The Welfare Impacts of Commodity Price Volatility: Evidence from Rural Ethiopia

Transcription

1 The Welfare Imacts of Commodty Prce olatlty: Evdence from Rural Ethoa Marc F. Bellemare Chrstoher B. Barrett Davd R. Just March 26, 2013 Abstract How does commodty rce volatlty affect the welfare of rural households n develong countres, for whom hedgng and consumton smoothng are often dffcult? And when governments choose to ntervene n order to stablze commodty rces, as they often do, who gans the most? Ths aer develos an analytcal framework and an emrcal strategy to answer those questons, along wth llustratve emrcal results based on anel data from rural Ethoan households. Contrary to conventonal wsdom, we fnd that the welfare gans from elmnatng rce volatlty are ncreasng n household ncome, makng food rce stablzaton a dstrbutonally regressve olcy n ths context. JEL Classfcaton Codes: D13, D80, O12, Q12 Keywords: Commodty Prces, Ethoa, Prce Rsk, Prce Stablzaton, Prce olatlty, Rsk and Uncertanty Suggested Runnng Head: Prce Rsk wth Multle Commodtes * We thank Zack Brown and Pascale Schntzer for excellent research assstance as well as Stefan Dercon for addtonal hel wth the data. We also thank Davd Hennessy, two anonymous referees, semnar audences at Amercan, Florda, Illnos, Leuven, Mchgan State, Mnnesota, Namur, NC State, Ottawa, Pars School of Economcs, Tennessee, Texas A&M, Toulouse School of Economcs, as well as Western Mchgan, and artcants at the 2009 Mdwest Internatonal Economc Develoment Conference and the 2011 Mdwest Grou on Afrcan Poltcal Economy conference for useful comments and suggestons. All remanng errors are ours. Corresondng Author and Assstant Professor, Duke Unversty, Box 90312, Durham, NC , (919) , marc.bellemare@duke.edu. Stehen B. and Jance G. Ashley Professor of Aled Economcs and Professor of Economcs, Cornell Unversty, Ithaca, NY , (607) , cbb2@cornell.edu. Assocate Professor, Cornell Unversty, Ithaca, NY , (607) , dr3@cornell.edu. 1

2 1. Introducton Throughout hstory and all over the world, governments have frequently set commodty rce stablty the reducton of rce fluctuatons around a mean rce level as an mortant goal of economc olcy. Governments have tred to stablze rces usng a host of olcy nstruments, from buffer stocks to admnstratve rcng and from varable tarffs to marketng boards. These efforts have tycally met wth lmted success. After a erod of sgnfcant olcy research on the toc n the 1970s (Newbery and Stgltz 1981), by the early 1990s rce stablzaton had largely fallen off the olcy research agenda. Snce the md-1990s, however, commodty rces have been on a rollercoaster rde (Cashn and McDermott, 2002; Jacks et al., 2009; Roache, 2010). Food rce ten-year volatlty reached ts hghest level n almost 30 years n December 2010 (FAO, 2010). Food rce volatlty what we wll also refer to as rce uncertanty or rce rsk throughout ths aer over the ast decade or so, unctuated by the food crses of 2008 and of as well as the bggest one-month um n wheat rces n more than three decades n summer 2010, has rekndled wdesread oular nterest n commodty rce stablzaton. Several governments have recently rentroduced food rce stablzaton schemes. A smle search fnds more than fve tmes as many artcles on the toc n the meda over the last fve years as n the recedng fve years. 1 Meanwhle, maor nternatonal agences such as the Food and Agrculture Organzaton of the Unted Natons, the Internatonal Fund for Agrcultural Develoment and the World Bank have romnently dscussed olcy otons for food rce stablzaton for the frst tme n years (WB 2008, FAO 2010, IFAD 2011). The mulse toward state nterventons to stablze domestc food rces commonly arses because () households are wdely beleved to value rce stablty; () the oor are wdely erceved to suffer dsroortonately from food rce nstablty; and () futures and otons markets for hedgng aganst food rce rsk are commonly naccessble to consumers and oor roducers n develong countres (Newbery, 1989; Tmmer, 1989). Although few exerts would dsute clam () above, convncng 2

3 emrcal tests of clams () and () are notceably absent from the ublshed lterature. Indeed, gven the olcy mortance of the toc and economsts ast sketcsm about the net economc beneft of government rce stablzaton nterventons (Newbery and Stgltz, 1981; Krueger et al., 1988; Knudsen and Nash, 1990), our theoretcal and emrcal toolkts for understandng the relatonsh between rce volatlty and household welfare reman uzzlngly dated and lmted, esecally when t comes to emrcal alcatons. In ths aer, we address that mortant ga n the lterature by studyng whether ndeed () households value rce stablty and () the oor suffer dsroortonately from food rce nstablty. These are emrcal questons requrng household data and a clear, rgorous strategy for relatng a measure of household welfare to a measure of food rce volatlty. A smle regresson of household welfare ndcators (e.g., ncome, wealth, exendtures) on food rce varance s nfeasble for several reasons. 2 We therefore ta the establshed theoretcal lterature on rce rsk to derve an estmable measure of mult-commodty rce rsk averson and the assocated wllngness to ay for rce stablzaton. 3 We then use a well-resected household anel data set from rural Ethoa wth controls for household and dstrct-round fxed effects to generate llustratve estmates of multle commodty rce rsk averson across the household ncome dstrbuton. 4 As Sarrs et al. (2011,.48) note n ther nvestgaton of otental olcy resonses to food rce volatlty n low-ncome countres, the man roblem s not rce or quantty varatons er se, but rather unforeseen and undesrable deartures from exectatons regardng commodty rces. More recsely, we combne the theoretcal frameworks of Turnovsky et al. (1980) and Schmtz et al. (1981) wth the emrcal framework develoed by Fnkelshtan and Chalfant (1991) and extended by Barrett (1996). Recall that Turnovsky et al. showed how a ure consumer s reference for rce stablty deended only on a handful of arameters and then derved a smlar measure for multle commodtes. Our analyss nnovates by lookng at agrcultural households who are not ure 3

