vðPt ; Y Þ ¼ ð2Þ 1þu vðPt ; Y Þ as u ! 2 1. This specification remains consistent with vðPt ; Y Þ ! ln ^ with the isoelastic demand function, but its coefficient of relative risk aversion is Y 1Àh rðPt ; Y Þ ¼ h À u ð3Þ vðPt ; Y Þ ^ with u indexing the degree of risk aversion. For simplicity, the representative consumer is assumed to adopt hand-to-mouth behavior: he consumes current income and does not save to smooth out fluctuations. The dynamics are thus simplified because the consum- er’s “cash on hand” does not have to be included as a state variable. This as- sumption overlooks the role of self-insurance through saving. However, this self-insurance remains limited in practice and falls short of providing protection comparable to that delivered by a complete market due, inter alia, to borrowing constraints and to the rather large share of the budget accounted for by staple food in many developing countries, especially for poor households. Given the absence of saving, the consumer does not solve an intertemporal problem. At each period, he is concerned only with current-period demand, 78 THE WORLD BANK ECONOMIC REVIEW which is not affected by the degree of risk aversion. The spatial and intertempo- ral arbitrages made by traders and storers are thus independent of consumer risk aversion because the demand function is independent of the degree of risk aver- sion. This independence creates the need for public intervention. Storers The single representative speculative storer is assumed to be risk neutral and to act competitively. Storage allows a commodity to be transferred from one period to the next. Storing the quantity St from period t to period t þ 1 entails a pur- chasing cost, Pt St, and a storage cost, kSt, with k representing the unit physical cost of storage. A ( positive or negative) per-unit subsidy z t for private storage is also considered. The benefits in period t are the proceeds from the sale of previ- ous stocks: Pt St21. The storer maximizes his expected profit as stated by the fol- lowing sum of cash flows: ( ) X1 max Et bi ½Ptþi StþiÀ1 À ðPtþi þ k À ztþi ÞStþi Š ð4Þ fStþi !0g1 i¼0 i¼0 where Et denotes the mathematical expectations operator conditional on informa- tion available at time t, and b is the discount factor. Accounting for the possibility of a corner solution (i.e., the non-negativity constraint of storage), the first-order condition of this problem yields the following complementary condition:5 St ! 0 ? bEt ðPtþ1 Þ þ zt À Pt À k 0 ð5Þ which means that the inventories are null when the marginal cost of storage is not covered by the expected marginal benefits; for positive inventories, the arbitrage equation holds with equality. Thus, the storer buys when the present prices are sufficiently low compared to their expected future level. International Trade Because the model describes a homogeneous product for a small open economy, international trade modeling collapses to two arbitrage conditions: between the domestic price, on the one hand, and the export or import parity price, on the other hand. These equations are expressed in complementarity form as follows: À w Á Mt ! 0 ? Pt À nM t À Pt þ t 0 ð6Þ À w Á Xt ! 0 ? Pt À t À Pt À nX t 0 ð7Þ 5. Complementarity conditions in what follows are written using the “perp” notation ( ? ). This notation means that both inequalities must hold, and at least one must hold with equality. Gouel and Jean 79 where Mt and Xt are imports and exports; Pw t is the world price; and t represents the per-unit import and export costs, which are assumed to be constant and iden- tical. nM X t and nt denote ( positive or negative) per-unit taxes on imports and exports. The complementarity equations for trade (6)–(7) imply that the domes- tic price is restricted to evolving in a moving band defined by the world price, trade costs, and trade taxes, if any: Pw X t À t À nt Pt Pw M t þ t þ nt : ð8Þ Recursive Equilibrium The period t harvest is denoted 1H t and is an i.i.d. random variable. The model has three state variables: St21 , 1H w t , and Pt . In any time period, the first two can be combined into one variable, availability (At), which is the sum of production and private carry-over: At ¼ StÀ1 þ 1H t : ð9Þ The other state variable, the world price, follows a continuous Markov chain, defined in the next section and characterized by the following transition func- tion: À w w Á Pw tþ1 ¼ f Pt ; 1tþ1 ð10Þ where 1w is the random production in the world market, which is assumed to be uncorrelated