My dissertation has three chapters in econometrics. The first chapter, coauthored with Kenneth A. Couch, contains a proof that under one testable condition a measure of economic mobility formed by the ratio of permanent to total variance employing the methods of Gottschalk and Moffitt (1994) is equivalent to the Shorrocks R constructed with a Theil General Entropy Index. The second chapter, coauthored with Gautam Tripathi, tests the assumption of conditional symmetry used to identify and estimate parameters in regression models with endogenous regressors without making any distributional assumptions. The specification test proposed here is computationally tractable, does not require nonparametric smoothing, and can detect n 1/2 -deviations from the null. Since the limiting distribution of the test statistic turns out to be a non-pivotal gaussian process, the critical values for implementing the test are obtained by simulation. In a Monte Carlo study we use the approach proposed here to test the assumption of conditional symmetry maintained in the seminal paper of Powell (1986b). Results from this finite sample experiment suggest that our test can work very well in moderately sized samples. The last chapter develops a sequential procedure to determine the necessary sample size for estimating the parameters of interest with preassigned levels of type I and II errors in program evaluation studies. The procedure is shown to be consistent and first order efficient in determining the sample size for linear regression, regression discontinuity and propensity score matching designs. Simulation results demonstrate the good performance of the procedure.