4 consumers, as they can both consume and roduce a number of commodtes and dervng a measure of wllngness to ay for rce stablzaton as a roorton of household ncome. Secfcally, we derve an estmable matrx of rce rsk averson over multle commodtes. Based on that matrx of rce rsk averson coeffcents, we further show how to derve household wllngness to ay (WTP) to stablze at ther means the rces of a set of commodtes. As we show n the emrcal results, the largest net roducers exhbt the greatest wllngness to ay for rce stablzaton, underscorng the ractcal mortance of ths extenson. We then aly ths measure to estmate the heterogeneous welfare effects of food rce volatlty among rural Ethoan households who both roduce and consume several commodtes characterzed by stochastc rces. Prces n our data are hghly varable: the coeffcents of varaton (.e., standard devaton/mean) range from 18 to 39 ercent among the commodty rces we study. We fnd that the average household s wllng to gve u 18 ercent of ts ncome to fully stablze the rce of the seven most mortant food commodtes n the data. We also fnd that gnorng the covarances between rces would lead to very slghtly underestmatng household WTP to stablze rces n ths context. Fnally, nonarametrc analyss suggests that n the rural Ethoan context the welfare gans of rce stablzaton are ncreasng n household ncome, contrary to conventonal wsdom. In other words, although vrtually everyone benefts from rce stablzaton, wealther households beneft more than oorer households. Ths s smlar recent fndngs by Mason and Myers (2013), who fnd that the Zamban Food Reserve Agency, whose goal was to stablze maze rces, largely beneftted relatvely wealthy roducers wthout havng any notceable effect on oor households. Our emrcal estmates are merely a frst, necessarly merfect contrbuton that we hoe regntes emrcal economc research on ressng olcy questons concernng commodty rce stablzaton. Ths queston s ntrnscally roblematc for emrcal research because t requres lausble statstcal exogenety of both ncomes and multle commodtes rce dstrbutons. Jont randomzaton of (or, 4

5 more generally, nstrumentaton for) the full vector s nfeasble n our, or robably any other, context. When we get to the emrcal llustraton, we argue that our dentfcaton strategy whch reles on longtudnal data, household fxed effects, and locaton-tme fxed effects s the best one can do, at least wth the these data and erhas wth any exstng household data set. But we emhasze the mortance of careful attenton to and forthrght declaraton of lkely sources of bas n estmaton. Ths s far too mortant an economc olcy queston to gnore out of concern for statstcal erfecton that s ntrnscally unattanable n general equlbrum roblems such as those assocated wth nonsearable agrcultural household models of the sort we emloy. 2. Theoretcal Framework Ths secton exlores the welfare mlcatons of multle commodty rce volatlty by secfyng a twoerod untary agrcultural household model (see onlne aendx A (Bellemare et al., 2013) for the basc model) and then dervng the household s matrx of rce rsk averson coeffcents. The agrcultural household model framework (Sngh, Squre and Strauss 1986) encomasses households dual roles as both consumers and roducers of the commodtes consdered. Ths allows us to summarze demand and suly sde factors n a sngle varable: marketable surlus (.e., the dfference between roducton and consumton). Households can be net buyers, net sellers, or autarkc, and can swtch among these ostons over tme. The effects of rce volatlty on roducer behavor and roft have been well-exlored n the theoretcal lterature. Outut rce uncertanty generally causes frms to emloy fewer nuts, forgong exected rofts n order to hedge aganst rce volatlty (Baron, 1970; Sandmo, 1971; Schmtz et al., 1981). 5 The analyss of commodty rce rsk has been extended theoretcally to ndvdual consumers (Deschams, 1973; Hanoch, 1977; Turnovsky et al., 1980; Newbery and Stgltz, 1981) who, gven the quas-convexty of the ndrect utlty functon, are generally thought to be rce rsk lovng for a secfc 5

6 commodty when the budget share of that commodty s not too large. But because agrcultural households can be both roducers and consumers of the same commodtes, t s entrely ossble for some households to be rce rsk averse, for others to be rce rsk neutral, and for yet others to be rce rsk lovng, although ror emrcal analyses have focused on ust a sngle commodty (Fnkelshtan and Chalfant 1991, 1997; Barrett, 1996). And whle Turnovsky et al. (1980) consdered the rce volatlty of multle commodtes, they only dd so theoretcally and for ure consumers. Gven that ndrect utlty functons the usual measure of welfare n mcroeconomc theory are defned over both ncome and a vector of rces, the lterature s focus on ncome rsk, extended at most to a sngle stochastc rce, ants an ncomlete cture of atttudes toward rsk as well as the macts thereof. More concretely, the lterature s of lmted usefulness n nformng the growng oular debates that surround food rce volatlty and food rce stablzaton olces, esecally n develong countres where many households both consume and roduce the commodtes n queston. Our nterest n rce nstablty requres at a mnmum a two-erod model, 6 wth at least one erod n whch agents make decsons subect to temoral uncertanty wth resect to rces. In what follows, we assume away other sources of volatlty (e.g., outut and ncome volatlty, the macts of whch are well-documented n the lterature), so as to focus solely on the macts of rce volatlty on household welfare. A smler, sngle commodty verson of ths framework was used by Barrett (1996) to exlan the exstence of the nverse farm sze roductvty relatonsh as a result of stale food cro rce rsk. In what follows, we extend Barrett s framework to the case of multle goods wth stochastc rces. We abstract from credt market, storage, and nformal transfer consderatons. Whle ncororatng the credt and nformal transfer asects of household behavor would undoubtedly make for a more realstc model of household behavor, we ot for a smler secfcaton so as to focus on the behavor of households n the face of temoral rce rsk. As regards storage, Tadesse and Guttormsen 6

