WPS4607
Policy ReseaRch WoRking PaPeR 4607
Intertemporal Adjustment and Fiscal Policy
under a Fixed Exchange Rate Regime
Marcel Aloy
Blanca MorenoDodson
Gilles Nancy
The World Bank
Poverty Reduction and Economic Management Network
Vice President's Office
April 2008
Policy ReseaRch WoRking PaPeR 4607
Abstract
The paper presents a dynamic model for small to longrun equilibrium and alters the longterm balance
medium open economies operating under a fixed between exports and consumption, both private and
exchange rate regime. The model provides a partial public.
explanation of the channels through which fiscal The simulation applied to Argentina shows that if
and monetary policy affects the real exchange rate. the share of public spending in the economy is higher
An empirical investigation is conducted for the case than the share of imports, an increase in the tax rate will
of Argentina during the currency board period of stimulate capital stock slightly, at least in the short term,
19912001. and depreciate the real effective exchange rate.
Empirical estimates show that fiscal policy may indeed In the long run, the fiscal policy affects the value
be an efficient instrument for promoting macroeconomic of the real exchange rate and consequently external
stability insofar as it encourages convergence toward competitiveness.
This papera product of the Poverty Reduction and Economic Management Network, Vice President's Officeis part
of a larger effort in the department to deepen our knowledge on the conduct of fiscal policy in developing countries.
Policy Research Working Papers are also posted on the Web at http://econ.worldbank.org. The author may be contacted
at bmorenododson@worldbank.org.
The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development
issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the
names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those
of the authors. They do not necessarily represent the views of the International Bank for Reconstruction and Development/World Bank and
its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent.
Produced by the Research Support Team
Intertemporal Adjustment and Fiscal Policy
under a Fixed Exchange Rate Regime
Marcel Aloy,* Blanca MorenoDodson,** and Gilles Nancy*
* CEDERS, University of the Mediterranean
** World Bank, Washington, DC
JEL: C5, E0, E4, E5,E6, F4, H3
Intertemporal Adjustment and Fiscal Policy in a Fixed Exchange Rate Regime
Introduction
In the debate over the choice of exchange rate regimes in the 1990s, it became
fashionable to favor the extremes of fixed and free floating regimes, while eschewing
intermediate regimes as macroeconomically inconsistent.1 The proponents of fixed exchange
rates cite the credibility that monetary authorities can obtain by committing to macroeconomic
stability, the "disciplining effect" on price setters, and the anchoring impact on price
expectations.2
Unfortunately, recent exchange rate crises have shown that, perhaps owing to external
shocks or inappropriate monetary and fiscal policies, some emergent economies with a hard peg
regime, most notoriously Argentina in 2001, have lost control of their current accounts and fallen
into acute financial crisis and recession. In other cases, such as Korea and Thailand, currency
crises have occurred even though monetary and fiscal policies were perceived as fully consistent
with the exchange rate regime; in those cases, an excess of confidence in nominal anchors has
led to indiscriminate shortterm capital inflows that masked failures in the domestic banking
system and misled investors.
Since then, research in the field of financial crisis has found that fixing exchange rates,
while refraining from seignorage and adjusting the domestic credit supply to the rate of longrun
output growth, is indeed conducive to macroeconomic stability, though it does not guarantee it.3
Since the first currency board was set up in Mauritius in 1849 to enforce a fixed exchange
rate, up to the most recent one in Bosnia, about 80 currency boards have operated in small and
mediumsize countries.4 The monetary discipline implicit in these arrangements is often seen as
a means of preventing the depletion of foreign exchange reserves in the face of expanding
domestic credit. Moreover, history seems to support the idea that currency boards are an efficient
way of achieving shortterm price stability. With a fixed exchange rate, after all, the money
supply is endogenous, and both interest rates and inflation rates must converge toward
international levels.
1Frenkel, Fajnzylber, Schmukler, Serven (2001)
2See for instance Corbo (2002), Fisher (1996), and Quirk (1996).
3These points are discussed in Alberola and Molinas (2000).
4See for instance the excellent review provided in Ghosh et al (2000).
2
Intertemporal Adjustment and Fiscal Policy in a Fixed Exchange Rate Regime
Most recent studies of dynamic macroeconomic adjustment in a fixed exchange rate
regime have emphasized the influence of the relative prices of traded and nontraded goods on
changes in the real exchange rate, ignoring the money supply constraint to which all small open
economies operating under a fixed exchange rate regime are subject. This is a curious omission,
given that a key role of a hard peg system is to maintain equilibrium in the balance of payments.
For that reason, the money supply must be considered as part of the macroeconomic framework.
Only few studies have analyzed the problem of balanceofpayments equilibrium in the
context of monetary optimal intertemporal models in a pure fixed exchange rate regime.5
Furthermore, to our knowledge, no one has yet attempted a macrodynamic analysis of a strict
fixed exchange rate regime focusing on the interaction between the real exchange rate, monetary
determination, and the impact of fiscal policy. That is precisely what we undertake here. Given
an endogenous money supply, we ask how fiscal policy might influence both the real exchange
rate and the macroeconomic dynamics in the transition toward long run equilibrium , as well as
in the long run.
The paper presents a simple dynamic model for small to medium open economies
operating under a fixed exchange rate regime.6 The model provides a partial explanation of the
channels through which fiscal and monetary policy affects the real exchange rate. An empirical
investigation is implemented for the case of Argentina during the currency board period of 1991
2001.
The paper is organized as follows. The first section provides background on Argentina.
The second section describes an optimal monetary intertemporal model for an open economy
under a currency board, emphasizing the links between fiscal policy, monetary constraints, and
the real exchange rate. The third section applies the model to the currency board experience in
Argentina, simulating the dynamic effects of changes in the tax rate and foreign interest rates on
the paths of capital accumulation and the real exchange rate.
