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____________ Review ____________
Vol. 66, No. 9




November 1984

5 Money Growth and the Size of the
Federal Debt
17 Depreciation , Inflation and Investment
Incentives: The Effects of the Ihx
Acts of 1981 and 1982
31 Interest Rate Variability: Its Link to the
Variability of Monetary Growth and
Economic Performance

T h e Review is p u b lis h e d 10 t im e s p e r y e a r b y th e R e s e a r c h a n d P u b lic In fo r m a tio n D e p a r tm en t o f th e
F e d e r a l R e s e r v e B a n k o f St. L ou is. S in g le-c o p y s u b s c r ip t io n s a r e a v a ila b le to th e p u b lic f r e e o f c h a r g e .
M ail r e q u e s t s f o r s u b s c r ip tio n s , b a c k iss u es, o r a d d r e s s c h a n g e s to : R e s e a r c h a n d P u b lic In fo r m a tio n
D ep a rtm en t, F e d e r a l R e s e r v e B an k o f St. L ouis, P.O. B o * 442, St. L ou is, M is so u ri 63166.
T h e view s e x p r e s s e d a r e t h o s e o f th e in d iv id u al a u th o r s a n d d o n o t n e c e s s a r ily r e fle c t o ffic ia l
p o s itio n s o f th e F e d e r a l R e s e r v e B an k o f St. L ou is o r th e F e d e r a l R e s e r v e S y stem . A r tic le s h e r e in m a y b e
r e p r in t e d p r o v id e d th e s o u r c e is c r e d ite d . P le a s e p r o v id e th e B a n k ’s R e s e a r c h a n d P u b lic In fo r m a tio n
D ep a rtm en t w ith a c o p y o f r e p r in t e d m a ter ia l.




Federal Reserve Bank of St. Louis
Review
N ov em b er 1 9 8 4

In This Issue . . .




T h e re ce n t an d prosp ectiv e rise in th e fed eral debt-GNP ratio h a s given rise to
c o n c e rn am on g e c o n o m ic analysts. In th e first article o f th is R eview , “M oney
Growth an d th e Size o f th e Fed eral D ebt,” K eith M. C arlson ex am in es th e im p o r­
ta n ce o f m oney grow th assu m p tio n s in th e a sse ssm en t o f th is ratio. Sim ulations
o f a m odified version o f th e St. Louis m od el are u sed to d eterm in e th e effect o f
alternative grow th p a th s o f M l on fed eral d eficits an d th e fed eral debt-GNP ratio.
T h e co n clu sio n derived from th e se sim u lation s is th at faster m o n ey grow th
m akes it easier to re d u ce bu dget d eficits. T h erefo re, p lan s to re d u ce d eficits over
tim e m u st b e co o rd in ated w ith m o n etary p o licy a ctio n s if th ey are to achieve th eir
d esired results. F urther, th e u sefu ln ess o f red u cin g d eficits via faster m oney
grow th m u st b e w eigh ed against th e resu ltin g a sso cia te d in flatio n aiy co sts.
In th e se co n d article, "D ep reciatio n , Inflation, an d In v estm en t In cen tiv es: T h e
Effects o f th e Tax A cts o f 1981 an d 1982,” M ack Ott ex a m in es th e relatio n b etw een
th e value o f ad d itions to b u sin ess cap ital eq u ip m en t an d p lan t an d th e A cceler­
ated C ost Recovery System (ACRS) en a cte d in 1981. ACRS h a s b ee n con trov ersial
sin c e its en a ctm e n t b ec a u se it red u ced effective co rp o ra te tax rates; it is a cen tra l
issu e in th e ad m in istra tio n ’s cu rren t tax reform prop osal.
P ro p o n en ts o f ACRS have argued th at th e low ered tax rates on cap ital in co m e
have raised th e rate o f in vestm en t an d th u s co n trib u te d to faster U.S. eco n o m ic
grow th, b u t critics claim th at in vestm en t actu ally h a s b ee n less rapid sin c e ACRS
w as en a cte d . Ott finds th at ACRS h as provided e n h a n c e d in vestm en t incentives,
red u ced th e bias against long-term in v estm en t in co m m ercia l an d in d u strial
stru ctu res an d sharp ly raised in vestm en t sin c e th e en d o f th e 1 9 8 1 -8 2 recessio n .
However, h e co n clu d e s th at a m a jo r force exp lain in g th e re ce n t strong rate o f
b u sin ess investm en t in th e U nited States h as b een th e sign ifican t d eclin e in th e
ex p e cted inflation rate. U nd er eith e r ACRS o r p rio r tax law, th e m assive d eclin e in
inflation w ould have h ad a significant positive im p a ct o n U.S. investm ent.
T h e grow th rate o f th e m on ey stock w as m u ch m o re variable in 1 9 8 0 -8 3 th a n in
th e previous 27 y ears. T h is g reater variability in crea sed b u sin ess cy cle risk, w h ich
w as reflected in a rise in th e variability o f lon g-term in tere st rates. In th e third
article in th is R eview , Jo h n A. T atom exp lain s th e links b etw een th e variability of
m o n ey grow th and th e variability o f in terest rates an d b etw een th e la tte r an d
e co n o m ic perfo rm an ce.
T atom d escrib es th e th eo retica l ch a n n e ls th rou gh w h ich an in crea se in risk
affects th e econom y, in clu d in g h ow it re d u ce s b o th th e d em an d for an d th e
su pply o f cu rren t goods an d services. He ex am in es th e effects o f th e variability of
in terest rates on GNP, th e p rice level and real o u tp u t u sin g a sm all red u ced -fo rm
m odel o f th e eco n o m y an d finds th at in crea sed risk re d u ce s sp en d in g an d output
an d raises p rice levels. M oreover, th e evid ence in d ica tes th at ch an g es in a n tici­
pated, rath er th a n u n a n ticip a ted risk, in flu en ce spen din g, ou tp u t an d p rices.
Specifically, T atom finds a su b stan tial negative effect from in crea sed risk on
b o th GNP and ou tp u t grow th over th e 1 9 8 0 -8 3 p eriod . In ad d ition, ch a n g es in risk
in 1 9 8 0 -8 3 acco u n t, in part, for tem porarily h ig h er in flation in 1 9 8 0 -8 1 and
tem porarily low er observed inflation in late 1982 an d 1983.

3




Money Growth and the Size of the
Federal Debt
Keith M. Carlson

F

-M- EDERAL d ebt h eld by th e p u blic (includ ing the
F ed eral Reserve System ) h as risen relative to GNP over
th e p ast 10 y ears, w ith m o st o f th e in cre a se o ccu rrin g
sin ce 1981 (see ch a rt 1). T h is re ce n t in crea se in the
federal debt-GNP ratio reverses a dow nw ard tren d
th a t h ad prevailed from th e en d o f W orld W ar II. F u r­
th erm o re, as o f early th is year, th e C ongression al
Budget Office (CBO) p ro je c te d th a t a co n tin u a tio n o f
cu rren t bu dget p o licies w ou ld lead to fu rth er rises in
th e debt-to-G N P ratio th rou gh 1989.
T h is ch an g e in tren d is view ed w ith c o n c e rn by
m o st ec o n o m ic analysts. A ccord in g to th e CBO:
Historical experien ce suggests that in creases and d e­
creases in federal debt relative to GNP have been a c­
com panied by approxim ately offsetting changes in
non-federal debt as a percentage o f GNP. Similarly,
growth trends in the federal debt-GNP ratio appear to
have been m irrored by opposite trends in the capitaloutput ratio.'

Should history re p eat itself, th e rising federal d ebtGNP ratio will p ro d u ce slow er e c o n o m ic grow th and a
low er stand ard o f living th a n w ould oth erw ise o ccu r.
T h e a ccu ra cy o f th e C BO ’s p ro je c tio n s d ep en d s, o f
cou rse, on h ow accu ra tely it is able to p red ict bo th
d eficits an d fu tu re GNP.2 Tw o p ro blem s m ake it dif­

Keith M. Carlson is a research officer at the Federal Reserve Bank of St.
Louis. Thomas A Pollmann provided research assistance.
'CBO (February 1984), part I, p. 75.
2For a critique of the procedures used by the CBO and the Office of
Management and Budget, see Klein (1984).



ficult to o b tain a cc u ra te p ro je c tio n s o f th e se tw o varia­
bles. First, th e s e variables are in terrelated ; c o n s e ­
quently, th e ir feed b ack effects m u st b e taken into
a c c o u n t. S e c o n d , a s s u m p tio n s a b o u t th e fu tu re
co u rse o f m o n eta iy p o licy are cru cia l to th e analysis;
different a ssu m p tio n s w ill p ro d u ce w idely vaiying
p ro jectio n s o f b o th fu tu re d eficits an d future GNP.
T h e p u rp o se o f th is a rticle is to exam in e th e im p o r­
ta n ce o f m o n eta iy p o licy a ssu m p tio n s in th e a ss e ss ­
m en t o f th e fed eral debt-GNP ratio. To aid in th is ex ­
am ination, sim u latio n s from a m odified version o f a St.
Louis-type m od el are u sed in co n ju n c tio n w ith a
m od el o f bu d g et an d d ebt d eterm in atio n . B eca u se th is
m od el is sensitive to ch a n g es in m o n ey grow th, it ca n
b e u sed to d eterm in e th e effect o f alternative m o n eta iy
p o licies on th e federal debt-GNP ratio.

A FRAMEWORK FOR ANALYSIS
T h e role for m o n eta iy p o licy in th e d eterm in atio n o f
strategic bu dget variables ca n b e d escrib ed w ith th e
aid o f a sc h e m a tic d iagram (see page 6). F or a given tax
stru ctu re an d set o f outlay program s, th e e co n o m ic
variables — real GNP, u n em p loy m en t, th e p rice level
an d in terest rates — im p in g e stron gly to d eterm in e
th e bu d g et o u tco m e in a given period .3 T h e se varia­
bles, in tu rn, are affected by th e grow th o f th e m on ey
stock. T h e size o f th e fed eral d eb t h eld by th e p u b lic
3 this diagram, the connection between economic variables and
ln
budget variables is predominantly in one direction, reflecting primar­
ily the results of previous econometric studies.

5

FEDERAL RESERVE BANK OF ST. LOUIS

NOVEMBER 1984

A Schematic Diagram of Budget Determination

relative to GNP is a co n v en ien t w ay o f su m m arizing
bu dget policy u n d e r a set o f e c o n o m ic assu m p tio n s
over a period o f y ears.
W ith the aid o f th is sc h e m a tic diagram , th e key vari­
ables can be id entified easily. T h e m odel m u st b e c a ­
pable o f tracing a path throu gh tim e for real GNP, the
p rice level (GNP deflator) an d in tere st rates. Given the
re sp o n ses o f receip ts and outlays, a tim e p ath for th e
fed eral d ebt ca n b e derived. T h en , to exp lo re w h eth er

6


th e federal d ebt grow s explosively over tim e, th e size
o f th e debt ca n be co m p a red w ith GNP.

Summary o f the Model
T h e m odel u sed in th is article is an au gm en ted
m o n eta iy m od el.4 (For details, see a p p en d ix A.) T h e
key featu re o f the m o d el is th at n o m in al GNP is d eter4For further details on its properties, see Carlson and Hein (1983).

FEDERAL RESERVE BANK OF ST. LOUIS

NOVEMBER 1984

C h a rt 1

Federal Debt Held by the Public as a Percent of GNP

m ined by cu rren t an d lagged values o f th e m oney
stock (M l); in o th e r w ords, fiscal variables w ere not
found to be sign ifican t in th e d eterm in atio n o f GNP."1
GNP is th en divided b etw een o u tp u t an d p rices via a
p rice eq u ation . T h e GNP d eflator is sp ecified as a fu n c­
tion o f cu rren t an d lagged values o f th e relative p rice of
en erg y, d em a n d p re s s u r e an d a n tic ip a te d p rice
ch an ge. T h e 10-year T re a su iy b o n d rate is a fu n ctio n
o f past inflation. T h e 3 -m o n th T re a su iy bill rate is a
fu n ctio n o f cu rren t and lagged values o f ch an g es in
output an d prices.
T h e budget p ortion o f th e m od el c o n sists o f an o u t­
lays eq u ation an d a re ceip ts equation.'1 T h e se eq u a­
5
This specification contrasts with that used in Carlson and Hein in
that federal expenditures are omitted. For empirical support, see
Hafer (1982).
6
For further detail, see appendix B. See Carlson (1983) for further
discussion of these equations.



tion s d ep en d on a given outlay program an d a set of
tax law s, respectively, as w ell as th e grow th o f real GNP
an d inflation. In terest pay m en ts are sp ecified as a
fu n ctio n o f th e tw o in terest rates in th e m odel, the
p ortion o f th e bu dget d eficit fin a n ced by th e public,
th e size o f th e fed eral d eb t an d th e am o u n t o f debt
m aturing w ithin a y ear. Several o th e r bu dget id en tities
are specified to g en erate ad d ition al variables an d to
clo se th e m odel so th at it ca n b e solved.

Properties o f the Model
T h e p r o p e r tie s o f th e m o d e l a re m o n e ta ris t.
C hanges in th e grow th rate o f m o n ey ch a n g e th e
grow th o f n om in al GNP quickly, w ith th e full effect
achieved w ithin five quarter's. Initially, th is ch an g e in
n om in al GNP is tran slated in to a ch a n g e in output
(real GNP) b eca u se p rice s resp o n d to ch a n g es in

7

FEDERAL RESERVE BANK OF ST. LOUIS

m on ey grow th w ith a m u ch lo n g er lag th a n nom in al
GNP d oes. T h e 3-m on th T re a su iy bill rate resp o n d s to
a ch an g e in m o n ey via its effects on o u tp u t an d p rices.'
T h e T re a su iy bo n d rate, on th e o th e r hand, resp o n d s
m ore slow ly to m o n ey b ec a u se it d ep en d s only on
past prices.
Over th e lo n g er run, th e effects o f a ch an g e in m o n e­
tary grow th are reflected only in n o m in al variables,
th at is, n om inal GNP, inflation an d n om in al in terest
rates. T h e ach iev em en t o f full a d ju stm en t to a steadystate grow th p ath takes abou t 30 y ears. F o r th e fivey ea r tim e h o rizo n u sed by th e governm en t for budget
analysis, o u tp u t grow th is still in flu en ced by m o n ey
grow th; th at is, th e stead y-state eq u ilibriu m h as not
y et b ee n attain ed . T o gain m o re in sight into th e future
p ro sp ects for th e budget, th e m od el is sim u lated to its
stead y-state equilibriu m , w h ich o cc u rs aro u n d 2015.
T h is longer-ru n p ersp ectiv e y ield s co n clu sio n s that
differ from th o se th at resu lt from focu sin g on th e c o n ­
ventional five-year bu dget h orizon .

THE BUDGET EFFEC T S FOR
ALTERNATIVE MONETARY PO LICIES:
1 9 8 4 -8 9
E ach y ea r th e CBO provides a set o f estim ates th at it
calls "baselin e p ro jectio n s." T h e se are p ro jectio n s of
w hat fed eral re ceip ts and outlays w ould be if cu rren t
law s an d prog ram s w ere to co n tin u e for th e n ext five
y ears. In o th e r w ord s, d esp ite th e u se o f th e term
"p ro jectio n s," th e se are n o t forecasts o f th e bu dget;
they are m ean t to be u sed as b ase lin e estim ates
against w h ich p ro p o sed ch an g es in tax law s and
sp en d ing program s can be m easu red and assessed .
In th e p ro cess o f prep arin g th e se estim ates, th e CBO
develops a set o f ec o n o m ic a ssu m p tio n s* T h is is a
n ecessary part o f th e p ro cess b ec a u se re ceip ts and
outlays d ep en d cru cially on ec o n o m ic co n d itio n s. Re­
ceip ts d ep en d , o f co u rse, on taxable in co m e and sales
w h ich, in turn, d ep en d on inflation and real grow th.
Similarly, outlays also are in flu en ced by real growth,
m ainly via u n em p loy m en t, an d inflation, sin ce a large
n u m b er o f p rogram s are no w in d exed to th e co st o f
living. In terest on th e federal d ebt obviously d ep en d s

’ Normally a third effect is included — a liquidity effect. However,
using quarterly data the effect of contemporaneous changes in the
growth rate of money was not found significant.
8
For further discussion of the role of economic assumptions in the
budgeting process, see Carlson.

8


NOVEMBER 1984

on th e level o f in terest rates as w ell as th e size o f th e
deficit an d th e a m o u n t an d m aturity stru ctu re o f o u t­
stand ing debt.
T h e CBO 's 1984 rep ort on th e bu dget is particularly
bleak.9 A ccord in g to th e C BO ’s b a se lin e estim ates, th e
federal d eficit will co n tin u e to grow in d ollar term s
th rou gh ou t th e 1 9 8 4 -8 9 period . Even w h en scaled
against a grow ing GNP, th e CBO co n c lu d e s th at the
"deficit p ro je c tio n s are obviously alarm ing.""’ As su m ­
m arized in th e ratio o f federal d eb t to GNP, th e b a se ­
lin e p ro jectio n s in d ica te th at th e sh arp in cre a se in th e
ratio in 1 9 8 2 -8 3 will co n tin u e th rou gh th e 1 9 8 4 -8 9
period.

Economic Assumptions
To asse ss th e validity o f th e C BO ’s co n clu sio n s, th e
m on etary m od el w as sim u lated u sin g th ree different
m on etary scen a rio s — 4, 6 an d 8 p e rce n t grow th of
M l. T h e se th ree alternative m o n ey grow th a ssu m p ­
tion s p ro d u ced alternative p ath s for real grow th, in ­
flation an d in terest rates.
Table 1 su m m arizes th e C BO ’s b a se lin e p ro jectio n s
an d th e sim u lation s by th e m o n etary m od el. A lthough
th e CBO ’s p ro je c tio n s are derived u n d e r th e a ssu m p ­
tion th at m on ey grow th will b e 6 p ercen t, th e ir results
are n ot gen erally co n sis te n t w ith th o se o b tain ed from
th e m on etary m o d el u sin g 6 p e rce n t grow th in m oney.
In p articular, th e C BO ’s estim a te o f th e d o llar level of
n om in al GNP in 1989 falls ab o u t halfw ay b etw een the
resu lts from sim u latio n s u sin g 4 p e rce n t an d 6 p e r­
ce n t m o n ey grow th.
T h e d ifference b etw een th e C BO ’s p ro je c tio n s and
th e m on etary m o d el's sim u lation s tra n sla tes prim arily
into a d ifference in th e p ro je c tio n s for o u tp u t. T h e
CBO ’s p ro jecte d level o f real GNP for 1989 lies below
that g en erated by th e m od el u sin g 4 p e rce n t m on ey
grow th. T h e ir relatively low p ro je c tio n s o f o u tp u t tend

9
CBO (February 1984), part II. The analysis in this article (for both the
CBO and the administration) is based on reports prepared in Febru­
ary 1984. Since then the CBO has prepared new baseline estimates
(CBO, August 1984) and the administration has released its MidSession Review of the Fiscal Year 1985 Budget (OMB, August 15,
1984). The February estimates are used here because of their
comparability; both the baseline estimates and the administration
estimates are prepared on the basis of common CBO assumptions.
Such comparability is not available for the August estimates. How­
ever, examination of the CBO’s revised baseline estimates indicates
that the conclusions are not materially affected. The estimates de­
veloped in this article are meant to serve as illustrations rather than
precise projections.
,0CBO (February 1984), part II, p. 6.

FEDERAL RESERVE BANK OF ST. LOUIS

NOVEMBER 1984

Table 1
Economic Variables: Model Simulations vs. CBO Baseline1
1984

1985

1986

1987

1988

1989

$3763
(13.9)
3778
(14.3)
3793
(14.8)
3651
(10.3)

$3968
(5.4)
4045
(7.1)
4123
(8.7)
3995
(9.4)

$4254
(7.2)
4430
(9.5)
4609
(11.8)
4339
(8.6)

$4563
(7.3)
4852
(95)
5153
(11.8)
4704
(8.4)

$4893
(7.2)
5313
(9.5)
5761
(11.8)
5084
(8.1)

$5247
(7.2)
5819
(9.5)
6441
(11.8)
5481
(7.8)

Real GNP (billions of 1972 dollars)
M = 4%
$1669
(8.7)
M = 6%
1675
(9.2)
M = 8%
1682
(96)
CBO
1618
(5.4)

$1707
(2.3)
1737
(3.7)
1768
(5.1)
1685
(4.1)

$1762
(3.2)
1817
(4.6)
1874
(6.0)
1744
(3.5)

$1823
(3.5)
1891
(4.1)
1964
(4.8)
1805
(3.5)

$1882
(3.2)
1952
(3.2)
2031
(3.4)
1866
(3.4)

$1937
(2.9)
1998
(2.4)
2072
(2.0)
1927
(3.3)

232.5
(3.3)
232.9
(3.3)
233.2
(3.4)
237.3
(5.1)

241.5
(3.9)
243.8
(4.7)
245.9
(5.4)
248.9
(4.9)

250.3
(3.6)
256.5
(5.2)
262.3
(6.7)
260.6
(4.7)

259.9
(3.8)
272.2
(6.1)
283.7
(8.2)
272.3
(4.5)

270.8
(4.2)
291.2
(7.0)
310.8
(9.6)
284.0
(4.3)

GNP (billions of dollars)
M = 4%
M = 6%
M = 8%
CBO

GNP Deflator (1972 = 100)
M = 4%
M = 6%
M = 8%
CBO

Treasury Bill Rate (percent)
M = 4%
M = 6%
M = 8%
CBO
Treasury Bond Rate (percent)
M = 4%
M = 6%
M = 8%
CBO

225.5
(4.7)
225.5
(4.7)
225.5
(4.7)
225.8
(4.7)

9.6%
9.8
9.9
8.9

12.4%
12.4
12.4
11.7

8.8%
9.4
10.0
8.6

11.1%
11.1
11.2
11.2

7.5%
8.6
9.8
8.4

6.6%
8.2
9.8
8.2

6.2%
8.2
10.1
8.0

9.7%
9.9
10.2
11.0

8.9%
9.5
10.1
10.9

9.6
10.6
10.8

8.4%

6.1%
8.4
10.6
7.8

8.1%
9.8
11.4
10.6

'Percent change in parentheses. Simulations begin in 111/1984; thus, 1984 reflects actual economic performance in the first half.

to in crease th e ir estim ates o f th e baselin e deficit; th eir
estim ates o f outlays are h ig h er an d th e ir estim ates of
receip ts are low er. T h e C BO ’s p ro je c tio n s o f th e p rice
level, on th e o th e r hand, are qu ite clo se to th e m o d el’s
sim ulation using 6 p e rce n t m on ey grow th.
T h e d ifferences in in terest rate p ro jectio n s are c o m ­



pared at th e bo tto m o f table 1. T h e C BO ’s p ro jectio n s
o f th e T rea su ry bill rate are co n s is te n t w ith th e
m o d el’s sim u lation s u sin g 6 p e rce n t m o n ey grow th.
T h e C BO ’s p ro je c tio n s o f th e T reasu ry bo n d rate, on
th e o th e r hand , are n o t; in stead , th ey resem b le m ore
clo sely th e m o d el’s resu lt u sin g 8 p e rce n t m on ey
grow th. Even using th at co m p ariso n , how ever, the

9

FEDERAL RESERVE BANK OF ST. LOUIS

NOVEMBER 1984

Table 2
Budget Variables: Model Simulations vs. CBO Baseline
(billions of dollars)
1984
Receipts
M = 4%
M = 6%

1985

1986

1987

1988

1989

$ 678
680
682

$ 749

$ 788
822
857
795

$ 852
914

$ 921
1017
1121

$ 987

663

761
773
733

$ 930
928
926
941

$ 998
997

CBO

$ 860
860
859
866

Surplus
M = 4%

$-182

$-182

$-210
-174

M = 8%
CBO
Outlays
M = 4%
M = 6%
M = 8%

M = 6%
M = 8%
CBO

-180
-177
-203

Debt
M = 4%
M = 6%

$1306
1303

lit=8%
CBO

1301
1327

-168
-153
-207

$1487
1470
1453
1533

C BO ’s p ro jectio n s are generally h ig h er th rou gh o u t the
perio d ."
H igher in terest rate estim ates w ill p ro d u ce h ig h er
estim ates o f th e d eficit. F u rth erm o re, th ere is a cru cial
cum ulative effect — hig h er in terest rates add to th e
cu rren t deficit, w h ich carries over to fu tu re y ears in
th e form o f larger d ebt th at m u st b e fin an ced .

