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Cowles Foundation Discussion Papers

2015

Nonparametric identification

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Full-Text Articles in Economics

Identification In Differentiated Products Markets, Steven T. Berry, Philip A. Haile Aug 2015

Identification In Differentiated Products Markets, Steven T. Berry, Philip A. Haile

Cowles Foundation Discussion Papers

Empirical models of demand for — and, often, supply of — differentiated products are widely used in practice, typically employing parametric functional forms and distributions of consumer heterogeneity. We review some recent work studying identification in a broad class of such models. This work shows that parametric functional forms and distributional assumptions are not essential for identification. Rather, identification relies primarily on the standard requirement that instruments be available for the endogenous variables — here, typically, prices and quantities. We discuss the kinds of instruments needed for identification and how the reliance on instruments can be reduced by nonparametric functional …


Identification Of Nonparametric Simultaneous Equations Models With A Residual Index Structure, Steven T. Berry, Philip A. Haile Jul 2015

Identification Of Nonparametric Simultaneous Equations Models With A Residual Index Structure, Steven T. Berry, Philip A. Haile

Cowles Foundation Discussion Papers

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 …


Identification Of Nonparametric Simultaneous Equations Models With A Residual Index Structure, Steven T. Berry, Philip A. Haile Jul 2015

Identification Of Nonparametric Simultaneous Equations Models With A Residual Index Structure, Steven T. Berry, Philip A. Haile

Cowles Foundation Discussion Papers

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.