Risk in Developing Country

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The Review of Economic Studies Ltd.

Risk, Financial Markets, and Human Capital in a Developing CountryAuthor(s): Hanan G. Jacoby and Emmanuel SkoufiasSource: The Review of Economic Studies, Vol. 64, No. 3 (Jul., 1997), pp. 311-335Published by: Oxford University Press

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Reviewof EconomicStudies 1997)64, 311-335 0034-6527/97/00150311$02.00j 1997The Reviewof EconomicStudiesLimited

R i s k , Financial Markets,a n d Human Capital i n aDeveloping Country

HANAN G. JACOBYUniversity of Rochesterand

EMMANUEL SKOUFIASThe Economics Institute, BoulderFirst version received May 1994; final version accepted December 1996 (Eds.)

This paper exploresthe link betweenfinancialmarket ncompleteness nd human capitalaccumulation.We examinehow child school attendance esponds o seasonalfluctuations n theincomeof agrarianhouseholdsusing paneldata from ruralIndia. To pinpointmarket mperfec-tions,westudyresponseso aggregate nd diosyncratic,s wellasto anticipated nd unanticipated,incomeshocks. Our mainfinding s thatseasonal luctuationsn school attendance re a form ofself-insurance, ut one whichdoes not result n a substantialoss of humancapitalon average.

I. INTRODUCTIONDifferencesn the extent of financialmarketdevelopment ndhumancapitalaccumulationhaveboth beenput forth as explanations orwhysome countriesgrowfasterthan others.'But these two potentiallyimportantfactors in economic growth are linked: financialintermediationacilitateshumancapital nvestment.Whenfinancialmarketsarecomplete,investmentdecisions, ncluding hose in humancapital,are determined olely by rates ofreturn.Butwhen marketsareincompleteor imperfect, he separationof consumptionandhuman capital investmentdecisionsno longer holds, and time devoted to schooling isinfluencedby familyresources see, e.g. Beckerand Tomes (1986)). In under-developedeconomies,where ncomesaretypically ow anderratic, he impactof market ncomplete-ness on human capital accumulation s potentiallylarge. Yet, as an empiricalmatter,the connectionbetweenfinancial markets and educationalinvestmentsremainslargelyunexplored.2n this paper,we use panel data from ruralIndia to examine the responseof humancapitalinvestment n children o fluctuations n familyincome.A numberof studieshave used micropaneldata on consumption romthe U.S., orfrom developingcountries,to test the implicationsof completefinancialmarkets(see

1. On financialmarkets, ee Bencivenga nd Smith(1991) andGreenwoodand Smith(1993).Onhumancapital,see Lucas (1988); Barro(1991); Mankiw,Romerand Weil (1992).2. A handfulof empirical tudiesexamine he effectof borrowing onstraints n humancapitalaccumula-tion in the contextof U.S. college education.Lazear 1980)and Langand Ruud(1986) infer mplicitdiscountrate differentialsrom educationaldecisions.Johnson(1978)estimatesa modelof laborforceparticipation ycollegestudentsunder he assumptionof borrowing onstraints. acoby(1994)tests for the effectof borrowingconstraints n the timingof child schooling n a developing ountry.311


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312 REVIEW OF ECONOMICSTUDIESAltonji, Hayashi and Kotlikoff (1992), Altug and Miller (1990), Cochrane 1991), Mace(1991) and Townsend (1994)), or the weaker implicationsof the Rational ExpectationsLife Cycle model (see, e.g. Altonji and Siow (1987), Hall and Mishkin (1982) and Zeldes(1989)). But these studies shed little light on the mechanismsby which consumptionsmoothing is accomplished. f householdsadopt costly self-insurance trategies,such asliquidationof productiveassets in lean times (see Rosenzweigand Wolpin (1993)), thenconsumptionsmoothing no longer entails a simplereallocationof resourcesacross timeand states that holds expectedwealth constant. Instead,householdsmay trade-offwealthfor smooth consumption.Our interest ies in the possibilitythat poor, agrarianhouseholds acking access toformal inancialmarkets,or perfectly ubstitutablenformal xchange see, e.g. Rosenzweig(1988) and Cox (1990)), may draw upon the labourof their childrenwhen faced with anincome shortfall.Insofaras the erraticschool attendance hat resultscontributes o lowereducationalattainment,and thus to lower futureproductivity, his self-insurance trategymay perpetuatepoverty and under-development. o assess this cost of using child labouras insurance,we propose and estimate a dynamic,structuralmodel of human capitalinvestment.Although many previousstudies haveexamined he role of family incomeindeterminingchoolattendance, nrollment r attainmentnbothdevelopedanddevelopingcountries(see Taubman 1989) for a reviewof the U.S. literature),none has explored hedynamicsof school attendance.We also attemptto pinpointthe sources of marketfailureby studyinghow schoolattendancecovaries with differentcomponentsof income. Our empiricalapproachthusbuilds on the work of Altonji and Siow (1987), who regressconsumptionchangesondecompositionsof incomechanges.An advantageof school attendancedata is that oneavoidshaving o makeuntestedassumptions egardingntra-temporaleparability etweenconsumptionand leisure,or betweenvariouscomponentsof consumption e.g. food andnon-food, durableand non-durable).Of course,interpreting chool attendancedata alsorequires mposing some theoreticalstructurea priori, so this study should be viewedascomplementary,ather hanas a rivalapproach, o the consumption-basedests of finan-cial marketstructure.3Our strategy s to test down to progressivelymore autarkicmarket structures.Forinstance,the hypothesisthat marketsare completewithin villages is much weaker thanthe hypothesisthat marketsare completeacross and within villages.In the formercase,we expectchildschool attendance o respond o aggregate hocks(e.g. regionaldroughts)but not to idiosyncraticshocks. Similarly,the hypothesisof perfectcredit markets isweakerthan the hypothesisof complete markets. Even though credit marketsenableconsumption smoothingin the face of anticipated ncome fluctuationsand provideex-post insurance n the form of emergency oans, unless households are insuredex-ante,theywillbe worse off if incomefallsunexpectedly.4 ninsuredhouseholds houldthereforewithdrawchildrenfrom school in responseto unanticipatedncome shocks, but not inresponseto anticipated hocks.

3. One criticism f consumption ata, particularlyn the contextof paneldata studies, s that it is typicallymeasuredwith considerable rror (see, e.g. Altonji and Siow (1987)). One reason we might expectschoolattendance o be measuredwithlesserror hanconsumption, speciallyat high frequencies, as to do with thefact that most consumption oods are storeable.Thus, over short intervals, ctualconsumptionmaynot corre-spond closely to purchases,uponwhich measured onsumption s based,while school attendancedoes reflectthe intensityof currenthumancapital nvestment.4. The distinctionbetweencreditand ex ante insurance s not necessarily lean in practice.Udry (1994)shows that loan repaymentsn ruralNigeriaaremadecontingentupon cropoutputs,thus servingan insurancefunction.


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JACOBY & SKOUFIAS RISK AND HUMAN CAPITAL 313We examineseasonality n farm income, which has receivedsome attention recently(see Sahn (1989) and Paxson (1993)). Although seasonalfluctuationsare largely antici-pated by households,neitherthe timing nor the intensityof the Indian monsoon is fullypredictable.The key to distinguishing redit marketfrominsurancemarket imitations s

a decompositionof incomechanges nto anticipatedand unanticipated omponentsalongthe lines of Altonji and Siow. However, our agrarianhouseholddata provide us with abetter nstrument or unanticipatedncomeshocks than wasavailable o Altonji and Siow,namely, village level rainfall"surprises".We exploit the fact that rainfallsurprisesaffectfarmers differentlyto estimate the impact of idiosyncratic ncome shocks on schoolattendance.In Section II, we use a model of human capital investmentunder uncertainty opredict he responseof school attendance o income fluctuationsundermarketstructuresranging rom complete o autarkic.SectionIIIdiscusses heICRISATdata set and SectionIV develops the econometricspecificationsused to test the hypotheses.After presentingourempirical esults n SectionV, weuse ourestimatedparameterso simulate heimpactof financialmarket ncompleteness n humancapitalaccumulation. ectionVI summarizesour findings.