with domestic production shocks.6 The market equilibrium can be written as follows: At þ Mt ¼ DðPt Þ þ St þ Xt : ð11Þ Based on the above, we can define the recursive equilibrium of the problem without public intervention: Definition In the absence of a stabilization policy (i.e., zt ¼ nM X t ¼ nt ¼ 0), a re- w w cursive equilibrium is a set of functions, S(A,P ), P(A,P ), M(A,Pw), and X(A,Pw), defining private storage, price, import, export over the state fA,Pwg and transition equations (9)–(10) such that (i) the storer solves (4), (ii) trade obeys the arbitrage equations (6)–(7), and (iii) the market clears. World Price Modeling world price dynamics is a crucial issue. The world price level directly influences the domestic price through arbitrage with export and import parity prices. Furthermore, by influencing storage decisions and domestic price 6. It would not be difficult to allow for correlated production shocks, if needed. 80 THE WORLD BANK ECONOMIC REVIEW expectations, which are central to the issues considered here, the world price may also affect expectations about the future price level. In single-country models, the world price is generally represented as a sto- chastic process following a standard distribution, in some cases including first- order autocorrelation (Brennan 2003; Srinivasan and Jha 2001). These types of simplifications are not consistent with the stylized facts on agricultural prices (Deaton and Laroque 1992), which appear to be correctly represented by a storage model (Cafiero, Bobenrieth, Bobenrieth, and Wright 2011). Taking full account of this storage-based representation of world prices would require a two-country model, in which the rest of the world is modeled alongside the economy being studied. The complexity cost of such an option would be high and difficult to reconcile with our objective of identifying the optimal policies. Following Williams and Wright (1991, Ch. 9), a way out of this dilemma would be to consider the small open economy model as a limit case of a two- country model as the size difference between the two countries increases. In this limit case, the small economy is negligible compared to the large one, meaning that the rest of the world can be modeled without paying attention to the small economy under study. In other words, overlooking the influence of the economy on the world market allows the world prices to be modeled as a separate process that is exogenous from the economy’s point of view. This as- sumption of a price-taker economy allows us to disregard the motivations that are linked to the influence of government decisions on world markets and greatly simplifies the analysis. World prices are thus assumed to result from a storage model with random in- elastic production. They are set as a result of a system of three equations equiva- lent to (5), (9), and (11), without import and export variables and without storage subsidy. This system has one state variable: availability. All variables and functions corresponding to the world market are indicated with the superscript w. Given the model’s structure, the observation of price allows us to define the state of the system; price dynamics can thus be defined as a continuous state Markov chain. The expression can be derived using equation (9) and the decision rules, Pw(Aw) and Sw (Aw), which provide the following: À w Á Pw w t þ 1 ¼ P At þ 1 ð12Þ À À Á Á ¼ P w S w Aw w t þ m1tþ1 ð13Þ   À Á  ¼ Pw Sw ðPw ÞÀ1 Pw t þ m1w t þ1 ð14Þ from which equation (10) follows. m is a scale parameter that allows a shift in the world yield distribution. We want to focus on economic mechanisms independent of structural differ- ences between the economy and the rest of the world, so we consider a perfectly Gouel and Jean 81 symmetrical situation in which the world market is calibrated with the same pa- rameter values as the domestic country (thus in the benchmark calibration m ¼ 1). Given that we consider an asymptotic situation in which the rest of the world is infinitely larger than the country, trade does not affect the world equilibrium, and the calibration does not need to account for any size difference. The symme- try between the rest of the world and the economy may appear to be arbitrary. For instance, the diversification of risks across the many countries that are part of the rest of the world could be assumed to lead to a lower variability of output. If the rest of the world is richer on average than the country considered, it could also be argued that