A Generalized Measure of Farm- Specific Technical Efficiency

Transcription

1 A Generalized Measure of Farm- Specific Technical Efficiency Philip J. Dawson, John Lingard, and Christopher H. Woodford Single measures of farm-specific technical efficiency over time are calculated for rice farms in Central Luzon, the Philippines, from the residuals of a stochastic frontier production function. Panel data from the Intemational Rice Research Institute's pe "Loop Survey" are used. Results show a narrow range of efficiency between 84% and 95% across the twenty-two farms, so that there is limited scope for increasing output by resource reallocation. A comparison is made with measures of technical efficiency using traditional covariance analysis. Key words: Philippines, stochastic production frontier, technical efficiency. Lingard, Castillo, and Jayasuriya; and Dawson and Lingard have measured farm-specific technical efficiency on rice farms in Central Luzon, the Philippines, using IRRI's "Loop Survey." In particular, Lingard, Castillo, and Jayasuriya estimate a production function for thirty-two farms from panel data for 1970, 1974, and 1979 using covariance analysis. Measures of technical efficiency are then calculated from the farmspecific dummy variables. The results show that the least efficient farm achieves only 29% of the output of the most efficient farm for identical input levels. More recently, Dawson and Lingard present estimates of farm-specific technical efficiency from a stochastic frontier production function using data for 1970, 1974, 1979, and For each year, a cross-section stochastic production function is estimated using the composed error model of Aigner, Loveli, and Schmidt and of Meeusen and van den Broeck. From the residuals, a measure of technical efficiency is then calculated for each farm in each year using the method of Jondrow et al. The results show an even greater range of efficiency than that calculated by Lingard, Castillo, and Jayasuriya: the least efficient farm in all years is in the 10%- 19% range, while the most efficient is in the 90%- 100% range. Hall and Bardsley draw attention to the large range of technical inefficiencies obtained by Lingard, Castillo, and Jayasuriya. However, the results substantiate those of Timmer in that covariance analysis often produces large differences in comparative efficiency. This technique tends to bias the production function elasticities downward, with large neutral shifts occurring in the intercept terms of individual farms. The intercept terms thus capture a substantial proportion of the impact of differential input use, leaving little for the factor elasticities to explain. As a result, measures of technical efficiency from covariance analysis tend to be biased downward. l Analysis of covariance was initiaily used by Timmer asa means of calculating farm-specific technical efficiency. 2 The method overcomes some criticisms associated with estimating deterministic production frontiers by mathematical programming techniques whereby estimates of the residuals provide measures of efficiency Philip J. Dawson and John Lingard ate both senior lecturers in agricultural economics, and Christopher H. Woodford is a computer programming advisor at the University of Newcastle upon Tyne, UK. The data for this paper were kindly provided by the Intemational Rice Research Institute, the Philippines. The authors ate appreciative of this provision and also acknowledge the cont and encouragement of John Flinn and Bart Duff of the Department of Agricultural Economics at IRRI. They would also like to thank three anonymous referees for helpful comments on an earlier draft. t This phenomenon is similar to the omission of a managerial input from cross-section production function estimates: specification error biases the estimates of individual production elasticities which, in turn, leads to a downward bias in the estimated returns to scale (Griliches). 2 Timmer refers to the index of efficiency ratings obtained from covariance analysis as ~Hoch's efficiency index" (p. 124). Hoch suggested the use of covariance analysis in estimating production functions as a means of overcoming management bias and estimating "entrepreneurial capacity." Copyright 1991 American Agricultural Economics Association

