Inverse problems can be described as functional equations where the value of the function is known or easily estimable but the argument is unknown. Many problems in econometrics can be stated in the form of inverse problems where the argument itself is a function. For example, consider a...

In nonparametric instrumental variables estimation, the mapping that identifies the function of interest, g say, is discontinuous and must be regularised (that is, modified) to make consistent estimation possible. The amount of modification is contolled by a regularisation parameter. The optimal...

A parameter of an econometric model is identified if there is a one-to-one or many-to-one mapping from the population distribution of the available data to the parameter. Often, this mapping is obtained by inverting a mapping from the parameter to the population distribution. If the inverse...

This note shows that adding monotonicity or convexity constraints on the regression function does not restore well-posedness in nonparametric instrumental variable regression. The minimum distance problem without regularisation is still locally ill-posed

We provide general compactness results for many commonly used parameter spaces in nonparametric estimation. We consider three kinds of functions: (1) functions with bounded domains which satisfy standard norm bounds, (2) functions with bounded domains which do not satisfy standard norm bounds,...

We study the identification and estimation of covariate-conditioned average marginal effects of endogenous regressors in nonseparable structural systems when the regressors are mismeasured. We control for the endogeneity by making use of covariates as control variables; this ensures conditional...

This paper considers estimating general spatial autoregressive models using the generalized method of moments (GMM). I propose nonparametric estimates of the optimal instruments based on conditional second moment restrictions. I show that these instruments are optimal over all possible...

Empirical models of differentiated products demand (and often supply) are widely used in industrial organization and other fields of economics. We review some recent work studying identification in a broad class of such models. This work shows that the parametric functional forms and...