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Vol. 29, NO. 2

v
?

ECONOMIC REVIEW
1993 Quarter 2
Using Bracket Creep to Raise
Revenue: A Bad Idea Whose
Time Has Passed

2

by David Altig and Charles T. Carlstrom

Cyclical Movements of the
Labor Input and Its Implicit
Real Wage

12

by Finn E. Kydland and Edward C. Prescott

Money and Interest Rates under
a Reserves Operating Target
by Robert B. Avery and Myron L. Kwast




FEDERAL RESERVE BANK
OF CLEVELAND

24

1993 Quarter 2
Vol. 29, No. 2

Using Bracket Creep
to Raise Revenue:
A Bad Idea Whose
Time Has Passed

2

by David Altig and Charles T. Carlstrom
Temporarily suspending indexation of the personal income-tax code is
often suggested as a means for raising federal revenues. Here, the
authors argue-that this method of taxation is inefficient in that it is inferior
to direct increases in marginal tax rates. They conclude that attempts to
use bracket creep in future deficit-reduction efforts should be viewed
with appropriate skepticism.

Cyclical Movements of the
Labor Input and Its Implicit
Real Wage

12

The standard measure of the labor input in aggregate production is the
sum of employment hours over all individuals. The validity of this
measure for cyclical purposes requires that the composition of thework force by skill and ability remain approximately unchanged over
the cycle. Here, the authors investigate the accuracy of aggregate
hours as a cyclical measure of the labor force and find that it is much
more cyclically volatile than the labor input. Using data for almost
5,000 men and women in the Panel Study of Income Dynamics, they
conclude that the labor input’s real wage is strongly procyclical, but
that average compensation per hour is not.

24

by Robert B. Avery and Myron L. Kwast
This study examines the short-run dynamic relationships between
nonborrowed reserves, the federal funds rate, and transaction ac­
counts using daily data from 1979 through 1982. Separate models
are estimated for each day of the week, and simulation experiments
are performed. The results suggest that the funds rate responded quite
rapidly to a change in nonborrowed reserves, but that the short-run
nonborrowed reserves multiplier for transaction accounts was only
about 18 percent of its theoretical maximum. In addition, the Federal
Reserve appeared to accommodate about 65 percent of a permanent
shock to money, and lagged reserve requirements seemed to delay
depository institutions’ response to a money shock.




Coordinating Economist:
William T. Gavin
Advisory Board:
Jagadeesh Gokhale
Erica L. Groshen
Joseph G. Haubrich

by Finn E. Kydland and Edward C. Prescott

Money and Interest Rates
under a Reserves
Operating Target

Economic Review is published
quarterly by the Research Depart­
ment of the Federal Reserve Bank
of Cleveland. Copies of the Review
are available through our Public
Affairs and Bank Relations Depart­
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Editors: Tess Ferg
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Design: Michael Galka
Typography: Liz Hanna

Opinions stated in Economic Re­
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eral Reserve Bank of Cleveland or
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Federal Reserve System.

Material may be reprinted pro­
vided that the source is credited.
Please send copies of reprinted
material to the editors.

ISSN 0013-0281

Using Bracket Creep to Raise
Revenue: A Bad Idea Whose
Time Has Passed
by David Altig and
Charles T. Carlstrom

Introduction
The Clinton administration, seconded by a ma­
jority in Congress as well as many economic
experts, has made the adoption of new revenue
sources a central element of its deficit reduction
efforts. According to Congressional Budget
Office (CBO) projections, over fiscal years (FY)
1994 to 1998, the federal government would
borrow about $355 billion less under the Clin­
ton budget proposals than if it merely contin­
ued with the tax and spending programs in place,
or planned, at the beginning of FY1993. Almost
75 percent of this difference is accounted for by
new federal receipts.1
However, even if the Clinton budgets unfold
as envisioned, the federal deficit relative to
gross domestic product (GDP) in FY1998 will
differ little from the level realized in FY1989,
the year just prior to the confluence of a pro­
tracted economic slowdown and the significant,
but unusual, outlays associated with the savings
and loan crisis. Worse yet, virtually all forecasts
suggest that after FY1998, deficits will again begin


■
http://fraser.stlouisfed.org/ 1 See Altig and Gokhale (1993) for a detailed explanation of these
Federal Reserve Bank estimates.
of St. Louis

David Altig is an economic advi­
sor and Charles T. Carlstrom Is
an economist at the Federal Re­
serve Bank of Cleveland. The
authors thank W illiam T. Gavin,
Jagadeesh Gokhale, and Finn E.
Kydland for helpful comments
and suggestions.

to climb dramatically. Given these circumstances—
and the probability that some of the tax changes cur­
rently on the table will be scaled back or rejected—
it is likely that many of the revenue alternatives the
administration has opted against will find their way
back into policy deliberations in the near future.
One of the alternatives reportedly considered
in the early stages of the Clinton team’s budget
deliberations was the suspension of adjustments
to income-tax rate brackets that automatically oc­
cur when the Consumer Price Index (CPI) rises.
In fact, this alternative has been periodically dis­
cussed ever since inflation indexation was intro­
duced by the Economic Recovery Tax Act of
1981 (ERTA).2
The fact that monetary policy can influence
government revenues is at the heart of tradi­
tional concerns about central-bank independ­
ence. Indeed, recognizing the temptation for
governments to compromise long-run price sta­
bility in the service of short-run fiscal pressures
is the key to understanding the history and

■

2 See Tatom (1985) and Altig and Carlstrom (1991a) for moredetailed descriptions of these provisions.

3

evolution of centralized monetary institutions.3
For those who, like us, believe that great skepti­
cism should accompany any policy that introduces
an inflationary bias into the economic environ­
ment, making government receipts positively re­
lated to the inflation rate is sufficient reason to be
wary of abandoning indexation.
Quite apart from these considerations, how ­
ever, is the simpler issue of efficiency. Suspen­
sion of inflation indexing raises revenues by
permanently increasing the income base to
which tax rates are applied. A straightforward
alternative would be to continue adjusting the
tax base for price-level changes while simulta­
neously increasing the applicable rates. The for­
mer approach is preferable to the latter only if
the economic costs of allowing inflation to ex­
pand the tax base are less than the costs of in­
creasing tax rates to levels sufficient to raise an
equivalent amount of revenue.
In this article, we formally address this issue,
asking whether, in the long mn, the utility of
an average consumer is higher when a given
amount of revenue is raised by temporarily
abandoning inflation indexation, as opposed
to adopting a comparable, but explicit, change
in the rate structure. Our analysis employs the
well-known quantitative framework pioneered
by Alan Auerbach and Laurence Kotlikoff (an
extensive discussion of which can be found in
their 1987 book D ynam ic Fiscal Policy), and a
rate structure similar to the one found in the
current U.S. federal tax code. In all of the cases
we consider, direct changes in tax rates are
superior to the strategy of raising revenue by
forgoing inflation adjustments.
Although a rising price level can affect tax
liabilities in many ways, the channel relevant
for our discussion is associated with bracket
creep, or the tendency for taxpayers to be
pushed into higher rate brackets as a result of
inflation-induced increases in nominal income. In
section I, we briefly review the specifics of indexa­
tion in the U.S. tax code, emphasizing the bracketcreep issue and its relation to another important
effect of inflation, capital-income mismeasurement. Section II then illustrates the effect of sus­
pending inflation indexation and contrasts this
approach with one involving stmctural changes
in the tax code. In section III, we lay out the ba­
sic model from which we calculate the welfare


http://fraser.stlouisfed.org/ A more complete articulation of this position is contained in the
■ 3
Federal Reserve Bank of St.Reserve Bank of Cleveland's 1990 Annual Report.
Federal Louis

costs of bracket creep as a revenue source. The
balance of the article contains our results.

I. What Does
Indexation
Really Index?
Indexation of the personal tax code formally
commenced in 1985 under provisions of ERTA.
Ad hoc indexation, in the form of infrequent
adjustments of nominal tax brackets, personal
exemption levels, and so on, was periodically
legislated prior to 1985, but ERTA represented
the first time that regular, ongoing inflation ad­
justments were codified in the tax laws.
Under ERTA, indexation required annual ad­
justments in the dollar value of tax-bracket limits
and personal exemption levels based on a costof-living index derived from the Bureau of Labor
Statistics’ CPI for urban wage earners (CPIU).
The indexing provisions of ERTA were in effect
for only two years before being superseded by
the Tax Refonn Act of 1986 (TRA86). However,
TRA86 extended ERTA’s indexing scheme with
only minor modifications.
The particulars of ERTA and TRA86 are such
that inflation adjustments are made with a lag
of approximately one year. For example, to im­
plement inflation adjustments for tax year 1986,
a cost-of-living index was calculated by divid­
ing the average CPIU for 1985 by the average
for 1984. The adjusted tax-bracket limits and
personal exemption levels were then obtained
by multiplying those in effect for the 1984 tax
year by the resulting cost-of-living index. Thus,
the procedure effectively adjusts the tax code
in a given year using realized rates of inflation
through the prior year.4
Because inflation adjustments are not con­
temporaneous, the accumulated effects of
bracket creep might not be zero in any given
year. However, if indexation is otherwise per­
fect, this is not an issue in the long run, which
is the focus of our analysis. To clarify, suppose
that real income is constant and equal to y,
and that nominal income in year t grows by
1+71,, where Kt is the annual rate of inflation.
Ignoring exemptions, deductions, and other ad­
justments to gross income, the ERTA and TRA86
indexation schemes can be thought of as pro­
cedures that effectively deflate nominal income
in each year by one plus the rate of inflation

■

4 This statement is not precisely correct, since ERTA provided formulas for annual cost-of-living indexes that used October through September data.

MBSM

methods would exist even if all adjustments
were contemporaneous. To see this, note that
nominal income in year t, relative to year t- 1
(which for simplicity we will henceforth as­
sume is the base year), is given by

B 0 X 1

The Effects of Bracket Creep:
A Simple Hypothetical Example
Let the marginal tax-rate schedule be given by
Marginal Tax Rate
(Percent)
0
25

y = w t ( l + n t) + R tA t_ 1 ,

Tax Bracket
(Dollars)
0 - 1,000
> 1,000

If an individual has a constant real income of $1,000, the an­
nual inflation rate is 3 percent, and indexation is suspended
for two years, then the sequence of taxable income levels,
marginal tax rates, and average tax rates is given by

Time

Nominal
Income
(Dollars)

Real
Income
(Dollars)

0
1
2

1,000
1,030
1,061

3
4
5
6
•
•

1,093
1,126
1,159
1,194
•
•

Nominal
TaxBracket
Limit
(Dollars)

1,000
1,000
1,000
1,000
1,000
1,000
1,000
•
•

Marginal Average
Tax
Tax
Rate
Rate
(Percent) (Percent)

1,000
1,000
1,000
1,030
1,061
1,093
1,126
•
•

0
25
25
25
25
25
25
•
•

0
0.7
1.4
1.4
1.4
1.4
1.4
•
•

SOURCE: Authors’ calculations.

for the previous year? Thus, taxable income in
year t is given by
'

y*=y F I
j= 1

(1+7lj)
(1 +7Cy_ j )

where we have designated the year in which
indexing commences as time period 1. Be­
cause the long run, or steady state, is charac­
terized by the condition K = n , a (for all j ) , it
is clear from the above expression that longrun taxable income just equals real income y
if timing lags are the only flaws in the adjust­
ment provisions.
Unfortunately, timing lags are not the only
flaw; problems with our current indexation

■

5 Formally, the law requires that the income limits to which particu­
lar rates apply in year t be inflated by the factor P,_x
/Pb, where P Is the

appropriately defined C IUand b refers to the base year used in the ad­
P
justment. However, because Pt _ ^ / P b just equals n J f+1(1 + rcy),

the
http://fraser.stlouisfed.org/indexing procedures are equivalent to holding the rate limits constant
Federal Reserve Bank andSt. Louisnominal income as described.
of adjusting

where w is real wage income, A is the house­
hold stock of assets (from the previous period),
and R is the nominal rate of return on these
assets. Real income, on the other hand, is
given by
y t = w t + A t_1( R t - n t) / ( l + n t) .
Although deflating nominal income by
1 + 7 t is fine for obtaining real wage income,
t
this adjustment is not appropriate for capital in­
come. Specifically, dividing nominal asset in­
come ( R t • At_ j) by one plus the inflation rate
would result in an overstatement of capital in­
come by an amount equal to 71,^4/— /(1 + n t).
1
This capital-income mismeasurement prob­
lem is logically distinct from the bracket-creep
problem per se: Although distortions from
bracket creep would vanish under a flat-tax re­
gime, distortions from capital-income mismeas­
urement would remain. Furthermore, as shown,
indexation as currently implemented does not
address the problem of overstating real capital
income in inflationary environments.
On the other hand, because capital-income
mismeasurement does result in an overstatement
of real income, it contributes to bracket-creep
effects. In what follows, we provide calculations
that examine the effects of suspending indexation
with and without the capital-income mismeasure­
ment problem.

