ECON 3141/4141: International macro and finance
Comments to the spring 2004 home assignement.
Ragnar Nymoen
The expectations augmented Phillips curve
I have prepared a Give batch file called SwillPhil.fl which is referred to
below. The file documents the estimations underlying equation (1) and (2). It
also contains the calculations that are required in question 1b) -d), and it provides
additional comments and suggestions that might be of interest. It can be downloaded
from the usual course page.
The extension fl identifies SwillPhil.fl as a PcGive batch file that allows
you to collect and execute several PcGive commands “in one go”. It is an alternative
to using Calculator for algebra and the PcGive menus for estimation. It is convenient
for documentation. SwillPhil.fl is a human readable file, so you can inspect it
using Word, Notepad or any other text editor. (Why not try Oxedit, which can
be downloaded from http://www.nuff.ox.ac.uk/Users/Doornik/?). If you use Word,
take care not to (accidentally) save the file as a Word document, since this will
produce a file which is unrecognizable for GiveWin and PcGive. (If you run the
batch file in GiveWin (see instructions below), the contents of the batch file will in
any case be written to the results window of GiveWin).
As mentioned, SwillPhil.fl contains both comments and commands. A
single lines of comment starts with //. A multi line comments starts with /* and
ends with /*. Everything else is commands.
To execute SwillPhil.fl: 1) Start GiveWin. 2) Load the data set SwissPhill 3) From
the Tools menu, click Batch Editor to open the dialogue box called Batch [PcGive]. 4) In
the dialogue: click the Load button and then open SwissPhill.fl from whatever directory it
is located in on you system. 5) In the Batch [PcGive] dialogue, click OK:run or Run button.
Either one will execute the file, but OK:Run closes the dialogue after execution, which is
convenient. After execution, you will find that the following is written to the GiveWin
result window: The contents of the SwillPhil.fl, and the results of PcGive commands just
executed.
Just for the record: Nobody have been penalized for not using GiveWin/PcGive,
or other software, to draw the graphs of the Phillips curves! I only use GiveWin
here in order to provide you with documentation, which you can consult to check
your own calculations.
1. (a) Here, “full score” only requires that you produce the scatter plots. However, as professionals to be, you should make it a habit to include at least
one or two sentences of explanation (since graphs are seldom self explanatory), comments and evaluation (for example, a relevant issue here is: “is
there sign of non-linearity?” (or “does the log-transform help produce
a good linear relationship?”). SwillPhil.fl contains some suggestions
(though some of you had (even) better ideas in your answers!). Those
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answers that include some comments/discussion have been given “more
than full” credits in the markings.
(b) The slope of the curves are −0.38 and −0.83, respectively. To draw the
lines in a diagram you also have to plug in α̂ = 0.5411, β̂ 0 = 2.0941
and, in the short run curve, a value for INF Lt−1 . Many of you use
INF Lt−1 = 0, which is OK. SwillPhil.fl uses the value 3 (as you can
see from the batch file). The upper panel of SwissPhill.gwg plots the
curves.
Some of you make the remark that the long term Phillips curve “really”
should be vertical. This is fine, but only if you first answer the question
for the model in the exam-set, i.e., using the parameter values given
for (1)! After doing so, you can point out that a vertical long term
Phillips curve entails α = 1 in equation (1) (and in (2) for that matter),
and not 0.54 as given. In fact, as an optional exercise, you can test
the hypothesis that α = 1 is a statistically valid restriction: (From the
estimation results: (0.54 − 1)/0.21 = −4.22. Compare this with the tdistribution with 13 degrees of freedom (use Tools–Tail probability in
GiveWin). This gives t(13,2-sided) = 4.22 [0.0010], hence he restriction
is not valid using the conventional levels of significance.) As some of you
remark, the sample is rather short, and for longer samples the estimated
α may become closer to 1. But it is also possible that the downward
sloping long run Swiss Phillips curve is robust to extensions of the data
set. Further investigation is needed to settle the issue.
(c) Equation (2) is sometimes referred to as a semi-logarithmic model, since
we have applied the log transform on the right hand side only. See the
non-linear part of SwillPhil.fl for the algebra (which most of you tackles nicely in your answers). The lower panel of SwissPhill.gwg contains
my empirical non linear Phillips curves (using 3% for lagged inflation in
the short run version).
