Asymptotic Refinements of a Misspecification-Robust Bootstrap for GMM Estimators
Journal of Econometrics (2014) 178(3), 398-413
I propose a nonparametric iid bootstrap that achieves asymptotic refinements for t tests and confidence intervals based on GMM estimators even when the model is misspecified. In addition, my bootstrap does not require recentering the moment function, which has been considered as critical for GMM. Regardless of model misspecification, the proposed bootstrap achieves the same sharp magnitude of refinements as the conventional bootstrap methods which establish asymptotic refinements by recentering in the absence of misspecification. The key idea is to link the misspecified bootstrap moment condition to the large sample theory of GMM under misspecification of Hall and Inoue (2003). Two examples are provided: Combining data sets and invalid instrumental variables.
Supplementary Appendix [pdf]
MATLAB code: Coverage probability (Table 3 & Figure 1, Table 4 & Figure 2), Size-corrected Power (Figure 3, Figure 4)
Figure 2 from the paper showing the empirical coverage probabilities of 95% confidence intervals (CI) under model misspecification (the x-axis)
Blue: the misspecification-robust bootstrap CI proposed in the paper
Green: the Hall-Inoue (2003, Journal of Econometrics) asymptotic CI
Light Blue: the Hall-Horowitz (1996, Econometrica) bootstrap CI
Pink: the Brown-Newey (2o02, Journal of Business and Economic Statistics) bootstrap CI
Red: the conventional asymptotic CI