II. Raising
Revenue with
Bracket Creep:
A Simple Example
Bracket creep effectively raises the income tax
base by an amount equal to the inflation rate
realized for the period over which indexation
is suspended. Although this point is fairly obvi­
ous, we provide a simple example to make the
discussion a bit more concrete.
Suppose that the marginal tax-rate schedule
is as described in box 1, that a representative
taxpayer has a constant real income of $1,000,
and that the price level increases by 3 percent
every year. Treating time 0 as the base year,
assume that indexation is forgone in years 1 and

5

2. As shown in the box, in the long run (after
period 2) this policy causes nominal income to
exceed the 0-percent rate bracket by about 6 per­
cent in every period. As a consequence, the
marginal tax rate faced by our average tax­
payer is higher from time 1 onward, even
though real income is unchanged.
Reflecting the simple two-bracket rate struc­
ture proposed in this example, temporarily
shelving inflation adjustments for two years (or
longer) has exactly the same effect on m argin­
a l tax rates as would a one-year suspension:
In both cases, the marginal tax rate rises from
0 to 25 percent. However, as seen in the last
column of the second table in box 1, the aver­
age tax rate increases as long as indexation is
suspended. This reflects the fact that inflation
expands the amount of income subject to the
25 percent rate, even when the marginal rate it­
self does not change.6

III. A Quantitative
Framework
In subsequent sections, we quantitatively com­
pare the long-run effects of raising revenue
through bracket creep with those that arise from
raising the same amount of revenue by proportion­
ately increasing statutory marginal tax rates. The
analysis uses a general-equilibrium overlappinggenerations model, similar to that of Auerbach
and Kotlikoff (1987), in which individuals face a
tax-rate schedule and indexing scheme much
like those legislated by TRA86. In this section, we
outline the model’s structure and discuss its param­
eterization. More-detailed discussions of similar
frameworks can be found in Auerbach and Kotli­
koff and in Altig and Carlstrom (1991b, 1992).

subject to
(2)

A s = 1 + rs( l - x s) A s_j
+ esco(l - ts)(1 - /,)- cs+ T
s,

where c s is real consumption expenditure at age
s, ls is leisure (where the total time endowment
has been normalized to one), r is the pre-tax real
interest rate (R - 7t)/(l + 7t), to is the pre-tax real
market wage, £s is an exogenous human capital
productivity endowment, xv is the individual’s
marginal tax rate, and Ts is a lump-sum transfer
payment equaling the individual’s total tax pay­
ment. The parameters o t. and a / represent,
respectively, the inverse of the intertemporal elas­
ticities of substitution in consumption and in leisure.
The parameter (3 is the subjective time-discount
factor, given by 1/(1 + p ) , where p is the rate of
time preference.

Capital and
the Production
Technology
The aggregate production technology is of the
standard Cobb-Douglas form
(3)

Y= A k Q
,

where Y is aggregate output per unit of labor,
A is an arbitrary scale variable, k is the aggre­
gate capital-labor ratio, and 0 is capital’s share
of production. The steady-state value of the
capital stock satisfies

(4)

k-

Y- C
n +6

where C is aggregate consumption per labor
unit, n is the rate of population growth, and 8
is the rate of depreciation on physical capital.8

Preferences and the
Budget Constraint
Assuming that productive life starts at age 1, a
representative member of each generation in
the model’s steady state maximizes a timeseparable utility function of the form
55

( 1)

f/=SP
5 =

■

S- 1

l- o

+ a

n - a '}
1-a,

1

6 Simulations in this paper consider the effect of bracket creep
only on marginal tax rates. Because tax revenues are returned to agents in
a lump sum, increases in tax revenues that are independent of marginal
http://fraser.stlouisfed.org/ hikes have no effect In equilibrium.
tax-rate
Federal Reserve Bank of St. Louis

■

7 The basis for the human capital productivity profile is the labor
efficiency estimates reported by Hansen (1986). We transformed Han­
sen's discrete function into a continuous function by linear extrapolation.
Because we will be focusing exclusively on steady states, we have
dropped time subscripts for exposltional convenience.

■

8 Equation (4) Is obtained from the goods-market-clearlng condition

Y ,= C t +
+ n)ku 1 -(1 -5 )/r/
and the requirement that k f +1 = k, in a steady state.

T A B L E

The Benchmark
Tax Code

1

Benchmark Parameters
Parameter

Description

1

Value

Intertemporal elasticity of
substitution in
consumption
Intertemporal elasticity of
substitution in leisure

°/
p

0.200

Subjective rate of time
preference

1

1.000

Throughout the remainder of this paper, we
focus specifically on the pure distortionary ef­
fects of the different tax regimes considered.
Accordingly, we assume that all revenues raised
through income taxes are rebated to the affected
cohort via lump-sum transfers, so that both
income-tax payments and lump-sum transfers
are given by

0.010
(5)

a

Utility weight of leisure

0.500

n

Population growth rate

0.013

e

Capital share of output

0.360

5

Capital depreciation rate

0.100

SOURCE: Authors.

7>

for y * < y
x Ly+ x H(y*

y)

for

y*>y,

where y* is taxable income and y defines the
maximum level of taxable income for which
the lower m arginal tax rate, x L is applicable.
,
In the benchmark case, we choose x L = 0.15,
x 1 = 0.28, and set y using the 1989 tax sched­
1
ule for married persons filing jointly. Appendix
1 explains how we calibrated the model to this
tax schedule.

Model Calibration
Solving the Model
As a benchmark, the parameters in equations
(1) through (4) are set at the values shown in
table 1. Given the tax code described below
and interpreting a time period as one year,
these parameters yield a steady-state capital/
output ratio of 2.59, compared to 2.68 for the
U.S. economy over the post-World War II peri­
od.9 With respect to the labor supply, our bench­
mark parameterization implies that, on average,
individuals spend about 28 percent of their total
time endowment in market-wage-generating ac­
tivities. How this matches the actual data depends
on the total hours that individuals have available
for leisure. If we assume that an average of six
hours per day is required for sleeping, over the
postwar period U.S. workers have devoted ap­
proximately 31 percent of their available time to
market-labor activities.1
0

■

9 We use the constant-cost net stock of fixed reproducible tangible
wealth reported in the January 1992 SurveyofC
urrentBusiness as our
measure of the U.S. capital stock. This measure includes consumer dur­
ables and government capital.

 ■ 10 The Bureau of Labor Statistics’ survey of payroll establishments
implies that nonfarm employees worked an average of 36.5 hours per
http://fraser.stlouisfed.org/
week over the 1959-92 period.
Federal Reserve Bank of St. Louis

The model is solved using numerical techniques.
Our procedures involve conjecturing values for
the aggregate capital stock and labor supply, cal­
culating steady-state consumption and leisure
paths conditional on the factor prices (wages and
interest rates) implied by those conjectures, and
iterating on updates of the aggregate variables
until individual choices are consistent with all rel­
evant market-clearing conditions. More-detailed
discussions are contained in appendix 2 and in
Altig and Carlstrom (1992).

IV. The Welfare
Costs of Raising
Revenue through
Bracket Creep
The policy in question involves temporarily for­
going indexation of the tax code. As discussed
in section II, this is equivalent to raising the tax
base by an amount equal to the rate of infla­
tion prevailing over the period when inflation
adjustments are suspended. In this section, we
focus on the pure bracket-creep case, meaning
that we abstract from problems associated with
capital-income mismeasurement. Accordingly,
for each age 5 individual, the new steady-state
tax base obtained after repealing indexation
for T periods is

F I G U R E

1

W elfare Lo sse s from
Suspending Indexation

N um b e r o f years
NOTE: The m odel parameters are set to their benchmark values (see table 1).
SOURCE: Authors’ calculations.

t'+ T -l

(6)

(1 + 71,)
t=

/'

+ A s_ x(R - n ) / ( l + 7 1 ) - ds,
where t ' is the time at which inflation adjust­
ments are repealed and t' + T is the time at
which they are reinstated. The term 7 repre­
t
sents the steady-state rate of inflation. Note
that this definition of taxable income assumes
that deductions are eventually adjusted for in­
flation and incorporates the assumption that in­
flation causes no further overstatement of real
income once indexation commences.
Our experiments contrast the welfare effects
of raising revenue through bracket creep, which
we will refer to as the inflation-revenue regime,
with an alternative strategy of directly increasing
marginal tax rates, which we will refer to as the
structural-revenue regime. All adjustments to the
statutory rate stmcture involve proportionate in­
creases in both x L and X H. 1
1
Our welfare measure is the amount of wealth
that must be given to a representative individual
to compensate for utility losses resulting from

raising revenue by suspending inflation indexa­
tion. Specifically, if we let U be the lifetime
nR
utility level of each member of a generation liv­
ing in a steady state under the inflation-revenue
regime, and US be that of an individual under
R
the stmctural-revenue regime, then welfare
losses are measured as the share of full wealth
that must be transferred to individuals in the in­
flation regime in order to equate U and USR.1
nR
2
The solid line in figure 1 plots welfare
losses under our benchmark parameterization
for T equals 1-5 years, assuming an annual in­
flation rate of 2.7 percent.1 Suspending in­
3
dexation for one year would result in a loss
equivalent to about 0.07 percent of wealth.
This number grows, although at a decreasing
rate, as the number of years over which in­
dexation is suspended (and hence the cumula­
tive rate of inflation) increases. Eliminating
inflation adjustments for five years, which in
our examples corresponds to price-level
growth of about 14 percent, results in welfare
losses of roughly 0.14 percent of wealth.1
4
The welfare losses indicated by our bench­
mark simulations indicate that the exploitation
of bracket creep is a relatively inefficient
method of taxation. The source of these losses
can be more fully understood by examining
the broken lines in figure 1. These experi­
ments decompose welfare changes into a “tax
effect” and a “price effect.” The tax effect is the
welfare loss due to changes in the marginal tax
rate alone, absent any general-equilibrium price
effect. That is, the tax effect is determined by
setting prices r and (0 at their steady-state levels
from the structural-revenue regime, and by set­
ting the age-specific marginal tax rates at the
levels determined from the inflation-revenue
regime. The welfare loss is the share of full
wealth that must be transferred under these cir­
cumstances in order to maintain the utility level

■

12 Full wealth is defined as the present value of maximum labor in­
come, that is, the amount of market wealth that could be generated if indi­
viduals allocated their entire time endowment to working. If welfare
losses are negative, then the inflation-revenue regime generates higher
utility than does the structural-revenue regime. In this case, the welfare
measure would be the share of wealth that must be taken away In order to
lower UR to the appropriate level.
n
■

■

11 We have also attempted experiments in which only the top mar­
ginal tax rate is increased. Interestingly, “Laffer curve” effects render this
 alternative Infeasible. That Is, tax receipts begin to decrease as t H rises
before
http://fraser.stlouisfed.org/ revenues in the structural-revenue regime can be equated to those
Federal Reserve Bankin the inflation-revenue regime.
of St. Louis

13 This corresponds to the inflation rate assumed by the CBO in
its most recent estimates of the revenue effects of suspending indexation.
See CBO (1993).

■ 14 When indexation is suspended for five years, the equal-revenue
structural alternative to the inflation-revenue regime implies marginal tax
rates of 16.5 and 30.8 percent.

8

F I G U R E

2

Life -C y c le Paths of M arginal T a x Rates

Tax rate
0.30

(—1

0.28
0.26

Inflation
regime

0.24 -

- Structural
regime

0.22 0.20

0.18 0.16

1111111111111111111111111111
1
0.14 ■
1 5 9 13 17 21 25 29 33 37 41 45 49 53
Age

NOTE: The model parameters are set to their benchmark values (see table 1).
Indexing is suspended for two years in the inflation regime.
SOURCE: Authors’ calculations.

F I G U R E

3

Life -C y c le S avin g Profiles

Units of output
1.0

NOTE: The model parameters are set to their benchmark values (see table 1).
Indexing is suspended for two years in the inflation regime.
SOURCE: Authors’ calculations.

F I G U R E

4

Life -C y c le Le isu re Profiles

UnR ,1 Analogously, the price effect is then de­
5
termined by setting taxes at their steady-state
levels from the structural-revenue regime and
by setting prices at the levels obtained in the
inflation regime.1
6
These partial-equilibrium experiments clearly
indicate that the welfare losses from suspending
indexation are driven by the direct effects of taxa­
tion: The differences in interest rates and wages
between the two regimes actually dampen the in­
efficiency of the inflation-revenue case relative to
the structural-revenue case, which is apparent
from the fact that price effects are negative.
The reasons for a strong tax effect are sug­
gested by examining the life-cycle paths of
marginal tax rates, which are shown in figure 2
for the case where indexation is suspended for
two years. Although the rates are marginally
higher in the structural-revenue regime over
much of the life cycle, they are substantially
higher in the inflation-revenue case at some
critical ages, specifically, 23-30 and 37-40.1
7
These effects show up clearly in figures 3 and
4, which depict life-cycle saving and leisure pro­
files in steady states under the two tax regimes,
again assuming that inflation adjustments are for­
gone for two years. In both cases, saving and
work effort are depressed near the “kinks” in
household budget constraints— the points at
which taxable income equals y — induced by
jumps in marginal tax rates. Because the equilib­
rium outcomes are such that distortions are more
severe in the inflation-revenue regime, welfare is
lower relative to the structural-revenue case.
Table 2 reports results from various sensitivity
experiments in which welfare losses are calcu­
lated under alternative settings for the model’s
parameters. Suspending indexation creates wel­
fare losses relative to our structural alternatives in
all cases considered. Although these alternatives
are clearly not exhaustive, we conclude from this
evidence that our basic finding is robust to plaus­
ible changes in the model’s parameterization.