5Chang and Tsai (1998) have offered an optimizing monetary model of an open economy operating under
purchasing power parity, assuming capital immobility and equilibrium in the government budget balance. More
recently, Daniel (2001) suggests an analysis of an open economy in a fixed exchange rate regime under the
restrictive hypothesis of an exogenous income endowment. Other papers, such as Turnovsky (1996) and Normandin
(1999), deal with fiscal policy issues in a small open economy without money.
6"Small to medium" denotes economies that are not big enough to influence international prices or interest rates.
3
Intertemporal Adjustment and Fiscal Policy in a Fixed Exchange Rate Regime
1. Argentina's currency board experience
Argentina's experience with a currency board is an attractive subject of study because of
the dramatic macroeconomic events that occurred during and after the decade during which the
board was in place, and because of the lessons that Argentina's experience holds for other open
economies that may be considering a fixed exchange rate regime.
Argentina's central bank failed with its currency board because of an explosive
combination of factorschief among them the impossibility of conducting monetary policy (by
definition endogenous), foreign currency developments in the leading country to which the
currency was pegged (the United States), difficulties in designing and implementing fiscal policy
to compensate for imbalances in other sectors (monetary, financial, labor), institutional rigidities,
and issues of political economy issues (Carrera 2002). 7
For some time, the results of the currency board were considered impressive for their
stabilizing effect. Hyperinflation was reduced to almost zero, and growth rates increased until the
verge of the crisis (figure 1.1).
Figure 1.1 Argentina's GDP at constant prices, 19912001
Millions of pesos
288000
272000
256000
240000
224000
208000
192000
1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001
Source: IFSFMI.
7We do not analyze the political economy or institutional failures in this paper.
4
Intertemporal Adjustment and Fiscal Policy in a Fixed Exchange Rate Regime
Over the period of our analysis, inflation in Argentina dropped dramatically, falling
below the U.S. rate by 1996 (figure 1.2). And, during the entire currency board period,
Argentina's economy was spared a liquidity shortage because of increases in net foreign assets
(figure 1.3).
Nevertheless, over the period, Argentina's external competitiveness worsened because
fiscal policy was unable to offset deterioration in the current account by a voluntary increase in
the tax rate or a slowdown in public expenditures (figure 1.4).
In 1991, when the currency board was adopted, the real exchange rate stood higher its
longrun equilibrium (Carrera 2002), so competitiveness was already a problem. Subsequently,
the peso continued to rise further in real terms, boosting imports and discouraging exports, which
served to increase current account deficits (figures 1.5 and 1.6).
Figure 1.2 Inflation in Argentina (solid line) and United States, 19902001
Percent
0.075
0.050
0.025
0.000
0.025
1990 1992 1994 1996 1998 2000
Source: IFS IMF.
5
Intertemporal Adjustment and Fiscal Policy in a Fixed Exchange Rate Regime
Figure 1.3 Net foreign assets in Argentina, 19912001
Millions of pesos at current prices
25000
20000
15000
10000
5000
0
5000
10000
1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001
Source: IFSFMI.
Figure 1.4 Public expenditures in Argentina, 19912001
Millions of pesos, current prices
56000
48000
40000
32000
24000
16000
8000
1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001
Based on data from IMF.
6
Intertemporal Adjustment and Fiscal Policy in a Fixed Exchange Rate Regime
Figure 1.5 The real exchange rate in Argentina, 19902001
Real Exchange Rate Index = 100 1990
100
90
80
70
60
50
1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001
Based on data from IMF.
Figure 1.6 The current account deficit in Argentina, 19902000
Millions of dollars
1800
900
0
900
1800
2700
3600
4500
1990 1992 1994 1996 1998 2000
Based on data from IMF.
7
Intertemporal Adjustment and Fiscal Policy in a Fixed Exchange Rate Regime
Turning to fiscal policy, immediately following the adoption of the currency board the
fiscal deficit fell to zero from an average of 5 percent of GDP during the 1980s. By 1994, the
current account had moved into surplus thanks to past growth achievements and better fiscal
policies. That year ended in deficit, however, and the deficit worsened throughout the remainder
of the currency board period, reaching around 3.5 percent of GDP by 2001 (figure 1.7).
Figure 1.7 Ratio of fiscal deficit to GDP in Argentina, 19912001
0.02
0.01
0.00
0.01
0.02
0.03
0.04
0.05
1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001
Source: Centro de Economía Internacional.
The procyclical reaction of revenues to GDP, combined with less downward flexibility of
fiscal expenditures, contributed to this result. In general, however, both public expenditures and
government revenues were sensitive to business cycles, causing the fiscal balance to fluctuate
widely during the entire period.
The country's deficits were financed by capital inflows stimulated by a policy of capital
liberalization. The inflows led, however, to higher external indebtedness, which seems to have
been the only feasible adjustment mechanism, given the existence of the currency board.
When the currency board was adopted, Argentina's total public debt was $87 billion, or
40 percent of GDP. By 2001, it had reached $145 billion (53 percent of GDP)a 67 percent
increase.
8
Intertemporal Adjustment and Fiscal Policy in a Fixed Exchange Rate Regime
Figure 1.8 Argentina's public debt, 19922003
Millions of dollars
200.000
180.000
160.000
140.000
120.000
100.000
80.000
60.000
40.000
20.000

1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
Source: Ministry of Economy, Republic of Argentina.
