A Study of Economic Efficiency of Utah Dairy Farmers: A System Approach

A Study of Economic Efficiency of Utah Dairy Farmers: A System Approach Author(s): Subal C. Kumbhakar, Basudeb Biswas and DeeVon Bailey Source: The Review of Economics and Statistics, Vol. 71, No. 4 (Nov., 1989), pp. 595-604 Published by: The MIT Press Stable URL: http://www.jstor.org/stable/1928101 Accessed: 17-09-2015 16:52 UTC

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A STUDY OF ECONOMIC EFFICIENCY OF UTAH DAIRY FARMERS: A SYSTEM APPROACH Subal C. Kumbhakar,Basudeb Biswas,and DeeVon Bailey* the three types of inefficiency empirically.The motivationforthisstudyis to explain the growth of dairy farmsin Utah during the past twenty years. The marketshare of large farms(having more than 100 milkingcows) has increaseddramatically.This trend suggests that large farms gained groundrelativeto the small farms(having less than50 milkingcows). It is possible thatlarge farmscan cope witheconomicchangesmore efficientlythan small farms.If large farmsare more efficient than small farms,as a group,one could also ask whethereach of the large farmsis more I. Introduction efficient than the small farms.The presentpaper to answer this question by estimating attempts is imin production HE studyof efficiency of Utah technical, allocative,and scale efficiency portant.Whetherone considersa freeenterfarms dairy individually. prise economy or a centrallyplanned economy, incomein the agricultural sector or the manufacturing We also examinethe role of off-farm of the the farm The analysis efficiency. larger sector, a developed economy or a developing the off-farm of the income component operator's has economy, the study of productiveefficiency will less time he on the farm. One spend likely importantimplications.This study is primarily is concerned with investigatingthe productiveeffi- consequence that the productiondecision,now on will be based less economicinformation, being of dairyfarmsin Utah. ciencyof owner-operators relatively inefficient. Another source of ineffiineffiThe main implicationis that if significant associated with is rooted ciency part-time farming ciencies exist, identificationand eliminationof in the indivisibility of the farmoperator.Given will resultin moreprofit. these inefficiencies kind of the operating decisions that characterize For a profitmaximizingfarmthe observedoutthe dairy farms, operator may be viewed as an put supply and input use will coincide with the indivisble factor. When the owner-operator takesa profitmaximizingoutput supply and input deoff job the will more farm he earn total part-time allocamand if and onlyif thefarmis technically, income but the farming sector may suffer from tively, and scale efficient(see F0rsund et al. (1980)). Thus one cannot infer anythingabout inefficiency. II simplyby estimating The paper is organizedas follows.Section is total or economic efficiency devoted to and modelling technical, allocative, as in Aigneret al. (1977), Bagi technicalefficiency in scale a simultaneous inefficiency equation and Huang (1983), Huang and Bagi (1984), is followed by the method of Kumbhakar and Summa (1989), Kalirajan and framework.This in III. The descriptionof data estimation section Shand (1985), Pitt and Lee (1981). The objective in IV is section the empirical results are and of the present study is to investigatethe three in discussed section V. Finally, section VI concomponentsof inefficiencytechnical,allocative, of the tains the conclusions presentstudy. forUtah dairyfarmers.To and scale inefficiencies

concernedwithinvestigating Abstract-This studyis primarily of owner-operthe technical,allocativeand scale inefficiency ators of dairy farmsin Utah. A stochasticproductionfrontier The results has been applied to analyse these inefficiencies. indicate that there is positive association between years of is of labor and capital.Productivity education and productivity income.Regardalso foundto be negativelyrelatedto off-farm it is foundthatlarge ing the effectsof farmsize on efficiency of all sizes considered.Separate farmsare the most efficient indiestimatesof technical,allocativeand scale inefficiencies cate that large and medium-sizedfarmsare technicallymore than small farms.Large farms,on average,are found efficient to be performingmuch betterthan medium-sizedand small are concerned. farmsso faras allocativeand scale inefficiency

tT

our knowledge,thisis thefirstattemptto estimate Received for publicationJune 21, 1988. Revision accepted forpublicationMarch 29, 1989. * Universityof Texas at Austin,Utah State University,and Utah State University,respectively. We are gratefulto two anonymousrefereesfor theircommentson an earlierversionof thepaper.

of theModel -II. Formulation Let the production functionfor Utah dairy farmersbe representedby n

m

Y = A H X'HiH i=1

k=1

Zk exp(v)

