1 chapter 5 fiscal deficits, public solvency, and the macroeconomy © pierre-richard agénor and...
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1
Chapter 5Fiscal Deficits, Public
Solvency, and the Macroeconomy
© Pierre-Richard Agénor and Peter J. Montiel
2
The Government Budget Constraint. Policy Consistency and the Solvency Constraint. Macroeconomic Effects of Fiscal Deficits.
The Government Budget Constraint
4
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.
5
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.
6
Consolidated budget identity of the general government:
L + B + EFg = P(g-) + iB + i*EFg + icL,
L: nominal stock of credit allocated by the central bank;
B: stock of domestic-currency-denominated interest-bearing public debt;
Fg: stock of foreign-currency-denominated interest-bearing 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;
E: nominal exchange rate; P: domestic price level.
. . .(1)
7
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.
8
Central bank balance sheet:
M = L + ER - ,
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.
(2)
.
9
Counterpart of these profits is increase in the central bank's net worth:
= i*ER + icL + ER.
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.
. .(3)
10
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.
From equation (2):
L = M - ER - ER + .
. . . . .
. . . . .
(4)
11
Substitute this in (4):
M + B + EF* = P(g-) + iB + i* EF*,
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) - .
. . .(5)
12
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.
13
Figure 5.1Mexico: Public Sector Fiscal Balance
(In percent of GDP)
Source: International Monetary Fund.
1965 1968 1971 1974 1977 1980 1983 1986 1989 1992 1995
-15
-10
-5
0
5
10
Primary balance
Operational balance
14
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.
15
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 quasi-
fiscal operations are common in developing countries.
16
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.
17
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.
18
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.
19
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,
M: base money stock;
P: price level;
M/M: rate of growth of the monetary base;
m: real money balances.
.(9)
.
.
20
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.
.
21
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.
.
.
22
Figure 5.2Seigniorage and Inflation Tax
(Percentage averages over 1980-91 and 1992-96 )
Belgium
Burundi
Canada
Colombia
Gabon
Germany
India
Indonesia
Jamaica
Japan
Kenya
Lesotho
Malaysia
Mexico
Morocco
Nigeria
Pakistan
Philippines
Singapore
Sri Lanka
Thailand
United Kingdom
United States
Venezuela
0 5 10 15 20 250
Seigniorage(percent of government revenue)
Belgium
Burundi
Canada
Colombia
Gabon
Germany
India
Indonesia
Jamaica
Japan
Kenya
Lesotho
Malaysia
Mexico
Morocco
Nigeria
Pakistan
Philippines
Singapore
Sri Lanka
Thailand
United Kingdom
United States
Venezuela
0 1 2 3 4 50
Seigniorage(percent of GDP)
Belgium
Burundi
Canada
Colombia
Gabon
Germany
India
Indonesia
Jamaica
Japan
Kenya
Lesotho
Malaysia
Mexico
Morocco
Nigeria
Pakistan
Philippines
Singapore
Sri Lanka
Thailand
United Kingdom
United States
Venezuela
0 1 2 3 4 5
Inflation tax(percent of GDP)
1980-91 1992-96
Source: Authors' calculations based on International Financial Statistics.Note: Seigniorage is measured in terms of the change in the base money stock as a percentage of either total government revenue or GDP. Inflation in measured as the annual rate of change in consumer prices. Inflation tax revenue is measured as tt-1 divided by GDP.
23
Figure 5.3Inflation and the Inflation Tax
(Averages over 1980-96)
Source: Authors' calculations based on International Financial Statistics.1/ The inflation tax is measured as t Mt-1 divided by nominal GDP. M is the base money stock and inflation is the annual rate of change in consumer prices.
Inflation (in percentage averages)
Infla
tion
ta
x (in
per
cen
t o
f G
DP
) 1
/
0 10 20 30 40
0
0.5
1
1.5
2
2.5
3
Germany
Thailand
Gabon
Singapore
Malaysia
Japan Canada
United States
Burundi
Indonesia
Belgium
Cameroon
PhilippinesIndia
United Kingdom
Sri Lanka
France
KenyaPakistan
Morocco
Lesotho
Jamaica
Colombia
Nigeria
Italy
Venezuela
24
Seigniorage accounts for a higher share of government tax and nontax revenue in developing countries compared to industrial countries.
