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2
Firm Siz©sExchange Rates,
and interest Rates
I.
The Economics of Firm Size:
Implications from Labor-Market Studies ....................................5
Michael C. Keeley
II. Dynamic Adjustment in Money D em an d ................ .................. 22
Brian Motley
III.
Intervention, Deficit Finance and
Real Exchange Rates: The Case of Japan .................................. 27
Michael M. Hutchison
IV.
Indicators of Long-Term Real Interest Rates
. . . . . . . . . . . . . . 45
Charles Pigott
Editorial Committee:
I. Randall Pozdena, Jack Beebe, Frederick Furlong
II. Joseph Bisignano
III. Joseph Bisignano, Brian Motley, Michael Keeley
IV. Michael Hutchison, Adrian Throop, James Wilcox
3
Michael C. Keeley*
One hypothesis about why large and small firms coexist in many
industries is that entrepreneurial ability determines firm size. More able
entrepreneurs managefirms whose sizes vary more than proportionately
with their talents. However, because larger firms also face higher costs
(per worker) in monitoring worker performance, they have more specialized methods of production, require more specialized training and
hire more skilled workers to economize on monitoring. Empirical results
tend to confirm this hypothesis. Moreover, the evidence implies that
significant economic losses may be associated with public policies that
prohibitfirms from attaining their optimum size.
interstate banking, may have resulted in less concentrated market structures.
On the other hand, there is a concern about the
potential costs of preventing finns from operating at
their most efficient or optimal scales. For example,
breaking up a large finn into several smaller ones,
or prohibiting the merger of smaller firms, may
have substantial costs if there are economies of
scale. Thus, possible anti-competitive effects due to
concentration should be balanced against possible
increases in productive efficiency in fonnulating
regulatory or antitrust policy.
For example, some economists have argued for a
repeal of the antitrust laws so that the United States
can compete mory effectively with Japan. 4 Proposals for the elimination of restrictions on interstate
banking are also often based on the notion that a
more efficient provision of services would result
and benefit consumers. Opponents to this type of
deregulation are concerned that the elimination of
restrictions would lead to a more concentrated
banking industry with less competition.
Until recently, there was no theory of finn-size
that was able simultaneously to explain actual finnsize distributions and several empirical regularities
in production associated with finn-size. However,
new developments in economic theory that focus on
entrepreneurial ability as a fixed factor of produc-
Many industries are characterized by the coexistence of finns of widely varying size, often with
output concentrated in a few large finns. Understanding why this is so is extremely important for
regulatory and antitrust policy.
On the one hand, it is widely believed that a high
concentration of output (that is, a positively skewed
distribution of finn size) leads to reduced competition. lOne of the rationales for the regulation of
many industries is to reduce concentration, prevent
increased concentration, or to restrict how finns in
J:oncentrated industries may operate, especially
/ those that are believed to be natural monopolies. 2
itrust law also grew out of a concern with conation and may have had substantial effects on
m
t structure through the prohibition of mergers,i;~nd until recently, suits aimed at breaking up
successful large businesses. 3 Regulation in industries such as trucking, airlines, rail transportation
and banking, may also have had significant effects
on the finn-size distribution in these industries. For
example, in banking, various restrictions on geographic competition, such as prohibitions against
*Economist. Helpful comments from Jack Beebe,
Fred Furlong, Randall Pozdena, and research assistance from Jennifer Eccles are much appreciated.
5
tion and on the organization of production are cap"
able of explaining firm"size distributions and differ"
ences in production methods among different"sized
firms. In this paper, these new theories are re"
viewed, some of their implications for differences
in production are tested indirectly, and the public
policy implications are explored. The empirical
analysis focuses on differences in the employment
practices among different"sized firms, in particular,
differences in wage levels, wage growth and tum"
over. Hopefully, the results provide useful evidence
about the determinants of the distribution of firm"
size so that public policies aimed at influencing
market structure can be better informed.
The organization of this paper is as follows. In
Section I, I review the implications of neoclassical
theory regarding firm"size distributions and present
evidence that contradicts these implications. Next,
in Section II, several new developments in eco"
nomic theory explaining the determinants of firm
size are reviewed and their empirical implications
regarding differences between various characteristics of the labor forces of large and small firms are
discussed. Then, in Section III, empirical evidence
is presented that tends to support these hypotheses.
Finally, the summary and conclusions are presented
along with policy implications.
I. Neoclassical Theory and Facts
To analyze the determinants of the firm-size distribution, it is first necessary to define what a firm is
and explain why firms exist. Our current understanding of what firms are and why they exist is due
to Coase (1937), who hypothesized that economic
activity takes place in firms instead of markets
because of the transactions costs involved in organizing economic activities in markets. A firm substitutes a command-and-control system for the allocation of resources that could have been achieved
through the market economy. Presumably, an economic activity (production) takes place within a
firm if it is less costly than if it took place using the
market. Alchian and Demsetz (1972) extended this
basic concept by emphasizing the importance of
group or team production. Group production implies the need for monitoring workers because the
separate contribution of each iIlf.iividual cannot be
assessed simply by observing ~~tput. Thus, group
production might be very diffj''Sl1lt to achieve in a
market setting.
If entrepreneurs in a given competitive industry
have available the same technology of production,
face the same relative prices for transactions within
the firm and outside, and face identical input prices,
all firms in the industry (that is, firms producing the
same products) would have identical cost functions.
Assuming V-shaped average cost functions, all
firms would produce at the minimum point on their
average cost curves and the number of firms would
equal total market demand (at a price equal to minimum average cost) divided by the output of a typical
firm at its minimum average cost. Thus, if such
conditions held, all firms in an industry would be
the same size. 5
However, even casual observation contradicts
the notion that all firms in an industry are the same
size. For example, in banking, the size distribution
is positively skewed and the variance in firm-size is
very large (with a standard deviation approximately
four times the mean), with firms ranging in size
from those with less than $5 million in assets to
those with over $100 billion. Furthermore, the relative variance of firm-size in many other industries is
even larger, and the skewness of the size distribution function in banking is considerably less than
that in many other industries.
To analyze the extent to which industry type can
explain firm-size, I have estimated the fraction of
the overall variance in firm-size that is explained by
industry type. The variance in firm-size is analyzed
using three regressions of firm size on
2-digit, and 4-digit SIC (Standard Industrial
fication) codes. The regressions are of the toJllQJwulg
general form:
SIZE, = A
+ Lj Bj SICij + e
j
(I)
where: SIZE; = the size of firm i, measured at
the establishment level, in terms
of number of workers,
SIC;j = a set of dummy variables indicating whether firm i is in the
Standard Industrial Classification
code (SIC) category j,
ei
6
= a random error term.
The data for these regressions are from an employer survey of over 5000 establishments. 6 (Establishments are defined as places of business regardless of ownership, and thus differ from firms.)
Establishment-level data are used (as opposed to
firm-level data), and since the overall variance in
establishment size is probably less than the variance
in firm-size because some firms are comprised of
many establishments, the variance in establishment
size within an industry is probably less than the
variance in firm-size.
The regressions indicate that the SIC code explains 6 percent at the I-digit level, 14 percent at the
2-digit level, and 47 percent at the 4-digit level of
the variance in establishment size. Thus, even at the
4-digit level, over 50 percent of the variance in
establishment size is within industries, and this may
be an understatement since in some cases the 4-digit
SIC code level may be too detailed in disaggregating firms that are really in the same industry. 7
These regression results do support the hypothesis that production technology (and hence, industry) is related to firm-size because firm-size does
depend on industry, but they also strongly suggest
that other factors must be responsible for the large
within-industry variation in firm size. One reason
may be that average cost functions are not U-shaped
but flat, exhibiting constant returns to scale over a
wide range, perhaps with initial economies of scale
(and declining average costs) over only a relatively
small initial interval. x This type of cost function
would imply a rectangular distribution of firms
within the flat portion of the average cost function,
since firms outside this range would be unlikely to
survive (because of their higher average costs), and
because within the range there is no reason for any
particular size to be observed more frequently.
However, this implication of neoclassical theory
is also contradicted by the data: the distribution of
firm-size within industry is highly skewed, not rectangular. For example, in Chart I, the distribution
of firm-size in the banking industry shows a highly
skewed distribution with a long right tail, and distributions in most industries are very similar. 9
One attempt to reconcile this skewness with neoclassical theory is the application of stochastic
models to the growth of individual firms. Much of
this analysis is derived from the work of Gibrat
(1931), who showed that if all firms have an equal
chance of growing (or declining) by a given percentage amount, then a log normal size distribution of
firms will result even if all firms are initially the
same size. There does seem to be evidence that the
growth of firms is independent of size, as well as
evidence that, at least for some industries, the
observed distribution is log normal. This theory of
the firm-size distribution, taken literally, implies
that there are no differences in production technologies of firms of different sizes (in the same
industry), that average costs are independent of
size, and that the existing size distribution at any
moment in time is simply due to the cumulative
effects of luck (random factors). That is, there
should be no systematic differences between large
and small firms since they have the same cost functions, and since differences in size are due only to
random shocks.
Because this theory implies that the size distribution of firms under competition is due simply to
randomness, one very important policy implication
is that there would be no losses in economic efficiency with the dissolution of large firms, or opposition to the consolidation of smaller firms through
mergers, as long as firms were operating on the flat
portion of their average cost curves. For example,
interstate banking could be prohibited without any
concern for possible losses in output due to an
Chart 1
Distribution of Firm Size
in the Banking Industry
Percent of All Banks
50
40
30
20
't~
o~oCb
-"'-/----..;;::--------~
~
%
Asset Size in Millions
Source: 1981 Statistics on Banking. Washington: FDIC. 1982,
Table 104.
7
hibiting mergers. Much of the empirical evidence
presented in this paper, however, shows that there
are many systematic differences between large and
small firms that cannot be explained by purely
statistical models of firm size.
inefficient scale of operation. Furthermore, since
less concentrated industries may be more competitive, one need not worry about balancing gains from
increased competition against losses due to nonoptimal size when breaking up large firms or pro-
II. New Explanations of the Firm-Size Distribution
economies due to the hierarchical organization are
limited by the increasing costs of monitoring workers. Monitoring workers requires direct worker contact and, therefore, is not subject to the same sorts of
scale economies as the coordination and allocation
of resources.
Rosen's model has some interesting implications
for the structure of firms' cost functions. First, in
equilibrium, any given firm will be subject to
increasing average costs if it expands output beyond
its equilibrium level, holding managerial talent
constant. Second, firms of different sizes, in equilibrium, may well have identical measured average
costs because the economies realized by the larger
firm due to its superior management talent will be
captured by the management whose talent is assumed to be in perfectly inelastic supply and
because managers' compensation is often recorded
as a cost, not a profit. Thus, evidence that measured
average costs are independent of firm size does not
necessarily imply that breaking up large firms
would not result in significant economic losses.
Rosen's model of firm size implies quite the opposite: there are economic benefits from allowing managers with superior talent to manage larger firms.
Oi (1982a, b) also developed a model that emphasizes entrepreneurial ability, but Oi's model more
fully develops the implications of monitoring costs.
His model, like Rosen's, assumes entrepreneurs
perform two functions: they coordinate production
and they monitor the performance of workers, but
Oi does not assume a hierarchical production technology and thus Oi's model is unable to explain the
skewed distribution of firm size in most industries.
In Oi's model, more able entrepreneurs are assumed
to be more productive at coordination but all entrepreneurs are assumed to be equally productive at
monitoring. Although it might seem somewhat arbitrary to assume more able coordinators are not
also more able monitors, Rosen's model of hierarchical production suggests why this might be so.
To explain differences in firm size, recent theoretical research has emphasized differences in
entrepreneurial ability, which is assumed to be in
perfectly inelastic supply. For example, Lucas
(1978) developed a model in which individuals are
alike as workers but differ in entrepreneurial ability.
In his model, the distribution of entrepreneurial
ability leads to an equilibrium distribution of firm
size, with more able entrepreneurs running larger
firms.
Rosen ( 1981 a, b, 1982) also developed a model in
which entrepreneurial ability explains the size
distribution of firms. His model focuses on the
hierarchical structure of production in firms where
decisions at each level of the hierarchy affect the
efficiency of labor inputs at the next lower level.
This production technology implies that there is a
multiplicative effect in assigning persons of superior talent to the top ranks because they increase
productivity by more than the increments of their
talents. A more productive chief executive officer,
for example, affects the productivity of everyone
below him or her in the organization, and thus even
a small increment in his or her talent may have a
very large overall effect on productivity. Even if
entrepreneurial ability were distributed normally,
the firm-size distribution would be skewed because,
in equilibrium, this production technology implies
that output and labor input rise more than proportionately with talent.
These same characteristics of production imply
that managerial compensation rises more than proportionately with ability. This, in turn, implies a
skewed distribution of compensation as well, a
finding confirmed by the work of Roberts (1956)
and Fox (1978), who both find managerial compensation varying with the log of the number of
employees. The reason this type of production technology does not lead to an equilibrium in which
there is only one firm managed by the most talented
individual (at least in each industry) is that the
8
(which are presumably associated with less monitoring), more reliable workers (who require less
monitoring), and more reliable capital equipment
(which requires fewer repairs and therefore less
monitoring of workers who perform the repairs).
The monitoring-cost hypothesis has several empirical implications. First, it implies that larger
firms invest in more specific human capital (that is.
skills specific to the firm) than small firms because
larger firms have higher costs per worker in monitoring worker performance. These higher monitoring costs lead larger firms to have more rigid and
specialized methods of production, which in tum
require more firm-specific training (that is, specific
human capital). Since large firms find it optimal to
invest in more specific human capital than small
firms, turnover rates (both quit and fire/layoff rates)
should be lower in large firms.
. Second, this theory implies that large firms will
hire more productive employees-that is, employees with higher levels of human capital (which
depends on commonly measured variables such as
education as well as traits such as intelligence or
reliability that are more difficult to measure). This
is the case because more productive workers allow
firms to lower monitoring costs per unit of output
and thus to economize on those costs, assuming that
they depend on the number of workers and not total
output.
Below, we present some indirect tests of these
hypotheses by estimating differences in wage
levels, wage growth, and turnover among firms of
different sizes and types.
A more efficient monitor cannot reap the same sort
of efficiencies in monitoring that he or she can in
making coordinating and aliocative decisions
because monitoring cannot be delegated in a hierarchical structure.
Since an increase in entrepreneurial talent leads
to an increase in the number of employees, and
more employees implies more time spent monitoring and less time spent making coordinating and
allocative decisions, the implicit costs of monitoring worker performance should be higher in larger
firms. They should be higher because the alternative use of time is coordination (or allocation of
resources), for which there are economies of scale
implicit in hierarchical organizations and because
of the lack of such scale economies in monitoring.
These scale economies make coordination more
valuable in large firms, and, as Rosen points out,
this strengthens the implication that firm size will be
skewed because superior managerial talent can be
economized by "subordinating" monitoring
through a more hierarchical structure.
The dependence of monitoring costs on firm size
means that firms of different sizes will have different types of workers, different types of managers.
different types of capital, and different sorts of
production methods. Thus, this new theory stands
in sharp contrast to the stochastic explanations of
the firm-size distribution that predict no systematic
structural differences among firms of different
sizes. For example, the monitoring-cost hypothesis
predicts that large firms should have more hierarchical structures, less flexible production methods
III. Empirical Evidence on the Monitoring-Cost Hypothesis
Although specific and general human capital are not
directly observable, wage rates, wage growth and
turnover are. Thus, one can test the monitoring-cost
hypothesis indirectly by analyzing these observable
variables. Below, I first discuss the implications for
wage levels.