II. THEORETICALFRAMEWORKA model of human capital investment under uncertaintyOur centralassumption s that householdsperceivea positivereturn to educatingtheirchildren.So, beforepresentingour model, it is worthdiscussing he payoffsto schoolingin village India. Returnsto education n the agriculturalabour market,given the menialnature of the work, are likelyto be negligible we presentevidencesupporting his claimbelow). Nevertheless,averagegradeattainmentn the six ICRISATvillagesthatwe studyin this paper rose steadilyby cohort for both males and females, nearly doublingin ageneration.Walkerand Ryan (1990) arguethat education n thesevillagesis a route tomore lucrative employmentoutside of agriculture.Education may also enhance farmmanagementability, particularlyhe abilityto employnew technologies see Rosenzweig(1995) and Foster andRosenzweig 1996)). To investigate hishypothesis or oursample,we estimatea conditional armprofitfunctionwith household ixedeffectsusingdata forsixICRISATvillages.Ourspecification llows the educationof the householdhead(whichaveragesabout 2 7 years)to shift the level of profitsas well as to interactwiththe use ofhigh-yielding eed varieties(HYVs), whichpresumablymakes education more valuable.The estimates,reported n AppendixA (Table A.1) indicatesignificantlypositivereturnsto educationthat increasewith the fractionof land underHYVs. Thesefindingssuggestthat childrenare sent to school at least partlyin the expectationthat they will becomemoreefficient armers,better able to managetechnicalchange.5Considera household thathas a singlechildeligible or school overthe time interval[0, T], where the timeindext refersto consecutiveagriculturaleasons.Denote the state(cumulativehistoryof shocks)at timet by c,, and assumefor simplicity hat the numberof statesis finite. Schoolattendance,Si( ) = Sit (henceforthwe deletereferences o state),augmentsthe child'sbeginningof periodstock of humancapital,Hi,, accordingto the

5. This motive is certainlymore relevant or boys, who will ultimately nheritpartof the familyfarm.However, f there s positiveassortativematingon education, henschoolinggirls may improve heirmarriagemarketprospects.Among16-30year-oldsnoursixvillages, hemeaneducation f females s 2-1yearscomparedto 3 2 yearsfor males.


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314 REVIEW OF ECONOMIC STUDIESlearning echnology

Hi,+ =g(Sit, Hi,; Oit), (1)whereg is increasing n Si, and Hi,, and incorporates he possibility of human capitaldepreciation.An educationproductivity hifter,Oi,, s included o reflect,e.g. child illness6or aggregateeffects such as school closings. The form of g determines he cost, in termsof human capital, of using child labour as insurance.In particular, f g=Hitf(Sit; Oit)and f is log concave (i.e. log (f ) is concave), then a simple Taylor expansion argumentshows that stable school attendanceyields a larger final stock of human capital than avariableattendancerate with the same mean.The householdchooses total consumptionCi,and timein school, Si,t[0, KY],whereQ)4s the child time endowment,so as to maximizethe expected discountedvalue of atime separableutility function

EoEt=oP U(Cit) 0 (HiT+ , BiT+I) (2)where B s a subjective iscount actor,andEodenotesexpectations onditionalon informa-tion availableat time zero.At the endof the schoolingphase,households eavea "bequest"of financialassets,BiT+ I, anda child humancapital stockHiT+ I, thejoint value of whichis given by the increasing oncave function4. We ignore leisure,both of the child and ofotherfamily members,as an unessentialcomplication.The only cost of attendingschool is foregone productionor earnings(there are noschool fees in India), so that the price of child timeis the spot wage for child labour W,,assuminga child labour market.7n contrastto standardhumancapitalmodels (e.g. Ben-Porath (1967)), we assumethat the child wage is independent f the humancapital stock,at least while the child is still attendingschool. This assumptionnot only simplifies heempiricalmodel but is also plausible n the presentcontext.Wage regressions stimatedon the ICRISATsample see AppendixA, TableA.2) and on othersamplesof agriculturalworkers e.g. Rosenzweig 1980, 1995))showthat the returns o education n farm abourare not significantlydifferent rom zero.Our main concernin this paperis with responsesto changes,or "shocks", n fullincome,Fi,, definedas non-labour ncome or profit plus the valueof the householdtimeendowment.Sincefull incomereflects he total value of householdassets(includingwork-ers) priorto any consumption ransfersor ex post adjustmentsn familylaboursupply,changes n Fi,can be said to be truly exogenousto the household.To characterize he dynamicsof school attendanceat a general level, consider themarginalrate of transformation etweenschool attendance n adjacentperiods,

_ dS,I gs(t-l)zit=- - =9H(t) , (3)wheregH (t)= g(Sit, Hit; Oi)/aHi, and so forth are partialderivativesevaluated withrespect to the appropriate ime t, state c,, arguments.Regardlessof the structureof

6. Temporary hildillnessalso reduces he child'stimeendowment nd hence household ncome, houghsuch income effectsare not likelyto be large.7. The childwageis the appropriate riceof time evenif the child worksexclusively t home, providedthat his timeis eitherperfectly ubstitutablen homeproductionwith that of a siblingwho does participatenthe labourmarket,or perfectly ubstitutablewith that of hired labour.We considerthe consequencesof animperfect hild labourmarket n more detail later.


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JACOBY & SKOUFIAS RISK AND HUMAN CAPITAL 315financialmarkets, our model impliesthat school attendance s governedby the Eulerequation (see AppendixB for the derivation)8

E,_}jpi,(W,/W,_} )Zit=1, (4)wherepi, is the "shadowprice"of date t consumptionrelative o date t - 1 consumption,in a sense thatwill be clarified hortly.ThisEulerequation s simplya dynamic,stochasticversionof the statement hatthe marginal ate of transformation etween wo inputsmustequalthe ratio of their prices.Financialmarketstructureplaysa role in equation(4) bydetermininghe relevantpit.The impact of incomefluctuationson school attendanceunderalternative inancialmarket structures s most easily discussedusing an empiricalspecification or equation(4). So, letg(Si,, Hi,; Oi,)= (1- 6 )Hi,f(Si,; Oi,),where6 is the humancapitaldepreciationrate (0 < 8 < 1) and where

f(Si,;Oi,)=exp y-yexpt y[sit ji]})0.(This function has several desirable properties, namely, f(O; 0) = 1, f '> 0, f is log-concavefor all y, and log (Zi,)= (ASi, A0i, /y, whereA is the first-differenceperator.Note alsothatf ' is increasing or S< y log (y) and diminishing hereafter,making it necessary ocheckthat the resultingEulerequationdoes not in fact characterize local minimum.9To focus on incomeuncertainty, uppose that all changes n Oi,are anticipated thiscan be relaxed n the estimation).Removingexpectations romequation(4), taking logs,and rearranging ives

ASi,=- y(log (pi.) + A log ( W,) - log (1 + Xi'))+ A0i, (6)whereXi,is the mean-zeroerrorin forecastingpi,(W, W,t )zi.. Equation (6) says thatschool attendance alls with an increase n the child wage or with an adverseeducationproductivity hock (a negativeA0i,). Before turning o the role of financialmarkets,notethat if we allowf to dependupon Hi,, then the unobservablehumancapitalstock entersour empirical pecificationn a complicatedway. We return o this issuein the empiricalsection.CompletemarketsSupposethat households can trade in state contingentconsumptionclaims. This is anabstraction,of course,intendedto represent he potentialrole of informal nstitutions ninsuringconsumption see Townsend(1994)). Householdscovered by completefinancialmarketsare able to reallocate esourcesacrossbothtime andstatesat fixedprices;equiva-lently, they face a lifetimeexpectedwealthconstraint.Thus,pitis constantacross house-holds in the samemarketand is nothingmorethan the ratio (scaledby ,B)of the priceofa consumption claim in state c, say P(c, ), to that in state ,_-I, P(t,- I). Because equation(4) thus includesonly marketprices,along with zit, it impliesa separationbetweenahousehold'shumancapitalinvestmentdecisionsand its consumptiondecisions.

A complete-markets quilibrium(or an incomplete-marketsquilibrium, or thatmatter)may involve a whole constellationof villages,each diversifyingocal aggregate8. Throughout this paper we assume an interior solution for Si, at all dates and for all states. We willhave more to say on zeros in hours of school attended in the empirical section.9. An alternative form, f(S&,; Oi,)= exp ((-1 /y)(S1, O, )-y), has similar properties, except that log (zi,) isproportional to A log (S&,).For our simulations in Section V, (5) provides a somewhat more convenient form.


