This study focuses explicitly on the methodological implications of the endogenous theory of governance as applied to firm performance. In particular, if firms choose their governance structures as part of a constrained performance maximization process, then application of an appropriate empirical methodology should reveal statistical evidence of such behavior. In this study we take advantage of the endogenous switching regression model framework to determine whether such predicted optimizing behavior can be corroborated by the data. The model allows us to test explicitly for selection behavior in accordance with comparative advantage and, concomitantly, the presence of selectivity bias, in estimating the impact of CEO duality on firm performance. The selection and performance equations are modeled in accordance with the extant accounting, economics, and management literature on the impact of the dual governance structure on firm performance. Overall, we tested four performance measures for the entire sample of firm-year observations as well as for the largest three industries in terms of sample sizes. The major finding, robust in all cases, is that there is no evidence to support a contention that CEO duality is a structure purposefully chosen for optimizing performance. If firms are indeed choosing the dual leadership structure, they are doing so for reasons other than improving performance from what it would be otherwise. In fact, for performance measured as market return and earnings per share, there is evidence of a significant selectivity bias that acts to lower performance below what it would have been under random assignment. For performance measured by Tobin's q and return on assets, we found neither evidence of selectivity bias, nor any significant marginal performance impacts of CEO duality. Such findings are inconsistent with an endogenous governance theory, at least when applied to firm performance.