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A joint Initiative of Ludwig-Maximilians-Universität and Ifo Institute for Economic Research
CESifo-Delphi Conferences 2001
Managing EU Enlargement
CESifo Conference Centre, Munich
14-15 December 2001
The Repercussions of EU Enlargement
for the Equilibrium Value
of the Euro
Jerome Stein
CESifo
Poschingerstr. 5, 81679 Munich, Germany
Phone: +49 (89) 9224-1410 - Fax: +49 (89) 9224-1409
E-mail: [email protected]
Internet: http://www.cesifo.de
J. L. Stein, ENLARGEMENT OF EURO AREA
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September 29, 2001
The Repercussions of EU-enlargement for the Equilibrium Value of the Euro
Jerome L. Stein
Division of Applied Mathematics, Box F, Brown University, Providence RI 02912, FAX
(401) 863-1355, e-mail [email protected], and CESifo
ABSTRACT
The EU is in the process of expanding its membership, with the planned subsequent
integration into the EMU. Our paper addresses several questions. What is the underlying
theoretical structure linking the "fundamentals" to the equilibrium or sustainable value of
a synthetic Euro? What are the likely effects of enlargement upon the value of the Euro?
What is the explanatory power of the model used to explain the equilibrium value of a
synthetic Euro?
Key words: Euro, NATREX, equilibrium exchange rates, international capital flows,
misalignment, Enlargement of euro area
JEL classification: F02, F3, F21, F36, F43
Seminars at: European Central Bank, October 24, 2001;
Deutsche Bundesbank/National Bank of Hungary/Center for Financial Studies Johann
Wolfgang Goethe Universitat in Frankfurt, October 26, 2001;
CESifo DELPHI conference, Munich December, 2001.
J. L. Stein, ENLARGEMENT OF EURO AREA
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29 September 2001
The Repercussions of EU-enlargement for the Equilibrium Value of the Euro
Jerome L. Stein
I. AIMS OF THE STUDY
1.1 The equilibrium value of the exchange rate
The EMU is in the process of expanding its membership. The new members, the
enlargement countries, are primarily the Central and Eastern European Countries
(CEEC). The enlargement will affect both the existing EU countries (denoted E1) and the
enlargement countries.
The CEEC countries are and will be undergoing structural changes in moving
from a centrally planned to a market economy; and it is difficult to predict their
development. Gerlinde and Hans-Werner Sinn explain why the optimistic, unrealized,
anticipations of the effects of German unification/enlargement were based upon a faulty
theoretical economic framework and upon the failure to predict social/political
developments.
Our paper presents a theoretically consistent framework that can be used to
evaluate the effect of enlargement upon the equilibrium, defined as a sustainable, value of
the real Euro under different scenarios. The CEEC countries would add about 11 % to the
GDP of the E1, and hence represent a significant but not drastic change in the EU. The
saving, investment and trade balance equations of the new members will affect the
equilibrium real exchange rate of the enlarged union, and the latter will affect the existing
members.
In order to answer the question: what will be the effect of enlargement upon the
equilibrium nominal value of the Euro, we must know what have been the determinants
of the equilibrium real value of a synthetic Euro. Notable quantitative, objective studies
concerning the equilibrium real value of the Euro are the papers by: Clostermann and
Schnatz; Maseo-Fernandez, Osbat and Schnatz; Detken, Dieppe, Henry, Marin and
Smets; Detken and Marin Martinez, and Duval. The hypothesis is that a valid theory
concerning the actual real value euro, whose birth was only a few years ago, should be
J. L. Stein, ENLARGEMENT OF EURO AREA
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able to explain the real value of the synthetic euro over the past thirty years. The advent
of the ECB can be expected to change monetary policy and relative prices, but monetary
policy should not affect the determination of the longer-run equilibrium real value of the
euro. Our paper addresses several questions.
•
What is the underlying theoretical structure linking the "fundamentals" to the
equilibrium value of a synthetic Euro?
•
Based upon the answer to the first question, what are the likely effects of
enlargement upon the value of the Euro?
•
What is the explanatory power of the model used to explain the equilibrium value
of a synthetic Euro?
The equilibrium value of the euro depends upon both real and nominal variables.
The nominal exchange rate is N(t) = dollars/ Euro. The real exchange rate R(t) of the
Euro, where a rise is an appreciation of the real Euro relative to the $US, can be defined
in several ways. Generally, the researchers use equation (1), where the ratio p(t)/p*(t) is
the Euro/foreign GDP price deflators. The period covered in the studies of the synthetic
euro1 is generally 1973:1 - 2000:1.
(1) R(t) = N(t)p(t)/p*(t)
The logarithm of the equilibrium nominal exchange rate log N*(t) in equation (1a)
is equal to the logarithm of the equilibrium real exchange log R*(t) rate minus log
p(t)/p*(t) the logarithm of relative (domestic/foreign) GDP price deflators (PD). The
logarithm of the actual nominal exchange rate log N(t) in equation (1b) is equal to log
N*(t) from (1a), plus a transitory term e(t). Speculative and "one time" effects are
contained in the e(t) term. This term has a zero expectation and may or may not be
serially correlated.
(1a) log N*(t) = log R*(t) - log p(t)/p*(t)
(1b) log N(t) = log R*(t) - log p(t)/p*(t) + e(t).
Equation 1b is plotted in figure 1. The log N(t) is denoted EUUSNERMAL, and
log p(t)/p*(t) is denoted EUUSPDMAL. The variables are 4Q moving averages (MA) and
1
All of our data have been supplied by Liliane Crouhy-Veyrac, unless otherwise noted.
Her study of the euro was presented at a Banque de France conference.
J. L. Stein, ENLARGEMENT OF EURO AREA
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in logarithms (L). In logarithmic terms, the equilibrium nominal exchange rate is a line not a point - whose intercept is an equilibrium real rate R*(t) and whose slope is -1. For
each equilibrium real exchange rate, there will be a different intercept. The PPP
hypothesis is that the equilibrium real rate R*(t) is a constant, say R*(t) = R(0), and the
equilibrium nominal rate is given by points along a line whose intercept is a constant
equal to R(0). It is clear from figure 1, and confirmed by the econometric studies cited
above, that there have been significant changes in the intercept corresponding to R*(t) as
well as changes in relative prices.
Any derived equilibrium exchange rate must be an attractor: There are market
forces that bring the nominal exchange rate back to the appropriate line. Convergence can
be produced either by changes in the nominal exchange rate or by changes in relative
prices. Our question is: how will the enlargement of the euro area affect the equilibrium
real rate R*(t)?
J. L. Stein, ENLARGEMENT OF EURO AREA
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Figure 1.
Log nominal exchange rate ($US/euro) EUUSNERMAL
Log EU/US GDP deflators EUUSPDMAL
4Q mov. avg.
0.6
EUUSNERMAL
0.4
0.2
0.0
-0.2
-0.4
-0.6
-0.4
-0.2
0.0
0.2
EUUSPDMAL
FIGURE 1 log N(t) = log R*(t) - log p(t)/p*(t)
1.2 Modes of Research
The authors of the studies of the synthetic euro carefully examined the theoretical
literature concerning the determination of exchange rates, in order to evaluate the
explanatory powers of the various techniques, models and hypotheses. They ended up by
going in two directions. In one direction, they took an empirical/econometric approach
that is not based upon a specific model. This research may be grouped under the heading
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BEER, behavioral equilibrium real exchange rate used by Clark and MacDonald,
Clostermann, Schnatz, Osbat and Maseo-Fernandez . In the other direction the
researchers used the NATREX model, which is a theoretical model that implies
econometric equations. Makrydakis, de Lima, Claessens and Kramer describe the
alternative approaches as follows.
“The BEER, unlike the ...NATREX approaches that rely on a structural
equilibrium concept, is based upon a statistical notion of equilibrium...[BEER] attempts
to explain the actual behaviour of the real exchange rate in terms of a set of relevant
explanatory variables, the so called ‘fundamentals’. The fundamental exchange rate
determinants are selected according to what economic theory prescribes as variables that
have a role to play over the medium to short-term....[In BEER]… the underlying
theoretical model does not have to be specified. The exchange rate equilibrium path is
then estimated by quantifying the impact of the ‘fundamentals’ on the exchange rate
through econometric estimation of the resultant reduced form.”
