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A joint Initiative of Ludwig-Maximilians-Universität and Ifo Institute for Economic Research
CESifo-Delphi Conferences:
Managing EU - Enlargement
Delphi Conference Centre, Delphi
13-14 September 2002
The Euro Under Alternative Scenarios of
Enlargement
Jerome L. 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, DELPHI - ENLARGEMENT OF EURO AREA
8-07- 02
DELPHI CONFERENCE
The Euro under alternative scenarios of Enlargement
Jerome L. Stein*
ABSTRACT
The EMU is in the process of expanding its membership. An analytic framework is
presented whereby one can explain how the enlargement of the euro area will affect the
equilibrium or sustainable real value of the Euro under different scenarios/policies. Then
we show what is the explanatory power of the model that we use 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
*Division of Applied Mathematics, Box F, Brown University, Providence RI 02912,
FAX (401) 863-1355, e-mail [email protected]
I thank my referees: Helge Berger, Thomas Moutos, Hans-Werner Sinn and Euclid
Tsakalatos, for their excellent guidance in revising my paper, and to Palle Andersen for his
discussion of an earlier version presented at a conference sponsored by the Deutsche
Bundesbank, National Bank of Hungary and the Center for Financial Studies in Frankfurt.
1
J. L. Stein, DELPHI - ENLARGEMENT OF EURO AREA
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8-07-02
The Euro under alternative scenarios of Enlargement
Jerome L. Stein
I. AIMS OF THE STUDY
The Euro Area - defined as the countries using the Euro/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). Enlargement will affect both the existing
EMU countries and the accession countries. The latter are and will be undergoing structural
changes in moving from a centrally planned to a market economy. Since elections have resulted
in changes in economic and social policies, it is difficult to make unconditional predictions. Our
paper presents an analytic framework to evaluate the effect of enlargement upon the
equilibrium, defined as a sustainable, value of the real Euro under different scenarios. Each
scenario corresponds to a different set of policies. In scenario I, there are populist policies
which emphasize the "welfare state". In scenario II, policies emphasize the liberalization of
economies and economic growth. Each scenario has different implications for the value of the
euro in the enlarged euro area. The realization will be a linear combination of the two scenarios
or policy options chosen, with variable weights resulting from the political process.
In order to answer the question: what will be the effect of enlargement of the euro area
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 during the period 1973 - 2000. A valid theory
concerning the actual real value euro should be able to explain the real value of the synthetic
euro over the past thirty years.
Monetary policy is not discussed here because the European Central Bank (ECB) is
committed to price stability1, regardless of what happens in the enlargement process. Moreover,
monetary policy should not affect the determination of the longer-run equilibrium real value of
the euro. Our paper addresses several questions.
1
See the discussion in section 1.2 below.
J. L. Stein, DELPHI - ENLARGEMENT OF EURO AREA
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•What is the underlying theoretical structure linking the "fundamentals" to the
equilibrium value of a Euro? What are the effects of enlargement upon the value of the
Euro, under different scenarios? Each scenario represents a different policy option.
•What is the explanatory power of the model used to explain the equilibrium real
value of a synthetic Euro?
1.1 The equilibrium value of the exchange rate
The equilibrium value of an exchange rate is a sustainable rate satisfying conditions
(C1) - (C4). Conditions (C1) - (C2) are referred to a medium run equilibrium. Conditions
(C1)-(C4) are referred to as longer run equilibrium.
(C1) Internal balance prevails where the rate of capacity utilization is equal to its long run
stationary mean.
(C2) External balance exists where there are no speculative capital movements or changes in
reserves, and domestic and foreign long-term real rates of interest are equal.
(C3) The ratio of net2 foreign liabilities/GDP is constant.
(C4) As a result of market forces, the actual exchange rate converges to a distribution whose
conditional mean is the "equilibrium" rate.
The equilibrium value of the nominal euro depends upon both real and nominal
variables. The nominal exchange rate is N(t) = dollars/ Euro. The real exchange rate of the Euro
R(t), where a rise is an appreciation of the real Euro relative to the $US, can be defined in
several ways. Generally3, the researchers use equation (1), where the ratio p(t)/p*(t) is the
Euro/foreign GDP price deflators.
(1) R(t) = N(t)p(t)/p*(t)
The logarithm of the equilibrium nominal exchange rate log Ne(t) in equation (2) is
equal to the logarithm of the equilibrium real exchange log Re(t) rate minus log p(t)/p*(t) the
2
Net foreign assets are negative foreign liabilities. We include debt and equity in "net foreign
liabilities", and call it "foreign debt".
3
Empirical results are sensitive to the way the real exchange rate is defined. See Stein and
Paladino (2001a), pp. 140-41.
J. L. Stein, DELPHI - ENLARGEMENT OF EURO AREA
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logarithm of relative (euro/foreign) GDP price deflators. Superscript “e” denotes equilibrium.
(2) log Ne(t) = log Re(t) - log p(t)/p*(t)
Uncovered interest rate parity/rational expectations links the actual real exchange rate to
the equilibrium rate. The real exchange rate R(t) converges to its equilibrium value Re(t) in
proportion to the real long-term 4 interest rate differential r*(t) – r(t) in equation (2a), where the
asterisk refers to the foreign rate. It follows that the actual nominal exchange rate log N(t)
differs from the equilibrium nominal rate by a term u(t), in equation (2b). The hypothesis is that
the term u(t) is stationary with a zero expectation and positive variance. It contains the stationary
real long term interest rate differential plus transitory factors ε(t).
(2a) log Re(t) – log R(t) = a [r*(t) – r(t)], a > 0.
(2b) log N(t) = log Re(t) - log p(t)/p*(t) + u(t), u(t) =a[r(t) – r*(t)] + ε(t)
A synthetic euro for the 11 euro countries, relative to the $US, has been computed in
many studies. We use the measures of the synthetic euro derived by Liliane Crouhy-Veyrac.
She used backward GDP weights following the OECD methodology5. Equation 2b is plotted in
figure 1 for the synthetic euro relative to the $US. In logarithmic terms, the equilibrium nominal
exchange rate is a line - not a point - whose intercept is an equilibrium real rate Re(t) and whose
slope is -1. For each equilibrium real exchange rate, there will be a different intercept. It has
been confirmed by the econometric studies cited below that the equilibrium real rate is not a
constant, but is affected by well defined real variables. That is, the intercept in equation (2) defining a family of lines - has been changing significantly over the period. A linear regression
line, with a constant slope and intercept, has been drawn in figure 1 as a benchmark.
4
The hypothesis of uncovered interest rate parity/rational expectations is rejected when one
uses short term rates.
5
All the data used in my paper come from Crouhy-Veyrac's work. They are very similar to
those used in the studies by the ECB researchers cited in this article.
J. L. Stein, DELPHI - ENLARGEMENT OF EURO AREA
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Figure 1.
Log nominal exchange rate ($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 Re(t) - log p(t)/p*(t) + u(t)
log N(t) = EUUSNERMAL, log p(t)/p*(t) = EUUSPDMAL, 4Q MA
1.2 The Importance of Knowing the Equilibrium Value of the Euro
Vitor Gaspar-Otmar Issing (2002) explained the role of the exchange rate in the
context of the European Central Bank (ECB) policy. The ECB announced a stability oriented
monetary policy strategy with several characteristics. First, the primary goal is to keep price
inflation in the medium term below 2% p.a. Price stability provides an important contribution to
J. L. Stein, DELPHI - ENLARGEMENT OF EURO AREA
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sustainable growth and efficiency in resource allocation. Second, a prominent role is assigned to
the growth of M3 as the main systematic determinant of the price level, but the ECB also uses
other instruments and indicators. Third, the exchange rate is not considered as an appropriate
target because it may be inconsistent with the goal of price stability.
Suppose that foreign prices are growing at 2% p.a, and that the ECB policy is to use
monetary policy to keep log (p(t)/p*(t)) = 0. The enlargement of the euro area will not affect
ECB monetary policy. This is why we ignore the monetary variables. If enlargement of the Euro
area results in changes in the equilibrium real rate, the intercept or line equation (2b) will shift.
Given the ECB policy to keep relative prices constant, the equilibrium nominal exchange rate
will shift up/down the vertical axis. If the ECB had attempted to keep the nominal exchange rate
constant, then variations in the equilibrium real rate - the intercept - would have produced
variations in the rate of inflation. That result is unacceptable to the ECB. Our question is: how
will the enlargement of the euro area affect the equilibrium real rate Re(t)?