Fraction of total hours
0.85

■

15 Thus, for purposes of calculating the tax effect, the modified
inflation-revenue regime involves solving for the consumption and lei­

sure profiles given

r R co and the marginal tax rates obtained from
S , s/?,

the regime’s original steady-state solutions.

Structural regime

I ■ 1 1 1 1 » 1 1 » 1 1 1 » I » I » 1 1 1 » » 11 » I » I » « » 11
13 17 21 25 29 33 37 41 45 49 53

1 1 1 . 1 » 1 . 111 » 111 »

1

5

9

Age
 parameters are set to their benchmark values (see table 1).
NOTE: The model
http://fraser.stlouisfed.org/ for two years in the inflation regime.
Indexing is suspended
Federal Reserve Authors’ calculations.
SOURCE: Bank of St. Louis

■

16 Thus, for purposes of calculating the price effect, the modified
inflation-revenue regime involves solving for the consumption and lei­
sure profiles given r (onR, and the marginal tax rates obtained from
nR,
the general-equilibrium steady-state solutions for the structural-revenue
case.

■

17 Age here refers to a period of adult life. If we assume that adult
economic activity begins at biological age 20, then ages 2 3 -30 and 3 7 40 in the model correspond to biological ages 4 3 -5 0 and 57-60.

9

TABLE

2

Welfare Losses under
Alternative Parameterizations
Indexing
Suspended for
Two Years

Indexing
Suspended for
Four Years

Benchmark

0 .0 6 1 1

0.1023

Utility weight of leisure
a = 0.25
a = 1.0

0.0743
0.0465

0.1126
0.0811

0.0582

0.1001

0.1021

0.1271

Elasticity of substitution
in consumption
l / o c= 0.33
l / o c = 0.2
.

0.0601
0.0793

0.1282

Elasticity of substitution
in leisure
1 / 0 ,= 0.14
1 / 0 / = 0.33

0.0468
0.0719

0.0759
0.1219

0.0515

0.0690

0.0850
0.1111

Capital depreciation rate
5 = 0.07
8 = 0.13

0.0623
0.0522

0.1031
0.0857

Population growth rate
n=0
n = 0.03

0.0665
0.0552

0.1096
0.0924

In table 3, we provide a comparison of the
welfare losses wr and without capital-income
ith
mismeasurement. Results are reported for sev­
eral different parameterizations of the model
and pertain to experiments in which indexa­
tion is suspended for one year. Not surpris­
ingly, the added, but realistic, complication of
capital-income mismeasurement serves only to
reinforce the welfare losses associated with the
bracket-creep strategy of taxation.

Rate of time preference
P- 0
p = 0.04

Capital share of output
0 = 0.3
0 = 0.45

0.0988

SOURCE: Authors’ calculations.

V. Welfare Costs
with Capital-lncome
Mismeasurement
Implicitly, the experiments conducted in the pre­
vious section assume that taxable income is cal­
culated as follows: First, an individual’s real
income is determined, then it is multiplied by the
appropriate inflation adjustment to obtain nomi­
nal income. It is this measure of nominal income
to which inflation adjustments are applied.
The actual procedure, of course, omits the
first step: Nominal taxable income is obtained
directly and then deflated according to the rele­
vant inflation index in order to determine the
appropriate tax liability. As noted in section I,
while the difference in these two procedures is
not critical for calculating real wage income,
the second approach overstates real asset in­
come by 7t • A/{1 + 7 t ) .



VI. Concluding
Remarks
In its recent analysis of alternative deficitreduction options, the CBO argues that increasing
revenue by suspending indexation is inappropri­
ate because it amounts to “unlegislated tax in­
creases.” However, because such a suspension is
possible only by a vote of Congress and the sig­
nature of the President, it is unclear why taxes
raised through this approach should be consid­
ered unlegislated. Although it is true that the ad­
ditional amount of revenue obtained over the
course of several years would be determined by
the inflation outcomes associated with Federal
Reserve policy, Congress has ample scope to ex­
press itself on the issue of an appropriate infla­
tion trend.
We suggest a more straightforward objection:
Raising revenue by temporarily suspending in­
dexation is inefficient relative to the more direct
approach of raising marginal tax rates. This ineffi­
ciency arises because distortions of private work
effort and saving decisions associated with rising
marginal tax rates are more severe when reve­
nues are raised through bracket creep. The net
result is that the utility of the average individual
is higher in the long run if inflation indexation is
maintained and if tax revenues are raised by per­
manently adjusting structural tax rates.
O f course, a multitude of additional factors
are ignored in the type of highly stylized
model we have employed here. For instance,
there is no lifetime heterogeneity and therefore
no distributional issues of which to speak. De­
spite this caveat— w'hich, after all, applies to
any model— our analysis suggests that the deci­
sion to abandon the bracket-creep tax strategy
is a wise one. As the public debate on deficit
reduction inevitably continues into the future,
taxation through suspending inflation indexa­
tion is probably one option we should keep
off the table.

na
T A B L E

3

Welfare Losses from CapitalIncome Mismeasurement
Without CapitalWith CapitalIncome
Income
Mismeasurement Mismeasurement
Benchmark

0.0343

Utility weight of leisure
0 = 0.25
1

a = 1.0

Rate of time preference
P -0
p = 0.04
Elasticity of substitution
in consumption
l / o t. = 0.33
l / o t. = 0 .2

0.0506
0.0256

0.0776
0.0655

0 .0 3 18

0.0639

0.0624

0.0652

Capital depreciation rate
8 = 0.07
8 = 0.13
Population growth rate
0

0.0344
0.0488

0.0774
0.0793

0.0277
0.0396

0.0578
0.0975

0.0285
0.0438

0.0684
0.0840

0.0378
0.0291

0.0812
0.0678

0.0373

Elasticity of substitution
in leisure
1 / 0/ = 0.14
1/0/=0.33
Capital share of output
0 = 0.3
0 = 0.45

n -

0.0718

0.0868
0.0550

0.0318

n = 0.03

NOTE: Simulations assume indexation is suspended for one year.
SOURCE: Authors’ calculations.

Taxable income levels are obtained by adjusting
gross income levels for deductions and personal
exemptions. In the benchmark case, we assume
that all taxpayers take the 1989 standard deduction
of $5,200. The personal exemption level in 1989
was $2,000. Multiplying by 3-13, the average fam­
ily size in 1988, yields total personal exemptions of
$6,260. Thus, our simulations assume that d =
$11,460 per household at every age.

Appendix 2 Outline of
Solution Strategy
Given a marginal tax-rate structure that is a con­
tinuous function of taxable income, the model
can be solved using the following algorithm:
(i) Conjecture values for K and L (and
hence for r and (o).
(ii) Conjecture a sequence of marginal tax
rates, T,, for t = 1-55.
(iii) Let uit, i = c,l, denote the age t marginal
utilities of consumption and leisure, respectively,
and let Xl denote the LaGrange multiplier associ­
ated with the time t budget constraint in equa­
tion (2). Given the conjectured net prices, use
equation (2) and the first-order conditions
(Al)

(A2)

0
u ll- X le l m , ( l - i , ) = 0,

and

Appendix 1 Calibration
of the Tax Code
Because our simulation model is geared toward
capturing the average effects of life-cycle behav­
ior, we calibrate gross income so that the highest
level of steady-state cohort income matches the
highest median income in the data. Taking 1988
as the reference year, this value was $42,192, as­
sociated with families headed by individuals aged
45-54. This number was obtained from the Cur­
rent Population Reports (series P-60, No. 166,
published by the Bureau of the Census) and was
converted to 1989 dollars according to the CPIU
inflation rate from 1988 to 1989 (4.8 percent).
This yields a value for high income in 1989 dol­
lars of $44,217. The scale of incomes in the
model is chosen so that the highest steady-state
income generated with the chosen tax code and
4 percent inflation is equal to this value.




(A3)

- X , _ j + ?i , ß 11 + r ( l - I , ) ] = 0

to solve for the optimal consumption and lei­
sure plans for members of each generation.
(iv) Apply the implied path of wage and as­
set income to the tax code and update the
path for marginal tax rates. Updates can be ob­
tained using the Gauss-Seidel algorithm.
(v) Repeat steps (iii) and (iv) until the opti­
mal paths of consumption and leisure are con­
sistent with the marginal tax rates they imply.
(vi) Aggregate individual labor and asset
supplies to obtain updates for K and Z.
(vii) Repeat steps (ii) through (vi) until aggre­
gate labor and asset supplies are consistent with
individual consumption and leisure decisions.
Altig and Carlstrom (1992) demonstrate how a
simple change-of-variables strategy can be used
to apply this algorithm to the case where margin­
al tax rates are a step function of taxable income.

References
Altig, David, and Charles T. Carlstrom.
“Bracket Creep in the Age of Indexing:
Have We Solved the Problem?” Federal Re­
serve Bank of Cleveland, Working Paper
9108, June 1991a.
______ , a n d _______ . “Inflation, Personal
Taxes, and Real Output: A Dynamic Analy­
sis,” Jo u rn a l o f Money, Credit, a n d B ank­
ing, vol. 23, no. 3, part 2 (August 1991b),
pp. 547-71.
______ , a n d _______ . “The Efficiency and Wel­
fare Effects of Tax Reform: Are Fewer Brack­
ets Better Than More?” Federal Reserve
Bank of Minneapolis, Discussion Paper 78,
December 1992.
Altig, David, and Jagadeesh Gokhale. “An Over­
view of the Clinton Budget Plan,” Federal
Reserve Bank of Cleveland, Econom ic Com­
m entary, March 1, 1993Auerbach, Alan J., and Laurence J. Kotlikoff. Dy­
nam ic Fiscal Policy. Cambridge: Cambridge
University Press, 1987.
Congressional Budget Office. Reducing the D efi­
cit: Spending a n d Revenue Options. Wash­
ington, D.C.: U.S. Government Printing
Office, February 1993Hansen, Gary D. Three Essays on Labor In d iv isi­
bility a n d the Business Cycle. University of
Minnesota, Ph.D. dissertation, 1986.
Tatom, John. “Federal Income Tax Reform in
1985: Indexation,” Federal Reserve Bank of
St. Louis, Review, vol. 67, no. 2 (February
1985), pp. 5-12.




Cyclical Movements of the
Labor Input and Its Implicit
Real Wage
by Finn E. Kydland and Edward C. Prescott

Introduction
The standard measure of the labor input is the
sum of market-sector employment hours over
all individuals. Validity of this measure requires
that the composition by skills and ability of
those working at each point in time be approx­
imately the same. Over the long term, the ex­
perience and educational achievements of the
work force have changed markedly, and vari­
ous methods have been devised to correct for
this transformation in quality (Jorgenson, Gollop, and Fraumeni [1987]) or in composition
(Dean, Kunze, and Rosenblum [1988]). From a
secular point of view, these corrections are
large, with the size of the correction being sen­
sitive to the method employed. But from a cy­
clical accounting point of view, as we show in
section IV, it makes little difference whether the
standard measure or these alternative measures
are used.
The question addressed here is whether, on
a cyclical basis, aggregate hours is a good
measure of the labor input. It could very well
be an adequate cyclical measure despite being
a poor secular measure. In particular, if the
 composition changes are slow relative to cycli­
http://fraser.stlouisfed.org/
cal variations in the labor input, it would be a
Federal Reserve Bank of St. Louis

Finn e . Kydiand is a professor of
economics at Carnegie-Mellon
University and a research associ­
ate at the Federal Reserve Bank of
Cleveland. Edward C. Prescott is
a professor of economics at the
University of Minnesota and a re­
search advisor at the Federal Re­
serve Bank of Minneapolis. The
authors thank Lawrence Christiano, Jagadeesh Gokhale, Victor
Rios-Rull, and Robert Townsend
for useful discussions, and David
Runkle for both useful discus­
sions and the permission to use
his PSID data tapes.

good yardstick from the point of view of cycli­
cal accounting.
Prior to this study, the evidence on this
question was mixed. Clark and Summers (1981)
find considerable differences in cyclical em­
ployment variability across age and sex groups.
Hansen (1986), using Current Population Sur­
vey data, aggregates the labor input by weigh­
ing the hours worked for different age and sex
groups by their relative wages. He reports that
his measure of the labor input is only slightly
more stable than is aggregate hours. Thus, if
differences in cyclical variability within such
groups were small, as he implicitly assumes,
then composition changes would not hinder
evaluation of the cyclical variability of the
labor input. Kydland (1984), however, main­
tains that there are in fact strong systematic dif­
ferences for males (ages 30 and over) in the
Panel Study of Income Dynamics (PSID). He
states that for this group, the more-educated
workers had higher average compensation per
hour and less variability in annual hours. Further­
more, the empirical sensitivity of this group’s
hours with respect to the unemployment rate
decreased with the level of education. Using
Kydland’s estimates, Prescott (1986b) finds that
if one adjusts a group’s average hours for

13

quality by multiplying it by that group's average
wage, quality-adjusted hours worked are only
half as sensitive to the unemployment rate as
are the quality-unadjusted hours.
In this paper, we systematically examine the
issue for all individuals in the PSID sample. We
treat each person’s time as being a different
type of labor input. The rental prices used to
construct the sample’s aggregate labor input for
each of the 14 years from 1969 to 1982 are that
person’s total labor compensation divided by
his total number of hours for the entire period.
Because each person’s human capital weight is
constant over time, these weights are orthogo­
nal to the cycle.
Our measurement procedure is in the na­
tional income and product accounting tradition
of Kuznets (1946) and Stone (1947). With this
approach, aggregate real time series are ob­
tained by evaluating output in different periods
using the same set of prices. This is precisely
what we do with respect to the labor input.
We determine that, cyclically, our measure
of the labor input varies by about one-third
less than the measure obtained by the standard
method for the PSID sample in the 1969-82 pe­
riod. Such a large correction, if it held for the
entire population, would dramatically change
the business cycle facts. If the labor input ac­
counts for a lesser share of the cyclical variation
in output, then the residual (the Solow technol­
ogy parameter) must account for more.
To see this point more clearly, suppose that
output, y, is determined by a standard aggre­
gate production function, y = z k a n 1-ct, where
z is the level of technology, k and n are the
capital and labor inputs, and a is a parameter
whose value generally is determined from the re­
spective income shares of GNP. To undertake
growth accounting, as proposed by Solow
(1957), one then proceeds to take logarithms of
the production function and rewrite as follows:
log z = log

y- c log
l

k - (1 - a) log n.