(1)

l 595

Copyright'? 1989

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1

596

THE REVIEW OF ECONOMICS AND STATISTICS

whereY is output,and Xi and Zk are endogenous and exogenous inputs,respectively.A is the efficiencyparameterand v is the randomnoise. The distinctionbetween endogenous and exogenous inputsis relevantin any productiondecisionsince the choice of the endogenousinputsis based on some optimizingbehaviorlikeprofitmaximization or cost minimizationwhereas the exogenous inputs are not derived fromsuch an optimization framework-at least in the short run. Thus the production relation in (1) can be treated as a short-run productionfunction.It can be relatedto introducedby the stochasticproductionfrontier, Aigner et al. (1977) and Meeusen and van den Broeck (1977), by specifyingA as

of may enhance productivity the owner-operator the endogenousinputsand hence increaseoutput. income of the owner-operator Similarly,off-farm may have some adverseeffecton productiondue to negligence,absenteeism,etc. Farm size may be productivaffecting anotherfactorsystematically The randomnoise v ityand technicalinefficiency. includes factorsnot in the controlof any farm, like weathervariation,machine breakdown,etc. and can affectproduction both favorablyand unfavorably.This makes the productionfrontier stochastic. One can estimate the stochastic production functionspecifiedin (lb)-using data on inputs and output-by the maximumlikelihood (ML) assumptions providedsome distributional method < 0 (la) A = aoexp(T) are made about theerrorcomponentsT and v. In where a0 is a parametercommonto all farmsand doing so, one allows the productionprocessto be that varies across only technicallyinefficient T is the technical inefficiency in the sense thatactual farms.The productionfrontiercan be viewed as outputis less than the maximumpossible output composed of thosepartsof the farms'production for a given input bundle. A productionprocess functionsthat yield maximumoutputfora given can also be allocativelyinefficient in the sense of set of inputs. Thus, some part of each farm's not using inputs by equating ratios of marginal productionfunctionbelongs to the frontierpro- products with the input price ratios-when the ductionfunction.However,it is quitepossiblethat objective is to minimizecost given output and in a profitmaximizing a farmwith its scale of operation,observedat a inputprices.Furthermore, a productionprocess can be scale insingle cross-section,may not be able to reach the framework in the sense of not producingan output frontier-the productionfunctionfor the indus- efficient try.On the otherhand,theremaybe farmswhose level by equating the product price with the giventheirlevels marginalcost (see F0rsundet al. (1980)). Thus in outputsare closer to thefrontier, the of inputs.The notionof how close the individual orderto estimatetotal or economicefficiency, are introducedin estiproductionplans are to the maximumlevels as threetypesof inefficiency giveninputlevels,is cap- matingthe productionfunction.For this we foldefinedby the frontier, turedby exp(T) whichessentiallymeasurestechni- low the frameworkin Kumbhakar(1987). Howcal efficiencyfor each farm. Thus, farms with ever,we distinguishbetweenscale and allocative A farm inefficiency, T = 0 operate on the productionfrontier. which are combined in Kumbhakar fora givenset (1987). is said to be technicallyinefficient are introduced of inputsif its outputlevel lies insidethe frontier. Allocativeand scale inefficiency This is represented by a negative value of in the followingform: T-which can be interpretedas the percentage MPi =- W.'exp(u) reduction in potential output due to technical MP1 exp(T) can be interAlternatively, inefficiency. WI which is bounded preted as technical efficiency between1 and 0. This makesthe rangeof techni- and to be 100% and 0%. cal efficiency dC = Pexp( ), (2) The productionrelationin (1) with(la) can be as rewritten fl where MPj is the marginalproductof input Xj, nt (lb) C = Z=1W XI is the total variable cost, WT Y = aoHl x,a1 Zf8k exp( + v). k=1 i=i is the price of Xi and P is the output price. Exogenous factorssuch as the educationlevel of uj(j = 2,..., n) and ( representallocative,and

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EFFICIENCY OF UTAH DAIRY FARMERS

597

cient outputs according to the KBB and FLS measures, respectively.Consequently,the optiMCKBB $ mum level of output correspondingto the FLS FLS Mc /k measureis greaterthan thatof the KBB measure. The magnitudeof thisdifference willincreasewith the size of technicaland allocativeinefficiency. So P: far as the directionof scale inefficiency is concerned,a farm'soutputplan is said to be underoptimal (over-optimal)by both measuresif Y < > yFLS) yKBB(y If Y lies between yKBB and Y C y FLS y KBB the opposite conclusion will be reached yFLS, regardingthedirectionof scale inefficiency. It can scale inefficiency, respectively.When u = 0 for also be seen fromthe figurethat these two meaall j-the productionprocess is allocativelyeffi- sures give differentmagnitudesof scale inefficient. On the other hand, if U > 0 for some j, ciency. inputXj is relativelyunder-utilized given Wj and The systemof simultaneousequations incorpoW1.Similarly, inputXj is over-utilizedif U < 0. ratingtechnical,allocative,and scale inefficiency The scale inefficiency "parameter"( is zero only (as definedin (2)) in a profit-maximizing framewhen the productionplan is optimal,given P. On workcan be writtenas the other hand, t is positive(negative)when acln Y=ln ao + Lain X+ klnZk +T+ V tual outpujtis less (greater)than the optimallevel k of output. The definitionof scale inefficiency, (, in (2) ln X1 - ln Xj= ln(al/aj)-ln W (hereafterKBB) is somewhatdifferent fromthe + ln Wj + Uj? Fosund et al. (1980) definition(hereafterFLS) which is based on efficientmarginalcost (MC) (net of technicaland allocativeinefficiency). Thus ln X, - lnY= lnP - lnWW+ lna, + lnr scale inefficiency, accordingto the FLS definition, FIGuRE 1.-MEASURES