Both approaches are positive, and not normative, economics. There is no welfare
significance, or value judgments, implicit in the derived equilibrium real exchange rate.
There is no implication that exchange rates should be managed. The principal difference
between the BEER and the NATREX, is that the NATREX takes as its point of departure
a specific theoretical dynamic stock-flow model, with explicit fundamentals. The
NATREX model stresses the transmission mechanism linking the real fundamentals to
the equilibrium exchange rate. It is a flexible model that can be modified according to the
particular structure of different economies and underlying scenarios. In this manner, the
NATREX model provides a framework whereby we can evaluate the effects of different
scenarios involved with enlargement upon the equilibrium value of the euro.
1.3 BEER Empirical/Econometric results
The conclusions to be drawn from the BEER studies are can be summarized.
•
The real value of the synthetic euro has been practically identical to that of the real
Deutschmark.
•
There are real variables Z(t) that produce a cointegration equation with the real
exchange rate. Each cointegrating equation passes the usual econometric tests and tracks
the real value of the synthetic Euro and the real value of the DMark.
J. L. Stein, ENLARGEMENT OF EURO AREA
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7
The equilibrium real value R[Z(t)] of the Euro/$US is not a stationary, constant mean
reverting, variable. It is a function of time varying real fundamental Z(t). The PPP
hypothesis of a constant equilibrium real rate is rejected over the sample period.
•
The real exchange rate based upon broad based indexes, such as the CPI or GDP
deflators, is almost identical to the real exchange rate of traded goods. The BalassaSamuelson (B/S) effect has a feeble effect upon the real exchange rate of the euro and of
the Deutschmark.
•
Generally, relative productivity and the terms of trade appreciate, and relative
fiscal policy depreciates, the long run real exchange rate
All of the BEER studies used the Balassa-Samuelson variable as a candidate for a
fundamental determinant of the equilibrium real exchange rate. The Balasssa-Samuelson
hypothesis is that the real exchange rate R(t) = R(CPI) equation (2) based upon broad
based price indexes such as the CPI is the product of the constant "external" price ratio
R(T) of traded goods in the two countries [equation (2a)] and R(NT) an "internal" price
ratio [equation (2b)].
The "law of one price" for traded goods is that R(T) = C a constant. The BalassaSamuelson (B-S) effect, represented by variable R(NT) the ratio of non-traded/traded
goods in the two areas, is generally measured as the relative CPI/WPI . The ratio R(NT)
of nontraded/traded goods in the two countries is called the "internal" price ratio. The
weight of non-traded goods in the CPI is fraction w. The B-S hypothesis is equation (2c):
Variations in the real exchange rate R(t) derive from variations in R(NT), since R(CPI) is
proportional to R(NT).
(2) R(CPI) = N(t)p(t)/p*(t) = R(T)R(NT)
(2a) R(T) = [N(t)p(T;t)/p*(T;t)]
(2b) R(NT) = [p(N;t)/p(T;t)]w/ [p*(N;t)/p*(T;t)]w
(2c) R(CPI) = C*R(NT)
Balassa/Samuelson hypothesis
p(t)= CPI, * = foreign country, p(T;t) = price of traded (T) goods at time t; p(N;t) = price
of non-traded (N) goods at time t; C = constant
The empirical studies consider regression (2d), where Z is a vector of real
fundamentals affecting R(T), the real exchange rate of tradables, and R(NT) is the B/S
J. L. Stein, ENLARGEMENT OF EURO AREA
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variable defined in (2b). The question is whether coefficients B and b are statistically
significant. The term in brackets on the left hand side is the definition of the real
exchange rate in (2).
(2d) log R(CPI) = [log R(T) + log R(NT)] = B.Z(t) + b log R(NT)
Some studies find that that coefficient "b" of variable R(NT) in an equation for
R(CPI) is significant, and others find that it is not significantly different from zero. One
issue is whether variable R(NT) has a statistically significant t-value in a regression with
other variables. Another more important question is whether variable R(NT) is important
in explaining variation in R(CPI).
Figure 2, derived from the Clostermann-Friedmann (1998) study of the real value
of the DMark, is a convincing demonstration that the Balassa-Samuelson effect R(NT)
has a feeble effect upon the real exchange rate. Duval (2001:346) presents a similar graph
for the Euro. The curve R(CPI) is the real exchange rate of the DM based upon the CPI.
The curve R(T) is the ratio of the prices of traded goods. The curve R(NT) is the BalassaSamuelson variable. Figure 2 shows that the real exchange rate R(CPI) for the DM is
almost identical to the ratio R(T) of traded goods. Both experienced significant variations.
By contrast, the internal price ratio R(NT) was practically constant2. Variations in the real
exchange rate R(CPI) are explained by variations in the relative price of traded goods
R(T). The reason that some researchers find that coefficient "b" in (2d) is significant is
that log R(NT) is on both sides of the regression.
2
Clostermann and Friedman (1998:213-214) write: "[The figure] shows Germany's
relative internal price ratio compared with a trade-weighted average of this group of 10
countries…It is remarkably constant, and - accordingly - the real effective exchange rate
on the basis of the overall CPI…seems to be nearly identical with the real exchange rate
based upon prices for tradables…On balance so far, not much evidence in favour of a
"Balassa-Samuelson effect" in broadly defined real effective D-Mark exchange rates
seems to exist in the data under consideration".
J. L. Stein, ENLARGEMENT OF EURO AREA
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Figure 2 Germany
R(CPI) = R(T)R(NT)
110
105
100
95
90
85
80
75
74
76
78
80
82
RCPI
84
RT
86
88
90
92
RNT
FIGURE 2 GERMANY R(CPI) = R(T)R(NT)
For US/Euro and for the real value of the DM, the B/S effect has to be viewed
differently from the way it is usually done in equation (2c). We do this in the section
below on the determinants of the trade balance.
The BEER studies do not provide a framework to answer the following questions.
What structural equations will be affected by enlargement, under different scenarios?
What is the transmission process from the structural equations to the value of the euro?
The next part briefly describes some aspects of the enlargement process. The NATREX
model provides a theoretical framework, whose explanatory power is shown below, to
answer the questions posed
J. L. Stein, ENLARGEMENT OF EURO AREA
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II. ENLARGEMENT OF THE UNION
2.1 Salient Characteristics
Several salient facts concerning the enlargement should be considered in our
analysis. First: The enlargement (CEEC) countries would add 11% to the GDP of the EU1, and hence would have a weight of 0.1 in the new vector Z(t) of fundamentals. Average
GDP per capita for the union would fall by 13%. Second: The gap in GDP per capita
between the CEEC countries and EU is much greater than existed during the previous
enlargements, as is shown below.
Enlargement
1973 Denmark, Ireland, UK
1981 Greece
1986 Portugal, Spain
1995 Austria, Finland, Sweden
1999 Transition (CEEC)
GDP per capita, (candidates/EU)
1.02
0.62
0.689
1.042
0.387
Third: The defining characteristic of the transition economies is their decision to
abandon central planning and move to market oriented economies with private
ownership. These economies suffered a substantial output contraction at the start of
transition. Almost 10 years after the transition process took off in Europe, only a handful
of countries are estimated to have returned to the levels prevailing at the start of
transition. One must exercise caution in using past national income statistics in order to
obtain quantitative estimates the real fundamentals and the structural equations of the
CEEC countries that will be relevant for the enlarged Euro area. Fourth: As the CEEC
countries have become more market oriented, they have become more integrated with
Western Europe. The majority of their trade and capital transactions are now occurring
with the EU.
The enlargement will affect the saving (S), investment (I) and current account
(CA) functions, in equation (3), of the entire euro area. The enlargement will affect the
functions within the CEEC countries, and the new CEEC functions will interact with the
existing EU-1 functions to form new EU functions vis-à-vis the rest of the world ($US).
