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Chapter 5
Fiscal Deficits, Public
Solvency, and the
Macroeconomy
© Pierre-Richard Agénor and Peter J. Montiel
1



The Government Budget Constraint.
Policy Consistency and the Solvency Constraint.
Macroeconomic Effects of Fiscal Deficits.
2
The Government Budget
Constraint



The Consolidated Budget Constraint.
The Measurement of Fiscal Deficits.
Seigniorage and Inflationary Finance.
 The Optimal Inflation Tax.
 Collection Lags and the Olivera-Tanzi Effect.
 Collection Costs and Tax System Efficiency.
4
The Consolidated Budget
Constraint



Consider a small open economy operating under a
predetermined exchange-rate regime.
Central bank provides loans only to the general
government.
Government can finance its budget deficit by
 issuing domestic bonds;
 borrowing abroad;
 borrowing from the central bank.
5

Consolidated budget identity of the general government:
. .
.
L + B + EFg = P(g-) + iB + i*EFg + icL,
(1)
L: nominal stock of credit allocated by the central bank;
B: stock of domestic-currency-denominated interestbearing public debt;
Fg: stock of foreign-currency-denominated interestbearing public debt;
g: real public spending on goods and services;
: real tax revenue (net of transfer payments);
i: domestic interest rate; i*: the foreign interest rate;
ic  i: interest rate paid by the government on central
bank loans;
6
E: nominal exchange rate; P: domestic price level.




In (1), there is no nontax revenue and foreign grants,
although these may be sizable in developing nations.
Right-hand side of (1): general government deficit.
Left-hand side: sources of financing of the fiscal
imbalance.
Fiscal deficit is financed by
 increase in domestic and external debt, or
 credit from the central bank.
7

Central bank balance sheet:
M = L + ER - ,

(2)
M: nominal stock of base money (currency held by the
public and reserves held by commercial banks);
R: stock of foreign exchange reserves;
: central bank's accumulated profits (net worth).
Profits of the central bank:
 interest received on its loans to the government;
 its interest earnings on foreign reserves,
.
 capital gains from the revaluation of reserves ER.
8

Counterpart of these profits is increase in the central
bank's net worth:
.
.
 = i*ER + icL + ER.



(3)
Assumption: interest rate earned on reserves is the same
as that paid on the government's foreign debt.
Overall public sector deficit is obtained by combining
general government budget constraint and that of the
central bank.
Central bank profits need to be subtracted from the
general government deficit.
9


Increase in its net worth must be deducted from the
general government's increase in liabilities.
From (1) and (3):
.
.
.
.
.
L + B + EFg -  = P(g-) + iB + i*E(Fg-R) - ER.
(4)

From equation (2):
.
.
. .
.
L = M - ER - ER + .
10

Substitute this in (4):
.
.
.
M + B + EF* = P(g-) + iB + i* EF*,
(5)
where net public foreign debt:
F* = Fg – R.

Primary (noninterest) fiscal deficit in real terms:
d  D/P  g - .

Conventional fiscal deficit in real terms:
d  g + i(B/P) + i*(EF*/P) - .
11

Inflation-corrected operational fiscal deficit:
d  g + (i-)(B/P) + i*(EF*/P) - ,



: domestic inflation rate.
This deficit is an approximate measure of deficit the
government would face at a zero inflation rate.
Figure 5.1: behavior of the primary and operational fiscal
balances for Mexico over the period 1965-1994.
While the two measures correlate well until the beginning
of the 1980s, sharp divergences emerged subsequently.
12
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13
The Measurement of Fiscal
Deficit




Measurement of fiscal deficits in developing nations
raises a host of conceptual and practical issues due to
the lack of uniformity among countries.
Another problem arises in countries where controls on
interest rates or key public and private prices are
pervasive.
If expenditure is measured at official prices, the deficit
may be largely underestimated.
Appropriate solution is to determine an adequate
“shadow” price for the goods or services whose prices
are subject to government regulations.
14





But it has empirical and conceptual difficulties.
Determining the appropriate degree of coverage of the
“consolidated public sector” can be difficult in practice.
In that regard, treatment of central bank operations is
important.
In many countries, central banks perform a variety of
“quasi-fiscal” operations, such as
 implicit levy of taxes;
 management of government subsidy programs, debt
service and transfers;
 provision of preferential credit, and emergency loans
to the financial system or other industries.
Significant central bank losses related to these quasifiscal operations are common in developing countries.
15





In 1990 central bank losses were 2.2% of GDP in Chile,
5% in Jamaica, and 3.6% in Uruguay.
In the same year the nonfinancial public sector balance
was a surplus of 3.8% in Chile and 0.5% in Uruguay, and
a deficit of 1.3% in Jamaica.
Operations performed by public financial intermediaries
other than the central bank may also account for sizable
quasi-fiscal deficits.
Quasi-fiscal deficits may exceed conventional fiscal
deficits in overall size.
Quasi-fiscal deficits should be included in a
comprehensive measure of the public sector balance.
16



In practice, separating monetary and quasi-fiscal
operations of central banks raises methodological
questions:
 appropriate treatment of capital gains or losses
resulting from valuation changes;
 proper way to estimate quasi-fiscal activities
performed outside the central bank's profit-and-loss
account.
Exchange-rate or loan guarantees provided by the
central bank may remain completely off its balance
sheet.
Governments and central banks use different accounting
systems.
17

Asymmetric accounting treatment:
 When a central bank operates profitably, it transfers its
profits to the government.

When it operates at a loss, the central bank runs down
its reserves.
18
Seigniorage
and Inflationary Finance


Seigniorage: amount of real resources appropriated by
the government by means of base money creation.
Seigniorage revenue:
.
.
Srev = M/P = m = m + m,
(9)
M: base money stock;
P: price level;
.
  M/M: rate of growth of the monetary base;
m: real money balances.
19




First part of (9): seigniorage is the change in the nominal
money stock divided by the price level.
Second part of (9): seigniorage is the product of the rate
of nominal money growth and real balances held by the
public.
 is the tax rate and m is the tax base.
Third part of (9): seigniorage is the sum of
.
 m: increase in the real stock of money;
 m: change in the real money stock (occurred with a
constant nominal stock due to inflation.
20

Inflation tax:
Itax = m,
so that



.
Srev=Itax + m.
.
This implies that in a stationary state (m = 0), seigniorage
is equal to the inflation tax.
If money creation causes inflation, seigniorage can be
viewed as a tax on private agents' domestic-currency
holdings.
Figures 5.2 and 5.3: considerable differences across
nations in the use of seigniorage.
21
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23

Seigniorage accounts for a higher share of government
tax and nontax revenue in developing countries
compared to industrial countries.
24
The Optimal Inflation Tax
Phelps (1973): inflation rate can be determined optimally
by policymakers in a public finance context.
Assumptions:
 There are no commercial banks.
 So base money consists of real cash balances held by
private agents.
 Economy is in a steady-state equilibrium.
 Rate of output growth is zero.
 Expectations are fulfilled.
s
 Inflation rate is constant at  .

25

Inflation tax revenue:
Itax = sm.

(12)
Money demand function follows the Cagan specification,
so that real money balances vary inversely with the
actual inflation rate:
m = m0
s
-
e ,
(13)
m0: a constant.
26

Combining (12) and (13) and setting m0 = 1 :
Itax =





s
s
-
e .
(14)
Right-hand side of (14): Inflation tax Laffer curve in
Figure 5.4.
When s = 0, the revenue from the inflation tax is also
zero.
With an increase in the inflation rate, revenue rises at
first and begins falling beyond a certain point.
Maximum revenue: when dItax/ds = 0 (at point A).
For any given level of inflation tax revenue lower than
that corresponding to point A, there are two equilibrium
levels of inflation.
27
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28

Unique revenue-maximizing rate of inflation:
tax = -1.
s
This is the inverse of the semi-elasticity of the demand
for money.
 Governments levy the inflation tax also on noninterestbearing required reserves that they impose on
commercial banks.
Cox (1983):
 Revenue-maximizing rate of inflation when government
bonds and privately issued bonds are imperfect
substitutes.
 He shows that traditional formulations may considerably
underestimate the revenue-maximizing rate of inflation.
29

Fischer (1983): how optimal inflation tax considerations
affect the choice between exchange rate regimes.
 Végh (1989a): the higher the degree of currency
substitution, the higher the optimal inflation tax is for a
given level of government spending.
Khan and Ramírez-Rojas (1986):
 Revenue-maximizing rate of inflation is lower in the
presence of currency substitution.
 Reason: elasticity of the demand for domestic real
money balances is higher in this case.
 Brock (1984): when a reserve requirement is imposed on
capital inflows, inflation tax revenue increases when the
economy becomes more open to world capital markets.

30
Collection Lags and the Olivera-Tanzi Effect



Link between inflation and the collection lag in
conventional tax revenue is emphasized by Olivera
(1967) and by Tanzi (1978).
In developing countries:
 average collection lags is high;
 share of revenue generated by taxes collected with
progressive rates and withheld at the source is small;
 taxes are levied at specific rates.
In such conditions an increase in the inflation rate will
bring a fall in real conventional tax revenue.
31


The extent depends on
 average collection lag;
 prevalent tax burden (initial ratio of taxes to output).
Real value of conventional tax revenue at s on an
annual basis:
Tax(s) =
Tax(0)
(1+M)n
=
Tax(0)
(1+s)n/12
Tax(0): real value of conventional taxes at a zero inflation
rate;
n: average lag in collection of conventional taxes
measured in months;
M: monthly inflation rate.
32

Total government revenue:
T = s e- +
s

Tax(0)
(17)
(1+s)n/12
Setting the derivative of (17) with respect to s equal to
zero gives the value of the inflation rate that maximizes
~
total real revenue, :
~
dT/d = (1-)e- - (n/12)
Tax(0)
~
(1+)(1+n/12)
=0
33







Figure 5.5: graphical determination of the solution.
Curve I: inflation tax Laffer curve.
Curve N: revenue from conventional taxes. It depends
negatively on inflation and is maximized at a zero
inflation rate (point F).
Curve T: horizontal sum of I and N and gives total
revenue.
~ is lower than the rate that maximizes revenue from the
issuance of money, 1/.
At that level of inflation, revenue from the inflation tax is
OB and conventional tax revenue is BC.
Net contribution of the inflation tax to total revenue is FC
(lower than the gross contribution OB).
34
F
i
g
u
r
e
5
.
5
I
n
f
l
a
t
i
o
n
,
I
n
f
l
a
t
i
o
n
a
r
y
F
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e
,
a
n
d
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o
t
a
l
T
a
x
R
e
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n
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e

