Eric Zivot

Further Evidence on the Great Crash, the Oil-Price Shock, and the Unit-Root Hypothesis

Recently, Perron has carried out tests of the unit-root hypothesis against the alternative hypothesis of trend stationarity with a break in the trend occurring at the Great Crash of 1929 or at the 1973 oil-price shock. His analysis covers the Nelson–Plosser macroeconomic data series as well as a postwar quarterly real gross national product (GNP) series. His tests reject the unit-root null hypothesis for most of the series. This article takes issue with the assumption used by Perron that the Great Crash and the oil-price shock can be treated as exogenous events. A variation of Perrons test is considered in which the breakpoint is estimated rather than fixed. We argue that this test is more appropriate than Perrons because it circumvents the problem of data-mining. The asymptotic distribution of the estimated breakpoint test statistic is determined. The data series considered by Perron are reanalyzed using the test static. The empirical results make use of the asymptotics developed for the test statistic as well as extensive finite-sample corrections obtained by simulation. The effect on the empirical results of fat-tailed and temporally dependant innovations is investigated. In brief, by treating the breakpoint as endogenous, we find that there is less evidence against the unit-root hypothesis than Perron finds for many of the data series but stronger evidence against if for several of the series, including the Nelson–Plosser industrial-production, nominal-GNP, and real-GNP series.

Why Are the Beveridge-Nelson and Unobserved-Components Decompositions of GDP So Different?

This paper reconciles two widely used decompositions of GDP into trend and cycle that yield starkly different results. The Beveridge-Nelson (BN) decomposition implies that a stochastic trend accounts for most of the variation in output, whereas the unobserved-components (UC) implies cyclical variation is dominant. Which is correct has broad implications for the relative importance of real versus nominal shocks. We show the difference arises from the restriction imposed in UC that trend and cycle innovations are uncorrelated. When this restriction is relaxed, the UC decomposition is identical to the BN decomposition. Furthermore, the zero-correlation restriction can be rejected for U.S. quarterly GDP, with the estimated correlation being -0.9.

Inference on a Structural Parameter in Instrumental Variables Regression with Weak Instruments

In this paper we consider the problem of making inference on a structural parameter in instrumental variables regression when the instruments are only weakly correlated with the endogenous explanatory variables.

A Structural Analysis of Price Discovery Measures

We analyze the structural determinants of two widely used measures of price discovery between multiple markets that trade closely related securities. Using a structural cointegration model, we show that both the information share (IS) and component share (CS) measures account for the relative avoidance of noise trading and liquidity shocks, but that only the IS can provide information on the relative informativeness of individual markets. In particular, the IS of one market is higher if it incorporates more new information and/or impounds less liquidity shocks. Use of the CS in conjunction with the IS can help sort out the confounding effects of the two types of shocks. Furthermore, we find that the IS only accounts for the immediate (one-period) responses of market prices to the news innovation, which implies that the IS estimates based on high sampling frequencies may be distorted by transitory frictions and may miss important price discovery dynamics.

A Bayesian Time Series Model of Multiple Structural Changes in Level, Trend, and Variance

We consider a deterministically trending dynamic time series model in which multiple structural changes in level, trend, and error variance are modeled explicitly and the number, but not the timing, of the changes is known. Estimation of the model is made possible by the use of the Gibbs sampler. The determination of the number of structural breaks and the form of structural change is considered as a problem of model selection, and we compare the use of marginal likelihoods, posterior odds ratios, and Schwarzs Bayesian model-selection criterion to select the most appropriate model from the data. We evaluate the efficacy of the Bayesian approach using a small Monte Carlo experiment. As empirical examples, we investigate structural changes in the U.S. ex post real interest rate and in a long time series of U.S. real gross domestic product.

Markov Regime-Switching and Unit Root Tests

We investigate the power and size performance of unit root tests when the true data generating process undergoes Markov regime-switching. All tests, including those robust to a single break in trend growth rate, have very low power against a process with a Markov-switching trend growth rate as in Lam (1990). However, for the case of business cycle non-linearities, unit root tests are very powerful against models used as alternatives to Lam (1990) that specify regime-switching in the transitory component of output. Under the null hypothesis, the received literature documents size distortions in Dickey-Fuller type tests caused by a single break in trend growth rate or variance. We find these results do not generalize to most parameterizations of Markov-switching in trend or variance. However, Markov-switching in variance can lead to over-rejection in tests robust to a single break in the level of trend.

Practical Issues in the Analysis of Univariate GARCH Models

This chapter gives a tour through the empirical analysis of univariate GARCH models for financial time series with stops along the way to discuss various practical issues associated with model specification, estimation, diagnostic evaluation and forecasting.

THE POWER OF SINGLE EQUATION TESTS FOR COINTEGRATION WHEN THE COINTEGRATING VECTOR IS PRESPECIFIED

In this paper I present an alternative derivation of the asymptotic distribution of Kremers, Ericsson and Dolados (1992) conditional ECM based t-test for cointegration with a single prespecified cointegrating vector. This alternative distribution, which is identical to the distribution of Hansens (1995) covariate augmented t-test for a unit root, is valid for weakly exogenous regressors and depends on a consistently estimable nuisance parameter that takes on values in the unit interval. I show analytically, using asymptotic power functions based on near-cointegrated alternatives, that the ECM t-test with a prespecified cointegrating vector can have much higher power than single equation tests for cointegration based on estimating the cointegrating vector. I also characterize situations in which the ECM t-test computed with a misspecified cointegrating vector will have high power.

A Bayesian Analysis of the Unit Root Hypothesis Within an Unobserved Components Model

In this paper we extend some of Phillipss [4] results to nonlinear unobserved components models and develop a posterior odds ratio test of the unit root hypothesis based on flat and Jeffreys priors. In contrast to the analysis presented by Schotman and van Dijk [9], we utilize a nondegenerate structural representation of the components model that allows us to determine well-behaved Jeffreys priors, posterior densities under flat priors and Jeffreys priors, and posterior odds ratios for the unit root hypothesis without a proper prior for the level parameter. The analysis highlights the importance of the treatment of initial values for inference concerning stationarity and unit roots.

A Bayesian Analysis of Trend Determination in Economic Time Series

In this paper we provide a comprehensive Bayesian posterior analysis of trend determination in general autoregressive models. Multiple lag autoregressive models with fitted drifts and time trends as well as models that allow for certain types of structural change in the deterministic components are considered. We utilize a modified information matrix-based prior that accommodates stochastic nonstationarity, takes into account the interactions between long-run and short-run dynamics and controls the degree of stochastic nonstationarity permitted. We derive analytic posterior densities for all of the trend determining parameters via the Laplace approximation to multivariate integrals. We also address the sampling properties of our posteriors under alternative data generating processes by simulation methods. We apply our Bayesian techniques to the Nelson-Plosser macroeconomic data and various stock price and dividend data.