Relative Efficiency in Wheat Productionin the Indian Punjab

By SURJIT S. SiDHU*

In recent contributions to this Review,Lawrence Lau and Pan Yotopoulos (L-Y)applied the profit function concept to theanalysis of relative efficiency of Indian agri-culture. They developed an operationalmodel to measure and compare economicefficiency and its components of technical effi-ciency and price (or allocative) efficiency forgroups of firms. By comparing the actualprofit functions of small and large farms atgiven output and input prices and fixedquantities of land and capital, they foundthat smaller farms had higher profits (totalrevenue minus the total cost of the variablefactors of production, in this case labor) thanlarger farms within the range of outputstudied and hence were economically moreefficient. Further, they were able to showthat the relative economic superiority ofsmall farms was due to their technical effi-ciency since both types of farms were priceefficient. Their results also indicate constantreturns to scale in Indian agriculture. Boththese findings have far-reaching implicationsfor the optimal allocative struct;ure of Indianagriculture.

In this paper, the L-Y model is confrontedwith new and recent data for wheat farms^in the Indian Punjab. My results run counterto their findings in that I do not find anydifferences in the economic efficiency (or itscomponents of technical efficiency and priceefficiency) of small and large wheat farms.

* Assistant professor, department of agricultural andapplied economics. University of Minnesota. This paperis based upon my Ph.D. thesis at the University ofMinnesota. Acknowledgement is made for financial sup-port from the Rockefeller Foundation and EconomicDevelopment Center, University of Minnesota. I wouldlike to thank Lee R. Martin, Vernon R. Ruttan, WillisL. Peterson, Martin E. Abel, and Hans P. Binswangerfor many helpful suggestions and discussions.

' The Punjab farms are multi-enterprise farms. Thisinvestigation deals only with wheat, not all farm enter-prises.

Using their model, I also compare the eco-nomic performance of old Indian wheat va-rieties with Mexican varieties, and tractor-operated with non-tractor-operated wheatfarms. The last mentioned two comparisonshave considerable relevance in the context ofthe "green revolution" and the absorption ofa rapidly growing labor force in India andother LDCs. Section I of the present paperestablishes a link between my estimationprocedure and the L-Y model and briefiy de-scribes the data and the variables. Section IIprovides empirical estimates, derives theimplications of these results, and comparesthem with those of L-Y. Section III sum-marizes my conclusions.

I. Estimating Procedure and the DataIn order to study relative economic effi-

ciency and its components of technical effi-ciency and price efficiency, the profit func-tion formulation used by Lau and Yo-topoulos seems to be an ideal tool. Since thispaper is an extension of their work, it is un-necessary to reproduce the model and therelated derivations. I provide a brief de-scription of the data and the variables asthey relate to the estimating equations.

To start with, let the wheat productionfunction be written as:

(1) Y = F{N; L, K)

where Y is output, N is the variable inputlabor, and L and K are the fixed inputs ofland and capital, respectively. Following theL-Y papers, the estimating equations for theCobb-Douglas case of this production func-tion are presented in Tables 2, 3, and 4.

For statistical specification I assume addi-tive errors with zero expectation and finitevariance for each of the two equations. Thecovariance of the errors of the two equationsfor the same farm may not be zero but thecovariances of the errors of either equation

742

VOL. 64 NO. 4 SIDHU: EFFICIENCY IN WHEAT PRODUCTION 743

TABLE 1—BREEP SUMMARY OF THE SAMPLES AND DATA

1)

2)3)

Sample

Ferozepur

Tractor CultivationRegionally Stratified

GeographicCoverage

District-Ferozepur

PunjabPunjab

VillagesIncluded

IS

197

Farms

150

304128

CropYear

1967-681967-681968-691969-701970-71

WheatType

NewOldNewNewNew

ObservationsAvailable

105132144287128

Sources: 1) Directorate of Economics and Statistics, Ministry of Food and Agriculture, Government of India; 2) TheEconomic Adviser, Government of Punjab; 3) I was responsible for the design and supervision of data collectionwork for this sample.

corresponding to different farms are assumedto he zero. With these assumptions anasymptotically efficient method of estima-tion as proposed hy Arnold Zellner is used'' toestimate jointly the parameters, of the twoequations. A hrief description of the variablesand the notation used is as follows:

F = physical output of wheat measuredin quintals per farm including by-products.'

iV=the labor input per farm used forwheat production measured in hours.It includes both family and hiredlabor.

