We suggest two nonparametric approaches, based on kernel methods and orthogonal series, respectively, to estimating regression functions in the presence of instrumental variables. For the first time in this class of problems we derive optimal convergence rates, and show that they are attained by...

This paper uses average monthly returns and linear spline regressions to investigate the relation between expected return and firm size during 1980-1994. We find that the average monthly returns are approximately constant across size deciles. The estimated spline regressions vary substantially...

Censoring of outcomes (selection) is a common consequence of survey nonresponse and attrition in panels, and has received much attention. Joint censoring of regressors and outcomes is also common, but it has remained unexplored. This paper shows that the problem of identification when regressors...

The bootstrap is a method for estimating the distribution of an estimator or test statistic by resampling one's data. It amounts to treating the data as if they were the population for the purpose of evaluating the distribution of interest. Under mild regularity conditions, the bootstrap yields...

In nonparametric instrumental variables estimation, the mapping that identifies the function of interest, g, is discontinuous and must be regularized to permit consistent estimation. The optimal regularization parameter depends on population characteristics that are unknown in applications. This...

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...

Modern econometrics requires implementation of highly specialized software. In contrast to mathematical arguments used in implementing new econometric techniques the corresponding software algorithms require specific platforms. The specialization of hardware and software, in fact, seriously...