25
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. Inflation rate is constant at s.
26
Inflation tax revenue:
Itax = sm.
Money demand function follows the Cagan specification, so that real money balances vary inversely with the actual inflation rate:
m = m0 e-,
m0: a constant.
(12)
s
(13)
27
Combining (12) and (13) and setting m0 = 1 :
Itax = s e-.
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/ds = 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.
s (14)
28
Figure 5.4Inflation and Revenue from Inflationary Finance
A
taxI
1/
I
I
29
Unique revenue-maximizing rate of inflation:
tax = -1.
This is the inverse of the semi-elasticity of the demand for money.
Governments levy the inflation tax also on noninterest-bearing 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.
s
30
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.
31
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.
32
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.
The extent depends on average collection lag; prevalent tax burden (initial ratio of taxes to output).
33
Total government revenue:
(1+s)n/12 T = s e- +
s Tax(0)
Setting the derivative of (17) with respect to s equal to zero gives the value of the inflation rate that maximizes total real revenue, :
~
(17)
(1+)(1+n/12)dT/d = (1-)e- -
Tax(0) ~(n/12)
~= 0
34
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).
~
35
Figure 5.5Inflation, Inflationary Finance, and Total Tax Revenue
A
taxI ,Tax()
~A'
D F C
0
IN T
B
G
Source: Adapted from Tanzi (1978, p. 435).
1/
36
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?
~
~
37
Figure 5.6Inflation, Inflationary Finance, and Tax Revenue
Source: Adapted from Tanzi (1978, pp. 446 and 448).1/ n denotes the collection lag, in months. The calculations reported assume that = 1 and that the ratio of money to GDP and the ratio of total tax revenue to GDP (both at a zero inflation rate) are equal to 20 percent.
5 10
15
20
25
30
35
40
45
50
60
70
80
90
10
0
12
0
14
0
16
0
18
0
20
0
25
0
30
0
35
0
40
0
45
0
50
0
Annual inflation rate (percent)
0
5
10
15
20
25
30
n = 2
n = 4
n = 6
Revenue from inflationary finance Total tax revenue 1/F
isca
l re
ven
ue
(in
pe
rce
nt
of
GD
P)
38
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.
39
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.
40
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.
41
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.
42
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.
Policy Consistency and the Solvency Constraint
44
The Intertemporal Solvency Constraint. Financing Constraints and Policy Consistency.
45
The Intertemporal Solvency Constraint
Consolidated public sector deficit in real terms:
(M/P) + (B/P) + (EF*/P)
= g + i(B/P) + i*(EF*/P) - .
. . .
46
(19) can be rewritten in terms of the behavior over time of stocks and flows per unit of output:
[M/(Py)] + b + zf *
= 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.
.
.
(20)
..
47
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.
.
. ^ ^
. ^
48
Defining augmented primary deficit as
d d ’ + (i*+z-r)zf*,
yields
= (r-n) + d - s.
Difference between primary deficit plus interest payments on the existing debt and seigniorage revenue must be financed by domestic or foreign borrowing.
.
^
(23)
(22)
49
Integrating forward (23) yields the public sector's intertemporal budget identity:
(rh-nh)dhk
t_
= E
t(sk-dk)e dk + lim Ee (rh-nh)dh
k
t
_
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.
50
Solvency thus requires that government's prospective fiscal plans satisfy the present-value budget constraint
dk. E
t(sk-dk)e
(rh-nh)dhk
t
_
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
0. (rh-nh)dhk
t
_ lim Ee
k(26)
As of time t, expectation of the present value of the consolidated future public debt cannot be positive in the limit.
51
(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).
52
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.
53
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).
54
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.
55
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.
56
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.
57
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.
Macroeconomic Effects of Fiscal Deficits
59
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.
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.
(27)
60
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.
61
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.
62
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,
63
private agents are subject to uncertainty incidence of taxes.
Haque and Montiel (1989), Veidyanathan (1993), Corbo and Schmidt-Hebbel (1991), Easterly and Schmidt-Hebbel (1994) reject debt neutrality.
64
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.
65Source: International Monetary Fund.
