World Bank Reprint Series: Number 109

Howard N. Barnum and Lyn Squire

An Econometric Applicationof the Threoryrof the FarxaHouseholLd

Reprinted with permission from Jouirinal of Dzeelo)pui?icit ec0o11(7?o7ics, vol. 6 (1979),pp. 79-102

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Journal of Development Economics h 11979) 7t) 102. : Not ili-Holland, [)ulkhing Comparny

AN ECONOMNIETRIC APPLICATION OF THE l1 HEORYOF THE FARM-I'IOU SEH1OI D*

Howard N. BARNU?M

Cenrtr ftoi ReNvarch on Economic Dvielopown ) t, U nitvrsitv C?! A!ti hi li. -A11n Arbor.V/14S19Q. USA

Lyn SQUIRE,

1,'Orld Bank. t11tisino,, n.( D 1)4 233 USI

Received M,la\ 197T. Flnal wersion receixed August 1978

Employing a Cobb D)ouglas specil'icauioIii tie prtiductioni uILnction iandL a modified linearexpenditure ssteil. the patper presents an economllletric model olf household production.consumption and labor pls hell behimour far a setil-comrinmerial Farm si, it a eompenitw i-ltbor

market. The model. estimatetd fromt primary. cross-sectionial. Malaxsian datl. is uLsed t) analx setihe imnpact ol nlipi .il,ri, ouitput price initerxeniiooi aniid technological chiatnge oni the agricultmltsector. III dLoilln so, tile 'la s-rist is tnealted as an endogenotis ariable to he determin2ed b-, thic

interaction ot iaggregate labor deicmanild and suppk curwsN obtained tol'mt thc estimated mil ot'

fulnctionIs.

1. Introduction

The theory of thtie !'fa -hot11tscl a,il has n 1 zt1 ch\ d a c plrI lit it icit p isil i tt

inl theto tite l ciop n sic I i t l. in CIs litetltLlic buit atall, del'icicie 1i1cs \h cliLLt tlthe 1itL111thbe of emiipirical applications.) As a,Iti Il, little iS I II- , Ith0tLt1 the

LuatiLli I,i '(i\% s LI i, c nc , ot-about the p.olicy itplpiclitimits ol' thle tlheor-etical

i rtL!L l;i..ti of 1htti( itld pridtiduction and const,tiption (d.cisioii. In thispapei-, x e tSe pr-imarv crOs, section data to) estin:ttc a Moodel Of ,1ort-run

houlosehiold hlha\oinur wiit the specific inil,entWln of c\.,,t.ni ,n the po.lcysienllifican,cC of the theorv of the liriu-ituschiold. 01,:r aue1itiOu iS prlttlhl\diiec.cL to thle 5 lltanitpi. tc ipaCct of calllne s ll ttlhe 1llowil fourt exo-

*111C T Iets p ic"icd l hele are tIIhoe of the auithorls adlitl nolt those of the VNkorld alnk II eallort rtle Li a' I Ft1'r l Ie 1re 4 Iearh assis'tancet'l ' 01 I Ca It. -i III I )i ne'.

Tlle seminal i ef5i cut 1 i ( hCIis : I')'. t 192 i also 'c. Sen11 t I C I.9Beti .SlI9qintand SiIO t's

Nakaiaia (1t96)0t. Khriilihna t1 9691, t. sd .10,t ., ti-i andi I au 1i()91th1e t'Io i applicationl ,1ots i to the . 1ii'i s t tic estimllatio it :.1i,ii lihoi'ldioldl 1,del, .,1

aisman b1 Lall. 1.11 inrid Yotopotuil, tI I '8

Xt) II.N. Barman t t it c .L. Squirt. Flu t'1l 4t tilt r l-11 4 cllu'sltl

genous variables whichi have beenI of cenitral i1mportnalnce in the theoreticalliterature iimilvirnu the larmn-li0t.sChold:

(i) the size of the family labor force. The miodel alilt, US to a 8scs thleimpact of iniglatiii on 110Uu\eliold output3 coau.,iiipitilimi and labor slulpp\

(ii) the price Of thie main agricuil t rral Oti put. (f ilntelet here are tllec.hsticitic. of botlh total outtpLIt and niLi,rketll suL Lui (sl

(iii) tMllo loi y. ('Ii alrmg, in farmi Icliiii 0l 'g\ ar-e basic itigrel tleiit of' aillruLrail dcCxelupiieiit strategies atnd cani be expected to laxe iinajoi reper-cus'iorr; on lhousehold decioions: and

(ij ) thle Wa(Te-rate for agricuiltural labor. In plart icilair. we are itierlestcdin. the elat icities of ho11uell0old labor sUpply and demandml for hired labor.

T'otall income or total exniitdiltire is not icludLedLL. inI the list Of exOUenous1Nariiblc since the inte-ratio n Of tlle prodluctio1l and. coi1sunl111iiir LiC6ioiv0lallows the model to determine both farm profit and wan;e incomle. It is this1eaturc of the miodel wvhich deterin iiie, tlle policy 'iiiirifc;ine of the farnii-hlous"cho1(l thieorv. F'or example. consider a chliige itn the price of the maiLtinali. rCeltur:al output. Ignoring the productiOnl side olf the model, the chlia e inprice will affect own-coiisumlil't io of the outilput as well ias the co*rtripnhio011nof olther items incldleiilln leiS.ure. If the prOd1ricu(o side ol the moelI isiintroduced. hoxexcNer. the change in pirice will also affTect ILrin output andhence lfrrn prorit and total household inicome. xlilhli will i1iiit ioe at ullrtlhechange in thie hlousehold's corisuiliptiii pattern. TIhS, thle p eLt itii0 Sr(ide Otfthe imiodel influenc CoWilsuinpiOll LIdL .i0iori tlr1 rough ItS imiipatct on totallhOLuseoll0d inicomie and e ctl)rditUti.

In sectioin 2 we presenit ai simple model Of lhoulseoltl behav-ior x hicllMl Ltides the salient featLtri.e Of the prott '\ piclcl fairiii-loslold'a ailid VhliclirfleCts thle plr-oduction anid itwitutiiuiral clhar. Icriitlics of rice -^110LdLuLcirLhouIehol.c0d's ill tlhe Nv 1Lda Rixer \'allex\ of NAV. \1.ll.ivsna. hli sectioni . wereport the results of a prodtlri,ii ulrin,ti'ir aiirlx,is based onI a CobbDotiulls specification and derive a profit `irlnetioll. We tlhenl specif\ thec0n.sMu1npliion side of tlhe model to Ct011'01ii tto i n1ti0dil xersiori of tlle linleare,xpendit tire s3: tem anld presenit the restults of' e-ttimnatioi. In seclioni 4 weproxiide an illdiCatilll Of tlle Iltid111til HIta ix c'1eiriifican of the theorx of thleI'arm 1 seh1M oldC1L] by,' co1Plr.n l pirin selected c.1nsLumpt11io0 Cldsticities. clla3lli11tedfirst uide(lreil he asstnL1pti0l that cosUlmptiolll ilrid pdtctiCo deciionlls areilideledenilt anid thieni tinider the iio c reatlistic zrssumiiptii tllalt wcmisLillrtirIMdecision sre (teepentdeint onl thle n(LIseli lt1Xs ipll0dlut iolb IbCeiarxi. Iti sectiiii 5xxe a'>ses tile polic\ innificari.c ol oui r sillt xvithi respectC to tile f`our ,sulesouitlinied abt xc. Thie paper is sUiniai. i;l.Cl ilo ctCi' 0rn 6. roakMd l01 .11o aalysiscon1filrm11s thec ox \rall imp1)ortlalloce of the tl,, ri-l,oislol.L thcoKrx as a basic toolfor the predictioii Of 110trehi10olu1 :e1spo1se to at x Mriet) Ofe W\o'lti chagesllue.

