ECON 3410/4410: Seminar exercises,
spring 2004
January 21, 2004
There are (only) 9 exercises in this document. This is to allow for one or two “open
seminars”, to be planned and organized by the students and seminar leader. Altogether
the seminar groups will have 11 meetings.
The zipped data sets referred to in the exercises can be downloaded from
http://folk.uio.no/rnymoen/rnyteach.html, just follow the link to ECON 3410,
spring 2004.
Exercise 1
It is a mistake to attend this opening seminar without working with the exercise,
as it gives you training in finding macroeconomic data (from the web or from other
sources) and to start analyzing them using e.g., graphs.
1. Inflation can be measured in different ways, using different price indices.
Which operational definition of the consumer price index is used by Norges
Bank (The Central Bank of Norway)? What about Bank of England? Use the
internet for information!
2. For an economy (country, region or “economic area”) of your choice, find time
series for inflation and/or wage increases and unemployment for a relatively
long period (for example 1980-2000). You may obtain data from the internet,
or from statistical publications and even textbooks. Take care to make a note
of variable definitions and sources. Save the data set in Excel file format, and
make sure that PcGive can read the xls file (if you want to use GiveWin for
the graphs you are asked to produce).
Note: A ready-made dataset (wage price prod.zip) is available from the
work-page of the course.
3. Show inflation and unemployment in a scatter plot, i.e., so called empirical
Phillips curves (B&W Fig 12.1 shows an example of such a graph)
(a) Draw a line which, intuitively, represents the average relationship between
the rates of inflation and unemployment. (In GiveWin: choose Graphics
properties and click 1 (sequential) regression line).
(b) Are there signs of a non-linear relationship in your data set? Explain
your findings. (Hint: make a scatter plot with inflation and the log of
the rate unemployment).
1
(c) Are there periods (“sub samples”) where the Phillips curve “fits better”
than in other periods? If so, do you have you any explanation for this
phenomenon?
(d) Are there any signs of “supply side shocks” in your data set? (Hint: a
supply shock could affect both the regression coefficient and the intercept)
Exercise 2
1. Assume that the rate of inflation is given by
(1)
∆pt = β 0 + β 1 it + α∆pt−1 + εt ,
t = 1, 2, .....
where the subscript t denotes time period (e.g., quarter or year) and ∆ denotes
the difference operator, i.e., ∆pt ≡ pt − pt−1 where pt denotes the (natural)
logarithm of the domestic price level. it denotes the interest rate controlled
by the central bank (this variable is a rate, it it not log-transformed). εt is
the disturbance.
(a) Why is it convention to use ∆pt as an approximate measure of the rate
of inflation?
(b) Show that (1) is an example of an ADL model.
(c) Assume that the impact multiplier of ∆pt with respect to a change in the
rate of interest from 0.04. to 0.05 is 0.0025. What does this imply for the
value of β 1 ?
(d) Assume that the long run multiplier is 0.01.Using the answer to c., what
is the implied value of α?
(e) In your own words: explain the concept of long-run multiplier.
(f) Assume that the long run multiplier is 0.01, and the data is quarterly.
Try to find values of β 1 and α which are consistent with 80-90% of the
long run effect is being reached within 2 years.
2. Using wage price prod.zip: is there wage Phillips curve in this data set.
Note that there are three unemployment series, you have to choose one of
them for your analysis. Are there sub-periods where the relationship is more
pronounced? Does it matter whether the rate of unemployment is in log or
not?
3. Using the data in wage price prod.zip, discuss the relevance of the statement in chapter 12.3 in B&W about a positive relationship between wages and
labour productivity, while there (still according to B&W) is no such relationship between the price level and productivity.
2
Exercise 3
1. Use the data in Norw wage shares.zip, and try to formulate a view on the
following issues
(a) The degree of correlation between the exposed sector wage rate and the
components of the “main-course” (labour productivity and the product
price) in the long-run (use a scatter plot).
(b) What about the short-run correlation?
(c) Comment on the degree of constancy over time in the two wage shares
(you may want to use the smoothed version of the series)
(d) Are there any evidence that the rate of unemployment is correlated with
the e-sector wage-share, and that it can explain some of the shifts in the
share?
Note that the file Norw wage shares.txt explains the variable definitions.
2. How can the idea of a supply side determined equilibrium rate of unemployment (so called “natural rate of unemployment”, or “NAIRU”) be reconciled
with the Norwegian model of inflation?
