UNIVERSITY OF OSLO
DEPARTMENT OF ECONOMICS
Home assignment: ECON5110 Econometrics of financial markets
Handed out: Friday, April 2, 2004
To be delivered by: Thursday, April 22, 2004 no later than 13:00 hrs.
Place of delivery: Department office, 12th floor
Further instructions:
 The questions are in English, but you can write your answers in English, Norwegian,
Swedish or Danish.
 The home-exam will be marked and counts 20% towards the overall mark in this course.
The scale for the overall mark will be A-F, with F as a fail.
 After completion, you must hand in two (2) copies of your written work. Please remember
to use the printed cover page (two copies of which are enclosed)
 In addition, you must fill in the enclosed declaration
 It is of importance that the home-exam is delivered by the deadline (see above). Papers
delivered after the deadline, will not be corrected.*)
 All papers must be delivered to the place given above. You must not deliver your paper to
the course teacher or send it by e-mail. If you want to hand in your paper before the
deadline, please contact the department office on 12th floor.
 If the home-exam is not accepted, you will not be permitted to take the ordinary written
exam in this course. You will then be withdrawn from the exam, so that this will not be
an attempt.
*) If a student believes that she or he has a good cause not to meet the deadline (e.g. illness) she or he should
discuss the matter with the course teacher and seek a formal extension. Normally extension will only be granted
when there is a good reason backed by supporting evidence (e.g. medical certificate).
The term paper is composed of three parts. The first part contains some “definitions”
that are necessary that you get acquainted with in order to be able to solve the problems
presented in the third part. The second part describes the data.
Just as a reminder, note that the application of the different econometric methods you
are learning in this course, requires that you have some theories as a background.
FIRST PART
OVERVIEW OF THE THEORY OF TARGET ZONES
1. Background
-
The daily data that we are providing for this term paper covers the period October 1st,
1986 until February 9th, 1990. During this period Norway adopted a unilateral target
zones. What is a target zone?
-
In a target-zone exchange-rate (or currency band) system, governments announce the
limits that their exchange rates can move within. The gap between the upper limit (when
the exchange rate is weakest) and the lower limit (when the exchange rate is strongest)
defines a zone of flexibility. There will be a realignment if the exchange rate moves
outside those limits. In such case there will be a change in the central parity (i.e. this is
usually the mid-way between the upper and the lower limits). In practise (and in theory),
central banks needed to intervene in the foreign exchange market in order to avoid the
exchange rate to move out of the target zone or currency band. It should be noted however
that in certain cases, interventions also tok place to avoid big variations of the exchange
rate even within the currency band.
-
When the target zones are credible (i.e. there are not expectations that a realignment will
occur), there should be a negative relationship between the interest rate differentials and
the exchange rate deviation from the central parity of the target zone. For example, if
today the exchange rate starts to move (or it is found) in the weak (upper) area of the
band, the market should expect that in the near future, the exchange rate will move toward
its central parity (i.e. an appreciation within the band should be expected). As a
consequence today's domestic interest rate should decrease. The interest rate differential
should then also decrease.
Krugman, P. (1991), “Target zones and exchange rate dynamics”, Quarterly Journal of
Economics, 106, 669-682, developed the theory of target-zone exchange-rate systems. If
you are interested in reading more about it, here is the link to his paper:
http://www.jstor.org/cgibin/jstor/printpage/00335533/di971082/97p0045r/0.pdf?userID=8
1f03059@uio.no/018dd5534000501084211&backcontext=table-ofcontents&config=jstor&dowhat=Acrobat&0.pdf
Svensson, L.E.O. (1992), "An interpretation of recent research on exchange rate target
zones", Journal of Economic Perspectives, 6, 119-144, presents a non-technical
description of a target zone and experiences about implementing it. Here is also the link to
his paper, in case you are interested:
http://www.jstor.org/cgibin/jstor/printpage/08953309/di980573/98p0062o/0.pdf?userID=8
1f03059@uio.no/018dd5534000501084230&backcontext=table-of
contents&config=jstor&dowhat=Acrobat&0.pdf
On central bank interventions in the foreign exchange market in general, see L. Sarno and
M.P. Taylor (2001), “Official intervention in the foreign exchange market: Is it effective
and, if so, how does it work?”, Journal of Economic Literature, 34, 839-869.
