`Objective' Bayesian Unit Root Tests

SUMMARY
Due to weaknesses in traditional tests, a Bayesian approach is developed to investigate whether unit roots
exist in macroeconomic time-series. Bayesian posterior odds comparing unit root models to stationary
and trend-stationary alternatives are calculated using informative priors. Two classes of reference priors
which are informative but require minimal subjective prior input are used. In this sense the Bayesian unit
root tests developed here are objective. Bayesian procedures are carried out on the Nelson-Plosser and
Shiller data sets as well as on generated data. The conclusion is that the failure of classical procedures
to reject the unit root hypothesis is not necessarily proof that a unit root is present with high probability

1. INTRODUCTION
Bayesians frequently criticize classical hypothesis-testing procedures, arguing that the relevant
question in a modelling exercise question should be: How probable is a hypothesis relative to
other competing hypotheses? For classical econometricians the usual outcome of a hypothesistesting
exercise is that a researcher either rejects or fails to reject a hypothesis. But classical
procedures cannot tell the researcher the probability that a hypothesis holds.
When the hypothesis tested is the unit root hypothesis, Bayesian methods are preferable to
traditional unit root tests. This is because most traditional unit root tests have extremely low
power, especially against trend-stationary alternatives (see, e.g. DeJong, Nankervis, Savin, and
Whiteman (1988), hereafter DNSW). Whether explicitly stated or not, studies such as DNSW
aim to discover the probability of the unit root hypothesis relative to the hypothesis of trendstationarity.
DNSW discover that classical procedures are poorly suited to this purpose in the
absence of time-consuming Monte Carlo studies. Koop (1991) develops Bayesian unit root tests
which overcome many of the problems of traditional unit root tests, but these new tests are
computationally burdensome and, for the most part, require the elicitation of informative
priors. Given the hesitation of some researchers to use informative priors and carry out
numerical or Monte Carlo integration, there is a clear need to develop Bayesian unit root tests
that are computationally easy and do not depend on the researcher's prior opinions. The
purpose of this paper is to propose several such tests (called here 'objective' Bayesian tests)
and compare them with some traditional alternatives.