ECON 3410/4410: Seminar exercises,
autumn 2003
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,
autumn 2003.
Exercise 1
It is mistake to attend this opening seminar without working seriously with the exercise, as it gives you essential training in finding macroeconomic data (from the web
or from other sources) and to analyze them using e.g., graphs.
1. 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
about 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).
2. Show inflation and unemployment in a scatter plot, i.e., so called empirical
Phillips curves (B&W Fig 12.1 shows one example of such a graph)
(a) Draw a line which, intuitively, represents the average relationship between
the rates of inflation and unemployment.
(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).
(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?
3. Inflation can be measured in different ways, using different price indices. Try
to find an alternative to the price index that you used in question 2 and repeat
the analysis in 2a)-2b). Discuss.
1
4. If you have been able to find data for wages (e.g., per hour worked, or per
employed person): is there a wage Phillips curve in your data?
5. 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.
Exercise 2
1. Use the data in Norw wage shares.zip, and formulate your 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. Discuss similarities and differences from
how the concepts are used in B&W chapter 12. What is the Norwegian model’s
counterpart to B&Ws concepts of “core inflation”?
4. 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. How is steady state rate unemployment determined in the version of the Norwegian model of inflation with a direct link from (lagged) profitability to wage
increases?
2
Exercise 3
Dynamic multipliers in a AS/AD set-up.
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 + εs,t
yt = ad0 + adp ∆pt−1 + adz zdt + εd,t
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. 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. Finally, εs,t and εd,t denote small,
random and insignificant shocks.
1. Explain why ∆pt is (an approximate) measure of the rate of inflation.
2. Explain, intuitively, how you would sign the two slope coefficients asy and adp .
3. Derive the final form equation for the rate of inflation, and show that it takes
the form of a 1. order difference equation.
(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) What are the dynamics of y with respect to zs ?
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. How can the model (1)-(2) be modified so that it can (logically) accommodate
more realistic inflation response to a change in zs .
Exercise 4
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?
3
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
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. 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.
4
Exercise 6
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
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
(7)
∆pt = β pw αwp ∆pet − β pw αwu (Ut−1 − Ū) + β pb ∆pbt
∆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 a (linear)
function of 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?
5
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.
(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 are the rate of inflation (∆p), and unemployment (U) and the real exchange rate (rex) 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
6
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 7
1. Assume first the following simple dynamic model for the rate of inflation
(1)
∆pt = δ + α∆pt−1 + εt , t = 1, 2, 3...T , − 1 < α.
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 ). 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 .
2. Derive the expressions for ∆p̂T +1 and ∆p̂T +2 as functions of the initial value
of the rate of inflation ∆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). In economic dynamics, the left hand side of (3) is called the
steady state rate of inflation.
4. 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):
E[pt ] = π ∗
7
5. 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?
6. 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.
7. Show that the dynamic forecasts for inflation and the rate of unemployment
h period ahead are given by
(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 ),
∆p̂T +h−1 ≡ ∆pT and ÛT +h−1 ≡ UT for h = 1, ∆iT +h = 0 for h = 2, 3,
8. Assume that the Bank sets the interest rate so that the inflation target is
reached in the first forecast period.
(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 8
For this seminar you should read part 1 of De Grauwe’s (2003): ”Economics of
Monetary Union” as a background.
8
Group 1: Prepare a presentation (20 minutes) based on chapter 1 and make a
summary (4-5 pages) of this chapter.
Group 2: Prepare a presentation (20 minutes) based on chapter 3 and make a
summary (4-5 pages) of this chapter.
These summaries are to be handed out to all the students attending the class
to help exam preparations.
After the presentations you should be prepared for debating/discussing whether
Norway should join the EMU, comparing the costs and benefits.
Exercise 9
For this seminar you should read part 2 of De Grauwe’s (2003): ”Economics of
Monetary Union” as a background.
Group 1: Prepare a presentation (20-30 minutes) based on chapter 6 and make
a summary (4-5 pages) of this chapter. Use relevant data to discuss whether Norway
would be allowed to join the EMU.
Group 1: Prepare a presentation (20-30 minutes) based on chapter 9 and make
a summary (4-5 pages) of this chapter. Use relevant data to discuss whether Norway
historically has “broken” a hypothetical “Stability and Growth Pact”.
The summaries are to be handed out to all the students attending the class to
help exam preparations.
9