2 Dawson, Lingard, and Woodford (Farrell). 3 Timmer (p. 124) draws attention to the main difference between the two methods: The frontier index is determinate. There is no random error term. The Hoch index is estimated along with an error term. AII variation from the frontier is due to efficiency differences according to the frontier measure. Only variation that persists over time is cast into the Hoch measure; all remaining variation is considered part of the random error term. The Farrell frontier.., is designed to use a single year's cross-section observations. AII variation not attributable to differential input use.., becomes part of the efficiency index... The net result is to cast doubt on the value of an efficiency estimate based on any of the frontier techniques that use only one year's data. Notwithstanding this criticism, deterministic production frontiers which are estimated statistically and not by mathematical programming methods were subsequently developed (Forsund, Lovell, and Schmidt). In this approach, OLS is used to estimate the average production function, and then the intercept is adjusted upward or corrected until one residual is zero and none of the residuals are positive. 4 Again, estimates of the residuals provide measures of farmspecific technical efficiency so that Timmer's criticisms remain valid. However, with the development of the stochastic frontier production function based on the composed error model of Aigner, Lovell, and Schmidt and of Meeusen and van den Broeck and the subsequent method of calculating firm-specific technical efficiency by Jondrow et al., Timmer's criticisms have now been answered. However, a remaining problem is that the frontier model will have as many efficiency estimates for each firmas there are time periods (Dawson and Lingard). Thus, technical efficiency is somewhat ephemeral, relating only to the technology available in a given year or at a given point in time. In this paper, we attempt to overcome this criticism. Using panel data from the International Rice Research Institute's pe "Loop Survey" for a subsample of twenty-two rice farms in Central Luzon, the Philippines for 1970, 1974, 1979, 1982, and 1984, we estimate a stochastic frontier production function embodying a composed error term. 5 The residuals are then used 3 See Timmer (pp ) for a comprehensive list of these criticisms and Forsund, Lovell, and Schmidt for a survey of frontier production functions. 4 The term, "corrected OLS" or COLS has been used to describe this technique. s While the "Loop Survey" has 61, 57, 143, and 135 observations for , 1979, and 1982, only 22 were available for Farm-Specific Technical Efficiency 1099 to calculate a single measure of technical efficiency for each farm over the whole fifteen-year period. These results are then compared with those obtained from covariance analysis. Except for Kalirajan and Shand, our use of a stochastic frontier production function contrasts with previous studies. In particular, we assume that technical efficiency persists and is enduring over time; common sense and intuition suggest that farmers who use today's technology more efficiently than others are likely to use tomorrow's technology more efficiently also. 6 Efficiency differentials should be fairly enduring over a fifteen-year time span. Accordingly and in keeping with Lingard, Castillo, and Jayasuriya, we return to the spirit of Timmer and examine and evaluate farm-specific technical efficiency over time. Statistical Model and Estimation Procedure Following Pitt and Lee, considera stochastic production function model with multiplicative disturbances of the form: ( 1 ) Y = f(x)e ~, where y is observed output, x is a vector of inputs ande is a stochastic error term. Aigner, Lovell, and Schmidt; and Meeusen and van den Broeck specify the error term as being composed of two independent elements: (2) e = u + v. The symmetric component, v, permits random variation in output resulting from factors outside the control of the fama like weather, disease, and so on. The one-sided component, u -< 0, reflects technical efficiency relative to the stochastic frontier, f(x)e v. Thus u = 0 for any farm's output lying on the frontier and is strictly negative for any output lying below the frontier. The model can be generalized to consider cross-section and time-series data. Assuming that the production can be represented by a log-linear function, combining (1) and (2) gives a variance components model of the form (3) y, =/30 I--[ ~~e'"" u,,), m k-i where x.k is the kth input (k = 1... m) of the ith farm (i = 1... n) in time period t (t = 1, 6 However, see Schmidt (pp ) for a contrary view.