IH.N. Barmnu ait (i L. Squire, Thelr;vr 't 1ft' Jarin-housold.( Xl

2. A theory of houselhold behavior

The model of household behavior we present describes a semi-comm11erciallfamily farm with a competitive labor market.3 It has been inoted that themajor part of world agriculture is consistent with this genre of model w'1hichis located intermediately on a continuum betweeni a wholly coimi1ericial farmemploying only hired labor and nmarketing all output and a pure su.bsistenlccfarm using only family labor and proditucinig nio marketed sLirplts.' I4particular the essential characteristics of agriculture in our study regioni inN.W. Malaysia are consistent with this model.

The study area from which our sample was taken is in the Muda RiverValley and comprises the state of Perlis and fotur ad-miniistrative distl ictk inthe state of Kedah. An average hOLISell. d in the Tegioin retains about otlefifth Of agricultural production for lhousehiold con1suLMpLion and n1 iaikLts theremainder. Further, there is an active iabor marke, for agricUltural and othertypes of labor and all households participate in the labor nmarket eitlher a;buyers or sellers of labor. Thus the use of labor time and the disposal ofoutput are determined with reference to market wages and prices, and theaverage farm is aptly described as semi-commercial. It is als) important forour choice of theoretical model that padi is grownl on all farms included inthe sample to the virtual exclusion of oth-ecr crops, tlhc-ereore malilkinig itunnecessary to estimate more thani one production ifuntiCliOnl to a;lid thecrop composition problems often enicounitered in prodtuctionl filiCntiOnl sLtlhtide

in multicrop region-ls. Finally we niote that land is rented by mneans of Fi\cdcharges and there are no sharecroppinig or other contriactlial arranleiencillhwhich might lead to noni-standard profit maximizing coniditionis.

With these points in mind, we formulate the hoLusehold model as follows:

ET=UL(L, C,M -, Ici), i=l (1)

F=F(D, tljA). j=1 (2)

T=H+L+D, (3)

and

qMI + pvC = ii,H + R + pF - .; j, (4)

where

L =leisure,

C = own-conmsimlptioni of agriciitw ral oUtplt,A -Con1suMpt6i0n of 1lari1lkCt-pu rlClu.etd goods,

3THis termuinoloov lias been u.igge.ilcd by Nakaitniri, t969yi.4 Khrishna (1969).

82 H.N. Barnum mdntl L. Squire, Theor i tl7e /hr:tin-hmusehold

a,=household characteristics (for example, number of depenidents),F =total output of C,D ==total labor input (both family and hired) used in F production,dj =other variable inputs used in F production,A ==area of land used inr F production,T ==total household ti- --i vailable for labor,H =net quantity of labor time sold if H1>0 and net quantity of labor time

purchased if H <O,R =non-wage, non-crop net other income,q = price of M,p =price of C,tv - wage-rate,wj=prices of other variable factors.

The household is assumed (o maximise its utility function Leq. (1)] subject toa production function [eq. (2)] and time and income conistraitiis [eqs. (3)and (4)].

The p)lanningi horizon is assumed to be one agricultural cycle. As a resuilt.decisions relating to the total supply of 11hou1shold factors of productioll aretreated as given. Thus migration, wlhich affects total available hLouseholdlabor supply, is onmitted from the aiialysis. as is the renlt dechioin, \x iichlaffects the total avxai11ble hueh1Lold land supply. Land may, therefore. betreated as a fixed fiactor. Rent paymenits or receipts, howe. r. are calptured illthe definition of R, n(on-w%age, non-crop net other income. Otlher lonlg termidecisionis are also omitted from the anal\sis. In partiCLlar1 it is a1Ns,iinied thatthe household has already made some decision about its desired level ofsavina and that this quantity is inClUded in the definition of R. Finally, theanalysis ignores risk, again on the grounds that, while ri4k man play acrucial role in the miaration decision or thei retit cckionii. it 1l)a s a lessimportant role in the short term Mileni it mav be assumed thath ic longerterm decisions have alreazd been made and the houschold Is. at least tosome extent, committed to a fairl\. well-defined coursLle of action for thedluration of the agpriculturIall cycle.

Mfaximising eq. (1) subject to eqs. (2) ilironeLbl (4) and elimintinif theLagl ran iani m_ultipliers, yields the following first-order eLquLat io)ns:

Lc(I.r=p (51)

"L" Ut =it, tq, (i)

pFD . (71)

I)Fd,-lj =j 1, S. ,

II.N. Barum and tel. LSquire., Theory o the fin-m-hou'schold 83

antd

qA.\ +pC'+ wvL = II + R + wT ~9)x%herc

Eqs. (5) and (6) express, the traditional first-order Coii1ditionl of' ell'-Iieeccionomics: that is. the niarginal r-atC Of ,Ub.stitL1tionT ill Consump11tionl mulstequl,1 thie miarginal rate of 1 raMnsforinationi ini prOdLuctioni. Eqs. (7) and (8) arethe pro[it-miaxiiniising con1ditionsN for the allocation of labor and othiervariable factors. Eq. (9) combines the inlcme and time con,traints as well asthe tchn11oo0iCal conStNmint dCescred by the prodLlCtion function. The left-han.d side of eq. (9) includes the expendit r'Ol n leisUre and ti(ihtle righlt-hiaiidside is anin miennced ecrsioni of Becker's (1965) conicept of 'tibll inicomle'wixhich in this case includCS the net profit (II) from houoliosl ld prodILuCtionll.

Labor is SinleIdi ot for separate treatment in eq. (7) to ernplabic th1at thelevel of labor inpuit is determinied sole byvtll e profit mna6ii,ini conlition.In the absenc of labor miiarket participatioln the dicliotomy betweeni the

rodUCtiono and conu ilmptin side wouild not be as coimplete. In this case teleid1ntis tyt a of labor used inll pO Bcldtionl N%oild be a ffected directly byi tlie

subjhective ti ailuation of ieorks the t oul I)sehold. 10io%Ce\Ci'. with an aeiltilabor imaril-ket thie subjectie evaluation. of work determini(7 es the lexel of laborsLipplied bv th1- h10LusCli0ld buit niot theC househoMld'S total dLn1ia11d for- labor inproduct ion. Instead total labor demand is deiteriiii medL by the prcofit maxni\i/-ing codiition and the IRLductioti and coll nuption segiients of the modelcani be estimnated separately.

Given ani indepruend1eilt e,timate of the pr1-Od IUClol Iu nelCtiol, eqls. (7) and (8)can be used to deiterm;l iine the ariable inp)LuI into F producIt ioL, and. 'mincethe land inpUt is determiniied e.xoigeiou *f thie total output or Ff ''lThe

out3.Io011in for thei N ariable iputs and F can tleti be used to derite II, iiet

farm profit. Fqs. (7) and 08, therelore, represenit the produictioni side of thieiimodel, and tlle ifntipct Of pr1'OduCilcl Oiloln thle C11sU11pttion 0 ie istnlletraniismitted throughl tlle aliie of II in the inicomec conistrainit. Turni ng to thec011onUlzeptione WI.etlc.if V% e afsume that the seccond or-der Coi1d itions aresatisfied. eqls. (5). (6) andIL (91 cMn be N0l'%0d for deiamIidiL funct ions for the thireecOnu inp111 ionlu gOds. C. .l and I. in ter of the ic mee prices, c it and 1:. the

olitiselhold cluiracteri,t ics, ti, and total hous ,ehold xpenidi tiner, E. wlhci isderit'1Aii as the sutmii of II. R and wT, Io iimptl leeinilit (lte modtiilel eeoiiomneto icallit reCmaiiS to SpeCify ; thle ri t s Of thle prod nertio hi net ion nll it,ll d 'or 1 thle

contlllipinmom dexIpeditUre SyStem).

