Dr Daniel Wilhelm

Nonparametric instrumental variable estimation under monotonicity

The ill-posedness of the inverse problem of recovering a regression function in a nonparametric instrumental variable (NPIV) model leads to estimators that may suffer from poor statistical performance. In this paper, we explore the possibility of imposing shape restrictions to improve the performance of the NPIV estimators.

We propose a simple model selection test for choosing among two parametric likelihoods which can be applied in the most general setting without any assumptions on the relation between the candidate models and the true distribution. That is, both, one or neither is allowed to be correctly specied or misspecied, they may be nested, non-nested, strictly non-nested or overlapping. Unlike in previous testing approaches, no pre-testing is needed, since in each case, the same test statistic together with a standard normal critical value can be used. The new procedure controls asymptotic size uniformly over a large class of data generating processes. We demonstrate its finite sample properties in a Monte Carlo experiment and its practical relevance in an empirical application comparing Keynesian versus new classical macroeconomic models.

In a randomized control trial, the precision of an average treatment effect estimator can be improved either by collecting data on additional individuals, or by collecting additional covariates that predict the outcome variable. We propose the use of pre-experimental data such as a census, or a household survey, to inform the choice of both the sample size and the covariates to be collected.

Cross-validation is the most common data-driven procedure for choosing smoothing parameters in nonparametric regression. For the case of kernel estimators with iid or strong mixing data, it is well-known that the bandwidth chosen by crossvalidation is optimal with respect to the average squared error and other performance measures. In this paper, we show that the cross-validated bandwidth continues to be optimal with respect to the average squared error even when the datagenerating process is a -recurrent Markov chain. This general class of processes covers stationary as well as nonstationary Markov chains. Hence, the proposed procedure adapts to the degree of recurrence, thereby freeing the researcher from the need to assume stationary (or nonstationary) before inference begins. We study finite sample performance in a Monte Carlo study. We conclude by demonstrating the practical usefulness of cross-validation in a highly-persistent environment, namely that of nonlinear predictive systems for market returns.

This paper addresses the issue of choosing the corresponding smoothing parameter (or bandwidth) so that the resulting point estimate is optimal in a certain sense.

The ill-posedness of the inverse problem of recovering a regression function in a nonparametric instrumental variable model leads to estimators that may suffer from a very slow, logarithmic rate of convergence. In this paper, the authors show that restricting the problem to models with monotone regression functions and monotone instruments significantly weakens the ill-posedness of the problem.

This paper provides a constructive argument for identification of nonparametric panel data models with measurement error in a continuous explanatory variable.

This paper addresses the issue of choosing the corresponding smoothing parameter (or bandwidth) so that the resulting point estimate is optimal in a certain sense.

We propose a simple model selection test for choosing among two parametric likelihoods which can be applied in the most general setting without any assumptions on the relation between the candidate models and the true distribution.