World Bank Reprint Series: Number Niinety-four

Howard N. Bamum and Lyn Squire

Technology andRelative EconomicEfficiency

Reprinted vwith permission from Oxford Economic Paipers,

vol. 30, rno. 2 (July 1978), pp. 181-98

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TECHNOLOGY AND RELATIVE ECONOMICEFFICIENCY1

By HOWARD N. BARNUMI and LYN SQUIRE

IntroductionTHE analysis of ecoiionoie efficiency nimongst. clearly differentiated groupsof farms has assumed an important place in the literature on agriculturaldevelopment. In the main, the analysis has been confinied to Indian dataanid to a comparison of small and large farms.2 The analysis, however, isperfectly general and can be applied to anty grouipinig of farms which seemssensible on the basis of a priori reasoninig. The application of the analysisto adaptive efficiency, for example, has beeni accomplished by dividingfarms according to their use of new or old varieties of seed.3

The interest in relative economic efficiency arose out of the observationthat for Indian farms labour intensity and yield are inversely related tofarm size. Most researchers initerpretedl this result as an indication thateither small and large farns faced differe'nt configurations of ilnpult andoutpult prices, or small and large farms differed with resspect to economicefficiency. This latter was further (liNided into technical and allocati-eefficiency: a group of farms may be considered techniially more efficientthan another group of farms if it can pro(duice a given output with less ofsome or all inputs; a group of farms m-av be considered allocatively moreefficient than another group of farms if it is more sticessftul in equatingmarginal revenue product and factor cost for each of its var;able inputs(i.e. more successful in maximizing profits).

It should be noted, however, that the observed relationship betweenlabour intensity, yield, and farm size is perfectly consistent with thehypothesis that all farms are econoniically efficient and with the hypothesisthat all farms face the samie configuration of input and output pricesprovided it can be denlonst.rated that the production function exhibitsdecreasing returnis to scale. In fact, the observred relationslhip betweenlabour intensity, yield, and farm, size warrants an analysis of relativeeconomic efficiency only if the production techllology can be chlaraeterizedby a linear homogeneous4 function. In other words, tests of ecoiomic.

1 The authlors aclknowledge gritefilly tlio researeh assistanco of LeafiuTJiong I )D1g. Tlhconstructive cornments of an anonymous referee are aLso ac1nowledgeod with tlhanks.

2 See, for example, Yotopoulos and Lau [10].3 For furthor details see SiC .i L9].4 onoiogeneity implies the, QA? Q(AX 1, AX,...)

where Q is output, Xi inputs, and A is a constanit. Tho paraiieter r indicates the (1egreo ofhomogeneity (returns to scale). Linearity implies r 1 (constant returns to senlo). For

Reprinted by permission of Oxford University Press

182 TECHNOLOGY AND 1ELAT'I VE ECONOMIC EFFJCIENCY

efficiency should be preceded by tests of the nature of technology especiallywith respect to the important assumption of constalnt retuirns to scale.

Similarly, the observed relationship between labour intensity, yield, andfarm size is perfectly consistent with the hypodiesis that all farms areeconomically efficient and with the hypothesis that all fatrmns face the sameconfiguiration of input and output prices 1 )ro?vided it can be (led onstrat.edthat stwall and large farms face (lifferenit production technologies. If one

group of farms has access to a new technology, then tests of econiomiciefficiency which assume that all farnis have the same production functionare clearly inadequate. Thus, in order to exeltu(le this possiblity, tests ofecoilonic efficiencY should be preceded by tests of the hypothesis that the

various groups of farms under consideration face the same technology.In this paper we l)resent tests of relative technical an(l allocatkive efflciency

for hflree pairings of padi farms innorth-west M\lalay-sia. Tests are conductedwith respect to farm grotupinirs based on (i) area operated, (ii) tenancystatus, and (iii) the number of years the farm has been double-cropped.

With regard to area operated, it is by niow well established that in many

countries yield and labour intensity are inversely related to area operated.As Bardhan [1] has iioted there are at least two reasons whyi this result hasatt,racted so muich attention: first., it has olbious policy imllplication.s withrespect; to land reforiii, in that, undi(ler certain eircumiiistances, it signifiesthe possibility of simnultaneously increasing output anid improving thedistribution of that output; anid secondlh, attempts to explain this pheno-menon are crucial to our understandingih of develophig agriiculture. Muchof the empirical research oni this jiuestion, however, has used Indian datarelating to group aicrage. and has taken the valule of total crop productionin mutlti-criop situations as the depenident variable. By way of contrast,the results roported here are for Malaysia, are based oni farim-level data,and relate solely to one rol)p (pad i). This last is important since the use ofthe valuie of outptut in multi-crop farms as the (lependlent variable implies

that all results are subject to a 'crop-oonllu)(sitjion effect' whielh may bias

results in unforeseen dIireet.ions.lThe effect of tenancy status on economic efficiency has also attracted

considerable attention in the deveflopmuent literature. In the main thedebate htas eentre(l on the issue of whether or not sharecroppinigr results inallocative illefficielcies. In the stiidy area, however, v irtually all landrenital conttracts are specified in termis of a fixed cash paymelnt. This

a two-fact or lirnear, liomogeneous pro lduetion function

QX - g(X(i,'.Y) an(i X NX .-\-, I-.J1

Tl hat is, average and mnarginal productivity are fiiiietion-Ll of the ratio of iinputs.

` Seeo Bardlhan L11.

H. N. 13BARNUMA AND L. ISQUIRE; i83

observation implies that (according to theory) allocative mdlin e lencicscannot arise from the nature of the rental contiract, since the fixe(d rentaldoes not influence the marginal, profit-muaximizingp conditions. Nelver-theless, it has been de.monstrated that in this region of north-west Malaysiatenants and owner-tenants consist.enitly have hitrhel' yields than pireoowners, and that after standardizing for farm size, the differencies in yieldsbecome even greater.1 Ac(ordingly, we test for (liffcrence.s in economllieefficiency for farms grouped by tenancy status, those rentinig in at leastsome of their land vonstit ut ilg oIne group .and(l owner-oper ators conist it tit ingthe, other group.