7 (2011, ) note that n Ethoa, smallholder farmers sell the bulk of ther roduce rght after harvest to ay taxes and loans and to meet ther cash requrements for socal servces, ( ) few farmers store gran for long erods n order to beneft from temoral arbtrage, and how storage cost s generally very hgh n Ethoa. Enhancements to our admttedly arsmonous framework, whch wll have to be combned wth more detaled emrcal data, are thus left for future research Prce Rsk Averson over Multle Commodtes Suose a household maxmzes ther utlty of consumton subect to a budget constrant that reflects roducton decsons made subect to uncertanty about the vector = (,, ) of commodty rces faced by the household n a subsequent erod. The household can both consume and roduce each commodty, yeldng a vector of marketable surlus (roducton less consumton) of the observed commodtes, =,,. Negatve (ostve) values of any x ndcate net consumton (surlus). The household receves ncome from a number of sources: the cros t sells, ts labor endowment, ts endowment of other nuts, and transfers (e.g., remttances). As demonstrated n the more detaled model found n the onlne aendx A (Bellemare et al., 2013), ths model mles a varable ndrect utlty functon (, ), where s the exectaton oerator. Let denote the rce of commodty and denote the rce of commodty. Lkewse, let denote the frst dervatve of the ndrect utlty functon wth resect to ncome, denote the vector of second dervatves of the ndrect utlty functon wth resect to rces, and denote the vector of second dervatves of the ndrect utlty functon wth resect to ncome and rces, resectvely. We start from the matrx of second dervatves of the household s ndrect utlty functon relatve to the vector of rces faced by the household,.e.,, whch s such that, (1) 7

8 and derve the followng matrx of rce rsk averson coeffcents n onlne aendx B (Bellemare et al., 2013): where = = =, (2) = +, (3) s the marketable surlus of commodty (.e., the household s net suly of commodty, or the quantty suled mnus the quantty demanded by the household of commodty ), s the rce of commodty, s the budget share of the marketable surlus of commodty (.e., = ), s the ncome elastcty of marketable surlus of commodty, s the Arrow-Pratt coeffcent of relatve rsk averson of the household, and s the cross-rce elastcty of the marketable surlus of commodty relatve to the rce of commodty. The elements of the A matrx vary among households, leadng to heterogenety of rce rsk references n oulaton. There are no theoretcal restrctons on the sgn of any of the elements of. Indeed, the sgn of deends on () whether the household s a net buyer or a net seller of commodty,.e., on the sgn of ; () the sgn of the budget share of the marketable surlus of commodty,.e., ; () whether the household s coeffcent of relatve rsk averson s less or greater than the ncome elastcty of the marketable surlus of commodty,.e., ; and (v) the sgn and magntude of the elastcty of the marketable surlus of commodty wth resect to rce,.e.. That sad, however, matrx has a straghtforward nterretaton: the dagonal elements are analogous to Pratt s (1964) coeffcent of absolute (ncome) rsk averson, but wth resect to ndvdual rces nstead of ncome. Therefore, 1. > 0 mles that welfare s decreasng n the volatlty of the rce of,.e., that the household s rce rsk averse over, 8

9 2. = 0 mles that welfare s unaffected by the volatlty of the rce of,.e., that the household s rce rsk neutral, and 3. < 0 mles that welfare s ncreasng n the volatlty of the rce of,.e., that the household s rce rsk lovng over. Prce rsk averson s the classc concern of the lterature on commodty rce stablzaton (Deschams, 1973; Hanoch, 1974, Turnovsky, 1978; Turnovsky et al., 1980; Newbery and Stgltz, 1981). The dagonal elements, measure the drect macts on welfare of the volatlty n each rce,.e., the mact on welfare of the varance of each rce, holdng everythng else constant. But rces almost never fluctuate alone commodtes are, to varyng degrees, tycally substtutes for or comlements to one another. 7 The nterretaton of the off-dagonal terms s a bt trcker. Because rces commonly covary, the off-dagonal elements of the matrx of rce rsk averson measure the ndrect macts on welfare of the volatlty n each rce,.e., the macts on welfare of the covarance between a gven rce and the rces of all the other commodtes consdered, holdng everythng else constant. Ths reflects the mact on welfare of changes n covaraton wthn a ortfolo. To obtan the welfare macts of rce volatlty, one thus needs to consder both () the varance n each commodty rce seres as well as () the covarances among these rce seres. Ignorng the covarances between rces leads n rncle to a based estmate of the total (.e., drect and ndrect) welfare macts of rce vector volatlty, although the sgn of the bas s mossble to determne ex ante. The off-dagonal terms (.e., the ndrect effects of rce rsk, or rce covarance effects) of the matrx of rce rsk averson have so far been gnored n the lterature. Our analyss s the frst to quantfy ther mortance relatve to the dagonal terms (.e., the drect effects of rce rsk, or rce varance effects) of the matrx of rce rsk averson. Taken as a whole, the matrx of rce rsk averson coeffcent thus seaks drectly to household references wth resect to multvarate rce rsk. 9

10 Although there are no restrctons on the sgn of the elements of matrx, the theory mles a testable symmetry restrcton on the estmated rce rsk averson coeffcents. Wth adequate data, one can test the null hyothess : = for all (4) whch, for a matrx of rce rsk averson defned over K commodtes, reresents ( 1)/2 testable restrctons. Intutvely, the emrcal content of equaton (4) s smly that the mact on household welfare of the covarance between rces and should be the same as the mact on household welfare of the covarance between rces and. Ths s analogous to symmetry of the Slutsky matrx; the followng rooston summarzes ths result. Prooston 1: Under the recedng assumtons, f the cross-artals of the household s ndrect utlty functon exst and are contnuous at all onts on some oen set, symmetry of the matrx of rce rsk averson coeffcents s equvalent to symmetry of the Slutsky matrx. Proof: See onlne aendx C (Bellemare et al., 2013). Moreover, the symmetry of the Slutsky matrx and the symmetry of the matrx of rce rsk averson coeffcents have the same emrcal content n that they both embody household ratonalty. So ths offers a useful alternatve ath to testng canoncal neoclasscal assumtons of household behavor that are often dffcult to test usng Slutsky matrces Wllngness to Pay for Prce Stablzaton As we dscussed n the ntroducton, olcy makers routnely try to stablze one or more commodty rces. But what are the welfare effects of such efforts, f and when they are successful? Ths subsecton derves the WTP measures necessary to establsh the welfare gans from artal rce stablzaton,.e., from stablzng one or more commodty rces. 8 10

