On the First Round Effects of Food Price Shocks: the Role of the International Asset Market Structure Preliminary and Incomplete, Please Do Not Cite

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1 October 30, 2013 On the irst Round Effects of ood Price Shocks: the Role of the International Asset Market Structure Preliminary and Incomplete, Please Do Not Cite Rafael Portillo, elipe Zanna ABSTRACT We develop a tractable small open economy model to study the determinants of first round effects of food price shocks in low income countries (LICs). We define first round effects as changes in inflation that, holding core inflation constant, help implement relative price adjustments. The model features three sectors, flexible prices, varying degrees of tradability of the food basket, and alternative asset market structures (complete and incomplete markets, and financial autarky). irst round effects depend crucially on the asset structure and the different transmission mechanisms they trigger. Under complete markets, inter temporal substitution prevails, making the inflationary impact of international food prices proportional to the food share in consumption, which in LICs is typically large. Under financial autarky, the income channel is dominant, and first round effects are instead proportional to the countrys food balance the difference between the countrys food endowment and its consumption which in LICs is typically small. This holds regardless of the degree of food tradability. Incomplete markets yield a combination of the two cases. A similar contrast emerges for changes in domestic food supply. 1

2 2 I. INTRODUCTION Low income countries (LICs) have faced large swings in international food prices in recent years. A common adage on the response to these shocks and commodity prices in general is that the central bank should accommodate first round effects but respond to second round effects. 1 What is meant by first round effects is not always explicit but is usually assumed to depend on the weight of the commodity in the consumer price index (CPI). This direct effect is usually contrasted with possible spillovers from commodity prices to core inflation and wage inflation second round effects. Implicit in the policy advice is the notion that an increase in commodity prices requires an adjustment in relative prices and macroeconomic aggregates. Holding core inflation constant, an increase in headline inflation helps implement these necessary relative price changes; this reasoning supports the first part of the adage. In addition, the choice of nominal anchor is not innocuous. Core inflation embodies the distortions resulting from nominal rigidities. Stabilizing core rather than headline inflation is desirable from a welfare perspective, and therefore justifies the second part of the adage. 2 Most of the academic literature on this topic has focused on wether the objective of core inflation stabilization is robust to various assumptions about the structure of the economy. 3 Not surprisingly, various caveats have emerged. 4 Yet there has been little work in understanding first round effects and how they themselves depend on the structure of the economy. The purpose of this paper is to fill this gap. As food makes up a large share of consumption expenditure in these economies, policymakers in LICs worry that the inflationary effects of food price shocks could be large. According to the Governor of the Central Bank of Tanzania:. Nor is this concern limited to national authorities. According to the managing director of the IM:. The experience during the 2008 food and fuel crisis is supportive of this concern, as developing and emerging economies experienced larger increases in inflation than did developed countries, with the bulk of the increase accounted by higher food prices (see IM 2011). But is it always the case that first round effects depend positively on the share of food in consumption, so that countries with higher food shares should inevitably experience larger increases in inflation? Or are there other, possibly mitigating, factors? We study the determinants of first round effects in a tractable small open economy model with three sectors (non traded, food and a generic traded good), flexible prices, a domestic 1 To our knowledge, this advice has its origins in policy decisions taken by the Bundesbank in the 1970s, which in the face of shocks to the international price of oil raised its one year ahead inflation objective to accommodate the inflation caused by the shock (see Bernanke et al (1998)). The standard advice likely became more clearly articulated with the adoption of inflation targeting regimes, as these helped focus the policy discussion on better understanding the sources of inflation and tailoring the policy response accordingly. rom an academic perspective, although not explicitly stated, the advice can be traced back to the seminal work of Robert Gordon (197X). 2 See Aoki (2001). 3 See... 4 A terms of trade externality and real wage rigidities...

3 3 and time varying endowment of food, varying degrees of tradability of the food basket, and various specifications of the country s access to international financial markets (complete markets, financial autarky and incomplete markets). The tractability of our model allows us to provide analytical solutions and a graphic representation of various equilibria. We use the model to analyze the real adjustment to a temporary increase in international food prices and a shock to the domestic endowment of food. We define first round effects as increases in inflation that holding non traded (core) inflation constant help implement the required relative price and macroeconomic adjustment. 5 In this case inflation is given by minus changes in the relative price of non traded goods (real wages), relative to the consumer price index. The larger the decline in the relative price of non traded goods, the larger the first round effects of food price shocks. With the help of the model we obtain the following results. irst, holding the share of food in the CPI constant, the range of first round effects of an international price shock is in principle large, depending on the share of non traded goods, the elasticity of substitution between goods, the inter temporal elasticity of substitution, and the labor supply elasticity. irst round effects rarely coincide with the weight of (traded) food in the CPI, which we refer to as the direct effect of the shock, except for very specific parameter values. Differences between the direct and the first round effect are accounted for by movements in the nominal exchange rate and sometimes by movements in the nominal price of non traded food. Second and more importantly, first round effects crucially depend on the asset structure: Under complete markets, the preferred specification in open economy new Keynesian models but the one that is least likely to capture the state of affairs in LICs, the inflationary impact of international food price shocks is proportional to the food share in the CPI. The reason is the following. Under complete markets, the real effects of international food shocks depend solely on the inter temporal substitution effects they trigger, which themselves depend on the share of food in the CPI. The larger the food share, the larger the increase in the relative price of the domestic consumption basket, and the larger the incentive to temporarily reduce aggregate consumption. This larger decline in consumption is then associated with a larger decrease in the relative price of non traded goods and therefore with larger first round effects. 6 The overall effect also depends on the degree of tradability of the food basket: the lower the share of food that is traded, the smaller the inflationary effects. In addition, the domestic endowment of food does not play a role in the adjustment, and only serves to pin down the trade surplus/deficit that would follow the increase in international food prices. As low income countries have large food shares, this specification predicts large first round effects. 5 Our assumption of constant inflation allows us to abstract from nominal rigidities altogether, which is why we focus on a model with flexible prices. Our setup assumes that the central bank has the technology to perfectly stabilize core. 6 Note that the presence of food in the basket drives a wedge between the real exchange rate and the inverse of the relative price of non traded goods: the former can appreciate even though the relative price of non-traded goods decreases. This point has been emphasized by Catao and Chang (2011).