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316 REVIEW OF ECONOMIC STUDIESshocks,or it maybe confined o a village n isolation.Consider irst he undeniably xtremecase of completefinancialmarketsboth within and acrossvillages, in which all incomerisk is insured.Not only is pi,= p, constantacross householdswithin each village,but itis also constant acrossstates of nature(in particular,p,= 1/(1 + rf), whererf is the risk-free interestrate). Income shocks do not affect school attendance n this case, but Xi, nequation (6) is still nonzero becauseof wage shocks.'0Sincewages are presumably et ina village market,the forecasterror s the same for all households(cit = 4t).In a world of no inter-village rade,but whereeach villagehas completemarkets,pitis againconstantacrosshouseholdswithina village.However,becauseof aggregatencomerisk,pi,is uncertainand thus also contributes o ,it.As in thepreviouscase, theseforecasterrorsare common. To understandwhy,considerthe "representative"illagehousehold,which is autarkic by assumption;in other words, its consumptionC, (droppingthe isubscript)equalsits full incomenet of schooling costs, Ft- WtS,. For this household,ptis equal to the intertemporalmarginal ate of substitution n consumption.Consequently,shocksto Ft(aggregatencome)aretransmitted o school attendance.An aggregatencomeshortfallraises the shadowpriceof consumption n the periodin which it occurs therebymakingschool attendance n thatperiodmoreexpensive.Regardlessof the financial inksacross villages,complete intra-villagemarkets imply that a child's school attendance snot affectedby idiosyncraticncomeshocks."IncompletemarketsWhen consumption s not insurable x ante, so that financialmarketsare incomplete, heseparationbetween humancapital investmentand consumptiondecisionsbreaks down.Thedegreeof non-separation ependsupontheabilityof households o transfer esourcesacrosstime.To examine hepossibilities, onsidera functionRt,relatingnet assetsbroughtinto period t, A*, to net assets at the end of the previous period, Ai,tI, such thatA*= Rt(Ai_j). At one extreme is a perfect credit market, in which caseRt= (1+ rt l )A,i- I, where r,t is the market interest rate. At the other extreme is intertem-poral autarky, n which case R, 0. Moregenerally, he marginalcost of borrowingmaybe increasing,so that R' I when A, -I0as a resultof depreciation f stocks.


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JACOBY& SKOUFIAS RISK AND HUMAN CAPITAL 317under ntertemporal utarkywhereeventhisequationdoes not hold). Droppingexpecta-tions againand takinglogs gives

log (pi,) =-log (R,(A, - ))I+ log (1 +co,), (7)wherew,i is themean-zero orecasterror n pi,R'.This forecasterrorarisesbecauseunanti-cipatedincomeshockslead to revisions n a household's ntertemporalmarginalrateofsubstitution n consumption.The presenceof pitin (6), meansthat the forecasterrorinthat equation,X,i,and thusschoolattendance,mustalso dependon unanticipatedncomeshocks,eitheraggregate ridiosyncratic, ot merelyon aggregate hocksas undercompletemarkets.'3This statement s trueirrespective f the specific ormof R,.Theformof R, doesdeterminehow schoolattendance esponds o anticipatedncomeshocks.Underperfectcreditmarkets, orexample,Pitaccording o (7) dependsonlyuponthe realizedmarket nterestrateand a forecasterror,neitherof whichis affectedby theanticipated ncome shock of a particularhousehold. Consequently,school attendancedoes not respondto anticipated hocks.By contrast,withan increasingmarginalcost ofborrowing or storage),R,(Ai,t, ) and hencepitis affectedby anticipatedncomeshocks,and thus so is school attendance.However,the impactof anticipated ncomeshocks onattendance s generallyasymmetric.To see why,considera household hatexpectshigherincomenext period,and thereforewantsto borrowto raisecurrentconsumption.Doingso raises R, and thereby eadsto an increase n school attendancenext season accordingto equation(6). Onthe otherhand,if an income decline s anticipated, henthehouseholdwantsto pay off debt, resulting n a decline n R, and with it a fall in schoolattendance.Now, if R',"


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318 REVIEWOF ECONOMICSTUDIESTABLEI

A taxonomy f income ffectsonschoolattendanceIdiosyncratic Aggregate village)

Marketstructure Anticipated Unanticipated Anticipated UnanticipatedComplete ntra-villagemarketsand:Complete nter-villagemarkets None None None NoneInter-villagereditonly None None None YesVillageautarkyand:Complete ntra-villagemarkets None None Yes YesIntra-villagereditonly None Yes Yes YesHouseholdsavingonlya Asymmetric Yes Yes YesHouseholdautarky Yes Yes Yes Yesa Also if borrowings possiblebut at an increasingmarginal ost.

relieson variation n the childwage,as this is the only variableon the right-hand ideof(6) that is directlyobservable.

III. DATAThe VillageLevel Studies(VLS) survey,conductedby the InternationalCropsResearchInstitutefor the Semi-AridTropics (ICRISAT), selectedten villages to represent ourbroadagroclimatic ones of semi-arid ndia (Walkerand Ryan (1990)). In each village,a stratifiedrandom sampleof forty householdswas chosen,consistingof equalnumbersof landless,small, medium,and large scale farm households.We use data on the timeallocationof childrenages 5 to 18 from six of these villages:Aurepalleand Dokur inAndhraPradesh;and Shirapur,Kalman,Kanzara,and Kinkheda n Maharashtra.Aurepalleand Dokur have red soil with limitedwaterstoragecapacity,and rainfallin these villagesis highlyunpredictable.Castor,paddyand sorghumare the main crops,cultivatedmainlyduringthe rainyseason.Shirapurand Kalmanhave blacksoils, whichretain more moisture, so the main crop, sorghum,is cultivatedduring the post-rainyseason. Both the level and timing of rainfallare also erraticin these two villages. InKanzaraand Kinkheda, armerscultivatemainlycotton, mungbeansand sorghum,andhave more reliablerainfall. Overall, rrigation s relativelyuncommon,except in Dokurwhereirrigated and is about 30%of grosscroppedarea.Detailed time allocation data, based on a one-day recall, was collected for eachhouseholdmemberon a monthlybasis from June 1975to the end of 1978 (the surveyended earlierin Dokur, Kalmanand Kinkheda).Since in none of the villagesis thereappreciable ultivationduringthe summer when,interestingly,he main schoolvacationis taken), we divide each agriculturalyear into two crop seasons; the rainy (Kharif)season and the post-rainy(Rabi) season. Plantingand sowingoperationsof the Kharifseasoncontinuethroughthe thirdquarterof the calendaryear,whilethe Kharifharvesttakesplacein thefourthquarter.The firstandsecondquarterof the calendaryearcoincidewith the harvest of the Rabi season crops. Farm incomes also fluctuatewithin theseseasons, as the plantingperiod is typicallya time of scarcitycomparedto the harvest.Althoughschool attendancemay also fluctuatesubstantiallywithinseasons,we focus onchangesbetweenseasons.One reasonfor doing so is to avoid cuttingthe data too finely


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JACOBY & SKOUFIAS RISK AND HUMAN CAPITAL 319and therebyexacerbatingmeasurement rror.Moreimportantly, ull incomeis not a welldefinedconcept exceptover a completeproductioncycle.'4We take two alternative easonalaveragesof schoolinghours,whichinclude traveltime to school. SI') averagesall of a child's monthly observations n a given season,including hose of zero reportedhours,and thus takes into account missedschool days.However,to the extent that zero reportedhours in school reflects he day of interview,S") may be subjectto measurement rror.Householdsweresupposedly nterviewedonregularworkdays, but it is not clear that the previousday, the day of reference,was notsometimesa Sundayor holiday.S(2) averages ust thepositivemonthlyobservations, huscapturingadjustmentsn the lengthof the school day.Fromour initial sampleof 475 children,we excludethose who neverattendedschoolduringthe survey period (we addressthe potentialsampleselectivitybias below). Afteralso deletingobservations o eliminate non-consecutive easons (32 cases) and childrenwith only a singleobservation 19 cases), we are left with 1256season-yearobservationson 258 children;161boys and 97 girls.Of theseobservations, here are212 cases of zeroschoolhours for a wholeseason,84 of whichoccurbetween wo seasonsof positiveschoolattendance; n otherwords,they are transitorywithdrawals rom school. The remaining128zeros occurat thebeginningor the endof thesamplingperiodforthe child n question,and thus are more likelyto reflecteither a delayin startingschool or a permanentdropout. Figure 1 plots villagemeansof the two school attendancemeasures,S(t) (excludingthe 128 zero observations ust mentioned)and S(2). The smoothertime series of S(2)relativeto S(1) points to the need for a sensitivityanalysis.

A SMl) Hours/Day)0 ChildWage/Hr Rps.x 20) + S(2) (Hours/Day)Aurepalle Dokur Shirapur8-0 -7.9 67

2 ~ ~ ~ ? ? u 2 i i 2 I 2 . . 3-2 2*61234567 12A4567 1 23456Kalman Kanzara Kinkheda6-0 5.7 -7*1

30 2-7 - 4.0123 4 567 1 23 4 567 12 34 56 71= 75:Kharif,2= 75:Rabi, 3 =76: Kharif, tc

FIGURE ISeasonalschool attendance nd childwages

14. In subsequentwork (Jacobyand Skoufias 1995)), we have examined onsumption moothingwithinthe Kharifseason.Usingdata from threeof the villages,Aurepalle,Shirapur nd Kanzara,we find no evidencethat consumptionrespondsto within-season hanges in farm income. Notwithstanding he possibilitythatconsumptionmay be measuredwith greatererror han schoolattendancen thisdata set, these resultssuggestthat within-season choolingfluctuationsmight not be very large.In any event,not takinginto accountsuchwithin-season ariationwould bias our tests of completemarkets n favourof the null, which,in the end, wereject.