The non-linearity is striking, and it is an attractive and realistic feature
that the slope is steep for low values of U and becomes flat for high values
of U. (Interestingly: If unemployment for some reasons rises to the flat
segment, inflation becomes almost unresponsive to a small change in U
and adjustment back to low level of U is hampered).
(d) Use the long run versions of the Phillips curve to calculate the two estimates of the natural rate of unemployment, see SwissPhill.fl, if you
want to check your own algebra. Some of you base you answers on the intersection point between the plotted short and long term Phillips curves.
But this is only correct if you used 3% for INF Lt−1 when you drew the
graphs. Since (1) and (2) are two different models, it is not surprising
that they give different estimates of the natural rate. If the semi-log
model gives the best fit, the lowest estimate is also the most credible.
(e) In question (d), the value of the equilibrium (steady state) rate of inflation was given at 3%. In the answer to (e) it is relevant to say that, due to
openness of the Swiss economy, the steady state rate of inflation (if it exists) must be “given from abroad”, i.e., we introduce an assumption that
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the foreign rate of inflation determines the equilibrium rate of inflation.
Given this assumption, the natural rate is affected. Only at higher steady
state level of unemployment can the long term Phillips curve be reconciled with a permanently lower foreign inflation rate, see SwissPhill.fl
for the calculations.
2. For example: Assume first that U is an exogenous variable. If U0 (the initial
value) is below U ∗ then both unemployment is stuck at U0 and inflation is
permanently higher than the equilibrium rate given from abroad. (competitiveness is lost over time). Conversely if Ut is exogenous and U0 > U ∗ there
are permanent gains in competitiveness (as domestic prices and wages grow
at a lower rate than foreign prices and wages). Clearly the assumption about
exogenous U is untenable: Sooner or later the gain/loss in competitiveness will
force the rate of unemployment towards U ∗ . Hence the key issue here has to
be the endogeneity of U (not how core inflation/expectations are adjusted, as
some of you seem to think). No formalization is expected here, but one simple
equation which does the trick is Ut = a + b(INLFt−1 − INF L∗ ) + et , b > 0,
INLF ∗ denotes the foreign long run inflation rate. The relationship between
inflation and aggregate demand (i.e., the demand side of the AS-AS model) is
another relevant mechanism to mention.
Some of you point out that adjustment of U in the direction of U ∗ also can
come about as a result of deliberate economic policy. This is a relevant and
valid remark.
The real-exchange rate and the AD-AS model
3. Straight forward from almost everyone. However care must be taken when you
formulate the definitions. In particular avoid expressions like “the nominal
exchange rate, S, is the ratio between the Euro exchange rate and the Kroner
exchange rate”. Although there are two currencies (for example Euro and
Kroner) there is only one exchange rate: The nominal exchange rate between
the two currencies is simply the amount of Euros you exchange for 1 Krone
(alternatively; how many Kroner you pay for one Euro).
One other notification: at the end of the course, you are expected to be aware
that, in practice, one has to choose operational definitions of P, P ∗ and S .
Most frequently, the operational definition of P is the domestic consumer price
index, but other possibilities exists, for example an import price index can be
used. Sometimes S is a bilateral exchange rate (most often Euro in Norway
nowadays, and then P ∗ is the consumer price index in the Euro currency
area), but usually a weighted sum of several rates are used, with P ∗ defined
correspondingly. The weights reflect the importance of the currency in imports
or exports. Such operational definitions are called effective real exchange rates.
Finally, since we always use price indices for P and P ∗ , the nominal exchange
rate is also always in index form, with the same base-year as the price indices.
Hence, in practice, real exchange rates are indices.
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4. Many of you state carefully (and correctly) that the reasonable interpretation
is that it is the relative version of the PPP which concerns us here.
The hypothesis of purchasing power parity, PPP, states that any changes in
P ∗ is cancelled out by movements in the nominal exchange rate and/or P . If
PPP holds on a year-to-year basis, then adjustment is very swift. Hence, in
(3), α = 0 and β 1 = β 2 = 0 are a relevant/correct set of zero-restrictions on
the parameters of the ADL equation of the real exchange rate. It leaves us
with
σt = β 0.
Since σ t ≡ St Pt /Pt∗ , a rise is foreign prices in period t, is immediately “cancelled out” by a revaluation/ appreciation and/or rise in the domestic price
level.
