Strategy and Sample Selection: A Strategic Selection Estimator

The development and proliferation of strategic estimators has narrowed the gap between theoretical models and empirical testing. But despite recent contributions that extend the basic strategic estimator, researchers have continued to neglect a classic social science phenomenon: selection. Compared to nonstrategic estimators, strategic models are even more prone to selection effects. First, external shocks or omitted variables can lead to correlated errors. Second, because the systematic parts of actors' utilities usually overlap on certain key variables, the two sets of explanatory variables are correlated. As a result, both the systematic and the stochastic components can be correlated. However, given that the estimates for the first mover are computed based on the potentially biased predicted probabilities of the second actor, we also generate biased estimates for the first actor. In applied work, researchers neglect the potential shortcomings due to selection bias. This article presents an alternative strategic estimator that takes selection into account and allows scholars to obtain consistent, unbiased, and efficient estimates in the presence of both selection and strategic action. I present a Monte Carlo analysis as well as a real-world application to illustrate the superior performance of this estimator relative to the standard practice.