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320 REVIEW OF ECONOMIC STUDIESAveragehourlywage rates for adult males, adult femalesand children n each villagefor each season-yearare calculated rom observationson daily wages and hours of casuallabourers.Child labour market participation s only about 20% overall (based on theinitial sample of 475 children),an issue addressed n the next section. Figure1 indicates

that villagemean childwages generally end to move in the opposite directionof schoolattendance,exceptin Dokur.Full income is calculated as F= (wvmNm wfNf+ w,N,)Q + HI+ V, where the Ni, i=m, f, c, are, respectively, he numbersof adultmales, adultfemales,15and childrenresidingin the household n any given season; the wiare the respectivevillage averagedaily wagerates;Q is the totaltimeendowment,assumed o equal 156days each season; nI s seasonalprofit from crop cultivation,defined as value of output (includingby-products, uch asfodder) minus expenseson variable inputs inclusive of family labour16; and V is netseasonal revenuefrom sales of livestockproducts (e.g. milk and bullockrental), handi-craftsproducedwithinthehousehold,and landrental.17"18 ealsoexaminea conventionalincome measure,denoted by Y, whichis likely to reflectthe ex post adjustmentsof thehousehold (Y=w,,,Lm wfLf+ w +.L. H+ V, where the Li are the total labour supplyofmales, femalesand children).In calculating Y,we use reported abourearnings cashandin-kind) receivedby family membersemployedeither as regularor casual workers.Figure2 plots the village means of both income measures,deflated by the districtlevel price index with base year in 1975. As with schooling hours, Figure 2 suggestshigh intertemporal ariabilitywithin any given villageas well as considerablenter-villagevariability.The plot for Kanzarashows the most distinctseasonal incomepattern,con-sistent with rainyseason cultivationof its main crop. Incomeseasonality s reversed nShirapurand Kalman becauseof sorghumcultivationduringthe Rabi season.

IV. ESTIMATION STRATEGYTesting for complete markets within and across villagesTo obtain an empirical pecificationor equation (6) thatallows us to test the hypothesesin Table 1, we first project the shadow price and forecast error terms,log (pi,) - log ( + i,), linearly on the idiosyncratic and aggregate components of thehousehold-specificull incomechange. Thus,we obtain the regression

ASiv, ao+ a A log Fiv,+ a2A og Fv,-yA log Wv, civ,, (8)whereASiv, s the changein school attendanceof child i, in village v, from season-yeart - 1 to season-year ; Alog Fiv, s the deviationof the changein log full incomefromthe

15. Rosenzweig 1988)excludes he value of the female imeendowment rom his measureof full incomebecause,over the nineyearsof the ICRISAT urveyhe uses, the numberof women n the household luctuatesconsiderably ue to marriage,whichmay reflect ntra-familynsurance rrangements. incewe look at a muchshorterpanel,and becausedemographicnformation s reportedon a yearlybasis, thus not contributingowithinyear changes n full income,we include he value of the female ime endowment.16. Expense tems are seeds, fertilizers,manure,pesticides,machineservices,owned and hired bullocklabour,hired and family male, female and child labour (all valued at the gender/age specificvillage averagewage rates). Someof theseinputsmay have been purchasedn priorseasons,but this is difficult o tell from thedata. 17. Note that V is not a pure profitmeasure, incethe allocationof familial imeto livestockand handi-crafts activities s unknown.Thus,F may be contaminatedby ex post laboursupply adjustments,houghthiscontaminations unlikely o be serious.18. Forty-seven bservations re droppedbecauseof missingfull income,and four aredroppedbecausefull income s negative sincewe later takelogs).


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JACOBY & SKOUFIAS RISK AND HUMAN CAPITAL 321A Full Income +'Conventional' Income

Aurepalle Dokur Shirapur6741 8013 - 4862

1082 -1305 656123 4 5 6 7 4 5 67 12 34 5 6 70 Kalman Kanzara Kinkheda

- 3365 5205 3315 -

> 90 802 - _ __ _ __ _ 404 AI I1 2 3 4 5 67 1 2 3 4 5 6 7 1 2 3 4 5 6 7= 75: Kharif, 2 = 75: Rabi, 3 = 76: Kharif, etc

FIGURE2Alternative seasonal income measures

village-season-yearmeanchange(theidiosyncratichock)andAlog F", s this meanchangeitself (the aggregateshock); and Alog We,, s the changein the log of the villagemeanchildwage.'9Thedisturbance ermciv,captures choolproductivity hocks,AO,i,assumedinitially to be orthogonal to changes in full income and child wages,20and possiblyunmeasured omponentsof income shocks.Thehypothesisof completemarketsboth withinand acrossvillages mpliesthat a =a2= 0. For a cleanertest of this hypothesis,we will also use dummyvariables o controlfor season-specificaggregateeffects. If we find that al >0, then we have evidencethatmarketsare incompletewithinvillages.But a, = 0 is only a joint test againstthe failureof intra-village redit and insurancemarkets.To makefurtherprogress hroughTable 1,we must use informationon rainfallsurprises.

Distinguishing between credit and insurance marketfailureThe key to decomposingAlog FiV,nto anticipatedand unanticipated omponents s toallow the effect of rainfallsurpriseson farm incometo vary across farms.So, considerthe regression

A log Fivl= Ovv,+Xi,-1 ,PI + (Xiv,0-DRv,)'32 + uiv, (9)

19. Child abourmarket mperfections ould break heseparation etweenhumancapital nvestment ndfarmproductiondecisions mplicit n our model. In thiscase,changes n the shadowwage(seeJacoby(1993)),ratherthan the mean village wage, belong in (8). The sign of the omittedvariablebias depends upon thecorrelationbetween he change n the shadowwageand the change n full income,which s uncleara priori. Ifthe correlations positive, hen the incomeeffectswould be underestimated, iasingourresults n favourof thenull hypothesis.20. Shocksdue to child illnessmaynot be uncorrelatedwithchanges n full income f parentaland childillness are correlated.To the extent that predeterminedarmcharacteristics re orthogonal o current llness,our instrumental ariables chemeappliedbelowwillcorrect or this problem.


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322 REVIEW OF ECONOMICSTUDIESwhere 3ov, is a village-season-yearntercept,Xi,,_1 is a vectorof farmcharacteristicsaggedone season, DRV, s the deviationof rainfall from the long-run village mean in season-year t, and uiV,s a randomcomponentconsistingof unobserved actors affecting ncomechangesand measurement rror.The Kroneckerproduct(0) generatesa vectorof inter-actionterms.Our estimatesof the anticipatedand unanticipated omponentsof the idiosyncraticincomechange are thus, respectively,

A log Fi,vtX',, _ l l (10)A log Fuvl (Xiv_I0 DRV. ' 2*( )

The anticipatedcomponentis the projectionof the actualchangein income (net of anaggregatecomponent)on informationavailable o the household at time t- 1, while theunanticipatedcomponentis predictedfrom informationunknown to the household att - 1, namely Xiv,_1?DRv,. 21 These interactions between farm characteristics and rainfallare indispensableor identifying he idiosyncratic,unanticipatedncomechange,sincebyitselfDRv,would be swept out with the village-season-yearntercepts n (9).Returningto the school attendanceequation, we focus on idiosyncratic hocks byintroducingvillage-season-yearntercepts,a0v,, to purgeaggregateshocks (and wages).We then allow Alog Ff"v,nd Alog F,u, o have separatecoefficientsand estimate22

ASiv, aov,+ alaA log Fav,+aIuA og Fuvt,+livt. (12)This equation provides a test for perfect intra-village redit markets(aia = 0) as well asfor perfect insurance markets (alu=0).Our specificationdiffers n threeways from Paxson's(1992) use of rainfalldata topredicttransitory ncome and estimateits effect on savings in Thailand. First, Paxsonignoresvillageor region-specific ggregateshocksin her savings equation;althoughsheincludesregion and time dummies,she does not include interactionsbetween the two.Thisimplicitlyassumes hat interestrates n different illagesmovetogether, husimposinginter-village reditmarkets.Second, n Paxson's ncomeequation,the effectof unexpectedrainfalldoes not dependon farmcharacteristics,o that differencesn transitory ncomeacrosshouseholdsarepurelyrandom.Third,Paxsonpredictsevels,as opposedto changesin income.Thus,unobservedhousehold ixed effectscorrelatedwith householdcharacter-istics could bias herestimatesof permanentncome.Finally,note that in estimatingequation (12), standarderrorsmust be corrected orgeneratedregressors,namely,(10) and (11). This calculation s complicatedby fact thatthe uiV, ontain unobservedcomponentsof income changesand thus will generallybecorrelatedwith the Thw,becausethe latter contain unobserved esponses o these incomechanges.We base our covariancematrixestimateson formulaeprovided n MurphyandTopel (1985),modified o accountforarbitraryormsof heteroskedasticitynd autocorre-lation. Details of the calculationsare availableupon request.