SECOND PART
DATA DESCRIPTION
-
As mentioned above, the daily data that we are providing for this term paper covers the
period October 1st, 1986 until February 9th, 1990.
-
The data in excel format, termpap1.xls (the link to the data can be found on the
webpage of the course), contain in the first and second columns the Norwegian krone
against a basket of foreign currencies (these currencies were of the largest trader partners
of Norway) observed daily at 09.00 and 15.00, respectively. In the third column is
reported the 3-month (annualised) interest rate differential between the Norwegian interest
rate and the basket of foreign interest rates (which correspond to the same currencies that
form the currency basket to which the Norwegian krone was pegged to). The fourth
column contains a dummy variable indicating when the Norwegian Central Bank (Norges
Bank) decided to intervene in the foreign exchange market, by either buying or selling.
There are two additional dummies in the fifth and sixth columns, respectively. In the fifth
column, the dummy indicates whether Norges Bank bought foreign currency (mostly
because the Norwegian krone was too strong) while the third dummy (in the sixth column)
indicates whether Norges Bank sold foreign currency (mostly because the Norwegian
krone was too weak).
-
Note then from the data that the upper limit of the Norwegian target zone was then 114.5;
the lower limit was 109.5; while the central parity (the midway in the target zone) was
112.
-
Before you proceed in answering the questions below, it would be useful that you plot the
data and analyse them. We provide figure 1 which shows both the Norwegian exchange
rate and the net amount of central bank interventions (CBI). Just note that a positive
(negative) number implies that Norges Bank bought (sold) foreign currency.
THIRD PART
THE PROBLEMS
1. Testing the credibility of the Norwegian target zone
Consider the provided data and the following equation:
it – i*t = a0 + a1(t - CP) + t
(1)
where CP is the log of the central parity of the exchange rate (i.e. log(112)). t is the log of the
exchange rate at day t, it – it* is the interest rate differential at day t, as we defined above.
a. Interpret equation (1) in light of the Target Zone model explained above.
b. Explain how equation (1) can be estimated by the Generalised Method of
Moments (GMM).
c. Estimate then (1) by using, for example PC give.
d. Estimate (1) under the assumption that t follows an ARCH or GARCH process.
Explain why you have chosen either ARCH or GARCH.
e. Interpret the results in light of the target zone model
2. The effect of Central Bank Interventions on the exchange rate
Consider the change in the log of the Norwegian exchange rate. In light of the data
provided, you should intuitively decide whether you would like to consider an
intradaily, daily, weekly or quarterly change.
f. Setup an ARCH or a GARCH model for your chosen change in the exchange rate.
(Hint: You may want to assume an autoregressive process for your chosen change
in the exchange rate, and assume that the disturbance of this process follows an
ARCH or a GARCH process.
g. Estimate the model that you have setup in f.
h. Find how intervention decisions (make use of the dummies) will affect the
estimates that you have obtained in g. Interpret not only the value of the
parameters but also interpret them in light of the Target Zone model.
i. Find how intervention decisions (make use of the dummies) will affect not only
the conditional mean of your chosen change in the log of the Norwegian exchange
rate but also its conditional variance. Also here, interpret not only the value of the
parameters but also interpret them in light of the Target Zone model.
j. Have you consider a constant term in the conditional mean equations above? Do
you think it is reasonable to include this constant? Why?
k. Consider now the conditional mean without the constant term and estimate again
your ARCH or GARCH model as you did in h and i. Interpret these new results.
Are these new estimates any different from the ones you found above?