II. ANALYTICAL TOOLS TO IDENTIFY KEY PARAMETERS FOR
POLICY EFFECTS OF ENLARGEMENT ON THE EQUILIBRIUM VALUE OF
THE EURO
There have been many econometric studies of the determinants of the value of the
synthetic euro, which are summarized in the European Central Bank, Monthly Bulletin (January,
2002: Box 2). Most of the studies are driven by econometric techniques rather than by
economic theory. The concept of "equilibrium" in the purely econometric studies is just a
statistical concept derived from a VEC approach, where the authors seek a cointegrating
equation which links the real rate to an eclectic set of variables6. Ronald MacDonald (2002)
describes this approach as "…essentially an atheoretical (i.e., statistical) way of constructing an
equilibrium exchange rate".
In order to understand what will be the effect of different scenarios/policy options upon
the equilibrium value of the euro, we use the economic concept of equilibrium, satisfying
6
See part IV below.
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conditions (C1)-(C4) in part 1.1 above. Outstanding recent studies of the synthetic euro, based
upon the economic concept of equilibrium, are by: Carsten Detken, Alistair Dieppe, Jérôme
Henry, Carmen Marin, Frank Smets, and Romain Duval. Similar studies based upon the
concept of economic equilibrium have been done for two of the main underlying currencies7: the
DMark by Christoph Fischer and Karlhans Sauernheimer, and for Italy by Daniela Federici and
Giancarlo Gandolfo.
Their main conclusions8 concerning the synthetic euro, over the sample period 1970:11999:4, are the following. (1) The Purchasing Power Parity hypothesis is not a satisfactory
concept in the medium to longer run. The extreme length of deviations from PPP implies that
they cannot be explained solely by monetary disturbances combined with nominal price
rigidities. (2) In the case of the European countries, the Balassa-Samuelson (B/S) hypothesis is
only weakly supported - if at all- when direct measures of the relative price of nontraded/traded goods are used. The direct measures to test the B/S hypothesis are based upon
sectoral price deflators of traded and non-traded goods.9 (3)The presence of non-traded goods
explains only a very small portion of the long run behavior of the real exchange rate. In most
cases, relative PPP is also rejected for traded goods. (4) Any credible theory for the long run
equilibrium real exchange rate should also embody a theory for the equilibrium real exchange
rate for traded goods.
The analytic framework that we use to discuss the implications of different
scenarios/policy options is the NATREX model. Knut Wicksell defined the "natural rate of
interest" as a long run sustainable equilibrium for the economy. Analogously call the equilibrium
or sustainable real exchange rate, which satisfies conditions (C1)-(C4) above, the NATural
Real EXchange rate. 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
7
Liliane Crouhy-Veyrac and Michèle Saint Marc did the same thing for the French Franc/DM
real exchange rate.
8
A discussion of these papers is in Stein and Lim, Introduction (2002).
9
Indirect measures such as the ratio of the CPI/WPI are inadequate for the test of the B/S
hypothesis. The B/S effect has been trivial for Germany. See Clostermann and Friedmann
(1998) figure 3.
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several factors10. (a) The short-term approaches rely very heavily upon anticipations, whose
explanatory power has proven to be unsatisfactory. (b) The state of macroeconomics, that aims
to explain shorter- term movements in the rate of capacity utilization or inflation, is extremely
controversial. Therefore, our focus is upon the equilibrium/sustainable real exchange rate.
The NATREX model is a method of analysis11 that we use to evaluate the effects of
enlargement under various scenarios. This is the model used in the studies cited in table 4 below
that use the economic concept of equilibrium. The technical details underlying the NATREX
model are contained in Stein (1997)(1999), as well as in some of the papers cited above, and
the discussion here will be primarily graphic and expository. The model is associated with a
"story", an economic explanation of the transmission mechanism that links the equilibrium real
exchange rate to policy and exogenous variables. 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.
The equilibrium real exchange rate is a relative price that evolves in a growing economy
subject to changes in policy and to external shocks. Part 2.1 states the reduced form structure,
which generalizes the macroeconomic balance models, and characterizes the class of NATREX
models. A distinction must be made between: endogenous variables, control variables and
exogenous variables. Policy scenarios are associated with changes in the control variables.
Endogenous variables in the NATREX model are the real exchange rate, the stock of
net foreign liabilities, debt plus equity /GDP, investment/GDP, saving/GDP, and the growth rate
of Y(t) the real GDP. 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 control models developed by Fleming and Stein. For the
economy as a whole, the public plus private sectors, decisions may be far from optimal.
Part 2.2 explains the microfoundations of the underlying equations and how they are
affected by social/economic policies. On the basis of theoretical parts 2.1 and 2.2 we have an
10
See Stein and Paladino (1997) for an evaluation of recent models used in international
finance.
11
Allen explains the logic and flexibility of the NATREX model, to take account of different
economic structures, and its relevance for policy decisions.
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analytical framework to explain, in part III, the effects of different scenarios of enlargement of
the euro area upon the equilibrium real exchange rate. The empirical evidence in support of the
NATREX model/analysis is discussed in part IV and draws upon the recent studies cited
above.
2.1 Dynamics of The Natural Real Exchange Rate
The reduced form dynamics, concerning the equilibrium real exchange rate in a
growing economy, are equations12 (3) (4) and (5). The micro-foundations of these equations are
discussed in an intuitive way in section 2.2 below. Equation (3) corresponds to conditions of
medium run equilibrium (C1) and (C2) above. It is the macroeconomic balance equation
evaluated at medium run equilibrium, where the rate of capacity utilization is equal to its
stationary mean - internal balance - and where real long term rates of interest are equal at
home and abroad - portfolio balance. The medium run equilibrium real exchange rate13 R(t)
equates the sum of the current account CA plus the non-speculative capital inflow, equal to
investment less social saving (I - S), to zero. Social saving is the sum of the saving of firms,
households and the government. Government saving is the high employment budget surplus
(+)/deficit (-). The current account is the trade balance B(t) less the net flow of income transfers
r(t)F(t) from the Euro area to the US (rest of the world). 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) = r*(t). We may view the left hand side
of (3) as the excess demand for euros relative to the dollar. If it is positive, then the euro
appreciates (rises) relative to the dollar, reduces the trade balance and restores the equality to
zero. Vector Z(t) = [Z1(t), Z2(t), Z3(t), Z4(t)] contains policy variables and exogenous variables
such as the relative price of materials such as oil or exogenous terms of trade. Vector Z(t) is
discussed in part 2.2 below.
12
All the variables, except the exchange rate and interest rate, are measured as fractions of
GDP.
13
We omit a superscript "e" and just denote the equilibrium real rate as R(t).
J. L. Stein, DELPHI - ENLARGEMENT OF EURO AREA
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The NATREX model generalizes the macroeconomic balance models by adding
dynamic equations (4) and (5) for the change in the debt-equity and the growth rate. When
there is macroeconomic balance, the current account can be positive or negative. A current
account deficit equals the capital inflow, which is the change in net foreign claims in the form of
either debt or equity. Refer to debt plus equity as "debt" or net foreign liabilities, and F(t) is the
ratio of debt/GDP. The change in the debt affects the current account and feeds back upon the
macroeconomic balance equation (3).
Equation (4) states that dF(t)/dt, the rate of change of debt/GDP has two components.
The first is I(t)-S(t) the investment ratio less the saving ratio, equal to the capital inflow, equal to
the current account deficit. The second part is the product of the growth rate g(t) of the GDP
and the debt ratio F(t).
Equation (5) is the growth rate of GDP. It is the sum of two parts, an endogenous and
an exogenous component. The endogenous part is bI(t) proportional at constant rate b to I(t)
the investment/GDP ratio and the exogenous/control part is contained in vector Z4. Whereas the
macroeconomic balance models are exclusively concerned with equation (3), the NATREX
adds dynamic equations (4) and (5), which feed back upon the macroeconomic balance
equation (3). The implications of the additions are that many effects of changes in control and
exogenous variables are more than reversed in the transition from the medium to the longer run,
as is shown in part 3 below..
