American Economic Association

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1 American Economic Association A Test for Relative Economic Efficiency: Some Further Results Author(s): Pan A. Yotopoulos and Lawrence J. Lau Source: The American Economic Review, Vol. 63, No. 1 (Mar., 1973), pp Published by: American Economic Association Stable URL: Accessed: 12/01/ :16 Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at. JSTOR's Terms and Conditions of Use provides, in part, that unless you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in the JSTOR archive only for your personal, non-commercial use. Please contact the publisher regarding any further use of this work. Publisher contact information may be obtained at. Each copy of any part of a JSTOR transmission must contain the same copyright notice that appears on the screen or printed page of such transmission. JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org. American Economic Association is collaborating with JSTOR to digitize, preserve and extend access to The American Economic Review.

2 A Test for Relative Economic Efficiency: Some Further Results By PAN A. YOTOPOULOS AND LAWRENCE J. LAU* Economic efficiency can be decomposed into two components: technical efficiency and price efficiency. A firm is said to be more technically efficient than another if it consistently produces larger quantities of output from the same quantities of measurable inputs. Differences in technical efficiency among (groups of) firms can therefore be captured by quantifying their differences in "technology."' On the other hand, a firm is said to be price-efficient if it maximizes profits. Since profit maximization implies equalization of the value of the marginal product of each variable input to its price, analysis of price efficiency involves also variables that are not ordinarily included in production function analysis-prices.2 Differences in economic efficiency among (groups of) firms may be caused by differences in technical and/or price efficiency. We compare relative economic efficiency of two firms with varying degrees of technical and price efficiency. For this purpose we compare the actual profit functions of the two firms, at given output and input prices and quantities of measurable fixed inputs. The firm which has higher profits (i.e., total revenue minus the total cost of the variable * Associate professor, Food Research Institute, and assistant professor, department of economics, Stanford University, respectively. Earlier drafts of this paper benefitted from comments of Richard R. Nelson and Vernon W. Ruttan. Wuu-Long Lin provided competent research assistance. The research was partially supported by National Science Foundation grant GS Al to Stanford University. We alone are responsible for any errors therein. 1 Examples of studies that focus on technical efficiency are Michael Farrell, Yair Mundlak, W. D. Seitz (1970), Robert Solow, and C. Peter Timmer (1970). 2 Examples of studies of price efficiency are W. David Hopper, Theodore W. Schultz, and Yotopoulos (1967a, 1968). These studies, however, are more limited than our approach to price efficiency since they allow onlv for inter-group (instead of both inter- and intra-group) variations in factor prices. The difference is further spelled out in J. Wise and Yotopoulos (1969). 214 factors of production) within a certain specified range of output and input prices is considered to be the more economic-efficient firm (within that range of prices). By applying this concept in the comparison of small and large Indian farms, we found in our previous paper (see Lau and Yotopoulos (1971)) that small farms are more economic-efficient. For many purposes, however, it is important to assess the relative importance of the two factors responsible for observable differences in relative economic efficiency. In this paper, we extend our earlier work with the specific purpose of identifying and isolating the causes for such difference between small and large farms. As an illustration we apply our technique to the same body of data as used in Lau and Yotopoulos (1971). Knowledge of the values of the technicaland price-efficiency parameters may be crucial in the formulation of policies. Suppose that differences in relative economic efficiency stem from differences in behavioral decision rules associated with the ability to maximize profits, then identifying the two components of technical and price efficiency can lead to better predictions. Again, suppose it were socially desirable to bring about the "value of the marginal product equals cost" rule, it would be possible, if the actual decision rules are known, to work out a system of ad valorem taxes and subsidies on the variable inputs and lump sum taxes and subsidies so that the social optimum would be attained. Finally, such knowledge may have important implications on agrarian reform, agricultural education, and agricultural extension policies. As a by-product of our analysis we also perform a simple statistical test of the hypothesis of constant returns to scale within the framework of the profit function. In our specific application the question of whether agriculture is characterized by increasing returns, constant, or decreasing returns is a