3. In the context of the Norwegian model of inflation: Discuss the concepts of
short- and long-run Phillips curves. What is the Norwegian model’s counterpart to B&Ws concept of “core inflation” in Ch 12?
4. Discuss in seminar: The Phillips curve version of the Norwegian model of
inflation: Assume that the economy is initially in equilibrium, but that the
next a situation where the actual rate of unemployment is higher than the
natural rate and the discuss the dynamic adjustment, from the initial situation
to the equilibrium situation.
5. Discuss in seminar: In the version of the Norwegian model of inflation with a
direct link from (lagged) profitability to wage increases there is no natural rate
of unemployment similar to the Phillips curve version of the model. How then
is the long run rate of unemployment determined if this model of inflation is
correct?
Exercise 4
Dynamic multipliers in a small macro model.
Assume that the rate of inflation and the output-gap of an economy can be
represented by the following two equations:
(1)
(2)
∆pt = as0 + asy yt + asz zs,t
yt = ad0 + adp ∆pt−1 + adz zdt
where the subscript t denotes time period (e.g., quarter or year) and ∆ denotes the
difference operator, i.e., ∆pt ≡ pt − pt−1 where pt denotes the (natural) logarithm
3
of the domestic price level. yt denotes the output-gap in period t (relative deviation
from full employment output). zs,t and zd,t are catch-all indicators of important exogenous supply-side and demand-side shocks. We could have included disturbances
εs,t and εd,t , but omit them for simplicity.
1. Explain, intuitively, how you would sign the two slope coefficients asy and adp .
2. In (1), substitute yt by the right hand side of (2) to derive the so called final
form equation for the rate of inflation, and show that it takes the form of an
ADL model with two exogenous variables, zs,t and zd,t .
3. Once you have found the final form equation for ∆pt , and have used that
equation to calculate the inflation multipliers (for example ∂∆pt+j /∂zs ), it is
possible to also find the multipliers for yt by taking the derivate of (2) with
respect to zs,t or zd,t . Use this method to answer the following:
(a) Assume a permanent increase in zs,t . Calculate the impact multiplier,
the first four cumulated dynamic multipliers and the long-run multiplier,
for both the rate of inflation and for the output gap. Use the following
coefficient values for the calculations: asy = 0.1, asz = 0.5 and adp =
−0.01.
(b) Are the multipliers of y with respect to zd very different from the multipliers in a.?
4. Try to illustrate the dynamics in a diagram with AD/AS curves (i.e., after a
shift in the AS curve).
5. Using the data set in Dp.zip, investigate whether the inflation dynamics that
you found in your answer to question 4 is realistic for that data set. (note:
read the exercise file carefully, it contains explanations and essential hints!).
6. Discuss in seminar: How can the model (1)-(2) be modified so that it can
(logically) accommodate more realistic inflation response to a change in zs .
Exercise 5
Simple portfolio model.
1. Explain the difference between a flow based and stock based model of the
market for foreign exchange.
2. Derive equation (1.18) in Rødseth’s Open Economy Macroeconomics (OEM
hereafter), defining the supply of foreign currency to the central bank. Show
also that the derivative of Fg with respect to the exchange rate Fg is given by
equation (1.19).
3. How does the degree of capital mobility influence the functional relationship
between the supply of foreign currency and the exchange rate?
4
4. Assume that there is an exogenous shift in the foreign currency supply function. How are
(a) the equilibrium exchange rate (in the case of floating exchange rate regime),
and
(b) the equilibrium foreign currency reserve (in the case of fixed exchange
rate)
affected by whether the degree of capital mobility is high or low?
5. Assume that government uses the interest rate i as an instrument to reach its
policy targets:
(a) In the case of a fixed exchange rate. How is i affected by an rising
expectation of a currency depreciation
(b) In the case of a floating exchange rate regime: How is the exchange
rate affected by a an increase in the interest rate. What could be the
underlying policy target in this case?
6. Explain the terms uncovered and covered interest rate parity. Assume that
the central bank trades in the forward marked, how is the spot exchange rate
affected (if at all)? Assume perfect capital mobility.
Exercise 6
For this seminar you should read part 1 of De Grauwe’s (2003): ”Economics of
Monetary Union” as a background.
Details will be given in the seminar.
