A SPECIFICATION TEST
NONPARAMETRIC INSTRUMENTAL VARIABLE REGRESSION
GAGLIARDINI, P. *, and SCAILLET, O. **
* University of Lugano and Swiss Finance Institute ** HEC Genève
and Swiss Finance Institute
We consider testing for correct specification
of a nonparametric instrumental variable regression. First we study the notion
of correct specification, misspecification and overidentification in this ill-posed
inverse problem setting. Second we study a test statistic based on the empirical
minimum distance criterion corresponding to the conditional moment restriction
evaluated with a Tikhonov Regularized estimator of the functional parameter.
The test statistic admits an asymptotic normal distribution under the null hypothesis,
and the test is consistent under global alternatives. A bootstrap procedure
is available to get simulation based critical values. Finally, we explore the
finite sample behavior with Monte Carlo experiments, and provide an empirical
illustration for an estimated Engel curve.
Keywords : Specification Test, Nonparametric Regression, Instrumental Variables, Minimum Distance, Tikhonov Regularization, Ill-posed Inverse Problems, Generalized Method of Moments, Bootstrap, Engel Curve.
JEL : C13, C14, C15, D12.
MSC 2000 : 62G08, 62G20.