POLICY RESEARCH WORKING PAPER 1299
Fiscal Policy in Classical and In this model of cbssical and
Keynesian open economies,
Keynesian Open Economies bothpermanentafid
transitory disturbances cause
Klaus Schmidt-Hebbel changes in iong-lun output
Klaues Schmidt-Hebbel
Ltuis Serven and capacity - and transitory
and permanent shocks may
have opposite effects on thie
current account. In the
Keynesian economy, money-
financed fiscal expansion
causes real exchange rate
depreciation, and non-
money-financed fiscal
expansion, appreciation
'1'l,. Woerldl Iank;
Ikollcv ResLarch Dcpu-m"1ent
Mlacrocconotmiics and Growth DiVis;OI)X
Mlav 1 994
PLICY RESEARCH WORKING PAPER 1299
Summary findings
Sciimidt-Hebbel and Serven analyze the impact of fiscal lJsing parameters for a representative open econorny,
policy changes in open economies, using a rational- the model is simulated to compare the dvoamic effects o.f
expectations framework that nests two prototype increases in public spe?nding financed by taxatlimn, debt,
economies: a neoclassical full-employment benchmark and money. The results illustrate four points:
economy, with intertemporally optimizing consumers * Both permanent and transitory disturbances cause
and firms and instant clearing of asset, goods, and factor changes in loiig-run output and capacity.
markets; and a Keynesian economy, with liquidity * Transitory and permanent shocks may have opposite
constraints and wage cigidity, which results in transitory effects on the current account.
deviations from full employment. * liquidity constraints and wage rigidities tend to
The model is forward-looking in that .he economy's amplify the cyclical adjustment to fiscal policy changes.
short-run equilibrium depends or, current and * The Keynesian economy's response to fiscal shocks
anticipated future values of all exogenous variables, and depends critically on the way the budget is financed:
displays hysteresis (that is, its long-run equilibrium is money-financed fiscal expansion causes real depreciation;
path-dependent). non-money-financed fiscal expansion causes
appreciation.
T'his paper - a product of the Macroeconomics and Growth Division, Policy Researcii Department - is part of a larger effort
ill the dcpartment to model macroeconomic adjustment in open economics. Copies of the paper are available free from the World
Bank, 1818 H Street NW, Washington, DC 20433. Please contact Emily Khine, room NI 1-061. extension 37471 (47 pages). May
1994.
I 'I'he Policy Research Wtorking Paper Series disseminates the findings of u 0. This specification has the useful property that adjustment costs vanish in steady-state
equilibiium - i.e., when gross investment per unit of effective labor is just sufficient to maintain the
capital/effective labor ratio. The evolution of the latter is described by:
(13) k = inv - (g + 8)k
Market value maximization for unconstrained firms, as well as current profit maximization for
constrained firms, yields the standard marginal productivity conditions for variable inputs (labor and
imported materials).'"
(14) Id = al v-l y
(15) m = (I - a 2l - ) (e pmr)-l y
Investment demand is, as described above, a combination of the market-value maximizing
investment rule of unconstrained firms and the profit-constrained investment of restricted firms:
(16) inv = - (g6 j+(1jp ~
0 [2 [piq pilc g + (g + 6) k]I + (1 - 0 ) [p2 + igA
where 0, is the share of non-constrained firms and 02 is the marginal propensity of liquidity-constrained
firms to invest out of operational profits; 0 5 0 2 5 1.
Unconstrained investment (the content of the first large right-hand side parenthesis) is derived
from maximization of the value of the firm. This component of aggregate investment demand is geared
to Tobin's maU& q -- i.e., average q minus the present value of the public investment subsidy per
unit of capital". This reflects the fact that optimal investment is determined by the addition to future
dividends of the marginal unit of capital, which excludes the subsidy due to its lump-sum nature. By
' The derivation of them conditons. an wei u of dte unconsauined componeot of invesment in equaiion (16) below,
foUows die standard maxunzauon of the value of the firm, subject to equa_o (I 1) - (13), not preented here for brvity.
II 'Me genwal remuom dat cause maginal nd averag q to diverge are spoUed out in Hayashi (1982).
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contrast, the average value of existing capital (i.e., the present value of the dividends associated with an
installed unit of capitai) must include the subsidy. In turn, investment by constrained firms (the last term
in the right-hand of (16)) rises one-for-one with tlhe investment subsidy.