I
N T

A
1
/
G
~

A
'
DF C
B
0
S
o
u
r
c
e
:
A
d
a
p
t
e
d
f
r
o
m
T
a
n
z
i
(
1
9
7
8
,
p
.
4
3
5
)
.
I
,
T
a
x
(
)

t
a
x
35







Reason: revenue from conventional taxes falls by DF as
a result of higher inflation.
If fall in conventional revenue resulting from an increase
in inflation may be so large that it yields an overall
decline in total real revenue.
Figure 5.6: some of Tanzi's results.
When n is 2 months, ~ is 70%.
When n rises to 6 months, ~ drops to 50%.
In that case, inflating at a rate of 70% would increase
revenue from the inflation tax, but total tax revenue
would fall.
How potentially relevant is the Olivera-Tanzi effect?
36
F
i
g
u
r
e
5
.
6
I
n
f
l
a
t
i
o
n
,
I
n
f
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F
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f
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a
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T
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a
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t
a
x
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v
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n
u
e
1
/
3
0
2
5
=
2
n
2
0
n
=
4
n
=
6
1
0
5
0
510
1250
2350
3450
4550
6700
8900
11020
114600
12800
23500
34500
45500
Fiscalrevnu(ipercntofGDP)
1
5
A
n
n
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f
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(
p
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)
S
o
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:
A
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(
1
9
7
8
,
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.
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4
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)
.
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.
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=
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.
37
Choudhry (1991):





Average collection lag is about 6 months for total
revenue but varies widely among the different categories
of revenue.
These lags vary considerably across countries.
In countries where n is high, raising the Itax may be
counterproductive, as a result of the Olivera-Tanzi effect.
Available evidence: at least in high-inflation countries,
the rate of inflation has been higher than the rate that
maximizes steady-state revenue from Itax.
Explanation for the existence of chronically high inflation
can be found in need to finance external and internal
obligations with internal resources.
38
Collection Costs and Tax System Efficiency



In most developing economies:
 tax base is inadequate;
 share of small-income earners is large;
 evasion is endemic;
 tax administration is weak, inefficient, and subject to a
large degree of corruption (Goode, 1984).
In such conditions, compare total cost of inflationary
finance and the benefits (additional consumption in the
future due to higher level of government expenditure).
Illustration of the effect of the efficiency of the tax system
on the optimal inflation tax rate.
39
Végh:
 Relationship between government spending and
inflationary finance.
 Government’s budget constraint:
g - y = m,

g: government spending;
0 <  <1: conventional income tax rate;
0 <  <1: coefficient that reflects the efficiency of the tax
system (fraction of tax liabilities actually collected);
y: tax base.
(1 - ) : unit collection costs that are wasted by the
inefficiencies of the tax system.
40





Government's objective is to maximize potential revenue
y with respect to the conventional tax rate and the
inflation rate, subject to the budget constraint.
De Gregorio (1993): reduction in the efficiency of the tax
system (fall in ) leads to
 increase in the optimal inflation rate;
 fall in the inflation tax base.
Effect on the optimal tax rate is ambiguous.
But share of income tax revenues falls as the share of
revenue from the inflation tax increases.
Thus, even when the optimal conventional tax rate
increases, it will not outweigh the effects of the fall in 
on the revenue collected from the income tax.
41





Aizenman (1987) and Végh (1989b): decline in the
efficiency of the tax system raises the inflation rate.
Conventional taxes are subject to increasing marginal
collection costs.
As a result, Itax depends positively on the level of
government spending.
Improvement in the efficiency of tax collection would
reduce the government's reliance on Itax.
Cukierman, Edwards, and Tabellini (1992): efficiency of
the tax system in developing countries is highly
correlated with
 composition of output;
 degree of instability and polarization of the political
system.
42
Policy Consistency
and the Solvency Constraint


The Intertemporal Solvency Constraint.
Financing Constraints and Policy Consistency.
44
The Intertemporal Solvency
Constraint

Consolidated public sector deficit in real terms:
.
.
.
(M/P) + (B/P) + (EF*/P)
= g + i(B/P) + i*(EF*/P) - .
45

(19) can be rewritten in terms of the behavior over time
of stocks and flows per unit of output:
.
.
.
[M/(Py)] + b + zf *
(20)
= g -  + (i--n)b + (i *+--n)zf *,
lower-case letters: upper-case quantities expressed as a
proportion of nominal output;
n: rate of growth of real output;
z = E/P: real exchange rate;
: devaluation rate;
.
M/Py: seigniorage as a fraction of output.
46




d’  (g-)/y: primary public sector deficit as a fraction of
output.
.
s  M/Py: seigniorage as a share of output.
  b + zf*: total public debt as a fraction of output.
. ^ ^
Using d(zf*)/dt  zf* + zzf* (z is rate of depreciation of the
real exchange rate) (20) can be written as
.
^
 = (r-n) + d ’ + (i*+z-r)zf
* - s,
r: domestic real interest rate.
47

Defining augmented primary deficit as
yields

^
d  d ’ + (i*+z-r)zf*,
(22)
.
 = (r-n) + d - s.
(23)
Difference between primary deficit plus interest
payments on the existing debt and seigniorage revenue
must be financed by domestic or foreign borrowing.
48

Integrating forward (23) yields the public sector's
intertemporal budget identity:
=E



t
_
(sk-dk)e  t
k
(rh-nh)dh
_
dk + lim Ee
t
k
(rh-nh)dh
k
E: expectations operator, conditional on information
available at period t.
Government is solvent if the expected present value of
the future resources available to it for debt service is at
least equal to the face value of its initial stock of debt.
49

Solvency thus requires that government's prospective
fiscal plans satisfy the present-value budget constraint
E




t
_
(sk-dk)e  t
(rh-nh)dh
dk.
Public debt must be equal at most to the present value
as of time t of seigniorage revenue minus the present
value as of time t of future primary deficits.
These conditions imply the transversality condition
_
lim Ee  t
k

k
k
(rh-nh)dh
 0.
(26)
As of time t, expectation of the present value of the
consolidated future public debt cannot be positive in the
50
limit.





