Three papers on Weak Identification Robust Bootstrap Inference Public Deposited

Downloadable Content

Download PDF
Last Modified
  • March 22, 2019
    • Affiliation: College of Arts and Sciences, Department of Economics
  • This manuscript is composed of three chapters that develop bootstrap methods in models with weakly identified parameters. In the first chapter, joint with Jonathan B. Hill, we introduce an asymptotically valid wild bootstrapped t-test, which provides robust inference for models with unknown identification category. Under weak identification, the wild bootstrap needs to be constructed using residuals imposing lack of identification, because the usual regression residuals are non-consistent. The robust t-test has better small sample properties compared to the asymptotic approximation counterpart and is simpler to estimate in practice, especially when the underlying Gaussian process has an unknown form and/or is high dimensional. A simulation exercise shows the benefits of using a robust t-test exposing the large-size distortions of the standard t-test when weak identification is present. In the second chapter, joint with Jonathan B. Hill, we introduce a parametric bootstrap that provides an alternative approach to construct statistical tests when parameters are weakly identified. The method extends the parametric bootstrap in regression models, to cases where some of the parameters cannot be consistently estimated, reducing the number of nuisance parameters that arise in the asymptotic distribution of the test statistic under weak identification. Unlike the known statistical tests in the literature, this parametric bootstrap method can mimic the true distribution without nuisance parameters in some important cases. We establish robust critical values of the t-statistic that lead to correct asymptotic size when the identification category is unknown. The simulation exercise shows that the parametric bootstrap can lead to very accurate test sizes and considerable test power comparable to the (infeasible) test statistic that assumes nuisance parameters are known. In the final chapter, we consider the mixed data sampling (MIDAS) model proposed by Ghysels, Santa-Clara, and Valkanov (2005) to evaluate the empirical performance of the wild bootstrapped robust t-test of Chapter 1 and the parametric bootstrapped robust t-test of Chapter 2. To test the statistical significance of the MIDAS estimators, we derive the bootstrapped t-test assuming weak identification because the parameters of the MIDAS model cannot be separately identified under the null hypothesis. Contrary to the results by Ghysels, Santa-Clara, and Valkanov (2005), the bootstrapped t-tests suggest that the estimators of the MIDAS model are not statistically significant, implying that the proposed functional form has low explanatory and predictive power in the study of the risk-return trade-off. We extend the empirical results to different sample frequencies to evaluate the small sample performance of the bootstrap methods and propose an alternative MIDAS specification constructed with the absolute value of excess returns.
Date of publication
Resource type
  • Kim, Ju Hyun
  • Doctor of Philosophy
Degree granting institution
  • University of North Carolina at Chapel Hill Graduate School
Graduation year
  • 2018

This work has no parents.