3 VOL. 63 NO. 1 YOTOPOULOS AND LAU: RELATIVE ECONOMIC EFFICIENCY 215 crucial point that has important policy implications. In Section I, the model is briefly described. In Section II, the relevant statistical tests are formulated in the context of the Cobb- Douglas function. Section III is on empirical implementation and statistical results. Section IV contains a brief summary and conclusions. I. The Model The model that we use is identical to the one in Lau and Yotopoulos (1972). The basic extension that allows us to identify separately the components of technical and price efficiency lies in the utilization of the factor demand functions. Let there be two firms3 denoted by the superscripts, with the production functions, respectively,4 (1) V1 = A'F(X', Z'); V2 = A2F(X', Z2) where V is output, X and Z are vectors representing the variable inputs and the fixed inputs of production, respectively. Equation (1) incorporates firm-specific technical efficiency,5 captured by the neutral differences in the production function, AI and A2. Two firms are equally technical-efficient if, and only if, Al=A'2 The marginal conditions are given by aa 'F(X1, Z') 1 1 (2) A kj1c ax-. aa 2F(X2, Z2) 2 2 ax2j 2 k2> 0; where c4 is the money price of the jth input I This analysis can be easilv extended to n firms. I In the notation that follows, we will continue at times to use the variables X, Z, k, and c unsubscripted in order to denote vectors. 5 Consistent with the "technical progress" literature, these parameters represent differences in environmental factors, in engineering entrepreneurial ability and in other nonmeasurable fixed factors of production. -vv divided by the money price of output faced by the ith firm. The cj's will be referred to as normalized prices. Equation (2) allows a firm to be unsuccessful in its attempts to equate values of the marginal product of its inputs to their respective normalized prices. This is introduced through the firm-specific and variable input-specific kj and it represents differences in managerial-entrepreneurial ability. If, and only if, two firms are equally price-efficient with respect to all variable inputs, then ki=k2, for.j= 1,..., r.6 To the production function F(X, Z) corresponds a Unit-Output-Price (UOP) profit function,7 (3) H = G(cl,..., cm; Zi,...,Zn) where II is UOP profit (i.e., current revenues less current total variable costs) divided by the money price of output and cj is the normalized price of variable input Xj. As shown in our 1971 article, the actual demand functions are given by i -A i OG(kicilA i;zi (4) Xj= d. i= 1,2;j= 1,...,m The supply function is given by (5) Vi = Ai (G(kici/Ai; zi) m i og(kici,aiz;,i, =1 j i = 1, 2;j =11...., m 6 In our formulation, ki reflect a general systematic rule of behavior-a decision rule that gives the profitmaximizing marginal productivity conditions as a special case. That the decision rule for the firm consists of equating the marginal product to a constant times the normalized price of each input may be rationalized as follows: (i) Consistent over- or under-valuation of the opportunity costs of the resources by the firm; (ii) Satisficing behavior; (iii) Divergence of expected and actual normalized prices; (iv) Divergence of the subjective probability distribution of the normalized prices from the objective distribution of normalized prices; (v) The elements of ki may be interpreted as the first-order coefficients of a Taylor's series expansion of arbitrary decision rules of the type (over)

4 216 THE AMERICAN ECONOMIC REVIEW MARCH 1973 From the actual supply and demand functions, we can obtain the actual UOP profit function, (6) Ila = Vt-Z cx j=l = Ai G(kici/Ai; zi) + E m i=l (1 - ki) d9g(kic/a i; Zi)\ i = 1, 2;j = 1,..., m Note that even if there exists no difference in technical efficiency (i.e., the At), there may be more than one set of ki's that correspond to the same actual UOP profit function. It should be emphasized at this point that Xj, Vi, and IHV as given in (4), (5), and (6) are the actual quantities of inputs demanded, output supplied, and UOP profits received by firm i given the firm-specific A i and the firm- and input-specific kj2. When appropriate functional forms are specified for G in equation (3), then equations (4)-(6) may be derived and estimated. Note that because of the profit identity only (m+1) of the (m+2) equations in (4), (5), and (6) are independent. Hence only (m+1) of the functions need be estimated. Observe that: (i) ai1'/0ai>o, i.e., actual profit always increases with the level of technical efficiency for given normalized input prices and ki; (ii) When k,= I for j= 1,..., m, the firm is a true profit maximizer; (iii) If, and only if, A1=A2 and k1=k2 the actual UOP profit functions and the demand functions of the two firms coincide with each other. From these observations a number of tests for relative economic efficiency become possible. First, one can test the null hypothesis of equal relative economic efficiency. This hypothesis is equivalent to testing whether a-x = f,(ci), i = 1, 2, i where f (0) =0 and f '(ci)?0. A wide class of decision rules may be encompassed under this formulation. 