Simulating the Monetary Model with
CBO's Baseline Estimates
T able 2 su m m arizes th e m o d el's sim u lation o f re ­
ceip ts an d outlays an d co m p ares th em w ith th e CBO's

"The CBO projects a continuation of the large disparity between
interest rates and inflation rates that has been observed recently.
The monetary approach assumes implicitly that interest rates even­
tually will return to levels consistent with past relationships with
inflation.

10


995
1025

-138
-229

$1696
1643
1590
1761

979
863

1122

945

1273
1016

$1071

$1157

$1245

1075
1078
1125

1172
1185
1240

1281
1309
1355

$-219

$-235

$-259

-161
-98
-261

-155
-64
-294

-159
-36
-338

$1914

$2148
1957

$2406
2115
1785
2652

1803
1688
2021

1750
2314

estim ates. T h e C BO ’s estim a ted re ceip ts are slightly
m ore th an th e m o d e l’s estim a tes u sin g 4 p e rce n t
m o n ey grow th. By 1989, th e C BO ’s estim a te o f receip ts
is $106 billion b elo w th at g en erated by th e m od el u s ­
ing 6 p ercen t m on ey grow th. T h e co m p o sitio n o f GNP
is in stru m en tal in p ro d u cin g th is resu lt. B eca u se the
CBO h as a relatively low estim ate o f real grow th, th eir
estim ate o f th e grow th o f re ceip ts is also low er.
T h e CBO 's estim ated outlays are w ell above the
h igh est estim ate derived from th e m od el. T h is differ­
e n c e again reflects th e relatively low level o f o u tp u t
that th e CBO p ro jects. As a result, outlays for u n e m ­
ploym ent co m p en sa tio n an d th e am o u n t o f d eficit to
be fin an ced are h ig h er as is th e C BO ’s estim a te for th e
in terest rate on T reasu ry b o n d s. D ifferen ces in fore­
ca sts for in terest rates ca n a ccu m u la te quickly into
h ig h er d eficits via th e ir effect on outlays. T h e m od el
sim u lates in terest p aym en ts u sin g an eq u atio n esti­

FEDERAL RESERVE BANK OF ST. LOUIS

m ated over a sam p le period o f 19 5 5 -8 3 (see ap p en d ix
B). T h e CBO d oes n o t estim ate a sin g le-in terest pay ­
m ents eq u atio n ; in stead , its estim ates are based on a
d etailed analysis o f th e co m p o n e n ts o f th e federal
d eb t.'2
W hen th e m o d el’s estim ates o f re ceip ts an d outlays
are co m bin ed , th e resu lting bu dget p ictu re is less
b lea k th a n th e C B O ’s p r o je c tio n s in d ic a te . T h e
m o d el’s surplus/deficit p ro jectio n s sh ow clearly th at
the size o f th e p ro jecte d d eficit is very sensitive to the
rate o f m on etary grow th assu m ed . W ith 4 p ercen t
m oney grow th, th e d eficit in crea ses in d ollar am ou n ts
th rou gh 1989; how ever, th e rise is sm aller th a n w hat
th e CBO p ro jects. W hen 6 p e rce n t m o n ey grow th is
assu m ed , th e budget deficit slow ly d eclin es. W ith even
m ore rapid m oney grow th, th e bu d g et m oves tow ard
su rp lu s after 1989, but, o f co u rse, inflation also is m ore
rapid.
P erhaps th e m ost d ram atic d ifference b etw een the
C BO ’s p ro jectio n s an d th o se o b tain ed from th e m od el
ap p ears w hen th e tim e p ath s for fed eral d ebt h eld by
the p u blic are co m p ared . T h e cum ulative effect o f defi­
cits over six y ears g en erates a p u b lic debt o f $2,406
billion w ith 4 p e rce n t m o n ey grow th, $2,115 billion
w ith 6 p e rce n t m o n ey grow th, and $1,785 billion w ith 8
p e rce n t m oney grow th. B eca u se th e CBO p ro jects
h ig h er d eficits for every y e a r th a n d oes th e m odel,
federal d ebt held by th e p u blic rises to $2,652 billion in
1989 u n d er th e CBO p ro jectio n s.

Simulating the Monetary Model with the
Administration’s Budget
Given th e m o d el’s sim u lations, eith e r the budget
situ ation or th e outlook for inflation is bleak. A lthough
th e situ atio n p ro je c te d by th e m o n etary m od el is not
quite as bad as that see n by th e CBO, th e broad c o n ­
clu sio n s about co n tin u in g large budget d eficits are
generally th e sam e. To d eterm in e w hat m ight be re­
quired to prevent co n tin u ed large deficits, th e ad m in ­
istra tio n ’s budget, as p rep ared in February 1984 and
recalcu lated w ith th e C BO ’s e c o n o m ic assu m p tio n s, is
su b je cted to th e sam e ex ercise u sed in the previous
s ectio n .’3

1 For further discussion of the CBO’s procedures, see CBO (Septem­
2
ber 1984).
,3OMB (February 1984), and CBO (February 1984), An Analysis of the
President's Budgetary Proposals tor Fiscal Year 1985.



NOVEMBER 1984

T h e ad m in istratio n 's budget for 198 5 -8 9 , su m m a­
rized in table 3, ca n b e co m p a red w ith th e CBO b a se ­
lin e estim ates in table 2. Note th at th e ad m in istration
prop osed m o d est in cre a se s in revenues, am oun tin g to
only an ad d ition al $23 billion in 1989. A ccord ing to the
CBO ’s analysis o f th e a d m in istratio n ’s budget, th e p ro ­
posed revenue in cre a se s stem from th e follow ing:
(1) taxation of health insurance prem ium s;
(2) "structural reform" proposals, mainly in the form of
lim itations on tax-exem pt leasing and on private-purpose tax-exem pt bonds; and
(3) restrictions on tax shelters and on accounting and
corporate tax abuses.

T h e p ro p o sals are n o t m ajo r; th e CBO estim a tes that
by 1 9 8 7 -8 9 prim ary reven u es w ould b e in creasin g
only at a slightly fa ste r rate th an th e CBO baselin e
estim ates, 8.8 p e rce n t vs. 8.5 p ercen t.

W ith regard to outlays, th e ad m in istratio n program
is som ew h at m o re a m b itiou s; outlays are p ro je c te d to
be $62 b illion less th an th e C BO ’s b aselin e estim ate by
1989. T h e a d m in istra tio n ’s program p ro p o ses c o n sid ­
erable ch a n g e in th e co m p o sitio n o f fed eral spending.
For 1989, relative to th e C BO ’s b a selin e p ro jectio n s,
d efen se sp en d in g w ou ld b e $11 billion higher, en title­
m en t program s w ould b e $15 b illion low er, n o n d e ­
fen se d iscretio n ary sp en d in g w ould b e $17 billion
low er, "offsetting re ceip ts" w ould b e h ig h er by $6 bil­
lion and n et in terest w ould b e low er by $10 billion.
Although th e se d ifferences do n o t ap p e a r large, the
ad m in istratio n 's estim a te for prim ary outlays for th e
1 9 8 7 -8 9 period w ould b e in creasin g at a 7.1 p e rce n t
rate, w h ich co m p a res w ith th e CBO 's b a selin e e sti­
m ate o f an 8.9 p e rce n t rate o f in crea se.

T h e sim u lation resu lts for th e m od el using ad m in is­
tration estim ates are su m m arized in table 3. W hen
co m p ared w ith table 2, th e co n to u rs o f th e d eficit to
GNP ap p ear little different, esp ecially in th e early
y ears. C loser in sp e c tio n reveals that, for a given m on ey
growth, th e ad m in istratio n program m oves eith e r to ­
w ard su rplu s o r tow ard a sm a ller d eficit by 1989. T his
show s how relatively sm all ch a n g es in th e grow th
rates o f re ceip ts an d outlays ca n alter significantly th e
outlook for th e d eficit an d th e federal debt, even by
1989. It is to be n oted , how ever, that th e p ro sp e cts for
th e d ebt im prove in co n ju n c tio n w ith an inflationary
m onetary policy.

11

FEDERAL RESERVE BANK OF ST. LOUIS

NOVEMBER 1984

Table 3
Budget Variables: Model Simulations vs. Administration
Budget (billions of dollars)1
________
1984

1985

1986

1987

1988

1989

$ 680
682
684

$ 757
769
781
741

$ 800
835
870
807

$ 866
929
995
878

$ 940
1037
1143
964

$1009
1147

$1002
1000
999
1028

$1067
1070
1073
1119

$1132
1148
1160
1212

$1193
1227
1254

866

$ 937
935
933
947

Surplus
M = 4%
M = 6%
M = 8%
Admin.

$-178
-176
-173
-201

$-181
-166
-152
-206

$-202
-166
-129
-221

$-200
-141

$-192
-110
-17

$-184
-80
47
-254

Debt
M = 4%

$1302

$1482

1300
1297

1465
1448
1529

$1682
1629

$1882
1769
1653
1990

Receipts
M = 4%
M = 6%
M = 8%
Admin.

665

1301
1039

Outlays
M = 4%
M = 6%
M = 8%
Admin.

M = 6%
M = 8%
Admin.

$ 858
857
857

1326

1576
1749

-78
-241

-248

$2073
1879
1669
2237

1293

$2255
1958
1622
2490

'Administration's February budget as estimated using CBO’s economic assumptions.

THE BUDGET EFFEC T S FOR
ALTERNATIVE MONETARY PO LICIES:
THE LONGER-TERM
T h e previous co m p ariso n s d em o n strate th at th e
m o n eta iy m od el y ield s sm aller d eficit estim ates th an
th o se u sin g th e CBO b aselin e p ro jectio n s. T h e ch ie f
co n clu sio n from th e sim u lation s derived from th e
m od el is th at faste r m o n ey grow th w ill p ro d u ce
sm aller d eficits up to 1989.1
4
B eca u se pu blic d iscu ssio n o f th e effects o f future
d eficits su ggests that they are co n c e rn e d w ith period s

,4This result suggests that a goal of a balanced budget is meaningless
unless there is an explicit accounting for monetary growth. No at­
tempt is made here to assess the costs and benefits of aiming
toward a balanced budget. What is clear is that the specification of
such an objective requires a consideration of the possible accompa­
nying inflation and variations in the rate of real growth.

12


o f tim e lo n g er th a n five y ears, an d b ec a u se th e m od el
d oes n ot re a ch its full eq u ilibriu m in five y ea rs tim e, it
is inform ative to carry on w ith th e sim u lation th rou gh
tim e. To m ake a co m p a riso n p o ssib le b etw een th e
CBO 's analysis an d th e m o d el’s sim u latio n s for th is
lo n g er period, b o th th e C BO ’s b a se lin e estim a tes for
p rim aiy re ceip ts an d outlays an d th e a d m in istra tio n ’s
estim ates w ere ex ten d ed beyon d 1989 at th e ir average
grow th rates for th e 1 9 8 7 -8 9 period . T h is provided
sufficient inp ut for th e m odel to co n tin u e th e sim u la­
tion s past 1989. T h e m o d el w as sim u lated throu gh
2015, w h en it re a ch es stead y -state equilibrium .

Long-Term Simulations o f CBO
Baseline Estimates
C hart 2 su m m arizes th e sim u lation resu lts u sin g
th e m odel an d th e CBO b a selin e p ro jectio n s for th e
full period. B eca u se d ollar a m o u n ts are gen erally dif-

NOVEMBER 1984

FEDERAL RESERVE BANK OF ST. LOUIS

C h a rt 2

Federal D ebt H eld by the Public as a Percent of G N P
Sim ulation Results U sing CBO Baseline Estimates
Percent
300

Percent
300

A n n u a l D a ta

250

250

200

200

M *= 4%

150

150

...•-***

100

......

.....

M = 6°
/
o
....
......

19 84

I
86

I
88

90

I
92

I
94

96

I
98

ficult to in terp ret m eaningfu lly w h en co n sid ere d over
long tim e p eriod s, th e resu lts for th e federal d ebt are
p resen ted relative to GNP.
C hart 2 yield s a su rp rising resu lt. Here, federal debt
held by th e pu blic, ex p ressed relative to GNP, rises
w ith ou t lim it for 4 and 6 p e rce n t m o n ey grow th. Only
w ith 8 p e rce n t m o n ey grow th d o es th e d ebt ap p ear to
eventually d eclin e relative to GNP.
W hy th e d ifference in th e sh o rt-ru n and long-run
resu lts? Isolating th e re aso n s for th is d ifference re ­
quires d etailed exam in ation o f th e tim e re sp o n se o f
receip ts and outlays to real grow th, in flation an d in ter­
est rates. T h e n atu re o f th e lo n g -term re su lts reflects
prim arily th at outlays resp o n d m ore slow ly to in ­
flation th an re ceip ts do. In ad d ition, b ec a u se it takes
tim e for th e d ebt to bu ild up in re sp o n se to deficits,
th e cu m u lative effect o f d eficits takes th e form o f in ­
c r e a s e d o u tla y s. T h e s e d elay s a re fu rth e r c o m ­



I
2000

^_-

M = 8%

50

I

100

I
02

04

I
06

50

II

I
08

10

12

I|

I

2014

p o u n d ed b ec a u se inflation resp o n d s m ore slow ly to
m on ey grow th th an o u tp u t does.

Long-Term Simulations o f the
Administration's Budget
C hart 3 su m m arizes th e lo n g -term sim u lation s o f
th e a d m in istra tio n ’s b u dget. H ere th e d ifferen ces from
th e 1 9 8 4 -8 9 h o riz o n are also striking.
Using 4 p e rce n t m o n ey grow th, th e sim u lation s
sh ow only a m o d est upw ard drift in th e fed eral d ebt as
a p e rce n t o f GNP over th e 30-year p erio d . W ith 6 an d 8
p e rce n t m on ey grow th, d eb t d eclin es relative to GNP
an d is eventually elim in ated , resu ltin g in a n e t cred ito r
position for th e fed eral gov ern m en t.”

1Currently, because the federal government borrows more than it
5
lends, it is a net debtor. Simulations showing the government as a
net creditor are only meant to be illustrative. They should not be
construed as forecasts.

13

FEDERAL RESERVE BANK OF ST. LOUIS

NOVEMBER 1984

C h a rt 3

Federal D e b t Held by the Public as a Percent of G N P
Sim ulation Results U sin g Adm inistration Budget

SUMMARY
T h ere is a d eveloping co n se n su s th at budget defi­
cits are grow ing at d isquieting rates. T o exam ine the
likelihood o f future deficits, a m o n etary m o d el w as
exp an d ed to in clu d e th e d eterm in atio n o f bu dget vari­
ables. Key bu d g et variables w ere re calcu lated using
th e CBO 's b ase lin e estim ates an d th e ad m in istratio n 's
February 1984 bu dget. T h e se sim u lation resu lts in d i­
cate th at th e p ro sp e cts for a b alan ced budget d ep en d
on th e tim e p ath o f m o n etary grow th. In particular,
achieving a b a la n ced bu d g et is facilitated by faster
m on ey grow th.
A n other co n c lu sio n th at derives from th is stud y is
th at a five-year p lan n in g h o rizo n seem s too sh o rt to
jud ge w h eth er a p articu lar set o f p o licies is really re­
d ucin g th e se q u e n ce o f future d eficits. B eca u se o f th e
lag stru ctu re b etw een p o licy variables and e co n o m ic
variables, a d ecad e o r m ore m ight be n ecessa ry before
th e full im p act o n d eficits ca n b e d iscern ed .
T h e ch arts an d tab les in th is article sh o u ld n o t sug­
gest th at co n sid erab le p re cisio n is p o ssib le in the

14


p rep aratio n o f b u d g et estim a tes — esp ecially th o se for
a far d istan t p eriod . T h e sim u lation s are m ea n t to be
illustrative; th ey are co n d itio n e d by a large n u m b er of
assu m p tion s, n o t th e least o f w h ich is th e m od el c h o ­
sen to derive th e sim u lation s. N evertheless, th e m a jo r
co n clu sio n sta n d s: th e lon g-term p ro c e ss o f red u cin g
bu dget d eficits is difficult, b u t possib le. In particu lar,
receip ts an d outlays d ep en d on key ec o n o m ic varia­
bles like real grow th, inflation an d in terest rates; th ese,
in turn, d ep en d cru cially on th e rate o f m o n etary e x ­
p an sion . T h u s, fiscal p lan s to re d u ce d eficits over tim e
m u st b e co o rd in a ted w ith m o n etary p o licy a ctio n s if
th ey are to be su cce ssfu l; an y c h o ice o f d eficit re d u c­
tion via faster m o n ey grow th m u st b e a ssessed in c o n ­
ju n ctio n w ith th e p o ssib le inflationary co sts involved.

REFERENCES
Carlson, Keith M. "The Critical Role of Economic Assumptions in
the Evaluation of Federal Budget Programs," this Review (October
1983), pp. 5-14.

NOVEMBER 1984

FEDERAL RESERVE BANK OF ST. LOUIS
Carlson, Keith M., and Scott E. Hein. "Four Econometric Models
and Monetary Policy: The Longer-Run View," this Review (January
1983), pp. 13-23.
Congressional Budget Office. The Economic Outlook, A Report to
the Senate and House Committees’ on the Budget — Part I (U.S.
Government Printing Office, February 1984).
Congressional Budget Office. Baseline Budget Projections for Fiscal
Years 1985-1989, A Report to the Senate and House Committees
on the Budget — Part II (GPO, February 1984).
Congressional Budget Office. An Analysis of the President’s Budg­
etary Proposals for Fiscal Year 1985, prepared at the request of the
Senate Committee on Appropriations (GPO, February 1984).

Congressional Budget Office. The Economic and Budget Outlook:
An Update, A Report to the Senate and House Committees on the
Budget (GPO, August 1984).
Congressional Budget Office. Federal Debt and Interest Costs, Spe­
cial Study (GPO, September 1984).
Hafer, R. W. 'The Role of Fiscal Policy in the St. Louis Equation,"
this Review (January 1982), pp. 17-22.
Klein, L. R. 'The Importance of the Forecast," Journal of Forecasting
(January-March 1984), pp. 1-9.
Office of Management and Budget. Budget of the United States
Government: Fiscal Year 1985 (GPO, February 1984).
Office of Management and Budget. Mid-Session Review of the 1985
Budget (GPO, August 15,1984).

Appendix A
A Monetary Model
T h e m od el u sed for sim u latio n s o f th e eco n o m ic
variables is su m m arized below . A d ot over a variable
in d ica tes co m p o u n d ed an n u al rate o f ch an g e. M ost

eq u atio n s are estim ated w ith Alm on co n stra in ts on
th e co efficien ts. A bsolute values o f t-sta tistics are in
p a ren th eses.

(1) GNP equation

(4) Treasury bond rate equation

Sample period: I/1960-IV/1981

Sample period: I/1960-IV/1983

4

20

RL, = 2.88 + .96 2 P ,,
(1.96) (3.75) i = 0

Y, = 2.67 + 1.14 2 M,_,
(2.601 16.30) i = 0
R: = .36

SE = 3.65

DW = 2.11

R2 = .13

SE =

.51

DW = 1.77

p = .95

(5) GNP identity
Y, = (P,/100) X,

(2) Price equation
Sample period: 1/1960—
1V/1983
4
P, =

(6) Dem and pressure definition
5

.87 + .14 2 PE, , + .09 2 IX,., - XF*)
12.30)
i= 1
(5.80) i = 0
+

(7) Price anticipations definition

1.11 PA,
(12.35)

R2 = .72

21

PA, = .96

SE = 1.41

DW = 2.01

Sample period: I/1960-IV/1983
10

10

.55 2 X,_, + .99 2 P,_,
(3.28) i = 0
(6.45) i = 0

R- = .15

SE =




.90

DW = 1.90

p = .91

2 P,„
i= 1

p = .15

(3) Treasury bill rate equation

RS, =

XF* = ( (XF/X,_,r - 1) •100

Y
M
P
PE
X
XF
RL
RS

=
=
=
=
=
=
=
=

nom inal GNP
m oney stock (Ml)
GNP deflator (1972 = 100)
relative price of energy
output in 1972 dollar's
potential output (Rasche-Tatom )
Treasury bond rate
Treasury bill rate

15

FEDERAL RESERVE BANK OF ST. LOUIS

NOVEMBER 1984

Appendix B
Budget Model
To estim ate th e effect o n bu dget p ro jectio n s o f an
a lte rn a tiv e s e t o f e c o n o m ic a s s u m p tio n s , th e
follow ing b u d g et variables w ere estim ated :
1) primaiy receipts: total receipts minus earnings
of the Federal Reserve System
2) primary outlays: total outlays minus net interest
3) net interest
T h e b a sic so u rce for estim ates o f th e relevant
elasticities w ere estim ates p u b lish ed by th e CBO
(February 1984), Part I. Net in terest w as estim ated
using fiscal y e a r d ata for 1955—
83.

