Econometrica: Jan 2018, Volume 86, Issue 1
Identification of Nonparametric Simultaneous Equations Models with a Residual Index Structure
Steven T. Berry, Philip A. HaileWe 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 results demonstrate identification when instruments have only limited variation. Even when instruments vary only over a small open ball, relatively mild conditions on the joint density suffice. We also show that the primary sufficient conditions for identification are verifiable and that the maintained hypotheses of the model are falsifiable.
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Supplement to "Identification of Nonparametric Simultaneous Equations Models with a Residual Index Structure"
Berry and Haile (2017) consider identification in a class of nonparametric simultaneous equations models, providing several combinations of sufficient conditions on the joint density of structural errors and the support of instruments. We show here that, even when the instruments vary only over a small open ball, their requirements on the joint density may be viewed as mild in at least one formal sense.