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...

Economists who use survey or administrative data for inferences regarding a population may want to combine information obtained from two or more samples drawn from the population. This is the case if there is no single sample that contains all relevant variables. A special case occurs if...

This chapter considers methods for evaluating the impact of social programs in the presence of nonrandom program placement or program selection. It first presents the evaluation problem as a missing data problem and then considers various solutions proposed in the statistics and econometrics...

Children in households reporting the receipt of free or reduced-price school meals through the National School Lunch Program (NSLP) are more likely to have negative health outcomes than observationally similar nonparticipants. Assessing causal effects of the program is made difficult, however,...

This paper studies the identifying power of conditional quantile restrictions in short panels with fixed effects. In contrast to classical fixed effects models with conditional mean restrictions, conditional quantile restrictions are not preserved by taking differences in the regression equation...

Nonparametric estimators of treatment effects are often applied in settings where clustering may be important. We provide a general methodology for consistently estimating the variance of a large class of nonparametric estimators, including the simple matching estimator, in the presence of...

Empirical Work on the wage impact of training has noted that unobserved heterogeneity of training participants should play a role. The expected return to training, which partly depends on unobservable characteristics, is likely to be a crucial criterion in the decision to take part in training...

Central limit theorems are developed for instrumental variables estimates of linear and semiparametric partly linear regression models for spatial data. General forms of spatial dependence and heterogeneity in explanatory variables and unobservable disturbances are permitted. We discuss...

This chapter provides a comprehensive overview of decomposition methods that have been developed since the seminal work of Oaxaca and Blinder in the early 1970s. These methods are used to decompose the difference in a distributional statistic between two groups, or its change over time, into...