We assume, as a first approximation, that the CEEC countries trade with and receive
capital flows solely from the EU-1 countries. Denote the EU-1 by E1 and the enlargement
countries by (C). Then the macroeconomic balance equation, whereby investment less
J. L. Stein, ENLARGEMENT OF EURO AREA
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saving plus the current account, is zero, is equation (3). Since each variable is a ratio
relative to GDP, in the aggregate country E1 has a weight of 0.9 and country C has a
weight of 0.1.
(3) {0.9[I(E1) - S(E1)] + 0.1[I(C) - S(C)]} + CA(E1) = 0.
An excess of investment less saving of the CEEC countries will mean that there is a
capital outflow from the country E1 to country C. If investment less saving in country E1
is unchanged, the desired capital inflow into the entire EU would increase by the same
amount. The desired capital inflow into the entire EU is the term in braces. The only
relevant current account function is that of the EU-1, because we assume that the CEEC
countries only trade with the E-1.
2.2 Outline of the Paper
Part III contains the structural and the resulting dynamic equations of the
NATREX model. The structural equations and the "fundamentals" will vary according to
the particular characteristics of the underlying economy. The "story" linking the
"fundamentals" under various scenarios of enlargement to the exchange rate is the
transmission mechanism, which is told in part IV. Part V shows to what extent the
NATREX model has been able to explain the value of the synthetic euro over the period
1971:1 - 2000:1. The econometrics provides a range for the expected change in the
trajectory of the euro, resulting from the enlargement under different scenarios.
III. STRUCTURAL EQUATIONS DETERMINING THE NATREX
The NATREX is not a point, but is a trajectory associated with both internal and
external balance. The focus upon the equilibrium trajectory has been motivated by several
factors. (a) The short-term approaches rely very heavily upon anticipations. The
explanatory power of such short-term models has been proven to be unsatisfactory3. (b)
3
The researchers agree with the study of the Reserve Bank of Australia, quoted in Lim
and Stein (1997: 91), that: "No economic hypothesis has been rejected more decisively,
over more time periods, and for more countries than UIP [short run uncovered interest
rate parity /rational expectations]."
J. L. Stein, ENLARGEMENT OF EURO AREA
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The state of macroeconomics, that aims to explain shorter- term movements in the rate of
capacity utilization or inflation, is riven by controversy; and the explanatory power of the
dominant theories is weak. Therefore, we have focused upon the equilibrium/sustainable
real exchange rate where the rate of capacity utilization is at its stationary mean.
The NATREX model is a method of analysis to evaluate the effects of
enlargement under various scenarios. I focus upon the key micro foundations in as simple
and general way as possible, so that we can evaluate how enlargement may affect these
key micro equations. The model is associated with a "story", the economic explanation of
the transmission mechanism. A convincing story is essential, if we are to have confidence
in the econometrics, and/or if we are to have a rational guide to policy.
Part 3.1 contains the reduced form structure, which generalizes the
macroeconomic balance models, and characterizes the class of NATREX models. Parts
3.2 - 3.5 derive the underlying structural equations. The specific characteristics of these
equations will vary according to the economy. The NATREX model has a rational
expectations foundation for the private sector, based upon stochastic optimal models
developed by Fleming and Stein. For the economy as a whole, the public plus private
sectors, decisions may be far from optimal.
3.1 The Reduced Form Equations in a growing economy
The reduced form dynamics in a growing economy are equations (4) (5) and (6).
Endogenous variables are: R(t) = the real exchange rate, F(t) = the stock of net foreign
liabilities, debt plus equity /GDP, I(t) = investment/GDP, S(t) = saving/GDP, g(t) = the
growth rate of Y(t) the real GDP. The micro foundations of the equations for the private
sector are discussed below.
The medium run equilibrium real exchange rate equates the sum of the current
account plus the non-speculative capital inflow to zero, when the domestic less foreign
real long term rates of interest r(t)-r*(t) have converged to zero, and the deviation of the
rate of capacity utilization from its stationary mean u(t) has converged to zero. The
current account is the trade balance B(t) less the net flow of income transfers r(t)F(t) from
Europe to the US (rest of the world). We may view the left hand side of (4) as the excess
J. L. Stein, ENLARGEMENT OF EURO AREA
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demand for euros relative to the dollar. If it is positive, then the euro rises relative to the
dollar, reduces the trade balance and investment and restores the equality to zero4.
Variable F(t) is the stock of net debt plus equity claims of the US on Europe, and r(t)F(t)
is the corresponding flow of interest and dividend payments evaluated at real rate of
interest r(t).
Equation (5) states that the percentage change in the ratio F(t) of net debt/GDP is
equal to: (i) the capital inflow/debt, equal to I(t) investment/GDP less S(t) social
saving/GDP, divided by F(t) less (ii) the growth rate g(t) = (dY(t)/dt)/Y(t) of GDP. Social
saving is the sum of the saving of firms, households and the government. Government
saving is the budget surplus (+)/deficit (-). Equation (6) is the growth rate of GDP, the
sum of two parts, an endogenous and an exogenous component.
BOX 1
REDUCED FORM EQUATIONS OF THE NATREX MODEL
(4) [B(R(t); Z3(t)) - r(t)F(t)] + [I(R(t); Z2(t)) - S(F(t); Z1(t))] = 0
(5) dF(t)/dt = [I(R(t); Z2(t)) - S(F(t); Z1(t))] - g(t)F(t)
(6) g(t) = b I(R(t); Z2(t)) + Z4
F(t) = net liabilities to foreigners in the form of debt plus equity/GDP; R(t) = real
exchange rate = N(t)p(t)/p*(t), N(t) = $US/Euro, p(t)/p*(t) = GDP price deflators
(euro/US); Y(t) = real GDP, I(t) = investment/GDP; S(t) = saving/GDP. The Z(t) vector
of exogenous and control variables. Growth rate of GDP = g(t) = [(dY(t)/dt)/Y(t)]. The
functions are evaluated at: u(t) = 0, deviation of rate of capacity utilization from its
stationary mean ; r(t) = r*(t) equalization of domestic r(t) and foreign r*(t) real long term
interest rates.
Whereas the macroeconomic balance models end with equation (4), the NATREX
adds dynamic equations (5) and (6). The implications of the additions are that many
4
Equation (5) states that the actual real exchange rate R(t) = N(t)p(t)/p*(t) is evaluated at
the medium run equilibrium. In reality, the convergence occurs at a finite rate, because it
takes time for the real long term interest rate differential and the deviation of the rate of
capacity utilization to converge to zero. If the nominal exchange rate were not free, then
the speed of adjustment also reflects the degree of price flexibility.
J. L. Stein, ENLARGEMENT OF EURO AREA
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effects of changes in control and exogenous variables are more than reversed in the
transition from the medium to the longer run.
3.2 The Production Function
The production, growth and investment functions are interrelated. Easterly (2000)
wrote that: "A growing body of research suggests that after accounting for physical and
human capital accumulation, 'something else' accounts for the bulk of output growth in
most countries." Although physical and human capital accumulation are certainly critical
characteristics of the growth process, Easterly questions the historical focus on factor
accumulation per se, and upon the traditional smooth Neoclassical production function in
capital and labor. The production function is equation (6), without direct recourse to the
concept of capital.
The endogenous growth (1/Y(t))dY(t)/dt in GDP has two components. The first is
a mean gross return on investment b times I(t) the ratio investment/GDP. The additional
labor and materials inputs are in fixed proportions to investment, discussed below. The
second is a stochastic term. The mean marginal gross return on investment is the ratio of
the growth in output (1/Y(t))(dY(t)/dt) divided by investment/GDP ratio I(t). The return
b(t) is stationary in both the EU-1 and the US. Capital accumulation per se in either the
US or in the EU explains less than 10% of the growth. The "something else" is contained
in the Z4 term. There is no explicit capital, but one can define capital in the sense of
Frank Knight K(t) = Y(t)/b. It is the current GDP capitalized at the stationary gross return
b on investment.
