Prior and posterior distributions Sample Clauses

Prior and posterior distributions. Table 4 reports prior and posterior medians with a 90 percent probability interval for the structural parameters and shock processes of the models Mmp+vol and M(freq+mp)+vol. The priors for constant param- eters are similar to those reported in the previous section, as well as the standard deviations of the shocks. We now discuss the prior distributions of the monetary t t policy rule. We impose an asymmetric prior for the interest rate response to infla- tion across the two regimes. In particular, the prior for the second regime [s1 = 2] corresponds to a more aggressive response to inflation—with a Normal distribution, the mean is 2.50 and the standard deviation is 0.20—than for the first regime with a Gamma distribution, the mean at 1.00 and the standard deviation at 0.20. The prior for the reaction to an output gap is symmetric across regimes. It follows a Gamma distribution with the mean at 0.30 and the standard deviation at 0.10. Finally, the interest rate smoothing parameter ρr follows the Beta distribution with 0.60 as the mean and 0.20 as the standard deviation. Finally, the prior mean probabilities for the process smp are equal to 0.95 and are associated with tight standard deviations, implying that the regimes are very persistent. Therefore, we label the Regime 1 as the “passive policy” regime and the Regime 2 as the “active policy” regime. The estimates for structural parameters, other than monetary policy coefficients, for the Mmp+vol and M(freq+mp)+vol models are close to those previously outlined. For this reason, we focus our attention on the monetary policy parameters. For Mmp+vol, t t the estimate for the interest rate response to inflation under the “passive policy” regime, ψπ(s1 = 2), is 0.8237 with the error bands [0.6412; 1.1755], covering the mode of a similar parameter ψπ(s1 = 2) = 0.8350 in M(freq+mp)+vol. This parameter is per- mitted to go below 1—leading to the indeterminacy region in a constant parameters model, but not necessary in a Markov-switching rational expectations model. The estimated posterior mode accepts the idea that the Federal Reserve has raised the nominal interest-rate less than one-for-one in response to higher inflation since post- World War II. In the “active policy” regime, both models imply that the estimate t for ψπ(s1 = 2) is about 2.45. The probability intervals of these parameters are very similar and clearly cover the estimates from the previous studies in DSGE literature [Christiano, Eichenbaum, and X...