Net interest
T h e estim atio n form o f th e n et in terest eq u a ­
tion w as derived from th e follow ing eq u atio n :
i, = i,( - is; + S")j + ii, -

^ - 1 ^ +
D ,-,

i,.,

M ,_ ,

w here
I,
= n et in tere st in fiscal y e a r t
i,

= average y ield on 3 -m o n th T reasu ry bills
an d 10-year T reasu ry b o n d s in y ea r t

T h e im p lied co efficien ts for receip ts as derived
from estim ates p rep ared by th e CBO w ere:

S,1

= bu dget su rp lu s in fiscal y e a r t = SJ’ — I, +

A Rf = .75 A X, + .81 A X,_, - .01 A X,_, + .26 A X,_3

S|
'

= prim ary su rp lu s in fiscal y e a r t

tt|
k

= earn in gs o f th e F ed eral R eserve System in
fiscal y e a r t

S”

= fin a n cin g from o th e r th a n b o rro w in g
from th e p u b lic in fiscal y e a r t

D,

= fed eral d ebt h eld by th e p u b lic in fiscal
y ea r t

M,

= average len gth to m aturity o f fed eral debt
(in years) at en d o f fiscal y e a r t

Primary receipts

+ .14 X,_4 + .21 X,_s + .75 A P, + .36 A P, ,
+ .02 A P, , + .16 A P,

< K

- .06 A P, 4 + .13 AP, -

w here
ARf

= deviation o f p e rce n t ch an g e in prim ary
re ceip ts from b a se lin e estim ate in fiscal
year t

AX,

= deviation o f p e rce n t ch an g e in real GNP
from b a se lin e estim ate in y e a r t

AP,

= deviation o f p e rce n t ch an g e in GNP defla­
to r from b a se lin e estim ate in y ea r t

Primary outlays
T h e im p lied co efficien ts for outlays as derived
from estim ates p rep ared by th e CBO w ere:
A Of = .25 AX, + .06 A X,_, + .03 A X, , - .03 A X,.:,
+ .01 A X,_4 - .02 A X,_, + .00 A P, + .39 A P, ,

T h e first term on th e righ t-h an d sid e rep resen ts
borrow ing from th e p u b lic in th e cu rre n t fiscal year.
T h e seco n d term is an ap p roxim ation o f th e ch an g e
in in terest co st d ue to refin an cin g m atu rin g debt.
T h is eq u ation w as solved for I, in th e form sh ow n
below . Sin ce it is an ap p roxim ation , th e eq u ation
was estim ated using d ata from 1 9 5 3 -8 3 :

+ .21 A P,_, + .14 A P , + .00 A P,_4 + .15 AP,.,

where
A Of = deviation of percent change in primary
outlays from baseline estimate in fiscal
year t


16


RJ = .99

SE = 2.05

DW = 1.95

p, = -.34

p, = .17

Depreciation; Inflation and
Investment Incentives: The Effects
of the Tax Acts of 1981 and 1983
Mack Ott

T

M . HREE y ears after its en actm en t, controversy still
su rro u n d s th e E co n o m ic Recovery T ax A ct o f 1981
(ERTA) an d its su cce sso r, th e Tax Equity and Fiscal
R esponsibility Act o f 1982 (TEFRA). On th e o n e hand,
th e Reagan ad m in istratio n claim s that th e 1981 tax
red u ctio n s su bstan tially in creased U.S. b u sin ess in ­
vestm en t an d co n trib u te d to th e strong recovery from
th e 1 9 81-82 re c e s sio n 1. On th e o th e r hand , so m e c o m ­
m en tato rs argue th at th e tax red u ctio n s have failed to
in crea se b u sin ess investm en t.2 M oreover, o th e r critics
o f ERTA argue that, alth o u g h investm ent h as in ­
creased , it h as d o n e so in an u n b alan ced fashion: too
few re so u rces are going into plant, w hile too m any are
going into p ro d u ce rs’ d urable eq u ip m en t.3 O m itted
alm ost en tirely from th e d ebate over th e effectiveness
o f th e tax red u ctio n s h as b een th e in d ep en d en t im ­
p act o f the re ce n t disinflation. T h at is, to w hat exten t
w ould investm ent have b een in creased sim ply by th e
d eclin e o f th e inflation rate an d how d o es su ch an
in flu en ce co m e about?
T h is article develops th e fou n d ation for assessin g
th ese issu es. First, th e ec o n o m ics o f d ep reciatio n d e­
d u ctio n s is d iscu ssed . Seco n d , d ep reciatio n a c c o u n t­
ing is reviewed. Third, th e legislatively en acte d effects
of ERTA an d TEFRA are set forth. Follow ing this, the
relation o f U.S. cap ital investm ent to d isto rtion s in
d ep reciatio n an d inflation during th e last th ree d e­

Mack Ott is a senior economist at the Federal Reserve Bank of St.
Louis. Paul G. Christopher provided research assistance.
'Economic Report of the President (1984), p. 34.
2 example, see Editorial, Washington Post, April 22, 1984.
For
’Greenhouse (1984).



cad es are review ed. In e a c h o f th e se step s, th e p a rtic­
u lar im p act o f a d eclin in g inflation rate is exam in ed to
w eigh its relative im p o rta n ce in ch an g in g th e invest­
m ent in cen tives d ue to d ep recia tio n d ed u ctio n s from
taxable in co m e.

THE ECONOMICS OF DEPRECIATION
DEDUCTIONS
In th e co u rse o f an y b u sin ess activity, eq u ip m en t
an d p lan t gradually are co n su m ed : eq u ip m en t w ears
out from u se o r b e co m e s o b so lete an d m u st b e re­
p laced ; stru ctu res d eteriorate, u ltim ately requiring
renovation o r d em o litio n an d re co n stru ctio n . C o n se­
quently, d ep recia tio n is a n orm al ex p en se o f b u sin ess
activity and, like o th e r n orm al ex p e n ses — w ages and
salaries, in su ra n ce p rem iu m s, u tilities an d m aterial
co sts — is d ed u cted from gross revenu es to d eterm in e
taxable in co m e.4

7Wo Types o f Depreciation:
Physical Deterioration and
Economic Obsolescence
An in h e ren t d ifference b etw een d ep recia tio n an d
o th e r d ed u ctib le b u sin ess ex p en ses, how ever, is that
d ep reciatio n ca n b e d eterm in ed on ly im plicitly; o th er

"From the institution of the federal income tax with the sixteenth
amendment to the Constitution in 1913, depreciation has been an
allowable deduction in computing taxable income. Under the Reve­
nue Act of 1913, taxpayers were allowed to deduct "a reasonable
allowance for the exhaustion, wear and tear of property arising out of
its use or employment in the business." Internal Revenue Service
(Vol. 1971-2), C.B. 504.

17

FEDERAL RESERVE BANK OF ST. LOUIS

ex p en ses ca n b e su b stan tiate d exp licitly by s u ch p o si­
tive d o cu m en tatio n as invoices.
Tw o d istin ct types o f e c o n o m ic value lo ss are cov­
ered by d ep reciatio n : First, th ere is th e obvious d eteri­
oratio n d ue to u se w h ic h le sse n s th e rem ain in g value
in p ro d u ce rs’ d urable eq u ip m en t an d stru ctu res. T h e
rate o f su ch d eterio ration is difficult to estab lish o b je c ­
tively b e c a u se w ear an d te a r o n a given type o f eq u ip ­
m e n t o r stru ctu re m ay o c c u r at different rates in dif­
feren t ap p lication s. Seco n d , th e re is th e eco n o m ic
value th at is lo st w h en e ith e r a n im proved m a ch in e is
developed — th at is, b e tte r quality o f output, faster
rate o f o u tp u t o r m o re frugal in its in p u t u se for a given
ou tp u t rate — o r a ch an g e in th e relative p rices o f an
in p u t (such as energy) o cc u rs th a t requ ires a ch an g e in
p ro d u ctio n te ch n iq u e s an d eq u ip m en t design. Al­
th ou gh th e e c o n o m ic lo ss d ue to o b so le sce n c e is obvi­
ously difficult to p red ict, it h as b ee n a te n et o f b u si­
n e s s in c o m e ta x p r o c e d u r e s r e s u lt in g in th e
acceleratio n o f d ep reciatio n sin c e w ell b efo re th e ex ­
plicit ad op tion o f a cc e le ra te d d ep reciatio n a c c o u n t­
ing sy stem s in 1954.5
To estab lish an ex p licit b asis for d e p reciatio n ex­
p en ses, th en , th e taxing au th ority co u ld eith e r allow
ea ch firm to estim ate its ow n cu rre n t d ep reciatio n
ex p en ses or provide g u id elin es in th e form o f so m e­
w h at arbitraiy sch e d u les o f allow able p e rce n ta g e d e­
d u ctio n s. F o r th e first 20 y ears o f th e fed eral in co m e
tax, individuals w ere given th e freed om to d eterm in e
th e ir ow n d ep reciatio n allo w an ces su b je ct to IRS re ­
view. T h e U.S. tax c o d e n ow prim arily takes th e seco n d
ap p roach .6

Elements o f Depreciation
T h e re are th ree elem e n ts o f d ep reciatio n exp en sin g
im plied by th e foregoing d iscu ssio n , only tw o o f w h ich
are exp licit in th e d ep reciatio n sch e d u les: First, th ere
is th e len gth o f tim e, th e a s s e t’s tap life, over w h ich

5
See Internal Revenue Sen/ice, p. 505.
6For example, the original IRS Bulletin F of 1920, which set forth
depreciation guidelines, clearly allowed the freedom to choose (and
imposed the burden to substantiate) depreciation deductions both
for deterioration and obsolescence:
The Bureau does not prescribe rates to be used in computing deprecia­
tion and obsolescence, as it would be impractical to determine rates
which would be equally applicable to all property of a general class or
character. For this reason, no table of rates is published. The rate
applicable and the adjustment of any case must depend upon the actual
conditions existing in that particular case. (Internal Revenue Service, p.
505, note 13.)

From 1934 onward, however, this procedure was tightened in large
part due to the declining prices of replacement capital. In response to
criticism (and proposed legislative action), the Treasury switched to a

http://fraser.stlouisfed.org/
18
Federal Reserve Bank of St. Louis

NOVEMBER 1984

th e asset, fo r tax p u rp o ses, is a ssu m ed to d eterio rate.7
Secon d , th e re is th e p a ttern o f d ed u ctio n s; th is c o m ­
p o n en t d eterm in es th e a c c e le r a t io n o f th e d ep recia ­
tion sch ed u le, w h ich varies from eq u al d ed u ctio n s in
ea ch p erio d — n o a cc e le ra tio n — to pro p o rtio n ally
large in itial-p erio d d ed u ctio n s, w h ich d eclin e a cc o rd ­
ing to sp ecified a cco u n tin g p a tte rn s over th e a s s e t’s
tax life. Third, th e re is th e p ro b lem o f h o w to treat
s c r a p o r salvage value. Given th e d ifferen ces in d eterio ­
ration th at exist in different a p p licatio n s, th is problem
w ould exist even if tax life an d useful life w ere equal.
In general, tax lives are sh o rte r th a n th e durability
im plied by th e rate o f p h y sical d eterio ration so th at
scrap value — m ore p articularly, after-tax scrap value
— is a p ro b lem for all cap ital u sers. M oreover, th e
lo n g er th e p h y sical life o f a n a sset, th e m ore u n certa in
its scrap value; te ch n o lo g ica l advance, ch a n g es in rela­
tive p rices o f in p u ts o r evolution in u se p attern s m ay
m ake th e m arket value at d isp osal m u ch le ss th a n th e
value im p lied by its rem ain in g p h y sical life given its
original p u rch a se p rice . F o r exam p le, a 30-year-old
ind u strial bu ild in g m ay b e phy sically so u n d bu t o f
little value b e c a u se o f a ch a n g e in regional in d u strial
use, d em o g rap h ic ch a n g es o r a shift in tran sp o rtatio n
m eth od s.
Th erefore, b o th th e sh o rten in g o f tax lifetim es and
th e a ccelera tio n o f d ep recia tio n d ed u ctio n s ca n b e
eco n o m ically ratio n alized as app roxim ating th e a c­
tual w ear an d o b s o le s ce n c e p a tte rn s o f a ssets. M ore­
over, as d iscu sse d in th e n ex t sectio n , a ccelera tio n
m ay offset a n a s s e t’s rising re p la cem e n t c o st d ue to
inflation, th o u gh th e m o re prag m atic ratio n alization
usually ad vanced is th at a ccelera tio n o r sh o rte n ed tax
lives provide in d u ce m en ts to in v estm en t.8 In an y case,

procedure requiring substantial documentation to support the opera­
tional as opposed to the procedural validity of depreciation deduc­
tions. Ibid, p. 505.
7 least since 1956 (and perhaps as early as 1942), the Internal
At
Revenue Code's provisions for depreciation have been moving from
a physical concept of asset life to a useful life, where the latter is
intended to accord with business practice rather than a potential
period of use. Ibid., p. 506. In general, the useful life would be shorter
than physical life due to obsolescence, optimizing of salvage value
and the benefits of replacing the asset when its net economic value of
output, while still positive, declines below that of a replacement asset.
8For example, President Kennedy argued that the shortening of tax
lives by 30-40 percent in 1962 (by an administrative not a legislative
procedure) was justified in spite of the large revenue loss because of
the investment impact:
Business spokesmen who have long urged this step estimate that the
stimulus to new investment will be far greater — perhaps as much as
four times greater — than the $1.5 billion [revenue loss] made available.
In any event, it is clear that at least an equal amount will go into new
income producing investment and eventually return to the Government
in tax revenues most, if not all, of the initial costs. Ibid., p. 507.

NOVEMBER 1984

FEDERAL RESERVE BANK OF ST. LOUIS

Depreciation Accounting Methods
S tra ig h t lin e — A nnual d ed u ctio n o f 1/N o f original
value o f asset, w h ere N is tax life o f asset.
D eclin in g b a la n c e — A nnual d ed u ctio n o f a sp e ­
cified (a) m u ltiple o f 1/N o f rem ain ing (i.e., u n d e p re­
ciated asset value). M ost co m m o n form s are 150
p ercen t, 175 p ercen t, and 200 p e rce n t d eclin in g
balan ce. Sin ce th is form u lation o f th e d ep reciatio n
d ed u ctio n takes a fractio n o f th e d eclin in g b alan ce
ea ch period, its d ed u ctio n s w ould never a cc u m u ­
late to th e total value o f th e asset. H ence, th e tax
co d e allow s a sw itch over to straight lin e at any
tim e; th e m axim izing sw itchover p o in t (N*) is
N* = 1-HN (— )];

w h en N* is n o t an integer, th e sw itchover o cc u rs at
th e next year. T h u s, th e o ptim al sw itch over for a 15y ea r asset u n d e r 200 p e rce n t d eclin in g b alan ce is
y ea r 8, for 175 p e rce n t d eclin in g b a la n ce it is y ea r 7,
an d for 150 p e rce n t d eclin in g b a la n ce it is y e a r 5.
To illu strate th e ch an g eo ver to straight line, c o n ­
sid er a 10-year asset w ith an original p u rch a se p rice
o f $1,000. T h e d ed u ctio n s u n d e r 150 p e rce n t d e c lin ­
ing b alan ce w ould b e as show n in th e table.
Note thafc if th e straig ht-line d ed u ctio n w ere u sed
in th e fou rth year, it w ould b e sm aller th an the
150 p e r c e n t d e c lin in g b a la n c e d e d u c tio n —
(1/7MS614.12) = $87.73 vs. $92.12; conversely, if the
150 p e rce n t d eclin in g b a la n c e d ed u ctio n w ere

th e co n co m ita n t gain at d isp ositio n o f th e fully d ep re­
ciated asset, scrap value, is treated as ordinary in co m e
to th e taxpayer.9

DEPRECIATION ACCOUNTING
T h e 1954 tax co d e explicitly au th o rized a variety of
a ccelerated d ep reciatio n acco u n tin g m e th o d s: su m of
th e y e a rs’ digits an d variations on d eclin in g b ala n ce
m eth o d s.1 T h e se m eth o d s are d escrib ed in th e ac0

9
Economic Recovery Tax Act of 1981, p. 188.
1As early as 1946, there was recognition that declining balance
0
depreciation could bring accounting practice closer to the deteriora­
tion and obsolescence rates implicit in business organization; how


Annual Deductions for Depreciation for a
$1,000,10-Year Asset under Various
Depreciation Methods
SL

150 DB

200 DB

SYD

1
2
3
4
5
6
7
8
9
10

$ 100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00

$ 150.00
127.50
108.38
92.12
87.00
87.00
87.00
87.00
87.00
87.00

$ 200.00
160.00
128.00
102.40
81.92
65.54
65.54
65.54
65.54
65.54

$ 181.81
163.63
145.45
127.27
109.09
90.91
72.73
54.54
36.36
18.18

Total

$1,000.00

$1,000.00

$1,000.00

$1,000.00

Year

NOTE: Columns may not add to total due to rounding.

taken in y e a r 5, it w ould b e sm aller th an the
straig h t-lin e — (1.5)(1/10)($522.00) = $78.30 vs.
$87.00.
S u m o f th e y e a r s ' d ig its — A nnual d ed u ctio n is a
d eclin in g fractio n o f th e a sse t's value; th is fraction
is th e ratio o f th e n u m b e r o f y ea rs rem ain ing in the
asset 's tax life at th e beg in n in g o f th e tax y ea r to the
sum o f th e y ea rs (1 + 2 + 3 + ... + N) in th e a s s e t’s tax
life. For a sse ts w ith a tax life o f six y ears o r m ore,
SYD w as th e m o st a ccelera ted d ep recia tio n sc h e d ­
ule allow ed in th e tax co d e p rio r to th e en a ctm e n t
o f ERTA in 1981.

com p anyin g in sert. A ssum ing th at tax life an d useful
life are equal, th e im p a ct o f a ccelera ted d ep reciatio n
a cco u n tin g is to retu rn th e in v ested cap ital to th e firm
earlier in th e a s s e t’s life th a n u n d e r straight-line d e­
p reciation , th ereb y red u cin g th e im p act o f inflation.
As a result o f th e h ig h er d ep recia tio n d ed u ctio n s, the
taxable p ro p o rtio n o f th e a s s e t’s in co m e is red u ced .

ever, in contrast to the 1954 tax code which allowed the taxpayer to
use declining balance methods, the 1946 IRS ruling imposed the
burden of proof on the taxpayer:
The declining balance method of computing depreciation would be
approved for federal tax purposes, provided it accorded with the method
of accounting regularly employed in the books of the taxpayer and

resulted in reasonable depreciation allowances and proper reflection of
net income for the taxable year or years involved. [Emphasis added],
Internal Revenue Service, p. 505, note 14.

19

FEDERAL RESERVE BANK OF ST. LOUIS

NOVEMBER 1984

C h a rt 1

Rem aining D epreciable V a lu e C om pared w ith
Rem aining Economic V a lu e
D o l la r s

D o l la r s

Year

This raises th e p re se n t value o f th e a s s e t’s an ticip ated
after-tax in co m e stream relative to its p rice. C o n se­
quently, in creasin g d ep reciatio n d ed u ctio n s sh o u ld
in d u ce a h ig h er rate o f investm en t, all o th e r thin gs th e
sam e.1
1
G raphically, th is early retu rn o f cap ital can b e see n
in ch a rt 1 w h ere th e rem ain ing u n d e p re cia ted value o f
an a sse t w ith a 10-year tax life is displayed. T h e u n d e ­
p recia ted o r rem ain ing value is sh ow n for fou r d ep re­
ciatio n acco u n tin g m e th o d s: straight lin e (SL), 150 p e r­

"The theoretical foundations for this exist in a variety of sources: Hall
and Jorgenson (1967) is the classic reference and Nelson (1976)
provides a clear exposition of the issues most germane to this
article. Auerbach (1983) surveys the literature on corporate finance
as it relates to taxation and the cost of capital. Kopke (1981) ad­
dresses the choices confronting tax policymakers regarding the
most effective form of tax reductions to stimulate investment.

http://fraser.stlouisfed.org/
20
Federal Reserve Bank of St. Louis

ce n t d eclin in g b a la n ce (150 DB), 200 p e rce n t d eclin in g
b alan ce (200 DB) an d su m o f th e y e a rs’ digits (SYD). As
a ben ch m ark , th e rem ain ing ec o n o m ic value — th e
a sset's initial value le ss cu m u la te d d eterio ration — is
also plotted ; eco n om ically , th e asset is a ssu m ed to
d eteriorate at an ex p o n en tia l 10 p e rce n t rate — th at is,
in inverse p ro p o rtio n to its original u seful life. Note
th at th e d ep recia tio n sc h e d u le s all provide fo r a n e a r­
lier retu rn o f cap ital th a n w arran ted by ph y sical d e te ­
rioration alon e. T h is o cc u rs for tw o rea so n s: First,
sin ce th e p h y sical d eterio ra tio n is a fra ctio n o f th e
d eclin in g b a la n ce, it w ill never co n su m e th e asset;
th ere will alw ays exist a positive scra p value.1 In co n 2

t2lf an asset's economic deterioration is proportional — e.g., geomet­
ric or exponential — it will always have a scrap or salvage value at
the end of any finite period. For example, if the asset’s output
deteriorates at a rate 8 , 0 < 8 < 1, and has a tax life N = 1/8, then the

NOVEMBER 1984

FEDERAL RESERVE BANK OF ST. LOUIS

C h a rt 2

The Im pact of Inflation on Rem aining Economic V a lu e
D o l la r s

D o l la r s

Year

trast, d ep reciatio n sch e d u les are d esign ed to exh au st
th e a s s e t’s value over its tax life. Seco n d , th e a c c e le r­
ated sch e d u les take a larger p o rtio n o f d ep reciatio n
earlier th an d o es th e a s s e t’s d ecay rate.

scrap value per dollar of initial value (S) will be about 3/8:
N

S = 1 - / 5„-«dt

0

N
= 1 - ( - e-s*i ), 8 = 1/N

0
= e-6 = e-'
"
= .368.