3 - e qb(t~r~/o-~)}), 1100 November T). A measure of farm-specific technical efficiency is given by Yit 9 (4) e ~" f(xi,k)ev,,, that is, the ratio of observed output to the maximum achievable stochastic level given that technical efficiency is fully realized. The coefficients flo, flk (k = 1... m) and measures of technical efficiency can be estimated once dist for u and v are assumed. Following Aigner, Lovell, and Schmidt; and Meeusen and van den Broeck, assume that vis normal; that is, v ~ N(0, tr~) and u halfnormal, that is u -< 0, u ~ IN(0, tr The production function in (3) can now be estimated by maximum likelihood methods. Pitt and Lee use an algorithm requiring the specification of first derivatives only. However, we use both fu'st and second derivatives so that all the information in the data can be maximized. This technique has greater power than Pitt and Lee's technique and results in more reliable and efficient convergence to the maximum. Moreover, there is no need to spetcify precise starting values for the parameters. Farm-specific technical efficiency in (4) depends upon the decomposition of e. Assuming that the technical efficiency of each farm is the same between time periods, define the efficiency of a particular farm as E[u ] e]: g 0 (5) E[u[91 =/ uf(ul[:)du,.!- where (6) 1 T t~ = -- E 6t' Tt=l and F(.) is the conditional density function of u given e, that is, F(u I e) = F(u, e)/f(e), where F(u, e) and F(e) are the joint probability density function of u and e and the probability density function of e, respectively. Now, in similar notation to (6), we have (7) ~ = u + ~. Since v, (t = 1,..., T) is normally distributed, then v ~ N(0, tr2v/t). It follows that the joint density function of u and ~ is given by 7 A derivation of the likelihood function for this model is available from the authors. (8) V~ Amer. J. Agr. Econ. 2 _(ll2u~la~) _Crl2~21~2) F(u l ~) - ~ e ~ 2~u 2~v Substituting (7) into (8) and rearranging gives F(u, e:) - e 7ro'uo'v - 1/2(u z/cr~ + {r~ - u)2}/ah F(e) is now given by F(e) = f0_~ F(u,e)du, which can be written as (9) V~ F( 91 ) - 0"~ e t{- ~ 2~ "troruo" v where = o'w,./to', + Crv and q)(.) is the cumulative standard normal distribution function. Returning to the evaluation of (5), (10) uf(u, i)du f - oc -- 7rOruO'v~ e(_~2a2r/2~2~h f_~ ue(-l/2~~{u-~~2t/crl}2)du Using a standard integral to evaluate (10), dividing by (9) to obtain (5), technical efficiency is given by (11) E[u l i] = Z o ~ o(:) where Z = o'2/o2~ E r,= i e, and 4~(.) is the standard normal density function. Equation (11) corrects the error in Kalirajan and Shand [eq. (11)]. Since u -< 0, then 0 -< e" -< 1. The population mean level of technical efficiency is given in Pitt and Lee as (12) E[e ~] = 2e(~~/2){1-4~(o'D}. Data and Model Specification Time-series data on changes in farming practices in developing countries ate scarce, but IRRI has monitored two sets of Philippine rice producers since The data used in this study come from one of these--the "Central Luzon Loop Survey"--which details information on rice production practices on the same farms on a highway loop north of Manila in Central Luzon. The survey respondents are dispersed geograph-

4 Dawson, Lingard, and Woodford ically over a 200-mile area, but all cultivate fields close to a major highway. Data are obtained by two interviews conducted each season with farm operators, one following transplanting and one post-harvest. Herdt discusses some of the main changes that have occurred at farrn level. The data used in this paper consist of a subsample of twenty-two identical farms in 1970, 1974, 1979, 1982, and Wet-season data only are considered and analyzed. AII the farms plant modern rice varieties (MVs) with IR36 the most common variety.8 Except for the typhoonaffected year of 1974, yields in general increased steadily over the period from 2,738 kilograms per hectare in 1970 to 4,570 kilograms per hectare in Since then, in the Philippines, rice yields have displayed a slightly negative trend and fell to 3,621 kilograms per hectare in 1984 for this sample. AII farms have used increasing amounts of inorganic fertilizers, from 32 kilograms per hectare in 1970 to 62 kilograms per hectare in both 1982 and 1984, and almost all farmers were applying some insecticides. Many were using herbicides, too. By 1984, over two-thirds of the area covered by the twentytwo farms was annually double cropped with rice. Labor use is a changing mixture of hired and family labor, with an initial substitution of hired for family labor between 1970 and 1974 gradually shifting back toward family labor thereafter which, in 1984, provided about 40% of the total farm labor. Transplanting, harvesting, and threshing are mainly done by hired labor, but other activities are carried out by both family and hired workers. Total labor use has fallen from a peak in 1974 of fifty-nine man-days per hectare to forty-six