21. We investigatebelow whetherseasonalrainfalldeviationsare predictablebasedon laggedrainfalldeviations,and thusindeedrepresenturprises.22. We do not includethe residuals rom (9), ui,,, becausethey generallycontainboth (unexplained)anticipated ndunanticipatedomponents.Enteringhem ntoequation 12) imposes hepossibly nvalidrestric-tion that the effect of anticipated nd unanticipatedncomeshocksare identical.


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JACOBY & SKOUFIAS RISK AND HUMAN CAPITAL 323Testing against borrowingconstraintsAs seen in Section II, increasingmarginalcosts of borrowingpresent a more restrictivealternative han autarky(which says that ala=0), because they may imply asymmetriceffects of anticipatedncomechanges.To test against this alternative,we estimate

ASiv,= aov,+ a+ D+,A log Fav,+aK(I -Di,)A log Fv,+ alA log Fv, + T7ivt, (13)whereD+, = 1 if A log F,a,> 0, and D+,= 0 otherwise.The null hypothesisof perfectcreditmarkets is a+ = a = and the alternative hypothesis of borrowing constraints isaj > al, whichsays that householdsadjustchild school attendancemorein response oanticipated ncomegrowth.23'24reditrationing s implied f ala= 0, since school attend-ance should not respondat all to income declines hat householdscan anticipate hroughsaving.

V. ESTIMATION RESULTSBaseline specificationWe firstexplore ssues of variablespecificationby regressing hanges n school attendanceon a setof villagedummies,andon changes n log incomeandwages.25Row (1) of Table2reportsOLS estimatesusingV), the unconditional easonal meanof school attendance,and trimsconsecutivezeros from the beginningand end of each child's time series aspreviouslydiscussed.26 ow (2) does the sameon the untrimmed ample ("+ zeros").Inbothrows,the effectof changes nchildwagesand full incomearein theexpecteddirectionand areremarkably ignificant t-valuesare corrected or arbitraryorms of heteroskedas-ticityand autocorrelation).Row (3) replicates ow (1) usingthe conditionaleasonalmeanof schoolattendance,S(2) (droppingobservationswith zero school attendance or a seasonlowers the samplesomewhat).The resultingwageeffect s substantiallyweakerandthe income effect is nowinsignificant, uggestingthat most of the economically meaningfulvariationin schoolattendance s in days attendedrather han in the lengthof the schoolday.Row (4) replaces ull incomewith the conventionalmeasureof income Y(the samplesizeis lower due to missingearningsdata). The income effect s much smaller hanin row(1), consistentwith an expecteddownwardbias from an income measurecontaminatedby ex post adjustments.

23. Altonjiand Siow (1987) proposea similar est for symmetryn the responseof consumption o incomechanges. As noted above, unless there is credit rationing, he hypothesison the directionof the asymmetryrequires n assumptionon the sign of R"',which s not intuitively bvious.24. A caveat in interpreting his test is that some childrenmay be constrainedby the upperbound onhours per day in school. If a child is alreadyattending choolfull-time, hen an increase n incomecannotleadto increasedattendance ven if borrowing s constrained. n other words, it may appearas though borrowingis unconstrainedven though it is constrained, hus diminishing he power of the test. However,as we will seebelow, most of the variation n school hours is in days attended,whichare less likely to be constrained romabove.25. At thispoint,we impose he constraint hat a = a2 in equation 8). Relaxing his constraintdoes notaffectthe conclusions n this subsectionand only clutters he analysis.26. Wealso test this semi-logspecification gainsta log-log specification cf. footnote 9) usingthe trans-formation AS1', =SiA'!-, ASi,, proposed by Layson and Seaks (1984). The Maximum Likelihood estimate of A isI 20 (100 observationswitheitherSi,,, or Si,- equalzero are dropped).Althoughwe reject he semi-log,A=I (x( =22-8), we do not reject t nearlyas decisivelyas we do the log-log specification,X=0 (x(1 = 1411!).Moreover, he semi-log specification nd the model with the transformed ependentvariableA producesimilar ncomeand wage coefficients.


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324 REVIEWOF ECONOMICSTUDIESTABLE2

Baseline specificationfor school attendanceSpecification A Incomea A log (We,) R2 Nobs

Including village dummies:(1) ASi',, 0 536 -2-094 0-078 867(3-81) (6-26)(2) AS(,,,),+zeros 0-511 -1 911 0-070 995(3-88) (6-22)(3) AS,2,) 0-071 -0-744 0045 767(0 97) (3-77)(4) AS(,,,)A log Yi,, 0-216 -1 800 0-068 788(3-45) (5 03)(5) ASj,,,),ncludingadultmale wageb 0-571 -1 393 0-093 867(4-16) (3 52)Including village-season dummies:(6) AS(,,,) 0 257 -1-030 0-144 867

(1-65) (2 50)(7) ASi,,,)Childfixed effects) 0-266 -1 803 0 337 867(1-67) (4-26)(8) AS3,,,)Childfixedeffects nstrum.variablesc) 0-185 -1 407 0 355 612(125) (189)Note. Absolute -values n parentheses, orrectedor arbitraryormsof heteroskedasticitynd autocorrelation.a Change n log full income,unlessotherwisenoted.b The coefficient n change n adult male wageis -2-536 (t=3-83)cAlog ( W, ) instrumentedy thechange n child wages aggedone period,rainfalln t - .1and t- 2, andvillage-seasoninteractiondummies.T-values orrected or generated egressors.

If childlabourmarketsarethin, then villagemeansof child wagescouldbe unrepre-sentativeof the shadowvalue of childtime. The significance f the childwagevariable nTable2 is thus encouraging.However,childwagechangesmay also reflectother villageshocks, such as changesin adultproductivity.Row (5) shows that includingchangesinthe log of the villageaverageadultmalewagestill leadsto a stronglynegativechildwageeffect and an income effectclose to that in row (1). We obtain similarresultswhen weincludechanges n adultfemalewages (not reported).We now considerequationspecificationssues nmoredepth,basingallfurther egres-sions on the variables and samplein row (1). Row (6) sweepsout permanent,village-specific,seasonalfactorsusinga full set of village-seasonnteractiondummies, he mainimpactof whichis a drop in the size and significanceof the income effect.We returntothis point shortly.Row (7) takesout, in additionto village-season ffects,child fixed effects.Thispro-cedurecorrects or possiblesampleselectionbiasdue to the exclusionof the 195 childrenwho neverattendedschoolduringthe samplingperiod.Selectivitymayleadto downwardbiasedestimatesof income and wage effects,becausethe childrenwho would have beenmoreresponsive o income and wagechangesendup quittingschoolearlyor neverenrollin the firstplace. Furthermore, ixed effectspartiallyaddressthe functionalform issue.Recall that if our specificationof the learningtechnology s incorrect, hen the stock ofhumancapital,which variesovertime,entersthe school attendance quation.It is impos-sible to test directlyfor the presenceof Hi, since, not only do we not have a tractablealternative ormforg, but Hi, is unobservable.27 owever,we can treatthe initial(i.e. as

27. If the stock of humancapitalis correlatedwithchanges n income,then we might falsely reject hecompletemarketshypothesis.Unfortunately, he ICRISATdata set does not providea measureof humancapitalthat variesovertime,suchas achievement est scores.Moreover,gradeattainments only recordedbylevel(primary, econdary, ndso forth),whichvaries ittleoverthe shortsampleperiod hat we have.Although


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JACOBY& SKOUFIAS RISK AND HUMAN CAPITAL 325of the beginningof the sampleperiod) stock of humancapital as a fixed effect, if weassumethat it entersthe school attendanceequationlinearly.The fixed effectsestimatesin row (7) are significantlydifferent romthose in row (6), but mainlydue to the higherwagecoefficient; he incomeeffectis practicallyunchanged.