(26): debt/output ratio must grow at a rate below real
interest rate minus rate of growth of output.
This restriction rules out an indefinite Ponzi game: the
government cannot pay forever the interest on its
outstanding debt simply by borrowing more.
At some point the debt must be serviced by reducing
primary deficits or by increasing seigniorage revenue.
Solvency restriction ensures only that the existing debt is
ultimately serviced; it does not imply that the debt is
actually paid off.
Implication of the analysis: solvency is ensured even if
debt/output ratio grows at a positive rate, as long as this
rate remains below the long-run value of (r-n).
51





If r < n, for all t, (22) will not be binding: government will
be able in each period to service the existing debt by
further borrowing.
Assume that this condition does not hold for an indefinite
period of time, thus exclude Ponzi games.
Solvency requires positive values for (s-d).
Although running a conventional surplus is not necessary
to ensure solvency, positive operational surpluses are
required in the absence of seigniorage revenue.
Generally: to ensure solvency requires reducing primary
deficit or increasing the present value of future
seigniorage.
52
Problems:
 In practice, use of the solvency constraint to determine a
sustainable path of fiscal policy is fraught with difficulties.
 These difficulties result from uncertainty about future
revenue and expenditure flows.
 Solvency is a weak criterion with which to evaluate the
sustainability of fiscal policy (Buiter, 1985).
53
Financing Constraints
and Policy Consistency




Macroeconomic programs consist of specifying targets
for inflation, output growth, domestic and foreign
borrowing, and the overall balance of payments.
These targets restrict the use of alternative sources of
financing of the public sector deficit.
Government budget constraint determines a sustainable
level of the fiscal deficit given the authorities' policy
targets.
If the actual deficit exceeds its sustainable level, one or
all macroeconomic targets must be abandoned, or fiscal
policy adjustment must take place.
54
Analysis of consistency requirements between fiscal
deficits, inflation, output growth, and the balance of
payments in a small open economy is provided by (21).
Is a given fiscal policy path sustainable?
 This can be determined by projecting the future course of
the debt/output ratio for given predictions about
 evolution of money demand,
 desired inflation rate,
 real interest rate,
 growth rate of the economy.
 If debt/output ratio to be rising continually, fiscal
adjustment or adjustment in other targets is required.

55




If the policy target is to maintain a fixed debt/output ratio
for both internal and external debt, real debt cannot grow
faster than real output.
Using (21) and inflation target yields the primary deficit
plus interest payments on domestic and foreign debt.
Then, it is possible to determine the inflation rate at
which revenue from the inflation tax covers the difference
between the government's financing needs and its
issuance of interest-bearing debt.
Given primary deficit and inflation targets, appropriate
path of foreign and domestic borrowing is determined.
56


Resulting path of policy variables depends on
 assumptions about the behavior of the predetermined
variables;
 estimated form of the demand for real money
balances.
Given path of fiscal policy is sustainable does not imply
that it is necessarily the optimal choice.
57
Macroeconomic Effects of
Fiscal Deficits

Conventional public deficits (Ig - Sg) are financed by
surpluses from the private sector (Sp - Ip) and the rest of
the world, CA (current account deficit):
D  (Ig-Sg) = (Sp-Ip) + CA.


(27)
Effects of large public deficits on the macroeconomy
depends on the components of this equation that actually
adjust.
Adjustment depends on
 scope for domestic and foreign financing,
 degree of diversification of financial markets,
 composition of the deficit.
59





Expectations about future government policies also play
a critical role in the transmission of fiscal deficits.
Ricardian Equivalence.
Deficits, Inflation, and the “Tight Money” Paradox.
 The Analytical Framework.
 Constant Primary Deficit.
 Constant Conventional Deficit.
Deficits, Real Interest Rates, and Crowding Out.
 Expectations, Deficits, and the Real Interest Rates.
 Deficits, Investment, and the Crowding Out.
Deficits, the Current account, and the Real Exchange
Rate.
60
Ricardian Equivalence





Ricardian equivalence: deficits and taxes are equivalent
in their effect on consumption (Barro, 1974).
Lump-sum changes in taxes have no effect on consumer
spending, and a reduction in taxes leads to an equivalent
increase in saving.
Reason: consumer endowed with perfect foresight
recognizes that the increase in government debt will be
paid off by increased taxes.
So consumer saves today the amount necessary to pay
future taxes.
Ricardian equivalence implies that fiscal deficits have no
effect on aggregate saving or investment or on the
current account of the balance of payments.
61



When does Ricardian equivalence to hold?
 Existence of infinite planning horizons;
 certainty about future tax burdens;
 perfect capital markets;
 rational expectations;
 nondistortionary taxes.
The available evidence for developing and industrial
countries has failed to provide much support for the
Ricardian equivalence hypothesis.
In developing countries, many of the considerations
necessary for debt neutrality do not hold because
 financial systems are underdeveloped,
 capital markets are highly distorted or subject to
financial repression,
62
private agents are subject to uncertainty incidence of
taxes.
Haque and Montiel (1989), Veidyanathan (1993), Corbo
and Schmidt-Hebbel (1991), Easterly and SchmidtHebbel (1994) reject debt neutrality.