Looking at these results, one might conclude that the currency board produced a degree
of macroeconomic stability and may have protected the country temporarily from effects of
exchange rate volatility, with a positive impact on growth. However, the nation's economic
system proved incapable of making sound fiscal adjustments and restoring competitiveness. In
the end, the explosion of external debt led to an acute recession.
2. A model of intertemporal adjustment in an open economy with a fixed
exchange rate
The model analyzes the process of intertemporal adjustment in a small to medium size
open economy operating with a fixed exchange rate regime. Individuals live in an infinite
horizon world with perfect foresight, and the home country produces and consumes a single
good, referred to in the paper as the domestic good, while also consuming a good imported from
abroad. Since the nominal exchange rate is pegged, the real exchange rate is the relative price of
domestic and imported goods.
Individuals face sequential decisions in order to optimize their welfare. First, within each
period, they choose an allocation of consumption between domestic and imported goods. This
process determines the relationship between the consumption price index and the real exchange
9
Intertemporal Adjustment and Fiscal Policy in a Fixed Exchange Rate Regime
rate. Second, individuals have to decide on the intertemporal distribution of consumption and
savings within the standard dynamic of an open economy over an infinite horizon.
The resolution of the intertemporal open macroeconomic model provides us with a set of
two firstorderdifference equations for capital accumulation and the real exchange rate.
2.1. Intratemporal optimization: consumption patterns and price level
determination
Denote by dt the consumption at time t of the good produced domestically and by zt the
consumption of the imported good. ct is the aggregate consumption of dt and zt. The consumption
price level is Pt. The aggregate consumption ct at current price is equal to:
Ptct = Et Pft zt + Pdtdt (1)
Pf and Pd represent respectively the prices of the imported good and the domestic good.
Aggregate consumption can be defined as a weighted combination of d and z:
ct = dt 1 zt (2)
is the weight of the imported good in aggregate consumption.
With regard to the prices of the domestic and imported goods, the real exchange rate Rt
can be written as:
Rt = Et Pft (3)
Pdt
Under a hard peg regime the nominal exchange rate Et is irrevocably fixed. Since
exchange rate fluctuations are not allowed, Et can be normalized to one.
Consumers optimize the allocation of consumption expenses between domestic and
imported goods according to their relative price. In order to achieve an optimal consumption
distribution between the goods, they maximize real consumption (equation 2) under the
constraint defined by equation (1).8 The optimal relationship between the consumption of the
two goods is given by the firstorder condition:
dt = 1 zt Pft (4)
Pdt
Solving equations (1) and (2) for zt produces the following expression:
8Max {dt 1 zt + (Et Pft zt + Pdtdt  Ptct )
}
10
Intertemporal Adjustment and Fiscal Policy in a Fixed Exchange Rate Regime
zt = Ptct (5)
Rt Pdt
and therefore:
dt = (1 ) Ptct (6)
Pdt
Replacing in equation (2) dt and zt with their value in terms of aggregate consumption
provides a determination of the consumption price as a loglinear function of the real exchange
rate and the domestic production price. The consumption price index is given by one of the
following equations:
Pt = Rt Pdt or Pt = Rt
1Pft (7)
where = 1 1
1
The aggregate consumption price level is a combination of the real exchange rate and
domestic or foreign prices.
These results will be reintroduced hereinafter in the form of Euler equations generated by
the intertemporal optimization program.
2.2. Macroeconomic equilibrium
2.2.1. Goodsmarket equilibrium
The economy produces only the domestic good. The output at time t, denoted yt, is
governed by a production function depending on the stock of capital9:
yt = F(kt ) (8)
Assuming no capital depreciation, the investment (made up solely of domestic goods) is
equal to:
It = kt  kt
+1 (9)
Exports are a function of exogenous world demand W and the real exchange rate:
xt = X(Rt ,W) X R > 0, XW > 0 (10)
The government raises a proportional tax and commits itself to purchase only domestic
9All variables are expressed in per capita terms. We assume no population growth. Population size is normalized to
one.
11
Intertemporal Adjustment and Fiscal Policy in a Fixed Exchange Rate Regime
goods gt. Under these hypotheses, the instantaneous domesticgoodsmarket equilibrium for this
small open economy is given by the following equation:
yt = gt + dt + X (Rt,W ) + It (11)
2.2.2. Balanceofpayments equilibrium in nominal and real terms
For simplicity, our approach here relies on the assumption that all government debt is
held by foreigners who feel secure because of the fixed exchange rate. In such a regime,
regardless of private capital movements, which are unpredictable in most emerging economies,
the balanceof paymentsequilibrium in current prices at time t is given by:
Mt  Mt + At  At 1+ i* = Pdt yt  Pc  Pdtgt  PdtIt
+1 +1 ( ) (12)
t t
The constant nominal foreign interest rate10 is denoted by i*.
The left side of equation (12) refers to the change in net foreign assets. In this simple
appraisal, movements of net foreign assets are equal to the algebraic sum of changes in money
supply (Mt+1Mt) and net foreign public assets (At+1At).
Transferring debt service i*At to the right side, we obtain the current account at time t.
Substituting (1) and (11) in (12) implies the conventional balanceofpayment equation:
Mt  Mt + At  At = Pdt X (Rt,W )  EtPftzt + i*At
+1 +1 (13)
From equation (12), the balanceofpayments equilibrium in real terms (at consumption
price), denoted by small letters, is:
(1+ t+1)at+1  at 1+ i* + (1+ t+1)mt+1  mt = (kt + F(kt )  gt  kt+1)
( )
Pdt  ct (14)
Pt
where t+1= Pt
+1
Pt 1 is the rate of growth of the consumption price index.
Equation (14) is the wealth dynamic constraint in an open economy under a fixed
exchange rate regime.
It does not seem unrealistic to consider public expenditures as being endogenous.
