semi-parametric stochastic regression in which the unobserved productivity is under control by capital and intermediate input (electricity expense). Estimating the semi-parametric model leads to consistent parameter estimate of labor. Next, we follow OP/LP’s algorithm, along with selection equation, to eliminate simultaneity and selectivity biases, assuming the presence of potential technical inefficiency. In order to jointly estimate the production frontier and selection equation, we introduce the copula function to model the dependence structure of their residuals. On the basis of the above framework, this dissertation further performs a metafrontier analysis to compare the TGR and metafrontier TE between exit and continuing firms.
Some interesting results are worth mentioning. First, the SFSS model can solve the problems of simultaneity and selectivity in the context of a production frontier where the two problems would cause a upward bias in labor coefficient and a downward bias in capital coefficient. Second, the omission of simultaneity and sample selection, such as the conventional stochastic frontier model, is found to incur a serious downward bias in the estimate of technical efficiency. Third, the results of metafrontier analysis confirm that there is little difference in TGR between exit and continuing firms, which implies that the primary determinant on whether a firm can keep operating in the industry is its managerial ability, rather than its adoption of technology.
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Appendix A. Deriving the Likelihood Function of the SFSS Model
We follow the procedure of Lai et al. (2009) to derive the likelihood function of the SFSS introduced in Chapter 3. Equations (14) and (15) are repeated as follow
1 and
f
(·) their corresponding pdfs. According to the Sklar’s theorem, there exists a unique copula functionC
(·) such that( , ) ( ( ), ( )),
F
C F
F
(A3)and
C
(·) is unique if bothF
(·) andF
(·) are continuous.Since
y
it* in (A1) is only observed whenI
it 1
in the selection regression, we can modify (A3) to build conditional probability of
:
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log-likelihood function given by (A8) can be written as
The log-likelihood functions (A11) and (16) are the same.
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Define a sign function as:
1, if 0;
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Figure 1: Technical Efficiency Measures, Electronics Industry.
Figure 2: Technical Efficiency Measures, Food Products Industry.
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(a) Stochastic metafrontier analysis
(b) Nonlinear programming method
Figure 3: TGR of Continuing and Exit Firms, Electronics Industry
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(a) Stochastic metafrontier analysis
(b) Nonlinear programming method
Figure 4: TGR of Continuing and Exit Firms, Food Product Industry
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(a) Stochastic metafrontier analysis
(b) Nonlinear programming method
Figure 5:
TE Score of Continuing and Exit Firms, Electronics Industry
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(a) Stochastic metafrontier analysis
(b) Nonlinear programming method
Figure 6:
TE score of Continuing and Exit Firms, Food Product Industry
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Table 1: Descriptive Statistics, Electronics Industry Panel A: All Firms
# of
Obs. # of Firms Mean Median Std. Dev. Minimum Maximum Output
(value-added) 16344 5512 314833.662 23757.154 2541198.781 8.745 1.43738E+8
Labor 16344 5512 115.473 28.000 400.434 1.000 14533.000
Capital 16344 5512 337110.422 8874.771 4116611.128 1.698 2.71092E+8 Electricity 16344 5512 6073.872 390.623 44130.733 0.947 2304933.750
CPTL2OUTPUT 16344 5512 0.623 0.160 11.412 0.000 1422.703
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Table 2: Descriptive Statistics, Food Products Industry Panel A: All Firms
# of
Obs. # of Firms Mean Median Std. Dev. Minimum Maximum Output
(value-added) 8303 2535 88473.283 8988.226 400718.803 3.825 12636700.000
Labor 8303 2535 45.211 13.000 124.868 1.000 6399.000
Capital 8303 2535 35693.318 3032.811 202730.714 1.588 7867883.500 Electricity 8303 2535 3108.244 414.148 12697.164 0.949 330558.531
CPTL2OUTPUT 8303 2535 0.575 0.139 3.479 0.000 160.928
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Table 3: Correlation Coefficient of Variables, Electronics Industry
(A) Correlation Coefficient: Variables of Production Function Output
(value-added) Labor Capital Electricity Output
(B) Correlation Coefficient: Variables of Selection Regression
It Capital Electricity CPTL2OUTPUT AGE PCM GDPForecast EXCHANGE
It 1.000 Note: (a) Symbols ***, **, and * denote significance at the 1%, 5%, and 10% levels, respectively. (b) Numbers in parentheses are t statistics.
