Instrumental Variable Estimation of Nonparametric Models

• Published in: Econometrica Vol. 71; no. 5; pp. 1565 - 1578
• Main Authors: Newey, Whitney K., Powell, James L.
• Format: Journal Article
• Language: English
• Published: Oxford, UK and Boston, USA Blackwell Publishing Ltd 01.09.2003; Econometric Society; Blackwell
• Subjects: Applications; Approximation; Consistent estimators; Distribution economics; Distribution theory; Econometrics; Economic models; Economic structure; Economics; Estimation; Estimators; Exact sciences and technology; Identification; instrumental variables; Instrumental variables estimation; Insurance, economics, finance; Inverse problems; Least squares method; Mathematical functions; Mathematics; nonparametric estimation; Nonparametric inference; Nonparametric models; Notes and Comments; Parametric models; Probability and statistics; Sciences and techniques of general use; Series convergence; Statistics; Structural models; Economics; Instrumental variable; Conditional distribution; Statistical distribution; Least square approximation; Statistical moment; Regression; Non parametric estimation; Statistical estimation; Moment estimation; Dependent variable; Inverse problem; Numerical approximation; Statistical method; Sufficient condition; Consistent estimator; Least squares method; Distribution function; Exponential family; Approximation theory; Econometrics; Random variable
• ISSN: 0012-9682; 1468-0262
• DOI: 10.1111/1468-0262.00459

In econometrics there are many occasions where knowledge of the structural relationship among dependent variables is required to answer questions of interest. This paper gives identification and estimation results for nonparametric conditional moment restrictions. We characterize identification of structural functions as completeness of certain conditional distributions, and give sufficient identification conditions for exponential families and discrete variables. We also give a consistent, nonparametric estimator of the structural function. The estimator is nonparametric two-stage least squares based on series approximation, which overcomes an ill-posed inverse problem by placing bounds on integrals of higher-order derivatives.