With time series for y, k, and n, a time series for
z is computed as a residual. More recently, this
relation has been used with quarterly data as the
basis for evaluating the statistical properties of cy­
clical technological change.1
Cyclical movements in the real wage have
been the subject of numerous empirical investiga­
tions. In an early study, Dunlop (1938) examines
British real-wage movements from I860 to 1913-


http://fraser.stlouisfed.org/
1 For more
Federal Reserve Bank of St. Louis details, see Prescott (1986a).

■

He finds that real wages tended to increase in
most expansions and decline in contractions.
Tarshis (1939) corroborates these findings for
the U.S. economy in the 1932-38 period, also
noting that changes in both the real wage and
hours worked were slightly negatively corre­
lated. Fischer (1988, p. 310) reviews these and
subsequent studies and concludes “...the weight
of the evidence by now is that the real wage is
slightly procyclical.” This is consistent with
Lucas’s (1981, p. 226) assessment that “...ob­
served real wages are not constant over the cy­
cle, but neither do they exhibit consistent proor countercyclical tendencies.”
These findings are problematic for any busi­
ness cycle theory that assigns an important role
to real-wage movements. As Phelps (1970)
points out, this is a concern for theories with
nominal-wage rigidities because they imply
countercyclical movements of the real wage. It
is also a problem for theories in which technol­
ogy shocks induce fluctuations. Unless leisure
is highly intertemporally substitutable, as it is
in the Hansen (1985) economy, the real wage
is strongly procyclical for this class of theories.
As emphasized by Christiano and Eichenbaum
(1992), and implicitly also by McCallum (1988),
the essentially zero correlation of cyclical hours
and compensation per hour is especially bother­
some for these theories.
Panel studies have examined the sensitivity of
individuals’ real compensation per hour to the
aggregate unemployment rate, with Bils (1985)
and Solon and Barsky (1989) finding very strong
procyclical movements and Keane, Moffitt, and
Runkle (1988) much weaker procyclical move­
ments.2 For some theoretical frameworks, this is
an appropriate procedure for determining how
the real wage moves cyclically, but for others it
is not. This method assumes that the nature of
the employment contract is such that the worker
chooses hours and is compensated in proportion
to the number of hours worked. This contractual
arrangement is the exception rather than the rule,
however. Because it is usually the employer who
chooses hours given some explicit or implicit
compensation schedule, we did not adopt the
real-wage definition implicit in the cited panel
studies and in the implied measurement proce­
dure. Rather, we employed the approach used

■

2 The samples used in these studies are much narrower than that
used in this paper. Bils and Keane, Moffitt, and Runkle use the National
Longitudinal Survey of Young Men (ages 14-24) as of the beginning of
the sample period. In the section of the Solon and Barsky paper that uses
PSID data, the sample is restricted to 357 men who worked in every year
of the sample period.

by Kuznets for other series, with the real wage
being defined implicitly as total labor compen­
sation divided by the aggregate labor input us­
ing a fixed set of wages to value the many
different types of labor inputs.
Our finding of strongly procyclical laborinput compensation contrasts sharply with most
previous findings. The reason for the difference
does not appear to be the special nature of the
PSID sample. For this sample in this period, real
compensation per hour is weakly procyclical
and, cyclically, real compensation per hour and
hours are only weakly correlated, as they are for
U.S. aggregate data. The disparity arises because
we use an alternate definition of the labor input.

I. Measuring the
Labor Input and
Its Rental Price
The standard measure of the labor input is sim­
ply aggregate hours. Let hit be individual-/
hours of work in year t. Aggregate hours per
person is

« ,=

1

h „ /N „

i

where Nt is the number of individuals in the
population in year t. The real rental price in
period t is

=l

e, / X
i

h,„

i

where eit is real earnings of individual i in
period t.
O ur measure of the labor input is

Z / = X ‘P A / N <
<
i-

where cp( is the “normal” price of individual-/
labor services. For the sample period, there was
little long-term change in real compensation per
hour. This led us simply to use as weights real
compensation per hour for the entire period.
Thus,

< =X
p<
/

e« /yL ha ’
t

where the summations are over years for which


individual hours and earnings are available.


Following standard procedures, the implicit real
wage of labor services is

wt = l

e« /yL

i

i

«PA.

where, as before, the summation is over those
in the sample at date t.

II. Data
The PSID data covered the years 1969-82. In­
cluded in the study were individuals in the Sur­
vey Research Center’s representative national
sample of families; those in the additional sam­
ple of low-income families drawn from the Sur­
vey of Economic Opportunity were not included.
Family information was used to construct indi­
vidual data for the head of the household (de­
fined in the PSID as the male, if present) and, in
the case of a married couple, for the wife as
well. All people with at least four years of posi­
tive annual work hours were included, resulting
in a sample of 4,863 individuals.
We obtained labor incomes for heads of
household by summing reported income for
regular labor, overtime, the labor portion of unin­
corporated family business, professional practice
or trade, and farm activity. Annual hours worked
is the sum of hours devoted to these activities.
We did not include 1967 and 1968 in the sample
because some of the income series went unre­
ported in these years.
Dollar figures were posted for regular income
in all years and for the other income categories
after 1974. In the 1969-74 period, only an in­
come bracket was reported for each of the other
categories, so these observations were assigned
income numbers based on the respective bracket.
The mle we use for that assignment is specified
in appendix 1. Typically, the head of the house­
hold reported his or her labor hours and various
incomes in the interview. If this person was a
married male, he also reported his wife’s income
and hours. These were the figures used for the
married females.
In some cases, the interviewers made major
assignments because of insufficient data; we
treated these years as missing observations.
For some people in some years, the reported
annual hours are substantial. We treated fig­
ures larger than 365 x 12 = 4,380 hours per
year as missing observations.
The tables in appendix 2 present aggregate
statistics for the entire sample population as
well as separately for males, married females,

and single females. The marital status of some
women changed over the sample period, so
that they appear in the married female group in
some years and in the unmarried female group
in the other years. The men are not subdivided
by marital status because of the small number
of unmarried males in the sample.

Cyclical Labor Input, Real Wage,
and Real GNP: PSID Sample, 1969-82
Percentage
Standard
Deviation

Correlations with

Hours (ZZ)
Compensation
per hour ( W H )
Real GNP

WL

GNP

—

0.52

0.52
0.75

—
0.51

0.75
0.51
—

H

Labor input (Z)
Real wage ( W L)
Real GNP

Z

WH

GNP

1.42

—

0.25

0.80

0.51

0.25
0.80

—
0.12

0.12

2.50

1.02
0.84
2.50

—

III. Findings
For purposes of this study, the cyclical compo­
nent of a time series is defined as the deviation
from the time trend.3 Because it is the percent­
age variation of each series that is of interest,
the logarithms of the various aggregates are
the time series whose properties are examined.
Key statistics for the full sample are presented
in table 1.

Empirical Elasticities with
Respect to GNPa
Labor input (Z)

0.30
(0.08)
0.45

Hours (ZZ)

(0 .10)
a. Standard errors are in parentheses.
SOURCE: Authors’ calculations.

FI GURE

1

Labor Input (L), Aggregate Hours (H
),
and Real GNP: Full Sample, 1969-82
Percent

Cyclical Behavior of
Aggregate Hours
and Labor Input
Figure 1 plots the cyclical component of aggre­
gate hours, the aggregate labor input, and real
GNP versus time. Clearly, both hours and the
labor input vary with GNP, but the hours com­
ponent varies much more. As shown in table
1, the percentage standard deviations are 1.42
for hours and 1.02 for the labor input, yielding
a ratio of the two volatility figures of 1.39.
Insofar as the behavior of the PSID sample is
similar to that of the entire population, the use
of aggregate hours as a proxy for the labor in­
put gives a highly distorted picture of the cycli­
cal movement of the labor input and therefore
of productivity as well. The empirical elasticity
of hours with respect to GNP is 0.45, while the
empirical elasticity of the labor input with re­
spect to GNP is 0.30— only two-thirds as large.

SOURCE: Authors’ calculations.




■ 3 Some view aggregate time series as the sum o ta cyclical and a
growth component. We do not (see Kydland and Prescott [1982]). One
should think of these elements as well-defined statistics that adequately
capture for this sample period what are commonly referred to as business
cycle fluctuations.

F I G U R E

2

Labor Input (L and Real Wage (M^):
)
Full Sample, 1969-82
Percent

SOURCE: Authors’ calculations.

FIGURE

3

Aggregate Hours (H and Real
)
Compensation (W ): Full Sample,
H
1969-82
Percent

SOURCE: Authors' calculations.




Cyclical Behavior
of the Labor Input
and Its Implicit
Real Wage
Part of the conventional wisdom is that real
wages and the labor input do not move together
cyclically. This reflects the Tarshis (1939) findings
for the 1930s and the Christiano-Eichenbaum
(1992) results for the postwar period. For our
sample in the 1969-82 period, aggregate hours
and average compensation did not move to­
gether much: The correlation is only 0.25. Thus,
the Tarshis findings hold for this period as well if
the measure of the labor input is aggregate hours.
But the labor input and its implicit real wage—
that is, real aggregate compensation divided by
the labor input — are strongly and positively as­
sociated, with a correlation of 0.52. Figure 2 plots
the labor input and real wage versus time, which
can be contrasted with aggregate hours and
hourly compensation in figure 3
Clearly, for the human-capital-weighted
labor input, the Tarshis result does not hold.
The real wage and the labor input move to­
gether cyclically. Both average compensation
per hour, W H, and the real wage, W L are posi­
,
tively associated with GNP. The correlation for
the real wage is 0.51, but it is only 0.12 for av­
erage compensation per hour.

Behavior of
Growth Rates
The more traditional (and, given current compu­
tational capabilities, we think inferior) method of
deducing the cyclical behavior of real wages,
hours, and employment is to examine relations
between changes in variables. This is the meth­
odology employed by Dunlop (1938) and Tarshis
(1939) in their pioneering studies. A question
that naturally arises is whether our disparate find­
ings are due in part to the difference in method­
ology. To answer this question, the statistics
calculated for cyclical components and reported
in table 1 were also calculated for growth rates
and are shown in table 2.
We find that growth rates of hours are much
more variable than those of labor inputs, with
the difference exceeding that for the cyclical
components. Growth rates of the labor input
and its real wage are positively correlated,
while those of hours and compensation per
hour are nearly uncorrelated. Similar relations
hold for the empirical elasticities of growth
rates of the labor input and hours with respect

T A B L E

to GNP. Thus, examining cyclical components
versus growth rates does not account for the
difference in our findings. The conclusions are
the same independent of the method.

2

Growth Rates of Labor Input,
Real Wage, and Real GNP:
PSID Sample, 1969-82
Percentage
Standard
Deviation

Correlations with

Hours (ZZ)
Compensation
per hour ( W H )
Real GNP

WL

GNP

0.94

—

0.21

1.13
2.75

0.21

0.87
0.36

0.87

—
0.36

H

Labor input (Z)
Real wage ( W L)
Real GNP

Z

WH

GNP

—

0.01

0.88

1.37

—

0.83

0.01

—

0.02

2.75

0.88

0.02

—

Empirical Elasticities with
Respect to GNPa

Labor input (Z )

0.30
(0.05)
0.44
(0.07)

Hours (ZZ)
a. Standard errors are in parentheses.
SOURCE: Authors’ calculations.