Therefore, we introduce them into the utility function.
10Against this simplifying assumption, it can be argued that i* should be a function of the debtoutput ratio, as in
models with countryrisk premium or models with imperfect capital mobility (see, for example, Agénor 2006). But,
according to Fisher (1996), "The monetary theory of the currency board is exactly that of the gold standard.
12
Intertemporal Adjustment and Fiscal Policy in a Fixed Exchange Rate Regime
2.2.3. Intertemporal optimization
The satisfaction of individuals relies on private consumption, public expenditures, and
real cash balances. For a given time preference factor , agents optimize each control variable
time path, benefiting from the availability of foreign loans in an open economy.
In such a framework, agents maximize the utility function below under the motion
constraint specified in equation (14). The optimization program can be expressed as:
MaxVt = (ln( j ct+ ) + ln( gt+ ) + ln mt (
j j + j))
j=0
uc: (1+ t+1)at+1  at 1+ i* + (1+ t+1)mt+1  mt = (kt + F(kt )  gt  kt+1)
( )
Pdt  ct (15)
Pt
The log linear11 utility function Vt is maximized under the balanceofpayments
constraint analyzed above. The firstorder conditions are:
gt = Pc
t t (16)
Pdt
ct = (1+ t ) +1
(1+i*) ct+1 (17)
Mt = Pt c
+1 t+1
+1 (18)
i*
1+ Fkt =
+1 ct
ct RRt
+1 t+1 (19)
Equation (19) results from price definition (7).
In the rest of the paper, the real foreign interest rate r* is assumed to be time invariant. We
1+ i*
use * to denote the foreign inflation rate. Since 1+ r* = 1+ *t , the assumption of a constant
real foreign interest rate implies that the foreign rate of inflation is also constant [(Pft /Pft1)1 =
*t=*].
Provided the arrangement is credible, it brings the benefit of rapid convergence toward international inflation and
interest rates, as can be seen in the Argentine experience."
11Supportive empirical evidence of the hypothesis of separability with respect to government spending is provided
by Karras (1994), McGrattan, Rogerson, and Wright (1997), Chiu (2001), and Okubo (2003), among others.
13
Intertemporal Adjustment and Fiscal Policy in a Fixed Exchange Rate Regime
2.2.3.1. Moneydemand dynamics
Equations (17) and (18) can be solved to obtain the dynamics of money demand. The
solution results in an Euler equation for the demand for nominal cash balance:
Mt = 1
(1+i*) Mt +1 (20)
At the steady state Mt
+1 = Mt
Pdt +1 Pdt time preference coincides with the discount rate
= 1
1+ r* . Since and r* are exogenous, we assume that this condition is always fulfilled: it
implies that the optimal money growth rate must be equal to the foreign inflation rate, which is
assumed to be constant:
Mt = (1+ *)Mt
+1 (21)
and at the steady state, the inflation rate on domestic prices will be equal to the foreign
inflation rate:
Pdt +1 =1+* (22)
Pdt
This result complies with one of the main expected results of a currency board
arrangement (see footnote 10).
2.2.3.2. Real interest rate parity
Expanding the domestic inflation rate according to the aggregate price level definition,
and in terms of the real exchange rate (7), the firstorder condition (17) becomes12:
1
ct = ct+1
1+ r*
( ) Rt +1 (23)
Rt
Solving (18) and (19) with respect to the real exchange rate provides us with an
12From the aggregate consumption price definition (equation 7), Pt = Rt 1 Pft , it follows that
1 1
Pt+1 =1+t+1 = . Inserting this definition of the inflation rate and the
Pt Rt+1 Pft+1
Rt Pft = (1+*) Rt+1
Rt
1+ i*
ratio1+ * = (1+r*) in (17) leads to the result in 23.
14
Intertemporal Adjustment and Fiscal Policy in a Fixed Exchange Rate Regime
expression of the intertemporal real exchange rate adjustment:
Rt = 1+ r*
(24)
1+ Fk,t+1Rt+1
This relationship demonstates that in our fixed exchange rate model, the ex ante real
interest rate parity between the home country and the rest of the world holds.
2.2.3.3 Money supply
Money supply is at the heart of the model because it determines the dynamic between the
real exchange rate and capital stock.
By inserting the optimum value of imports (5) into the balanceof paymentsequation (13)
we obtain the money supply dynamic:
Mt  Mt = Pdt X( Rt ,W ) Ptct ( At (1+ i* )At )
+1 +1 (25)
The dynamics of public foreign debt (assets) are governed by a natural accumulation
process, where stands for the proportional output tax, andPtct for nominal public expenditures
(equation 16):
At = (1+ i*)At + PdtF(kt )  Pc
+1 (26)
t t
Substituting public debt (asset) accumulation in (25) we obtain:
Mt  Mt = Pdt [X (Rt,W )  PdtF(kt )] + (  ) Pc
+1 (27)
t t
Demand for government spending and demand for imports are both proportional to
consumption. That being so, if >, (goods and services provided by the government weigh more
than imported goods) an increase in private consumption spending will automatically affect the
money supply because of the resulting drop in foreign assets (26). Given the mechanical reaction
of the money supply, fiscal policy remains the government's only instrument of economic. If
private consumption leads to an increase in the delivery of public services, for example, a tax
increase will be needed to maintain the balance of payments (27).
To move toward resolution of the model it is necessary to express nominal consumption
in terms of money demand. From equation (18) it follows that:
Pc = Mt
i *
(28)
t t
Given that, on the demand side, the optimal flow of money depends solely on the foreign
15
Intertemporal Adjustment and Fiscal Policy in a Fixed Exchange Rate Regime
inflation rate (21), and that the money supply is endogenous (because it results from the balance
of payments in a currency board regime), equation (28) demonstrates that consumption is driven
by the nominal quantity of money.
