Raising Food Prices and Welfare Change: A Simple Calibration. Xiaohua Yu

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1 Rasng Food Prces and Welfare Change: A Smple Calbraton Xaohua Yu Professor of Agrcultural Economcs Courant Research Centre Poverty, Equty and Growth Unversty of Göttngen CRC-PEG, Wlhelm-weber-Str Göttngen, Germany Tel:+49-() / Emal: xyu@un-goettngen.de Please cte: Yu. X.(214): Rasng Food Prces and Welfare Change: A Smple Calbraton. Appled Economcs Letters. Vol. 21(9): Runnng Ttle: Rasng Food Prces and Welfare Change Abstract: Ths paper proposes a smple and straghtforward method whch only requres the nformaton of expendture share and the compensated own prce elastcty to calbrate ex ante consumer welfare change due to prce change, whle specfc prce nformaton s not requred. It s appled to calculate the welfare loss due to recent food prce nflaton, and fnd that recent food prce nflaton after Jan. 29 n the world causes 22%, 14% and 9% welfare loss respectvely for low-, mddle- and hgh- ncome countres. Key Words: Compensatng Varaton, Food Prce, Welfare Loss, Low-Income Countres. JEL: Q11, I32 1

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3 Rasng Food Prces and Welfare Change: A Smple Calbraton Abstract: Ths paper proposes a smple and straghtforward method whch only requres the nformaton of expendture share and the compensated own prce elastcty to calbrate ex ante consumer welfare change due to prce change, whle specfc prce nformaton s not requred. It s appled to calculate the welfare loss due to recent food prce nflaton, and fnd that recent food prce nflaton after Jan. 29 n the world causes 22%, 14% and 9% welfare loss respectvely for low-, mddle- and hgh- ncome countres. Key Words: Compensatng Varaton, Food Prce, Welfare Loss, Low-Income Countres. JEL: Q11, I32 Introducton Recent food prce nflaton has sgnfcant negatve mpact on household welfare, partcularly for the poor households (Ferrera et al. 213; Meyer and Yu 213). The prevalent method to calculate consumer welfare change n response to prce change s the Hcksan Compensatng Varaton (CV), whch assumes expendture s constant. The man stream of the current lterature uses the frst-order approxmaton (Ferrera et al. 213; Deaton and Muellbauer 198 pp.186) or the so-called exact welfare measure (Hausman 1981) whch s derved from ntegratng the Marshallan demand functon, to calculate CV. The method of frst-order approxmaton suffers from serous bas f the ncome effect s very large, whlst the method of exact welfare measure nvolves complcated ntegraton and may also ental substantal bas f the demand functon s not correctly specfed. Even though Fredman and Levnsohn (22) and Robles and Torero (21) provde second order approxmatons for CV, they requre prce nformaton for specfc products, and hence are ad hoc. From the polcy perspectve, t s mportant to know the welfare mpact n advance, so that some smple calbratons would be very appealng. 3

4 Ths paper smplfes the second-order approxmaton by Fredman and Levnsohn (22), and proposes a much straghtforward method to calculate the welfare mpact of prce changes. It only requres the nformaton for expendture share (Engel ndex for the case of food) and compensated own prce elastcty to calbrate ex ante welfare change due to prce change. Such a method can provde precautonary polcy to offset negatve mpact of prce change promptly. Methodology defned as Suppose the prce for good changes from p to p 1, then the compensatng varaton s CV E p u E p u 1 (, ) (, ) (1) where p, u, and E() respectvely denote prce vector for m goods, utlty, and expendture functon; The superscrpt j,( j,1), denotes tme: j and j 1 respectvely for before and after prce change. CV can be normalzed by expendture as CV M (2) E ( p, u ) M n equaton (2) can be explaned as the proporton of addton expendture entaled by prce change to the expendture before prce change n order to keep the welfare constant. Followng 1 Fredman and Levnsohn (22) and Robles and Torero (21), E( p, u ) can be approxmated as 1 E( p, u ) E( p, u ) q p s p p 2 (3) 1 k k kj k j where 2 C( p, u ) hk skj p p p k j j by Shephard s Lemma, and hk s the Hcksan demand for Good k. Then we have, 4

5 1 CV q p s p p 2 k k kj k j. (4) If 1 p s farly close to p, or f 1 p s almost proportonal to p, or f substtuton s lmted, the second order term wll be small, and the bas for the frst-order approxmaton s small (Deaton and Muellbauer 198 pp.174). In practce, polcy makers usually concern about the mpact of prce change for a specfc good or a group of goods, such as food group. Suppose the prce for group (e.g. food) changes, whle the prces for other goods are fxed. By Equaton (4), we have 1 h CV q p p 2 ( ) 2 p (5) Defne p G as the prce growth rate. Combnng equatons (2) and (5) yelds p p 1 2 M w[ Gp ] pgp ( 6 ) 2 where hp w s the expendture share for good before prce change, and E p ( p, u ) h p p h s the compensated own prce elastcty (Proof can be seen n Appendx 1). Dfferent from Fredman and Levnsohn (22) and Robles and Torero (21), Equaton (4) provdes a smple calbraton for welfare change n response to prce change for good, but t only requres the nformaton for budget share w and compensated prce elastcty p, whch are often avalable n the lterature. We then can ex ante calbrate the welfare change, and provde precautonary polcy to offset negatve mpact of prce change promptly. In the case of food prce change, w s smply the Engel Index. Obvously, Equaton (6) ndcates that welfare loss due to hgh food prces s postvely correlated wth Engel Index when 5