According to human capital theory, (see Becker
( 1964) ), wage rates depend on general and specific
human capital. General human capital is a set of
skills and knowledge that can be transferred from
one employer to another, while specific human
capital is a set of skills and knowledge that are
The monitoring-cost hypothesis implies that
large firms invest more in specific human capital
than small firms because large firms have higher
costs (per worker) of monitoring worker performance. These higher monitoring costs lead large
firms to institute rigid and specialized methods of
pr?dnction, which, in tum, require more specialized training. This hypothesis also implies that large
firms hire workers with more general human capital
in order to reduce the costs (per unit of output) of
monitoring, assuming that monitoring costs depend
on the number of workers and not total output.
9
other things being equal, a given amount of specific
training will lead to higher observed current wages
than the same amount of general training because
only a fraction of specific training costs are borne by
the worker. Marginal products, of course, depend
on the accumulation of human capital, and the share
of the marginal product being paid to the worker
depends on the share of the training costs that are
borne by the worker. Wage levels thus may differ
among tinns of different sizes and types because of
differences in the levels of their workers' general
and specific human capital and differences in the
provision of current general and specific training. 12
Workers with more general human capital require
less monitoring per unit of output if monitoring
costs depend on the number of workers and not total
output, or ifthere are other aspects of production in
which managers' and workers' skill levels complement each other. Large firms thus should
be more likely to hire highly skilled workers than
small finns; that is, there should be a positive
matching of more able entrepreneurs with more able
workers. This consideration alone implies that
larger finns would pay higher wages. However, if
large finns provided sufficiently more training and
this training were paid for by employees, such a
training effect could conceivably offset the higher
wages in large finns due to the greater skill levels of
their employees.
Whether large finns would provide more on-thejob general training than small finns depends on
whether training activities require more monitoring
than production activities because large finns face
higher monitoring costs. It seems likely that such
training does require much individual attention
(monitoring). If so, large finns would simply hire
workers with more general training that had been
acquired elsewhere. This lower rate of general
human capital accumulation would lead to even
greater wage differences between large and small
finns. Although large finns are expected to offer
more specific training (\vhich would depressobserved wages somewhat), it is unlikely this would
dominate the higher wages large finns pay due to
higher skill levels and their practice of Ptoviding
less general training. Thus, on balance, large firms
are expected to pay higher wages. Below, this hypothesis is tested.
useful only in a specific finn. Since this theory
predicts that wage levels differ among finns of
different sizes because of differences in human capital, to analyze the implications of the monitoringcost hypothesis for differences in wage rates one
needs to assess its implications for human capital.
General human capital is, by definition, equally
valuable in any finn. Workers are therefore expected to bear the full costs of acquiring general human
capital since they take their general human capital
with them when they leave the finn. If such general
human capital is acquired on the job, then observed
earnings would be net of investment costs (that is,
observed earnings would equal the potential marginal product minus the costs to the employer of
providing general training). Since such general
human capital is equally valuable at all finns,
workers must be paid the full retum on any investments in such capital (or they will leave and find
employment in a new finn).
The allocation of costs and returns between
employer and employee of specific and general
human capital is quite different. Since specific
human capital is only valuable in the finn where it is
acquired, this type of capital completely depreciates
when the worker leaves the finn. Thus, if the finn
had entirely bome the costs and received the benefits of such investments, the finn would lose its
investment if a worker quit. Similarly, if the worker
paid the entire cost of the investment and received
the full benefit and then was fired, the worker would
lose his capital. Becker shows that such considerations lead workers and finns to share in the costs and
benefits of investments in specific hum~~;capital to
ensure that both decisions to fire and t~yquit take
into account the loss of specific human.~apital that
would result. 10
To summarize, human capital theory implies that
observed wages depend on (opportunity) marginal
products, II the amount of training currently being
undertaken, and the share of the training costs being
paid implicitly by the worker. Higher marginal products lead to higher wages as do lower workers'
shares of training costs (because workers pay for
their training implicitly with lower wages) and
greater amounts of on-the-job general or specific
training (holding constant the share of costs that are
borne by the worker) lead to lower wages. Thus, all
10
Data and Samples
survey.) Three different specifications of this
model, with different control sets, were estimated:
one with no control variables, one with a set of
2-digit SIC industry dummies, and one with the
same industry dummies and other control variables.
In the model with no control variables, B i measures the mean difference in the natural log of the
wage rate between category i and small private
businesses (the excluded category). The natural-log
specification is used since it fits somewhat better
than a linear model, and because the coefficients
can be interpreted as percentage effects (if they are
small). 10 Industry control variables are included to
control for possible differences in wages that might
be correlated with firm size across industries. It
should be noted that the coefficient estimates of the
government category, when industry dummies are
included, cannot be easily interpreted since government employment is largely but not entirely captured in SIC codes 91 through 97.
Finally, the complete set of control variables are
added to hold observable differences in the characteristics of the individuals and their employers
constant. These control variables are described in
Appendix A: they include not only the usual human
capital variables (education, experience, demographic characteristics) but also dummies for occupation of the worker and whether the worker was a
union member. Finally, there are a number of site
characteristics (unemployment rate and SMSA
size). This control set is far more comprehensive
than those normally available. 17
In Table I, the estimated coefficients of these
models are presented for four demographic groups.
The results from the specification with no control
variables indicate that for all groups, workers in
large private businesses receive considerably higher
wage rates than workers in small private businesses.
The effects are large and statistically significant for
all groups, indicating that employees of large firms
earn between 17 and 40 percent (exp.. 16 = I. 17 and
expo .34 = 1.40) more than workers in small private
businesses. This table also shows some statistically
significant differences for other types of employers,
with government workers earning less than workers
in small private businesses for married men and
youth, but earning more in the case of married
women and single female heads. (F Tests of the
joint significance of the four firm-size-and-type
The data analyzed come from the Employment
Opportunity Pilot Projects (EOPP) baseline household and employer surveys. These surveys were
designed to obtain pre-program measures of a variety of variables, such as wage rates, earnings,
employment, and unemployment as part of the evaluation of EOPP. 13 The household survey covered
the period January I, 1979 through the date of the
interview (most interviews occurred between May
and September 1980).14
The household survey was conducted in 10 pilot
and 10 matching control sites throughout the U. S. ;
and the employer survey was conducted in 10 pilot
sites and 19 control sites. The employer and household surveys have in common 7 pilot and 7 matching control sites where the two surveys are linked.
The linked surveys are used when analyzing the
household data since firm size comes from the
employer survey. 15
When analyzing differences among firms of different types and sizes in wage levels, wage growth,
and turnover, all firms are classified into one of five
types:
Large private business (an establishment with
500 or more employees)
Small private business (an establishment with
less than 500 employees)
Government-federal, state or local
Self employed
Special government-(CETA, WIN, EOPP,
Manpower or youth program)
Analysis of Firm Size on Wage Levels
To test the hypothesis that wage rates are higher
in large firms, the following sorts of models were
estimated:
Inw
=
A" + A I C + BID I + B 2 D 2
+B 3 D 3 +B 4 D 4 +e
(2)
where: Inw is the natural log of an employee's wage
rate, C is a vector of control variables, D j = I if the
job is of the ith type (i = I, ... , 4), and. the As and
Bs are parameters to be estimated. In this analysis,
wage rates are defined as earnings divided by hours
of work, and include tips, bonuses and commissions but not fringe benefits. (There were no measures of fringe benefits in the EOPP household
II
The results with the complete set of control variables are generally similar except that estimated
wage differences are smaller, ranging from 10 to 15
percent depending on the demographic group.
However, all estimated differences between large
and small private businesses are statistically significant at the I percent level or better, except for youth
for whom the effects are significant at the 5% level.
These results show that large firms do hire
workers with higher levels of general human capital
(since the inclusion of the human-capital control
variables leads to smaller differences) than do small
firms, but they also show that, even controlling for
industry type and a large number of observable
differences between the employees of large and
small businesses, large businesses pay significantly
higher wages. These results are consistent with the
monitoring-cost hypothesis that large firms hire
more productive workers, both in terms of higher
levels of measurable characteristics and factors
such as intelligence that are not observed. This
would explain the smaller wage differences when
variables presented in Table I indicate they are
jointly significant at the I % level or better.)
Likewise, special government workers eam lessprobably an indication of the low-paying nature of
these special jobs. Self-employed married men and
women eam significantly less than their counterparts in small private businesses, but there are no
statistically significant differences for self-employed single female heads and youth.
These results strongly confirm the hypothesis
that workers in large firms are paid more than
workers in small firms. 18 These results affirm those
of other researchers [see Schiller (1982), Mellow
(1981), and Oi (1982)].
When industry-control variables are included,
the results show similar, although generally somewhat smaller, effects. F tests indicate one can reject
the hypothesis that industry has no effect on wages,
holding firm size constant. This is not surprising
since different industries probably have workers
with different skill levels and, hence, different
wages.
12
training requires relatively more monitoring than
other activities. Thus, there is no strong prior reason
to expect differences in wage growth between small
and large firms since the more rapid wage growth in
large firms due to the higher rate of specific human
capital accumulation may be fully or partially offset
by less rapid general human capital accumulation.
Starting and ending wage rates for hourly workers are used to analyze wage growth on a particular
job. (For salaried employees, however, no measure
of wage growth on the job is available, so such
workers are excluded.) The empirical models
employed to analyze wage growth are very similar
to those used to analyze wage levels. They are of the
general form:
all control variables are included, as well as the
persistence of significant wage differences even
after controlling for many factors.
However, the results also would be consistent
with the idea that lower levels of specific or general
training are being provided by large firms (whose
costs are partially or fully borne by workers), although our theory predicts the opposite: that large
firms provide more specific and less general training than small firms. Since training leads to more
rapid wage growth, we can test this alternative
theory by analyzing wage growth.
Firm Size and Type and Wage
Growth on the Job
Real wage growth on a particular job, according
to human capital theory, is due to the accumulation
of human capital. More rapid human capital accumulation that is paid for by the employee leads to
more rapid wage growth. Although we expect large
firms to provide more specific training, they would
provide less general training if providing general
In (we/w)/length = Ao+A,C+B,O , +B 2 0
+ B3 0 3 + B4 0 4 + e
where: w s = starting wage rate
We =
13
ending wage rate
2
(3)
spell ended, if it ended (quit, laid off, or fired) were
not significantly different from those using no control variables. The one difference was that they
showed no significant differences between large
and small private businesses for youth.
Since wage growth does not appear to differ
significantly between large and small firms, to the
extent that large firms provide more specific training (which is paid for by employees) than small
firms (which would lead to more rapid wage growth
in large firms), it must be offset by less general
training being provided by large firms. These results, along with the existence of higher wage levels
in large firms, suggest that such firms are hiring
more highly skilled workers (in terms of both measurable and unmeasurable characteristics), and that
observed wage differences are due to differences in
skill levels and not differences in on-the-job human
capital accumulation. Also, if large firms do provide more specific human capital (as both theory
and the empirical work on turnover presented below
suggest), then these results imply that small firms
••
19
.,
provide more general trammg. The momtonng-
length = length of the period (in years)
over which the starting and
ending wages are measured, and
the Dis, Ais, Bis and C are
defined as before.
The model therefore measures the relative wage
growth of various sizes and types of employers
compared to small private businesses. The same
three specifications of the control set that were used
in the wage-level regressions also are used here.
The estimates of this wage-growth model are
presented in Table 2. When no control variables are
included, there are no statistically significant differences in the rate of wage growth between small and
large firms, with the exception of the youth d~m~
graphic group. For youth, wage growth on the Job ~s
greater in large businesses. The only pattern that IS
consistent across demographic groups is a lower
rate of growth for special government jobs.
Estimates using industry control variables only
and estimates using industry, human capital and
additional control variables for the reason the job
14
cost hypothesis predicts higher skill levels, more
specific training and less general training in large
firms. Thus, these results confirm the predictions of
the monitoring-cost hypothesis.
This framework can be used to model various
discrete events. For example, to model job turnover, let the rate of leaving employment for the jth
person be given by rjk , where k is the destination
state, and k= I indicates being fired or laid off and
k=2 indicates quitting. We assume that the turnover
rate depends on the type and size of the ernployer
and various control variables:
Analysis of Turnover Rates
Since the monitoring-cost hypothesis predicts
more specific human capital in large firms, turnover
rates should be smaller. To determine if turnover
rates depend on firm size and type, models determining the (instantaneous) transition rates between
employment and leaving that employment (either
finding new employment or not working) are
estimated.
The instantaneous rate of an event occurring, ret),
is the limit, as dt approaches zero, of the probability of the event occurring between t and t+~t
[pet, t+dt) ] per unit of time:
ret) = lim
dt-~o
P(t,t+~t)
Inrjk = A ok + A k C j + B Ik DIj + Bck Dei
+ B 1k D 1j + B 4k D 4j
(5)
where,
D ij = a dummy variable indicating a firm
of size and type i.
C j = a vector of control variables including
those described in Appendix A and, in
addition, I-digit SIC industry dummies. cO
(4)
The As and Bs are parameters to be estimated.
In this model, the rate of leaving employment
depends on whether the person quits or was fired,
the characteristics of the individual, and the size and
type of the person's employer. cl
The vector of parameters in equation (5) can be
dt
If ret) were constant over time, then the expected
duration until the event occurs would be Ifr and the
duration until the event occurs would be distributed
exponentially.
IS
16
small businesses, and for single female heads they
are 58 percent less. The only type of employer that
has higher turnover rates than small private firms is
special government programs, which is not surprising given that the intention of these programs is to
provide short-term employment. These results also
suggest that turnover rates are not, in general,
significantly different among the government, the
self-employed, and large private businesses.
In Table 4, we present the coefficients of the
turnover model described by equation (5), which is
identical to the model in Table 3 except that quits are
distinguished from lay-offs. Sample sizes are somewhat lower because some observations lacked information on why a job ended. The results suggest
that for all demographic groups, quit rates are considerably higher than fire/lay-off rates, with the
smallest differences for married men and the largest
differences for youth. These results also suggest
that large private businesses have lower quit rates
and lower fire/lay-off rates than small businesses,
with somewhat larger differences for quit rates.
Both the self-employed and large private businesses generally have lower quit and fire/lay-off
rates than small businesses. Not unexpectedly, the
estimated by the method of maximum likelihood
using individual data on observed lengths of employment spells. 22 The observed length of employment (in a particular job) equals the last time the
person is employed (either when the person leaves
his or her job or when the observation period ends)
minus the time the person is first employed in that
job (or July I, 1979, depending on which is later).
In Table 3, we present the results of a simplified
version of the model described by equation (5) in
which there is only one destination state-leaving
the current job. Mean annual turnover rates (from a
rate model with only a constant term) show that
turnover rates are relatively high in our sample,
ranging from .39 per year for men to l.51 per year
for youth. Since the inverse of the turnover rate
gives the expected duration at that particular job,
these numbers imply lengths of employment at a
particular job ranging from 2.56 years for married
men to .66 years for youth. 23
The results in this table strongly suggest that
small businesses have much higher turnover rates
than large businesses, government, or the selfemployed. For example, for married men, turnover
rates are 44 percent less in large businesses than
17
highest turnover rates of all five categories of firms
analyzed. This suggests that very little specific
human capital is accumulated by workers in small
firms.
However, the fact that the self-employed have
significantly lower turnover rates than employees of
small businesses indicates that owners of Small businesses are much less likely to quit and close their
businesses than the employees of small businesses
are likely to leave-. This is consistent with the notion
that many owners of small businesses have substantial specific capital, both human and physical, invested in their businesses.
government has lower fire/lay-off rates than large
private businesses.
The results in Tables 3 and 4 are consistent with
the hypothesis that large private firms provide more
specific training than small businesses. Since specific human capital is fully depreciated when a
worker leaves, both the firm and the worker have an
incentive to avoid this potential loss of wealth.