Substituting (28) in (27), the final expression of the moneysupply adjustment in terms of
variables, Rt and kt is:
,
Mt = 1+ (  )
+1 i* Mt
+ Pdt (X(Rt,W)F(kt)) (29)
Equation (29) describes the change in money supply change (identical to the change in
foreign exchange reserves) resulting from the balanceofpayments equilibrium,
(M = CA  A) , in a fixed exchange rate regime, where CA A = (X Z) + (T G).
From the equation above, we infer the following conclusions:
· Other things being equal, a tax cut will increase both the domestic money supply (29) and
foreign debt (26). This is the consequence, in the absence of sterilization, of the capital
inflow required to ensure equilibrium in the balance of payments.
· A depreciation in the real exchange rate will increase exports, and therefore external
reserves and the money supply.
· Because consumption is driven by the quantity of money (equation 28), the bracketed
term in equation (29) conveys a simple relationship between the dynamics of money and
the balance between public expenses G and imports Z, both of which are proportional to
the consumption level and therefore to the existing money stock. For example, the rate of
growth of money supply will be greater if > , other things being equal. In this case, the
quantity of money will stimulate government spending (inducing a public deficit, capital
inflows, and an increase in the money supply) more than imports (which induce a current
account deficit, depletion of external reserves, and a decrease in the money supply ).
2.2.3.4. Money market equilibrium
Substituting the expression for optimal money demand (equation 21) into the equation
for the money supply or balance of payments (29), gives the condition for money market
equilibrium:
16
Intertemporal Adjustment and Fiscal Policy in a Fixed Exchange Rate Regime
Mt = Pdt [X (Rt,W )  F(kt )] (30)
* +(  ) i*
This equation shows the optimal money balance at each period. Given the endogenous
moneysupply dynamics reflected in equation (29), Euler equation (21) will always be
satisfiedthat is, the rate of money growth will be equal to  provided individuals hold this
particular amount of cash balance in period t.
Following equation (29), a tax cut, other things being equal, will induce an increase in
money supply at time t+1. Whenever >, individuals must hold less money at time t in order to
compensate for this undesirable money growth.
2.2.3.5. Capital accumulation
Because the optimal real cash balance (30) is endogenous and depends on the real
exchange rate and capital stock, the model must be completed by adding the dynamics of these
two variables. The dynamics of the real exchange rate are given in equation (24). After
simplifications, the combination of the balanceofpayments equilibrium (equation 12), first
order conditions (16, 18), and equations (26) and (20), yields the following equation for capital
accumulation:
kt+1 = (1 )F(kt ) + kt  * +
i* Mt
Pdt (31)
Equation (31) is nothing else but the movement of the balance of payments under a fixed
exchange rate regime expressed in terms capital stock change. The capital stock is defined as the
difference between the level of production (net of taxes) and the sum of change in cash balances
and the level of private consumption. Thus, the terms between the brackets introduce the two
following elements:
· First, from (21) it is easy to show that *Mt = Mt+1. For any given foreign inflation rate,
the greater the predetermined cash balance, the greater its variation. Other things being
equal, this will reduce capital accumulation, as domestic agents will increase their cash
balance instead of physical capital.
· Secondly, from (28), the term (i*/).Mt drives household consumption: higher real cash
balances induce greater consumption and, in consequence, less capital accumulation.
17
Intertemporal Adjustment and Fiscal Policy in a Fixed Exchange Rate Regime
2.3. The dynamics of the model
2.3.1. The reduced form
The structural form of the model is composed of equations 30, 31, and 24. The reduced
form is obtained replacing the real money assets with their equilibrium level (substituting
equation 30 in equation 31). This substitution provides a backwardforward system of two first
orderdifference nonlinear equations:
kt = (1 )F(kt ) + kt + [X (Rt,W )  F(kt )]
+1 (32)
Rt = 1+ r*
(24)
1+ Fk,t+1Rt +1
In equation (32), we define: =  * + i*
.
* +(  ) i*
The coefficient is <0 if < or if  <
13 *
, and positive otherwise.
i*
In equation (32), the standard withdrawal effect of fiscal policy on transitional dynamics
is captured by the term:  F(kt ) . A new term (  F(kt )) is introduced to account for the
endogeneity of the money supply. The latter effect encompasses all of the mechanisms described
in the sub section 2.2. Provided that > (public expenditures are lower than imports) and
<1+ , is negative and less than 1. As long as < 1, a tax increase stimulates capital
accumulation during the transitional dynamics, contrary to the standard withdrawal effect.
Econometric estimates (see section 2.3.3) appear to verify this assumption.
The reduced form of the model requires some commentary. First, as the tax rate goes
up, the stock of capital rises in accordance with equation (32), owing to the relationship between
the money supply and the tax rate, as analyzed in the previous section. Second, the capital stock
increase induces a drop in the marginal productivity of capital . As a consequence, the real
exchange rate depreciates (24), exports are stimulated, and capital stock returns to its longrun
value.
13 and denote the share of imports and of public consumption in global consumption.
18
Intertemporal Adjustment and Fiscal Policy in a Fixed Exchange Rate Regime
The country may be also face an external shock, for instance a rise in the foreign real
interest rate. In that case, a depreciation in the real exchange rate (equation 24) will strengthen
exports and deplete capital stock. This pushes up the marginal productivity of capital , causes the
real exchange rate to appreciate, and, as exports dwindle, capital stock increases. If the increase
in the real interest rate is permanent, capital stock converges toward a new and lower longrun
level.
