EC924 - Monetary Economics
Irfan Qureshi
University of Warwick
February, 2016
Irfan Qureshi (University of Warwick)
EC924 - Monetary Economics
February, 2016
1/8
Monetary Policy rule
it = ρ + φπ π + φỹ ỹ + vt
(1)
Monetary Policy shock
vt = ρv vt−1 + vt
(2)
at = ρa at−1 + at
(3)
Technology shock
We write this in state space representation
Then we ’shock’, at and vt ⇒ ↑ at and ↑ vt ⇒ yt
Irfan Qureshi (University of Warwick)
EC924 - Monetary Economics
ỹt
πt
...
February, 2016
2/8
Dynare output:
Dynare does 1000 replications of yt ỹt πt ... and displays the
mean, standard deviation, variance of those 1000 series.
The ”constant” in the policy and transition functions are just steady
state values.
Dynare produces a matrix of correlations as well as coefficients of
autocorrelation variables at different lags.
Irfan Qureshi (University of Warwick)
EC924 - Monetary Economics
February, 2016
3/8
Question 1(c)
What happens after a shock to monetary policy vt ?
Increase in it
This reduces expected inflation Et πt+1
This increases the real interest rate, through the Fischer equation, rt
This is a demand side model:
I
I
I
I
A high it generates an incentive for households to postpone
consumption and save
This fall in consumption reduced the output gap
Actual output must fall with the fall in consumption
Deflationary pressure reduces inflation.
In order to bring this effect the C.B engineers a reduction in the
money supply.
M.P shock does not affect the flexible price output
Irfan Qureshi (University of Warwick)
EC924 - Monetary Economics
February, 2016
4/8
Question 1(d)
The sign of output and employment to a positive technology shock is in
general ambiguous, since it depends on parameter values (calibration),
including the interest rate coefficients.
n =1
Baseline calibration, σ = 1 → ψya
In this case a technological improvement leads to a persistent decline
in employment.
Improvement in technology is partially accomodated by the Monetary
Authority, which lowers nominal interest rates, while increasing the
money in circulation.
This policy is not sufficient to close a negative output gap, which is
responsible for the decline in inflation.
Irfan Qureshi (University of Warwick)
EC924 - Monetary Economics
February, 2016
5/8
Question 1(d)
Under the baseline calibration output increases, though less than its
natural counterpart, and employment declines
n
n
nt = [(ψya
− 1) − σψya
(1 − ρa )(1 − βρa )Λa ]at
(4)
Since Λa > 0
negative
z
}|
{ positive
z}|{
nt = [0 − (1 − ρa )(1 − βρa )Λa ] at
nt < 0
Irfan Qureshi (University of Warwick)
EC924 - Monetary Economics
(5)
February, 2016
6/8
Question 1(e)
φπ < 1, violates the Taylor principle
Monetary Authority should respond more than 1-1 to expected
inflation
Self fulfilling expectations.
Taylor rule
it = πt + rt + aπ (πt − πt∗ ) + ay (yt − yt∗ )
(6)
aπ > 0, aπ = 0.5
ay > 0, ay = 0.5
1% rise in inflation → it should respond more than 1 + aπ
Irfan Qureshi (University of Warwick)
EC924 - Monetary Economics
February, 2016
7/8
Question 1(f)
Variance Decomposition: indicates the amount of information each shocks
contributes to the variables in the model.
y n : natural output
n
ytn = ψya
at + θyn
(7)
r n : natural rate of interest
n
(1 − ρa )at
rtn = −σψya
Irfan Qureshi (University of Warwick)
EC924 - Monetary Economics
(8)
February, 2016
8/8