11 Recall that we model rsky choce as a two erod model n whch decsons are made n the frst erod, before the realzaton of rce uncertanty, and rces (and thus utlty) are realzed n the second erod. We can then defne the WTP to elmnate all rce rsk as the amount of money whch, when subtracted from wealth gven exected rce levels ( ), results n the ndvdual beng ndfferent to the random rces and ncome, or,, = (, ), (5) where ncome may be random. Followng the standard rocedure n the lterature, we aroxmate the left hand sde of ths equaton usng a frst order Taylor seres exanson n drectons of certanty around the mean rce and ncome, and usng a second order Taylor seres exanson around mean rce and ncome n all dmensons nvolvng rsk (see, for examle, Arrow s (1971) dervaton of the coeffcent of absolute rsk averson). Followng the dervatons n onlne aendx D (Bellemare et al., 2013) we ultmately obtan the followng measure of WTP to stablze the rces of all commodtes: = + 2. (6) Assumng that ncome (whch s lkely to be locally determned) s uncorrelated wth rces (whch are lkely to be globally determned), 9 then ths smlfes to =. (7) Thus, WTP s ust the sum of the covarances of rces weghted by the money metrc mact of rce varaton on ndrect utlty. If nstead one s nterested n stablzng only the rce of a sngle commodty, WTP smlfes to = (8) The WTP fgures derved above rovde the transfer ayment a olcymaker would need to make to the household n order to comensate the household for the uncertanty t bears over. Fnkelshtan 11

12 and Chalfant (1997) ntroduced a smlar measure, but ther framework consdered only one stochastc rce, whch necessarly gnored the covarance between rces. Equaton (8), however, ndcates that even (.e., the WTP to stablze the rce of a sngle commodty ) deends on the covarance between the rce and the rces of other commodtes. Stablzng the rce of one commodty wll have mlcatons for the roducton and consumton of substtutes and comlements that can mact welfare through ortfolo effects. In other words, a rce stablzaton olcy focusng solely on the rce of commodty would bas the estmated WTP for commodty, unless = 0 or = 0 for all. It s mossble to determne a ror the sgn of the bas, whch deends on the sgn of the covarances and on the sgn of the off-dagonal terms of the matrx of rce rsk averson. Lastly, note that n what follows, WTP s always exressed as a roorton of household ncome, so as to make WTP comarable across households. Therefore, the remander of ths aer dscusses / rather than. 3. Data and Descrtve Statstcs We emrcally llustrate the theory develoed n the revous secton by estmatng the rce rsk averson coeffcent matrx and household WTP for rce stablzaton usng the 1994a, 1994b, 1995, and 1997 rounds of the wdely-used and well-resected Ethoan Rural Household Survey (ERHS) data. 10 Tadesse and Guttormsen (2011,. 88) note that, n Ethoa, [a] rse or declne n rce trend s not as bad as ts varablty. ( ) [P]rce volatlty and, more recently, food rce nflaton reman the overrdng natonal concerns. Post-reform gran rces are subect to sgnfcant and contnung nterannual rce volatlty that ranks among the hghest n the develong world. 12

13 The ERHS recorded both household consumton and roducton decsons usng a standardzed survey nstrument across the rounds we retan for analyss. The samle ncludes a total of 1494 households across 16 dstrcts (woreda) wth an attrton rate of only 2 ercent across the four rounds selected for analyss (Dercon and Krshnan, 1998). 11 The average household n the data was observed 5.7 tmes over four rounds and three seasons (.e., three-month erods), 12 wth only 7 households aearng only once n the data. The estmatons n ths aer thus rely on a samle of 8,518 observatons. 13 In what follows, we focus on coffee, maze, beans, barley, wheat, teff, and sorghum, whch are the most mortant seven commodtes n the data when consderng the fracton of households roducng or consumng them. Table 1 resents descrtve statstcs: a ostve mean marketable surlus ndcates that the average household s a net seller of a commodty, and a negatve mean marketable surlus ndcates that the average household s a net buyer of a commodty, so the average household s a net buyer of every commodty. For each commodty, a sgnfcant number of households have a marketable surlus of zero, however, because they nether bought nor sold that commodty. 14 Per equaton (3), a household s rce rsk neutral for any commodty for whch ts net marketable surlus equals zero. If a household nether buys or sells of a gven commodty, t s unaffected by fluctuatons n the rce of that commodty. Table 2 further characterzes the deendent varables by focusng on the nonzero marketable surlus observatons and by comarng descrtve statstcs between net buyers and net sellers. Excet for coffee and wheat, the urchases of the average net buyer household exceed the sales of the average net seller household. For every commodty, there are many households n both the net buyer, autarkc, and net seller categores, reflectng otentally heterogeneous welfare effects wth resect to commodty rce volatlty n rural Ethoa. Table 3 lsts the mean real (.e., corrected for the consumer rce ndex) rce n Ethoan brr for each of the seven commodtes we study, 15 the average seasonal household ncome, and the average 13