Sec Sen tL)6u and (S e.lc; 11d

84 H.N. Barnutmi atnd L. Squiire, i7lie'orv o* thU firln-houschol)d

3. The econometric model

Recently, Lau, Lin and Yotopoulos (1978) have unified the production andconsumption aspects of an agricultural hoLoSCeliold in an emipirical mliodel.Employing group means for farms in several regioni !,- Taiwan they estimatethe consumption parameters of a linear logaritlihnic expend(litture sy)sten"(LLES) and characterize lhouselhold production activity with an estilatedpr'zit function.' The general approach we follow parallel.s that of Iau et al.;however, the empirical specification we use departs fromn their specifi-cation in several respects which improve the model's applicability to policyanalysis. First the production segment of our model einploys a directestimate of a production function. This has the advantage that we cani tusesample data on the intensity of factor use directly in the estimiation of theproductiorn function8 rather than employing factor prices, which are nIotlikely to vary greatly over a cross section sample. in the es-tin-tation of aprofit function. Second we dlevelop a modified %ersion of the linear expendi-ture system which, unlike the LLES. does not restrain the elasticit% ofconsumption with regard to expenlditure to be unity.9 In sectilon 4 we shalldemonstrate the crucial role of the expenditure elasticities in liiiking theconsumption and production sides of the farmn-houeheiold moodel and, tlhus.the importance of using an expenditure system N% hichi allows thie bud etshares to varv. Third, we empl oy a transformation introduced by Abbott aidAshenfelter (1976) which allows the direct estimationi of a h .lIo Lmhold laborsupply function rather than the indirect derik ation of a sutpply function ft-omlthe household leisure demand function. This is desirable because it avoldsnmajor data problems which ine%itabl\ arise in defining leisuire and flhirel0reallo)\\N a more reliable estimate of holuselold labor suipply respoinse. Finallywe emrploy primary cross section data -athered at weekly initervals oxer aone year period and coxcring the time antd incomie alloca.itions of a set ofhotiseh(olds. wlich are 1iormogeneous wvith Fes'pect to crop grown ainid soilquality.

hThle linear loga;riihnuic expenditure system is des eloped in Lau and NItchlell t19t70).See Lau and Yotopoulos t1971 for an application of the piolit function. Ihe hasic

ihLeorceical reference is Mcl Tdden F1'0)i'It has been pointed oUt that direct estimates of a production function nsiole a poteotiial

simultaneous equations bias [Nowshlrvani (1166)] This criticism has been Huccessfultl answeredby. among otheri, Zellner, KJnenta and IDreze u1966i who demionstrate that, ei%cln thle lagbetweeni itiput decisions and output which occurs in agri.ultu1 ordinary least sqiuares wkill gixeunbiased estimates of the production function.

'1Ihe LfES does imply that the ratio of the own priLc elasticities to thie expenditire elasticitie,will be Lppro,inmatle proportional across commodities I Deaton t1974)l lihe pmtioplitilnalitlrestrictioni will, hosewer. 'otnl-v be close for all goods if the lexel ol Adlh.Lggfle.si I .s.I1llQd 1i

high' [l)eaton (11)74. p. 3-4it I 1or the presenit stuidIN tihe ratio o' thle pfrice alnid inicoimle Clastil.utmsaries atid the approxiimate proportionality restriction was not substantiated, thiis resiult i1attributed to the fact that tile buidget share of each commodtiti is hit igh al th ie lexel otdisaggregation low.

FIN. Barminm amii L. Sqtiire. TIheory 0/ tIh farmn-h1nusehold 85

The production segmnent of the household model is introdUced by derivinginput demand functions and a profit function basedi upon an estimnatedproduction function. The production function is speciFied in Cobb D)ouglasform as

F= X,Y,4'IDl'2P;K`X4,

where K is the flow of capital services (nl.achitiery), and V are tlle othiervariable inputs.

The estinmated prodtiction fuinction1 ° is

F-- 19.1 1A(1 "2D` '' -08 K`(IXKI . If)

An analysis of allocational efficienicy revealed that paadi farmers in the stud',area maximise profits with respect to labor, nmachiniery and other %ariahleinputs and treat land as a fixed factor. Accordingly, we can derivc (lernanidfunctions for the three variable factors from eq. (11) and the profit nmaximi-zation conditions, eqs. (7) and (8). For examiiple, the total demand for padilabor is

=2-( p w)F. (12)

Substituiting the de11an;lld functions in eq. (1t)) anid rearrangingig yields anexpression for the level of restricted'1 farm profits (1) at difrfrelclt levels ofoutput,

II-= pF,

= 0.62 pF. (13)

Sub-tit'.tini the demanid functionis for the N ariable inputs in (11), thieproduction funiction cani be rewritten in terms of the fixed factors and therelative prices of D, V and K as

4 ' Ix

F i : H -) .4 (p ) I I'(p %,,P _23 l( .p W1)24,21,

-42.11 -_(1p W)(1. 4 " (1) 10. )0.1 1 ' w,i(O. 1 2. (14)

'"All oeilicieiiis .IIc sigLnificant at the 5 ,, lemel, except that on the flosw of capital serlices, W10.6. and returns to scale proved to be constant. The estimation of thie production function

and tests (f allocational efficiency are diwcosbed in Barnum and Squire W 178 1.

Eq. (13) measures land's share of output if each factor is paid its marginal produlct.

86 ] ,N. Barnum and L. S,. S Iquir, T n C? the farin-lholaehold'Iz

Fitnallv. sUstitutiIg eq. (14) in eq. (13) gives an expriessioni for profits. as afinction or factor prices. whlichi can iow be incorporated in tim hlusehlol(dmodel as a coMponlenlt of thle inco me side of total expentditIlue.

The C0onsum1.EpltiOll side of the household miodel is specified ecoioninteiritmllusitng the linear cxpenditure system. To differ-entiate, be%%.en the uise of' tirmieby dependents and Working famNlily' miembers the system is developed in percapita terms. For an mcl'Midual1l llelbel Of the falin iFI tilC Iliiity funcio3n iS'a it ten as;

U , I =N' i n (x'. Jl I,

Wihere Xi illdiCaltes VPe aitaZil(l COnsuiiption of tlle ith COinnIolditi I, and ;', arerfunction, of a xarietv of' hotiuIehcld chla-racteristics. DepnllLdlent are assu;1med1CLto conwsuine all their a\ailable timc in thie form of lcisuir-e and to conlltime thtsame qiiaiitide.> of other goods as do working family nmeiibers. We furthlera.suil]ne tilat tile h1oLusehold Utilit%y fun1Ction1 iS idenlit cal ror eaclh inember andadditi e across illndi%idlils. so that muinimino over the n1 worlkinig familyjemierlicls and the 11, LeIp11endenlts anid subhstituting ti ts. :, L II,) for leisurleC0IuN Mptioi per workin lilliln 11eIberC, tIle houehlC01d C01onsumpIrti on pro-blem is to nia\imi/e

In It 7-) +n1 1 It -; In

t 1n;. In I t nfl, In - ti

su1bl et to

"i, rpC + qAI IE

where lower case letters indicate pr C' - liaita amn1onn0 t s(of oc an1d 11i zaniLl t is thetotal timile a\; ilable per imdikidIMdl. N is tile qLnilltit\ ol .labor tilmle supplnliedper rfaiilk wOi'kcrI and 11:-211 + 11'.

D)i.i1i-ig throUgh bv 2I the Litilitx inammimi/tion problemii nmay he writtenequi6alenlth as

Maxt' :, klXl, Inil (I A)/), In l-A8i(t - ;,j

subject to

kwu(t -,o s ) ± t -ill : ' n1.

