SBP Working Paper Series STATE BANK OF PAKISTAN

In this model, the central bank directly transfers money to households and real money balances evolve as
in equation (17). The real money balances are no longer part of the utility function and household
maximizes the following utility function
U
i
= E
t i i
t ln ct
Aht
(31)
t=0
subject to cash-in-advance constraint in equation (29) and budget constraint in equation (20). The first
order conditions for this model are:
w
Et
w
t
1
=
t
R
t
(32)
t1
A 1
= Et
i
wt
t1ct
1
(33)
1 1 k
= Et
(1 rt
1
)
wt
wt
1
(34)
3.3 Interest Rate Targeting Model
In this model, the central bank operates by following a Taylor type interest rate rule by reacting to the
fluctuations in output and inflation from their steady state values.
This way of modelling central banks’ behaviour has become the workhorse of DSGE models for
analyzing the role of monetary policy in both developed and developing economies. Even though, in our
empirical section, we only found a weak link between interest rates and short run fluctuations in output,
we still wanted to evaluate the role of short term interest rate as a tool of monetary policy in propagating
business cycles in a developing economy. The best way to do this was to use the well established
theoretical framework in literature of modelling monetary policy as a Taylor type interest rate rule in a
simple New Keynesian DSGE model.
For this model, we assume that the economy is cashless and we briefly discuss households’ behavior and
monetary policy in this scenario.
3.3.1 Households
The households maximize utility function represented by equation (31) subject to combined budget
constraint obtained by addition of budget constraint in equation (18) and capital accumulation constraint
in equation (19)
The first order conditions of households are same as those found in equation (21), (22) and (23).
3.3.2 Monetary Policy
In this set up, the central bank conducts monetary policy through Taylor type interest rate rule by
changing policy rate in response to fluctuations of output and inflation. The interest rate reaction function
is given as:
19