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BOX 1
REDUCED FORM EQUATIONS OF THE NATREX MODEL
(3) [B(R(t); Z3(t)) - r(t)F(t)] + [I(R(t); Z2(t)) - S(F(t); Z1(t))] = 0
(4) dF(t)/dt = [I(R(t); Z2(t)) - S(F(t); Z1(t))] - g(t)F(t)
(5) g(t) = bI(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. Z(t) = vector of exogenous and control
variables. Growth rate of GDP = g(t) = [(dY(t)/dt)/Y(t)]. The functions are evaluated at a rate
of capacity utilization equal to its stationary mean and the equalization of domestic r(t) and
foreign r*(t) real long term interest rates.
2.2 The Structural Equations14
2.2.1 Production and Growth Functions
The production, growth and investment functions are interrelated. Easterly and Levine (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 and Levine question the historical focus on factor accumulation per se,
and upon the traditional smooth Neoclassical production function in capital and labor. Our
production function15 is equation (5). There is no explicit capital, but we define capital K(t) in the
sense of Frank Knight where K(t) = Y(t)/b. It is the current GDP capitalized at the stationary
gross return b on investment.
14
Technical details and derivations of the structural equations for investment, saving and the
current account are in: Lim and Stein (1997: ch. 4), Fleming and Stein (2001) (2002), and Stein
(1997)(1999). Here, we discuss the results in a more intuitive fashion.
15
Our production function generalizes the AK function.
J. L. Stein, DELPHI - ENLARGEMENT OF EURO AREA
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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/GDP16. The second is a
stochastic term. The return is stationary in both the EU 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 is the total factor productivity Z4 term.
2.2.2 The Investment Function
Fleming and Stein (2002) considered continuous and discrete time models of
international finance where both the GDP and the interest rate for borrowing/lending are
stochastic, and may be correlated. In these models, the future is unpredictable and there is risk
aversion. No certainty equivalence is used. 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
dynamic programming, and the control variables are in closed loop form17. There is no unstable
saddle point characteristic. The dynamic programming-stochastic optimal control solution
guarantees stability in a stochastic sense. Drawing upon their work, we derive equations for the
optimum ratios of investment/output and consumption/output.
The ratio of investment/GDP equation (6.1) is a non-linear function of the "q-ratio". It
can be defined in several equivalent ways. It is the expected return on investment less the real
interest rate. Alternatively, the q-ratio is the present value of expected profits, divided by the
supply price of investment goods18. In Fleming and Stein, the investment ratio is zero until qratio exceeds an explicit measurable risk premium. Then I(t) rises linearly with the q-ratio to a
maximum called I-max. Corresponding to I-max is a maximum debt/GDP ratio, called debtmax. The maximum is such that default will occur if the "bad" state of nature occurs. Stein and
Paladino (2001b) applied the Fleming-Stein (2001) analysis to country default risk. They
16
The additional labor and materials inputs are in fixed proportions to investment.
Closed loop optimal investment in a growth model was developed in Infante and Stein. We
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.
17
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showed that the relation between the actual debt/GDP and the debt-max could explain the
probability default/renegotiation among emerging market countries.
(6.1) I(t) = I(q(t)).
The determinants of the q-ratio that are relevant in the scenarios discussed below are as
follows. Suppose that the goods produced are sold at home and abroad, and the investment
good is domestically produced. The numerator of the q-ratio is the increase in the quasi-rents or
cash flow, capitalized at the real rate of interest. The denominator is the supply price of the
investment good. The increase in the quasi-rents is equal to the productivity of the investment
less the labor input cost less the cost of imported materials. It then can be shown that the qratio, equation (6.2), is positively related to the total factor productivity Z4(t), and to the terms
of trade T(t), and is negatively related to the real wage w(t), the real exchange rate R(t) and r(t)
real long term rate of interest. The vector of exogenous variables Z2(t) = [Z4(t), T(t), w(t), r(t)].
(6.2) q(t) = Q[R(t); Z2(t)].
Investment function (7), derived from (6.1)(6.2), is used in equations (3)-(5) above.
(7) I(t) = I(Q(t)) = I[R(t); Z2(t)].
Enlargement will affect the investment function insofar as it leads to changes in
exogenous vector Z2 .
2.2.3. Social Saving Function
Social consumption C(t) is private consumption plus government consumption. Social
saving is GNP less social consumption, where GNP is the GDP less net payments of interest
and dividends to foreigners.
The infinite horizon/continuous time stochastic optimal control models (Fleming-Stein
(2002)) imply19 that optimal private consumption is related to current net worth, equal to
18
The q-ratio is due to Keynes, Treatise on Money, and Tobin.
The Fleming-Stein model generalizes the Merton model to an international finance context.
Both use similar techniques, dynamic programming, which are fundamentally different from those
that use an “intertemporal budget constraint”. There is no saddle point instability or requirement
that one can predict the future. See Fleming and Stein (2002) for a comparison of alternative
approaches.
19
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capitalized disposable current income less foreign debt. For the private sector, disposable
income is GDP less taxes plus transfers. If the utility function is logarithmic, the factor of
proportionality is the social discount rate is δ. Whereas the private consumption is presumed to
result from a utility maximization process, government consumption Cg results from the political
process.
Social consumption C(t) is optimal private consumption, the first term on the right hand
side of (8a), where τY represents taxes less transfers, and L(t) is the net foreign debt; and
government consumption is Cg(t). Divide (8a) by Y(t) and the social consumption rate c(t) =
C(t)/Y(t) is (8b), where F(t) = L(t)/Y(t) is the ratio of the net foreign debt/GDP and cg(t) =
Cg(t)/Y(t) is the ratio of government consumption/GDP
(8a) C(t) = δ[(1−τ)Y(t)/b – L(t)] + Cg(t)
(8b) c(t) = C(t)/Y(t) = δ[(1−τ)/b – F(t)] + cg(t)
Social saving, equal to Y(t) – rL(t) – C(t), is GNP less social consumption, where
GNP is GDP less net interest and dividend payments to foreigners. The ratio S(t) of social
saving/GDP is equation (8).
(8) S(t) = [1 – δ(1−τ)/b] + (δ – r)F(t) – cg(t) = S[F(t), Z1(t)], δS/δF = (δ - r) > 0,
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”20.
Scenario I concern the policies that affect social saving. The effect of the enlargement
of the euro area upon saving is reflected in changes in the elements of vector Z1 = (δ, τ,
cg) discussed below. Saving function (8) is general and consistent with many sensible
approaches. It does not rely upon any one restrictive hypothesis.
2.2.4 The Current Account Function
Scenario II in section (3.2) below concerns the current account and growth functions.
Enlargement will affect the current account function CA = B - rF equal to the trade balance B
less interest and dividend payments to foreigners rF, relative to GDP. The trade balance
20
A stability condition is that the discount rate exceed the real interest rate δ > r.
J. L. Stein, DELPHI - ENLARGEMENT OF EURO AREA
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depends upon the competitiveness of the tradable sectors. Measure competitiveness as the
optimal output of tradables /GDP, evaluated at a given the real exchange rate.
The optimal output of tradables X(t) is such that marginal cost MC in $US is equal to
the external dollar price P*. Enlargement of the euro area to include the CEEC will affect the
international competitiveness of the EMU insofar as it affects X(t).There are several possibilities.
(i) The firms in the old EMU invest directly/build plants in the CEEC, where the latest
technology is used, but labor costs are 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 euro area to lower cost plants in the CEEC. (ii)
The firms in the old EMU outsource some of their inputs to the CEEC.
Marginal costs are positively related to the level of output, the labor cost and the cost of
imported materials, and are negatively related to the level of productivity. Solve the equation P*
= MC for the optimum output of tradables X(t) and derive equation (9). The exchange rate
converts the dollar price P* and the foreign price of imported materials into a common
currency. The vector which determines marginal cost contains the elements: the terms of trade
T(t), equal to the ratio the selling price in the world market to the price of imported materials,
the real exchange rate is R(t), labor productivity y(t) and the real wage w(t).
(9) X(t) = X(R(t), w(t), T(t), y(t)).
The value of imports/GDP depends upon the real exchange rate and the level of income.
Ratio B of the trade balance/GDP is equation (10). The most important components of vector
Z3 are: relative productivity at home and abroad, the relative real wage and the terms of trade.
(10) B(t) = B(R(t); Z3(t))
Investment and competitiveness are related. Relative productivity contains two parts.