7 For a more detailed discussion of these derivations, see our 1971 article. there exists significant differences between the profit functions. Such a test has been carried out in our 1971 article, in which the hypothesis of equal relative economic efficiency is rejected. Second, it is possible to test separately the hypotheses of equal technical efficiency, i.e., A1= A2, and of equal price efficiency, i.e., kl= k2, or both. Note that one can have equal relative economic efficiency without necessarily having both A1=A2 and kl=k2. Finally, one can compute Ai and ki explicitly to isolate the sources of differences in economic efficiency. These are the specific tasks of this paper. Il. The Formulation of the Cobb-Douglas Case A Cobb-Douglas production function with decreasing returns in the m variable inputs and with n fixed inputs is given by8 where V = m n A IIXi1IZjI i=1 j=1 m - aj < 1 j=l The UOP profit function for this Cobb- Douglas production function is II* = A (1-A)'1(1 - y) j=l ( 7.(f (1-P) ) j=l aj By direct computation, the actual UOP profit function for this Cobb-Douglas production function for firm i, with efficiency parameters At and kt is i i -1 (1_A) i Ha = A - cj/kj k) -1 j=1 / I The value of,u< 1 is required since constant or increasing returns in the variable inputs are inconsistent with profit maximization.

5 VOL. 63 NO. I YOTOPOULOS AND LAU: RELATIVE ECONOMIC EFFICIENCY 217 It ( t (Ci)-a(-u j=l1 (I (zi (')) i = 1, 2 or, by substitution from equation (8) (11) i i -c1a[1 i -1 i-1 * *i - = (k1) (k*) al or (8) H =A4 (Cj)a2] [ i (Zr)] where j=1 i(1-pt-i 1#) f (kz) l) H i= 1, 2 i=1, 2; l= 1,...,m Equation (8) indicates that the actual UOP profit functions of the two firms differ by a constant factor, which is a function of kj and Ai. In addition, from equation (11) all the demand functions differ across firms by constant factors. The basic estimating equations for this study are (8) after taking natural logarithms, and (11). The first hypothesis we can investigate within our framework is that of equal relative economic efficiency. This implies that 1 2 (12) A* = A* a1 -a=(l - *,Bj -j (I I)1 < 0 i= 1, 2 - IA) > O j- 1,..., Similarly by direct computation the demand functions for variable inputs are given by X1= A ( (ailkic ) (Z(ki)-a b-y)-1) * ( mi (ai})(1u)-) ( II(4)-aJ(1-$)-) 3=1~~~~= (10) X (I (Z>dJ ai (1M})-) i = 1,? 2; = - j=1 ji = 1 1 = 1 i = 1, 2; 1) =2,., or that In (AI/A2) = 0. Note that it is possible for two firms to be equally economicefficient without being equally technicalefficient or equally price-efficient or both. We note, moreover, that if, and only if, A1=A2 and k1 = k2 then Al =A' and a*,l= a, 1 = 1,..., m and the two functions IH and HI (or In H' and In II2) should be identical. This implies the following linear relations: 1 2 (13) (i) A* = A* and (ii) *1 *2 We can therefore test for the two components of economic efficiency, i.e., for equal relative technical and price efficiency by testing statistically the joint hypotheses in (13). Furthermore, we observe that if, and only if, k k= then *1 *2 (14) ai al I, Hence a test of equal relative price efficiency (but not equal economic efficiency) consists of testing the joint hypotheses in (14). In our model we may also investigate the absolute price efficiency hypothesis, i.e., whether one or both firms have maximized

6 218 THE AMERICAN ECONOMIC REVIEW MARCH 1973 profits subject to given prices. Observe that perfect profit maximization in the ith firmn or group of firms implies (15) (i) k = , m and (ii) k *= 1 From (15) it follows that (16) a * I = 1,...=, m This furnishes a necessary and sufficient statistical test of the hypothesis of profit maximization. 9 Next we turn our attention to the question of the degree of returns to scale. For the case of a Cobb-Douglas profit function, the necessary and sufficient condition for homogenity of degree k of the underlying production function is 10 or alternatively, (k- 1) n * - Laj +L_ j= k =1 k= n j= k - (km 4a j=1 9 To see that (16) implies (15), and hence is a necessary and sufficient condition for profit maximization for firm i, just observe that (16) implies ki- k. = 1 1 = 1,..., m which in turn implies that Hence i-i which leads to i-i k1 =k1', I,l'= 1,..., m k =k* (1- kl OL t _(1i- ke j~l i-i k1 = 1 1=1... tj) Equation (16) therefore furnishes a strong statistical test of the hypothesis of profit maximization. 