L = the land input measured as acres ofwheat grown per farm.

K=Si measure of flow of capital servicesgoing into wheat production perfarm.^

p=the price of wheat per quintal as re-ported for each farm.

' This will also make our results comparable to thoseof L-Y.

' The by-products are converted into quintals ofwheat by dividing the total value of by-products bywheat price.

* Child and female labor is converted into man equiv-alents by treating two children (or women) equal toone man.

' An hourly flow of services is derived for each durableinput including capital in the form of livestock that thefarm uses in wheat production. It includes depreciationcharges, interest charges, and operating expenses. De-preciation schedules are based on the specific life of eachinput, but interest costs are estimated at a uniform in-terest rate of 10 percent per annum. The actual numberof hours of use times the hourly flow of services of eachdurable input gives its total service flow. Aggregation ofthese asset-specific service flows plus the seed and fer-tilizer costs yields a measure of the capital services.

wN = the total wage bill in rupees forwheat production per farm.'

w = the hourly wage rate of labor. I t isobtained simply by dividing the totalwage bill wN by total labor input A''.

P = t h e profit from wheat production:total revenue less total variablelabor costs.

IT = the profit function.

A brief summary of the samples and dataused in this study is provided in Table 1. Ascompared to the group average data used byL-Y and most earlier Indian studies, I havebeen fortunate to have access to micro levelprimary data.

II. Empirical Results

A. Old versus New Varieties of Wheat

The first test for relative economic effi-ciency in wheat production in Punjab com-pares the economic efficiency of new varietiesof wheat with the old varieties of wheat. Forthis purpose 1967-68 data are used from theFerozepur Sample (see Table 1). The twoequations (the profit function and the labordemand function) are estimated jointlyusing Zellner's method of estimation by im-posing the restrictions that;3i = /3i in the twoequations and requiring that fii-]-^s= 1, thatis, assuming constant returns to scale.^ Theseresults are presented in Table 2. They indi-cate that the new wheats are economically

' Family labor services are valued as equivalent tothose of the annual contract labor for each farm.

' This assumption is based on the earlier tests carriedout in my dissertation and tests carried out in subse-quent sections.

744 THE AMERICAN ECONOMIC REVIEW SEPTEMBER 1974

TABLE 2—RESULTS or JOINT ESTIMATION OP COBB-DOUGLAS PROFIT FUNCTION AND LABOR DEMANDFUNCTION FOR WHEAT, 1967-68, PUNJAB, INDIA

Parameter

X=

ft =

/33 =

EstimatedCoefficient

4.8720.4850.2540.6700.330

StandardError

0.9650.1290.013"0.1550.155

Note: The estimating equations are:

Irnr = X + S"D" + fiilnw -^p,lnL -{• fizlnK

wN 0= |3i, where X = /« * + (1 - /3i) In p

»In both equations.

more efficient compared to the old wheats by48.50 percent. From \ = ln ^^ + (l-/3i) In pwe evaluate ^J by substituting the samplemean value of In p for old wheat. Then weget A" the efficiency parameter in the Cobb-Douglas production function for old wheat,the computed value of which is 5.641. In thesame way, fromX = /« ^Sl+5^+(l—ft) In p,we get A'^ the efficiency parameter for newwheat = 8.166. Thus maintaining the hy-pothesis of neutral technical shift,^ we find thatthe efficiency parameter for the new wheatproduction function is larger by 44.70 per-cent.

