TY - JOUR
AU - Kim,Kyoo il
AU - Petrin,Amil
TI - A New Control Function Approach for Non-Parametric Regressions with Endogenous Variables
JF - National Bureau of Economic Research Working Paper Series
VL - No. 16679
PY - 2011
Y2 - January 2011
DO - 10.3386/w16679
UR - http://www.nber.org/papers/w16679
L1 - http://www.nber.org/papers/w16679.pdf
N1 - Author contact info:
Kyoo il Kim
Department of Economics
Michigan State University
18D Marshall-Adams Hall
East Lansing, MI 48824
Tel: 517-353-9008
E-Mail: kyookim@msu.edu
Amil Petrin
Department of Economics
University of Minnesota
4-101 Hanson Hall
Minneapolis, MN 55455
Tel: 612/625-0145
Fax: 612/624-0209
E-Mail: petrin@umn.edu
AB - When the endogenous variable enters the structural equation non-parametrically the linear Instrumental Variable (IV) estimator is no longer consistent. Non-parametric IV (NPIV) can be used but it requires one to impose restrictions during estimation to make the problem well-posed. The non-parametric control function estimator of Newey, Powell, and Vella (1999) (NPV-CF) is an alternative approach that uses the residuals from the conditional mean decomposition of the endogenous variable as controls in the structural equation. While computationally simple identification relies upon independence between the instruments and the expected value of the structural error conditional on the controls, which is hard to motivate in many economic settings including estimation of returns to education, production functions, and demand or supply elasticities. We develop an estimator for non-linear and non-parametric regressions that maintains the simplicity of the NPV-CF estimator but allows the conditional expectation of the structural error to depend on both the control variables and the instruments. Our approach combines the conditional moment restrictions (CMRs) from NPIV with the controls from NPV-CF setting. We show that the CMRs place shape restrictions on the conditional expectation of the error given instruments and controls that are sufficient for identification. When sieves are used to approximate both the structural function and the control function our estimator reduces to a series of Least Squares regressions. Our monte carlos are based on the economic settings suggested above and illustrate that our new estimator performs well when the NPV-CF estimator is biased. Our empirical example replicates NPV-CF and we reject the maintained assumption of the independence of the instruments and the expected value of the structural error conditional on the controls in their setting.
ER -