EC924 - Monetary Economics
Irfan Qureshi
University of Warwick
March 2016
Irfan Qureshi (University of Warwick)
EC924 - Monetary Economics
March 2016
1 / 15
Today
We will discuss the Summer 2014/2015 exam.
Irfan Qureshi (University of Warwick)
EC924 - Monetary Economics
March 2016
2 / 15
Question:1
Consider the Baseline New Keynesian model that we discussed in
class.
(a) List the agents (decision makers) in this economy. Formalise
their behaviour mathematically and find the conditions that
describe their optimal decisions. Discuss the intuition behind
these conditions.
Two types: Production sector is not split into two parts, and in which
households directly buy intermediate goods from intermediate goods
producers (these producers are monopolistically competitive). In both they
ε
R
ε−1
ε−1
1
ε
di
, and maximize
would have demand given by Ct ≡ 0 Ct (i)
their lifetime utility subject to their budget constraint:
Z
1
Pt (i) Ct (i) di + Qt Bt ≤ Bt−1 + Wt Nt − Tt
0
Irfan Qureshi (University of Warwick)
EC924 - Monetary Economics
March 2016
3 / 15
Question:1
i Consider the setup where we split production sector into two parts:
final good producer (competitive), and intermediate goods producers.
Final good producer packs intermediate goods to produce a single final
good which it then sells to households. Therefore, households problem
will be exaclty the same as before.
ii Households maximize lifetime utility:
Et
∞
X
β t U (Ct , Nt )
t=0
subject to their budget constraint:
Pt Ct + Qt Bt ≤ Bt−1 + Wt Nt − Tt
C 1−σ
N 1+ϕ
t
t
− 1+ϕ
Consider the following utility function: U (Ct , Nt ) = 1−σ
σ - inverse of the intertemporal elasticity of substitution and ϕ - inverse of
the Frisch labor supply elasticity.
Irfan Qureshi (University of Warwick)
EC924 - Monetary Economics
March 2016
4 / 15
Question:1
Household’s problem is standard:
(∞
"
#)
1+ϕ
1−σ
s
X
N
C
B
+
W
N
t−1
t
t
t
t
−
+ λt
4 = Et
βt
−Tt − Pt Ct − Qt Bt
1−σ 1+ϕ
t=0
First-order conditions:
∂4
∂Ct
∂4
∂Nts
∂4
∂Bt
= Ct−σ − λt Pt = 0
= −Ntϕ + λt Wt = 0
= −λt Qt + βEt {λt+1 } = 0
So optimality conditions of the household are standard and do not change.
Irfan Qureshi (University of Warwick)
EC924 - Monetary Economics
March 2016
5 / 15
Question:1
Simplifying:
Ctσ (Nts )ϕ =
Ct−σ
= βEt
−σ
Ct+1
Wt
Pt
1
Qt Πt+1
i Notice that because of the monopolistic firms equilibrium level of
employment in this setup will be lower than in the case with flexible
prices assumed in an RBC model.
ii This is because monopolistically competitive firms will offer wage that
is lower than in the case of flexible prices (difference will be a markup
that they will charge).
iii They can do this because they have ‘some’ power in the market.
Irfan Qureshi (University of Warwick)
EC924 - Monetary Economics
March 2016
6 / 15
Question:1
The final good firm, as described above, packs intermediate goods using
the following “technology”
Z
1
Yt =
Yt (i)
ε−1
ε
ε
ε−1
di
(1)
0
Final good producer sells final good to households at price Pt . Therefore,
its problem is to
Z
max Pt Yt −
1
Pt (i) Yt (i) di
0
s.t their production technology given by (1) .
Irfan Qureshi (University of Warwick)
EC924 - Monetary Economics
March 2016
7 / 15
Question:1
Plug in the expression for Yt
1
Z
Pt
Yt (i)
ε−1
ε
ε
ε−1
di
0
Z
−
1
Pt (i) Yt (i) di
0
and take the first order condition with respect to Yt (i) The first order
condition will be
ε
Pt
ε−1
Z
1
0
ε
ε−1
−1
ε−1
ε
Yt (i) ε −1 − Pt (i) = 0
ε−1
1
ε−1
Z 1
ε−1
1
Pt
Yt (i)− ε − Pt (i) = 0
Yt (i) ε di
Yt (i)
ε−1
ε
di
0
Irfan Qureshi (University of Warwick)
EC924 - Monetary Economics
March 2016
8 / 15
Question:1
Write the same expression for the j − th good, as follows:
1
ε−1
Z 1
ε−1
1
ε
dj
Yt (j)− ε − Pt (j) = 0
Pt
Yt (j)
0
Then combining these two expressions (dividing them) one can get:
1
Pt (j) Yt (j) = Pt (i) Yt (i) ε Yt (j)
ε−1
ε
Intergrating out:
Z 1
Z 1
ε−1
1
ε
Pt (j) Yt (j) dj = Pt (i) Yt (i)
Yt (j) ε dj
0
|0
{z
}
Yt
Finally, using that Pt Yt =
ε−1
ε
R1
Pt (j) Yt (j) dj obtain:
Pt (i) −ε
Yt (i) =
Yt .