FIGURE
Labor Input (L) and Aggregate
Hours (//): Males, 1969-82
Percent

4

Robustness of
the Findings
These results strongly support the view that, cy­
clically, the labor input varies significantly less
than does aggregate hours and consequently
that productivity fluctuates much more. There
would be a problem if the human capital
weights were systematically too low for indi­
viduals with the most cyclically variable hours
of employment. We can think of no reason for
such a pattern. O n the contrary, a study by Kotlikoff and Gokhale (1992) suggests why the op­
posite may be the case. Measuring life-cycle
compensation and productivity profiles, they
find that for highly skilled workers, compensa­
tion is lower than productivity in the first half
of the life cycle, usually until individuals reach
their mid-forties. Especially in the early part of
the life cycle, this difference is substantial. Be­
cause our sample period includes years in
which the baby boomers had just entered the
work force (the average age is under 40 in all
years before 1980), our sample may include an
unusually large number of such highly skilled
workers whose measured quality weights
understate their productivity.
Neither do we believe that cyclical variations
in human capital are a concern. The stock of hu­
man capital is several times larger than annual
output. The variations in the human capital in­
vestment would have to be huge to induce signifi­
cant cyclical variation in the human capital stocks.
If they were, cyclical GNP would be a poor meas­
ure of cyclical output, for it would not include this
large and highly volatile investment component.
Other capital stocks are roughly orthogonal to cy­
clical output, and we can think of no plausible rea­
son for the human capital stock to differ.4
We multiplied the weights by identically
and independently distributed log-normal ran­
dom variables with a mean of 1 and a standard
deviation of 0.1. This did not affect any of the
findings, which indicates that errors in measur­
ing the weights that are not systematically re­
lated to the cyclical variability of individuals’
hours are not a problem.

SOURCE: Authors’ calculations.




■

4 See Kydland and Prescott (1982).

F I G U R E

Over time, people enter and exit the PSID
sample and there are missing observations. The
number of people in the sample varied smoothly
over time and did not fluctuate with GNP. Conse­
quently, our surprising findings do not appear to
be the result of missing observations being sys­
tematically related to the business cycle.
Some wage observations are sufficiently
extreme that they are almost certainly errors.
To see how our measurements could be af­
fected by such observations, we omitted year t
for person i if eu / hit exceeded both three times
(p; and $15 in 1969 dollars. The findings were es­
sentially the same with these extreme observa­
tions deleted.

5

Labor Input (L) and Aggregate
Hours (H Single Females, 1969-82
):
Percent

1969

1971

1973

1975

1977

1979

1981

SOURCE: Authors’ calculations.

FI GURE

6

Labor Input (L) and Aggregate
Hours (//): Married Females, 1969-82
Percent

0.05
0.04
0.03
0.02
0.01

0.00
-

0.01

-

0.02

-0.03
-0.04
-0.05
-

0.06

1969

1971

1973

1975

1977

1979

1981

1979

1981

SOURCE: Authors' calculations.

FIGURE

7

Labor Input (L), Aggregate Hours (//),
and Real GNP: Weighted Sample, 1969-82
Percent

1969

1971

1973


http://fraser.stlouisfed.org/
SOURCE: Authors' calculations.
Federal Reserve Bank of St. Louis

1975

1977

Cyclical Behavior
of Variables by
Demographic Groups
The sample was subdivided into males, single
females, and married females. Men were not
classified separately by marital status because
in half of the years, the number of single males
in the sample was less than 200, which is far too
small for our purposes. Men accounted for ap­
proximately two-thirds of the hours supplied by
the total sample and for four-fifths of the labor in­
put. Given this, it would be surprising if the ag­
gregate statistics for males and those for the
entire sample were dissimilar. Figures 1 and 4
show only a slight difference in the aggregate be­
havior of males and that of the entire sample.
An interesting finding is the disparity in the
behavior of single and married women. Figures
5 and 6 present plots of their hours and labor
input versus time. Given the small size of the
samples (less than 600 single and 1,700 mar­
ried women) and the fact that coefficients of
variation are about 0.6 for singles and 0.8 for
marrieds, random sampling variability is not
small. The empirical elasticities of hours and
the labor input with respect to GNP are re­
ported in table 3 along with the standard errors.
We find that the labor inputs for males and
single females are much less responsive to real
GNP than are their hours of work in the busi­
ness sector. The estimated elasticities are larg­
est for single women.

T A B L E

IV. Implications of
the Findings

3

Empirical Elasticity of Hours and Labor
Input with Respect to Real GNP for
Demographic Groups, 1969-82
Empirical Elasticity with Respect to Real GNPa
Hours
0.45
(0.10)
0.47
(0.06)
0.69
(0.21)
0.28
(0.27)

All

Males
Single females
Married females

Labor Input
0.30
(0.08)
0.27
(0.11)
0.26
(0.21)
0.35
(0.24)

The results for the PSID sample indicate that,
cyclically, workers’ aggregate hours are not a
good measure of their aggregate labor input.
To make the PSID sample more representative
of the U.S. population, we weighted the three
demographic groups by their relative numbers
in the U.S. population. Figure 7 plots both the
weighted-sample hours and labor input along
with real GNP. These hours move in closer
conformity with GNP than do the unweighted
figures. Table 4 presents some summary statis­
tics, which are essentially the same as those for
the unweighted sample as reported in table 1.

a. Standard errors are in parentheses.
SOURCE: Authors’ calculations.

Bias of Measures of
Relative Volatility
■ ■ ■ ■ I T A BL E 4
Cyclical Labor Input, Real Wage,
and Real GNP: Weighted Sample,
1969-82
Percentage
Standard
Deviation

Correlations with
Z

GNP

Hours (ZZ)
Compensation
per hour ( W H ~
)
Real GNP

0.55

0.82

0.80

0.55

—

0.51

2.50

0.82

0.51

H

Labor input (Z)
Real wage ( W L)
Real GNP

0.98

W1

w"

GNP

0.01

0.83
-0.09

1.50
0.43

0.01

—

2.50

0.83

-0.09

Empirical Elasticities with
Respect to GNPJ

Labor input (Z)
Hours (ZZ)
a. Standard errors are in parentheses.
SOURCE: Authors’ calculations.




0.32
(0.06)
0.50
(0.10)

The statistics reported are nonlinear functions
of sample moments. A question is how close
they are to the statistics for the population
from which the sample was drawn. For a ran­
dom sample of a given size, there is generally
a sampling distribution, which is a function of
the distribution of characteristics in the sampled
population. This sampling distribution is a con­
tinuous function of the distribution of popula­
tion characteristics.
We used Monte Carlo techniques to deter­
mine the sampling distribution for the population
for which the PSID sample is representative. If
this distribution is close to the actual population
distribution, continuity implies that the distribu­
tion of sampling errors for the actual population
will be close to the computed one. Insofar as it is
sufficiently close (which is true asymptotically),
the sampling-error distribution for the ratio of the
standard deviations of hours and the labor input
has a negative bias of 0.13 and a standard devia­
tion of 0.16. If the true value were 1.25, which is
a large number from the point of view of busi­
ness cycle accounting, in only one of the 100 ran­
dom samples was the statistic as much as 0.28
above its true value. This, we think, indicates
that the difference in volatilities is most likely
greater than 25 percent for the actual population
in this period.

Comparison with
Other Measures of
the Labor Input
The standard measure of the labor input is ag­
gregate hours. W hen it is adjusted using the
composition adjustment factor of Dean, Kunze,
and Rosenblum (1988), the measure’s cyclical
variability is reduced from 2.34 to 2.07 percent,
implying that hours are 13 percent more vola­
tile than their adjusted hours in the 1969-82
period. Similarly, for the Jorgenson, Gollop,
and Fraumeni (1987) adjustment, the variability
of hours is 2.20, while it is 1.84 for their labor
input in the 1969-79 period. Thus, hours are
19 percent more variable than is their labor in­
put. Finally, comparing Darby’s (1984) total
hours and quality-adjusted hours for the same
period, the cyclical variability of the former is
3.02 percent, while that of the latter is 3.06.
In all three studies, there is considerable ag­
gregation within each group, and quality
weights are computed on this basis. From a cy­
clical accounting point of view, these adjust­
ments are somewhat significant, but are
dwarfed by the adjustments suggested by our
study. We, of course, use separate weights for
each individual. The weighted-sample hours
variability is 1.50 percent— a full 53 percent
larger than the labor-input variability, which is
only 0.98 percent.

Implications for
Accounting for
Cyclical Variations
in Output
To the extent that the relative variabilities of
hours and the labor input found for the weighted
PSID sample hold for the entire U.S. population,
our findings call for major revision of the tradi­
tional view of the nature of business cycles.
Rather than productivity and the labor input be­
ing slightly negatively correlated, they become
strongly positively associated. The importance of
variations in the labor input in accounting for
fluctuations in aggregate output is substantially
reduced. Given that cyclical components of capi­
tal stocks and output are roughly orthogonal,
variation in the Solow technology coefficient
must account for much more of business cycle
fluctuations in output. This factor, then, is nearly
as important as are variations in the labor input.




21

Figures Used for Bracketed
Income Variables, 1969-74
Income Bracket
(Annual Dollars)_____________________________ Value Used
250
750
1,500
2,500
4,000

1-499
500-999
1,000-1,999
2,000-2,999
3,000-4,999
5,000-7,499
7,500-9,999
10,000 and over

6,000
8,500
14,000

SOURCE: Authors.

■
■
Ei
m

Sample Averages: Full Sample
and Males, 1969-82
Males

Full Sample
Year

H

L

E

Age

No.

Year

H

L

E

Age

No.

1969

1,657
(962)

1,754
(1,502)

5,981
(5,568)

38.8

2,710

1969

2,210
(659)

2,647
(1,427)

8,999
(5,745)

40.4
(13.1)

1,425

(13.1)

1,634
(951)

1,704
(1,440)

5,979
(5,542)

(13.4)

1,628
(954)

1,681
(1,436)

5,900
(5,507)

1972

1,623
(968)

1,657
(1,387)

1973

1,625
(963)

1974

1,580
(961)

(1,351)

1,540
(950)

38.6

2,914

1970

2,149
(699)

2,530
(1,387)

8,863
(5,782)

40.1
(13.5)

1,534

38.5
(13.7)

3,161

1971

2,135
(715)

2,491
(1,403)

8,682
(5,814)

40.0
(13.9)

1,666

5,939
(5,549)

38.3
(14.0)

3,374

1972

2,142
(733)

2,456
(1,314)

8,799
(5,793)

39.7
(14.2)

1,779

1,637
(1,390)

5,965
(5,569)

38.4
(14.1)

3,596

1973

2,114
(767)

2,396
(1,366)

8,744
(5,892)

39.7
(14.4)

1,905

1,600

5,901
(5,711)

38.6

3,757

1974

2,048
(796)

2,330
(1,322)

8,607
(6,200)

39.8
(14.5)

1,990

(14.3)

5,694
(5,956)

38.4
(14.3)

3,889

1975

1,983
(819)

2,281
(1,432)

8,290
(6,803)

39.6
(14.6)

2,026

(1,386)

1,555
(957)

1,553
(1,367)

5,798
(5,929)

38.9
(14.5)

4,037

1976

1,992
(843)

2,269
(1,414)

8,445
(6,714)

40.1
(14.8)

2,102

1,562

1,553
(1,348)

5,899
(5,884)

39.2
(14.5)

4,149

1977

2,002
(843)

2,280
(1,374)

8,648
(6,549)

40.2
(14.8)

2,143

(963)
1,578
(946)

1,544
(1,336)

6,012

39.4
(14.7)

4,287

1,983
(846)

2,222
(1,392)

8,707
(6,570)

40.5
(14.9)

2,221

(5,891)

1979

1,588
(939)

1,532
(1,339)

6,053
(5,827)

39.7
(14.7)

4,474

1979

1,972
(852)

2,186
(1,422)

8,680
(6,483)

40.6
(14.9)

2,330

1980

1,564
(947)

1,496
(1,315)

6,019
(5,964)

40.7
(14.8)

4,401

1980

1,926

2,127
(1,406)

8,611
(6,724)

41.7
(15.1)

2,286

(875)

1981

1,537
(949)

1,470
(1,287)

5,922
(5,888)

41.8
(14.7)

4,376

1981

1,892
(881)

2,089
(1,361)

8,467
(6,631)

42.6
(14.9)

2,271

1982

1,502
(968)

1,431
(1,316)

5,841
(6,627)

42.7
(14.7)

4,309

1982

1,832

2,028
(1,439)

8,319
(7,872)

43.6
(14.9)

2,223

1970
1971

1975
1976
1977
1978

1,561

1978

(928)

NOTES: H = annual hours of work; L = annual labor input; and E = annual real labor earnings in 1969 dollars. Standard deviations are in
parentheses.
SOURCE: Authors’ calculations based on PSID data.




Sample Averages: Single and
Married Females, 1969-82
__________________ Married Females

Single Females___________________
Year

H

L

E

Age

No.

Year

H

L

E

Age

No.