A finalissue to explore s the endogeneityof A log (W,,,)due to correlationwith theforecasterror in equation (6). Note that we do control for ex post changes in pi, byincludingthe incomechangevariable.To instrumentA log (Wv, we use changesin thechild wagelaggedone seasonback,laggedrainfallvariables,andvillage-seasondummies,but not the change in full income, as this variablereflectsnew information.28 he IVestimatesin row (8) are based on a smallersamplebecauseusing lagged variablesasinstrumentsmeansdroppingthe first seasonof data. However,a Wu-Hausmantest (p-value=0 32) indicatesthat the estimateof y is not significantlydifferent rom its fixedeffect counterpart stimatedon the same sample,nor from the estimate n row (7) on thelargersample.In fact, the IV estimateof y lies in betweenthe 1-03and 1 80 estimatedfromour otherspecificationswithvillage-seasondummies. t is also worthnoting thatforthis rangeof y the marginalproductof school attendancebeginsto decreasewell beforeattendance eaches ts samplemean,whichsuggests hattheEulerequation ndeedcharac-terizesa local maximumon this sample.Aggregate vs. idiosyncraticshocksTable3 beginsour analysisof financialmarketstructurewithchildfixedeffectsestimatesof equation (8). Row (1) decomposesthe change in full income into its idiosyncraticandaggregate omponentsand includesonlyvillagedummies.Aggregate ncomechanges(village-season-yearmeans) attract a much largercoefficient han idiosyncraticchanges(i.e. a2> a, ). However,beforewe can concludethatvillage-wide luctuationsn seasonalincomeareharder o insure hanidiosyncratichocks,wemust controlfor seasonal actorsthat affectschool attendance hroughother channels hanincome or wages.Thus,in row(2) of Table 3 we reintroduce he village-seasondummies,with the resultthat a2 is nolonger significantlydifferent rom zero, and in fact becomesnegative.Two conclusionsemerge:Eitheraggregatencomeshocksarefully nsured, venthough diosyncratichocksarenot, whichseems mplausible; r, mostaggregate easonal luctuationsarepredictableand hencecollinear with the village-seasondummies.A problemwith the latterview isthat inspectionof Figure 2 suggests that village-wideseasonal income movements areprobablynot highlypredictable, xceptperhaps n Kanzara.To make furtherprogress,we turn now to village-specificegressions.Rows(3)-(5) of Table3 reportseparate stimatesof equation 8) for thethreevillageswith all seven seasons of data: Aurepalle,Shirapurand Kanzara.In both Aurepalleand Shirapur, diosyncratic hocks have significant,and about equal, effectson schoolattendance,whilein Kanzarawe cannotstatisticallyrejectcompletemarkets.That childlabourplaysless of a self-insurance ole in Kanzaracould reflect he fact that its rainfallis the highestand least erraticof the threevillagesor it may reflectthe abundanceofformalcredit institutions n Kanzararelative o Aurepalleand Shirapur see WalkerandRyan (1990)). We also find importantdifferencesacross villages in responsiveness oaggregate ncome shocks. While the estimateof a2 is negativebut insignificantn bothnot a directmeasureof humancapital,currentage of the childcouldbe included,but the effectof agingwouldbe compoundedn the village-season-yearummies hatwe use later.28. The analogous ssue arisesin intertemporalaboursupplymodelswith uncertaintysee, e.g. Ham(1986)),where ime dummiesare excluded romthe instrumentet wheninstrumenting agechanges.


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326 REVIEWOF ECONOMIC STUDIESTABLE 3

Effectsof aggregate nd idiosyncraticncome hangeson schoolattendanceSpecification a, a2 -Y r2 Nobs

(1) Full sample 0-391 0-936 -2-88 0-299 867w/village dummiesa (2.14) (4.08) (7T24)(2) Full sample 0-384 -0-628 -1-29 0 343 867w/vil.-seasondummiesa (2 23) (1*37) (2 82)By village:(3) Aurepalle 0 703 -0 128 -2 52 0 292 155w/season dummya (2'09) (0 09) (0 96)(4) Shirapur 0-714 1-42 -0-85 0 335 247w/season dummy' (2-05) (2-79) (1-60)(5) Kanzara 0-292 -1-25 -3-26 0-321 204w/season dummy' (1-30) (1-28) (4'84)Including illage-season-yearummies:(6) Full Samplea 0-388 0-449 867

(2-35)(7) Full sample 0-320 0-261 867(1-96)(8) Small armb(OLS) 0-187 0-243 501(0 64)(9) Smallfarm(2SLS)C 1 00 0 224 501(2-68)(10) Large arm (OLS) 0-510 0-368 366(2-23)(11) Large arm(2SLS)c 0495 0368 366(1-56)Note: Absolute -values nparentheses,orrected or arbitraryormsof heteroskedasticitynd autocorrelation.a Specificationncludeschild fixed effects.b Small farmers nclude andless, mall and medium armhouseholds.c First-stage egression esultsreportedn AppendixTable A.3.Aurepalleand Kanzara, n Shirapur t is significantlypositiveand twice the estimate ofa,. Thus,households n Shirapurappearto conformto our priorthat school attendanceshouldrespondmoreto aggregate han to idiosyncratichocks.Consistentwiththisfindingis the comparative rregularity f seasonal ncomepatterns n Shirapur eenin Figure2.The rest of Table 3 prepares he way for our analysis of idiosyncratic hocks. Theimportanceof these shocks, and thus our rejectionof intra-village ompletemarketsonthe full sample, s reinforcedn rows(6) and (7), which takeout all aggregate hocks(andwagesin the process)usingvillage-season-yearnteractiondummies.Row (6) displays hechildfixed effectsestimates,and row (7) removesthemagain,which has little impactonthe income coefficient as in Table2). We thus ignorechildfixed effects n the remainderof the analysisto preservebetween-child ariation n the data.The last four rows of Table3 focus on farmsize.If accessto villagefinancialmarketsis positively relatedto householdwealth (see Morduch (1990) and Townsend (1994)),then we expect idiosyncraticncome shocksto have moreof an impacton children romsmallfarmsthanon those fromlargefarms.However,rows(8) and (10) appearto showjust the opposite.The OLS estimates ndicatethat school attendanceof children rom thelargefarm households,but not that of childrenfrom landless,small and medium farmhouseholds,respondssignificantlyo idiosyncraticncomechanges.29However,as it hap-pens,these resultschangewhen we instrument ncome.Rows (9) and ( 11) report he2SLS

29. Note that landlesshouseholdsreceiveminimal armprofits,so most of theirincome is fromwages.Sincewe usevillageaveragewages, he landless xperience nlysmall diosyncraticncomechanges manyreportincomefrom non-farmself-employment ctivities).When we exclude landlesschildren rom the small farmsubsample,he resultsarenot appreciably ffected.


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JACOBY& SKOUFIAS RISK AND HUMAN CAPITAL 327estimatesusingthe sameinstrument et (describedbelow)thatwe use in estimatingequa-tion (9). Row (9) indicatesa significantbias towardzero in the OLS estimates or smallfarmers,whichwe attribute o measurement rrorin income.Thereis no such evidenceof attenuationbias for large farmsin row (11), nor for that matteron the full sample(resultsnot reported),whereinstrumenting nly reducesthe precisionof the estimates.We conclude,therefore,that small farmersare not, after all, better insuredthan theirlargerneighbours.30

Anticipated vs. unanticipatedshocksWe next decompose diosyncraticncomechanges nto theiranticipatedand unanticipatedcomponentsusingequation(9). Givenour results n Table3, we do so separately or thesmall and largefarmsubsamples.As seenin AppendixA (TableA.3), the instrument etincludes aggedfarmcharacteristics, s well as interactionsbetweenthese characteristicsand: (i) current deviationsof quarterly(three-month)rainfallfrom ten year averages(1975-1984); (ii) the squaresof these deviations;and (iii) the day (since January1) ofonset of the monsoon. Preliminaryo our income decomposition,we checkedwhethertheserainfalldeviationsrepresent urprises r whethercurrent ainfall s partlypredictablebasedon previousrainfall,and adjusted he rainfalldeviationsaccordingly.31'32Table4 reportsestimatesof equation(12), whichallows the anticipated nd unantici-pated componentsto have separatecoefficients.The full sampleregression n row (1),

TABLE4Effects of anticipatedand unanticipatedidiosyncraticincome changes on schaoolattendance: instrumentalvariables estimatesSample al,, alu R2 Nobs

(1) Full sample 0-195 0-250 0-258 867(1-70) (1-48)(2) Smallfarms 0-939 1 00 0-251 501(2-34) (2 69)(3) Large arms 0-639 0-361 0-356 366(1-98) (0 98)Note. Absolute -values n parentheses,orrectedorarbitraryormsof het-eroskedasticity nd autocorrelation nd for generated egressorssee text).All specificationsncludevillage-season-yearnteraction ummies.First-stageregression esultsreportedn AppendixTable A.3.

30. Oneexplanation or this farmsizedifferential,uggestedby a referee,has to do with labourmarketconstraints. diosyncraticabourproductivity hocks(not capturedby villagewages)mayaffect argefarmersmore than small farmersbecause the former are more constrained n the hiringof child labour.If so, andunobservedabourproductivityhocksarepositively orrelatedwith observed ncomeshocks, hen the estimateof a, for largefarmersmay have a greaterdownwardbias than that for small farmers.31. Specifically,usingten yearsof weatherdata, we ranregressions f first and secondquarterrainfalltotalson rainfall otals laggedone quarter, eparatelyby season andvillage.We repeated his procedureor atwo-quarterag. Out of these48 regressions,hereareonly 5 casesin which aggedrainfall ignificantly redictscurrent easonfirstor secondquarter ainfall. n thesecases,we use theresidual romthe regression ather hanthe deviationof rainfall rom the quarterlymeanas a measureof DRU,.32. Interactions etween armcharacteristicsndthe monsoononset dateare included n the anticipatedcomponent, ince the onsetdate is knownpriorto anyplantingdecision.Overall, he variablesusedto predictanticipatedncomechangesarejointlysignificant smallfarmers:F(I1,444)= 25-1; largefarmers:F( 11,309)67), as are those used to predictunanticipated ncome (small farmers:F(16,444)=10-7; large farmers:F(16,309) = 7 6).