Exercise 7
Consider the following model, representing wage and price setting, the market of
foreign exchange (float) and aggregate demand of a small open economy
(1)
(2)
(3)
(4)
(5)
(6)
∆wt
∆pt
et
Ut
rext
pbt
=
=
=
=
=
=
−αwu (Ut−1 − Ū) + αwp ∆pet , 0 ≤ αwp ≤ 1
β pw ∆wt + β pb ∆pbt , 0 ≤ β pw + β pb ≤ 1
γ 0 − γ 1 (it − i∗t ) + γ 2 F EXt
φ0 + φf p F Pt − φrex rext + φri (it − ∆pt )
pbt − pt
p∗t + et
it and i∗ represent the domestic and foreign interest rates respectively. The other
variables written with lower case Latin letters denote natural logarithms of the
original variables, i.e., wt = ln(Wt ) where Wt is the wage rate.
The variables: w = wage per hour worked; U = rate of unemployment; ∆pt
= inflation rate (substrict e denotes expectations); ∆pbt = rate of change in import
5
prices; et = nominal exchange rate (log of e.g., kroner/USD) ; F EXt = catch-all
variable for factors that affect the nominal exchange rate at a constant interest rate
differential; F Pt = catch-variable for financial policy; rex = real exchange rate; p∗t
= foreign price level (in foreign currency).
1. Show that the price Phillips curve takes the form
∆pt = β pw αwp ∆pet − β pw αwu (Ut−1 − Ū) + β pb ∆pbt
(7)
∆pet denotes the expected price increase in period t.
2. Sketch graphically the short and long-run price Phillips curve under two alternative hypotheses for ∆pet : a) Perfect expectations and b) ∆pet is the inflation
rate in period t − 1. Which (extra) assumptions on the model’s parameters
are necessary to secure a vertical long-run Phillips curve in the two cases?
3. Check that your results in 2. carry over to the wage Phillips curve.
In the following we assume that inflation expectations are formed according
to b) in question 3.
4. Which parameter restriction(s) are needed to ensure that an increase in the
rate of interest has a positive impact on the rate of unemployment?
e
i
Figure 1:
5. Equation (3) can be interpreted a “linearization” of the equilibrium condition
for the market for foreign exchange in OEM (see chapter 1 and/or chapter
3.1), for example if we let the exogenous variable F EXt represent the effects
of (foreign) price levels and initial values of bonds on the supply of foreign
currency to the central bank.
6
(a) Figure 1 shows three possible relationships between e and i. Indicate (in
the figure) for each line, the appropriate sign/size of the coefficient γ 1 .
(b) Try to describe in more detail what is the underlying characteristics of
the market for foreign exchange in the three cases covered by the graph.
6. Which variables are endogenous in the model made up of equation (1)-(6)?
7. How is the rate of inflation, ∆pt , affected by a permanent rise in the interest
rate, in the period of the rise and in the following period? Hint: Note that the
system of equations can be written more compactly as two dynamic equations
for ∆pt and Ut :
(8)
(9)
∆pt = β pw αwp ∆pt−1 − β pw αwu (Ut−1 − Ū )
+β pb {∆p∗t + [−γ 1 (∆it − ∆i∗t ) + γ 2 ∆F EXt ]}
Ut = φ0 + φf p F Pt − φrex {p∗t + [γ 0 − γ 1 (it − i∗t ) + γ 2 F EXt ]
−(pt−1 + ∆pt )} + φri (it − ∆pt )
8. Let (the unique) steady state equilibrium of the model be defined by ∆pt =
∆pt−1 , ∆et = 0, Ut = Ū , ∆rext = 0 and ∆pit = ∆p∗t ≡ π ∗ . Explain why
the long-run multipliers of the real exchange rate, the rate of inflation and the
level of the nominal exchange rate can be derived from the long-run system:
Ū = φf p F Pt − φrex rext + φri (it − ∆pt )
∆pt = β pw αwp ∆pt + β pb ∆p∗t
et = γ 0 − γ 1 (i − i∗ ) + γ 2 F EXt
9. Derive the long-run effects of a permanent increase in the interest rate on
inflation, output and the real exchange rate. How are the long-run effects
compared to the short-run effects of question 3? Explain.
Exercise 8
Issues in inflation targeting.
Assume the following dynamic model for the rate of inflation
∆pt = δ + α∆pt−1 + εt , t = 1, 2, 3...T , 0 < α < 1.
