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.

In welfare theory it is standard to pick the consumption stream that maximizes the welfare of the representative agent. We argue against this position, and show that a benevolent social planner will generally place a greater weight on future consumption than does the representative agent.