B. Relative Efficiency

There are different policy irnplicationsassociated with each component of differ-ences (technical efficiency or price efficiency)in economic efficiency of small and largefarms. For example, the finding that smallfarms are more technical efficient and thatboth small and large farms are absolute priceefficient could lead to the conclusion thatsmall farms serve the national interest better(leaving aside the equity considerations). Ifwe find that smaller farms are less priceefficient, policies which improve market in-

' In my dissertation I compared production functionsfor old and new varieties of wheat, small and largewheat farms, and tractor-operated and non-tractor-operated wheat farms and found that the differences inthese production functions are only of the neutral type.

formation for them may improve their allo-cative efficiency. Similar implications wouldfollow if tractor-operated farms were moreprice efficient than non-tractor-operatedfarms. It is thus important to obtain knowl-edge of the source of differences (technical orprice) in economic efficiency.

For the new varieties of wheat the estima-tion results using Zellner's method for eachof the four years 1967-68 to 1970-71 and forthe four-year combined data comparingsmall and large' wheat farms are presented inTable 3. For comparing tractor-operated andnon-tractor-operated farms, the results em-ploying data for Tractor Cultivation Sample1969-70 (as described in Table 1), are pre-sented in Table 4. In order to provide an-swers to the questions of relative efficiencyposed above we carry out the following sta-tistical tests:

1) The hypothesis of equal relative eco-nomic efficiency of small and large andtractor and nontractor wheat farms:

(i) Ho-. 5^ = 0

(ii) Ho-. 8^ =0

2) The hypothesis of equal relative priceefficiency with respect to labor demand ofsmall and large and tractor and nontractorwheat farms:

(i) Ho =j3i

- • • - - ' T - NT' ' • '

• ( i i ) Ho-, [ Pl -Pl : • • •

3) The joint hypotheses of equal relativetechnical and price efficiency of small andlarge and tractor and nontractor wheatfarms:

(i) Ho-- = 0 and

T T NT(ii) Ho-. 5 = 0 and /3i = /3i

' In this study farms with more than 10 acres ofwheat are defined as large farms and farms with 10 acresor less as small farms. This seems to be a realistic divid-ing line between large and small wheat farms for Punjabwhere the average farm size is 12.5 acres. (See MartinBillings and Arjan Singh, 1971.) Also it facilitates com-parisons of our results with those of L-Y (1971, 1973)who also used this criterion for small and large farms.

VOL. 64 NO. 4 SIDHU: EFFICIENCY IN WHEAT PRODUCTION 745

TABLE 3—RESULTS OF JOINT ESTIMATION OP COBB-DOUGLAS PROFIT FUNCTIONAND LABOR DEMAND FUNCTION FOR NEW WHEAT, PUNJAB, INDIA

1967-68Single Equation

Ordinary LeastSquares {OLS)

Unrestricted

1 Restriction"

2 Restrictions'"

3 Restrictions"

1968-69Single Equation

OLSUnrestricted

1 Restrictions'

2 Restrictions'"

3 Restrictions"

X

3.7990.748

3.4330.6413.4460.6413.0190.6673.8850.636

4.1150.9943.7140.6923.7250.6913.3910.6733.3090.655

UOP Profit Function

S'-

-0.1410.144

-0.0640.137

-0.1120.123

-0.1380.1310.0930.115

-0.0410.1600.0490.1330.0260.1110.0610.1090.0150.070

ft

0.1070.159

0.2630.1360.2620.136

-0.2440.034

-0.2360.034

-0.5070.2070.0240.1440.0240.144

-0.3810.041

-0.3810.041

02

0.6140.115

0.5060.0980.5060.0980.5200.1040.5370.109

0.7130.1790.5140.1240:5140.1240.4770.1220.4980.114

ft

0.4870.125

0.5640.1070.563

o.m0.5990.1130.4620.109

0.3340.1700.4540.1180.4540.1180.4950.1160.5030.114

Labor

-0.2210.075

-0.2210.075

-0.2740.035

-0.2440.034

-0.2360.034

-0.4060.065

-0.4060.0(J5

-0.4210.043

-0.3810.041

-0.3810.041

Demand Function

|3f

-0.2890.040

-0.2890.040

-0.2740.0J5

-0.2440.034

-0.2360.0i4

-0.4330.05P

-0.4330.05P

-0.4210.043

-0.3810.041

-0.3810.041

0.923

0.771

Zellner's method of estimation was used to obtain joint estimates of the UOP Profit Function and the LaborDemand Function.