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Table 4: Correlation Coefficient of Variables, Food Products Industry
(A) Correlation Coefficient: Variables of Production Function Output
(value-added) Labor Capital Electricity Output
(B) Correlation Coefficient: Variables of Selection Regression
It Capital Electricity CPTL2OUTPUT AGE PCM GDPForecast EXCHANGE
It 1.000 Note: (a) Symbols ***, **, and * denote significance at the 1%, 5%, and 10% levels, respectively; (b) Numbers in parentheses are standard errors.
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Table 5: Parameter Estimates of the Electronics Industry
Without Unobserved Productivity With Unobserved Productivity
Capital and Electricity YES YES YES
1.460*** 0.827*** 0.904***
Note: (a) Symbols ***, **, and * denote significance at the 1%, 5%, and 10% levels, respectively. (b) Numbers in parentheses are standard errors.
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Table 6: Parameter Estimates of the Food Products Industry
Without Unobserved Productivity With Unobserved Productivity
Capital and Electricity YES YES YES
1.213*** 3.009*** 0.428***
Note: (a) Symbols ***, **, and * denote significance at the 1%, 5%, and 10% levels, respectively. (b) Numbers in parentheses are standard errors.
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Table 7: Average Firm-specific Productivity Changes of the Electronics Industry Without Unobserved Productivity With Unobserved Productivity
OLS Heckman SFA SFAS OP/LP SFSS
(1) (2) (3) (4) (5) (6)
1998-1999 -0.647% -0.808% -1.101% -0.814% -1.854% -5.230%
1999-2000 5.798% 5.655% 5.388% 5.626% 4.546% 4.381%
2003-2004 0.192% 0.102% -0.067% 0.086% -0.543% -1.136%
Table 8: Average Firm-specific Productivity Changes of the Food Products Industry Without Unobserved Productivity With Unobserved Productivity
OLS Heckman SFA SFAS OP/LP SFSS
(1) (2) (3) (4) (5) (6)
1998-1999 -2.351% -2.816% -2.762% -2.745% -4.370% -5.443%
1999-2000 -1.243% -0.995% -0.958% -0.953% -1.905% -2.677%
2003-2004 -3.742% -4.006% -3.979% -3.964% -4.931% -5.653%
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Table 9: Descriptive Statistics of Technical Efficiency, Electronics Industry
Technical Efficiency Mean Median Standard Deviation
SFA 0.50024 0.49933 0.12420
SFAS 0.63858 0.64155 0.08689
SFSS 0.61470 0.62087 0.10006
Table 10: Descriptive Statistics of Technical Efficiency, Food Products Industry
Technical Efficiency Mean Median Standard Deviation
SFA 0.543919 0.546093 0.117619
SFAS 0.358143 0.331322 0.169162
SFSS 0.78899 0.79087 0.037304
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Table 11: The Group-specific Stochastic Frontier Estimates
Electronics Firms Food Product Firms
Exit Firms Continuing
Note: (a) Symbols ***, **, and * denote significance at the 1%, 5%, and 10% levels, respectively. (b) Numbers in parentheses are standard errors. (c) The critical value at the 1% level with 10 degrees of freedom is 23.209.
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Table 12: The Estimates of the Industry’s Metafrontier
Electronics Firms Food Product Firms
Stochastic
Note: (a) Symbols ***, **, and * denote significance at the 1%, 5%, and 10% levels, respectively. (b) Numbers in parentheses are standard errors.
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Table 13: Summary Statistics of Industry Efficiency Measures Panel (A): Electronics Industry
Stochastic Metafrontier NP Metafrontier
Mean Std. Dev. Min Max Mean Std. Dev. Min Max
(t-statistics) (0.804) (51.884)
Diff TEM 0.021*** 0.070***
(t-statistics) (7.472) (53.296)
Panel (B): Food Product Industry
Stochastic Metafrontier NP Metafrontier
Mean Std. Dev Min Max Mean Std. Dev Min Max
(t-statistics) (-0.060) (171.177)
Diff TEM 0.093*** 0.277***
(t-statistics) (27.224) (152.001)
Note: (a) Symbols ***, **, and * denote significance at the 1%, 5%, and 10% levels, respectively. (b) Numbers in parentheses are standard errors.