Much smaller turnover rates for large firms are
consistent with the notion that large firms provide
more specific on-the-job training than small firms.
Also, we find that small firms generally have the
IV. Summary and Conclusions
dustry, occupation and various individual characteristics, employment practices depend strongly on
firm size.
To summarize, large firms hire more highly
skilled workers and consequently pay higher
wages, provide more specific on-the-job training,
provide less general on-the-job training, and retain
their workers much longer than small firms. Stochastic models of firm size (taken at face value) are
not consistent with these systematic differences
among firms of different sizes. Thus, the results in
this paper support the monitoring-cost hypothesis.
The evidence supports the notion that firm size
does matter-that firm size is the result of a deterministic process depending on the distribution of
managerial or entrepreneurial talents, the economics of a hierarchical organization of production
within firms and the costs of monitoring workers'
performance. This model of the firm also explains
the skewed distributions of firm size within industries, why large and small firms coexist, and suggests that there may be economic losses associated
with public policies that prohibit finns from attaining their optimum size.
After controlling for industry type and a large
number of individual characteristics, we find striking differences in wage levels and turnover among
different-sized firms. Large private businesses pay
significantly higher wages than small private businesses. However, no significant differences are
found between the rates of wage growth of large
and small businesses. This suggests that large private firms are hiring more highly skilled workers,
both in terms of measurable and unmeasurable characteristics, than small private firms, and that the
observed wage differences are due to differences in
levels of human capital, not differences in the rate
of accumulation. This is consistent with the hypothesis that large firms hire more highly skilled workers because such workers have lower monitoring
costs (per unit of output). The finding that large
firms also have significantly lower turnover than
small firms supports the hypothesis that large finns
have more rigid and specialized methods of production and therefore provide more on-the-job training.
These results taken together provide strongsupport
for the hypothesis that, even holding constant in-
18
Ap~ndixA
Control Variables Employed in the Wage-Level Regression
Site Characteristics
occupation Characteristics
Large SMSA dummy (population over 1 million)
Small SMSA dummy (population under I million)
Not SMSA dummy-excluded category
Site unemployment rate
Dummy for union member
Dummy for occupation executive/administration
Dummy for occupation engineer/scientist/doctor
Dummy for occupation teacher/librarian
Dummy for occupation health technician/
nurse/pharmacist
Dummy for occupation marketing/sales
Dummy for occupation clerical
Dummy for occupation service
Dummy for occupation transportation
Dummy for occupation mechanical
Dummy for occupation production
Dummy for occupation not known because person
was not working when occupation question was
asked (excluded occupations include material
handler, technologists, writer/artist, and any
unknown occupations)
Spell Characteristics
Dummy for spell being truncated by the end
of the period
Duration of the spell
Dummy for spell being truncated at 7-1-79
Dummy for job coming from 2-job file
Dummy for job being continued from prior spell
Demographic Characteristics
Race dummy for Black
Race dummy for Hispanic
Low-income strata dummy (from EOPP survey)
Age in years
Number of persons in the family
Income and Labor Force Characteristics
Human Capital Variables
Dummy for not working first half of 1979
Dummy for receiving AFDC first half of 1979
Dummy for receiving VI first half of 1979
Dummy for receiving Food Stamps first half of 1979
Non-Labor income first half of 1979
Disability dummy for disability that limits
the amount of work
Number of years of school
Number of years worked since age 17
'Number of years worked squared
FOOTNOTES
1. There is also concern about the concentration of political
power as well as the distribution of income that would result
from such concentration.
7. In the data set analyzed, the 4-digit SIC code resulted in
548 different categories of firms (i.e., industries) out of a
sample of 5271 observations.
2. For example, it is widely believed that public utilities
repres~nt natural monopolies, which, if unregulated, would
. restrictoutput and charg.e higher prices to consumers.
8. SeeStiglehifl958), Simon and Bonini (1958), Hoit aha
Prais (1956), anq Ijiri and Simon (1964) .
\...>.............................
.
9. Studies by Hart and Prais(1956), Sim()n .and Bonini
(1958), Quandt (1966) and Ijiri and Simon (1964) all show
that the distribution of firm-size within specific industries is
skewed. Analysis of the EOPP data indicates that the firmsize skewness in banking is less than most, but not all, other
.
3. For example, the government's IBM case was brought
primarily because of IBM's large market share in mainframe
computers.
4.• S~e LesterThurow, "Abolish the Antitrust Laws," Dun's
Re;;ie~ (February 1981, p. 72.)
industries defined at the 2.. digit SIC level.
10. This framework has been used by Pencavel (1972) to
explain differences in turnover rates.
11. That is the marginal product that could be achieved if
no time were devoted to training. Opportunity marginal
products themselves depend, of course, on the accumulation of both general and specific human capital.
12. Another reason why observed wages may differ
among firms is because of differences in the nonpecuniary
5. Seeaaumol (1982) for a recent discussion of industry
emphasizes the technology of production.
Viner (1932) originally developed this theory of market
structure.
structurei~hat
6. Data arefrom the first wave of the employer survey that
was performed as part of the evaluation of the Employment
Opportunity Pilot Projects (EOPP). See Section IV for a
description of the data.
19
conditions of work. For example, Masters (1969) has
argued that large firms have to pay higher wages because
of their more rigid and inflexible working schedules. However, one can think of many cases where the working
environment is superior in large firms.
In
1J
WOi ---[ WOi = 0
1
WOi =
B or - - - = exp B,·
"wOi = 0
17. In addition to these sorts of control variables there are
also variables that hold constant various ways in which the
observations were created. There is control for left- and
right-censoring of the spell whether the job was continued
from a previous spell, whether the job was from the 2-job
spell file (indicating that the person held 2 jobs at least part
of the time during which the job in question is being analyzed), and whether this job was a second job (indicating
that two jobs were held and that the job being analyzed is
less important in terms of hours worked).
13. EOPP was designed to test a structured job-search
program combined with a work and training program that
was a key part of President Carter's welfare reform proposal. The program began in some sites on a very Umited
basis in the summer of 1979 but was not into full operation
until the summer of 1980. The program never reached the
scale of operation originally intended and was soon phased
out during 1981 under the Reagan Administration. However, the operations and purpose of this program are not
pertinent to this study in which only preprogram data are
analyzed.
18. Workers in large private firms also earn more than
government workers or self-employed workers.
19. Schiller (1982) finds that workers in small firms have
more rapid rates of wage growth than workers in large firms
for new entrants to the labor force. This evidence is also
consistent with the notion that small firms provide more
general training.
14. An important characteristic of the sample is that the
period covered by the interview (January 1, 1979 through
June 1, 1980, on average) is artificially divided into a sixmonth "control" period from January 1, 1979 through June
30, 1979, and an analysis period from July 1, 1979 through
the end of the interview. This is done because the statistical
models employed in this paper are based on the assumption that variables measured during the first six-month period are exogenous with respect to the dependent variables
that are analyzed during the second period. If such variables were calculated during the analysis period it might be
difficult to infer the direction of causaUty.
20. Two digit SIC industry dummies were not used in the
analysis of turnover because of computational cost.
21. This equation is based on a number of assumptions.
For example, it assumes that the explanatory variables and
their coefficients do not vary over time, that the rate of
leaving employment does not depend on the length of time
of employment, that the rate of leaving one spell is independent of characteristics of previous spells and that unobserved variables do not affect the rate (heterogeneity). By
including a large number of variables in C, we hope to
account for some of these effects.
15. In this study, firm size is from the employer survey.
Since all firms with 500 or more employees were included in
the sample frame of the employer survey, it is possible to
determine firm size for the employers of all individuals in the
household survey by inference. Thus, samples are many
times larger than they would have been were we to restrict
the analysis to only matching cases. Only 6,788 jobs in the
household survey were matched to the employer survey
out of approximately 35,000 jobs. For all matching cases,
firm size is taken directly from the employer survey and for
all non-matches firm size can be inferred to be less than
500, assuming that the matching was d
urately. For
matching cases, firm size is taken from th
oyer survey
sample records, which contain informa .) n the .entire
sample frame of employers in the sites c0rllrll0n to both the
household and employer surveys regardless of whether the
employer survey was actually completed.
22. If we define ej to equal one if individual j is observed
leaving his or her job due to being fired or laid off and zero
otherwise, 0 j to equal one if individual j is observed leaving
his or her job due to quitting, and zero otherwise and then
the likelihood function, assuming independence among
length of spells, may be written as:
L = 11 [rli H(t j)] ej [r 2j H(9] oj [H(t j)] 1-8j-oj
J=l
where
H(t j)
exp [-r ljtj - r2jti)
is the probability the individual is still employed at the
job at time t j is the length of the observed spell. Maxi,. zation of L with respect to the Bs from the above eqyation
gives the maximum Ukelihood estimates of the • • Bs. F9r.
further details on the structure of this model, see Turlla
(1976), Tuma and Robins (1980), or Tuma, Hannan, and
Groeneveld (1979).
16. Since InwDi=l - InwDi=O = Bi, the exponential of the
coefficient is the ratio of the wage when Oi = 1 to the wage
when Oi = O. That is,
23. Very high turnover rates for youth are one reason II'Ihy
youth have such high observed unemployment rates.
20
REFERENCES
Alchian, Armen A., and Harold M. B. Demsetz, "Production,
Information Cost and Economic Organization," American Economic. Review, Vol. 62, Dec. 1972, pp.
777-795.
Oi, Walter, "Heterogeneous Firms and the Organization of
Production," Working Paper No. E-82-10, The Hoover
Institution, Stanford, California, April 1982a, and Economic Inquiry, Vol. XXI, No.2, April 1983.
Baumol, w'J., "Contestable Markets: An Uprising in the
Theory of Industry Structure," American Economic
Review, Vol. 72, No.1, 1982.
Pencavel, John H., "Wages, Specific Training, and Labor
Turnover in U.S. Manufacturing Industries," International Economic Review, Vol 13, No.1, February
1972.
Becker, Gary S., Human Capital: A Theoretical and
Empirical Analysis with Special Reference to Education, New York: National Bureau of Economic
Research, 1964.
Quandt, Richard E, "On the Size Distribution of Firms,"
American Economic Review, Vol. LVI, No.3, June
1966.
Coase, Ronald, "The Nature of the Firm," Economica, Vol.
4,1937,pp.386-405.
Roberts, D.R., "A General Theory of Executive Compensation Based on Statistically Tested Propositions,"
Quarterly Journal of Economics, Vol 20, 1956, pp.
270-294.
Federal Deposit Insurance Corporation, 1981 Statistics on
Banking, Office of Public Information, FDIC, Washington, D.C., 1982.
Rosen, Sherwin, "Output, Income and Rank in Hierarchical
Firms," Working Paper No. E-81-10, The Hoover Institution, Stanford, California, August 1981a.
Feller, William, An Introduction to Probability Theory
and its Applications, 3rd Edition, New York: John
Wiley and Sons, 1968.
Rosen, Sherwin, "The Economics of Superstars," American Economic Review, Vol. 71, No.5, December
1981b.
Fox, H., Top Executive Compensation, (1978 Edition),
New York: National Conference Board, 1978.
Rosen, Sherwin, "Authority, Control and the Distribution of
Earnings," The Bell Journal of Economics, Vol. 13,
No.2, Autumn 1982, pp. 311-323.
Gibrat, R., Les Inegalites Economiques, Paris: Recueil
Sirey, 1931.
Hart, P.E, and S.J. Prais, "An Analysis of Business Concentration," Journal of the Royal Statistical Society,
Ser. A, Vol. 119, Pt. 2. 1956, pp. 150-181.
Schiller, Bradley R., "Human Capital Transfers from Small
to Large Businesses," research report prepared for the
Office of Economic Research, U.S. Small Business
Administration, June 1982.
Hymer, Stephen and Peter Pashigian, "Firm Size and
Rates of Growth," Journal of Political Economy, Vol.
LXX, No.6, December 1962, pp. 556-569.
Simon, Herbert A., and Charles P. Bonini, "The Size Distribution of Business Firms," American Economic
Review, Vol. XLVIII, No.4, September 1958, pp.
607-617.
ljiri, Y. and H.A. Simon, "Business Firm Growth and Size,"
The American Economic Review, Vol. 54, No.2,
March 1964, pp. 77-89.
Stigler, George J., "The Economics of Scale," Journal of
Law and Economics, Vol. 1, Oct. 1958.
Keeley, Michael C., and Philip K. Robins, "Job Search and
the Duration of Unemployment," SRI International,
November 1982.
Stigler, George, The Organization of Industry, Richard D.
Irwin: Homewood III., 1968.
Lewellen, W, G., and B. Huntsman, "Managerial Pay and
Corporate Performance," American Economic
Review, Vol. 60, No.4, 1970.
Stoikov, Vladimir and Robert L. Raiman, "Determinants of
Differences in the Quit Rate Among Industries," Americ~n Economic Review, Vol. LVIII, No.5, Part 1,
December 1968.
Lucas, Robert E, Jr., "On the Size Distribution of Business
Firms," The Bell Journal of Economics, Vol. 9, pp.
508-523, Autumn 1978.
Tuma, N~hcy B., "Rewards, Resources, and the Rate of
Mobility," American Sociological Review, Vol. 41,
April 1976.
Lester, A.A., "Pay Differentials by Size of Establishment,"
Industrial and Labor Relations Review, Vol. 7, No.
167, pp. 57-67.
Tuma, Nancy B., Michael Hannan, and Lyle Groeneveld,
"Dynamic Analysis of Event Histories," American
Journal of SociolOgy, Vol. 84, No.4, 1979.
Masters, Stanley H., "An Inter-Industry Analysis of Wage
and Plant Size," Review of Economics and Statistics, Vol. 51, August 1969, pp. 341-345.
Tuma, Nancy B., and Philip K. Robins, "A Dynamic Model of
Employment Behavior: Evidence from the Seattle and
Denver Income Maintenance Experiments," Econometrica, 1980.
Mellow, Wesley, "Employer Size and Wages," Washington,
DC: Bureau of Labor Statistics, draft, 1981.
Oi, Walter, "The Fixed Employment Costs of Specialized
Labor," Working Paper No. E-82-16, The Hoover Institution, Stanford, California, June 1982b.
Viner, J., "Cost Curves and Supply Curves," Zeitschrift fOr
Nationalokonomie, Vol. 3, 1932, pp. 23-46.
Williamson, O.E "Hierarchical Control and Optimum Finm
Size," Journal of Political Economy, Vol. 75, 1967,
pp. 123-138.
21
.
I
Brian Motley*
Models of money demand generally assume that in the short-run,
actual real balances may diverge from their desired level. This paper
compares two alternative explanations. The first is that the central bank
fixes the nominal money stock but prices change slowly so that the real
money stock adjusts to its desired level with a lag. The second is that
transactions costs cause individuals to change their nominal money
holdings slowly. Empirical evidence mildly supports the second hypothesis, even during the 1979-82 period when the Federal Reserve closely
monitored the nominal M1 stock.
Models of money demand generally take it for
granted that, in the short-run, the actual stock of real
money balances may diverge from the "desired
stock" determined by the prevailing levels of
income and interest rates. The standard explanation
for this divergence is that there are "transaction
costs" to adjusting money holdings, which render it
non-optimal for individual transactors to alter their
stocks of money continually to hold them at desired
levels. These transaction costs include not only
such explicit charges as brokerage fees for buying
and selling financial assets but also the psychological and "shoe-leather" costs of deciding upon
and then implementing a change in average money
holdings.