(F,

OF SCALE INEFFICIENCY

can be specified as

d9C* d = P exp(0F)'

-

ln{a

+ Eaj exp(-uu)

(2a)

+ , (3)

whereC* is the totalvariablecost netof technical where r = Y-ai. Equations in (3) representa sysand allocative inefficiency. The FLS measure is temof (n + 1) equations to be solved for(n + 1) appealing in the sense that it makes the three unknownsXi and Y, whichare the unconditional sources of inefficiency complementone another. input demand and output supply functions.The The measurebased on actual cost-the KBB mea- conditional input demand functionscan be obsure- is also interesting. It focuseson findingthe tained by solving the firstn equations and the optimal level of outputforeach farmconditional output supplyfunctionfromthe last equation. It on its technicaland allocativeinefficiency. How- is shown in Schmidtand Lovell (1979) that the ever, these two measures are not the same and conditional demand for each of the inputs will thereforemay not lead to the same conclusionso increaseby the same proportiondue to technical However, the presence of technical far as over-(under-)production of output is con- inefficiency. reducesoutputsupplywhich,in turn, inefficiency cerned.This is illustratedin figure1.' Let MCFLs be the MC curvebased on totalcost netof techni- requires less inputs. The net effectis to reduce cal and allocative inefficiency. Since inefficiencydemand for each input,as can be seen fromthe always increases cost, MC"KBB-the MC curve unconditionalinput demand and output supply based on observed total cost, is drawn above the functions(see Kumbhakar(1987) fordetails). For MC FLs. Thus, yKBB and yFLS are the scale effi- estimationit is easier to use the equations in (3) than the input demand and output supply func1 We owe thispoint to an anonymousreferee. tions.

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THE REVIEW OF ECONOMICS AND STATISTICS

598

where

1II. Methodof Estimation To estimatethe systemof equations in (3) by the ML method,we need to derivetheprobability densityfunction(pdf) of theerrorvector

2 2

(2G

+

0,2)

2 (T

v, u',

+

In(a ?+

-

(gV2 +

ajexp(-u

z12

g,2)

fromthepdfof T, v and ( whereu = (u2,..., uJ)'. IL ( Cl2 + (7g,2) The distributionalassumptionson these random errorsare and ID(.) is the cumulativepdf of a standard (i) T is iid N(O, au2) truncatedat zero from normalvariable.The log likelihoodfunctionfora sample of F farmsis thengivenby above, T

(ii) u is lid N(fL, E),

F

(5) L= is iid N(O, at2),and lnf(zl, u, Z2) + FlnjJj, f=1 T, u, and ( are independentof each other and also independentof input prices W, where f indexes farm (f = 1, 2, . . ., F). and exogenousinputsZk. f(ZI, U, Z2) is defined in (4) and z1, u, ( are to be replaced by their observable counterpartsfrom Let of the Jacobianof the (3).2 IJIis the determinant z1 = T + V fromz1, u, Z2 to ln Y, ln Xi. In the transformation presentcase it is (1 - r). The ML estimatesof the and parameterscan be obtained by maximizingL in (5). However,the burdenof estimationcan some(i + a1 exp(-u1)). -n an what be reduced by concentratingthe above log Z2 = likelihoodfunctionwithrespectto j and E. At the maximumof L, the estimateof It is Then thejoint pdf of (iii) (iv)

(

(Zl,

U, Z2)'

F

f(ZI,

U, Z2)

= fl(zl)f2(U)f3(z21U) =

7 I~j 1=Ff=l

fA(ZI)f2(U)f3(),

=

_

_

In X1 + ln W1- ln X

wherefi(.), f2(.) and f3(.) are thepdfof zl, u and -ln W + ln(aj/al), (6) (, respectively.After some algebraic manipulawhere a bar over a variable designatesan arithtions,the above joint pdf can be writtenas meticmean. Similarly,Ujk, the (j, k)th elementof 2 exp( -b/2) a ID(-MILT/a E can be estimatedfrom z (ZlUl f (fZ1, U, z2) =) n/2YaTaly (gjk

xexp(Xexp{-

+ ln al +

1(u -

'

l(u - .))

FI

Ff

(Ujf

-

U)

(U kf-

_uk)

j, k = 2,..., n, (7) which is independentof the parameters.Thus E becomes a constant.The concentratedlog likelihood functioncan be writtenas (for a single

Z2

ai exp(-ui) (4)

2 The farm subscriptf on , and ui are omitted for notationalconvenience.Similarare thecases withinputs,input prices, output and output price-Xi, W, Y and P, respectively.

