Research Database

For the first-order univariate autoregression without constant term, the joint p.d.f (corresponding to a flat prior) for the true coeffecient p and the least squares estimate p-hat is estimated by Monte Carlo and graphically displayed. The graphs show how the symmetric distribution of p|p-hat coexists with the assymetric distribution of p-hat|p. Treating tail areas of the p-hat|p distribution as if they summarized evidence in the data about the location of p amounts to ignoring the shrinkage in the variance of p-hat|p as p approaches one. Prior p.d.f.'s implicit in treating classical significance levels as if they were Bayesian conditional probabilities are calculated. They are shown to depend sensitively on p-hat and to put substantial probability on p's above one.

This paper reports an optimistic forecast of U.S. output and inflation trends in 1990–91. Generated by a Bayesian vector autoregression (BVAR) model of the U.S. economy using data available on November 30, 1989, the forecast is more optimistic than a consensus forecast. The key to the model's greater optimism for real growth is its outlook for strong consumer spending. The model's optimism is defended by examining historical precedents as well as comparing the track records of the model and consensus forecasts. The model's measures of forecast uncertainty, however, suggest that its predictions should be taken cautiously. An appendix explains how the model can be used to generate conditional forecasts.