Eric Zivot's Working Papers

Last updated: December 31, 1998

1. Title: The Power of Single Equation Tests for Cointegration when the Cointegrating Vector is Prespecified.
   
   • Co-authors: None
   • First version: September 1995; Latest revision: August 1998.
   • Abstract

     In this paper I present an alternative derivation of the asymptotic distribution of Kremers, Ericsson and Dolado's (1992) conditional ECM-based t-test for no-cointegration with a single prespecified cointegrating vector. This alternative distribution, which is identical to the distribution of Hansen's (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.

     Adobe Acrobat file for text: ecm.pdf
     Adobe Acrobat file for tables: ecmfigs.pdf
     GAUSS code: (not available)
     

2. Title: Cointegration and Forward and Spot Exchange Rate Regressions.
   • Co-autors: None
   • First version: December 1996; Latest revision: October 1998.
   • Abstract:
     
     In this paper we investigate in detail the relationship between models of cointegration between the current spot exchange rate, s_t, and the current forward rate, f_t, and models of cointegration between the future spot rate, s_t+1, and f_t and the implications of this relationship for tests of the forward rate unbiasedness hypothesis (FRUH). We argue that simple models of cointegration between s_t and f_t more easily capture the stylized facts of typical exchange rate data than simple models of cointegration between s_t+1 and f_t and so serve as a natural starting point for the analysis of exchange rate behavior. We show that simple models of cointegration between s_t and f_t imply rather complicated models of cointegration between s_t+1 and f_t. As a result, standard methods are often not appropriate for modeling the cointegrated behavior of (s_t+1, f_t)' and we show that the use of such methods can lead to erroneous inferences regarding the FRUH.
     
   • Adobe Acrobat file: forward.pdf
   • GAUSS code: coming soon!

    

3. Title: Asymptotic Distributions of Dummy Variable Coefficients in Unit Root Regressions with Level and Trend Breaks.
   • Co-authors: Christian Murray
   • First version: (manuscript in preparation)
   • Abstract: (not available)
   • Adobe Acrobat file: (not available)
   • GAUSS code: (not available)

    

4. Title: Bayesian and Classical Approaches to Instrumental Variables Regression
   • Co-authors: Frank Kleibergen
   • First version: August 1998
   • Abstract

We estabilsh the relationships between certain Bayesian and classical approaches to instrumental variables regression. We determine the form of priors that lead to posteriors for structural paameters that have similar properties as classical 2SLS and LIML and in doing so provide some new insight to the small sample behavior of Bayesian and classical procedures in the limited information simultaneous equations model. Our approach is motivated by the relationship between Bayesian and classical procedures in linear regression models: i.e., Bayesian analysis with a diffuse prior leads to posteriors that are identical in form to the finite sample density of classical least squares estimators. We use the fact that the instrumental variables regression model can be obtained from a reduced rank restriction on a multivariate linear model to determine the priors that give rise to posteriors that have properties similar to classical 2SLS and LIML. As a by-product of this approach we provide a novel way to dtermine the exact finite sample density of the LIML estimator and theprior that corresponds with classical LIML. We show that the traditional Dreze (1976) and a new Bayesian Two Stage approach are similar to 2SLS whereas the approach based on the Jeffreys' prior corresponds to LIML.

• Adobe Acrobat file:papziv2.pdf
• GAUSS code: