Tables 5 and 6 present parameter estimates of the production and selection equations for the two chosen industries. Columns 1-4 of the upper panel, respectively, list estimates of OLS, Heckman’s sample selection model, the conventional SFA, and the SFA with sample selection (SFAS) of Lai et al. (2009).6 These four models do not take the simultaneity problem into account, since the unobserved productivity
is precluded from the production function. Columns 5-6 of the upper panel summarize estimates of OP/LP and our proposed SFSS model, respectively. The latter two models consider both simultaneity and selection problems, but the SFSS further generalizes the OP/LP model to a stochastic frontier framework.[Table 5 and Table 6 here]
The OLS estimates of labor and capital are 1.000 (1.081) and 0.153 (0.170) for the case of electronics (food products) industry. The sum of the two coefficients is equal to 1.153 (1.251), suggesting that these plants in both industries are operating under technology of increasing returns to scale. The coefficient of labor is found to be more than six times as large as that of capital in both industries. One may suspect that labor coefficient is inclined to be overestimated, while capital coefficient
The estimation procedure is similar to (16). Note that their model ignores the simultaneity problem.
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simultaneity and selectivity problems, where the former problem entails an upward bias in the labor coefficient and a downward bias in the capital coefficient and the latter problem incurs a downward bias in the capital coefficient, as pointed out by OP.Column 2 gives the corrected estimates from the Heckman’s (1979) sample selection model. Estimated
that describes the correlation between unobserved determinants of propensity to exit the market
it and unobserved determinants of outputv
it for electronics (food products) industry is statistically significant, suggesting that the unobservables (i.e.,I
it
0) is correlated with one another (i.e.,it 1
I
). The correlation further implies the firm’s liquidation decision affects its production non-randomly and hence affects its production process. Compared to the OLS estimates, the coefficient of labor is slightly decreased, but the coefficient of capital is slightly increased in both industries.Columns 3 and 4 include an extra non-negative random variable
u ,
representing technical inefficiency, in the production function, while the unobserved productivity
it is still excluded from the two models. Column 3 corresponds to the conventional SFA and Column 4 is the SFAS model that considers a firm’s liquidation decision. Differing from the OLS and the Heckman’s approach, attributing all deviations from the production frontier to noise (e.g., measurement error, random shocks, etc.), the stochastic frontier framework assigns all deviations to both noise and inefficiency. For the case of electronics (food products) industry, the estimated labor coefficient of the SFA is slightly decreased, but the estimated capital coefficient is somewhat increased as compared to the OLS results. Similar outcomes can be detected from the SFAS estimates. In sum, the coefficient estimates of labor and capital are, respectively, decreased and increased when technical inefficiency is included in the production function, irrespective of the liquidation decision.Aside from the foregoing four models, columns 5 and 6 present the parameter
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methods deal with the problems of simultaneity and selectivity, but the SFSS further deliberates technical inefficiency. To eliminate the positive bias of the labor coefficient, we reformulate the SFSS model to a semi-parametric stochastic frontier model of (11) to control for the unobserved productivity and re-estimate the production function. This leads to a consistent parameter estimate of labor. For the case of electronics (food products) industry, the labor coefficients in columns 5 and 6 are 0.927 and 0.900 (0.819 and 0.809), respectively, which are 7.30% and 10.00%(24.93% and 25.07%) lower than those of OLS.
The above results confirm that the production function considering the unobserved productivity is indeed able to fix the upward bias in labor coefficient at least to some extent. In addition, the upward bias of labor coefficient in food products industry is much larger than in the electronics industry. This uncovers that firms’
decision on labor hiring in food products industry is positively and more closely related to their current productivity
t than in the electronics industry. One possible explanation is that labor input plays a more important role in food products plants than in electronics plants that undertake a highly capital-intensive technology.We next attempt to estimate
k after correcting for selection in the production function. OP/LP recommend the use of polynomial series expansion in1 1 1
ˆ
it( ˆ
it kk
it)
h
and predicted survival probabilitiesP ˆ
it to control for both simultaneity and selectivity. Note that our SFSS model uses powers ofh ˆ
it1 to control for simultaneity in production frontier and uses selection equation to simultaneously account for firm’s decision of exit, in addition to consider potential production inefficiency. Our estimation results of the electronics industry show that the capital coefficient increases from 0.153 (OLS) to 0.191 for the OP/LP and to 0.250 for the SFSS model, indicating that the capital coefficients of the OP/LP and SFSS are, respectively, raised by 24.84% and 63.40% relative to that of OLS. This is congruent with the expectation that the presence of simultaneity and selection‧
problems is likely to predict a downward bias in coefficient of capital. Moreover, the capital coefficient of SFSS is about 30.89% higher than the OP/LP. This validates the inclusion of technical inefficiency in the production function. Likewise, both capital coefficients of OP/LP and SFSS in food products industry are greater than that of OLS and the capital coefficient of SFSS exceeds that of OP/LP.
