Identifying Structural Effects in NonseparableSystems Using Covariates

This paper demonstrates the extensive scope of an alternative to standardinstrumental variables methods, namely covariate-based methods, for identifying and es-timating effects of interest in general structural systems. As we show, commonly usedeconometric methods, speci…cally parametric, semi-parametric, and nonparametric ex-tremum or moment-based methods, can all exploit covariates to estimate well-identi…edstructural e¤ects. The systems we consider are general, in that they need not impose lin-earity, separability, or monotonicity restrictions on the structural relations. We considere¤ects of multiple causes; these may be binary, categorical, or continuous. For continu-ous causes, we examine both marginal and non-marginal e¤ects. We analyze e¤ects onaspects of the response distribution generally, de…ned by explicit or implicit moments oras optimizers (e.g., quantiles). Key for identi…cation is a speci…c conditional exogeneityrelation. We examine what happens in its absence and …nd that identi…cation generallyfails. Nevertheless, local and near identi…cation results hold in its absence, as we show....