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EFFICIENCY OF UTAH DAIRY FARMERS observation)

solutionof In Y from(3)-which is b

L = const. -n

-

+ n a- lnna a + In (-D

, -In

1

lnY= m-

2ut

(Z2

+ ln(1

-

In(ai + Za exp(-u})))

-

r).

T +

T

a 1

[T

ln Wi

T/A)~~~~~~9 /

where11, 6fare theestimates of

1T

k

zk + l-rn

In P

v

1-r

(8)

The ML estimates of In ao, a1,. .., an, ov, , I can be obtained by maximizing(8) afteraddingit over all the farms.The ML estimatesof j and elementsof Y can be obtainedfrom(6) and (7). Following Kumbhakar(1987), it can be shown that T given z1 (the residual of the production function)is normallydistributedwith mean and variance a 2 truncatedat zero. Thus, point estimate of technicalinefficiency for each farm can be obtained fromthemean of T, i.e.,

=

Ea

/uf

1-r

T

599

-

1 - rnIna + Eajexp(-uuj) 1

1-r

Eau Ea'

r 1-r

+(12)

where m =(ln ao + rln ?r + ailn aj)/(1 -r). It can be seenfrom(12) thatonce t is estimated, an estimate of thedegreeof under-(over-)production of output(in logarithms) can be obtained from

(9)

rt

1-r'

(13)

and a. Given wherer and t are to be replacedby theirestimates.Similarly, OUF can be calculated replacing t by(F in (13), namely,

X and Z, the percentageloss in output due to technicalinefficiency, T, can be obtainedfrom PT=

(Y-

Y*)/Y* = l-exp(T),

(9a)

rF OUF= (13a) where Y* is the frontier output(conditionalon X 1- r and Z) obtained by settingT = 0. thedifference in themagniAllocative inefficiency for each farm and for As pointedoutbefore, tudes of OU and oUF will depend on thesizesof everyendogenousinput(X) can be obtainedfrom

technicaland allocativeinefficiency. If no such inefficiency existsbothOU and oUF willbe the same. On the otherhand,if over-production is (10) indicatedby boththemeasures, themagnitude of Since both positiveand negativeuj increasecost, over-production will be higherunderthe KBB it mightbe of some interestto estimatethe per- measure. The oppositeis truewhenunder-producbyboththemeasures. centage increase in cost due to allocative ineffi- tionis evidenced ciency, CA, for each farm,Once uj is estimated, To maketheformulas in (13) and (13a) operaCA can be estimatedfrom(see Schmidtand Lovell tional,we needto findtheestimates of ( and (F. Once allocativeinefficiency (1979) fordetails) is estimated,t for eachfarmcan be estimated fromthelastequation CA = exp(E-lnr)-1, (11) in (3). Thisis givenby U = ln X1 - ln Xj-

ln(a/laj) +lnWI -lnInWJ, j=2,...,n.

where E=

n

(

Zdaj uj/r + ln a I+

j=2

=

ln X1 -ln Y-ln

n1

j=2

adjexp(-u)j).

-

P + lnW1- ln a^

ln + ln{ a1 + E a^X,exp(-f U)},

(14)

The effectof scale inefficiency on outputcan be whereUj is obtainedfrom(10). On the other obtained from the output supply function-the hand, (F can be obtained fromthe relation(2a)

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600

THE REVIEW OF ECONOMICS AND STATISTICS

whichcan be rewritten as (F=

TABLE 1.-MARKET SHARES OF UTAH DAIRY (MILK PRODUCTION)

ln C* - In r - In Y - In P =In X

-

Size of Farma (percentage of Utah total)

InY - Ea1uj/r

+ zl/r-ln

P + ln W1- ln a,.

(14a)

