Poverty Analysis Using an International Cross-Country Demand System

Transcription

1 Publc Dsclosure Authorzed Publc Dsclosure Authorzed Publc Dsclosure Authorzed Publc Dsclosure Authorzed Polcy Research Workng Paper 4285 Poverty Analyss Usng an Internatonal Cross-Country Demand System The World Bank Development Research Group Trade Team July 2007 J. A. L. Cranfeld Paul V. Preckel Thomas W. Hertel WPS4285

2 Polcy Research Workng Paper 4285 Abstract Ths paper proposes a new method for ex ante analyss of the poverty mpacts arsng from polcy reforms. Three nnovatons underle ths approach. The frst s the estmaton of a global demand system usng a combnaton of mcro-data from household surveys and macro-data from the Internatonal Comparsons Project (ICP). Estmaton s undertaken n a manner that reconcles these two sources of nformaton, explctly recognzng that per capta natonal demands are an aggregaton of the dsaggregated, ndvdual household demands. The second nnovaton relates to a methodology for post-estmaton calbraton of the global demand system, gvng rse to country-specfc demand systems and an assocated expendture functon whch, when aggregated across the expendture dstrbuton, reproduce observed per capta budget shares exactly. Ths leads to the thrd nnovaton, whch s the establshment of a unque poverty level of utlty and an approprately modfed set of Foster-Greer-Thorbecke poverty measures. Wth these tools n hand, the authors are able to calculate the change n the head-count of poverty, poverty gap, and squared poverty gap arsng from polcy reforms, where the poverty measures are derved usng a unque poverty level of utlty, rather than an ncome or expendture-based measure. They use these technques wth a demand system for food, other nondurables and servces estmated usng a combnaton of 1996 ICP data set and natonal expendture dstrbuton data. Calbraton s demonstrated for three countres for whch household survey expendture data are used durng estmaton Indonesa, the Phlppnes and Thaland. To show the usefulness of these calbrated models for polcy analyss, the authors assess the effects of an assumed 5 percent food prce rse as mght be realzed n the wake of a multlateral trade agreement. Results llustrate the mportant role of subsstence expendtures at lowest ncome levels, but of dscretonary expendture at hgher ncome levels. The welfare analyss underscores the relatvely large mpact of the prce hke on poorer households, whle a modfed Foster-Greer-Thorbecke poverty measure shows that the 5 percent prce rse ncreases the ncdence and ntensty of poverty n all three cases, although the specfc effects vary consderably by country. Ths paper a product of the Trade Team, Development Research Group s part of a larger effort n the group to support poverty analyss and trade program. Copes of the paper are avalable free from the World Bank, 1818 H Street NW, Washngton, DC Please contact Paulna Flewtt, room MC3-333, telephone , fax , emal address pflewtt@worldbank.org. Polcy Research Workng Papers are also posted on the Web at worldbank.org. J. A. L. Cranfeld may be contacted at jcranfe@uoguelph.ca. July (49 pages) The Polcy Research Workng Paper Seres dssemnates the fndngs of work n progress to encourage the exchange of deas about development ssues. An objectve of the seres s to get the fndngs out quckly, even f the presentatons are less than fully polshed. The papers carry the names of the authors and should be cted accordngly. The fndngs, nterpretatons, and conclusons expressed n ths paper are entrely those of the authors. They do not necessarly represent the vews of the Internatonal Bank for Reconstructon and Development/World Bank and ts afflated organzatons, or those of the Executve Drectors of the World Bank or the governments they represent. Produced by the Research Support Team

3 POVERTY ANALYSIS USING AN INTERNATIONAL CROSS-COUNTRY DEMAND SYSTEM J. A. L. Cranfeld 1, Paul V. Preckel 2 & Thomas W. Hertel 2 JEL Classfcaton: D1, C4, I3 Keywords: Aggregaton, consumer demands, expendture dstrbuton; poverty 1. Assocate Professor and contact author, Department of Agrcultural Economcs and Busness, Unversty of Guelph, Guelph, Ontaro, Canada, N1G 2W1, Telephone: (519) , Fax: (519) , e-mal: jcranfe@uoguelph.ca. 2. Professor, Department of Agrcultural Economcs, Purdue Unversty, West Lafayette, Indana, U.S.A., Any errors or omssons reman the responsblty of the authors. The authors would lke to thank Wll Martn for hs contnued support of our research. As well, the fnancal support of the Bank Netherlands Partnershp Program of the World Bank s gratefully acknowledged.

4

5 INTRODUCTION Recent research nto the evoluton of the world dstrbuton of ncome focuses on usng a combnaton of cross country and wthn country nformaton to estmate the dstrbuton of ncome from an ex post perspectve (Schultz 1998; Bourgugnon and Morrsson 2002; Quah 2002; Sala--Martn 2002a, 2002b, 2006). These analyses have arrved at mxed results, suggestng on the one hand no change, or slower growth, n the extent of poverty worldwde (Bourgugnon and Morrsson 2002) or fallng poverty on the other hand (Sala--Martn 2006). Whle useful from a hstorcal perspectve, such analyses do not permt us to predct how nequalty, and ndeed poverty rates, mght change n the future. Ths s partcularly mportant for analyzng the poverty mpacts of trade polcy changes, where the mpact on low-ncome households s lkely to be very dfferent from hgher-ncome households. Developng such a characterzaton of the poverty mpacts of trade polcy could be done on a country-by-country bass wheren household expendture survey data are employed to approxmate compensatng varaton as a budget share weghted average of prce changes arsng from polcy shocks (Chen and Ravallon 2003; Levnsohn et al. 2000). However, such an approach does suffer from a number of weaknesses. Inconsstences between natonal accounts and household survey data (Sala--Martn 2006) renders results from household survey based analyss suspect n makng predctons about aggregate mpacts. Moreover, consderable dffcultes arse n obtanng systematcally comparably dsaggregated expendture nformaton from household surveys for a large number of countres. Even more substantal dffcultes are encountered when attemptng to map these dsaggregated expendture patterns on partcular goods or servces from household survey data to aggregate data, such as those contaned n the Internatonal Comparsons Project (ICP) partcularly when many countres are nvolved. Obtanng the prce data needed to fully characterze preferences n terms of Engel and substtuton elastctes from household survey data s another problem. Lastly, the shareweghted summaton approach to approxmatng CV lacks theoretcal rgor. Indeed the absence of substtuton effects can be qute problematc for large prce changes (Fredman and Levnsohn 2002). 1 All-n-all, t s often dffcult to compare mpacts across countres based on country-by- 1. More specfcally, these authors fnd that ncorporaton of substtuton effects dampens by 50% the welfare loss from prce ncreases followng the Asan fnancal crss. 1