\% l'I.he A .- 1 I 11. If \cM let /|I -kJII, and 11. Ank . tlheln it is ;mpp1;rclr;mc thlalt thepiroblem is that of the -,tandarcdl Iicsallr e\pen)Lit lre s\xl.eii for which the

'N. 3arinwn atndttl L Stqiiire. Thu'orv o/ theJr ma'-hozuseh1ld 87

eXpedlliture e(uLtions are

wv(t -s)=',' 1w +/3 (F/n- W',' -P^,2 q7'. (15a)

p- -I2p+±fl (E,n-v'TI -pml2 -. 15b)

(I'll , '3q + fl (E n - w'T '- 17,1, -- (11'3) (I 5e)

This system can be altered to avoid a data specification error wlhich Couldarise thriouigh the ComIIputatioin of leisure as the residual after time allocatedto work aCti\ities ts) is suibtracted from total discretionary time available Ut).The possible error occurs beCalLse of the necessity of making arbitraryassum,nption0s witll ret;ad to SUbsistenice time r euIlli relmletlts in the defCillitioll ofdiscretionar-y time. To avoid this problem we adopt a modirication SULeeested

bv Abbott and Ashenfetter (1976), which involves substituting t--, for ;,' ineq. (15). Substitution yieldst 2 the estinmatin,g eq(lLations.

- WS - - fl Ih ± 4 . p-',2 1 ( 16a)

.116c)

here-

h) -~ w'.% 4-pc' 4-qm

This t ransforination hias the duial Iad anW1 taC that nleithlel lei.su-r nor totalaxailable lhoturs are inluldetILCL as \ariableh aind we obtaini a direct estimate ofthle hOloulehold labor SuLI1pl\ fLunction [eq. l 6a)].

12 Fxpanding, eql. (15al IieIlds

ntI -i n , -; pCi qM) 'a A ; w t:A'('

I ' It n1o ) + 17' tr -- it ; " 4'-11|

Sth,urtitiuy I. n, -t- and t - we obtaini

lnt II'. utt ;,t + ft n pt IC's u p( 111 ' ;

s hlich can be rearranged to) ItOrmn eq1 (16a). Similtr dermiations can he tisedi to obtain eqv i (10b)and c(1c).

88 H.N. Barnum antd L. Squire. Tlheory qf thefarml-hIosehold

To simplify, we can write the system in matrix notation as

-ws X b O O 0PC 0 b ° F2

-qni ] 0 0 b 03

- , - t'k -pfl -qll/1 ]'s+ S'12 ( -32) ( . 32

-13 -p1/3 q(l -/3) -' 3or

Yit= B# + Pi.

Household characteristics are introduced1 3 by making the vector of j,'s alinear fLinction of a vector of household characteristics G,

fis7 r60b 611 012 613 6147 F1 l

^J2 = 20 621 022 623 624 . 1

Lr3 6 L 530 ('31 632 633 634 - 7,

or

Thus the final system of equations to be estimated can be written as

=B/i + P6G. (17)

Because the elements of 0 appear in each of the three expend(iituireequations [note that 7,y 72 and -3 each appeaer in (15a), (15b) anid (15c)] wechoose an estimation procedure which conistrains the estimates of 6 to beconsistent across equations. Further, since the marginal buidget shares sum toone. /31 +32± +,1X3 must equal unity; that is, an estimate of fl3 can be obtainedfrom estimates of /32 and /33. Therefore it is necessary to estimate only thesecond two equations in the system in order to derive a complete set ofestimated parameters and we can eliminate the first row in Y, B, / and P forpurposes of estimation.14

The model is estimnated for households in the Muda River Valle) ofMalaysia tusinlg the primary cross section data described in the appendix. Inour samiiple neiliher p nor q xaries but in the systen described by eq. (17)variation is required in only one price (w in our analysis). in alddition tohouLIselhold chaiacteristics aind expejnditur,es. for all pararneters to be de-

`SeeTh il (1975)."4ibid.

II... Barnim anl L. Squire, 1 h1e1)13 (11 the Ii ,n-l lu,ld 59

termined. FT sination, of the 5stein proceeds tinder the as>umptwn thalt thedistUrbmnce terms in each eqLuationi are iindependenit aId lave zero meanisand ullifolorll a.lriances. We apply ordiniary leasL .Sliquares Llsinlg a imlo(liricttillof the iteraltie least squares proeetirLe Lused bv Stonie (1954). Settinig fl, andfi3 equal to their values obtained from inconst rained estim.ation, the I'matrix is coustimicted atnd o1 diid a least Nsq11a .e's iS uSed to Cstli[in; t. the ,iand f? inn rices. T'lie new \:1u'I u Of I and fl; are thenil dedto ItWrollNt tI Pand the procedure-c continutles iteiutit,cly unttil co erolence is obtain ed.Con erle2ene1e occurred in less than ten iterations ainid the resuiliug ckt)ctiel. iihproved renmarlhahly c)siintciit with uicout,rtillLed C'stiI i 1t- Of thr e ti Ineequta;tions>.

After a pirelimlinar\ set of resLults wkaIs obtailied, ilariable,s \%illl hcoelficicil tswvhich were n(ot siginifiicant at lcast at the niniety perccnt co:nFidenice lexel(Using a one-tailed t-test) were droppedl and thle ..)tln a was reestimnated.Speciieall\, none of the coefficiceins oni age (u) were founld to he 4inialieat,with regard to family labor force (iul) only (561 was found to be sinidficant,and with iegau-d to edUcation (e), (13 and `l 33 were found to be siniiicaicit.The final pai m tcinte r estmimtes are ireporte(d in table 1. The signs of allcoefficients are siuniificilt alt ahob c tthe ninety-five percent confidence level.

[lable 1I:stimratekl paramieter, of thie liuear espeniture systemn fot an .agricutl

ttiratl household in Mal.ti;sa

('oteficient Fstimate T-statistic

flu"' (1.311()t)5 2.72

/t( 7X '11(l

79.87 1691376.06 8.62

131.31 3.1()

-i 9.15 8.742.18 2.431.83 4.725.02 2.09

201.53 2.06a,, 7.45 231

.N 21)7.DI)eriNed from Ithe restriction thlat k/fI e 2 +t -1 1. In calculatitig gt

k- was set at its meani salue of (0.56.

The pcr capilhl eplpendiilltC fuictions miay be obtained by substitutilIg thleresults of table i inito eq. (17). The family e.penditiitire fuinctions may theni bedici-ed by nlulltiplying Ltle labor stipply ftincti(n by --= n (tlhe number of

90 H.N. Barnllm and L. Squire, Theoryv of the.Mrmn-household

working family members) and the expenditure functions for padi and non-farm goods by n (the number of family members). The final set of householdequations may be written as follows:

FWvs k 0 0 -0.30pC (E- wn1 t) 0 1 0 0.05L(IAI 0 0 1 L 078-

(I-w0.30k) wk 0.30 klp 0.30 kq]

+ n 0.05 wk 0.95 p -0.05 q0.78 wvk -0.78 p 0.22 q

F- 79.87 9.35 -2.18 1.83 I 7x 76.66 0 5.02 2' I (18

131.36 0 -20.53 7.45 Ll2

4. The interaction of production and consumption decisions

An imiportant feature of the theoretical model ol farm hoUsehold heha% iol

lies in the recociliition that thCe 11hu1schold res,ponse to a elhnnec in ane.\xoienoLis xariable bothi in a restructuirinig of conisuiilmptionl patiterlsattributed to expenditLiure anid con1 v 1.sumption suLb.stituLtion effects and inproduction res,ponsc. Estimates of the impact of changes in, for examplep1,labo i market conditions or padi prices are apt to be more accurate if basedoin a conpilete farm household model than if they are based on either thecon0UMption or production segments alone, To g-ain an indicatilon or the(ilLIMtit:itieC sinifiMCa CCe of thle in tegrated model., we first de'rke parltialhollehold response elasticities under the as1,,SUmptl1ionl that n1et farm prorit. II,is exogenous, thereby -inoring the produ0L1ctionl side of the mzodel. Then wederixe total rcsIponse elasticities for the full model by inseitinsg the profitfiunctioin into the expeCndfitLureC equation, thereby allowing, profits to bedeterminie( CendoCenolMIxy anid incorporating the produCtion side of thein oddl.

The comilplete h1ouLSehold miodel consists, on the consLum1ption side, of thedemni;id functions whichi can be deri\c d from the first order coni(ditionis, andtilh CXpemCILiditt're con1stiraint.