man-days per hectare in Before 1973, most of the farms were sharecropped, but subsequent land reform converted the tenancies to leaseholds with the rice farmers paying a fixed rent in kind. A further stage of land reform has also occurred whereby the tenants receive a certificate of land transfer converting them into amortizing land owners purchasing their farms over a fifteen-year period. This changing land tenure accounts for the changing size of farms from an average of 2.82 hectares cultivated in 1970 to 1.83 hectares in It also partly explains the changing pattern of machinery use on the farms. In the 1960s, four-wheel tractors and large rice-threshing machines were predominant as landlords controlled 8 The switch to modern va across the wider "Loop Survey" (149 farms) had been completed by Farm-Specific Technical Efficiency 1101 the harvesting operations to ensure that they obtained their rent in the form of crop share. With the shift to leaseholding, it was unnecessary for landlords to supervise threshing, and small portable threshers were developed and introduced in the mid- 1970s. Similarly, two-wheel power tillers replaced large tractors, although secondary tillage operations (harrowing and levelling) are still carried out using water-buffalo. Changing price relationships in the 1980s in the Philippines have reduced the economic incentives for rice farmers and cont to the lowering of recorded yields. Real rice prices have declined; paid out costs by farmers as a proportion of the value of production have risen over time as material input prices and hired capital charges increased. Factor prices, especially land and labor, are expected to rise in the long term asa result of increasing cropping intensities and off-farm employment opportunities. The real price of rice is also expected to continue to decline on world markets, and net returns to rice producers on this technological treadmill will continue to stagnate. The economic prospects for Philippine rice farmers are thus not good, and it is therefore essential to determine the extent of the efficiency gap between "best" and "average" farmers and attempt to narrow it in order to maintain rice production levels and to defend farmers' incomes. The production function for rice is estimated on a whole-farm basis. Output (y) is defined as the physical amount (kgs.) of rice produced. There are four inputs, three of which are measurable and one which is qualitative. The measurable inputs are area (A) measured in hectares, pre-harvest labor (L) measured in man-days, and kilograms of inorganic fertilizer (N). 9 The qualitative input, represented by a dummy variable, is irrigation (DI) where D/= 1 for irrigated (pump or gravity) and = 0 for rain-fed, lo In addition, 9 Nonessential chemicals are excluded from the production function: IR36 is both disease and pest resistant so that use of agrochemicals implies a problem. Accordingly, it is expected that farrn yields will be low if chemicals ate being used, and it is reasonable to assume tht such inputs do not have the conventional production response. Indeed, no significant effect on rice output could be found for chemical inputs in the forro of weedicides or insecticides. ~o Dummy variables representing mechanization and soil texture were initially included in the production function but then omitted. For the mechanization dummy, results substantiate those previously obtained in that no significant effect on rice output could be found for two-wheel power tillers or four-wheel tractors. Data on ~soil texture" were divided into three: clay, clay/loam, and sandy/silty. Clay soils generally lead to higher productivity of wetland rice production. Using clay as the base, perverse (positive) signs on the clay/ioam and sandy/silty dummies were obtained, a result similar to that obtained by Herdt and Mandac. Such a result is counterintuitive.

5 1102 November 1991 time-specific dummies ate included to account for interyear differences (D,) where D74, for example, is the time dummy for The functional form chosen was derived experimentally using OLS prior to eventual estimation by maximum likelihood methods. A transcendental logarithmic function was estimated at first, but serious multicollinea problems among the cross-product terms led us to prefer a Cobb-Douglas specification. The production function to be estimated is (13) In Yi, = q +/3~ In Ai, +/3z In Li, T + /33 In Ni, +/34Dtit + Z "yjdj i' + eit' j=2 where i = 1... n; t = 1... T; Dj,.t = 1 if j = t, and = 0 otherwise. Results The estimated stochastic production frontier is In 33i, = In Ai, In Li, (53.29) (22.00) (7.08) In Ni, Dti, D74 (8.93) (10.26) (11.18) D D D84, (7.23) (10.80) (5.47) where log-likelihood is , 6 "2, = 0.020, (2.05) 6.2 = 0.146, and asymptotic t-statistics are in (30.62) parentheses. All coefficients on the variables are significant and accord with prior beliefs as to