The present value of the public investment subsidy is implicitly defined by the dynamic equation:
(17) pvig = (r-g) pvig - piig
Aggregate operational profits -- which determine capital formation by liquidity-constrained firms
-- are defined as:
(18) op = y - v -e pmr mr
and dividends are the sum of operational profits, net of investment expenditure, the investment subsidy
and the proceeds of new issues of equity:
(19) d = op - piinv - pi iac + piig + q(k + gk)
After determining aggregate investmnent according to equation (16), the second-stage investment
decision involves allocating investment expenditure between domestic goods and imports, according to
a Cobb-Douglas aggregation which renders constant expenditure shares:
(20) in = y pi inv
(21) im = (1-y) e p'|imv
where y is the share of national-goods investment in aggregate investment expenditure, satisfying
O s 5 1. Therefore the aggregate investnent deflator is a Cobb-Douglas average of national-goods
investment prices and imported investment-goods prices:
(22) pi = (epim)(l1Y
2.4 Conaumers
Consumer preferences also allow two-stage budgeting distinguishing between intertemporal
aggregate consumption decisions and intratemporal consumption composition choices. Intertemporal
preferences reflect unit intertemporal elasticity of substitution (i.e., logarithmic intertemporal utility);
intratemporal preferences also display unit elasticity of substitution between domestic and imported goods.
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Private sector non-human wealth includes four assets: base money, domestic public bonds, foreign
assets, and equity claims on the domestic capital stock.
(23) a = hb + bg + e fbp + q(k-fe) - pvihb
where the present value of money holding costs pvihb has to be subtracted from financial wealth; it is
implicitly defined by the dynamic equation:
(24) pvihb = (r-g) pvihb - i hb
Human wealth is the present value of future labor income, net of taxes, and inclusive of current
external transfers."2 Under the assumption that indiviouals can freely borrow against their future labor
income at the going real interest rate, the path of human wealth is characterized by:
(25) hu - (r-g)hu + [td - vI - e ftrp3
Consumption of non-liquidity constrained consumers is derived from standard maximization of
intertemporal utility over an infinite horizon, subject to the intertemporal budget constraint equivalent of
the private sector flow constraint in equation (3) -- which is exactly consistent with wealth definitions
in equations (23) - (25). Solving the maximization problem yields the standard result that private
consumption of unconstrained households is equal to the subjective discount rate (net of effective labor
growth) times total (human and non-human) wealth."
Unconstrained consumers are of course Ricardian, as they internalize the government's
intertemporal budget constraint b)y anticipating the entire stream of current and future tax payments.
B%.cause liquidity-unconstrained consumers face the same discount rate as the government'4, they are
indifferent between tax, debt, or money financing. Therefore government debt -- although included in
equation (23) -- ultimately "is not wealth" (Barro. 1974).
Total private consumption demand is an aggregate of consumption by unconstrained and
constrained consumers. with the latter consuming their current net labor income:"5
'" For expositionsl convenience, all txes and transfers have been lumped together in the human capital flow equation.
Since both accrue in lump-sum fashion, dui is of no consequence for the model's properties.
"As before, the analytical derivazions are stadard and can be omitted.
''Me assumption of equal discount rates is crucul for Ricardian equivalence to hold. Higher pnvate sector discount
rates, whether due to finite lifetim (reflected by a given probability of death, as in Blanchard, 1985) or to a rsk premum
on consumer.' debt relative to the borrowing cost of the government (e.g., McKibbin and Sachs, 1989) would cause
Ricarchan equivalence to break down.
'5 For discussion and enmprical analyses of the irplications of liquidity conSatiint for consumer behavior - as wel as
for Ricardian equivalence - see, for example. Hayahi (1985), Hubbard and Judd (1986), Bernheim (1987), Leiderman and
Blejer (1988), and Seazr (1993).
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(26) cp = x1 [ (X2 g 8I)a j 2 - A)
PC j + PC-X1)
where 0 s A, s 1 is the share of unconstrained consumers, and X2 is the subjective discount rate.
Disposable income is defined by:
(27) yd = v I + e ftrp - td
After determining aggregate private consumption levels according to equation (25), the second-
stage private consumption decision allocates it to domestic goods and imports, according to Cobb-Douglas
intratemporal preferences:
(28) cnp = npc cp
(29) cmp = -T) cp
Le pcmp
where 0 5 71 S 1 is the share of national-goods in aggregate private consumption expenditure. Therefore
the aggregate private consumption deflator is a Cobb-Douglas index of national-goods prices and imported
consumption goods prices:
(30) pc = (e p=p)(l -11)
2.5 Govemmn
The public sector could either determine policy exogenously or derive it from optimization of
some objective function; for realism and simplicity, we choose the first option. Thus public consumption
and investment expenditures are exogenously given. To finance its activity, the public sector can choose
among taxes, money, domestic debt or external borrowing (or any combination of them).
The accumulation of per capita real balances can be characterized as:
(31) hb = [ng - (P/P) - g]hb
where it is worth noting that the rate of money growth nmg will be endogenous under money finance of
the deficit and exogenous otherwise.
