Demand Analysis as an Ill-Posed Inverse Problem with Semiparametric Specification
In this paper we are concerned with analyzing the behavior of a semiparametric estimator which corrects for endogeneity in a nonparametric regression by assuming mean independence of residuals from instruments only. Because it is common in many applications, we focus on the case where endogenous regressors and additional instruments are jointly normal, conditional on exogenous regressors. This leads to a severely ill-posed inverse problem. In this setup, we show first how to test for conditional normality. More importantly, we then establish how to exploit this knowledge when constructing an estimator, and we derive results characterizing the large sample behavior of such an estimator. In addition, in a Monte Carlo experiment we analyze the finite sample behavior of the proposed estimator. Our application comes from consumer demand. We obtain new and interesting findings that highlight both the advantages, and the difficulties of an approach which leads to ill-posed inverse problems. Finally, we discuss the somewhat problematic relationship between nonparametric instrumental variable models, and the recently emphasized issue of unobserved heterogeneity in structural models.
|Date of creation:||06 Aug 2008|
|Date of revision:|
|Contact details of provider:|| Postal: |
Web page: http://fmwww.bc.edu/EC/
More information through EDIRC
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Ait-Sahalia, Yacine & Bickel, Peter J. & Stoker, Thomas M., 2001. "Goodness-of-fit tests for kernel regression with an application to option implied volatilities," Journal of Econometrics, Elsevier, vol. 105(2), pages 363-412, December.
When requesting a correction, please mention this item's handle: RePEc:boc:bocoec:752. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Christopher F Baum)
If references are entirely missing, you can add them using this form.