14 seasonal nonzero household ncome n the full samle. The ncome measure used n ths aer s the sum of roceeds from labor ncome (both off-farm emloyment and non-farm self-emloyment), cro sales, remttances, sales of assets, ncludng lvestock, and sales of anmal roducts for each erod. Average ncome from the aforementoned sources s dfferent from zero n only about 82 ercent of cases, whch exlans why the average seasonal ncome of about $94 ($376 annually) may seem low. When focusng on nonzero ncome, the average seasonal ncome ncreases to about $106 ($424 annually). These fgures, whle seemngly low, encomass all the sources of ncome avalable n the data and reflect the extreme overty revalent n rural Ethoa. Table 3 also resents the budget share of each stale commodty. Food reresents the overwhelmng maorty of rural Ethoan household exendtures, at least 85 ercent. Ths falls on the uer end of global estmates of such budget shares, reflectng the extreme overty of ths oulaton, the conscuous absence of much other than food to urchase n rural Ethoa, and our nablty to mute the value of land rental ncome and exendture n the ERHS data. Purchases of teff and coffee reresent the largest budget shares, wth 21 and 15 ercent of the average household budget, resectvely. Although a budget share of 15 ercent may seem very hgh for coffee, recall that coffee lays an mortant role n Ethoan culture, where the coffee ceremony s culturally central (Pankhurst, 1997). Note that households both urchase and sell green coffee beans, so that the same commodty s beng comared as art of the marketable surlus of coffee. Fnally, because rce varances and covarances lay an mortant role n comutng household WTP for rce stablzaton, table 4 reorts the varance-covarance matrx for the rces of the seven stale commodtes. Coffee exhbts by far the most rce volatlty. Snce coffee s also one of only two cros (along wth wheat) where net sellers mean net sales volumes exceed net buyers mean net urchase volumes recall that net sellers are always rce rsk averse n the sngle stochastc rce settng (Fnkelshtan and Chalfant 1991, Barrett 1996) these descrtve statstcs suggest that 14

15 stablzaton of coffee rces s more lkely to generate welfare gans than would stablzaton of other commodty rces. But that remans an emrcal queston, and our estmaton results (Secton 5) actually suggest otherwse. 4. Emrcal Framework For each commodty, we estmate a reduced form regresson of the marketable surlus of that commodty as a functon of outut rces and household ncome wth controls for a range of observables and unobservables. We use dstrct-round fxed effects to control for the nut rces and weather condtons faced by each household n each dstrct n each round as well as for macroeconomc factors such as nflaton, nterest rates, the nternatonal rce of commodtes, etc. Tme-nvarant household fxed effects rovde further control for household-secfc references, roducton skll, transactons costs and bohyscal condtons related to locaton, socal relatonshs that may confer referental rcng or access to ncome-earnng oortuntes, and other household-secfc transacton costs that determne whether a household s a net buyer of a commodty, autarkc wth resect to t, or a net seller of the same commodty (de Janvry et al., 1991; Bellemare and Barrett, 2006). The use of household and dstrct-round fxed effects also controls for access to storage, so that our estmates should largely account for what lttle commodty storage there s n rural Ethoa (Tadesse and Guttormsen, 2011). We estmate the followng marketable surlus functons for the seven commodtes dscussed n the revous secton: l = + l + l + + l + l (9) where an astersk (*) denotes a varable transformed usng the nverse hyerbolc sne transformaton a logarthmc-lke transformaton that allows keeng negatve as well as zero-valued observatons and whch allows nterretng coeffcents as elastctes suggested by Burbdge et al. (1988), and used by 15

16 MacKnnon and Magee (1990), Pence (2006), and Moss and Shonkwler (1993) 16 and where denotes a secfc commodty (.e., coffee, maze, beans, barley, wheat, teff, or sorghum), 17 k denotes the household, l denotes the dstrct, and t denotes the round; denotes household ncome; s a vector of the rces of all (observed) commodtes (ncludng ); s a vector of household dummes; l s a vector of dstrct-round dummes; and s a mean zero, d error term. The estmated coeffcent on household ncome n equaton 9 s the ncome elastcty of the marketable surlus of commodty, or n the notaton of equaton 3 n secton 2. Lkewse, the estmated coeffcent on rce n equaton 9 s the elastcty of the marketable surlus of commodty wth resect to rce, or n the notaton of secton 2. We estmate equaton (9) by seemngly unrelated regressons (SUR), snce SUR estmaton brngs an effcency gan over estmatng the varous equatons n the system searately when the deendent varables are all regressed on the same set of regressors. We estmate equaton (9) over 1,494 households across seven erods (.e., four rounds and three seasons), clusterng standard errors at the dstrct level. No household was observed over all four rounds and three seasons; the number of observatons er household ranged from one to sx. 18 We also nclude all commodty rces avalable n the data (.e., coffee, maze, beans, barley, wheat, teff, sorghum, otatoes, onons, cabbage, mlk, tella, 19 sugar, salt, and cookng ol) as exlanatory varables. Comutaton of own- and cross-rce elastctes (.e., the ε terms) as well as of ncome elastctes (.e., the η terms) s straghtforward, as the estmated coeffcents on own- and cross-rce as well as on ncome n equaton (9) are elastctes gven the nverse hyerbolc sne transformaton. We then combne these estmates to obtan the ont estmate = +, (10) whose standard error s obtaned by the delta method. Gven that marketable surlus s often zero, we use the mean of the and varables to comute budget shares. 20 Because our data do not allow 16