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2.6 Foreigners
The demand by foreigners for the domestically produced good is given by a conventional export
function, which embodies imperfect substitution between the national good and the foreign final good and
a normal relation to foreign income:
(32) x = p1 (e px)P2 yfP2
where pV, P2, p3 2 0-
Finally, the path of foreigners' equity holdings remains to be described. At every instant, foreign
investors use dfi units of foreign currency (in real per capita terms) to purchase domestic shares, whose
price in terms of domestic output is q. Hence their per-capita holdings of equity evolve according to the
equation:
(33) fe = e i g fe
q
In turn, profit repatriation equals the total volume of dividends earned by foreign investors, which
is given by the product of the share of foreign-held equity and total dividends:
(34) prem = fe d
k
3. STEADY STATE AND STABILITY
3.1 The Steady State
The long run equilibrium of the model is characterized by constant asset stocks in real per capita
terms, constant asset prices (i.e., Tobin's q and the real exchange rate), and constant real wages with full
employment. Thus, the government's budget must be balanced, and the current account deficit must equal
the exogenously given flow of foreign investment, which in turn is just sufficient to keep foreign equity
holdings (in real per capita terms) unchanged.
Since the per capita real money stock is constant, long run inflation equals the rate of expansion
of per capita nominal balances nmg-g. In turn, with a constant real exchange rate, domestic and foreign
real interest rates are equalized by uncovered interest parity, and nominal exchange depreciation is
determined by the difference between domestic and (exogenously given) foreign inflation. Hence, across
steady states changes in the rate of money growth are fully reflected in the inflation rate (and thus in the
nominal interest rate) and in the rate of nominal depreciation.
By combining the model's equations, tne steady-state equilibrium can be reduced to two
independent equations in the real exchange rate, real wealth, and the real interest rate: a goods market
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equilibrium condition, and a zero private wealth accumulation condition (in real per capita terms).16
Together they imply a constant stock of per capita net foreign assets. Real wealth accumulation can cease
only when per capita consumption equals the per capita return on wealth. But the latter is just (rf-g) times
the wealth stock (because of the assumption of perfect asset substitutability), while in the steady-state the
former equals (XA-g) times the wealth stock (from (25)-(27))." Hence, this implies the well-known
result that the rate of time preference X, must equal the exogenously given foreign real interest rate:
(35) 2 - Rf
Since (35) provides no information on the steady state wealth stock, we would be left only with
the goods market equilibrium condition to determine both wealth and the real exchange rate-an obviously
impossible task. This means that their steady-state values (and hence also those of all variables that
depend on them) depend not only on the long-run values of the exogenous variables, but also on the
initial conditions and on the particular adjustment path followed by the economy -- and therefore on
parameters governing the speed of adjustment such as the degree of real wage rigidity or the magnitude
of adjustment costs associated with investment. In other words, the model exhibits hysteresis. As noted
by Giavazzi and Wyplosz (1984), this follows from the assumption of forward-looking consumption
behavior derived from intertemporal optimization by infinitely-lived households with a constant rate of
time preference and facing perfect capital markets.
Nevertheless, certain important features of the steady state can easily be determined." On the
production and investment side, long run equilibrium is characterized by full employment and a constant
capital stock in per capita terms. From (13), gross investment is just inv = (g + 6)k, and adjustment ccsts
are identically zero (from (12)). In turn, from (7), (17), (18) and (19), Tobin's q in steady state is given
by:
(36) q Fkipl (g+6)
(rf-g)
where Fk is the marginal productivitv of capital. If no firms are liquidity constrained (that is, B, = I in
(16)), then (16) further guarantees that marginal q equals the price of capital goods or, equivalently, that
average q equals the price of capital plus the unit investment subsidy (i.e. q = pi + pvig/k). Thus, from
the above equation the marginal product of capital equals its user cost:
(37) Fk = pi (rf+6)
16 See Serven (1994) for an analysis of the steady-state and dynamic properties of the non-monetary neoclassical vermon
of our model.
This is sictly correct only in the absence of liquidity constrints (XA = I). However, when XA < 1 wealth
accumuluion would stUll equal (r - X,) times the wealth stock of unconsuained consutters (a + ), hu).
Giavazzi and Wyplo:Z (1985) provide a method to solve analytically certain linear models with hysteresis. They show
tdua the long-sun equilibrium depends on irntal conditions and on the speed of adjustment of the system. Since our model is
nonlinear, however, a compnmble solution technique is not available.