The final pairing of farms is accordlina to the number of years the farmhas been double-cropped and repre etiAs an attempt to examiiine the adap-tive behaviour of Malaysian padi farmers and also to examine the impactof repeated double-croppinig on the technical efficiency of pa(li production.The area under stuldy has recently b)enefitedl from the prGvision of irri-iigtionfacilities (the -Muda River Project) wlich ha- enabled farmers to switchfrom single-to (loul)le-eriopp)Lng. The change in technology can be ex)eted,

of course, to have had a marked impact on the demanmd for laf)imi. Irlieobvious impact comes froIm tlh ad(it ion of a I1W (lelnaind for padi ll)ourin a season where thlre hadl lprev-i(isly- been nIo padi prio(ductioni. A mnodi-ficaiioni of the initial inpl).a(t oni labour deni)imd caii be expecte(d if thetechnical efficiency of pi-odluction (luring; the secoinl orop cycle changes,or if the allocational efficiencey of padi farmers chan-es, with the leuui¢th oftime a farm has been (ldouble-crioppedI. The (ross-sectioln sali-le used inthis study (distilluislhes b)etw(11een !luns which lurv 1been (dotllble-vop,pedfor one year and those which have hevil douhc -cropped for t(.o or moreyears. A comparative analysis of tlese two ,guoulmps of fairms will enaible usto aseertain the effect of farm experience oin allocational and techniicalefficienexv. This analysis is of particiul1ar interest since the distribution ofthe benefits of the new t(eC1mlltg011V thll'rlglul thIe labour' mlarket will depeInd,

atleast to somen extent., on the impact. ofthenew t i ewhnoior\0 t clhciencvof factort use in pa(li pioducetion.

Study area and data baseThe stud(ly area is in the extremie nor-th-w-est of peiniilular Mal]Iysia andI

comiipiris(es the state of Perlis taind four R(lmnhiTIiStI'attiVe dtistricts ill tHe state

of Kedal. Pndi (iultia ion is the mn oeuupatiOI of over 4iO,Otu') familiesin the area w\hich contains about 30 per ent of the p)adi land in Marilai sia.and accournts for almost 50 per cenit. of total pa(hi out.puit. 'he receltswitch from Siigle- to (louble-er oppinlg as a resuilt. of niew irrigation fatcilit ies

2 Soo Iuing [41.

184 TlE"CHNOLOGY AND RELATIVE ECONOMIC EFFICIENCY

has been accompanied by a significant increase in output from 277,000 tonsin 1965 to 678,000 tons in 1974.

The data for this study were collected durinig the course of one calendaryear commev; iw .u November 1972 and runniing through to Novemlber1973 as part of' the FAO/IBRD co-operative programme. The householdsfor this survey were sampled as follows. Inl the first stage of the two-stage sampling proceduire, a simple random sample of all rural populationcensus enumeration blocks within the commanci area of the Muda RiverIrrigaticoni Project (642 in total) was taken using a 25 per cent samplingfractioni. Of the resuilting 14,788 households, 10,196 were identified asbeinig primarily engaged in padi work either as padi farmers or as padifarmi workers, The sample was then stratified by (i) the number of yearsthe farm had beein double-cropped; anid (ii) wiether the land operated wasacid or non-acid. Within each stratum thus identified, the sample size

was chosen such that it bore a proportioniate relationship to the standarddeviation of mean annual cash income. The final sample size was 839bouseholds, or slightly more than 8 per cent of the popuflation.

Eaeh household in the sample was interviewed fifty-four times duringthe course of the year. These interviews comprised an openinig and closinginventory (whliel collected informationi on a variety of stock variablessuch as asset ownership and family size) and fifty-two weelly interviews(which collected infonmation on a variety of flow variables such as ex-pendi-ture, inlcomie, output, and labour isafge). The data from the fifty-twow cel; interviews have been agg regaated into tliirteen, four-weekly periods.The data base, therefore, constitutes a relatively high quality source ofinformiiation, on the main flow variables as a result of the comiparativelyshort period of recall for the respondent.s (one week).

For the purposes of our study, we have concentrated on those farmswhich have been double-cropped for one or more years and which operatenon-acid land. This concenitration enisuires a relatively homogeneoussample: it omiiits those operating on the qualitatively inferior acid. soils

(p per centof the original sanmple), thosewhowereinthe)1rocess of switchingfro llsilitelo- to dolule-cropping during the period of observation (20 per centof the original sanmple), and those. households not operating any land at all

(5 per cent' of the original sa.rnple). In addition, our study focuses on thesilngle, agrricuiltujral cycle for which a complete record of inputs and olutputsis available. Thia:t is, the sttdy is confined to the second agricultuiral crop

eycle in the 1972-3 seasoni. Of the two padi crops grown in the MudaR ivr Valley, the second is that which relics on irrigation water and whichrun3 from.i April/Miay to August/September.

The samlple was fuirther adjuisted to exclude (i) all households whichfailed to report labour usage for land preparation, plant-Ig, harvesting, or

II. N. BAlRNUMI AND L. SQUIRE 185threshing; (ii) all households which failed to report padi ouitpuit; and(iii) all households which did not hire labour. The last adljustmenit onlyinvolved the removal of 17 farms, since most households participatteextensively in the labour market. The final sample size for the productionfunction analysis is 386 houselholds.