price elasticity should be assumed to be smaller in the rest of the world. This assumption would make sense, although the symmetry assump- tion adopted here means that international trade is not motivated by a structural difference but only by the existence of country-specific production shocks that are uncorrelated to worldwide shocks. The sensitivity of the results to the as- sumption of self-sufficiency, and thus to the symmetry between the country and the world market, is analyzed in a supplemental appendix (section S4, available at http://wber.oxfordjournals.org/). Calibration The rational expectations storage model does not allow a closed-form solution; it must be approximated numerically. The numerical algorithm that we use is based on a projection method and is described in detail in the supplemental ap- pendix. The parameters are set such that at the non-stochastic steady-state equilibri- um, price, production, consumption, and availability are equal to 1, and imports and exports are equal to 0 (see table 1 for parameter values). As a result, the country is self-sufficient in the steady state, and no trade takes place. An annual interest rate of 5 percent is used for discounting. Based inter alia on Korinek and Sourdin (2010), we set trade costs to 20 percent. This cost is more than the average cost cited in this study for agricultural products, reflecting our focus on grains for poor countries.7 Seale and Regmi (2006) estimate elasticities for food consumption for 144 countries. From their research, we choose cereal elasticities that are typical of low-income countries: –0.4 for price elasticity and 0.5 for income elasticity. We assume that consumers spend, at the steady state, g ¼ 15 percent of their income on the staple, an intermediate value between what is observed for rice consump- tion in poor and affluent households in Asia (Asian Development Bank 2008). Because steady-state consumption and price are equal to 1, income, which is assumed to be constant, is equal to the inverse of the commodity budget share, 1/ g. At the steady state, we assume a relative risk aversion parameter of 2, implying u ¼ 2 2.62. 7. International trade also frequently entails above-average domestic transport costs. 82 THE WORLD BANK ECONOMIC REVIEW T A B L E 1 . Parameterization Parameter Economic interpretation Assigned value b Annual discount factor 0.95 h Income elasticity 0.5 a Own-price demand elasticity 2 0.4 g Commodity budget share 0.15 Y Income 6.67 d Normalization parameter of demand function 0.39 u Parameter defining risk aversion 2 2.62 k Physical storage cost 0.06 t Trade cost 0.2 m Normalization parameter of world yield distribution 1 1 H , 1w Probability distribution of yield B(2, 2) . 0.5 þ 0.75 We follow Brennan (2003) and assume a per-unit storage cost of 6 percent of the steady-state price (i.e., k ¼ 0.06). Combined with the opportunity cost, this physical storage cost entails an overall storage cost at the steady state equal to 11.3 percent of the steady-state price. For the yield at a country level, we assume that the random productions, 1H and 1w, follow a beta distribution. The beta dis- tribution has the advantage of being empirically supported and popular in sto- chastic yield modeling at a local level (see, among others, Babcock and Hennessy 1996; Nelson and Preckel 1989) and of having bounded support, which is com- putationally convenient. We assume that the distribution has shape parameters 2 and 2, which makes it unimodal at 0.5, and we assume that it is symmetric. The distribution is translated and rescaled to vary between 0.75 and 1.25, implying a coefficient of variation of 11.2 percent. I II. DY N A M I C S WITHOUT PUBLIC POLICY To understand the consequences of public policies, the situation without public intervention is a natural and useful benchmark. Because the model used here differs significantly from those discussed in the literature so far, we analyze this benchmark case in some detail.8 Stock, price, and trade behavior as a function of availability are represented in figure 1(a) for four different values of the world price. Figure 1 also includes similar representations for situations with policy in- tervention in panels (b)–(d), which we discuss below. To understand this figure, first consider the central panel, where domestic price is represented as a function of availability. The demand function with no storage and no trade, represented in light gray, is a useful benchmark. Consider, for example, the solid black line, corresponding to a world price equal to 0.9. When availability is lower than 1 by at least 3 percent, the domestic price is equal 8. The effects of different trade and storage costs in the situation without public intervention are discussed in the working paper version of this article (Gouel and Jean 2012). Gouel and Jean 83 F I G U R E 1 . Stock, Price, and Trade Behavior Notes: Negative trade values refer to imports. The gray curve in the central panels refers to the demand schedule with no storage and no trade. 