- 16 -
Notice, however, that pi is an increasing function of the real exchange rate because of the import
content of capital goods. In turn, for a given capitai stock Fk is a decreasing function of the real exchange
rate, due to the use of imported materials in production. Hence, (37) defines an inverse relationship
between the steady-state capital stock and the real exchange rate: across steady states, a real depreciation
must reduce the capital stock, and (from (11) and (14)) also output and the real wage. It also follows that
the long-run values of these variables depend, like the real exchange rate, on initial conditions and on the
adjustment path of the economy. I9
What if some firms are liquidity constrained (i.e., l3, < 1) ? The negative long-run relationship
between the capital stock and the real exchange rate is unaltered; however, in the steady state q does not
equal the subsidy-inclusive price of capital goods, nor does Fk equal the user cost of capital. Provided
the marginal propensity to invest of constrained firms (B2 in (516)) is not too large,a' the marginal product
of capital must exceed the user cost, and Tobin's q must exceed the price of capital goods plus the
Investment subsidy. Formally:
(38) Fk= pi ((rf+8) + fl
where f > 3 is a term that depends positively on the adjustment cost coefficient t and the rate of
depreciation of capital, and negatively on B,, 82 and the investment subsidy.21 Tobin's q under liquidity
constraints becomes:
(39) q = pi f(rf+6) + +
The intuition behind these results is simple: with binding liquidity constraints, firms cannot invest
as much as they would want and therefore cannot close the gap between the shadow value of one
additional unit of capital and its cost. This implies that, for a given long-run real exchange rate, liquidity
constraints will cause the economy to achieve a lower capital stock and output, and a lower real wage
as well, than in the fully unconstrained case.
Using (37) or (38), the steady-state goods market equilibrium condition (4) can be rewritten as:
19 See Serven (1994) for further elaboution Tis is in contimt to similar dynamic modes (e.g., Sachs (1983), Giavam
et al. (1982)), where capial goods have no import contot and thus the ueady-stat marginal product of capital (" wvll as
the capital stock and real output) depends only on the relatve -price of mateials in terms of domestc goods (e pmr in our
notaion). Hem the import con- of capital goods creae a negative relationship between the real exchange rae and .,
even for a given real cost of imported inputs. Gavin (1991) ud Serven (1991) have shown tha this has unportant
consequences for the effet of macroeconomic policies on inve
20' Te exact condition is 82 < (g+6)/(rf+6) - ig/(a2y).
' The exact expresion for f is f = X___f___ ________2____f__g - (rf+6), where Z * - i the
0, + (1-,) 2g (rf-g 62+--)
public invennegt/pros output ratio.
- 17 -
(40) y(e,-..) T1 (rf-g)(a+hu) + cg + y pi (g+8) k(e,...) + x(e,...)
which defines an inverse relationship between the long-run real exchange rate and real wealth: an increase
in the real exchange rate (a real depreciation) generates excess demand for domestic goods and requires
a fall in private wealth and consumption to restore market equilibrium.' As noted before, the particular
levels of real wealthi and the real exchange rate that will obtain in the long run depend on the initial
conditions and on the dynamic path followed by the economy.
Aside from real wealth, the other key element in the determination of the long-run real exchange
rate is the distribution of demand between the public and private sectors. Since public consumption is
assumed to have no import content, an increase in cng creates excess demand for domestic gpods and
leads to a real appreciation. As argued before, this would cause the capital stock and output to rise as
well.
An important implication of the model's hysteresis property is that transitory disturbances have
long-run effects. For the case of fiscal policy, this has been recently highlighted by Turnovsky and Sen
(1991).? In our framework this also means that even transitory monetary disturbances can have
permanent real effects: if some consumers are liquidity constrained (or myopic), a transitory incrcea in
inflationary taxation matched by a reduction in direct taxes will raise disposable income and consumpion,
leading to reduced wealth accumulation and eventually causing a fall in long-run wealth and a peff ient
real depreciation.'
3.2 Dypamics. Stability and Model Sotuion
The precise dynamics of the model depend on the way the public deficit is financed. Under tax
or money finance, the model is driven by ten dynamic equations. Four of them describe the time paths
of predetermined variables: the capital stock, private foreign assets, foreign holdings of equity, and the
real wage. At each moment in time, these variables are given by current and past values of endogenous
and exogenous variables. Further, the four predetermined variables have to satisfy well-defined initial
conditions. Under debt (domestic or foreign) finance, a fifth dynamic equation describes the time path
of dte relevant debt stock.
