CAPACITY AND ASYMMETRIES IN MONETARY POLICY
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which is assumed to follow an AR(I) stochastic process13
(2-28) xt = (1 -px)x + pxxt-ι + εxt
with 0 < px < 1 and ε3,4is an i.i.d. shock to xt with zero mean and standard
deviation σx. The random variable εxt is assumed to be orthogonal to all other
variables in the model.
2.4. Households. The economy is populated by a continuum of homogeneous
households of unit measure. These agents value alternative stochastic streams of a
(composite) consumption good Ct and labor Lf, according to the following lifetime
expected utility function
(2.29) E0∑βtU(Ct,l-Lst)
t.=o
where β > 0 represents households’ intertemporal discount factor. Here, Et denotes
the expectation operator conditional on the information at date t. Throughout the
paper, it is assumed that the function U (∙) is given by
f [c7(ι-L4s)1-γ]1^"-ι , . 1
(2.30a) I7(C,t,Lf) = < ------------. , . for σ ≠ 1
( y log (Ct) + (1 - 7) log (1 - Lf) for σ = 1
Here I-Lt denotes the quantity of leisure time, and the total time for work -the
time endowment- is set at 1. The curvature parameter σ measures the relative
risk aversion. The parameter 7 is a scalar between 0 and 1 and it represents the
consumption expenditure share in the utility function.
The representative household begins period t holding an amount Mt of liquid
assets that represent the economy’s stock of money. At this point in time, it decides
how much money is going to be deposited in a saving account, Dt. The remaining
currency Mt - Dt, together with labor income, will be used to finance purchases of
a consumption good. Therefore, the household faces the following cash constraint
in the final goods market:
(2.31) PtCt ≤ Mt D1 + WtLst
where Lf represents the fraction of time actually devoted to work and Wt is the wage
paid in the competitive labor market for each unit of time supplied. Importantly,
portfolio decisions take place before the realization of the monetary shock. As
a result, the equilibrium rate of interest falls, and output and employment rises.
Income for the household is derived from several sources: labor income, WtLf,
which are the only source of income available to finance current period transactions;
profits from financial intermediaries ∏6 and from input firms W, and rents from
bank deposits. Thus, the stock of money, Mt+ι, in the hands of the household at
the end of period t is given by
(2.32) Mt+ι ≤ Mt -Dt + WtLst - PtCt + (1 + Rt) Dt + Hf + ∏6
13Christiano, Eichenbaum and Evans (1998) show that this is a good approximation when
money is measured by broad monetary aggregates such as М2, but when the concept of money
refers to Ml or even the monetary base, the monetary policy shock is better represented by a
second order MA process.