4 4 Under financial autarky, the inflationary impact is instead proportional to the country s net food balance rather than the food share in the CPI. In particular, a country that is self sufficient in food should not experience any increase in inflation! The striking difference between the two specifications can be explained as follows. Under financial autarky, the effects of the international price shock depend solely on their effects on the country s external income (income effects). If the country is self sufficient there are no balance of payment pressures from increases in international food prices, hence no pressures for the relative price of non traded goods to change. If this relative price were to fall, the country would demand less traded goods overall and an incipient current account surplus would arise. This incipient surplus will appreciate the nominal exchange rate and reduce the relative price of non traded goods up to the point where the balance of payment clears again. This striking result stems from the inability to run a current account surplus (or deficit) in response to the shock. In addition, for a given food balance, the degree of tradability of the food basket is irrelevant for the inflationary impact of the shock, since the food balance itself is all that matters for the effect of the shock on the balance of payments (and therefore on inflation). As food balances are relatively small in LICs on average, one or two percentage points of GDP, this specification predicts tiny increases in inflation (or even deflation if the country is a net food exporter). Under incomplete markets, domestic agents can accumulate non contingent bonds subject to a portfolio adjustment cost and can in principle run current account surpluses or deficits in response to the shock. In this case, the first round effects depend on both the share of food in consumption and on the country s overall food balance, and the solution is a weighted combination of the first two specifications. While the weight of food in the CPI still captures the substitution effects associated with the shock, the food balance now captures its wealth effects; the more persistent the shock is, the larger the wealth effects and the more important the country s food balance becomes in conditioning the inflationary response. Larger portfolio adjustment costs also push the equilibrium toward the financial autarky case. The effects of shocks to the domestic food endowment also vary starkly depending on the asset market structure. Under complete markets, shocks to the domestic endowment have an inflationary impact only if the endowment is not fully traded, and if so because of inter-temporal substitution considerations. Under financial autarky the opposite holds: it is the overall size of the endowment (and not its degree of tradability) that matters for the inflationary impact of the shock, and because of income rather than substitution effects. The effects of the shock under incomplete markets again fall somewhere between the two polar cases. Third, when we calibrate the model to a generic/median sub-saharan African country, alternative specifications yield very different inflationary pressures. Under complete markets a 1 percent increase in international food prices can result in an increase in first round inflation of as much as 0.27 percent, if food is fully traded. This is large but considerably smaller than the direct effect, which corresponds to the median food share times the shock (0.5 percent). Under financial autarky, the median increase in inflation is tiny (0.01 percent).

5 5 Under incomplete markets, the median increase in inflation falls somewhere in between (0.09 percent if food is fully traded). We draw from this exercise that is far from obvious that first round effects should be large in countries with relatively high food shares in consumption. In addition, while the inflationary effect varies, in all cases a nominal appreciation offsets either a large part or most of the direct effect of the shock. The paper is organized as follows. Section 1 is this introduction. Section 2 presents the model, Section 3 provides an analytical solution, while section 4 discusses the model s calibration and provides a graphic representation of the solution. Section 5 provides a sensitivity analysis and section 6 extends the model to analyze the case of the incomplete tradability of the food basket. inally, section 7 concludes. II. THE MODEL A. The consumer The representative consumer chooses a stream of consumption baskets c t, labor efforts n t and holdings of nominal assets to maximize lifetime utility: ( ) E 0 β t c 1 σ t 1 σ ι n1+ψ t, 1 + ψ subject to the budget constraint: t=0 ( P t c t + B t+1 + ϕ 1 E t [Q t,t+1 D t,t+1 ] + ϕ 2 S t B t+1 + Q(Bt+1) ) = W t n t + Π NT,t Pt y,t + Pt T y T + R t 1 B t + ϕ 1 D t + ϕ 2 S t R Bt. P t is the consumer price index (CPI), W t is the nominal wage and Π NT,t are profits from the non traded sector. We assume the agent is endowed with two types of traded goods: a time varying supply of food y,t and a constant supply of a generic traded good y T, valued at prices Pt and Pt T, respectively. Regarding nominal assets, D t,t+1 denotes time t holdings of contingent claims, which pay one unit of currency if a specific state of nature is realized (in period t + 1) and nothing otherwise, and Q t,t+1 is the one period stochastic discount factor for that state of nature. B t+1 is a non contingent bond, denominated in foreign currency, that pays gross interest R, and S t is the nominal exchange rate. These assets contingent claims and non contingent bond B are traded internationally. We follow Schmitt-Grohe and Uribe (2003) in assuming that holdings of B t+1 are subject to portfolio adjustment costs Q(B t+1): Q(B t+1) = v 2 (B t+1) 2.