The remaining six dynamic equations describe the time paths of 'jumping' variables: Tobin's q,
the real exchange rate, real money balances, human wealth, the present value of the investment subsidy,
2 Tis is guaanted Ly our assumption of conrtat expediture shar of domesic goods and impots in privae
connipton Dt inveetmmnt With more general specification. ailowing lower substtuability etweenV dometic and forogn
goods, a positive association between real wealth and tde real exchange rate in steady state (i.e., a 'conactionary
devaluation' of dhe type analyzed by Krugnan and Taylor (1978)) could not in principle be ruled out
I Turnovsky and Sen (1991) use a non-monetary model with intentemporiy optimizing consumers to show diat
ansitory fiscal disurbances have long-run effects. Their result deperAs critically on the endogeneity of labor supply in
thie frahework, wbic makes long-rn employment endogenous. In our cue, the dependence of tde long-run capitl sock
on the real exchange rate ensures that ransitory fiscal shocks have permanent effecs despite the conancy of full
eMployment acoss weady stae.
I Without liquidity consaints, a monetary accelemaion (an increae in nmg) holding constant public consupohn would
just amount to a change in the composition of txation between the inflation tax and (proent or futvre) direct taxes (or
trafers), witaut any effect on wealth, conwumption, or any other real variable.
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and the present value of the cost of holding money. They are not predetermined by the past and can react
freely to 'news' about current and future values of exogenous variables; their equilibrium values at any
point in time depend on the entire future anticipated path of the forcing variables. For the complete
dynamic system not tc explode, these jumping variables have to satisfy certain terminal (transversality)
conditions. Solving the model basically amounts to finding initial values for the non-predetermined
variables such that, rollowing a shock, the model will converge to a new stationary equilibrium.
The necessary and sufficient conditions for the existence and uniqueness of such initial values in
linear models of this type have been investigated in the literature and will not be discussed -here,
However, this is not the case for large nonlinear models such as this one.' While a formal proof of
stability cannot be provided, numerically the model was always found to converge to the new long-run
equilibrium under reasonable parameter values.
The requirement that the predetermined variables satisfy initial conditions, while the jumping
variables must satisfy terminal conditions, poses a two-point boundary-value problem, for whose
numerical solution severai different techniques exist. One leading example is the "multiple shooting"
method proposed by Lipton et al. (1982), which solves the model over a fixed time horizon starting from
arbitrary ,uesses for the initial and future values of the jumping variables. The second is the "extended
path" algorithm of Fair and Taylor (1983), which first solves the model also over a fixed time horizon,
but starting from arbitrary guesses for the expected values of the jumpers, which are updated until they
become sufficiently close tc the actual values obtained from the model's equations, and then gradually
extends the horizon until the solution path is unaffected by the addition of more time periods.
For the simulations below, we combine both techniques. First, we solve the model over an
arbitrarily chosen time horizon using multiple shooting. To prevent the solution from being distorted by
the choice of too short a time horizon (which would force the model to reach the terminal conditions too
early), we then extend the horizon and recompute the solution path until the resulting changes in the
solution trajectory of the endogenous variables fall below a certain tolerance,' at which time the process
stops. In practice, the length of the simulation horizon required for this procedure to converge is strongly
affected by two parameters governing the speed of adjustment of the system: the elasticity of real wages
to employment (i.e., the slope of the augmented Phillips curve), and the magnitude of adjustment costs
associated with investment. Finally, the model is made discrete for the numerical simulations, so for any
variable x, x = x,1 - x.
4. SIMULATION; RESULTS
This section discusses the dynamic response to external shocks, by presenting simulation results
for the model introduced above. In a companion paper (Schmidt-Hebbel and Serven, 1993) we have
D See BlanchLrd and Kahn (1980) and Buita (1984).
26 In pinciple, we could lirnearze the dystem around a steady gtate to detummi analytically the conditions under whici
tie tramtion malnx posseues the saddle-pont property. For a tenth-order gysem, however, diis would be an inbsetrbbe
task
r We used a very act convergence cntenon, requLring thd tde maximum relative change between solutions in any
varable at any time penod not exceed one-dhouaansz of one percent. Mis typically required a horizon between nxty Nd
eighty perods for convergence.
- 9
explored the model's response to a favorable foreign transfer shock (an external grant) and a favorable
terms-of-trade shock (a decline in the price of the intermediate import used in production, say oil). We
simulate the dynamic adjustment to fiscal and manetary policy shocks. The first-round magnitude of both
shocks is common, equivalent to a 4% gain of initial steady-state output. We start by introducing the
values of model parameters and exogenous variables and presenting the values of the endogenous
variables at the initial steady-state equilibrium. Then we discuss the simulation results.
