This research covers four difficult areas of applied econometrics. The first project is adaptive estimation of semiparametric and nonparametric models. In many econometric models, such as the smoothed maximum score estimator, the optimal rate of convergence of an estimator depends on an unknown smoothness, say s, of some function(s). This project will specify a general method that takes existing estimators designed for given values of s and use them to construct an estimator that does not depend on s but obtains the optimal rate of convergence for the case of known s up to a logarithmic factor. This method is a generalized variant of Lepskii (1990) method.
The second project considers the block-block bootstrap, a method that is useful in time series GMM contexts. The block-block bootstrap, proposed by the PI, yields larger asymptotic refinements than the block bootstrap. This research will develop the block-block bootstrap to cover cases in which an HAC variance matrix estimator is required. The third project deals with optimal tests in an instrumental variable regression model with weak instruments. For models with normal reduced-form errors and known covariance matrix, this project will develop a class of similar invariant tests that have maximum weighted average power in finite samples and develop analogous asymptotic tests for models with non-normal errors and unknown covariance matrices. The research will also develop heteroskedasticity-robust and heteroskedasticity and autocorrelation-robust versions of these tests.
The fourth project is on inference in cross-section and panel models with common shocks, such as macroeconomic and political shocks. This research explores the implications of a new asymptotic framework that the PI has developed for cross-section models that allows for general forms of cross-section dependence but yields simple asymptotics. It investigates the properties of GMM estimators and tests in nonlinear cross-section models with common shocks and various procedures in panel models with large numbers of cross-section and time series observations and common shocks.
This research contributes original ideas to solve many difficult problems in econometrics. The results will be extremely helpful to applied econometricians, and in the process, improve economic policy-making.
