ECON 3410/4410: Seminar exercises,
spring 2005
November 24, 2004
There are (only) 9 exercises in this document, although each seminar group will
have 11 meetings.This is because it may require more than one seminar to get through
some of the exercises. It is also possible to drop the whole of (or part of) some of the
exercises and to organize one or two “open seminars”, This is up to the students and
their seminar leader.
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 3410/4410,
spring 2005.
At the back of the set there are 3 extra exercises. The first fits into the first part
of the course. The last two are exam questions from 2004.
Note that the Observator journal has printed answers to the 2003 exams for this
course.
Exercise 1
As “warm-up” exercises, the questions to the two first seminars review some central
concepts and their empirical (“observable”) counterparts, as well as some much used
operations involving logs.
1. From the internet, from a textbook (or maybe you already know this one), try
to find out what is meant by the terms “effective exchange rate” and “bilateral
exchange rate”. Is there a relationship between these concepts?
2. From NORKVAR.zip, which can be downloaded from the course internet page,
obtain the datafile NORKVAR.xls. The dataset contains a quarterly time series CPIVAL, which is an effective exchange rate index for Norway.
(a) The so called base year of the series is 2001. What does that mean?
(b) There are two bilateral exchange rates in the dataset: SPEURO and
SPUSD, between kroner and Euro and kroner and USD respectively. Consider the correlation between CPIVAL and SPEURO on the one hand,
and CPIVAL and SPEURO on the other.1 Which one is largest–and
why?
1
Before the introduction of the EURO (and the abolition of national currencies in most EU
countries), the SPEURO series represent the exchange rate between kroner and the European
Currency Unit, ECU.
1
(c) Derive a series for the bilateral exchange rate between USD and EURO.
What are the most conspicuous developments over the available period?
(d) Use available resources (library, newspapers, internet) and extend the
USD/EURO series, and comment on the most recent developments.
3. Make a graph (using Excel or GiveWin/PcGive for example) of the variables
CPIVAL and CPI in the datafile NORKVAR.xls. CPI is the official Norwegian
consumer price index (published by Statistic Norway). The two series have in
common that they are averages of nominal prices of individual commodities
(which?). Still, the two series appear markedly different in the graphs. Why?
4. Calculate the time series of the quarterly rate of change of CPI. What is
the common name of this series? Calculate also the 4-quarter rate of change
in CPI. Plot the two series in a graph. Why is the annual rate of change
“smoother” than the quarterly rate of change?
5. Calculate also the approximate growth rate, based on the log transform of CPI
(see e.g., the appendix to Introductory Dynamic Macroeconomics). How good
is the approximation?
6. Try to classify the following economic concepts as either stock or flow variables
(discuss in seminar)
(a) The labour force
(b) The rate of unemployment
(c) The trade surplus
(d) The money stock
(e) Private consumption expenditure
(f) Government dept
(g) Government deficit
(h) The price level
(i) Inflation
(j) The supply of foreign currency to the central bank.
7. Stock variables often change gradually: at each point in time their rate of
change is finite. The consumer price index is a much used example. Other
stock variables can jump from one value to another at any given point in time.
In such instances the derivative of the variable with respect to time is infinite–
at least in principle: with actual data (quarterly, monthly, daily, hourly) the
rate of change is finite, but for the observations when jumps occur, that rate
will be huge. Such stock variables are dubbed jump-variables.
In this course. we will often consider the nominal exchange rate as a jump
variable. Given the behaviour of for example, CPIVAL. Is there any realism
in such an assumption?
2
Exercise 2
1. In the dataset CY.xls on the web pages, there are observations of two variables
C and Y . Try to decide whether the underlying relationship between these
two variables are linear or log-linear. What is the approximate value of the
derivative/elasticity of C with respect to Y ?
2. In this course we learn how to analyse the dynamics of linear economic models.
Hence it is important to be able recognize a linear model when you see it! The
key property is “linearity in parameters”, which is (in fact) compatible with
non-linearity in variables. For example, consider the three alternative models
of the relationship between the two variables Y and X:
(1)
(2)
(3)
Y
ln Y
ln Y
= α + βX
= α + β ln X
= α + βX
(a) A model which is linear (also) in variables has the property that the first
derivative is a constant (independent of X). Which of the three equations
has this property?
(b) A model which is linear (only) in parameters has the property that the
first derivative is itself a function of X. Describe how the first derivatives
of (1)-(3) depend on X.
(c) Which equation implies a constant elasticity of Y with respect to X?
(d) There are still more specifications of linear models to consider. Let for
example Y denote the rate of inflation in %, and let X denote the rate
of unemployment (also in %). What is the qualitative difference between
the ‘linear Phillips curve’ in (1) and the two ‘concave Phillips curves’
given by the two alternative specifications:
(4)
Yt = α + β ln Xt , and
1
(5)
Y = α+β ?