4.1 Model Parameterization and Initial Steady-State Solution
Within the general structure spelled out above, two economies will be considered: (i) a
neoclassical (NC) benchmark, and (ii) a Keynesian benchmark combining liquidity constraints and
unemployment. Table 2 summarizes the common and distinct parameter values for these three
economies. Under the neoclassical benchmark, liquidity constraints on consumption and investment are
ruled out (B, = X, = 1.0). For the Keynesian case, the latter coefficients are reduced to 0.5. For the
full-employment cases, the elasticity of real wage changes with respect to current employment is set at
a very high level (w - 1,000) and indexation to lagged consumer-price inflation is ruled out (e = 1.0).
By contrast, wage-setting behavior in the Keynesian benchmark gives rise to unemployment, as a result
of a low employment elasticity (w = 0.25) and an important role of lagged inflation (O = 0.5). The
latter feature reflects nominal stickiness of wages.
Numerical values for other coefficients in the structural equations were borrowed from empirical
estimates (Serven and Solimano, 1991, Elbadawi and Schmidt-Hebbel, 1991) and preceding simulation
models (McKibbin and Sachs, i989, Giavazzi and Wyplosz, 1984) for various countries, complemented
by estimates deemed to be representative for open economies. Table 2 also reports these parameter
values shared by the three economies. Base money demand exhibits unit income elasticity. The interest
semi-elasticity is 0.5, implying a seignorage-maximizing inflation rate of 200%. The share of labor,
capital and intermediate imports in production (gross of imported materials) is 0.6, 0.3, and 0.1,
respectively. The quadratic adjustment coefficient of investment is 2.5 andk the rate of capital depreciation
is 0.04. The import component of aggregate investment is relatively large (0.4), exceeding that of private
consumption (0. 1). The rate of discount of consumers is set at 0.06, which, according to equation (35),
is also equal to the foreign real interest rate. Export demand exhibits a unitary foreign-income elasticity.
The price elasticity of foreign demand for exports is 1.5.
Before discussing the values of exogenous variables, a remaining question on model clos,ure has
to be addressed: one residual endogenous variable for each of the two independent budget constraints
remains to be chosen. For the simulations discussed below, the adjusting variable for the public sector
will be either taxes (td), or domestic debt (bg), or money growth (nmg); and for the private sector the
residual budgetary variable is foreign asset holdings (fbp).'
The numerical values for exogenous variables are also based on both representative country
magnitudes (as ratios to output) and previous models. Table 3 summarizes the exogenous variables for
the initial steady state, common to the three economies. While the simulations show the response to
changes in one exogenous variable (public consumption), all other exogenous variables are maintained
at the levels summarized in table 3. Because in the initial steady-state domestic output per efficiency
n Acul odl imulaios aume dim the pnvate sector intratmporal budget conatrain (eqution (3)) is the redundaa
budget conswuit by Walras' Law, hence it is excluded from the set of model equaons. (Obvioualy the iuAtewporal
budget conwmt is still used in deiving optml private consumpion leveb). Hence fbp is dte endogenous variable
assocad to the extrnl ector budget consaint (2).
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labor force unit is 1.0, all exogenous variables can be interpreted as ratios to initial steady-state output.
Both the public and private sector benefit from foreign transfers, at 0.015 each. Foreign income is
normalized at 1.0. Foreign direct investment flows amount to 0.005. Public indebtedness in foreign and
domestic capital markets is 0.30 and 0.20, respectively. The sum of public consumption and investment
is 0. 19, with a relatively large share of consumption. All absolute foreign price indices are normalized
at 1.0, with zero foreign inflation. The rate of growth of the labor force in efficiency units is equal to
the sum of population growth (2 %) and the rate of Harrod-neutral technical progress (I %). The foreign
real (and nominal) interest rate is 6 %. Finally, nominal base money grows at 5%.
The initial steady-state values of endogenous variables for the NC economy (and of most
endogenous variables for the K)9 are reported in Table 4. Initial (and final) rteady-state output growth
is determined by the rate of growth if the labor force in efficiency units (3%). Hence output per
efficiency labor is constant; parameter values were chosen so that its numerical value is 1.0.
At the initial steady-state equilibrium, total private sector (or consumer) wealth is almost 20 times
output, corresponding to the sum of non-human wealth (4.990) and human wealth (14.417). The four
components of non-human wealth (other than the exogenous public debt) are domestic base money (0.15),
the domestic-currency value of foreign assets (0.874), the net value of equity given by the product of q
(0.6) and the difference between the total c4pital stock (3.0) and the equity owned by foreigners (0.115),
and minus the present value of costs derived from holding base money (0.4).
Steady-state inflation at 2 % is given by the difference between money growth and output growth.
Seigniorage is defined as the product of base money holdings and its rate of growth. At initial and final
steady-state equilibria, seigniorage is 0.75% of output - the amount required to finance an operational
public sector deficit of the same magnitude. Note that only at steady-state positions seigniorage is equal
to the sum of the inflation tax (0.3% of output) and the growth effect on money demand (0.45% of
output). At non-stationary equilibria, accumulation of money holdings drives a wedge between
seigniorage and the latter sum.
