Food prices and inflation targeting in emerging economies

International Economics ∎ (∎∎∎∎) ∎∎∎–∎∎∎

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Food prices and inflation targeting in emerging economies Marc Pourroy a,n, Benjamin Carton b, Dramane Coulibaly c a

CRIEF (EA2249), University of Poitiers, 2 rue Jean Carbonnier Bat A1, TSA 81100, 86073 Poitiers cedex 9, France CEPREMAP, France c EconomiX-CNRS, University of Paris Ouest, France b

a r t i c l e i n f o

JEL classification: E32 E52 O23 Keywords: Monetary policy Commodities Food prices DSGE models

abstract The two episodes of food price surges in 2007 and 2011 followed by a drop in 2014 have been particularly challenging for developing and emerging economies’ central banks and have raised the question of how monetary authorities should react to such external relative price shocks. We investigate the optimal monetary policy that manages food price shocks. To this end, we develop a new-Keynesian small open-economy model that incorporates world food price shocks. We show that the optimal monetary policy depends on country income level. In low and medium income countries, overall consumer price targeting is optimal, while in high-income countries non-food inflation targeting is the best option. This result holds not only because food represents a significant share in total consumption in low and medium income countries, but also because of food good composition. Indeed, the poorer the country, the higher the share of purely domestic food in consumption and the more detrimental lack of attention to the evolution in food prices. & 2016 CEPII (Centre d’Etudes Prospectives et d’Informations Internationales), a center for research and expertise on the world economy. Published by Elsevier B.V. All rights reserved.

n

Corresponding author. E-mail addresses: [email protected] (M. Pourroy), [email protected] (B. Carton), [email protected] (D. Coulibaly). http://dx.doi.org/10.1016/j.inteco.2015.12.001 2110-7017/& 2016 CEPII (Centre d’Etudes Prospectives et d’Informations Internationales), a center for research and expertise on the world economy. Published by Elsevier B.V. All rights reserved.

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1. Introduction The last few years have been intensely challenging for central bankers. The financial crisis has had tremendous negative effects on developed economies and major spillover effects on emerging economies (large capital inflows and outflows). At the same time central bankers had to manage the dramatic volatility in food prices. According to the United Nations Food and Agriculture Organization (FAO), in the period 1996–2006, world food prices rose on average by only 0.05% per semester in real terms; from 2007 to 2011 they have risen by an average of 2% per semester,1 that is, by 25 times more. This period of fast increase in food prices has been followed by a similar decline: between February 2011 and May 2015 food prices have dropped by 41%. The most frequently mentioned causes of food price volatility include extreme weather conditions, increased demand from emerging countries caused by growth in incomes, increased costs volatility to farmers due to high oil prices volatility, rapid development of biofuels, adoption of restrictive trade policies by major net exporters of key foods products such as rice, and speculation in commodity markets. So, for the monetary authorities of almost all small open economies, these shocks were perfectly exogenous from their policies or their own country situations, and were unanticipated. The high fluctuation in food prices is questioning how monetary policy should react to these external shocks. The present paper tries to find some answers. Specifically, we examine how monetary authorities in developing countries should respond to food price shocks. The case of developing countries is interesting for two main reasons. First, in low-income and emerging economies, food consumption represents a significant share of household expenditure. Table 1 shows that food budgets represent around 50%, 30% and 20% of the household budgets in low-income, middle-income and high-income countries, respectively. Therefore, in these countries, changes in food prices will induce significant variations in their headline inflation. Second, low- and middle-income countries are characterized by a large share of non-tradable products in their food consumption. For instance, even if a country is an exporter of a given agricultural product, the domestically consumed variety is often of a different (e.g. lower) quality, is produced in different fields and does not share the logistics infrastructure of the exported variety. Different cultures induce different diets, some cereals and tubers are country specific and not traded. Even if volumes of agricultural imports are large, they represent at most half of the country's food consumption (see Table 1). Thus, developing economies are characterized by a large domestic food sector. This is a crucial aspect of this analysis of the effects of a world price shock on a small open economy. Since the domestic food sector is country specific, it evolves with the domestic environment. Pricing strategies do not reflect directly the world market. But since domestic and tradable food goods are highly substitutable, the domestic food sector is impacted on by the evolution in the world market. So, in studying the pass-through from the world market price to the domestic overall consumer price index (CPI), a major issue is the passage from the tradable food goods price to the non-tradable food goods price. This channel is a striking feature of developing economies and a major concern for monetary authorities. In this study, we examine particularly the performance of an inflation targeting framework to manage food price shocks in developing countries. By definition, an inflation targeting framework requires the choice of a measure of inflation as the target. Targeting countries generally use core inflation as the target. There are several methods used to compute core inflation. The most common approach, which is exploited by many countries, is the exclusion method, which computes core inflation by removing the prices of a fixed, pre-specified set of items from the CPI basket. The excluded components are chosen because they are considered either volatile or susceptible to supply 1 The period beginning in 2006 (or post-great moderation) has been characterized by two price surges: the FAO price index increased by 54% between January 2006 and June 2008, declined of 34% between June 2008 and December 2008, then rose by 53% before stabilizing in December 2010.

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Table 1 Food budget shares. Source: International Comparison Program (ICP) (World Bank, 2005), tradable shares (FAO, 2007) and own calculations. Note: Tradable share is defined as the percentage of the food products documented by the 2007 FAO Food Balance Sheet database for which the sum of import and export is less than 5% of domestic consumption. The 144 countries covered by the 2005 ICP and the 162 countries covered by the 2007 FAO Food Balance Sheet database are divided into low-, middle-, and high-income countries, based on their income relative to that of the United States. Low-income, middle-income and high-income countries represent those with real per capita income less than 15 percent, between 15 and 45 percent, and greater than 45 percent of the U.S. level, respectively. Items

Low-income (%)

Middle-income (%)

High-income (%)

Food in consumption Tradables in food

48 37

31 59

20 81

disturbances; they typically consist of food and energy items.2 The other approach is a statistically based method that removes extreme price changes or outliers (both positive and negative) from the overall inflation rate.3 This method is more sophisticated, however it generally leads to the same result: food and energy items are generally considered as outliers and therefore are excluded from core inflation. In order to analyze the response of monetary policy to food price shocks, we construct a small open economy model where food can be produced domestically or imported. More precisely, the consumption bundle consists of food and manufactured goods, where each kind of good consists of two varieties: one is non-tradable (domestically produced and sold in a monopolistic competition market) and one is tradable (both imported and produced at home, and sold in a competitive market under the law of one price). This allows us to assume that food price volatility is related to both technological shocks (such as weather) and imported price shocks (such as world price hikes). Therefore our model allows us to decompose the channel from the world price to the overall CPI, through the effects on domestic food prices, food and non-food substitutability, and exchange rate effects on non-food tradable goods competitiveness. We consider three important issues:


Firstly, we model an economy in which the non-tradable food share in consumption is large,







implying a non-negligible part of non-tradable food prices in the CPI. Thus, monetary authorities cannot look at food price shocks as short term volatility only. World food price movements impact on domestic non-tradable sticky prices in food and non-food sectors, implying a low-pace return to the equilibrium. Secondly, our model allows us to distinguish two price indices: the overall consumer price index and the non-food index (as in the exclusion method). We do not consider a monetary policy rule based on a model-based core inflation as the relevant price index is not observable by the central bank.4 Thirdly, we examine whether the fact that food is a first necessity matters for the ranking of monetary policy rules. In this case, we employ a Klein-Rubin form with minimum amount of consumption.

Our results suggest that in low-income and medium-income countries central bank should target CPI rather than core inflation. We demonstrate that this result does not hold for high-income 2 The exclusion method is based on the idea that these excluded items are prone to supply shocks that are beyond the control of the central bank, and is used by Canada, New Zealand, Peru, Thailand and the United Kingdom among others. 3 In the statistics-based method, the set of excluded items changes each period, depending on which items show extreme price movements. For example, Chile uses a statistics-based approach and computes its core inflation by excluding the 20 percent largest negative price changes and the 8 percent largest positive price changes. This method is more sophisticated but is also more costly to implement, since the list of the goods included in core inflation need continuous updating. 4 In our framework, non-food inflation is different from a model-based core inflation as some non-food items have flexible prices whereas some other food items have sticky prices.

