The simplest econometric method for carrying out an estimation is, of course, OLS regression. However, the validity of OLS estimates depends critically on the homogeneity of the disturbance term of the equation. If the regression is run on panel data, the estimates are likely to be biased due to heterogenous intercepts and slopes.
To illustrate this problem, let us consider technical efficiency to be a linear function of the indicators of reform in the goods market, labour management, capital management and the tax system. The econometric model can then be written as:
Te, = a + ^ x , + u, (6.1) where X, = is a vector of socio-economic variables representing four
reform measures, (3 = (Pp[32,^3,^4) is the vector of corresponding coefficients, and is an error term with mean zero and variance O^. In the literature, this is caUed a pooled regression model.
A theoretical assumption underlying the OLS estimation is that the data are generated fi-om well-controUed experiments and the outcomes are random variables with a probability distribution that is a function of variables describing the conditions of the experiments. In our case, this means that the technical efficiency of each enterprise is generated by a parametric probability distribution function p{Te.^ / 0), where 9 is a four-dimensional vector, identical for all enterprises and in all six periods. The equation of the pooled regression model implies that the observations of variables are drawn from an identical probability distribution for each enterprise in each period, since all enterprises share the same parameters.
This assumption does not seem to be valid for this study. Two factors undermine the assumption. First, government policy towards state enterprises differs according to locality, which may in turn lead to a differing response from state enterprises to economic reforms (chapters 4 and 5). Second, the initial conditions for sample enterprises in 1980, such as their physical capital intensity or human capital, could vary greatiy among enterprises. The parameters of the probability distribution for different enterprises are therefore unlikely to be identical. In fact, our estimation results for technical efficiency revealed substantial inter-enterprise variation (Figures 5.1 and 5.2) in both heavy and light industrial sectors over the whole time period as well as in 1980 (Table 5.5). If we ignore such heterogeneity, we may come up with inconsistent and misleading estimates of the parameters of interest. This is called heterogeneity bias in the literature on panel data analysis.
In the case of panel data, heterogeneity bias can take place both among cross- sectional units in a particular time period and among observations in different time periods. In this study we call the former intra-temporal heterogeneity bias and the latter
170 inter-temporal heterogeneity bias. For simplicity, only the former case is illustrated here; inter-temporal bias can be understood in the same way. In the following discussion, it should be noted that inter-temporal homogeneity is implicitly assumed.
Three types of heterogeneity bias may occur when Te.^ is regressed on all other variables using the OLS method.^
Type 1: Intercept Heterogeneity and Slope Homogeneity
In this case, equation (6.1) will be written as:
+ for (6.2) where / = 1,..., N is the index of enterprises. In the literature, equation (6.2) is called the
individual-mean or ceU-mean corrected regression model. The coefficients of this equation are called within-group estimates.
Given that technical efficiency is consistently and positively correlated to the indicators of economic reform, the heterogenous intercept bias includes four cases. These are illustrated in Figures 6.1-6.4. In these figures, the broken-line circle represents the scatter point for an individual enterprise over time, and the broken line represents the true underlying relationship between technical efficiency and the indicators of economic reform (this wiU be the OLS regression line if we estimate observations for individual enterprises separately). The solid line represents the OLS regression line based on equation (6.1).
In case 1 (Figure 6.1), the OLS estimates understate the true coefficient, since the solid line is flatter than the broken lines. If the solid line were steeper, then the OLS estimates of (3 would overstate the true relationship between technical efficiency and reform indicators. In both situations, the estimates of p are biased.
In case 2 (Figure 6.2), the OLS estimates of (3 are unbiased since solid and broken lines have the same slope. They are not, however, efficient The estimates may turn out to be statistically insignificant, while the true relationship between efficiency and its explanatory variables is consistent across enterprises.
The two cases presented in Figures 6.3 and 6.4 cause even more serious concern. In the former case, the OLS estimate predicts that technical efficiency bears no relationship to economic reform measures; in the latter case, it points in the wrong direction. If the null hypothesis is that technical efficiency is positively correlated to economic reform posited in these figures, then from the statistic point of view, type I error will occur based on the OLS estimation. The OLS estimation will certainly lead to false inference in both cases.
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