An Estimated DSGE Model of the Indian Economy.

In this utility function σ ≥ 1 is a risk-aversion parameter which is also the inverse of the
inter-temporal rate of substitution. The parameter % ∈ (0, 1) defines the relative weight
households place on consumption and this form of utility is compatible with a balanced
growth steady state for for all σ ≥ 1.³ For later use, we write down the marginal utilities
of consumption and leisure as, respectively,

_{ΛC,t = (1 - %)Ct}(1-%)(1-σ)-1_Lt%(1-σ)                           ₍₂₎

The value function at time t of the representative household is given by

where β is the discount factor. In a stochastic environment, the household’s problem at
time t is to choose state-contingent plans for consumption {Ct}, leisure, {Lt} and holdings
of financial savings to maximize Ω_t given its budget constraint in period t

Bt+1 = Bt(1 + Rt) + Wtht - Ct

where Bt is the net stock of real financial assets at the beginning of period t, Wt is the real
wage rate and Rt is the real interest rate paid on assets held at the beginning of period t.
Hours worked are h_t = 1 - L_t and the total amount of time available for work or leisure is
normalized at unity. The first-order conditions for this optimization problem are

ΛC,t ⁼ βEt [(1 + Rt+1)ΛC,t+1]

= Wt

ΛC,t

Equation (6) is the Euler consumption function: it equates the current marginal utility of
consumption with the discounted marginal of consumption of a basket of goods in period
t + 1 enhanced by the interest on savings. Thus, the household is indifferent as between
consuming 1 unit of income today or 1+Rt+1 units in the next period. Equation (7) equates
the marginal rate of substitution between consumption and leisure with the real wage, the
relative price of leisure. This completes the household component of the RBC model.

Turning to the production side, we assume that output Yt is produced by the rep-
resentative competitive firm using hours, ht and beginning-of-period capital Kt with a
Cobb-Douglas production function

Yt = F(At,ht,Kt) = (Atht)^αKt^1-α
3See Barro and Sala-i-Martin (2004), chapter 9.

<<   5   6   7   8   9   10   11   >>

More intriguing information