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countries where the share of food prices in core inflation is low enough to make non-food inflation a good proxy for core inflation. Therefore, our policy recommendations are highly dependent on the country specificities. The share of food in consumption is not the only information that matters: the share of tradable varieties in food goods is also highly relevant. In high income countries, the share of purely domestic varieties in food goods consumption is low, implying that food price goods mostly depend on the world market where a small open economy is price taker. Hence, the central bank has no power on such price and would better not to react to this source of volatility. In contrast, in low-income countries, the share of food goods in the economy is simply too large to be set aside by the monetary authorities. Many studies focus on oil price rather than food price shocks. Some analyze the choice of index (core or headline inflation) to target in the presence of oil price shocks. Bodenstein et al. (2008) use a stylized Dynamic stochastic general equilibrium (DSGE) model with an energy sector to study the optimal monetary policy response to an adverse energy supply. They find that policies that react to a forecast of headline inflation following a temporary energy shock induce different effects from policies that react to a forecast of core inflation, with the former causing greater volatility in core inflation and the output gap. Batini and Tereanu (2009), using a small open-economy DSGE model to design an appropriate response from inflation targeting countries to oil price shocks, find that the optimal response of inflation targeting central banks is an aggressive increase in real interest rates in order to close the inflation gap with the minimum efficient policy horizon. This focus on oil price shocks (see e.g. Blanchard and Galí, 2007; Gomez-Lopez and Puch, 2008 or Schubert and Turnovsky, 2011 among others) is of limited help in an analysis of food price shocks. They focus mainly on shocks to the input price, while food price shocks are more likely to be shocks to consumption goods with extremely low elasticity of substitution with other goods. This applies to the paper by Anand and Prasad (2010) which proposes a model of a closed developing economy in which food producers are credit constraints. Anand and Prasad (2010) show that overall CPI targeting is the best policy in the presence of financial restrictions. Since they model a closed economy, the volatility of food prices is due only to technological shocks. Thus, their model does not allow analysis of the monetary policy response to a world price shock. Our paper is related also to the study by Catao and Chang (2010) which examines how monetary policy should react to imported food price shocks. Similar to our approach, they assume that food price shocks are relative price shocks. These authors propose a small open economy in which all food is imported. They find that broad CPI targeting is welfare-superior to alternative policy rules once the variance in food price shocks is as large as in real world data. The restriction that food is only imported (and not domestically produced) does not capture the passthrough mechanism from the world to the domestic food price, as is the case in our paper. Moreover, low- and middle-income countries are sometimes importers and sometimes exporters, but there is no net trend in the data to characterize them as net food importers. The remainder of the paper is organized as follows. Section 2 collects stylized facts on low-, middle- and high-income countries and the behavior of international prices. Section 3 describes the model and its calibration. The simulation results are presented in Section 4. Section 5 introduces fixed consumption. Finally, Section 6 sums up the results and discusses some policy implications.

2. The business cycle and the behavior of international prices Before presenting the model to assess optimal monetary policy in the different countries when facing food price shocks, we collect some statistics on the business cycle for low-, medium- and highincome countries. We also collect evidences on the behavior of international prices. The current section aims to understand how the three groups of countries differ in terms of the business cycle and how to calibrate the model on realistic data. However, there is nothing like a representative country in each group: a lot of heterogeneity remains after grouping in low-income, middle-income and highincome. The calibration exercise is not only limited by the lack of data (for middle- and low-income countries in particular) but also by the large differences in each group. Please cite this article as: Pourroy M, et al. Food prices and inflation targeting in emerging economies. International Economics (2016), http://dx.doi.org/10.1016/j. inteco.2015.12.001i

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Fig. 1. The distribution of some business cycle moments in high, medium and low income countries: standard deviations, autocorrelations and cross-correlations. Source: WEO October 2014. Statistics on annual data after filtering (HP-filter with λ ¼ 10).

2.1. Stylized facts on the business cycle We compare some business cycle statistics for low-, medium- and high-income countries. Lowincome countries are defined as countries for which GDP per capita is lower than 0.14 times the GDP per capita in the US (PPP terms). Medium-income countries are between 0.15 and 0.45 the US level. We use the WEO annual database from 1960 to 2013 for 160 countries (October 2014 release) for real GDP (GDP), inflation (INFL) and the trade balance (TB). The FAO index is used to measure world food price changes (FP). We first detrend the data using an HP-filter (with smoothing parameter λ¼ 10). The distribution of main statistics are given in Fig. 1. Some robust differences appear between our three groups. The business cycle in low-income countries differs from high income countries in three dimensions. First, the variance of macroeconomic variables is higher in low-income countries, in particular for inflation (about 2.5% against 1% for high income) and GDP (about 2.5% against 2% for high income). Second, shocks are less persistent in low-income countries, particularly on GDP (autocorrelation on annual data average at 0.2 against 0.35 for high-income countries). Third, the role of domestic demand shocks appears lower in low-income countries (the correlation of GDP and the trade balance is close to zero) whereas around  0.3 in high income countries. In medium-income countries, the negative correlation of trade balance and GDP may be caused by large financial shocks, like the Asian crisis in 1998. World food price changes and total inflation are marginally more correlated in low income countries. Together with the highest volatility of inflation, this implies a larger effect of food price on domestic inflation.

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Fig. 2. Share of food consumption in total consumption.

Fig. 3. Share of tradable food in food consumption.

2.2. Stylized facts on food consumption The three groups of countries moderately differ in terms of the business cycle. But the share of food in the consumption basket depends much more on the level of development. We estimate the equation
log

Si 1 Si

 ¼ α1 logðGDP i Þ þ α2 logðGDP i Þ2 þα3 þ εi

where S is either the share of food consumption in the total consumption or the share of tradable food in food consumption. We used a GLS estimator in order to take into account heteroscedasticity. The residual is explained by logðε2i Þ ¼ β1 logðGDP i Þ þ β2 logðGDP i Þ2 þ β3 þ νi . Results are displayed in Figs. 2 and 3. The share of food in the consumption basket reaches around 60% for the poorest countries whereas this share is smaller than 20% for every high-income country. More importantly, the share of tradable varieties (for which the price is highly related to international prices) is much higher in high-income countries than in low-income countries. More than half of lowincome countries consume at least 50% of domestic non-tradable food items (see Fig. 3).

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Table 2 Estimated VAR. Variables

itw

P FT⋆ t

iw t 1

P FT⋆ t 1

0.99 (11.3)  0.20 (  2.7) 0.03

 1.64 (  2.7) 1.76 (2.9) 1.03

P FT⋆ t 2

(2.5)  0.02

(12.6)  0.42

(  1.9)

(  5.16)

iw 2

P MT⋆ t

P MT⋆ t 1

1.11

P MT⋆ t 2

(13.5)  0.42

R-2 D-W Obs.

(  5.07) 0.71 2.00 126

0.60 1.81 126

0.68 1.91 126

t-stat in parenthesis.

2.3. Behavior of international prices The behavior of international prices is described by a VAR model of dimension three, including:


tradable food goods price, P FT⋆ , proxied by Reuter's DataStream food commodities composite price t index;


tradable non-food goods price, P MT⋆ , proxied by Reuter's DataStream world export index; t
world interest rate, itw, proxied by the yield on one year US Treasury bonds. The quarterly dataset range from 1980 first quarter to 2011 last quarter. We consider two lags, according to the correlograms shape, AIC or BIC criteria and the estimated residuals (Gaussian) distribution. We have also estimated other models, like VARMA, and had similar results. Missing values in Table 2 refer to non-significant parameters. Significant figures are used for model calibration. As international prices are purely exogenous in the model, we do not try to identify structural innovations.