their various influences on rice production; namely, the production elasticities are positive and less than unity. The time dummies are positive except for 1974, when abnormal typhoon damage lowered the rice harvest considerably. The positive time dummies reflect an upward drift of technology over time, improved farmer learning, and so on. The irrigated farms not surprisingly obtain higher output levels than the rainred ones, as implied by the positive and significant coefficient on the irrigation dummy. There is a small but significant fertilizer effect; the labor input is important; and, as with previous studies, the influence of land on farm-level rice output is dominant. The validity of the measures of technical efficiency subsequently computed rest upon the estimates of the production function; we are convinced that our estimated production Amer. J. Agr. Econ. function is a good one both in terms of plausibility and statistical properties. Indeed, it is much better than our other previous published results (Lingard, Castillo, and Jayasuriya; Dawson and Lingard). Table 1 and figure 1 present the frequency distribution and probability histogram of the technical efficiency ratings. A range of efficiencies is observed across the twenty-two farms; but the spread is not large, with the best farm being over 95% efficient while the worst is only 84% efficient. Fourteen farms are 90% or more efficient, and three are less than 85% efficient. The mean efficiency and the median from the sample is 89.3% and 89.5%, respectively; the population mean efficiency from (12) is 89.7%. There is no significant evidence of skewness or kurtosis; the distribution is mesokurtic, that is, neither flat nor peaked with respect to the general appearance of the frequency curve. A c assumption of the analysis is that technical efficiency is time invariant. In principle, it is possible to test this assumption; but, as noted by Pitt and Lee (model III), "[this] is precluded because of the difficulty in specifying Table 1 Frequency Distribution of Technical Efficiency Ratings Number of Farms Efficiency Stochastic Covariance Rating (%) Frontier Analysis Mean Standard deviation Median Coefficient of skewness (0.491) (0.491) Kurtosis (0.953) (0.953) Note: Standard errors are in parentheses.

6 Dawson, Lingard, and Woodford Farm-Specific Technical Efficiency 1103 Pe.rceatage of Sample Stochagª Fronª [] Covariaace Analysis Figure 1. ~ o ~~~ ~,~,n,,, R.![~.,I Pezce.atage Effideacy Probability histogram of the efficiency ratings a flexible multivariate distribution (uil... u;r) with each u, -< 0. The multivatiate truncated normal distribution is a possible candidate but the implied likelihood function is computationally intractable" (pp ). A key issue here is the provision of a useful algorithm for evaluating T-dimensional integrals of cumulative normal distribution functions. In general, currently available algorithms are too time consuming to be repeatedly invoked in a conventional minimization procedure. An alternative is to follow Dawson and Lingard and calculate farmspecific efficiency ratings from year-specific cross-section data using maximum likelihood methods. This is impractical with the small data sets of twenty-two because of convergence problems. These results are not compared with those using covariance analysis. Covariance Analysis The equation to be estimated using covariance analysis is (13), where the error term, e,, is replaced by vt anda set of farm-specific dummy variables, Di, is included. The additional terms ate E,"=2 A~D~it, where D~, = 1 if s = i, and = 0 otherwise. By setting the base as the most efficient farm, the estimates of A~ (s = 2,..., n) and Al are used to calculate the technical efficiency for each farm, 0 -< e a -< l: the best farm is 100% efficient, and those of all others are measured in relative terms. The estimated equation is ln33it = lna,-, lnlª (13.05) (4.70) (2.12) in N, D,, D74 (0.75) (1.66) (3.16) d D D D84 (2.18) (3.28) (1.65) n + ~_~ isdsi, R 2 = 0.81 s--2 (t-statistics in parentheses). The signs and magnitudes of all coefficients are similar to those obtained from the stochastic frontier approach, although those on fertilizer and the irrigation and 1984 time dummies are now insignificant; over 81% of the variation in the (log of) output is explained. Table 1 and figure 1 again present the frequency distribution and probability histogram of the technical efficiency ratings. The mean efficiency and the median from the sampie are 58.6% and 57.6%, respectively. The range of efficiencies across the twenty-two farms is large with the worst producing only 36% of the output of the best, given identical input levels. These results substantiate those of Lingard, Castillo, and Jayasuriya in that cova analysis produces large differences in comparative efficiency. The coefficient of skewness implies that the distribution of efficiency ratings is positively and significantly skewed, but there is no evidence of kurtosis. It is clear from table 1 and figure 1 that the distributions of efficiencies obtained from both