E-- II 1+ i t +± R.

nil On1 thle pr(odLtiOctin Side, of the pro)fit fuLnCtiOnl derviel fromil theproduiCtionl fiunct ion and first order profit ma:.%imi/ingi conlditiOns. O1r itn termsofnthe es,tiniated tt t i,th completc miiodlel consists Of thle de1man.lld runction(S

1I. V. Barnuimtel tantd L. Squire, Theori, of t/h' fitri-llhous'hld 9 1

which can be derived directly fiom eq. (18), and the prorit functionii (13)

with F given as written in eq. (14).Totally differenitiating the full system of household equlatiolns and rewriting

allows the deriatini of the set of total response zlaisticities wlhich give theproportional change in any CndloInCIIOLs Nariable, Y. in response to aproportionIal clhange in an exogenotus variable, A. The total responseela.sticities caln be broken down into coin-ipoinenit partial elaisticities.

1 %x xriabl) (II constant)L Y X' Y

Y .} E)\ (tE 11 H .> \'\

tE (' - M t1 E ) (`X\ II

cr, using a more concise notation,

^1)Y=1)*x + 11 ± 11 li, (19)

where 6, represcits the elasticity obtained if farm profitk( are alloweed tovarx and )1*, represenits the elasticitv obtained if farm proFits are eld

constant. A simple 1measofl11c of the sienifican-ce of integratingl prOdLuctioin anld

consumption decisions can be obtainied by coipailnluring ijy/ anld ?1

elalstcitiecs comiipultel for chloseni depenideiit a1nd1 i1ndepCIndLC1nt Ixariablcs. (.3iventhat wve lh:i el chosell to part ition the total elasticity tusiing the N araiahitIii orprorits as a criterlin it is utseftil to compare elasticitiCs forl' eXotgenOuS variables

which are arguments in the profit fuLnttiii1.iSTable 2 presen-ts elashticitiec, calculated at the arilithmetic means or the

sample used for Lstimiation, for hoLuseh1d Co0suinpL11tion1 of padi (C). jion-fa rmg(oods (MI1, and 11houehllOld labor supply, (81( with resppct to the price of padi(1)) the wage rate 1w) anld the iieu tral tech iicl fiieiicy parameter (z,).Comparhi ii the values of )1*x and ij, *NVe note thlait of the niine pairs ofelasticities, six have a changle in sign dependiiig on whether or not profit is

endogenous. (Comparing by cmx-CeIOL1s variable we niote that all of thieelas.ticitic with es,pect t) price have d'iffelrenii sigins and of thcse two differ byat least + 0.5. Al.] of the elasticitieN \%iti respect to the wage rate also have a

An ' sessiient o thile qualititlae significiictce of tire [arm 11hLosellhOld ilioel codi( hbe carriedotiut with other a l.ants of the procedure sunmmalri/ed by eq(i )1 1or' Insta1Ce,. Otle Cutildi

Compare elastitiles obtailled h\ first hiolding expend(titure (instead of t01I is i oIlstanIlt ;iiId thellallow-in ev\endiltiire ito Xalr In this case. 'or thle Net of elIsticitiles ttli e\xedlidtiture Constant

l les in. );s ii would ntot altflect expedliture although clearly tilh totial alue ttil disci etionarslitmler. wil, NWould hac Increased. Vse hawe chosen as nore instructis e. to hokd li ini lprol aiieon,tallt since this is the mio,i likes pi ocedti e to be 1011oNed b\ anl eonomistwlho \% hoIses itocaltcu lte tar tIll 10 e 111pii elastiities, 1s . m1111.1111 o.f tile roet (ot ilhe expellditur c lstrailnlit,. aidti

\N i'hs ditat on11 the costnptionll sIde olf tile mlldlel hot whl lacks illntoillilotll about tile

Prtt,06 ilOll lslartles.

92 Hl.N. Barum-iit ma!t L. Squire. TI'hori- of thc Iai,u-hi-ouisehllo(

Trable 2Selected household response elasticities with farm profits alternatively exogenious and

ciidoL'noii.'

Endogenous variable

Owni consumption Consumption of LaborExogenous of padi non-farm goods supplyvariable (C) (Ml) (S)

Price of padi (p)-0.04 -0.27 0.0

IIP0.38 t.94 -0.58

Wage rate (w)n 0.06 0.29 -0.07

fl.--0.08 - 0.35 0.12Neutral technologyparameter (a,)

Y"0 t),.,0.42 2.21 -0.65

Total expenditure (E) 0.52 2.74 -- 0.81

'The elasticities are computed at the mean values of the variablcs. tl* represcints elasticitiescomputed under the aNsumiption that net farmi profit is ex09Cil0liS. 'h) represents elasticitiescomputed withi profits cendoyetnou,. The components of q,j , are obtainedI as follows: tl* and i,,.are computed fromn eq. (18); and tl, equals II E. iqj~ is comlpuIted fromn eqls. (131 anid (141.

change in sign,' 6 although the absolute v-alues of the diffei-ences are not asgreat as for price. We conclude that, for our study area, the theory of thlefarm household is of considerable imnportanice wheni examining the Ilik-el)impact of changes in the price of the maini agricuiltural ouptiut, anld is also ofimportance, althouigh relatively less so. when lo)okmig at the imipact ofchanges in the wage rate.

We also note that the theory of the farmi householdI is important whenlexamnining tLhe likely impact of a nieutral shift in the production function. Forneutral chaniges in technolotiv, the first term in eq. (19) equals zero since,with the production side of the model excluded, conistimipticin is indepcndenitof techinology. The seconid term is, oee, potentially large since farmprofits are hig-hly elastic withi respect to chaniŽcs in the neutral technologicall

''In particular note that withi the profit funiction excludedi thec labor supply schledule withres,peci to the wage rate is negative. a fact -which is conisistent withi the resuilts derived by B3armcland MacDonald (1973) for houisehiolds with a h,oinoiheiic uitility function and inisufficienit assetincomne to provide for minimumn subsistence levels of consumiption. This iiegaiii\c respon)se ismiore than offset by thle iniclusioni of the produiction side of the mnodel; withi the aidditioni ol thieprofit functioni the supply response is positive. Sinice four-fifths of all labour in the Muida valleycomes from farm hiouseholds onle cani expect that the aggregate labor market response ispositive. This issue is discussed fuirLlici in the subsequient section.

fI.N. Barnumn tanid L.. Squire, Theory o fthe firm-househlwd 93

parameter of the production function. ' The extent of the overall impact onC, NM or S depends crucially on the size of the expenditure elasticity (seetable 2) for the endogenous variable qLuestion.

Examining the table by endogenous variable, it cani be noted that theelasticities of ,A[ and S have the greatest change in magnitude with theincorporation of the profit function. The distinguishing featulre of these twovariables is that they ha\e, in aIbsolIte terms, the highest expenditureelasticities of the three %ariables coinMledered. These results give a uLantitiltatiVebasis to the observation made abhoe of the inmportance of the expenditureelasticities and the necessity of usitig a consLuMP1tion system which will allowunrestricted estimates of the exlpeniditLure clasticities.' The results alsoindicate that the theory of the farm household is qLLantiLtti%iel) important (interms of the differences betweeni elasticities based on only the conistilointioIlside of the model and elasticities derixed from the integrated niodel) if eitherthe expenditure elasticity is absolutely large (as is the case, in this study, fornon-farm goods and labor supply) or if the impact of a change in ancxo ge1o Lus variable on farm profits is large (as is the case of a chalige inoutput price or te[clinolog ,: the theory is especially important in the eventthat both occur simultaneouslS (as is the case of the elasticity of deniand fornon-farm goods with respect to clhaniges in otutput price or technology).