X
(e) Calibrate equation (4) and (5) in way that makes both models consistent
with the following: At a 4% initial unemployment, a 1 percentage point
increase in unemployment reduces inflation by 1 percentage point.
(f) Equation (5) is called the reciprocal model. Using for example the β
value form question (e), sketch the Phillips curve (i.e., for different values
of U ). Discuss in class: What could become main policy issues if the
reciprocal model was the correct model of inflation in an economy?
3. Using the variables CPIVAL, CPI and CPIKONK in the datafile NORKVAR.xls,
calculate a real exchange rate index for Norway. Draw a graph of the series,
call it REX for example.
4. According to an economic hypothesis, called purchasing power parity (PPP),
real exchange rates typically have a constant mean? Is there any evidence in
support of PPP to be hauled from the real exchange rate you calculated in
question 3?
3
5. In many macroeconomic models (e.g., the AD-AS model used in the B&W
book) one makes the assumption that REX is constant in each period (a
stronger version of the PPP hypothesis). Comment on the realism of such an
assumption.
6. Take the (natural) log of REX, and obtain its (approximate) growth rate.
Comment on how much the three components have contributed to the rate of
change of REX.
Exercise 3
1. In practice, inflation is measured in different ways, using for example 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. A ready-made dataset is available in the file wage price prod.zip on the
course page.
(a) 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)
(b) Draw a line which, intuitively, represents the average relationship between
the rates of inflation and unemployment. (Hint: in GiveWin: choose
Graphics properties and click 1 (sequential) regression line).
(c) 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).
(d) 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?
3. Assume that the rate of inflation is given by the augmented Phillips curve
(6)
∆pt = β 0 + β 1 Ut + 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. Ut denotes the unemployment rate (i.e.,
this variable is a rate, it is not log-transformed). εt is the disturbance.
(a) Give (a least) one economic theoretical argument for inclusion of the
lagged inflation rate on the right hand side of the equation.
(b) Show that (6) is an example of an ADL model of the relationship between
inflation and the of unemployment.
(c) Assume that the impact multiplier of ∆pt with respect to a change in the
rate of unemployment is −0.01. What does this imply for the value of
β1?
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(d) Assume that the long run multiplier is −0.20. Using the answer to c.,
what is the implied value of α?
(e) In your own words: explain the concept of long-run multiplier in this
application.
(f) A majority of modern economists now routinely sets α = 1. What is
their rationale?
(g) Assume that α = 1, and that the NAIRU rate of unemployment is 0.05.
What is the corresponding value of β 0 ?
4. Using wage price prod.zip: is there a 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?
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 4
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?
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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 5
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 of
the domestic price level. yt denotes the output-gap in period t (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 derivative 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.?
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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 6
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.
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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 (subscript 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-all 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 proportional
to 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?
8
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 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
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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 .
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
δ
1−α
(where E[pt ] denotes the long-run mean which is identical to the mathematical
expectation).
(3)
E[∆pt ] =
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 ∗
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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. 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 (School exam 2004)
Dynamics and wage and price setting.
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1. Consider the ADL model
(6)
yt = β 0 + β 1 xt + β 2 xt−1 + αyt−1 + εt ,
where εt denotes the disturbance term in period t. The other Greek letters denote coefficients. Assume that xt is an exogenous variable (i.e., not influenced
by yt or yt−1 ).
(a) Consider a permanent shock to the exogenous variable. Give the expression for the impact multiplier, the 2nd multiplier, and the long run
multiplier.
(b) What is the condition for stability of (6)?
(c) Figure 2 contains graphs of two solutions of an ADL equation of the type
given in (6). The solutions are based on identical coefficient values, and
the same numbers for the exogenous variable have been used in both
cases. The thicker line shows a solution where the first solution period is
1990. The thinner line has 2000 as the first solution period.
Consider the following statement:
The ADL model is unstable, or even explosive, since both graphs show
persistent growth in yt .
Do you agree? Give a brief justification for your answer.
2.2
y t solution, start 1990
y t solution, start 2000
2.1
yt
2.0
1.9
1.8
1990
1995
2000
time
2005
2010
Figure 2: Two solutions of an ADL equation for yt .
2. Consider the case where yt in (6) denotes the hourly wage rate in the exposed
sector of an open economy, and where xt is an exogenous main-course variable.
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Assume that the main-course model’s hypothesis about a constant long run
wage share holds.
(a) Re-write the ADL model (6) as an error-correction model for the hourly
wage rate.
(b) Give a brief economic interpretation of wage setting in the exposed sector.
The market for foreign exchange.
Consider the system of equations given as Model 1, attached to the exam set.
3. How is the currency supply function defined by the system of equations in
Model 1?