3. Model and calibration The current section briefly presents the structure of the model, which is extensively developed in Appendix A, and its calibration for low-income, middle-income and high-income countries. 3.1. The model in a nutshell Households: The small open economy is populated by infinitely lived households. They consume C and supply labor L. Households can own domestic firms and can accumulate foreign assets in the form of one-period risk-free bonds in the world currency B⋆ with exogenous interest rate iw. A complete set of contingent claims is available to domestic households but these claims are not internationally traded (no international perfect risk-sharing). The consumption bundle: Households consume food F and non-food M goods. Each kind of good consists of two varieties: a non-tradable one N (domestically produced and sold in a monopolistic competition market) and a tradable good T (both imported and produced at home, and sold in a competitive market under the law of one price). The price of each variety is denoted P FT , P FN , P MT , Please cite this article as: Pourroy M, et al. Food prices and inflation targeting in emerging economies. International Economics (2016), http://dx.doi.org/10.1016/j. inteco.2015.12.001i

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Table 3 Estimated residuals matrix. iw

P FT⋆

P FT⋆

1 0.089

1

P MT⋆

 0.023

0.56

Country groups Shocks correlation iw

Shocks covariance iw P FT⋆

3.8e  5 2.4e  5

1.8e  3

P MT⋆

 3.4e  6

5.7e  4

P MT⋆

1

5.6e  4

FT⋆ and P MN . The law of one price for tradable varieties implies P FT and P MT ¼ St P MT⋆ where S is t ¼ St P t t t FT⋆ MT⋆ the nominal exchange rate, and P and P the exogenous international prices. Two important parameters will distinguish countries by their level of development: the share of food in consumption, γ, and the share of tradable in food consumption, γF (see Table 5). Firms: The production function of each firm ðY ¼ AL1  α Þ has only one factor of production, labor, with decreasing return to scale function and a sector-specific productivity denoted AFT ; AFN ; AMT and AMN . Non-wage income implicitly remunerates land (in the food sector) or capital (in the non-food sector).5 Firms in a tradable sector take as given the wage level and the price of the good they produce. They choose the level of production to maximize profits. Firms in a non-tradable sector are in monopolistic competition and face price rigidity à la Calvo. Monetary policy: We consider two options for the monetary authorities: either to react to food prices or not to react. Hence, considering monetary policy rules in which central bank moves interest rates systematically as a function of price inflation, the central bank can target either the overall (including the four varieties) CPI index inflation, denoted by π, or the non-food prices (including P MT and P MN only) denoted by π M . These interest rate rules take the following forms:

h


Headline inflation targeting: logðit Þ ¼ ρi logðit  1 Þ þ ð1 ρi Þ logðiÞ þΦ logðπ t Þ h

i


Non-food inflation targeting: logðit Þ ¼ ρi logðit  1 Þ þ ð1 ρi Þ logðiÞ þ ΦM logðπ M t Þ

i

where i is the steady-state level of interest rate i. For each interest rate rule, the value of the parameters is set in order to maximize the welfare associated with this rule (see Section 4). Note that πM is generally used by central banks as a proxy for core inflation: excluding food prices from the CPI. Shocks: There are two kinds of perturbations: shocks to productivities in each sector AFT ; AFN ; AMT and AMN and shocks to foreign prices, P FT⋆ , P MT⋆ and iw.


Productivity shocks are assumed to evolve exogenously over time, following an AR(1) process


xt ¼ ρx xt  1 þ ϵxt , where 0 o ρx o 1 and ϵx  Nð0; σ ϵ Þ, for x ¼ AFT , AFN , AMT , AMN . Foreign variables ðP FT⋆ ; P MT⋆ ; iw Þ follow a VAR(2) process (see Section 2.3) (Table 3).

5 Following Anand et al. (2015) we do not incorporate physical capital in the production function and we use a simple and unique production function for any sector. A sector is not defined by the production function used but a sector is defined by a price setting mechanism: domestic goods are produced by price setter firms on monopolistic markets with sticky prices while tradable goods are produced by price taker firms following the law of one price. Also introducing different types of physical capital in the model would limit our ability to use a unique framework to compare low-, middle- and high-income countries.

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Table 4 Parameters calibration. Description

Symbol

Value

Utility function Discount factor Inverse of intertemporal elasticity of substitution Inverse of elasticity of labor supply Share of tradable in non-food consumption Elasticity of substitution between food and non-food good Elasticity of substitution between food T and N Elasticity of substitution between non-food T and N

β ρ χ γM θ θF θM

0.99 2 0.83 0.5 0.3 1.4 1.4

Food sector Probability of domestic food price non-adjustment Monopoly power Scale effect on labor, non-tradable Scale effect on labor, tradable

ϕFN ηFN αFN αFT

0.5 6 0.25 0.25

Non-food sector Probability of non-food price non-adjustment Monopoly power Scale effect on labor, non-tradable Scale effect on labor, tradable

ϕMN ηMN αMN αMN

0.75 6 0.25 0.25

Adjustment cost Parameter of bonds adjustment cost

ζ

0.001

Shocks persistence Productivity, domestic food sector Productivity, tradable food sector

ρFN ; σ FN ρFT ; σ FT

0:25; 0:03 0:25; 0:03

3.2. Calibration Most of the parameters are set according to the typical values in the literature; others are set in order to reproduce some basic ratios, mainly food sector size (see Table 4). The representative household is assumed to have no foreign debt at equilibrium (Bn ¼ 0). We assume also that both the food and the manufacturing sectors have a closed economy steady-state (Y FT ¼ C FT and Y MT ¼ C MT ).6 All relative prices are set to 1 at the steady-state ðP FT ¼ P FN ¼ P MT ¼ P MN ¼ 1Þ. Similarly, the parameter that weights labor in utility (ψ) is set such that total values for labor and consumptions at the steady-state are equal to unity (L¼1 and C¼1). The quarterly discount factor β is set equal to 0.99 which implies a yearly real world interest rate of 4% at the steady-state. The risk-aversion parameter is set to ρ ¼ 2 , which means an intertemporal elasticity of substitution of 0.5, as is usual in the literature (see for instance Devereux et al., 2006; Schmitt-Grohé and Uribe, 2007; De Paoli, 2009). The share of food in consumption, γ, is calibrated according to International Comparison Program (ICP) data that cover 144 countries. Depending on the group to which the country belongs (low-, middle- or high-income countries) it is set to 48%, 31% and 20%, respectively (see Table 5) and the share of tradable goods in food consumption is set to 37%, 59% and 81%. The elasticity of substitution between food and non-food goods, θ, is a key parameter in our model. Because the demand for food is inelastic, θ is lower than 1. To our knowledge Anand and Prasad (2010) is the only study to provide a clear calibration.7 We follow Anand and Prasad (2010) and set elasticity 6 In low-income and middle-income group, countries can experience surplus or deficit in the agricultural balance. On average, the data know no systematic imbalance. 7 Anand and Prasad (2010) write in page 26: Since the demand for food is inelastic, we set [elasticity of substitution] ¼ 0.6 as the baseline case. With a subsistence level of food consumption, this parameter choice implies a price elasticity in demand for food of about  0.3 at the steady-state, which is close to the USDA estimate. In our case, we have no subsistence level of food consumption as a baseline (this assumption is removed in Section 5). Thus, for this parameter we set the elasticity in utility at θ ¼ 0:3.