» 1 Restriction: i85'=/3i."' 2 Restrictions: /3t=ft; /3f=/3i." 3 Restrictions: /3i=A; /32-Fft= 1; /3i = |8,.

The estimating equations for the four individual years are:

In T = \ -\- S^'D^ +

The estimating equations for the four-years' pooled data are:

In

= Pi

S 1 L

-\-S D

-|-j3iD

i-l

where

jr=profit (total receipts less wage bill)w=money wage rate

Z) = dummy variable taking the value of one if wheat area is greater than ten acres and zero otherwiseD'5= dummy variable taking the value of one if wheat area is less than ten acres and zero otherwiseZ). = three year dummy variables taking the value of one for 1968-69, 1969-70, and 1970-71, respectively, and

zero otherwiseiV=labor in hours per farm used in wheat production2, = land in acres used for producing wheatX'=total costs of capital services for wheat per farm

Asymptotic standard errors are in italics.

746 THE AMERICAN ECONOMIC REVIEW SEPTEMBER 1974

1969-70Single Equation

0X5Unrestricted

1 Restriction"

2 Restrictions'"

3 Restrictions"

1970-71Single Equation

OLSUnrestricted

1 Restriction"

2 Restrictions'"

3 Restrictions"

X

4.6510.4774.7480.4114.7440.4104.7440.4184.6940.408

2.859O.tf'//3.2870.5953.2910.5P43.3860.5W3.4380.576

inAi

1967-68 to 1970-71Single Equation

OLSUnrestricted

1 Restriction"

2 Restrictions'"

3 Restrictions"

404040

.405

.JJ4

.479

.301

.475

.JO/4.410040

.JOJ

.568

.297

I

- 00

- 00

- 00

- 0000

0000

TABLE 3

I/OP Pro^/ Function

.093

.108

.136

.OP*0.14200000

00

- 00

- 00

- 00

- 00

.025

.059

.021

.05tf

.012

.015

.054

.075

.OJ*

.OPJ

.142

.0P4

.099

.055

.056

.110

.048

.104

.051

.102

.057

.101

.010

.05P

ft

-0 .2780.124

-0 .0580.106

- 0 . 0 5 80.016

- 0 . 2 4 80.081

-0 .2470.081

- 0 . 4 8 10.189

- 0 . 1 8 4O./7(5

- 0 . 1 8 40.175

- 0 . 2 5 50.025

- 0 . 2 5 40.025

UOP Profit

Sl «2

- 0 ,0,

- 0 ,

,411 - 0 . 3 9 3M8 0.063,384 - 0 . 3 5 3

0.0(5/ 0.057- 0 ,

0- 0

0- 0

0

,384 - 0 . 3 5 3.061 0.057.377 - 0 . 3 4 7.062 0.057.336 - 0 . 3 0 5.000 0.054

(Continued)

0.0.0.0.0.0.0.0.0.0.

0,0,0,0,0,

ft

7400987140<?5714055716086742072

,477.131,496.121.496./2/

0.512000

.//7

.477

.//O

Function

S3

-0 .2420.07/

- 0 . 2 4 10.064

- 0 . 2 4 00.064

- 0 . 2 0 00.063

- 0 . 1 6 30.061

ft

0.2590.0820.2600.0700.2600.0700.2560.0720.2570.072

0.5810.1120.5390.1030.5390.1030.5230.1000.5230.100

ft

- 0 . 2 4 30.079

- 0 . 0 8 50.072

- 0 . 0 8 50.072

- 0 . 2 7 90.042

- 0 . 2 7 10.042

0000000000

Labor Demand Function

|3f

-0 .5010.153

-0.5010./5J

-0.4820.122

-0 .2480.0<?/

-0 .247O.OW

- 0 . 2 3 40.051

- 0 . 2 5 40.05/

- 0 . 2 5 90.025

- 0 . 2 5 50.025

- 0 . 2 5 40.025

ft 03

.709 0.359

.058 0.056

.690 0.358

.05J 0.051

.690 0.358

.052 0.051

.700 0.358

.053 0.051

.663 0.337

.050 0.050

- 00

- 00

- 00

- 00

- 00

- 00

- 00

- 00

- 00

.449

.204

.440

.204

.482

./22

.248

.081

.247

.081

.304

.048

.265

.046

.259

.025

.255

.025- 0 . 2 5 4

0 .025

R^

0.776

Labor Demand

- 0 . 4 1 10.078

-0 .4120.07,?