6 country analyses whch utlze survey data. In ths regard, a theoretcally rgorous, nternatonally comparable analyss of the poverty mpacts of nternatonal prce changes should be a welcome addton to the lterature. However, to date, most nternatonal demand studes have been done usng only per capta data whch s of lmted value to those nterested n the dstrbutonal consequences of polcy reform. One excepton s the recent work by Cranfeld (1999) and Cranfeld et al. (2004) usng maxmum entropy and treatng the per capta observaton as an explct aggregaton over households. Ths paper bulds on that prevous work and contrbutes a framework whch enables estmaton of the future mpact of poverty arsng from exogenous polcy shocks. It does so by ncorporatng more dsaggregated household survey data nto an entropy-based estmaton procedure n whch the demands for fnal goods and servces at dfferent ponts of the expendture dstrbuton are estmated. Ths demand system, n turn, provdes the bass for analyzng the mpact of a global food prce ncrease of the sort antcpated by nternatonal trade models n the wake of WTO reforms. Recovery of dsaggregate demands at each pont of the natonal expendture dstrbuton s acheved usng a global demand system (.e., a demand system wth the same set of parameters for each observaton) whch embodes more flexble ncome (expendture) effects compared to alternatve demand systems. The value of the demand system s further enhanced va postestmaton calbraton of the parameters so that each country-specfc demand system reproduces observed per capta demands. The resultng country-specfc, calbrated demand systems appear to be well-suted to predctng expendture patterns across the ncome spectrum n the three focus countres n our study: Indonesa, Thaland and the Phlppnes. As such t provdes a useful vehcle for evaluatng the welfare mpacts of changes n consumer prces due to nternatonal trade reforms. 2 One of the great benefts of ths approach to poverty analyss derves from the fact that we are able to establsh a unque poverty level of utlty for each country. The poverty level of utlty s nvarant to the nternatonal trade shock and resultng prce changes and therefore deally suted for assessng the mpact of a prce change on the poverty level. Ths leads us to 2. Of course, one mportant lmtaton of the work n ths paper s that we do not take nto account factor earnngs. However, the approach to dong so s relatvely straghtforward, provded estmates of the earnngs mpacts are 2

7 defne a modfed Foster-Greer-Thorbecke (FGT) poverty measure useful n conductng ex ante poverty analyss stemmng from exogenous polcy shocks. Specfcally, snce our approach yelds a sngle, calbrated expendture functon for the entre populaton n a country, we replace the ndvdual s expendture level n the FGT measure wth an expendture functon defned across a prce vector, calbrated demand parameters and the ndvdual s level of utlty. In a smlar ven, the threshold level of expendture used n FGT s replaced wth the expendture functon defned across the same prce vector, the same calbrated demand parameters, and the poverty level of utlty. Use of the calbrated expendture functon and the poverty level of utlty to defne the threshold level of expendture s advantageous, as there s no ambguty about how the threshold level of expendture n the modfed FGT measure must change n the wake of polcy reform. In ths framework, the threshold level of expendture s that whch s requred to attan the ntal poverty level of utlty, at the new prces. As such, t reflects optmal adjustments n demand, n response to these prce changes. Use of an explct expendture functon n the FGT measure s therefore a valuable nnovaton and clearly preferable to other ncome or expendture-based approaches, whch rely on the ndexaton of a fxed bundle of goods and servces to establsh a poverty lne. In addton to beng theoretcally more satsfyng, the expendture functon approach lends tself to ease of use n the type of partal and general equlbrum modelng often used for trade polcy analyss. Ths work draws together several recent strands of lterature n consumer demand, poverty and trade polcy analyss. On the demand sde, t represents another step n the long lne of lterature related to estmaton of nternatonal consumer demands (e.g. Thel and Clements 1987; Thel et al. 1989; Rmmer and Powell 1992; Cranfeld et al. 2002; Seale et al. 2003). By treatng per capta natonal demands as the explct aggregaton of a dstrbuton of demands across the expendture spectrum, t also adds to the lterature whch merges marco (.e. per capta) and mcro (.e. ndvdual or household survey based) data for use n the analyss of nequalty and poverty (e.g. Ravallon and van de Walle 1991; Schultz 1998; Cranfeld 1999; Bourgugnon and Morrsson 2002; Quah 2002; Sala--Martn 2002a, 2002b, 2006), thus allowng us to look beyond the averages (see, for example, Ravallon 2006). Ths paper has especally avalable. For an llustraton of how ths can be done, see the paper by Hertel et al. (2004). 3