6 the absolute value of prce elastcty and prce growth rate are small. As the poor usually have hgher Engel ndex, the loss of welfare would be greater. Applcaton and Dscusson Recently, food prce nflaton has attracted a lot of attenton (Ferrera et al. 213, Robles and Torero 21) from a polcy perspectve. As shown n Fgure 1, the world has experenced two food crses n the past decade: one n 28, and the other one after 29. For the recent food crss, food prce has ncreased by almost 5% compared wth the data n January 29. Hgh food prce can nevtably mpact consumer welfare, and the number can be easly calbrated by Equaton (6). The current lterature has provded ample nformaton about food budget shares (or Engel ndex) and own prce elastctes. The largest database for cross-natonal comparable budget share nformaton would be the Internatonal Comparson Program (ICP) (World Bank 28) 1. Then USDA estmated ncome and prce elastctes, ncludng compensated own prce elastctes needed n ths study by usng the 25 ICP data 2 (Muhammad et al. 211). Gven the budget share and compensated own prce elastctes, we can calculate the welfare loss n dfferent scenaros for dfferent countres. We only report the aggregate results for low-, mddleand hgh-ncome countres n Table 1. Table 1 ndcates that when food prce grows by 5%, whch occurred after Jan. 29 n the world, 22%, 14% and 9% of the ncomes are needed to compensate the welfare loss respectvely for low-, mddle- and hgh- ncome countres. The numbers are qute huge. Fnally, t should be mentoned that the method s based on the second-order approxmaton, so that there mght be some bas when the prce growth rate s hgh. 1 The most recent ICP program was set up n 211, but only 25 ICP data s avalable at : 2 Avalable at: 6

7 Appendx 1: Proof of Equaton (6). Combnng equatons (2) and (5) yelds 1 1 h M [ q p ( p ) ] E p u p 2 (, ) 2 hp p 1 h p p E( p, u ) p 2 p h p 2 [ ( ) ] 1 2 w[ Gp ] pgp. 2 References: Deaton Angus and John Muellbauer (198),Economcs and Consumer behavor. Cambrdge Unversty Press. Uk. Ferrera F. H. G., A. Fruttero, P. G. Lete and L. R. Lucchett (213) Rsng Food Prces and Household Welfare: Evdence from Bbrazl n 28. Journal of Agrcultural Economcs, Vol. 64(1): Fredman, J. and Levnsohn, J. (22) The dstrbutonal mpacts of Indonesa s fnancal crss on household welfare: A rapd response methodology, World Bank Economc Revew,Vol. 16: Hausman J. A. (1981) Exact Consumer s Surplus and Deadweght Loss, Amercan Economc Revew, Vol.71(4): Meyer S. and X. Yu (213): The Impacts of Producton Uncertantes on World Food Prces, Chna Agrcultural Economc Revew. Vol.5(4): Muhammad A., J. L. Seale, B. Meade, and A. Regm (211) Internatonal Evdence on Food Consumpton Patterns: An Update usng 25 Internatonal Comparson Program Data. Economc Research Servce, techncal Bulletn No USDA. Avalable: Robles, M. and Torero, M. (21) Understandng the mpact of hgh food prces n Latn Amerca. Economa, Vol. 1: World Bank (28) Global Purchasng Power Partes and Real Expendtures, 25 Internatonal Comparson Program. World Bank, USA. Avalable at : 7

8 25 Fgure 1, World Food Prce Index ( Jan. 25 Dec. 212, and 25=1 ) M1 25M5 25M9 26M1 26M5 26M9 27M1 27M5 27M9 28M1 28M5 28M9 29M1 29M5 29M9 21M1 21M5 21M9 211M1 211M5 211M9 212M1 212M5 212M9 Source: IMF Prmary Commodty Prces 8

9 Table 1, Welfare changes (M) n response to food prce change wth dfference scenaros Budget share for Food, Beverages & tobacco Compensated Own Prce Elastctes Welfare Change for Dfferent Scenaros of Prce Change Rates 1% 2% 3% 4% 5% Low-ncome Mddle-ncome Hgh-ncome Note: Low-ncome countres represent those wth real per capta ncome less than 15 percent of the U.S. level; mddle-ncome countres are those wth real per capta ncome between 15 and 45 percent of the U.S. level, and hgh-ncome countres wth have per capta ncome equal to or greater than 45 percent of the U.S. level. Budget share and prce elastctes are reported n Muhammad et al. (211)., 9