Strategic misspecification in regression models

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) misspecification. The misspecification can be equivalently written as a form of omitted variable bias, where the omitted variables are nonlinear terms arising from the players' expected utility calculations and often from data aggregation. We characterize the extent of the specification error in terms of model parameters and the data and show that typical regressions models can at times give exactly the opposite inferences versus the true strategic data-generating process. Researchers are recommended to pay closer attention to their theoretical models, the implications of those models concerning their statistical models, and vice versa.