6 6 B t+1 denotes holdings of a non contingent nominal bond that pays gross interest R t at time t + 1. The bond is not traded internationally. 7 Parameters ϕ 1 and ϕ 2 take values of either one or zero; together they determine the international asset market structure facing the country. Three cases are considered: the pair (ϕ 1 = 0, ϕ 2 = 0), which implies financial autarky, (ϕ 1 = 1, ϕ 2 = 0), which implies complete (contingent) markets, and (ϕ 1 = 0, ϕ 2 = 1), which implies access to the international non contingent bond. We will refer to the latter case as the incomplete markets case. In this specification, the portfolio adjustment cost ensures the stationarity of the country s net foreign asset position (B ) and allow us to model various degrees of international capital mobility (captured by the value of v). Utility maximization leads to the following first order conditions: { } c σ Rt σ t = βe t c t+1, (1) π t+1 ιn ψ t = w t c σ t, (2) where π t (π t = P t /P t 1 ) is the gross inflation rate and w t (w t = W t /P t ) is the real wage. If ϕ 1 = 1, profit maximization over the set of contingent assets results in a state specific Euler equation: c σ β t = c σ t+1, (3) Q t,t+1 π t+1 which holds across all states of nature. If ϕ 2 = 1, profit maximization over Bt+1 results in another Euler equation: { } c σ t = βr st+1 1 σ E t, c s t 1 + vbt+1 t+1 (4) where s t is the CPI based real exchange rate (s t = S tp P t ) and P is the foreign CPI (assumed constant). B. The consumption basket The consumption basket is the following: c t = [ α 1 η η 1 N c η N,t + α 1 η η 1 c η,t ] η + (1 α N α ) 1 η 1 η 1 η c η T,t. The triplet (c N,t, c,t, c T,t ) denotes consumption of non traded goods, food and the generic traded good, respectively, α N (α ) is the share of non traded goods (food) in consumption, 7 The net supply of B is zero.

7 7 and η is the elasticity of substitution. Cost minimization leads to the following demand functions: c N,t = α N ( P N,t P t ) η c t = α N p N,t η c t, (5) c,t = α ( P,t P t ) η c t = α p,t η c t, (6) c T,t = (1 α N α )( P T,t P t ) η c t = (1 α N α )p T,t η c t. (7) P N,t is the price of non-traded goods. The triplet (p N,t, p,t, p T,t ) denotes the price of each good relative to the CPI, which is given by: P t = [ α N P 1 η N,t + α P 1 η,t ] + (1 α N α )P 1 η 1 1 η T,t. (8) C. Traded prices In our baseline specification, we assume the domestic prices of food and the generic traded good are given by the law of one price: P,t = S t P,t, P T,t = S t P, (9) where P,t is the international nominal price of food. This assumption implies the following domestic relative prices: p,t = s t p,t, p T,t = s t. (10) Lower case p,t (p,t = P,t P ) is the international relative price of food, which we assume is exogenous and time varying. D. The non traded sector irms hire labor to produce non traded goods, using a linear production function: y N,t = n t. (11) Profit maximization results in the following labor demand condition: p N,t = w t, (12) which implies zero profits (Π NT,t = 0). Equilibrium is given by c N,t = y N,t. This perfectly competitive specification replicates the monopolistically competitive one used in new Keynesian models under a monetary policy that perfectly stabilizes

8 8 non traded (sticky price) inflation when firms in that framework receive an employment subsidy that corrects market power distortions. 8 E. Closing the model Under financial autarky (ϕ 1 = 0, ϕ 2 = 0), the representative agent cannot buy or sell financial assets from foreigners. Total demand for traded goods must therefore equal the value of domestic endowments: s t p,tc,t + s t c T,t = s t p,ty,t + s t y T. (13) Under complete markets (ϕ 1 = 1, ϕ 2 = 0), we can combine equation (3) with a similar condition for foreign consumers and derive the following equilibrium condition (see Backus and Smith (1992)): c t = φs 1 σ t c, (14) where c is foreign consumption and φ denotes initial conditions. Under complete markets, c t will deviate from φc only if the domestic basket becomes more or less expensive than the foreign one, i.e., only if the real exchange rate appreciates or depreciates relative to its steady state value. Under incomplete markets (ϕ 1 = 0, ϕ 2 = 1), the country s balance of payment now includes the accumulation of foreign assets, interest income from abroad and portfolio adjustment costs: s t p,tc,t + s t c T,t + s t (b t+1 + Q(b t+1)) = s t p,ty,t + s t y T + R b t, (15) where b = B /P is the value of net foreign assets in units of foreign consumption. or simplicity, we set P = 1, which implies Q(B t+1) = Q(b t+1). III. ANALYTICAL SOLUTION A. Steady state The steady state is the same across all specifications. We impose the condition βr = 1, which in the case of incomplete market imposes b = 0. More generally, we set aggregate consumption, relative prices, and gross inflation to 1: c = s = p N = p = w = π = 1. Steady state values of (c N, c, c T ) are given by (α N, α, 1 α N α ), respectively. Variables y N and n also equal α N, which requires ι = α ψ N. inally, we set y = κ, which imposes y T = 1 α N κ. 8 See Appendix.