8 strong tes to Sala--Martn (2002a, 2002b, 2006) n that we use per capta expendture and consumpton data coupled wth expendture nequalty data to recover an approxmaton to the expendture dstrbuton and data sources drectly lnked to those that author has used n prevous work. 3 However, we dffer from Sala--Martn (2002a, 2002b, 2006) n that we are nterested n country-specfc effects arsng from polcy shocks and we have the means to recover nformaton useful n welfare analyss. In partcular, the demand system used here has an explct expendture functon whch we use not only for welfare analyss, but also for poverty analyss. Therefore, our poverty calculatons are ted drectly back to mcro-theory and the behavour of economc agents; the value of ths theoretcally grounded approach to welfare and poverty analyss has been hghlghted prevously n Ravallon (1998) and Neary (2004). The next secton presents a bref dscusson of the demand system we estmate. The emprcal methods and data are then dscussed. Results of the econometrc estmaton are then presented, followed by development of the calbraton scheme and subsequent results. The calbrated demand systems are then used to evaluate the consumpton-based poverty mpacts of nternatonal trade reforms. Whle ths paper only performs these calculatons for three countres n Southeast Asa, Indonesa, Phlppnes and Thaland, the approach could be extended to evaluatng the poverty mpacts of consumer prce changes for all countres n the nternatonal data set. Ths knd of comprehensve, econometrcally-based analyss of the nternatonal poverty mpacts of trade reform has htherto been mssng from the lterature. AN IMPLICIT, DIRECTLY ADDITIVE DEMAND SYSTEM The demand system used to characterze consumer preferences s an mplct, drectly addtve demand system (ncknamed AIDADS). AIDADS s best characterzed as a generalzaton of the Lnear Expendture System (LES) whch allows for non-lnear Engel curves whle mantanng a parsmonous parameterzaton of consumer preferences. Rmmer and Powell (1996) developed AIDADS 4 based on Hanoch s (1975) semnal work on mplct addtvty. Wrtten n budget 3. Granted, Sala--Martn (2006) used per capta GDP and ncome nequalty measures rather than expendture measures. Note, however, that use of expendture data s consstent wth the World Bank s approach to modelng poverty ssues. 4. AIDADS s n the famly of demand systems satsfyng Cooper and McLaren s (1992) condtons for effectve 4

9 share form AIDADS appears as: w pγ = y α + β exp + 1+ exp ( u) ( u) p γ 1 y where s the th good s budget share, p s a n vector of prces wth typcal element w p R + + s expendture, utlty and q α, > γ, β γ are unknown parameters, γ s a n vector wth typcal element (1) γ, u s 0. In AIDADS, the followng parametrc restrctons are used to ensure well-behaved demands: 0 α, β 1 for all, and. n α = n = 1 = 1 Further detals on AIDADS can be found n Cranfeld et al. (2002, 2004); however, a few ponts are worthy of menton here. Frstly, as wth the LES, AIDADS characterzes consumpton at the subsstence level usng the parameters γ whch represent the quantty of good requred for survval, and therefore not subject to dscretonary adjustment. Estmaton of the subsstence quanttes permts us to say somethng meanngful about consumers behavoral response (or rather the lack of t) at extremely low ncome levels. Whle AIDADS and the LES share the subsstence parameters, AIDADS generalzes the LES wth a re-parameterzaton of the margnal expendture share, such that the margnal expendture shares change wth the level f expendture. When β = 1 α = β, AIDADS collapses to, y the LES and the margnal expendture share on good s constant. The parameter α characterzes the margnal expendture shares on good n the neghborhood of subsstence ncome, whereas If α > β true when α < β β descrbes the margnal budget share at extremely hgh levels of expendture., then the margnal (and average) budget share falls wth rsng ncome. The opposte s. From the pont of vew of characterzng consumpton behavor at very low ncome levels, ths addtonal flexblty s very mportant, as the margnal expendture shares of the very poor are generally qute dfferent from ther counterparts evaluated at natonal, per capta ncome levels. global regularty (see Rmmer and Powell 1996 for detals). AIDADS also has rank three (see Gorman 1980 and Lewbel 1991 for further dscusson on demand system rank). 5

10 EMPIRICAL METHODS & DATA As the man purpose of ths paper s to utlze an nternatonal, cross-country demand system for poverty analyss, we do not focus on estmaton methods per se. Indeed, the entropy-based emprcal methods used to recover the approxmaton to the dstrbuton of expendture, estmate parameters of AIDADS and recover unobservable levels of consumpton have been publshed prevously n Cranfeld et al. (2004). However, snce the present analyss ncorporates a more refned approach to the estmaton problem, a techncal appendx contanng the emprcal model accompanes ths paper. Nevertheless, to contextualze the results, note that the emprcal framework s developed n a mathematcal programmng envronment, wheren the underlyng demand system parameters and approxmaton to the dstrbuton of expendture are calculated. The numercal optmzaton program mnmzes an objectve functon composed of a concentrated log-lkelhood functon and entropy functon; the former allows for estmaton of the demand system parameters, whle the latter enables recovery of the approxmaton to the dstrbuton to expendture. Constrants are used to defne the AIDADS demand system, assocated parametrc restrctons and regresson error terms, as well as the level of utlty n the AIDADS model. Addtonal constrants are ncluded to ensure the recovered approxmaton to the expendture dstrbuton matches the known moment condtons for expendture and to ensure that the recovered dsaggregate demands aggregate back to the observed level of per capta demand. As orgnally developed, maxmum entropy methods provde a means to recover unobservable nformaton from an observable, but nosy sgnal or message. More recent usage, however, has focused on recovery of unobservable nformaton from observable statstcs of an underlyng dstrbuton. For example, f one observed the frst j-moments of a random varable and knew the support of the underlyng dstrbuton, one could use maxmum entropy methods to recover an approxmaton to the true dstrbuton, such that the frst j-moments of the approxmatng dstrbuton exactly match the observed moments, but reflects maxmum uncertanty wth respect to the j+1 moments and beyond. Recovery of the approxmatng dstrbuton takes the form of a constraned optmzaton problem, wheren Shannon s measure of uncertanty s maxmzed subject to constrants requrng the moments of the approxmatng dstrbuton to exactly match the known moments (see Jaynes 1957a, 1957b; Kapur and Kesavan 6

