ECON 3410/4410. Spring 2006
Annotated version of question set to the term paper.
2 May 2006.
Ragnar Nymoen
1. Choose one of the two titles below and write an essay. The essay should not be
more than 2500 words long, and good essays can be considerably shorter. Important: cite the number of words (for example using the word count function
in MS-Word) in a footnote. Graphs and formulae do not count as words.
Title 1: On the role of static and dynamic models in macroeconomics.
Title 2: On the role of stabilization policies in modern economies.
2. Assume a small open economy with a fixed 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 Ch 3.2.), and let Ut denote the rate of unemployment
(not in logs)
Assume the following model for the wage rate
(1)
∆wt = β w0 + β w1 Ut + β w2 ∆mct − (1 − αw )(wt−1 − mct−1 ) + εw,t
where εw,t represents an exogenous (and random) disturbance term.
Give signs to the coefficients in (1), and explain your reasoning.
Comment:
This was meant to be brief (should have said so, perhaps.). Also, in general,
when answering this type of question in economics courses: don’t bother with
the interpretation of the constant term (intercept), they are usually without
any economic interpretation. Economic theory is about the derivative coefficients in models (β w1 , β w2 and αw here).
3. Assume that the rate of employment is exogenous, for example determined by
government policy (which we need not specify in this model).
(a) Explain why the formulation in (1) is consistent with the so called wagecurve, namely a relationship between the wage rate and the rate of unemployment.
Answer
Assume steady-state. Ut = U, ∆mct = gmc . ∆wt = gw , εw,t = 0. Solve
for w along a steady state growth path
(3.1)
w = mc +
where
k=
β w1
U +k
1 − αw
β w0 + β w1 gmc − gw
1 − αw
1
(3.1) is consistent with a real-wage curve model since it can be expressed
as
β w1
U +k
w−q =a+
1 − αw
where a is (log) of productivity, and q is the product price. Of course
could have log U instead.
w1 −1)gmx
Some students may note that, for consistency k = β w0 +(β
1−αw
(b) What are the dynamic multipliers of the wage level with respect to a
permanent change in the rate of unemployment?
Answer
(1) in ADL form:
wt = β w0 + β w1 Ut + β w2 mct + {1 − αw − β w2 } mct−1 + αw wt−1 + εw,t
Impact: β w1 . Second: β w1 (1 + αw ).Third: β w1 (1 + αw + α2w ). Long-run:
β w1 /(1 − αw )
(c) What is the response of the wage level if the change in U is not permanent,
but instead lasts for two time periods before returning to its initial value?
Answer
Impact: β w1 . Second: β w1 (1 + αw ). Third: αw β w1 (1 + αw ). Fourth:
α2w β w1 (1 + αw ). Long-run: 0
4. Next, assume that the rate of unemployment is endogenous and given by
Ut = β U 0 + β U 1 (wt−1 − mct−1 ) + εU,t
(2)
The main-course variable and the two disturbances εw,t , εU,t , are exogenous
variables in the dynamic system made up of (1) and (2). For simplicity set
β w2 = 1.
(a) Give the conditions for the existence of a solution to the system (1) and
(2).
Answer
Parameters take fixed (and known) values. Values of exogenous variables
(mct , εw,t and εU,t ) have to be set over the solution period, t = 1, 2, ...T .
Known initial conditions: mct−1 and wt−1 .
(b) Give the condition (on the coefficients) which ensure that the system has
an asymptotically stable solution.
Answer
With β w2 = 1, (1) can be written as
(4.1)
wt − mct = β w0 + β w1 Ut + αw (wct1 − mct−1 ) + εw,t
Use (2) to obtain:
wt − mct = β w0 + β w1 β U 0 + {β w1 β U1 + αw } (wct1 − mct−1 ) + εw,t
2
The stability condition for the variable wt −mct is thus {β w1 β U1 + αw } <
1. Ut is stable as long as wt − mct is stable. So the same condition for
the system.
Note: Some students may have answered the question with β w1 = 1. OK
since the typo was corrected only after a week.
(c) Assuming that the system has an asymptotically stable solution, give the
expressions for the long-run solution of Ut and wt − mct .
Answer
β w0 + β w1 β U 0
1 − β w1 β U1 − αw
β + β w1 β U0
U = β U 0 + β U 1 w0
1 − β w1 β U 1 − αw
w − mc =
3