Small Medium Large

FARMS

1969

1974

1978

1982

43.0% 35.7% 21.3%

26.0% 32.5% 41.5%

17.3% 33.3% 49.4%

10.6% 29.3% 60.1%

Given thatfirmscan makea mistakeby producing suboptimumlevels of output and that these Small = less than 50 milk cows. Medium = between 50 and 100 milk mistakesare costly,it mightbe worthestimating cows. Large = over 100 milk cows. loss in profitdue to such mistakes.The percentage loss in profit due to scale inefficiency can be of 116 farmfamilies,froma populationof 510 in estimatedfrom these counties,was interviewed.The sample was stratifiedby county dairy farm population and =1H(P, W, Z, , v) farm size. Eightynine of the surveyswere coms fl* plete enoughto be includedin thisanalysis.Quesexp{4r/(1 - r -Prexp(()} tions regardinga wide range of farmand family 1-(1-r) characteristics wereobtainedincludingdebt situa(15) tion, managementstyle, numbers of acres and cows, inputcosts,capital structure, operator'sedwhere 11* is the profitfrontierdefinedby II* = ucation level, off-farm income,etc. The response PY- YEiW1Xi when ( = T = Uj= O and rate,3definedas thepercentageof familiesactually LI(P, (W, Z, v) is profitwith only scale ineffi- interviewed out of thetotalcontacted,was 66.67%. ciency (i.e., T = U.= 0). Similarly,HF1 can be The observationswere separatedby size based calculated by using the FLS measure of scale on dollar sales during1985 (U.S. Departmentof in (15). It has been shownin sectionII inefficiency Commerce).Dollar sales representedapproximate that if t and (F are both positive(negative),the grossfarmincomebased on averageherdproducmeasured magnitude of over-(under-)production tion, annual average milk price for the type of is greater(less) thanthatof by the KBB definition milksold (gradeAA and/or manufacturing grade), the FLS definition.This in turnindicatesthatthe income from the sale of dairy cattle and other percentageloss of profitusingthe formermeasure livestock,and crop income. is greater(less) thanthatusingthe lattermeasure. Table 1 depictsthechangein the size distribuNo such conclusioncan, however,be reachedif t tion of Utah dairy farms.The numberof dairy and (F are of different signs.If the interestis in cows is a convenientproxy for farm size. In the measureof dollar cost of scale inefficiency (in 1969-1982, the productionshare of small farms termsof forgoneprofit),Cs, foreach farm,it can (havingless than 50 milking cows) declined from be calculatedfromCs = rI* -Is usingbothmea- 43% to 10.6% while largefarms(havingmorethan sures of scale inefficiency. 100 milkingcows) gained ground. The market shareof largefarmsincreasedfrom21.3% in 1969 IV. Descriptionof Data to 60.1% in 1982. This was accomplishedthrough Data for this studywere obtained froma ran- several avenues includingnew entry,expanding dom sample of dairyfarmersin Utah surveyedby herd size on existingfarms,and increasesin averthe Department of Economics, Department of age milkproductionper cow caused by improved Family and Human Developmentand theDepart- feedingprogramsand improvedgenetics. Table 2 presentssome socio-economiccharacment of Home Economics and ConsumerEducation at Utah State University, Logan. The purpose teristicsof the farmerssurveyed.Larger farms of the surveywas to determinemajor factorslead- tendedto be operatedby the slightlyyoungerand ing to eitherfinancialsuccess or failureand ecoexcluded nomic efficiency of Utah dairyfarmers.The sur- 3Since the non-respondentsand the twenty-seven were not in a "special category"in termsof the farm vey was based on the fivecountiesthat were the families and familycharacteristics,the possibilityof selectivitybias major dairyproductioncentersin Utah. A sample could be ignored. a

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EFFICIENCY OF UTAH DAIRY FARMERS TABLE 2.-AVERAGE

Category (AverageValues) Operator'sage Operator'seducation level(years) Milk cows Rollingherd average(lbs.) Annual off-farm income/year Farm assets Farm debts

FARM AND FARM FAMILY CHARACTERISTICS OF UTAH DAIRY FARMERS, 1985

Small (under$100,000 sales)

Medium ($100,000-$250,000 sales)

601

FROM SURVEY

Large (over $250,000 sales)

50.4

52.5

49.7

14.0 34.0

13.0 71.7

13.0 159.3

14,613

16,519

17,685

$11,145 $237,078 $59,500

$5,553 $433,689 $108,704

$4,512 $759,706 $302,428

slightlyless educated farmers.Large farmerswere for each of these groups. The resultsare listed also carryingthe largestdebt loads but had 21% undermodels B-D in the orderof small,medium higher average productionper cow than small and large farms.4This was done to determine producers. Small producershad the largest off- whetherthe production structurediffersacross farmincomes,tendedto be slightlymoreeducated farmsof different sizes. If so, as evidencedby the and worked more hours offthe farm(both hus- likelihoodratio (LR) test,estimatesfor the proband and wife). duction parametersas well as inefficiency based We consideredtwo endogenousinputs-capital on model A are inappropriate.However,forpurand labor. Labor representedthe time,in hours, poses of comparison,we presenttheresultsforall spent in activitieson the farmby the husband, the models(models A-D). wifeand hiredlabor. Additionallabor was considThe parameterestimatesare reportedin table 3. ered to be available at a cost of $5 per hour(Utah The labor coefficient (elasticity)is about twiceas AgriculturalStatistics).The opportunitycost of large as that of capital in each of these models. capital consisted of depreciationand interestex- For labor the highestvalue is 0.382 and is associpenses on the farm (Jorgensonand Griliches ated withsmall farms(model B). The large farm (1970), Jorgenson(1969)). All capital was depreci- has the smallest labor elasticity.This indicates ated using the straightline method.An interest thatincreasingmanagementand/or labor timeon rate of 11% was used to calculate the opportunity the small farmswill have a greaterimpact on a cost of capital. We consideredland an exogenous percentagebasis than on the large farms,suggestinput. Consequentlya short-run productionfunc- ing that small farmswould benefitif the ownertion is estimated. operator spent more time on the farmor hired Other exogenous inputs are years of formal additionallabor. The orderof the magnitudefor education of the farmoperator,off-farm income, the capital coefficientsis similar to that of and two dummy variables for three farm sizes. labor-highest for small farms and lowest for Off-farm income affectsnot only the farm'scash large farms.The coefficient of land is quite small flowsituation,but is also a measureof effort in all thegroupsas well spent but statistically significant in non-farmactivities.Size may influenceeffi- as in the fullmodel (model A). For exogenousfactorsaffecting ciencyif economiesof size are present.The farm's the productivity, output is measured in pounds of milk produced crucial variables are education,off-farm income, (adjusted forwaste and disease). V. EmpiricalResults Consideringthe diversefarmsizes we divided the sample into three subgroups, viz, small, medium,and large,and estimateda separatemodel