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328 REVIEWOF ECONOMICSTUDIESbased on separatefirst-stageregressions or the small and large subsamples (with thesecond-stage ovariancematrixappropriately djusted),offersno conclusiveresults.How-ever, for the small farms in row (2), both the anticipatedand unanticipated omponentsof idiosyncraticncome changeshave significantlypositive coefficients.This findingsug-gests that small farms are not well insured ex ante nor do they have perfect access toseasonal borrowingand lendingopportunities.In fact, the effects of the two types ofincome shocksare indistinguishable.As for largefarms, only anticipated ncome shocksseem to matter,and even they have less of an impacton child school attendancethanthey do for small farms. But, these results shouldbe viewed with caution, as they couldreflect the poor predictivepower of the instruments or large farms (cf. Table 3, row(1)).33Finally,we look explicitly or borrowing onstraintsby testingwhether chool attend-ance respondssymmetrically o anticipated diosyncraticncome changes,using equation(13). We focuson the small farmsubsamplebecauseonly about 4%of anticipated ncomechanges for large farm householdsare predicted o be positive. The estimate of a',, theeffect of anticipated ncreases n income, is 1-44 (t-value=2 52) for the small farmers,whilea l , the effectof anticipateddeclines n income s only0 534 (t-value= 1 33).Thougha'a is largerthan a,, as predictedunder increasingmarginalcosts of borrowing,thedifference s not statisticallysignificantat the 5% level. Moreover,we cannot rejectala = 0, which s consistentwithcreditrationing.Of course,thesenonrejectionsmayreflectnothing morethan the low statisticalpower of the tests.Simulating the impact of market incompletenesson humancapitalGiventheapparentvulnerability f households,particularlymallfarmers, o idiosyncraticshocks, we would like to know the cost of using child labour to self-insure.Since ourmodel assumes hat school attendanceprovidesno directutility,thiscost can be expressedsolelyin terms of humancapitalforegone.Of course,withoutknowingthe marketrentalprice of humancapitalwe cannot estimatea monetarycost, but someinteresting ompari-sons are still possible (as in Trostel (1993) who simulateschangesin the humancapitalstock in a differentcontext).Consider hildA in villagev,whose household s insuredagainst diosyncratichocks,and whose school attendance n period t is equal to the villagemean S9,. Supposethatchild B in the same village is uninsured,so that his school attendanceresponds toidiosyncratic ncome shocks. Let eB, be a draw from household B's distributionofidiosyncraticncome shockswith var (eB,) = CB . ChildB's school attendance s obtainedby drawingan eB1 for each t, multiplying t by a', the estimate of responsiveness oidiosyncratic hocks,and addingit to Sv,. If childA and childB both share the learningtechnologyproposed n SectionII, and the same initial stock of humancapital,then theexpectedpercentagedifferencen final humancapitalstocksbetweenthemis

E og (HT+I HT+BI=7[Eexp(-aleB,/Y)-1] t=0exp (-St). (14)33. An underestimatef a1, mightresult f some of the season'sschool attendanceoccurspriorto therealizationof the unanticipated hock,but thereis no reason to expectthis bias to be larger or largefarmsthan for small farms.We also test whether he unanticipated omponent s indeedunanticipated. o do so, wereestimate ows (2) and (3) by including he season-aheadunanticipated omponent(this leads to a drop insamplesize as we lose a seasonof data). Underthe null that households houldnot adjustschool attendancein response o unexpectedhocksthathavenot occurred et,wewouldexpecta zero coefficient n theseseason-aheadshocks.In fact, the t-testhas a p-valueof 0 58 forsmall farmsand0 47 for largefarms.


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JACOBY & SKOUFIAS RISK AND HUMAN CAPITAL 329If, for example,eB,is normallydistributedwith meanzero, then the term in expectationson the right-hand ide of (14) is simply exp {of2 (a1 /y)2/2}. Thus, as we would expect,child B falls fartherbehindA when a, and o2 are higher; that is, when childB is moreexposedto idiosyncratic isk.

All the quantities in (14) are either estimatedparameters rom our model or caneasily be calculated rom the data. To estimatethe expectations ermin bracketswithoutimposing a distributionalassumption, we begin with each household's time series ofAlog Fj, (the idiosyncratic ncome shock) and subtract ts intertemporalmean to createa mean zero shock.34By centring he shock at zero, we avoid confounding he effectsofdifferencesn means and variancesof school attendance.We thenreplace he expectationterm with a mean over time for each child (using only those childrenwith at least fourseasons of dataafterdropping he firstseason),and take means of the estimatedexpecta-tion across childrenwithin a village.TABLE 5

Predicted deviations from human capital stock under ull insuranceAurepalle Shirapur Kanzara

2 a 0-241 0-048 0-095S., 595 455 4 15(standard deviation) (1 42) (0 60) (0-79)E log (H I/HB+ )x 100:

(I) Full sample a1, y 0-16 0-05 0-15(2) Full sample y, 0-57 0-17 0 09village-specific a,(3) Village-specific a1, y 1-58 0-04 0-21Notes. Full sample estimates from row (2), Table 3, village-specific estimates fromrows (3)-(5) Table 3.aVillage mean of household-specific intertemporal variance of idiosyncratic fullincome shock.

Table 5 presents simulatedhuman capital differentials or childrenin Aurepalle,Shirapurand Kanzara.To gauge the influenceof differentparameters,we presentthreeestimatesof Elog (HTA+1HT+ 1). In row (1), we applythe full sampleestimatesof a, andy to childrenin all three villages; in row (2), we account for differences n a, acrossvillages;and,in row(3), we allow forvillage-specific 's as well. In allcases,the estimatedhumancapital ossesexperiencedby uninsured hildrenaresmall,if not negligible.Lossesare largest n Aurepalle, he villagewith the highestaverageCB. Still,over the course ofthreeand a half years,the typicalchild in Aurepalle s estimated o lose less than 2%ofhuman capital relative to a hypothetical child who is completely insured againstidiosyncratic isk.35Finally,we compareestimatesof E og (HTA+1HT+1 ) for children from small andlargefarmhouseholds,basedon the results n rows (9) and (11) of Table3. Samplesizeconstrainsus fromperforming eparateanalyses by farm size and village,so we use the

34. Note that, within each village, the cross-seasonal mean of idiosyncratic income shocks is zero for allt by construction.35. Although we find aggregate income shocks to be an important source of fluctuation in school attend-ance in Shirapur (or, at least, we can separate out their impact from permanent seasonal variation in attendance),our calculations indicate that the human capital cost of aggregate uninsured risk is negligible in Shirapur. Thisresult is largely due to the low estimate of y in Shirapur.


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330 REVIEWOF ECONOMICSTUDIESfull sample estimate of y. Even though large farm householdshave almost twice thevarianceof idiosyncraticncomeon average, heir estimateof al is only half that of smallfarmhouseholds,andis less thanunity.Thus,the gain from nsuring mallfarmhouseholdsturnsout to be aboutthreetimes arger hanthe gain frominsuring argefarm households,althoughboth gainsare under 1%of humancapital overthree and a half years.We mustemphasizethat these are only the gains from eliminating"excess"variability n schoolattendance due to income shocks, and thus do not includethe gains from raisingtheaverage evel of school attendance hat might result, for example,from a relaxationofcredit marketconstraints.

