Dependent Variables: A Constrained Optimization Method

The methodological problems of the panel regression can be summarized and put into three
categories: boundary violations, parameter estimation, and model specification. Throughout this paper, I use the
example in the first column of Table 1 from Thomas Hansford and Brad Gomez's 2010
article "Estimating the Electoral Effects of Voter Turnout" from *American Political Science Review*
to discuss these problems and present the results of the revised models. The dependent variable is county-level
democratic vote share in presidential elections from 1948 to 2000. The independent variables include (1)
*Partisan composition*, measured as the moving average of the Democratic vote share in the three most recent
elections, (2) *Turnout*, meaning voter turnout, (3) the two interaction terms *Turnout$\times$GOP Incumbent*
and *Turnout$\times$Partisan composition*, where *GOP Incumbent* is a dummy variable for a presidential
election in which the incumbent is Republican, and (4) 13 time dummy variables indicating the temporal units from 1952
to 2000. The default category, represented by the constant, is the presidential election in 1948 in which the incumbent
is Democrat. The dataset, comprised of typical TSCS data with a sample size of 27401 that covers 1964 counties and 14
presidential elections, was compiled by the two authors from various sources. We confine our discussion to the
fixed-effect model.