Three essays on predictive regression, low-frequency variation, and dynamic stochastic general equilibrium models
OA Version
Citation
Abstract
This dissertation investigates several important issues related to filtering, estimation, and inference in time series econometrics. The applied focus is on financial and macroeconomic models that include predictive regressions and dynamic stochastic general equilibrium models as prominent examples.
Chapter 1 studies inference in predictive regression with a nearly integrated predictor. Conventional tests for predictive regressions exhibit substantial size distortions while existing valid inference procedures usually require multiple steps for their implementation. I propose a simple procedure using an augmented regression that requires only one step to test the coefficients in a predictive regression with a nearly integrated predictor. I prove that the usual $t$-test using conventional standard normal critical values is conservative. Furthermore, to address the situation where the predictive test is uninformative because of possible outlying events or regime changes, I propose a class of robust tests and study their asymptotic properties. In the empirical application, I find considerable evidence of the predictability of NYSE/AMEX returns using nearly integrated predictors, such as the log dividend-price ratio or the log earning-price ratio.
Chapter 2 (joint with Alessandro Casini and Pierre Perron) establishes theoretical results about the low frequency contamination
induced by general nonstationarity for estimates such as the sample
autocovariance and the periodogram, and hence deduces consequences for heteroskedasticity and autocorrelation robust (HAR) inference. We show that for short memory nonstationarity data these estimates exhibit features akin to long memory due to low frequency contamination, to which, however, estimates based on nonparametric smoothing over time are robust. The theoretical findings are further confirmed by simulations. Since inconsistent long-run variance (LRV) estimation tends to be inflated when the data are nonstationary, HAR tests based on LRV can suffer from low frequency contamination, being more undersized with lower power than those based on HAC, whereas tests based on the recently introduced double kernel HAC estimator do not.
The last chapter (joint with Zhongjun Qu) develops a new particle filter for dynamic stochastic general equilibrium (DSGE) models by mapping the state vector into two subvectors: a subvector whose components are observed and a subvector whose components are latent. By only sampling and propagating particles of the latent variables, we avoid the need to introduce measurement errors, a convenient but questionable practice. For implementation, we propose to approximate the observables' density conditional on the latent variables using series expansions. As an important feature, the new filter also allows us to study singular DSGE models using the composite likelihood, therefore providing a unified treatment of both singular and nonlinear DSGE models.
Description
License
Attribution-NonCommercial-NoDerivatives 4.0 International