generate a sample from the posterior distribution. Two parallel chains are used in the
MCMC-MH algorithm and in all the estimations reported in this paper, the univariate
diagnostic statistics produced by Dynare indicate convergence by comparing between and
within moments of multiple chains (Brooks and Gelman (1998)).
Thus, 100,000 random draws (though the first 30% “burn-in” observations are dis-
carded) from the posterior density are obtained via the MCMC-Metropolis Hastings algo-
rithm (MH), with the variance-covariance matrix of the perturbation term in the algorithm
being adjusted in order to obtain reasonable acceptance rates (between 20%-40%).11 The
estimation results for the US report the Bayesian inference in Table 2. Table 3, fourth
column, reports posterior means of all estimated parameters using the Indian data, along
with the approximate 95% confidence intervals based on the approximate posterior standard
deviation obtained from the inverse Hessian at the posterior mode.
As shown in Table 2, the estimation results are plausible and are generally similar
to those of Levin et al. (2006) and Smets and Wouters (2007) for the US. In particular,
the posterior mean estimates for the Calvo price-setting parameter, ξ, imply an average
price contract duration of around 2.5 quarters, similar to the findings of Christiano et al.
(2005), Levin et al. (2006) and Smets and Wouters (2007). It is interesting to note that the
risk-aversion parameter (σ) is estimated to be slightly greater than assumed in the prior
distribution, indicating that the inter-temporal elasticity of substitution (proportional to
1 /σ) is estimated to be about 0.54 in the US, which is plausible as suggested in much
of RBC literature. As usual, monetary policy disturbances (eMPS) are less important in
driving inflation and output in the US.
As expected, the policy rule estimates imply a fairly strong response (θ) to expected
inflation by the US Fed Reserve and the degree of interest rate smoothing (ρ) is fairly
strong. Our posterior results also suggest that the point estimates of the policy reaction to
past inflation appear small, which is in line with our prior belief. The estimated degree of
backward lookingness is well below the prior mean, further suggesting that the practice of
the Fed is consistent with a substantial degree of forward-looking behaviour. This reinforces
previous findings in the literature, in particular Gabriel et al. (2009).
Turning to the estimates for India, the estimated ξ is well below its prior of 0.75,
suggesting that firms adjust prices quite frequently, between 1 and 3 quarters, and implying
only mild price stickiness. Similarly, the estimated model undershoots α, suggesting a
labour share of 62%. Note, however, that structural parameters like σ and ζ deviate little
from their prior means, in fact the posterior distributions overlap with the prior ones, which
might suggest that the data is not very informative about these parameters. %, on the other
hand, is pinned down with better precision at around 0.4.
In terms of the policy parameters, we find a substantial degree of policy inertia, with
ρ reaching 0.81. More importantly, the estimated Calvo rule seems to suggests that the
RBI sets interest rates reacting strongly to expected inflation (with the feedback coefficient
11See Schorfheide (2000) for more details.
13