Initial steady-state private consumption is 0.58, mostly comprised by national-goods consumer
spending. Stationary gross domestic investment is 0.21, all of which goes to replace depreciated capital
per efficiency labor force unit. 60% of investment f-ls on domestically-produced goods. Investment
adjustment costs are zero at the steady state, because they are only incurred on net investment. Exports
are 0.20, intermediate imports are 0. 10, and total hnports reach a level of 0.242. The corresponding
trade deficit of 0.042 and profit remittances (0.01) are financed by foreign transfers (0.03), the net return
(net of growth) on foreign-held assets, which yields 0.017, and direct foreign investment flows (0.005).
The latter flow finances an initial current account deficit (net of accumulation of foreign assets to maintain
constant asset/output ratios) of 0.005.
The steady-state nominal interest rate of 8% equals the sum of long-run domestic inflation and
the real interest rate. At a al exchange rate of 1.0, all relative goods prices are also equal to 1.0. The
29 As disussd in secton 3.1, Tobin's q ts higher and investnent is lower under binding liquidity consamints than in the
neoclAsl ecoomy. In fact, ina seady-ate values n the K economy ae 1.479 for q and 0.208 for gron domec
inveetmeeg. which can be compared to the iaonary values in die NC economy, repot in Table 4. The saioary capitl
ock is slighdy lower in die K economy (2.973), but the total equity value (q tunes k) is larger. Higher eqtuty moe than
offsets lower foreig assets held by the private sector (equal to 0.853 in the K economy). Hence steady-state tota come
weald and consumn are slighdy larger in die K economy. The stationary tred deficit is lighly lower in the K
economy, as the retuir on foreigi ast holdinp bas lighdy deteriorated due to the lower aock of pnvate foreign ast
hodinp. All otder variable reman unchaged in the K econory as comqaed to the NC case.
- 21 -
price of equity in units of national goods (q) is 1.444. Having normalized employment at 1.0. and with
a labor share in production of 0.6, the real product wage is also equal to 0.6.
TABLE 2: PARAMETER VALUES EOR SIMULATIONS
Sae money demand - 0.16,0 - ' L., - -0.5
Watg settiing nrle - 1,000 (NC) or 0.25 (K), e - 1.o (NC) or 0.5 (K)
- 0.91,a - 0.6, - 0.3
Production function = - 2.5
Investment adjustment costs 6 - 0.04
Physical capital deprocazon rate B- 1.0 (NC) o. 0.5 (K), 12 = 0.5
Private investment demand y 0.6
Domes ontent of investment XI 1.0 (NC) or 0.5 (K), X2 = 0.06
Private u imption demand l- 0.9
Domestic .cent of consufmption p = 0.2, p2 = 1.5, p, = I
Export demand
TABLE 3: INITIAL VALUES OF EXOGENOUS VARlABLES
Income. Transfer and Capital Flows All Forewtn Price Levels 1.0
Foreign tmnsfer to public sector (ftrg) 0.015 Raw
Foreign truanfer to pnvate sector (ftrp) 0.015
Foreign uncome (yf) 1.0 Populamion growth (pg) 0.02
Foreign direct investment (dfi) 0.005 Harrod-neutral technical progress (tg) 0.01
Foreign real interest (rf) 0.06
Stocks Nominal base money growth (nmg) 0.05
Domestic debt of public sector (bg) 0.2
Foreign assets held by public sector (e fbg) -0.3
Goods Flows
Public nanioial-goods consumption (crip) 0.15
Public investment subsidy (ig) 0.04
- 22 -
TABLE 4: INITIAL STEADY-STATE VALUES OF ENDOGENOUS VARIABLES
Income, Capital and Transter Flows Ermlovmenc (1) 1.0
(erational profits (op) 0.300 Ouput (y) 1.0
Dividends paid (d) 0.260
Taxes itd) 0.183 Ranes
Pnvae disposable inwome (yd) 0.433
Profit Rr.uttances (prem) 0.01 Nominal intenest rate on public debt (i) 0.08
Real interest rmte on public debt (r) 0.06
S_ocks Infiabon rate 0.02
Total pnvate sector wealth (a+hu) 19.407 All Reative Goods Prices 1.0
Non-humaz wealth of pnvate sector (a) 4.990
Stock of domesuc equity held by foreigners (te) 0.115 Other Prices
Domemuc base money (hb) 0.15
Human wealth of private sector (hu) 14.417 Real equity price (Tobin's q) 1.444
Physical capWal (k) 3.0 Real wage per effetve labor unut 0.6
Present value of government investment subsidy (pvig) 1.233 Real exchange rate (e) 1.0
Present value of cost of holding money (pvihb) 0.40
Foreign asets held by pnvate sector (e fbp) 0.874
Goods Flows
Privae aggregate consuimpuon (cp) 0.582
Private uipored-goods consumption (cnp) 0.058
Private national-goods consumpton (cnp) 0.524
Gross domestic investment (inv) 0.210
Private natonal-goods investment (in) 0.126
Private imported-goods investment (in) 0.084
Investnent adjustrnent costs (iac) 0
Exports (x) 0.20
Intermediae imports (mr) 0.10
Total imports (mr) 0.242
Trade balance -0.042
Current account balane -0,005
- 23 -
The simulations below explore three alternative tyTes oi shocks: a permanent unanticipated (P)
disturbance (hitting the economy from period I to terminal period T), a transitory unanticipated (TU)
shock (bitting during periods 1 -4), and a transitoiy anticipated (TA) shock (bitting during periods 2-5).