One part comes from the rate of capital formation, where investment is directed to the
export/tradable sectors. If the investment is not directed at exports/tradable, but is in shopping
centers, office buildings, and residential construction, then the MC of producing
exports/tradable does not decrease. Another part comes from the improved efficiency of
resource allocation, which will be stressed in scenario II.
J. L. Stein, DELPHI - ENLARGEMENT OF EURO AREA
16
Enlargement will affect the international competitiveness of the euro area insofar as it
affects vector Z3 in equation (10). Insofar as the marginal costs of producing export/import
substitutes shifts downwards to the right, the current account function CA(t) = B(R(t);Z3(t)) r(t)F(t), of the enlarged EMU will increase.
III. POLICY EFFECTS OF ENLARGEMENT: TWO SCENARIOS
The equilibrium real exchange rate of the Euro will change as more countries are
admitted into the euro area. Countries will enter at different speeds, depending on the rate that
they satisfy the criteria. The International Monetary Fund, in its publication "The Road to EU
Accession", described some of the challenges over the medium run of enlargement. " The
overarching aim of fiscal policy over the medium-term should be to support convergence
towards EU income levels - fostering growth that is both strong and sustainable. This will place
major demands on the public finances. Resources are needed to complete transition, adopt the
acquis, modernize infrastructure, protect the environment, and reform pensions and health care
so as to contain long-term costs. Moreover, tax burdens - and notably tax rates on labor - need
to be reduced…"21.
The IMF quotation above is a “wish list” that must be translated into policies. It is
impossible to predict what policies will be followed in the enlarged euro area both in the
accession countries and in the initial members. Our strategy is to use the NATREX
model/analytical framework to explain what will be the effects upon the equilibrium value of the
euro under different scenarios. These scenarios correspond to policies that are related
analytically to variations in the exogenous variables Z in BOX 1.
There are basically two distinct scenarios, which have some overlap. Scenario I
describes the effects of policies that try to raise the welfare/consumption level of the present
generation and to reduce current income inequality. Analytically, these policies are associated
with parameter Z1, declines in the social saving function. I shall refer to these populist polices as
“consumption/egalitarianism” policies. Scenario II describes the effects of growth-oriented
21
Introduction and Overview, p.6.
J. L. Stein, DELPHI - ENLARGEMENT OF EURO AREA
17
policies that aim to raise the welfare of future generations. These policies aim to make future
generations better off than their parents were, by raising growth and by providing more
opportunities for the younger generation. Policies in scenario II involve the liberalization and
privatization of economies to increase competition and encourage entrepreneurship.
Egalitarianism is subservient to growth as an objective. Analytically, these policies correspond to
policies that increase Z3 in the current account and Z4 in the growth functions. I refer to these
policies as “growth/liberalization”, and they are definitely not populist policies. The conclusions
are summarized22 in table 1. I explain these conclusions graphically and in terms of
scenarios/stories in the following sections.
Table 1. Implications of Two Scenarios
Scenario
I. Consumption/
Real exch. Rate,
Real exch. rate,
Debt-equity/GDP
medium run
long run
long run
Appreciate
Depreciate below
Increase debt ratio
egalitarianism; decline in Social
initial level
saving
II. Growth/ liberalization; rise
in current account and growth
Appreciate
Appreciate above
Decrease debt
medium run level
ratio
functions
22
See Stein (2002) for the mathematical derivations of the medium and longer run effects of
changes in the elements of vector Z upon the real exchange rate and ratio of net foreign
debt/GDP.
J. L. Stein, DELPHI - ENLARGEMENT OF EURO AREA
18
3.1 Scenario I. Policies fostering Consumption and Egalitarianism
In scenario I the policies aim to raise the levels of consumption of goods, services,
health care and the environment for the current generation, and also to reduce the inequality of
income among the current households. There are many ways to implement these policies,
without violating the Maastricht treaty.
(Ia) The government may increase cg(t) expenditures for social consumption, health, welfare the
environment. The budget deficit/GDP= G(t)/Y(t) is, in terms of equation (8a):
G(t)/Y(t) = cg(t) – τ < M
where M is the maximum permitted under the Maastricht treaty.
(Ib) The government may tax the profits of business firms to finance the cg(t) expenditures that
are directed to raise the consumption of lower income groups/implement egalitarian policies. In
this manner, the M constraint above is satisfied. In this case, social consumption rises at the
expense of productive 23 investment.
(Ic) The government provides loan guarantees to firms that produce consumer goods,
particularly those where expenditures are high proportions of the budgets of lower income
households. These guarantees are not items in the government budget.
(Id) The government is biased towards labor in the wage bargaining process, and intervenes to
raise wages and fringe benefits for lower income employees.
(Ie) The government guarantees the retirement income and future health care needs of the
present generation. Thereby, the incentives to save for retirement and for a “rainy day” are
reduced.
In terms of our framework, policies in Scenario I involves changes in the elements of
vector Z1 in the saving function, equation (8). The rise in cg is case (Ia) above. Policies (Ic) –
(Ie) correspond to a rise in the discount rate δ, which is the ratio of consumption/net worth, via
changes in the distribution of income and a reduced incentive to save for the future.
The past is a poor predictor of what will happen in the CEEC countries after
enlargement. All we can expect is diversity in the policies among countries and changes in policy
J. L. Stein, DELPHI - ENLARGEMENT OF EURO AREA
19
within each country as a result of elections where populism waxes and wanes. Table 2 shows
the diversity of changes in the saving ratios among the CEEC during the period 1994-99.
Table 2
Changes in S = saving/GDP, 1994-1999
Country
∆(S)
Bulgaria
4.6
Croatia
-7.1
Czech R.
-1.3
Estonia
-1.5
Hungary
11.7
Latvia
-8.6
Lithuania
-4.5
Poland
1.4
Romania
-7.3
Slovakia
-1.5
Slovenia
0.2
Turkey
-2.4
Source: Bank for International Settlements (2001:table 20)
The NATREX analytical framework is used to explain24 the effects of scenario I upon
the equilibrium real value of the euro. Figures 2a and 2b are simple graphic expositions of the
transmission mechanism in the scenarios of the model, and permit us to understand the
distinction between exogenous, control and endogenous variables. I juxtapose the two figures to
facilitate a comparison of scenarios I and II, whose implications are summarized in table 1.
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
converged25, and the output gap is zero. The negatively sloped CA curve describes how an
appreciation of the real exchange rate decreases the trade balance and current account. The
23
Productive investment is investment where the expected return on investment b > r the real
long term rate of interest.
24
The mathematical derivations are in Stein (2002), and the discussion here is intuitive.
25
Prior to the enlargement of the euro area, the CEEC nominal interest rates will embody an
inflation expectations term so that, although nominal interest rates differ, real long term interest
rates are close to those in the original EMU. With the entry into the EMU, the inflation
expectations decline and so does the nominal rate of interest. However, real long term interest
rates do not change.
J. L. Stein, DELPHI - ENLARGEMENT OF EURO AREA
20
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 then declines relative to saving. That
is why S-I rises with the real exchange rate. The intersection of SI and CA curves, described by
equation (3), implies the medium run equilibrium exchange rate.
Figure 2a
Scenario I. Decline in Saving less Investment.
R(0) initial real exchange rate, R(1) medium run, R(2) long run.
Initially, saving less investment is described by curve SI(0), and the current account by
curve CA(0). They are equal at real exchange rate R(0). Scenario I involves a decline in social
saving in the enlarged EMU, resulting from policies (Ia)-(Ie) above. The SI curve in figure 2a
shifts from SI(0) to SI(1). If all of the increased demand were directed to home goods, then the
CA curve is unaffected26. At exchange rate R(0), the ex-ante current account CA(0) now
exceeds ex-ante saving less investment SI(1), the desired capital outflow.
Several things happen. Domestic firms/government borrow abroad what they cannot
borrow at home. 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), evaluated at the inital level of net foreign assets F(0) and productivity. The medium run
the real exchange rate appreciates in Scenario I, where there is a rise in investment less
saving.
Whereas the macroeconomic balance (Mundell-Fleming) models stop at movement
R(0)-R(1), the NATREX model continues by taking into account the endogenous changes in
net foreign claims, which will feed back upon the macroeconomic balance equation. At
appreciated real exchange rate R(1), investment less saving produces a capital inflow equal to
the current account deficit 0A per unit of time. The foreign debt/equity is rising at rate 0A per
unit of time, equation (4). The implications for the trajectory of the real exchange rate are
26
Since the marginal propensity to import is a fraction, the graphic exposition in figure 2a is
adequate.
