TY - JOUR
AU - Lochner,Lance
AU - Moretti,Enrico
TI - Estimating and Testing Models with Many Treatment Levels and Limited Instruments
JF - National Bureau of Economic Research Working Paper Series
VL - No. 17039
PY - 2011
Y2 - May 2011
DO - 10.3386/w17039
UR - http://www.nber.org/papers/w17039
L1 - http://www.nber.org/papers/w17039.pdf
N1 - Author contact info:
Lance Lochner
Department of Economics, Faculty of Social Science
University of Western Ontario
1151 Richmond Street, North
London, ON N6A 5C2
CANADA
Tel: 519/661-2111 ext. 85281
Fax: 519/661-3666
E-Mail: llochner@uwo.ca
Enrico Moretti
University of California, Berkeley
Department of Economics
549 Evans Hall
Berkeley, CA 94720-3880
Tel: 510/642 6649
Fax: 510/643 7042
E-Mail: moretti@econ.berkeley.edu
AB - Many empirical microeconomic studies estimate econometric models that assume a single finite-valued discrete endogenous regressor (for example: different levels of schooling), exogenous regressors that are additively separable and enter the equation linearly; and coefficients (including per-unit treatment effects) that are homogeneous in the population. Empirical researchers interested in the causal effect of the endogenous regressor often use instrumental variables. When few valid instruments are available, researchers typically estimate restricted specifications that impose uniform per-unit treatment effects, even when these effects are likely to vary depending on the treatment level. In these cases, ordinary least squares (OLS) and instrumental variables (IV) estimators identify different weighted averages of all per-unit effects, so the traditional Hausman test (based on the restricted specification) is uninformative about endogeneity. Addressing this concern, we develop a new exogeneity test that compares the IV estimate from the restricted model with an appropriately weighted average of all per-unit effects estimated from the more general model using OLS. Notably, our test works even when the true model cannot be estimated using IV methods as long as a single valid instrument is available (e.g. a single binary instrument). We re-visit three recent empirical examples that examine the role of educational attainment on various outcomes to demonstrate the practical value of our test.
ER -