Research in Econometric Methods

Yale University, New Haven CT

Investigators

Abstract

This proposal describes research on several new topics and continued research in several areas. First, the PI will consider bias-reduced semiparametric estimation of the long memory parameter 'd'. The most common estimator of this parameter, the Geweke and Porter-Hudak (GPH) estimator, has been found to have substantial finite sample bias. The PI and P. Guggenberger, a graduate student at Yale, will develop an alternative GPH estimator whose bias is reduced by an order of magnitude, whose variance is increased only by a multiplicative constant, and whose rate of convergence is faster than that of the GPH estimator. We plan to establish the optimal rate of convergence of estimators of 'd' when the normalized spectral density is smooth of order s at zero and show that the bias-reduced GPH estimator attains this rate, but, for s > 2, the GPH estimator does not. Working with Yixiao Sun, a graduate student at Yale, the PI will develop a local polynomial Whittle estimator that behaves like other local Whittle estimators, but has reduced bias and a faster rate of convergence. The second area of proposed research is on the bootstrap for nonlinear estimators. This research continues work already reported by the PI.. We aim to obtain higher-order improvements for bootstrapping minimum distance and indirect inference estimators, stronger higher-order improvement results for the iid nonparametric bootstrap than those currently available, and new results for residual-based and BCa bootstraps and Lagrange multiplier (LM) and likelihood ratio (LR) tests. The third area of research is to develop some new asymptotic optimality properties of the classical LM, LR, and Wald tests. The idea is to generalize the finding that the LM test for serial correlation against AR(1) errors is the same as that against MA(1) errors. This finding implies that the LM, LR, and Wald tests have Wald-type asymptotic optimality properties for testing against both AR(1) and MA(1) errors. Results of this type hold more generally, both in this model and in many other models. The object of the proposed research is to obtain some general results that determine different classes of alternative models for which a given LM, LR, or Wald test has asymptotic optimality properties. The fourth area of proposed research continues the PI's research on testing problems when a parameter is on the boundary of the maintained hypothesis and a parameter appears under the alternative but not under the null hypothesis. Numerous examples of such problems already exist, and we believe that problems of this sort will become increasingly prevalent as researchers rely more and more on nonlinear models. We aim to show that the LR, LM, and Wald tests are asymptotically admissible, develop new tests that maximize weighted average power for certain weight functions, construct a complete class of tests, and establish the asymptotic null distribution of the LR, LM, and Wald tests in the Markov regime switching model. Finally, we plan to show that the LR, LM, and Wald tests for testing for conditional heteroskedasticity of GARCH(1, 1) form are consistent against any form of serial correlation in the squared errors.