EC924 - Monetary Economics
Irfan Qureshi
University of Warwick
February, 2016
Irfan Qureshi (University of Warwick)
EC924 - Monetary Economics
February, 2016
1 / 18
Today
1
Housekeeping - 1
2
Housekeeping - II
3
Housekeeping - III
4
Empirical motivation
5
A Classical Monetary Model
Irfan Qureshi (University of Warwick)
EC924 - Monetary Economics
February, 2016
2 / 18
About me
Irfan Qureshi
i.a.qureshi@warwick.ac.uk
Office:
I
I
I
Location: S2.94, Department of Economics
Hours: Friday 2:30 p.m - 3:30 p.m
No booking required
www.warwick.ac.uk/iqureshi
Irfan Qureshi (University of Warwick)
EC924 - Monetary Economics
February, 2016
3 / 18
Organisation of the course
3 seminars
In the second seminar we will be working with DYNARE. Please bring
your laptops to class.
Irfan Qureshi (University of Warwick)
EC924 - Monetary Economics
February, 2016
4 / 18
Organisation of the seminars
Interactive
I
Go through each problem set together.
Organised
I
Finish each problem set
Revise
I
Any concepts you might have missed out in class
Feedback
I
I
I
An opportunity for you to receive feedback on your own thoughts
about the course.
Time to think about your dissertation
Will mention frontier literature where needed
Irfan Qureshi (University of Warwick)
EC924 - Monetary Economics
February, 2016
5 / 18
SVAR - CEE(1999)
Classic paper on identifying and studying the effects of monetary
policy shocks
Numerous others:
I
I
Romer and Romer: Use meeting level data to identify and study the
impact of monetary policy shocks on the real and nominal economy.
(AER 2004).
Nakamura Steinsson: Use increase in the volatility of interest rate news
in a 30-minute window surrounding scheduled Federal Reserve
announcements arises as news about monetary policy. (AER
forthcoming)
Irfan Qureshi (University of Warwick)
EC924 - Monetary Economics
February, 2016
6 / 18
Question 1:(a)
Intuition:
CEE first represent the monetary policy instrument using the
following equation:
I
I
instrument
feedback rule
z}|{
St
z }| {
f (Ωt )
=
exogenous variations
+
z}|{
σs st
Ωt : Monetary authority’s information set (systematic part) - example
inflation and output.
st : Measure of monetary policy shock (unsystematic part) - exogenous.
Partition set of variables in their VAR(Yt ) as Yt = Y1,t
I
I
I
St
Y2,t
0
Y1,t : contains variables whose time t elements are in the information
set of the Monetary Authority
St : represents a monetary policy instrument (federal funds rate)
Y2,t : other variables that are in the information set but respond
contemporeneously to the monetary policy shock.
Irfan Qureshi (University of Warwick)
EC924 - Monetary Economics
February, 2016
7 / 18
The recursiveness assumption:
Find a lower triangular matrix A0 which relates structural VAR
(SVAR) errors, ut and reduced form VAR errors t as following:
A0 ut = t
(1)
Finally they assume that A0 is lower triangular matrix. (special case
of LU decomposition)
Indeed by Cholesky factorisation there exists the unique representation
−1 0
V = A−1
0 (A0 )
(2)
This assumption is in fact the recursiveness assumption which implies
that monetary policy shocks are orthogonal to the information set of
the monetary authority.
Irfan Qureshi (University of Warwick)
EC924 - Monetary Economics
February, 2016
8 / 18
Response to an expansionary monetary policy shock:
Nominal interest rate falls → Real interest rate falls
Output will rise
Inflation will rise
...but what is the transmission mechanism? Need a structural model to
study the transmission mechanism of monetary policy. We could do this in
a VAR but will have to include other variables.
Classic paper on the transmission mechanism: Mishkin (1995).
Irfan Qureshi (University of Warwick)
EC924 - Monetary Economics
February, 2016
9 / 18
Question 1:(b)
Money Demand
mt − pt = yt − ηit
I
I
I
I
I
(3)
mt : log of money balances
pt : log of price levels
yt : log of output level
it : net nominal interest rate
η: interest semi elasticity of money demand
Monetary policy summarised by an exogenous path for the growth
rate of money supply, ρm ∈ [0, 1]
∆mt = ρm ∆mt−1 + m
t
(4)
Note: Gali (2008, chapter 2) normalises coefficient on output to 1.