This inverse relation of depreciation and tax life holds for a variety of
assets under the ADR system — for example, autos (8 = .333,
N = 3), railroad equipment (6 = .066, N = 15) and metal working
equipment (8 = .1225, N=7.8). Gravelle (1982), table 1, p. 8. Even
when 8>1/N, however, there will be a positive scrap value. For
example, aircraft (8 = .1818, N = 9.2) and office, computing and ac­
counting equipment (8 = .2729, N-7.0) have 8s about twice the recip­
rocal of their respective Ns for which S would be about 1/8: S = e-“
= e-2= .135.



D espite th e a p p aren t e x cess o f d ep recia tio n over
eco n o m ic d ecay d ep icted in ch art 1, a ccelera ted d e ­
p reciatio n a cco u n tin g is in su fficien t to provide for re ­
p la cem en t if th e rate o f inflation is high en ou gh . C hart
1 im plicitly assu m es a zero inflation rate in th at e c o ­
n o m ic d ecay is d isp layed relative to a h isto rica l p u r­
ch a se p rice.
C hart 2, draw n w ith th e rem ain in g value a d ju sted
for an inflation rate o f 9 p ercen t, illu strates th e im pact
o f inflation on th e relatio n o f e c o n o m ic an d a c c o u n t­
ing m easu res o f d ep recia tio n . T h is h a s th e effect o f
pivoting e a c h o f th e a cco u n tin g d ep recia tio n profiles
co u n te r-clo ck w ise a ro u n d th e z ero -tim e in tercep t
d ue to th e rising n o m in al p rice o f th e rep la cem en t
asset relative to its h isto rica l n o m in al p u rch a se p rice.
At a 9 p e rce n t inflation rate, th e $1,000 p u rch a se p rice
o f th e asset w ill rise to $2,367 over its 10-year tax life.
C on sequen tly, at an y p o in t in th e a s s e t’s 10-year tax
life, a sm aller p o rtio n o f th e real re p la cem e n t co st (the
e co n o m ic rem ain ing value) is recov ered w ith a high

21

FEDERAL RESERVE BANK OF ST. LOUIS

inflation rate (chart 2) th a n w ith a zero inflation rate
(chart I).1
3

INFLATION DISTORTIONS IN
DEPRECIATION SCHEDULES AND
THE CHANGES DUE TO ERTA
AND TEFRA
To evaluate th e co m b in ed effects o f a cc elera ted d e­
preciation , inflation, scrap value an d sh o rte n ed tax
lifetim es, w e first exam in e th e d ep reciatio n sch e d u les
applied to asse ts u n d e r th e a ssu m p tio n th at tax lives
an d eco n o m ically u seful lives are equal. In th is exam i­
nation, p re sen ted in table 1, th e relative ad eq u acy of
d ep reciatio n d ed u ctio n s is asse ssed for asse ts o f 3-, 5-,
10-, 15- and 30-year d urabilities. T h e table also in c o r­
porates o n e final co m p licatio n — th e in vestm ent tax
credit.
Sin ce 1962, th e investm en t tax cred it (ITC) h as been,
in effect, a seco n d form o f a cc elera ted cap ital retu rn in
the tax co d e. In p rin cip le, b e c a u se it is a retu rn of
cap ital at th e en d o f th e a s s e t’s initial tax year, ITC
au gm ents th e d ep reciatio n d ed u ctio n ; ad ju stin g for
its bein g a cred it ra th e r th a n a d ed u ctio n ca n b e a c ­
co m p lish ed by dividing by th e tax rate.1
4
E ach entry in table 1 is th e su m o f th e real p resen t
d isco u n ted value o f th e tax -d ed u ctio n equivalent of
th e in vestm ent tax cred it p lu s th e d ep reciatio n d e­
d u ctio n s p lu s th e after-tax a n ticip ate d p ro ceed s from
th e sale o f th e asset (scrap value) in ratio to th e p re sen t
d isco u n ted value o f th e re p la cem e n t co st o f th e asset.
A real after-tax in tere st rate o f 3 p e rce n t w as u sed in
the co m p u ta tio n s.1 T h e en tries are co m p u ted over a
5

,3The inflation effect is symmetric: rising prices lower the value of
depreciation deductions and falling prices raise it. Consequently, it
is not surprising that in 1934, during a period of sustained deflation,
legislation was introduced in Congress to lower depreciation allow­
ances. Internal Revenue Service, p. 505, note 10.
1 For the first two years after its introduction, the depreciable base of
4
an asset was reduced by the credit; from 1964 to 1982, no such
reduction was required. In 1982, the enactment of TEFRA has
restored a reduction in the depreciation base — by 50 percent of the
credit. ITC is currently 10 percent of the asset’s price in the case of
equipment with a tax life of five years or more and 6 percent for
shorter-lived equipment; structures, generally, are not eligible for
ITC, although some equipment associated with structures and cer­
tain low-income housing does qualify. Tax Equity and Fiscal Respon­
sibility Act of 1982, pp. 41-43.
,5This is the commonly used rate in the literature, going back to Hall
and Jorgenson (1967) and continuing through Kopke (1981).
Gravelle (1982) uses 5.5 percent following Hendershott and Hu
(1981); all of the ratios reported in this article were also recomputed
with a 5.5 percent real rate, and neither the qualitative nor quantita­
tive results using 5.5 percent were appreciably different.

http://fraser.stlouisfed.org/
22
Federal Reserve Bank of St. Louis

NOVEMBER 1984

range o f inflation ra tes typ ical o f th o se ex p erien ced
during th e last th ree d eca d es. T h e h ig h er th e inflation
rate, th e lo w er th e real value o f th e d ep recia tio n d e­
d u ctio n s sin ce th e d ed u ctio n s are b a se d o n a fixed
n om in al value — th e h isto rica l p u rch a se p rice o f th e
asset. In co n trast, th e d en o m in a to r is u n a ffected by
inflation sin ce it is ca st in real te rm s to m e a su re th e
d eclin in g value in p ro d u ctio n o f th e a sset. Note th at
th e se are actual, n o t ex p ected , in flation rates. It is th e
actu al in flation rate th a t d eterm in es w h e th e r d ep reci­
ation d ed u ctio n s w ill b e ad eq u ate to provide fo r th e
re p la cem en t a sset; how ever, as th is im plies, th e h ig h er
th e ex p e cted in flation rate over th e a s s e t’s life, th e
low er th e value o f th e asset.
T h e se ratios d eterm in e w h e th e r th ere is ad equ ate
provision in th e tax co d e for th e a n ticip a te d n e t c o st o f
asset re p la cem e n t (net o f scrap value). T h e fund is
exactly ad eq u ate if th e ratio eq u als 1.0. R atios le ss th a n
1.0 in d icate th a t th e fu n d is in ad equ ate, a n d im p licit
su bsid ies are p re se n t in ratio s th at e x c e e d 1.0. T h e
ratios are co m p u te d for a variety o f d ep reciatio n
sch ed u les, b o th straig h t-lin e an d a ccelera ted . T h e A c­
celerated C ost Recovery System (ACRS) m a n d a ted by
ERTA an d m odified by TEFRA also is in clu d ed in th e
table; ACRS-ERTA is b a sed on th e 150 DB m eth o d .
ACRS-TEFRA is ACRS-ERTA w ith th e re d u ctio n in d e ­
p reciation b ase — 50 p e rce n t o f th e in vestm en t tax
cred it — m an d ated by TEFRA.1
6
T h e table su ggests that, even at an inflation rate as
high as 9 p e rce n t, th e p re sen t value o f d ep reciatio n
d ed u ctio n s is su fficien t to provide for re p la cem e n t o f
a ssets w ith tax lives u p to 10 y ea rs u n d e r an y o f th e
sch ed u les; w ith two ex cep tio n s, th is also h old s for 15y ea r assets. W hile th e ratio s are lo w er u n d e r cu rren t
law (TEFRA) th a n u n d e r p rio r law, th e y rem ain a d e­
qu ate fo r re p la cem e n t funding. In m arked co n tra st, for
th e m ost d urable a sse ts — th o se w ith 30-year lifetim es
w h ich are, generally, stru ctu res an d o th e r p lan t — th e
d ed u ctio n s are in a d eq u a te even at an inflation rate as
low as 3 p e rce n t. W hile th e m o re a cce le ra te d d e p re ci­
ation sch ed u les, 200 DB an d SYD, ap p e a r to overcom e
th is shortfall, stru ctu res an d p lan t w ere restricted ,
before ERTA, to u sin g 150 DB. C on sequen tly, for in ­
vestm en t in plant, d ep recia tio n d ed u ctio n s w ere w o e­
fully in ad eq u ate to provide fo r re p la cem e n t at th e in ­
flation rates e x p e rie n ce d in th e U nited States over th e

1 More accelerated versions of ACRS were mandated by ERTA for
6
1985 (175 percent declining balance) and for 1986 and beyond (200
percent declining balance); however, these later changes were re­
pealed by TEFRA. See Tax Equity and Fiscal Responsibility Act of
1982, pp. 40-43.

FEDERAL RESERVE BANK OF ST. LOUiS

NOVEMBER 1984

Table 1
Ratio of Present Value of Depreciation Deductions to Replacement Cost
with Scrap Value
Prior Tax Law

Tax Life
(years)

ACRS

"<% )

SL

150 DB

200 DBI

SYD

ERTA

TEFRA

3
3
3
3

0
3
6
9

1.323
1.262
1.204
1.151

1.330
1.276
1.224
1.176

1.339
1.293
1.249
1.207

1.333
1.280
1.231
1.184

1.319
1.255
1.194
1.138

1.289
1.227
1.168
1.114

5
5
5
5

0
3
6
9

1.424
1.333
1.251
1.176

1.433
1.351
1.276
1.207

1.445
1.373
1.306
1.245

1.444
1.370
1.301
1.238

1.420
1.327
1.242
1.165

1.370
1.281
1.200
1.127

10
10
10
10

0
3
6
9

1.453
1.300
1.173
1.067

1.468
1.327
1.208
1.109

1.489
1.363
1.255
1.163

1.499
1.378
1.274
1.183

1.460
1.311
1.187
1.083

1.408
1.266
1.148
1.049

15
15
15
15

0
3
6
9

1.483
1.274
1.114
0.991

1.505
1.309
1.159
1.042

1.535
1.359
1.220
1.110

1.556
1.390
1.255
1.144

1.497
1.296
1.142
1.021

1.445
1.253
1.106
0.991

30
30
30
30

0
3
6
9

1.223
0.889
0.688
0.561

1.265
0.949
0.755
0.630

1.325
1.033
0.846
0.719

1.379
1.096
0.904
0.767

N/A
N/A
N/A
N/A

N/A
N/A
N/A
N/A

NOTE: Each entry in the table is computed as
N
(ITC/x)e-<-*> + (1-0ITC) 2 D(t)e-"+’ » + (1- r)e^ '+,,N
t=1
8

r+ 8

8 ,
+ erl' «N(1--------'
r+ 8

where ITC = Fraction of asset’s purchase price received as investment tax credit, 6 percent for three-year assets and 10 percent for
longer-lived assets, except structures for which it is zero; in the table, 30-year assets are assumed to be structures
t

= Corporate tax rate, .46

0 = .5 for ACRS-TEFRA; for other schedules, 0 = 0

D(t) = Depreciation deduction under the specified schedule in year t
ir = inflation rate
r = Real after-tax discount rate, assumed to be 3 percent
N = Tax life of asset; assumed equal to useful life in table 1
8 = Real economic rate of deterioration, assumed to be 1/N

15 y ears p re ce d in g ERTA. As w e sh all see below , o n e o f
ERTA’s clea rest im p acts h as b e e n to rectify th is sh o rt­
fall for stru ctu res.

The Uncertain Effect o f Anticipated
Salvage Value
F o r asse ts w ith tax lives u n d e r 15 y ears, th e en tries
in table 1 suggest th a t th e p re sen t value o f d ep recia ­



tion d ed u ctio n s co m b in ed w ith th e in vestm en t tax
cred it have b e e n su fficien t to provide for rep lacem en t.
Yet, in clu d ed in th e se en tries is th e after-tax p ortion o f
th e a s se t’s a n ticip a te d scrap o r salvage value. T h at is,
for exam ple, th e re p la cem e n t o f an electric typew riter
is in p art fin a n ce d by th e a n ticip a te d sale o f th e old,
u sed typew riter. Yet, th e in clu sio n o f s u ch a n ticip ated
scrap value in th e in vestm en t d ecisio n en tails signifi­
ca n t risks: te ch n o lo g ica l o b so le sce n ce , eco n o m ic o b ­

23

FEDERAL RESERVE BANK OF ST. LOUIS

so le sce n ce d ue to ch an g es in relative p rices an d (in
th e ca se o f stru ctu res) lo catio n al o b so le sce n ce. T h e
first o f th e se is exem p lified by th e w id esp read u se o f
w o rd -p ro cessin g m ach in es, w h ich h as red u ced th e
value o f even th e m o st so p h isticate d electric type­
w riters. T h e se co n d ca n b e ap p reciated by co n sid er­
ing th e effect o f th e m id -1970s’ ru n -u p in oil and gas
p rices on th e value o f stan d ard -sized A m erican u sed
cars. T h e third is an obvious risk en tailed in p u rch a s­
ing any co m m ercial, in d u strial o r resid en tial stru c­
ture. M oreover, e a c h o f th e se risks rises w ith th e d u ra­
bility o f th e a sse t.1
7
B eca u se scra p value is so u n certain , esp ecially for
longer-lived a ssets, it is inform ative to re co m p u te th e
ratios in table 1 w ith ou t scrap value. T h e resu lts are
show n in table 2. W ithout scrap value, th e m o st a c c e l­
erated d ep reciatio n sch e d u les u n d e r p rio r law w ere
ad equ ate for re p lacem e n t ex cep t for assets o f 10- or
15-year tax lives at 9 p e rce n t inflation an d 30-year
a sse ts at any inflation rate. U nd er cu rre n t tax law (TE­
FRA), how ever, even th ree-y ear asse ts in th e fa ce of
m o d erate inflation, say 6 p e rce n t, co u ld n o t have th e ir
re p la cem en t fin an ce d th rou g h d ep reciatio n d ed u c­
tion s alone.
N on eth eless, th e sh o rte r is th e a sse t life, th e sm aller
is th e risk en tailed in th e a n ticip ate d scrap value; thu s,
a th ree-y ear asset (for exam ple, an au to m o bile o r light
truck acco rd in g to th e tax code) su rely d oes have a
m ore secu re resale m arket th an , say, an a sse t w ith a
sev en-year life (for exam ple, acco u n tin g , co m p u tin g or
o th e r office eq u ip m ent). C onsequ en tly, th e ratios p re ­
sen ted in tables 1 an d 2 sh o u ld b e in terp reted as
defining a range o f u n certain ty w ith in w h ich th e sp e ­
cific values o f p articu lar asse ts can be co n sid ere d in
1That is, suppose that there is a 1 percent likelihood that during any
7
single year an innovation in technology will make an existing asset's
value decline due to the improvements in newer machines. Then,
the probability that an investment will not have its scrap value low­
ered is 97 percent for a three-year asset, 90 percent for a 10-year
asset and 74 percent for a 30-year asset.
Further, consider the uncertainty associated with relative prices.
Every manufacturing process makes use of a variety of inputs —
labor, various raw materials and energy — so that the optimal
design based on existing technology of a machine used in that
process will depend on the relative prices of the inputs. Suppose
that the likelihood during any single year of a significant change in
relative input prices (sufficient to induce an alteration in capital
design) is 1 percent and is independent of the likelihood of techno­
logical innovation. Then, the probability that an asset’s salvage
value will not be lowered by either event is 94 percent for a threeyear asset, 82 percent for a 10-year asset and only 55 percent for a
30-year asset.
Finally, if we add a third source of obsolescence, the problem of
neighborhood decline or a change in locational use patterns, also an
independent likelihood of 1 percent, this final obsolescence risk
which is peculiar to structures causes the 30-year asset probability
of no decline in salvage value to plummet to 40 percent.

http://fraser.stlouisfed.org/
24
Federal Reserve Bank of St. Louis

NOVEMBER 1984

relation to th e ir d ep recia tio n allo w an ces an d scrap
values.

Shortened Tax Lives under ACRS and
the Impact on Specific Asset Types
A lthough ERTA co n ta in s a bew ild erin g array o f fea­
tures, th e p rin cip a l ch a n g es to p rio r tax law are low er
p erso n al in co m e tax rates, ch a n g es to gift an d estate
tax rules, in cen tiv es fo r saving a n d th e ACRS d ep recia ­
tio n d ed u ctio n sch e d u les. In th e co n tex t o f d ep recia ­
tion, th e prim ary im p act o f TEFRA w as to rep eal th e
m ore a ccelera ted ACRS sch e d u les, w h ich w ould have
b eco m e effective in 1985 an d 1986, an d to re d u ce th e
d ep reciab le a sse t b a se by o n e -h a lf o f th e ITC . ACRS
u n d e r eith e r ERTA o r TEFRA, as tab les 1 an d 2 show , is
n o t as a cc elera ted for a given tax life as w ere som e
o p tio n s available ea rlier — fo r exam ple, 200 DB an d
SYD. T h e m a jo r im p act o f ERTA, how ever, w as in
sh o rten in g th e tax life o f a ssets, an im p a ct n o t revealed
by eith e r o f th e se tab les.
U nder ERTA, fo u r ACRS sc h e d u le s re p la ced th e vari­
ous o p tio n s available to a sse t o w n ers u n d e r p rio r
law .1 T h e old er sy stem w as b a se d o n surveys c o n ­
8
d u cted by th e U.S. T reasu ry D ep artm en t from w h ich
asset life d istrib u tio n s w ere co m p u te d . T h e system
b a sed on th e se d istrib u tio n s, ca lle d th e A sset D ep reci­
atio n Range system (ADR), w as th e b a sis for d eterm in ­
ing th e tax life over w h ich a n a sse t co u ld b e d ep reci­
ated u sin g th e various d ed u ctio n form u las.1
9
T h e n ew system , ACRS, re p la ced m o re th a n 100
cla sses o f asset lives w ith four: 3-year, 5-year, 10-year
a n d 15-year. T h e 3-year cla ss p rim arily co n ta in s a u to ­
m obiles, light tru cks an d re se a rc h eq u ip m en t. M ost
eq u ip m en t is in clu d ed in th e 5-year cla ss. T h e 10-year
cla ss prim arily co m p rise s sp ecia liz ed m a ch in ery of
th e p u b lic utility ind ustry. All stru ctu res an d som e
o th e r u tilities' cap ita l are in th e 15-year cla ss.20 T h u s,
th e a ccelera tio n o f th e d ep recia tio n allo w an ce u n d e r
ERTA relative to p rio r tax law is n o t d ue to th e form ula
applied .2 Rather, th e saving is prim arily d ue to a p ro ­
1
,8See Economic Recovery Tax Act of 1981, pp. 6-7, 67-68, and 7585.
,9ln particular, the 30th percentile of the survey responses was the
minimum allowable tax life.
“ Certain manufactured housing and tank cars also fall into the 10year class. See Economic Recovery Tax Act of 1981, pp. 78-80.
2 The schedules for equipment are based on 150 DB with a switch to
1
straight line at the deduction optimizing point (see insert). There is a
half-year convention in these schedules — the asset is assumed to
be acquired at mid-year so the initial year’s depreciation is one-half
of the 150 DB schedule in the insert. The ACRS schedule for struc­
tures is 175 DB with a switch to straight line at year 8; the structures’
schedules are specific to the month of asset acquisition. See Eco­
nomic Recovery Tax Act of 1981, pp. 40-41.