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Table 5 Calibration per country type. Description

Symbol

Value

Low-income countries Share of food in consumption Share of tradable in food consumption Persistence, non-food sector productivity Volatility, non-food sector productivity

γ γF ρMN ; ρMT σ MN ; σ MT

0.48 0.37 0.65 0.025

Middle-income countries Share of food in consumption Share of tradable in food consumption Persistence, non-food sector productivity Volatility, non-food sector productivity

γ γF ρMN ; ρMT σ MN ; σ MT

0.31 0.59 0.7 0.0225

High-income countries Share of food in consumption Share of tradable in food consumption Persistence, non-food sector productivity Volatility, non-food sector productivity

γ γF ρMN ; ρMT σ MN ; σ MT

0.20 0.81 0.75 0.02

Table 6 Sectors shares. Source: World Bank. Note: Calculations form the authors of the mean for 144 countries, divided into low-, middle-, and highincome countries, based on their income relative to that of the United States. Low-income countries represent those with real per capita income less than 15 percent of the U.S. level, middle-income countries are those with real per capita income between 15 and 45 percent of the U.S. level, and high-income countries with have per capita income equal to or greater than 45 percent of the U.S. level. Value added (% of total)

Low income Middle income High income All countries

Employment (% of total)

Agriculture

Industry

Services

Agriculture

Industry

Services

23 7 2 14

29 35 32 31

48 59 66 56

40 16 4 16

18 26 26 24

42 58 69 60

in utility at θ¼0.3. The elasticity of substitution between tradable and non-tradable goods, θF and θM , is set to 1.4, as estimated for developing countries by Ostry and Reinhart (1992). At the steady-state, agricultural sector value added represents around one-third of total GDP (which is a key feature of emerging economies, as seen in Table 6). Labor in the agricultural sector represents around one-third of total employment. Generally, the literature on Calvo-style pricing behavior sets the probability of price nonadjustment at around ϕ ¼ 0:75, which implies that on average price adjustments occur every four quarters. However, empirical studies show that food prices are less sticky than the prices of manufactured goods (see Loupias and Ricart, 2004; Bils and Klenow, 2004; Baudry et al., 2005). Thus, following this literature we set ϕF ¼ 0:5 for the food sector and ϕM ¼ 0:75 for the manufactured sector. This ensures the robustness of our results, other values for ϕF and ϕM are proposed and analyzed in Table C1. The scale effect on labor equals 0.75 for each sector ðαFN ¼ αFT ¼ αMN ¼ αMT ¼ 0:25Þ. The standard deviation of productivity shocks in the non-food sector (σ) is set to 2% in highincome countries, in line with the business cycle statistics in Section 2.1, those in Ravenna and Natalucci (2008) or Gali and Monacelli (2005), and average those in the international business cycle literature. The associated persistences (ρMT and ρMN ) are set at 0.75 on a quarterly basis (delivering 0.3 on an annual basis). In middle- and low-income countries, standard deviation are set higher Please cite this article as: Pourroy M, et al. Food prices and inflation targeting in emerging economies. International Economics (2016), http://dx.doi.org/10.1016/j. inteco.2015.12.001i

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(2.25% and 2.5%, respectively) and the autocorrelation is lowered (0.7 and 0.65, respectively). Productivity shocks in the food sectors (mainly weather events) are calibrated following Anand and Prasad (2010): persistences (ρFT and ρFN ) are set at 0.25, and standard deviation (σ) at 0.03 for the three groups of countries. We estimate a VAR model in order to calibrate variances and covariances in world food price shocks, the world manufacturing (non-food) price shocks and the world interest rate shocks. The results are given in Section 2.3. For the described structure of shocks and the low-income countries calibration, the variance decomposition of the main variables of the model is given in Table B2 in Appendix B. The model is solved numerically up to second-order approximation using Dynare (see Adjemian et al., 2011).

4. Welfare and model's response under alternative monetary policy rules 4.1. Welfare calculation To assess the normative implications of the two monetary policies we numerically evaluate the welfare derived in each case, for any country category. As discussed by Benigno and Woodford (2012) two approaches are possible for welfare analysis in DSGE models. The first is to compare a given policy with the optimal Ramsey policy (see Woodford, 2003). The second is solving the model using a second-order approximation to the structural equations for a given policy and then evaluating welfare using this solution (see Kim and Kim, 2003 on the limitations of first order solutions and SchmittGrohé and Uribe, 2004 on second order solutions). Considering our model distortion (market power exercised by monopolistically competitive firms in the two non-tradable markets) we take the latter option for two reasons. First, as opposed to the calculation of a Ramsey policy, computing a second order solution does not require re-writing the model without inefficiency. Second, as opposed to a first order solution, computing a second order solution is not required to assume that government can access a subsidy to factor inputs, financed from lump-sum taxes, aimed at dismantling the inefficiency. However, following Schmitt-Grohé and Uribe (2006) we have to define price dispersion and aggregate production function in a recursive form (see Eq. (25)) to accurately approximate welfare up to second order. Our welfare criterion is defined following Faia and Monacelli (2007), also in line with Coenen et al. (2008), De Paoli (2009) and Kolasa and Lombardo (2014) among others. We use the following criterion: ( W ¼ E1

1 X

t¼0

)   βt uðC t ; Lt Þ  

x0 ¼ x

where x denotes the set of predetermined variables. Following Schmitt-Grohé and Uribe (2004) and Adjemian et al. (2011) the second-order welfare approximation takes the form of the following conditional expectation: W ¼ E  1 fW 0 gjy  1 ¼ y ¼ W þ

 1  1  g þ E0 ½g uu ðu1  u1 Þ ; 2 σσ 2

where W denotes the welfare value at the (non-stochastic) steady-state, g σσ is the second derivative of the policy function (g) with respect to variance in the shocks, and guu is the Hessian of g with respect to the shock vector u. We present the results in terms of the percentage conditional welfare gains relative to non-food targeting. Welfare gains are defined as additional perpetual consumption needed to make the level of welfare under non-food price inflation targeting identical to that under the evaluated policy. Thus, a positive number indicates that welfare is higher under the CPI inflation targeting policy than under strict non-food price inflation targeting policy. Please cite this article as: Pourroy M, et al. Food prices and inflation targeting in emerging economies. International Economics (2016), http://dx.doi.org/10.1016/j. inteco.2015.12.001i

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Fig. 4. IRF under alternative monetary policy rules: low-income countries.

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Table 7 Taylor rules: calibration that maximizes welfare. Target Low-income countries Headline inflation Non-food inflation Middle-income countries Headline inflation Non-food inflation High-income countries Headline inflation Non-food inflation

Optimal rule

W

logði=iÞ ¼ 119 logðπ Þ

logði=iÞ ¼ 930 log π M

24.46

1

0.00

2

3.38

1

0.00

2

 0.93

2

0.00

1

logði=iÞ ¼ 1001 logðπ Þ

logði=iÞ ¼ 1001 log π M logði=iÞ ¼ 1001 logðπ Þ

logði=iÞ ¼ 1001 log π M

Rank

4.2. Discussion over alternative monetary-policy rules Fig. 4 displays the model's response to a shock to the world food price for a typical low-income country. We consider an unanticipated one percentage point transitory increase in the world food price. Inflationary pressure leads the central bank to tighten its monetary policy. Aggregate consumption drops and the currency appreciates. Whatever the monetary policy rule, around twothird of the shock passes through domestic prices, while one-third is absorbed by exchange rate appreciation. The increase in the domestic price of tradable food leads to a large fall in domestic demand for this good. Because tradable and non-tradable food goods are substitutable ðθF ¼ 1:4Þ this fall in tradable food consumption is partly compensated for by an increase in non-tradable food consumption. Thus the price of non-tradable food also increases despite the monetary policy. Appreciation of the currency makes the tradable non-food goods cheaper, and causes demand for them to rise. Consumption of non-tradable non-food goods decreases while consumption of tradable non-food goods rises. The increase in food exports dominates the fall in non-food exports such that the trade balance becomes positive, and the net foreign position is cleared through ownership of more foreign assets. When the central bank targets the overall CPI, the interest rate increases at the time of the shock. The price of non-tradable goods does not increase, firstly because wages are a constraint, secondly because the exchange rate appreciation reduces the passthrough. During the transition, the interest rate decreases, and global demand, wages and prices rise. Thus non-tradable prices increase progressively, and domestic inflation is spread over a long period. When the central bank excludes food prices from its target, the interest rate does not move with world food price hikes. Thus, the food price shock heats the domestic economy more heavily. The shock is absorbed less by the exchange rate appreciation. Wages and non-tradable goods prices increase dramatically. During the transition, the relative price of tradable food falls gradually because of nominal rigidity. Since our model includes tradable food and non-food goods, the exchange rate turns to be a key channel for the transmission of monetary policy. If the central bank raises its interest rates following a world food price shock, this will cause appreciation of the domestic currency and will reduce the relative price of tradable non-food goods. This keeps inflation in non-food goods at a low rate. Results in Table 7 give the optimal parameters and the welfare associated with non-food inflation targeting and CPI inflation targeting. In a first step, we assume no autoregressive term in the policy function ðρi ¼ 0Þ. Alternative assumptions as well as other sets of parameters are presented in the robustness analysis in Appendix C. In particular Table C4 shows that results are similar when ρi a 0. We present here only optimized parameters in order to make sure that the results describe what any