Table I presents the basic information oIn mean input and olitplot levelsfor the second padi crop for the three pairings of farmis. In line with theresults reported for other countries, the total labolur input pCer relml-decreases with farm size from 203 hours per relong on farms of less than5 relong (small farms) to 164 hours per relong on farms of more than5 relong (large farms).' Similarly, yield decreases with farm size from499 gantang per relong on small farms to 474 gantang per relong oIl largefarms but, unlike labour intensity, the difference- in yields is not signi ificanitabove the 95 per cent confidence level.2 The joint influenice of (hclngCs inlabour intensity andyieldis captured i t,he figures for labour plO(l u(tiv-it\.:an hour's labour on a small farm producees 2 8 gantang comiipared to afigure of 3-1 gantang on a large farm. The flow of capitil services anld tlheuse of other variable iniputs (mainly fertilizer and pesti(idle), however,remains relatively constant. as farm size clanmges.3

Turning to the influenice of tenancy status, at a 5 per cent level of sig-nificance it may be concluded tllat tenarits use less labour but more othervariable iniputs per reloiir than owners and have similar yields. Rathersurprisingly, how-ever, tenants operate 6-6 relong on average compared toa figure of only 5-1 for owners. The observation that teniants have a higher(but not statistically difflerent) yield aln(d lower laibour initensity (497gantang per relong and 176 hours per relong) than owviers (478 garnlltlangiper relong and 199 hours per relong) is in accord with results reportedelsewhere for Malaysia and sug-ests that tenants are eitlher technicall orallocatively more efficient than owners.

The most surprising result, however, arises in the case of the brea ik-dowinby experience with dotuble-croppinig. Although operators of f.airms whiichhave only beeni douible-cropped once use similar (quanitities of inpluts tooperators of farms which have been (louible-eropped at least twice, thenewly double-cropped farms achieve a yield of 543 gsmitani,< per relongcompared to the 468 gantang per relong achieved on farmns double-croppedover a longer period. The simiiilarity in the input levels and yet the coll-qiderable difference in yields su--est thlalt, in spite of the greater experience

A relong equals 0-71 aores, 2 A gantang equals 5-32 lbs.Yield and labour intensity data for a finer breakdown by farm sizo are given below:

Farm size (relong) <2 2-4 4-6 6-8S 8-10 >, 10

Yield (gantang per relong) 523 465 505 450 504 453Labour intensity (hours per relong) 225 204 174 163 168 1 52

TADLE IArithmeic m* of i*puM and tu ptW

Labour input in hoursr LaC)Area Yield i7 per relong Capital OWler ductivaOxy

Parm operated in gp.tang - flou per inptls per in Vnriutezg G

cl ion N reon* relongt Male F¢male 3otk s'elang§ relangj par htour,p

223 3.3 499 98 105 203 18 11 2 8

> 5 163 9*6 474 78 86 164 17 11 381

4tMioll 18*44 0.97 4-40 4-07 6-31 0-70 0-78 1-72

Owner-oRorators 173 5.1 478 95 104 199 18 10 2 8

T.-nts 213 6.6 497 86 90 176 18 12 3V0

t-atat4,stie 3.35 0,75 1 7 2-99 3-08 0.11 2-27 1-04

DoQAbl-cro)rpp.d:One yefr 106 5.7 543 83 97 180 17 10 3.4 H

Two or mnore years 280 6-1 408 92 96 180 18 11 2 7

t-Atatistie 0374 2-73 488 008 1810 0158 1.15 3-80

All farmns 386 6-0 488 90 97 386 18 11 249

Area oporated is measured in relong (1 relong = 071 acres) and we have controlled for soil quality differences by omitting all 0

households operating acid land. t

t A gantang equals 5-32 lbs.$ The labour of household members less than 15 years of age is not inoludod since information obtained. from tho survoy indicated

that the use of child labour is essentiaUy nill.§ The capital variable measures the flow of capital services to padi produotion in physical torms. That is, the flows of bufralo t

and two- and four-wheel tractors are uggre,gateod to form a single measure of the flow of eapital servieos. The ieiglt iisou(i in the Q

aggregation represont the relative time needed for each power source to bring a constant area to the samo stato of readiness for

planting. To arrive at buffalo-equivalents, the flow of four-wheel tractor hours is weighted by 14 and that of two-wheel tractor hours Zby 3-5.

Other variable inputs inelude various fertilizers and pesticides in value terms (MS per relong).

II The t-statistic tests for the difference between the means of the two groups. The means are statistically differenlt at a 5 per cent

level if t > 1-96.

H. N. BARNUM AND L. SQUIRE 187

of the latter group of farmers which would be expected to improve alloca-tional and technical efficiency, production is technologically more efficieIton the more recently double-cropped farms.

Methodology

Our approach involves a direct estimate and comparison of prodlictionfunctions for each of our six groupings of farmers.' We test first for factor-neutral and factor-biased, diffTr mces in technology for each pairing offarmers and then piroceed to tests of retirns to scale. Finally, we comparemarginal revenue products aind factor costs in an analysis of absolute andrelative allocative efficiency. Our basic estimating equation may be writtenas: Qj = eao+'xoDj1[ Xy+aDj ec (1)

(i=I , 4; j -1,.,N),

where Qj = output of the jth farm, X1 = area operated, X2 labour,X3 = capital serv-ices aind X 4̀ = other variable inputs.2 The error terun,ej, is assumed to have a zero mean and a unifori variance, and. to bedistributed independently of the Xi 3 One regression is run for each of ourthree pairings of farms; Dj is a duimmy variable which takes thei value ofunity for (i) large farms, (ii) tenant farmers, and (iii) farms double-croppedfor two or more y,ears; and zero for (i) small farms, (ii) owner operators,and (iii) farms double-cropped for only one year. The coefficients of theproduction :fuinction in each pairing for that grouip of farms for whichD = f 0 re thleni givein bvyo aind i,; while the coefficients of that group offarms in each pairiing for which D =1 may be recovered from the sumsa,+a' and xi+oz'

For each pairing of farms, tests of the hypothesis that the two groupsof farms face the szame pro(duictioni technolocrg are conducted, using ananalysis of covariance, by reference to the statistical significance of theshift coefficienits (a' and ar). If for the pairing of farms under considerat ionaz is statistically (litleref-it from zero, then a shift in the neutral technicalefficiency parnimter is conifirmlied. Similarly, if for the pairing of farms

1 This rnothiduology has been crilieized by Nowshirvani [5j and others on tlhe groun(dsthat the pro(dtuction function estimate is subject to simnulta[1Coi1Her qiuJLti0ii bias. Thiscriticisin has been successfully answered by ainong othlrs. Zolloer, Knienta, anl I)roze tll]who demonstrate that., given the lag between input (lIcisions and output whichl occurs inagriculture, orlinary least squares will give unjbiasedl e'itiiiattps of the production func-tion. An alternati-te approach iiivolves tle. use of the profit function. See Yotopoulos andLau £101.

