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.

Leamer (1983) suggested to study the range of estimators β˅0 in the model y=Xβ + δ when imposing linear constraints of the form M (Cβ - c) = 0 where only C and c are fixed. However the extremes may come from models with a bad R^2, say. In this paper we give the exact bounds when only considering models with R^2 ≥ (1 - δ) R^2 max + δR^2 min. These exact bounds can be found from calculating only two regressions. We apply our techniques to study the velocity of money.