TY  - JOUR
AU  - Lochner,Lance
AU  - Moretti,Enrico
TI  - Estimating and Testing Non-Linear Models Using Instrumental Variables
JF  - National Bureau of Economic Research Working Paper Series
VL  - No. 17039
PY  - 2011
Y2  - May 2011
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  - In many empirical studies, researchers seek to estimate causal relationships using instrumental variables. When only one valid instrumental variable is available, researchers are limited to estimating linear models, even when the true model may be non-linear.  In this case, ordinary least squares and instrumental variable estimators will identify different weighted averages of the underlying marginal causal effects even in the absence of endogeneity.  As such, the traditional Hausman test for endogeneity is uninformative.  We build on this insight to develop a new test for endogeneity that is robust to any form of non-linearity. Notably, our test works well even when only a single valid instrument is available. This has important practical applications, since it implies that researchers can estimate a completely unrestricted non-linear model by OLS, and then use our test to establish whether those OLS estimates are consistent.  We re-visit a few recent empirical examples to show how the test can be used to shed new light on the role of non-linearity.
ER  -