2 A moro precise dlefinition of the variables is presented in tlie footnotes to Table I.3 The regressions reporte(l in Tables II and III below wore examixned for a hoteroskedastic

relationship between the residuals and the farm size variable. .Using tho Spearman lIanilcCorrelation Test the hypothlois of homnoskedlasticity was not rojected at a 5 per cont levelof significanco.

188 TECHNOLOGY AND RELATIVE ECONOMIC EFFIC IENCY

under consideration the slope shift coefficients (a') are significantly differentfrom zero as revealed by a joiiit. F test, it is concli(lded that there are factor-biased differences in techlology. On the other hand, if neither the interceptshift coefficient nor the slope( shift coefficients prove to be (liftereilt fromzero, it is conelt(ledd that botlh groups of farmis face the same technlololgy.

Deipjending on the results of the above exercise we l)roeeCd in one of twopossible w ays. If for any pairing of farrms it is concluided that technologyis the same for both groups, then the production function is re-est.imatedover the entire samiple. Tests of returns to scale mray then be based onthe estinatcd coefficients of this regression: constant retuirns to scale isconfirined if i a-- 1. The fintal set of tests coincernmig allocative efCicienicy

is then coniducted with respect to the, ratio (kc) of marginal productivity andfactor cost. For example, with respect to labour, the relevant equationmav be w,vritten as

k = ,' (2)

whe-ce x2 is the expoie] nt on the labouir variable and is the sianlme for both

groups of farms in any pairing and Q, X2, wV (wage-rate, divided by outlputprice) are lpeific to each group of farms. Tests are first condlucted fordifferencves in the conifiguration of iniput and output prices facing eachgroup, aId then for allocati-e efficienicy-. Absolute alocative efficiency foreither group is coniflrmned if k = 1 (that is, marginal product equals factorcost), andi whether or not absolute allocative efficieiey is confirme(d, thetwo groups are considered eq(ually alloc-atively eflikieiit if their respectivek values are the sai tie.

An alt eni five procedure is a(lopted.l hoi-vever, if the technology for anytwo groups of farms is showni to be different. In this event, separate pro-ducetion ftuimctiims arc re-estimiated for eachi group of farmts with. 7ie restric-

tion that any eoeflien-jits sholwnv not to be statistically (liIlerent on thebasis of the estiniatet of (quation (1) are held constant for this new estiim.ate.Tests of allocative eflicienicy are ag.ain based on equation (2) but now thepc.itsihitvr that tihe productioii ftiunction is different for the two groups is

t Twvo) t1alifieations of thlis test slu nlti he noted. First, an implici.t ass1umjjption in the useof a t or atn P trest on a Hubset of etrieficioits is that tiie copfficients omittetd from tla teUstare correct. S'ujitlvnintary P tests aro p)resented in Table II to illu-itrlLto that the resultsobtained aro tiblei witi other formulations of the test discusssed in the text. Steond,the test proeoduro we have used assume.s that! tlho orror ttrm bas a tmiiorin varianee overtlite entire ITamplt'. An alternative procedturei restricts the varianices to ho utniforni witlbiireach v-ubsanpfi, bxut allows them to differ amnonig subsamples. The alternative test inlvolvesa comparison of the residutal sum of squares froni soparate rogressions -with the residualsutmn of quares frnmi a pooled regression constrainedl undler th(e null hYputhtewis. For our

h1imjl., },Ii iwer, the alternativo tests yi1ld idntiec.Jl concluslions. We hliave oen to

repo¢rt results using the dhurimy shifb alterilative because it is more compact andl alsoprovides iinfiriuiation oln tle individual shift cooefciernts. For further discussion of thesetests seeo hliow t23 axnd Rae and 'Mill(er [7].

H. N. BARNUM AND L. SQUIRE 189

fully allowed for by admitting intergroup variations in the exponents ofthe factor inputs, ai.

Technical efficiencyThe results of our estimates of equiationi (1) for our three pairings of

farms are presented in Table II. At this stage, we are interested primarilyin the statistical significance of the shift coefficients. Exam-nining thevalue of pja, we see that the hypothesis that the factor coefficients are thesame cannot be rejected at a 5 per ceint significance level for these pairingsof farms. This conclusion is further supported by employing a two-tail

TABLE II

Begression 1 (Equation (1))*

Farm Tenancy Don?ble-croppi?igCoefficientt size statwu experience

In oO 3-36 2 98 3-80In acD -0'95 (0-70) -0 29 (0-58) -1A41 (0(60)Land o: 0-72 (010) 0-72 (0.10) 0-81 (0.13)

c4D -0-29 (0.18) -0 21 (014) -0 27 (016)Labour cU2 0<19 (0-09) 0-22 (0-10) 0 10 (0.13)

4aD 0 23 (0<15) 0<19 (0<15) 0 30 (0t15)Capital a, -0 02 (0 04) 0C01 (0 04) 0 03 (0 05)

a'D 0-10 (0-07) 0 (0-06) -0-01 (0.06)Other variable inputs

U'A 0-08 (0-04) 0-08 (0.04) 0.02 (0-05)c4D 0 02 (006) -0 02 (006) 0 09 (0)06)R2 0-67 0-67 0-68Fat 1-94 0-75 1-76pFbT 1-55 1-44 4-18Fef 0-21 2-72 13-76N 386 386 386SEE 048 0-48 0-48

* Standard errors presented in parentheses after estimates.t D 1 in(licates large farms (> 5 relorug), tvnant.9, and farms (dul(-eA-roppcd

two or more years. D -3 0 indlicates small farms (< 5 relong), owners, all(n farmsdouble-croppe(d.

t Fa tests the hypothesis that a 0 for i 1,.,, 4. That is, F" tests the hypo-thesis that output elasticities are the same in separate regressions for each group.The critical value of P at a 5 per cent significance is 2-39. Fb tests the liyp otlcsi sthat a' 0 and 0x' 0 for i 1,..., 4. That is, P tests the hypothesis that allcoefficients are the same in separate regressions for each group. The critical valueof F at a 5 per cent significance level is 2 23. Fp tests the hypothesis that et - 0in a reg,ressioni with cX ; 0 for i 1,..., 4. The regfressioa used to obtain Fc isnot reported here. The critical value of Fc at a 5 per cent. significanee level is 3-86.The maintaited hypothesis examined in the text does not invrolve Fb and Fo. Thesetests are included only to show the interested reader that the conclusion reachedin the text could be obtained using other formulations of the mnaintained hypothesis.