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policy rule can do at best.8 Results for non-optimized rules are similar and are given in Table C3. The explanation for optimal parameters' values are twofolds. First, Φ (optimal parameter for CPI targeting policy rule) and ΦM (optimal parameter for non-food targeting policy rule) are large enough to fully stabilize the targeted inflation rate. In other words, it is similar to implement these optimal parameters or to have π t ¼ 0 or π M t ¼ 0, respectively. Second, these parameters depend on sectors shares. For example, there are more tradable food goods in the CPI of high-income countries than in the CPI of low-income countries. Therefore, a central bank targeting headline inflation would optimally have a stronger reaction to a world food price shock in high-income countries than in low-income countries. The results in Table 7 clearly point out that the best policy is to target non-food prices in highincome countries. However, in low-income countries or middle-income countries, the best policy option turns to be CPI inflation targeting. This result can be enlightened by previous studies and especially by Aoki (2001) who shows that in case of relative price shock, the optimal policy is to target the sticky prices. However, in our case sticky prices are widespray among the economy's two sectors: these (sticky) prices are located in the non-tradable sectors. Also, following Table 1, the poorer the country, the bigger the weight on non-tradable food in CPI inflation.9 This explains the ranking of the interest rate rules: in high income countries, the share of non-tradable food in the CPI is extremely low, thus it can be virtually neglected by the monetary authorities with the consequence that nonfood inflation is a better target than headline inflation. However, in middle-income countries, the share of non-tradable food in the CPI is higher than in high-income countries, and thus it cannot be neglected by the monetary authorities. Consequently, in middle-income countries targeting non-food inflation is less effective than targeting headline inflation. This result is even stronger in low-income countries, where the welfare cost of shocks under CPI inflation targeting is 0.03% better than under non-food inflation targeting, expressed in perpetual utility loss of consumption. In low- and middle-income countries, a surge in imported food prices generates inflationary pressures in the large non-tradable food sector. Thus, the trade-off between headline and non-food inflation differs for high-income countries and lower-income countries. This result is robust to changes in the calibration of the main parameters of the model (see Table C1 in Appendix C).

5. Fixed consumption and monetary policy Food is not a good like other goods: it is basic consumption need. Some might argue that because food is a good of first necessity, a food price shock will not spread to the economy in the same ways as other relative price shocks. Consumption cannot decrease freely. A part of consumption is not related to relative prices and thus is inelastic. In this section, we examine whether the fact that food is a first necessity influences the ranking of monetary rules. We can conclude that our results are robust to a change in the definition of food in the utility function. Following Anand and Prasad (2010), to account for food being a necessity, households must FN

FT

consume a minimum amount of each kind of food in order to survive, denoted C and C , respectively. We assume also that the household always has enough income to buy the subsistence level of food. Thus, the food index in utility is given by a generalized Klein–Rubin utility function (see e.g. Gollin et al., 2002). The model without fixed consumption is taken as a baseline. We then add subsistence levels of 5, 10, 15, etc. up to 95% of the food consumption and evaluate in each case the optimal monetary policy as described in Section 4. The welfare cost of shocks obtained by a given rule for a given value of fixed food consumption should not be compared to the welfare value obtained by the same rule for another value of fixed 8 To insure the robustness of our results, Taylor rules optimal parameters are computed while considering the entire set of shocks fAFT ; AFN ; AMT ; AMN ; P FT⋆ ; P MT⋆ ; iw g. 9 The share of non-tradable food relatively to non-tradable non-food goods in the CPI is around 4% in high-income countries, 12% in middle-income countries and 30% in low-income countries.

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Fig. 5. Welfare gain associated to CPI targeting relatively to non-food targeting.

consumption, because it does not come from the same utility function. Since the utility function has changed, it does not allow for welfare comparison. However, for a given value of fixed consumption we can compare different policies and rank them according to their welfare. We can also compare the rankings from one fixed consumption value to another. Our main result is that the rankings do not change. Graphically this is represented by the fact that in Fig. 5 the lines never cross. Thus the results described in Section 4 are ongoing: targeting overall CPI is better than targeting a proxy for core inflation given by non-food inflation.

6. Conclusion In this paper, we examine how central banks react to food price shocks. In particular, we analyze the performance of an inflation targeting regime to deal with a shock to the world price of food products. We developed a small open economy New Keynesian model. We consider that both food and non-food goods are made of tradable and non-tradable goods, and we calibrate our model on real data. We defined a non-tradable food good as a product that is produced at home and whose price does not depend directly upon the world market. This setup allowed us to describe the channel between the world market and domestic consumer prices, through the relative demand for tradable goods and purely domestic varieties. It is well-known that central banks cannot calculate the exact core inflation indices of their economies because they generally lack micro-level data on prices behaviors, particularly in less-developed and emerging economies. They tend to use a proxy for core inflation that is based on excluding oil and food prices from the CPI. We showed how confusion between core inflation and non-food inflation can lead to badly formulated policies. This result holds for low-income and middle-income countries, where the share of food goods in the CPI, and particularly the share of non-tradable food goods, is large. In high-income countries, the share of non-tradable food in consumption is small enough to be ignored by central banks in their definition of core inflation. Thus, our results suggest that in low- and middle-income countries central banks should target headline inflation rather than a core inflation index that excludes food prices. This finding holds not because food is a first necessity, but because non-tradable food represents a significant share in total consumption. When food is described as a first necessity good the ranking of monetary rules does not change. In fact, a high share of non-tradable food in consumption implies a non-negligible part of sticky food prices in the CPI giving room for monetary policy action toward food price shocks.

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Therefore, the results from our work provide important policy recommendation for countries that are inflation targeting and intend to implement such policies in the future. For high-income countries, food prices can be virtually ignored in the target index. For low- and middle-income countries where non-tradable food is not negligible, central bank should not ignore food price evolution and should target headline inflation.

Acknowledgments We thank Philippe Aghion, Agnès Bénassy-Quéré, Christian Bordes, Gunther Capelle-Blancard, Charlotte Emlinger, Pierre-Olivier Gourinchas, Yannick Kalantzis, Jean-Christophe Poutineau and Fabien Tripier for helpful comments and suggestions. The views expressed in this paper are solely the responsibility of the authors.

Appendix A. Technical description of the model A.1. Households The representative household of the domestic economy maximizes the following intertemporal utility: E0

1 X

βt U ðC t ; Lt Þ

with U ðC; LÞ 

t¼0

C1  ρ L1 þ χ ψ 1ρ 1þχ

where 0 o β o 1, E is the expectation operator, ρ 4 0 is the inverse of intertemporal elasticity of substitution, χ 40 the inverse of elasticity of labor supply and ψ 4 0 is a scale parameter. The portfolio of the household at the end of period t includes a set Bt þ 1 of domestic contingent claims priced dt;t þ 1 , 10 a set B⋆ t of one-period risk free bonds in foreign currency and the ownership of domestic firms. The budget constraint is given by n o t þ1 ⋆ ⋆ MN þ Π FN P t C t þ Et dt Bt þ 1 þ B ⋆ t þ Bt þ 1 þ it Bt  1 =St ; t =St ¼ W t Lt þ Π t where P denotes consumption price, S the nominal foreign exchange rate and Π the dividends of domestic firms. To avoid a multiplicity of steady-states and a unit root of the dynamic system related to the accumulation of foreign assets, the household is assumed to face an interest rate that is increasing in the country's net foreign debt, following Schmitt-Grohé and Uribe (2003). The interest w rate perceived by the household, denoted by i⋆ t , is the sum of the world interest rate, it , and a risk premium that depends on the net foreign asset position: ⋆

w B  1Þ; i⋆ t ¼ it þ ζðe

where ζ 4 0 is a parameter of bond adjustment cost. The first order conditions related to domestic contingent claims, foreign bonds holdings and labor supply are given by
 

tþ1 Pt Ct þ 1  ρ St þ 1 t þ1 ; ð1Þ ¼β ; 1 ¼ Et 1 þ i⋆ dt t dt Pt þ 1 Ct St Wt ¼ ψLχt C ρt : Pt

10

ð2Þ

Their is no international trade of contingent claims in order to avoid muting the current account channel.

