An Estimated DSGE Model of the Indian Economy.

Demand for capital by firms must satisfy

Et h(1^^ ^α) ∣+. ₊    + (1^^ ^δ)Qt+ɪi

Qt

In (15) the right-hand-side is the gross return to holding a unit of capital in from t to t + 1.
The left-hand-side is the gross return from holding bonds, the opportunity cost of capital
and includes an exogenous risk-premium shock RPSt, which, for now, we leave unmodelled.
We complete the set-up with investment costs by defining the functional form

S(X) =φX(Xt-(1+g))²

The RBC model we have set out defines a equilibrium in output, Yt , consumption Ct ,
investment It , capital stock Kt and factor prices, Wt for labour and Rt for capital, and the
price of capital Qt , given exogenous processes for technology At , government spending Gt
and the risk premium shock RP S_t.

2.2 From RBC to NK

The NK framework combines the DSGE characteristics of RBC models with frictions such as
monopolistic competition - in which firms produce differentiated goods and are price-setters,
instead of a Walrasian determination of prices, and nominal rigidities, in which firms face
constraints on the frequency with which they are able to adjust their prices. Therefore,
we now introduce a monopolistically competitive retail sector that uses a homogeneous
wholesale good to produce a basket of differentiated goods for consumption

where ζ is the elasticity of substitution. This implies a set of demand equations for each
intermediate good m with price Pt(m) of the form

Ct ( m )= μ PtPm ) ^ζ Ct

where P_t = [R_q^l P_t(m)ɪ^-ζdm ^{1 z} is the aggregate price index. A competitive capital-
producing sector is modelled as for the RBC model

Conversion of good m from a homogeneous output requires a cost cY_t^W (m) where whole-
sale production uses the production technology (8). Thus

Yt(m) = (1 - c)Y_t^W (m)

YtW = ( Atht ) ^αK1^-α

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