2.3.3. Dynamic analysis of the linearized system
At this point, we need to identify the steady state vector. Equation (24) provides a value
for longterm capital stock. At the steady state Rt = Rt . Therefore:
+1
Fk(k) = r* k = Fk (r*)
1 (33)
To compute the value of the real exchange rate in the steady state, we insert this result in
equation (32) at the point:kt = kt = k , Rt = R . After simplifications, we obtain the following
+1
value for the longrun real exchange rate:
X (R) = (1 )1F(k) R = X1 (34)
(1) 1F(k)
Since the functions of F and X are monotonic and concave, their inverses allow us to
compute steadystate solutions (equations 33 and 34). The two firstorderdifference equations
can be linearized in the neighborhood of their longterm values.
We must observe that while the longrun value of capital stock is independent of the tax
rate, the longrun value of the real exchange rate is influenced by the tax rate. At equilibrium,
whatever the time horizon considered, the higher the tax rate, the lower the money supply and
consumption. So, a higher level of exports, accompanying reductions in consumption, will
correspond to a depreciated real exchange rate. Thus it is clear that fiscal policy may have a
significant influence on economic patterns, even in the long run, by turning the economy toward
or away from exports.
As agents are assumed to have perfect foresight, the model can be solved by writing the
_
two equations backward. In the long run Fk = r = r* . A Taylor series expansion of equations (32)
19
Intertemporal Adjustment and Fiscal Policy in a Fixed Exchange Rate Regime
and (24) in the neighborhood of R, k leads to the expressions below.14
kt = 1+ r*  r* (1+)kt +XRRt + cst (35)
1 1
Rt = 1+ 1+ Rk
k
RXRFk Rt1
(36)
1+ r*  11+ r* Fk Rkt1 +1
r* k + r*
In matrix form, the linear system becomes:
kt a0
Rt b0 =
b1
a1kt a2
1
Rt b2
+ (37)
1
with: a0 = 1+r*( +1)r* ; a1 =XR; b0 =(1+r*( +1)r* )1+r* ; b1 = XR RFkk RFkk +1
1+ r*
In the rest of the paper, we consider the case where < 1, as assumed in the previous
sections.
The characteristic polynomial of the above matrix is: P( )=2+(b1a0 )+a0b1  a1b0
The values of the characteristic polynomial for = 1 and = 1 are, respectively:
P(1) = RFk XR
k
(1+r* ) <0 and P(1) = 3+(1+r*+RFk* kXR )2(+1)r*+2r* >0
1+ r
From the signs of P(1) and P(1) we conclude that the system is unstable, and the steady
state is a saddle. We verified these conditions for any tax rate between zero and one.
Turning to fiscal policy, it appears that the tax rate selected by the government can magnify or
diminish the impact of a change in the real exchange rate on capital accumulation. The
eigenvector associated with the characteristic root ( ) corresponding to the stable path can be
defined by the following equation:
(
v1 = +1)r* +r* +1( )u1 (38)
XR
If < 1 and for all positive values of < 1, the expression in brackets is negative, with
the consequence that the eigenvector slope corresponding to the stable path is positive. Thus,
14Xv, Fw denote derivatives with respect to variables v and w.
20
Intertemporal Adjustment and Fiscal Policy in a Fixed Exchange Rate Regime
along the stable path an increase in capital stock is followed by depreciation of the real exchange
rate. This mechanism relies on the fact that capital increases as the foreign real interest rate falls.
That is one of the reasons why if the interest rate parity holds the real exchange rate depreciates,
other things being equal, and a given value of the real exchange rate in the next period (24). But,
as we have already seen in the previous section, in a fixed exchange rate regime a tax increase
triggers an increase in exports. This effect is also included in relation (38).
To strengthen this result, we experimented with numerical simulations.15 These show that
for relevant values of parameters, roots are positive. The derivative of the eigenvector slope with
respect to the fiscal ratio is also positive, but its value is small with respect to the tax rate. As a
consequence, a tax increase will raise the numerator of the above equation (38) and will push the
ratio up.
In conclusion, with a fixed exchange rate regime, an active fiscal policy designed to
reduce external debt and promote exports should gradually raise the tax rate until the desired
export level is reached. Used in that way, fiscal policy may be an efficient way to promote
macroeconomic stability. In the transition period it encourages convergence toward longrun
equilibrium, while in the long run it modifies the distribution of exports and consumption,
private and public.
15A program written using MAPLE software is available on request.
21
Intertemporal Adjustment and Fiscal Policy in a Fixed Exchange Rate Regime
3. Empirical investigations
The objective of our empirical investigations is to estimate the parameters involved in our
dynamic model. Our ultimate purposes are to test the model's ability to explain Argentina's
currency board experience and to measure the dynamic effects of changes in fiscal policy and
foreign real interest rates.
The model, based on nonlinear simultaneous equations, can be written in the following
form:
kt = (1 )F(kt) + kt +[X (Rt,W )  F(kt)]
+1
kt = (1) yt yt1 (39)
1
kt1 kt1+ X (Rt ,W )
1 
kt1 kt1
Rt = 1+ r*
(40)
1+ Fk,t Rt log(Rt) = r*  Fk,t + log(Rt+1)
+1
To estimate equation (39) we assume that exports expressed in constant prices are a
function of the real exchange rate (R) and world demand (WD). Their relationship is given in a
linear logarithmic expression:
log(Xt ) = x0 + x1 log Rt + x2 log(WDt ) + SVt
1 1 (41)
in which:
· SV denotes seasonal dummies.
· R is the effective real exchange rate released by the International Monetary Fund. The
nominal exchange rate gives the amount of local currency in foreign currency terms. An
increase in R, for example, corresponds to a depreciation that would be likely to improve
exports.
