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Bayesian approaches to cointegratrion

Gary Koop (), Rodney Strachan (), Herman van Dijk and Mattias Villani

No EI 2005-13, Econometric Institute Research Papers from Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute

Abstract: The purpose of this paper is to survey and critically assess the Bayesian cointegration literature. In one sense, Bayesian analysis of cointegration is straightforward. The researcher can combine the likelihood function with a prior and do Bayesian inference with the resulting posterior. However, interesting and empirically important issues of global and local identification (and, as a result, prior elicitation) arise from the fact that the matrix of long run parameters is potentially of reduced rank. As we shall see, these identification problems can cause serious problems for Bayesian inference. For instance, a common noninformative prior can lead to a posterior distribution which is improper (i.e. is not a valid p.d.f. since it does not integrate to one) thus precluding valid statistical inference. This issue was brought forward by Kleibergen and Van Dijk (1994, 1998). The development of the Bayesian cointegration literature reflects an increasing awareness of these issues and this paper is organized to reflect this development. In particular, we begin by discussing early work, based on VAR or Vector Moving Average (VMA) representations which ignored these issues. We then proceed to a discussion of work based on the ECM representation, beginning with a simple specification using the linear normalization and normal priors before moving onto the recent literature which develops methods for sensible treatment of the identification issues.

Date: 2005-03-11
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https://repub.eur.nl/pub/1915/ei200513.pdf (application/pdf)

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Working Paper: Bayesian Approaches to Cointegration (2004) Downloads
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