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We implicitly assume the cashless limiting utility (Woodford, 2003) such that the central bank is able to set the nominal one-period risk-free interest rate defined by the following equation: n o tþ1 1 ¼ Et ð1 þ it Þdt : ð3Þ

A.2. The structure of the consumption bundle The consumption bundle C is a CES of food goods, CF, and non-food goods, CM, with θ being the elasticity of substitution between food and non-food goods, and γ the share of food in consumption: 

ðθ  1Þ=θ

ðθ  1Þ=θ θ=ðθ  1Þ C t  ð1  γÞ1=θ C M þ ðγÞ1=θ C Ft : t Both food and non-food goods include a tradable commodity (international price) and a bundle of non-tradable domestic varieties (domestic sticky price), the two components are aggregated in a CES function with elasticity of substitution θF and θM and where the share of the tradable component is denoted γ F and γ M , respectively. Food and non-food bundles are given by 

ðθF  1Þ=θF

ðθF  1Þ=θF θF =ðθF  1Þ 1=θ C Ft  ð1  γ F Þ1=θF C FN þ γ F F C FT ; t t h iθM =ðθM  1Þ 1=θ 1=θ M MN C t ðθM  1Þ=θM þ γ M M C MT : CM t  ð1  γ M Þ t ðθ M  1Þ=θ M Given the price of each good P FN , P FT , P MN and P MT , optimal allocation of consumption expenditure over the four varieties leads to a definition of aggregate price for food P F , non-food P M and aggregate consumption P:  1=ð1  θF Þ FT P Ft ¼ ð1  γ F ÞP FN ; t 1  θ F þ γ F P t 1 θ F

ð4Þ

 1=ð1  θM Þ MN 1 θM þ γ M P M;T 1  θM ; PM t ¼ ð1  γ M ÞP t t

ð5Þ

 1=ð1  θÞ F P t ¼ ð1  γÞP M : t 1 θ þ γP t 1  θ

ð6Þ

The demand for food and non-food goods are given by !θ PF C Ft ¼ γ t Ct ; Pt

CM t ¼ ð1  γ Þ

PM t Pt

!θ Ct :

ð8Þ

The demand for each good have the following expressions: !  θF P FT FT t Ct ¼ γF C Ft ; P Ft C MT ¼ γM t

P MT t

ð7Þ

ð9Þ

!  θM

PM t



P FN t C FN ¼ 1  γF t P Ft

CM t ;

ð10Þ

!  θF C Ft ;

ð11Þ

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P MN t C MN ¼ 1  γM t PM t

!  θM CM t :

ð12Þ

Non tradable varieties: Non-tradable food and non-tradable non-food goods are assumed to be a composite of a continuum of differentiated varieties, ct(i) with iA ½0; 1, via the aggregate CES function !ηFN =ηFN  1 Z  C FN t

C MN  t

1

cFN t ðiÞ

0

Z

1 0

ηFN  1 ηFN

;

di

!ηMN =ηMN  1 cMN ðiÞðηMN  1Þ=ηMN di t

;

where ηFN and ηMN are the elasticity of substitution across food and non-food varieties, respectively. FN Let P FN t ðiÞ and P t ðiÞ be the nominal price of variety i at time t in the food and non-food sectors, respectively. The aggregate price in the sector in each sector is defined by !1=ð1  ηFN Þ Z ¼ P FN t

P MN ¼ t

1

0

Z 0

1  ηFN P FN di t ðiÞ

1

; !1=ð1  ηMN Þ

P MN ðiÞ1  ηMN di t

:

The consumer minimizes its total expenditure for any given level of consumption of the composite good, subject to the aggregation constraint. The optimal level of cN ðiÞ is then given by !  ηFN P FN t ðiÞ cFN ð i Þ ¼ C FN t ; t P FN t cFT t ðiÞ ¼

P FT t ðiÞ

!  ηFT

P FT t

C FT t :

A.2.1. Tradable goods producers The production technology for tradable goods is given by FT FT 1  αFT Lt ; Y FT t ¼ At

ð13Þ

MT 1  αMT ¼ AMT Lt ; Y MT t t LFT t

LMT t

ð14Þ AFT t

AMT t

where and denote the unit of labor employed in each sector, and and the level of technology. The firm takes the price and the wage as given, and chooses the quantity produced and the labor required to maximize its profit. For the two tradable sectors, one has FT FT FT Π FT t ¼ P t Y t W t Lt ; MT ¼ P MT  W t LMT Π MT t Yt t : t

The first order condition implies FT FT W t LFT t ¼ ð1  αFT ÞP t Y t ; MT ¼ ð1  αMT ÞP MT W t LMT t t Yt :

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Together with the production function we get demand for labor ! FT 1=αFT FT P t ¼ ð 1  α ÞA ; LFT FT t t Wt

¼ LMT t

ð1  αMT ÞAMT t

P MT t Wt

ð15Þ

!1=αMT :

ð16Þ

A.2.2. Non-tradable goods producers In a non-tradable sector (being food or non-food), the variety i is produced by a single firm according to a technology common across sector firms and using labor as the only input. The production function is given by

1  αFN FN FN Y FN Lt ðiÞ ; t ðiÞ ¼ At MN 1  αMN Y MN ðiÞ ¼ AMN Lt ðiÞ : t t or Y MN is the level of production for food or non-food sectors, respectively, AFN or AMN is where Y FN t t t t FN MN productivity in the sector, Lt ðiÞ or Lt ðiÞ the level of employment in the firm i. Firms are allowed to set prices according to a stochastic time-dependent rule as in Calvo (1983): in each period, a firm faces a probability ϕFN or ϕMN of not being able to re-optimize its price. In a given sector, all firms that reset their price at t will choose the same P tjt in order to maximize the expected present discounted value of profits, under the constraint that the firm must satisfy demand at the posted price. Thus, the firm program is given by 8
 P tjt  η > > > Y t þ kjt ¼ Ct þ k ðdemandÞ > 1 < Pt þ k X   tþk
1=ð1  αÞ max Et dt ϕk P tjt Y t þ kjt  Ψ t þ kjt subject to > Y t þ kjt P tjt > k¼0 > ðcostÞ > : Ψ t þ kjt ¼ W t þ k At þ k Optimal price setting and inflation dynamic: From the demand function for the variety i, one has Y ¼  η tPþtjtkjt . The first order condition (FOC) is given by 2 3 1 X η t þk k 5 ¼ 0: Et dt ϕ Y t þ kjt 4P tjt  ∂Ψ kjt η  1 ∂Y tt þþ kjt k¼0

∂Y t þ kjt ∂P tjt

Let mct ¼

 1=ð1  αÞ α=ð1  αÞ W t 1 Yt 1  α At Pt .