5. Policv conclusions

Up to this point we haxe Llsed the estimated response elalsticities todemonst;rate the signiricance of thle lheor% of the farm hoLuI:sehold anid theiMP01ortLance of the expend(liturle elas.tiCitiCe. We now use our results to draw a

variety of policy conclusiolis with respect to mii-ration, the effect of olutputprice intcr%\ention oti nmark-eted surplus, anid the incomlie distributionalimplications of clhanges in output price and teclinology. Otther results may bederiked from the estimated model but the one,s diescribred hiere appeared to usto be of particular interest. The policy analysis is lhased onl the responseelasticities, for the integrated model, liresented in table 3.

In each of the applications considered it is necessary to distinLuislhbetween the responise of an indki idtial houLIsChold and the aggrcelate marketrespoiise. ThIuLS, the elasticities coniipuLted from the 1ho0Usehold model show theimpact of a ch;-igc in an exogenous i arialile on hlouschold helha% ior when all

?%Vc 1tiso estimated the c' hlnlmption side of the miodel Lising the linear loigildimiicexpenditure systetn applied b I ani et al. (197S). Foir most of the endogenious tariahles therehpoil;i ' ie, obtainiedi li'on,i thie consuption1ci)0 1 liullt or tIle molelt; ar'e siMilam itlmagnitude for bothi the I I IFS anl IFS sxtenm hut the t0tal response elasticities obtained tIrmthe to svystems tililer greatix Aieii the productioni sde is incorporalte(l. Fhe (illferenice is.atiribuLaible to the Il'at thalt tiie 1.1.S restricts the expenditure elasticities to be unity while theITS only restricts the expenditure elasticities to be positi\e.

Table 3

Selected lioLuseloldk response elasticities.d

Endogenous variable

Conisump-Own con- (ioll of labor Labor Marketed larmii

F weewiiloul sa mpiion( of non-lfarm stIpplx dean'llid OLutput Surplus profitvariable padi ((C1 goods (I) (St (ID) 11 (., C) (1il

Number ofworking familymembers (n 1) (0.44 - 06 .62 0(.0

Price orpadi (p) (038 1.94 (1.58 1.61 0.61 0.66 1.61

Neutraltechnologyparameter Ix,,) 1 0.42 2.21 ().65 1.61 1.61 1 '5 1.61

W:g,e rate (0i (t).t)8 -01.35 (t -1.47 0(.47 015i 0.47

1Tie elasticitics are deriwed from the integrated moidel anled are compu ted at mean valties ofthe variables.

other exogenous variables are hleld COInItaniit aiid ani if teimipt to driaw macro,general eqU ilibritimi coiclutsiowK must face the pribleniis ol agggregation andof the macro iitcrdepcndenic% among \ariab!es whliclh at the micro le\el calnbe treated as cxog nuis.>. To allow ani e\trapol tioln of thle imicrlo !Il;vs\yis tothie mlar-ket level, it is asumLlied that the :ele\%ant aggreg"atc rela tiolIlips catnbe obtained by multiplying the correspolndine nmicioeConomic l0 liuoInIi".by the total number of hIoLIseholds in the padi sector or equi'.dalently rathlierthan attempting a numerical agigrcuutio n we asssume that the estili:itedmodel describes a representrti\ e h1oLusehold. It is also assumed that the onlyimiacro) economlic ilnerdepenidency betweeni % iriaiblcs wllichi aue eoeilmeols atthe micro level is between the wage rate and all otlher \l ariables. To jLstifythis assumption, we note that the prices of the main inpu)LIts anid outputs.including padi and the prices of manv conuimsiler items are determined inworld markets, sub'ject to tariff policy. Other vLriables which are exogenousat the micro level (that is, family labor force, number of dependents, areaioper.ated, etc.) are also exogenous at the macro level, becatuse our focus is on'hie short-runri during wlhich period these variables may be conisidlereed fixed.i"

The eqU.utiOll for labor market eqLilibrlillum for the repiereslentalive holise-11old is

D==S+(,

'IIn the terninology introdduced by Yotopoulos and La.u (1974). the aglpiculr iral sector asmodelled here is closed witlh respect to the labor marnket and regulated s iih respect to theoutput market.

7U.N. Barjuun ant! L. Sqiire ih1eori' of' thte farnm-household 95

where G is the supply of labor conmino from :10on-uricuCltural households.After differeintiating thii eCtLM;tioll with respect to \wages ancd a givenexogenous ;ariable X. the resulting labor market conidition for Ceulilibratingproportional changes in wages and X can be written in terms of ehisticiliesas

=I 1,(S(; D) i( )xfiX 'i~~- ~S D)- I~( (;D)(20)

wlhere t; is the elaslticitv of hired labor, G. witlh respect to the wige. Thetotal response, imt(atti.is m)uitaiidis, of a chosen en1do0genu1sLI. variable, Y, to achanige in a giveni exogenous Nirialble. X. cani now be \i itlei

lihece the First termi on the right-lhand side gives the response, ceteris ihus,

and the second term gives the part of the total responise attributable to theinduced change in wages. In the analysis below eqs. (20) anld (21) are appliedusing the values of the elasticities in table 3 and setting S D= 0.81. It is alsoassumed that the eliasticil\ of non,-padi lired labor- with respect to a wagrechange is -0.07. as it is for p;aIdi h 1ouseh1old6 s in the Niltull ieioln with theproduction side of tle mnodel oimitLed 2

0 (see table 2).We look first at the qtuestion of sur1 plLus labor and thle Cfecto rO lural-urbani

migrotioni on a''Iirc tlt ural output, a subject \I1cli has receCied c0onsiderabl-1e

2"I his assutlmption is salid if the utilitx funetioii and tihe mean \alues of the exogenotu,Nariables delihieating the charaeteristlcs of a representatixe household are the same foi padi andnon-padi households. Barzel and lMcDonald (197'3. deiemoinstrate the tlheoretical possibilitN of aiegati.il\\- leoped labor uippl\ ctur\e using the specification of tile utilit i clvttlon emljoyetd Inour emilpirical analysis. Other possible \alties lor the elahstiCits of off-fllari labor response weretrie(i anl(d the results contrasted with those obtained unider the assuml;tion tlihat q,, t07.t. ItwNas founid that the policy results were not highly sensitixe to a range of \ailuesF lio fr hom

t).1 to 2. That is ,i. can be negati%e. or positiNe and inelastic, or positixe itald nioderatelxelastic without ika iii ilfl affecting¢ tilhe policy implications. In contrast, for higils elasticxalues of olff-farim labor respollne the resuilts challge nllLrkcdll. For Instance if either labor fromoutside the Nlud;a area is in perfectly elastic huppls to farmis in Nluida or a po(ol or surpltis laborexists, then (, + r anid the inarket elasticities wNould approach the househiold \altes iein

table 3.llowexer. tinlike mani reemons of Soutileast Asia. the \Iuda Ri\er Vallex is char;acteri,ed b\

an actxe labor imazr-ket and an apparent lack o; surpltis labor A ii oin indication that tIleOutside habor suplyI is Ii ilml inelastic is gixeni by obser\ing tlhat after tle Nlutida irrigationftli0cc was cnmpiplett thiere was a large iincrease in l ,itze%. mroneyN wage rates mo re tllhandotibled betwseen 1970 mpme-pio wci i and JI 93 p m oleii. whereas tihe conisuimiier price indtextexclusise of rice) increased b\ oak\ 15",, and rice prices sb less tlihan 51) during the samieperiod. Thus, we hase chosen to assumrie aLn itnelastic labor supplyl and to con,sider thle labomarket interactions in the policy applications. Blitt for househlled mod )(.els estimated f0i otliejregions, w here lici e is a strong p-i,"bmlity o!' surplus latlOr ll' an fllliltelt elatiC labor spl11,otne would apply the lhousehiol(d response elasticities Iconiparable to those in table 3i directly toobtain estimates (or thie .iggi et ;e mnark-et response.

