Strategic Misspecification in Regression Models

Abstract

Common regression models are often structurally inconsistent with strategic interaction. We demonstrate that this "strategic misspecification" is really an issue of structural (or functional form) (Signorino 1999(Signorino , 2000Smith 1999) suggests that, when analyzing strategic behavior on the part of individuals or states, failure to reflect that strategic interaction in one's statistical model can result in invalid inferences. Signorino (1999) demonstrates this with a Monte Carlo example in which the inferences from logit regressions are far from (at times completely opposite to) the strategic data-generating process. Signorino (1999), however, is not a complete analysis of the misspecification, but more a warning and demonstration that the misspecification exists. As of yet, the form of the misspecification has not been characterized in a way that most practitioners readily understand or in a manner that allows us to state when the effects of strategic misspecification should be mild versus severe. The primary goal of this article is to do exactly that.As we demonstrate in this article, strategic misspecification is really an issue of structural (or functional form) misspecification. Because this type of misspecification is not well known among political scientists, we begin in the next section by illustrating the problem of functional form misspecification as it applies to the classical linear regression model. It is easy to show in this case that functional form misspecification is actually a type of omitted variable bias, where the omitted variables are nonlinear terms in a Taylor series approximation of the true functional form.We then move to the strategic setting and construct what we believe is the simplest model possible: a twoplayer deterrence game. We assume the data in this case represents whether a particular outcome (war) has occurred or not, and we analyze the misspecification of using logit or probit with the ubiquitous linear X B specification of the latent variable equation. As in the OLS case, it is easy to rewrite the strategic misspecification as a form of omitted variable bias, where the omitted variables are nonlinear terms in a Taylor series expansion of the true functional form and where the nonlinearity is due to the players' expected utility calculations. Because of the misspecification, parameter estimates are not only biased, but inconsistent. Therefore, throwing more data at the problem does not make it go away.In the third section, we analyze the misspecification when the dependent variable is the action taken by the first player, the attacker. By construction, this choice is

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