This note establishes that the fully nonparametric classical errors-in-variables model is identifiable from data on the regressor and the dependent variable alone, unless the specification is a member of a very specific parametric family. This family includes the linear specification with...

This chapter provides background for understanding and applying special regressor methods. This chapter is intended for inclusion in the "Handbook of Applied Nonparametric and Semiparametric Econometrics and Statistics," Co-edited by Aman Ullah, Jeffrey Racine, and Liangjun Su, to be published...

Assume individuals are treated if a latent variable, containing a continuous instrument, lies between two thresholds. We place no functional form restrictions on the latent errors. Here unconfoundedness does not hold and identification at infinity is not possible. Yet we still show nonparametric...

We propose a generalization of random coefficients models, in which the regression model is an unknown function of a vector of regressors, each of which is multiplied by an unobserved error. We also investigate a more restrictive model which is additive (or additive with interactions) in unknown...

A new uniform expansion is introduced for sums of weighted kernel-based regression residuals from nonparametric or semiparametric models. This result is useful for deriving asymptotic properties of semiparametric estimators and test statistics with data-dependent bandwidth, random trimming, and...

We consider estimation of means of functions that are scaled by an unknown density, or equivalently, integrals of conditional expectations. The "ordered data" estimator we provide is root n consistent, asymptotically normal, and is numerically extremely simple, involving little more than...

For vectors z and w and scalar v, let r(v,z,w) be a function that can be nonparametrically estimated consistently and asymptotically normally, such as a distribution, density, or conditional mean regression function. We provide consistent, asymptotically normal nonparametric estimators for the...

Let r(x,z) be a function that, along with its derivatives, can be consistently estimated nonparametrically. This paper discusses identification and consistent estimation of the unknown functions H, M, G and F, where r(x, z) = H[M (x, z)] and M(x,z) = G(x) + F(z). An estimation algorithm is...

Regression discontinuity models, where the probability of treatment jumps discretely when a running variable crosses a threshold, are commonly used to nonparametrically identify and estimate a local average treatment effect. We show that the derivative of this treatment effect with respect to...

Suppose V and U are two independent mean zero random variables, where V has an asymmetric distribution with two mass points and U has a symmetric distribution. We show that the distributions of V and U are nonparametrically identified just from observing the sum V+U, and provide a rate root n...