We present new results on the identiﬁability of a class of nonseparable nonparametric simultaneous equations models introduced by Matzkin (2008). These models combine exclusion restrictions with a requirement that each structural error enter through a “residual index.” Our identiﬁcation results encompass a variety of special cases allowing tradeoﬀs between the exogenous variation required of instruments and restrictions on the joint density of structural errors. Among these special cases are results avoiding any density restriction and results allowing instruments with arbitrarily small support.
Berry, Steven T. and Haile, Philip A., "Identification of Nonparametric Simultaneous Equations Models with a Residual Index Structure" (2015). Cowles Foundation Discussion Papers. 2443.