9 9 B. The log linear version of the model We log linearize the equations of the model around the steady state. inancial Autarky (A) Under A, the model (eqs. (2), (5) (13)) can be reduced after some algebra to a system of two equations: ĉ t = 1 + ηψ ψ + σ ˆp N,t, (16) α N ĉ t = ηˆp N,t α κ ˆp,t + κ ŷ,t. (17) 1 α N 1 α N 1 α N A hat (ˆ) indicates percent deviations from steady state, with the exception of ˆb t, for which it indicates deviations in percent of consumption. Equation (16) describes internal balance: the relation between aggregate consumption (c) and the relative price of non traded goods (p N ) that ensures equilibrium in the non traded goods sector and the labor market. The relation is straightforward: an increase in p N results in an decrease in the demand for non traded goods and an increase in the supply of labor; an increase in overall consumption is therefore required to increase non traded demand and reduce labor supply (via the ritsch labor supply curve (2)). Equation (17) describes external balance the clearing of the balance of payments. In this case, an increase in p N results in an increase in traded goods demand; a decrease in c is then required to clear the bop. ˆp,t and ŷ,t operate as exogenous shifters of the external balance curve. Complete Markets (CM) Under CM, internal balance remains the same. We derive an alternative external balance condition, by combining the log-linear version of equations (8) and (14): ĉ t = α N 1 1 α N σ ˆp N,t α 1 1 α N σ ˆp,t. (18) Note that, unlike eq. (17), this alternative condition does not reflect the need to clear the bop. Instead, it describes how changes in relative prices affect the representative agent s demand for current consumption, through their effect on the risk sharing condition (14). Because of this, external balance under complete markets does not depend on the economy s endowment of food (either its steady state or current value). This will have important consequences for the inflationary effect of food shocks. Incomplete Markets (IM) inally, under IM, the solution of the model can be reduced to a system of three equations. irst, the internal balance equation, which is the same as (16). The second equation is the

10 10 relation between p N, c and b that clears the balance of payments (by combining eqs. (15),(6),(7),(8), and (10)): ĉ t = α N ηˆp N,t α κ ˆp,t + κ 1 ŷ,t ˆb 1 α N 1 α N 1 α N 1 α t+1 + R ˆb N 1 α t. (19) N Unlike financial autarky, accumulation or decumulation of foreign assets now allow the representative agent to consume more or less traded goods than the value of his endowment. The third equation is the relation between present and future values of (c, p N, p ) and b t+1 implied by combining the Euler equation (4) with eq. (8): ĉ t = ĉ t+1 α N 1 1 α N σ (ˆp N,t ˆp N,t+1 ) α 1 ) (ˆp 1 α N σ,t ˆp,t+1 + vˆb t+1. (20) Consumption now depends on future values of domestic and foreign relative prices, while the portfolio adjustment cost encourages agents to increase consumption when they accumulate net foreign assets (as these lower their net return). Because of the forward looking nature of the Euler equation, the solution of the model is no longer static. To characterize expectations of future variables, we need to specify stochastic processes for international relative prices and the domestic endowment: ˆp,t = ρ p ˆp,t 1 + ϵ p,t, ŷ,t = ρ y ŷ,t 1 + ϵ y,t, 1. Link between inflation and relative prices Under the assumption of constant non traded gross inflation (ˆπ N,t = 0), headline inflation is given by (minus) changes in the relative price of non traded goods: ˆp N,t = ˆπ N,t ˆπ t ˆπ t = ˆp N,t. (21) In the case of shocks to ˆp,t it is helpful to compare the impact on ˆπ t to the direct effect of the commodity price shock, i.e., the effect of the shock on inflation holding all domestic nominal prices constant (except the nominal price of food). As mentioned in the introduction, this is often interpreted as the first round effect of the shock. This direct effect is given by α ˆp,t : ˆπ t α ˆp,t = ( ˆp N,t + α ˆp,t). If the relative price of non traded goods falls by less than the direct effect of the shock ( ˆp N,t > α ˆp,t ) then inflation also increases by less than the direct effect. As will be shown below, there is no guarantee that inflation will increase by this amount. Of further interest is that, given the assumption of full tradability of the food basket and the choice of

11 11 the nominal anchor, differences between actual inflation and the direct effect must come from changes in the nominal exchange rate Ŝt: ˆπ t = (1 α N ) Ŝt+α ˆp,t Ŝt = 1 ) (ˆπt α ˆp 1 ( ),t = ˆpN,t + α ˆp,t. 1 α N 1 α N In the case of ŷ,t 0, where ˆp,t = 0, any resulting increase in inflation would come from a nominal depreciation. C. Solving for ˆπ We now provide analytical solutions for the impact of food shocks on the economy, under financial autarky, complete markets and incomplete markets. In the first two cases, the solution is straightforward since the models are static. In the third case, we rely on the method of undetermined coefficients to find the policy rules that ensure non-explosive dynamics. 9 inancial autarky Under A, equilibrium changes in inflation are given by: ˆπ A t = Φ p A ˆp,t Φ y A ŷ,t, (22) with: Φ p A = (ψ + σ)(α κ ), Φ y A (1 + ηψ)(1 α N ) + η(ψ + σ)α N = Φ A p κ α κ. Complete markets Under CM, inflation is instead given by: ˆπ CM t = Φ CM p ˆp,t Φ CM y ŷ,t, (23) where Φ CM p and Φ CM y are as follows: Φ CM p = (ψ + σ)α (1 + ηψ)σ(1 α N ) + (ψ + σ)α N, Φ CM y = 0. Incomplete markets 9 In the latter case, we verified the analytical solutions by comparing them with simulations of the model (using Dynare).

