Three Essays in Time Series Econometrics

Abstract

This thesis deals with different topics in time series econometrics that belong, broadly speaking, to the area of macroeconometrics. That is, topics and methods are investigated which are of interest to applied researchers that want to analyze the behavior of aggregate measurements of the economy by means of time series data. For instance, macroeconomic time series often display specific nonlinear characteristics. Chapter 1 applies one of the recently proposed techniques to capture nonlinearity to U.S. interest rate data. Another important area of macroeconomic research is the identification of structural shocks that have an economically meaningful interpretation, in contrast to prediction errors. Chapter 2 compares some alternative structural estimators in the context of a recent discussion on the reliability of standard structural estimators. Finally, the third chapter compares different estimators of so-called vector autoregressive moving-average (VARMA) models that are a potential alternative to vector autoregressive models which are used predominantly in applied macroeconomic research. In the following, I will briefly describe each chapter in more detail. Chapter 1 reviews some simple extensions of the threshold cointegration models forwarded by Balke and Fomby (1997). These are models designed for non-stationary series with non- linear dynamics that are tight together by a long-run equilibrium relationship. I apply one of these models to the U.S. interest rate spread and show that there is evidence in favor of a threshold model of this kind. The model suggests that the spread is probably not mean- reverting in a large band around the equilibrium. However, the model is not found to provide better forecasts relative to a linear benchmark vector error-correction model. In chapter 2 Karel Mertens and I compare different structural estimators in the context of a recent discussion on the reliability of long-run identified structural vector autoregressions (SVARs). Several authors have suggested that SVARs fail partly because they are finite- order approximations to infinite-order processes. In the second chapter we estimate VARMA and state space models, which are not misspecified, using simulated data and compare true with estimated impulse responses of hours worked to a technology shock. We find little gain from using VARMA models. However, state space models do outperform SVARs. In particular, subspace methods consistently yield lower mean squared errors, although even these estimates remain too imprecise for reliable inference. Our findings indicate that long- run identified SVARs perform weakly not because of the finite-order approximation. Instead, we find that the simulated processes used in the previous studies are nearly violating the most basic assumptions on which long-run identification schemes are based. Chapter 3 compares different estimation methods for VARMA models. Classical Gaussian maximum likelihood estimation is plagued with various numerical problems and has been considered difficult by many applied researchers. These disadvantages could have led to the dominant use of vector autoregressive (VAR) models in macroeconomic research. Therefore, several other, simpler estimation methods have been proposed in the literature. In chapter 3 these methods are compared by means of a Monte Carlo study. Different evaluation criteria are used to judge the relative performances of the algorithms. The obtained results suggest that the algorithm of Hannan and Kavalieris (1984a) is the only algorithm that reliably outperforms the other algorithms and the benchmark VARs. However, the procedure is technically not very reliable and therefore would have to be improved in order to make it an alternative tool for applied researchers.