NOVEMBER 1984

FEDERAL RESERVE BANK OF ST. LOUIS

Table 2
Ratio of Present Value of Depreciation Deductions to Replacement Cost
without Scrap Value
Prior Tax Law

ACRS

Tax Life
(years)

7T(%)

SL

150 DB

200 DBI

SYD

ERTA

TEFRA

3
3
3
3

0
3
6
9

1.131
1.069
1.012
0.959

1.138
1.084
1.032
0.984

1.147
1.101
1.057
1.015

1.141
1.088
1.039
0.992

1.127
1.063
1.002
0.946

1.097
1.035
0.976
0.922

5
5
5
5

0
3
6
9

1.236
1.145
1.063
0.989

1.246
1.163
1.088
1.020

1.258
1.185
1.119
1.057

1.256
1.182
1.114
1.050

1.233
1.139
1.054
0.978

1.182
1.093
1.012
0.939

10
10
10
10

0
3
6
9

1.276
1.123
0.996
0.890

1.292
1.150
1.031
0.932

1.312
1.186
1.078
0.987

1.322
1.201
1.097
1.006

1.283
1.134
1.010
0.906

1.231
1.090
0.972
0.872

15
15
15
15

0
3
6
9

1.317
1.108
0.948
0.825

1.338
1.143
0.993
0.876

1.369
1.193
1.054
0.943

1.390
1.224
1.089
0.978

1.331
1.130
0.976
0.855

1.278
1.087
0.940
0.825

30
30
30
30

0
3
6
9

1.088
0.754
0.553
0.426

1.129
0.814
0.620
0.494

1.190
0.898
0.711
0.584

1.243
0.961
0.768
0.632

N/A
N/A
N/A
N/A

N/A
N/A
N/A
N/A

NOTE: Entries in the table are computed as in table 1 except the present value of anticipated scrap value does not appear in the numerator:
N
ITC (1/t ) e-*'*"1 + (1- © ITC) 2 D(t)e-"+-»
t=1

n o u n ced sh o rten in g o f th e tax lives o f e a c h a sse t class.
T h e m ean red u ctio n s in asset tax lives from ADR to
ACRS for eq u ip m en t an d for stru ctu res w ere, re sp e c ­
tively, 44 p e rce n t an d 49 p e rce n t.2 T h e re d u ctio n s in
2
tax lifetim es varied w idely. T h e tax life o f th e th reey ea r cla ss w as sh o rte n ed by only h a lf a y e a r from ADR
to ACRS, bu t for longer-lived assets, th e red u ctio n s
in clu d ed 22.5 y ears for co m m ercial stru ctu res (15-year
category), 4.7 y ears for aircraft (five-year category) and
5.5 y ears for railroad eq u ip m en t (10-year category).
T h u s, in evaluating th e ad eq u acy o f d ep reciatio n
d ed u ctio n s in providing for rep lacem en t o f any sp e ­
cific asset, th e re are six elem e n ts to be co n sid ered : the
d ep reciatio n sch ed u le, th e an ticip ated inflation rate,
th e a s se t’s tax life, its investm en t tax cred it, e co n o m ic
^Computed from ADR data by producers’ equipment and structures
classes in table 1 of Gravelle (1982).



life an d scrap value. T h e effects o f th e se elem e n ts are
revealed in th e ratio s o f d ep recia tio n to rep lacem en t
co st for sp ecific a sse ts in table 3.
C olum n a o f tab le 3 lists th e sp ecific asset types
analyzed; th e n in e a sse ts w ere selecte d to cov er a
variety o f ec o n o m ic d ep recia tio n rates, durability and
ACRS tax lives, w h ich are rep o rted in co lu m n s b, c and
d, respectively, for e a c h asset. C olum n e lists th e in ­
flation rate assu m ed in e a c h ratio, th e range o f rates
b ein g th e sam e as in tab les 1 an d 2. In th e n ext th ree
co lu m n s, th e ratio o f th e p re sen t values o f d ep recia ­
tion, ITC an d after-tax salvage value to e co n o m ic d e­
p reciatio n an d scra p value are rep o rted ; th e ratios are
co m p u ted u n d e r p rio r tax law in co lu m n f, u n d er
ERTA in co lu m n g an d u n d e r TEFRA in co lu m n h.
C olum ns i an d j disp lay th e ratio o f th e en tries in
co lu m n s g an d h to co lu m n f; if th e ratio is g reater
(less) th an 1.0, th e n th e tax trea tm en t u n d e r ERTA or

25

Table 3
Comparison of Present Values of Depreciation Tax Deductions with ITC and
Scrap Value to Replacement Cost for Selected Assets
Economic
Asset Type
Depreciation Rate1
(a)________________ (b)

Ratios of Present Value of
Depreciation Deduction
to Replacement Cost3

Tax Life
(years)2
ADR
(c)

ACRS
(d)

u(% )
(e)

ADR*
(f)

.3333

3.0

3

Office, computing
and accounting
equipment

.2729

7.0

5

Aircraft

.1818

9.2

5

Mining and oilfield
machinery

.1650

9.2

5

Communications
equipment

.1179

11.5

5

Ships and boats

.0750

16.0

5

Railroad
equipment

.0660

15.0

10

Industrial
structures5

.0330

36.0

15

Commercial
structures5

.0230

37.0

15

0
3
6
9
0
3
6
9
0
3
6
9
0
3
6
9
0
3
6
9
0
3
6
9
0
3
6
9
0
3
6
9
0
3
6
9

1.339
1.293
1.249
1.207
1.305
1.215
1.135
1.062
1.389
1.276
1.178
1.091
1.415
1.301
1.202
1.114
1.511
1.371
1.251
1.150
1.501
1.331
1.193
1.082
1.559
1.393
1.258
1.147
1.192
0.853
0.660
0.540
1.361
0.981
0.766
0.634

Automobiles,
light trucks

Ratios of
Present Value of
Deductions

ACRS-ERTA ACRS-TEFRA ACRS-ERTA/ADR ACRS-TEFRA/ADR
(g)___________(h)_____________ (I)________________(j)

1.319
1.255
1.195
1.138
1.301
1.207
1.123
1.047
1.365
1.268
1.181
1.101
1.391
1.293
1.205
1.125
1.464
1.362
1.269
1.186
1.594
1.483
1.382
1.291
1.570
1.407
1.272
1.158

1.289
1.227
1.168
1.114
1.251
1.162
1.081
1.008
1.314
1.221
1.137
1.062
1.339
1.245
1.161
1.085
1.409
1.312
1.224
1.144
1.534
1.428
1.333
1.246
1.514
1.359
1.230
1.131
1.495
1.239
1.045
0.895
1.713
1.427
1.210
1.042

0.985
0.970
0.956
0.943
0.997
0.994
0.990
0.985
0.983
0.994
1.003
1.009
0.983
0.994
1.003
1.009
0.969
0.993
1.014
1.031
1.062
1.114
1.158
1.194
1.007
1.010
1.011
1.010

0.963
0.949
0.935
0.923
0.959
0.956
0.953
0.949
0.946
0.957
0.966
0.973
0.946
0.957
0.966
0.973
0.933
0.957
0.978
0.995
1.022
1.073
1.117
1.152
0.971
0.975
0.978
0.978
1.254
1.452
1.584
1.657
1.259
1.456
1.580
1.644

'See Graveile (1982), table 1.
2
Actual tax lives for equipment under ACRS are .5 years less than shown due to an assumption, implicit in the schedules, of acquisition at
mid-year; for structures, the ACRS schedules explicitly allow for actual month of acquisition.
3Entries are as in table 1 except ADR uses ADR tax life and ACRS uses ACRS tax life for numerator of ratios; denominator for both ADR and
ACRS use ADR tax life as proxy for useful life.
4
For structures, the depreciation schedule utilized is 150 DB with a switch to SL after 12 years (for industrial structures) or 13 years (for
commercial structures). For autos, 200 DB was used (200 DB is more accelerated than SYD for assets with tax lives less than 6 years); all
other assets used SYD.
5
Note that TEFRA did not change the ERTA tax schedules for structures.

TEFRA h as in crea sed (decreased ) th e value o f d e p re ci­
atio n fo r th a t a sse t.
N o tice th a t fo r stru c tu re s,
co lu m n s g an d h are co m b in ed as are co lu m n s i an d j;
th is reflects th e fact th a t in v estm en ts in stru ctu res do
n ot qualify for ITC, and, th u s, th e 50 p e rce n t o f ITC

26


red u ctio n in th e d ep recia b le b a se m an d ated by T E ­
FRA d oes n o t affect stru ctu res.
Scan n in g d ow n th e co lu m n s o f ratio s in co lu m n s f - j
o f table 3 provides an overall a sse ssm e n t o f th e im p act

on d ep reciatio n ad eq u acy u n d e r ERTA an d TEFRA
relative to p rio r tax law. C olu m n f reiterates th e g en ­
eral m essage o f table 1 for sp ecific asse ts — nam ely
th at eq u ip m en t, esp ecially shorter-lived eq u ip m en t
su ch as au tom obiles, w as m o re th an ad equ ately p ro ­
vided for u n d e r th e p rio r tax law, w hile stru c tu re s’
d ep reciatio n d ed u ctio n s w ere in ad eq u ate at even low
inflation rates. C olu m n s g an d h sh o w th at th e n ew tax
laws have re d u ce d th e ben efits o f fast d ep reciatio n for
sh o rt-liv ed e q u ip m e n t, b u t sh a rp ly ra ise d th e s e
b enefits for stru ctu res at all inflation rates. F o r ex am ­
ple, at a 6 p e rce n t inflation rate, th e d ep reciatio n ratio
for office, co m p u tin g an d a cco u n tin g eq u ip m en t d e ­
clin es from 1.135 u n d e r p rio r tax law to 1.081 u n d e r
TEFRA, w hile for in d u strial stru ctu res it rises from
0.660 to 1.045. Finally, th e en tries in co lu m n s i an d j
affirm th at longer-lived assets have h ad th e ir d ep recia ­
tio n ra tio s re d u ce d le ss o r in c re a se d m o re th an
shorter-lived a ssets. F or exam ple, co m p arin g th e ra­
tios in co lu m n j at a 6 p e rce n t inflation rate, co m m u n i­
catio n s eq u ip m en t h as 0.978 o f its p rio r tax law d ep re­
ciatio n ratio u n d e r TEFRA, w hile th e shorter-lived
asset aircraft h as 0.966 an d th e longer-lived asset co m ­
m ercial stru ctu res h as 1.580.
In sum m ary, th e ratio s in co lu m n h reveal th at th e
shift to ACRS h as provided in d u ce m en ts to p u rch ase
n ew cap ital eq u ip m en t th a t rise w ith th e d urability o f
th e e q u ip m e n t. M o reo v er, re la tiv e to p r io r law
(colum n j), th e ad d itio n al incentives are esp ecially
stron g for n o n resid en tial stru ctu res, particu larly at
low inflation rates. C om p ared w ith p rio r tax law, ACRS
d im in ish es th e d eleterio u s effects o f inflation on th e
value o f d ep reciatio n d ed u ctio n s for long-lived assets
an d re d u ce s th e attractiv e n ess o f in v estm en ts in
eq u ip m en t relative to stru ctu res. F o r exam ple, th e
p resen t value o f th e d ep reciatio n d ed u ctio n s p lu s
scrap for in d u strial stru ctu res u n d e r ACRS is g reater
th a n th e p resen t value o f th e re p lacem e n t c o st at in ­
flation rates u p to 6 p e rce n t; m oreover, th e d ed u ctio n s
are in crea sed m assively relative to p rio r tax law at till
inflation rates.2 In particu lar, th e ratios for ind u strial
3
stru ctu res in co lu m n h e x c e e d th o se for au to m o biles
an d aircraft at low in flation rates w h ere, as co lu m n f
show s, th e ranking w as th e reverse u n d e r p rio r law.

The Combined Effects o f Tax Changes
and Disinflation in the 1980s
To fo cu s o nly o n th e ch an g es in th e d ep reciatio n
sch e d u les an d th e ir effects o n various asse ts at any

a \ part, this higher present value of depreciation deductions is offset
n
by the lack of investment tax credit on investment in nonresidential
structures. Moreover, the tax act of 1984 has lengthened the depre­
ciation term for structures from 15 to 18 years, which will slightly
reduce the impetus. See Tax Reform Act of 1984, p. 178.



sp ecific inflation rate u n d e rsta tes th e in v estm en t in ­
cen tiv es provided by th e ch a n g es in th e 1980s. T h e
red u ctio n in th e observed in flation ra te and , p resu m ­
ably, th e a n ticip a te d in flation ra tes over th e invest­
m en t term provide a n o th e r stron g im p etu s. F o r exam ­
ple, th e ra te o f in flatio n m e a su red by th e im p licit GNP
d eflator h a s b ee n falling over th e p a st fo u r y ea rs —
from an average rate o f over 9 p e rce n t d uring 1 9 78-81
to betw een 3 an d 4 p e rce n t d urin g 1 9 8 2 -8 4 . C o n se­
quently, th e m o st p e rtin en t a sse ssm en t o f th e im p act
on in vestm en t in cen tiv es afforded by th is su b stan tial
d eclin e in th e in flation rate is to co m p a re (using th e
d ata in tab le 3) th e ratio o f d ep recia tio n to re p la ce­
m en t co st u n d e r pre-ERTA sc h e d u le s at 9 p e rce n t
inflation w ith th e ratios for 6 p e rce n t inflation u n d er
TEFRA. T h e se in flation ra tes ap p roxim ate th e ex ­
p e cted inflation rates, b a se d o n survey data, w h ich
prevailed in late 1980 an d la te 1984, respectively.2
4
W hen th is co m p a riso n is m ad e for co m m u n ica tio n s
eq u ip m en t, th e ratio rises from 1.150 to 1.224 in stead
o f d eclining. In th e ca se o f au to m o b iles, th is e n h a n ced
co m p a riso n show s a slight d e clin e — from 1.207 to
1.168 — w hile in th e ca se o f in d u strial stru ctu res it
reveals a n e a r d ou blin g — from 0.540 to 1.045.

THE HISTORICAL RELATION
BETWEEN DISTORTIONS IN
DEPRECIATION DEDUCTIONS
AND INVESTMENT
As sh o w n above, th e re are tw o so u rce s o f d isto rtion
in d ep recia tio n d ed u ctio n s: O n th e o n e h an d , th ey
m ay provide m o re e x p e n se d ed u ctio n th a n requ ired
for th e eventual re p la cem e n t o f th e u sed -u p asset.
T h is ca n re su lt e ith e r from a sh o rten in g o f th e tax life
b elo w th e sp an o f its e c o n o m ic u sefu ln ess, o r from an
accelera tio n o f th e d ed u ctio n s. O n th e o th e r hand ,
th ey m ay b e in a d eq u a te to provide for th e p u rch a se o f
th e re p la cem e n t a sse t given a rise in its n o m in al p rice
d ue to inflation. T h a t is, sin c e th e d ed u ctio n s are
b ased on th e p u rch a se p rice — its h isto rica l co st —
inflation will progressively m ake th e d ep recia tio n al­
low an ce in ad eq u ate for th e p u rch a se o f th e re p la ce­
m ent.
As sh ow n in tab les 1 an d 2, th e se tw o d isto rtion s
w ork in o p p o sitio n . F o r exam ple, in table 1 co n sid er

2
4The short-term (one-year period) expected inflation rate in June
1980 was 10.22 percent and 5.47 percent in June 1984; these
estimates are from a semi-annual survey of economists conducted
by Joseph Livingston of The Philadelphia Inquirer, as revised by
Carlson (1977). The long-term (10-year period) expected inflation
rate in October 1980 was 8.82 percent and had fallen to 5.79 per­
cent in October 1984; these estimates are from a decision-makers
poll conducted by Richard B. Hoey of Drexel Burnham Lambert,
Incorporated.

27

FEDERAL RESERVE BANK OF ST. LOUIS

NOVEMBER 1984

C h a rt 3

Depreciation Distortion and the Growth Rate
of the Corporate Capital Stock

Sources: B oard o f G o v e rn o rs o f the F e deral Reserve System and U.S. D e p a rtm e n t o f C om m erce
S h a d e d a re a s re p re s e n t p e rio d s o f business re cessions.

th e effect o f in creasin g a cc e le ra tio n o n th e ratio o f
d ep reciatio n to re p la cem e n t c o st fo r a 10-year a sse t at
a 6 p e rce n t inflation rate: as th e d ep reciatio n sch e d u le
is a cce le ra te d from SL to 150 DB to 200 DB, th e ratio
rises from 1.173 to 1.208 to 1.255, a n in c re a se o f n early 7
p ercen t. Conversely, co n sid e r th e im p act o f risin g in ­
flation on th e 10-year a s s e t’s ratio u n d e r 200 DB: as
inflation rises from 3 p e rce n t to 9 p e rce n t, th e ratio
falls from 1.362 to 1.163, a d e cre a se o f over 17 p e rce n t.
C on sequently, th e rate o f investm en t sh o u ld vaiy p o si­
tively w ith th e n et d isto rtion o f d ep reciatio n — th at is,
th e d ifference b etw een th e se tw o o p p o sin g d isto r­
tions.
T h is asso ciatio n , in fact, can be see n in ch a rt 3
w h ich d isplays th e grow th rate o f th e cap ital sto ck and
th e ratio o f th e C apital C on su m p tio n A d ju stm en t
(CCA) to estim ated e c o n o m ic d ep reciatio n for U.S.
n o n fin an cial co rp o ra tio n s beginnin g 1955. CCA, as
estim ated by th e C om m erce D ep artm en t, is th e dif­
fere n ce betw een d e p reciatio n claim ed by co rp o ra ­
tio n s on th e ir tax retu rn s an d th e estim ated “e c o ­
n o m ic d ep recia tio n ” o f th e ir cap ital eq u ip m en t; th e
C om m erce D ep artm en t d efin es e c o n o m ic d ep recia ­

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28
Federal Reserve Bank of St. Louis

tion as straig h t-lin e d ep recia tio n w ith an a d ju stm en t
(an in crea se in th e d ep recia b le base) for inflation. By
co m p u tin g th e ratio o f CCA to e c o n o m ic d ep reciatio n ,
w e o b tain a p ro p o rtio n a l m ea su re o f d ep reciatio n
d istortion .
C hart 3 reveals im p o rtan t ch a ra cte ristic s o f th e last
30 y e a rs ’ cap ital sto ck grow th rates. First, th e interval
o f h ig h est cap ital sto ck grow th over th e p erio d c o in ­
cid ed w ith th e interval d urin g w h ich th e CCA ratio
w as h ig h est — from late 1961 th rou gh early 1974.2
5
From m id -1973 th rou g h early 1982, CCA w as negative,
h e n c e its ratio w as b elo w zero, an d cap ital grow th w as
“ The simple correlation coefficient between the variables in chart 3 is
.42, significant at the .0001 level. However, the association appears
to have changed during the 1981-82 recession: from 1955-80, the
correlation was .65, significant at .0001, but from 1981-84 it was
- .08 and insignificant. Yet the sharp rise of CCA during the 198182 recession, due to disinflation and ERTA, is out of keeping with its
behavior in the earlier recessions shown in chart 3. During the
1969-70 and 1973-74 recessions, CCA fell sharply and during the
1980 recession it was roughly constant. The other two recessions,
1957-58 and 1960-61, during which CCA rose moderately, had,
like the current recovery, much sharper upturns in capital growth
than the recoveries following the recessions with declining or un­
changed CCA.

NOVEMBER 1984

FEDERAL RESERVE BANK OF ST. LOUIS

C h a rt 4

Investment in Structures and the Rate of Inflation
R a tio

Q u a rte r ly D ata

P e rce n t

S ources: B oard o f G o v e rn o rs o f the F e deral Reserve System an d U.S. D e p a rtm e n t o f C om m erce
|J_ T w o -q u a rte r m o vin g a v e ra g e .
[2 T w e lv e -q u a rte r m o vin g a v e ra g e .
S ha d e d a re a s re p re s e n t p e rio d s o f business re cessions.

co rresp o n d in g ly slow er. Seco n d , cap ital sto ck grow th
ap p ears to follow th e grow th rate o f real o u tp u t: it rises
th rou gh ou t ex p an sio n s an d p lu m m ets in recessio n s,
ceteris p aribus. T h u s, th e tw o p ro n o u n ced n o n -re ce s­
sion d eclin es in cap ital grow th in ch a rt 3 — 1 955-5 6
an d 1 9 6 6 -6 7 — e a c h o ccu rred in y ears w h en su b sta n ­
tial slow dow ns in th e grow th rate o f real o u tp u t o c ­
cu rred — year-over-year d eclin es o f 4.6 p e rce n t and
3.3 p ercen t, respectively. Third , th e sh arp est rise in
cap ital sto ck grow th in any single y e a r o ccu rred in
1983 co in cid e n t w ith th e largest rise in th e p ro p o rtio n
o f CCA to e c o n o m ic d ep reciatio n .
A seco n d qualitative in d icatio n o f th e effects o f d is­
tortion in d ep reciatio n d ed u ctio n s is its im p act on the
relative sh are o f investm en t devoted to stru ctu res. As
is clea r from tables 1 o r 2, u n d e r p rio r tax law, invest­
m en t in stru ctu res w as p en alized — in th e sen se of
low ering th e ratio o f d ep reciatio n d ed u ctio n s to re­
p lacem en t co st — by su stain ed inflation relatively
m ore th an investm en t in shorter-lived assets. As a c o n ­
seq u en ce, it is n o t su rp risin g th at p erio d s o f su stained
high in flation are also p erio d s in w h ich in vestm ent in



stru ctu res is relatively low .2 C hart 4 d ep icts th e p ro ­
6
p ortion o f total U.S. n o n resid en tia l in vestm en t in n on resid en tial stru ctu res an d th e rate o f inflation sin ce
1955. As ex p ected , in v estm en t in p lant h as b een p ro ­
portionally low est d uring p erio d s o f relatively high
an d su stain ed in flation. T h e en h a n c e d in cen tiv es for
investm ent in stru ctu res d isp layed in table 3 an d th e
drop in th e inflation rate suggest th at th e s tru c tu re s’
share o f in v estm en t sh o u ld rise from its cu rren tly low
proportion .

CONCLUSIONS
Elem en tary cap ital th eo ry im plies th at low ering
taxes on cap ital by in crea sin g th e a ccelera tio n o f d e­
“ Nelson (1976), pp. 928-30, develops the simple analytics of this
proposition, which are that the present values of shorter-lived proj­
ects rise relative to longer-lived ones, as implied by the data in
tables 1, 2 and 3. The simple correlation between the variables in
chart 4 during 1955-84 is - .89, significant at the .0001 level. More­
over, a regression of the plant share variable on the Livingston 6month expected inflation rate yields a coefficient of -1.81, signifi­
cant at the .0001 level.

29

FEDERAL RESERVE BANK OF ST. LOUIS

NOVEMBER 1984

p reciatio n d ed u ctio n s o r sh o rten in g th e term over
w h ich d ep reciatio n is tak en raises th e value o f cap ital
and, o th e r th in gs th e sam e, raises th e rate o f invest­
m ent. T h e tax re d u ctio n s in ERTA co n siste d prim arily
o f a sh o rten in g o f th e tax lifetim es over w h ich assets
are d ep reciated ; th e ch an g es in TEFRA, w hile rep ea l­
ing th e m ore a cc e le ra te d d ep reciatio n sch e d u les that
w ould have follow ed in 1985 an d 1986, left in tact th e
b asic sh o rten in g o f a sse t tax lives. T h is low ered the
portion o f n e t p ro ceed s on w h ich co rp o ratio n s w ould
pay taxes an d raised th e value o f cap ital.

abou t w h at in flatio n rate p o licy m ak ers w ill bring
abou t in th e future. W ith out q u estio n , th e ren ew ed
vigor o f co rp o ra te in v estm en t is d ue to b o th so u rces o f
effective tax re d u ctio n s — ACRS an d th e low er rate o f
inflation.2
*

Yet, th e rise in investm ent o ccu rrin g sin c e th e e n ­
a ctm en t o f ERTA ca n n o t b e attribu ted solely to faster
a cceleratio n o f d ed u ctio n s o r sh o rte r tax lives. In large
part, th e rise in CCA sin c e 1980 h as b ee n due to th e
sh arp d eclin e in th e inflation rate from ab o u t 9 p e r­
ce n t to abou t 3 to 4 p e rce n t an d th e a sso ciate d d eclin e
in inflation ex p ectatio n s. Previously, su stain ed shifts
in th e inflation rate also have b e e n asso ciated , in ­
versely, w ith ch an g es in th e rate o f cap ital stock
grow th. Part o f th e rapid rise in cap ital stock grow th in
1983 m ay be due to th e proxim ity an d severity o f th e
1980 an d 1 9 8 1 -8 2 re cessio n s. In n o o th e r recovery,
how ever, h as cap ital grow th risen as rapidly o r as long
as in th e cu rren t exp an sio n .

Carlson, John A. "A Study of Price Forecasts," Annals of Economic
and Social Measurement (Winter 1977), pp. 27-56.

