A note on budget deficits, debt service payments, and interest rates

The QuarterlyReviewof lkon~mics and Fmce, Vol. 33, No. 4, Winter, 1993, pages 439-445 Copyright 0 1993 Trusteesof the Universityof Illinois All rightsof reproductionin any form reserved. ISSN 00335797

A Note on Budget Deficits, Debt Service Payments, and Interest Rates Richard J. Cebula and Rupert G. Rhodd Georgia Institute of Technology and Florida Atlantic International

The potential

impact

has been investigated 1984,

of federal

1985; Evans 1985,

Makin

1983; Mascaro

and Khan

1988).

budget deficits on interest

extensively

(Barth

and Bradley

1987; Feldstein

and Meltzer

and Eckstein

1983; McMillin

Most of these studies examine

short term interest rates, most commonly somewhat

differently,

attention

in the literature.

tional macroeconomics transmit because

nominal

This neglect

generally

the effect of federal the interest-sensitive

to variations decompose Bradley

in long-term

upon

components

Ostrosky

interest

rates.

have received

deficits upon only limited

in view of the fact that conven(not short term) interest

Furthermore,

of the budget

and cyclical

debt outstanding

None of this literature

rates This is

such as business are most sensitive

of this research

although components

has

a few studies (Barth

and

the deficit in terms of

(Dwyer 1982; Holloway

has attempted

to examine

1986;

the impact of

that is, no study has examined

impact of the deficit net of (less) debt service payments. analysis below, however, measuring

most

deficit,

1990) or define

the deficit after allowing for debt service payments, empirical

1990;

of private sector spending,

into its structural

in the real national

1986; 1987).

1986, 1987,

of budget

and new home construction,

1988; Barth et al. 1984; 1985; Ostrosky

the net change

1986;

budget deficits to the real side of the economy.

the N.1.P.A measure

the total deficit

is unfortunate

1983,

US Treasury bill rate. Stated

rates of interest

argues that long-term

outlays on new plant and equipment focused

1986; Ostrosky

the impact

States

Iden, and Russek

1970; Hoelscher

the three-month

long-term

rates in the United

1981; Barth,

As argued in the section

the on

the deficit thusly may be very appropri-

ate. This note seeks to add to the literature upon the nominal

long-term

interest

allow for debt service payments

referred

on the national

our insights into the deficit-interest

to above in two ways: (1) it focuses

rate; and (2) it adjusts the value of the deficit to debt. The analysis seeks to improve

rate relationship.

QUARTERLY REVIEW OF ECONOMICS AND FINANCE

440

THE MODEL To a large extent

paralleling

Hoelscher

(1983;

1986),

long-term

nominal

Barth

and Bradley

and Zahid

rate of interest

rium of the following

(1988),

(1989),

Barth

the model

as being determined

et al. (1984;

adopted

here

by a loanable

1985),

regards

the

funds equilib-

form: D-S=B-M-C

(1)

where: D= S =

real domestic

private sector demand

real domestic

private sector supply of long-term

for long-term

M=

real net purchases

of securities

B =

real net borrowing

by the federal

C =

real net capital flows into the nation from other nations.

The following

standard

behavioral

by the central

bonds

bonds

bank

government

relationships

are hypothesized:

D=D

(R,P,RSR),

DR>O,DP
(2)

S=S

(R,P,RSR),

SR < 0, Sp > 0, SRSR> 0

(3)

where: R=

the nominal

P=

the expected subscripts

It is hypothesized function

of the expected

(1986))

it is argued

the real demand more

real short-term

interest

that the higher

extensively

rate and where

the

partial differentiation.

is an increasing

smaller investors

(ex ante)

denote

rate

that, in accord with the standard

for bonds

decreasing

rate of interest

future inflation

the expected

RSR=

demand

long-term

funds model,

of the nominal

inflation

rate. In addition,

the expected

for long-term substitute

loanable

function

short-term

following

real short-term

ceteris @ibus.

