Fixing Boundary Violations: Applying Constrained
Optimization to the Truncated Regression Model
Abstract
Much political science research involves analysis of a dependent variable that has boundary restrictions. In econometric textbooks, these studies should apply the truncated regression model, otherwise the OLS estimate is likely to generate out-of-bounds predicted values. However, political scientists seldom use truncated regression and are unaware of this methodological problem. In this article, I investigate this issue and finds that both the OLS and truncated regression models suffer from boundary violations. To resolve this problem, I propose a revised truncated regression model with constrained optimization and successfully eliminates boundary violations. Simulation results found via various settings confirm the superiority of the revised model. Further analysis indicates that hypothesis testing results are quite sensitive if different models are applied. This finding significantly challenges the appropriateness of the current model. Through a replication study, I demonstrate how the revised model can be applied to political studies and why it is preferable to OLS and the current truncated regression model.
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