J. L. Stein, DELPHI - ENLARGEMENT OF EURO AREA
21
derived by combining equations (3) and (4). There are both stabilizing and destabilizing effects
of the debt.
(i) The rise in the debt raises the interest payments rF(t), which further deteriorate the
current account. In figure 2a, the higher interest-dividend payments shift the CA curve to the left
of CA(0). The leftward shift of the CA function along the SI(1) function depreciates the
exchange rate below R(1) and widens the deficit on current account. The steady decline in the
CA function- due to a steady rise in the debt - along a given SI function produces
instability. The debt will explode and the euro exchange rate will depreciate steadily.
(ii) The stabilizing effect arises from an endogenous the shift of the SI curve to the right.
The rise in the debt/GDP lowers net worth and social consumption, and increases social
saving/GDP, according to equation (8). For example, the higher net foreign debt may cause the
government to restrain its expenditures and reverse some of policies (Ia) - (Ie) above. As saving
rises, the capital inflow equal to (I – S) declines. The SI curve in figure 2a shifts to the right
towards SI(2). Thereby, the capital inflow and the rise in the debt are reduced.
The long run debt/GDP rises as a result of the cumulative current account deficits. The
current account curve declines to CA(2), due to the need to make income transfers on the
higher debt. The SI curve shifts to the right to SI(2) because the decline in net worth raises
social saving, by the totality of firms, government and possibly households. The new sustainable
equilibrium real exchange rate depreciates to R(2) below27 the initial level R(0). In a growing
economy the equilibrium current account deficit/debt is equal to the growth rate. From equations
(3) and (4) when the debt/GDP stabilizes at F* and the real exchange rate converges to R* =
R(2) < R(0):
(11) B(R*, Z) = (r – g)F*,
27
(r – g) > 0.
The long run effect upon the real exchange rate 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 (rg) > 0. For 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 below R(0).
J. L. Stein, DELPHI - ENLARGEMENT OF EURO AREA
22
Since the debt is higher, resulting from the accumulation of current account deficits, the trade
balance must be higher28. Therefore, the real exchange rate must depreciate to increase the trade
balance.
In this manner, the NATREX model shows that scenario I leads to longer run
depreciation, not appreciation as claimed by the traditional Mundell-Fleming models.
Policies (Ia)-(Ie) above also affect elements Z3 in the current account function and Z4 in the
growth function. Their negative effects will be understood by considering scenario II below.
3.2 Scenario II. Policies fostering Growth and Liberalization
Scenario II concerns the policies that emphasize growth and competition in the enlarged
EMU area. Drawing upon the studies by the International Monetary Fund 29 and by the Bank for
International Settlements, the growth in the CEEC countries can be described as follows.
28
See the footnote above why (r – g) > 0.
Doyle, Kuijs and Jiang, Real Convergence to EU Income Levels in International Monetary
Fund (2001),The Road to EU Accession.
29
J. L. Stein, DELPHI - ENLARGEMENT OF EURO AREA
23
(i)There is a significant diversity of policies and performance among the countries. (ii) The
remarkable increases in labor productivity in Poland and Hungary appear to reflect total factor
productivity rather than increases in the capital stock. (iii) In the more rapidly growing countries,
growth derives from total factor productivity, whereas in the less successful countries growth
results from factor inputs. (iv) The growth is broad based. (v) Quarterly data for a panel of
Eastern European Countries 1996-99 suggest that the Balassa/Samuelson effect is small30.
Productivity growth is not greatly differentiated between tradable and non-tradable sectors. (vi)
Firms controlled by a foreign strategic investor performed better in deep restructuring, and the
latter is associated with improved performance and labor productivity.
Scenario II focuses upon the policies (IIa) and (IIb) reflected by parameters of the
growth and current account functions.
Policy (IIa) is the liberalization and privatization of the economy. It is related to parameter Z4.
Policy (IIb) concerns the exchange rate selected when the countries enter the euro area. It is
related to parameter Z3.
Equation (5) above described the growth as the product of a mean productivity of
investment b times I(t) the investment/GDP ratio plus a term Z4 that can be called the growth of
total factor productivity. Given the current endowment of resources, capital and labor, the
maximization of real GDP occurs when the marginal conditions of resource allocation are
satisfied. Then the economy will be operating close to its production possibility surface. The real
value of the GDP will rise without any change in factor inputs, and the effect of improved
resource allocation can be called a rise in total factor productivity. Only when the economy is
liberalized and privatized with a free price system can the marginal conditions be met. Parameter
Z4 in the growth function is primarily the result of the growth of total factor productivity, which
comes from liberalization of the economy.
Enlargement will increase the current account function of the euro area if it shifts the
marginal cost function of producing tradable goods to the non-euro area downward to the right.
This will occur if the marginal cost, at the initial level of output, is lower in the entering countries
30
The studies of the synthetic euro and the DM conclude that the Balassa/Samuelson effect is
J. L. Stein, DELPHI - ENLARGEMENT OF EURO AREA
24
than in the older members. Let the quantity of exports – or tradables - be X, the world price be
P* and marginal cost in euros is MC. The marginal cost function can be written in a simplified in
equation (9a). It rises with output and the slope is labor cost in euros, WN/A. The wage in local
currency is W, the exchange rate at which the j-th country enters the euro area is Nj euros/local
currency j, and A is a level of productivity.
(9a) P* = MC = (WN j/A) X
Solve for the output X of tradables and derive (9b).
(9b) X = P* / [(WN j/A)]
The higher the exchange rate at which the country enters the euro area, times the wage
in local currency, the less competitive will be the country in producing tradables. The crucial
variables here are: the wage/productivity and the entering exchange rate. These variables are
subsumed under parameter Z3 of the marginal cost function of producing exports. Populist
policies tend to raise the real wage, growth oriented policies tend to raise productivity and the
choice of the exchange rate affects competitiveness. There are significant differences among the
CEEC countries in their search for the exchange rate to enter the euro area. Table 3 shows that
from 1994-98, the growth of real unit labor cost has varied among the countries. It has declined
in Hungary, Poland and Slovenia, and has risen in most of the others. It is impossible to predict
the overall effect upon productivity/real wage and exchange rate Nj when these countries enter
the euro area.
feeble, if it exists at all. See the articles discussed by Stein and Lim (2002).
J. L. Stein, DELPHI - ENLARGEMENT OF EURO AREA
25
Table 3
Growth of: real product wage ∆w, productivity ∆y and real unit labor cost (∆w/w-∆y/y)
1994-98, % p.a.; Growth 1991 - 1999; Ratio of TFP growth/growth;
Country
∆w/w1991-99
GDP growth:
∆w/w ∆y/y %
∆y/y % TFP /growth % 1999/1991
% pa
pa
pa
Czech.
9.1
6.6
2.5
51 %
9.1 %
Hungary 1.0
12.5
-11.5
122
16.6
Poland
7.8
9
-1.2
44
47.9
Slovenia
5.7
7
-1.3
82
25.6
Croatia
22.7
4.4
18.3
Slovakia
7.2
5
2.2
9
21.8
Estonia
11.7
5.8
5.9
Lithuania 21.4
4.6
16.8
Latvia
13.4
7.7
5.7
Romania 5.5
5.9
-0.4
Bulgaria
-2.2
3.3
-5.5
Source: Bank for International Settlements, tables 6, and 6a. International Monetary Fund, "The
Road to Accession", Doyle et al, Table I p. 30. Real product wage w, productivity y.
Scenario II involves31 a rise in total factor productivity resulting from a liberalization of
the economy, which improves the allocation of resources and raises total factor productivity and
the growth rate. The NATREX model is used as our analytical framework when WN/A
declines and the growth rate rises.
The SI curve remains at SI(0) for the enlarged euro area, but the decline in WN/A or
rise in total factor productivity increases the trade balance and shifts the current account curve
for the enlarged euro area in figure 2b from CA(0) to CA(1). At the initial exchange rate for the
euro R(0), the current account CA(1) exceeds the capital outflow SI(0), and the real exchange
rate appreciates to R(1). The appreciation of the exchange rate to R(1) restores medium run
equilibrium by restoring S(0) - I(0) = CA(1), equation (3).
