ECON 3410/4410: Seminar exercises,
autumn 2008.
2 September, 2008.
The zipped data sets referred to in the exercises can be downloaded from
http://folk.uio.no/rnymoen/rnyteach.html, follow the Teaching-autumn-2008 link.
Note that the student magazine Observator 2/2008 contains an A graded answer to
the exam from June 2006.
Exercise 1
1. Consider the dynamic model made up of equation (1.3) and (1.4) in IDM.
Assume that in the initial situation (in period t = 0), "d;0 = "s;0 = 0 and
P0 = P and X0 = X where P and X are stationary values.
(a) Assume c < a, and draw a …gure similar to …gure 1.3 in IDM. Assume
that "d;1 < 0 and that all other values of "d;t and "s;t are zero, ie a
temporary demand shock. Use the graph to illustrate the behaviour of
Pt and Xt in period t = 1; 2 and 3. What happens when t becomes really
large?
(b) Re-do the analysis, but with one change in the set of assumptions: that
c > a.
2. Using the same model as in question 1, illustrate the behaviour of Pt and Xt
in period t = 1; 2 and 3 in the case of a permanent demand shock. (You can
represent this either as "d;t < 0 for many periods (i.e., t = 1; 2; ::::::), or as a
reduction in the intercept b). Examine both constellation of slopes of the two
curves.
3. Consider the model de…ned by equation (1.5) and (1.6) in IDM.
(a) What is the expression for the slope of the long-run demand curve?
(b) What happens to the slope of the long-run demand curve if b1 = 1? Can
you think of an interpretation?
(c) Assume that in the initial situation (in period t = 0) "d;0 = "s;0 = 0 and
P0 = P and X0 = X where P and X are stationary values. Assume that
b1 = 1 and c1 = 0. Assume that "s;1 > 0 and that all other values of "d;t
and "s;t are zero, ie a temporary supply shock in period 1.
i. What are the long-run e¤ects of this positive supply shock?
ii. Show, graphically, that in period 1: X1 > X0 and P1 < P0 ; and in
period 2: X2 < X1 and P2 > P1 .
1
iii. If, instead of a < 0; we set a = 0, what are the e¤ects of the supply
shock on X1 and P1 ? What about period 2 and 3? Strictly speaking
this question only makes sense if b1 6= 1, so base your answer on
0 < b1 < 1.
4. Classify the following as either stock or ‡ow variables
(a) The labour force
(b) The rate of unemployment
(c) The trade surplus
(d) The money stock
(e) Private consumption expenditure
(f) Government debt
(g) Government de…cit
(h) The price level
(i) In‡ation
5. Figure 1 shows time series for three di¤erent nominal exchange rates, and their
respective rates of change.
a) Krone/USD exchange rate
b) Percentage change in krone/USD (quarter by quarter)
10
8
0
6
1960
9
1970
1980
1990
2000
2010 1960
1970
1980
1990
2000
2010
d) Percentage change in krone/USD (quarter by quarter)
c) Krone/euro exchange rate
5
8
0
7
1980
110
1990
2000
2010
e) Effective krone exchange rate index
1980
5
1990
2000
2010
f) Percentage change in effective krone index (quarter by quarter)
100
0
90
1970
1980
1990
2000
2010
1970
1980
1990
2000
2010
Figure 1: Bilateral and e¤ective rates of foreign exchange (Norwegian kroner). Quarterly data.
(a) Explain the di¤erence between a bilateral exchange rate and an e¤ective
exchange rate
2
(b) Panel a): What might be the explanation for the fall in on the krone/dollar
exchange rate the early 1970s?
(c) Panel a): Comment the peaks in the mid 1980s and in 2001.
(d) Based on panel a) and c), sketch how the bilateral exchange rate between
USD and EURO has developed over the period 1980-2008.
(e) The base year of the e¤ective exchange rate series in panel e) is 1995. How
would you proceed to change the two bilateral exchange rates (panel a)
and c) into index series with 1995 as the base year. How would this
change a¤ect the graphs in panel b) and d)?
(f) Are there any examples of jump-behaviour in these series?
Exercise 2
1. 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 that the models are linear in parameters, and linear models
may therefore be non-linear in the 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
=
=
=
+ X
+ ln X
+ X
(a) A model which is linear both in parameters and in variables has the
property that the …rst derivative is a constant (independent of X). Which
of the three equations has this property?
(b) A model which is linear in parameters but non-linear in variables has the
property that the …rst derivative is itself a function of X. Describe how
the …rst derivatives of (1)-(3) depend on X.