10 This result is derived in Lau (1972) and Lau and Yotopoulos (1972). Note that i=_1 ac*<o by the monotonicity conditions on the profit function. Hence, if k>1 (increasing returns), O3* > 1. If k= 1 (constant returns), Ei *= 1. If k< 1 (decreasing returns), 7J < 1. A test of the hvpothesis of constant returns in all inputs in the Cobb-Douglas case then becomes a test of the hypothesis 1 *= 1, where d* are the elasticities of the profit function with respect to the fixed factors of production. We shall test this hypothesis in our application. Finally, based on the definitional identities in equations (9) and (11) and the estimates of In A*, aj, j and a*, one can compute the values of Ai and the ki, as well as the direct production elasticities of the inputs aj and /j. III. Empirical Analysis In thi.s section we use the same data as used in our 1971 article from the Studies in the Economics of Farm AManagement (The Studies) of the Indian Ministry of Food and Agriculture to estimate jointly the UOP profit function and the labor demand function conditional on the given quantities of cultivable land and fixed capital.11 The profit function (8) and the labor demand function (11) mav be written (17) In HIa = In A* + 6LDL + al it 2w + flu ln,k + /32 In T (18) --= a, DL+ a1 DS where Ha is actual UOP profit (total revenue less total variable cost, divided by the price of output), w is normalized wage rate, K is interest on fixed capital, T is cultivable land, 5L=in (A4AS)? and DL and Ds are dummy variables taking the value of one for large and small farms, respectively, and zero otherwise. Large farms are defined as those with cultivable land greater than ten acres per farin. A maintained hypothesis is that the production function is identical on large and 11 A description of the data is available in :ur 1971 article. We shall not repeat it here.

7 VOL. 63 NO. 1 YOTOPOULOS AND LAU: RELATIVE ECONOMIC EFFICIENCY 219 small farms up to a neutral efficiency parameter. This implies that the coefficients corresponding to In w, In K, and In T are identical for large and small farms. A problem arises at this point. Our formulation of the UOP profit and labor demand functions is in terms of normalized prices. However, in our empirical application normalized prices are not available since the data on prices of output are rather poor. Fortunately, we note that (17) may be rewritten In Ha = In I' - or In p = In A* + 6LDL + a, In w' - al In p + Il In K + 02 In T In ri' = In A* + 6LDL + (1 - a) In p * + (l In 0 w' + I3 In K +,B2 In T where II' is actual money profit in rupees, w' is the money wage rate in rupees per day, and p is the price of the output in rupees. If the prices of outputs differ only across states, then one can insert state dummy variables to capture the effect of differences due to (1-a*) In p. This also allows interstate differences in the technical efficiency parameters. Observe that (18) holds independently of the price of output wl W'L *L *S - = -- -a, DL + a, DS 'Ta H't Hence our final estimating equations consist of 4 1nl H' = In A* + LDL + i Di (19) i= 1 and + -al + /2 In T In w' + f1 In K W'L *L * (20) - W a DLD + Sa D where ri' is farm profit in rupees and w' is money wage rate. A remark about the stochastic specification of the model is appropriate at this point. Not much is known about how disturbance terms in general should be introduced into economic relationships although Irving Hoch (1955, 1958) and Mundlak and Hoch and subsequently Arnold Zellner, Jan Kmenta and Jacques Dreze have proposed one possible assumption that is workable in the Cobb- Douglas case. Here we follow the usual, and admittedly ad hoc practice of assuming an additive error with zero expectation and finite variance for each of the equations (19) and (20).12 For the same farm, the covariance of the errors of the two equations is permitted to be nonzero. However, the covariances of the errors of either equation corresponding to different farms are assumed to be identically zero. Given this specification of errors, it is immediately apparent that Zellner's method provides an asymptotically efficient method of estimation. Moreover, the efficiency of estimation can be increased by imposing known constraints on the coefficients in the equations. Six statistical hypotheses are tested successively on the data. The results of these tests are reported in Table 1. They are: (i) Equal Relative Economic Efficiency HO: 6L = 0 i.e., A L= As* or In (A L/As) = 0. This hypothesis is rejected at the 10 percent significance level. Hence we conclude that small farms are relatively more economic-efficient than large farms. (ii) Equal Relative Price Efficiency *L *S Ho:i = a, This is not rejected at the 10 percent level. Hence we conclude that small and large 12 Marc Nerlove, in his pioneering study of cost functions, derives an additive error to the natural logarithm of the cost function. We can do the same here for our profit function, using the same assumptions as his. The additive error in the second equation may arise from different abilities to maximize profits or divergence between expected and realized prices.