Since, in th e ca se o f m o st interm ed iate-lived cap ital
equ ip m ent, th e ACRS-TEFRA d ep reciatio n sch ed u les
are actu ally less a cce le ra te d th a n th o se allow ed u n d e r
p rio r tax law, ACRS co u ld exp lain n eith e r th e re cen t
rise in CCA n o r in cap ital grow th in ch a rt 3. Yet, if th e
d eclin e in inflation ex p e cta tio n s co n tin u es to follow
th e d eclin e in observed inflation, th e n th e value of
d ep reciatio n d ed u ctio n s will have b een raised by 10 to
20 p e rce n t for m o st eq u ip m en t an d by m o re th a n 100
p e rce n t for stru ctu res.-7 T hu s, th e im p acts o f th e 1981
an d 1982 tax a cts have b e e n au gm en ted by th e su b ­
stantial d eclin e in th e in flation rate sin c e 1980 and,
m ore im portant, th e ch an g e in in v esto rs’ ex p ectatio n s

2 Specifically, the increases in the ratios of depreciation and scrap to
7
replacement cost as inflation declines from 9 percent to 3 percent
(from table 3, columns f and h) are: autos, 1.7 percent; office equip­
ment, 9.4 percent; aircraft, 11.9 percent; mining and oil field equip­
ment, 11.8 percent; communications equipment, 14.1 percent;
ships and boats, 32.0 percent; railroad equipment, 18.5 percent;
commercial structures, 125.1 percent; industrial structures, 129.4
percent.


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30
Federal Reserve Bank of St. Louis

REFERENCES
Auerbach, Alan J. 'Taxation, Corporate Financial Policy, and the
Cost of Capital," Journal of Economic Literature (September 1983),
pp. 905-40.

Economic Recovery Tax Act of 1981: Law and Explanation (Com­
merce Clearing House, Inc., 1981).
Economic Report of the President, February 1984 (U.S. Government
Printing Office, 1984).
Editorial.

Washington Post, April 22, 1984.

Gravelle, Jane G. "Effects of the 1981 Depreciation Revisions on
the Taxation of Income from Business Capital," National Tax Jour­
nal (February 1982), pp. 1-20.
Greenhouse, Steven. "Pitfalls in the Capital Spending Boom," New
York Times, June 3,1984.
Hall, Robert E., and Dale W. Jorgenson. 'Tax Policy and Investment
Behavior," American Economic Review (June 1967), pp. 391-414.
Hendershott, Patric, and Sheng-Cheg Hu. “ Investment in Pro­
ducers’ Equipment," in Henry J. Aaron and Joseph A. Pechman,
eds., How Taxes Affect Economic Behavior (The Brookings Institu­
tion, 1981), pp. 85-127.
Internal Revenue Service Announcement 71 -76. 'The Adoption of
the Asset Depreciation Range (ADR) System," Vol. 1971-2, C.B.,
pp. 503-24.
Kopke, Richard W. 'The Efficiency of Traditional Investment Tax
Incentives," in Public Policy and Capital Formation (Board of Gov­
ernors of the Federal Reserve System, April 1981), pp. 163-73.
Nelson, Charles R. "Inflation and Capital Budgeting," The Journal of
Finance (June 1976), pp. 923-31.
Tax Equity and Fiscal Responsibility Act of 1982: Law and Explanation
(Commerce Clearing House, Inc., 1982).
Tax Reform Act of 1984: Law and Controlling Committee Reports
(Commerce Clearing House, Inc., 1984).

2 The Economic Report of the President (1984) is also clear on this
8
apportioned credit:
The tax climate for business investment has also been substantially
improved in the past 3 years. During the 1970s the rising rate of inflation
combined with the old depreciation rules to raise very substantially the
tax rate on the income from investment in business plant and equip­
ment. The 1981 changes in the tax rules governing depreciation, as
modified in the Tax Equity and Fiscal Responsibility Act, and the sharp
reduction in inflation reduced this effective tax rate substantially, (p. 34).

Interest Rate Variability: Its Link to
the Variability of Monetary Growth
and Econom ic Perform ance
John A. Tatom

C
L _ 7 fN C E 1979, in terest rate volatility h as b ee n u n ­
u sually high, su b je ctin g investors to in creased risk on
th e ir retu rns. W hen investm ent is riskier, risk-averse
investors d em an d a h ig h er rate o f retu rn as an in c e n ­
tive to co n tin u e investing. Evans (1984) show s th at th e
rise in th e volatility o f in terest rates in 1980-81 had a
significant negative effect on o u tp u t in th e United
States, w h ich h e attribu tes to th e p o licy o f m onetary
stock co n tro l im p lem en ted in 1979.' O th er investiga­
tors have n o ted th at m o n ey grow th volatility in creased
su bstantially after 1979 an d have attribu ted m any of
th e u n u su al featu res o f e c o n o m ic p erfo rm an ce sin ce
1980 to th is in crease.2
T h e p u rp o se o f th is p ap e r is to exam in e bo th the
link betw een m o n ey grow th an d in terest rate variabil­
ity an d th e effects o f in tere st rate variability on U.S.
ec o n o m ic p e rfo rm an ce. T h is exam in atio n is c o n ­
d u cted using a m od el in w h ich m oney grow th is exog­
enou s, and p ast in terest rate an d m oney grow th varia­
bility are taken to be exo g en o u s for th e d eterm in atio n
o f cu rren t eco n o m ic p erform an ce.

John A. Tatom is a research officer at the Federal Reserve Bank of
St. Louis. Thomas A. Gregory provided research assistance.

'See Evans (1984). The 1979 policy change is discussed by Lang
(1980) and Gilbert and Trebing (1981). Subsequent policy altera­
tions are discussed by Thornton (1983) and Wallich (1984). For an
extensive set of criticisms of central bank policy aimed at money
stock control, especially the policies of the Federal Reserve from
1979-82, see the citations in Batten and Stone (1983), p. 5.
2
See Friedman (1983), Bomhoff (1983), Tatom (1983), Bodie, Kane
and McDonald (1983), Mascara and Meltzer (1984) and Belongia
(1984).



T h e article first ex am in es th e re cen t ex p erien ce
w ith u nu su ally high variability o f b o th m on ey grow th
an d in terest rates. T h is sectio n clarifies w hy variability
m atters, and d escrib e s th e type o f in terest rate varia­
bility that, in theory, affects e co n o m ic d ecisio n -m ak ­
ing. O th er m e a su res o f in terest rate variability that
w ere exam in ed in th e co u rse o f th is re sea rch are also
in d icated . A sp ecific m easu re o f variability that h as the
d esired th eo retica l prop erty is th en show n to b e p o si­
tively in flu en ced by th e level o f m o n ey grow th variabil­
ity. T his relatio n sh ip is d em o n stra ted u sin g th e ex p e­
rien ce o f th e p a st 60 y ears.
Next, th e article tu rn s to th e link b etw een in terest
rate variability an d e c o n o m ic p erform an ce. T h e th e o ­
retical ch a n n e ls o f in flu en ce o f b o th m on ey an d in ter­
est rate variability on e c o n o m ic p erfo rm an ce are ex ­
plained. T h e se h y p o th ese s are tested using a sm all
redu ced -form m od el o f th e eco n om y. T h e se tests also
d elin eate w h eth er it is an ticip a ted or u n an ticip ated
in terest rate volatility that a cc o u n ts for th e observed
effects. Finally, em p irical estim a tes o f the eco n o m ic
effects o f in terest rate variability over the past four
y ears are p resen ted .
T h e em p irical resu lts poin t to several d ifficulties in
im plem en tin g tests o f th e in terest rate variability hy­
po th esis. Only a few m easu res o f in terest rate variabil­
ity strongly su p p o rt th e h y p o th eses tested . W hile
th e se few have d esirable th e o retica l an d statistical
prop erties, o th e r stan d ard m easu res o f variability p ro ­
vide m ixed results, at best, in th e te sts o f th eir effects
on eco n o m ic p erfo rm an ce. T h is stud y fo cu ses on only
on e m easu re o f in terest rate variability. T h is m easu re
h as significant effects on th e levels o f GNP, p rice s and
real ou tp u t during th e p eriod s exam in ed ; it is also

31

NOVEMBER 1984

FEDERAL RESERVE BANK OF ST. LOUIS

Chart 1

Short-run an d Trend M o n e y G row th

---- ------------------------ ------------------------ ------------------------ --------------1954

Si

58

60

62

(4

66

68

70

72

---- ----------------------------- —
74

76

78

80

82

----- -----1.4
1984

U. Tw o-quarter ra te o f change of M l.
[2 Tw enty-quarter rate of change of M l.
Shaded areas represent periods of business recessions.

show n to b e in flu en ced by th e variability o f m o n ey
grow th.3

THE RECENT EXPERIENCE IN
PERSPECTIVE
T h e grow th rate o f th e m o n ey stock (M l) h as b een
m ore volatile sin c e 1979 th a n in th e previous 27 y ears.
3
The link between money growth variability and these other mea­
sures of interest rate variability was not examined because these
other measures do not appear to systematically affect economic
performance.

32


C hart 1 show s th e an n u al rate o f grow th for tw o-qu ar­
ter periods an d th e lon ger-term tren d rate o f ex p a n ­
sion (five years) sin ce 1953. E co n o m ic th eory an d e m ­
pirical ev id en ce in d icate th at sh arp sw ings in the
tw o-qu arter grow th rate o f th e m on ey stock tem p o ra r­
ily affect th e grow th rate o f o u tp u t an d em p loym en t.
T h e sh ad ed areas in th e ch art, w h ich in d icate periods
o f b u sin ess recessio n , are a sso cia te d w ith relatively
sharp slow ings in sh o rt-ru n m on ey grow th relative to
th e tren d grow th rate.
C hart 1 also show s th at th e gyrations o f m oney
grow th about tren d have b e e n u n u su ally w ide sin ce

FEDERAL RESERVE BANK OF ST. LOUIS

NOVEMBER 1984

C hart 2

Standard Deviations of Quarterly M l Growth
Perceat

1954

Percent

56

58

60

62

64

66

68

70

72

74

76

78

80

82

1984

H F o u r-q u a rte r s ta n d a r d d e v ia tio n o f M l g ro w th (400A ln).
[2 T w e n ty -q u a rte r s ta n d a r d d e v ia tio n o f M l g ro w th (400Aln).

1979. Statistical m easu res o f m o n ey grow th variability
strongly su p p o rt th is visual evid en ce. C hart 2 show s
th e stan d ard deviations for th e grow th rate o f th e
qu arterly m o n ey stock m easu red over th e m o st recen t
fou r an d 20 qu arters sin c e 1953. B o th m e asu res sh ow
relatively high levels o f volatility sin c e 1979.4

"There are several reasons for increased variability of money growth
since 1979. For example, Weintraub (1980), Tatom (1982), Hein
(1982) and Board of Governors of the Federal Reserve System
(1981) emphasize the effect of the credit control program on the
currency ratio and, hence, on the link between reserves and mone­
tary aggregates in mid-1980. This factor contributed to the rise in
the variability of money growth in 1980. Others have emphasized
problems associated with financial innovations, especially late in
1982 and early in 1983, that led to the temporary abandonment of
M1 targeting in October 1982.



The Variability o f Interest Rates
T h e variability o f e x p e cte d retu rn s affects d ecisio n s
b eca u se it in flu en ces th e variability o f w ealth (the
p re sen t value o f e x p e cte d in co m e stream s). F o r exam ­
ple, th e p resen t value o f real in co m e ex p ressed as a
p erp etu ity is inversely p ro p o rtio n al to th e ex p ected
yield . T h at is, w ealth (W) is th e flow o f in co m e p e r y ea r
(Y) d isco u n ted by th e rate o f in terest paid on a p e rp e­
tuity (i), W = Y/i.
W ealth h o ld ers are co n c e rn e d w ith th e likelihood o f
p e r c e n t a g e v a r ia tio n s in in terest rates ra th er th a n ab ­
so lu te p ercen ta g e p o in t ch an g es. T h e w ealth effect o f
a 100 b asis-p o in t ch a n g e in th e ex p e cted in tere st rate
is g rea ter w h en th e ex p e cted in tere st rate is 3 p e rce n t

33

FEDERAL RESERVE BANK OF ST. LOUIS

NOVEMBER 1984

th an w h en it is 15 p e rce n t. In th e form er case, w ealth
ca n ch an g e by ab o u t o n e-th ird ; in th e la tte r case,
w ealth ch an g es by a bo u t 6 p e rce n t. If risk is m easu red
relative to th e ex p e cted retu rn, th e variability o f re­
tu rns sh o u ld be m easu red relative to the m ean return.
T h e logarithm o f th e in tere st rate provides su ch a
m e a n -ad ju sted m easu re. T h e variability o f th e loga­
rithm o f w ealth is d irectly related to th e variability of
th e logarithm o f th e ex p e cted y ield .1 Risk is m easured
h ere u sing th e yield on Aaa bon d s, sin ce it is the lo n g ­
term yield th at is m o st im p o rtan t for cap ital a cc u m u ­
lation an d h as th e g reatest im p act on w ealth .

b esid es th e tw o m easu res in ch art 3, th e stand ard
deviations of: th e level o f th e qu arterly in terest rate,
th e ch a n g e in th e qu arterly in tere st rate an d th e
ch an g e in th e logarithm o f th e qu arterly in terest rate.
To test th e effects o f variability on e c o n o m ic p erfor­
m an ce, ea ch stan d ard deviation m easu re, as w ell as
th e logarithm o f e a c h m easu re, w as u sed . Tw o o th e r
m easu res w ere exam in ed as w ell: th e average a b so lu te
ch an g e in the level o f th e qu arterly in terest rate and
the coefficien t o f variation o f th e qu arterly in terest
rate. All m easu res w ere co m p u te d for four-, 12- an d
2 0 -q u a rter period s.

T h e ex p ected volatility o f rates o f retu rn is an im p o r­
tant d eterm in an t o f in vestm ent d ecisio n s. It is not
possible, how ever, to d irectly m easu re this risk.1 If
'
a sse ssm en ts o f th is risk are reflected in th e actu al
variability o f yield s, th e n th e variability o f in terest rates
in the re cen t p ast ca n b e u sed as an in d icato r o f risk.
Even th en , th e len gth o f th e relevant p ast is essen tially
an em p irical issue.

T h e b est resu lts (judged by ro b u stn ess a cro ss p eri­
ods o f tim e an d relative exp lan ato ry p o w er for e c o ­
n o m ic perform an ce) w ere fou n d u sin g th e 20-q u arter
stand ard deviation o f th e logarithm o f th e in terest rate;
th is m easu re is ca lled VR h ere. Virtually th e sam e
resu lts are o b tain ed u sin g th e 2 0 -q u a rter co efficien t o f
variation, w h ich is sim ply a n alternative w ay o f a d ju st­
ing th e variability o f th e in terest rate for different m ean
levels over tim e. As em p h a siz ed above, it is su ch
m ea n -a d ju sted m e a su res o f variability that, in p rin ci­
ple, sh o u ld m atter. O th er m e a su res gen erally do n ot
have sig n ifican t e c o n o m ic effects; in th o se ca s e s
w h ere sign ifican t e c o n o m ic effects are observed, rela­
tio n sh ip s u sually are eith e r n o t ro b u st o r are sta tisti­
cally in ferior in term s o f exp lan ato ry pow er. T h e se
excep tio n s are n o ted below .

C hart 3 show s th e stand ard deviation o f th e loga­
rithm o f th e qu arterly Aaa bo n d yield, m easu red for
th e fou r an d 20 quarter's en d in g in ea ch q u arter
show n, respectively, for th e p erio d from 1924 to 1983.
T h e se m easu res su m m arize th e riskiness o f yield s
during th e resp ective p ast period . B oth m easu res in d i­
ca te a sh arp ju m p to reco rd levels in th e variability of
in terest rates after 1979. In 1984, th e 2 0 -q u arter m ea ­
sure d eclin ed sh arply from its peak in early 1982, bu t it
rem ain ed n e a r previous peaks achieved in th e m id1930s, early 1960s an d early 1970s.

Other Measures o f Interest Rate
Variability
T h ere are a variety o f o th e r w ays to m easu re the
variability o f in tere st rates. F o r exam ple, Evans (1984)
u ses th e stan d ard deviation o f m onthly in terest rate
ch an g es over a o n e-y ear period. T h e list o f stand ard
deviation m easu res exam in ed for th is article in clu d es,

5
Given expected income, (Y), wealth is W = Y/i and the logarithm (In)
of wealth is In Y - In i. Thus, In W is inversely related to In i and the
variance of In W is proportional to the variance of In i. Note also that
the variance of (In i) is independent of the level of the interest rate
since Var [In (k i)] = Var (In i), where k is a scalar multiple.
6lt would be most useful to measure the variability of the expected
after-tax real rate of return and that of the expected rate of inflation
separately. Makin aqd Tanzi (1983) argue that an increase in both
factors account for the increased volatility of interest rates in 198082. Since both have qualitatively the same effect on investment,
production and money demand incentives, the distinction is ignored
here.

34


In terest rate variability m e a su res in h eren tly d ep en d
on past in terest rates. F or exam p le, a rise o r fall in
in terest rates from o n e level th at h as p ersisted for a
co n sid era b le tim e to a n o th e r th at will p ersist for a
long tim e to co m e, will lead to a tra n sito ry rise in th e
variability o f in tere st rates d urin g th e tra n sitio n from
th e form er to th e la tte r an d for so m e perio d su b se ­
quently. T h e Aaa b o n d y ield h as b road ly follow ed a
p attern o f th ree level shifts from 1955 to 1983; it rose
from abou t 3 p e rce n t d uring 1 9 5 0 -5 5 to n e a r 4.5 p er­
ce n t d uring 1 9 6 0 -6 5 , th e n ro se to ab o u t 8 p e rce n t from
1970 to early 1977, an d finally su rged upw ard to an
average o f 13 p e rce n t in 19 8 0 -8 3 .
T h e th ree m a jo r spikes for th e 2 0 -q u a rter m easu re
in ch art 3 are co n siste n t w ith su ch level shifts in in ter­
est rates. T h ere are tw o w ays to in terp ret th is rise in
variability. O ne w av w ould suggest th at th e rise is
purely arith m etic w ith n o ec o n o m ic c o n s e q u e n c e s for
perceived in v estm en t risk. T h e alternative view is th at
the rise in in terest rate variability a sso cia te d w ith su ch
level shifts in in terest rates m irrors th e in crea sed risk
p erceived from su ch u n fo reseen ch a n g es. M oreover,
this risk, like th e variability m easu re, is red u ced slow ly
over tim e. T h is article assu m es th at th e se co n d in ter­

NOVEMBER 1984

FEDERAL RESERVE BANK OF ST. LOUIS

C h a rt 3

Stan d a rd D e viatio n s of the Logarithm of the Q uarterly A v e r a g e A a a B o n d Yield

1926 28 30

32

34 36

38

40 42

44

46 48 50

52

54

pretatio n is m ore accu rately d escrip tive o f risk p e r­
cep tio n s follow ing su ch level shifts in in terest rates.

The Link Between Variable Money
Growth and Variable Interest Rates
B oth m easu res o f th e variability o f m o n ey grow th
sh ow n in ch a rt 2 ro se sh arp ly b eg in n in g in 1980 and
rem ain ed w ell above th e ir previous average during
198 0 -8 3 . T h e variability o f in terest rates ro se sim ilarly,
as ch art 3 show s. An em p irical investigation o f th e link
betw een th e variability o f m o n ey grow th an d th at of
in terest rates w as co n d u cte d for th e 2 0 -q u arter sta n ­
dard deviation m easu res sh o w n in ch a rts 2 an d 37
T he best univariant time series model for VR is a second-order
autoregressive and second-order moving average process during
the periods 1/1955—IV/1978 and 1/1955—IV/1983.



56

58

60 62

64

66

68 70

72 74

76 78 80 82 1984

Lags o f th e 2 0 -q u a rter stan d ard deviation o f quarterly
m on ey grow th sh ow n in ch art 2, VM, w ere in tro d u ced
to test w h eth er m o n ey grow th variability in flu en ces
in terest rate variability, VR. T h e resu lts for th e period
I/1955-1V/1983 are sh ow n in table 1.
T h e re is a sign ifican t positive link b etw een a rise in
th e variability o f m o n ey grow th an d th e variability of
in terest rates." W hen o n e co n tro ls for th e p ast two
qu arters o f th e variability o f in tere st rates (longer lags

8
These tests, including past information on interest rate and money
growth variability, use the Granger causality test specification. How­
ever, unidirectional causality is not asserted, necessary, or tested
here. Also, interest rate variability may be a function of other
sources of increased risk including increased variability of fiscal
policy variables. The importance of other factors is apparent over
the 1955 to 1978 period, when VR showed considerable variation,
but VM was essentially unchanged.

35

FEDERAL RESERVE BANK OF ST. LOUIS

NOVEMBER 1984

Table 1
The Effect of Money Growth Variability on the
Variability of Interest Rates_______________
Dependent Variable: VR,1
1/1955—IV/1983

111/1924— IV/1954

Coefficient
Constant
VR,,
VR,2
VM,,'
VM,2
R2
S.E.
0(12)
Pi
P2

t-statistic

Coefficient

t-statistic

0.245
1.877
-0.920
0.827
-0.762

1.96
51.52
-24.53
3.87
-3.41

0.117
1.763
-0.790
0.153
-0.147

1.62
34.86
-15.59
3.09
-2 .8 7

0.996
0.394
7.74
-0.185
0.380

0.993
0.282
11.62
-2 .1 5
4.42

—
—

—
—

1
VR, is the standard deviation of the logarithm of the Aaa bond yield over the 20 quarters ending in
quarter t; VM, is the standard deviation of money growth measured over the same period.

are n o t significant) an d for statistically significan t s e c ­
o n d -o rd er au to co rrelatio n , th e variability o f m o n ey
grow th over th e previous tw o qu arters h as significant
effects on th e cu rren t level o f th e variability o f in terest
rates.” A rise in m on ey grow th variability initially h as a
significant an d positive effect o n in tere st rate variabil­
ity; th is effect is offset in th e n ex t qu arter.1 A ccord ing
"
to table 1, th e sign ificant positive effect o f th e variabil­
ity o f m oney grow th on in terest rate variability is
tran sitory .1
1
A ttem pts to re p licate th e table 1 resu lts from 1/1955IV/1978 w ere u n su ccessfu l; th e variability o f m o n ey
grow th did n ot significantly affect th e variability of
in terest rates over th is earlier p eriod . A p rin cip al rea­

9
The Q-statistic indicates that the residuals in the equation estimate
are not significantly correlated with their own past for up to 12 past
quarters, although the same results holds for one to 24 past values
of the residuals.
1 The results do not arise from the computational relationship arising
0
from the use of moving standard deviations. Virtually identical
results are obtained by relating changes in VR to AVR„, VR,_2, and
either VM,, and VM,_2, or AVM,,. First-differences of VM or VR are
not computationally related.
"The steady-state response of VR to a rise in VM involves the lagged
adjustment of VR to its own past values. This response is 1.52, but
its standard error, found from the variance-covariance structure of
the coefficients on the lags of VM and VR, is 2.00. Thus, the effect of
a change in VM is transitory. Whether a rise in money growth
variability, in theory, has a permanent or transitory effect on interest
rate variability is a question that is not resolved here. The empirical
evidence clearly indicates that the effect is transitory.