17 drectly estmatng R, the coeffcent of relatve rsk averson, we estmate the coeffcents for = 1, whch s well wthn the range of credble values found n the lterature (Frend and Blume, 1975; Hansen and Sngleton, 1982; Chavas and Holt, 1993; Saha et al., 1994). What would the deal data set to estmate equaton (9) look lke? Ideally, one would want to ensure statstcal ndeendence of rces and ncome from the error term n the marketable surlus equaton and thereby obtan causal estmates of the, and elastcty arameters. Randomzng over a multdmensonal vector of rces and ncome s ractcally nfeasble, however, as s any other aroach to generatng a vector of vald nstrumental varables for rce and ncome regressors that could otherwse be endogenous. The best feasble oton for ths roblem s therefore anel data analyss, whch allows controllng for unobservable household, dstrct and erod characterstcs. Household fxed effects should control for the systematc way n whch each household forms ts rce exectatons, and dstrct-round fxed effects should control for deartures from the systematc way n whch each household forms ts rce exectatons by accountng for the rce nformaton avalable to each household n a gven dstrct n a gven tme erod. Lkewse, f a household s status as a net buyer, autarkc, or a net seller wth resect to a gven commodty s rmarly drven by ts references for roducng and consumng that secfc commodty, by nnate skll, by locaton-secfc endowments, or by the household-secfc transactons costs t faces (de Janvry et al., 1991; Goetz, 1992; Bellemare and Barrett, 2006), these factors are accounted for by the household fxed effect. Whle ths anel data aroach does not urge the error term of all rosectve correlaton wth the exlanatory varables n equaton (9), t surely urges much of t and s ultmately the best one can do n terms of emrcal dentfcaton on ths mortant emrcal queston, as we dscuss n greater detal n onlne aendx E (Bellemare et al., 2013). Stll, we cauton the reader aganst ether nterretng our estmates for the coeffcents n equaton (9) as strctly causal or gnorng crucal olcy questons for whch ronclad dentfcaton s nherently elusve. We subect our 17

18 estmates to a range of robustness tests as a check on our fndngs. The core, qualtatve fndngs rove nvarant to a bevy of robustness checks. In the emrcal work below, the arameters the rce elastctes of marketable surlus are dentfed by () the varaton n rces wthn each household over tme (gven our use of household fxed effects); and () the between-dstrct varaton wthn a gven round and over tme for each dstrct (gven our use of dstrct-round fxed effects). For examle, the rce of maze s common to all the households n a gven dstrct n a gven round, so controllng for the unobserved heterogenety between households and the unobserved heterogenety between dstrct-round, the vector of coeffcents the vector of rce elastctes of marketable surlus s dentfed because rces vary over tme for each household and because rces also vary between each dstrct-round both across sace and over tme. The dentfcaton of the ncome elastcty of marketable surlus s more straghtforward gven that ncome vares both wthn households over tme and between households n a gven dstrct wthn a gven round. Condtonal on a household s status as a net buyer, autarkc, or a net seller of a gven commodty, ts urchase or sales of that commodty s drven by ts references and by the household-secfc transactons costs t faces but also by clmatc and other envronmental fluctuatons that affect roducton (Sherlund et al., 2002), whch are largely accounted for by the dstrct-round fxed effect, and by rces and ncome, for whch we control. See onlne aendx E (Bellemare et al., 2013) for an extended dscusson of our dentfcaton strategy and of rosectve sources of bas n estmaton. 5. Estmaton Results and Hyothess Tests Ths secton frst resents estmaton results for the marketable surlus equaton (9) for all seven commodtes retaned for analyss. Gven that these results are ancllary, we only brefly dscuss them so 18

19 as to devote the bulk of our dscusson to the estmated matrx of rce rsk averson and, more mortantly, to our estmates of household wllngness to ay for rce stablzaton. Table 5 resents estmaton results for the seven marketable surlus equatons. Intutvely, one would exect the own-rce elastcty coeffcents,, to be ostve. That s, as the rce of commodty ncreases, households buy less or sell more of that same commodty, deendng on whether they are net buyers or net sellers to begn wth. In sx cases out of seven (coffee, maze, beans, barley, teff, and sorghum), estmated own-rce elastctes of marketable surlus are ostve, and those coeffcents are statstcally sgnfcant n three of those sx cases (coffee, maze, and barley). Only one estmated ownrce elastcty (wheat) s negatve, whch s lkely due to the roft effect dentfed by Sngh et al. (1986). The roft effect concerns the added mact on demand of the ncome the household enoys from the hgher rce for the commodty t grows; for net sellers wth a relatvely hgh ncome elastcty of demand (as dstnct from marketable surlus) for the commodty, one can get ths result. Ths seems lausble for wheat n ths settng. Smlarly, estmated ncome elastcty coeffcents are ostve and statstcally sgnfcant n sx out of seven cases (coffee, maze, barley, wheat, teff, and sorghum), wth the ncome elastcty of the remanng marketable surlus not sgnfcantly dfferent from zero. Ths could artly reflect resdual endogenety of ncome as a functon of marketable surlus but almost surely reflects the crucal role cash ncome lays n fnancng roductvty-enhancng nuts n ths settng, such that hgher ncome s routnely causally assocated wth hgher outut because t relaxes the lqudty constrant roducers face n fnancng the urchase of nuts, such as fertlzer and mroved seeds, that offer hgh margnal returns (Dercon and Chrstaensen 2011). We can llustrate the nterretaton of coeffcents n table 5 by takng coffee as an examle. In that case, for a 1 ercent ncrease n the rce of coffee, the marketable surlus of coffee ncreases by 0.5 ercent on average as a result of net buyers of coffee urchasng less coffee and of net sellers of coffee 19

20 sellng more coffee. Lkewse, for a 1 ercent ncrease n household ncome, the marketable surlus of coffee ncreases by 0.1 ercent Prce Rsk Averson Matrx We use the estmaton results reorted n table 5 to comute coeffcents of own- and cross-rce rsk averson and use these coeffcents to construct the matrx of rce rsk averson n table 6a. Because all rces are measured n brr and all quanttes are measured n klograms, the varous coeffcents of rce rsk averson n table 5 can be comared to one another. Lookng at the dagonal elements of matrx, t aears that households n the data are on average most sgnfcantly own-rce rsk averse over maze (591.46), barley (268.86), and teff (124.98) the commodtes wth the greatest net urchase volumes and least rce rsk averse over coffee (7.38), wheat (15.09), and beans (31.89). Of the latter three commodtes, two coffee and beans have the lowest mean net sales volumes among net sellers and the lowest mean net urchases volumes among net buyers, as reflected n Table 2. Most rural Ethoans rce rsk exosure to these latter commodtes s qute modest, hence the relatvely low rce rsk averson coeffcent estmates. The statstcal sgnfcance and magntude of the off-dagonal elements of the estmated matrx underscore the mortance of estmatng rce rsk averson n a multvarate context. Indeed, all 42 offdagonal elements of are statstcally sgnfcant at the 1 ercent level. Lookng at secfc coeffcents, note that when t comes to cross-rce rsk averson, the average household n the data s most rce rsk averse over the rces of maze and teff (readng coeffcents as row-column, gven the ostve sgns on the maze-teff and teff-maze coeffcents), and most rce rsk lovng over the rces of maze and wheat (gven the negatve sgns on the maze-wheat and wheat-maze coeffcents). In other words, whereas the average household n the data s hurt by covarance n the rces of maze and teff, t benefts from covarance n the rces of maze and wheat. In fact, for maze, those cross-rce effects clearly domnate 20