11 1992; or Golan et al for further detal). However, the resultng frst order condtons do not have a closed-form soluton, so numercal methods are used to solve the mathematcal programmng problem computatonally (see the techncal appendx for detals on ths mathematcal programmng model used n ths study). Our analyss uses prce, per capta expendture, and budget share data from a cross secton set of countres n the most recent (1996) Internatonal Comparsons Project (ICP). These data are useful n analyzng nternatonal demand patterns as they are provded n dentcal unts (.e., nternatonal dollars) and facltate comparson of prces and quanttes for dsaggregate commodtes across countres. The ICP data record fnal consumpton of 26 goods and servces n 114 countres, wth countres rangng n per capta expendture from Malaw to the Unted States. In keepng wth the addtve nature of AIDADS, the 26 goods and servces are aggregated nto three broad aggregate goods: food (FOOD); other non-durables (ONONDUR); and servces (SERVICES). Because of the dynamc nature of decsons wth respect to durable goods, and gven the crosssecton nature of the data, durable goods have been omtted from ths analyss. In other words, we focus only on the allocaton of expendtures across non-durables and servces. 5 Budget shares are constructed by dvdng nomnal expendture on each aggregate good by total nomnal expendture. The prce of each good equals the rato of nomnal expendture for that good to real expendture for the same good. Total nomnal expendture per capta serves as the per capta expendture term n AIDADS. Table 1 provdes summary statstcs of the ICP data used for estmaton. On the expendture dstrbuton sde of the data base, quntles and decles, are obtaned from an updated release of Dennger and Squre s (1996) World Income Inequalty Database (WIID). Only expendture or consumpton based quntles and decles are used. 6 Table 2 shows 5. Moreover, ntal estmaton of AIDADS wth data that ncluded durables resulted n an emprcal model that would not converge, nor would t converge after numerous attempts to resolve the ssue (e.g. changng startng ponts of the optmzaton program, changng the bounds on the choce varable set, etc). 6. The updated WIID s a complaton of Gn coeffcents and quntle and decle data for varous countres over tme. 7

12 the quntle and decle values, year of coverage, and measurement detals. 7 The household survey data show the mnmum, average and maxmum value of expendture for each percentle of the populaton n the three focus countres. As these are rather volumnous, they are not presented here. However, these data are drawn from household surveys for Indonesa (1993), Thaland (1996) and Phlppnes (1999). 8 ECONOMETRIC RESULTS Estmated parameters of AIDADS are shown n Table 3. Begnnng wth the estmates of subsstence quanttes, γ, note that the estmate for servces s at ts lower bound of zero, whle those for food and other non-durables are postve. The estmates of γ suggest, as one mght expect, that food and other non-durables are a requred part of the subsstence bundle of goods, whle servces are not strctly requred for survval. Premultplyng the γ s by ther respectve, country-specfc, prces and summng over the three goods permts us to establsh the cost of the subsstence bundle. Ths survval level of expendture on non-durables s equal to $14, $15 and $26, respectvely, for Indonesa, the Phlppnes and Thaland. The estmates of γ upon whch these subsstence bundles are based reflect the level of real expendture of the poorest household n the sample,.e. those households on the extreme lower end of the expendture dstrbuton (on a global scale). Not surprsngly, these survval expendtures are drastcally lower than poverty 7. The year of coverage often devates from 1996, but usually by no more than fve years, whle quntles are measured n dfferent unts across countres (.e., households versus ndvduals, gross versus net of taxes). Because expendture dstrbutons tend to change slowly over tme, the msmatch between years s assumed unmportant. Due to the hgh correlaton between expendture, gross and net of taxes, and for households versus ndvduals, ths msmatch n the data s also assumed away. 8. One may wonder why these household survey data were not drectly ncorporated nto the analyss. Sala--Martn (2006) outlnes three reasons why one should not use household survey means n such analyss. Albet weak, hs frst pont s that the lterature uses populaton-weghted dstrbuton, the mplcaton beng that comparson to the lterature requres use of data smlar n nature. Second, and perhaps more persuasvely, survey means have poorly understood propertes; the noton beng that dfferences n survey methodologes and strateges results n possble msleadng summary statstcs from household based surveys. Thrdly, surveys are not avalable for all countres and all tme perods. Ths latter pont hghlghts the dffcultes one mght encounter n attemptng to estmate a global demand system usng household based survey data. We would add to Sala--Martn s (2006) the fact that not all surveys collect the nformaton needed to estmate demand systems; some surveys do not (or cannot) collect prce data, whle others only collect partal nformaton on the household s consumpton bundle, both of whch make t nearly mpossble to estmate a useful demand system. 8

