Essays in Time Series Econometrics

Abstract

In this dissertation, I address issues related to both statistical and causal inference in time series in three independent chapters. In the first chapter, coauthored with E. Lazarus and J. H. Stock, we use higher-order expansions to derive a theoretical frontier for the size-power tradeoff for a class of heteroskedasticity and autocorrelation robust (HAR) estimators. Our results characterize the relative benefits of different estimators. We establish that tests using standard $t$ or $F$ critical values exhibit small worst-case losses compared to the optimal approach. We highlight the extent to which methods popular in the applied literature fall short of this envelope. The second chapter demonstrates that heteroskedasticity can identify structural shocks in macroeconomic models without structural assumptions of the type required in existing identification arguments. My approach relies on a new decomposition of the autocovariance of the variance of reduced form residuals, which has a unique solution under generic regularity conditions. This allows for the identification of SVAR-type models based solely on the presence of time-varying volatility in the structural shocks. In the third chapter, I show that models identified by exploiting multiple variance regimes, most commonly SVARs, can face a weak identification problem when the structural variances evolve in a linearly dependent manner. I propose tests for the presence of weak identification. I exploit specific features of the regime-based identification argument to prove the validity of more powerful weak identification-robust tests for parameters of interest in this familiar macroeconomic setting and extend the result to impulse response functions.