12 12 inally, under IM, equilibrium inflation now also depends on the country s net foreign asset position: ˆπ IM t = Φ IM p ˆp,t Φ IM y ŷ,t Φ IM b ˆb t, (24) The terms Φ IM p and ΦIM y are the weighted sums of the previous two solutions: Φ IM p = ω p ΦCM p + (1 ω p )Φ A p, Φ IM y = ω y Φ CM y The weights on the complete market solutions ω p + (1 ω y )Φ A y. and ω y, respectively, are given by: with: ϱ = ( ω p = ω y = 1 ρ p 1 ρ p + ϖ 1 (ϱ + v(1 α N )), 1 ρ y 1 ρ y + +ϖ 1 (ϱ + v(1 α N )), ϖ = (1 + ηψ)σ(1 α N) + (ψ + σ)α N (1 + ηψ)(1 α N ) + η(ψ + σ)α N, ϖ(r 1) v(1 α N ) + ((ϖ(r 1) v(1 α N )) 2 + 4v(1 α N )ϖr ) 2 The term Φ IM b also depends on ϱ: Φ IM b = (ψ + σ) (1 + ηψ)σ(1 α N ) + (ψ + σ)α N ϱ. ). We can interpret Φ p A, ΦCM p and Φ IM p as pass through measures consistent with first round effects of international food price shocks, under alternative asset market structures. D. Remarks On the effects of ˆp,t Inspection of Φ A p reveals that the impact of international food prices on inflation under financial autarky is proportional to the net food balance (α κ ). As mentioned in the introduction, this result derives from the role of the bop in the adjustment process. To see why, we begin by assuming that the increase in international prices initially results in the direct price increase mentioned earlier ( ˆp initial N,t = α ˆp,t ), and consider three cases: initial food balance (α = κ ), food deficit (α > κ ), and food surplus (α < κ ). If the country has an initial food balance the higher food bill is exactly offset by the higher value of

13 13 the food endowment. In this case, the initial change in p N would result in an incipient trade surplus, as consumers would switch away from traded goods (in general) and toward non traded goods. The excess net supply of traded goods would then result in a nominal appreciation, undoing the original increase in ˆp N,t and helping rebalance trade. The bop would clear only when the nominal appreciation has completely offset the direct effect of the food price increase: Ŝ t A = α /(1 α N ) ˆp,t, which implies inflation would not change ( ˆp N,t A = ˆπ t A = 0). 10 If the country is a net food importer, then p N must decline and inflation increase to help reestablish external balance, but the required adjustment depends on the initial bop pressure again, holding expenditure on traded goods constant at first which itself depends on the starting net food balance. If the country is a net food exporter, then p N must increase and inflation must decrease! The above results contrast sharply with the CM solution, under which κ has no impact on Φ CM p. In this case, changes in the international price of food have an effect on inflation only to the extent they affect the relative price of the domestic basket, and the representative consumer s demand for current consumption. This channel is proportional to α. inally, the IM solution combines both solutions, with the weight ω p pushing toward the CM case. The combination of the two solutions reflects two separate channels that are present when markets are incomplete. The first channel captures the inter temporal substitution effects associated with food shocks. This channel is proportional to the CM solution because it is the only channel present in that specification. The second channel captures the income or wealth effect of the shocks. Similarly, this channel is proportional to the A solution because it is the only channel present in that specification. We now provide a brief discussion of how each parameter affects Φ p A the sign of which depends on the country s food balance and Φ CM p. We also discuss how each parameter affects the weight ω p. or the latter term, the analysis focuses on whether the coefficient increases or decreases the relative importance of the two channels mentioned above (inter temporal substitution versus wealth effects). 11 The higher the elasticity of substitution between goods (η), the easier it is for agents to switch expenditure. In this case p N needs to fall by less (d Φ p A /dη < 0,dΦCM p /dη < 0). By reducing the impact of the shock on aggregate consumption under financial autarky, the higher elasticity of substitution also reduces the marginal value of accumulating net foreign assets. It therefore brings the IM solution closer to financial autarky (dω p /dη < 0). 10 In this case, the CPI based real exchange rate appreciates by the same magnitude as the nominal exchange rate: ŝ t A = Ŝ t A. Note that while inflation does not change, the increase in international food prices has real effects, namely on the composition of trade. The real appreciation increases consumption of the generic traded good and a generic trade deficit opens up, and the opposite occurs for food. Overall trade remains balanced, however. 11 The analysis is similar for Φ y A, Φ CM y and ω y.

14 14 Under A, the curvature of utility (σ) affects internal balance only. A higher σ makes labor supply more sensitive to a fall in consumption. or a given decline in consumption, say from an increase in ˆp,t, internal balance then requires a larger, offsetting, fall in w. Since p n = w inflation increases by more: d Φ p A /dσ > 0. Under CM, σ also affects external balance: it reduces the consumer s willingness to reduce c temporarily in response to an increase in the price of the basket (since 1/σ is the inter temporal elasticity of substitution). The latter effect dominates (dφ CM p /dσ < 0). A higher σ also increases the marginal value of accumulating net foreign assets an therefore brings the IM solution closer to the complete markets case (dω p /dσ > 0). A higher ψ has two offsetting effects. On the one hand, it makes labor supply less sensitive to w which results in larger movements in real wages to clear the labor markets. On the other hand, it makes labor supply less sensitive to movements in c which results in smaller offsetting movements in real wages when consumption falls. If ησ > 1 a condition we will return to below the second channel dominates and a smaller decrease in p N (real wages) is required. Inflation increases by less: d Φ p A /dψ < 0 and dφcm p /dψ < 0. A higher ψ also increases the effect of the shock on consumption (under A), thus raising the marginal value of b ; it brings the IM solution closer to the CM case (dω p /dψ > 0). A larger non traded sector (higher α N ) has two offsetting effects on the bop. On the one hand, it increases total consumption s sensitivity to changes in p N, to satisfy external balance, which reduces pressures on p N. On the other hand, it increases consumption s exposure to p, which increases pressures on p N (also to satisfy external balance). Under A the first effect dominates when ησ > 1 in which case p N decreases by less (d Φ p A /dα N < 0). The opposite holds under CM (dφ CM p /dα N > 0). A larger α N brings the IM solution closer to the CM case (dω p /dα N > 0). A higher autocorrelation of international food price shocks has no effect on Φ p A or. However, by increasing the persistence of p, it increase the wealth effect from Φ CM p changes in this variable, thus increasing the relative importance of the A solution in the IM case (dω p /dρ p < 0). A higher portfolio adjustment cost has no effect on Φ p A or ΦCM p. However, by increasing the costs associated with inter temporal smoothing, it reduces the relative importance of the CM solution in the IM case (dω p /dv < 0) A lower discount rate (higher β) lowers the annuity value from future income. It therefore lowers the wealth effects associated with a food shock, bringing the IM solution closer to complete markets (dω p /dβ > 0) inally, we ask under what conditions will the inflationary impact of the shock correspond to the direct effect (α ˆp,t ). Under complete markets, the answer is straightforward: when the intertemporal elasticity of substitution 1/σ equals the intratemporal elasticity η (ησ = 1). If the intertemporal elasticity is smaller than the intratemporal one (ησ > 1), then the effect on