4The appropriatenessof dividingthe sample into groupsis testedby the likelihoodratio (LR) test-where the restricted versionis model A (withpooled data fromall the groups)and the unrestricted versionis models B-D. The hypothesisof a single production function(model A) for all the farms of different sizes is rejectedat the 1% level of significance.

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B-D, we can see that education has the highest elasticity (0.5352) on medium-sizedfarmsand the (ASYMPTOTIC lowest elasticity(0.2327) on small farms.Thus Parameter Model A Model B Model C Model D gains fromincreasingeducationare highestforthe medium-sizedfarms.For off-farm income, these Constant 9.9890 7.6250 8.9983 10.0921 (0.423) (.2061) (0.733) (.0555) elasticitiesare - 0.0232, - 0.0143 and - 0.0065 on Labor .2681 .3820 .2558 .1902 small,medium,and largefarms,respectively. This (.0028) (.0199) (.0036) (.0035) indicatesthat the loss in productivity due to offCapital .1197 .1651 .1151 .1021 (.0034) (.0074) (.0038) (.0063) farmincomeis higheston the small farms. Land .0324 .0102 .0031 .0647 The size-relateddummyvariables in model A (.0005) (.0013) (.0005) (.0005) show that,on average,outputsof small farmsare Education .1372 .1054 .3367 .3071 (.0106) (.0159) 52.28% (1 - exp(-.7399)) lower and those of (.0143) (.0119) Off-farm - .0156 - .0105 - .0090 - .0046 medium-sized farmsare 32.73%(1 - exp(-.3965)) income (.0003) (.0018) (.0005) (.0004) lowercomparedwithlargefarms,ceterisparibus. Size dummy -.3965 (medium) (.0035) Some economiesof size are likelyto exist in the Size dummy - .7399 _ dairy industry whichwould accountforlargefarms (small) (.0063) being moreefficient than smallerfarms.However, .0393 .0371 .0402 .0326 >, (.0002) (.0005) (.0003) (.0003) since the data rejectmodel A in favorof separate .5522 .61766 .6653 .1491 modelsby farmsize, it would be interesting to see (.0787) (.0105) (.2011) (.0052) whether similar conclusions could be reached from .6131 .7425 .5217 .4204 194 (.1216) (.1210) (.0729) (.1234) the lattermodels. Incidental We now returnto the estimatesof technical parameters: inefficiency, T, allocativeinefficiency, uj and scale - .0213 - .2797 - .0248 .0083 Pk inefficiency, (. These inefficiencies can be esti.3808 .5366 .3415 .3106 Gkk mated for each farmby using (9), (10) and (13). Instead of reportingT, Uj, and (, we reportPT, and size-relateddummyvariables.5Educationhas percentageloss of output due to technicalineffia very high positive and statisticallysignificant ciency; CA, percentageincrease in cost due to coefficient. This suggeststhat educationincreases allocativeinefficiency; and 1IJ.percentageloss of output by increasingproductivityof labor and profitdue to scale inefficiency. These are givenin capital. The effectof educationis strongestforthe equations (9a), (11) and (15). To conservespace medium-sizedfarms(model C). Off-farm income we reportonly the mean values of PT, CA, and on the otherhand has a negativeeffecton output. E s by farm size. In table 4a, we report these This negativeeffectis strongest forthesmallfarms resultsbased on the pooled data (model A). The whichhave the largestoff-farm incomes.As noted estimatesof PT show that the large farmsare earlier,thelargertheoff-farm incometheless time technicallymore efficientthan small and methe operator will spend on the farm. Conse- dium-sizedfarms.Output of small farms,on the quently,the productiondecisionwill be based on average,could have been 52.12% higherhad these less economic information, whichtendsto reduce farmsbeen operatingon the productionfrontier. efficiency. The correspondingfiguresfor the medium and Effectsof education and off-farm income on large farmsare 31.56% and 20.02%, respectively. output can be examined more closely fromthe Thus, groupsof smalland medium-sizedfarmsare estimatesof elasticities.It can be seen from(12) (.5212 - .2002)100 = 32.10% and (.3156 that the elasticityof Zk on Y is 1k/(1 - r). .2002)100 = 11.54% less efficient (technically)relMoreover, the elasticityof Zk on Xi is also ative to the group of large farms.These numbers Ik/(l - r) for all i. Concentratingon models indicate how much potential exists for raising TABLE 3.-MAXIMUM