3.3 The Investment Function
Fleming and Stein considered continuous and discrete time models where both the
GDP and the interest rate for borrowing/lending are stochastic, and may be correlated. In
such a model, the future is unpredictable and there is risk aversion. The solution implies
what is "rational behavior". The object is to select capital, foreign debt and consumption
to maximize the expected present value of the utility of consumption over given finite or
infinite horizons, and where the foreign debt will not be defaulted. The technique used is
J. L. Stein, ENLARGEMENT OF EURO AREA
15
dynamic programming, and the control variables are in closed loop form5. There is no
unstable saddle point characteristic. The dynamic programming solution guarantees
stability, in a stochastic sense. Inspired by their work, we can derive equations for the
optimum ratios of investment/output ratio and consumption/output.
The ratio of investment/GDP equation (7) is a non-linear function of the expected
return on investment less the real interest rate. Call this the "q-ratio" defined in (8.1). The
investment ratio is zero until q-ratio exceeds a specific measurable risk premium. Then it
rises linearly with the q-ratio to a maximum called I-max. The maximum is such that
default will occur if the "bad" state of nature occurs. Corresponding to a I-max is a
maximum debt/GDP ratio, called debt-max. Stein and Paladino (2001) applied the
Fleming-Stein analysis to country default risk. They showed that the relation between the
actual debt/GDP and the debt-max could explain the probability default/renegotiation
among countries.
(7) I(t) = I(q(t)).
The q-ratio is the expected net return on investment less the real rate of interest.
Alternatively, the q-ratio is the present value of expected profits, divided by the supply
price of investment goods6. The real interest rate is r(t). The q-ratio is equation (8.1), if
we assume that relative prices, and the real rate of interest are martingales. The expected
rate of return is derived as follows.
An increment of capital dK(t) produces an expected increase in output of
dY(t) = b dK(t), which is sold for domestic currency at an average price P(t) =
(P*/N)α(P1)1-α . Fraction α of the GDP is sold in the world market at price P*(t) in $US,
and fraction (1-α) is sold at home at price P1(t) in domestic currency. There are fixed
proportions. To produce the output, an increment of labor of dL1(t) = a1 dK(t), and an
increment of imported materials dL2(t) = a2 dK(t) are required. The labor input price is
W1(t), and materials input price is W2(t). The investment good is locally produced at price
5
Closed loop optimal investment in a growth model was developed in Infante and Stein.
They used dynamic programming to produce convergence to the perfect foresight growth
path, when there is little knowledge of the quantitative values of the production function.
6
The q-ratio is due to Keynes, Treatise on Money, and Tobin.
J. L. Stein, ENLARGEMENT OF EURO AREA
16
P1(t).
(8.1) q(t) = (1/r)(P.b - a1W1 - a2W2) / P1
Define the real wage w = W1/P1, terms of trade T= P1/W2 as the ratio of export
price P1 to the price W2 of imported materials, the real exchange rate R(t) =
N(t)P1(t)/P*(t) as the ratio of domestic prices N(t)P1(t) to foreign prices P*(t) of
competing goods. For the US and the EU, materials prices are not significant components
of P1 and P*. Ratio P/P1= R-α is inversely related to the real exchange rate. Using these
definitions, the q-ratio is equation (8.2). The q-ratio is (i) negatively related to the real
exchange rate, real wage, the real rate of interest r and input coefficients a1, a2, and is (ii)
positively related to the mean productivity of investment b and the terms of trade T.
Vector Z2(t) = (r,b,wa1, a2 / T(t)) is exogenous.
(8.2) q(t) = (1/r) (b/R(t)α - wa1 - a2/T(t)) = Q(R(t); Z2(t)).
Investment/GDP, I(t) is positively related to the q-ratio in excess of a risk premium. Write
the investment function as (10), which is used in equations (5)-(6) above.
(9) I(t) = I(q(t)) = I[R(t); Z2(t)],
The US had a higher mean return on investment than did the EU, shown in table
1- column 3 below. Consistent with Easterly's observation, capital accumulation does not
explain very much about growth. It is extremely difficult to know to what extent the qratio will change as a result of the enlargement. We have rough estimates of the gross
return on investment b(t) for the EU countries and for the enlargement countries. We
attribute negative growth in some of the countries to the transition process from central
planning to market economies, and exclude those countries from our estimates. Table 1
presents the relevant data.
It seems that the gross return in the CEEC countries 1997-99 exceeds that in the EU-1
countries over the past 30 years. However, as shown above, the relative productivity in
the enlargement countries is 0.4 of that of the EU-1 countries, but I do not have data on
the real wage. Since the gross return b(t) is higher, and the ratio of the real wage/labor
productivity w(t)/a(t) is assumed to be similar, the q-ratio for the enlarged union may
rise.
J. L. Stein, ENLARGEMENT OF EURO AREA
17
Table 1
Country
1998
Czech republic
Estonia
Hungary
Poland
Slovenia
2000
Bulgaria
Latvia
Lithuania
Romania
Slovakia
EU-1
USA
real GDP growth
g(t)
-1.2% pa
4.6
4.6
5.2
4.5
investment rate
I(t)
28.5%
31
31.5
27.6
25.2
gross rate of return
b mean
14.8% pa
14.6
18.8
17.9
-0.4
4.1
2.6
-4.9
4.3
2.5
2.87
18
28.9
23
19.9
33.8
21.4
18.5
14.2
11.3
12.7
11.6
14.8
Note: For the enlargement countries: growth rates are for 1997-99, and investment ratio
for 1999; For the EU-1 and US, the period is 1971:2 - 2000:1. Source for g(t), j(t) for the
enlargement countries is WEO:2000, tables 4.1 - 4.2, pp140-41. Data for EU-1 and US is
from Crouhy-Veyrac.
3.4 Social Saving Function
The infinite horizon/continuous time stochastic optimal control models (FlemingStein, Merton) imply that optimal consumption/GDP is proportional to current net
worth/GDP: capital/GDP less foreign debt/GDP. If the utility function is logarithmic, the
factor of proportionality is the social discount rate is δ. Since the production function is:
Y(t) = b(t)K(t), capital/GDP is (1/b(t)). Optimal consumption/GDP is (10a). Optimal
saving is GNP less optimal consumption, and GNP is GDP less interest/dividend
payments to foreigners. Optimal saving/GDP is (10b).
(10a) C*(t)/Y(t) = δ (K(t)/Y(t) - F(t))
(10b) S*(t)/Y(t) = (1 - δ/b(t)) + (δ - r)F(t), b(t) > δ > r
If there were no debt, the optimal saving/GDP ratio is the first term. Positive
saving occurs if the gross return on capital exceeds the discount rate b(t) > δ. The second
term contains the role of the debt. We show below that a stability condition is that the
J. L. Stein, ENLARGEMENT OF EURO AREA
18
discount rate exceed the real interest rate δ > r. A rise in the debt decreases net worth and
raises saving.
Social saving is private saving, which we assume is the optimal S*(t)/Y(t), plus
government saving Sg(t)/Y(t) = taxes less transfers less government consumption, divided
by GDP. Government saving results from the political process, not from the optimization
of social utility; and the fiscal policy affects the actual private saving. Saving function
(10) is general and consistent with many sensible approaches. It does not rely upon any
one restrictive hypothesis. Social - private plus public - consumption depends positively
upon net worth equal to capital less net foreign debt plus equity F(t), and upon exogenous
factors Z1(t) such as fiscal policy (government consumption and the vector of tax rates),
and the particular characteristics of the population and its institutions such as the
"discount rate". The positive relation between social saving, by the sum of firms,
households and government, and net foreign debt, δS/δF > 0, is a stability condition for
“inter-temporal optimization”.
(10) S(t) = S*(t)/Y(t) + Sg(t)/Y(t) = S(F(t); Z1(t)), δS/δF > 0, δS/δZ1 < 0.