1 ∂Ψ

kjt P t þ k ∂Y tt þþ kjt ¼ mct þ k

Y t þ kjt Yt þ k

One has

α=ð1  αÞ

:

The FOC can be rearranged
ð1  α þ ηαÞ=ð1  αÞ Et P tjt η ¼ Pt η1

P1

k¼0

tþk

dt Et


ϕk Y t þ k

P1

Pt þ k Pt

ð1  α þ ηÞ=ð1  αÞ

t þk k ϕ Yt þk k ¼ 0 dt




X t and Y t have the following recursive expressions: n o ð1  αFN þ ηÞ=ð1  αFN Þ FN t þ1 FN FN ¼ Y FN Et dt π FN Xtþ1 ; X FN t mct þϕ t tþ1 n o tþ1 FN FN ¼ Y FN Et dt π FN Y FN t þϕ t t þ 1 ηY t þ 1 ;

Pt þ k Pt

η

mct þ k ¼

η η  1 XY tt :

ð17Þ ð18Þ

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n o ð1  αMN þ ηÞ=ð1  αMN Þ MN tþ1 X MN ¼ Y MN mcMN þ ϕMN Et dt π MN Xt þ1 ; t t t þ1 t

ð19Þ

n o t þ1 MN ¼ Y MN þ ϕMN Et dt π MN Y MN t t t þ 1 ηY t þ 1 :

ð20Þ

Given the definition of the consumption bundle, inflation dynamic in the sector is given by !1  η FN 1  η

P FN tjt FN FN ¼ ϕ þ 1ϕ ; ð21Þ πt P FN t MN 1  η

P MN tjt πt ¼ ϕMN þ 1 ϕMN P MN t

!1  η :

ð22Þ

Price dispersion and aggregate production function: Price dispersion in a given sector induces a misallocation of factors and decreases the productivity at the aggregate level comparing to productivity at the firm level. Schmitt-Grohé and Uribe (2006) develop the calculus in the constant return to scale case. We propose here the decreasing return to scale case. Labor demand from firm i is given by

 P t ðiÞ  η=ð1  αÞ Y t 1=ð1  αÞ Lt ðiÞ ¼ : At Pt Integrating over firms of the sector gives ! FN 1=ð1  αÞ FN Y t ¼ S LFN t t AFN t ¼ S MN LMN t t

Y MN t

ð23Þ

!1=ð1  αÞ ð24Þ

AMN t

where the effect of price dispersion on productivity is captured by the term S t ¼

R 1 Pt ðiÞ  η=ð1  αÞ 0

Pt

di,

which has the following recursive expression:
  η=ð1  αÞ Z
 P tjt P t ðiÞ  η=ð1  αÞ þ di S t ¼ ð1  ϕ Þ Pt Pt P t ðiÞ ¼ P t  1 ðiÞ
  η=ð1  αÞ
  η=ð1  αÞ
  η=ð1  αÞ P tjt Pt  1 P tjt η=ð1  αÞ ¼ ð1  ϕÞ þϕ S t  1 ¼ ð1  ϕÞ þ ϕπ t St  1 : Pt Pt Pt Applied to our two non-tradable sectors, we get: !  η=ð1  αFN Þ

P FN η=ð1  αFN Þ FN tjt FN FN þϕFN π FN St  1 ; St ¼ 1  ϕ t P FN t

P MN tjt ¼ 1  ϕMN S MN t P MN t

!  η=ð1  αMN Þ þ ϕMN π MN t

η=ð1  αMN Þ

S MN t  1:

ð25Þ

ð26Þ

A.2.3. Closing the model: monetary policy and the balance of payments Market clearing conditions are given by: ¼ C FN Y FN t ; t

ð27Þ

¼ C MN ; Y MN t t

ð28Þ

FN FT X FT t ¼ Y t  Ct ;

ð29Þ

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X MT ¼ Y MT  C MT t ; t t

ð30Þ

FT MN Lt ¼ LFN þ LMT t þLt þLt t :

ð31Þ

Monetary policy is described in Section 3. The monetary policy rule is given by

h i 8 > for headline inflation targeting: < ρi log it  1 Þ þ 1  ρi Þ logðiÞ þ Φ logðπ t Þ

h i log it Þ ¼ > : ρi log it  1 Þ þ 1  ρi Þ logðiÞ þ ΦM logðπ M for nonfood inflation targeting: t Þ

ð32Þ

where headline inflation is defined as πt ¼

Pt ; Pt  1

ð33Þ

and non-food inflation is given by πM t ¼

PM t PM t 1

:

ð34Þ

The trade balance is given by the sum of food tradable and manufacture tradable net exports. Aggregating the budget constraint of domestic firms and households leads to the evolution of the net foreign asset position in foreign currency: w ⋆ FT⋆ FT B⋆ X t þ P MT⋆ X MT t ¼ ð1 þ it  1 ÞBt  1 þ P t t t :

ð35Þ

A.2.4. Introducing fixed consumption Introducing a minimum consumption of food modifies the food consumption bundle  θF =ðθF  1Þ



 FN ðθF  1Þ=θF FT ðθF  1Þ=θF 1=θF FT  C þγ C C : C Ft  ð1  γ F Þ1=θF C FN t t F Notice that C Ft is not the amount of food consumed by the household, but the household's utility and C FT value derived from food consumption. The household consumes C FN t t . But since food is a necessity, we consider that consumption does not deliver pleasure (or utility) to the household before the minimum level is reached. This means that its utility starts to increase only when food consumption overtakes this subsistence level. Demand for each food variety (previously given by Eqs. (9) and (11)) can be rewritten as !  θF !  θF

P FN P FT FT FN FT F FN t t Ct þ C ; Ct ¼ 1  γF C Ft þ C : Ct ¼ γF P Ft P Ft Thus, in this case, the total consumption expenditure is given by P t C t þ P FN t C

FN

þ P FT t C

FT

:

The representative household now faces the following budget constraint expressed in units of domestic currency: n o

⋆ FN FT t þ1 FN MN þ P FT þ Et dt Bt þ 1 þ B⋆ þBt þ 1 þ i⋆ P t C t þ P FN t Bt  1 =St : t C t C t =St ¼ W t Lt þ Π t þ Π t We introduce fixed consumption in food and restrict the change in the utility function such that the economy's steady-state is maintained. This implies introducing minimum consumption in Eq. (A.6) and rescaling the share of food in the consumption bundle according to γ ¼ γð1  AÞ with A being the food subsistence level in proportion to total food consumption at the steady-state. The introduction of fixed consumption modifies the elasticity of substitution between goods. The CES elasticity, denoted by θ, is no longer the elasticity of substitution between goods, now denoted by E. The latter is given by E ¼ Aθ. As the share of fixed consumption in total food consumption rises, the elasticity of substitution falls to zero. Please cite this article as: Pourroy M, et al. Food prices and inflation targeting in emerging economies. International Economics (2016), http://dx.doi.org/10.1016/j. inteco.2015.12.001i

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A.2.5. The general equilibrium FN FT The dynamic equilibrium is a set of vectors ðX t Þt of endogenous variables Xt ¼ (Ct, C Ft , C M t , Ct , Ct , MN MT F M FT MT FN MN FT FN MT MN M FN MN FN FN MN C t , C , Pt, P t , P t , πt, πt , π t , π t , Y t , Y t , Y t , Y t , Wt, Lt, Lt , Lt , Lt , Lt , S t , S t , X t , MT ⋆ MN Y FN , Y MN , X FT t , X t , it, St, Bt ). The equilibrium conditions are given by Eqs. (1)– (35). t , Xt t

Appendix B. Main statistics of the model In order to illustrate the fluctuations generated by the model, we reproduce in Table B1 the autocorrelation of total GDP, Y, overall inflation, π, and the trade balance TB. We reproduce in Tables Table B1 Approximated coefficients of autocorrelation. Lags