Figure 5.7aInflation and Fiscal Deficit
(Average over 1964-92, in percent)
-15 -10 -5 0 5
0
10
20
30
40
50
60
70
80 Latin America
PanamaHonduras
Barbados
Guatemala Trinidad
El Salvador
Dominican Republic
Paraguay
Costa RicaJamaica Colombia
Ecuador
Mexico
Chile
Uruguay
Bolivia
Peru
Fiscal Balance/GDP
Infla
tion
66
Fiscal balance/GDP
Source: International Monetary Fund.
Infla
tion
Figure 5.7bInflation and Fiscal Deficit
(Average over 1964-92, in percent)
-20 -15 -10 -5 0 5 10
0
5
10
15
20 Other developing countries
SingaporeMalaysia
Malta
Thailand
Congo
Morocco Cyprus
Ethiopia
Togo
India
Seychelles
Pakistan
Fiji
SenegalSri LankaNiger
Jordan
BangladeshCameroonMadagascar
Mauritius Korea
Egypt AlgeriaIndonesiaPhilippines
Kenya
Syria
Côte d'Ivoire
67
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.
68
Figure 5.8aInflation and Broad Money Growth(Average over 1964-92, in percent)
M2 growth
Source: International Monetary Fund.
Infla
tion
0 10 20 30 40 50 60 70 80
0
10
20
30
40
50
60
70
80 Latin America
PanamaHonduras
Barbados Guatemala
Trinidad
El Salvador
Dominican Republic
ParaguayCosta Rica
Jamaica
Colombia
Ecuador
Mexico
Chile
Uruguay
Bolivia
Peru
69
Figure 5.8bInflation and Broad Money Growth(Average over 1964-92, in percent)
Broad money growth
Source: International Monetary Fund.
Infla
tion
5 10 15 20 25 30
0
5
10
15
20 Other developing countries
Singapore
MalaysiaMalta
Thailand
Congo
Morocco
Cyprus
EthiopiaTogo
SeychellesIndia
Pakistan
Ivory Coast
Fiji
Senegal
Sri Lanka
Niger
Jordan
Bangladesh
Cameroon
Madagascar
Mauritius
KoreaEgypt
Indonesia
Algeria
PhilippinesKenya
Syria
70
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.
71
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.
72
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.
The Analytical Framework
. .(28)
73
Assuming that transfers are constant over time, real wealth is:
a = m + b + (y+)/r.
Demand functions for goods and money:
c = a, > 0
m = (-)a / i, > ,
i = (1 + )r + : net nominal interest rate;
= (1 - )r : rate of time preferences.
(29)
(30)
(31)
74
Equilibrium condition in the goods market:
c = y - g,
g: noninterest government spending. Government budget constraint:
m + b = g - y + (1-)(+rb) - m.
Dynamics of real money stock:
m = ( - )m,
M/M: rate of growth of nominal money stock.
(32)
(33)
(34)
. .
.
.
75
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,
* = .
~ ~
~
76
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-).
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.
Constant Primary Deficit
~
~
+
(38)
77
Substituting (34) in (33) yields
b = (1-)rb - m - zb,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.
.(39)
78
Since, from (34), m = m - m, (30) and (31) imply
m = [ + (1-)r]m + zm,
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).
.
.(40)
. .
79
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 - m(s)]e[( + (1-)r)t ],
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).
(41)s~ ~
80
From (30), (31), and (32),
= [(-)/] (y-g)m-1 - (1-)r, 0 < t < T.
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.
...
. +
+
(42)
81
Condition m = 0 is satisfied by adjusting discontinuously the rate of money growth at T so as to satisfy (40)
mT = 0 = [ + (1-)r]mT + zm.
Since m < 0 for 0 < t < T, (43) implies that must be raised above.
Since mT < 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.
.+
.
~
. ~ +
+
82
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.
+
+
83
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.
84
What happens if conventional deficit remains fixed, rather than the primary deficit?
Using (37), (38) is replaced by
d = g - y + (1-)(+rb).
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.
Constant Conventional Deficit
~(46)
85
Using (29) - (32), (34), and (46) yields
b = -nb - m + zb, zb (1-)(y+) - (y-g).
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.
.
(47)
.
86
Figure 5.9Steady-State Equilibrium with Constant Conventional Deficit
m = 0.
b = 0.
E
m
b
m(~ h
b(h~
Source: Adapted from Liviatan (1984, p. 13).