The social saving function for the enlarged union can be expected to decline:
(δS/δZ)dZ1 < 0.The enlargement countries face the need for substantial real and financial
restructuring, they can be expected to increase social services and transfer payments to
conform to the EU social welfare standards, and also increase military expenditures upon
joining NATO. An extremely large expenditure is required to comply with EU
environmental standards. The decline in social saving will not be as drastic as occurred
with the German unification, since the CEEC countries will not be able to count on
massive transfers from the EU. To some extent, the Maastricht treaty may limit the
government deficit.
3.5 The Current Account Function: Relation to the Investment Function and a
reinterpretation of the Balassa-Samuelson effect
We assume that all trade and investment of the CEEC countries (C) are solely
with the EU countries. The relevant current account function CA for the enlarged EU visà-vis the rest of the world is that of the original EU-1, country E1. The current account
J. L. Stein, ENLARGEMENT OF EURO AREA
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function CA = B - rF is equal to the trade balance B less interest and dividend payments
to foreigners rF. Macroeconomic balance equation (4) corresponds to equation (3)
repeated here.
(3) {0.9[I(E1) - S(E1)] + 0.1[I(C) - S(C)]} + CA(E1) = 0.
How will enlargement affect the current account function? The trade balance
depends upon the competitiveness of the tradable sectors. We measure competitiveness as
the optimal output of tradables /GDP, evaluated at a given the real exchange rate. We
show how competitiveness, investment, and the underlying logic of the BalassaSamuelson effect are interrelated, even though B/S equation (2c) above is rejected.
The optimal output of tradables X(t) is such that marginal cost MC in $US is
equal to the external dollar price P*, equation (11a). Enlargement will affect the
international competitiveness of the EU insofar as it affects X(t).There are several
possibilities. (i) The EU-1 firms invest directly/build plants in the CEEC countries, where
the latest EU-1 technology is used, but labor costs, the real wage w(t) is lower. The output
of these plants is exported to, or replaces imports from, the non-euro area. The net effect
of the direct investment is that production is shifted from high cost plants in the EU-1 to
low cost plants in the CEEC countries. (ii) The EU-1 outsource some of their inputs to the
CEEC countries. For example, in Information Technology, there is a shortage of qualified
personnel in Germany, but Russia has ample low cost, talent with advanced degrees in
physics and mathematics. With enlargement, German firms employ Russian programmers
to write complex codes for use in German financial and manufacturing firms. (iii) Lower
cost labor migrates from the CEEC to the EU-1. The effective real wage of firms within
the EU-1 declines as a result the three possibilities.
Output is produced by labor L1(t) and imported materials L2(t), given the capital
and general level of technology/productivity. A rise in productivity means that the same
output can be produced with a smaller quantity of these inputs. The price equals the
marginal cost function MC*(t) measured in $US is (11a). The nominal wage is W1(t) in
domestic currency and N(t) = $US/euro. The price of imported materials in foreign
currency is W2* (t).
(11a) P*(t) = MC*(t) = [W1(t)N(t) dL1/dX ] + [W2* (t) dL2/dX]
J. L. Stein, ENLARGEMENT OF EURO AREA
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The increase in labor required to produce an additional unit of output is (11b), and
that of materials is (11c) - where "a" is the weight of labor and (1-a) is the weight of
materials in the marginal cost function. The rising marginal cost is reflected in the output
X(t) in the numerator. An increase in the level of "productivity" z(t) shifts the marginal
cost function downward to the right. A smaller quantity of both labor and imported
materials is required to produce output.
(11b) dL1/dX = a X(t)/z(t); (11c) dL2/dX = (1-a) X(t)/z (t)
The optimum output X(t) where marginal cost MC*(t) is equal to the world price P*(t)
satisfies equation (11d).
(11d) P*(t) = [N(t)W1(t)aX(t)/z(t)] + W*2(t)(1-a)X(t)/z(t)]
Define the real exchange rate R(t) = N(t)P(t)/P*(t), the real wage w(t) = W1(t)/P(t), and
the terms of trade7 T(t) = P*(t)/W*2(t). Using these definitions in (11d), the optimum
output of exports is equation (12).
(12) X(t) = z(t) / [R(t)aw(t) + (1-a)/T(t)]
Competitivity is defined as, the value of exports/GDP = Bx = P*X/NPY, equation
(13a). The GDP is the same as productivity for the economy as a whole, since total labor
is normalized at unity. Define variable Z3 = z/Y as "relative productivity": the ratio of the
"productivity" in exports/productivity in the entire economy. Changes in Z3 reflect the
shift in the supply (marginal cost) of exports function relative to the corresponding supply
of GDP. Competitivity is: (i) negatively related to the real exchange rate, and the real
wage, (ii) positively to relative productivity Z3 and to the terms of trade T. A rise in
relative productivity does not necessarily translate into a rise in the real wage in the
export sector, because the real wage is more closely related to total productivity in the
economy.
(13a) Bx = P*X/NPY = Z3 / R(awR + (1-a)/T) ,
Z3 = z/Y relative productivity
The value of imports/GDP depends upon the real exchange rate R. Thus the ratio B of the
trade balance/GDP is equation (13). The most important components of vector Z are:
7
Here the terms of trade T = world price P* of exports/world price imported materials
W2*. In the investment equation, we defined the terms of trade T = price of domestic
output P1/ price imported materials W2. We use the "terms of trade" T for either concept,
rather than call them T1 and T2.
J. L. Stein, ENLARGEMENT OF EURO AREA
21
relative productivity Z3, the real wage w, the terms of trade T.
(13) B = B(R(t); Z(t)), where Z =(Z3, T, w)
Investment, the B/S effect and competitiveness are related. Relative productivity
Z3 contains two parts. One part of its increase comes from the rate of capital formation,
where investment is directed to the export sectors. If the investment is not directed at
exports, but is in shopping centers, office buildings, and residential construction, then Z3
is close to zero. Another part comes from the dissemination of technology into the export
sector. For example, a rise in Z3 may occur via the use of information technology in
shipping, for communication between buyers and sellers, and for inventory management.
Enlargement will affect the international competitiveness of the EU-1 insofar as it
affects X(t) or vector Z in equation (13). Insofar as the investment of the EU is direct
investment in the lower cost CEEC countries and there is more outsourcing, the marginal
costs of producing export/import substitutes, shifts downwards to the right, and variable
Z3(t) rises. At any given real exchange rate and net debt, the current account function
CA(E1) = B(R(t);Z(t)) - r(t)F(t), will increase. The logic of the B/S effect is subsumed
under Z3 , the exogenous factor in the CA function in equation (4) BOX 1.
IV. THE DYNAMIC EFFECTS OF CHANGES IN THE REAL
FUNDAMENTALS UPON THE TRAJECTORY OF THE NATREX: THREE
SCENARIOS
What are the likely effects of enlargement upon the real value of the Euro.
NATREX explains the transmission mechanism whereby changes in the real
fundamentals Z(t) work their way through the economic system to affect the real
equilibrium exchange rate and the current account. There are four fundamental
determinants of the real exchange rate in the equations in BOX 1. The first two, Z1(t),
Z2(t), affect saving and investment. The third Z3(t) affects the competitivity of the
economy. The fourth is the exogenous part of the growth rate g. In reality, enlargement
will involve some combination of scenarios. Our procedure is to analyze the effect of
each scenario separately.
J. L. Stein, ENLARGEMENT OF EURO AREA
22
4.1 Three scenarios.
In scenario I, there is a rise in social absorption, equal to government plus private
consumption plus social investment, in the CEEC (C) countries. The investment is in
shopping centers, residential construction, hotels, public utilities, highways and
telecommunications. The budget deficit rises to finance an improvement in the social
standards to bring them closer to the EU-1 level. Scenario I involves a rise in investment
less saving. There are rises in Z1 and Z2, but the others parameters - relative productivity
Z3 and the growth rate g are unchanged8.