1

2

3

4

5

Low-income countries Y 0.66 π 0.64 TB 0.70

0.40 0.25 0.40

0.22 0.05 0.20

0.12 0.00 0.09

0.06 0.01 0.05

Middle-income countries Y 0.69 π 0.65 TB 0.71

0.42 0.28 0.42

0.24 0.08 0.21

0.13 0.02 0.10

0.07 0.02 0.05

High-income countries Y 0.71 π 0.67 TB 0.72

0.44 0.31 0.43

0.25 0.10 0.23

0.14 0.03 0.11

0.07 0.02 0.04

Table B2 Variance decomposition (%): low-income countries. Shocks

AFN

AFT

AMT

AMN

iw

P FT⋆

P MT⋆

C L Y Y FN

1.80 0.33 5.54 44.85

0.15 3.90 12.78 1.26

0.09 0.93 3.20 0.58

0.16 0.05 0.47 0.21

38.00 38.14 31.54 20.50

51.19 47.92 39.37 2.55

8.61 8.72 7.11 30.04

Y FT

0.10

30.28

0.52

0.01

10.53

54.21

4.36

Y MN

5.11

0.62

0.32

4.94

16.99

69.78

2.23

Y MT Π ΠF ΠM

0.37

5.85

11.88

0.05

30.37

2.73

48.74

1.43 10.71 10.46

0.05 0.17 0.16

0.01 0.03 0.03

0.02 0.17 0.17

35.42 9.47 9.68

56.02 48.14 49.05

7.05 31.30 30.44

Table B3 Variance decomposition (%): middle-income countries. Shocks

AFN

AFT

AMT

AMN

iw

P FT⋆

P MT⋆

C L Y Y FN

0.25 0.04 0.98 32.70

0.10 3.03 11.56 0.91

0.10 0.80 3.25 0.57

0.20 0.05 0.55 0.21

40.11 40.17 35.29 15.36

47.59 44.08 37.84 7.99

11.64 11.84 10.53 42.26

Y FT

0.01

30.89

0.50

0.01

9.00

53.40

6.19

Y MN

0.76

0.34

0.26

4.39

22.60

70.58

1.06

Y MT Π ΠF ΠM

0.07

6.44

8.88

0.06

31.66

2.74

50.15

0.18 2.05 2.05

0.01 0.01 0.01

0.01 0.00 0.00

0.03 0.09 0.09

34.69 9.64 9.63

54.80 61.09 61.19

10.29 27.13 27.03

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Table B4 Variance decomposition (%): high-income countries. Shocks

AFN

AFT

AMT

AMN

iw

P FT⋆

P MT⋆

C L Y Y FN

0.02 0.00 0.10 23.54

0.08 2.29 9.40 0.55

0.10 0.60 2.67 0.42

0.20 0.04 0.50 0.13

41.47 41.85 38.10 10.91

43.63 40.32 35.25 22.17

14.50 14.89 13.99 42.28

Y FT

0.00

30.71

0.39

0.01

8.37

53.24

7.28

Y MN

0.07

0.23

0.23

3.77

26.56

66.98

2.16

Y MT Π ΠF ΠM

0.01

5.83

5.94

0.05

34.78

3.35

50.03

0.02 0.24 0.24

0.00 0.00 0.00

0.00 0.00 0.00

0.03 0.04 0.04

34.58 9.67 9.65

51.87 65.46 65.57

13.50 24.58 24.48

B2, B3 and B4 the variance decomposition of the model's key variables for low-, middle- and highincome countries respectively. Total GDP and trade balance are ex-post variables defined by: MT MN þ Y FN ; Y ¼ Y FT t þYt t þY t

⋆ FT⋆ FT TB ¼ ð1 þ iw X t þ P MT⋆ X MT B⋆ t  1 ÞBt  1 þ P t t t t :

Appendix C. Robustness tests See Tables C1–C4. Table C1 Robustness test. Parameter

γ

γT

θ

θT

ρ

Baseline Test

0.31 0.20

0.61 0.10

0.30 0.90

1.40 2.50

2.00 0.50

Low-income countries CPI targeting: optimal ϕ Welfare associated to CPI targeting Non-food targeting: optimal ϕM Welfare associated to non-food targeting

118.9 24.46 930.2 0.00

118.9 24.46 930.2 0.00

135.8 22.24 462.2 0.00

92.6 29.57 98.4 0.00

23.7 25.76 1001.0 0.00

Middle-income countries CPI targeting: optimal ϕ Welfare associated to CPI targeting Non-food targeting: optimal ϕM Welfare associated to non-food targeting

1001.0 3.38 1001.0 0.00

1001.0 3.38 1001.0 0.00

1001.0 3.80 1001.0 0.00

1001.0 5.96 1001.0 0.00

1001.0  2.49 1001.0 0.00

High-income countries CPI targeting: ϕ Welfare associated to CPI targeting Non-food targeting: ϕM Welfare associated to non-food targeting

1001.0  0.93 1001.0 0.00

1001.0  0.93 1001.0 0.00

1001.0 0.15 1001.0 0.00

1001.0  0.08 1001.0 0.00

1001.0  7.65 1001.0 0.00

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Table C2 Robustness test for Calvo parameters. Parameter

ϕFN

ϕFN

ϕMN

ϕMN

Baseline Test

0.50 0.33

0.50 0.66

0.75 0.50

0.75 0.85

Low-income countries CPI targeting: optimal ϕ Welfare associated to CPI targeting Non-food targeting: optimal ϕM Welfare associated to non-food targeting

1001.0 21.74 1001.0 0.00

99.6 23.70 1001.0 0.00

63.6 12.34 34.1 0.00

1001.0 36.00 1001.0 0.00

Middle-income countries CPI targeting: optimal ϕ Welfare associated to CPI targeting Non-food targeting: optimal ϕM Welfare associated to non-food targeting

1001.0 3.30 1001.0 0.00

1001.0 3.00 1001.0 0.00

1001.0 0.84 62.6 0.00

1001.0 6.29 1001.0 0.00

High-income countries CPI targeting: ϕ Welfare associated to CPI targeting Non-food targeting: ϕM Welfare associated to non-food targeting

1001.0  0.94 1001.0 0.00

1001.0  0.99 1001.0 0.00

1001.0  1.34 986.7 0.00

1001.0 0.10 1001.0 0.00

Table C3 Welfare analysis for non-optimal policy parameters. Monetary policy reaction Φ or ΦM

2.50

3.50

4.50

5.50

Low-income countries Welfare associated to CPI targeting Welfare associated to non-food targeting

106.79 0.00

36.15 0.00

29.25 0.00

27.12 0.00

Middle-income countries Welfare associated to CPI targeting Welfare associated to non-food targeting

0.77 0.00

1.76 0.00

2.45 0.00

2.75 0.00

High-income countries Welfare associated to CPI targeting Welfare associated to non-food targeting

 19.62 0.00

 5.12 0.00

 2.99 0.00

 2.21 0.00

Table C4 Policy rules with autoregressive term. Autoregressive parameters ρi

0.00

0.25

0.50

0.75

Low-income countries CPI targeting: optimal ϕ Welfare associated to CPI targeting Non-food targeting: optimal ϕM Welfare associated to non-food targeting

118.9 24.46 930.2 0.00

1001.0 25.31 1001.0 0.00

1001.0 27.70 1001.0 0.00

1001.0 48.38 1001.0 0.00

Middle-income countries CPI targeting: optimal ϕ Welfare associated to CPI targeting Non-food targeting: optimal ϕM Welfare associated to non-food targeting

1001.0 3.38 1001.0 0.00

1001.0 3.48 1001.0 0.00

1001.0 3.72 1001.0 0.00

1001.0 5.54 1001.0 0.00

High-income countries CPI targeting: ϕ Welfare associated to CPI targeting Non-food targeting: ϕM Welfare associated to non-food targeting

1001.0  0.93 1001.0 0.00

1001.0  0.95 1001.0 0.00

1001.0  1.01 1001.0 0.00

1001.0  1.51 1001.0 0.00

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Appendix D. Impulse-response function See Figs. D1–D8.

Fig. D1. World food price shock, IRF for middle-income countries.

25

26

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Fig. D2. World food price shock, IRF for high-income countries.

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Fig. D3. World non-food price shock, IRF for low-income countries.

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Fig. D4. World interest rate shock, IRF for low-income countries.

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Fig. D5. Productivity shock, non-tradable food sector, IRF for low-income countries.

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Fig. D6. Productivity shock, tradable food sector, IRF for low-income countries.

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Fig. D7. Productivity shock, non-food non-tradable sector, IRF for low-income countries.

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Fig. D8. Productivity shock, non-food tradable sector, IRF for low-income countries.

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