(c) Which equation implies a constant elasticity of Y with respect to X?
(d) There are other non-linear models that are linear in parameters, that you
also will come across regularly. Let for example Y denote the rate of
in‡ation in %, and let X denote the rate of unemployment (also in %).
Consider the ‘linear Phillips curve’in (1) and the two so called ‘convex
Phillips curves’given by the two speci…cations:
(4)
Y
=
(5)
Y
=
+ ln X, and
1
?
+
X
Equation (5) is called the reciprocal model.
Evaluate the derivatives of in‡ation with respect to unemployment, at
X = 4, using = 4 in (1) and (4), and = 16 in (5)?
(e) Illustrate the shape of the tree di¤erent price Phillips curves by graphs.
3
2. With reference to Table 2.3 and the associated text in IDM, con…rm that in
the case of a distributed lag model, the two …rst multipliers of a temporary
change are equal the coe¢ cients of xt and xt 1 respectively, while j = 0 for
j = 2; 3;. . . . Show also that in the case of a permanent change, long run is
equal to 1 + 2 .
3. Using the de…nitions of dynamics, in what sense would you say that the Differenced data model of section 2.3 quali…es as a dynamic model, and in which
sense does it qualify as a static model?
4. Consider the price Phillips curve
(6)
t
=
0
+
11 ut
+
12 ut 1
+
e
21 t+1
+ "t ,
with the notation explained in Chapter 2.5 in IDM, and the model for anticipated in‡ation:
(7)
e
t+1
= (1
) +
t 1;
0<
(a) Show that (6) and (7) imply an ADL model of
1:
t.
(b) Give also the ECM form of the implied in‡ation model.
(c) Assume dynamic asymptotic stability of in‡ation, so that
t = 0 in the
long-run for a given constant rate of unemployment ut = u. Give the
expression for the long-run equation for in‡ation.
(d) Will the long-run rate of in‡ation be equal to the target value ?
Exercise 3
1. Formulate a dynamic model of the real exchange rate consistent with the PPP
hypothesis holding as a long-run proposition.
2. Let t denote the real exchange rate period t. Assume that the time period is
annual, and that we are given the following ADL model which explains t :
(1)
t
=
0
+
1 xt
+
2 xt 1
+
t 1
xt represents an exogenous variable. (For simplicity, the random disturbance
"t has been omitted).Economists have suggested that after a shock, the real
exchange rate can “overshoot”its (new) long-run level.
(a) With reference to (1), formulate a precise de…nition of overshooting.
(b) Illustrate the concept by drawing graphs (by hand or computer) of dynamic multipliers which are consistent with both overshooting with noovershooting.
(c) Give one example of speci…c parameter values which gives rise to overshooting, and of another speci…c set which does not imply overshooting.
Formulate a de…nition of overshooting that you …nd meaningful in the
light of (1)?
4
3. Consider the dynamic model made up of equation (1.3) and (1.4) in IDM. Assume that the models parameters are known with certainty. Give the necessary
and su¢ cient conditions for
(a) a unique solution, and
(b) an asymptotically stable solution.
4. Consider the model given in question 3 of Exercise 1.
(a) For the case of c1 = 0, …nd the …nal equation for Xt .
(b) Is the system stable?
(c) How is stability a¤ected by setting
i. b1 = 1?
ii. a = 0?
iii. b1 = 1 and a = 0?
Exercise 4
1. Figure 2.3 in IDM shows a solution for ln(Ct ) which trends upwards. This
may indicate an unstable solution for the logarithm of private consumption.
Assume that you did not have access to the value of in the consumption
function, only to Figure 2. Why does this …gure indicate that the solution is
in fact stable?
Simulated
Simulated
Simulated
12.00
Simulated
Simulated
11.95
11.90
11.85
11.80
11.75
11.70
11.65
11.60
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
Figure 2: 5 solutions of the consumption function in (1.20), corresponding to di¤erent initial periods: 1989(4), 1990(4) ,1992(4). 1995(4) and 1998(4).
5
2. In a dynamic system with two endogenous variables, explain why we only need
to derive one …nal equation in order to check the stability of the system.
3. In the model in section 2.8.1 i IDM derive the …nal equation for IN Ct . What
is the relationship between the demand multipliers that you know from Keynesian models, and the impact and long-run multipliers of INC with respect
to a one unit change in autonomous expenditure?
4. What are the main similarites and di¤erences between Solow’s growth model
and the RBC model?