Except for the consideration of technical inefficiency, our SFSS has another exclusive feature. That is, it explicitly models production frontier and selection equation as simultaneous equations. Such a model of structural equations is better to be jointly estimated like our SFSS. Conversely, OP/LP implicitly assume production function and selection equation to be uncorrelated and thus suggest using the two-step method to remove the selection bias. Since the SFSS results in the estimated values of the dependence being equal to 0.981 and 0.740 for the two industries, the uncorrelation assumption may not be desirable.
When both simultaneity and selectivity biases are eliminated and technical inefficiency is incorporated, the ratio of labor share to capital share is reduced from 6.535( 1.000 / 0.153)
to 3.600 0.900 / 0.250
for electronics industry and from 6.359( 1.081/ 0.170)
to 3.275 0.809 / 0.247
for food products industry. The measure of returns to scale in electronics (food products industries) lowers from 1.152 to 1.150 (from 1.251 to 1.056). The finding of increasing returns to scale seems to be reasonable, since most of the sample plants are small- and medium-sized as pointed out in the Chapter 5 of data description. These plants are anticipated to be operating at the decreasing portion of the long-run average costs.The determinants of a plant’s liquidation are also important. The less sunk costs and the older the plants are, the more likely they choose to stay in the market.
However, the former results contradict most of empirical studies, e.g., Dunne and Roberts (1991) and Fotopoulos and Spence (1998), that assert that capital requirements are barriers to exit. Moreover, a depreciation in domestic currency has
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likelihood of staying the market. Surprisingly, the economic condition has negative effect on the probability of staying in the market.[Table 7 and Table 8 here]
6.1 Productivity and Technical Efficiency
Given the parameter estimates of the production frontier, shown in Tables 5 and 6, we can calculate the firm-specific productivity measure, which is formulated as7
ˆ ˆ
1998-1999, 1999-2000, and 2003-2004, where 1998-1999 and 2003-2004 are recessionary periods and 1999-2000 is expansionary period.8First, the results show that the SFSS model in chosen industries yields lowest mean rate of productivity growth, indicating that models ignoring unobserved productivity (such as, OLS, Heckman, SFA, SFAS), technical inefficiency (OP/LP), or selectivity, tend to over-predict firms’ productivity growth. These over-predictions in the first five models may be attributed to high estimated labor coefficient and low estimated capital coefficient. Second, the productivity growth of electronics industry is generally higher than that of the food products industry. Third, the productivity growth in the expansionary year is higher than in the recessionary year as what we expect. However, the food products firms always have negative productivity changes, regardless of the state of the economy.
7 This measure is also referred to as the Solow residual.
8 Information on the date of the expansion and contraction over business cycles is judged by the Council for economic Planning and Development (CEPD), a central government bureau of Taiwan.
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立 政 治 大 學
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N a tio na
l C h engchi U ni ve rs it y
[Table 9, Table 10, Figure 1 and Figure 2 here]
Tables 9 and 10 present descriptive statistics of the TE measures for both industries. Clearly, there are significant differences in TE scores among models of SFA, SFAS and SFSS. Their average TE scores in electronics industry are 50.024%, 63.858%, and 61.470%, respectively. On the other hand, the mean TE score (standard deviation) of food products industry for the three models are 54.919% (11.762%), 35.814% (16.916%), and 78.899% (3.730%), respectively. These average TE measures of food products industry show that the TE measures from the SFA and the SFAS are respectively 43.664% and 77.970% lower than that of the SFSS. The foregoing reflects that the omission of simultaneity and/or selectivity can cause a severe downward bias in TE, especially for the food products industry. Figures 1 and 2 plot the kernel density functions of TE scores for the three frontier models and the two industries. As far as the electronic industry is concerned, the curves of the SFSS and SFAS are close to each other, but they lie on the right of the kernel density of the SFA, since their TE estimates exceed those of the SFA very much. For the food products industry, the kernel density function of the TE measure from the SFSS locates at the rightmost and the remaining two curves situate on its left-hand side.
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Before comparing technical efficiency between continuing and exit firms, the sample selection bias must be considered when estimating group-specific production frontiers.
In the first step, we estimate the probit model with the determinants that explain plants’ liquidation decisions and, in the second step, use the predicted probabilities to estimate the production frontiers of (7) and (23) for the two groups by adopting algorithm introduced in Chapter 3.
[Table 11 here]
Table 11 reports the estimation results of group-specific stochastic frontiers.
Using these estimates, we can test for the null hypothesis that exit and staying plants share the same technology. The LR test statistic is significant at the 1% level of significance in both industries, and hence the null hypothesis is rejected. One is led to conclude that the two types of plants are operating under heterogeneous technologies.
[Table 12 here]
Table 12 reports estimates of the metafrontier obtained by SMF and NP approaches. Except for the estimates of series expansions