(1)
where T denotes the end of the observation period and also the period where the
forecasts for the next H periods are made (and published). εt is a normally distributed disturbance term (with zero mean and a known variance denoted σ 2 ). δ and α
are known without uncertainty (in period T ).
1. Explain why the dynamic forecast of the rate of inflation in period T + h,
denoted ∆p̂T +h is given by
(2)
∆p̂T +h = δ + α∆p̂T +h−1 , h = 1, 2, ....H, with ∆p̂T ≡ ∆pT .
7
2. Derive the expressions for ∆p̂T +1 and ∆p̂T +2 as functions of the initial value
of the rate of inflation, i.e., ∆pT .
3. Show that, as H → ∞, the forecast approaches the long-run mean of ∆pt
according to (1) given by
(3)
E[∆pt ] =
δ
1−α
(where E[pt ] denotes the long-run mean which is identical to the mathematical
expectation).
4. In economics terminology, the left hand side of (3) is called the steady state
rate of inflation. Why?
5. In the model of exercise 7, inflation dynamics are more complicated than in
equation (1). Nevertheless, using the insight that if a steady state rate of
inflation exists, it corresponds to the long-run mean, show that the long-run
mean of inflation implied by the exercise 7 model is given by:
E[∆pt ] =
β pb
π∗
1 − β pw αwp
or, subject to homogeneity in wage and price setting (β pw + β pb = 1, αwp = 1):
E[pt ] = π ∗
6. Assume that the central bank is committed to inflation targeting and that
the model in exercise 7 represents the Banks beliefs about the transmission
mechanism between the interest rate i (controlled by the Bank) and unemployment and inflation. How, according to your view, should the Bank specify
its operational inflation target?
7. The Bank produces inflation forecast based on the model of exercise 7, information available in period T , exact knowledge about all parameter values and
the following set of assumptions about the exogenous variables:
a) F EXT +h = F EXT , F PT +h = F PT , for h = 1, 2, ...H.
b) p∗T +h = p∗T + hπ ∗ (and thus ∆p∗T +1 = π ∗ ), for h = 1, 2, ...H
c) iT +h = iT + ∆iT +1 , i∗T +h = i∗T , for h = 1, 2, ...H
Give a brief characterization of there assumptions.
8
8. The dynamic forecasts for inflation and the rate of unemployment h period
ahead can be written as
(4)
(5)
∆p̂T +h = β pw ∆p̂T +h−1 − β pw αwu (ÛT +h−1 − Ū)
+(1 − β pw )(π ∗ h − γ 1 ∆iT +h ),
ÛT +h = φ0 + φf p F PT − φrex {p∗T + hπ ∗
+[γ 0 − γ 1 (iT +h − i∗T ) + γ 2 F EXT ]
−(pT + ∆p̂T +h )} + φri (iT +h − ∆p̂T +h ),
Note :
∆p̂T +h−1 ≡ ∆pT and ÛT +h−1 ≡ UT for h = 1, ∆iT +h = 0 for h = 2, 3,
Assume that the central bank sets the interest rate so that an inflation target
of 2.5% is reached in the curse of the first forecast period (T + 1).
1. (a) Derive the expression for the period T +1 interest rate iT +1 . Which macro
economic variables affect interest rate setting in this case?
(b) Assume instead that the inflation target is the periods ahead. Compared
to a., will the interest rate be influenced by fewer or more macroeconomic
variables in this case? (hint: which variables “drive” the ∆p̂T +2 forecast!).
(c) Returning to a., what could cause that actual inflation in period T + 1
is different from the forecast, i.e., ∆p̂T +1 6= ∆pT +1 ? If the actual rate is
higher than the target, what would the Bank’s policy response be? How
could unemployment be affected by this policy actions?
Exercise 9
For this seminar you should read part 2 of De Grauwe’s (2003): ”Economics of
Monetary Union” as a background.
Details will be given in the seminars.
Additional exercise 1
B&W chapter 12 and B&W version of AD/AS model (chapter 13).
1. Answer exercise 1, 2, 3, 8 and 10 in on page 296-297 in B&W. In connection
with question 8: What is the operational definition of inflation used by the
Central Bank of Norway?
2. Discuss the statement in B&W summary point 3 on page 323. Is this statement
a possibility or a truism? Discuss its empirical relevance and plausibility using
the data set found in Money and infl.zip, or a similar data set of your choice.
3. Answer exercise 1, 3 and 9 in B&W chap 13 (AD/AS setup), p 324-325
9