Irfan Qureshi (University of Warwick)
EC924 - Monetary Economics
February, 2016
10 / 18
Question 1:(b)
Derive the equilibrium conditions of the model and log-linearise them
σct + ϕnt = wt − pt
(5)
wt − pt = at − αnt
(6)
yt = ct
(7)
yt = at + (1 − α)nt
(8)
at = ρa at−1 + at
(9)
1
(it − Et πt+1 − ρ)
(10)
σ
Solve this system to get the equilibrium level of employment, output, real
wage and real interest rate
ct = Et ct+1 −
Irfan Qureshi (University of Warwick)
EC924 - Monetary Economics
February, 2016
11 / 18
Question 1:(b)
Equilibrium level of employment
log(1 − α)
σ(1 − α) + ϕ + α
(11)
(1 − α) log(1 − α)
σ(1 − α) + ϕ + α
(12)
(σ(1 − α) + ϕ) log(1 − α)
σ(1 − α) + ϕ + α
(13)
nt = ψna at +
Equilibrium level of output
yt = ψya at +
Real wage will be given by:
ωt = ψωa at +
Real interest rate
yt = rt + σψya Et ∆at+1
Irfan Qureshi (University of Warwick)
EC924 - Monetary Economics
(14)
February, 2016
12 / 18
Question 1:(b)
What do all these equations mean?
I
I
Real variables are determined independantly of monetary policy, and
therefore monetary policy cannot affect them.
This is contrast with the data (evidence by CEE (1999))
Lets use the ad-hoc money demand and equation for money supply to
obtain equation for prices as a function of future money holdings
pt = mt +
k
∞ X
η
Et ∆mt+k + ut0
1+η
(15)
k=1
Unique solution to price level for exogenous money supply path
Irfan Qureshi (University of Warwick)
EC924 - Monetary Economics
February, 2016
13 / 18
Question 1:(b)
Write the exogenous money supply in recursive form and plug it in
equation 15...
pt = mt +
ηρm
∆mt
1 + η(1 − ρm )
(16)
Under standard parameters, the response of prices to exogenous
money supply shocks is quite large
This is contrast with empirical evidence
I
I
Inflation response was sluggish, meaning that prices did not respond
much
Response more than 1-1
Irfan Qureshi (University of Warwick)
EC924 - Monetary Economics
February, 2016
14 / 18
Question 1:(c)
Optimal Monetary policy?
Trick Question: Optimal monetary policy will not matter for the real
part of the economy.
In part (b) we just showed that real part of the economy does not
depend on monetary policy.
Since money does not enter the utility function of households, and
therefore does not affect the optimality conditions of the firms or the
households, stablising inflation will not have any effect of the utility of
agents in this ecoomy.
Irfan Qureshi (University of Warwick)
EC924 - Monetary Economics
February, 2016
15 / 18
Question 1:(d)
1
Introducing money in the utility function:
I
Depends on the way money is introduced in the utility function
F
F
Seperable: Same as before, money holdings will not affect the FOC wrt
consumption and labour, same logic of part (c)
Not seperable: Optimality conditions would be affected. Ramsey
problem means that social planner would maximize a sequence of static
problems of the form:
Mt
U(Ct ,
, Nt )
(17)
Pt
(1−α)
subject to Ct = At Nt
I
Optimality condition w.r.t to money balances will be given by:
−
Un,t
= (1 − α)At Nt−α
Uc,t
(18)
Um,t = 0
Irfan Qureshi (University of Warwick)
EC924 - Monetary Economics
(19)
February, 2016
16 / 18
Question 1:(d)
We know from the household problem that MRS betwen money
holdings is:
Um,t
= 1 − exp(−it )
(20)
Uc,t
The only way for this to be the case is for the nominal interest rate to
be equal to zero.
This is the well known Friedman rule
Irfan Qureshi (University of Warwick)
EC924 - Monetary Economics
February, 2016
17 / 18
Question 1:(d)
Increase in the utility of holding money balances has to be equal to
the cost: one monetary unit minus the cost of buying a bond that
gives one monetary unit in period t + 1. When it > 0
Um,t
Um,t
<
Uc,t
Uc,t
I
(21)
Only when the nominal rate is zero are the private and social costs of
holding money equated.
MB: transaction costs, MC: it
Since MC = 0, HH can hold as much money as they want to, the
Monetary Authority can supply as much as it wants to (since it is
costless), therefore it = 0
Irfan Qureshi (University of Warwick)
EC924 - Monetary Economics
February, 2016
18 / 18