- 0 . 3 7 90.052

- 0 . 2 7 90.0-^2

- 0 . 2 7 10.042

- 0 . 3 5 10.078

- 0 . 3 4 60.077

- 0 . 3 7 90.052

- 0 . 2 7 90.042

-0 .2710.042

From Table 5 we see that none of thesethree hypotheses can be rejected at the 90percent level of significance. Thus the hy-potheses 1) that small and large wheat pro-ducing farms have equal relative economicefficiency and equal relative price efficiencyand 2) that tractor-operated and non-tractor-operated wheat producing farms have equalrelative economic efficiency and equal rela-tive price efficiency are supported by theseresults. This implies that these farms alsohave equal technical efficiency. The view that

small and large farmers have the same degreeof economic motivation seems to hold. Be-cause wheat is a dominant enterprise onthese farms, one can argue that these conclu-sions would perhaps be equally applicable toall enterprises on these farms.

4a) Next maintaining the hypothesis ofequal price efficiency in 2), we turn to thehypotheses of:

(i) Absolute price efficiency of large farms.

Ho

VOL. 64 NO. 4 SIDHU: EFFICIENCY IN WHEAT PRODUCTION 747

TABLE 4—RESULTS OF JOINT ESTIMATION OF COBB-DOUGLAS PROFIT FUNCTIONAND LABOR DEMAND FUNCTION FOR NEW WHEAT, 1969-70, PUNJAB, INDIA

Function Parameter

UOP Profit XFunction

5^

ft

ft

Labor Demand j3fFunction

SingleEquation

OLS

4.830(0.501)0.089

(0.073)-0.286

(0.124)0.790(0.083)0.224(0.085)

-0.259(0.203)

-0.610(0.153)0.777

Estimated

Zellner's MethodUn-

restricted

4.778(0.433)0.075(0.070)

-0.062(0.107)0.785(0.071)0.241(0.073)

-0.259(0.202)

-0.610(0.153)

1 Restric-tion"

4.794(0.433)0.032(0.063)

-0.064(0.107)0.785(0.071)0.241(0.073)

-0.481(0.122)

-0.481(0.122)

Coefficients

with Restrictions2 Restric-

tions'"

4.811(0.441)0.041(0.064)

-0.253(0.081)0.788(0.073)0.235(0.075)

-0.252(0.081)

-0.252(0.081)

3 Restric-tions"

4.934(0.398)0.062(0.054)

-0.256(0.081)0.779(0.072)0.221(0.072)

-0.256(0.081)

-0.256(0.081)

Note: The estimating equations are:T T

wN

where 2?'' is a dummy variable taking the value of one for farms owning a tractor andzero otherwise; and D"'' is a dummy variable taking the value of one for farms notowning a tractor (animal operated) and zero otherwise. Asymptotic standard errors arein parentheses.

» See fn. a. Table 3." See fn. b. Table 3." See fn. c. Table 3.

TABLE 5—TESTING OF STATISTICAL HYPOTHESES

Hypotheses

Maintained Tested

1) 5^=02) p^=ps

i l i l 4) Pl^Pi

6) ft+ft= 11) 6''=02) |3f=^i'''3) «''=0

^^= '" 6'lft+ft:?'