96 IU.N. Barnum antl .. Squire. Theorv I l the ot tarn-hluehId

theoretical attentioni in the absence of inicroeconlfmlie empirical data. Basedon the model introduced by Sen (1966) the (lidiissNioin has focuissed on thelabor supply response following the departure of a family inemibher from a1h0tmehold which does not participate in the labor market. In Sens frame-work labor market particil)tion is considere,d a sLufficinlt condition for theConst.amicv of per capita labor s:ipply. silnce the eqluationl of the Illmargillalutility of leisure to aln exogenoLlJveleteriniie(d wage rate reCma1.illn uinaffectedL.By waN of conitrast our results establish that the 1per, C(IitaI labor stmlplph maybe a function of the size of the familk labor force, in whiclh case anexo(lellnosly deteiemiined wage-rate is no longer a sufficient conditioni for aconstant per capita labor supply. In our model the removal of a vmr-kingmember from an agricuiltural lioPelhOlOl will inl IuCece per Calp7ita Con-stimptioni patternis tlhrouglh a chane in the value of dliscretioniar-) timiiea% ailable to the 1hLousehold and tihroughl chlanges in the extent of thelhouschold participation in the labor market.

Since the household has access to the labor market, the priol'-maximniimnulevel of agricultural prodUCtion is detern,. ned independently of the numiber of\ior;king family members. Following the departure of one family worker, theprofit-maximi,inig level of OUtputi can be maintainied by either redtucinghousehold Con0sumption of leisuLre, or inlcreasillg tile lalmI n tit). of liredi laboror botlh. The ecCLonomllic cost of Jllilra1tionl is (ICtlrIllilnLeI, at lelst in part, bythe value of qsi,, the elasticity of family labor suppl) witlh re,peel tochanges in II. If Is,, 1 (i.e., the per callita labor sutpply of the renmininehousehold members remains conltant), tlheni the entire imipact of migrration istransmittedl to the labor market. Alternatively, if 1s, () (i.e., per capitalabor supply increaises proportiomlitel\ with decreases in the number ofworking family members), then there is n(o effect on the labor market. In theevent of the latter, the econoimiic cost of migration, in the sense of foregoneoutput. is zero, since the loss of one workin)g family miemiiber is r-estolredentirely by a reduction in the con.,IumIption of leisre by the rema;lining falmilymlemiibers. On the otlher lhand, if i1s, 1 migration will lead to a loss ofoutput, the extent of which will be determiniiied by the change in theagricultural wage-rate induced by the inicreasedI dematn;d for hlired labor.

In our study area in N.W. Malayia. qs,., is e.stimate(l to be 0.62. that is,38",, of the reduLction in hlous.holzd labor supply follohming the depart tire ofone workin- family nmcmhber is replaced by extra effort on the part of theremaininiig family members, ceteris paribs. It However the mi tn6a te effCt olloutput and thus the economic cost of migration will dlepend oni the responseof hired labor and the louiseliol(l to changes in the marlket x agc, If thlcsuiply of lhirecd labouir from landes i houseldokis is perfectly elastic tlheeconomic cost of migrati0in is zero since ad(itional labor can be lhirei

ilthout inicreasing the wage rate tand lhence without r-edLuCing.4 outpuLlt.Altern:itivcly, if we IssLumIc tlliht the nonl-pa(li hired labor supply lhas an

Iu.N. Bar.,nut,,m and L. Squire. , Thory fa thie farm-household 97

clisticit) of -0.07 as obtained from the COnIsulmlptionll side of the householdmodels, cqs. (20) and (21) can be used to calculate that the elasticity, E,I,,, oftotal labor hours used in padi pr-oductioni with respect to the number ofwvorking, family members is 0.47, mnutatis miiitandi's.2 ' It may be conIclldedthat migration from padi-producing houehldv60(Is in rural Malaysia is sociallybeneficial pro\ ided the migirant's marginial productivity at his point ofdestina,ition exceeds 0(47 of his marginal prodductivity at hiis poinit of origin.

We next turn to an analvsis, of the effects Of olutptLL price interventionwhich is an important component of current MI;alaysian agriculturail policiesdesigned to achieve self-sufficienicy in padi. Much of the past succ2ss of

Iaav.lhia's efforts in this directio;i must be attributed to tech1nologicalclhalle, IIo)%%er the g ernminent hias also intervened in the padi imarket tokeep the dom1estiC price hbo%e the cif price, thereby subsidizinig producers.

The eldsticities in table 3 establish that, at the nmicoecononiic level,Nala\siazn farm households respond positively to an increase in the price ofpadi output: the elasticity of total output is 0.61 and that of nmar-ketedoutput is 0.66. I1 l ever, these elisticiiies give the response. ceteri.s parihnts ofaii indi%idUL al 110Isclhold. If all 11household1Ls respoInd to the price increase asindicated in talble 2 the supply of labor from padi houLIsCeholds will decrease,the denmand for labor will increase and the resultinLg potential increase inInarket wage, may effect a reduction in outptut and niarkelcd sulrpltus wllichwill brinig ah)ut lower clasticitics mu1ttatis mnuiilaid,.s. T'he impact onl themarket wage will depend on the response of hired labor. isinig eqs. (20) and(21 ) and I(," 0(.07 we calctulate that the -:Isticitie.s of output andimiar'keted sulllrplu' with rL.spect to price are -0.02 anid - 0.08 respectively?2

We conclude that if the res(pons,e of hired non-padi labor is inelastic, as wehave a1ssumened it to be. the effects of -o\rnenient price intervenition on outputand mairketed s1urplus have hceen esentia;lll niil.2 .1

Turning to the issue of the inicomc disi ribLitiomiial imipaict of clianiges inoutput price and t1c noo1010`3, we first e\:anliinc tlheir imlplialct oni incomes inpadi hlouseholds and then consider the reper-cuLssions on otlher Sectors of theeconomy. As far as padi households are concerned, the miiicrocconioilnic effectof an increase in output price or an upward shift in the production functioncan be derived inimediiteLI from eq. (19). Thus, the elasticity of farm profitwith respect to price or the technology parameter is 1.61. Padi households.therefore, receive a major inicoeic benefit froim both price increases andtechnologicail advances, wlhich has substantial ex peiidi tuile efflcts on tllepatLI en IOf So110s1e COI1.1c11sptionl.

"Siiiiili.1rl%it can bec alculatedl that Es5 1)0.58, E,,,- u 1j()2. andE E,,, 0.15.''In cointrast, thie inutaris mnutandis elasticitiesi of output and marketed phi., withi respect to

neuitral ciel ilogicIl change are (0)96 and 1t)09 re,pecl'.ilN.'As 110 ,, ranges Irom - 0.1 tO 2.t), the Cl1.11r en'. of output with respect to) price ranges Only

rom -0.02 to 0.11.

98 H.N. Barm1un ntdt L. Squire, Tihavy (?t the farni-hot7useh.d

The associated changes in consumiption anid pro)d uction in padi hiouseholdscan be expected to have a major effect on other holusehold groups. Forexample, much of the increased expenditurec made possible by price illnlceasesor tcchnolo-ical advances is allocated to non-farm comlmodities (Al). Thehousehold elasticity of Al witlh respect to p is 1.94 and with respect to X,) it is2.21. ThuLs, the indirect elect.s through clhaniges in consumiption cani beexpected to lead to sinlific anlt incre;ses in income for those in botlh rural andurban areas whio prlduce or supply non-farm coninioditiec.

Of miore imnporitance. howe\er, is the impact of a price incrI.sce or atechnoloc0-ical advance on those members of the rural sectCo Who dCjependprimarilv on wage emiplo%nment as a source of income since this group isuSuially among the loorest in most develoqing countries. Increases in theprice of a mal;ljor con)sumnption iteml suchi as padi canl be expected to imposesevere hardships on this grfoup -. otunatlel howevcr, the e% idenicc fromN.W. W alayia indicates that this group cant e.\pect a comipensallno benefit inthe form of increased w'.aee income. Table 2 indicates ilhat the louLschl0dresr)ponise. ceteris paribus, to a price change will involl\e an increase iIldemand for padli labor (hotlh familn and hired) and a reduction ill huLsehCOldlabor supply. The comibinatiOll Of ani increased deCm11an11d and a reduced supplxof labor from padi hoL)Useholds w6ill effect ecomdarm changes in the \\ace-rateand the use of hiired labor or botlh.