The simulations examine the effects of a fiscal expansion reflected by a public consumption
increase of 4% of initial output, Ehree altrnative forms of financing are considered: lump-sum taxation
(a balanced-budget fiscal expansion,, debt-financing, and monetary-financing.
The discussion of the simulation results focuses on the deviations from an initial cady-state
equilibrium (represented by period 0), distinguishing between the impact effects (in period 1) and the
transition toward the new steady-state equilibrium (from period 2 to terminal period T). The discussion
is based on the figures depicting the dynamic paths of the main endogenous variables. For tne tax-
financed fiscal expansion, each figure page is divided into an upper panel, which reports the dynamic
trajectories under the three types of shocks (P, TU, and TA) for the Neoclassical case, and a lower panel
depicting the dynamic trajectories of the sarne shocks for the same variable in the Keynesian case.
Because Ricardian eauivalence holds in the NC economy, the response of the key variables is the same
regardless of th:.- financing alternative chosen. Thus, for the debt-financed case, we show the dynamic
trajectories of fojur variables for the K case only. For the money-financed case, we show the dynamic
trajectories of three variables for the NC economy and nine variables for the K economy. The terminal
pe.iod T varies between 70, 80, and 90 periods.
4.2 A Balanced-Budget Fiscal Expansion
Under a balanced-budget expansion, taxes are raised to finance higher government consumption
and any other net expenditure increase arising endogenously, such as higher interest payments on the
domestic public debt. The dynamic paths of the main endogenous variables in response to the tax-
financed fiscal expansion are shown in figures 1-10.
Ccnsider first the neoclassical (NC) economy and the case of a permanent tax-financed fiscal
expansion. Tax revenue increases by 4 percentage points (pp.) of output iii period I and thereafter (Fig.
I). A permanent increase in government consumption and taxes reduces wealth and private consumption
accordingly (Fig. 2). i z t. anrd FconrorT1ic Growth Ross Levine 38526
WPS1286 Econo- [' rF anistormation and the Luca Barbone April 1994 S. Harbi
Fiscal C lsis A Crit:cal Look at the Domenico ir. Marchetti 37143
Centr ' i%::.rcpean Experience of the 1990s
WPS1287 Unstable Inflat on and Seignorage Jacques Morisset April 1994 D. Jenkins
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Issues and (otions 37699
WPS1289 A Fiscal Needs Approach to Equali- Anwar Shah April 1994 C. Jones
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WPS1290 Oil Price Instab:iity, Hedging, and an Stujn Claessens April 1994 D. Gustafson
Oil Stabillzatiori Fund' The Case of Panos Varangis 33714
Venezuela
WPS1291 A Survey ot Viet Nam's Legal Natalie G. Lichtenstein April 1994 M. Rangarajan
Fra-:tivor, in' IT:'r 'a-1 -i 81710
Policy Research Working Paper Series
Contact
Title Author Date for paper
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in Russia and Other Former Soviet Martha de Melo 84768
States Gur Ofer
WPS1293 Product Standards, Imperfect Glenn Harrison April 1994 N. Artis
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WPS1 297 How Relative Prices Affect Fuel Charles C. Guo May 1994 C. Jones
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Plant-Level Evidence from Chile
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Exchange Rate, and the Current Account 37471
WPS1299 Fiscal Policy in Classical and Klaus Schmidt-Hebbel May 1994 E. Khinp
Keynesian Open Economnies Lu s Server 37471
WPS1300 Dynamic Response to External Klaus Schmidt-Hebbel May 1994 E. Khine
Shocks in Classical and Keynesian Luis Serven 37471
Economies
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Application to Jakarta
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and Economic Properties 37699