implications of the model and evidence from previous studies. However, as noted in the
introduction, estimated DSGE models for emerging economies, and India in particular, are
scarce, though one might infer potential priors by comparing the features and stylized facts
of developed and developing economies. In general, inverse gamma distributions are used
as priors when non-negativity constraints are necessary, and beta distributions for fractions
or probabilities. Normal distributions are used when more informative priors seem to be
necessary. In some cases, we use the same prior means as in previous studies (Levin et al.
(2006), Smets and Wouters (2003) and Smets and Wouters (2007), for example), but choose
larger standard deviations, thus imposing less informative priors and allowing for the data to
determine the parameters’ location. The first four columns of Table 3 provide an overview of
the priors used for each model variant described below in the case of India. For consistency
and comparability, all priors are the same across different specifications.
The risk aversion parameter σ allows significant room for manoeuvre, with a normal
prior defined with a mean of 2 and standard deviation of 0.5. The beta prior density for %
is centred in the midpoint of the unit interval with a standard deviation of 0.2, while the
Calvo-pricing parameter ξ has a mean of 0.75 and standard deviation of 0.1 as in Smets
and Wouters (2007), implying a contract length of 4 quarters. The labour share α has a
normal prior with mean 0.8 (approximately its steady state value10), while ζ has a mean of
7 with a standard deviation of 0.5.
For the policy parameters, priors were chosen so that a large domain is covered, reflecting
the lack of knowledge of the RBI reaction function. We choose beta distributions for the
parameters that should be constrained between 0 and 1, namely the smoothing coefficient
ρ (centred around 0.75 with a standard deviation of 0.1) and the forward-backward looking
parameters φ and τ, with a mean of 0.5 and a standard deviation of 0.2, a relatively diffuse
prior. The feedback parameters θ and φ have normal priors with a mean of 2 and a standard
error of 1, thus covering a relatively large parameter space.
The shock processes are the likeliest elements to differ from previous studies based on
the US economy. Adolfson et al. (2008), for example, argue for choosing larger prior means
for shock processes when analyzing a small open developed economy (Sweden). In the case
of India, it is natural to expect significantly larger swings in the macro observables and the
prior means for the standard errors are therefore set at 3 (3.5 for the risk premium shock,
higher than the US), using an inverted gamma distribution.
2.5.3 Posterior Estimates
The joint posterior distribution of the estimated parameters is obtained in two steps. First,
the posterior model and the Hessian matrix are obtained via standard numerical optimiza-
tion routines. The Hessian matrix is then used in the Metropolis-Hastings algorithm to
10We chose not to calibrate α to its steady state value and instead freely estimate this parameter. The
proximity of the estimated values for α will provide additional indications regarding the quality of the fit
for each model.
12