1969

1,527
(794)

1,174
(917)

4,068
(3,139)

41.7
(15.5)

263

1969

919
(844)

659
(726)

2,264
(2,495)

35.9
(11.7)

1,022

1970

1,482
(796)

1,142
(897)

4,037
(3,213)

41.2
(15.7)

290

1970

950
(845)

690
(743)

2,439
(2,663)

35.7
(12.0)

1,090

1971

1,483
(811)

1,150
(901)

4,106
(3,226)

42.3
(15.8)

306

1971

954
(845)

686
(732)

2,466
(2,664)

35.4
(12.2)

1,189

1972

1,472
(815)

1,122
(907)

3,943
(3,316)

42.1
(16.1)

333

1972

932
(842)

674
(739)

2,435
(2,694)

35.4
(12.4)

1,262

1973

1,488
(793)

1,115
(878)

4,009
(3,255)

42.4
(16.5)

358

1973

963
(841)

692
(738)

2,520
(2,693)

35.4
(12.4)

1,333

1974

1,409
(831)

1,056
(879)

3,813
(3,117)

42.6
(16.7)

388

1974

953
(831)

701
(755)

2,587
(2,804)

35.7
(12.5)

1,379

1975

1,329
(831)

999
(834)

3,738
(3,217)

42.0
(16.8)

429

1975

977
(829)

713
(745)

2,613
(2,749)

35.7
(12.6)

1,434

1976

1,302
(832)

958
(817)

3,657
(3,203)

42.7
(17.3)

454

1976

1,012
(831)

720
(723)

2,700
(2,785)

36.0
(12.6)

1,481

1977

1,357
(867)

964
(812)

3,626
(3,180)

42.9
(17.4)

478

1977

1,008
(833)

718
(731)

2,756
(2,931)

36.5
(12.7)

1,528

1978

1,348
(883)

955
(812)

3,645
(3,217)

43.3
(17.8)

493

1978

1,078
(830)

771
(750)

2,951
(2,996)

36.8
(12.6)

1,573

1979 \ 1,329
(872)

895
(747)

3,547
(3,081)

43.0
(18.1)

527

1979

1,118
(833)

799
(761)

3,087
(3,083)

37.4
(12.7)

1,617

1980

1,338
(906)

895
(769)

3,527
(3,107)

44.4
(18.0)

533

1980

1,116
(840)

789
(743)

3,115
(3,182)

38.1
(12.6)

1,582

1981

1,269
(931)

865
(778)

3,477
(3,216)

45.5
(17.9)

552

1981

1,112
(838)

781
(757)

3,070
(3,157)

39.2
(12.7)

1,553

1982

1,237
(938)

848
(788)

3,414
(3,334)

46.7
(17.8)

551

1982

1,120
(861)

776
(756)

3,126
(3,345)

40.0
(12.6)

1,535

NOTES: H = annual hours o f work; L = annual labor input; and E = annual real labor earnings in 1969 dollars. Standard deviations are in
parentheses.
SOURCE: Authors’ calculations based on PSID data.

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Money and Interest Rates
under a Reserves
Operating Target
by Robert B. Avery and Myron L. Kwast

Introduction
Between October 1979 and mid-summer 1982, the
Federal Reserve focused its attention on controlling
a narrow monetary aggregate (M l) and relied pri­
marily on nonborrowed reserves as the short-run
instrument for achieving its monetary target. This
brief but important period provides a unique op­
portunity to examine the dynamic effects of the
short-mn monetary supply process.
Although many interesting issues could be ex­
amined, we concentrate on two that have received
little empirical attention: 1) the speed and dynamic
response patterns of both money and short-term
interest rates to changes in nonborrowed reserves,
and 2) the extent of “feedback” effects between
short-run shocks to money and the central bank’s
provision of nonborrowed reserves.
We provide unique estimates of liquidity ef­
fects following changes in the supply of nonbor­
rowed reserves. This work originated over a
decade ago in the midst of heated debate about
Federal Reserve operating procedures and mone­
tary control. Although the debate has cooled,
there is renewed interest in understanding liquid­
ity effects because they are central to the mone­
tary policy transmission mechanism.1 Using

http://fraser.stlouisfed.org/
monthly data, Leeper and Gordon (1992) show
Federal Reserve Bank of St. Louis

Robert B. Avery is a professor in
the Department of Consumer Eco­
nomics and Housing at Cornell
University and a research associate
at the Federal Reserve Bank of
Cleveland. Myron L. Kwast is an as­
sistant director in the Division of
Research and Statistics at the Fed­
eral Reserve Board of Governors,
Washington, D.C. The authors
thank Allen Berger, John Carlson,
William Gavin, Jagadeesh Gokhale,
Joseph Haubrich, Donald Hester,
Robert Lltterman, Allan Meltzer,
and Steven Strongen for numerous
useful comments. Oscar Barnhardt
and Michelle Hamecs provided
able research assistance.

that evidence about the existence of liquidity
effects is ambiguous. They conclude that a suc­
cessful characterization of such effects requires
the identification of private and public behavior.
This paper identifies liquidity effects through tem­
poral disaggregation and a structural specification
based on the mechanisms of monetary control.
Our approach is to disaggregate the time di­
mension of the analysis into the shortest period
of practical concern for most monetary policy
decisions. Thus, our estimation procedures ex­
ploit daily data collected by the Federal Re­
serve. A simplified structural model of the
short-run money supply process is developed
that, because of the paucity of variables avail­
able on a daily basis, is estimated using lagged
endogenous variables. We further emphasize
the short-mn nature of the model by estimat­
ing separate statistical models, and therefore
separate effects, for each day of the week. Each
model includes controls for the Federal Open
Market Committee’s (FOMC) M l target growth
paths and is estimated in first-difference form.
Thus, the models focus only on very short-term

■ 1

Bernanke and Blinder (1992) make a persuasive case for the
presence of liquidity effects in the U.S. economy. Christiano and Eichenbaum (1992), Christiano (1991), and Coleman, Labadie, and Gilles
(1993) build explicit models of liquidity effects.

25

behavior and abstract from longer-term rela­
tionships and policymaking. In essence, we ex­
amine the reaction of money and interest rates
to deviations of nonborrowed reserves from
weekly and longer-term target growth paths.
Thus, we control for those factors that are gen­
erally the focus of monthly or quarterly models
and examine the variability that is averaged
out in such analyses.
Statistical tests of the importance of day-byday effects are performed. We then use the esti­
mation results to simulate the short-run dynamic
relationships between nonborrowed reserves,
the federal funds rate, and a measure of transac­
tion accounts. These experiments provide in­
sights regarding the short-run money supply
process that are not accessible using the more
time-aggregated data of previous studies.2

I. The Model
On October 6, 1979, the Federal Reserve an­
nounced that it was switching its short-mn op­
erating target from the federal funds rate to
nonborrowed reserves in an effort to better
control the money supply. By the latter part of
1982, the Fed had begun to deemphasize M l
as its monetary target, with a resulting decline
in the use of nonborrowed reserves as its oper­
ating target.3 During this brief period, however,
nonborrowed reserves appear to have been the
primary short-term instmment of central bank
policy, while the federal Rinds rate was deter­
mined primarily by market factors.4
Stevens (1981) characterizes Federal Reserve
nonborrowed reserves policy during this period
as consisting of five steps. Steps one and two
occurred at the FOMC meetings and involved
the setting of yearly and short-run (inter-FOMC
meeting) paths for Ml. In the third step, the staff

■

2 Other studies have used weekly and often monthly or quarterly
data to examine what are frequently very short-run issues. See, for exam­
ple, Spindt and Tarhan (1983,1987), Tinsley et al. (1982), Jones (1981),
Johannes and Rasche (1981), Feige and McGee (1977), and Gavin and
Karamouzis (1985).

■
■

3 See Axilrod (1982,1985).

4 Poole (1982) disputes this claim, arguing that the Fed actually
used borrowed reserves as its short-run target and that under the lagged
reserve requirements in effect at the time, it should have been using free
reserves. Notice, however, that since free reserves equal nonborrowed re­
serves minus required reserves, which are fixed in any given week under
lagged reserve requirements, over any weekly period nonborrowed re­
serves and free-reserves targeting are functionally equivalent. Spindt and
Tarhan (1987) present evidence supporting the view that over an inter FOMC operating horizon, the Federal Reserve, from fall 1979 through fall
1982,
http://fraser.stlouisfed.org/ followed a nonborrowed reserves operating target. Over shorter
Federal Reserve Bank (weekly)Louis however, their results are ambiguous.
of St. intervals,

derived the target growth paths for borrowed
and nonborrowed reserves on the basis of the
short-run path for Ml. Step four was repeated each
week. Incoming information about the money mul­
tiplier, unexpected changes in the mix of deposits,
and unexpected changes in the demands for cur­
rency, excess reserves, and borrowed reserves
were used to translate the inter-meeting objective for
nonlxDirowed reserves into a target for the reserve
maintenance week. “On Friday,” Stevens argues,
“...objectives ... can be set, reflecting any technical
corrections and judgmental adjustments to the inter­
meeting reserve objectives ....” Step five translated the
weekly objective into a daily program. At this level,
changes in nonborrowed reserves were primarily re­
active to very short-mn changes in the market factors
absorbing and supplying reserve funds. These fac­
tors included such items as Treasury operations, Fed­
eral Reserve float, and unexpected discount window
borrowing. Although federal funds rate targeting was
not explicitly used, funds rate changes were some­
times read by policymakers as indicators of changes in
these underlying factors, which would have prompted
daily adjustments in nonborrowed reserves.
We focus on the last two steps, examining
how unexpected shocks to money and the fed­
eral funds rate influenced weekly and daily re­
serve operations. We also examine how reserve
changes affected money and the funds rate.
Open market operations have a direct effect
on money via the creation or destruction of bank
deposits, while indirect effects may work through
the funds rate. The use of daily data allows us
to study feedback effects. That is, changes in re­
serves induce changes in money and the federal
funds rate, which may ultimately cause addi­
tional changes in reserves because policymakers
cannot distinguish them from other money or
interest-rate shocks.5
The general lack of daily data and the ana­
lytical complexity of combining five daily m od­
els into an empirically tractable system forces
us to restrict our description of the daily money
supply process to a straightforward structure.6
In this spirit, a reasonably accurate— but admit­
tedly simplified—model of the bank reserves

■

5 Avery (1979) models monetary policy as an endogenous vari­
able. His results suggest that over the 1955-75 period, feedback effects
occurred within a month.

■

6 A more complex model of short-run money supply over the pe­
riod studied here is provided in Goodfriend et al. (1986). Other authors,
including Judd and Scadding (1982), have suggested linkages between
the federal funds rate and money demand, working through interest-rate
term structures. Since the current model and subsequent empirical work
ignore interest rates other than the federal funds rate, the maintained as­
sumption is that the term structure shifts proportionately with changes in
the funds rate. Spindt and Tarhan (1987) provide results that support this
assumption for our sample period.

market during the November 1979 to mid­
summer 1982 period would focus on three key
variables: 1) nonborrowed reserves (NBR), 2)
the federal funds rate (FFRT), and 3) the equilib­
rium quantity of transaction money (TRAN). Such
a model may be written as

The functional relationships among the
reduced-form errors (the v ’s ) are identical to the
contemporaneous relationships that exist among
the endogenous variables in the structural model.
That is,
(7)

(1)

(8)
FFRTt —a 2 N BRt + a 2 X t + e 2t,
\
2

(2)
(3)

v u = a u v 2t+ e u >

N BRt = au FFRTt + a\ t + e lt,
2X

(9)

V2 t ~ a 2\ V \t + e 2 f

t

’

a 5 l V l t + a 32V 2t+ e 3 f

TRANt = a } l N BR, + a p FFRTt
+ a } iX t+ e5t,

where
X t is a vector of relevant exogenous variables,
a .. represents behavioral parameters (or vec­
tor a' of parameters), t is time measured in
days, and e lt is normally distributed random
disturbances, which are serially uncorrelated
(though they may be correlated with each other).
This is a block recursive model in which non­
borrowed reserves and the funds rate are deter­
mined simultaneously in the federal funds market
(equation [1 represents NBR supply and equa­
]
tion [ ] NBR demand), and the equilibrium quanti­
2
ties of NBR and FFRT help to contemporaneously
determine TRAN. Thus, feedback is allowed be­
tween FFRT and NBR, but not between TRAN
and NBR. The rationale for this is based both on
the institutional fact of lagged reserve requirements,
under which required reserves held in week three
were based on transaction accounts held in week
one, and on the view that neither the Federal Re­
serve nor the market observed changes in aggre­
gate money during the day.
Analysis of the dynamic relationships
among the endogenous variables is facilitated
by considering the reduced form of the model:
(4)

N BRt = P\Xt+ v lt,

(5)

FFRT,= P'2X,+ v 2n

(6)

TRAN,= P's X,+ v i r

where the P's are reduced-form coefficients, and

6111 e

2t + e \t

1 —a

v~,=


V 3t ~


a 2i

ii

a 2 i e \t

+

e 2t

1 —a

u

a 2i

a 5l V\t

+

a i2 V 2 t + e 5f

Thus, analysis of the reduced-form errors in
equations (7)-(9) will provide impulse-response
functions identical to those obtained by analyz­
ing the structural model directly.7
The reduced-form equations (4)-(6) are esti­
mated as a set of vector autoregressions (VARs),
where the X s in each equation are a set of lagged
endogenous variables (with some minor additions).
This particular choice of exogenous variables im­
plies that the v’s in (7)-(9) will be one-step-ahead
forecast errors.
The VAR methodology, pioneered by Sims
(1980, 1982), was adopted primarily because of
the difficulty of collecting more-traditional ex­
ogenous variables on a daily basis.8 Many ex­
ogenous variables that have been used in weekly
or monthly money-demand models are simply
not available on a daily basis. Use of the VAR
methodology allows us to get around this prob­
lem by thinking of the lagged endogenous vari­
ables as instruments for a more complex set of
Xs. An additional advantage of using lagged en­
dogenous variables is that it allows us to perform
a relatively simple calculation of the dynamic

■ 7 Briefly, this can be seen as follows. Consider the simultaneous
equation system
Y ,= B Y t + P X t + e v
where Yf , X , , and e, are vectors of endogenous, exogenous, and ran­
dom errors, respectively, and B and P are matrices of coefficients. The
reduced form of this system is
Y , = ( I - B Y ' P X , + u t,
with
u , = (I - £ ) " 1 et.
From the latter relationship, it is clear that
u t = B u , + e t,
of which equations (7) - (9 ) are but a special case.