21 the own-rce effect. Indeed, the maze-teff (195.78), teff-maze (282.49), maze-wheat ( ), and wheat-maze ( ) coeffcents of cross-rce rsk averson are all much larger n absolute value than the wheat-wheat coeffcent of own-rce rsk averson (15.09). We llustrate the necessty of our mult-commodty aroach wth the examle of teff, gven the ostve coeffcent (124.98) of own-rce rsk averson for teff. Frst, note that n table 6a, households are, on average, rsk averse over the rce of teff. Ths s the drect effect of fluctuatons n the rce of teff. Recall, however, that the covarances between rce of teff and the rces of other commodtes were all ostve n table 4, so that an ncrease n the volatlty of the rce of teff s correlated wth varaton n other food rces, over whch households are ether rsk averse (coffee, maze, and wheat) or rsk lovng (beans, barley, and sorghum). Ths generates an ndrect welfare effect of volatlty n the rce of teff through ts covarance wth other food rces. To obtan the total welfare effect n the rce of teff, one needs to consder the coeffcent estmates n the teff row or the coeffcent estmates n the teff column of matrx, as we dscuss n the next secton. In addton, we unool the data and resent the dagonal terms of the matrx of coeffcents of own-rce rsk averson for each commodty by slttng the samle between the net buyers and net sellers n table 6b. In that case, we note that net buyers of all commodtes but wheat are on average rce rsk averse, net sellers of coffee, wheat, teff, and sorghum are on average rce rsk averse, whle net sellers of maze, beans, and barley aear rce rsk lovng, on average. Recall that the theoretcal framework n secton 2 mled symmetry of matrx. We thus conduct a Hotellng (1931) test of multvarate means equalty whose null hyothess of symmetry s such that : = for all. Gven that there are 21 coeffcents on ether sde of the dagonal of matrx, the test contans 21 restrctons and s run over all 8518 observatons, so that the F-statstc of for the test should be comared wth the (21,8497) crtcal value. One restrcton s droed due to multcollnearty, however, so we comare (20,8498) crtcal value. As n most other studes 21

22 concerned wth testng household ratonalty (see, for examle, Brownng and Chaor, 1998), and as the reader wll most lkely already have nferred from lookng at the off-dagonal coeffcent of matrx, we reect the null hyothess of household ratonalty at less than the one ercent level Wllngness to Pay Estmates for Prce Stablzaton Recall from secton 2.4 that the WTP for stablzaton of a sngle commodty rce can be estmated by consderng ether the rows or columns of matrx of rce rsk averson, but that for total WTP, both values concde by constructon. Table 7 shows the estmated average household WTP (exressed as a roorton of household ncome) to stablze the rces of ndvdual commodtes as well as to stablze the rces of all seven commodtes consdered n ths aer. We start by estmatng WTP gnorng the covarances between rces (Fnkelshtan and Chalfant, 1991), an omsson that bases downward commodty-secfc and total measures of WTP to stablze rces. In that case, note that the commodty-secfc WTP estmates are all statstcally sgnfcant and that the average household n the data would be wllng to gve u 17 ercent of ts ncome n order to stablze the rces of all seven commodtes retaned for analyss. If ths seems a rather hgh fgure, kee n mnd that full rce stablzaton s ractcally nfeasble, so ths fgure reresents an uer bound on the welfare gans assocated wth rce stablzaton. Lookng at the WTP derved from the columns of n the second column of table 7, the average WTP estmates are all statstcally sgnfcant. The commodty for whch the average household would be wllng to ay the hghest roorton of ts budget to stablze the rce s coffee wth 11 ercent, and the commodty for whch the average household would be wllng to ay the smallest roorton of ts budget s beans wth -2 ercent. In other words, consderng the columns of matrx, the average household n the data would be wllng to gve u 11 ercent of ts ncome to stablze the rce of 22

23 coffee, but t would need to be ad 2 ercent of ts ncome n order to accet a stablzaton n the rce of beans. Lkewse, lookng at the WTP derved from the rows of n the thrd column of table 7, the average WTP estmates are once agan all statstcally sgnfcant. The commodty for whch the average household would be wllng to ay the hghest roorton of ts budget to stablze the rce s once agan coffee wth 8 ercent, and the commodty for whch the average household would be wllng to ay the smallest roorton of ts budget s barley, less than 1 ercent. Ultmately, columns 2 and 3 of table 7 suggest that the average household n the data would be wllng to gve u 18 ercent of ts ncome n order to smultaneously and comletely stablze the rces of coffee, maze, beans, barley, wheat, teff, and sorghum. That estmate s statstcally sgnfcant at the one ercent level, whch suggests aggregate wllngness to ay to stablze food commodty rces n rural Ethoa under the assumton that the average household s coeffcent of relatve rsk averson = 1. The reader mght wonder why there s a seemng contradcton between the magntude of the estmate coeffcents of rce rsk averson n matrx n table 6a, n whch the average household seemed to care most about food stales (.e., maze, barley, teff) and the magntude of the estmated WTPs for rce stablzaton n table 7, n whch the average household seems to care most about a nonstale (.e., coffee). The dscreancy between the coeffcents n matrx and the WTP measures s due to the fact that whle the WTP measures n equatons (7) and (8) nclude rces varances and covarances, the coeffcents of rce rsk averson n equaton (3) do not nclude these varances and covarances. So although households are a ror relatvely less rsk averse wth resect to the rce of coffee than they are for other commodtes, the fact that ther WTP to stablze the rce of coffee domnates ther WTP to stablze the rces of other commodtes s due to the consderably more volatle rce of coffee. In other words, whereas equaton (3) denotes references for margnal tradeoffs 23