4. Explain intuitively the case of an upward sloping supply curve.
5. Consider the following two regimes: a) A fixed exchange rate regime where
the central bank targets both the nominal exchange rate and foreign currency
reserves, and b) a clean-float exchange rate regime with an endogenous domestic interest rate. Compare the effects of a reduction in the foreign interest
rate in the two regimes.
Fiscal and monetary policy.
6. Make use of the AD-AS model, listed as Model 2 at the back of the exam
set. Analyse the short and long run effects of a permanent reduction in the
exogenous tax level. Consider both a fixed and a floating exchange rate regime.
7. What are the main arguments in favour of inflation targeting in small open
economies?
8. Discuss some of the challenges to the successful operation of an inflation targeting regime.
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Model equations and symbols
Model 1
Taken from Chapter 3.1 in Rødseth’s book (note: only 7 independent equations)
B + M + EFp
P
−M − B + EFg
P
r
M
P
B
P
EFp
P
Fg + Fp + F∗0
B0 + M0 + EFp0
= Wp
P
−M0 − B0 + EFg0
=
= Wg
P
= i − i∗ − ee (E), e0e (E) S 0 (i.e., unsigned)
=
= m(i, Y ), mi < 0, mY > 0
= Wp − f (r, Wp ) − m(i, Y )
= f (r, Wp ), fr < 0, 0 < fW < 1
= 0
The symbols are defined (in accordance with the book):
Volumes
Y
Output (income)
W
financial wealth
Financial assets, nominal values
M
money
B
bonds (interest bearing assets in domestic currency)
F
foreign bonds (interest bearing assets in foreign currency)
Prices, interest rates
P
price level
E
nominal exchange rate, domestic currency per unit of foreign currency
i
nominal interest rate
r
risk premium on domestic relative to foreign bonds
Functions
ee
expected rate of depreciation
m
(real) money demand function
f
(real) demand for foreign currency bonds
Subscripts
p
private
g
government
∗
foreign
0
initial value
Partial derivatives of behavioural relationships are indicated by subscripts, e.g., mi .
The derivative of the expected depreciation function is written e0e .
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Model 2
Adapted from the book by Burda and Wyplosz.
Y = C(Y − T ) + I(ρ) + G + P CA(Y, Y ∗ , σ)
0 < CY < 1, Iρ < 0, P CAY < 0, P CAY ∗ > 0, P CAσ < 0
SP
σ= ∗
P
ρ = i − π̄,
M
= L(Y, i), LY > 0, Li < 0
P
i = i∗ − se (S), s0e (S) S 0 (i.e., unsigned)
π = π̄ + a(Y − Ȳ ) + z, a > 0
Volumes
Y
GDP (output)
Ȳ
full employment trend output
T
net taxes
G
government consumption and investments
Prices, interest rates
i
nominal interest rate
ρ
real interest rate
σ
real exchange rate
S
nominal exchange rate, foreign currency per unit of domestic currency
P
price level
π
inflation
π̄
“core inflation”
z
variable representing a supply side shock.
Financial assets, nominal values
M
money
Functions
se
expected rate of appreciation
L
(real) money demand function
C
consumption function
I
investment function
P CA
primary current account function
Superscript
∗
foreign
Subscript
Partial derivatives of behavioural relationships are indicated by subscripts, e.g., CY .
The derivative of the expected appreciation function is written s0e .
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Extra 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.
Extra exercise 2 (postponed exam 2004)
1. Consider the expectation augmented Phillips curve for the rate of inflation,
πt:
(7)
π t = β 0 + απ et + β 1 Ut + β 2 Ut−1 + εt ,
where εt denotes the disturbance term in period t. Ut denotes the rate of
unemployment in period t, and π et+1 represents the inflation rate expected to
prevail in period t + 1.
(a) Consider a permanent shock to the rate of unemployment. Give the
expression for the impact multiplier, the 2nd multiplier, and the long run
multiplier in the following cases
i. Inflation expectations are correct.
ii. Inflation expectations are based on inflation in period t − 1.
(b) In the two cases: Which restriction(s) secure(s) a vertical long run Phillips
curve?
2. In 1(a), it is implicitly assumed that Ut is exogenous (independent of π t and
π t−1 ). Assume instead that Ut is endogenous. Consider the case in 1a (ii) and
discuss the dynamic effects of a temporary and permanent shock to unemployment in this case. Hint: In order to simplify the discussion: set β 2 = 0 in
equation (7).
3. Unlike the model in equation (7), the main-course model of inflation makes
special reference to the openness of the economy.
(a) Explain how wages and prices develop according to the main-course model.
(b) Can the idea of a natural rate of unemployment be reconciled with the
main-course model? Explain.
4. Consider the system of equations given as Model 1, attached to the exam set.
Give the simplified system of equations corresponding to the case of perfect
capital mobility. Explain.
