Calvo vs. Rotemberg in a Trend Inflation World - Wiwi Uni-Frankfurt

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the more appealing from a "structural" standpoint. To gauge the statistical relevance of the di¤erence in the estimated indexation parameters, Figure 2 displays the distribution obtained by plotting 10,000 pairwise di¤erences computed by subtracting the draws sampled from the posterior of the parameter under Calvo from those sampled from the posterior under Rotemberg. Positive draws from this distribution suggests a higher degree of indexation associated to Rotemberg with respect to Calvo. Notably, the larger part of the mass is clearly associated to positive realizations, with a share of about 82%. While the standard [5th pct, 95th pct] credible set includes the zero value, the stricter [25th pct,75th pct] credible set - recently employed by e.g. Cogley, Primiceri, and Sargent (2009) - does not. Thus, the data support a lower indexation parameter called for by the Calvo model. The estimation of a constrained version of the two models, i.e., with the degree of indexation set to zero, also con…rms the superiority of the Calvo model. As shown by Table 2, all the structural parameters display an appreciable stability across the di¤erent model versions. Interestingly, the marginal likelihood gives an even more clear indication: the …t of the Calvo framework improves (suggesting that indexation is just unwarranted), while the one of the Rotemberg set up deteriorates (suggesting this model needs the indexation assumption to …t the data at hand). Consequently, the Bayes factor, which in this case reads 188:67, leads to a more solid preference in favor of the Calvo model, i.e., a "very strong" evidence in the language of Kass and Raftery (1995). 3.3 Robustness checks In comparing Calvo and Rotemberg, our empirical exercises support (i) trend in‡ation equipped models, (ii) the empirical superiority of the Calvo model, and (iii) the lower degree of indexation to past in‡ation called for by the Calvo model. These conclu- 20
sions have been drawn by relying on some assumptions whose relevance for our …ndings deserves further scrutiny. Therefore, we performed some robustness checks along dif- ferent relevant dimensions. With respect to the exercises documented in this Section, we considered (a) alternative calibrations of the trend in‡ation rate, i.e. 2% and 3%; (b) indexation to trend in‡ation, i.e. = 0; (c) a more informative prior for the indexation parameter, i.e. Beta(0:25; 0:10); (d) a di¤erent measure of in‡ation, i.e. the "in‡ation gap" computed by taking raw in‡ation in deviations with respect to its Hodrick-Prescott "trend". This exercise is conducted to account for possible drifts in trend in‡ation in the sample at hand; (e) a di¤erent proxy of the business cycle, computed by modeling output’s low-frequency component with a piecewise quadratic trend with a break in 1973:I as suggested by Perron and Wada (2009); (f) alternative calibrations of the Frisch labor supply elasticity ' drawn from the interval [0:5; 1:5]. Our …ndings (i)-(iii) turn out to be robust to these perturbations. Our robustness checks are reported in the Appendix. 4 Policy implications In their theoretical paper, Ascari and Rossi (2009) show that trend in‡ation enlarges the determinacy region in the Rotemberg model. Di¤erently, a positive in‡ation rate in steady state shrinks the determinacy region under Calvo pricing. This di¤erence is clearly of great importance from a policymaking perspective, in that the set of optimal and implementable simple policy rules (rules which do rule out self-ful…lling expectations leading to ine¢ cient macroeconomic ‡uctuations) is clearly di¤erent under the two pricing schemes in presence of trend in‡ation (for an analysis on implementable optimal policy rules in models with trend in‡ation, see Schmitt-Grohé and Uribe, 2007). Of course, di¤erent regions would emerge if di¤erent model calibrations were used. However, not all the possible regions enjoy the same likelihood from an empirical point 21
Page 1 and 2: Calvo vs. Rotemberg in a Trend In
Page 3 and 4: in‡ation to 1984:I-2008:II U.S. m
Page 5 and 6: constant trend in‡ation for the p
Page 7 and 8: h R 1 0 " 1 " Y i;t di i " " 1 to Y
Page 9 and 10: adjusted by a (geometric) combinati
Page 11 and 12: the steady-state, trend in‡ation
Page 13 and 14: as well as the coe¢ cient of real
Page 15 and 16: espect to its long run trend y obs
Page 17 and 18: models, which are log-linearized ar
Page 19: the Calvo models (unrestricted) rea
Page 23 and 24: The stark di¤erence in the determi
Page 25 and 26: in‡ation on the convolutions of t
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Page 35: 1 0.5 0 Inflation vs. price dispers

Calvo vs. Rotemberg in a Trend Inflation World - Wiwi Uni-Frankfurt

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