between the two sectors in terms of labour intensity (αF and αI), the degree of price stick-
iness (ξF and ξI), market power (ζF and ζI), the elasticity of substitution between goods
in the formal and informal sectors (μ), the degree of real wage rigidity (rw), the size of the
informal sector (w, relY and reln), and financial frictions (χF and χI, nkF and nkI , ξFe and
ξIe). We also allow for sector-specific technology and mark-up shocks, and we attempt to
estimate the relative size of the informal sector.
In terms of priors for the new set of parameters, we maintain those used for the aggregate
economy model estimated in the previous section. In terms of the size of the informal
sector, given by 1 - w, for which we have no prior information, we estimate a dimensionless
quantity: the relative nominal outputs for the two sectors relY instead of estimating w. We
normalize AI = AF = 1.0 and choose prior means (that will hit reln = 0.2 approximately),
of rw = 0.75, relY = 1.0, αF = 0.6 and αI = 0.8. See Appendix B for more details on
the calibration and prior settings of the parameters related to the size of informality. For
the additional parameter μ, we assume a normal prior centred around 1.5 with a standard
deviation of 0.2. On the other hand, we impose a beta distribution centred at 0.75 for the
degree of wage rigidities rW, with a standard deviation of 0.1. Note that the model depends
on other parameters, which we calibrate, namely a sector-specific financial accelerator risk
premium (ΘF and ΘI), the latter fixed at 1.06, as one would expect a higher risk premium
associated with the informal sector.13
The posterior estimates and confidence intervals for this model are presented in the right-
most column of Table 3. The two bottom lines of Table 3 report the log marginal likelihood
and posterior model probabilities comparing the three models under study. A striking
result is the substantial improvement in fit achieved by the two-sector model over the
simpler financial frictions model. Indeed, the difference in the log likelihoods is remarkable,
lending unequivocal support to the third model compared with the second and very strong
support for the second compared with the first.14
The model also produces other interesting results. In terms of the formal-informal
dichotomy, the data is informative about the size of the informal sector as the relative
nominal outputs for the two sectors is 1.15 and the relative numbers of workers employed
in the formal sector are 0.28, which gives us a rather lower estimate for the size relative
to our prior assumptions, but still consistent with much of the evidence on informality in
India. In addition, we learn that the shock processes are more persistent and more volatile
in the informal sector, which seems a plausible outcome. Likewise, the estimated model
indicates that the informal sector is more labour intensive, as αI is larger than αF .
In terms of the financial friction mechanisms, differences are less marked. Although the
13See Haugen (2005) for some empirical support for this prior.
14Using pi = p1BF (i, 1) and (38) the model probabilities calculated from the estimated posterior distri-
bution are 0.9959, 0.0039 and 0.0003 for the third, second and first model respectively. According to Jeffreys
(1961) this constitutes “decisive evidence” in favour of the third over the second model, and “strong to very
strong evidence” of the second over the first - see Dejong and Dave (2007), chapter 9 for a useful discussion
of model comparison.
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