15 15 inflation is smaller than the direct effect (ˆπ t CM < α ˆp,t ).12 Under financial autarky, inflation would increase by the direct effect only if the steady state food endowment equals a threshold value κ DE : κ DE = [ 1 (1 + ηψ)(1 α ] N) + η(ψ + σ)α N α. ψ + σ Any value of κ above κ DE implies the inflationary effect will be smaller than the direct effect (ˆπ t A < α ˆp,t ). or a broad range of parameter values, unless the elasticity of substitution η is very small (η << 1, see discussion below), the threshold value κ DE will be quite small (much lower than α ). In other words, the food balance must be in substantial deficit before the inflationary effect is comparable to the direct effect. Under IM, inflation will correspond to the direct effect if a weighted combination of the two conditions above holds. On the effects of ŷ,t Under financial autarky, a decline in the domestic endowment of food ( ŷ,t < 0) results in an increase in inflation (Φ y A > 0), with the effect proportional to the relative size of the endowment (κ ). This result also derives from the impact of the shock on the bop. A decline in the endowment creates an incipient trade deficit, which can only be undone with a nominal (and real) depreciation that switches spending away from both food and the generic traded good. The nominal depreciation is the source of the increase in inflation: ˆπ t = (1 α N ) Ŝt. 13 The Under complete markets, domestic agents can perfectly insure themselves against unexpected changes in the endowment of traded goods (both food and the generic traded good), by buying and selling contingent assets that pay off in those states of nature. Changes in the endowment have therefore no effects on inflation: Φ CM y = 0. Just as in the case of p the IM solution combines both solutions, with the weight depending (among other factors) on the persistence of the shock and the cost of adjusting the country s international asset position. IV. CALIBRATION AND A GRAPHIC REPRESENTATION We now quantify the first round effects of shocks to p under various calibrations of the model. 14 Throughout these simulations we keep all parameters constant, with the exception of the food endowment κ. 12 This specification corresponds to the case where goods are Edgeworth-Pareto substitutes, see Svensson and van Wijnbergen (1989). 13 The cpi based real exchange rate depreciates by: ŝ t = α N Ŝt. 14 We skip the quantitative analysis of shocks to y for the sake of brevity.

16 16 A. Calibration We do not calibrate the model to a specific country but draw instead on evidence from the universe of low income countries. Our choice of parameters is summarized in Table 1. α α N σ η ψ β v ρ p Our choice is justified as follows. The average share of food in the CPI in sub-saharan African countries is 48.5 percent, so we pick α = In a group of 3 African countries (Kenya, Ghana, Uganda) the share of non-traded goods and services (housing, health, education, recreation, transportation and communication) is 33 percent on average (we pick alpha N = 0.3). 16 We calibrate σ from Ogaki, Ostry and Reinhart (1997), who estimate the inter temporal elasticity of substitution for low income countries: their average estimate is 0.337, which implies σ 3. We infer ψ from Goldberg (2011), who estimates the wage elasticity in the day labor market in rural Malawi. She finds an elasticity of While her estimate is not directly applicable to our specification she focuses on the extensive margin of labor supply we set ψ = 5, which implies a risch elasticity of 0.2. The choice of the intertemporal discount rate is standard in the literature. Two parameter choices are worth discussing in some detail. irst, we draw η from Seale, Regmi and Bernstein (2003), who estimate compensated own-price elasticity for food and beverages. Their average estimate for the 40 countries with the lowest income per capita in their sample is slightly lower than -0.5, which implies η 1. This value is higher than elasticities used in other studies (see Anand and Prasad (2010)) so we will consider alternative values below. Second, we draw on Akitoby and Stratmann to calibrate v. These authors regressed interest rate spreads in emerging markets on a number of various gross external assets and liabilities (and policy variables). When combined to form a net asset value, their estimates imply a relatively low value of v (v = ). We believe their estimate provides a lower bound on the value of v in low income countries, which is likely to be much higher as many of these countries do not even have access to international capital markets (and would therefore be excluded from their sample of countries). However, we will use this value as a starting point and discuss alternative values later. inally, we pick ρ p using data on an international food price index compiled at the IM, deflated by the US CPI. 17 We extract the business cycle component using a band pass filter, 15 See IM (2011). 16 On Uganda, see Consumer Price Index April 2001, available at On Ghana see Time Series P1, available at On Kenya see CPI December 2008, available at 17 The data is available at...