Since the question explicitly says that xt is an exogenous variable, the following
interpretation is also allowed: The equilibrium value of the real exchange rate
is not completely invariant to all changes in the economy, exogenous events
can occur that lead to a permanent change in. Hence, α = 0 and β 2 = 0,
leading to
σ t = β 0 + β 1 xt
is also allowed here.
Many of you take another starting point, namely that if PPP is to hold on a
period to period basis, then σ t = σ t−1 is implied. This amounts to an assumption about the real exchange rate always being in steady state (from period
to period), which is a stricter and less relevant than the two interpretations
above. However, in the marking of the papers, we have decided to give some
credit also to this interpretation, as long as you formulate the coefficient restrictions needed to make (3) become consistent with ∆σ t = 0 as α = 1 and
β 0 = β 1 = β 2 = 0. If you wonder why we like this interpretation less than the
first, think about the implications of having σ t = σ t−1 as the dynamic equation
for the real exchange rate: You will recognize this as an unstable equation for
σ t , and the idea that the real exchange rate follows an unstable path seems to
be inconsistent with PPP (which is an equilibrium condition). The exceptional
case where the logical consistency between PPP and σ t = σ t−1 is maintained,
is when the initial value σ0 happens to coincide exactly with the equilibrium
value of the real exchange rate, and there are no shocks thereafter.
Some of you suggest α = 1 and β 1 = β 2 = 0, but this gives
∆σ t = β 0 ,
implying that from an initial value σ 0 , the real exchange rate is trending,
either upward or downward. This is definitively inconsistent with the PPP
hypothesis and it has not been credited in the markings.
5. If the PPP hypothesis is to hold as a long run property then the parameter
constellation in (3) must be such that there is stable steady state solution of
(3). However, there is no requirement of quick and immediate return to steady
state after a shock (in P ∗ or x). Restriction set b) is consistent with this. If we
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allow a permanent change in the exogenous variable xt to have a permanent
effect on σ t , then also c) is consistent with PPP holding as a long run property.
6. α = 1. In this case even an temporary change in xt (increases by example
0, 01 unit for one period only) will affect the level of σ t permanently, because
the solution of σ t is unstable.
7. The question gave the following 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)”. Many of you have interpreted this very liberally, and you move directly
to the graph with the AD-AS model without reference to any defining equations at all. If you read again, this is not what the hint tells you to do! As
always in macroeconomics, conclusions depend on assumptions, and they are
represented by the equations of the AD-AS model, short and long run version,
and the corresponding lists of endogenous and exogenous variables. So, in the
answer you should list the model(s) and explain how the equations translate
into the AD and AS curves. This is possible with the use of only one or two
sentences.
That said, she analyses that you give are rather promising, and some of them
are very good. In the second part of the course, you will get further training
in the use of the AD-AS model.
In brief the main elements of good answers is the following: Short run effects:
In both cases increased demand (due to devaluation in a) and tax reduction
in b)) shifts the AD-curve to the right (a positive horizontal shift). The shortrun AS curve does not change. Assuming equilibrium initially, the effects are
higher output and inflation in both a) and b). Long run effects: The vertical
long run Phillips curve ties down Y in the long run. Hence there in traces of
the initial increase in Y in the long run. In the long run π = π ∗ , so also the
initial rise in inflation is reversed. The real exchange rate, which was initially
reduced in a) is also unchanged compared to the initial situation (applies to
question a)). Many of you missed that in b), the long run effect, is a rise in
σ (since the the tax reduction is permanent, the current account has to be
crowded out to make room for permanently increased private consumption).
Dynamics: If π̄ is exogenous, the short run AS curve does not shift and in
both a) and b) there is a gradual change from the intersection marking the
short run effects in π and Y , and back towards the long run equilibrium. The
period with π > π ∗ wipes out the initial fall in σ (applies to a)), and serves
to permanently increase σ in b). If you instead assume that π̄ changes in
response to the initial increase in π, you need to include a sequence of shifting
AS curves in your account of the dynamics. Remember that the long-run AS
curve is not changed in this case either!
In (b) some of you introduce the government budget constraint in order to
tie down the long run solution. However, given the long run version of the
AD-AS model this is not formally required: Even with a permanent reduction
in T̄ there is well defined new steady state, since σ appreciates to give room
for higher private consumption (by reducing P CA). After finishing the analy-
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sis, you are however free to criticise the model, and its long run equilibrium
concept on the grounds that it fails to take account of the government budget
constraint. However, if we interpret “long-run” in this model as corresponding
to, say, 5-7 years, this omission may not be damaging.
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