Testing the Correlated Random Coefficient Model

69 Pages Posted: 3 Nov 2009 Last revised: 25 May 2012

See all articles by James J. Heckman

James J. Heckman

University of Chicago - Department of Economics; National Bureau of Economic Research (NBER); American Bar Foundation; Institute for the Study of Labor (IZA); CESifo (Center for Economic Studies and Ifo Institute)

Daniel Schmierer

University of Chicago - Department of Economics

Sergio Urzua

Northwestern University

Multiple version iconThere are 2 versions of this paper

Date Written: October 2009

Abstract

The recent literature on instrumental variables (IV) features models in which agents sort into treatment status on the basis of gains from treatment as well as on baseline-pretreatment levels. Components of the gains known to the agents and acted on by them may not be known by the observing economist. Such models are called correlated random coefficient models. Sorting on unobserved components of gains complicates the interpretation of what IV estimates. This paper examines testable implications of the hypothesis that agents do not sort into treatment based on gains. In it, we develop new tests to gauge the empirical relevance of the correlated random coefficient model to examine whether the additional complications associated with it are required. We examine the power of the proposed tests. We derive a new representation of the variance of the instrumental variable estimator for the correlated random coefficient model. We apply the methods in this paper to the prototypical empirical problem of estimating the return to schooling and find evidence of sorting into schooling based on unobserved components of gains.

Suggested Citation

Heckman, James J. and Schmierer, Daniel and Urzua, Sergio Samuel, Testing the Correlated Random Coefficient Model (October 2009). NBER Working Paper No. w15463. Available at SSRN: https://ssrn.com/abstract=1498964

James J. Heckman (Contact Author)

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Daniel Schmierer

University of Chicago - Department of Economics ( email )

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United States

Sergio Samuel Urzua

Northwestern University ( email )

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Evanston, IL 60208
United States

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