TY  - JOUR
AU  - Heckman,James J.
AU  - Schmierer,Daniel A.
AU  - Urzua,Sergio S.
TI  - Testing the Correlated Random Coefficient Model
JF  - National Bureau of Economic Research Working Paper Series
VL  - No. 15463
PY  - 2009
Y2  - October 2009
UR  - http://www.nber.org/papers/w15463
L1  - http://www.nber.org/papers/w15463.pdf
N1  - Author contact info:
James J. Heckman
Department of Economics
The University of Chicago
1126 E. 59th Street
Chicago, IL 60637
Tel: 773/702-0634
Fax: 773/702-8490
E-Mail: jjh@uchicago.edu

Daniel A. Schmierer
Department of Economics
University of Chicago
1126 E. 59th Street
Chicago  IL  60637
E-Mail: dschmier@uchicago.edu

Sergio S. Urzua
Department of Economics
Northwestern University
2001 Sheridan Road
Evanston, IL 60208
Tel: 847/491-8213
Fax: 847/491-7001
E-Mail: s-urzua@northwestern.edu
AB  - 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.
ER  -