Nonparametric instrumental variable derivative estimation

ABSTRACT

The focus of this paper is the nonparametric estimation of the marginal effects (i.e. first partial derivatives) of an instrumental regression function ϕ defined by conditional moment restrictions that stem from a structural econometric model , and involve endogenous variables Y and Z and instruments W. The derivative function is the solution of an ill-posed inverse problem and we propose an estimation procedure based on Landweber–Fridman regularisation. We provide theoretical underpinnings of the proposed approach, examine finite-sample performance, and consider an illustrative application.

Keywords:

• Nonparametric
• derivatives
• endogeneity
• instrumental variables
• ill-posed problem
• regularisation
• Landweber-Fridman
• Engel curve

Acknowledgments

We would like to thank Richard Blundell for providing the data used in the empirical application, Frédérique Fève for her helpful comments, Andrew Chesher and the research group at CeMMAP, University College London, and participants at ISNPS 2012 for their comments and suggestions.

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Samuele Centorrino  http://orcid.org/0000-0001-8713-7197

Additional information

Funding

Racine would like to gratefully acknowledge support from the Natural Sciences and Engineering Research Council of Canada (NSERC:www.nserc.ca) and the Social Sciences and Humanities Research Council of Canada (SSHRC:www.sshrc.ca).