An alternative reason for expecting diver~Fnces
between actual and desired real balancesl!; that
although individual transactors can increase/or decrease their nominal money holdings, the economy
as a whole cannot, as long as the central bank is
controlling the stock of money closely. In other
words, if the Federal Reserve fixes the nominal
stock, money becomes a "hot potato", so that the
desired stock of money must adjust to match the
actual stock rather than conversely. As a result,
divergences between the desired and actual stocks
may occur not because economic agents are individually slow to adjust their actual money holdings
to their desired levels but because the factors determining those desired holdings-prices, income and
interest rates-do not adjust instantaneously to
close such gaps.
The so-called "buffer-stock" approach to the
demand for money in a sense lies between these two
views of the adjustment process. According to this
approach, an essential function of money is to serve
as a "buffer" between streams of receipts and expenditures, both of which are somewhat unpredictable. The phrase "quantity of money demanded ...
does not refer to an amount of money which an
(individual economic) agent will want to hold at
each and every moment, but rather, to an amount
which he will want to hold on average over some
time interval." I The agent anticipates that his actual
money holdings will vary around this average, rising when outlays are unexpectedly low or receipts
are unexpectedly high, and falling when the converse is the case.
Indeed, it is largely because agents anticipate
such variations (that is, they expect the unexpected)
that they hold stocks of money. 2 As a result, when
money holdings do rise or fall, agents do not
immediately seek to move their holdings back to
their desired average level. This explains whyeven at the level of the individual agent-' 'actual"
money may diverge from "desired"money, and
also why the factors determining the total desired
*Senior Economist,
Federal Reserve Bank of San
Francisco. Research assistance was provided by
Roger Weatherford.
22
stock-income, prices and interest rates-do not
adjust rapidly to eliminate such divergences.
In a recent article in this Review, Judd and Scadding compared a variety of alternative dynamic
models of money demand. 3 They concluded that
models in which divergences between desired and
actual real balances resulted from slow adjustment
in prices provided the best explanation of U. S. data.
Judd and Scadding used quarterly data and their
estimation period ended in 1974. The purpose of
this short paper is to compare the performance of
this "price-adjustment" model with the conventional approach using monthly data over the period
since mid-1976 and, in particular, to examine
whether changes in the central bank's policy target
have affected the results of this comparison.
The use of monthly data raises the issue of
whether the "adjusting variable" may be different
according to the length of time considered. Most
theoretical models assume that, in the short run,
income and prices are essentially fixed and that it is
the interest rate that moves to equate money supply
and money demand. Interest rate changes are then
transmitted to income and prices over a longer time
period. Judd and Scadding found that a model in
which interest rates move in response to divergences
between money supply and money demand was
unable to explain U.S. quarterly data. A possible
explanation for their result would be that the interest
rate adjustment process is completed within a quarter and so cannot be captured in quarterly data.
However, in preliminary tests, I obtained similarly poor results using monthly data, casting some
doubt on the standard view that interest rates are the
adjusting variable in the short run. In view of these
initial results, I decided to limit this study to
a comparison between the conventional moneyadjustment approach, in which the nominal money
supply adjusts to the public's demand for nominal
money balances, and the price-adjustment approach
in which the nominal supply of money is fixed and
prices adjust to equate the real money supply with
the public's demand for real money balances.
(1)
where all variables are in logarithms and m~ represents the desired stock of real balances given the
levels of real income, y" and interest rates, it,
(2)
Substituting Equation (2) into Equation (1) and
adding an error term yields
P,=(l-'y) PH + I'M,
-l'ao-l'a,y,-l'a2it+u;
(3)
This equation also may be written in an alternative
form:
M,- Pt = (l-I')(M,- PH)
+l'ao+l'a,Yt+l'a2it-u; (3a)
The Judd-Scadding version of the money adjustment model begins with the assumption that the
nominal money stock responds to the difference
between the currently desired money stock and the
actual stock in the preceding period, after adjustment for the effect on the actual stock of the change
in bank loans:
LlM, = 8LlBL,
+A[m~+Pt-(MH+8LlBLt)]
(4)
Substituting Equation (2) into Equation (4) and
adding an error term yields
Mt=(l-A)Mt_I-APt+8(l-A)LlBLt
+Aao+Aa,y,+Aa2it+uMt
(5)
As in the case of the price-adjustment model, this
equation also may be written in an alternative form:
(M t- P,) = (1- A)(M t_1 - PI) + 8( 1-A)ABL t
(5a)
+Aao+Aa,y,+Aa2it+uM,
It is important to note that in Equation (3) the
price level is the dependent variable and the nominal money stock is exogenous, whereas in Equation (5) nominal money is endogenous and prices
are exogenous. Although the models may be transformed algebraically to appear to have the same
dependent variable, such transformations do not
alter the estimated parameters as long as the appropriate coefficient restrictions are imposed. In comparing the models, it is important to bear this in
mind, since the variance of prices is substantially
less than the variance of the nominal money stock. 4
Alternative Models of Dynamic Adjustment
The price adjustment model begins with the
assumption that prices change in response to the
difference between the actual money stock determined by the central bank and the desired stock:
23
Empirical Results
The results of estimating Equations (3a) and (Sa)
over the period 1976.08-1983.08 are shown in
Table I. The entries represent the underlying structural parameters of the models: the long-run elasticities with respect to real income and the interest (ate
[a l and a z in Equation (2)] and the adjustment
coefficients (A and y). It is striking that the elasticity
estimates are extremely close. Moreover, both the
income elasticity (not significantly different from
unity) and the interest rate elasticity are close to
estimates made with the San Francisco Money MarketModel. 5
The standard error of the price-adjustment equation is noticeably lower than that of the moneyadjustment model. This result is the same as that
reached by Judd and Scadding using quarterly data
over an earlier sample period. However, this finding does not necessarily imply that the price-adjustment model.is superior because the variance of the
dependent variable also is lower in the price-adjustment equation. In terms of the proportion of total
variance explained, the models are quite similar
and, in fact, the money-adjustment model provides
a slightly better fit. Allowing for degrees of
freedom, the price model explains 28.5 percent of
total variance while the money model explains 34.4
percent. 6
The underlying theory of these models suggests
that their appropriateness should depend on the
monetary policy rule being followed by the central
bank. If, for example, the authorities pursue an
interest rate target in the short run, the stock of
nominal money is endogenous and hence the
money-adjustment model is appropriate. With a
money-stock target, on the other hand, money
becomes a "hot-potato," making the priceadjustment model more appropriate.
To test the idea that the policy rule may influence
the adjustment mechanism, the full sample period
(1976.08-1983.08) was divided into two subsamples. In 1979.10-1982.07, the Federal Reserve
was assumed to be fixing the nominal money stock
in the short run; hence the price adjustment model
should be the appropriate one. In 1976.08-1979.09
and 1982.08-1983.08, the Federal Reserve was
assumed to be allowing the nominal money stock to
be endogenous in the short run; hence the moneyadjustment model should be appropriate. Separate
equations were estimated for these two periods. The
results are shown in Table 2. The coefficients
shown in the first and second columns of the table
are unconstrained estimates, while those in the third
and fourth columns were made subject to the restriction that the underlying long-run income and interest rate elasticities remained constant over the full
1976-83 sample period. This restriction reflects the
assumption that these long-run elasticities do not
depend on the policy regime. Under this restriction,
the estimated elasticities are not much different
from those estimated in Table I.
The results in Table 2 cast some doubt on the
price-adjustment model. When this model is estimated over the period for which theory suggests it
should be most appropriate (the period from October 1979 to July 1982, during which the Federal
Reserve was targeting MI), the income and interest
rate elasticities are implausibly low. These elasticity estimates change dramatically when the constraint that they are constant over the full 1976-83
period is imposed 7 [compare columns (I) and (3) of
Table 1
Money Demand Equations
(1976.08-1983.08)
Price
Adjustment
Model
Money
Adjustment
Model
Adjustment Factor*
0.038
(2.760)
0.109
(3.768)
Real Personal Income
(Elasticity)
1.110
(2.635)
1.018
(3.958)
Commercial Paper Rate
(Elasticity)
-0.194
(3.221)
-0.182
(4.645)
Change in
Bank Loans**
0.276
(2.070)
Constant
(Long Run Value).
-2.872
(0.927)
-2.021
( 1.087)
RHO I
0.247
(2.207)
-0.020
(0.183)
0.002095
0.186
( 1.523)
-0. i77
( 1.453)
0.004504
RH02
SEE
"Explained" Sum
0.285
0.344
* ')I in Equation (3); A in Equation (5)
** 8 in Equation (5)
*** Based on monthly growth rates of prices and nominal
money. and adjusted for degrees offreedom. See footnote 6.
24
the table]. By contrast, the money equation yields
plausible parameters that do not change much when
the restriction is imposed.
I would interpret these results as giving some
support to the money-adjustment model and casting
some doubt on the price-adjustment model, but the
evidence is not strong either way. One possible
explanation for the results is that although the Federal Reserve targetedMI over the 1979-82 period, it
did not control it sufficiently closely in the short run
for it to be genuinely exogenous. Even over this
period, then, Mlwas not a true "hot potato."
Another explanation could be that the sample period
for the price-adjustment model is short and includes
highly unusual interest rate and income volatility as
well as a period of credit controls.
money supply adjusts to real demand with a lag
because prices adjust slowly. Judd and Scadding
concluded that the price-adjustment modeloutperformed the money-adjustment specification.
I have argued that the appropriate specification,
in principle, depends on the policy regime in effect.
If the central bank is pursuing a nominal MI target,
money becomes a "hot potato" and the conventional specification in which nominal money is the
adjusting variable will not be appropriate. Such a
specification would be suitable if the Federal Reserve had an interest rate or nominal income target
and, in the short run, allowed the nominal supply of
money to adjust in response to changes in demand.
I also argue that it is not appropriate to compare
these models in terms of the standard errors of the
estimated equations under the rival specifications.
Under the conventional specification, the dependent variable is the nominal money stock, whereas
under the alternative, the dependent variable is the
price level. Since the variance of prices is less than
that of nominal money, one expects an equation
with prices as the dependent variable to have a
lower standard error. The models cannot be rearranged to have the same dependent variable, so
Summary and Conclusions
The principal purpose of this paper was to reexamine the question raised by Judd and Scadding
as to the appropriateness of the conventional assumption in money demand studies that nominal
money demand responds to changes in its determinants (income, prices, interest rates) with a lag.
The alternative view considered here is that the real
Table 2
Money Demand under Varying Policy Regimes
Unconstrained
Price
Adjustment
Model
(79.10-82.07)
Price Adjustment
Coefficient
Money Adjustment
Coefficient
Real Personal
Income (Elasticity)
Commercial Paper
Rate (Elasticity)
Change in I
Bank Loans
Constant
RHOI
RH02
SEE"
Unconstrained
Money
Adjustment
Model
(76.08-79.09,
82.08-83.08)
0.0953
( 1.925)
Constrained
Price
Adjustment
Model
(79.10-82.07)
Constrained
Money
Adjustment
Model
(76.08-79.09,
82.08-83.08)
0.0236
( 1.197)
2.871
( 1.62)
0.0707
(4.50)
1.155
(9.68)
- 0.182
(7.54)
0.184
(1.35)
- 2.93
(3.39)
0.230
0.180
- 0.338
- 0.257
0.353
(1.41 )
0.006
(1.41 )
0.003053
2.837
(3.85)
0.0739
(4.65)
1.096
( 11.70)
- 0.171
(8.24)
0.192
( 1.38)
- 2.503
(3.68)
0.256
0.182
0.331
- 0.249
1.096
(11.70)
- 0.171
(8.24)
0.003087
I. 13 in Equation (5)
2. These standard errors refer to the full sample period and measure the ability of the combined models to explain the data.
25
FOOTNOTES
that it is not possible to set up a "nested" equation
that includes each model as a special case.
There is some weak evidence that the moneyadjustment specification provides a superior explanation of the U.S. experience. The estimated
parameters appear to be more stable under this
specification. On the other hand, the empirical
results suggest that the estimates of the underlying
long-run parameters are not sensitive to the dynamic structure chosen. This is a very useful result
since it implies that, at least in the long-run, predictions of the effects of changes in the stock of nominal money on income, prices and interest rates will
not be affected much by the adjustment assumptions
made in estimating the money-demand relation.
1. David Laidler, "The Buffer Stock Notion in Monetary
Economics," 1983 Harry Johnson Lecture, April 12, 1983.
2. The fact that agents hold this buffer in the form of money
rather than of other assets which yield interest is explained
by the existence of transactions costs of switching between
money and these other assets.
3. John P. Judd and John L. Scadding, "Dynamic Adjustment in the Demand for Money: Tests of Alternative
Hypotheses," Economic Review, Federal Reserve Bank of
San Francisco, (Fall 1982).
4. The variance of the monthly change in the logarithm of
prices (I.e. the monthly growth rate) over the period from
August 1976 to August 1983 is 6.30 x 10-6 whereas that of
the monthly change in the logarithm of nominal money is
3.17 x 10.- 5 Thus nominal money was approximately five
times more variable than was the price level.
5. John P. Judd, "A Monthly Model of the Money and Bank
Loan Markets" Working Papers in Applied Economic Theory and Econometrics, No. 83-01, May 1983.
6. For each equation this proportion is computed as
1- [(RSS/n-k)/(TSS/n-1)]
where n is the number of observations, k is the number of
parameters estimated, RSS is the residual sum of squares
of each equation and TSS is the total sum of squares of the
monthly growth rate of the dependent variable in each
equation (I.e., prices and nominal money respectively).
7. An F-test of this restriction cannot reject it at the 5% level
of significance. The computed F-statistic is 1.72, compared
to a critical value of 3.13.
26
Michael M. Hutchison*
How official sterilized (non-monetary)foreign exchange market intervention may influence the exchange rate by changing the relative supply
ofgovernment bonds denominated in domestic andforeign currencies is
shown in this paper. Recent Japanese experience is investigated in the
context of a simple asset market model of exchange rate determination.
The empirical estimates suggest that Japanese official intervention has
had only a small influence on the real value ofthe yen-dollar exchange
rate largely because its impact was dwarfed by the role of large fiscal
deficits in changing the relative supply ofgovernment bonds.
The Williamsburg economic summit took place
last Spring amidst great concern over the general
strength and dramatic volatility of the dollar in
world currency markets. A major issue on the agenda was whether central banks should increase their
intervention in the foreign exchange market and
attempt both to hinder the dollar's climb and to
reduce its fluctuations. As a basis for discussion,
summit participants used the Report of the Working
Group on Exchange Market Intervention (the Jurgensen report) commissioned at the 1982 Versailles
summit. Although the report gave few policy
recommendations, it did help to identify the important issues and to clarify the meaning of intervention. In particular, the Jurgensen report distinguished between "monetary" intervention and
"sterilized" intervention, and emphasized that the
effectiveness of central bank foreign exchange
market operations will largely depend upon the
distinction.
Official foreign exchange market intervention
may be viewed as a process through which the
central bank shifts the composition of its portfolio
between foreign and domestic assets. In the case of
monetary intervention, the central bank changes its
net foreign asset holdings through purchases and
sales of foreign exchange and allows a corresponding change in its monetary liabilities, that is, the
monetary base (total reserves plus currency held by
the non-bank public). Sterilized intervention, on the
other hand, means that the central bank allows the
change in its net foreign asset holdings to be offset
by a corresponding change in its net domestic
assets. Monetary liabilities of the central bank
remain unchanged in this case, and the monetary
base is "sterilized" from foreign exchange market
intervention operations. In both instances, foreign
assets held by the public will change. Monetized
intervention, however, will change the public's
holdings of base money, while sterilized intervention will change the public's holdings of domestic
bonds.
