Understanding unit rooters: a helicopter tour
For the first-order univariate autoregression without constant term, the joint density (corresponding to a flat prior) for the true coefficient and its least squares estimate is estimated by Monte Carlo and graphically displayed. The graphs show how a symmetric distribution for the coefficient conditional on the estimate coexists with an asymmetric distribution for the estimate conditional on the coefficient. Prior densities implicit in treating classical significance levels as if they were Bayesian posterior probabilities are calculated. They are shown to depend sensitively on the estimated coefficient and to put substantial probability on values of the coefficient above one. Copyright 1991 by The Econometric Society.
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