■

8 A few examples will give the flavor of the types of variables that
might be used in a more explicit model. Under the system of lagged reserve
requirements in existence during the study period, required reserves were
fixed within each reserve maintenance week (Thursday—
Wednesday) and
were determined by required reserve ratios and the two-week lagged values
of reservable liabilities. The demand for excess reserves is affected by a num­
ber of factors, including the volume of reserve account transactions and the
risk preferences of individual banks. The supply of reserves is influenced by
the demand for borrowed reserves, which depends in part on the spread be­
tween the federal funds rate and the discount rate, and the degree of “moral
suasion” exerted at the discount window.

27

reaction of the system to shocks without having
to specify or estimate the dynamic behavior of
the exogenous variables separately.
Even with the assumption that money is de­
termined recursively, the structural parameters of
equations (7)-(9) cannot be calculated from the
reduced-form equations without further restriction
because of the simultaneous determination of
NBR and FFRT. A traditional identifying assump­
tion would be that the reserve supply is set dur­
ing the previous period and thus is exogenous.
However, we decided that this assumption is in­
appropriate in the daily model, since we are fo­
cusing on the reaction of the Federal Reserve
Open Market Desk to unforeseen changes in the
economic environment. Moreover, as shown in
the next section, it also turns out to be inconsis­
tent with the positive contemporaneous relation­
ship observed empirically between the two
variables (or between their one-step-ahead fore­
cast errors, vx and v2). An alternative, albeit arbi­
trary, restriction was therefore imposed.
We assumed that the structural coefficient
representing the effect of a contemporaneous
change in reserves on the federal funds rate, a 21,
was identical to the structural coefficient of the
previous day’s reserve change on the funds
rate (an element of a '7 ). This additional as­
2
sumption, which identifies the entire system,
centers around the belief that banks trading in
the federal funds market smooth the price of
reserves from day to day. This may occur for
two reasons. First, because of lags in the sys­
tem, it isn’t clear that traders can actually de­
tect “new” reserves within a day. Second,
during the study period, reserve accounting
took place on a weekly rather than daily basis.
Reserves on any one day of the maintenance
period were almost perfect substitutes for re­
serves on another day. Thus, the relevant re­
serve quantity in determining the funds rate
was an estimate of “weekly” reserves, which
would be equally affected by contemporane­
ous and one-day-lagged shocks.9

tion accounts. Data on each of these variables
were collected for the five working days
(Thursday through Wednesday) of the 139 re­
serve maintenance weeks from November 7,
1979 through June 30, 1982. This represents a
relatively homogeneous period with respect to
the operating procedures of monetary policy
following the Federal Reserve’s October 1979
adoption of reserve targeting. The only likely
deviation occurred during the April-August
1980 period of credit controls. Our calculations
for this interval are characterized by an inter­
cept shift in all estimated equations.
Data were collected from several sources.
Systemwide nonborrow'ed reserves were taken
from the Federal Reserve’s daily balance sheet
and then corrected for “as-of” adjustments and
overdrafts.1 Transaction accounts were meas­
0
ured as the sum of gross demand deposits, auto­
matic transfers from savings accounts, telephone
and preauthorized transfer accounts, and NOW
accounts and share drafts, minus demand bal­
ances due from depository institutions in the
United States, less cash items in the process of
collection. These data, designated TRAN, were
gathered at the individual bank level and then ag­
gregated daily across all Federal Reserve member
banks.1 The federal funds rate was measured as
1
the daily weighted average computed by the Fed­
eral Reserve.
Sample means and standard deviations for
the variables used in this study are presented
in table 1. Average levels for each variable are
given, as are average changes by day of the
week. The data show substantial variation in
the day-by-day change in every variable. For
example, Friday and Monday appear to have
been especially atypical for member-bank
transaction accounts. Each Friday, an average
of $9-8 billion flowed out of these accounts,
and on Monday $13.4 billion flowed in. The
Friday outflow may have resulted either from
the weekend migration of transaction accounts
to higher yields, from Eurodollar arbitrage be­
havior by the big banks that was common

II. Data
Our empirical analysis is based on the dynamic
relationships of the three variables discussed
above— nonborrowed reserves, the federal
funds rate, and money as measured by transac-

■

9 The robustness of this assumption was tested in estimating the
impulse-response functions (presented in the next section) by resetting the
coefficient a 21 to one-half and to two times the structural coefficient of the

previous
http://fraser.stlouisfed.org/ day’s reserve change. In neither case were the substantive conclu­
sions drawn from
Federal Reserve Bank of St. Louis calculating the impulse-response functions changed.

■ 10 As-of adjustments are corrections made up to three weeks later
to reflect errors in the original accounting. Overdrafts are negative bal­
ances not reflected in the original accounting.
■ 11 TRAN is taken from the Report of Deposits submitted to the Fed­
eral Reserve for the purpose of computing required reserves. The data used
are final “hard” numbers subject to little revision. It should be noted that the
money supply data were released each Friday and were computed from dif­
ferent sources than those used for TRAN. However, the TRAN definition
was chosen after extensive conversations with the Federal Reserve staff re­
sponsible for computing the monetary aggregates over the sample period.
They indicated that TRAN would be extremely highly correlated with the ag­
gregate measures of transaction money used at the time.

m
T A B L E

1

Sample Means9
Average
uany
Level

Variable
NBR

Average Daily Change
Thursday

Friday

Monday

Tuesday

Wednesday

149
(3,549)
40
(88)
570
(3,751)
-873
(3,839)
-1,052
(1,298)

-126
(2,055)
-9
(52)

-39
(3,079)
3
(62)
13,432

-726
(2,599)
-10
(67)
-4,394

(8,753)
-220
(3,087)
-181
(395)

(9,109)
-778
(2,662)
-52
(332)

690
(3,115)
-25
(110)
421
(3,972)
1,721

40,361

FFRT

1,467

TRAN

213,329

Total system excess reserves
Total system reserve borrowings

531
1,426

-9,849
(7,308)
116
(2,037)
247
(431)

(3,543)
1,031
(1,433)

a. The federal funds rate is measured in basis points. All other variables are measured in millions of dollars. All data are nonseasonally adjusted.
NOTE: Standard deviations are in parentheses.
SOURCE: Board o f Governors o f the Federal Reserve System.

over part of the estimation period, or from
banks’ attempts to reduce reservable liabilities
over the Friday to Sunday period.
The more-than-compensating Monday in­
flow may reflect the return of Friday’s funds
and the Monday posting of weekend transac­
tions.1 In addition, it is interesting to observe
2
that the average federal funds rate fell on both
Tuesday (10 basis points) and Wednesday (25
basis points). However, these declines were
more than offset by the 40-basis-point average
increase on Thursday. This may reflect either a
falloff in reserve demand tow'ard the end of
the reserve maintenance week (because riskaverse banks obtained their reserves earlier) or
an expansion of reserve supply. It may also in­
dicate risk-averse actions on the part of the
Federal Reserve Board to supply reserves and
thus avoid a large swing in the funds rate.
Prior to use in the regression analysis, the
raw data had to be adjusted. To control for
trends, we converted each variable to a daily
first difference. Because data were not other­
wise seasonally adjusted, variables were fur­
ther transformed to deviations around seasonal
(monthly) means. We computed values for the
10 bankers’ holidays per year using predicted
values from auxiliary regressions similar in


■
http://fraser.stlouisfed.org/ 12 Such transactions include deposits by retail stores and auto­
Federal Reserve Bank mated teller machine activity.
of St. Louis

form to those ultimately used in the analysis,
but employing only those observations with
complete data.
The basic VARs were estimated utilizing all
three variables: NBR, TRAN, and FFRT. Results
for these regressions are available in Avery and
Kwast (1986). We regressed the daily change
in each variable against both the lagged daily
changes in the current and previous reserve
week and the wr
eekly changes of the second
through fourth lagged reserve weeks for each
of the three series.1 In addition, we used vari­
3
ables representing the FOMC’s short-run path
for M l, an intercept shift for the April-August
1980 credit control period, and binary vari­
ables for the day, the day after, and two days
after a Social Security payment (generally the
third of each month), as well as for the end of
a quarter. These variables were designed to
capture what are commonly recognized as the
most important seasonal effects not accounted
for by the transformation using monthly means.
Each regression was fit separately for all five
days in the reserve week, utilizing the 139 sam­
ple weeks of data.
The first-differencing and VAR forms of the
regressions appear to have removed most first-

■

13 The choice of lag structure reflects a trade-off between nonrestrictive completeness and estimation parsimony. Once daily observations for the
previous week were included, the model results were not particularly sensi­
tive to the lag specification of the endogenous variables.

29

FI GURE

1

Cumulative Response to a $200Million-per-Day Net Shock to N R
B
Maintained for Five Days
Millions of dollars

Basis points

order serial correlation from the equation re­
siduals, with estimated first-order serial correla­
tion coefficients of 0.02, -0.02, and 0.06 for
NBR, TRAN, and FFRT, respectively.1 The av­
4
erage contemporaneous residual correlation is
0.27 between NBR and TRAN, 0.10 between
FFRT and TRAN, and 0.15 between NBR and
FFRT. As mentioned earlier, the positive corre­
lation between NBR and FFRT led us to adopt
our somewhat arbitrary identifying restriction
for the model. W hen structural parameters
were determined using the lagged identifying
restriction, the imposed coefficient was the
“right” sign and “a reasonable order of magni­
tude” in all five cases (there is a separate
model for each day of the week).1
5

III. Dynamic
Behavior
NOTE: Cumulative net change.
SOURCE: Authors’ calculations.

TABLE

2

Cumulative Response to a $200Million-per-Day Net Shock to N R
B
Maintained for Five Days

Variable

One
Week

Two
Weeks

Three
Weeks

Four
Weeks

Five
Weeks

NBR changea

1,000

1,000

1,000

1,000

1,000

Percent change0

(-)
2.48

(-)
2.48

(-)
2.48

(-)
2.48

(-)
2.48

FFRT changec

-87.7
(15.5)
Percent changeb -5.98

-113.0
(31.5)
-7.70

-56.9
(2 6.6)
-3.88

-90.9
(27.3)
-6.20

-91.0
(40.9)
-6.20

447.8
(170.0)
Percent changeb 0.21

-209.4
(601.0)
-0.10

-734.2
(822.3)
-0.34

122.8
(788.4)
0.06

1,098.7
(896.7)
0.52

TRAN change“

a. Cumulative net change, millions of dollars.
b. Based on average values over the estimation period.
c. Cumulative net change, basis points.
NOTE: Standard errors are in parentheses.
SOURCE: Authors’ calculations.




We are concerned here with the magnitude,
sign, and significance of the impulse-response
functions of each endogenous variable with re­
spect to an exogenous shock to both itself and
the other endogenous variables. The contem­
poraneous effects follow directly from estimates
of the ciy s computed by solving the sample
analog of equations (7)-(9). The effect of ex­
ogenous shocks on future values of the endo­
genous variables does not follow as straight­
forwardly. However, given a solution to the
contemporaneous relationships of (7)-(9), fu­
ture effects could be computed by solving for
the moving-average representation of the VAR
structure in equations (4)-(6).
Below, we examine the reactions of the sys­
tem to two different shocks. The first is the esti­
mated impact of an unexpected change in non­
borrowed reserves, and the second is the reaction
of policymakers to a shock to money demand.

Response to
a Change in
Nonborrowed
Reserves
Figure 1 displays calculated responses of each
variable to a net $1.0 billion positive shock to

■

14 Higher-order serial coefficients were smaller in absolute magni­
tude than these, and none was statistically significant.
■ 15 The structural parameter estimates are not reported here be­
cause the impulse-response functions derived from them are, for pur­
poses of this paper, more meaningful. The impulse-response functions
are presented in the next section.