Table I illustrates the effect of intervention on
asset supplies in more concrete terms. The table
shows a stylized central bank balance sheet and the
consolidated private sector claims on foreign and
domestic governments. The domestic central bank
holds two assets, domestic government bonds and
* Economist. Research assistance for the article was
provided by Mary~Ellen Burton-Christie. I have
benefitted from helpful comments from my colleagues in the FRBSF Research Department. I am
also indebted to Steve Haynes, Peter Hooper, Ralph
Langenborg, Raymond F. Mikesell and Joe Stone
for their comments on earlier drafts of this paper.
27
With a stylized case of sterilized foreign currency
support intervention, the domestic central bank follows all of the steps outlined above for monetary
intervention and then takes one additional step-it
sells a domestic bond in order to hold domestic base
money unchanged. The net effect, shown by (2) in
Table I, is that the central bank holds more foreign
bonds and fewer domestic bonds, leaving base
money unchanged, while the private sector holds
fewer foreign bonds and more domestic bonds.
The Jurgensen report emphasized the distinction
between monetary and sterilized intervention because the form intervention takes will largely determine its effectiveness. Few disagree that monetary
intervention may have a significant influence on the
exchange rate. By changing base money, monetary
intervention will influence the broader money aggregates, interest rates, and prices in the economy.
These variables are important determinants of
exchange rates. Sterilized intervention, on the other
hand, amounts to a switch of a domestic (foreign)
bond for a foreign (domestic) bond held in private
portfolios. This form of intervention will only be
effective if investors view the bonds as less than
perfect substitutes, and relative yields adjust as a
consequence of the change in their relative supply.
The change in relative yields is the channel through
which sterilized intervention may exert an influence
on the exchange rate. The debate surrounding the
efficacy of intervention thus largely concerns sterilized intervention, and the degree to which changes
in the distribution of foreign and domestic bonds in
private portfolios will influence relative yields.
A major difficulty facing the central bank, however, is that sterilized intervention is but one source
of change in the public's bond holdings. The sale of
government bonds to finance government budget
deficits will likely playa larger role than intervention in determining the bond mix in private portfolios. The public's domestic government bond
holdings (B) is determined by the interaction of
moneta.ry policy, government budget deficits, and
official exchange market intervention.· A government budget deficit over any given period, for
example, must be financed by the private sector.
The government bond can be sold either to the
public or to the central bank. In the formercase,B
will increase; in the latter case, base money will
foreign government bonds, and has one liability,
domestic base money. (For the sake of simplicity,
we assume that central bank domestic credit equals
domestic bond holdings and that central bank net
foreign asset holdings equal net foreign bond holdings). The consolidated private sector aggregates
the foreign private sector and the domestic private
sector and focuses on total claims on government,
that is, "outside" assets. Consolidated private sector claims on foreign and domestic governments are
distributed between domestic base money, foreign
base money, domestic government bonds and foreign government bonds.
Monetary foreign currency support intervention
occurs when the central bank purchases foreign
currency from the private sector with domestic currency, and in tum purchases a foreign bond with its
foreign exchange receipts. 1 The net effect on the
central bank balance sheet and private asset holdings from this operation is indicated by (1) in Table
I. The central bank increases its holdings of foreign
bonds and increases domestic base money. Reflecting the new composition of the central bank portfolio, the private sector holds more domestic base
money and fewer domestic bonds.
Table 1
(A)
Domestic Central Bank Balance Sheet
Assets
liabilities
Foreign Bonds
1+
Domestic Base Money
.2 +
Domestic Bonds
1+
2 nc
1 nc
2 ,-
(B)
Consolidated Private Sector Claims on
Governments (Foreign and Domestic)
Domestic Base Money
Foreign Base Money
1+
20c
Inc
2m:
Domestic Bonds
[ or
:'+
Foreign Bonds
Notes:
1-
+: increase
-: decrease
nc: no change
28
stock of yen-denominated government bonds in private portfolios at a rate far surpassing that of
most other major industrial nations since the midseventies. An empirical study of the Japanese case
therefore provides some interesting insights into the
complications central banks face in their attempts to
manage exchange rates.
Section I presents a model of real (price-adjusted)
exchange rate determination that is later employed
to measure the effectiveness of Japanese sterilized
intervention operations. The model is a variant of
the "asset market approach" which views the exchange rate as an asset price whose value is largely
determined by the relative demand and supply of
asset stocks denominated in various national currencies and which is prone to large fluctuations as
asset risk-return characteristics are perceived to
change. The foreign exchange market is viewed as
an asset market in this model, with exchange rates
determined not by the balancing of flow demands
and supplies of currencies, but rather by the values
at which the market as a whole is willing to hold the
outstanding stocks of assets. 4 Sterilized intervention can be conveniently analyzed within this
framework because of its influence on relative bond
supplies.
Section II discusses Japanese foreign exchange
market intervention policy and describes the growth
of fiscal deficits in Japan. This provides the background for an account of the growth of Japanese
government bonds in private portfolios in comparison to the United States. An empirical test of the
model using Japanese-U .S. data from 1973 through
1982 is the subject of the third section. The paper
concludes with a short summary and discussion of
several policy implications.
increase. On the other hand, B will also be influenced by the central bank when it purchases or sells
domestic bonds in conducting monetary policy
through open market operations, even in the absence of current government budget deficits. In
short, the public's domestic bond holdings equal the
cumulative domestic budget deficit (fDEF) minus
cumulative open market purchases of government
bonds in exchange for domestic base money (MB d )"
plus cumulative sales of home-country domestic
bonds by official foreign~exchange intervention
authorities (fINT), that is, sterilized intervention in
both the home and foreign countries combined:'
B = fDEF - MB d
+ fINT
(I)
From equation (I), it is apparent that a domestic
bond sale either to finance a home-country budget
deficit, or to finance exchange market intervention
in support of the foreign currency will increase the
supply of domestic currency denominated bonds in
private portfolios. The ability of the central bank to
influence the relative supply of bonds through sterilized foreign exchange operations alone during any
given period will therefore be complicated by these
other sources of supply.
Purpose
This paper investigates the Japanese experience
with sterilized intervention in the foreign exchange
market over the 1973-82 floating rate period. The
Japanese case is particularly interesting both because the Bank of Japan pursues an active foreign
exchange market intervention policy-it is among
the most active of central bank participants in the
foreign exchange market-and because large central government budget deficits have increased the
I. Real Exchange Rate Model
domestic and foreign relative prices, it is an important factor in determining a country's position in
international competition, and its determinants are
of special policy significance.
The exchange rate equation is derived initially
from the covered interest parity condition. This
condition states that the return on domestic securities must equal the return available on (equally
The basic formulation of the real exchange rate
model follows Isard (l980a, 1980b) and may be
viewed as a simplification of Hooper and Morton's
(1982) extension of the sticky-price monetary
model of exchange rate determination developed by
Dornbusch (1976).5 The focus dependent variable
is the real (price-adjusted) value of the exchange
rate. Because the real exchange rate is a measure of
29
to the interest differential between domestic and
foreign securities over a similar holding period, less
any expected yield differential.
It is convenient to think of the future expected
exchange rate as linked to the current spot exchange
rate through the interest differential. Equation (4')
illustrates this relationship. A given interest differential (including <p e ) is consistent with any given
spot exchange rate level, and only indicates the
expected change in the (log) level of the exchange
rate over the maturity of the bonds in question.
Once expectations about the expected future spot
rate are identified, however, the spot rate is determined at a given level. The link between the current
(spot) price of a currency and its expected future
price is hence quite strong, as it is in the case of any
asset price.
To show that (4') holds in real (price-adjusted)
terms as well as nominal, we define the real exchange rate (q) and expected future real exchange
rate (qe) as the difference between the nominal
exchange rate and current and expected future relative prices expressed in logs, respectively:
risky) foreign securities once investors have covered their open positions (and hedged against exchange risk) by forward market purchases or sales: 6
(l + R) = (F/S) (I + R*)
(2)
where: R
= domestic nominal interest rate over
maturity t
R* = foreign nominal interest rate over
maturity t
S = spot exchange rate (domestic price
of foreign currency)
F = forward exchange rate
In log form, (2) may be expressed as (3)
r=f-s+r*
f-s=r
(3)
or
r*
(3')
where r = log (I + R), r* = log (I + R*.), s = log S
and f = 10gF
The expected yield differential between domestic
and foreign bonds is the difference between the
forward rate and the future spot rate, 7 cf> e = f - se.
To see this, we may substitute f = cf>e + se into (3)
and solve for the expected yield differential: cf>e = r
- [r* + (se - s)]. The return on domestic bonds is
given by the domestic interest rate (r) and the return
on foreign bonds is given by the foreign interest rate
(r*) plus the expected percent appreciation of the
foreign currency, se - s. The forward rate will
generally not equal the expected future spot rate cf> e
i= 0 (and expected yields on government bonds
denominated in different national currencies will
generally not be equal), if investors view the bonds
as imperfect substitutes. A simple model relating
the yield differential to government bond supply
and demand is developed below.
Rearranging and substituting the yield differential and expected future spot exchange rate for the
forward rate gives:
se -
S
= r - r* - cf> e
q = s - (p - p*)
qe = se _ (pe _ p*e).
(5')
where: q = real exchange rate (log)
qe = expected future real exchange
rate (log)
p = domestic price level (log)
p* = foreign price level (log)
pe = expected future domestic price
level (log)
p*e = expected future foreign price
level (log)
Equations (5) and (5') are both identities and
differ only in that (5') is an ex ante relationship
based on market expectations of future spot exchange rates and of future domestic and foreign
price levels. The real exchange rate measures deviations from purchasing power parity, that is, the
extent to which the nominal exchange rate moves
beyond simple adjustment to relative price shifts.
Expected future price levels may now be disaggregated into their current price and expected inflation components,
(4)
or
s = (r* - r) + cf>e + se
(5)
(4')
Equation (4) is a condition which will hold in
internationally integrated financial markets with
rational behavior on the part of investors. It simply
states that the market expectation of domestic currency depreciation over a given period will be equal
pe = p +
30
7T
(6)
pe* = p*
+ 1T*
path moving towards its long-run sustainable value.
The real exchange rate is a major component in the
current account adjustment process because it reflects the relative price between domestic and foreign goods and services. An unexpected current
account surplus or deficit, to the extent that it is
considered permanent, is therefore assumed to indicate to market participants that a real exchange rate
shift may be necessary to return the current account
back to its sustainable level or path. 8
This process may be formalized by stating the
change in the expected long-run future real exchange rate (dqe) as a function of unexpected current account movements or "surprises" (CN) over
period t:
(6')
where 1T = In (l + p), 1T* = InO + p*), and p, p*
equal the expected percent change in the domestic
and foreign price levels, respectively. Substituting
(5) - (6') into (4') then gives the basic real exchange rate identity:
q
= (r*
- 1T*) - (r - 1T)
+ cPe + qO
(7)
This equation expresses the real exchange rate as
a function of domestic and foreign real interest
rates, the yield differential, and the expected future
real exchange rate. Up to this point, we have made
no behavioral assumptions about the way expectations are formed, and have derived (7) by manipulating the covered interest arbitrage condition,
introducing the definition of the real exchange rate
and disaggregating the expected future price level
into its current price and expected inflation components. The formation of expectations regarding the
future real exchange rate and the yield differential
need to be identified, however, before the model
can be implemented.
dqe
=
g[CN(t)] dt
(8)
This relationship assumes that all changes over
period t in the expected future long-run real exchange rate are unexpected, and that no time trend,
and hence predictable element, is discernable during the period under investigation. Market participants thus employ all available current account
information in their formation of expectations about
the future real exchange rate, and only additional
information imbedded in the unexpected component of the contemporaneous current account will
cause them to revise their expectations. We are, in
effect, assuming that market participants form their
expectations "rationally," but we limit the set of
relevant information upon which they base their
expectations to the current account.
Integrating (8) from an initial period to the
present gives the level of the expected long-run
future real exchange rate at a point in time t as a
function of unexpected cumulative current account
developments:
Expected Equilibrium Real Rate
Among the more important influences of expectations about future real exchange rates (qe), is the
market's perception of a sustainable balance of
payments. The ~urrent account of the balance of
payments is perhaps the most logical choice as a
measure of external equilibrium from an asset
market view of exchange rate determination. This is
because the current account equals the difference
between the sale of domestic goods and services
(and net transfers) to foreigners and the purchase of
foreign goods and services by domestic residents.
Whenever the current account does not equal zero, a
nation exports more or less than it imports. In the
absence of official reserve flows, the current
account imbalance reflects the net accumulation
(current account surplus) or decumulation (current
account deficit) of private domestic resident claims
on foreigners. It is in this sense that a sustainable
long-run· current account must be consistent with
the rate of foreign asset accumulation or decumulation desired by private investors (both foreign and
domestic) in the long-run. If an unexpected current
account surplus or deficit arises, some adjustment
may be necessary to restore the current account to a
qe
= f g[CA'(t)] dt
(9)
It is assumed that the (log) level of the expected
future real exchange rate, qe, may be expressed as a
simple linear function of the cumulative sum of
unexpected current account developments: 9
(0)
Yield Differential Determinants
The expected yield differential is of particular
importance because it is through this channel that
3\
analogous to (13) and (14). We do so by defining
wealth as total holdings of bonds, both foreign and
domestic. Domestic wealth (foreign wealth) relevant for portfolio choice in this model thus consists
of domestic resident (foreign resident) holdings of
both domestic and foreign bonds. This implicitly
assumes that investors first allocate a portion of
their total wealth to total bond holdings, and then
decide between foreign and domestic bonds. This
assumption, though restrictive, allows us to drop
the foreign bond demand functions explicitly, and
to infer the percentage of domestic and foreign
residents' wealth devoted to foreign bonds directly
fromf3d andf3r. For example, the percentage oftotal
domestic wealth, so defined, invested in foreign
bonds equals one minus the percentage of domestic
wealth invested in domestic'bonds, (1- f3ct).
W can now define total "world" wealth as W =
Wd + Wr; sum (13) and (14) to get total domestic
bond demand (B = Bd + B r); and solve for the yield
differential:
(15)
cf>e = ~ {(B)}- (ad - ar) {(Wd)}- ~
b W
b
W
b
foreign exchange market intervention influences
the exchange rate. The yield differential is determined by the interaction of demand and supply for
assets in both home and foreign countries. Under
certain assumptions, it may be expressed as a function of the relative supply of government bonds,
relative wealth, the perceived exchange rate risk
associated with holding foreign bonds, the degree
of investor risk aversion and the currency' 'habitat"
preferences of investors (Dornbusch, 1980).
For the purpose of empirical estimation, we
assume a simple bond demand function similar to
Frankel (1982) to derive the yield differential determinants. 1O Total private demand for domestic government bonds (B) is the sum of domestic private
demand (B d) and foreign private demand (B r). The
domestic and foreign demand functions, in tum,
may be expressed as a proportion (f3) of domestic
and foreign wealth invested in domestic government bonds:
B d = f3d W d
(II)
Br = f3r Wr
(12)
From (I) and (15), it is apparent that a domestic
bond sale either to finance a home-country budget
deficit, or to finance foreign-currency support exchange market intervention, will increase the supply of domestic currency denominated bonds in
private portfolios and, consequently, increase their
expected relative return (that is, increase the yield
differential), if investors view the bonds as less than
perfect substitutes (b =/= (0). This will immediately
depreciate the exchange rate through (7) in our
model. The larger the degree of substitutability
between foreign and domestic bonds, that is, the
larger the value of b, the smaller will be the increase
in the yield differential, and hence, the effect on the
exchange rate, of any given change in relative bond
supply. An increase in domestic wealth relative to
total wealth, on the other hand, will increase the
relative demand for domestic bonds (assuming that
domestic investors display a greater preference for
home securities than do foreign investors, that is, ad
> ar) and lower the yield differential. This will
appreciate the value of the domestic currency.