84 THE WORLD BANK ECONOMIC REVIEW to 1.1: storage is zero (see left panel for storage behavior), and the country imports at an import parity price (1.1) that is equal to the world price (0.9) plus transport costs (0.2). Conversely, when availability is large enough (in this case, when it exceeds 1 by at least 2 percent), the domestic price is higher than the demand schedule would imply because of storage. No trade occurs in this case (see right panel for trade behavior), given that the domestic price is consistently above the export parity price (0.7, in this case). More generally, for this small open economy without any trade taxes, domes- tic prices necessarily lie in a moving band defined by world prices plus or minus trade costs. Compared to a closed economy, this context radically modifies storage behavior and its consequences. Abundant availability usually favors storage, but exporting is another potential profitable outlet; when scarcity pre- vails, the stabilizing effect of selling inventories may be redundant in the face of the price ceiling imposed by import competition. The first salient feature is that there is no storage when the country imports (see figure 1(a)). To see why this case is necessarily true, note that the domestic price is exactly equal to the world price plus trade costs when the country imports. Equation (5) can thus be rewritten as follows: bEt ðPtþ1 Þ À Pt À k ¼ bEt ðPtþ1 Þ À Pw t À t À k: ð15Þ Because the storage arbitrage condition (5) holds for the rest of the world (as assumed here, given how world prices are determined), À Á À Pw t Àk ÀbEt Pw tþ1 ð16Þ which, combined with (15), gives À Á bEt ðPtþ1 Þ À Pt À k b E t P t þ1 À P w t þ1 À t: ð17Þ Given (8), the domestic price is always inferior or equal to the import parity price, which also holds in expectations terms. As a result, bEt ðPtþ1 Þ À Pt À k ðb À 1Þt , 0: ð18Þ This equation implies that domestic storage is not profitable when importing because the expected value of next year’s difference between domestic and world prices cannot exceed trade costs. This feature, emphasized inter alia by Williams and Wright (1991) in a two- country framework, reflects the fact that importing for storage never makes eco- nomic sense when intertemporal arbitrage is the same at home and abroad. It is always preferable to defer the decision about whether importing will be neces- sary until the next year. Gouel and Jean 85 Storage and exports may coexist in cases where availability is relatively abun- dant. When the country exports, the domestic price equals the export parity price, and the storage arbitrage equation becomes St ! 0 ? bEt ðPtþ1 Þ À Pw t þtÀk 0: ð19Þ For a sufficiently high world price, the expected domestic price cannot be high enough to make speculative storage profitable; exporting is more profitable than storing, and no storage takes place. The coexistence of storage and exports is only observed for intermediate world price levels that are high enough compared to domestic prices to make exporting profitable but not high enough to make the first unit of storage less profitable than exporting.9 The interrelations between storage and exports are also illustrated by the storage rule (left panel of figure 1[a]) for a world price equal to 1.1, where exports are reflected in a flat storage curve for relatively large availabilities. For a world price equal to 1.3, ex- porting is always more profitable than storing, so the storage rule is flat through- out. The current world price affects domestic storage even in the absence of trade. Indeed, world prices are positively autocorrelated because they are generated by a storage model. As a result, a higher current world price entails higher world price expectations for the next period. Accordingly, storage outside of trade situ- ations moves slightly upward for higher world prices. This relationship is illus- trated in figure 1(a) by the two situations of a world price equal to 0.9 and 1. In both cases, the