Figure 2b Scenario II Rise in Competitiveness
31
Mathematically, we are considering rises in Z3 and Z4.
J. L. Stein, DELPHI - ENLARGEMENT OF EURO AREA
26
R(0) initial real exchange rate, R(1) medium run, R(3) long run.
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 per unit of time, which implies a
rising foreign debt-equity. In scenario II, there is a capital outflow equal to a current account
surplus of 0B per unit of time, which implies a declining foreign debt-equity.
The story is the reverse of scenario I. The debt declines. The decline in the net
interest/dividend payments on the debt/equity shifts the CA curve further to the right to CA(2),
and thereby strengthens the effect of the medium run impact upon the real exchange rate. The
decline in the debt increases net worth and decreases the saving ratio. The SI curve shifts to the
left to SI(2). The long run real exchange rate R(3) equilibrates CA(2) = SI(2) and the real
exchange rate appreciates to R(3) > R(1) > R(0). The debt/GDP may be converted into a net
asset position/GDP, where the country is a net creditor.
At the new long run equilibrium, the growth rate is higher and the debt is lower. The
debt F* may become negative: net foreign assets are positive. The right hand side of equation
(11) B(R*,Z) = (r-g)F*
is lower. Hence the appreciation of the real exchange rate to R* = R(3) generates the required
trade balance. There are sustainable current account surpluses32 and net asset position grows at
the rate g(t) of real GDP.
IV. ESTIMATION OF THE VALUE OF THE SYNTHETIC EURO
In order to answer the question: what will be the effect of enlargement upon the
equilibrium value of the Euro under different scenarios, we must have confidence in the
explanatory power of our model. Have we isolated the "real fundamentals"? How valid is the
"story" that we have told? A valid theory concerning the real value euro, whose birth occurred
only a few years ago, should be able to explain the real value of a synthetic euro as well as the
32
If F* < 0, then CA/(-F*) = g > 0, and CA > 0. There are sustainable current account
surpluses that keep F* constant. However B, the trade balance/GDP, is B = (r-g)F* < 0. The
negative trade balance offsets the receipts of interest income from abroad, adjusted for growth.
J. L. Stein, DELPHI - ENLARGEMENT OF EURO AREA
27
real values of the major component currencies – the DMark, the French Franc and Italian Lira over the past thirty years. We must show that market forces drive the real exchange rate to
what is claimed to be the equilibrium/sustainable value33.
There have been many quantitative-econometric studies concerning the equilibrium
real value of the synthetic Euro. As a rule the synthetic euro is based upon the European Central
Bank area wide model data set over the period 1970 - 2000. Clostermann and Schnatz show
that variations in the real value of the DMark and in the synthetic euro have been similar from
1975 - 99. We refer the reader to the following surveys and evaluations of research on the
synthetic euro: the European Central Bank, (2002), Schnatz and Smets (2001), Stein (2001)
and the OECD (2001).
Most of the studies do not specify the underlying model. These studies take an eclectic
approach that simply searches for cointegrating equations in "sensible" variables34, which pass
the usual econometric tests. The VECM vector error correction method used by the authors
restricts the long run behavior of the endogenous variables to converge to their cointegrating
equations, while allowing a wide range of short run dynamics. As MacDonald (2002) noted, the
authors obtain a statistical/atheortetic concept of the "equilibrium". The statistical/atheoretical
approach does not correspond to any particular analytical framework and it is often difficult to
know how to interpret the econometric results. That is why it cannot easily be related to the
different policies of enlargement.
The NATREX model is an economic concept of equilibrium. It is the analytic
framework that is used here to describe the scenarios and dynamics associated with
enlargement, summarized in figures 2a and 2b and table 1 above. The economic concept of an
equilibrium corresponds to the intercepts log Re(t) in equation (2b) above.
33
We claim that the deviation between the actual real exchange rate and the NATREX has a
distribution with a zero expectation. See Stein and Paladino (2001a), BOX 2, p. 129.
34
Outstanding papers using this approach are by Clostermann and Schnatz for the DMark, and
by Maseo-Fernandez, Osbat and Schnatz for the synthetic euro.This class of studies is referred
to as the BEER (Behavioral Equilibrium Exchange Rate) approach. See MacDonald and Stein
(1999: ch.1) and Stein and Lim (2002) for a discussion of these approaches.
J. L. Stein, DELPHI - ENLARGEMENT OF EURO AREA
28
Some of the empirical tests of the NATREX model estimate the underlying structural
equations and others estimate the reduced form dynamic equations for the equilibrium real
exchange rate. Several of the studies concern the synthetic euro and others concern the
component currencies.
Table 4
Estimates of NATREX for the synthetic euro and component currencies
author
currency
estimation
Detken, Dieppe, Henry,
synthetic euro
structural equations
synthetic euro
structural equations
Duval (2002)
synthetic euro
reduced form dynamics
Maurin (2000/01)
synthetic euro
reduced form dynamics
Fischer, Sauernheimer (2002)
DMark
reduced form dynamics
Stein and Sauernheimer
DMark
reduced form dynamics
Federici, Gandolfo (2002)
Italian Lira
structural equations
Crouhy-Veyrac, Saint Marc
French franc/DM
reduced form dynamics
Stein (1999)
$US/G7
reduced form dynamics
Verrue and Colpaert (1998)
Belgian franc
structural equations
Stein, Paladino (2001a)
French franc/DM, Italian
reduced form dynamics
Marin and Smets (2002)
Detken and Marin Martinez
(2001)
(1997)
(1997)
Lira/DM
The NATREX model is an analytical tool, mapping control and exogenous variables
into the trajectories of the real exchange rate and the foreign debt/GDP. These trajectories are
the “stories”. Table 4 summarizes the major NATREX studies of the European currencies,
which the reader may consult for the research design, measurement of variables and technical
J. L. Stein, DELPHI - ENLARGEMENT OF EURO AREA
29
econometric details. Whereas all obtain similar qualitative results concerning the parameter
estimates and their statistical significance, the quantitative results differ substantially depending
upon: the method of estimation, the lag structure used, and the precise measurement of
variables. Therefore, much more confidence should be placed upon qualitative than upon
quantitative results.
The scenarios of enlargement in figure 2a concern policies (Ia)-(Ie)/section (3.1) that
change the social saving function. Stein and Sauernheimer showed that variations in the social
saving function in Germany were associated with regime changes between the Social Democrats
and the Conservative parties. Stein and Paladino (2001a: 117-122) showed that a similar
situation occurred in Italy and France. In figure 2b, the policies (IIa) – (IIb)/ section (3.2)
change the current account function, growth and total factor productivity.
Any of the econometric studies of the synthetic euro cited in table 4 can be used to
simulate the effects of the enlargement of the euro area. Empirically, one can vary the basic
fundamentals vector Z(t) in the structural equations and simulate the resulting change in the
equilibrium real exchange rate. Alternatively, one can vary the fundamentals in the reduced form
dynamic equation, and estimate the change in the trajectory35.
The studies cited in table 4 show that the NATREX model does indeed explain the
evolution of the synthetic euro. We stressed that there is a wide range of estimation methods
and quantitative results. A simple example is given here to give the reader a feel for the results.
The simple example or application of the model here is done in two steps. First: in part 4.1 we
provide an estimate the longer run equilibrium R*(t) = BZ(t). Second: in part 4.2, we use the
long run estimate and uncovered real long term interest rate parity/rational expectations equation
(2a) to show the explanatory power of the model. Part 5 draws upon the theory and
econometrics to summarize our conclusions concerning the effects of EMU enlargement upon
the equilibrium value of the euro.
35
The mathematical analysis is in Stein (2002) appendix.
J. L. Stein, DELPHI - ENLARGEMENT OF EURO AREA
30
4.1 Estimation of NATREX in a Reduced Form Dynamic Equation
The dynamics of the equilibrium real exchange rate in figures 2a and 2b, based upon
BOX 1, imply a vector-matrix differential equation, which corresponds to econometric VECM
equation (12). The real exchange rate R(t) and vector Z(t) do not revert constant means: they
are not stationary variables.