5. Use the following equation, with notation explained in Chapter 2 of IDM,
(1)
y =
k
1
k =
s y
(2)
to …nd an expression for the long-run capital intensity k.
approximation
(3)
kt
1
s
+
k
1+n 1+n
1
kt
1
+s
Then use the
1
k
1+n
for the dynamics of the capital intensity to …nd the dynamic multipliers with
respect to a temporary and a permanent drop in the savings rate s.
6. In the RBC model of Chapter 2 in IDM, derive the …nal equation for the real
wage. Will the real wage typically be pro-cyclical or counter cyclical? Explain
the economic interpretation.
Exercise 5
1. In‡ation is measured in di¤erent ways, using di¤erent price indices. Which
operational de…nition 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 data set is available in the …le wage price prod.zip on the course workpage.
(a) Show in‡ation and unemployment in a scatter plot, i.e., an empirical
Phillips curve.
(b) Try to draw a line which, intuitively, represents the empirical relationship
between the rates of in‡ation and unemployment.
(c) Are there signs of a non-linear relationship in your data set? (Hint: make
a scatter plot with in‡ation and the log of the rate unemployment).
(d) Are there periods (“sub samples”) where the Phillips curve “…ts better”
than in other periods? If so, do you have you any explanation for this
phenomenon?
6
3. Assume that the rate of in‡ation is given by the dynamic price Phillips curve
(1)
pt =
0
+
1 Ut
+
pt
1
+ "t ,
t = 1; 2; :::::
where the subscript t denotes time period (e.g., quarter or year) and denotes
the di¤erence 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). "t is the disturbance.
(a) 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
1?
(b) Assume that the long-run multiplier is
what is the implied value of ?
0:20. Using the answer to a.,
(c) In your own words: explain the concept of long-run multiplier in this
application.
(d) A majority of modern economists would probably set
their rationale?
= 1. What is
(e) Assume that = 1, and that the NAIRU rate of unemployment is 0:05.
What is the corresponding value of 0 ?
4. Consider again question 4 in Exercise 2. Assume, that the credibility of the
target rate of in‡ation is regarded a depending essentially on long-run in‡ation
being equal to in the long-run. How can this be be achieved given (6) and
(7) in that question?
5. Consider the Figure 3 and 4.
(a) What can be said about the degree of correlation between the exposed
sector hourly wage costs and the “main-course”(labour productivity and
the product price) in the long-run.
(b) What about the short-run correlation?
(c) 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
wage-share?
Note: There is …le on the internet pages called Norw wage shares.zip
with the data and variable de…nitions.
7
a) Wage per hour, valued added price index and productivity
250
b) Scatter plot: wage cost (vertical axis) and value added price index.
200
1.0
Hourly wage cost
150
Average labour productivity
100
0.5
50
1970
250
1980
1990
2000
c) Scatter plot: wage cost (vertical axis) and labour productvity .
250
200
200
150
150
100
100
50
50
125
150
175
200
225
250
275
0.2
0.4
0.6
0.8
1.0
d) Scatter plot: wage costs and m ain-course variable
50
100
150
200
250
1.2
300
Figure 3: Hourly wage costs, value added price index and labour productivity in the
Norwegian ’exposed sector’. 1966(1)-2001(4).
8
a) Scatter plot of log hourly wage costs and log 'main-course'.
b) Scatter plot of quarterly growth rates, wage cost and main-course
0.10
5
∆w
t
t
0.05
w
4
0.00
3
3.0
3.5
4.0
m c t4.5
5.0
-0.10
5.5
0.00
∆ m ct
0.05
0.10
0.15
d) Scatter plot of log wage share and log unemployment rate
-0.25
c) Scatter plot of annual growth rates, wage cost and 'main-course'.
-0.05
0.20
log wage-share
0.15
∆4 w
t
-0.30
0.10
-0.35
0.05
-0.05
0.00
0.05
∆
4
0.10
m ct
0.15
-4.5
0.20
-4.0
-3.5
-3.0
log unemploy ment rate
-2.5
Figure 4: Panel a()-c): Scatter plots of level and growth rates of Norwegian e-sector
hoursly wage cost and ’main-course’, 1966(1)-2001(4). Panel d): Scatter plot of the
e-sector wage share and the log of rate of unemployment, 1980(1)-2001(4)).
9
Exercise 6
1. What would you say is the Norwegian model’s counterpart to the modern
concept of “core in‡ation”?
