The Triangular Model with Random Coefficients

Stefan Hoderlein, Hajo Holzmann and Alexander Meister
Additional contact information
Hajo Holzmann: Marburg University
Alexander Meister: University of Rostock

No 894, Boston College Working Papers in Economics from Boston College Department of Economics

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: 2015-06-24, Revised 2016-02-01
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://fmwww.bc.edu/EC-P/wp894.pdf main text (application/pdf)

Related works:
Journal Article: The triangular model with random coefficients (2017)
Working Paper: The triangular model with random coefficients (2015)
Working Paper: The triangular model with random coefficients (2015)
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:boc:bocoec:894

Access Statistics for this paper

More papers in Boston College Working Papers in Economics from Boston College Department of Economics Boston College, 140 Commonwealth Avenue, Chestnut Hill MA 02467 USA. Contact information at EDIRC.
Bibliographic data for series maintained by Christopher F Baum ().