Investment less saving in the enlargement countries is financed by the EU-1, in
the form of direct (FDI) and indirect investment. The EU-1 investment in the CEEC does
not crowd out investment in the EU-1 on a 1-1 basis. Therefore, the desired capital inflow
(I-S) = I(E1) - S(E1) + I(C) - S(C) for the entire union rises. Investment less saving for the
1998 and 2000 CEEC groups, for the two combined and for the EU-15 is described
below. For scenario I, we make three assumptions: (A1)-(A3).
Investment rate
Saving rate
I-S
CEEC total
26.9
21.5
5.4
EU-15
20.7
20.9
-0.2
Source: IMF, WEO, (2000; table 4.2); After enlargement: Weight EU = 0.9, weight
CEEC = 0.1
(A1) The desired capital inflow of the enlargement countries I(C)-S(C) rises by
about 10 per cent: from 5.4% pa to 6% pa. A weighted average of (I-S)(E1) and (I-S)(C)
would convert a desired capital outflow for the EU-15 of 0.2 % pa into a desired capital
inflow of 0.42 % pa = .9(-0.2% pa) + .1(6% pa ) for the enlarged union. Investment will
exceed saving in the enlarged EU vis-à-vis the US.
(A2) None of the investment in the CEEC countries affects the trade balance
function of the EU-1. Vector Z3(t) in trade balance equation (13) does not change.
Assumption (A2) corresponds to a situation where the investment in CEEC is directed to
producing goods solely for the internal European market.
(A3) None of these policies affects the growth rate of GDP of the entire union.
8
One may think of this as similar to the scenario of German unification, enlargement of
Germany. We have also considered the growth rate in equation (6) and let the exogenous
disturbance be Z4. The analysis is more complicated, but the results are not changed
drastically. We are using the simplest possible approach.
J. L. Stein, ENLARGEMENT OF EURO AREA
23
In scenario II, the enlargement increases the competitivity of the EU-1. The
enlargement induces outsourcing by EU-1 firms and/or direct investment into the
enlargement countries. The resulting output is exported from the EU-1 to the rest of the
world. Investment is diverted from the EU-1 to the CEEC countries, and I-S for the entire
union is unaffected. Formally, there is a rise in Z3(t) in trade balance equation (4) or (13),
without any permanent change in either Z1(t) and Z2 (t), which affect the (I-S) for the
union. Growth g(t) in the union is unaffected.
In scenario III, the growth rate of the EU rises. For example, both saving and
investment rise by the same amounts. Investment rises because the gross return on
investment increases, and this induces a rise in business saving to finance the higher
business investment. The investment is directed to all sectors of the economy. Relative
productivity in exports Z3 = z(t)/Y(t) does not change, but the growth rate g in equation
(6) increases.
Realistically, the enlargement will be associated with some combination of the
three effects. Their respective magnitudes cannot be predicted, but the analysis provides a
framework for analyzing alternative scenarios. Our procedure is to analyze the effect of
each scenario separately. In section 4.2, we develop the mathematical structure, which is
used in sections 4.3-4.5 to explain the three scenarios of enlargement.
4.2 Mathematical Structure
The equilibrium implied by system described in BOX 1 has two components.
The medium run corresponds to equation (4) and figure 3. The NATREX model
generalizes macroeconomic balance equation (4) by also considering endogenous changes
in F(t) , the ratio of debt plus equity as a fraction of GDP, equation (5). The longer run
equilibrium is described by both equation (4) and equation (5) when dF(t)/dt = 0, the debt
grows at the rate g of real GDP. A linear approximation of the equilibrium system,
equations (14)-(15), is in BOX 2. We require that the deterministic system be stable.
J. L. Stein, ENLARGEMENT OF EURO AREA
24
BOX 2
Equilibrium of model.
Medium-run (14); longer run adds (15) where dF(t)/dt = 0
(14) (IR + BR) dR - δ dF = - dz1 - dz2 - dz3
(15) IR dR - (g + δ - r) dF = - dz1
- dz2
+ F dg
Stability conditions:
∆ = [-(IR + BR)] (g + δ - r) + δIR > 0; T = (IR + BR)- (g + δ - r) < 0.
Where: dz1 = -SzdZ1, dz2 = IzdZ2, dz3 = BzdZ3 . Rise in investment less saving is (dz1+dz2)
> 0; rise in relative productivity/competitivity is dz3 > 0, rise in growth is dg > 0.
Coefficient SF = (δ - r) from equation (10b).
The effects of changes in the fundamentals dz and dg upon the long run values of
the real exchange rate R*= BZ(t) and the debt/GDP ratio F*, derived from (14)-(15) are
stated in BOX 3. In the following sections, we discuss the dynamics and the economic
scenarios, which explain these results.
BOX 3
Long run effects of changes in real fundamentals upon the equilibrium real exchange rate
R*= BZ(t) and debt plus foreign equity F*. A rise in R is an appreciation.
Scenario
I. rise dz1 + dz2 > 0
II rise in competitivity, dz3 > 0
III rise in exogenous growth, dg > 0
B = dR*/dz
-(r-g)/∆ < 0
(δ -r + g)/∆ > 0
δF/∆ > 0
dF*/dz
(-BR)/∆ > 0
IR/∆ < 0
F(ΙR + ΒR)/∆ < 0
Note: ∆ > 0, (δ -r + g) > 0, (ΙR , ΒR) < 0. F > 0, debtor; F < 0 creditor; present value of
GDP is finite if (r > g).
J. L. Stein, ENLARGEMENT OF EURO AREA
25
4.3 The process of adjustment: medium run
Figure 3 is a simple graphic exposition of equations (4) or (14), the medium run of
the transmission mechanism. The curve SI relates saving less investment to the real
exchange rate, and curve CA relates the current account to the real exchange rate. They
are evaluated when real interest rates have converged r(t) = r*(t), and the output gap u(t)
= 0. The intersection of SI and CA gives us the medium run equilibrium exchange rate,
equation (4) or linear equation (14).
The negatively sloped CA curve describes how an appreciation of the real
exchange rate decreases the trade balance and current account. The positively sloped SI
curve describes how an appreciation of the real exchange rate raises domestic costs and
prices relative to world demand and reduces the present value of expected profits. The
Keynes-Tobin q-ratio declines, and investment declines relative to saving. That is why S-I
rises with the real exchange rate. Initially, saving less investment is described by curve
SI(0), and the current account by curve CA(0). Real exchange rate R(0) produces internal
balance.
J. L. Stein, ENLARGEMENT OF EURO AREA
26
4.4 The dynamics to the longer run equilibrium
The medium run equilibrium real exchange rate in equation (16) is derived from
equation (14), which corresponds to figure 3.
(16) R(t) = R(F(t), Z(t)].
The dynamics to the longer run equilibrium arises through equation (5), the rate of
change of the ratio of debt-equity/GDP. Although Scenarios I and II have similar effects
upon the medium run exchange rate in equation (16), the three scenarios have vary
different effects in the long run equilibrium in BOX 3.
Substitute the medium run real exchange rate (16) into the investment less saving
function and derive equation (17), where J(t) = I(t)- S(t) evaluated at the medium run
exchange rate.
(17) J[F(t), Z(t)] = I[R(F(t),Z(t)] - S[F(t), Z(t)].
Substitute (17) into (5) and derive the differential equation (18) for the rate of change of
the deb/GDP. It is graphed in figure 4, for the three scenarios .
(18) dF(t)/F(t) = J(F(t); Z(t)) - gF(t)
The stability condition is that the curve, equation (18), intersects the abscissa with
a negative slope: (δJ/δF - g) < 0. At the equilibrium F* rise in the debt should lower J(t)
investment/GDP less saving/GDP below the growth rate times g of the GDP. The
stability conditions ∆ > 0, T < 0, indicated in BOX 2, correspond to this condition. In
figure 4, equation (18) is described by curves I-I II-II and III-III for the three scenarios.
J. L. Stein, ENLARGEMENT OF EURO AREA
27
4.4 Scenario I.
Scenario I involves a rise in investment less saving, dz1 + dz2 > 0. The SI curve in
figure 3 shifts from SI(0) to SI(1). If all of the increased demand were directed to home
goods, then the CA curve is unaffected9. At exchange rate R(0), the ex-ante current
account CA(0) now exceeds ex-ante saving less investment, the desired capital inflow.
