3.1 Bayesian Estimation for India
The model with financial frictions defines extra parameters which we now try to estimate for
India. These are the proportion of liquidity constrained consumers λ, the elasticity of the
external finance premium with respect to leverage χ in (43), the entrepreneurs survival rate
ξe and the leverage ratio nk . Additionally, the model depends on the financial accelerator
risk premium parameter Θ, which we choose to calibrate at 1.01 (additional sensitivity
analysis suggests that other reasonable values for Θ delivers similar results).
Thus, we maintain the priors used for the baseline model and define additional priors
for newly estimated parameters. In the case of χ, we assume an inverse gamma with a
mean of 0.05, following Bernanke et al. (1999). Given that the remaining parameters are
expected to be between 0 and 1, we use beta distributions. For λ, we assume that 40% of
households in India are unable to optimize their consumption, with standard error of 0.1.12
We follow Gertler et al. (2003) in setting the mean of ξe equal to 0.93, with a standard
deviation of 0.05. For the leverage ratio parameter nk, required to set k in (43), we choose
the midpoint of the unit interval, with a standard deviation of 0.1.
The sixth column of Table 3 contains the posterior estimates of the model discussed
above. First, the improvement in model fit is significant. The log marginal density is now
-356.3, which corresponds to a Bayes factor of nearly 15, with a posterior model probability
of 94%. This means that the data indicates that adding the financial frictions discussed in
this section is indispensable.
The added parameters are all statistically significant, estimated with reasonable pre-
cision and within the expected bounds, apart from λ. Indeed, the proportion of liquidity
constrained households is found to be around 20%, somewhat below our prior.
Nevertheless, the quality of this model can also be gauged by analyzing the parameters
estimated previously. In general, estimates are more precise and sensible. α, for instance,
is now retrieved with great accuracy, with its estimate nearly coinciding with the long run
average in the data. Importantly, the parameters of the estimated Calvo-type interest rate
feedback rule imply that the RBI assigns a larger weight to inflation, both expected and
past, with values of 2.42 and 1.64 for θ and φ, respectively. The corresponding forward-
backward looking horizons, given by φ and τ remain similar to the previous model, though.
12There is an important connection between the size of non-Ricardian households (λ) and model inde-
terminacy. For instance, Gali et al. (2004) find that the presence of non-Ricardian consumers may alter
dramatically the properties of simple interest rules using an otherwise standard NK model. In particular,
one of their main results is that the size of the inflation coefficient that is required in order to rule out mul-
tiple equilibria is an increasing function of the weight of rule-of-thumb consumers in the economy. Following
Gali et al. (2004), we carry out a number of simulations using a standard NK model with rule-of-thumb
consumers and a Taylor-type interest rate. Based on a set of conventional parameter values, our simulation
results indeed confirm that the size of λ is an increasing function of the inflation coefficient θ. For a set of
θ = [1.5, 2, 3, 15], the threshold values of λ must be around 0.30, 0.31, 0.32, 0.40, respectively, in order to
guarantee the uniqueness of system equilibrium. When λ takes a high value under such a rule, the size of
θ required for the avoidance of indeterminacy may be too large to be credible. For this reason, we choose
a truncated prior for λ that has an upper bound of 0.4 in this and following sections. The detailed set of
simulation results is available upon request.
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