13 lne(s) prevously reported n the lterature. 9 The nvarance of these subsstence purchases to expendture wll have mportant mplcatons for the overall behavor of consumpton at the lowest expendture levels as wll be shown below. Next, turn to the two sets of parameters descrbng the behavor of margnal budget shares. For FOOD, the estmated value of α ndcates that, at subsstence expendture levels, 73 percent of an addtonal dollar of expendture s devoted to food, as opposed to18 percent for other non-durables and just nne percent for servces. Ths hghlghts the crtcal role of food n the budget decsons of very poorest households. The estmates of β provde the target value towards whch the margnal budget share evolves as expendture rses wthout bound. Not surprsngly, ths s zero for food at some pont the household s satated wth respect to food but over two-thrds for servces; at extremely hgh expendture levels slghtly over two-thrds each addton dollar of expendture s allocated to servces. The value of the margnal budget shares, ftted budget shares and Engel elastctes for all three goods, calculated at the means of the data, are presented n Table 4. As expected, when evaluated at the means of the data, the margnal budget share for food s low (0.068), whle that for servces s large (about 0.6). Ths hghlghts the danger of usng the more restrctve LES specfcaton when one s nterested n the behavor of households n poverty. By restrctng the margnal budget share to be constant, the LES s lkely to understate the margnal budget share on food at the subsstence level by a full order of magntude (0.73 versus at mean prces and expendture). Ideally, we would lke to be able to compare the recovered and observed budget shares across the expendture spectrum. However, n our experence, attempts to do so are tenuous at best. In partcular, there s an nherent dscordance between the ICP data and the household survey data. Frstly, the defnton of specfc goods and servces dffers. Secondly, the data collecton methods dffer; ICP bulds on the natonal accounts, whle the household data are based on surveys mplemented usng a samplng approach. (Sala--Martn (2006) devotes consderable dscusson to these ssues.) As such, any comparson between actual budget shares 9. For nstance, Ravallon et al. (1991) conclude that $23 per month (n 1985 PPP unts), or $276 per annum, s a reasonable lower bound to the poverty lne. 9

14 from the household surveys and recovered budget shares tends to be domnated by dfferences n the measurement of dsaggregated spendng, and as such, s not terrbly nformatve. Moreover, our prmary nterest les n how one mght use the recovered shares to undertake polcy analyss. As foreshadowed above, the frst step n ths regard s a post-estmaton calbraton scheme whch turns a global demand system nto natonal demand systems. We turn attenton next to ths scheme. POST-ESTIMATION CALIBRATION Whle t s a useful analytcal construct, the assumpton of globally common preferences and the subsequent nvarance of the AIDADS parameters across countres s problematc for polcy analyss. And so, as s commonly done wth mcro-smulaton analyss, t s useful to have a strategy for post-estmaton calbraton, n whch the nternatonal demand system s natonalzed by forcng the calbrated system to pass through the observed per capta expendture levels. In ths context post-estmaton calbraton of AIDADS s acheved by frst rescalng α and β, and then re-computng a value of κ. However, n keepng wth our focus on nternatonally comparable measures of poverty, we do not alter the subsstence quanttes,, whch we assume to be a functon of human needs and, as such, s nvarant across regons. Our calbraton scheme works as follows. Frst, gven that the subsstence parameters are nvarant across countres, the subsstence shares (.e. prce tmes γ dvded by expendture) are known and constant. Thus, t makes sense to parse the AIDADS equaton n share form nto two components a subsstence share and a dscretonary share (the latter could also be referred to as the super-numeracy share). We then calculate the ftted dscretonary budget shares at per capta expendture as: αˆ ˆ + βˆ exp( ut ) p δˆ = (1- t γ t ), (2) 1+ exp( u ) y t t where αˆ and βˆ are estmated values, γˆ s the vector of estmated subsstence quanttes, and u t s the value of utlty arsng from choce of the optmal consumpton bundle at the per capta γ level of expendture, y t. The calculated value of δˆ t s smply the value of the dscretonary 10

15 budget share at the per capta level of expendture, calculated usng the estmated values of AIDADS parameters. Next, add the estmaton resduals for the th equaton n the tth observaton back to obtan observed dscretonary budget shares as follows: t t ( wt - wˆ t δ = δˆ + ) (3) δˆ t to where w t s the per capta budget share, ŵ t s the ftted value of the budget share evaluated at the per capta level of expendture, calculated usng the econometrcally estmated value of the AIDADS parameters. Here, the regresson errors (stated n terms of budget shares) are added back nto the dscretonary porton of AIDADS. Dong so assumes that all of the regresson error s attrbutable to an mperfectly observable dscretonary budget share. The next step n the calbraton scheme s to adjust the orgnal estmates of wth the rato of ftted to observed dscretonary budget shares as follows: ~ αt = αˆ δˆ t δt and ~ ~ βt = β δˆ t δt. Fnally, normalze the values of α ~ t and β ~ t to ensure they sum to unty: C α = ~ α α ~ ~ t t jt and β = β β ~ C t t jt, where the superscrpt C denotes the parameters have j j been calbrated. These country specfc, calbrated values of α and β are then fxed and used n calbratng utlty and the κ α and parameter by solvng a non-lnear system of equatons for each country. Ths system contans the defnng equaton of utlty for AIDADS and the AIDADS system wth quanttes fxed at ther observed per capta consumpton levels, but evaluated at the per capta level of expendture. 10 Hence, each country for whch post-estmaton calbraton s undertaken has ts own values of α, β and κ. These calbrated parameters have the desrable property that reproduce the observed per capta natonal budget share at the per capta level of expendture. 11 Moreover, ths calbraton scheme results n a calbrated set of budget shares β 10. Ths normalzaton s requred, as ntegraton of the calbrated demand system back to an underlyng dual functon requres a constant of ntegraton. Adjustng κ accordngly provdes such normalzaton. 11. The only potental problem wth ths procedure occurs f the actual consumpton level for a gven good s not larger than the subsstence level. Ths suggests that t may be of nterest to constran the subsstence levels to be strctly less than the lowest level of observed consumpton. 11

