Asymptotic Sizes of Subset Anderson-Rubin Tests with Weakly Identified Nuisance Parameters and General Covariance Structure (Job Market Paper)
Abstract: In Guggenberger et al (2012), subset AR test under conditional homoscedasticity is shown to have correct asymptotic size under critical values from the Chi-squared distribution of reduced degrees of freedom, and thus provide power improvement over the projection based test. This paper shows that it is not the case under general covariance structure. We provide a thorough simulation results to show that the break-down of the result under general covariance structure can be observed in wide range of parameters that is plausible in empirical applications, including inferences on New Keynesian Phillips Curve. The simulation results suggests that empirical researchers should rely on more conservative projection based tests when applying subset AR test with potential heteroscedasticity and autocorrelation.
Panel data models with non-additive unobserved heterogeneity: Estimation and inference (with Ivan Fernandez-Val), Quantitative Economics, Vol.4, pp.453-481, Nov, 2013
Abstract: This paper considers fixed effects estimation and inference in linear and non-linear panel data models with random coefficients and endogenous regressors. The quantities of interest—means, variances, and other moments of the random coefficients—are estimated by cross sectional sample moments of generalized method of moments (GMM) estimators applied separately to the time series of each individual. To deal with the incidental parameter problem introduced by the noise of the within-individual estimators in short panels, we develop bias corrections. These corrections are based on higher-order asymptotic expansions of the GMM estimators and produce improved point and interval estimates in moderately long panels. Under asymptotic sequences where the cross-sectional and time series dimensions of the panel pass to infinity at the same rate, the uncorrected estimators have asymptotic biases of the same order as their asymptotic standard deviations. The bias corrections remove the bias without increasing variance. An empirical example on cigarette demand based on Becker, Grossman, and Murphy (1994) shows significant heterogeneity in the price effect across U.S. states.
Inference on Quasi-Bayesian Estimators Accounting for Monte-Carlo Markov Chain Numerical Errors
Abstract: Quasi-Bayesian method of Chernozhukov&Hong (2003) and related approaches have been applied to numerous applications to tackle the non-convex shape arises in certain extremum estimations. The method involves drawing finite number of MCMC (Monte Carlo Markov Chain) chains to make inference and thus some degree of numerical error is inevitable. Most applied researches, however, ignore such error and treat the draw as if it is infinitely many. This paper quantifies the degree of numerical error arising from the finite draws and provides a method to incorporate such errors into the final inference. We show that a sufficient condition for establishing correct numerical standard errors is geometric ergodicity of the MCMC chain. It is also shown that geometric ergodicity is satisfied under Metropolis Hastings chains with quasi-posterior for the whole class of extremum estimators where the quasi-Bayesian method is applicable.
Research in Progress
An Improved Method of Testing Asymmetric Correlation of Equity Portfolios: Application to International Equity Indices
Abstract: It is widely documented that correlation between many equity portfolio returns is much higher conditioning on downside move than on upside move. Formal testing of the correlation asymmetry is problematic because of the conditioning bias. Bivariate normal distribution has been widely used in the literature as a benchmark distribution for the testing. In this paper, I find potential problems of using normal distribution as a benchmark and propose an alternative non-parametric benchmark distribution based on normal copula that controls for the effect of marginal distributions in observed correlations. I apply the method to 25 major international stock indices and find that correlation asymmetry still exists, but the degree and significance is undermined compared to the result using normal benchmark. The bias of using normal benchmark is found to be large for some statistics. I also find the bias is positively correlated with the unconditional correlation.