2. In the ECM version of the Norwegian model of in‡ation, with a direct link
from (lagged) pro…tability to wage increases, there is no implied natural rate of
unemployment. This is di¤erent from the Phillips curve version of the model,
and also from any other Phillips curve variant. Does this mean that if the
ECM main-course model is correct, no long-run rate of unemployment exists?
Discuss.
3. Answer question 1-4 and 5 in the exercises to chapter 3 in IDM.
4. Exercise 5, question 1,2 and 3, to chapter 18 in IAM.
Exercise 7
1. Exercise 1, to chapter 17 in IAM.
2. Exercise 2, to chapter 17 in IAM.
3. Assume that the rate of in‡ation 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 di¤erence 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 "s;t and "d;t , but omit them for simplicity.
4. Explain, intuitively, how you would sign the two slope coe¢ cients asy and adp .
5. In (1), substitute yt by the right hand side of (2) to derive the so called …nal
form equation for the rate of in‡ation, and show that it takes the form of an
ADL model with two exogenous variables, zs;t and zd;t .
6. Once you have found the …nal form equation for pt , and have used that
equation to calculate the in‡ation multipliers (for example @ pt+j =@zs ), it is
possible to also …nd 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 …rst four cumulated dynamic multipliers and the long-run multiplier,
for both the rate of in‡ation and for the output gap. Use the following
coe¢ cient values for the calculations: asy = 0:1, asz = 0:5 and adp =
0:01.
10
(b) Are the multipliers of y with respect to zd very di¤erent from the multipliers in a.?
7. Try to illustrate the dynamics in a diagram with AD/AS curves (i.e., after a
shift in the AS curve).
Exercise 8 (questions sampled from earlier exams)
1. Consider the two equation model:
(1)
Xt = a Pt + b0 + b1 zt + "d;t , demand, and
(2)
Xt = c Pte + d + "s;t , supply.
<0
>0
where the symbols take the same meaning as in quotation (1.1) and (1.2)
in IDM with the following modi…cations: Pte denotes the expected price in
period t. b0 is the intercept term of the demand equation, b1 > 0 is the partial
derivative of demand with respect to the exogenous economic variable zt .
Consider two hypotheses for Pte : H1) Pte = Pt and H2) Pte = Pt 1 .
(a) Comment brie‡y on the possible economic interpretations of the two hypotheses.
(b) Compare how the two endogenous variables react to a one-period positive
shock to demand, depending on whether H1) or H2) applies.
(c) Compare how the two endogenous variables react to a permanent shock
to demand, depending on whether H1) or H2) applies.
(d) Give the mathematical conditions for stability of the system in the case
of H2) Pte = Pt 1 .
2. Assume a small open economy with a …xed exchange rate, and that one single
wage rate applies to all sectors of the economy. The natural logarithm of the
wage rate in period t is denoted wt . Let mct denote the main-course variable
(as explained in IDM), and let Ut denote the rate of unemployment (not in
logs).
Assume the following model for the wage rate:
(3)
wt =
w0
+
w1 Ut
+
w2
mct
(1
w )(wt 1
mct 1 ) + "w;t
where "w;t represents an exogenous (and random) disturbance term. Remember that wt = wt wt 1 ; and mct = mct mct 1 . Assume that Ut is an
endogenous variable, and that the following equation:
(4)
Ut =
u0
+
u Ut 1
+
u1 (w
mc)t
1
+
u2 zt
+ "u;t
u1
0
together with (3) de…ne a system that determines wt and Ut . zt denotes an
exogenous variable, representing government policy for example.
11
(a) Give signs to the coe¢ cients of the system (ie. those not already signed),
and explain your reasoning very brie‡y.
(b) Assume that the system is dynamically stable. What are the e¤ects of a
permanent change in zt ?
(c) Replace (3) with a wage Phillips curve. How does this change in the
model speci…cation a¤ect your answers to (b)?
(d) Is there a “natural rate of unemployment”in one of both of these models
(meaning that the equilibrium level of unemployment is independent of
the rate of in‡ation)?
(e) Simplify the system by setting u = 0. What are the dynamic responses
of wt , Ut , and wt to a permanent increase in the main-course variable
mct ?
Exercise 9 (question 3 and 4 are from earlier exams)
1. Exercise 3 in chapter 20 in IAM.
2. Exercise 1 in chapter 23 in IAM.
3. Explain brie‡y what are: i) Rational expectations, ii) The Lucas critique, and
iii) Ricardian equivalence.