Using eq. (21) vc. ,an calculk !e that E,,.,. the elasticity ofl the niar-ket Nkagewitlh respect to a clhanige in price mnaU zi\ Inltalmdis is 1.34 andLi that E,,, theelasticity of hired labor uLse with respect to price, is 0.10. tlhus. the largeincease in wages more thani offsets the slight (leciine in employmient anldJOuseholds Micich depend to a sionificant extent on wage employiment as asourLe of income can e\pect an increase in their income as a result of anIincrease in the price of padi.

A similar effect may be e.Xpected xitlh respect to a. 1kan11& in t11c1m10ol .Previous treatniWients of the effects of teclnolo-g ical chalinge on the labormarket have tended to concentrate on the demnand lor labor. that is. oni theproductioni side of the model, and ncglected the impact of teclhnology oin theallocation of househlold time betweeni leisure and labor. 24 Ho\\V'ee oLurappflicaliOll of the farm houLIsehol(di model inLdicaltes thlat thiere will be a'i/eable response from padi farmers onl botlh the dendlld and supply side ofthe labor nuimret. Since the elaistici1\ of demlnld for labor (bothi faily andhired) witlh respect to i,, is 1.61 and the elasticity off flnmil\ labor .,npply withi'e>llcct to Xl iS -0.65. it Can be expected that raCLItN;l technologica-!l clhanigewill increase the wage bill. Using eq. (20) we calculate the !mIati mulwidela.sticilt of the wage with1 respect tO X, to be 1 .38. Similala l. we calculate the171ulwtitis nniiu,,di e lastichi of lircd labor tise witlh re.pI)ect to X, to he (0.16.

24 tor exam-ple see Sidhlu t19741.

U.N. Barnum and 1.. Squire., ! heor lo tit, larmn-hzu'hold 99

xNhich implies that, although there wvill be somile r.ed[uLctio iin minployment.neutral technologyical chan-e will have a sie.able positixe imipact on the wagebill. Tlahis result is of cons,iderable significancc becauise it indicatcs that thetrickle dowin' approaclh to econioiviic growthi is at least partially valid in thatthe beniefits of iniprxemuents. in farm leclhnoloov are being transilmnittedtihrough the labor mnarket to those whtlo are n(ot tlhensel\cs primarily padiiirnimr., AFricL1hltuail projects. \Iuichli benefit directly those memilbers of ruralsociety who contr)l the Imainl productixe alssets, can also be eXpeCCtedl to

benefit those xhio owni little or nio land thiouIgh changes in wage-rates andthe w,-age hill.

6. C(onclusions

In this paper we demionstrate thle policy significance of an integratedtreatment of production and consumption decisions in the theory of the110 1o1uhL)1d. Consider ii o the impnaitct of changes in x ogenuslIO x ar'iables weconclude thiat since the prodtiction side of the miodel e\erts its influence onthe C0onUl ptio0ii side thirotigih the expenditure claslticity, thie integrated

theory is espceiall\ imporurtiit if eithier the e.\pend itui re elast icit\ is higil or ifthe product ion effect is domlinalit.

In opeciric applications the resuilts of the .stin:i ted model indicate that theeconiomic cost of Iruri-al-uribaii nmiiir,itimn in N.W. Nlala\Nia is ini:lil inrelationi to the 1n1 11gilmll pdneot lLix it\ of the migranit prior to hiis depalrILtirethat outpLut price intervention is not effectixe in increalsinqg imarketed surplus:and tliat the beiiefits of' increasesC- in a11gr-icultuLrLal ouItput prices anid ofimi1prox0e\mnents in leclhnoloo\ are ditributled througih the labor market tothose Wvho relV 11CLIe i\ oiio wage emiiplo miieiti as ar major source of income.

Appendix

Dtit .sourceS

The data for tIlis study were Collected during the CouIse of one calendaryear ctmnmencing I)eceinber 1972 and running through to N'oxemiber 1973 aspart of the FAO IBRI) cooperatiuxc program. The liouisehiolds for tIlis surVeywverc s.ampled as lollo\\ s, In the lirs-t stage of the two-stage samplingprocltire, a simplc random samiiple of all rural population celluLIS en-umlcratioii blocks xx itlhin the command area ol the Mlu(dai River IrrigationProject (642 in total N\,ias taken using a 25 ") sampling fraction. Of theresultino 14,788 households, 10,196 \xcrc identified as being primarily engagedin, pa3di work eilither as padi fairinmers or as padi farm xx orkers.

The sample was thieni s,tratified by ti) the numiihbe- or fears the h1ousehlol(dhlad beena double-crop!liilg: and lii) wiether the lanid operated uwas. acid or

10B0 Ifr. Barni tan1 L. Squire, Theorv qi the, lrm-huwsehold

nioni-acid. Withiin eaclh stratum thlus identified, the sample size was chosensuch that it bore a proportionnate relationship to the standard deviation of

mean annual cash income, For the purposes of our study, we haveconcentrated on those households which have been double-cropping for one

or more years and which operate non-acid land. This concentration ensuresa relatikely homogeneous sample: it omits those operating on the qualit-atively inferior acid soils (8"(, of the original samnple) and those who were in

the process of sw%itchinig from single- to double-cIropling dIlring the period ofob6er%ation 20O l of the original sample). The remainhing sample was thenfurther adjutsLed to exclude (i) alt 11oLSeIhOlds which failed to report labor

usage for land prepanrtioin, plantinhg, harvesting or threshing, (ii) all house-lholds which failed to report padi output, and (iii) all households whichfailed to report wage paymeniits. The finial sample size is 207.

During the course of the sr\ey each household was inlerviewved fifty-fourtimes. These inter\ie\ws comlprised an openiing and closing in entlory (whichcollected information on a \arietv of stock variables such as asset ownershipand family size) and fifty-two weekly interviews (whichi collected inforiiatiohlion a variety of flow variables such as e\peniditure, income, output and laborusage). The data from the fifty-two wekly inter-views liave been agereeatedinto thirteen f'ur-weeklh periods.

Because the survey commnceIdCL ill the imidldle of the fij-st crop productiLo

period, our sttidy is conindl to thle secold crop. That is, the phlalninighorionll is asN"uMed to be the secoind crop cycle anid all variables are definedwith respect to that cycle.

Dt'/l!ivitl H } L) C?f uariabt'.8

C =own-constusmptiOll of p-adi in gantang,qMAI-constumptioi of noni-farmii coiiinmdities ill AS,

S =famnily labor SluplidiC to on-farm padi prodimctioii and off-farm wageemployment in man-days. 1Mafle aind female Nv)ork time is weightedeq11111),

T ttotal time i%a'.ilaibl in nizan-ciii.s. for all w\orking members of thefamily. Days lost thirough s,ickniiess, ab*Isences or other nuctuiations in thenumber of w%orking family imienmbers were netted out,

, number of working family members defileld as all miiemiibers of thc.family of 16 years of age and o'ver,

11, IlInum r of dcepenidenits defined as all imeimiber-s of the family under 16years of age,

a1 aie of tIle oLuSehCIol1d hea.dnumber of yea;irs of diucation recei% eLi by the hou(sehold lhead,

p =--price of padi in 1S per gamintung..v wage-rate in AIS per ian-day. \Vapes for off-farm employnment were

If.N. Bartmon aindi L. Squire, 7heury o/ ihelfirm-niouselld 101

calculated by dividing the total value of wages received in kind ormoney by reported hours worked off the farm. The construction of thisvairiable entails the use of the weakest data obtained fromn the surveysince some households were inconsistent in reporting wage income,especially in kind. Households with obvious discrepancies in theNepO)rting process were omitted,

L =-a residual which is called 'leisure' aiid is imieasuired in mandays L=TS- f'8 on the issliniption of an eight hour working day,

E =total expenditure in MS. E=pC + qM + itL.

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