world price is too low to make exports profitable. For availability above the steady state, storers accumulate stocks, but stock levels are higher for a world price of 1 than for a world price of 0.9 because of the expectation of higher future world prices, which increases the profitability of storage. This in- creased profitability also translates into higher domestic prices for a world price of 1 because of the increased stock accumulation. Under the assumption of a small economy, exporting implies a complete dis- connect between domestic prices and availability, as reflected in the flat segments of the price curves that are observed for large enough availabilities for world prices equal to 1.1 and above in the central panel of figure 1(a). Similarly, for limited availabilities, the domestic price is disconnected from availability when it reaches the import trigger price, which is equal to the world price plus trade costs. Between these two cases, the price curve takes a standard form in the pres- ence of storage, with a strongly downward sloping curve for availabilities below a given threshold under which no storage takes place and a smoother curve there- after. For trade, assuming exogenous world prices implies that the net trade curve has a unitary slope whenever trade is not zero. A sample simulation of world and domestic prices illustrates the link between them (figure 2). The domestic price tends to be set to the import parity price when 9. The returns to storage are declining due to its negative influence on expected future domestic prices. 86 THE WORLD BANK ECONOMIC REVIEW F I G U R E 2. Simulated History of Prices without Public Intervention the world price is low and to the export parity price when the world price is high. Most world price spikes are imported through trade to the domestic market. I V. O P T I M A L S TA B I L I Z AT I O N PO L I C Y When modeling the relationships between storage and trade policies, we do not want to only analyze specific cases; we also want to assess the optimal use of these policies. To perform this assessment, we assume that the government cannot commit to future policies and must follow time-consistent policies. To design this optimal stabilization policy, we need to formulate a meaningful objective. The op- timization problem of the discretionary optimal policy can then be stated. Social Welfare Function Policy design is usually based on maximizing the sum of all agents’ surpluses. This standard practice is not valid here because the expected surplus is not a suit- able measure of risk-averse consumers’ welfare. Helms (1985b) shows that, in contrast, the ex ante equivalent variations are meaningful welfare indicators. This corresponds to the amount of income that, in the price regime without inter- vention, would bring the same change in expected utility as the intervention con- sidered here. In the intertemporal framework used in this paper, in which savings are not taken into account, the temporal allocation of this equivalent income is not neutral.10 Assuming that equivalent variation takes the form of a constant income flow, the corresponding amount EVt is implicitly defined at period t by ( ) X1 h  t  i Et ~ ; Y þ EVt À vðPtþi ; Y Þ bi v P ¼0 ð20Þ tþi i¼0 where P~t tþi refers to the price in period t þ i when the policy intervention is stopped from t onward. A first-order Taylor series expansion of the first term 10. Gollier (2010) shows, in a different context, how savings behavior ensures equivalence between alternative patterns of allocation of replacement income over time. Gouel and Jean 87 around the path followed without further intervention gives 1Àb X 1 h  t i EVt % Et ~ ;Y bi vðPtþi ; Y Þ À v P ð21Þ t þi wt i¼0 P  t  where wt ¼ ð1 À bÞEt 1 i¼0 b i v Y ~ P tþi ; Y is the discounted average of the future marginal utility of income in expected terms. Social welfare can be measured by combining this ex ante equivalent variation for consumers with the surplus of other agents:11 1 X 1 h  t i Wt ¼ Et ~ ;Y bi vðPtþi ; Y Þ À v P tþi wt i¼0 ð22Þ X 1  à þ Et i b Ptþi 1H tþi þ Ptþi StþiÀ1 À ðPtþi þ k À ztþi ÞStþi À Costtþi i¼0 where Costtþi denotes the period t þ i fiscal cost of public policies. We neglect the distortionary cost caused by revenue collection, so the fiscal cost of policy intervention is the cost of subsidizing private storage plus the net tax cost of trade policy: Costt ¼ zt St À nM X t Mt À nt Xt : ð23Þ Using (9) and (23), social welfare can be simplified to 8 À Á   9 1 X