(12) ∆R(t) = α[R(t-1) - BZ(t-1)] + Σb(i)∆Z(t-i) + + Σc(i)∆R(t-i) + ε(t), a < 0
Term BZ(t) is the longer run equilibrium36 associated with the "fundamentals" Z(t), defined in the
scenarios above. Term α[R(t-1) - BZ(t-1)] is the error correction (EC) term. In the NATREX
model graphed in figures 2a - 2b , the cointegrating equation R(t) = BZ(t) reflects the long run
equilibrium R(2) or R(3) respectively, associated with fundamentals Z(t), and the EC term
represents trajectory [R(0) - R(1) - R(2)] or [R(0) -R(1) - R(3)]. The term ε(t) represents
stationary/ transitory/ I(0) forces with zero expectations. An appealing aspect of the NATREX
model is that there is a clear relation between the dynamics of the model and the VECM
econometrics.
A difficult and important problem is to decide what are the appropriate empirical
measures corresponding to the fundamentals37 Z in the model BOX 1. We must use variables
that correspond to the theory, are objectively measurable 38 and easy to calculate. The real
exchange rate R(t) = N(t)p(t)/p*(t), where the weights are GDP deflators. A rise is an
appreciation of the real Euro. We measure the parameter describing the shift of the saving
function in curve SI as c(t)/c*(t) as the ratio of social39 consumption/GDP in Euroland c(t)
relative to c*(t) in the US. Social consumption is private plus public consumption. A rise in
36
Insofar as: (i) R(t) and vector Z(t) are all integrated I(1), (ii) there is only one cointegrating
equation, (iii) the Z(t) vector is weakly exogenous, then R(t) = BZ(t) is the cointegrating
equation.
37
This problem is discussed in all of the papers that use the NATREX. The statistical/atheoretic
approach does not face this problem, since there is no underlying explicit theoretical structure.
38
My data were supplied by Liliane Crouhy-Veyrac, whose study was presented at a Banque
de France conference. The euro data are aggregates of the 11 euro countries, using backward
GDP weights. These data are very similar to those used by the ECB.
J. L. Stein, DELPHI - ENLARGEMENT OF EURO AREA
31
c(t)/c*(t) represents a leftward shift in the SI curves in figure 2a/ scenario I. The parameters in
the current account function are: (i) relative Euro/ US productivity, GDP per worker40 y(t) /
y*(t) and (ii) the terms of trade T(t). The exogenous real price of oil41 T* = 1/T(t), is an inverse
measure of the terms of trade. An increase in relative productivity or a decrease in the real price
of oil corresponds to the scenario II in figure 2b where there is a rightward shift of the current
account function. The longer run equilibrium real exchange rate is R*(t) = BZ(t).
Table 5 displays a cointegrating equation42 in variables {log R(t), log c(t)/c*(t), log
y(t)/y*(t), log Τ∗(t)}. Consistent with the theory in table 1, relative time preference c(t)/c*(t)
depreciates the long run real exchange rate, relative productivity y(t)/y*(t) appreciates the long
run real exchange rate, and the real price of oil T* depreciates the long run exchange rate. Note
that the result that a rise in social consumption depreciates the longer run real exchange
rate is the opposite of the Mundell-Fleming result. The latter just looked at movement R(0)R(1) in figure 2a, and not at the entire trajectory R(0)-R(1)-R(2).
Most of the studies cited in table 4 also estimate the error correction terms and the
disturbance terms in equation (12). An estimate of coefficient α in the error correction term in
equation (12) is α = -0.05. Therefore an inverse measure of the speed of response to the
equilibrium is (1+α) = 0.95, discussed in the next part.
39
Some of the studies in cited in table 4 use relative government consumption instead of social
consumption as the “exogenous” parameter. See Stein and Paladino (2001a) for a discussion
of these issues for France, Germany and Italy.
40
Some of the studies cited in table 4 use productivity per worker and others use total factor
productivity per worker. Total GDP per worker y(t) is closely related to total factor
productivity per worker. Since the relative EU/US real wage is highly correlated with relative
productivity, we just use the relative productivity variable.
41
The real price of oil is: $price oil/US producer price index.
42
We use the Johansen method with lag 4, since the variables are generally 4Q MA. The real
return on investment b(t) = g(t)/I(t) is the ratio of the growth rate g(t) to the investment ratio I(t).
Since b(t) and g(t) are I(0), they were not used in the cointegrating equation.
J. L. Stein, DELPHI - ENLARGEMENT OF EURO AREA
32
Table 5
Sample: 1975:3 2000:1; Included observations: 95; 4 quarter moving averages
Test assumption: Linear deterministic trend in the data; Lags interval: 1 to 4
Series: Log R(t), log c(t)/c*(t), log y(t)/y*(t), log real price of oil T*, C
Likelihood
Ratio
Eigenvalue
5 Percent
1 Percent
Hypothesized
Critical Value Critical Value No. of CE(s)
0.475358
83.67247
47.21
54.46
None **
0.131479
22.39377
29.68
35.65
At most 1
0.069664
9.002238
15.41
20.04
At most 2
0.022299
2.142353
3.76
6.65
At most 3
*(**) denotes rejection of the hypothesis at 5%(1%) significance level
L.R. test indicates 1 cointegrating equation(s) at 5% significance level
Normalized Cointegrating Coefficients: 1 Cointegrating Equation(s)
Log R(t)
1.00
log c(t)/c*(t)
4.136
(0.87)
Log likelihood 496.8615
log y(t)/y*(t)
-2.88
(0.395)
log real-oil
0.001444
(0.00054)
C
-0.612693
Coefficient α = -0.05 in equation (12).
4.2 The Explanatory Power of the Model for the Real Synthetic Euro
Each study derives confidence intervals for each parameter, but the parameter estimates
differ quantitatively among studies. The first type of uncertainty can be called statistical
uncertainty and the second can be called model uncertainty. The latter is considerable. In
view of the model uncertainty, quantitative estimates should not be given undue weight. A lesson
to be learned from the empirical studies is that undue emphasis should not be placed upon
quantitative precision.
The medium run equilibrium real value of the euro is the trajectory in R(0)-R(1)-R(2) in
figure 2a or trajectory R(0)-R(1)-R(3) in figure 2b. The medium run equilibrium value satisfies
conditions C(1) – C(2) along the trajectory and C(1)-C(4) at the longer run equilibrium R(2) or
R(3) in figures 2a/2b.
J. L. Stein, DELPHI - ENLARGEMENT OF EURO AREA
33
At any one time, conditions (C1)-(C4) will not be satisfied. We therefore view the real
exchange rate as depending upon two factors. The first involves the longer run NATREX
directly. The second is related to uncovered real long term interest rate parity/rational
expectations, as described in equation (2a) above. We discuss each in turn. The real exchange
rate is written as equation43 (13).
(13) log R(t) = a1 log R*(t) + a2 [r(t) - r*(t)]
The longer run equilibrium R*(t) = BZ(t) is derived from the cointegration equation in
table 5. The R* corresponds to R(2) in figure 2a or to R(3) in figure 2b. The speed of
convergence of the real exchange rate to the longer run equilibrium R* is derived from
coefficient α = -0.05 in equation (12). This means that:
[R(t) – BZ] = (0.95) [R(t-1) – BZ] = (0.95)t [R(0) – BZ]
The equilibrium NATREX real exchange rate R(t) converges to its longer run value R* =
BZ with a half-life of 13.5 quarters. We view the longer run equilibrium R*(t) = BZ(t) as the
rational expectations value.
The actual real exchange rate at any one time does not necessarily satisfy conditions
(C1) and (C2) where rates of return are equalized, and where the rate of capacity utilization is
at its stationary mean. These variables are mean reverting to zero, but the convergence takes
some time. This is where the second factor enters.
The second factor in equation (13) is connected with “uncovered real interest rate
parity/rational expectations”. The speed at which the actual real exchange rate R(t) converges to
its equilibrium value along the trajectory is given by differential rates of return44.”Misalignment”,
defined as R(t) - BZ(t), is explained by a systematic factor45 “uncovered real interest rate parity”
the second term in equation (13). We use the real long term interest rate differential [r*(t) – r(t)]
43
For simplicity, we write the real exchange rate as R(t) without specifying that it is a logarithm,
unless necessary. This type of decomposition is in Lim (2002).
44
Most of the studies cited in table 4 take into account the error correction. Here, we illustrate
the approach by taking a short cut.
45
There are also non-systematic factors, which consist of variables not taken into account in the
model. Bubbles are among these non-systematic factors. They are noise with zero expectations.
J. L. Stein, DELPHI - ENLARGEMENT OF EURO AREA
34
as the second driving force behind the convergence of the actual rate to the longer run
equilibrium. This differential is stationary with a zero expectation.
