An Estimated DSGE Model of the Indian Economy.

To introduce price stickiness, we assume that there is a probability of 1 - ξ at each
period that the price of each intermediate good m is set optimally to P_t⁰(m). If the price
is not re-optimized, then it is held fixed.⁵ For each intermediate producer m, the objective
is at time t to choose {P_t⁰(m)} to maximize discounted profits

∞

Et X ξk Dt,t+k Yt+k ( m ) £ Pt ( m ) - Pt+k MCt+k ]                 (21)

k=0

subject to (18), where D_t,t+k is now the nominal stochastic discount factor over the interval
[t, t + k]. The solution to this is

In setting up the model for simulation and estimation, it is useful to represent the
price dynamics as difference equations. Using the fact that for any summation St ≡
^P_k^∞₌₀ β^kXt+k , we can write

St = Xt+^X∞ β^kXt+k = Xt + ^X∞ β^k0+1Xt+k0+1 puttingk⁰=k+1
k=1                   k⁰=0

= Xt + βSt+1                                                   (24)

and defining here the nominal discount factor by D_t,_t+k ≡ β^λCjt+^k∕^pt_t^+k■ inflation dynamics
are given by

Ht-ξβEt[Πt^ζ+^-1¹Ht+1]

Jt-ξβEt[Πt^ζ+1Jt+1]

1

Real marginal costs are no longer fixed and are given by

P^W

MCt = t.                                  (28)

Pt

⁵Thus we can interpret ι^ as the average duration for which prices are left unchanged.

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