17 17 and find that the sample autocorrelation is We will also experiment with other parameter values below. B. Graphic representation The inflationary impact of a 1 percent increase in ˆp is represented in igure 1. The figure plots the impact on inflation against the country s net food deficit (α K κ ). The straight black line represents the inflationary impact under financial autarky (Φ p A ), the dashed dotted line represents the inflationary impact under complete markets (Φ CM p ), and the straight grey line represents Φ IM p. The dashed line represents the direct effect (α ). As previously discussed, the inflationary impact under CM does not depend on κ. Under our calibration ησ > 1, which implies this case generates an increase in inflation that is smaller than the direct effect (Φ CM p = 0.27 < α ). On the other hand, the impact under A ranges from percent when the country s endowment of food is 70 percent (the highest possible value for κ ) to 0.61 percent when κ = 0. The A solution coincides with complete markets when κ = 0.28 (point b in the figure). This is the value of κ for which the complete markets solution is associated with ex post balanced (overall) trade. The A solution coincides with the direct effect when κ = (point c). The IM solution is closer to the A solution: under the current calibration, the weight on the CM case ω p is less than one third (ω p = 0.32). By construction the IM solution matches both A and CM at point b. While the A and IM solutions provide a range of possible first round effects, we need to discipline the choice of κ to provide a quantitative estimate. We therefore draw on trade data from a sample of 28 sub-saharan countries, for the period The median food balance in this sample was a deficit of 0.9 percent of GDP, with the highest food deficit being percent and the highest food surplus being percent. In our model this implies a median food endowment κ = 0.481, with a range (0.389, 0.641). In this case, the median inflationary effect predicted under A is 0.01 percent, with a range (-0.17,0.12). Under incomplete markets, the median is 0.09 percent, with a range (-0.03,0.17). V. SENSITIVITY ANALYSIS A lower η While the baseline calibration has drawn on empirical work using data from low income countries, there is considerable uncertainty over possible parameter values, and other calibrations are also possible. In particular, it can be argued that the elasticity of substitution between food and non food items is lower than one, reflecting the view that poor households 18 See Baxter and King... and Sargent...

18 18 may be severely limited in their ability to substitute away from food consumption. or this reason, we now explore how results change when η goes from 1 to 0.1. The inflationary impact from a 1 percent increase in ˆp is now represented in igure 2. The impact under financial autarky is represented with a black dotted line, the impact under complete markets is represented with a long dashed dotted line, and the impact under IM is represented with a grey dotted line. We have also included the previous lines for Φ p A, ΦCM p, and Φ IM p (black straight, dashed dotted, and grey straight lines, respectively). When η falls below 1/σ, which is the case here, the product ησ falls below 1 and goods become Edgeworth-Pareto complements (see Svensson and van Wijnbergen (1989)). In this case, the line for Φ CM p shifts up, and the inflationary impact jumps above the direct effect: = 0.72 > α. Φ CM p Under financial autarky instead, the line for Φ A p rotates, becoming steeper. While a net food balance still implies zero inflation, food deficits now lead to larger inflationary pressures. The median food balance from the sample of African countries (0.9 percent of GDP)is now associated with an increase in inflation of percent. With the highest food deficit in the sample (10.12 of GDP), the increase in inflation is now 0.62 percent, above the direct effect. The flip side is that food surpluses now result in larger deflations: the highest food surplus in the sample (14.12 percent of GDP) is now associated with a deflation of percent! Under complete markets, the line for Φ IM p shifts up and become steeper. The inflationary impact of food price increases is now greater over a large range of food balances, but it also becomes deflationary at a faster rate following some threshold food surplus. The median food balance in the sample is now associated with an increase in inflation of 0.29 percent, with a range (-0.24,0.66). In sum, lower elasticities of substitution lead to higher inflation rates in a number of cases (complete markets, financial autarky when the food balance is in deficit, incomplete market under food deficits and a range of food surpluses). However, they also result in larger deflations in other cases (under A when the country is a net food exporter, and under IM over a threshold food balance value). Varying v We now explore what happens when portfolio adjustment costs v vary. igure 3 displays Φ CM p and Φ A p under the median food balance in the sample. It also displays values of ΦIM p as the portfolio adjustment costs increases (using a log scale). As previously discussed, the IM solution approximates the A solution as v increases. Concretely, a doubling of v from to 0.375, which is a relatively small adjustment, lowers ω p (the weight of the CM solution) from 0.32 to A tripling of v lowers ω p to Varying ρ p igure 3 also displays values of Φ IM p as ρ p increases. Note that, as ρ p approaches one, small changes in this parameter bring the IM solution increasingly closer to the A case.

19 19 Concretely, raising ρ p from 0.87 to 0.9 lowers ω p from 0.32 to Setting ρ p = 0.95 lowers ω p to VI. EXTENSION: INCOMPLETE TRADABILITY O THE OOD BASKET So far, the model has assumed the food basket is fully tradable. However, the nominal price of many items in the food basket may depend directly on domestic demand and supply factors independently of how these factors affect the nominal exchange rate rather than international factors. 19 We now explore how the results of the model change when the assumption of complete tradability is abandoned. ood consumption is now a basket, with two items: c,t = [ς 1η η 1 c η T,t + (1 ς) 1 η 1 η c η N,t ] η η 1. c T,t and c N,t are the consumption of traded and non traded food, respectively, with nominal prices (P T,t, P N,t ). ς measures the share that is tradable. A unit value for ς corresponds to the original version of the model (which we will refer to as the baseline). or simplicity the elasticity of substitution is assumed the same as that between food and non food (η). Utility maximization results in the standard demand equations: c T,t = ς( p T,t p,t ) η c T,t = ςα p η T,t c t, (25) c N,t = (1 ς)( p N,t p,t ) η c T,t = (1 ς)α p η N,t c t, (26) where we have made use of eq.(6). The terms p T,t and p N,t denote relative prices of traded and non traded food, which are now combined to create a relative price index for food: p,t = [ ] ςp 1 η 1 1 η T,t + (1 ς)p1 η N,t. (27) A similar equation holds for the nominal price of food (P,t ). The representative agent now has two food endowments: (y T,t, y N,t ). In the non traded case, consumption must equal the endowment: c N,t = y N,t, with p N,t adjusting to ensure equilibrium. In the traded case there is no such requirements. Instead, p T,t is given by the law of one price: p T,t = s t p,t. The steady state is similar to the baseline case, with p N = 1 and y T + y N = κ. The non traded food endowment must equal (1 ς)α, which implies y T = κ (1 ς)α. 19 Trade costs may render certain staples effectively non tradable within a certain price band (see Bergin and Glick (2009)). Trade restrictions have similar effects. Non tradability may be endogenous, with large changes in international prices increasing the tradability of certain food items. or simplicity, we treat tradability in food as exogenous.

