The triangular model with random coefficients

Stefan Hoderlein (), Hajo Holzmann and Alexander Meister
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Stefan Hoderlein: Institute for Fiscal Studies and Boston College
Hajo Holzmann: Institute for Fiscal Studies
Alexander Meister: Institute for Fiscal Studies

No CWP33/15, CeMMAP working papers from Centre for Microdata Methods and Practice, Institute for Fiscal Studies

Abstract: The triangular model is a very popular way to capture endogeneity. In this model, an outcome is determined by an endogenous regressor, which in turn is caused by an instrument in a first stage. In this paper, we study the triangular model with random coefficients and exogenous regressors in both equations. We establish a profound non-identification result: the joint distribution of the random coefficients is not identified, implying that counterfactual outcomes are also not identified in general. This result continues to hold, if we confine ourselves to the joint distribution of coefficients in the outcome equation or any marginal, except the one on the endogenous regressor. Identification continues to fail, even if we focus on means of random coefficients (implying that IV is generally biased), or let the instrument enter the first stage in a monotonic fashion. Based on this insight, we derive bounds on the joint distribution of random parameters, and suggest an additional restriction that allows to point identify the distribution of random coefficients in the outcome equation. We extend this framework to cover the case where the regressors and instruments have limited support, and analyze semi- and nonparametric sample counterpart estimators in finite and large samples. Finally, we give an application of the framework to consumer demand.

Keywords: Random Coefficients; Endogeneity; Nonparametric; Identification; Radon Transform; Demand. (search for similar items in EconPapers)
Date: 2015-06-30
New Economics Papers: this item is included in nep-ecm
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Citations: View citations in EconPapers (21)

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Related works:
Journal Article: The triangular model with random coefficients (2017)
Working Paper: The Triangular Model with Random Coefficients (2016)
Working Paper: The triangular model with random coefficients (2015)
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