Several things happen. (a) The excess demand raises the domestic interest rates. Domestic
firms/government borrow abroad what they cannot borrow at home. (b) The desired
capital inflow tends to appreciate the exchange rate to R(1) > R(0), to restore internal and
external balance. This is a movement to the medium run equilibrium R(1) = AA',
evaluated at the given level of net foreign assets F(t) and productivity. The medium run
impact upon the real exchange rate in Scenario I, where there is a rise in investment less
saving
dzi > 0 for i = 1,2 is dR/dzi = -1/(BR + IR) > 0. At real exchange rate R(1), investment less
saving equal to the capital inflow equal to the current account deficit is 0A. This means
that the foreign debt/equity is rising. The implications of this for the trajectory of the real
J. L. Stein, ENLARGEMENT OF EURO AREA
28
exchange rate are discussed in connection with figure 4, the synthesis of equations
(14),(15) and (18).
The appreciated exchange rate generates a current account deficit to finance the
capital inflow of 0A in figures 3 and 4. The dynamics of the debt are described by curve
I-I figure 4, in scenario I. The debt rises along I-I in figure 4 in the direction of the
arrows. There are several effects of the debt subsumed under equation (18): one
destabilizing effect and three stabilizing effects.
(1) The rise in the debt raises the interest payments rF(t), which further
deteriorates the current account. In figure 3, the rise in the interest payments shift the CA
curve further to the left of CA(1). This shift depreciates the exchange rate and widens the
deficit on current account. The steady decline in the CA function along a given SI
function produces instability: the debt will explode and the euro exchange rate will
depreciate steadily.
Two stabilizing effects arise from the shift of the SI curve to the right. (2a) One
stabilizing effect is that the rise in the debt/GDP lowers net worth and consumption, and
increases saving/GDP, according to equation (10b). As saving rises, the capital inflow
equal to the rise in the debt declines. (2b) The appreciation of the real exchange rate
lowers the q-ratio, equation (8.2), and reduces investment. These two effects reduce
investment less saving, and shift the SI curve in figure 3 to the right. Thereby, the capital
inflow and the rise in the debt are reduced.
(3) The ratio F(t) of debt/GDP in (5) rises as long as the capital inflow/debt
J(t)/F(t), equal to the growth of the debt, exceeds the growth rate g of the GDP. Even if
the capital inflow J(t) is constant, the growth of the debt per se reduces the growth of the
debt steadily to the growth rate g(t) of the GDP.
The long run effect in scenario I is that the debt/GDP rises along curve I-I from
point A to F(I). This is effect dF*/dz > 0 in BOX 3. The long run effect upon the real
exchange rate dR*/dz depends upon the difference between the real long term rate of
interest and the growth rate, (r-g). The present value of real GDP is finite if (r-g) > 0. For
9
Since the marginal propensity to import is a fraction, the graphic exposition in figure 3
is adequate.
J. L. Stein, ENLARGEMENT OF EURO AREA
29
the EU during the period 1973:1 - 2000:1, the real long term interest rate r = 4% pa has
exceeded the growth rate g = 2.48% pa. In that case, in scenario I the real exchange rate
of the euro will depreciate, dR*/dz = -(r-g)/∆ < 0 below R(0).
4.5 Scenario II
Scenario II involves are rise in relative productivity dz3 > 0, without a change in
investment less saving. The SI curve remains at SI(0), but the current account curve in
figure 3 increases to CA(1). At the initial exchange rate R(0), the current account exceeds
the capital outflow S-I, and the real exchange rate appreciates to R(1). The appreciation of
the exchange rate to R(1) restores medium run equilibrium by reducing investment and
the trade balance. In the medium run, the change in the real exchange rate resulting from
a rise in relative productivity z3 is dR/dz3= -1/(BR + IR) > 0, based upon equation (14).
In the medium run there is a difference between scenarios I and II. In scenario I,
there is a capital inflow equal to the current account deficit of 0A. This implies a rising
foreign debt-equity. In scenario II, there is a capital outflow equal to a current account
surplus of 0B.This implies a declining foreign debt-equity.
Figure 4 describes the difference in the dynamics, the trajectory to the longer run
equilibrium. In scenario II, the medium run equilibrium is at point B' in figure 3. The real
exchange rate is also R= R(1), but investment less saving J(1) = 0B < 0. In figure 4,
equation (18) is described by curve II-II. At a zero debt/GDP, the debt is declining by 0B
per unit of time in figures 3 and 4, whereas in scenario I the debt/GDP was
rising at rate 0A per unit of time.
The story is just the reverse of scenario I. The debt declines along trajectory II-II
from point B to F(II). The decline in the debt strengthens the effect of the medium run
impact upon the real exchange rate. As shown in BOX 3, the long run real exchange rate
appreciates above R(0), and the debt/GDP may be converted into a net asset
position/GDP equal to F(II). The country is a net creditor. At the new long run
equilibrium, there are sustainable current account surpluses and net asset position grows
at the rate g of real GDP.
J. L. Stein, ENLARGEMENT OF EURO AREA
30
5.6 Scenario III
Scenario III just involves a rise in the growth rate g, with no change in investment
less saving, or in relative productivity. Initially, there is no change in either the SI or the
CA curves in figure 3. However there are long run effects, as seen in figure 4 and BOX 3.
Initially, the debt was growing at the same rate as the GDP. When the growth rate
rises, then the debt/GDP ratio will decline. The rise in the growth rate is represented in
figure 4 by a rotation of the curve to III-III from point 0A. The debt/GDP ratio declines to
F(III) in figure 4. The decline in the debt increases the current account and appreciates the
real exchange rate. At the new equilibrium, the debt/GDP is constant at an appreciated
real exchange rate.
V. ESTIMATION OF THE VALUE OF THE SYNTHETIC EURO
We first show to what extent the NATREX model can explain the equilibrium value of
the synthetic euro. Then we can estimate to what extent enlargement will change the
equilibrium real value, under the three different scenarios. Equation (1b) relates the
nominal rate N(t) to the equilibrium real rate R*(t) and to relative prices p(t)/p*(t). In
section 5.1, we estimate the NATREX, the real equilibrium rate, and in (5.2) we estimate
the equilibrium nominal rate. Our conclusions are consistent with those obtained in the
other studies10, evaluated in Stein (2001).
5.1 The NATREX, real equilibrium rate
Differential equation (18) for the dynamics of the debt/GDP can be transformed
into difference equation (19) for the dynamics11 of the equilibrium real exchange rate
R(t). Term BZ(t) is the longer run equilibrium associated with the "fundamentals" Z(t),
defined above. Vector B consists of the dR*/dZ terms in column 1 in BOX 3. Insofar as
R(t) and vector Z(t) are integrated I(1), R(t) = BZ(t) is the cointegrating equation. The
second term a[R(t-1) - BZ(t-1)] is the error correction (EC) term. In the NATREX model
10
See the the papers by: Clostermann and Schnatz; Maseo-Fernandez, Osbat and
Schnatz; Detken, Dieppe, Henry, Marin and Smets; Detken and Marin Martinez, and
Duval.
11
Solve (16) for F(t) = F[R(t), Z(t)] and use it in (18).
J. L. Stein, ENLARGEMENT OF EURO AREA
31
graphed in figure 4, the cointegrating equation R(t) = BZ(t) reflects the long run
equilibrium associated with fundamentals Z(t), and the EC term represent movements
along the curves. The third term represents short-term shocks from variables Z(t). The
fourth term represents stationary/ transitory/ I(0) forces and have zero expectations.
(19) R(t) = BZ(t) + a[R(t-1) - BZ(t-1)] + Σb(i)∆Z(t-i) + ε(t)
(1b) log N(t) = log R*(t) - log p(t)/p*(t) + e(t).
A difficult and important problem is to decide what are the appropriate empirical
measures corresponding to the fundamentals12 Z in the model BOX 3. We must use
variables that correspond to the theory, are objectively measurable and easy to calculate.