8 220 THE AMERICAN ECONOMIC REVIEW MARCH 1973 TABLE 1-STATISTICAL HYPOTHESES TESTED Maintained Tested Hypothesis Hypothesis Ho Computed F Critical Fo.10 i) al = 0 F(1, 57) = 3.96 F(1, 57) = 2.79 ii) i) *L *S *3 F(1, 57) = 1.93 F(1, 57) = 2.79 el = O iii) *L *S F(2, 57) = 4.19 F(2, 57) = 2.39 al1 = E *L *3 *3 a1 = iv) (X1 = 1 F(1, 58) = 0.09 F(1, 58) = 2.79 *L *3 *L * C = O v) al =a F(1, 58) = 0.09 F(1, 58) = 2.7/9 *L ** Ce = a, vi) 31 +,B2 = 1 F(1, 59) = 2.01 F(1, 59) = 2.79 ai = t1 Note: For definition of variable see Table 2. Source: Table 2. farms do not have different price-efficiency parameters, ki, i.e., they both succeed to the same degree in maximizing profits. (iii) Equal Relative Technical and Price Efficiency * HO:6L = 0 *L *S This hypothesis is rejected. This actually can be anticipated in view of the rejection of hyphothesis (i). (iv) Absolute Price Efficiency of Small Farms *s * HJo:al al Maintaining the hypothesis of equal price efficiency in (ii), we test for absolute price efficiency of small farms. This hypothesis is not rejected at the 10 percent level, implying that the small farms have maximized profits, i.e., ks=1. (v) Absolute Price Efficiency of Large Farms *L * Ho:al =a Also maintaining the hypothesis of equal relative price efficiency of (ii) we test for the absolute price efficiency of large farms. This hypothesis also cannot be rejected at the 10 percent level. This means that large farms have also maximized profits, i.e., k = 1. One could have expected this finding from the results of (ii) and (iv). (vi) Constant Returns to Scale Ho0l = 1 Maintaining the hypotheses (iv) and (v) we test for constant returns to scale to all factors of production. Again, this hypothesis cannot be rejected.'3 Once a hypothesis is not rejected, we proceed to obtain estimates of parameters incorporating the hypothesis. The estimation results are tabulated in Table 2. As predicted by economic theory, the profit function is decreasing and convex in wage rate, and increasing in land. The wrong sign of the coefficient of capital can be attributed to a misspecification of this variable. Defining capital as interest charges on fixed assets per farm involves the implicit assumption that the service flow of capital, which is the appropriate input in production analysis, is proportional to the capital stock. As shown 13 At this point compare the discussion of A. M. Khusro.