Real Exchange Rate Equation
Substituting the expected equilibrium real exchange rate determinants ( 10) and yield differential
where Wd(Wr) is domestic (foreign) wealth and
f3d(f3r) is the proportion of domestic (foreign)
wealth devoted to domestic government bonds. By
assuming that f3d and f3r are simple linear functions
of the expected yield differential, that is,
f3d = ad + b cf>e and f3r = ar + b cf>e, we may write
( II) and (12) as:
Bd = (ad
+ bcf>e)Wd
(13)
B r = (ar
+ bcf>e)Wr
(14)
where ad' a r are the desired percentages of total
domestic and foreign wealth, respectively, held in
domestic government bonds independently of
expected relative yields, and bcf>c measures the proportion of wealth devoted to domestic bonds in
response to differential yields. This formulation
assumes that domestic and foreign demand for
domestic government bonds, measured as a percentage of total wealth, differs only by a constant term
which is presumably higher in the domestic country
because domestic investors prefer the home currency "habitat."
To close the model we need to introduce the
foreign bond market and develop demand functions
32
as market participants perceive a shift in the tenus
of trade necessary to return the current account to a
sustainable long-run equilibrium position.
An increase in the share of domestic government
bonds in total wealth, other things being equal, will
depreciate the home currency as investors demand a
higher yield to absorb the bonds into their portfolios. Holding interest rates and the future expected real exchange rate constant, the increased
yield may come about through an exchange rate
depreciation. An increase in the share of domestic
wealth in total wealth, on the other hand, will increase the relative demand for domestic bonds and
appreciate the exchange rate, ceteris paribus.
This process can be explained in intuitive tenus
as the macro-economic adjustment process set in
motion from domestic disturbances that work partially through the foreign exchange market. In this
case, the disturbance is an increase in domestic
government bonds which necessitates an increase in
their expected relative return. Part of this adjustment may be reflected in higher relative interest
rates in the home country, and part may come about
through an increase in the expected appreciation of
the domestic currency. The increase in the expected
appreciation of the currency may come about by an
immediate spot depreciation beyond any drop in
expectation regarding the future equilibrium rate
(which is determined by the long-run current account equilibrium condition). This then sets up a
greater appreciation of the home currency, or less
of a depreciation, than was expected before the sale
of a domestic bond, either to finance a domestic
budget deficit or to finance foreign-currency support intervention (purchases of foreign bonds with
domestic bonds). 12
detenuinants (15) into the basic real exchange rate
equation (7), and rearranging, gives the model to be
estimated in Section III of this article:
q = bo + b l (r*-7T*) + b2 (r-7T)+ b3 (B/W)
+ b4 (Wd/W) + bs (2:eA')
where:
(16)
bo = !xo - (arlb);
b,>O
b2 <0
b3 = l/b>O
b4 = [-(ad-af)/b]<O
bs=!XI<O
Equation (16) expresses the real exchange rate as
a function of foreign and domestic real interest
rates, the proportion of domestic government bonds
in total wealth, the proportion of domestic wealth in
total wealth and the cumulative sum of current account surprises. The real exchange rate will depreciate (that is, increase) with a rise in the foreign real
interest rate, and appreciate with a rise in the home
real interest rate. The size of the real interest rate
coefficients (b l and b 2 ) equal, in theory, the tenu to
maturity (in years) of the foreign and domestic bonds whose interest rates are included in the
equation. For example, a one percentage point increase in the five-year domestic bond rate (expressed at annual rates), ceterius paribus, should
immediately appreciate the real exchange rate by
five percent. The exchange rate appreciation keeps
expected relative yields unchanged by creating an
expected home currency depreciation of approximately one percent annually over the five-year
maturity of the domestic bond. Unexpected current
account surpluses in the home country (b s), on the
other hand, will appreciate the domestic currency,
U. Exchange Market Intervention and Budget Deficit Finance in
Japan
relative to other major industrial nations. On the
other hand, the surplus of Japanese private savings
over investment during the last decade has meant
that financial wealth in Japan available for portfolio
investment has also grown at a more rapid rate than
most other industrial nations.
Table 2 gives two measures of the Bank of
Japan's foreign exchange market intervention in
relation to changes in the yen-dollar exchange rate
The real exchange rate model outlined above,
with its focus on the influence of privately held
government bonds and financial wealth on the exchange rate, is particularly appropriate for an analysis of. the Japanese experience since the mid1970s, On the one hand, Japan's large fiscal deficits
and active exchange market intervention policy
have combined to increase greatly the supply of
Japanese government bonds in private portfolios 13
33
quarter of 1979, for instance, was met with strong
yen-support operations by the Bank of Japan and a
$5 billion decline in official reserves. The foreign
exchange funds account indicates that the Japanese
sold $6.2 billion in foreign exchange during the
quarter.
The Bank of Japan has generally followed a
"leaning against the wind" intervention policy,
that is, it usually sells yen when it appreciates and
buys yen when it depreciates. This is indicated by
the figures in the table. Japanese reserves generally
fall when the yen is depreciating and rise when it is
appreciating, and the Bank of Japan both buys and
sells large amounts of foreign exchange over a period of several quarters. Empirical evidence derived
from estimating the Bank of Japan's foreign exchange market intervention functions also supports
this conclusion. Quirk (1977) estimates that the
over the course of the floating rate period. The
intervention proxies are gross changes in official
Japanese reserves (less gold) and changes in the
Japanese foreign exchange funds account. 14 By
either measure, Japanese intervention in foreign
exchange markets is significant and the Bank of
Japan is generally recognized as among the most
active of the central bank participants in the foreign
exchange markets. During 1982, for instance,
Japan lost almost $5 billion in foreign exchange
reserves in an attempt to slow the slide of the yen
against the dollar. The foreign exchange funds measure suggests that the Bank of Japan sold $8.9
billion (net) foreign exchange during 1982. Furthermore, Japan in the past has gained or lost similar
amounts of international reserves in a single quarter
in its foreign exchange operations. The sharp drop
of the yen following the oil price shock in the fourth
Table 2
Official Japanese Foreign Exchange Market Intervention:
Reserve Change, Foreign Exchange Funds and Exchange Rate Change
Gross Change in 1
Official Reserves
(less gold)
(Billion Dollars)
1974
1975
1976
1977
1978 I
II
III
IV
1979 I
II
III
IV
1980 I
II
III
IV
1981 I
II
HI
IV
1982 I
II
III
IV
u.s.
$
Foreign Exchange 2
Funds Account
(Billion Dollars)
L3
-0.6
3.8
6.6
6.3
-1.9
1.9
3.8
U.S.
$- L3
Percent Change in 3
Yen-Dollar
Exchange Rate
(Yen Depreciation (+»
-2.1
2.6
6.2
7.7
1.1
2.9
3.1
7.5%
1.6%
0.0%
9.4%
- 3.8%
- 7.0%
12.7%
- 1.1%
-4.2
-4.1
0.4
-5.0
-3.9
-4.1
0.8
-6.2
5.7%
8.0%
0.5%
9.0%
-1.8
4.1
1.1
1.6
-3.7
2.4
0.9
1.2
2.0%
4.5%
5.4%
4.2%
1.9
1.0
0.2
0.6
1.5
0.3
11
-0.6
2.4%
7.0%
5.4%
3.1%
1.1
1.7
-1.4
-0.7
1.9
-2.6
-2.5
1.9
-
-
3.9%
4.6%
6.0%
0.3%
Notes: (I) Source: IMF. International Financial Statistics
(2) Bank of Japan, Economic Statistics Monthly; converted to dollars with period average yen-dollar exchange rate.
(3) Period average yen-dollar exchange rate.
34
reducing exchange volatility, while not hindering
longer-term trends.
Table 3 illustrates the development of Japanese
general government budget deficits, as a percent of
GNP, in comparison to the U.S. and Germany. The
rapid growth of these deficits and their large size,
both by historical standards in Japan and relative to
the U. S. , Germany and other major industrial countries, is a fairly recent phenomenon.
Japanese government budget deficits surged in
the mid-1970s, as Table 3 demonstrates. The rising
fiscal deficits are attributable to both cyclical and
structural developments in the pattern of revenues
and expenditures. On the revenue side, the 19741975 recession in Japan brought on a cyclical shortfall in government revenues, more so than in most
industrial countries, because Japan is highly dependent on corporate taxes, and consequently highly
variable corporate profits, for its tax revenue. The
structural problem on the revenue side is that the
Japanese income growth rate, and hence, the
growth of tax receipts, has slowed substantially
since 1973.
Bank of Japan bought (sold) U.S. $160 million in
foreign currency in the current month in response to
a one-percent appreciation (depreciation) ofthe yen
against the dollar during the March 1973-0ctober
1976 period. Argy (1982) calculates a somewhat
stronger response (U.S. $210 million) for a given
percent change in the effective (trade-weighted)
value of the yen over the March 1973-December
1979 period. Policy statements by Japanese central
bank officials do not refute these findings. 15
One implication of the Japanese leaning-againstthe-wind intervention policy, however, is that,
while it may influence relative government bond
supplies in the short-term, it will have little effect
over extended periods as intervention on either side
of the market is eventually reversed. This suggests
that month-to-month and perhaps, quarter-to-quarter, changes in the yen exchange rate may be influenced by Japanese intervention policy through this
channel, but that longer-term effects are probably
small. This is, of course, the intent of a leaningagainst-the-wind policy-to slow, but not to
reverse, exchange rate movements in the hopes of
Table 3
International Comparison of General Government
Fiscal Balance, 1972-81
(In percent of GNP)
1972
1973
1974
1975
1976
19n
1978
1979
1980
1981
Japan I
Receipts
Disbursements
Balance
United States 2
22.1
21.8
0.3
24.0
21.9
2.1
25.1
25.0
0.1
23.1
26.7
- 3.6
24.0
27.5
- 3.5
24.7
28.8
4.1
26.5
30.7
- 4.1
27.2
31.7
- 4.4
28.7
32.7
- 4.0
30.0
33.7
3.7
Receipts
Disbursements
Balance
31.4
31.7
0.3
31.5
31.0
0.5
32.2
32.5
- 0.3
30.6
34.9
- 4.2
31.3
33.5
- 2.1
31.6
32.5
0.9
31.5
31.5
31.6
31.1
0.6
31.8
33.1
1.3
32.6
33.5
1.0
Germany2
Receipts
Disbursements
Balance
38.7
39.2
0.5
41.2
40.0
1.2
41.5
42.9
1.4
40.8
46.6
- 5.8
42.3
45.9
3.6
43.5
45.9
- 2.4
43.3
46.0
- 2.7
I Fiscal year.
2 Calendar year.
35
42.9
45.8
- 2.9
-
42.8
46.3
3.5
Table 4
International Comparison of
Gross Private Savings
Less General Government Fiscal
Deficit, 1972-80
(percent of GNP)
Chart 1
Relative Japanese/U.S. Government Debt
Percent
45
40
35
30
25
20
15
10
5
0
Japan
United States
Gennany
1972
1975
1978
1980
31.7
15. I
:2L0
25.7
12.8
16.0
24.9
17.3
18.1
24.9
15.3
17.3
Notes: Calculated as gross private savings less general budget
deficit. as percent of GNP Japan data is for fiscal year;
U.S. and Gennan data cover calendar years.
1972
in private portfolios in comparison to the U.S. over
the last decade.
Another reason the model developed above is
particularly relevant for the Japanese case is that it
explicitly accounts for the influence of relative
financial wealth on the exchange rate. Japanese
financial wealth, similar to government debt, has
grown at a rapid pace over the last decade, and at a
rate much faster than that of other major industrial
nations. 16 This phenomenon is due both to the high
private savings rate in Japan, which has continued
unabated over the decade, and the sharp drop in the
growth of Japanese private domestic investment
since the 1973 oil-price shock. The combination of
the two factors has resulted in a large increase in
Japanese financial wealth that has been available to
finance domestic government budget deficits (see
Table 4) as well as to export capital (through current
account surpluses) to the rest of the world over the
greater part of the period. One advantage of the
present model is that it allows us to identify the
separate int1uences of relative wealth from relative
bond supply on the real exchange rate.
While it is true that the rapid growth of financial
wealth in Japan has largely "filled in" the financing
requirements of government budget deficits, it is
nevertheless useful to look at the pa..rtial influence of
each variable on the exchange rate. 17
On the expenditure side, the government sector
in Japan has grown rapidly in recent years, led by
increases in social security benefits, social assistance grants, and interest on the public debt. These
developments have increased the size of general
government expenditures from its historically small
percentage of GNP to a ratio approximately equal to
that of the U.S. in 1981-33 percent.
The net result of these developments is that the
government began issuing "deficit finance" bonds
in 1975 to cover the shortfall in revenues over
current expenditures. The amount of deficit-financing bonds issued by the government increased
rapidly from 1975 through the remainder of the
decade. Total government bond issues as a percent
of both general account expenditure and GNP
peaked in fiscal 1979-80. These developments have
correspondingly spurred the growth of Japanese
government bonds held privately. The ratio of outstanding government bonds to GNP increased in
Japan from 6% to 36% from the end of fiscal
1974/75 to the end of 1982/83. In less than a
decade, Japan moved from having a ratio of (central
government) outstanding bonds to GNP that was
among the lowest in industrial countries to one that
was among the highest. Chart 1 illustrates the
growth of Japanese national government debt held
IU. Empirical Results
exchange rates. Long-term real interest rates are
used as the interest rate variable in the model because expectations of the future real exchange rate,
qC, are based on an equilibrium current account
This section presents the empirical results from
testing the two-country real exchange rate model
given by equation (16) with monthly data for Japan
and the U. S., over the 1973-82 period of floating
36
condition that will hold only in the long run. 18
The real value ofthe yen/dollar in log form (q) is
calculated as the log of the spot yen/dollar exchange
rate less the log of the Japanese wholesale price
index plus the log of the U.S. wholesale price
index. Long-term real interest rates (r l,) are constructed from the nominal interest rate on long-term
governmental securities less a two-year centered
moving average of the monthly percent change in
the consumer price index. 19. Japanese government
bonds held privately (Bj) is measured by total
Japanese national government debt, net of Bank of
Japan and government agency holdings.
"World" financial wealth (W) is calculated as
the sum of U. S. base money, U. S. national government debt privately held, Japanese base money and
Japanese national government debt privately
held. 20 Japanese financial wealth (Wi) is calculated
as the sum of Japanese national government debt
privately held, Japanese base money, and the cumulative sum of Japanese current account surplus from
March 1973, the beginning of the floating rate period in Japan. Bj/W and wj/W state total Japanese
privately held bonds and financial wealth, respectively, as a percent of total financial wealth. 21
The current account surprise variable is the cumulative sum of the residuals from the equation regressing the difference in the Japanese and U.S.
current account (JCA-USCA) on six of its lagged
values and three lagged values of the real exchange
rate.
Estimation results are given in Table 5. Column
(4) of the table shows the fully specified model
given by equation (16), and columns (1)-(3) show
the sensitivity of the coefficient estimates to dropping particular variables from the regressions.
Turning to column (4), all of the signs of the variable coefficients conform to theoretical predictions,
and are significant at the 90% level of confidence or
higher with the exception of the current account
surprise variable. A one percentage point increase
in the Japanese long-term real interest rate is estimated to appreciate the real value of the yen by 0.77
percent, ceterius paribus. The U.S. real interest
rate estimate is significantly higher than its Japanese counterpart, however, and suggests that a one
percentage point increase will depreciate the yen by
1.35 percent.