Pt
Irfan Qureshi (University of Warwick)
0
EC924 - Monetary Economics
March 2016
9 / 15
Question:1
(b) What is the empirical motivation behind the introduction of
price stickiness in this model? How is price stickiness
introduced in this model?
i We (and after project 1, you!) observe in the data that after a
monetary policy shock prices do not respond much. In fact, their
response is quite sluggish.
ii In addition, researchers like Nakamura and Steinsson, Bills and Klenow,
using large datasets for the United States, show that prices stay fixed
on average for 6 months, which would suggest quite large price
stickiness.
iii One needs to introduce this stickiness into the model. The way we
discussed in class is Calvo price stickiness. Each intermediate goods
firm can change the price of their differentiated product with an
exogenous probability θ in each period. Therefore, firms will take this
into account when setting their prices.
Irfan Qureshi (University of Warwick)
EC924 - Monetary Economics
March 2016
10 / 15
Question:1
(c) Given your answer in part (b), explain the difference between
nominal and real rigidities. Discuss how Kimball-type
preferences, as an example of real rigidity, can lead to price
stickiness.
i Real rigidities are not exogenous like nominal rigidities, in a sense that
not-changing prices come out from the optimal behaviour of the firm.
For example, with Kimball-type preferences elasticity of substitution is
not the same for all price levels. When price level is high, elasticity of
substitution is very high which makes firms reluctant to increase their
price.
ii On the other side, for lower price levels, elasticity of substitution is very
low, meaning that decreasing price would not influence much demand
of the firm and therefore they would not change the price. The
important thing is that they recognise that elasticity of substitution is
not fixed as it is in case of the CES preferences.
Irfan Qureshi (University of Warwick)
EC924 - Monetary Economics
March 2016
11 / 15
Question:1
(d) One of the critiques of the classical model is that it delivers a
very high correlation between hours and output due to a
technology shock, which might not be in line with the data.
Explain how the NK model can generate a negative correlation
between output and hours after a positive technology shock.
i In this case, once there is a positive technology shock, marginal cost
decreases and aggregate demand increases.
ii However aggregate demand does not increase as much as it would in
case of flexible prices, since not all the firms will change the price
putting a limit on the increase of aggregate demand.
iii Therefore, since aggregate demand does not match the increase in
productivity, for certain calibrations, it can be the case that
employment can go down.
Irfan Qureshi (University of Warwick)
EC924 - Monetary Economics
March 2016
12 / 15
Question: 2
(a) What does the term “Great Moderation” refer to? Discuss at
least three proposed explanations for this phenomenon. Why
does it matter which of the explanations is correct?
i Great moderation: reduction of macroeconomic volatility in the US
after 1980s. This expression was first coined by Stock and Watson.
ii Explanation 1: ”Good Luck” : reduction in the volatility of exogenous
shocks, especially technology shocks.
iii Explanation 2: ”Good policy”: refers to a better conduct of monetary
policy after 1980s. After 1980s monetary policy changed its objective
to inflation targeting.
iv Explanation 3: Change in the structure of the economy. Inventories are
run better, services become more dominant in the creation of GDP,
and they are less volatile.
If the dominant explanation is 1 then shocks might become large
again, increasing the overall volatility. If one believes the second
explanation, then volatility can be held in check as policymakers have
learned from their past mistakes and therefore would not allow for the
volatility to reach the levels as before 1980s.
Irfan Qureshi (University of Warwick)
EC924 - Monetary Economics
March 2016
13 / 15
Question:2
(b) What are the main findings of Clarida, Gali and Gertler in their
paper “Monetary Policy Rules and Macroeconomic Stability:
Evidence and Some Theory”, regarding the Great Moderation?
Discuss the procedure they used to derive their results.
i They estimate a forward-looking monetary policy reaction function for
the postwar United States economy, before and after Volcker’s
appointment as Fed Chairman in 1979.
ii They use GMM estimation as a basic tool.
iii Their results point to substantial differences in the estimated rule
across periods.
iv In particular, interest rate policy in the Volcker-Greenspan period
appears to have been much more sensitive to changes in expected
inflation than in the pre-Volcker period.
v They then compare some of the implications of the estimated rules for
the equilibrium properties of inflation and output, using a simple
macroeconomic model, and show that the Volcker-Greenspan rule is
stabilizing.
Irfan Qureshi (University of Warwick)
EC924 - Monetary Economics
March 2016
14 / 15
Question:2
(c) Explain the Orphanides’ critique of Central Banks following
Taylor-type rules when conducting monetary policy.
i The main critique of Orphanides is that Taylor-type rules use
unobservable objects, such as output gap, which can be significantly
mismeasured.
ii In particular, when CB decides how to respond to output gap and
inflation it uses real time data (data available at that particular
moment) which are usually wrongly estimated, and which might lead
to wrong responses of monetary policy.
iii Therefore, high inflation prior to 1980s can be directly a consequence
of bad measure of the output gap and too much focus of monetary
policy on stabilizing the real economy.
Irfan Qureshi (University of Warwick)
EC924 - Monetary Economics
March 2016
15 / 15