Note: Critical F-ratios are: i

1967-68

0.22;0.64;

0.73;7.72;7.72;

839.81;

P'o.io (1, aPo.io (2, 0

(1,203)(1,203)

(2,203)(2,203)(2,203)(1,203)

:) = 2.7O;

Computed F-Ratio and Degrees of Freedom

1968-69

0.14; (1,265)0.10; (1,265)

1969-70

1.93; (1,567)0.04; (1,567)

0.08; (2,265) 1.20; (2,567)4.71; (2,265) 3.44; (2,567)4.71; (2,265) 3.44; (2,567)

373.61; (1,265) 384.94; (1,567)1.13; (1,567)1.92; (1,567)1.09; (2,567)

4.31; (2,567)4.31; (2,567)

914.14; (1,567)

Fo.osd, « ) = 3.84;Fo.o6(2, « ) = 3.00;

Fo.,o(l, « ) =; Fo.oi (2, ot) =

1970-71

0.23;0.02;

0.14;0.10;0.10;

306.41;

•6.63

(1,249)(1,249)

(2,249)(2,249)(2,249)(1,249)

1967-68 to 1970-71

0.15;0.34;

0.20;5.58;5.58;

1812.13;

(1,1302)(1,1302)

(2,1302)(2,1302)(2,1302)(1,1302)

748 THE AMERICAN ECONOMIC REVIEW SEPTEMBER 1974

(ii) Absolute price efficiency of small farms,

For the first two years 1967-68 and 1968-69and for the four years pooled data, we rejectthese hypotheses at 99 percent level of sig-nificance and for the year 1969-70 at 95 per-cent level of significance. But, for the latestyear 1970-71, we cannot reject these hy-potheses at 90 percent level of significance.This means that during the years 1967-68,1968-69, and 1969-70, both small and largefarms were not in a state of equilibrium inthe sense of equating the value of marginalproduct of labor to its wage rate. For theyear 1970-71, however, we find that bothsmall and large farms were in equilibrium,i.e., maximizing profits.

4b) Maintaining the hypothesis of equalprice efl&ciency in 2), we also test the hy-potheses of:

(i) Absolute price efficiency of tractorfarms, Ho:fil = Pi

(ii) Absolute price efficiency of nontractorfarms, Fo:;8r = /3i

The meaning of these tests is whethertractor and nontractor farms maximizeprofits by equating the value of marginalproduct of labor to its opportunity price.The null hypothesis is rejected in both cases.The conclusion is that both tractor and non-tractor farms were not able to maximizeprofits during the year 1969-70. In light ofthe results for the hypothesis of equal rela-tive price efficiency in statistical test 2), weconclude that, with respect to labor, tractorand nontractor farms were equally unsuc-cessful in their efforts to maximize profits byusing the optimum amount of labor.

5) Lastly, we test the hypothesis of con-stant returns to scale in all factors of produc-tion:

This hypothesis is rejected at the 99 percentlevel of significance in all cases. The sum((32-fi33)>l for the years 1967-68, 1970-71,and for the four-year pooled data. But

for the years 1968-69 and1969-70. These differences from unity arequite small in either case. Also, perhapsslightly increasing returns for the years1967-68 and 1970-71 resulted because alarger number of observations for theseyears were below the respective sampleaverages.

Important policy implications follow fromthese findings. The most substantive one isthat policies with respect to land redistribu-tion and ceilings on ownership of land can bebased primarily on social and political con-siderations. Secondly, governmental policieswith respect to pricing, supply of agricul-tural inputs, marketing facilities, provisionof credit and extension services, etc. need notfavor either large or small farms (or farmshaving tractors or without tractors) on thebasis of their economic efficiency or its com-ponents of technical efficiency or priceefficiency.

The results of statistical test 4) have inter-esting implications with respect to theprofit-maximizing behavior (or rationality)of the wheat producers. They have a bearingon earlier price and allocative studies.'" Theresults appear to indicate the existence of adisequilibrium between the profit-maximiz-ing attempts and the actual results achievedby wheat producers. It is most likely createdby a shift to the right in the labor demandfunction, resulting from the introduction ofhigh-yielding wheats." During the first threeyears, 1967-68, 1968-69, and 1969-70, pro-ducers were not in equilibrium in the sense ofequating the marginal value product of laborto its opportunity cost. And during the lastyear 1970-71, we cannot reject the hypothe-ses of absolute price efficiency. That is, wefind that producers on the average (bothsmall and large) were able to equate themarginal value product of labor to its goingopportunity cost. These results seem to sug-gest that in a changing agriculture one should

" See for example David Hopper, A. M. Khusro,Theodore Schultz, G. S. SahoU and L-Y (1971, 1973).