bonds,

the real

rate of interest

and a

Hoelscher

rate of interest, That

the

is, as RSR rises,

bonds for long-term

bonds

in their

portfolios. It is also expected bonds is a decreasing Hoelscher

(1986),

rate, the greater

it is argued

the incentive

of new short-term

bonds,

supply of long-term Substituting

that, in accord function

with conventional

of the expected that the greater

for bond suppliers

R=R(P,RSR,B,M,C)

the real supply of

real short-term

to issue new long-term

function

2 and 3 into Equation

wisdom,

rate. Furthermore,

the expected

ceterh paribus. Therefore,

bonds is an increasing

Equations

inflation

it is hypothesized

following interest

bonds in lieu that the real

of RSR.

1 and solving for R yields: (4)

BUDGET DEFICITS, DEBT PAYMENTS, 8cINTEBEST BATES

441

The expected signs on the partial derivatives in Equation 4 are:

The first two signs are based upon the behavioral assumptions underlying Equations 2 and 3 above. Thus, it is expected that the nominal long-term interest rate is an increasing function of the expected inflation rate since bond supply increases and bond demand decreases when the expected inflation rate rises. Next, the sign on R~R should be positive because the real long-term bond supply increases and the real long-term bond demand decreases when the expected real short-term interest rates rises. Also, it is expected (in accord with the “conventional wisdom”) that interest rate should be, ceterisparibus, an increasing function of federal government borrowing. In other words, as conventional macroeconomic theory argues, as the federal govemment attempts to finance a deficit, it presumably generates upward pressure on the interest rate as it attracts funds to absorb its debt issuance. In the section of empirical analysis below, it is argued that the deficit should be measured net of debt service payments. Next, because of the fact that the central bank purchases of securities act to offset the effects of government borrowing, it is argued here that RM is negative. Finally, the expected sign on RC is negative to reflect the fact that net capital inflows from other nations act to absorb domestic issues and thereby to produce downward interest rate pressure.

EMPIRICAL ANALYSIS: THE NOMINAL LONGTERM RATE OF INTEREST Based upon the model summarized in Equations 4 and 5, we estimate the following quasi-reduced-form equation:

where: Et=

the nominal average interest rate yield in quarter t on ten-year US Treasury notes, expressed as a percent per annum;

ao’ P,=

constant term; the expected inflation rate in quarter t, expressed as a percent per annum;

R!SR=

the ex ante real average interest rate yield in quarter t on three-month US Treasury bills, expressed as a percent per annum;

BSY, =

the ratio of the seasonally adjusted total federal budget deficit in quarter t, net of (less) debt service payments on the national debt in quarter t, to the seasonally adjusted middleexpansion trend GNP in quarter t, expressed as a percent;

442

QUARTFSLY REVIEW OF ECONOMICS AND FINANCE MJY,

=

the ratio of Mt, which is defined as the average of the seasonally adjusted current

and preceding

market

instruments

quarters’

adjusted middle-expansion CJY,

=

States in quarter

trend GNP in quarter stochastic

CL= The model Zahid (1988)) of fixed because

is quarterly rates

(Bretton

expectations

inflation

rate in quarter rate

three-month

(P,)

capital into the

middle-expansion

Woods)

began

to collapse. Income

Next,

US Treasury

We end with 1985:4

Accounts

from Thies

in 1986.

(1986),

Variable P, represents

t. The variable RSR, is computed t from

Following

during which the system

the Economic Report of the President. The

from

expectations.

in quarter

1971%1985:4.

this is the quarter

the nominal

who generates

the averageexpected

by subtracting

average

interest

the expected rate yield

the

Specifically,

deficit

bills in quarter

variable

is defined

the deficit is defined

service payment

here

as nowhere

are reinvested

deficit per se effectively credit markets.

overstates

Focusing

accurately

because

to the extent

the magnitude

of net federal

borrowing

the net drain in billions

that deficits

of current

impose

dollars.

from the

may enable

on our credit

us to

markets.