9 VOL. 63 NO. 1 YOTOPOULOS AND LAU: RELATIVE ECONOMIC EFFICIENCY 221 TABLE 2-JOINT ESTIMATION OF COBB-DOUGLAS PROFIT FUNCTION AND LABOR DEMAND FUNCTION Single Zellner's Method with Restrictions Equation 1 Restriction 2 Restrictions 3 Restrictions Ordinary a7 1= Parameter Least atl =a* i3+0*=i Squares Unrestricted a =als a; =a a =t; UOP Profit Function In As* (.470) (.413) (.416) (.289) (.202) al (.217) (.200) (.192) (.186) (.148) (.471) (.412) (.416) (.399) (.388) (1.093) (.955) (.964) (.568) (.535) (.416) (.364) (.367) (.224) (.229) (.613) (.536) (.541) (.447) (.419) al (1.029) (.900) (.908) (.373) (.374) (.235) (.206) (.207) (.202) (.175) (.200) (.175) (.176) (.170) (.175) Labor Demand Function at (.549) (.549) (.412) (.373) (.374) as (.582) (.582) (.412) (.373) (.374) Notes: Numbers in parentheses are asymptotic standard errors. The estimating equations are where InH = In As + 8LDL + E4 i Di + a1 In w?fh + In K + 32 In T w'l *L *S --II'-a=1aDL al Ds i'1 II' =profit including interest on fixed capital and land rent w' = money wage rate DL =a size dummy variable taking the value of one for farms with a physical area greater than ten acres and zero otherwise Ds=a size dummy variable taking the value of one for farms with a physical area less than ten acres and zero otherwise. D= regional dummy variable with D1, D2, D3, D4 taking the value of one for only West Bengal, Madras, Madhya Pradesh and Uttar Pradesh, respectively. L =labor in days per year per farm K=interest on fixed capital per farm T =cultivable land in acres per farm Source: The Studies, Delhi, Reports for the year : Madras, Punjab, Uttar Pradesh, West Bengal; Report for the year : Madhya Pradesh. elsewhere (Yotopoulos (1967a, b)), this measure of capital leads to biased coefficients. From our estimated parameters, we can compute, by (9) and (11), indirect estimates of the production elasticities of labor, capital and land as well as those of the technicalefficiency and price-efficiency parameters of the large and small farms. These are tabulated in Table 3. We note that the production elasticities thus estimated appear generally large by comparison with estimates of directly fitted Cobb-Douglas agricultural production functions reported in other studies. The obvious reason for this discrepancy

10 222 THE AMERICAN ECONOMIC REVIEW MARCH 1973 TABLE 3-INDIRECT ESTIMATES OF THE INPUT ELASTICITIES OF THE PRODUCTION FUNCTION AND THE EFFICIENCY PARAMETERSa 1 Restriction 2 Restrictions 3 Restrictions *L * *L * *S * Parameter al al = al 1a 12? = 1 Labor a, Capital i Land Sum of Elasticities (al + f1 + (2) AL Large Farms L ki A Small Farms ks s Note: For definition of variables, see Table 2. a The indirect estimates of the coefficients of the production function are computed from the identities in (9). The efficiency parameters are computed from (9) and (11). is the constraint of constant returns to scale combined with the negative coefficient of capital. 14 Conceptually, however, the indirect estimates of production coefficients are statistically consistent, as opposed to those obtained directly from the production function by ordinary least squares, which are in general inconsistent because of the existence of simultaneous equations bias. By examining the technical efficiency component for small and large farms in Table 3 we find that the former are approximately 20 percent more efficient than the latter. IV. Summary and Conclusions An operational model to measure separately relative technical efficiency and price efficiency between (groups of) firms has been developed and applied to Indian agriculture. Needless to say, the usefulness of the approach here is not restricted to agriculture; neither is it specific for comparing large and small farms. The conclusion of the test of relative economic efficiency is in favor of the small 14 The negative coefficient of capital has also appeared in other application with the same data. See Lau and Yotopoulos (1971) and Yotopoulos, Lau, and K. Somel. farms, i.e., farms of less than ten acres, in agreement with our previous result in our 1971 article. Given the fixed inputs (land and fixed capital), and within the ranges of the observed prices of output and variable inputs (labor), the small farms of the sample of The Studies have higher actual profits. The relative economic efficiency of the small farms, however, is not due to superior price efficiency. In fact, we have found that both large and small farms are price-efficient.15 It may, after all, be true that the marginal calculations which the market place requires of the farmer are relatively easy to make. More importantly, we have established the superior technical efficiency of the small farms."6 We have also found that there exist constant returns to scale in Indian agriculture. Hence one cannot argue for a consolidation of small farms on the grounds of economies of scale. These findings imply that in agriculture the direct supervisory and leadership role of 15 This finding is inconsistent with Amartya Sen's (1964, 1966) hypothesis that large farms maximize profits while small farms maximize utility. 16 One possible explanation that has been advanced is an inverse proportional relationship between farm size and intrinsic fertility.