36


so n for th is resu lt is th at th e variability o f m o n ey
grow th over th e p eriod I/1955-III/1979 w as relatively
co n sta n t; th e stan d ard deviation o f VM over th is p e ­
riod is 0.3 p ercen t, o n ly 15.3 p e rce n t o f th e m ean level
of m on ey grow th variability over th e period . T h e varia­
bility o f m o n ey grow th from 1955 to 1979 w as to o sm all
an d stead y to provide in form ation o n th e p o ten tial
im p act o f ch a n g es in m o n ey grow th variability on in ­
terest rate variability.'-

Earlier Evidence: 1924 to 1954
Prior ev id en ce o f a sy stem atic relatio n sh ip betw een
th e variability o f m o n ey grow th an d in terest rates d o es
exist, how ever. F ried m an an d Sch w artz (1963) have
sh o w n th a t m o n ey g row th variability w as m u ch
g reater b efore W orld W ar II th a n it w as from th e en d o f
W orld W ar II to th e early 1960s.1 T h e variability o f
3
m oney grow th also flu ctu ated m u ch m ore before
W orld W ar II. T h e average level o f VM from 1/1924—
IV/
1954 is 7.5 p e rce n t, a n d its stan d ard deviation is 3
p ercen t; th e form er is m ore th an th ree tim es as large,

,2The mean of AVM from 1/1955-111/1979 is 0.0021 and its standard
deviation is 0.1101. Over this period, AVM is an independently
distributed random variable with a Q-statistic, Q(12), of 7.34, which
indicates that AVM is not correlated with its past history. Over the
longer period to IV/1983, AVM is described by a first-order moving
average process.
'3Friedman and Schwartz (1963, pp. 592-638). Their M1 data until
1947 is used to compute VM below.

FEDERAL RESERVE BANK OF ST. LOUIS

an d th e la tte r m easu re is abo u t 10 tim es as large as
th at observed from 1955 to 1979. T hu s, th is earlier
p eriod sh o u ld provide u seful in fo rm atio n on th e ef­
fect o f m o n e ta iy grow th variability on in terest rate
variability.
Over th e period III/l 924-IV/l 954, th ere is a statisti­
cally sign ificant positive relatio n sh ip betw een VR and
VM (see table 1). T h e resu lts are sim ilar to th o se for th e
1 9 5 5 -8 3 p eriod . In p articu lar, for th is earlier period,
in crea ses in th e volatility o f m o n ey grow th tem p o rar­
ily an d significantly raised th e volatility o f in terest
rates. A u to co rrelated erro rs are not significant in the
earlier p eriod acco rd in g to th e Q -statistic. T h e dy­
nam ic stru ctu re for in terest rate volatility is about the
sam e as in th e la ter p erio d .M T h e difference in th e
m agnitu d e o f th e m o n ey grow th variability effect in
th e tw o p eriod s is n o t m eaningfu l; th e m on ey stock
data u sed in th e early p eriod are largely b ased on end o f-m on th data, w hile th o se in th e later period are
b ased on averages o f daily figures.

VARIABILITY OF MONEY GROWTH
AND INTEREST RATES: THE
AGGREGATE DEMAND CHANNELS
M ascaro and M eltzer (1984) have attribu ted part o f
the su b stan tial ju m p in in terest rates an d th e d eclin e
in real GNP grow th in 1980-81 to th e in creased u n c e r­
tainty arising from g reater variability o f m o n ey grow th.
T h ey attribu te a 1.3 p ercen tag e-p o in t rise in th e aver­
age lon g rate an d a 3.3 p ercen tag e-p o in t rise in th e
average sh o rt rate over th e n in e qu arters, IV/1979-IV/
1981, to a rise in m o n e ta iy u n certain ty .1
3
M ascaro an d M eltzer em p h asize a m oney d em an d
ch a n n el for th e effect o f m o n eta iy u n certain ty on th e
econom y. A rise in m o n e ta iy u n certain ty in creases th e
d em an d for m oney. T h ey in d ica te th at an in crea se in
th e d em an d for m o n ey raises th e in terest rate and
red u ces aggregate d em and . In add ition, they argue,
p rices an d real o u tp u t fall b eca u se o f th e red u ctio n in
aggregate d em an d . F u rth erm o re, th ey suggest th at th e
grow th ra tes o f output, p rices an d GNP are likely to be
fu rth er affected by th e re d u ce d d em an d for cap ital.
T h eir em p irical an alysis fo cu se s on th e rise in in terest
rates on b o th sh o rt- an d long-term d ebt d ue to th e risk
p rem iu m .1
6
1 0ver this period, the t-statistic for the steady-state response of VR to
4
VM is 0.12; the response of VR to VM is transitory.
'5
Belongia has argued that nominal GNP growth was depressed by
the rise in monetary uncertainty in 1980. Both Mascaro and Meltzer
and Belongia use a measure of the variability of unanticipated
money growth rather than that of actual money growth.



NOVEMBER 1984

T h e re is a s e c o n d d e m a n d c h a n n e l, how ever,
th rou gh w h ich m o n ey grow th variability low ers in ­
v estm ent. W hen m o n ey grow th is m o re variable, the
variability o f th e o u tp u t o f good s an d services, em p loy ­
m ent an d earn in gs w ill rise. T h ere will also b e greater
risk a sso cia ted w ith th e ex p e cted retu rn s from both
existing cap ital an d p ro sp ectiv e in vestm en ts. If sto ck ­
h o ld ers an d len d ers are risk averse, an d if existing
ex p an sio n p lan s an d so u rce s o f fin an cin g are to be
m aintain ed m arket rates o f retu rn m u st rise to c o m ­
p en sate for in crea sed risk. Of co u rse, w ith h ig h er co sts
o f cap ital fun d s an d g reater risk a sso cia te d w ith p ro ­
spective in v estm en t p ro jects, in v estm en t m anagers
will b o th re d u ce in v estm en t an d e n h a n c e th e flexibil­
ity o f th e ir asset p o rtfo lio s.1 T h u s, b ec a u se it co n trib ­
7
u tes to m o re v olatile in v e stm e n t re tu rn s, erra tic
m oney grow th raises th e level o f observed m arket rates
and retard s an d re d irects th e d esired stocks an d u s ­
age o f p lant an d eq u ip m en t.
At u n ch an g ed in terest rates an d co sts o f fund s for
firms, a rise in th e varian ce o f ex p e cted retu rn s from
in vestm en t in p lant an d eq u ip m en t re d u ce s th e in ­
centive to invest. T h e portfolio shifts em p h a siz ed by
M ascaro an d M eltzer, an d G ertler an d G rinols (1982),
involve an in crea se in m o n ey d em an d th at raises in ­
terest rates. Investm ent d em an d in th e ir an alysis d e ­
clin e s along a given in vestm en t d em an d curve. But
even at an u n ch an g ed co st o f cap ital, firm s faced w ith
riskier ex p e cted in co m es w ill re d u ce in v estm en t.

,6Bodie, Kane and McDonald (1983) find evidence of a rise in the risk
premium on long-term bonds. Gertler and Grinols (1982) show that
a rise in monetary growth uncertainty raises money demand and
reduces investment, but their result follows primarily from an in­
crease in the variability of expected inflation, not from an increase in
the variability of the real rate of interest. If variations in money
growth affect real output and employment in the short run, as mone­
tary explanations of the business cycle indicate, then monetary
randomness also affects the variability of the expected real rate and
investment incentives. Indeed, this is more likely if the link between
money and prices has long lags as shown in the model used below
or in Barro (1981). A rise in monetary variability raises the variability
of yields on capital and reduces investment, either through in­
creased variability of expected inflation or of real rates of return
(both of which are captured in the variability of nominal interest
rates), or both.
Makin and Tanzi attribute the high volatility of interest rates from
1980 to the end of 1982 to increased volatility of both expected
inflation and after-tax real rates of return. Their evidence for the
former, however, is survey data on expected inflation for a six-month
horizon during a period in which substantial price level shocks were
occurring.
"Obviously a rise in risk tends to reduce both the supply of saving and
investment demand at given market interest rates. Thus, the effect
on observed market rates is not as straightforward as it may appear
in the text. If suppliers of credit are more risk averse than firms that
invest in plant and equipment, then market rates (not risk-adjusted)
will tend to rise. This result also depends on relative interest elastici­
ties of supplies and demands for credit and equities.

37

FEDERAL RESERVE BANK OF ST. LOUIS

NOVEMBER 1984

Figure 1
The Channels of Influence of Increased Risk

Su ch a d eclin e in th e d em an d for good s and services is
a cco m p an ie d by a re d u ctio n in th e d em an d for cred it,
so th at in terest rates ten d to fall along w ith aggregate
dem and .
T h e left side o f figure 1 su m m arizes th e tw o aggre­
gate d em and ch a n n e ls. T h e se effects arise in th is in ­
sta n ce throu gh in crea sed m o n ey grow th variability.
O th er ch an g es th at raise risk a sse ssm en ts abou t fu­

38


ture e co n o m ic co n d itio n s or b u sin ess cy cle risk cou ld
alter in terest variability as well, how ever. T h ere ap ­
pear, th en , to b e at least tw o ch a n n e ls th rou g h w h ich
m o n eta iy grow th variability affects aggregate d em an d :
in crea sed m o n ey d em an d an d re d u ce d in vestm en t. Of
co u rse, th e two ch a n n e ls have o p p o site im p licatio n s
for in terest rates; both, how ever, im ply re d u ce d aggre­
gate d em an d and, h e n c e , low er n om in al GNP, real
output an d p rices. T h e M ascaro -M eltzer evid en ce on

NOVEMBER 1984

FEDERAL RESERVE BANK OF ST. LOUIS

in terest rates suggests th at th e rise in m o n ey d em and
d om in ates risk-related red u ctio n s in th e d em an d for
goods an d services.
Figure 2

Evans (1984) an d T atom (1984a) sh o w th at a rise in
the variability o f in terest rates h as a significan t n ega­
tive effect on th e level o f a n n u al o u tp u t. T h is effect is
co n siste n t w ith th e tw o aggregate d em an d ch an n els
sh ow n on th e left side o f figure 1, bu t it en co m p asses
o th e r so u rces o f a rise in su ch variability b esid es a rise
in m o n etary variability. To th e ex ten t that su ch varia­
b ility a rise s from m o n e ta ry variability, it sim p ly
reflects th e ch a n n e ls throu gh w h ich m o n ey grow th
variability affects th e levels o f in terest rates, spending,
ou tp u t an d p rices.

The Effect of an In c re a se in R isk on Output and P ric e

VARIABILITY OF INTEREST RATES
AND MONEY GROWTH: AGGREGATE
SUPPLY
A rise in risk im plies, at th e p ro d u cer level, in ­
crea se d variability o f ex p e cted sales, real ca sh flows or
profits. A rise in th e variability o f retu rn s to p ro d u ctio n
may b e view ed as eith e r an in crea sed co st o f u sin g the
firm ’s cap ital to p ro d u ce o u tp u t o r a re d u ctio n in th e
value o f given ex p e cted in co m e. In eith e r case, ex p o ­
sure to th e in creased risk can be le ssen e d by red u cing
ex p ected output, p ro d u ctio n an d cap ital em p loy m en t
in p ro d u ctio n . T hu s, an in crea se in risk re d u ce s d e ­
sired supply, given ex p e cted p rices o f in p u ts and o u t­
put."1T h is effect is su m m arized in th e third ch a n n e l of
in flu en ce show n in figure 1. W h eth er su pply is re ­
d u ced m ore th an d em an d is not obvious. T h u s, w hile
th e co n se q u e n ce s o f in creased risk for sp en d in g and
output are u nam biguous, given th e p rice level, the
co n se q u e n ce s for th e p rice level are not.
Figure 2 show s th e effect o f a rise in risk, VR, on
aggregate d em an d an d supply. Initially, th e eco n om y
is a ssu m ed to o p erate at p o in t A w here, at p rice level
P„, th e q u an tities o f good s and services d em an d ed and

,8De Vany and Saving (1983) provide a model of the firm in which
greater variability of demand will yield higher pecuniary prices, the
substitution of inventory for plant and equipment at a given expected
output rate to the extent the product is storable, and, a reduction in
expected output relative to capacity. Such reductions in the effi­
ciency of firms indicate an overall loss in economic capacity or, for a
given stock of plant and equipment and employment, less expected
output. The firm in their model can be risk-neutral. Sandmo (1971)
and Holthausen (1976) show that risk-averse firms reduce capacity
and output in response to increased uncertainty, yielding similar
price and output implications.



output

su p p lied (y0) are equal. An in crea se in risk red u ces
aggregate d em an d to AD,; at (P0, y,), m arket in terest
rates, w h ich are im p licit in AD an d AD,, are h ig h er
than at (P0, y j . Aggregate su pply is red u ced as well,
how ever. As draw n in figure 2, AS shifts leftw ard m ore
th an AD, so th e p rice level rises to P,. Thu s, th e e c o n ­
om y o p erates at p o in t B. Of co u rse, th e p rice o u tco m e
d ep en d s on th e relative m agn itu d e o f th e su pply and
d em an d shifts.
Earlier stu d ies o f m o n etary u n certa in ty an d in terest
rate variability have focu sed prim arily on th eir effects
on n om in al an d real GNP an d on th e in terest rate. T h e
co m m o n assu m p tio n a p p ears to be th at th e effects on
sp en d in g an d o u tp u t arise from an u n a n ticip a ted shift
in aggregate d em an d , so th at th e p rice level ch a n g es in
th e sam e d irectio n as sp en d in g o r output. T h e m odel
u sed below to asse ss th e effects o f in terest rate varia­
bility is a red u ced -fo rm m od el for GNP, p rice and o u t­
put grow th th at p erm its all th ree effects to be exam ­
ined ; th is m od el is sh o w n in table 2.
In th e m od el w ith ou t in terest rate variability, GNP
grow th d ep en d s on cu rren t an d p ast grow th rates of
th e m oney stock, cy clically a d ju sted federal ex p en d i­
tures, energy p rices an d a strike variable."' Inflation

39

NOVEMBER 1984

FEDERAL RESERVE BANK OF ST. LOUIS

Table 2
The Reduced-Form Model________________________________
4
(1) GNP = 0„ +

2

4
fJ„, M,_, +

i= 0
20

(2) P =

2 y, M +
,_,
i= 0

2

6
PJ+6 ^

+

j= 0

2

pk+„

+ P,8 AS,

k=0

4

2 7j, 2 p'^ + yx D1 + y1 D2
1
7
j= 1

(3) X = GNP - P
where
GNP = gross national product
P = GNP deflator
X = real GNP
M = money stock (M1)
E = cyclically adjusted federal expenditures
p* = the producer price index for fuel and related products and power deflated by the business sector
price deflator
AS, = the quarterly change in the ratio of days lost due to strikes to the civilian labor force
A dot over a variable, for example a, represents 400 Ain a

d ep en d s on cu rre n t an d p ast grow th rates o f th e
m o n ey stock, energy p rice s an d dum m y variables for
the w age-p rice co n tro l an d d eco n tro l period s o f the
early 1970s.
In tro d u cin g in terest rate variability in to this m odel
perm its its effects on GNP an d th e p rice level to be
exam in ed d irectly. T h e real o u tp u t grow th effect sim ­
ply equals th e d ifference b etw een th e GNP grow th and
inflation effects. In ad dition , th e eq u ation in table 1
(1/1955—
IV/1983) ca n b e u sed to d elin eate an ticip ated
an d u n an ticip ated in terest rate variability. T hu s, the
issue o f w h eth er in tere st rate variability effects arise
from u n an ticip ated o r an ticip ated ch an g es in variabil­
ity ca n b e exam ined .

,9The model estimation uses quarterly data for growth rates. Evans
and Tatom (1984a), use annual data for the level of output and, in
the latter, the level of prices.
The strike variable, S, is based on days lost due to work stop­
pages. The details for its construction are available upon request
from the author. The coefficients for money and expenditure growth
were estimated using a fourth-degree polynomial with head and tail
constraints. The energy price coefficients were estimated using a
third-degree polynomial and were constrained to sum to zero. This
constraint cannot be rejected in either period.

40


INTEREST RATE VOLATILITY AND
ECONOMIC PERFORMANCE
To exam in e w h eth er re ce n t ch a n g es in in terest rate
variability affected to tal sp en d in g or GNP, th e m o d i­
fied version o f th e A n d ersen -Jo rd an eq u atio n show n
in table 2 w as u sed for GNP. Sin ce in terest rate variabil­
ity ro se sh arp ly b egin n in g in 1979, tests w ere c o n ­
d u cted for tw o p erio d s: I/1955-IV/1978 an d 1/1955IV/1983.-0
T h e resu lts for GNP grow th are given in table 3. In
bo th period s, a rise in th e variability o f in terest rates in

“ The level of interest rates can be controlled for in tests such as
these, but this raises an identification problem; a change in interest
rate variability affects the level of interest rates and vice versa. Such
an attempt to control for interest rates would capture variability
effects in the interest rate effects, or vice versa. The interest rate
specification in Tatom (1983), the contemporaneous and five lagged
values of the changes in the logarithm of the Aaa bond yield, was
added to the GNP equation in table 3 to check for their importance.
The lagged variability of interest rate measure remains significant in
both periods, despite the inclusion of these interest rate controls, so
that the results reported do not arise from changes in the level of
interest rates. Similar controls were examined for the price equation;
see footnote 28 below.

FEDERAL RESERVE BANK OF ST. LOUIS

NOVEMBER 1984

Table 3
Interest Rate Variability and GNP
Dependent Variable: GNP,
Independent
Variables
Constant

M

4
2 Pi.,
i= 0

£

4
2
j=0

AS,
pr
p’ ,
p«
p«
P
*M
p«
p«
VR_,
R2
SE
DW

I/1955-IV/1983
Coefficient

I/1955-IV/1978

t-statistic

Coefficient

t-statistic

5.389

6.02

3.992

4.01

1.061

8.10

1.142

7.99

-0.000

-0 .0 0

-0.006

-0 .0 8

-0.520
-0.041
0.005
-0.005

-3 .9 8
-1 .6 6
0.28
-0 .3 6
-2 .1 2
-1 .9 3
0.99
2.68
-4 .8 5

-0.497
-0.035
0.011
-0.004
-0.038
-0.046

-3 .9 3
— 1.18
0.52
-0 .2 3
-2 .1 8
-2 .2 8

0.015
0.097
-0.152

0.38
2.85
-2 .0 9

-0.031
-0.033
0.029
0.075
-0.297
0.52
3.099
1.88

0.57
2.892
2.05

th e previous q u arter sign ifican tly an d p erm an en tly
red u ces th e grow th rate o f GNP.2 Lon ger lags (up to
1
eight quarters) o n th e variability o f in tere st rates w ere
exam ined , bu t n o n e ad d ed significantly to th e table 3
equation, w ith o r w ith ou t an insignifican t co n te m p o ­
ran eou s term . In th e m o re re ce n t period, th e effect is
larger th a n in th e p re-1979 sam p le period, bu t bo th
resu lts in d icate th a t variability m atters. T h e eq u ation
in table 3 w as also estim ated to th e th ird q u arte r o f
1981, th e previous cy clical peak. T h e co efficien t on
in terest rate variability, VR,_„ is ab o u t th e sam e as in
th e p re-1979 case, -0 .1 3 8 (t = -2 .0 3 ); thu s, th e ch an g e

in th e volatility co efficien t o cc u rre d as a resu lt o f th e
ex p e rie n ce from m id-1981 to th e en d o f 1983.”
T h e variability m e a su re VR, c a n b e d eco m p o sed into
an an ticip a ted co m p o n e n t, VR,, th e p red icted value
from th e 1/1955—
IV/1983 estim a te in tab le 1, an d an
u n a n ticip a ted co m p o n e n t, VRE„ th e resid u al from th e
eq u atio n . T h e te sts o f th e GNP effect c a n b e co n d u cte d
u sin g ea ch o f th e se m e a su res to clarify th e so u rce o f
th e in terest rate variability effect. W hile e ith e r effect is
co n siste n t w ith th e theory, th e im p o rta n ce o f m o n eta iy variability as a m a jo r so u rce o f th e GNP effect is
stren g th en ed if it is fou n d th a t th e a n ticip a te d co m p o -

2 For the longer period (1/1955-IV/1983), the coefficient of a contem­
1
poraneous four-quarter standard deviation of interest rate changes
is significantly negative in the GNP growth equation. The lagged
value of the average absolute change in the level of interest rates
also significantly and negatively affects GNP whether measured
over four, 12 or 20 quarters, and in both periods. None of the latter
measures provide as much explanatory power as VR in the text.

“ The equation estimated to the end of 1978 is stable when extended
to 111/1981. The F-statistic for the additional 11 observations is F1 8
13
= 0.93. When the equation ending in 111/1981 is extended to IV/
1983, it is not stable; the F-statistic for the additional nine observa­
tions is F994 = 2.89. The critical F is 1.98 (5 percent) or 2.60 (1
percent), th e instability of the equation during late 1981 and 1982 is
also discussed in Tatom (1984b).




41

FEDERAL RESERVE BANK OF ST. LOUIS

n en t o f variability, w h ich d ep en d s, in part, o n m o n ey
grow th variability, is resp o n sib le for th e GNP effect.
T ests o f cu rre n t an d lagged values o f b o th VR and
VRE w ere co n d u cte d . It m ight seem th at only th e a n ­
ticip a te d an d u n a n tic ip a te d c o m p o n e n ts o f VR, ,
sh ould be exam in ed b ec a u se it is th e sign ifican t varia­
ble in table 3. But VR, an d lagged VR term s beyond one
lag are co n strain e d to zero in table 3, a result that may
only have b een su p p o rted in th e lag sea rch over VR by
co n strain in g th e a n ticip ate d an d u n an ticip ated co m ­
p o n en t to be equal in e a c h o f th e o m itted period s.
T h u s, it is u seful to ex am in e all o f lags o f VR an d VRE,
regard less o f th e actu al VR lags selecte d above. C ur­
ren t o r lagged values o f u n an ticip ated volatility, VRE,
a re n o t s ta tis tic a lly sig n ifica n t in e ith e r p erio d ,
w h eth er an ticip ated in terest rate variability is in ­
clu d ed o r not. T h e cu rren t o r first lag o f an ticip ated
volatility, VR, o r VR,_,, are significant, in b o th period s;
ad d itional lags are not sign ificant for eith e r sp ecifica ­
tion in eith e r period.
T h e resu lts u sin g eith e r VR, o r VR,_, are virtually
id en tical; th o se u sin g VR, are rep o rted h ere. T h e co e f­
ficient on VR, is -0 .1 5 8 (t = -2.181 in th e I/1955-IV/1978
p eriod a n d -0 .2 8 9 It = —
4.75) in th e lo n g er period . B oth
estim a tes are essen tially id en tical to th o se sh ow n for
VR,_, in table 3. Further, n o n e o f th e o th e r co efficien ts
in table 3 are affected w h en VR, is u sed an d th e stan d ­
ard erro r o f th e estim ates co m p are favorably. In the
period en d in g in IV/1983, th e stan d ard erro r is 3.111; in
th e earlier period it is 2.886. T h e a d ju sted R2s are the
sam e as in table 3. T h u s, th e so u rce o f th e in terest rate
variability effect in table 3 is an ticip ated variability.-3
T h e resu lts in d icate th a t th e effect o f in tere st rate
variability o n GNP grow th sin c e 1979 d iscu sse d below
is th e sam e w h eth er th e m easu re ch o se n is th e actual
past level o f volatility, VR, ,, o r co n tem p o ra n e o u s or
lagged an ticip ated volatility (VR, orVR,_,).