4. Explain the ”credibility problem”in monetary policy, including the mechanism
that can lead to an in‡ation bias under discretionary policy. Indicate also how
the problem can be avoided.
Exercise 10 (exam, November 2007)
1. Assume a small open economy with a …xed exchange rate, and that one single
wage rate applies to all sectors of the economy. The natural logarithm (or
“log”for simplicity) of the wage rate in period t is denoted wt . Let mct denote
the log of the product of the foreign price and productivity (which are both
exogenous), and let Ut denote the rate of unemployment (not in logs).
Assume the following model for the wage rate :
(1)
wt =
w0
+
w1 Ut
+
Recall that wt = wt wt 1 ; and
0
1, 0 < w < 1.
w2
mct
w2
(1
mct = mct
w )(wt 1
mct 1 ):
mct 1 . Assume that
w1
0,
(a) Explain brie‡y, and with reference to for example wage bargaining theory,
how this dynamic wage equation can be given an economic interpretation.
12
(b) Consider an exogenous increase in unemployment that lasts one period.
How is wt a¤ected by this shock to unemployment? Give the two …rst
multipliers, and the long-run multiplier (Assume that w1 < 0).
In the rest of Question 1, we assume that Ut is an endogenous variable,
and that equation:
(2)
Ut =
1 <
+ u Ut 1 + u1 (w mc)t
< 1; u1 > 0; u2 < 0
u0
u
together with (1) de…ne a dynamic system.
variable.
1
+
u2 zt ;
zt denotes an exogenous
(c) What are the impact and long-run e¤ects of a permanent increase in zt
on the endogenous variables of the system?
(d) If equation (1) is replaced by a wage Phillips curve, how would this change
a¤ect your answers to Question 1(c)?
(e) Simplify the system (1) and (2) by setting u = 0. What are the dynamic
responses of wt , and Ut to a permanent increase in the variable mct ?
In addition to any mathematical and/or graphical results that you might
present, try to explain in words the dynamic process that is triggered by
the change in mc.
2. Consider the closed economy AD-AS model:
(3)
(4)
(5)
(6)
yt
y = 1 (gt g)
r); 1 > 0; 2 > 0
2 (rt
e
r t = it
t+1
it = r + et+1 + h( t
) + b(yt y); h > 0; b > 0
e
y) + st
t = t + (yt
which you will recognize from the book Introduction to Advanced Macroeconomics by Sørensen and Whitta-Jacobsen.
(a) Which equation represents the Taylor-rule?
(b) What is meant by the Taylor-principle?
(c) Consider two expectations hypotheses: i) backward-looking expectations
(in the book sometimes called static expectations), and ii) rational expectations. Explain why in the case of i), the solution of the model is
dynamic, while in case ii) the solution is static.
3. Consider the following graph with short-run aggregate demand and supply
schedules for an open econony:
13
Inflation
πf
R-III
R-VI
R-I
ȳ
Real GDP
Figure 5: Open economy AD-AS curves.
The line market R-I represents a ‡oating exchange rate regime where the nominal
money supply is the target variable for monetary policy. Line R-VI corresponds to
a …xed exchange rate regime, where the interest rate is the instrument of monetary
policy. Line R-III represents an in‡ation targeting regime.
1. (a) Give the economic interpretation of the di¤erences in slope between the
three demand curves.
(b) Consider a positive supply shock. What are the short-run e¤ects (the
impact multipliers) of the shock on in‡ation and real GDP in the three
regimes? Explain.
(c) What are the impact e¤ects of an expansionary …scal policy in the three
regimes? Explain.
(d) If the shocks in b. and c. are permanent, what are be the long-run e¤ects
on GDP? Explain.
14
Reference to Exercise 10: an open economy AD-AS model
System of equations adapted from Introduction to Advanced Macroeconomics by
Sørensen and Whitta-Jacobsen:
(7)
(8)
yt = 0 +
r t = it
(9)
(10)
ert =
t =
(11)
(12)
(13)
(eet+1
mt
r
1 et
e
t+1
et + ft
e
t + (yt
f
it + (eet+1
+ e et
it =
et ) =
pt = m0
2 rt
+
+ ert
y) + st
t
3 gt
+
f
4 yt
1
et )
m 1 it + m 2 y t
Variables that are measured in (natural) logarithms
y : real GDP.
y : level of GDP corresponding to full employment.
g : real government expenditure.
y f : real foreign GDP.
m: nominal domestic money stock.
e: nominal exchange rate.
ee : expected nominal exchange rate.
er : real exchange rate.
p: domestic price level.