11 VOL. 63 NO. 1 YOTOPOULOS AND LAU: RELATIVE ECONOMIC EFFICIENCY 223 the owner-manager may be crucial for attaining high levels of economic efficiency. More studies are needed to further explain the so-called "unmeasureable factors" which apparently cause the difference in technical efficiency. REFERENCES M. J. Farrell, "The Measurement of Productive Efficiency," J. Royal Statist. Soc., 1957, 120, I. Hoch, "Estimation of Production Function Parameters and Testing for Efficiency," Econometrica, July 1955, 23, "Simultaneous Equation Bias in the Context of the Cobb-Douglas Production Function," Econometrica, Oct. 1958, 26, W. D. Hopper, "Allocation Efficiency in a Traditional Indian Agriculture," J. Farm Econ., Aug. 1965, 47, A. M. Khusro, "Returns to Scale in Indian Agriculture," Indian J. Agric. Econ., Oct. 1964, 19, L. J. Lau, "Applications of Profit Functions," in D. L. McFadden, ed., An Econometric Approach to Production Theory, Amsterdam 1972, forthcoming. and P. A. Yotopoulos, "A Test for Relative Efficiency and an Application to Indian Agriculture," Amer. Econ. Rev., Mar. 1971, 61, and, "Profit, Supply, and Factor Demand Functions with Application to Indian Agriculture," Amer. J. Agric. Econ., Feb. 1972, 54, D. L. McFadden, "Cost, Revenue, and Profit Functions," in D. L. McFadden, ed., An Econometric Approach to Production Theory, Amsterdam 1972, forthcoming. Y. Mundlak, "Empirical Production Function Free of Management Bias," J. Farm Econ., Feb. 1961, 43, and I. Hoch, "Consequences of Alternative Specifications in Estimation of Cobb-Douglas Production Functions," Econometrica, Oct. 1965, 33, M. Nerlove, "Returns to Scale in Electricity Supply," in C. F. Christ et al., eds., Measurement in Economics: Studies in Mathematical Economics and Econometrics in Memory of Yehuda Grunfeld, Stanford 1960, T. W. Schultz, Transforming Traditional Agriculture, New Haven W. D. Seitz, "The Measurement of Efficiency Relative to a Frontier Production Function," Amer. J. Agric. Econ., Nov. 1970, 52, A. K. Sen, "Size of Holdings and Productivity," Econ. Weekly, Feb. 1964, 16, , "Peasants and Dualism With or Without Surplus Labor," J. Polit. Econ., Oct. 1966, 74, R. M. Solow, "Technical Progress and the Aggregate Production Function," Rev. Econ. Statist., Aug. 1957, 39, C. P. Timmer, "On Measuring Technical Efficiency," Food Res. Inst. Stud. in Agric. Econ., Trade, Develop., 1970, 9, J. Wise and P. A. Yotopoulos, "The Empirical Content of Rationality: A Test for a Less Developed Economy," J. Polit. Econ., Nov. 1969, 77, P. A. Yotopoulos, (1967a) Allocative Efticiency in Economic Development: A Cross Section Analysis of Epirus Farming, Athens 1967., (1967b) "From Stock to Flow Capital Inputs for Agricultural Production Functions: A Microanalytic Approach," J. Farm Econ., May 1967, 49, ,"On the Efficiency of Resource Utilization in Subsistence Agriculture," Food Res. Inst. Stud. in Agric. Econ., Trade, Develop., 1968, 8, L. J. Lau, and K. Somel, "Labor Intensity and Relative Efficiency in Indian Agriculture," Food Res. Inst. Stud. in Agric. Econ., Trade Develop., 1970, 9, A. Zellner, "An Efficient Method for Estimating Seemingly Unrelated Regressions and Tests for Aigregation Bias," J. Amer. Statist. Ass., June 1962,.57, J. Kmenta, and J. Dreze, "Specification and Estimation of Cobb-Douglas Production Function Models," Econometrica, Oct. 1966, 34, Government of India, Ministry of Food and Agriculture, Studies in the Economics of FarXm Management, Delhi , reports for the year : Madras, Punjab, Uttar Pradesh, West Bengal; report for the year : Madhya Pradesh.