190 TECHNOLOGY AND RELATIVE EC'ONOMIC F1'FICFI,ENCY

t test to examine the significance of the coefficients on the individual factorshift variables. Final',y, with respect to the constant term, only the shiftcoefficient on the neutral teclmical efficiency parameter for the pairing offarms based on experience with (double-croppingr is significantly differentfrom zero at a 5 per cexnt signiificance. level. We colluhide, thelefore, thatsmall and large farms, and tenants and owniers face the same technology,but that farms which have been double-cropped for only one year aretechnlically rmore efficienit than farms which have been double-croppedover a longer period of ti me in the sense that their neutral technical efficiencyparameter (a0) is larger.'

Accordingly, the production function is re-estiiimated over the entiresample for larg, and small firms and owners and tenants, but sepa.rateproduction funcietioni.s are estimated for farms which havie been double-croppeed one year and farms which have been double-cropped two or moreyears with the restriction that. axx c 0 for all i # 0. These results arereported in Table Ill. For these regressions all coefficients are statisticallysignificant exep)t. that on eapital.2 Land and labour are tl imost i pl)ortan-ltinpiuts, as ones woutldI (expect, annd retuirns to scale are constant. 3 Fromthese results we eoni clude that:

(i) large an(l small fiarms are equally teelhically efficienit, (that is, theyface the same linear homogeneous p)rodldltioni function);

(ii) ownlers and teniants are equtially teclinicallY efficient (that is, theyface tlhe sane p1r o(ldtiction fnlctioni); and

(iii) newly doubfle-cropped fafrms are teelhically more efficient thanfarms douible-cropped for two or iore y,ears (that is, thle neutitral efficiency-Parameter is larger for newly douible-cropped farm's).

It miay be eoncluded fromi (i) and (ii) that yield anid input intelisity'shioufld be the sam,e regardless of fiarm size or tenancy statuts unless eitherthlie different groups of farms face dlifferenit configurationss of input and

1 Sidhu [91 arrives at a similar fii d imlj as a result of his Iunl,iRV-S of thin shift from old tonrew Nhoat varieties in the In(lian PulnjldL. wklthugh lie finds that pro(ductio)n with newvar'twics is tecunically more effiieont than J)rloduction with thle old vtiriLltis, he finds thatthe neutral .lliA piti a otr of tho Colb) Douglas prodluction function (ouir ao) in(licates a(decr(aw;~ in *l1inifitx of produictio)n of the3 new wleat vnrieti-i as; experieneo wvith the( newseedZs !r.)%.4 bo)th gv,egrrnlldically an(I in time. See .SidIIIu [91, table 3 aoudu pagesH 222 3. Withrespect to thle size breakdown of farins, results for India usilig the profit fiuntioni pliarohare rmixed. 'iitl.p andl Lau (101 conclude that small farms in the l 1950,4 were ttwlmlie-ally nmore iicieivnt than linrgt, farmns. ,siullhu [81,1h wv r, fin(ds small anid lnrgse farms in the1960.s to be euqually teclnilically el'bioont. Note. lit evi-r, that the tests based on the profitfiuntMini only allow for differences in neuitral technical etlieviicny between the two groupiH;apart. from this, the two gni,ups are asu med to face the sanie toehil-11,gy.

a It i-i pio-iildi that the capital input, which is required ent ir,ly for pdlohLzlhing, is bringingland of (itifereut qi(lalit up) to a comornn standlard of readiness for plianting. In this event,the contribution of eapitail to output would be captured in the coefiievivit on landl.

I This is contrary to Bardhan's con1clusion [1] for paddy farms in India. Ito fln(ds.1'wrok.iirg re.urns to scale for pa(dLdy farms but constant returns to scales for wheat farms,

H. N. BARNUM AND L. SQUIURE 191

output prices, or they are not equally allocatively efficient. And it may beconcluded from (iii) that newly double-cropped farms should have yieldsapproximately 22 per cent higher and a labour intensity approximately39 per cent higher than farms double-cropped for two or more years unlesseither the different groups of farms face different configurations of iniputand output prices, or they are not equally allocatively efficient.' Comptuted

TABLE III

Regression 2*

Farnm size/ Double-croppingCoefficieNtj tenancy status experience

In N 2*94 2.99ln oD -0 20 (0 05)Land ca 0-62 (0-07) 0-61 (007)Labour a 2 0 29 (0 07) 0 31 (0 07)Capital a3 0 01 (0 03) 0 02 (0-03)Other variable inputs a4 0-08 (0-03) 0 08 (0-03)

R2 0-66 0-67N 386 :%6SEE 0-49 0n48

Returns to seale 1'01 1-02

* Standard errors are reported hil parentheses after estimates.t D = 1 indicates farms double-cropped two or more years; D 0

iindicates f.;rms double-cropped one year.$ Not significantly different from 1 using a 1 per cent significance level

for either group.

at the geometric means the adtual difference in yields between the twogroups is 19 per cent indicating that the observed difference in yields isadequately explained by the neutral shift in the production function.However, with regard to labour intensity contrary to expectation, farmsdouble-cropped two or more times uise 6 per cent more labour than farmsin their first year of double-cropping, which suggests that either they facedifferent wages or else the profit maximizing ability of thle two groups isdifferent with respect to the labour input.

