Identification of Nonparametric Simultaneous Equations Models with a Residual Index Structure

We present new identification results for a class of nonseparable nonparametric simultaneous equations models introduced by Matzkin (2008). These models combine traditional exclusion restrictions with a requirement that each structural error enter through a “residual index.” Our identification results are constructive and encompass a range of special cases with varying demands on the exogenous variation provided by instruments and the shape of the joint density of the structural errors. The most important of these results demonstrate identification even when instruments have limited variation. A genericity result demonstrates a formal sense in which the associated density conditions may be viewed as mild, even when instruments vary only over a small open ball.