The data to compute

B, were

from the Economic Rqboit of the President.

obtained

Following

Barth

M, is computed

and Bradley

by averaging

(1989))

moving

in the monetary loanable

funds in the economy.

et al. (1984))

adjusted

of credit

average is adopted

base to influence

data were obtained

Barth

the seasonally

values of the net acquisition

two-quarter

market

in order

banking

quarter

instruments

to allow adequate

system liquidity

M, is expressed

and Hoelscher

current

in billions

in billions

of current

(1983))

and preceding by the Fed. This

time for changes

and hence of current

from the Flow of Funds Accounts of the Federal

The C, data are also expressed

the supply of dollars. The M,

Reserve

GNP (YJ was obtained of current

dollars.

Hoelscher

this is because

from Holloway

In principle (1983;

1986))

(1986, Table 2) ; it too is expressed

following

Barth

and Holloway

it can be reasonably

argued

and Bradley

(1986))

(1989))

from trend

in billions

Evans

(1985;

we divide B,, M,, and Cr by Yr;

that the budget

and net capital flows should all be judged

System.

dollars and were obtained

the Flow ofFun& Accountsof the Federal Reserve System. The middleexpansion

actions,

that

in more US Treasury debt, the size of the current

on the deficit net of debt service payments

evaluate

B, is expressed

else in the literature.

here as the N.1.P.A federal budget deficit L%SS the debt

on Treasury debt. We follow this procedure

debt service payments

1987))

on

t (TBR,) . Both P, and TBR are expressed as per annum. TBR, was obtained from the Economic Report of the President.

a percent

Variable

adjusted

as a percent;

data (P,) were obtained

data on inflationary

inflation

of credit

to the seasonally

net flow of foreign

and initially covers the period

monthly

quarter

t, expressed

data for Rr were obtained

inflationary

System,

error term.

of the major revision of the US National

The

more

adjusted

t to the seasonally

we begin with 1971:4 because

exchange

Reserve

trend GNP in quarter t, expressed as a percent;

the ratio of the seasonally United

values of the net acquisitions

by the Federal

deficit,

monetary

policy

relative to the size of the economy.1

BUDGET DEFlClT!S, DEBT PAYMENTS, & INTEREST RATES Since

the federal

genous, its inclusion bias. Accordingly,

budget

Equation

nique, with the instrument

(lagged

two quarters),

President. In addition,

explains

adjusted

rate data were obtained

instruments

rate of the consumer

of the nominal

average interest

The criteria for choosing CPI,2

(CPI,2)

Equation

variable

variables,

(+lo.la)

DW = 1.71, where terms in parentheses

positive and statistically

significant

significant

using Ut_2, CPI,s

(7)

(-3.42)

DF = 50.

For example,

DW =

(+9.74)

1.72,

(net of debt service payments)

is

level. Thus, it appears exercises

a positive and

Rr in terms of other long-term

& as the nominal

average interest

+ 0.45B, /Yr - 2.03M,/Y, (+3.07)

coefficient

- O.lOC&

(8)

(-1.81)

(-1.55)

DF = 50. on variable

B/k’, is positive and

level, so that we infer once again that the deficit

exercises

rate of interest.

level. Of

on the deficit variable

(Mood,) ,3 the IV results are:

Rho = 0.10,

8, the estimated

at beyond the one percent

the expected

rate of interest.2

if we measure

bonds

exhibit

the one percent

coefficient

if we measure

corporate

(+4.06)

coefficients

the one percent

long-term

Mood, = 4.29 + 0.43P, + 0.83RSR,

long-term

(IV) technique,

at or beyond

at beyond

is also reached

yield on Moody’s Aaa-rated

nominal

parallel those of choosing

(net of debt service payments)

impact upon the nominal

This same conclusion

significant

lag

US Treasury notes (Three,*).