" Results reported in my dissertation indicate thatthe per acre factor demand functions shifted to the rightby 25 percent as a result of the introduction of Mexicanwheat varieties in Punjab.

VOL. 64 NO. 4 SIDHU: EFFICIENCY IN WHEAT PRODUCTION 749

expect the existence of a fair amount of in-efficiency in the labor market but that pro-ducers do seem to react to overcome theexistence of a disequilibrium.

C. Comparison with Findings byLau and Yotopoulos

We provide two brief comparisons of ourresults with the research of L-Y (1971, 1973)regarding relative efficiency in Indian agri-culture.

Estimates for the Cobb-Douglas produc-tion function elasticities for various inputswere derived indirectly from the profit func-tion estimates (Table 3) using four-year(1967-68 to 1970-71) data, and are presentedin Table 6. These estimates are obtainedfrom identities which link the coefficients ofthe profit function and those of the produc-tion function. The main advantage of theseindirect input elasticities over the ones ob-tained from direct estimates of the produc-tion function is their statistical consistency.Since Pi appears in both the profit and labordemand equations, imposing the restrictionthat it be equal in both equations improvesthe efficiency of these estimates. Further-more, since these estimates are derived fromfour-year data they should be quite reliablefor predictive purposes.

All the estimates of output elasticities withrespect to various inputs (including capital)have the expected signs and reasonable mag-nitudes. I seem to be fortunate in havingdata which yielded reasonable elasticityestimates for capital. L-Y obtained (becauseof the problem of measuring the capital in-put) negative elasticity for capital and,under constrained estimation with constantreturns to scale, relatively large elasticityvalues for labor and land.

Secondly, whereas my findings agree withL-Y regarding equal relative price efficiencyand equal absolute price efficiency of smalland large farms, the findings regarding equaltechnical and thus equal overall economicefficiency differ. They find small farms rela-tively more efficient technically and thusmore efficient economically, whereas my re-sults indicate no differences in technical oreconomic efficiency of small and large farms.

TABLE 6—ESTIMATES OF THE INPUT ELASTICITIES OFTHE COBB-DOUGLAS PRODUCTION FUNCTION DERIVED

FROM THE PROFIT FUNCTION FOR NEW WHEAT1967-68 to 197O-71," PUNJAB, INDIA

LaborLandCapital(ai-\-at +

• Tableh See fn' See fn<• See fn

1 Restric-tion**

ai 0.078as 0.636a, 0.349a,) 1.063

3, last column.. a, Table 3.. b, Table 3.. c. Table 3.

2 Restric-tions"

0.2180.5470.2801.045

3 Restric-tions'"

0.2130.5220.2651.000

A possible explanation for this discrepancymight be as follows:

Their findings pertain to the mid-1950's.Indian agriculture at that time could becharacterized as traditional and in a state ofequilibrium with available technology (seeSchultz). Modern inputs like chemical fer-tilizers were conspicuous by their absence.Smaller farms which had more labor avail-able per unit of land'^ perhaps used it formore intensive land improvement programswhich resulted in superior technical efficiencycompared to the larger farms. Also as empha-sized by L-Y, under these circumstances thetechnical-managerial input becomes more in-tensive on smaller farms. Their finding ofsuperior technical efficiency of smaller farmsthus seems to be consistent with these ob-servations.

Since the mid-1950's, however, Indianagriculture has undergone a great trans-formation, especially in Punjab. The level ofland fertility which formerly depended onthe level of labor input and could be higheron small labor-surplus farms no longer de-pends upon intensive labor input alone. Theavailability of fertilizers, other chemical in-puts, and increased irrigation input reducesthe fertility (productivity) differences ofland on small and large farms. Thus a majorsource of greater technical efficiency of

" At this point a reference is made to the studies byAmartya Sen, the survey article by Jagdish Bhagwatiand Sukhamay Chakravarty, and T. N. Srinivasan.

