An Estimated DSGE Model of the Indian Economy.

where consumption, technical LAP, the real wage and tax rates, and government spending
(all indicated by X_t) are growing at a common growth rate.

There are three parameters A_F, A_I and w that are dependent on the units chosen and
therefore cannot be calibrated nor estimated. By choice of units of labour in both sectors,
and units of capital and labour, we can normalize AF = AI = 1. Then instead of estimating
w for which we can have no priors we estimate a dimensionless quantity: the relative nominal
outputs for the two sectors rel_Y . In terms of the endogenous steady state variable w we
then have

PfYf ₌ 'w Pt 1-- Ct + (PF) (It + Gt)
Pi Y- =      (1 - w) ( P ´¹ -^μ CIt

From (B.1) we can solve for w to obtain

relγ ( P ´^{1 μ} Ct - ( P ´ (It + Gt)
⁽ P )¹ ~^μ Ct + relY ⁽ P )¹ ~^μ Ct

so we can solve for w as a post-recursive variable. This completes the specification of the
model which now includes relY as a parameter to be estimated, which has been switched
with w which is now an endogenous variable in the steady state.

We can also use data for the the relative numbers of workers employed in the formal
sector reln given in the model by

_rel =     ^{(1 -} ʌ) nF

n (1 - A)(1 - nF) + A

From Marjit and Kar (2008) we learn that in 2001 80% workers in industry were informal
and they contributed 28% to GDP. This implies reln = 0.25 and relY = 2.6 implying
a formal-informal labour productivity ratio of around 10:1. Sen and Kolli (2009) suggest
estimates reln = 0.1 and relY = 1.1 implying a slightly higher productivity ratio 1:11. Rada
(2009) provide estimates reln = 0.075. relY = 0.68 implying a slightly lower productivity
ratio 1:9.¹⁶

The question is: how can the model be calibrated to reproduce this high productivity
gap? There are two parameters we can vary that increase the size of the informal sector and
reduce its marginal product of labour: the mark-up of the real wage in the formal sector
over that in the informal sector, rw, and labour shares in production, αI and αI . Figure
2 puts αF = 0.6 < αI = 0.8 and varies rw, Figure 3 puts αF = 0.5 < αI = 0.8 and again

¹⁶ This productivity gap seems very high. Ila Patnaik has pointed out that the informal sector employment
numbers may be exaggerated as they include all household members, employed or otherwise, in the household
sector. As a first attempt we therefore choose priors reln = 0.2, relY = 1 implying a productivity ratio of
1:5.

40

<<   41   42   43   44   45   46   47   >>

More intriguing information