(-1.16)

7, all five of the estimated

budget deficit

As shown in Equation

and (2) the twoquarter

- 1.69M,/Y, - 0.2OC&

(+3.11)

is the fact that the estimated

rate measures.

respec-

lag of the

are t-values.

As shown in Equation

interest

P, and ES&,

yields:

Rho = 0.10,

signs, with four of the coeffkients

significant

Economic Rgbort of the

from the BusinRFs

6 by instrumental

(+5.32)

that the federal

the contempo-

Conditions Digest (March, was obtained from the Economic Report of the President.

as the instrumental

interest

the

as instruments

Rr = 2.16 + 0.59P, + O.SORSR, + 0.58B,/Y,

particular

is

rate of the

(1) the two-quarter

rate yield on three-year

was obtained

rate

with the lagged unemployment

of the variables

price index

CPI,p and Three,2

1989) ; variable Three,2 Estimating

(IV) tech-

of instrument

unemployment

from

have been adopted:

actual inflation

Ut_2 above. Variable

variables

the budget deficit, whereas

to allow for endogeneity

tively, two additional

is partly endo-

Ut_% The choice

terms in the system are not correlated

rate. The unemployment

and Three,2

using an instrumental

the fact that the lagged seasonally

error

payments)

the possibility of simultaneousequation

being the seasonally adjusted quarterly unemployment

civilian labor force systematically raneous

(net of debt service

6 is estimated

of the civilian labor force based upon

deficit

in the analysis introduces

443

a positive and significant

impact

upon

the

QUARTERLY REVIEW OF ECONOMICS AND FINANCE

444

CONCLUSIONS Within an open-economy

loanable-funds

framework, the impact of the US federal

budget deficit upon long-term interest rates has been investigated. Unlike the existing literature,

the deficit has been defined here as the N.I.P.A. budget deficit less debt

service payments. This focus on the deficit net of debt service payments is based on the idea that to the extent that debt service payments are reinvested in more US Treasury debt, the size of the total current deficit per se effectively overstates the magnitude of net federal government borrowing from the credit markets. The analysis has focused upon the nominal long-term interest rate, which has received only limited attention in the literature to date. The empirical

results imply that the federal budget deficit, net of debt service

payments, elevates the nominal long-term rate of interest. This finding has important implications. For example, to the extent that interest rates are higher in the U.S. than otherwise would be the case, the probability of “Third World” debt crises is elevated. In other words, higher interest rates in the U.S. will raise the cost of borrowing to Third World nations and thereby increase the likelihood of defaults by Third World nations on interest and debt payments. In addition, the evidence would imply, strictly from the U.S. perspective,

the existence

result of the budget deficit). slower capital formation

of crowding-out

In turn, the crowding

and slower economic

of private investment

out of private investment

(as a

implies

growth in the U.S. over the long run.

NOTES 1.

It should be noted that the conclusions derived below are basically unchanged if we

simply express Bt, Mt, and Ct in billions of constant dollars. 2.

It should be noted that a similar conclusion is reached ifwe do not subtract debt service

from the deficit, that is, if we replace Bt in Equation 6 with the tot&federal budget deficit (Dt) per se. The IV results are given by: Rt = 3.55 + 0.4OPt + 0.48RSRt + 0.41DJYt (+3.10)

(+4.80)

DW = 1.51,

(+2.90)

Rho = 0.24,

- 0.60MJYt

- 0.18CJYt

(-0.43)

(-2.30)

(9)

DF = 50.

with the time period studied being 19’71:4-1985:4. Dt is expressed in billions of current dollars and was obtained from the Economic Rqbort of the President. As shown above, the total budget deficit variable also exercises a positive and significant impact upon nominal longer-term interest rate. 3. Variable Moodt was obtained from the Economic Rtprt

of the President.

BUDGET DEFICI-IS, DEBT PAYMENTS, & INTERFST BATES

445

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