Dynamic efficiency measurement: theory and application.

(9) No relation can be established between [A.sup.i.sub.gt1], [A.sup.i.sub.gt2], and [A.sup.i.sub.gt], yet [A.sup.i.sub.gt4] [greater than or equal to] [A.sup.i.sub.gtl] [greater than or equal to] [A.sup.i.sub.gt3] and [A.sup.i.sub.gt4] [greater than or equal to] [A.sup.i.sub.gt2] [greater than or equal to] [A.sup.i.sub.gt3]. A relationship between [A.sup.i.sub.gt3], [A.sup.i.sub.gt4], and [A.sup.i.sub.gt], can be established. [A.sup.i.sub.gt], = Eg(*)/[F.sub.g](*) [greater than or equal to] [E.sup.i.sub.gtl]/ [F.sub.g](*) [greater than or equal to] [E.sup.i.sub.gtl]/[F.sup.i.sub.gtu] = [A.sup.i.sub.gt3]. Similarly, [A.sup.i.sub.gt] = [E.sub.g](*)/[F.sub.g](*) [less than or equal to] [E.sup.i.sub.gtu]/[F.sub.g](*) [less than or equal to] [E.sup.i.sub.gtu]/[F.sup.i.sub.gtl] = [A.sup.i.sub.gt4]. Thus, [A.sup.i.sub.gt3] [less than or equal to] [A.sup.i.sub.gt] [less than or equal to] [A.sup.i.sub.gt4].

(10) The procedure to establish lower and upper bounds on the allocative efficiency of variable inputs is similar to the one used in footnote 9 to define bounds on the long-run allocative efficiency.

(11) The LCP is also an efficient algorithm to solve nonlinear programming problems (Ahn 1981; Al-Khayyal 1987, 1989; Cheng 1984). Interpretations of the LCP in the context of economics can be found in Paris (1979a, 1979b).

(12) Omitting the time index t, the variable cost function can be defined as C(z) = E[C(z)Iz]+ [epsilon] whereE[C(z) |z]= f C(z)[f(C . z)/[f.sub.1] (z)] dC, E[[epsilon] | z] = 0, and f(C, z) and [f.sub.1] (z) are the multivariate and marginal density functions, respectively. The variable kernel estimator of E[C(z) I z is obtained by replacing f(C, z) and [f.sub.1] (z) by their respective kernel estimators as follows:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

where

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

K(*) is the kernel function, [d.sub.c] is the window-width for the dependent variable, and [d.sub.z] =([d.sub.1], [d.sub.2] ..... [d.sub.m[+2o) is the window-width for the independent variables z. The standard multivariate normal density function is used for the kernel and the estimator in (A) can be rewritten as

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

The marginal cost of adjustment of the quasi-fixed factor h is estimated by differentiating [C.sub.n](z) in (B) with respect to [I.sub.h] leading

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

(13) The estimates of the behavioral shadow values of capital are not reported due to space restrictions. The results are available from the authors upon request.

(14) Point estimates of the shadow values close to zero do not necessarily imply the absence of adjustment costs. Instantaneous adjustment arises when the shadow value of the quasi-fixed factors is constant. Please, see Silva and Stefanou (2003) for a discussion on the value of these estimates.

(15) The Lilliefors test is used to test for normality. For details on this test, see Conover (1999).

(16) The Smirnov test is a nonparametric test to detect whether two distribution functions are identical or not. For details on this test, see Conover (1999).

(17) The Page test is a distribution-free test for ordered alternatives in the k-related-samples problem. Please, see Neave and Worthington (1988) and Conover (1999) for details on this statistical test.

(18) Inspection of the results indicates significant differences between technical and allocative efficiency scores. However, differences in the percentage of technical and allocatively inefficient farmers when the upper bounds on both efficiency levels are used may be due to the fact that the value of the measure generating the upper bound on the allocative efficiency is often greater than one.

