To Criticize the Critics: An Objective Bayesian Analysis of Stochastic Trends

In two recent articles, Sims (1988) and Sims and Uhlig (1988) question the value of much of the ongoing literature on unit roots and stochastic trends. They characterize the seeds of this literature as "sterile ideas," the application of nonstationary limit theory as "wrongheaded and unenlightening" and the use of classical methods of inference as "unreasonable" and "logically unsound." They advocate in place of classical methods an explicit Bayesian approach to inference that utilizes a flat prior on the autoregressive coefficient. DeJong and Whiteman adopt a related Bayesian approach in a group of papers (1989a,b,c) that seek to reevaluate the empirical evidence from historical economic time series. Their results appear to be conclusive in turning around the earlier, influential conclusions of Nelson and Plosser (1982) that most aggregate economic time series have stochastic trends. So far, these criticisms of unit root econometrics have gone unanswered; the assertions about the impropriety of classical methods and the superiority of flat prior Bayesian methods have been unchallenged; and the empirical reevaluation of evidence in support of stochastic trends has been left without comment. This paper breaks that silence and offers a new perspective. We challenge the methods, the assertions and the conclusions of these articles on the Bayesian analysis of unit roots. Our approach is also Bayesian but we employ objective ignorance priors not flat priors in our analysis. Ignorance priors represent a state of ignorance about the value of a parameter and in many models are very different from flat priors. We demonstrate that in time series models flat priors do not represent ignorance but are actually informative (sic) precisely because they neglect generically available information about how autoregressive coefficients influence observed time series characteristics. Contrary to their apparent intent, flat priors unwittingly bias (This abstract was borrowed from another version of this item.)