Another distinct feature is the persistence of the exogenous shocks, now estimated to
be higher, though not for the mark-up shock. The associated standard errors are somewhat
smaller, in particular the risk premium shock, perhaps reflecting the model’s ability to
capture additional uncertainty. Nevertheless, they are still high when compared to the ones
found in the literature in the case of developed economies. Note, however, that the Calvo
probability ξ is still below the prior, again indicating a large frequency of price adjustments
(every 1-2 quarters).
4 A Two-Sector NK Model with an Informal Sector
We now consider a two-sector “Formal” (F) and “Informal” (I) economy, producing dif-
ferent goods with different technologies which sell at different retail prices, PF,t and PI,t ,
say. Monopolistic competition prevails in both I and F retail sectors. In the competitive
wholesale sectors, labour and capital are the variable factor inputs and the informal sector
is less capital intensive. The capital-producing sector is competitive as before. Both capital
goods and government services are provided solely from the formal sector and the latter
are financed by an employment tax. Thus, unlike the previous two models, taxes are now
distortionary. In the general set-up, this can be shared by the formal and informal sectors,
giving us a framework in which the role of tax incidence can be studied as one of the drivers
of informality. The other drivers in our model are the degree of real wage rigidity in the
formal sector and the credit constraints facing the informal sector.
Again, we allow a proportion of all households 1 - λ to be Ricardian and λ to be non-
Ricardian. Those who are Ricardian consume C1,t . A proportion nF,t of their members
work h1F,t hours in the F-sector and a proportion 1 - nF,t work h1I,t hours in the I-sector.
Non-Ricardian (credit-constrained) households work h2I,t hours only in the I-sector and
consume C2,t out of current wage income.
4.1 Dynamic Model
Consider first the benchmark model without labour market or financial frictions. Ricardian
households are described by the following utility function
(1-%)(1-σ) %(1-σ) %(1-σ)
C CCrt C C ʌ C1 ,t (nF,tL 1 F,t +(1 - nF,t)L1 I,t ) - 1
λ1 ,t = λ(C1 ,t,L 1 F,t, L1 I,t) = --------------------------:--------------------------------
1-σ
which is a generalization of (1). As before we need their marginal utilities os consumption
and leisure given respectively by
(1-%)(1-σ)-1 %(1-σ) %(1-σ)
ΛC1t = (1 - %)C1,t (nF,tL1F,t + (1 - nF,t)L1I,t )
ΛL1it = %C1(,1t-%)(1-σ)(Li,t)%(1-σ)-1; i = I, F
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