63
Deficits, Inflation,
and the “Tight Money” Paradox

Explanation for the inflationary consequences of public
fiscal deficits in developing nations:
 lack of sufficiently developed domestic capital markets
that can absorb newly issued government debt.
central bank is under the control of government and
finances public deficits through money creation.
There may be no clear short-term link between fiscal
deficits and inflation.
Positive correlation in the long run is also not a clear-cut.
Figure 5.7: positive relationship between fiscal deficits
and inflation is discernible, although it appears weak.64

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65
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66
Possible reasons:
 nonlinear relationship between fiscal deficits and
inflation,
 other factors (behavior of world prices or supply-side
shocks).
Haan and Zelhorst (1990):
 Relationship between government deficits and money
growth.
 Long-run relationship between budget deficits and
inflation in high-inflation countries is positive.
 Figure 5.8: positive relation between money growth and
inflation in the long run.

67
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69
Reasons for the absence of a close correlation
between budget deficits and inflation in the short
run.
 Increase in fiscal deficits may be financed by issuing
bonds rather than money.
 Change in the composition of the sources of deficit
financing may lead to higher inflation without substantial
changes in the level of deficit.
 Money demand function may be unstable, expectations
may be slow to adjust, or inertial forces may prevent the
economy from adjusting rapidly to changes in inflationary
pressures.

Existence of strong expectational effects linked to
perceptions about future government policy.
70
Drazen and Helpman (1990):


If the public believes that the government will attempt to
reduce its fiscal deficit through inflation, current inflation
will rise.
If the public believes that the government will introduce
fiscal adjustment program to lower the deficit, inflationary
expectations will adjust downward and current inflation
will fall.
“Monetarist arithmetic” (tight money paradox) by
Sargent and Wallace (1981):
 When a government finances its deficit by inflation tax,
any attempt to lower the inflation rate today, even if
successful, will require a higher inflation rate tomorrow.
71
The Analytical Framework


Closed economy with zero rate of population growth
(n = 0).
Household's flow budget constraint:
.
.
m + b = (1-) (y++rb) - c - m,
m: real money balances; y: output;
b: government-indexed bonds held by the public;
: net lump-sum transfers from the government;
c: consumption expenditure;
: inflation rate; r: constant real interest rate.
0 <  <1: proportional income tax rate levied on all
components of gross income.
(28)
72

Assuming that transfers are constant over time, real
wealth is:
a = m + b + (y+)/r.

(29)
Demand functions for goods and money:
c = a,  > 0
m = (-)a / i,
 > ,
(30)
(31)
i = (1 + )r + : net nominal interest rate;
 = (1 - )r : rate of time preferences.
73

Equilibrium condition in the goods market:
c = y - g,

g: noninterest government spending.
Government budget constraint:
.
.
m + b = g - y + (1-)(+rb) - m.

(32)
(33)
Dynamics of real money stock:
.
m = ( - )m,
(34)
.
  M/M: rate of growth of nominal money stock.
74

In the steady state m = b = 0, using equations (28) to
(34) yields, with r = /(1 - ):
~
c = y - g,
~
m=
-
~
(1-)  + 
~
{m + b + r -1(y+)},
~
~
g - y + (1-)(+rb) = m,
* = .
75
Constant Primary Deficit

Consider a temporary reduction in the rate of money
growth during the time interval (0,T), with the primary
~
government deficit held constant at d:
~
d = g - y + (1-).



(38)
After T, stock of real government bonds is assumed to
remain constant at the level it attained at period T.
During the interval (0,T)  is exogenous and b
endogenous, while for t  T stock of bonds remains
constant at the level bT+, and  becomes endogenous.
Effects of this policy rule on the dynamics of inflation
and real money balances proceeds in two stages.
76

Substituting (34) in (33) yields
.
b = (1-)rb - m - zb,
(39)
where
zb = (1-)(y+) - c.


Since output and public spending are constant, private
consumption is also constant, at (y - g) from (32) along
the equilibrium path.
Hence zb is also constant.
77

.
Since, from (34), m = m - m, (30) and (31) imply
.
m = [ + (1-)r]m + zm,
(40)
zm = -[(-)/](y-g),


where zm is constant.
From (30), a constant level of consumption implies that
real wealth must
be constant along the equilibrium path,
.
.
so that m + b = 0.
Suppose that, starting at a steady state where  = h,
monetary authority reduces the rate of money growth
unexpectedly at time t = 0 to a value s < h over (0, T).
78




Although the price level is fully flexible, real money
balances will not jump at t = 0.
Reason: m0 is determined, from (30) and (31) by the
requirement that consumption remain constant and by
the fact that b0 cannot jump on impact.
From (40), a reduction in  implies m0 < 0, so that real
money balances will be declining over time.
Solving Equation (40) yields
m=

~
m(s)
+ [m0 -
~
s
m(s)]e[( + (1-)r)t ],
(41)
where m0 < m(s) = - zm/[s + (1-)r].
(41) indicates that real money balances will be declining
at an increasing rate over the interval (0, T).
79

From (30), (31), and (32),
 = [(-)/] (y-g)m-1 - (1-)r,
0 < t < T.
(42)




This implies that  increases continuously over (0, T).
Solution for t  T:
During
the interval
.
. . (0, T), b must be rising because
m < 0 and m + b = 0.
Because the latter condition must continue to hold for t
 T and the stock of bonds must remain constant at bT+
.
for t  T, we must have m = 0 for t  T.
So real money balances must remain constant at mT+ for
t  T.
80

.
Condition m = 0 is satisfied by adjusting discontinuously
+
the rate of money growth at T so as to satisfy (40)
.
~
mT = 0 = [
+ (1-)r]m+T + zm.
.