· WD is a world demand index measured by imports by the member states of the
Organisation for Economic Cooperation and Development.
· x0is the intercept.
Our reduced form defines a backwardforward dynamic system. Estimating the forward
equation for the real exchange rate is done by introducing an ad hoc expectation process for the
real exchange rate. The basic idea is to consider that the future real effective exchange rate,
REER (R t+1), stabilizes exports (the level of which is given in equation 41) over the long run at
the steady state (log(Xt ) = log(Xt ) ).
+1
22
Intertemporal Adjustment and Fiscal Policy in a Fixed Exchange Rate Regime
Therefore the REER equation is written as follows:
log(Rt ) = rus,t  a
yt 1
+ + (42)
kt x1 (log(Xt)  x2WDt  x0) + SVt
where:
· rus is the real U.S. interest rate (the Fed Funds rate minus a threemonth centered
,t
moving average of the rate of growth of the U.S. consumer price index).
· is the capital depreciation rate.16
· a.yt/ ktis the marginal productivity of capital (a is the exponent of the CobbDouglas
function).
According to exports equation (41), the second term of the right side of equation (39) is
the value of the REER required to maintain exports at the same level in the next period.17
The estimated equation for the rate of growth of capital is very close to the theoretical
equation:
kt  kt 1 1 1 + c0 + SVt (43)
kt1 = Xt txt y
1 1 t1 (1txt ) yt
kt1 +
kt1
where txt is the exogenous tax rate.
Finally, the form of the production function is assumed to be:
yt = gt1akta (44)
Since parameter (a) is estimated from equation (39), the index of exogenous efficient
labor units (gt) can be computed directly by solving (44) for gt:
1
gt = yt 1a
(45)
kat
Thus the production function is used to simulate yt at each period of time.
The set of equations (41), (42), and (43) is estimated using the nonlinear least squares
system. Estimation results are presented in table 3.1. All coefficients have the expected sign and
are very precisely estimated, using robust standard errors calculation. The elasticity of exports
16The capital stock time series is computed by adding gross investments data and using an initial value given in the
Argentina Central Bank database. We used a quarterly depreciation rate =0.01375 in order to obtain the same
profile as the annual series given in the database.
17log(Xt ) = x0 + x1 log REERt + x2 log(WDt) + SVt = log(Xt) . Solving for REERt yields the expression in
+1
brackets.
23
Intertemporal Adjustment and Fiscal Policy in a Fixed Exchange Rate Regime
with respect to relative price (2.18) and world demand (1.64) are relatively high. Moreover, the
estimated elasticity of production with respect to capital in the CobbDouglas specification
(0.33) is very close to the value expected in standard studies. The estimated value of the key
parameter is unambiguously negative and less than 1.
24
Intertemporal Adjustment and Fiscal Policy in a Fixed Exchange Rate Regime
Table 3.1 Estimation of equations 4143
Using nonlinear least squares system
Coefficients Estimates Standard error Tstat
x1 2.18464 0.28178 8.5915
x2 1.64126 0.00718 242.3771
a 0.33055 0.03944 8.2536
1.42972 0.102373 13.6523
x0 0.489195 0.687573 0.71148
c0 0.07861 0.000872 89.9925
Nonlinear system estimation
Robust standard error calculations with flat window and 4 lags
Observations
Quarterly data from 1991:04 to 2001:03
Usable Observations 40
Dependent variable LREER
Centered R² 0.5288 R Bar² 0.5406
Uncentered R² 0.5821 T x R² 23.286
Dependent variable XR
Centered R² 0.8086 R Bar² 0.8134
Uncentered R² 0.9998 T x R² 39.992
Dependent variable TVK
Centered R² 0.7099 R Bar² 0.709942
Uncentered R² 0.8379 T x R² 33.519
Using insample historical values for world demand, productivity, and the U.S. real
interest rate, and out of sample observations (from the third quarter of 2001) of the same series, a
dynamic simulation of the model demonstrates that the nonlinear procedure we adopted is
appropriate (figure 3.1). Correlation coefficients between observed and simulated time series
total 0.992 for GDP, 0.756 for REER, 0.997 for capital stock, and 0.797 for exports.
To learn the dynamics of the model we simulated a permanent 1 percent shock to the tax
rate and another shock, also 1 percent but lasting for just one period, to the foreign real interest
rate (figure 3.2). The panels in the figure show that an increase in the tax rate of one percentage
point exerts a slight stimulus on capital stock (0.6 percent), at least in the short term, while
causing a maximum depreciation of 0.7 percent in the REER. In the long run, these variables
converge toward their steadystate values, with capital unaffected since the REER remains
depreciated. Given the elasticity of exports with respect to the real exchange rate, we infer that
the dynamic path of exports is the same as that of the exchange rate, though at a larger order of
25
Intertemporal Adjustment and Fiscal Policy in a Fixed Exchange Rate Regime
magnitude. This implies that an increase of one percentage point in the tax rate leads to an
increase (about 1.4 percentage point) in exports over the medium and the long run.
The responses following a transitory shock in the foreign real interest rate (returning to its
initial level after one period) are instructive. During the dynamic transitional period, capital
accumulation decreases, and the real exchange rate depreciates, causing a rise in exports. These
effects are not symmetric with those observed in the case of a tax increasecapital moves
adversely in both cases.