The major decline in yields (22 per cent) with experience of double-croppinig wxarrianlits firther investigationi. An examlination of Table Irevealsthat productivity, both per unit of area and per iman hour, has (lecrea.sedwith duratioin of double-cropping in spite of the fact, that labour, capital,and other variable iniputs per unit of area have increased slightly. Animmi-aediate explanation which would be consistont with this pattern is

1 The ratio of yields is given by the ratio of the neutral toecnical officioeny parameters(a,), and, assuming profit maximization, the ratio of labour intonsitios is given by the ratioof the neutral technical efficienry parameters raised to the power of /1i,

o.B.r. 30.2 0

192 TECHNOLOGY AND RELATIVE ECONOMIC EFFICIENCY

that the soil has become less productive with repeated double-cropping.The results of Table II support this r ;1telntioll in t-ht they show:

(i) a decreasing constant term which could be an effect of the increaseddrain on soil nutrients due to the adoptioni of double-cropping;

(ii) a decreasing elasticity for the land input and an inereasiny elasticityfor other variable inputs (mainly fertilizer); and

(iii) a marked increase in the responsiveness of output to labour whichmight result from iincreased knowledge of the appropriate timing and mixfor the various tasks associate(d with the second crop but may also reflectthe use of labour in additional soil preparation and in techniques whichare adopted to compensate for the deterioration in, natural fertility.

Although the shifts in the coefficients of land, labour, and other variableinputs are consistenit with the hypothesis of decreasing fertility, they arenot strong enough to be confirmed statistically. A finer breakdown of thesample into three groups revealed essentially the same pattern. Farmswhich had been double-cropped only once had a higher constant term aindcoefficient for land but lower coeffiicient-s for labour and other variableinputs than farms wvhich had been double-cropped twice, and the sametrend was observed for the comparison of farms which had been double-cropped twice and those which had been double-cropped more than twice.In this case a comparison of the group of farms with one year's experiencedouble-cropping and the group of farms with more than two years' experi-ence indicated a shift in the coefficients that proved significant at below a5 per cent significance level.1 The resuilts ind(licatte a sharp decline infertility after one year's double-cropping which apparently levels offsomewhat but continues to decline through the second year of double-cropping. The results carry significant implications for Malaysia's self-sufficiency drive with respect to padi in that if the almost continuous useof farmland implied by double-cropping does reduce natural fertility, thennot only will the yields of the second crop be reduced, but so also willthose of the first crop. And if the decline in yields of the first crop parallelthose of the secon(d, then double-cropping will have resulted in an increasein annual yields, not of 100 per cent, but more like 50 per ceit.

The rulovant cooflicients are reported below:

in La7nd Labour Oihlrr vatriable(an) (a:) (- 2 ) input

one year 3-85 0.80 0.10 0-02two years 2-49 0 53 0-41 005two years+ 2-23 0-50 0-44 0-12

Using a joint F test, the null hypothesis that the coefficients for the one-year and more-than-two-years groups are the same is rejected. The calculated value of P is 4-79 with 5and 245 degrees of freedom.

H. N. BARNUM AND L. SQUIRE 193

While the results presented here are not conclusive, they are sufficientlypersuasive to warrant the recommendation that further field investigationsbe undertaken to determine whether or not natural fertility is decliningand, if so, whether or not the rate of decline is diminishing. The resultsalso illustrate the value of the methodology: conclusions of the sort pre-sented here can only be reached if other possible causes of yield differentials(e.g. different technologies and allocative inefficiencies) can be individuallyisolated and tested separately.

Allocative efficiency

Our tests of allocative efficiency are preceded by an examination ofintergroup differences in the configuration of output and input prices.Unfortunately, the FAO/IBRD price data are not as reliable as the quantitydata. Accordingly, in Table IV we present a breakdown of mean input andoutput prices drawn from an earlier survey conducted in the saime area.'Since this survey was completed only two years before the FAO/IBRDsurvey and contains carefully collected price information, we consider it amore reliable base for an intergroup comparison of prices.

The commercialized nature of padi production in the Muda River Regionleads one to expect that markets are reasoniably well integrated and thisis confirmed by the results presented in Table IV. At a 5 per cent signifi-cance level it may be concluded that tenants and owners face the same setof relative factor costs for labour, ploughing, and land, and that small andlarge farmers face the same set of relative factor costs for harvestinglabour, tractor ploughing, and land but that small farms face higher relativefactor costs for transplanting labour and buffalo ploughing. Similar testsfor the third pairing of farms were not possible, since the Doering Study[3] does not containi a breakdown of farms by double-cropping experience.Nevertheless, given the general level of variation in prices 2 and the absenceof any theoretical expectation that these two groups should face differentprices, we proceed on the assumption that farms double-cropped once andfarms double-cropped more than once confront the same set of prices.Accordingly, in the final row of Table IV we presenit our estimates of pricesin gantang which we assume confront all farms anrd which will be used inour analysis of allocative efficiency. These prices are drawn from theFAO/IBRD survey and seem to be consistent with those pr-esenlted inDoering [3].

Table V presents the results of our tests of allocatirve efficiency. At a5 per cent level of significance it may be concluded that all groups of farms

1 See Doering [3].2 The coefficients of variation vary from 0*37 for two-wheel tractor hire to 092 for har-

vesting labour.