Since m < 0 for 0 < t < T, (43) implies that  must be
raised above.
Since m+
T < m0, it follows that
s > h < ~.

This indicates that reduction in the money growth rate
during (0, T) below its initial value must be followed at T
by an increase beyond the initial value.
81

Using (42) in the post-adjustment steady state inflation
remains constant at T+ and
T+ > 0, t  T.



This indicates that the steady-state  that prevails
beyond T is higher than in the initial steady state.
Increase in  occurs during the interval (0, T), because
no jump can occur at time T as a result of perfect
foresight.
So temporary reduction in  raises  both during and
after the policy change.
82
Reason:
 Temporary reduction in  is offset by an increase in
bond finance.
 Thus, after the temporary policy is removed, higher
interest payments require that seigniorage revenue be
higher to finance the deficit.
 This requires a higher .
 Expectation of higher  in the future implies higher 
even while the contractionary policy is in place.
83
Constant Conventional Deficit
What happens if conventional deficit remains fixed,
rather than the primary deficit?
 Using (37), (38) is replaced by
~
d = g - y + (1-)(+rb).



(46)
For (46) to hold continuously with b endogenous,
assume that the government makes compensatory
adjustments in transfer payments to households, .
Because public spending and output are constant,
financing rule implies that  + rb is constant at .
Assume also that population growth n is positive.
84

Using (29) - (32), (34), and (46) yields
.
b = -nb - m + zb,



For  given, (40) and (47) form a differential equation
system in b and m whose steady-state equilibrium is a
saddlepoint.
Slope of the saddlepath coincides with the slope of the
[m = 0] curve in Figure 5.9.
Steady state is reached at point E, for a given value of
 = h.
Real balances may jump on impact since endogenous
transfers ensure that wealth, and consumption remains
constant initially.
.

zb  (1-)(y+) - (y-g).
(47)
85
F
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86



.
.
Varying  and maintaining m = b = 0 permits derivation
of alternative long-run equilibrium values of real money
balances and stock of bonds.
Alternatively, for a given value of b, treating m and  as
endogenous allows to derive the steady-state relation
between real holdings of money and bonds.
This relationship is given by
m = (nb - zb - zm)/(1-)r.



This equation is MM curve in Figure 5.10.
Initial long-run equilibrium with  = h obtains at E.
Consider a reduction of  from h to s over (0, T).
87
F
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88





New steady state solution associated with ( 400 and
(47) with  = h obtains at point E (located on MM).
Real money balances increase, in association with a fall
in price level and initial steady-state , and the system
jumps from E to A.
The economy then follows a divergent path over (0, T),
moving from A to B located on curve MM, which is
reached exactly at period T.
If at that moment the policymaker raises  to c > s and
freezes the stock of bonds at b+T, B will represent a
steady-state equilibrium.
During the transition period, real balances fall while the
stock of bonds and  rise.
89
However, at B real balances remain above their original
~ h
equilibrium level m( ), implying that  will remain
permanently below its initial steady-state level.
 Result: temporary reduction in  leads to permanent
reduction in .
Difference from the previous case:
 When the primary deficit is held constant, increase in
interest payments on the public debt is financed by the
inflation tax and is therefore inflationary.
 When the overall deficit is held constant, increase in
interest payments on government debt is financed by a
rise in taxes.
 “Tight” monetary policy (reduction in ) leads to a
dynamically unstable system during (0, T).

90
Solvency constraint requires a freeze of the stock of
government bonds.
 Result: for t  T, smaller stock of m, larger b, and
permanently higher .
Liviatan (1986):
 Instability disappears if a “tight monetary policy” is
defined as a reduction in the share of money financing
of the government deficit over (0, T).
 Ratio of money financing to bond financing  is
exogenous;  is endogenous.
 Monetary tightening: temporary reduction in .
 Modified model is saddlepath stable, if initial share of
money financing is not too small.

91


With constant primary deficit:
 temporary monetary tightening leads to an immediate
but temporary increase in inflation;
 permanent tightening leads to an immediate and
permanent increase in inflation.
If the deficit is defined as including interest payments on
the public debt, the Sargent-Wallace paradox is
reversed.
92

Further generalization can be obtained if the deficit
target is written as
~
d = g - y + (1-) + rb,




where 0 <  <1.
Constant primary deficit:  = 0.
Constant overall deficit:  = 1.
Assume composition of deficit finance  is policy
parameter.
Liviatan (1988b): policy trade-off emerges in the choice
of the optimal combination (, ).
93
There exists * such that
 for  < *, increase in  is deflationary;
 for  > * increase in  is inflationary.
 At any given level of inflation there exists a trade-off
between  and :
 negative when  < *;
 positive when  > *.
 Lack of a close correlation between fiscal deficits and
inflation may be due to uncertainty about policy
instrument that will be used to close the budget deficit.
Example:
 Government increases public spending and finances
the resulting budget deficit by issuing bonds.