LIKELIHOOD ESTIMATES OF MODELS A-D STANDARD ERRORS IN PARENTHESES)

T

6 If the objectiveis only to see whetherlarge farmsare, on S It is to be noted that these dummyvariables are used in model A withthe implicitassumptionthatfarmsizes affectthe the average,technicallymore efficient than mediumand small interceptsonly in the logarithmicform of the production farms frontiermodels may not be necessary(see Lau and function. Yotopoulos (1971), Sidhu (1974)).

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EFFICIENCY OF UTAH DAIRY FARMERS TABLE 4A.- MEASURES OF INEFFICIENCY BY SIZE OF DAIRY FARM (BASED ON MODEL A)

Measure PTa CAb II c

Ylf

TABLE 4B. -MEASURES OF INEFFICIENCY BY SIZE OF DAIRY FARM (BASED ON MODELS B-D)

Small

Medium

Large

52.12% 5.89% 18.56% 13.16%

31.56% 3.62% 11.18% 8.12%

20.02% 3.87% 7.96% 6.06%

Percentage loss in output due to technical inefficiency. Percentage increase in cost due to allocative inefficiency. Percentage loss in protitdue to scale inefficiency. The superscriptF in 11, indicates the Forsund et al. measure.

output without increasinginput use.7 The estimates of CA show thatcost of thesmall farms,on the average,is increasedby 5.89% due to allocativeinefficiency. For medium-sized and largefarms These such costs are 3.62% and 3.87%,respectively. is more resultssuggestthat technicalinefficiency serious for these dairyfarmsthan allocativeinefficiency.

603

Measure PTa cAb I-IC F)~_

Small (Model B)

Medium (Model C)

Large (Model D)

31.69% 5.91% 19.52% 13.73%

11.46% 3.74% 11.22% 9.21%

20.16% 3.58% 5.59% 3.45%

Note: See notes to table 4a.

farmsize. Results based on such separatemodels by farmsize are reportedin table 4b. Examining the resultsonly for small farms(model B) it can be seen thatthe estimatesof loss of outputdue to technicalinefficiency, PT, are much lower compared withmodel A. The estimatesof percentage increasein cost due to allocativeinefficiency and percentageloss of profitdue to scale inefficiency are more or less the same. Similar results are foundforthe medium-sizedfarms(model C). For largefarms,theresultsin thetwomodelsare quite similarexceptforHIS,whichare somewhatsmaller in model D forbothmeasuresof scale inefficiency. Resultsrelatingto technical,allocative,and scale inefficiencies fromthe single as well as the separate models by farmsize explain why over time the percentageof large farmsincreasedrelativeto small and medium-sizeddairy farms in Utah. Large farms,on the average, are 13.52% more efficient (technically)relativeto the small farms (table 4b). These are, on the average,more efficientthansmall farmsin allocatinginputsas well as choosing optimal level of output. These are reflectedin lower values of CA and Qs for the large farms.

The estimatesof OU (based on model A) show that actual outputs exceed optimum levels for 31.58% of the small farms.Actual outputexceeds the optimum, on the average, by 68.89% and 81.48%, respectively, formedium-and large-sized of scale inefficiency farms.If the FLS definition is used, the percentageof farmsproducingexcess output reduces to 26.31, 53.33 and 70.37, respectively.8These resultssuggestthatthe Utah indusespecially tryis characterizedby over-production, by the large farms.Milk prices decreased during the threeyears prior to this studyperiod (Utah AgriculturalStatistics).Consequently,thesefarms may not have fullyadjusted theirfactorsof production (cows, barns,corrals,etc.) to lower milk prices. However,theestimatesof FsJ suggestthat small farmsas a groupcould increasetheirprofit by 13.16% (18.56% if the FLS definitionis used) VI. Conclusions by producingmilkat optimumlevels.For medium and large farmsthesenumbersare 8.17% (11.18%) This paper has been primarilyconcernedwith and 6.06% (7.96%), respectively. investigating technical,allocative,and scale inefThe estimates of PT, CA, and Hs reported in ficiency of dairyfarmsin Utah. of owner-operators of The distinguishing table 4a are based on modelA, thespecification featureof themodel is estimatwhich is rejected in favorof separate models by ing theseinefficiencies in a simultaneousequation A stochasticproductionfrontiertechframework. One can, however,question whetherall the inputs have nique, whichgives estimatesof each typeof inefbeen captured,or whetherinputsare correctlycaptured.Simificiencyfor everyindividual farm,has been apfarmsmay be those larly,if soil quality varies,the inefficient plied forthispurpose. withpoor qualityof soil (Schmidt(1985)). xWe also findthatnumbersof farmsforwhichthedirection The results obtained indicate that there is a changes(frompositiveto negative)are 1, 7 of scale inefficiency associationbetweenfarmereducationand positive and 3 in the groupsof small,mediumand large farms,respecEducation is associatedwith productiveefficiency. is used. tively,when the FLS definition