The real exchange rate R(t) = N(t)p(t)/p*(t). In this paper we measure the parameter Z1 =
c(t)/c*(t) as the ratio of social consumption/GDP in Euroland c(t) relative to c*(t) in the
US. Social consumption is private plus public consumption.
The parameter Z3 reflects the relative productivity in the export sector. We
explained in section 1.3 above why it is not the ratio CPI/WPI. We measure Z3 as relative
labor productivity in Euroland/US, Z3 = y (t)/y*(t). The variables are 4Q moving averages.
Some authors used relative total factor productivity instead of relative labor productivity.
In either case, the assumption is that in equations (12)(13) above, Z3 = z/y and z = yγ+1,
γ>0. Productivity in exports is assumed to grow at a faster rate than general productivity,
Z3 = yγ.
A major factor that raises investment is the quantity b(t) in the q-ratio, eqn. (8.2).
It is the gross return on investment, which is an important part of variable Z2 in the
investment function. Variable b(t) is tied directly to the growth rate g(t), since b(t) =
g(t)/I(t), where g(t) is the growth rate of GDP and I(t) is the ratio investment/GDP. Both
b(t) in Europe and b*(t) in the US, and b(t)- b*(t) are I(0) stationary. Therefore we did not
include this variable in the cointegrating equation, but treat it as a trendless disturbance in
(19). Equation (12) indicates that the terms of trade also affects investment, and may be
included in Z2(t).
12
This problem is discussed in all of the papers that use the NATREX. See Stein (2001),
for an evaluation of the research. The authors use somewhat different measurements of
the fundamentals Z, but obtain consistent results.
J. L. Stein, ENLARGEMENT OF EURO AREA
32
The real NATREX rate depends upon the fundamentals Z(t) = [c(t)/c*(t),
y(t)/y*(t); b(t)-b*(t)] of relative social consumption, relative productivity, and the
trendless relative rates of return. As shown in Stein (2001), the qualitative/significant sign
results are robust across studies. The quantitative results are sensitive to the method of
estimation and measurement of variables. Consistent with the theory in BOX 3, relative
time preference c(t)/c*(t) = Z1 depreciates the long run real exchange rate, and relative
productivity y(t)/y*(t) = Z3 appreciates the long run real exchange rate. Equation (19) is
an example of an estimate13 of the longer run NATREX, the cointegrating equation R(t) =
BZ(t).
1971:1 - 2000:1
N=117; Adj. R-SQ = 0.34
(20) R(t) = 0.82 - 1.13 [c(t)/c*(t)] + 1.75 [y(t)/y*(t)];
(se)
(0.54)
(0.22)
(0.49)
[t]
[1.7]
[-2.1]
[7.9]
5.2 The Nominal Exchange Rat: NATREX and PPP
We may now synthesize NATREX and PPP, as graphed in figure 1. There are
several ways to estimate the equilibrium nominal exchange rate in equation (1b), log
N*(t) = log R*(t) - log p(t)/p*(t). Equation (19) writes the equilibrium real rate as the sum
of three elements: the longer run, the error correction and transitory terms. For R*(t) in
equation (1b), the intercept in figure 1, I use the long run equilibrium value BZ(t) in
equation (20), and the effect of the trendless relative rate of return [b(t)-b*(t)]. The error
correction, which contains lagged variables, always improves considerably the fit. An
overly stringent test of our theory in equation (21) excludes the EC term. The estimate of
the logarithm of the equilibrium nominal rate corresponding to (1b) is equation (21). The
R*(t) in equation (1b), the variable intercept in figure 1, corresponds to the term in
braces.
1971:1 - 2000:1
N=116
Adj. R-SQ = 0.3
(21) log N(t) = {1.08 log BZ(t) + 0.274 [b(t)-b*(t)] - 0.009}- 1.04 log p(t)/p*(t)
(se)
(0.43)
(0.115)
[t]
[2.35]
[2.38]
13
My data were supplied by Liliane Crouhy-Veyrac.
(0.26)
(0.06)
[-0.15]
[-3.9]
J. L. Stein, ENLARGEMENT OF EURO AREA
33
The estimate of the nominal rate N(t) = $US/euro is (22). The period is 1971:2 2000:1, and the variables N(t), p(t)/p*(t) are 4Q MA. Figure 5 graphs the actual nominal
exchange rate N(t), the fitted value N*(t), from equation(22), and the residual.
(22) N(t) = {1.19 BZ(t) + 0.26 [b(t) - b*(t)] + 1.26}- 1.48 p(t)/p*(t)
(se)
[t]
(0.46)
[2.5]
(0.12)
[2.1]
(0.22)
[5.6]
(0.34)
[-4.2]
Figure 5. Actual N(t) = $US/euro, Fitted from (22),
residual
1.8
1.6
1.4
1.2
0.4
1.0
0.8
0.2
0.6
0.0
-0.2
-0.4
75
80
Residual
85
90
Actual
95
00
Fitted
Equations (21)-(22) synthesize NATREX and the PPP. There is structural stability.
The recursive estimates of the coefficients of the medium run nominal NATREX
equation (22), estimated over the entire period 1971:1 - 2000:1, are stable from 1985:012000:01. The nominal exchange rate converges to the medium run nominal NATREX.
(iii)The deviation can be called "misalignment". The misalignment of the euro in year
J. L. Stein, ENLARGEMENT OF EURO AREA
34
2000 is less than 1 standard deviation of the value of the error over the entire period. (iv)
Since the inception of the euro, the real long term equilibrium rate BZ(t) from (20) has
been relatively constant. The recent decline in the Euro below the estimated longer run
NATREX is due to a large extent to the decline in the relative rate of return on
investment b(t)-b*(t). This decline has been associated with a capital inflow into the US
in the form of direct investment.
Figure 5 the actual nominal exchange rate N(t) = $US/Euro, the fitted value N*(t), from
equation (22), and the residual.
6. Conclusion In 1990 it was not possible to predict the quantitative value of the
Mark that would result from German unification. In 2001 it is impossible to predict with
a high degree of confidence what will be the quantitative value euro after enlargement. It
is however possible to predict within a range of values the consequences of different
scenarios involved with the enlargement. To do so, we must have a theoretical
framework that explains the transmission mechanism from policies and exogenous
variables to the economy. The NATREX model is a framework of analysis that
sufficiently flexible to explain the transmission mechanism; and it can be modified
according to the specific structure of the economy and specific scenarios.
In this paper we have stressed the microeconomic structure of the investment,
trade balance and consumption equations, and have shown what are the "fundamentals"
and how they exert their effects. The focus is upon the equilibrium, the attractor, rather
than upon short term fluctuations produced by non-systematic factors that average out to
zero. The hypothesis is that the actual rate converges to a distribution, whose mean is the
NATREX.
We showed to what extent the NATREX model has been able to explain the
evolution of the synthetic euro 1971:1 - 2000:1. On the basis of this study, and of the
applications of NATREX to the synthetic euro by other authors, we conclude that there is
agreement concerning the fundamentals and their qualitative effects upon the exchange
J. L. Stein, ENLARGEMENT OF EURO AREA
35
rate. The quantitative estimates vary according to the estimation technique used, and the
results should be taken as suggestive rather than as firm point estimates.
On the basis of estimates from equations (20)(22) above, the mean real
equilibrium value of $US/ synthetic euro can be explained by the following
decomposition.
(1)
(2)
Mean coefficient
product
Relative EU/US social consumption/GDP
0.93
-1.13
-1.05
Relative EU/US labor productivity
0.74
1.75
1.30
Constant
1
0.82
0.82
Relative rates of return on investment
Real exchange rate
-0.03 0.27
$1.06
-0.01
$1.06
The effect of enlargement upon the euro will depend upon how it affects the
fundamentals above. Each scenario is associated with a change in the mean value of the
variable in col. (1) times the assumed stable value of the coefficient in col. (2). More faith
should be placed upon qualitative estimates than upon quantitative estimates.
J. L. Stein, ENLARGEMENT OF EURO AREA
36
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