Variables which are rates
i: interest rate.
if : foreign interest rate.
r: real interest rate.
: in‡ation rate.
f
: foreign in‡ation rate.
e
: the expected in‡ation rate.
Other variables
s: variable representing a “supply-shock”.
Time subscripts
All variables of the model have subscripts for time period: t, t
For example yt is real GDP in time period t.
denotes time di¤erence, for example et = et et 1 .
1 or t + 1.
Notes
In equation (11) the expected rate of currency depreciation is denoted (eet+1
e
et ), corresponding to ln(Et+1
=Et ) in the book and lectures. In equation (12) the
symbol denotes the exogenous part of depreciation expectations (it can be positive,
negative or zero).
15
Exercise 11 (exam, May 2004)
1. Consider the ADL model
(1)
yt =
0
+
1 xt
+
2 xt 1
+ yt
1
+ "t ;
where "t denotes the disturbance term in period t. The other Greek letters denote coe¢ cients. Assume that xt is an exogenous variable (i.e., not in‡uenced
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 (1)?
(c) Figure 6 contains graphs of two solutions of an ADL equation of the type
given in (1). The solutions are based on identical coe¢ cient values, and
the same numbers for the exogenous variable have been used in both
cases. The thicker line shows a solution where the …rst solution period is
1990. The thinner line has 2000 as the …rst 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 justi…cation for your answer.
2.2
y t solution, start 1990
y t solution, start 2000
2.1
2.0
t
y
1.9
1.8
1990
1995
2000
time
2005
Figure 6: Two solutions of an ADL equation for yt .
16
2010
2. Consider the case where yt in (1) denotes the hourly wage rate in the exposed
sector of an open economy, and where xt is an exogenous main-course variable.
Assume that the main-course model’s hypothesis about a constant long run
wage share holds.
(a) Re-write the ADL model (1) as an error-correction model for the hourly
wage rate.
(b) Give a brief economic interpretation of wage setting in the exposed sector.
3. Make use of the AD-AS model given below. Analyse the short and long run
e¤ects of a permanent reduction in the exogenous tax level. Consider both a
…xed and a ‡oating exchange rate regime.
Y = C(Y T ) + I( ) + G + P CA(Y; Y ; )
0 < CY < 1, I < 0, P CAY < 0, P CAY > 0, P CA < 0
SP
=
P
=i
,
M
= L(Y; i), LY > 0, Li < 0
P
i=i
se (S), s0e (S) S 0 (i.e., unsigned)
=
+ a(Y
Y ) + z; a > 0
Volumes
Y
GDP (output)
Y
full employment trend output
T
net taxes
G
government consumption and investments
Prices, interest rates
i
nominal interest rate
real interest rate
real exchange rate
S
nominal exchange rate, foreign currency per unit of domestic currency
P
price level
in‡ation
“core in‡ation”
z
variable representing a supply side shock.
Exercise 12 (exam May/Aug 2005)
1. Assume that the rate of unemployment (Ut ) and in‡ation ( t ) is endogenous
in the dynamic system made up of equation
(1)
t
=
1
1 Ut
0
0, 0
17
+
2
2 t 1;
1:
and
(2)
Ut =
1
0
0;
+
1 (it 1
t 1)
+
2( t 1
t 1 );
0;
2
where it denotes the domestic interest rate and t is the foreign rate of in‡ation, both taken as exogenous. It is also assumed that the nominal rate of
foreign exchange is exogenous and constant (for simplicity, it is not speci…ed
as a separate variable in equation (2)).
(a) Suggest an economic interpretation of equation (2).
(b) Explain what is meant by a solution to the system de…ned by (1) and (2).
(c) Show that the condition for a stable solution of the system is:
(3)
2
+
1 1
1 2
< 1.
(d) Is a vertical long-run Phillips curve consistent with a stable solution of
the system? Explain.
(e) Assume that condition (3) holds. Denote the steady-state (long-run)
solution of the two endogenous variables by and U . Draw a …gure that
illustrates how and U are determined.
(f) Give the expression for U .?
(g) Can in‡ation be controlled by monetary policy in this model?
2. Try to answer the following questions concisely but without the use of mathematics.
(a) Consider an open economy of the type studied in the course. What will
be the e¤ect of an increase in government spending? How does the answer
depend on the exchange rate regime in this economy?
(b) Explain brie‡y what are: i) Rational expectations, ii) The Lucas critique,
and iii) Ricardian equivalence
18