The paper considers an elementary New-Keynesian three-equation model and compares its Bayesian estimation based on conventional priors to the results from the method of moments (MM), which seeks to match a finite set of the model-generated second moments of inflation, output and the interest rate to their empirical counterparts. It is found that in the Great Inflation (GI)
period---though not quite in the Great Moderation (GM)---the two estimations imply a significantly different covariance structure. Regarding the parameters, special emphasis is placed on the degree of backward-looking behaviour in the Phillips curve. While, in
line with much of the literature, it plays a minor role in the Bayesian estimations, MM yields values of the price indexation parameter close to or even at its maximal value of unity. For both GI and GM, these results are worth noticing since in (strong or, respectively, weak)contrast to the Bayesian parameters, the covariance matching thus achieved appears rather satisfactory.