Solving Problems in the Panel Regression Model for Truncated
Dependent Variables: A Constrained Optimization Method
5.2 Theoretical Implication
The above findings raise some potential problems that could significantly compromise the validity of political science research if the current panel regression method is applied to an analysis of a truncated dependent variable. The first concern is empirical boundary violations. Under no circumstances is a regression result that generates out-of-bound predicted value acceptable. Next, theoretical boundary violations must be considered. While some people might insist that regression results only explain the empirical data and do not extend to possible cases that do not appear in our sample, this view greatly limits the scope to which our analysis could apply. Third, in order to solve boundary violations with constrained optimization, different estimation methods must be into considered. The choice of least squares and maximum likelihood could generate very different results in panel data analysis. Fourth, if we select the least squares method, a full solution might not always be available, although we can always find a conditional solution that applies to a varying range of cases. On the other hand, despite the fact that maximum likelihood estimation is more likely to achieve a full solution, its results tend to be less significant.
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