194 TECHNOLOGY AND RELATIVE ECONOMIC EFFICIENCY

TABLE IV

Mean input prices in gantang*

I1r.ge per Cost per relongmanday for for ploughing by

RenzFarm per Trrans- Har- 2-wheel 4-wheel

cla8sification relong planting vesting Buffalo tractor tractor

Small 180-3 4-53 4-62 18-99 27-04 17-99Large 156-1 3 55 4 84 13-08 26-41 16-63t-statistic 1-52 2-03 0-28 2-22 0-10 1i10Owners 3.99 4-01 13-87 25-26 7-73Tenants 165-7 3-90 5-25 17-19 27-61 16-96t-statistic .. 0-17 1-54 0-94 0-32 0-59All fiarms 165-7 3-94 4-75 15-77 26-77 17-25Coefficient of

variation 0-42 0-64 0-92 0-71 0-37 0-39

Mean inrput price8 in gantangf

Rent per WVage per Cost per Other variablerelong manhour buiffalo-houir inputs

All Farms 157 0-66 1-29 1-61

* The price data presented here are from Doering [3]. This survey contains superiorprice data to the FAO/IBRD survey and is, therefore, preferred. The survey was con-ducted in the Muda River Region two years beofore the FAO/IBRD survey and is presentedhere, not as an indication of the prices actually facing farmors in the FAO/IBRD survey,but as a commentary on the nature of the input and output markets in the Muda RiverRegion.

t These prices are taken from the FAO/IBRD survey and are used subsequently in theanalysis of allocative efficiency. The price of padi used in arriving at prices in gantang isM$0-62 per gantang, the farm-gate price prevailing in tho major harvest month of September.The wage-rate is the average wage prevailing during the second crop cycle.

are allocatively efficient (i.e. k = 1) wihl respect to the three variableinputs, labour, capital, and other variable inputs, but not with respect tothe fixed factor, land.' In other words the results confirm the hypothesisthat padi farmers in the Muda Region maximize restricted profits: that is,land is viewed as a fixed factor and profits are maximized by the appropriatechoice of the variable inputs subject to the given quantity of land.

In our view, these results reflect fundamental differences in the marketsfor the two most important inputs, land and labour. We note first that thelabour market is very active: all 386 houiseholds employ hired labour, theaverage quantity hired being 51 per cent of the total labour input. Even

' Given the size of the standard errors, the hypothesis of profit maximization is establishedmuch more firmly with respect to the labour input than with respect to capital servicesand other variable inputs.

x. N. BARNUM AND L. SQUIRE 195

TABLE VMarginal productivities and allocative efficiency

Marginal products*

Farmr Other variableclaasificatiopi Land Labour Capital inputs

Small 275 (31-0) 0-68 (0-16) 0-41 (1.0) 4-36 (1-6)Large 263 (29.7) 0-80 (0-19) 0-43 (1.0) 4-07 (1.5)

Owners 260 (29-3) 0.66 (0-16) 0-43 (1.0) 4-61 (1-7)Tenants 279 (31-5) 0-79 (0.19) 0 41 (1.0) 3-95 (1.5)

Double-croppedone year 302 (34-7) 0-92 (0-21) 0-67 (1.2) 5-10 (1.9)

Double-croppedtwo or more years 253 (29.0) 0-73 (0.17) 0-51 (0-9) 3-95 (1-5)

Allocative efficiency-value of kt

Small 1-75 (0-20) 1-03 (0-24) 0-32 (0-78) 2-71 (0-99)Large 1-68 (0-19) 1-21 (0-29) 0-33 (0-78) 2-53 (0-93)

Owners 1-66 (0-19) 1-00 (0-24) 0-33 (0-78) 2-86 (1.06)Tenants 1-78 (0-20) 1-20 (0-29) 0-32 (0.78) 2-45 (0-93)

Double-croppedone year 1-92 (0-22) 1-39 (0-32) 0-52 (0-93) 3-17 (1-18)

Double-croppedtwo or more years 1-61 (0-18) 1-11 (0-26) 0-40 (0-70) 2-45 (0-93)

* Marginal products are computed at the geometric means and are expressed in gantang.Standard errors are reported in parentheses after the estimates. The production funotioncoeffioients are taken from the appropriate column of Table III.

t The estimate of k is obtained by dividing marginal productivity by the price in gantangas calcuilated from the FAO/IBRD survey and reported in tlhe last row of Table IV.

the smallest farms (< 2 relong) hire 31 per cent of their labour require-

ments while the largest farms (> 10 relong) hire as much as 67 per cent

of their requirements. Although most labour is hired from within the

kampong (village), labour is not hired from within kin groups and there is

enouah' seasonal migrant labour to indicate the presence of a competitive

labour market, By way of contrast, there is ample evidence to indicate that

the lalnd market is confined largely to intra-family transactions. Thus,

'71 per cent of the estimated 28,000 tenant householders are actually renting

their relatives' lands. Nearly a quarter of these are operating padi lands

which one day they will inherit from their parents. 1 In this event, it might

be expected that for many operators land is not treated as an econoniic

resource in the same sense as is labour. In addition, it may reflect the faet

that those who are most anxious to rent land are usually those who lest

have the financial resources to do so. For such farmers one would expect

the marginal product of land to exceed its market price. In other words,

I See Omar [6], p. 21.

196 TECHNOLOGY AND BH' LATlV yE ECONOMIC EFFICIEI-NCY

the market ren.tal of land is below the economic value of land because, onthe one hand, many transactions involve kin, and, on the other hand,imperfections in the credit market may prevent some operators eniterilng tlleland market.'

Recallilng the restilts of Table I (that both small farms and ownier fairmsuse more la,bour per relong than large farms and tenant farms, lrespectively),Table V shows that, although both small and large farms and owner anldtenant farms are absolutely allocatively eflient with respect to the labouriniput, all farms use less than the profit-maximising labour inlput (i.e.k > 1) and that the departure from the profit-maximising laboQur iniput isgreater for large farms and tenant farms than for small farms and ownerfarms. The tendency to underuse labour may reflect the practice of pro-viding meals to transplanting and larnvest workers, wvhich wotuld iniereasethe real cost of labour to the farmer.2