7 1104 November 1991 stochastic frontier and covariance analysis approaches are different; potential gains in technical efficiency are small for the former but are relatively large for the latter. Intuitively, measures of inefficiencies obtained from covariance analysis are too large to be maintained over time; those obtained from the stochastic frontier are preferred. Nevertheless, Spearman's correlation coefficient of 0.95 implies that there is a significant relationship between the rankings of technical efficiencies from the two approaches. Conclusions The responsibility for technical inefficiency rests mainly with management. As Liebenstein (p. 397) notes: "Managers determine not only their own productivity but the productivity of all cooperating units in the organization." Because it is reasonable to assume that management is fixed over a short period of time, it therefore follows that technical efficiency is fixed also; that is, technical efficiency is persistent and enduring over time. However, most previous studies which measure firm-specific efficiency from stochastic frontier production functions involve the use of year-specific cross-section data. But there are as many efficiency measures for each firmas there are time periods, implying that technical efficiency relates only to the technology available in a given period: it is nondurable and transient. With nonexperimental data, there is no method of validating measures of technical efficiency, rather they depend upon the production function estimates. 1~ In compa with previous studies using similar data (Lingard, Castillo, and Jayasuriya; Dawson and Lingard), the results presented here compare favorably, and the measures of technical efficiency accord more with intuition. We conclude that this small sample of Philippine rice farmers has adopted the new technology rapidly between 1970 and 1984, and all have quickly adapted their farming practices at a similar rate. There are no technological laggards within the sample, and significant yield gaps do not exist between best- and averagepractice farmers. Accordingly, there is little purpose in attempting to relate the very narrow spread of farm-specific inefficiencies to farmspecific socioeconomic factors like age of the I i In this context, see Herdt and Mandac, who compare production functions from experimental and nonexpe data. Amer. J. Agr. Econ. farmer, education, tenancy, access to credit, and so on. Increased rice production in the future, then, must come from further technological progress. [Received August 1989; final revision received January 1991.] References Aigner, D., C. A. K. Lovell, and P. Schmidt. "Formulation and Estimation of Stochastic Production Function Models." J. Econometrics 6(1977): Dawson, P. J., and J. Lingard. "Measuring Farm Efficiency Over Time on Philippine Rice Farms." J. Agr. Econ. 40(1989): Farrell, M. J. "The Measurement of Productive Efficiency." J. Royal Statist. Soc. 120(11I)(1957): Forsund, F. R., C. A. K. Lovell, and P. Schmidt. "A Survey of Frontier Production Functions and of Their Relationship to Efficiency Measurement." J. Econometrics 13(1980):5-25. Griliches, Z. "Specification Bias in Estimates of Production Functions." J. Farm Econ. 39(1957):8-20. Hall, N., and P. Bardsley. ~Dummy Variable Estimators of Technical Efficiency: A Comment." J. Agr. Econ. 38(1987): Herdt, R. W. ~A Retrospective View of Technological and Other Changes in Philippine Rice Farming " Econ. Develop. and Cultur. Change 35(1987): Herdt, R. W., and A. M. Mandac. ~Modern Technology and Economic Efficiency of Philippine Rice Farmers." Econ. Develop. and Cultur. Change 29(1981): Hoch, I. "Estimation of Production Function Parameters Combining Time-Series and Cross-Section Data." Econometrica 30(1962): Kalirajan, K. P., and R. T. Shand. "A Generalized Measure of Technical Efficiency." Appl. Econ. 21(1989): Liebenstein, H. "Allocative Efficiency vs. 'X-Efficiency'." Amer. Econ. Rey. 56(1966): Lingard, J., L. Castillo, and S. K. Jayasuriya. "Comparative Efficiency of Rice Farms in Central Luzon, the Philippines." J. Agr. Econ. 34(1983): Jondrow, J., C. A. K. Lovell, I. S. Materov, and P. Schmidt. "On the Estimation of Technical Efficiency in the Stochastic Production Function Model." J. Econometrics 19(1982): Meeusen, W., and J. van den Broeck. ~Efficiency Estimation from Cobb-Douglas Production Functions with Composed Error." lnt. Econ. Rey. 18(1977): Pitt, M. M., and L.-F. Lee. "The Measurement and Sources of Technical Inefficiency in the Indonesian Weaving Industry." J. Develop. Econ. 9(1981): Schmidt, P. "Frontier Production Functions." Econometric Rev. 4(1986): Timmer, C. P. ~On Measuring Technical Efficiency." Food Res. lnst. Stud. 9(1970):