16 across all expendture levels wthn each country s expendture dstrbuton. Table 5 shows the estmated and calbrated values of the AIDADS model. Recall that the subsstence parameters,, are assumed to be nvarant nternatonally and are not calbrated. In lght of the subsequent trade polcy experment whch we wll explore, we focus our attenton here on the behavor of food expendtures across the expendture spectrum. In ths regard, note that snce the orgnal estmate of β for food s zero, then so too are the calbrated values of β. However, relatve to ts value n the estmated nternatonal demand system, the calbrated value of α γ has ncreased for Indonesa and the Phlppnes, but fallen for Thaland. The calbrated values of κ have also changed relatve to orgnal estmate, wth Indonesa s and Thaland s calbrated κ values beng smaller than that estmated for all countres, whle the calbrated value of κ s larger for the Phlppnes. These calbrated values are not terrbly useful n conveyng the mpact of calbraton. Instead t s more nstructve to compare the recovered and calbrated budget shares for food across the expendture dstrbuton n the three focus countres. Fgures 1, 2, and 3 plot, among other thngs, the recovered and calbrated budget shares for food across the ncome spectrum. For Indonesa (Fgure 1), the calbrated food expendture shares now pass through the per capta based budget share (depcted by a blue damond), and vary only slghtly from the recovered shares. Specfcally, the calbrated shares are rotated n a clockwse manner around the per capta based budget share. Relatve to the recovered shares, ths means the calbrated shares are larger than the recovered shares at low expendture levels, whle the reverse s true at hgh expendture levels. However, the dfference between the calbrated and recovered shares s slght, whch makes ths rotaton dffcult to observe. These fgures also plot the horzontal lne correspondng to the calbrated value of α (for the respectve focus country) and we can see that α les well above all of the calbrated budget shares even for the poorest household. Ths s because α s a measure of the lmtng behavour of margnal expendtures as total expendture approaches our estmate of subsstence expendture. As the poorest household n the expendture dstrbuton for Indonesa has an expendture level well above the subsstence expendture at local (.e. Indonesan) prces, ths dfference s not surprsng. Snce Engel s law suggests the margnal budget share for food falls 12

17 as expendture grows, t s hardly surprsng that the calbrated per capta budget share for food s well below the lmtng behavour gven by α. Fgures 1 3 also plot the break-down of the calbrated budget shares nto the subsstence ( p γ y ) and dscretonary shares ( ( α ( ( ) + β exp u ) ( 1+ exp u )( 1- p γ y) ), respectvely. Ths permts us to examne how these ndvdual components adjust to changes n expendture level, thereby decomposng changes n the overall budget share. Comparng the subsstence and dscretonary shares for food n Indonesa, we see that the majorty of the change n food s budget share s drven by dscretonary expendture. As the subsstence share has expendture n the denomnator, ths share falls wth rsng expendtures; for Indonesa, ths means that as expendture approaches the level of the wealthest household, the subsstence share becomes nearly zero. Somewhat dfferent results are obtaned for the Phlppnes, where calbrated shares dffer a bt more from the recovered shares (see Fgure 2). Here, the calbrated shares have shfted upwards relatve to the recovered shares n order to pass through the observed natonal per capta budget share. Moreover, the dfference between the recovered and calbrated shares grows as one progresses upwards through the Phlppnes expendture dstrbuton. Calbrated food budget shares are very close to the calbrated value of for the Phlppnes (the horzontal lne n fgure 2), suggestng that total expendture on non-durable goods and servces by the poorest household n the Phlppne s recovered expendture dstrbuton s closer to subsstence expendture (at local prces) than n Indonesa. The subsstence share of food at the subsstence level of expendture s much hgher n The Phlppnes than n Indonesa -- approxmately 16 percent of total non-durable expendture n the poorest household. As wth Indonesa, t falls towards zero at the hghest expendture levels. It s also nterestng to note that the behavour of the dscretonary shares across the expendture spectrum s rather dfferent from Indonesa. Dscretonary shares for food n the Phlppnes ntally rse wth expendture, thereupon reachng a maxmum, before begnnng to fall after about 5.2 on the log expendture scale. As wth Indonesa, food s budget share s almost entrely accounted for by dscretonary expendtures on food at hgh levels of expendture. α 13

18 For Thaland the dfference between calbrated and recovered shares s much more pronounced (Fgure 3). As requred, Thaland s calbrated food budget shares pass through the per capta based budget share for food. Moreover, the calbrated shares have shfted down, relatve to the recovered shares, n near parallel fashon. Also note that the gap between the calbrated value of α for food and the food budget share for the poorest household n Thaland s expendture dstrbuton s even more pronounced than n Indonesa. And, as wth Indonesa, the subsstence shares and calbrated dscretonary shares fall as expendture ncreases, wth the dscretonary share accountng for a larger porton of food s budget share as one moves up the expendture dstrbuton. What should be clear from the precedng dscusson s that our calbraton strategy does not affect the subsstence shares. Calbraton only plays a role n changng the locaton and shape of the dscretonary shares; t does so by alterng the values of α, β and κ, and the subsequent value of utlty when the utlty functon s evaluated, subject to the budget constrant, usng the calbrated parameters. For the partcular estmates presented above, only the term ( u) ) ( 1 exp( )) ( α + β exp u s altered, and that drves the changes n the dscretonary + share. It s mportant to recognze, however, that any exogenous polcy shock to ether prces or expendture (ncome) levels wll alter both the subsstence and dscretonary shares. For nstance, a prce ncrease arsng from trade lberalzaton would ncrease the subsstence share for food, but may ncrease or decrease the dscretonary share. The latter s qualfed as the prce ncrease wll decrease the ( 1 - p γ y) component of the dscretonary share but ncrease the ( u) ) ( 1 exp( )) ( α + β exp u component (recall that the value of for food s zero); dependng + on the sze of these changes, the dscretonary share may ncrease or decrease. As such, t s dffcult to say a pror f food s share of expendture wll rse or fall n the wake of a prce hke. Of even greater mportance s how such a prce shock mght affect the poorest households and hence the ncdence of poverty. In the tradton of mcro-smulaton, we turn next to an exploraton of these questons by smulatng the mpacts of a fve percent global food prce rse usng the calbrated demand system. We wll focus partcular attenton on the resultng changes n consumer demand and poverty. β 14

