Bayesian Econometrics and How to Get Rid of Those Wrong Signs

In many instances, Bayesian Econometrics offers a more natural interpretation of the results of a statistical investigation than does the sampling theory approach. Furthermore, the Bayesian approach provides a formal framework for incorporating prior information which is frequently available from economic theory. Despite these advantages of the Bayesian approach, applied econometric work has generally been dominated by the sampling theory approach. A simple regression example with one coefficient is used to describe the Bayesian approach using three different priors: a natural conjugate informative prior, a non informative prior, and a prior with inequality restrictions on the sign and possibly magnitude of the coefficient. The differences between the sampling theory and Bayesian approaches are highlighted. Some practical problems with the first two priors are suggested as possible reasons for the non adoption of the Bayesian approach; it is argued that the inequality restricted prior provides a practical and meaningful alternative which is likely to increase the appeal of the Bayesian approach. The implications are outlined of extending the simple one coefficient model to one where the error variance is unknown and then one where there is an unspecified number of coefficients. An example is provided of how to compute Bayesian inequality restricted estimates using the econometric computer program SHAZAM.