24 n rce rsk, equatons (7) and (8) derve the WTP as a combnaton of those references and the magntude of the rce rsks nvolved. In order to be more secfc about the dstrbuton of the welfare gans from rce stablzaton, fgure 1 lots the results of a second-degree fractonal olynomal regresson of the estmated household-secfc WTP to stablze the rces of all seven commodtes on household ncome, along wth the assocated 95 ercent confdence band. 21 Fgure 1 ndcates that although the average WTP to stablze the rces of coffee, maze, barley, beans, wheat, teff, and sorghum all at once s ostve at all levels of ncome, households are wllng to gve u an ncreasng amount of ther ncome n order to stablze rces as they get wealther. Ths goes aganst the conventonal wsdom that holds that the oor n develong countres are the ones who are most hurt by rce volatlty. The ntuton behnd the result n fgure 1 s that snce roducers are more lkely to be hurt by rce volatlty (Sandmo, 1971), and snce the wealther households n our data are more lkely to be roducers, a ostve relatonsh naturally arses between ncome and WTP to stablze rces. The fact that relatvely wealther rural households aear to be hurt more by rce volatlty than oorer rural households may also go a long way toward exlanng the oltcal economy of food rces n the develong world, where commodty rce stablzaton n the sense of damenng varance, rather than reducng the lkelhood of rce skes s usually a concern of food roducers, who tend to be relatvely wealther rural households, rather than of food consumers (Lton, 1977, Bates 1981; Barrett, 1999; Lndert, 1991; van de Walle, 2001) Lmtatons The theoretcal dervatons n secton 2 and the emrcal framework n secton 4 rovde a useful methodology wth whch to study the welfare macts of rce volatlty. Lkewse, the results n ths 24

25 secton llustrate the emrcal alcaton of the methodology. Those results, however, suffer from mortant lmtatons that need to be acknowledged and dscussed. Frst, recall that we have assumed away other sources of volatlty (ncome, outut, etc.) n order to focus solely on rce rsk averson,.e., on the welfare macts of rce volatlty. But recall that n aled mcroeconomcs, welfare s reresented by the ndrect utlty functon, whch deends on both the rces faced by the ndvdual or household as well as on the ndvdual or household s ncome. In order to resent a comlete cture of rsk averson, then, one would need to take nto consderaton the fact that ncome s also stochastc. As derved n onlne aendx A (Bellemare et al., 2013) and dscussed n secton 2, the calculatons here are only vald f other stochastc sources of ncome are uncorrelated wth rce rsk. It haens that none of the bvarate correlaton coeffcents between rces and ncome n the ERHS data are statstcally sgnfcantly dfferent from zero at the ten ercent level, but ndeendence cannot be taken for granted. Second, n the exected utlty (EU) framework whch we adot n ths aer, the welfare costs of rsk generally tend to be of second order. As one revewer helfully onted out, ths leads to wellknown ssues such as the aarent low welfare cost of macroeconomc volatlty. If we take those ssues serously, however, t may mean that the welfare costs of volatlty are much hgher than normally acknowledged (Grant and Quggn, 2005). So whle the EU framework s a convenent tool wth whch to analyze behavor, t s far from erfect, as the lterature on behavoral anomales wth resect to and deartures from the EU framework demonstrates. Our reecton of the symmetry mlcaton of the matrx of rce rsk averson coeffcents renforces a vast lterature that calls nto queston canoncal assumtons of neoclasscal consumer and roducer theory. Extendng the analyss of rce rsk averson to more general models of behavor s an nterestng toc for future research. Thrd, the methodology develoed n ths aer only accounts for the statc costs of volatlty. But there are also dynamc costs, whch may be much more mortant. For examle, households may decde 25

26 to wthdraw ther chldren from school, forgo some nvestments n health, or draw down ther assets n order to mantan a secfc level of consumton after food rce shocks (Carter and Barrett, 2006). These cong behavors may have long-term consequences on household welfare whch our methodology cannot cature. So whle our emrcal results gve us a glmse of the generally negatve macts food rce volatlty can have on welfare, they rovde an ncomlete cture. Nestng analyss of the welfare effects of rce volatlty wthn a structural dynamc model esecally one wth rosectve nonlneartes that mght gve rse to overty tras would reresent an mortant extenson of the current model. Lastly, kee n mnd the emrcal concerns dentfed n secton 4.2. Whle our use of anel data allows controllng for much rosectve statstcal endogenety and s ultmately the best one can do n ths class of roblem, we once agan cauton the reader aganst nterretng Table 5 s estmates for the coeffcents n equaton (9) as strctly causal. We encourage readers to focus less on the recse quanttatve estmates than on the core qualtatve fndngs: the average rural Ethoan household s rce rsk averse over these seven commodtes, but the welfare loss due to commodty rce volatlty s ncreasng n ncome Robustness Checks An anonymous revewer and the edtor n charge encouraged us to dscuss the robustness of our results. In a revous verson, nstead of alyng the nverse hyerbolc sne transformaton to all marketable surluses, rces, and ncomes, we regressed marketable surluses n levels on the logarthms of rces and ncomes. Dong so led to results that were somewhat smlar to those n fgure 1, wth the exceton that, on average, households n the left tal of the ncome dstrbuton aeared rce rsk lovng (.e., they had a negatve WTP for rce stablzaton) rather than rce rsk averse, as n fgure 1. The fndngs 26