VI. CONCLUSIONIn this paper we have examineda complementaritybetween what have been widelyproposedas two enginesof economicgrowth,financialmarketdevelopmentand humancapital accumulation.Child labour, and therebyschool attendance,appearsto play asignificantrole in the self-insurance trategyof poor householdsin rural India. Givenpositive returns to education inside and outside of agriculture, his strategyis likelyto be costly to households n the long-run.Unfortunately,no conclusiveresearchexistson the direct consequencesof erratic school attendancefor educational attainmentorcognitive skills in developing countries. In light of our findings, efforts to uncoversuch a connection using data better suited to the task than those of ICRISAT arecertainly warranted.36Nevertheless,we have made use of our structuralparameterestimates to examine the cost of "excess"variabilityin school attendance.Althoughsmall on a yearly basis, this cost could become substantialwhen accumulatedoverthe entireschoolinghorizonfor childrenof smallfarmhouseholdswith exceedinglyuncer-tain incomes,and who live in villageswith poor financial nfrastructure.On the otherhand,if the cost of erraticschool attendance s too high,thenparentswould never resortto this self-insurance trategy n the firstplace, so our findingof a generally ow cost isperhapsnot surprising.Another goal of this paperwas to analysethe structureof ruralfinancialmarketsas revealed through school attendance patterns. Based on the response of schoolattendance o idiosyncratic hocks, we were led to rejectcompleteintra-villagemarketsoverall. However, idiosyncraticrisk has the smallest impact on school attendanceinKanzara,the village with the most assuredrainfall and the most developedfinancialmarkets. We were less successful in disentanglingthe impact of aggregate incomeshocks from other seasonalfactors that affectschooling,exceptin one village (Shirapur).There we found that aggregaterisk is indeed harder o insureagainstthan idiosyncraticrisk.Thesefindingsgenerally orroborateTownsend 1994),who rejectsperfect nsurancewithin three ICRISATvillagesbased on yearly householdconsumptiondata (see alsoMorduch(1990)). Notably, Townsendalso has difficulty stimating he impactof aggre-gate shocks withmuchprecision.Ouranalysisalso makesthe, admittedly ubtle,distinctionbetweencredit and insur-ance marketfailureby using rainfalldata to estimatethe anticipatedand unanticipatedcomponentsof idiosyncraticncomechanges.Thisdecompositions unique n the literature(see Deaton (1992)) because an observableaggregateshock, the village-levelrainfallsurprise, s allowedto affecthouseholdsdifferently.We findthat small farmhouseholds,

36. Finalgrade attainment,althoughcertainlynot a perfectmeasureof humancapital,was nonethelesspoorlyrecorded if at all) in the ICRISATdataafterthe 1975baseline urvey.


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JACOBY& SKOUFIAS RISK AND HUMAN CAPITAL 331but not large ones, are inadequatelyinsured ex ante; unanticipated ncome shockssignificantlyaffect their children'sschool attendance. Moreover, despite prima facieevidence of active seasonal loan markets in the ICRISAT villages (see Walker andRyan (1990)), we find that intra-villagecredit marketconstraints,possibly combinedwith limited storage opportunities,do play a role in the human capital investmentdecisions of both large and small farm households, though the evidence is lesscompelling or the formergroup.From the policy perspective,our resultssuggestthat effortsto expandeducationalopportunities or the poor (e.g. buildingmore rural schools) withoutan understandingof the economic risks and constraintsthat they face may be met with only limitedsuccess. Moreover, compulsory schooling laws or laws against child labour, to theextent that they can be enforced in rural areas, could subst?ntially ower householdwelfare. Conversely, nterventions n rural financialmarkets,not to mention financialmarketdevelopment,mayhaveunexpected onsequencesor humancapitalaccumulation(Foster (1995) makesa similarpoint in the contextof childbody size). For example,ourresultssuggestthatpoliciesdesigned o promoteshort-term reditandinsurance,particu-larly to smallfarmers,could haveimportant ong runeffectson economicgrowth.Theseeffectswouldbe strengthenedf educationhas spillovereffects(seeFosterandRosenzweig(1995)forrecentevidence n Indianagriculture).Futureresearch n both financialmarketsand human capital investment should thus pay close attention to their importantinteraction.

APPENDIX ATABLEA.l

The returns to schooling in farm production: fixed effets estimates of a linearprofit function for the six ICRISAT villages 1975-1983Regressor Value of Profitsa FarmerFixed Effectb

Education of Head (years) ... 119 14(2 44)Age of Head ... 25-45(2 02)Medium ranked caste ... -617 44(185)Low ranked caste ... -672-95(1 54)Cultivatedarea 231 62(8 54)Fraction irrigatedarea 143920(4*35)Fraction of HYV area -392 70(1 10)Education fractionof HYV 236 46 ...(2 50)R2 0-771 0-084Nobs. 1491 206Notes. Dependentvariable:Profitsin 1975 Rps. using state level deflators.Village-Yearnteractiondummiesare also includedas additionalregressors.a Absolutevaluesof t-statistics, orrectedor arbitraryormsof heteroskedastic-ity and autocorrelation,n parentheses.b Estimated ixed effect from profit functionregression.Absolutevalues of t-statisticsin parentheses.A constant term and village dummies are includedin this auxiliaryregression.


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332 REVIEWOF ECONOMIC STUDIESTABLE A.2

The returns to schooling in the casual agricultural labourmarket: Wage function estimates for adults in the sixICRISAT villages, 1975-1978Regressor Adult males Adult females

Years of schooling 0-007 -0-007(1-41) (1-30)Age 0-015 -0-002(2-85) (0-59)Age squared/ 00 -0-020 0-002(2-98) (0-63)Medium rankedcaste -0-016 0-012(0-54) (0-62)Low rankedcaste 0-012 0-023(0 30) (0-92)InverseMill's ratio (A)' -0-039 0-033(0-88) (130)Nobs: 387 533Notes. Dependentvariable:In(Wage per Hour). Additionalregressors ncludedbut not reported:constant term,millimetresof rainfall n the month of June, surplusrainfall nthe month of June, year dummies,and village dummies.Allmonetaryvariablesare in 1975 Rps. using state level deflators.Absolutevalues of t-statistics n parentheses.a The additionalvariablesused in the first-stageprobitregressions nclude: dummiesfor the marital status of theindividual,disability,value of farm assets, other assets andgender-specific ummiescontrolling or the age compositionofthe familymembersresiding n the household.

TABLE A.3First-stage regression for seasonal full income changes

Small farms LargefarmsRegressor Coeff. I -valuel Coeff. I -valuel

One-Season Lagged Farm Characteristics:No. Males Age 15+ -0-364 2-62 0-0121 0-85No. FemalesAge 15+ 0 0417 2 57 0-00256 0 14No. Children 0-0289 3-12 -0-00199 0-10(I) IrrigatedArea (hectares) 1-78 2-93 1-51 4-58(2) CroppedArea (hectares) -0 168 3-00 -0-0109 0-25(3) LivestockValue (Rps/1000) 0-348 3-38 -0-255 0-91(4) ImplementsValue (Rps/1000) -0-397 0 67 -0-0022 0-01Interactions with Lagged Farm Characteristics:(I) x Monsoon Onset Date" -0-00890 2 61 -0-00814 4 40(2) x Monsoon Onset Date 0-000701 2-33 0-000023 0 09(3) x Monsoon Onset Date -0-00165 3-46 0 00110 0 70(4) x Monsoon Onset Date 0-00208 0 59 -0 000093 0 05(1) x Rain Dev. Ist Qrt.C -0 00440 5-47 -0-00161 3-25(2)x Rain Dev. Ist Qrt. 0-000018 0 15 -0 000182 169(3) x Rain Dev. 1st Qrt. -0-000249 0 73 0 000935 3.93(4) x Rain Dev. 1st Qrt. 0 00070 0.99 0-000625 1-08(1) x Rain Dev. 2nd Qrt. -0-00331 3-32 0-000310 0-36(2) x Rain Dev. 2nd Qrt. 0-000499 3-32 -0-'000199 1-80(3) x Rain Dev. 2nd Qrt. 0 00124 2-33 0 00169 4-02(4) x Rain Dev. 2nd Qrt. 0-00275 2-43 0 000445 0 39


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JACOBY& SKOUFIAS RISK AND HUMAN CAPITAL 333Small farms Largefarms

Regressor Coeff. I -valuel Coeff. I -valuel(l)x(Rain Dev. Ist Qrt.)2 0-0107 506 000245 217(2) x (Rain Dev. Ist Qrt.)2 0-000197 0-64 0-000568 1 78(3) x (Rain Dev. Ist Qrt.)2 -0 000376 0 34 -0-00164 4-36(4) x (Rain Dev. Ist Qrt.)2 -0 00204 1 12 -0-000998 0-79(l)x(Rain Dev. 2nd Qrt.)2 0-0112 2-59 -000340 0-69(2) x (Rain Dev. 2nd Qrt.)2 -0-00216 3-16 0-00178 1-80(3) x (Rain Dev. 2nd Qrt.)2 -0-00636 2-38 -0-0113 448(4) x (Rain Dev. 2nd Qrt.)2 -0-'0125 2-41 -0-00464 0-65R2 0 6057 0 6795Nobs: 501 366Notes. Both specifications ncludevillage-season-yearnteractiondummies.a Corrected or arbitrary orms of heteroskedasticity nd autocorrelation.b Onset date is in days since January1.c Deviationof current eason quarterly ainfall in millimetres) rom ten-yearaverage adjusted or autocorrela-tion wherenecessary;see text).

APPENDIX BDerivation of Euler equations: complete marketsHouseholdsmaximize 2) subject o (1) and the expectedwealthconstraint

oT=0 A,[C,,+W,Si,-Fi,]


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