Figure 3.1 Dynamic response of Argentina's GDP, real exchange rate, capital stock,
and exports to simulated shocks
Bold line: actual values Dash line :simulated values in sample and out of sample
Argentina 1991:4 2001:3: Dynamic Simulations
72000 1.2
1.1
64000
1.0
56000
0.9
48000 0.8
1992 1995 1998 2001 2004 2007 1992 1995 1998 2001 2004 2007
GDP REER
700000 10800
9000
650000
7200
600000
5400
550000
3600
500000 1800
1992 1995 1998 2001 2004 2007 1992 1995 1998 2001 2004 2007
Capital Export
26
Intertemporal Adjustment and Fiscal Policy in a Fixed Exchange Rate Regime
Figure 3.2 Dynamic multipliers in Argentina
Percent change
Dynamic Multipliers
Capital REER
0.6 0.8
0.5 0.7
0.6
0.4
0.5
0.3
nge nge 0.4
hac 0.2 hac
% % 0.3
0.1
0.2
0.0 0.1
0.1 0.0
0 50 100 150 200 250 0 50 100 150 200 250
Quarters Quarters
Tax Rate +1% Tax Rate +1%
Dynamic Multipliers
Capital REER
1.6 0.56
0.48
1.4
0.40
1.2
0.32
1.0
0.24
nge 0.8 nge 0.16
hac hac
% 0.6 %0.08
0.00
0.4
0.08
0.2
0.16
0.0 0.24
0 50 100 150 200 250 0 50 100 150 200 250
Quarters Quarters
Productivity +1% Productivity +1%
27
Intertemporal Adjustment and Fiscal Policy in a Fixed Exchange Rate Regime
Dynamic Multipliers
Capital REER
0.1 1.08
0.96
0.0
0.84
0.1
0.72
0.2
0.60
nge 0.3 nge 0.48
hac hac
% 0.4 %0.36
0.24
0.5
0.12
0.6
0.00
0.7 0.12
0 50 100 150 200 250 0 50 100 150 200 250
Quarters Quarters
RIR +1% RIR +1%
4. Conclusions
The model proposed in this paper depicts a small to medium open economy that
produces a single domestic good and trading with the rest of the world. The intertemporal
optimization process leads, under market equilibrium constraints, to a reduced set of two
dynamic equations describing the movements of the real exchange rate and capital accumulation.
The money market equilibrium plays a major role in those movements insofar as the optimal rate
of growth of the money supply driving adjustments in the balance of payments is fixed by the
economy's structural patterns in the short run and by foreign inflation in the long run.
The model identifies two main structural patterns: the weight of imports, on the one hand,
and the weight of public expenditures, on the other. The comparative weight of the two variables
conclusively explains adjustments in the money supplythat is, the process of adjustment of the
balance of payments. Other things being equal, the money supply increases faster when the
weight of public expenditures exceeds that of imports. In this case, changes in the quantity of
money exert a stronger stimulus on government spending (which induces a public deficit, capital
inflows, and an increase in the supply of money) than on imports (which induce a current
account deficit, a drawdown of external reserves, and a reduction in the money supply).
In other words, with a fixed exchange rate regime controlled by the monetary authority,
the interaction between fiscal and monetary policies depends on the weight of the public sector
28
Intertemporal Adjustment and Fiscal Policy in a Fixed Exchange Rate Regime
visàvis the share of imports in total consumption.
If goods and services provided by the government outweighed imported goods, an
increase in private consumption would automatically raise the money supply because the drop in
foreign assets. Tax rates would be the government's only remaining instrument of economic
policy, given the endogeneity of the money supply. For example, if private consumption led to
an increase in the delivery of public services, a tax increase would be needed to maintain the
balance of payments.
On the other hand, if the share of imports in the economy were greater than the share of
public expenditures, an increase in domestic consumption would reduce the money supply (to
maintain equilibrium in the balance of payments). A tax cut would therefore be necessary to
offset the consumption effect and maintain the money supply.
Adapted to meet econometric standards, the model was applied to the Argentinean
economy during the country's decadelong experience with a currency boarda vivid case of
economic policy restriction. Indeed in a hard peg regime authorities wishing to diverge from the
natural dynamic path of their economy (to accelerate convergence with longrun equilibrium, for
example) have only fiscal policy at their disposal.
Econometric estimates confirm the sign of the parameters and thus uphold the theoretical
analysis in the case of Argentina during the currency board, when public spending was more
significant than imports in the composition of output. What this means for other countries is that,
with a fixed exchange rate regime, a fiscal policy designed to shrink external debt and promote
exports might consist of gradual increases in the tax rate until a desired level of exports was
reached. In this sense, fiscal policy may be an efficient instrument to promote macroeconomic
equilibrium because, in the transition period it encourages convergence toward longrun
equilibrium, and, in the long run, modifies the distribution between exports and consumption,
private and public.
To explore the dynamics of the model we simulated a permanent shock of one percentage
point to the tax rate and a transitory shock of like magnitude to the foreign real interest rate. The
simulations show that an increase of one percentage point in the tax rate exerts a slight effect on
capital stock, at least in the short term, and causes the REER to depreciate. In the long run, if no
action is taken to affect the money supply, the real exchange rate will stray from its longrun
value. This means that fiscal policy can be used to move the economy toward a desired real
29
Intertemporal Adjustment and Fiscal Policy in a Fixed Exchange Rate Regime
exchange rate.
In addition, given the elasticity of exports with respect to the real exchange rate, we
conclude that exports react similarly to the exchange rate, although with a higher order of
magnitude. This implies that an increase the tax rate will provoke an increase in exports over the
medium and the long run.
Finally, a transitory shock to the foreign real interest rate will decrease the stock of capital and
encourage exports. But the effects are not symmetric with those observed for a tax rate increase,
since capital moves adversely in both cases.18
18Volatility of foreign interest rates does not seem to have been the main cause of the decline in capital stock in
Argentina, since the U.S. interest rate remained quite stable after 1995.
30
Intertemporal Adjustment and Fiscal Policy in a Fixed Exchange Rate Regime
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