94
This policy is not sustainable and requires future
measures to close the deficit and satisfy the
intertemporal government budget constraint.
 But the public is not sure whether the government will
 increase taxes;
 use money financing; or
 use combination of the two options.
Kawai and Maccini (1990):
 Effects of this type of uncertainty in a closed economy.
 If “pure” money finance is anticipated to be used,
inflation usually displays a strong, positive correlation
with fiscal deficits.
 If tax finance is anticipated to be used, inflation and
deficits may be positively or negatively correlated. 95

Deficits, Real Interest Rates,
and Crowding Out
Rise in domestic public debt has
 increased the risk of default;
 reduced private sector confidence in the
sustainability of the fiscal stance.
 This leads to high real interest rates and further fiscal
deterioration, destabilizing mechanism.
Figure 5.11:
 For four middle-income developing countries, the
relationship is not conclusive.
 But in some countries the inverse relationship between
real interest rates and fiscal deficits holds.
96

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98

Reason for weak association:
 central bank regulations prevent a complete
adjustment of nominal interest rates to market levels.
 expectations about future, rather than current, fiscal
policy.
99
Expectations, Deficits, and Real Interest
Rates
Assumptions:
 Small open economy with three categories of agents:
households, the government, and the central bank.
 Domestic production consists of a tradable consumption
good and is assumed fixed at y.
 Purchasing power parity holds continuously and world
prices are normalized to unity.
 This implies that the domestic price level is equal to the
nominal exchange rate, which is devalued at a constant,
predetermined rate  by the central bank.
 Households hold two types of assets: domestic money,
100
and a government-indexed bond.






Domestic money bears no interest.
Transactions technology is such that holding cash
balances reduces liquidity costs associated with
purchases of consumption goods.
Capital is perfectly immobile internationally.
Government consumes final goods, collects income
taxes, and pays interest on the outstanding stock of
bonds.
It finances its fiscal deficit by issuing bonds or by
borrowing from the central bank.
Agents are endowed with perfect foresight.
101

Representative household maximizes discounted utility
over an infinite horizon:







t
(49)
[u(c, m)]e-tdt,
 > 0: rate of time preference (assumed constant);
c: consumption;
m: real money balances;
u(·): instantaneous utility function.
Assume that the function is separable in c and m:
u(c, m) =
c1-
1-
+  lnm,
: coefficient of relative risk aversion.
 > 0,
102

Real financial wealth of the representative household:
a = m + b,

(50)
b: real stock of government-indexed bonds.
Flow budget constraint gives the actual change in real
wealth as the difference between ex ante savings and
capital losses on real money balances:
.
a = (1-)(y++rb) - c - m,
(51)
r: real interest rate;
: lump-sum transfers from the government;
0 <  < 1: proportional income tax rate.
103


Assume: taxes are levied on gross income at a uniform
rate.
Using (50), (51) can be written:
.
a = (1-)a + (1-)(y+) - c - im,


(52)
i = (1 - )r + : net nominal interest rate.
Household treat y, r, , and  as given and maximize
(49) subject to (52) by choosing {c, m, b}
t = 0.
Hamiltonian for this problem:
H = u(c, m) + {(1-)a + (1-)(y+) - c - im},
: measures marginal utility of wealth.
104



Optimality conditions:
c / m = i,
(53)
.
c / c = [(1-)r - ],
(54)
 = 1/: intertemporal elasticity of substitution in
consumption.
(53): equates marginal rate of substitution between
consumption and real money balances to the nominal
interest rate (opportunity cost of holding money).
(54): dynamics of consumption are determined by the
difference between the after-tax real interest rate and
the rate of time preference.
105

(53) can be written as
m = c/i.


(55)
This relates the demand for money
 inversely to i;
 positively to the level of transactions.
Nominal money stock must satisfy
M = D + ER,
(56)
D: stock of domestic credit (from central bank to
government);
R: foreign-currency value of net foreign assets held by
the central bank.
106

Changes in the real credit stock:
.
d = ( - )d,



(57)
: rate of nominal credit growth.
Assume:
Net foreign assets and loans to the government do not
bear interest.
Net profits. of the central banks is capital gains on
reserves ER, which are transferred to the government.
In real terms, the government budget constraint
. .
d + b = g - y + (1-)(+rb) - m,
g: noninterest public spending.
(58)
107

Combining (52), (56), (57), and (58) gives the overall
budget constraint of the economy, which determines the
evolution of the balance of payments:
.
m = y - c - g.

(59)
Using (55), equilibrium condition of money market can
be solved for the equilibrium nominal real interest rate:
+
-
i = i(c, m),
(60)
which in turn yields the real interest rate:
r = [i(c, m) - ]/(1 - ).

(60): increase in c requires an increase in r to maintain
equilibrium of the money market.
108
Rise in m, due to expansion of domestic credit or
accumulation of net foreign assets, lowers r.
 Increase in  requires a compensating reduction in r.
Assumptions:
 Central bank expands nominal credit to compensate
government for the loss in the real value of outstanding
credit stock due to inflation ( = ).
.
 As a result, d = 0.
.
 b = 0.
 Government adjusts level of net transfers to households
to balance the budget.
 (58) becomes:

 = (1-)-1(y-g+m).
(61)
109

Since constant real stocks of domestic credit and bonds
are normalized to zero, seigniorage revenue is m.