19 POVERTY IMPACTS OF A GLOBAL FOOD PRICE RISE There has been consderable nterest recently n the potental mpacts of multlateral trade lberalzaton on poverty n developng countres. The clear consensus s that agrcultural reforms n the rch countres wll cause world farm and food prces to rse, as farm subsdes are elmnated and rch country border protecton s reduced (Beghn et al.; Clne; Anderson and Martn). Moreover, recent proposals for the exempton of so-called Specal Products from tarff cuts n developng countres would mean that the world prce rses would not be offset by tarff cuts for many staple food products. In addton, the G-33 proposal for a Specal Safeguard Mechansm could permt substantal tarff rses n the face of mport surges. In short, there s a strong lkelhood that food prces wll rse n developng countres, followng a successful concluson of the Doha Development Agenda. Regardless of ts orgn, a food prce rse may be expected to beneft agrcultural producers n the developng world, whle hurtng consumers. The net outcome s therefore ambguous (Hertel and Wnters 2005). Provdng a comprehensve analyss of the trade/poverty debate s beyond the scope of ths paper. However, the framework developed here offers an mportant mprovement n the way the consumpton mpacts of such a prce hke are evaluated. Instead of smply assumng that the poor consume the natonal per capta bundle of goods and servces (Clne 2004) or that they consume only food (Anderson et al. 2006), we a now n a poston to assess the dfferental mpact of a food prce ncrease across the entre expendture (ncome) spectrum. For llustratve purposes, we apply a fve percent ncrease n the prce of food and examne ts mpact on the demand for food and household welfare wthn each focus country. The change n welfare at the new prces s then used to assess the mpact on a modfed FGT measure of poverty. Tradtonally, the FGT measure s defned as: N -1 yn δ Pδ = N ( 1- ) Ι ( yn z ) z n=1 where 12 δ { 0, 1, 2}, N s the number of observatons (.e. households), s the nth household s y n expendture, z s a poverty lne threshold level of expendture and Ι( z ) s an ndcator y n 12. To avod confuson wth a parameter of AIDADS, we use δ as the subscrpt to the FGT measure (.e., ) α rather than the tradtonal. P δ 15

20 functon assumng a value of unty f the condton s true, and zero otherwse. P 0 measures the proporton of people n the populaton who are at or below the poverty lne threshold, P 1 s the poverty gap (.e., the per capta expendture short fall of those n poverty, expressed as a share of the poverty lne threshold level of expendture), and P 2 s a poverty measure whch s senstve to dstrbuton among the poor (Deaton 2000, p.147). In some respects, P 2 could be vewed as akn to a partal Herfndahl ndex. It s a partal measure because t only reflects the concentraton of expendture amongst the poor. P For purposes of ths paper, we redefne e( p ~, u N -1 n δ δ = N (1- ~ ) Ι( un u ) n=1 e( p, u ) ( n ) where e p ~, u ) s the calbrated AIDADS expendture functon evaluated at the prce vector p ~ and calbrated utlty for the nth household ( u ), whle e( p ~, u ) s the calbrated AIDADS expendture functon evaluated usng the prce vector p ~ and the poverty level of utlty, u. When p ~ s set equal to the base prce vector, e p ~, u ) and e( p ~, u ) measure household n P δ as: ( n expendture on non-durables and the poverty level of expendture, respectvely, before the prce shock. When p ~ s set equal to the shocked prce vector, the post-shock levels of expendture as well as cost of attanng the poverty level of utlty at the new prces are obtaned. Note that whle the poverty level of expendture, e ( ~p,u ), changes, the poverty level of utlty s nvarant to the prce shock. The use of utlty n the ndcator functon s advantageous as utlty wll vary wth expendture and prces, and consumer demands at the poverty lne are free to change as well. A natural queston to next ask s how one establshes the poverty level of utlty. We use two approaches to establshng the poverty level of utlty. The frst approach assumes one has a poverty level of expendture. In ths case, country specfc poverty levels of utlty can be calculated by maxmzng the AIDADS utlty functon, usng the calbrated AIDADS parameters, subject to the budget constrant evaluated at local prces and the poverty level of expendture. The resultng soluton wll nclude the optmal consumpton bundle at the poverty (4) 16

