Uncertainty, model selection, and the PPP puzzle

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This article employs a Bayesian methodology to measure the uncertainty involved in the long-run holding of the purchasing power parity (PPP) and in the half-life (HL) of deviations from it. Our Bayesian approach combines estimates obtained from ARMA, ARFIMA, and ARIMA specifications so that it is able to take into account model uncertainty. Exact posterior distributions corresponding to all the features of interest (fractional orders of integration, impulse responses, HLs, etc.) are derived. Our results suggest that model uncertainty is high, which implies that uncertainty estimates can be severely biased downwards when the former is not explicitly considered. In spite of that, support for the long-run holding of the PPP is substantial in most countries. However, the speed at which this happens seems to be much slower than what has been suggested, as shown by the fact that the probability of the HL lying in the three- to five-year interval is very small.