87
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).
. .
88
Figure 5.10Dynamics with Constant Conventional Deficit
M
B
E
A
C
m
E'
M
b
m(~ s
m(~ h
b(h~b(c~
b(s~
~m(c
Source: Adapted from Liviatan (1984, p. 14).
89
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 bT, B will represent a steady-state equilibrium.
During the transition period, real balances fall while the stock of bonds and rise.
+
90
However, at B real balances remain above their original equilibrium level m(h), 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).
~
91
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.
92
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.
93
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 (, ).
~
94
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.
95
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.
96
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.
97
Figure 5.11aFiscal Deficits and Real Interest Rates
Source: International Monetary Fund.1/ Bank deposit rates (rates offered to resident customers for demand, time, or savings deposits).2/ Government fiscal balance is calculated as the difference between Revenue and, if applicable, Grants Received, and Expenditure and Lending Minus Repayments.
1980 1984 1988 1992 1996-4
-3
-2
-1
0
1
2
0
-4 -10
-5
0
5
10
Korea
1980 1984 1988 1992 1996-20
-15
-10
-5
0
5
0
-20 -60
-50
-40
-30
-20
-10
0
10
20
Mexico
Real bank deposit rate, in percent per annum (right scale) 1/
Government fiscal balance, percent of GDP (left scale) 2/
98
Figure 5.11bFiscal Deficits and Real Interest Rates
Source: International Monetary Fund.1/ Bank deposit rates (rates offered to resident customers for demand, time, or savings deposits).2/ Government fiscal balance is calculated as the difference between Revenue and, if applicable, Grants Received, and Expenditure and Lending Minus Repayments.
1980 1984 1988 1992 1996-6
-5
-4
-3
-2
-1
0
1
2
-6 -40
-30
-20
-10
0
10
20 Philippines
1980 1984 1988 1992 1996-8
-6
-4
-2
0
2
4
6
-8 -10
-5
0
5
10
15 Thailand
Real bank deposit rate, in percent per annum (right scale) 1/
Government fiscal balance, percent of GDP (left scale) 2/
99
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.
100
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, and a government-indexed bond.
Expectations, Deficits, and Real Interest Rates
101
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.
102
Representative household maximizes discounted utility over an infinite horizon:
t
[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, > 0,
: coefficient of relative risk aversion.
(49)
103
Real financial wealth of the representative household:
a = m + b,
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,
r: real interest rate;
: lump-sum transfers from the government;
0 < < 1: proportional income tax rate.
(50)
(51).
104
Assume: taxes are levied on gross income at a uniform rate.
Using (50), (51) can be written:
a = (1-)a + (1-)(y+) - c - im,
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.
(52).
105
Optimality conditions:
c / m = i,
c / c = [(1-)r - ],
= 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.
.(54)
(53)
106
(53) can be written as
m = c/i.
This relates the demand for money inversely to i; positively to the level of transactions.
Nominal money stock must satisfy
M = D + ER,
D: stock of domestic credit (from central bank to government);
R: foreign-currency value of net foreign assets held by the central bank.
(56)
(55)
107
Changes in the real credit stock:
d = ( - )d,
: 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)
(57)
108
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. Using (55), equilibrium condition of money market can
be solved for the equilibrium nominal real interest rate:
i = i(c, m),
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.
.(59)
+ -(60)
109
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)
110
Dynamic system in c and m:
c
m=
ic im-1 0 m - m
c - c.
.~
~
r
m=
r m
-r -m m - m
r - r.
.
~
~
Dynamic system in r and m:
(62)
Since constant real stocks of domestic credit and bonds are normalized to zero, seigniorage revenue is m.
111
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 steady-
state 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.
..
112
r = 0.
Figure 5.12Steady-State Equilibrium with Zero Capital Mobility
E
m = 0.
r
S
S
mm~
113
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 SS, and begins rising along SS 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.
..
114
Figure 5.13Permanent and Temporary Increases in Government Spending
with Zero Capital Mobility
EE'
B
A
C
S'
S'
B'C'r = 0.
m = 0.
r
mm~
115
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 SS (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 BC.
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.
116
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 bT beyond period T.
+
117
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.
118
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.
119
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.
Deficits, Investment, and Crowding Out
120
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.
121
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.
122
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.
123
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.