30

FI GURE

2

Cumulative Response to a $200Million-per-Day Gross Shock to
T A Maintained for Five Days
RN
Millions of dollars

Basis points
3

NOTE: Cumulative net change.
SOURCE: Authors’ calculations.

NBR ($200 million per day for five days).1 A
6
net change was simulated to represent a shift in
the weekly objective for NBR growth, which pre­
sumably would be represented by a net rather
than a gross change in NBR. Because the model
is first-differenced, the figures presented are cu­
mulative moving averages. Approximate standard
errors at intervals of one through five weeks are
displayed in table 2. These were calculated using
bootstrap methods, since analytic derivation
would have been extremely difficult.1
As seen in the figure, FFRT responds quite
rapidly and inversely to the change in NBR. In
fact, the two-week response is greater than the
five-week response. By five weeks, FFRT has de­
clined more than 6 percent. Given the 2.4 percent
change in NBR, this implies a short-run elasticity
with respect to nonborrowed reserves of -2.5.

■

16 The linearity of the model makes the size of the shock unimpor­

tant, since the values of the multipliers are independent of the shock’s
size. The shock simulated is one that offsets any implied feedback (even
in the near future) and that provides an additional $200 million injection
per day for five days. Thus, the shock is equivalent to a net injection.
■ 17 The estimated covariance of the VARs was calculated assuming a
three-equation system with contemporaneously correlated, but serially un­
correlated, errors. The resulting coefficient covariance matrix was used to
generate 50 random multivariate normal coefficient vectors centered on the
estimated parameter vector. Simulated moving-average responses were then
derived for each of the random coefficient vectors (contemporaneous coeffi­
 cients were also adjusted), and the sample standard deviation of the cumula­
tive
http://fraser.stlouisfed.org/ responses was calculated at each point in time. These estimates suggest
Federal Reserve Bank of St. Louis moving averages are significantly different from zero.
that the cumulative

Initially, TRAN rises, fueled primarily by the
contemporaneous correlation that is probably
due to the open market operation itself. During
weeks two and three, cumulative TRAN changes
are actually negative, and it is not until week five
that there is any appreciable increase. Even then,
the implied “money multiplier” (ignoring currency
and other transaction accounts) is only slightly
larger than one. This suggests that most of the ef­
fects of an unexpected change in nonborrowed
reserves were absorbed by changes in borrowing,
excess reserves, or cash— not by changes in
transaction accounts. To investigate this possibil­
ity, reduced-form models identical to those of
NBR, FFRT, and TRAN (same independent vari­
ables and lagged endogenous variables) were
run for excess and borrowed reserves. Assuming
a recursive contemporaneous ordering, response
functions similar to those shown in figure 1 were
calculated for both variables. After three weeks,
declines in borrowing and increases in excess re­
serves were estimated to total $1,187 million
more than the injection of reserves. By week
five, decreases in borrowing totaled $423 million
and increases in excess reserves were estimated
at $323 million. Together, these results imply that
almost three-quarters of the reserve injection was
absorbed by these short-term “buffers.”

Feedback Effects:
Response of
Nonborrowed
Reserves to a
Change in Money
Demand
The short-run reaction of the money market,
particularly nonborrowed reserves, to a change
in money may be examined with calculations
similar to those utilized in the previous subsec­
tion. The difference is that in this case, a shock
is exerted on TRAN, and feedback (on TRAN)
is allowed. Figure 2 presents the results of a
$200-million-per-day gross positive shock to
TRAN maintained for five days.1 For reasons
8
that will become apparent below, the results
of this simulation are displayed out to seven

■ 18 Ceteris paribus, this is also a large shock and would increase
TRAN by 25 percent if continued for one year with no feedback. With
feedback, the shock would increase TRAN by 8.5 percent. We handle
contemporaneous correlations the same way as in the NBR simulations.
Neither NBR nor FFRT is assumed to react to contemporaneous TRAN;
thus, there is no intraday feedback.

31

T A B L E

3

Cumulative Response to a $200Million-per-Day Gross Shock to
T A Maintained for 5 Days
RN

Variable
NBR change3
Percent changeb
FFRT change0
Percent changeb
TRAN change3
Percent change5

One
Week

Two
Weeks

Three
Weeks

Four
Weeks

Five
Weeks

Six
Weeks

Seven
Weeks

-21.8
(23.2)
-0.05

-27.0
(30.7)
-0.07

80.2
(29.3)
0.20

37.1
(32.6)

-11.4
(32.6)
-0.03

21.0
(37.4)
0.05

43.0
(32.7)
0.11

-2.38
(1.27)
-0.16

-1.52
(1.67)
-0.10

0.43
(1.81)
-0.03

(1.83)
-0.001

-0.74
(2.16)
-0.051

-0.51
(1.82)

-1.96
(2.12)

-0.03

-0.13

607.9
(40.4)
0.28

427.5
(73.6)
0.20

360.3
(78.9)
0.17

168.2
(72.0)
0.08

342.9
(76.0)
0.16

404.7
(74.2)

413.0
(80.8)

0.19

0.19

0.09
-0.01

a. Cumulative net change, millions of dollars.
b. Based on average values over the estimation period.
c. Cumulative net change, basis points.
NOTE: Standard errors are in parentheses.
SOURCE: Authors’ calculations.

weeks. Approximate standard errors are given
in table 3
Without feedback, the gross change in TRAN
would have been $1.0 billion. The data plotted
in figure 2, however, show that at the end of
five weeks the net increase is only $343 mil­
lion. Thus, only about 35 percent of the gross
increase in TRAN persists for five or more
weeks. The path of this change is also of inter­
est. After an initial increase, TRAN declines
through week four and then begins to rise. The
time path of FFRT is similar (though reversed
in sign) to that of TRAN. After an initial decline,
FFRT rises through week three and then starts
to fall again. The decline in FFRT at the end
of five weeks is somewhat surprising, although
small and, as judged by estimated standard
errors, apparently insignificant.
The most interesting results of this simulation
are suggested by the NBR data. During the first
two weeks of the positive money shock, the
Federal Reserve withdraws reserves, perhaps
in response to the initial decline in the funds
rate. By the end of three weeks, however, $80
million of NBR has been injected. After five
weeks, $11 million has been withdrawn, while
a net addition of $43 million is observed at the
end of seven weeks. This pattern of withdraw­
als and injections is roughly consistent with the



changes in reserve demand that occur under
lagged reserve requirements. In that case, an
increase in money translates into greater re­
serve demand in the third week of these calcu­
lations (the second week after the monetary
shock). Thus, the simulated pattern for NBR, re­
flecting the timing required by lagged reserve
requirements, strongly suggests that under this
system, the Federal Reserve did accommodate
at least some of the increase in money.
An estimate of the extent of central bank ac­
commodation may be computed as follows.
Consider the $43 million net increase in NBR
supplied by the end of week seven. Clearly,
this would not support the total $1.0 billion
shock to TRAN However, the Federal Reserve
never really observes the $1.0 billion increase,
but sees only the net changes shown in figure
2. The appropriate procedure is to compare
the permanent increase in NBR with the in­
crease in required reserves resulting from the
permanent increase in TRAN. Assuming that
the shock to TRAN is the only shock to money,
that all of the net increase in nonborrowed re­
serves goes to member banks, and that the
marginal reserve requirement is the transaction
account limit in effect over the estimation
period (16.25 percent), then the data underly­
ing figure 2 imply that the Federal Reserve

Cumulative Response after Five Weeks
to a One-Day, $1.0 Billion Net Shock to
N R Administered on Different Days
B
Variable

Thursday

Friday

Monday

Tuesday

Wednesday

1,091.1
(941.0)
0.51

1,445.0
(984.0)
0.68

1,030.3
(953.3)
0.48

1,133.8
(977.5)
0.53

692.3
(797.2)
0.32

FFRT change0

-74.0

-81.2

(42.3)
-5.0

(43.9)
-5.5

-119.3
(45.1)
-8.1

-89.4

Percent change0

-95.3
(43.9)
-6.5

TRAN change3
Percent changeb

(37.3)
-6.1

a. Cumulative net change, millions o f dollars.
b. Based on average values over the estimation period.
c. Cumulative net change, basis points.
NOTE: Standard errors are in parentheses.
SOURCE: Authors’ calculations.

accommodated about 65 percent of the increase
in required reserves during the sample period.1
9
As an additional test, a shock was simulated
that was identical to that of figure 2 in week one,
but negative and offsetting in week two (so that
the cumulative change in TRAN was close to
zero after two weeks). In this case, we estimated
that the Federal Reserve would supply more than
100 percent of the reserves required (assuming a
16.25 percent reserve requirement) for the weekone shock. This suggests that the Fed may have
been even more willing to accommodate money
shocks when they appeared to be temporary.

for TRAN ranges from a high of $1.45 per dollar
of NBR for a Friday shock to a low of $0.69 for
a Wednesday shock. The five-week interest-rate
multiplier ranges from a Tuesday high of 1.119
basis points per million dollars of NBR to a low
of -0.074 for a Thursday shock. To examine
whether these differences are statistically signifi­
cant, we performed “Wald-type” chi-square tests
using the approximate covariance matrix of the
five-week multipliers. Chi-squares testing the
equality of daily coefficients were 3-46 for TRAN
and 8.49 for FFRT, with only the latter significant
at the 10 percent level. Thus, while the quantita­
tive variation is large, it is difficult to tell deci­
sively whether the daily variations are important.

Day-of-the-Week
Effects
IV. Conclusion
One of the premises underlying the use of the
particular model forms employed in this paper
is the view that causal relationships might have
differed by the day of the week. The estimated
model system allows us to test this premise.
To examine the importance of a given day,
we performed calculations identical to those
presented in figure 1, but with the shock ap­
plied to only one day of the week. Results are
displayed in table 4. The five-week multiplier

■

19 Using weekly data for the October 1 979-O cto b er 1982 period
and a somewhat different methodology, Spindt and Tarhan (1987) esti­
mate virtually the same degree of accommodation in nonborrowed re­
 serves. They suggest that “... of an increase in required reserves caused
by an
http://fraser.stlouisfed.org/ increase in money almost 2/3 were supplied in non-borrowed form
andSt. Louis in borrowed form.” (p. 113)
Federal Reserve Bank of about 1/3

The short-mn money multiplier for nonborrowed
reserves appears, at least over the period consid­
ered here, to be quite small relative to its poten­
tial long-run value. The estimated short-run
multiplier for total transaction accounts of 1.1 is
only 18 percent of the long-run value of 6.2 im­
plied by the highest reserve ratio in effect over
the estimation period. In the short am, banks ap­
pear to accommodate almost three-quarters of a
change in nonborrowed reserves by altering
their holdings of excess reserves and borrow­
ings. Thus, the size of the open market operation
needed to achieve a desired change in money ap­
pears to be much larger in the short m n than that
needed to effect the same change in the long run.

33

The Federal Reserve’s short-run influence
over the funds rate is considerably greater than
that over money. The estimated short-run elas­
ticity of the funds rate with respect to nonbor­
rowed reserves is -2.5. This contrasts with an
estimated short-run elasticity of transaction ac­
counts with respect to nonborrowed reserves of
0.2. Taken together, these results suggest that
(again over the time period considered) al­
though a short-run change in nonborrowed re­
serves could quickly and substantially affect
the federal funds rate, the induced change in
money in the short run was much smaller. Thus,
the Fed may have had to accept substantial
interest-rate volatility in counteracting short­
term shocks to money. Viewed from this per­
spective, the apparent Federal Reserve policy
in 1979-82 of supplying about 65 percent of
the increase in reserves needed to accommo­
date a short-run increase in money may have
been prudent, since it helped to avoid an even
larger increase in short-term interest rates.
Finally, over much of the period covered here,
there was considerable debate about whether,
given its reserves operating procedure, the Fed­
eral Reserve should have substituted a system of
contemporaneous reserve requirements for the
extant lagged reserves system. A contemporane­
ous system, it was argued, could have substan­
tially improved short-run money control.
The results presented here suggest that, during
the period under examination, depository institu­
tions at least partially delayed their response to a
money shock by two weeks— the exact timing
implied by lagged reserve requirements. Specifi­
cally, a positive shock to money was estimated
to lower the funds rate initially and then to put
upward pressure on it in the second week after
the shock. This suggests that contemporaneous
reserve requirements would likely have acceler­
ated the response of the funds rate to a change
in money demand, since reserve demand would
have responded contemporaneously rather than
with a lag. However, the modest short-run inter­
est elasticity of money estimated in this study sug­
gests that the quicker response of the funds rate
would not, ceteris paribus, have resulted in a sub­
stantial short-run reversal of the shock to money.
Thus, it appears that while contemporaneous re­
serve requirements would likely have resulted in
a modest improvement to short-run monetary
control, the Federal Reserve would still have
faced a rather sharp short-run trade-off between
interest-rate volatility and monetary control.2
0

 ■ 20 Indeed, the Fed implemented a contemporaneous reserves sys­
tem
http://fraser.stlouisfed.org/in February 1984, but only after switching to a borrowed reserves
Federal Reserve Bank(interest-rate-smoothing) procedure.
of St. Louis

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