Non-parametric Models with Instrumental Variables

Abstract

This paper gives a survey of econometric models characterized by a relation between observable and unobservable random elements where these unobservable terms are assumed to be independent of another set of observable variables called instrumental variables. This kind of specification is usefull to address the question of endogeneity or of selection bias for example. These models are treated non parametrically and in all the example we consider the functional parameter of interest is defined as the solution of a linear or non linear integral equation. The estimation procedure then requires to solve a (generally ill-posed) inverse problem. We illustrate the main questions (construction of the equation, identification, numerical solution, asymptotic properties, selection of the regularization parameter) by the different models we present.

Nonparametric Instrumental Variables Estimation Under Misspecification

“…Many useful results from functional analysis apply to operators that are compact, and so the compactness assumption simplifies analysis of the NPIV estimation problem. For some discussion of compactness in NPIV (including primitive conditions that imply this property) see, e.g., Florens (2011) and Horowitz (2011).…”