Some Problems with the G NP Estimates
It sh ould be n o ted that th e in terest rate variability
m easure, eith e r VR, , o r VR„ en ters th e GNP eq u ation in
level form. T hu s, a rise in th e level o f VR perm an en tly
affects th e grow th rate o f n o m in al GNP. T e sts o f ad d i­
tion al lags, esp ecially VR,_, and VR,.,, respectively, in d i­
ca te th at they are insignificant. T h is result suggests
th at a p erm an en t rise in th e variability o f in terest rates
red u ces bo th th e level o f GNP in th e sh o rt ru n and th e
grow th rate o f sp en d in g p erm an ently.
2 The significance of VR in both periods indicates that, given past
3
interest rates, VM significantly reduces GNP. When VM and its lags
are added alone to the table 1 equations, however, they are not
significant.

42


NOVEMBER 1984

T h e la tte r effect is th eo retica lly im p lau sib le; th e
cap ital stock eventually sh o u ld b e a d ju sted to its
low er d esired level. O n ce th is h a s o ccu rred , th e p e r­
m an en t effect o n th e grow th o f n o m in al sp en d in g an d
real ou tp u t sh o u ld d isap p ear. T h e d yn am ic stru ctu re
of VR in d icates, how ever, th at in tere st rate volatility
ten d s to revert to its m ean follow ing ch a n g es in m on ey
grow th variability o r ran d o m sh o ck s. T h u s, b eca u se
ch a n g e s in in te re s t ra te v o latility are tra n sito ry ,
ch an g es in th e GNP grow th rate arisin g from in terest
rate variability are tran sitory as w ell.
A seco n d c o n c e rn w ith th e GNP ev id en ce is th at
variability m easu red over tw o sh o rte r tim e h orizon s
(four an d 12 qu artersl d o es n o t have a significant effect
on GNP grow th, n o r do a few o th e r m easu res o f varia­
bility for any h o rizo n . T h e re are two w ays to in terp ret
the GNP resu lts. O ne in terp reta tio n is th at ch a n g es in
in tere st rate variability are o n ly im p o rta n t w h en
view ed from a lo n g er tim e h o rizo n and, even th en ,
only certa in m e a su res o f variability (such as VR, the
coefficien t o f variation o f th e in terest rate o r average
absolu te ch a n g es in th e in terest rate) ca p tu re th e re le­
vant risk. T h e o th e r alternative is th at th e GNP resu lts
are sp u riou s. T h e c o n siste n t resu lts from th e tests for
p rices b elo w suggest th at th e la tte r in terp reta tio n is
n o t valid.

The Effect o f Interest Rate Variability
on Prices
T h e th eo retica l d iscu ssio n in d ica tes th at th e effect
of in crea sed in tere st rate variability on p rices is an
em pirical issu e; it d ep en d s on w h e th e r aggregate su p ­
ply is affected m o re o r less th a n aggregate d em an d . To
a ssess th is relatio n sh ip , a stan d ard p rice eq u atio n
w h ich em p h asizes th e link b etw een m o n ey grow th
an d p rices, co n tro llin g for sh o ck s su ch as w age and
p rice co n tro ls an d energy p rice ch an g es, is em ployed.
T h e p rice eq u atio n u sed for th e test o f an in terest rate
variability effect is th e seco n d eq u atio n in table 2.-‘
Again, b o th p erm an en t an d tra n sito iy effects o f in ter­
est rate variability w ere exam in ed .
As w ith th e GNP ex p erim en ts, th e five-vear m easu re

2The coefficients on money growth are estimated to lie along a third4
degree polynomial.
“ A 12-quarter measure of the standard deviation of the logarithm of
the interest rate has a positive and statistically significant effect at
one lag in the period ending in IV/1983, but the equation has a
higher standard error than the same estimate using the 20-quarter
variability measure. The 20- and 12-quarter average absolute
change in the interest rate also significantly raises then lowers
inflation at lags one and two, respectively, over the longer period,
but no effect is significant in the earlier period. See also footnote 31
below.

FEDERAL RESERVE BANK OF ST. LOUIS

NOVEMBER 1984

Table 4
Interest Rate Variability and Prices_________________________
Dependent Variable: P,
Independent
Variables

1/1955— IV/1983
______________________
Coefficient
t-statistic

1/1955— IV/1978
______________________
Coefficient
t-statistic

20

0.939

20.41

1.010

24.05

D1
D2

-1.442
1.419

-2.07

-3 .3 7

Pm

0.008

P«
P'-3

0.051
-0.017

-1.942
1.306
0.012
0.041

Pm
AVR_,
A VR,_2

0.031
1.275
-0.951

-0.018
0.030
1.093
-0.963

-1 .1 5
2.11
3.38
-2.84

M

2 y,
i= 0

R2
SE
DW
P

0.80
1.179
2.11
0.37

of variability (VR) is significant and provides the great­
est explanatory pow er of the alternative m easures.-'1
Tests for statistically significant lags of VR indicate that
the past three quarters of interest rate volatility affect
inflation. The effects of VR sum to zero, implving that
there is no p erm anen t effect of a ch an ge in VR on
inflation.-" Thus, the ap p rop riate expression includes
AVR, , and AVR,_2. The price equation results for the
two periods are sum m arized in table 4. In addition,
these results indicate that there is no p erm an en t effect
of a change in VR on the level of prices, since the
coefficient on AVR,_, is opposite in sign and statistically
not significantly different from that for AVR,
A ccording to these results, a rise in VR initially raises
inflation and the p rice level one quarter later, then
depresses inflation and the price level in the subse­
quent quarter. After two quarters, both inflation and

“ The F-statistics for this constraint are Fi e = 0.85 for the 1/1955—
4
IV/1978 period and F, 1 5 = 0.00 in the 1/1955—IV/1983 period.
0
2 This result is at odds with that found using annual data where
7
interest rate variability appears to have a permanent positive impact
on the price level. See Tatom (1984a). It is shown below, however,
that a distinction between anticipated and unanticipated variability
yields results that are consistent with the annual result for the price
level.



1.97
0.74
4.19
-1.01
2.40
4.80
-3 .6 2

1.93
0.80
2.59

0.81
1.112
2.00
0.16

the price level are unaffected.-7 The sum of the coef­
ficients on the ch an ge in interest rate variability in
table 4 is positive, but not significantly different from
zero. In the I/1955-IV /1978 period, the sum is 0.130
(t = 0.62), while in the I/1955-IV/1983 period it is 0.283
(t = 1.27).2
R
The an ticip ated/u nan ticipated variability d istin c­
tion w as also em ployed to isolate the inflation effect.
W hen VR, ,, VR, , and VR, , are d eco m p osed into antici­
pated and u n an ticip ated co m p o n en ts using the table
1 equation, only the lagged unan ticip ated com p onen t,

2 The price equation is stable across the two periods in table 4. The
8
F-statistic for the last 20 observations is F^ M = 1.66, which is below
the critical value of 1.69 (5 percent significance level). The equation
is not stable without the interest rate variability term. See Tatom
(1984b), where tests of other variables (such as shifts to other
checkable deposits or unusual recent movements of exchange
rates, the volatility of money growth, unemployment or interest
rates) that might affect prices indicate that, since mid-1981, only
unemployment and the previous quarter’s change in the In of the
Aaa bond rate significantly affect the price level. The unemployment
result does not hold before IV/1981 and disappears even in the later
period when the past interest rate change is included. The bond
yield result is robust across the periods. When either of these varia­
bles is added to the estimates in table 4, however, it is not significant
in either period, and the interest rate variability result is unaffected.
This also indicates that controlling for the level of interest rates in
table 4 does not affect the result there.

43

FEDERAL RESERVE BANK OF ST. LOUIS

VRE,.,, is significant, and in b o th period s. T e sts o f lags
of VRE or VR y ield ed th e sam e co n c lu sio n for VRE and
in d ica te d th a t b o th VR, an d VR, , term s are s ta ­
tistically sign ifican t in b o th p eriod s. In addition, the
co efficien ts on th e tw o an ticip ated variability term s
ca n b e co n strain e d to sum to zero; in th e 1/1955-1V/
1978 period, F, h = 0.00, w hile in th e lo n g er period, F,
.
= 0.70.
T h e inflation eq u atio n s w ith VRE, , o r AVR, are
given in table 5, along w ith th e inflation equation
co n tain in g b o th variables.--’ T h e resu lts do n ot d is­
crim in ate betw een th e alternative h y p o th eses th at
only an ticip ated (AVR) o r u n a n ticip a ted (VRE) in ter­
est rate variability m atters in th e I/1955-IV/1983 period.
E ith er sp ecificatio n y ield s th e sam e a d ju sted R2 and
stand ard erro r o f estim ate; w h en o n e o f th e se variables
is in clu d ed , th e o th e r is not significant. In th e earlier
p erio d , ho w ever, lag g ed u n a n tic ip a te d v o la tility
slightly ou tp erform s th e a n ticip ate d variability sp e ci­
fication. M oreover, th e tests sh o w th at w h en VRE,_, is
in clu d ed , inform ation on a n ticip ate d variability is not
statistically significant.
T h e effect o f in tere st rate volatility on p rices is u n ­
am biguous, acco rd in g to th e re su lts in table 5. In p ar­
ticular, a rise in an ticip ate d variability tem porarily
raises inflation, leaving th e p rice level u nam biguously
higher. Although it m ay ap p e ar th at a rise in u n a n tic i­
pated variability p erm an en tly raises p rices a n d in ­
flation, only the form er co n clu sio n is co rrect; this
result is th e sam e as that o btain ed w h en only a n tici­
p ated inflation is co n sid ered . A rise in th e u n a n tic i­
p ated variability o f in tere st rates ca n n o t p e r m a n e n t ly
raise inflation b ecau se , by definition, th e level o f u n a n ­
ticip ated variability is only a tran sitory p h en o m en o n .
T h e evidence su p p o rts th e d o m in an t su pply-sid e

“ In table 4, the included lags of VR can be written as (VR„ VR,_,,
VR,_2, VR,_3 where the coefficient on VR, is constrained to zero. A
),
more general specification includes the anticipated (VR) and unan­
ticipated component (VRE) of each of the VR effects above, where
these components at each lag are not constrained to be equal. From
this specification, the constraints involved in table 5 can be tested
and found to hold. These constraints are that the coefficients on
V R „, VRE,_3, V F U VRE,_2, and VRE, are zero; and they hold when
tested jointly or separately. One cannot discriminate statistically
between the hypotheses that the coefficients on VR, and VR,., are
significantly different from zero and opposite in sign while that on
VRE,., is zero and the hypotheses that the coefficient on VRE,_, is
significantly different from zero and those on VR, and VR,_, equal
zero. An implication of these results is that the apparent insignifi­
cance of VR, in table 4 arises from the imposition of the unsupportable constraint that the effects of VR, and VRE, are the same. Thus,
the following constraints in table 4 do not hold: that the coefficient on
VR, is zero or that the coefficients on VR,_, equals that on VRE,.,.
When these constraints are relaxed, both components of VR,_2 and
VRm drop out.

44


NOVEMBER 1984

effect o f in terest rate variability: a rise in in tere st rate
variability u nam biguously raises p rices perm anently,
throu gh a tem p orary rise in inflation, but it h as no
p erm an en t effect on th e inflation rate. T h e evid ence,
however’, d oes not d iscrim in a te w ell b etw een w h eth er
the p erm an en t effect on p rices arises from ch an g es
in a n tic ip a te d v a ria b ility o r p a st u n a n tic ip a te d
variability.

The Effect o f Interest Rate Variability
on Output
T h e grow th rate o f real GNP in th e m o d el in table 2
equals th e d ifference b etw een th e grow th rate o f GNP
an d th e grow th rate o f p rices; it ca n b e w ritten as the
righ t-h an d -sid e o f th e GNP eq u atio n less th e righth an d -sid e o f the p rice eq u atio n . C on sequ en tly, the
effect o f in terest rate volatility on o u tp u t grow th is the
difference in th e VR co m p o n e n ts in th e ap p rop riate
GNP an d p rice eq u atio n s.
Sin ce a p erm an en t rise in in tere st rate variability
perm an en tly low ers th e grow th rate o f GNP an d te m ­
porarily raises th e in flation rate, th e p e rm a n en t effects
on real ou tp u t an d its grow th rate are u nam big u ou sly
negative. An estim ate o f th e effect o f in tere st rate varia­
bility on ou tp u t grow th is fou n d u sin g th e actu al varia­
bility results in tab les 3 an d 4. F o r th e I/1955-IV/1983
period, the ou tp u t grow th effect is (-1.572 A VR,_, +
0.654 A VR,_2- 0.297 VR,_.,I; t-sta tistics for th e th ree co e f­
ficien ts are -5 .7 6 , 2.42 an d -4 .8 7 , respectively. W hen
th e a n tic ip a te d in te re s t rate v a ria b ility m e a su re
resu lts are co m b in ed , th e real GNP grow th rate effect
is (-0.937 AVR, - 0.289 VR,_,I; th e t-sta tistics for th e two
co efficien ts are -5 .7 8 an d -4 .7 5 , respectively. T h e longrun effect on th e real GNP grow th rate in d ica ted by th e
last term is essen tially id en tica l for b o th sp e cifica ­
tion s, w h ile th e tim in g an d sh o rt-ru n effects are
slightly different. Of co u rse, th e sam e effects ca n be
estim ated using th e u n a n ticip a ted volatility effect on
p rices and th e a n ticip a te d volatility effect on GNP;
w hen th is is don e, o n ce again, th e d ifferen ces are
slight.

The Estimated Effects on Economic
Performance: 1980—
83
To gain som e in sigh t into th e m ag n itu d e o f th e esti­
m ated effects above, th e a ctu a l levels o f VR, from 1/1980
to IV/1983 are given in tab le 6, alon g w ith th e effects on
th e grow th rates o f GNP, p rices an d real GNP, d u e to
the d ep artu re o f VR from its I/1955-III/1979 m ean level
of 8.60 p ercen t. T h e effects for GNP, p rices an d ou tp u t

NOVEMBER 1984

FEDERAL RESERVE BANK OF ST. LOUIS

Table 5
Anticipated and Unanticipated Interest Rate Volatility and Inflation
Dependent Variable: P,
1/1955—IV/1983
Independent
Variables

M

20
2 7.
i= 0

Coefficient

t-statistic

Both

Unanticipated VR (VRE)
Coefficient

t-statistic

t-statistic

Coefficient

4
2 7i*2t
j= 1

A VR,
VRE_,

0.924

20.53

0.938

20.39

0.930

20.67

-1.185
1.712

D1
D2

Pe

Anticipated VR (VR)

-1 .7 3
2.41

-1.765
1.274

-2.51
1.79

-1.498
1.540

-2 .1 3
2.15

0.065

2.93

0.081

3.70

0.071

3.18

0.372
0.720

1.69
1.73

4.32

0.648

—

—

_

0.37

4.36

0.81
1.187

0.81
1.198

0.81
1.198
2.14

R2
SE
DW
P

_
1.234

2.13

2.13
4.26

0.40

4.53

4.34

0.38

1/1955—IV/1978
Independent
Variables

M

20
2 7i
i= 0

Anticipated VR (VR)
t-statistic

Coefficient

Both

Unanticipated VR (VRE)
Coefficient

t-statistic

Coefficient

t-statistic

0.990

23.02

1.004

26.42

1.003

26.39

D1

-1.641

-4 .4 6

1.489

-2 .8 6
2.15

-2.274

D2

1.323

2.12

-2.239
1.333

-3.90
2.10

0.071

2.73

0.068

2.90

0.068

2.88

0.029

0.14

1.350

2.50

P'

4
2 yhltl
i=1

A VR,
vrem

0.440
—

0.19

3.89

0.81
1.096
1.97

0.81
1.090
1.97

2.01

DW




_
1.408

0.80
1.125

R2
SE
P

2.85
—

1.85

0.10

0.94

0.10

0.97

45

FEDERAL RESERVE BANK OF ST. LOUIS

NOVEMBER 1984

Table 6
The Effect of Interest Rate Variability on GNP, Prices and
Real GNP: 1980-83
Period

Variability of
interest rates

Effect on GNP
growth rate

Effect on
inflation

Effect on
real GNP
growth rate

1/1980
II
III
IV

10.03%
11.33
12.70
14.83

0.1%
-1 .2
-1 .3
-1 .6

1.9%
2.9
0.3
0.6

-1.8%
-4.1
-1 .6
-2 .2

1/1981
II
III
IV

16.66
18.61
20.66
21.79

-2 .2
-2 .6
-3 .2
-3 .8

1.5
1.0
1.3
1.3

-3 .7
-3 .6
-4 .5
-5.1

1/1982
II
III
IV

22.57
22.62
21.90
20.55

-3 .8
-3 .9
-3 .8
-3 .4

0.2
0.3
-0 .3
-1 .0

-4 .0
-4 .2
-3 .4
-2 .4

1/1983
II
III
IV

19.29
18.02
16.62
15.22

-2 .9
-2 .6
-2 .2
-1 .8

-1 .0
-0 .8
-0 .8
-1 .0

-1 .9
-1 .8
-1 .4
-0 .8

in table 6 use the I/1955-IV /1983 estim ates of the im ­
p act of anticip ated variability rep orted above. The esti­
m ates based on actu al or unan ticip ated variability ef­
fects are about the sam e for the w hole period or for
subperiods su ch as the 1 9 8 1 -8 2 recession.
Changes in risk, as m easured by the five-year stan ­
dard deviation of the logarithm of Aaa bond yields
have h ad a substantial im p act on the econ om y since
1979, generally retarding the grow th rate of nom inal
and real GNP over the period. In 1980-81, the rise in
risk tem porarily raised the observed inflation rate. The
subsequent fall in risk tem porarily red u ced inflation
in 1982-83.
Table 6 indicates that g reater interest rate variability
red u ced the grow th rates of nom inal spending and
real GNP by an average of 2.3 and 3.8 percen tage

“ Evans also reaches this conclusion. Using the estimates based on
actual variability, the reduction in nominal GNP over the whole
period shown in table 6 is 2.7 percentage points, while during the
recession it is 3.9 percentage points; the reduction in real GNP
growth over the whole period is 2.8 percentage points and 3.6
percentage points during the recession. Similar estimates are found
using the unanticipated interest rate variability hypothesis for prices;
real output falls 2.6 percentage points over the whole period and 3.7
percent during the recession.

46


points, respectively, during the III/1981-IV/1982 re ce s­
sion.3 Thus, su ch variability played a m ajor role in the
0
relatively sluggish grow th of spending at a 2.8 p ercen t
rate over the p eriod an d the -2 .4 p ercen t grow th rate
of real GNP from peak to trough. Indeed, d epartures
from the m ean variability h ad a negative im p act on
real output grow th that exceed s the observed decline,
suggesting that, in the ab sen ce of in creased variability,
real GNP grow th w ould have been positive.3
1

3 When the measure of variability is the 20-quarter standard deviation
1
of the changes in the logarithm of the quarterly interest rate, similar
significant effects are obtained for GNP, prices and real GNP. Over
the period 1/1955—IV/1983, the current and past four levels of this
standard deviation measure significantly affect GNP growth. The
sum effect is significantly negative. In the price equation, only the
change in the standard deviation three quarters earlier is significant.
For both equations, the statistical results are inferior to those pre­
sented in the text, judged by the fit of the equations. Also, the
results are not as robust. In the 1/1955—IV/1978 period, no lag of this
measure adds significantly to the price equation; in the GNP equa­
tion, only the lagged change in the standard deviation approaches
significance (t = -1.92). The quantitative effects of higher variability
on GNP, prices and output using this measure, however, are similar
to those found from tables 3 and 4 or those given in table 6. For
example, over the recession period 111/1981—IV/1982, nominal and
real GNP growth were reduced by an average 2.7 percent, while
inflation was unaffected. The anticipated/unanticipated variability
tests were not conducted for this measure due to the inferiority of the
actual variability results.

FEDERAL RESERVE BANK OF ST. LOUIS

NOVEMBER 1984

SUMMARY AND IMPLICATIONS

________, and Anna Jacobson Schwartz. A Monetary History of the
United States, 1867-1960 (Princeton University Press, 1963).

T h e evid ence h ere generally su p p o rts re cen t stu d ­
ies w h ich in d icate th at in crea sed variability o f m on ey
stock grow th an d in terest rates in th e early 1980s had
d eleteriou s effects on ou tp u t and em p loy m en t. M ore­
over, th e evid ence provides a link b etw een th e rise in
m oney grow th and in terest rate variability. T h e rise in
the variability o f in terest rates, in p articu lar a n tici­
p ated variability, w as an im p o rtan t ch a n n e l throu gh
w h ich in creased m o n etary u n certain ty op erated to
red u ce GNP, o u tp u t and em p loym ent, an d to first
raise, th e n low er, inflation after 1979.

Gertler, Mark, and Earl Grinols. "Monetary Randomness and In­
vestment," Journal of Monetary Economics (September 1982), pp.
239-58.

T h e em p irical resu lts suggest th at th e rise in in ter­
est rate variability after 1979 exp lain s th e severity of
the 1 9 8 1 -8 2 re cessio n . T h e resu lts also sh ed som e
light on th e m agnitu d e o f th e sw ing in observed in ­
flation from 1 980-81 to 1 9 82-83. Inflation w as first
p u sh ed up tem porarily in 1980-81, th e n dow n in
1 9 8 2 -8 3 due to th e p attern o f ch an g es in in terest rate
volatility sin ce 1979.

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47