20 20 This condition and the constraint that the endowment of traded food cannot be negative place a lower bound on possible values of ς. The larger the steady state trade deficit in food (α κ ), the larger the lower bound on the share of traded food in consumption: ς ( ς, 1), with ς = max(0, (α κ )/α ). Intuitively, a country that relies on imports to secure its food consumption must have a large share of traded food in its basket. A. Analytical solution under incomplete food tradability We log linearize the model around the steady state, and make an additional simplifying assumption: the two food endowments comove perfectly: ŷ T,t = ŷ N,t = ŷ,t. As in the previous case, we can reduce the model to two equations. The internal balance equation is the same as before (eq. (16)) since conditions in the non traded goods market and the labor market (eqs. 2, 5, 11 and 12) have not changed: ĉ t = 1 + ηψ ψ + σ ˆp N,t, The second equation (a revised external balance condition) now incorporates two equilibrium conditions. Under financial autarky, it combines the clearing of the bop with the equilibrium in the non traded food market (the log linearized versions of equations 6, 7, 8, 10, 13, 25, 26, and 27). Given the structure of our model and the two simplifying assumptions made earlier same elasticities of substitution between food types and between food and non food, and the perfect comovement of the two food endowments the new external balance condition is the same as before: 20 α N ĉ t = ηˆp N,t α κ ˆp,t + κ ŷ,t. 1 α N 1 α N 1 α N Intuitively, the impact of international food prices on the balance of payments still depends on whether the country is a net food importer or exporter, independently of how large the share of traded food (ς) is. While there is a link between possible values for ς and the net food balance of the country (see above discussion), the latter variable contains all the necessary information about the structure of the food market to study the aggregate macroeconomic adjustment to food shocks. Similarly, the perfect comovement of the two endowments makes the effect of changes in the supply of food depend on the overall size of the food endowment, just like before. Under complete markets, the revised external balance assumption now combines the risk sharing condition with the equilibrium in the non traded food market (equations 14, 8, 25, 26, and 27). In this case, the external balance condition is the following: ĉ t = ϑ pn ˆp N,t ϑ p ˆp,t + ϑ y ŷ,t, (28) 20 Relaxing the restriction that the elasticity of substitution between food and non food is the same as the elasticity of substitution between different types of food does not change this result. The proof is available upon request.

21 21 ϑ pn = α N η ησ(1 α N ) α (1 ς)(ησ 1), ϑ p α ςη = ϑ pn α N η, ϑ α (1 ς) y = ϑ pn. α N η This new condition merits two comments. irst, the impact of p on c is now proportional to the share of traded food in consumption (α ς), rather than the total share of food (α ) as was the case before. Second, consumption is now sensitive to changes in the domestic food endowment (ϑ y > 0 if ς < 1), with the effect being proportional to the share of the non traded part of the endowment (α (1 ς)). The mechanism behind the latter result is as follows. A decline in the food endowment raises the domestic relative price of non traded food (p N ) and therefore the domestic relative price of the food basket (p N ). Holding p N constant, this raises the cost of domestic consumption (the cpi based real exchange rate appreciates) which elicits a decrease in overall consumption (through the risk sharing condition (14)). Note that the external balance condition reduces to the previous external balance condition (eq.(18)) if food is fully tradable. Equilibrium under A Under A, since internal and external balance remain unchanged, the inflationary effect of the two shocks (ˆp,t, ŷ,t) is the same as before, i.e., eq.(22) still holds. An important difference concerns the nominal price that implements the required increase in inflation. In the baseline specification, only the nominal exchange rate Ŝt adjusts. In the extension, we can combine eqs. (8), (9), and (27) to obtain the following relation: ˆπ A t = α ς ˆp,t + (1 α N α (1 ς)) Ŝ A t + α (1 ς)ˆπ A N,t, where ˆπ N,t A = log(p N,t) log(p N,t 1 ). or a given ˆp,t, equilibrium changes in inflation must therefore come from either Ŝ t A or ˆπ N,t A, i.e., changes in the nominal price of non traded food. To understand when and how each nominal price adjusts, we solve for the equilibrium changes in non traded food inflation by combining eqs. 16, 22, 26 and the identity ˆπ N,t A = ˆp A N,t + ˆπ t A. The solution for ˆπ N,t A is the following: Γ A p = (ησ 1)(α κ ) η [(1 + ηψ)(1 α N ) + η(ψ + σ)α N ], ˆπ A N,t = Γ A p ˆp,t Γ A y ŷ,t, Γ A y = Γ A p (ησ 1)(α N + κ ) + (1 + ηψ). (ησ 1)(α κ ) If ησ > 1, the effect of ˆp,t on non traded food inflation has the same sign as the food trade deficit (α κ ). As before, we can distinguish three cases. When food trade is balanced, non traded food inflation does not change (ˆπ N,t A = 0), which implies the nominal exchange rate appreciation is solely responsible for keeping overall inflation constant: Ŝ A = α ς/ (1 α N α (1 ς)) ˆp,t. If the food trade is in deficit (surplus), then non food traded inflation also increases (decreases) with changes in ˆp,t. inally, non traded food inflation always increases with negative shocks to the food endowment (Γ y A > 0).