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1.3 Empirical Validations

The first case is Timothy Hellwig and David Samuels's 2007 article, "Voting in Open Economies: The Electoral Consequences of Globalization" in Comparative Political Studies. I replicate Model I and II in Table 1 (p.292), which explains the incumbent party's vote share and find that the least predicted vote shares are $-4.797\%$ and $-3.163\%$ by OLS, and $-7.938\%$ and $-5.874\%$ by TRM.

[Replication of Hellwig and Samuels (2007)]

The second case is Thomas Hansford and Brad Gomez's 2010 article, "Estimating the Electoral Effects of Voter Turnout" in American Political Science Review. I replicate the model in the column 2 of Table 1 (p.277) that conducts an F-test for excluded instruments. The dependent variable is aggregate-level voter turnout when the incumbent is Republican. The least predicted value is $-8.287\%$ by OLS, and $-24.277\%$ by TRM.

[Replication of Hansford and Gomez (2010)]

The third case is Daron Acemoglu et al.'s 2008 article, " Income and Democracy" in American Economic Review. I replicate the pooled and fixed-effects OLS that explain the level of democracy in Table 2 (p.816). The dependent variable is a normalized Freedom House measure of democracy, ranging from $0$ to $1$. The least and greatest predicted values for the pooled model are $-0.031$ and $1.065$ by OLS and $-0.103$ and $1.202$ by TRM. For the fixed-effects model, the least and greatest predicted values are $-0.052$ and $1.077$ by OLS, and $-0.147$ and $4.488$ by TRM.

[Replication of Acemoglu et al. (2008)]

None of the three articles explains why the TRM model is not used, nor explains how to interpret the out-of-bounds predicted values. This scenario indicates that the current version of the TRM model is not widely perceived as the default method among political scientists. Moreover, if the TRM model were used, the problem of boundary violations would have been more significant considering the replication results. Therefore, even though the application of the OLS model is clearly at odds with the distributional assumption, most political scientists are not aware of this methodological problem. And thus far, there is no solution in the field to simultaneously resolve the violations of the distributional assumption and boundary restrictions.

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