INTRODUCTION

In the last fifteen years there has been much work on identification of causal effects under weak conditions in settings with endogeneity. Earlier, researchers focused on linear systems with additive residuals. However, such systems are often difficult to motivate by economic theory. In many cases it is the nonlinearity of the system and the presence of unobserved heterogeneity in returns (and thus nonadditivity 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 solely on assumptions that are more tightly linked to economic theory. Such assumptions typically 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. Although much of the earlier literature on simultaneous equations focused on larger systems (in fact, much of the theoretical literature studied systems with an arbitrary number of endogenous regressors and an arbitrary number of instruments despite the rare occurrence of systems with more than two endogenous variables in empirical work and the practical difficulty of even finding a single credible instrument), many applications have this two-equation form and the framework is sufficiently rich for discussing the nature of the identification problems that are studied here.