Advances in Economics and Econometrics: Nonadditive Models with Endogenous Regressors

In the last fifteen years there has been much work on nonparametric identification of causal effects in settings with endogeneity. Earlier, researchers focused on linear systems with additive residuals. However, such systems are difficult to motivate by economic theory. In many cases it is precisely the nonlinearity of the system and the presence of unobserved heterogeneity in returns (and thus non-additivity in the residuals) that leads to the type of endogeneity problems that economists are concerned with. In the more recent literature researchers have attempted to characterize conditions for identification that do not rely on such functional form or homogeneity assumptions, instead relying on assumptions that are more tightly linked to economic theory. Such assumptions often include exclusion and monotonicity restrictions and (conditional) independence assumptions. In this paper I will discuss part of this literature. I will focus on a two-equation triangular (recursive) system of simultaneous equations with a single endogenous regressor and a single instrument, with the main interest in the outcome equation relating the outcome to the (endogenous) regressor of interest. The discussion will include settings with binary, continuous, and discrete regressors. JEL Classification: C14, C21, C52

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