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cal Efficiencyfor Individual Farms in Tennessee," greater productivitybecause it improvesmanaCanadian Journalof Agricultural Economics31 (1983), gerial ability and enhances the productivityof 249-256. capital and labor. The empiricalfindingsalso indi- F0rsund,F. R., C. A. K. Lovell and P. Schmidt,"A Surveyof FrontierProductionFunctions and of theirRelationcate that productivity is negativelyrelatedto offship to Efficiency Measurements,"Journalof Econometfarmincome. The largerthe off-farm income the rics13 (1980), 5-25. less timethe farm-operator spendsmanagingfarm Huang, C. J.,and F. S. Bagi, "Technical Efficiency on Individual Farms in NorthwestIndia," SouthernEconomic operations. Consequently,production decisions Journal51 (1984), 108-115. information based on insufficient are less efficient. Jorgenson, D. W., "The Theory of InvestmentBehavior,"in On farmsize and efficiency the large farmswere Harold R. Williams and John D. Huffnagle(eds.), MacroeconomicTheory: Selected Readings (Appletonfound to be the mostefficient. CenturyCroftsPublishers,1969). Separate estimatesof technical,allocative,and Jorgenson, D. W. and Z. Griliches,"Explanation of Productivhave been made for all farms. scale inefficiencies ity Change," in AmartyaSen (ed.), GrowthEconomics (Middlesex,England: PenguinBooks Ltd, 1970). Results indicate that large farmsare technically K. P., and R. T. Shand, "Types of Education and more efficient than small farms.Output forthese Kalirajan, AgriculturalProductivity:A QuantitativeAnalysis of farms,on the average,is 11.53% higherthan the Tamil Nadu Rice Farming," Journialof Development Studies21 (1985), 223-243. small farms,ceterisparibus.However,the output Subal C., "The Specificationof Technical and of large farms,on the average,would have in- Kumbhakar, Allocative Inefficiencyin Stochastic Production and creased by 20.16% had thesefarmsbeen operating ProfitFrontiers,"Journalof Econometrics34 (1987), 335-348. on the production frontier.The corresponding S. C., and T. Summa, "Technical Efficiencyof figurefor medium-sizedfarmsis 11.46%. Due to Kumbhakar, Finnish Brewing Plants: A Production FrontierApallocativeinefficiency, costs of small farms,on the proach," Scandinavian Journal of Economics 91 (1) (1989), 147-160. average, are increasedby 5.91% whereasthe figL. J., and P. A. Yotopoulos, "A Test for Relative Effiures are 3.74% formedium-sizedfarmsand 3.58% Lau, ciency and an Application to Indian Agriculture," for large farms.Most of the farmersin all size AmericanEconomicReview61 (1971), 94-109. Loss of Meeusen, W., and J. van den Broeck,"EfficiencyEstimation categoriesare foundto be scale inefficient. fromCobb-Douglas ProductionFunctions with Comprofitdue to scale inefficiency rangesfrom5.59% posed Error,"International EconomicReview18 (1977), (for large farmsin model D) to 13.73% (for small 435-444. farmsin model B). One probable explanationis Pitt,M. M., and L.-F. Lee, "The Measurementand Sourcesof Technical Inefficiency in the Indonesian Weaving Inthat milk prices decreased duringthe threeyears 9 (1981), dustry,"Journalof DevelopmentEcononmics prior to this studyperiod and the farmsmay not 43-64. have fullyadjusted theiroutputsto the changein Schmidt, P., "Frontier Production Functions," Econometric Reviews4 (1985-86), 289-328. prices. Schmidt,P., and C. A. K. Lovell, "EstimatingTechnical and

Allocative Inefficiency Relative to Stochastic Production and Cost Frontiers,"Journalof Econometrics9 (1979), 343-366. REFERENCES in Wheat Productionin Sidhu, SurjitS., "Relative Efficiency Aigner,D. J., C. A. K. Lovell and P. Schmidt,"Formulation the Indian Punjab," The AmericanEcononmic Review64 and Estimationof StochasticFrontierProductionFunc(1974), 742-751. 6 (1977), 21-37. of Econometrics tion Models," Journial Utah AgriculturalStatistics,Utah Departmentof Agriculture, Bagi, F. S., and C. J. Huang, "EstimatingProductionTechni1987.

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