Elvira Silva is associate professor, Faculty of Economics, University of Porto, and Spiro E. Stefanou is professor, Department of Agricultural Economics and Rural Sociology, Pennsylvania State University. Table 1. Upper Bound on Technical Efficiency of Variable Inputs, by Year

1987 1988 1989 Mean (%) 99.58 99.69 98.88 Median (%) 100 100 100 Std. error (%) 3.28 2.02 5.25 IQR (a) (%) 0 0 0 Maximum (%) 100 100 100 Minimum (%) 74.36 84.50 65.20 Skewness (b) -7.62 -7.18 -5.44 Excess kurtosis 56.02 51.14 29.71 Normality 0.5346 0.5277 0.4974 (p-value) (<0.01) (c) (<0.01) (c) (<0.01) (c) Percent inefficient 1.6% 3% 9.8% farmers

1990 1991 1992 Mean (%) 100 98.80 99.78 Median (%) 100 100 100 Std. error (%) 0 4.60 1.57 IQR (a) (%) 0 0 0 Maximum (%) 100 100 100 Minimum (%) 100 77.54 87.85 Skewness (b) -- -4.07 -7.44 Excess kurtosis -- 15.73 54.14 Normality -- 0.5330 0.5243 (p-value) (<0.01) (c) (<0.01) (c) (<0.01) (c) Percent inefficient 0% 7% 3% farmers (a) IQR is the interquartile range. (b) The skewness coefficient is the ratio of the third central moment and the cube of the standard error. (c) The 0.99 quanile is the largest quantile presented in the Lilliefors table. Thus, the p-value is some value less than 0.01. Table 2. Lower Bound on Technical Efficiency of Variable Inputs, by Year

1987 1988 1989 Mean (%) 96.85 97.59 97.32 Median (%) 100 100 100 Std. error (%) 8.85 8.31 8.47 IQR (a) (%) 0 0 0 Maximum (%) 100 100 100 Minimum (%) 58.31 54.90 60.95 Skewness (b) -3.02 -3.84 -3.17 Excess kurtosis 8.30 14.33 8.84 Normality 0.4750 0.4994 0.5064 (p-value) (<0.01) (c) (<0.01) (c) (<0.01) (c) Percent inefficient 16% 12% 13% farmers

1990 1991 1992 Mean (%) 98.74 98.64 99.09 Median (%) 100 100 100 Std. error (%) 5.64 5.04 5.15 IQR (a) (%) 0 0 0 Maximum (%) 100 100 100 Minimum (%) 63.85 72.99 64.82 Skewness (b) -5.11 -3.70 -5.82 Excess kurtosis 26.28 12.95 33.49 Normality 0.5066 0.5131 0.5371 (p-value) (<0.01) (c) (<0.01) (c) (<0.01) (c) Percent inefficient 8% 9.8% 3% farmers (a) IQR is the interquartilc range. (b) The skewness coefficient is the ratio of the third central moment and the cube of the standard error. (c) The 0.99 quantile is the largest quantile presented in the Lilliefors table. Thus, the p-value is some value less than 0.01. Table 3. Lower Bound on Allocative Efficiency of Variable Inputs, [A.sub.x3], by Year

1987 1988 1989 Mean (%) 93.35 93.96 95.07 Median (%) 100 100 l00 Std. error (n/n) 15.06 12.50 14.11 IQR (a) (%) 0 0 0 Maximum (%) 100 100 100 Minimum (%) 26.07 53.09 28.94 Skewness (b) -2.57 -1.93 -3.04 Excess kurtosis 6.56 2.46 8.90 Normality 0.4411 0.4396 0.4986 (p-value) (<0.01) (c) (<0.01) (c) (<0.01) (c) Percent inefficient 23% 24.6% 18% farmers

1990 1991 1992 Mean (%) 94.43 95.41 97.25 Median (%) 100 100 100 Std. error (n/n) 16.80 12.39 8.80 IQR (a) (%) 0 0 0 Maximum (%) 100 100 100 Minimum (%) 18.51 29.52 59.55 Skewness (b) -3.26 -4.16 -2.95 Excess kurtosis 9.80 17.94 7.92 Normality 0.4658 0.4983 0.4884 (p-value) (<0.01) (c) (<0.01) (c) (<0.01) (c) Percent inefficient 16% 19.7% 15% farmers (a) IQR is the interquartile range. (b) The skewness coefficient is the ratio of the third central moment and the cube of the standard error. (c) The 0.99 quantilc is the largest quantile presented in the Lilliefors table. Thus, the p-value is some value less than 0.01. Table 4. Upper Bound on Allocative Efficiency of Variable Inputs, by Year