Dynamic system in c and m:
.
c
.
m

ic im
=
-1 0
~
c-c
~
m-m
Dynamic system in r and m:
.
r
.
m
r m
=
-r -m
~
r-r
~
(62)
m-m
110
Assume that the condition for the system (62) to be
saddlepath stable holds.
Figure 5.12:
.
 This condition requires that the slope of the [m = 0]
.
locus be steeper than the slope of the [r = 0] locus.
 Saddlepath SS has a negative slope, and the steadystate equilibrium obtains at E.
 As indicated by (54), real after-tax interest rate must be
equal to the rate of time preference at point E.
 Assume: economy is initially in a steady-state
equilibrium, and fiscal policy shock brought about by a
permanent, unanticipated increase in g.
 Increase in g generates on impact an excess demand
for goods, which requires a concomitant fall in c.

111
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112








So, r must fall to maintain equilibrium in the money
market.
Over time, c rises.
This leads to a gradual increase in r, until it returns to its
initial steady-state value.
Foreign reserves fall throughout the transition period.
Figure 5.13: adjustment process.
.
.
Increase in g shifts curves [r = 0] and [m = 0] to the left.
r jumps downward from E to A located on the new
saddlepath SS, and begins rising along SS toward the
new steady state, E.
Now assume that increase in g is announced at t = 0 to
occur at period T in the future.
113
F
i
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'
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C B
B
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.
r
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A
S
'
~
m
m
114






In the short run, dynamics of r will depend on the
horizon T.
If T is very distant, r will jump downward to a point such
as B, and will continue to fall along BC during (0, T).
New saddlepath SS (at point C) will be reached at the
moment the increase in g is implemented.
If T is short, r rises immediately after the initial
downward drop to B, along the divergent path BC.
New saddlepath will be reached at period T.
Result: r fluctuates in reaction to both
 actual fiscal policy shocks;
 expected changes in the fiscal stance.
115
If agents correctly anticipate an increase in g, r adjusts
immediately, with little effect occurring when the policy
measure is effectively implemented.
 Therefore, correlation between fiscal deficits and real
interest rates can be weak in the short run.
 Expectations may also be related to financing mix that
the government may choose in the future.
Example:
 Government may initially raise g and finance the
ensuing deficit by issuing bonds during (0, T).
 At the same time, it may announce its intention to either
reduce net transfers to households or scale down
expenditure on final goods to balance the budget.
 In this way b is maintained constant at a level b+
T beyond
116
period T.

Kawai and Maccini (1990):
 Effect of an alternative policy sequence on the behavior
of r.
 Inflation is endogenously determined.
 Government runs a fiscal deficit using bond finance for
a transitory period, and closes it at a given date in the
future by
 either raising taxes
 or using money finance.
 When agents anticipate the latter option to be used,
expected  rises and translates into an immediate
increase in i.
 As a result asset holders reduce their money balances
and shift into bonds, thereby reducing r.
117



So although current deficits and i are positively
correlated, there is an inverse relation between the
deficit and r.
Depending on the state of policy expectations, larger
fiscal deficits may lower r.
If uncertainty about financing options in the future varies
over time, correlation between current deficits and
interest rates can be subject to large fluctuations.
118
Deficits, Investment, and Crowding Out





When interest rates are flexible, large public deficits
financed by borrowing from domestic credit markets will
exert upward pressure on r.
This reduces private investment and output.
When interest rates are determined by government fiat,
excessive domestic borrowing crowds out private sector
expenditure due to reduction in credit allocated by the
banking system.
When there informal credit market, tighter restrictions on
official loans lead to a higher informal interest rate.
Whether fiscal deficits have a negative effect on private
investment, output, and growth depends on the sources
of the deficit and the composition of g.
119
Deficits, the Current Account,
and the Real Exchange Rate
If the opportunity to borrow internally is limited, a close
correlation exists between fiscal deficits and current
account deficits.
 Implication: reduction in the availability of external
financing requires
 either fiscal adjustment
 or increase in inflation and seigniorage revenue.
Carlos Rodríguez (1991):
 Mechanisms through which fiscal policies affect private
spending and the accumulation of foreign assets.

120




External deficit determines the real exchange rate that
is consistent with the clearing of the market for
nontraded goods.
Implication of such models: effect of deficits on the
current account and the real exchange rate depends on
both level and composition of g.
Alternative way to view the link between fiscal deficits
and the current account is through expectations about
future policy.
Suppose the government runs a bond-financed fiscal
deficit for a limited period of time.
121
Dynamics of the economy during the transition period
depend on whether the public expects government to
switch in the future to
 tax finance regime
 or money finance regime.
 If tax finance is expected to be used, current fiscal
deficits will be associated with a current account deficit.
 If money finance is anticipated to be used, fiscal deficits
may be associated with current account surpluses.
 Therefore “twin deficits” arise only when private agents
anticipate that the government will choose tax finance.
Empirical evidence:
 Existence of a positive relation between large fiscal
deficits and large external imbalances.

122
Khan and Kumar (1994):
 Econometric analysis of the role of public deficits, and
other domestic and external variables, in the
determination of the current account.
 Fiscal deficits have a highly significant effect on the
behavior of the current account.
123