Conclusion

Since most economic relationships predicted by economic theory are unknown, one has to count on a particular parametric form, which may lead to a biased estimation due to invalid parameterization. The importance of nonparametric and semiparametric regression techniques has drawn much attention from the econometricians and applied researchers recently. These techniques allow the functional form to be determined at least partially by the data. Fan et al. (1996) and Deng and Huang (2008) generalized the conventional linear stochastic frontier model to a semiparametric stochastic production frontier model. On the basis of previous works, this article adds to the current literature by considering both TE and AE in the context of a semiparametric stochastic cost frontier model using panel data.

This paper has solved two major problems faced by applied researchers. First, the cost system must be estimated simultaneously, suffering from computational difficulties. Second, the log-likelihood function of the expenditure equation cannot be maximized due to the presence of the nonparametric component. Even worse, the nonparametric function is unable to be estimated by existing nonparametric regression methods. We propose a five-step procedure to cope with these problems. Evidence from a set of Monte Carlo simulations tends to support the superiority of Model A at least for a moderate sample size, while the performance of Model B’s estimators is nearly as good as that of Model A’s, particularly when the time period of the panel data is long. In other words, Model B is appropriate for long panel data.

The first step estimators of the cost share equations perform reasonably well. We thus advocate using these estimates to compute the AE measure and treat the estimated allocative parameters as given in the following steps. It is noticeable that despite the uselessness of the parameter estimates obtained in the third step, this step is necessary to yield the residuals and to concentrate out variance ². Otherwise, estimators of Step 5 will perform poorly. Moreover, Models A and B are robust to include additional explanatory variables to both parametric and nonparametric portions of the cost function. When cross sectional data are available, the foregoing conclusions continue to hold in general, except that the bias of the estimated TE measure does not decrease as the sample size increases.

The three models are applied to investigate the TE and AE measures of the financial sectors of 14 East European countries over the period of 1993-2004. As expected, the average TE scores obtained by Models A and B are close to each other.

Model C underestimates the average TE scores, but exaggerates the rate of improvement on the TE. Financial deregulation appears to successfully prompt the TE of the sample banks over the transition period. Since the TI dominates the AI, bank managers are suggested to promote their managerial ability in such a way as to reduce the production costs for a given level of outputs, followed by adjusting for their input mix given the ratios of input prices.

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Appendix

Table II. The performance of the estimators of lnG, AE and TE for the case of ( ,  ², )= (-0.025 , 1.88 ,

Table III. The performance of the allocative parameter estimates setting M(‧)=2 ln(1y₁) as N=30

Table V. The performance of the parameter estimates from the third-stage setting M(‧)=2 ln(1y₁) as N=30 Model A

Table VI. The performance of the estimators of ( ,  ², ) setting M(‧)=2 ln(1y₁) as N=30

Table VII. The performance of estimated function lnG setting M(‧)=2 ln(1y₁) as N=30

Model A Model B

Table X. The performance of the first-stage parameter estimates using cross-sectional data assuming (², ) =

Table XI. The performance of the third-stage parameter estimates using cross-sectional data assuming ( ², )= (1.88,1.66)

Table XII. The performance of the estimators of ( ², ) and M(‧) using cross-sectional data assuming ( 2, )=(1.88,1.66) 1000 -0.0318 0.0621 -0.0609 0.0336 0.0231 0.0190

Model B 1000 -0.0339 0.0615 -0.0619 0.0335 0.0229 0.0298

Model C

 ^{2 M(‧)}

N Bias MSE Bias MSE Bias MSE

100 -1.1114 135.0659 11.9583 532.0402 0.8387 3.0253 300 -0.7597 18.1286 3.7948 50.6329 0.6325 1.4538 500 -0.7224 5.8017 1.8657 13.0069 0.5125 0.9517

1000 -0.5412 3.2962 0.9885 4.4140 0.3775 0.6153

Table XIII. The performance of the estimated lnG using cross-sectional data assuming ( ², )=(1.88,1.66)

Model A Model B

Table XIV. The performance of the estimated AE using cross-sectional data assuming ( ², )=(1.88,1.66)

Model A Model B

Table XV. The performance of the estimated TE score using cross-sectional data assuming ( 2, )=(1.88,1.66)

Table XVI. The performance of the parameter estimates in Step 1 setting M(‧)= y₁ ln(1y₁)

Table XVII. The performance of the parameter estimates from the third-stage setting M(‧)= y₁ ln(1y₁)

Translog

Table XVIII. The performance of the estimators of ( ,  ², ) setting M(‧)= y₁ ln(1y₁)

Table XIX. The performance of estimated function lnG setting M(‧)= y₁ ln(1y₁) ( ,  2, )= (0.025 , 1.88 , 1.66)

Table XX. The performance of estimated AE setting M(‧)= y₁ ln(1y₁) ( ,  2, )= (0.025 , 1.88 , 1.66)

Model A Translog

AE1 AE2A AE2T

( N , T ) Bias MSE Bias MSE Bias MSE ( 50 , 6 ) 0.0031 0.0027 0.0149 0.3992 0.0082 0.4110 ( 50 , 10 ) 0.0010 0.0015 0.0038 0.0008 0.0020 0.0012 ( 50 , 20 ) 0.0002 0.0007 0.0014 0.0004 -0.0006 0.0006 ( 100 , 6 ) 0.0004 0.0012 0.0030 0.0007 0.0011 0.0011 ( 100 , 10 ) 0.0002 0.0007 0.0013 0.0004 0.0002 0.0006 ( 100 , 20 ) 2.89E-06 0.0003 0.0009 0.0002 -0.0001 0.0003 (200, 6) 0.0001 0.0006 0.0013 0.0003 0.0004 0.0005 (200, 10) 2.89E-06 0.0003 0.0007 0.0002 0.0001 0.0003 (200, 20) 0.0004 0.0002 0.0006 0.0001 0.0001 0.0001

Table XXI. The performance of estimated TE scores setting M(‧)= y₁ ln(1y₁) ( ,  2, )= (0.025 , 1.88 , 1.66)

Model A Translog

( N , T ) Bias MSE Bias MSE ( 50 , 6 ) 0.0030 0.0093 0.0649 0.0833

( 50 , 10 ) 0.0048 0.0033 0.0508 0.0672 ( 50 , 20 ) 0.0214 0.0018 -0.2723 0.2523 ( 100 , 6 ) 0.0015 0.0065 0.0263 0.0452 ( 100 , 10 ) 0.0024 0.0029 0.0288 0.0342 ( 100 , 20 ) 0.0204 0.0017 -0.1862 0.2019 (200, 6) -0.0003 0.0060 0.0022 0.0111 (200, 10) 0.0009 0.0026 0.0044 0.0073 (200, 20) 0.0200 0.0016 0.0145 0.0722

Table XXII. Parameter estimates of the Translog model

Parametric Estimate Standard Error

Intercept 0.0086 0.2602

Table XXIII. Average AE and TE scores of the Translog model

Mean St. Dev.

AE (%) 89.21 0.1013

TE (%) 61.15 0.2033

國科會補助計畫衍生研發成果推廣資料表

日期:2011/07/18

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計畫名稱: A study of the economic efficiencies in East European countries using semiparametric approaches

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