The estimates for the yield differential determinants, relative Japanese debt (Bi/W) and relative
TableS
Regression Estimates of the Real Yen/Dollar Exchange Rate
(Monthly, March 1973-December 1982)
Explanatory Variables
Intercept
(1)
5.46
(145.80)
0.08
(- 0.13)
0.99
(1.96)
(2)
5.66
(130.90)
- 0.79
(- 1.91)
1.42
(3.20)
1.14
( 1.83)
1.47
(- 3.34)
(3)
5.44
(164.27)
- 0.09
(- 0.15)
0.97
(2.02)
-
LCA'
0.004
I
R2
Rho
aBS
.86
.81
.86
.91
118
"0
J 10
.87
.89
, '0
110
(4)
5.62
(110.90)
-
0.77
(-
1.81)
1.35
(2.96)
1.17
(1.86)
1.39
(- 3.19)
- 0.003
I.
.86
.82
118
Notes: (I) rl, (r~;) is constructed from nominal long-term rates less a twelve month centered moving average of monthly percentage
change in the Consumer Price Index. BJ/W is the ratio of Japanese national government securities to "world" private financial
wealth, proxied by the sum of Japanese and U.S. private financial wealth. WYW is the ratio of Japanese private financial
wealth to world private financial wealth. CA' is the cumulative current account surprise variable. The real yen/dollar rate in
log form is constructed as the log of the nominal yen/dollar rate less the log of the Japanese Wholesale Price Index (WPI) plus
the log of the U.S. WPI index. See statistical appendix for data sources and complete variable definitions.
(2) All equations are estimated with the Fair technique, with correction for first-order autocorrelation (il) and instruments for r i
and BYW. The t-statistics are in parentheses below each coefficient.
37
wealth (WJ /W), suggest that these factors also exert
an important influence on the yen rate. A one percentage point increase in the ratio of Japanese
national government debt to total financial wealth
depreciates the real value of the yen 1.17 percent. A
one percentage point increase in the ratio of Japanese financial wealth to total financial wealth, on the
other hand, appreciates the yen 1.39 percent. A one
billion dollar unexpected increase in the net Japanese-U. S. current account is estimated to appreciate
the yen by 0.3 percent. This coefficient is not statistically significant, however.
The first three columns in the table show the
results from regressing the real exchange rate on
Japanese and U.S. real interest rates alone (Column
1), real interest rates together with relative debt and
relative wealth (Column 2), and real interest rates
with the cumulative current account surprise variable (Column 3). All of the coefficient signs in the
regressions again conform to theory and, in addition, long-term U.S. interest rates, relative Japanese debt, and relative Japanese wealth are significant at the 90% level of confidence or higher. The
long-term Japanese real interest rate, however, only
becomes significant when relative debt and relative
wealth are included in the regression. The cumulative current account surprise variable, in contrast, is
only significant when these variables are excluded.
Overall, the regressions lend some support to the
real exchange rate model. Considering the length of
the period under investigation, and the great deal of
volatility the real yen-dollar rate has experienced,
the results may be viewed in a favorable light. Of
particular interest for our purposes is that relative
debt and relative wealth both enter significantly in
the regressions, and that the Japanese real interest
rate only becomes significant with the yield differential determinants included. This indicates that the
Japanese real interest rate is an important determinant of the real exchange rate, but that its influ~nce
can only be measured when the model is fully specified and other factors (relative debt and relative
wealth) are held constant.
To get a rough idea of the policy significanc¢of
the Bj/W coefficient estimate, consider the size of
the coefficient in relation to the total stocks<()f
Japanese government debt and total financial
wealth. For December 1982 values, a one percentage point increase in the ratio of Japanese debt to
total wealth would entail a U.S. $13.28 billion
increase in Japanese government bonds outstanding
in private portfolios (assuming financial wealth
remains unchanged). This increase causes an estimated 1. I percent depreciation in the real value of
the yen.
A comparison of this figure to the recent Japanese
budget deficit was 10,853 billion yen in 1982, or
approximately U.S. $43 billion calculated at the
period average yen/dollar exchange rate. At given
financial wealth and Japanese real interest rates, the
floatation of these additional government bonds to
finance this revenue shortfall would have caused the
real value of the yen to depreciate by an estimated
3 1/2 percent over the course of the year.
Turning to Japanese intervention, the yen was
generally weak in comparison to the dollar through
most of 1982 and, in response, the Bank of Japan
bought yen and sold dollars in the Tokyo foreign
exchange market. Assuming that the Bank of Japan
sold between $5-$9 billion in foreign exchange
over the year, the estimates suggest that this would
have appreciated the yen during the year by less
than one percent in real terms holding other factors
unchanged.
These examples serve to illustrate the large sums
involved if Japan wishes to influence the real value
of the yen through sterilized intervention operations. The sums are large because existing stocks.of
government bonds in private portfolios are large,
and very large purchases or sales of these assets are
involved in bringing about a significant change in
their relative supply. The examples also point out
that the large financial requirements of the central
government have caused new bond issues to dominate the limited domestic bond purchases by the
Bank of Japan needed to finance yen-support intervention operations in 1982. More generally, in the
Japanese case, it appears that the influence of sterilized intervention on the movements in the yen-dollar
real exchange rate since the mid-seventies has
probably been small. In addition, sterilized intervention may become even less effective as an
independent policy instrument. In the face of large,
and rapidly growing, privately held stocks of government bonds, it may take an enormous amount of
sterilized intervention to influence the exchange
rate.
Some words of caution regarding the interpreta38
bond issues may influence the exchange rate, and it
will work against the direct effect channeled
through the risk premium.
But, while the link between real interest rates and
real exchange rates is well-documented, there is
only scant evidence of a predictable link between
government bond supplies and real interest rates. In
the Japanese case, a recent empirical study by
Fukao and Okubo (1982) appears to refute the hypothesized positive link indirectly when it found no
evidence of such a link between government bonds
outstanding and nomina/long-term interest rates.
One explanation for their finding may be, as the
theory presented here suggests, that the foreign
exchange market absorbs some of the initial impact
resulting from government bond issues in Japan. In
the short run, the yen exchange rate is clearly more
flexible than Japanese long-term interest rates, a
reason being that Japanese long~term interest rates
have been subject to fairly rigid government controls. until recent years. Because of this rigidity,
the exchange rate may be the channel through which
relative yields adjust to reach a new equilibrium
following a shift in relative government bond
supplies. The empirical results do not refute this
hypothesis.
tion of these results are in order. First, while the
model appears to perform well overall by standard
goodness-of-fit (R2 ) measures, it has only moderate
success in tracking some of the more dramatic
swings in the real value ofthe yen. This is illustrated
in Chart 2 which shows actual and predicted values
of the real yen value (log) from the fourth regression
(Column 4) in Table 5. 22
A second point concerns the coefficient estimates
on the real interest rate variables. Both coefficients
are substantially less (in absolute value) than theory
suggests should be the case for long-term interest
rates. In addition, the Japanese real interest rate
coefficient is significantly less than that of the U. S.,
whereas theory predicts coefficient values roughly
equal in absolute value. These shortcomings in the
empirical estimates are important because. interest
rates play a central role in our model of exchange
rate determination. Both the generally low coefficient values and the asymmetry between Japanese
and U.S. variables shed some doubt on the plausibility of the underlying model. On the other hand,
the inherent difficulties in measuring expected
long-term inflation in both Japan and the U.S. may
explain these apparent inconsistencies.
Third, and perhaps most important, the model's
estimates only measure the direct or partial influence of relative debt on the exchange rate. To the
extent that additional bond issues increase domestic
real interest rates, the exchange rate will tend to
appreciate in value, and, thereby, offset some of the
initial downward pressure on the currency. That is,
budget deficits may cause real interest rates to rise
and appreciate the domestic currency. This constitutes an indirect channel through which govemment
Parameter Shift
The Japanese financial system has undergone a
process of rapid liberalization in recent years 23 that
has included the deregulation of interest rates and
relaxation of capital controls. These developments
suggest that Japanese and U.S. government securities. have probably been viewed by investors as
better substitutes during the latter part of the sample
period than previously, making the yield differential variable less pronounced and its determinants
less important in our exchange rate equation. To
investigate this proposition, we include a test to see
ifthe slope parameters on relative debt and relative
wealth have significantly changed from the 1973:03
-1978: 12 period to the 1979:Ql-1982:12period.The
a priori expectation is that both coefficients are
significantly less. in absolute value in the latter period than in the earlier period.
Test results are given in Table 6. Column (2)
presents estimates of the full model with the shift
dummy variables and, for purposes of comparison,
column (I) restates previous model coefficient
Chart 2
Real Yen/Dollar Exchange Rate
Log Scale
39
estimates. Neither parameter shift is significant at
the 90% level of confidence. However, the estimated coefficients for the earlier period do increase
substantially in absolute value-from 1.17 to 1.78
for relative debt and from -1.39 to -1.69 for relative
wealth-and the estimated coefficients in the latter
period approach zero. Both results are consistent
with our expectations. The estimated coefficients in
the latter period equal -0.48 [1.78 + (-2.26)]for
relative debt and -0.32 (-1.69 + 1.37) for relative
wealth.
These results suggest that the yield differential
variable may have become less important because
of the ongoing liberalization of the Japanese financial system. This implies that the relative supply of
government securities and relative financial wealth
will probably have less of an impact on the yen
exchange rate in the future than it had in the past. In
practical tenns, this means that the direct influence
of Japanese government budget deficits on the real
exchange rate may be less currently than what the
model estimates suggest was the case during the
greater part of the seventies. It also means, however, that sterilized intervention as a separate policy
instrument may be even less effective now than it
was during the earlier period.
From this viewpoint, a loss in effectiveness ofthe
sterilized intervention policy instrulTleIltlTlay have
been a necessary cost associated with the increased
internationalization of the Japanese financial
system. The results are inconclusive, but they do
suggest that even the limited effectiveness of this
policy instrument may overstate its importance.
West Gennany also has generally unregulated
capital flows. Consistent with the results presented
above, a recent study of the German case byObstfeld (1982) also found that sterilized intervention
Table 6
Regression Estimates of the Real
Yen/Dollar Exchange Rate
with Parameter Shift Dummy between
1913:03-1918:12 and 1919:01-1982:12
Explanatory Variables
Intercept
(1)
5.62
(109.57)
- 0.77
(- 1.81)
1.35
(2.96)
1.17
(1.86)
1.39
(- 3.19)
.003
(- 1.18)
D*(BifW)
D*(Wj/W)
(2)
5.62
(108.59)
- 0.95
(- 2.01)
1.61
(3.39)
1.78
(1.77)
1.69
(- 2.94)
.003
(- 1.35)
- 2.26
(- 1.54)
1.37
I
R"
Rho
OBS
.86
.82
118
.86
.81
118
Note: See Notes for Table 4. Dummy variable equals zero for
1973:03-1978: 12 period and unity for 1979:01-1982: 12.
has only a small effect on the exchange rate.
Through a series of experiments simulating a structural model of Gennan asset markets and prices, he
concluded that the Gennan central bank's " ... ability
to influence the exchange rate without altering
monetary conditions is very limited. It is accurate to
assert that the sterilized intervention considered
above has essentially no effect on the exchange
rate." (p. 24). This conclusion for Gennany is
consistent with the empirical results obtained in the
case of Japanese sterilized intervention in this study.
VI.. Conclusions and Policy Implications
This paper has analyzed how' sterilized foreign
exchange market intervention works< within a
simple model of real exchange rate determination.
We demonstrated that thisfonnofiritetvention
changes the relative supply of bonds denominated
in domestic and foreign currency. It willonlyinfluence the exchange rate when investors< view the
bonds as imperfect substitutes and relative yields
adjust as a consequence.
Because the central bank does not allow base
money to change in response to its foreign exchange
purchases and sales, sterilized intervention maybe
of limited usefulness as a separate policyinstrument. Nevertheless, the distinction between sterilized and monetary intervention is important because
it isolates the direct effects of intervention operations on the exchange market from those of monetary policy operations.
40
existing stocks of Japanese and U.S. government
bonds outstanding. Another complication is that the
Bank of Japan's intervention operations since the
mid-seventies, though sizable by international
standards, have been small relative to Japanese
government bond issues financing budget deficits.
In addition, some tentative evidence indicates that
the effectiveness of sterilized intervention in Japan
is further limited by the financial market liberalization measures implemented in recent years. These
measures have tended to increase the substitutability between Japanese and U.S. bonds, and reduces
the effectiveness of sterilized intervention.
It is difficult to draw strong policy conclusions
about the overall usefulness of sterilized intervention from these results, however. We have used a
very simple model in the analysis, and have identified only one channel through which sterilized
intervention may influence the exchange rate.
Sterilized intervention may influence the exchange
rate through other channels as well. For example,
sterilized intervention may have a "demonstration" effect, that is, it may influence expectations
about underlying economic conditions or policies.
This in tum might directly shift the expected future
real exchange rate, qe, and the current rate. In
addition, the results presented here are based on
monthly data while central bank intervention objectives may be of a shorter duration. Japanese intervention, even when sterilized, may have a considerable influence on short-term exchange rates (for
example, daily) that is not picked up by monthly
data.
Nevertheless, these results do support the simple
asset market model of exchange rate determination
presented here and suggest that the Bank of Japan's
sterilized intervention operations have had only a
small influence on the yen-dollar real exchange
rate. However, it appears likely that sterilized
intervention will become an even less potent policy
instrument as the Japanese financial system becomes· more closely integrated with its western
counterparts.
Sterilized intervention has two important limitations in particular. First, while sterilized intervention may influence the relative supply of government bonds at the margin, bond issues floated to
finance government budget deficits have played a
predominant role in changing relative bond supplies. In theory, the shift in the relative supply of
bonds is what influences the exchange rate, not
whether the source of the change is due to foreign
exchange operations or to finance budget deficits.
Sterilized intervention will shift relative bond
supplies to a greater extent than bond issues to
finance deficits for a given purchase or sale of
domestic bonds (because foreign bonds privately
held will correspondingly increase or decrease with
central bank domestic bond purchases or sales in the
intervention case). For a given shift, however, the
simple asset model predicts an equal influence on
the exchange rate.
Second, is the related point that the central bank's
ability to use sterilized intervention as an effective
policy instrument will be smaller the larger the
outstanding stocks of government liabilities. Quite
simply, the rapid growth of government bonds since
the mid-seventies has correspondingly increased
the amount of sterilized intervention necessary to
bring about a given exchange rate change (assuming
the elasticity of substitution between foreign and
domestic bonds remains unchanged) in Japan. In
this sense, the central bank must be willing to
commit ever growing resources in pursuit of their
exchange rate objectives.
A simple model of real exchange rate determination, applied to Japanese-U.S. data over the 197382 floating rate period, provided some interesting
results. The empirical results generally support the
theoretical model and suggest that the relative
supply of government bonds has influenced the
yen-dollar real exchange rate. However, the coefficient estimates also suggest that a very substantial
amount of sterilized intervention may be necessary
to bring about a. noticeable exchange rate movement. This result is primarily due to the large
Data Appendix
Data Sources: International Monetary Fund, lnterq
national Financial Statistics (lFS); Bank of Japan,
Economic Statistics Monthly (EMS); U.S. Treasury
P
Department, Treasury Bulletin.
41
real yen-dollar exchange rate (log) =
log(s) -log(P) + 10g(P*);
Japanese Wholesale Price Index,
(IFS, line 63);
p*
rj
It
[US
It
W
U.S. Wholesale Price Index, (IFS,
line 63);
Japanese long-tenn real interest rate;
weighted average of 5-10 year bond
rates in Japan (Source: FRB Macrodata library); less expected inflation
(see text for construction of expected
inflation)
U. S. long-tenn real interest rate;
IO-year U.S. treasury bonds (Source:
FRB macrolibrary); less expected
inflation (see text for definition)
Japanese national government debt
held privately; equal to total national
government debt less government
and Bank of Japan holdings. Converted to billion U.S. dollars with
period average exchange rate.
