Three essays in econometrics

This thesis consists of three essays. The first essay investigates the issue of local misspecification in instrumental variable models. We show that conventional tests often fail to give accurate inferences when the exogeneity conditions of some instruments are mildly violated. The sizes of those tests can be considerably distorted due to their non-centrally distributed test statistics under the null hypothesis. This paper proposes an adjusted score-type test to correct this size distortion while preserving good discriminatory power. Monte Carlo experiments are also conducted to demonstrate size improvement using our method. The second essay provides an improved inference for predictive quantile regressions with persistent predictors and conditionally heteroskedastic errors. Confidence intervals based on conventional quantile regression techniques are not valid when predictors are highly persistent. Moreover, the conditional heteroskedasticity introduces rather complicated nuisance parameters in the limit theory, whose estimation errors can be another source of distortion. We propose a size-corrected bootstrap inference, thereby avoiding the nuisance parameter estimation. The bootstrap consistency is shown even with the non-stationary predictors and conditionally heteroskedastic innovations. Our Monte Carlo simulation confirms the significantly better size performances of the new methods. The empirical exercises on stock return quantile predictability are revisited. The third essay studies the benefit of using the adaptive lasso method for predictive quantile regression. The commonly used predictors in predictive quantile regression typically have various degrees of persistence, and exhibit different signal strengths in explaining the conditional quantiles of the dependent variable. We show that the adaptive lasso methods have consistent variable selection and the oracle properties under the presence of stationary, unit-root and cointegrated predictors. Some encouraging simulation results are reported