Figures 3 and 4 show the explanatory power of the model. Figure 3 describes the
explanatory power of the longer run NATREX relationship. The actual real value of the
synthetic euro log R(t) is denoted EUUSREDPMAL. The real long term equilibrium exchange
rate log R*, given by the cointegrating equation in table 5, is denoted NATJLR. The R*(t) =
BZ(t) = NATJLR is the rational expectations equilibrium. The variables graphed in figure 3 are
normalized46 to facilitate quantitative comparisons. The actual rate converges to a distribution
whose mean is the long run NATREX, which is our rational expectations equilibrium.
Figure 3. Real value of synthetic euro log R(t) = EUUSREDPMAL
Long run NATREX, R* = BZ = NATJLR
4 Q MA, normalized variables
2
1
0
-1
-2
-3
76 78 80 82 84 86 88 90 92 94 96 98
EUUSREDPMAL
NATJLR
Figure 3. Convergence to the NATREX rational exectations longer run equilibrium.
J. L. Stein, DELPHI - ENLARGEMENT OF EURO AREA
35
Real value of synthetic euro log R(t) = EUUSREDPMAL and R*(t) = BZ(t) = NATJLR, long
run NATREX from table 5. Variables are normalized.
Regression equation (14) is the estimate of equation (13). Figure 4 displays the
explanatory power of equation (14). The first term is the longer run NATREX in figure 3, when
conditions (C1) - (C4) are satisfied. The second term is related to the uncovered real long term
interest rate parity (r - r*) = EUUSRLINT when condition (C2) is not satisfied.
(14) log R(t) = 0.28 log R*(t) + 0.06 [r(t) – r*(t)] + 0.03; ADJ-RSQ = 0.58
(se)
(0.04)
(0.006)
[t]
[6.1]
[9.7]
(0.01)
[3.03]
Figure 4. The real exchange rate of the synthetic euro log R(t) = EUUSREDPMAL, a
combination of longer run equilibrium R*(t) = BZ(t) = NATJLR and real long term interest rate
parity [r(t) - r*(t)] = EUUSRLINT
46
A normalization of variable X is X' = (X - mean)/standard deviation.
J. L. Stein, DELPHI - ENLARGEMENT OF EURO AREA
36
Figure 4.
ACTUAL log R(t); Estimate of equation (14), FITTED.
RESIDUAL = Actual - Fitted.
0.4
0.2
0.0
0.4
-0.2
0.2
-0.4
0.0
-0.2
-0.4
76 78 80 82 84 86 88 90 92 94 96 98
Residual
Actual
Fitted
The conclusions from figures 3 and 4 are as follows. The longer term trends in the
synthetic real euro are explained by the longer run NATREX. The longer run NATREX does
not have a constant value, but depends upon the real fundamentals described above. Significant
deviations, called "misalignments", from this value are explained by real long term interest rate
differentials. The real long term interest rate differential is stationary with a zero mean. When real
interest rate convergence occurs, then the systematic movements in the real exchange rate are
explained by the NATREX trajectory.
J. L. Stein, DELPHI - ENLARGEMENT OF EURO AREA
37
5. Conclusion
Enlargement of the euro area to include the CEEC would add 11% to the GDP; and the CEEC
would have a weight 0.1 in EMU. This is a significant but not a very large change. What will be
the resulting effects upon the euro? What are the lessons to be learned from history? The most
recent "enlargement" was the German reunification. Most of the predictions concerning the
effects of German unification were incorrect for several reasons. First, the predictions were
unconditional and not based upon alternative policy scenarios. Second, there was not a
theoretically consistent and empirically verified model underlying the predictions. Our
contribution is to provide an analytic framework to analyze effects of policies/scenarios of
enlargement. This is why we use the NATREX dynamic stock-flow growth model, with
endogenous changes in debt and growth. The analytic framework can be used to analyze any
set of policies. Two basic scenarios are considered as illustrations.
Scenario I can be described as Populism/egalitarianism. The policies emphasize the
welfare of current generation. Theoretically this implies a decline in social saving relative to
investment. A capital inflow will be induced, which tends to increase the foreign debt - without
raising the productivity of the economy.
Scenario II focuses upon Growth/liberalization of the economy. The emphasis is upon
the welfare of future generations. Theoretically this corresponds to a growth in total factor
productivity primarily brought about by a more efficient allocation of resources and improved
technology introduced by foreign direct investment. Another important aspect of the
competitiveness of the enlarged euro area concerns the exchange rates selected by the CEEC to
enter euro area. The higher the entering exchange rate(euro/local currency) relative to the real
wage and productivity, the less competitive will be the accession countries. That is, the euro
area would not benefit from an increase in the trade balance evaluated at the initial real exchange
rate of the euro relative to the US dollar. In scenario II, there is an improved allocation of
resources so that total factor productivity is raised, and the entering exchange rate does not
more than offset real wage and productivity differentials.
J. L. Stein, DELPHI - ENLARGEMENT OF EURO AREA
38
The NATREX model implies both medium run and longer run effects. The medium run
effects of changes in the vector Z(t) of fundamentals are similar to those in the macroeconomic
balance models. In scenario I, as saving declines relative to investment, there is a capital inflow
and an initial appreciation as in Mundell-Fleming. Unlike the Mundell-Fleming model, there will
be longer run depreciation due to higher debt and lower growth. At the longer run equilibrium
real exchange rate R* the ratio F* of debt/GDP stabilizes. This mean that the trade
balance/GDP denoted B(R*;Z) equals the net payments on the equilibrium debt/GDP, adjusted
for the endogenous growth rate, (r - g)F*. This is equation (11) repeated here.
(11) B(R*;Z) = (r - g)F*
(r - g) > 0
Since the debt is higher and the growth rate is not higher in scenario I, the real exchange rate has
to depreciate to raise the trade balance sufficiently to service the debt.
Scenario II implies an initial appreciation, because the enlarged euro area increases its
trade balance. The current account surpluses decrease the debt; and the investments are
productive. In the longer run there is a further appreciation due to a lower debt F*; and there is
a higher growth rate due to increases in total factor productivity produced by a more efficient
allocation of resources. The right hand side of equation (11) declines. Hence the real exchange
rate must appreciate to reduce the trade balance.
We have provided a general and flexible analytic framework whereby one can analyze
different scenarios of enlargement. The transmission mechanism is explicit. The next question is
whether the NATREX model has been able to explain the evolution of the synthetic euro and
the main component currencies: the DMark, French Franc and Italian Lira. We cite the studies
that examine both the structural and reduced form dynamic equations of the NATREX model.
There are several types of uncertainty: Statistical uncertainty and Model uncertainty. The
former concerns confidence limits of parameter estimates for a given model. The second
concerns the range of estimates derived from different methods of estimation and measurement
of variables. The studies cited in table 4 obtain similar qualitative results, but different
quantitative values. This means that we have confidence in the qualitative aspects of the model,
but one should not overemphasize quantitative results. A further implication is that we reject the
J. L. Stein, DELPHI - ENLARGEMENT OF EURO AREA
39
usefulness of target zones or exchange rate management, because they require quantitative
precision that is not possible.
With the caveat about relying upon precise quantitative results, we do provide some estimates,
based upon a short cut method of estimation. The real exchange rate R(t) converges to longer
run equilibrium log R*[Z(t)], based upon fundamentals Z(t), with a half-life 13.5 quarters. The
R*[Z(t)] is a Rational Expectations Equilibrium. A 1% increase in relative social
consumption/GDP leads to a long run depreciation of 4% in the long run. A 1% increase in
relative productivity leads to a 3% appreciation in the long run. Scenario I primarily affects
social consumption, and scenario II primarily affects relative productivity. It should be noted that
the CEEC only will have a weight of 0.1 in the euro variables. The "misalignment", the deviation
from the longer run equilibrium is explained to a significant extent by real long term interest rate
differentials. These are stationary with zero expectations. We have thereby answered our two
questions.
•What is the underlying theoretical structure linking the "fundamentals" to the
equilibrium value of a Euro? What are the effects of enlargement upon the value of the
Euro, under different scenarios/ policy options ?
•What is the explanatory power of the model used to explain the equilibrium real
value of a synthetic Euro?
J. L. Stein, DELPHI - ENLARGEMENT OF EURO AREA
40
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