Identifying Structural Effects in Nonseparable Systems Using Covariates

This paper demonstrates the extensive scope of an alternative to standard instrumental variables methods, namely covariate-based methods, for identifying and estimating effects of interest in general structural systems. As we show, commonly used econometric methods, specifically parametric, semi-parametric, and nonparametric extremum or moment-based methods, can all exploit covariates to estimate well-identified structural e§ects. The systems we consider are general, in that they need not impose linearity, separability, or monotonicity restrictions on the structural relations. We consider effects of multiple causes; these may be binary, categorical, or continuous. For continuous causes, we examine both marginal and non-marginal effects. We analyze effects on aspects of the response distribution generally, designed by explicit or implicit moments or as optimizers (e.g., quantiles). Key for identification is a specific conditional exogeneity relation. We examine what happens in its absence and find that identification generally fails. Nevertheless, local and near identification results hold in its absence, as we show.