文档介绍：Topics in Macroeconomic Policy: Optimal ary and Fiscal Policies
A Standard Framework To Study ary Policy
petition:
Production Technology:
Government Spending [assume GS is a fraction τ of output and hence g = -ln(1-τ)]:
Household Behavior:
By some approximations, we also have
The supply of labor satisfies:
From the labor supply equation, we have
The intertemporal equation yields
Finally, assume money demand as
Assume flexible price, from (1) and (2) one can see that money policy is neutral:
Note: (3) implies first best allocation can be achieved by setting v = μ. Moreover, (4) indicates optimal policy rule of real interest rate (mechanism). Finally, (3) and (4) show this is a model with prominent Keynesian properties.
where
Staggering Price
Assume each firm resets price in any period only with probability 1-θ. So the evolution of aggregate price can be approximated by the following
Note that this is different from simple sticky price assumption. Firm solves the following programming to set pt*
Subject to (5) and pt = pt*. With the static price rule p = mc + μ, we obtain
Here mcn denotes nominal marginal cost. From (1) and (3), we know
Then from (5) and (6), one can obtain a New Phillips curve
κ is a positive parameter (?). From (2) and (4), one can further obtain
(7) and (8) characterize the dynamics of the model.
Note that there are 4 distortions in the model. First, money-holding cost (Friedman Rule). We ignore this because of the ad hoc money demand assumption. Second, static distortion from petition (solved by the subsidy v). The Third is firms’ inability to adjust prices and the Fourth is the relative price distortion (due to the lack of synchronization in pricing), which induces allocation inefficiency. Intuitively, the optimal ary policy requires xt = πt = 0 to eliminate the last two distortions (mechanisms).
The Taylor Rule
Taylor (1993) finds . ary policy follows a simple rule (why not M?):
Generally the Taylor Rule is not optima