750 THE AMERICAN ECONOMIC REVIEW SEPTEMBER 1974

smaller farms during the mid-1950's seems tobe less important during the late 196O's.

Another explanation can be advanced inthe form of an hypothesis. There are twoelements to this hypothesis. First, we mayagree (in a somewhat qualified manner) withthe findings of L-Y (1971,1973) that in tradi-tional agriculture or in an agriculture in astate of equilibrium, smaller labor-surplusfarms have greater technical efl&ciency andthereby are more efficient economically.Second, we postulate that large farms havebetter access to research information becauseof relatively easier (often free) access to ex-tension services. The period covered by thepresent study immediately followed the in-troduction of high-yielding, varieties ofwheat. Thus, it may well be that largerfarms, because of their comparative ad-vantage in research information, assimilatedthe new wheat technology more rapidly thansmaller farms and this offset the technicalsuperiority of smaller farms. This hypothesiscan be verified only in the future.

D. Elasticity Estimates

Next I present a number, of importantelasticity estimates derived from the profitfunction estimates for four-year data (1967-68 to 1970-71), shown in the last column ofTable 3. The labor demand elasticities withrespect to wage rate w, land L, capital K,and price of output, respectively, are —1.271,0.663, 0.337, and 1.271.

All these elasticity estimates have the ex-pected signs. The price elasticity of demandfor labor indicates that demand is quiteresponsive to wage levels. Positive responsesfor labor demand to increases of land, capitaland output price have important implica-tions for labor absorption in wheat farming.

The elasticities of output supply with re-spect to the normalized wage rate and outputprice are -0.271 andO.271, respectively. Therelatively inelastic output response with re-spect to wage rate along with an elastic re-sponse of demand for labor with respect towage rate imply that exogenously enforcedwage rates for agricultural labor above themarket determined wage rates could resultin substantial increase in unemployment of

the agricultural labor force." The magnitudeof output response with respect to wheatprice is important for any effort to use theoutput price variable as a policy instrumentfor inducing increased supply of wheat.

We also obtain the reduced form outputelasticities with respect to land and capital,0.663 and 0.337, respectively. These elas-ticities indicate the output response of theaverage farm with respect to exogenous in-creases in land and capital, respectively,holding the normalized wage rate and notthe quantities of labor as constant. A givenincrease in the quantity of land (capital)shifts upward the marginal productivitycurves of labor and other factors of produc-tion. As a result, more of these inputs are em-ployed than before. Thus, holding wage rateconstant (but not the quantities of labor), a1 percent expansion in wheat land will resultin 0.663 percent increase in wheat output anda 1 percent increase in capital will result in0.337 percent increase in wheat output.

III. Summary and ConclusionsThere are two substantive conclusions that

follow from the analysis of our data. First,there seem to be limited possibilities forgrowth by improving allocative eflSciency inmoving toward production frontiers. This isthe inference from tests indicating rationalproducer response to disturbances in thelabor market generated by shifts in the labordemand function. On the other hand, techni-cal changes such as the shift in the wheatproduction function on the order of about 45percent, popularly known as the "green revo-lution," constitute the more importantsource for potential increases of output.Second, we find that tractor-operated wheatfarms are no better off in terms of their eco-nomic performance than non-tractor-oper-ated farms and that large farms are no betteroff than small farms. There are no differencesin the technical and price efficiency parame-ters of these classes of farms. Policy for cur-

" For excellent discussions of the impending problemof labor force absorption in the context of the "greenrevolution" and farm mechanization, see Bruce John-ston and John Cownie, Billings and Singh, and C. H.Hanumantha Rao.

VOL. 64 NO. 4 SIDHU: EFFICIENCY IN WHEAT PRODUCTION 7S1

tailing farm size may be based only on socialand political considerations. A qualificationabout this implication, however, is necessarybecause we have studied only the wheat cropout of the complete set of enterprises onPunjab farms. The picture may be differentif we study the production relationship be-tween aggregate output of all enterprises andthe inputs used.

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