21 level of expendture and local prces, but also the poverty level of utlty (.e. the utlty of the consumpton bundle purchased at local prces wth the poverty level of expendture). The advantage of such an approach s that the resultng poverty levels of utlty (across countres) reflect nter-country prce level dfferences that otherwse would not be accounted for f one used a poverty level of expendture only. We use ths approach to calculate poverty levels of utlty assocated wth one and two dollar a day poverty thresholds; specfcally, we use a one dollar a day poverty level of expendture (.e. $365 per annum) n calculatng the poverty level of utlty for Indonesa and the Phlppnes, and the two dollar a day (.e. $730 per annum) threshold for Thaland. 13 The one and two dollar a day poverty thresholds of expendture are employed n order to have some measure of consstency wth the second way n whch a poverty level of utlty can be establshed. In partcular, the World Bank s World Development Indcators (WDI) provdes natonal poverty rates (NPRs), defned as the proporton of natonal populatons whch fall below natonally defned poverty levels. These percentages are 15.7, 36.8 and 13.0 percent n Indonesa, the Phlppnes and Thaland, respectvely. Usng the recovered approxmaton to the expendture dstrbuton and ts support, t s easy to determne the poverty level of utlty and expendture. The share of a country s populaton s summed untl the cumulatve sum just exceeds the natonal level of poverty. The utlty level of the household group just below the pont at whch the cumulatve sum just exceeds the NPR s the poverty level of utlty. We can then map back from that household group to the expendture level consstent wth these NPR based thresholds; these values are $331 for Indonesa, $343 for the Phlppnes and $629 for Thaland. Moreover, t should now be clear why we choose the one dollar a day poverty level of expendture for Indonesa and the Phlppnes, and two dollars a day for Thaland n our frst approach to defnng the poverty level of utlty; dong so makes the analyss based on the two poverty level of utlty approaches more comparable n terms of poverty level of expendture. 13. The one and two dollar a day poverty lnes have been the subject of some dscusson n the lterature. Sala-- Martn (2006) notes that the World Bank s defnton of the poverty lne was stated as $1.02 per day (n 1985 prces) n 1990, but at $1.08 (n 1993 prces) n The ssue s what base year s used to defne the poverty lne, and the extent of prce nflaton snce that base year was establshed. Nevertheless, as our approach could accommodate any poverty lne, we do not address whether one ought to use one dollar a day, $1.02 per day or $1.08 per day, and focus nstead on how one mght use the approach wth any partcular poverty lne defnton. 17

22 The average percent change n demand for food when the prce of food ncreases by fve percent ranges from -3.8 percent for Thaland to -4.1 percent of the Phlppnes. To better llustrate these reductons n demand for food across the focus countres, Fgure 4 shows the level of demand for food n the focus countres before and after the prce shock. Prce shock nduced reductons n quantty demanded vary not only across focus countres, but also across expendture levels wthn each focus country. For nstance, Indonesa, the Phlppnes and Thaland have per capta non-durable expendture levels of $655, $763 and $1,454, respectvely, based the 1996 ICP data base. Fgure 4 shows that Thaland (a wealther country compared to Indonesa and the Phlppnes) generally has smaller changes n the quantty of food demanded, regardless of where one s located n the expendture dstrbuton. Changes n demand for food n Indonesa and the Phlppnes are larger compared to Thaland, but also reflect consderable wthn-country varaton. To better llustrate what s drvng the changes n demand arsng from the fve percent ncrease n prce, Fgure 5 plots the uncompensated prce elastcty for food n the Phlppnes and ts components based on the calbrated demand system. These components nclude the expendture (Engel) elastcty, budget share, the negatve of the product of the share and Engel elastcty and the compensated prce elastcty (.e. the components of the Slutsky equaton are plotted across the expendture spectrum). What s clear s that the expendture effect (.e. the negatve of the Engel elastcty tmes the budget share) domnates the compensated prce effect, and s the most sgnfcant drver of changes n the uncompensated prce elastcty. Moreover, the uncompensated own-prce elastcty for food becomes more nelastc as expendture grows. Consequently, the relatve change n demand falls as expendture grows due to the declne n both the budget share and Engel elastcty. However, because the level of demand ncreases from low to hgh expendture levels, these smaller relatve changes n demand actually translate nto larger absolute changes n demand at hgher expendture levels (Fgure 4). To relate the prce shock mpact back to the fundamental parameters of AIDADS, fgures 6, 7 and 8 show the breakdown of the change n food s budget share nto the change n the subsstence share and the change n the dscretonary share spent on food, across expendture levels n the focus countres. Recall that the subsstence share wll rse for any prce shock, whereas the dscretonary share may ncrease or decrease, dependng on the sze of change n 18

23 ( 1 - p γ y) versus α ( 1 exp( u)) (where we have reflected the fact that s zero n the + β calbrated demand system). Further nsght can be ganed by notng that when β equals zero (as s the case for food), the mpact of a prce change on the dscretonary share can be expressed as: δˆ p jt t αˆ p ˆ - α u t = {-γ + ( 1- t γ ) }. (5). 1+ exp( u ) y 1+ exp( u ) p t t t t Snce α ( 1 + exp( u )) s postve, the sgn of (5) depends on the two terms wthn the brackets t {}, but snce u t p t s negatve, the term n {} can be ether postve or negatve. In Indonesa (see fgure 6), the change n food s budget share ntally ncreases as expendture ncreases, reaches a maxmum and then declnes. As s evdent n the fgure, the change n the subsstence share becomes smaller as one progresses through the expendture levels, whle the change n the dscretonary share ncreases from a very small level, to a maxmum and then declnes. The latter effect suggests that 6.8 on the natural log of expendture scale s the crtcal pont after whch the reducton n ( 1 - p γ y) arsng from the prce ncrease overwhelms the ncrease n α ( 1 exp( u)) and the change n the overall budget share for food + begns to drop. As s clear from fgure 6, the change n the subsstence share domnates at low expendture levels, as assocated ponts n fgure 6 le above those representng the change n the dscretonary budget share for food. However, the change n overall food budget share s domnated by the change n dscretonary share at hgher expendture levels. The change n food s budget share for the Phlppnes (fgure 7) s somewhat dfferent; specfcally, the share ntally falls, reaches a local mnmum, rses to a maxmum and then falls agan. Ths wave pattern of adjustment reflects two competng sets of changes. On the one hand, the change n the subsstence share falls through the entre range of expendture (as expected). On the other hand, the change n the dscretonary budget share s ntally negatve, but ncreases, becomes postve, reaches a maxmum and then begns to fall. Based on ths, we may conclude that at low levels of expendture, the role of the subsstence parameter for food overwhelms the postve effect of the second term n brackets n equaton 5. Fgure 8 llustrates that results are also dfferent for Thaland, where the change n food s budget share arsng from the fve percent food prce rse s postve, but decreasng n expendture. However, as before, the change n food s share n the total non-durables budget 19