The other main result of Table I, that the yieldl of the secondcl crop offarms doluble-cropped onily one year, is considerablyI higlher than that offarms dc able-cropped two or more years, has alrealy b)eell accouinted forin terms of a neutral shift in the, pro(lllutioIL fuictioni. Qiven that shift,however, the labour init-ensities (that is, labour input pe)i unit of Ireaoperated) of the two groups of farms should also be very differenit, whereasTable I indicates that they are almnost the same. Co]plute(d at the geo-metric mealns, the observed ratio of labour intensity of farms double-croppedonce to that of farms double-cropped more than once is 0 95. The ratio ofthe demand curves for labour per' relorig, however, wYas coiuted edarlierto be 1,39. It is of some interest, therefore, to exaimine why the obser ve(lshift in the demoand for labour (liffeirs so (dr-amatically froiim the ex pectedshift given the neutra1 shift in the production function. The figure of 1'39was arrived at on the assumption of profit maximization with respect tolabour for both groups of farms; that is, k was set equal to unity for bothgroups. If, however, we use the observed vtalues of k reported in Table Vtorecompute theratio ofthe demand curves, we obtain 1*39 x 071 = 0.99,Swhich is approximately equal to the observed clhang-e in demand. Thlus, itappears that changes in the neutral technical efficiency I)aa paicter are beillnoffset by changes in allocative efficioncy such that labour intensity rIemainlsroughly coinstant. Moreover, the change in allocative efficieney rie.prsenitsan improvemelnt: the value of k falls from 1 39 for farmner.s who lack experi-

l Thus in Table V, k is cou,si.ently greaiter thani unity for land in(licatiiig underutiliza.tion of that input. Note that this holds for both owners and tenants.

2 Thus, Doering [3] reports that 92 per cenlt of farmer. liiring traiisplanting labour and84 per cent of farmers hiring hnrvestiing labour provided someo form of rofroshment forhired labour.

3 The adljustment factor required to obtain the ratio of demand curves for labour perrelong is the ratio of k for farms (IOUble-croplpC( more than oince to that for farms dlouble-cropped once, raised to the power of (L_X 1 L2)/y I

H. N. BARNUMl AND L. SQUIRE 197

ence with the second crop to 1.11 for experienced farmers indicating animprovement in allocative efficiency.' The results indicate that farmersare coping very well either by luck or judgement both with the adjustmentto double-cropping itself and to the neutral shifts in the production functionwhich occur as a result of continued double-cropping.

The final issue we address is that of relative allocative efficiency. Sirncewe have already shown for our three pairings of farms that absolute alloca-tive efficiency is confirmed with respect to the three variable inputs, thisanalysis is confined to the fixed factor, land. At a 5 per cent level of signi-ficance, we may conclude that large and small farms, owners and tenants,and farms double-cropped one and two or more years are equally allocativelyefficient with respect to land (i.e. have the same value of k). Land is con-sistently underused (k > 1) regardless of farm size, tenancy status, orexperience with double-cropping. As argued earlier, we attribute thisresult to imjp,,' rections in the land market especially the tendency to treatland as a non-economic factor in intra-family transactionis.

ConclusionsOur main conclusions are as follows:(i) small and large farms are equally ecoinomically efficient. There is

no statistically significaiit case, therefore, for any form of land reform orceiling on land ownership on efficiency grounds. Nor is there any need foragricultural policies relating to pricing, availability of inputs, marketingfacilities, provision of credit, etc. to distinguish between small and largefarms;

(ii) tenants and owners are equally economically efficient. This is animportant result since it demonistrates empirically that tenurial systemsexist wvhich are not cletriLiental to economic efficiency at least in a staticsense. It follows that land reformn policies which involve a redistributionof land ownership should be viewed primarily from a social or politicalperspective since on pure econiomic grounds a fixed rental tenurial systemis equally elficieiit; and

(iii) conlltine(l double-cropl)pinr results in a neutral, dowi,nward shift inthe production fuinction, such that farms double-cropped more than onceare economically less efficient than those double-cropped only once. If the(low nwaird shift is attributed to declining soil fertility, the results point tothe need for an iiiereased application of fertilizer to be introduced simul-titneotusly with double-cropping if yields are to be maintained.

MTniiversity of Michigan, Centrefor Research. on Economiiic DevelopmentWVorld Bank, Development Economics Department

1 This improvement., however, was not confirmed statistically since both groups wereiowr.w to bo absolutely allocatively efficient.

198 TECHNOLOGY AND RELATIVE ECONOMIC EFFICIENCY

REFERENCES

1. BARDiuN, P. K., 'Size, productivity, and returns to scale: an analysis of farm-levol data in Indian agriculture', Journal of Political Economy, vol. 81, no. 6,Nov./Dec. 1973, pp. 1370-86.

2. C-ow, G. C., 'Tests of equality between sets of coefficients in two linear regres-sions', Econometrica, vol. 28, July 1960, pp. 591-605.

3. DOERING III, 0. C., '1970 Muda Agric-Econ Survey', AIuda AgorictilturalDevelopment Authority, Kedah, Malaysia, 1972.

4. HIUANa, Y., 'Tenancy patterns, productivity and rentals in NaJlaasia', EconomicDevelopment an7d Cultural Change, vol. 23, ito. 4, July 1975, pp. 703-18.

5. NowsamvAnm, V. F., 'Allocation efficiency in tradib;ionrl Indian agriculture:comment', Journal of Farm Econzoinics, vol. 4S, Feb. 1964 pp. 218-21.

6. OmAa, A. H., 'Some aspects of the socioaeconomic value rwfemn of the Mudarice farmers in developmental perspectives', Muda jil`blieatio;i No. 24, MudaAgricultural Development Authority, Kedah, Malaysia, Aug. 1973.

7. RAO, P. M., and MiLLER, R. L., Applied Econometrics, Wadsworth Pub. Co.,Belmont, California, 1971

8. SIDHU, S. S., 'Relative efficiency in wheat production in the Indian Ptunjab',American Economic Review, vol. 64, no. 4, Sept, 1974, pp. 742-51.

9..- 'Economics of technical change in wheat production in the Indian Punjab',American Journal of Agricultural Elcononic.s, May 1974, pp. 217-26.

10. YOTOPOUnOS, P. A., and LAU, L. J., 'A test for relative economic efficienuc:some further results', American Econoinic Review, vol. 63, no. 1, Mar. 1973,pp. 214-23.

11. ZELLNER, A., KMENTA, J., and DREZE, J., 'Specification and estimatiorn ofCobb-Douglas production function models', Economnetrica, vol. 34, Oct. 1966,pp. 784-95.

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