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5. Assume that for some time, the central bank in a small open economy has
successfully been targeting the nominal exchange rate, but suddenly a strong
devaluation pressure arises in the market for foreign exchange. In such a
situation: what would your recommendation to the decision makers in the
central bank be?
6. Assume a floating exchange rate regime, and perfect capital mobility. Make
use of the AD-AS model, listed as Model 2 at the back of the exam set, and
analyse the short and long run effects of a permanent reduction in the foreign
rate of inflation.
Model equations and symbols
See exercise 9.
Extra exercise 3 (home exam 2004)
The two first questions address the expectations augmented Phillips curve and the
natural rate of unemployment. Question 3-7 centre around the real exchange rate
and the AD-AS model (case of fixed exchange rate regime)
The expectations augmented Phillips curve
1. The file SwissPhil.zip can be downloaded from the internet address
http://folk.uio.no/rnymoen/ECON3410_index.htm. The file contains annual data on inflation and unemployment in Switzerland. The variable definitions are given in the file with extension .txt, as well as in the comments to
each series in the PcGive file.
(a) Use the scatter plot option in PcGive (or a similar function in for example
Excel) to produce one or more graphs that illustrate the empirical Phillips
curve in Switzerland. (You may want to experiment both with the rate
of unemployment, U in the dataset, and its log, LU , in the dataset.)
(b) We next want to estimate an expectations augmented Phillips curve.
Expectations are assumed to be linked to INF Lt−1 . If we estimate (by
OLS) the regression
(8)
INF Lt = β 0 + β 1 Ut + αINF Lt−1 + εt
over the whole sample 1981 to 1996, we obtain (with four decimals) α̂ =
0.5411, β̂ 0 = 2.0941 and β̂ 1 = −0.3822. (If you want you can do the
estimation yourself, but this is not required). Using these parameters,
draw the estimated short and long-run Phillips curves in a diagram with
INF L on the vertical axis, and U on the horizontal axis.
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(c) If we instead estimate
(9)
INF Lt = β 0 + β 1 LUt + αINF Lt−1 + εt ,
the results are α̂ = 0.5224, β̂ 0 = 1.6134 and β̂ 1 = −0.8691. Draw the
short and long-run Phillips curves. Also for this case, use a diagram
with INF L on the vertical axis, and U on the horizontal axis. Discuss
any interesting differences from the curves you obtained in question b.
(d) Assume that the long run equilibrium rate of inflation is 3%. Compute
the natural rate of unemployment corresponding to equation (8) and, for
comparison, also the natural rate from the estimation of (9). Comment
on any differences found.
(e) Assume that the rate of foreign inflation falls from 3% to 1%, permanently. Is the natural rate of unemployment affected? Explain.
2. Assume that the Phillips curve model is given by equation (8), and let U ∗ denote the associated natural rate. Assume an initial situation where the actual
rate of unemployment is different from U ∗ . Discuss an economic mechanism
which secures that, starting from the initial situation, the rate of unemployment asymptotically approaches U ∗ .
The real-exchange rate and the AD-AS model
3. Explain briefly (maximum 150 words) what we mean by the term real exchange
rate, and why it is often referred to in discussions of international competitiveness.
Let σt denote the real exchange rate (defined in the same way as in B&W) in
period t. Assume that the time period is annual, and that we are given the
following ADL model which explains σ t :
(10)
σ t = β 0 + β 1 xt + β 2 xt−1 + ασ t−1
xt represents an exogenous variable. (For simplicity, the random disturbance
εt has been omitted).
4. If the hypothesis of purchasing power parity, PPP, holds on a year-to-year
basis, which coefficients in (10) are then set to zero? Explain.
5. Assume that the PPP hypothesis does not hold on a year-to-year basis, but as
a long run property. Which of the following possible parameter restrictions on
(10) are consistent with this version of the PPP hypothesis? Explain. (Hint:
depending on additional assumptions, which are for you to formulate, there
are more than one possible correct answer here).
(a) α = 1, β 1 = β 2 = 0
(b) 0 < α < 1, β 1 = −β 2
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(c) 0 < α < 1, β 1 > −β 2
6. Under which restrictions do a temporary change in xt have a permanent effect
on the real exchange rate?
7. In this question we make use of the AD-AS model discussed in the lecture
on 4th March 2004. (See for example slides posted 16th February, which also
contains references to the B&W book). Use graphs to analyse the short and
long run effects of:
(a) A devaluation (because we are considering a fixed exchange rate regime).
(b) A permanent reduction in the exogenous tax level.
Try also to explain the dynamics as fully as possible. Make sure to pay particular attention to the dynamic effects on the real exchange rate.
(Hint: Take the model specification as given, i.e., you should not spend time
discussing equations and the signs of derivatives, apart from what you find
relevant for the answers to the specific questions).
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