Source: ESM Table: "National
Government Debt. "
U.S. and Japanese financial wealth
proxy; W=Bj+Bus+Mj+M uS
U. S. central government debt held
privately; calculated as (I) "Estimated Ownership of Public Debt
Securities by private investorstotal privately held" (Table OFS-2)
JCASUM
2:CA'
less (2) "selected U.S. liabilities to
foreigners-total, official institutions" (Table IFS-2) less (3) "nonmarketable U. S. Treasury bonds and
notes issued to official institutions
and other residents of foreign countries" (Table IFS-3). Treasury
Bulletin
Bank of Japan Reserve Money, (IFS
line 14); (converted to billion U.S.
dollars with period average exchange rate).
U .S. Federal Reserve, Reserve
Money, (IFS line 14);
Japanese financial wealth; wj=
Mj + Bj + JCASUM
cumulative sum of Japanese current
account from 1973:03 (billion U.S.
dollars) (ESM) plus $11.5 billion
(U.S. liabilities to Japan, 1973:03,
IFS line 9a.d.)
cumulative current account surprise;
cumulative sum of residuals from
regressing Japanese current account
less U. S. current account on six own
lag values and three q lag values
(from 1973:03).
FOOTNOTES
ium in his empirical tests, however.
1. Central banks generally hold their foreign reserve
assets which are used for intervention operations in the
form of government interest-bearing securities, primarily
U.S. Treasury securities, as the dollar is the predominant
intervention currency.
6. The covered interest rate parity condition, equation (2),
generally holds in Japan once transactions costs are taken
into account. See Sea (1981).
7. The yield differential is usually called the risk premium in
the exchange rate literature. This is because risk adverse
speculators must expect some profit if they are to hold an
uncovered futures contract (and bear the risk associated
with unexpected exchange rate fluctuations) which the
interest rate arbitragers have purchased or sold to hedge
their portfolios against exchange rate risk.
2. Note that MBd created through open market purchases
of government securities does not necessarily equal the
total monetary base. Base money may be supplied through
central bank loans to commercial banks or through open
market operations using commercial bills, for instance.
3. See Dooley and Isard (1979), p. 5, for a discussion of
this issue.
8. This condition also implicitly sets the condition for goods
market equilibrium and has been introduced in this context
by Kouri (1976) and Hooper (1983), amongst others. Note
also that the sustainable long-run current account is
assumed constant in this model.
4. See Mussa (1979) and J. A. Frankel (1981) for convincing arguments in support of an asset market approach as
opposed to the more traditional "flow" models of exchange
rate determination.
5. Isard (1980a, 1980b, 1982) derives this model in a
similar fashion (in both nominal and real values) and terms
his an "accounting identity" approach because it is based
on an arbitrage condition and several identities. It is also
derived and tested for a weighted average of the dollar's
real value by Hooper (1983). Hooper ignores the risk prem-
9. A more complicated function is derived in Hooper and
Morton (1982). They attempt to distinguish between transitory and permanent elements in the current account.
10. The asset demand function employed here is a simplification of Frankel's (1982) general approach. Frankel
42
16. By the national income accounting identity, it can be
shown that the excess of private savings (S) over private
domestic investment (I) equals the current account surplus
(X-M) plus the government budget deficit (G-T): S-I = (X-M)
+ (G - T). Beyond running large government budget deficits
(measured either by the central or consolidated general
government accounts), Japan has run a current account
surplus over the greater part of the last decade and has
generally been a net exporter of capital to the rest of the
world.
extends the single foreign demand for domestic securities
function developed here into two components: a "focus"
foreign country demand function and a third-country investor demand function.
11. The few studies that have embedded exchange risk
determinants into empirical exchange rate models have
generally employed "abbreviated specificati9ns". (e.g.
Hooper and Morton (1982), p. 45) because of data considerations. These attempts have met with limited success in
modeling the risk premium, however. Misspecification of
the model may be one reason for the generally poor results
heretof()re. ThiS. model derives the determinants of the risk
premium along theUnes of Dornbusch (1980), Dooley and
Isard (1979) and Frankel (1982), and employs this more
complete specification in the exchange rate equationestimates. This formulation presents the risk premium as a
function of both the relative supply of government bonds
demonimated in domestic anf foreign currency and the
international distribution of wealth among investors.
17. See Hang-Sheng Cheng, "Crowding-Out: Japanese
Experience," Federal Reserve Bank of San Francisco
Weekly Letter, March 19, 1982, for an engaging discussion
of the "crowding out" versus "filling-in" issue in the Japanese context. The common opinion expressed by government publications in Japan is that there is no evidence of
government credit demands croWding out private investment thus far, but it is feared that it may become a problem
in the future if budget deficits are not reduced. See
Economic Survey of Japan 1979/1980.
12. Another explanation of the adjustment process given
changes in relative asset supplies or relative wealth considers therale ofprivate capital flows. An increase in domestic
assets at unchanged interest rates, for instance, will
increase the proportion of home securities in private portfolios beyond the ratio desired by investors. As investors
begin to sell home securities in favor of foreign securities in
an attempt to bring portfolios back into balance, the resulting capital outflows from the domestic country puts downward pressure on the exchange rate. Increases in relative
domestic wealth, On the other hand, will shift upward the
demand for home securities, cause an incipient capital
inflow and appreciate the domestic currency. If assets are
considered perfect substitutes, Le., investors do not differentiate between securities donominated in the home and
foreign securities, then neither relative asset supplies nor
relative wealth should influence the exchange rate through
this channel (Le., through the risk premium or "differential
return" channel).
18. The Fair estimation procedure is employed in all regressions. This is a statistical technique designed to provide Consistent coefficientestimates of an equation With
both autocorrelated error terms and endogenous explanatory variables. Which variablesare assumed endogenous
is particularly important because the empirical results are
sensitive to this choice. Japanese relative bond supplies
and Japanese real interest rates are treated as endogenous variables in the short-run. To the extent that Bank of
Japan reacts to real exchange rate movements in its intervention operations, Japanese bond supply will be correlated with the error term in the. exchange rate equation.
Interest rates in Japan, both nominal and real, may also be
systematically influenced by real exchange movements
and are treated as an endogenous variable in the model
estimation. The instruments for both endogenous explanatory variables are formed from the predicted values of a
reduced form equation which includes contemporaneous
and lagged exogenous variables i.n the system (r US, WVW,
CAS), the lagged endogenous variables (q, B/W, ri) and a
time trend. See Fair (1970).
13. This measures Japanese government securities not
held by the Bank of Japan or other Japanese government
agencies (e.g., Trust Fund Bureau, Industrial Investment
Special Account, Postal Life Insurance and Annuity). Of the
total government debt held privately in December 1982,
99% was held in long-term instruments (internal bondsconsisting of construction bonds and deficit-finance
bonds).
19. Thisrreasure. is similar to Hooper (1983) and Shafer
and Loopesko (1983).
20. The financial wealth. measure has been broadened
from that cJefined in the thaoreticalsection. To private bond
holdings have been added (U.S. and Japan~se) base
money. This adjustment has been made to help distinguish
better empirically between domestic bond supply and
domestic financial wealth.
21. All Japanese data used in computing Bi, Wand Wi are
converted from yento U.S. dollars at the average month-tomonth yen/dollar exchange rate.
14. QUirk(1977)argues that the foreign exchange funds is
the most appropriate proxy for Japanese official intervention because it includes "hidden intervention;' Le., Bank of
Japan foreign exchange deposits with its member commercialbanks, and excludes certain transactions with the
U.S. military in Japan which are includedIn officialreserve
figures.
22. A related point concerns the structural stability Of the
exchange rate equation and estimated coefficients to different sample periods, Changes in variable definitions, and the
choice of estimation technique. Exchange rate models
15.• See,for instance, "A Japanese View of Exchange Rate
Policy" written in.1982 by ShijuroOgata, Bank ofJapan
Executive Director, for Aussenwirtsehalf of the University
ofSt. Gallen.
43
have generally had poor out of sample forecasting performance in recent years, and have demonstrated significant
structural instability. The results here should therefore be
interpreted with this important qualification in mind.
23. See Charles Pigott's "Financial Reform in Japan," in
Federal Reserve Bank of San Francisco Economic
Review, Winter 1983, for a comprehensive review of the
process of liberalization in Japanese financial markets.
REFERENCES
Argy, Victor. Exchange-Rate Management in Theory and
Practice, Princeton Studies in international Finance,
No. 50, Princeton, 1982.
International Monetary Fund. International Financial
Statistics, September 1973, vol. 26, No.9-May 1982,
Vol. 35. No.5.
Bank of Japan. Economic Statistics Monthly, January
1974, No. 322-January 1982, No. 418.
Cheng, Hang-Sheng. "CroWding Out: Japanese Experience." Federal Reserve Bank of San Francisco
Weekly Letter, March 19, 1982.
Isard, Peter. "Expected and Unexpected Changes in
Exchange Rates: The Roles of Relative Price Levels,
Balance-of-Payments Factors, Interest Rates and
Risk." International Finance Discussion Papers, No.
156, Federal Reserve Board, April 1980. (a).
Dooley, Michael and Peter Isard. "The Portfolio Balance
f
Model 0 Exchange Rates." International Finance
Discussion Paper, No. 141, Federal Reserve Board,
May 1979.
Isard, Peter. "Factors Determining Exchange Rates: The
Roles of Relative Price Levels, Balance of Payments,
Interest Rates and Risk." International Finance Discussion Papers, No. 171, Federal Reserve Board,
December 1980. (b).
Dornbusch, Rudgier. "Expectations and Exchange Rate
Dynamics." Journal of Political Economy, 1976, vol.
84, no. 61.
Isard, Peter. "An Accounting Framework and Some Issues
for Modelling, How Exchange Rates Respond to the
News." International Finance Discussion Papers, No.
200, Federal Reserve Board, January 1982.
Dornbusch, Rudgier. "Exchange Risk and the Macroeconomics of Exchange Rate Determination." Paper
prepared for the Conference on the Internationalisation of Financial Markets and National Economic
Policy, New York University, April 10-11, 1980.,
Kouri, Pentti J.K. "The Exchange Rate and the Balance of
Payments in the Short-Run and the Long-run: A Monetary Approach." Scandinavian Journal of Economics, 78 (May 1976): 280-304.
Fair, Ray. "The Estimation of Simultaneous Equation
Models with Lagged Endogenous Variable and First
Order Serially Correlated Errors."Econometrica,
1970,38:507-516.
Mussa, Michael L. "Empirical Regularities in the Behavior
of Exchange Rates and Theories of the Foreign
Exchange Market." In Policies for Employment,
Prices, and Exchange Rates, edited by Karl Brunner
and Allan H. Meltzer. Carnegie-Rochester Conference
Series on Public Policy, vol. 11, (1979).
Frankel, Jeffrey. "The Diversibility of Exchange Risk."
Journal of International Economics, 1979, 9: 379393. (a)
Frankel, Jeffrey. "On the Mark: A Theory of Floating
Exchange Rates Based on Real Interest Differentials."
American Economic Review, 1979, 69:610-22. (b)
Frankel Jeffrey. "Tests of Monetary and Portfolio Balance
Models of Exchange Rate Detenmination." Revised
February 1982. Written for Bellagio, Italy NBER conference January 25-29, 1982.
Obstfeld, Maurice. "Exchange Rates, Inflation and the
Sterilization Problem: Germany, 1975-81" NBER
Working Paper Series, No. 963, August 1982.,
Otani, Ichiro and Siddharth Tiwari. "Capital Controls and
Interest Rate Parity: The Japanese Experience. IMF
Staff Papers, 1981: 28.
Piggot, Charles. "Financial Reform in Japan." Federal
Reserve Bank of San Francisco Economic Review,
No.1, Winter 1983, 25-46.
Frenkel, Jacob A. "Flexible Exchanges, Prices, and the
Role of 'News:' Lessons from the 1970s." Journal of
Political Economy, 1981, vol. 89, no. 4.
Quirk, Peter. "Exchange Rate Policy in Japan: Leaning
Against the Wind." IMF Staff Papers, 1977, 24:642664.
Fukao, Mitsuhiro and Takashi Okubo. "International Linkage of Interest Rates: The Case of Japan and the
United States." Bank of Japan Discussion Papers
Series No. 13., June 1983.
Seo, Jun'ichiro. "The Efficiency of Japan's Foreign Exchange Market and Features of Recent Yen Rate
Movements." Bank of Japan Discussion Paper Series
No.9, October 1981.,
Hooper, Peter. "Movements in the Dollar's Real Exchange
Rate over Ten Years of Floating: A Structural Analysis." unpublished paper prepared for the Third International Symposium on Forecastir:1g. Philadelphia,
Pennsylvania, June 7-8,1983.
Shafer, Jeffry R. and Bonnie E. Loopesko, "Floating
Exchange Rates After Ten Years." Brookings Papers
on Economic Activity, 1983.
Working Group on Exchange Market Intervention Established at the Versailles Summit of the Heads of State
and Government June 4-6, 1982. "Report of the Working Group on Exchange Market Intervention," March
1983. Chainman Philippe Jurgensen.
Hooper, Peter and John Morton. "Fluctuations in the Dollar:
A Model of Nominal and Real Exchange Rate Determination."Journal of International Money and
Finance, 1982, 1:39-56.
44
Indicators of Long-Term
Real Interest Rates
Charles Pigott*
Longer term real interest rates cannot be measured directly, but their
movements can be estimated from economic indicators they affect, particularly foreign exchange rates and nominal interest rates. An increase
in U.S. nominal.interest rqtes that is accompanied by arising dollW
indicates that U.S. longer term real interest rates probably also have
risen. On this basis, the unprecedentedly high level ofthe dollar in recent
years strongly suggests that U.S. long-term real interest rates remain
very high by historical standards.
Since October 1979, when the Federal Reserve
announced a major change in its operating procedures,. interest rates here and abroad have fluctuated
to a degree unprecedented in post-war experience.
These fluctuations have generated great controversy, both.about their origins and their consequences.
Most perplexing of all have been the gyrations in
longer-terminterest rates, particularly their apparent tendency to vary with seemingly shorHerm
disturbances in the markets. I This turmoiland confusion has come· at a particularly unwelcome time,
as financial innovation and deregulation sometimes
have made. it more difficult to predict the impact of
the monetary aggregates .targeted by the Federal
Reserve, and· hence increased the need for other
indicators of the effect of policy on the economy.
These circumstances have underscored the need
for measures of medium and long-tenn real interest
rates andexpeqted inf1<ltiqn. Inth~ory,mediumand
long~term relllinterestrates are importantdetenninants of investment and other real spending decisions, Knowledge of their level could be helpful in
gauging the future course of economic activity, as
well as the .effect of current monetary. and fiscal
policies on. the economy. Inflation anticipated over
the next several years would provide an indication
of public perceptions about the future course of
monetary policy, and thus about the credibility of
the authorities' public commitments to maintain
price stability. Unfortunately, it is very difficult to
measure lbnger-tenn real interest rates or expected
inflation, mainly because inflation expected over
the next several years need not depend in any predictable way on past trends.
The basic objective .of this paper is to demonstrate a practical method for measuring medium and
long-term real interest and expected inflation rates
for the U.S. This methbd uses several economic
variables affected by real interest rates and/or
expected inflation as "indicators" of their movements. Included among these variables are the spot
and forward exchange values of the dollar, which
are shown to be closely related to long-term real
interest rates and .expected inflation .•• Estimates of
longer-term real interest rates and ex~ctedinfla
tion can then be calculated from weighted averages
of the indicators. As explained in the next section,
underlying this approach is the observation that real
interest rates and expected inflation have verydifferent impacts on certain other financial variables,
such as exchange rates. Hence, the way in which
these variables move when nominal interest rates
vary provides a clue about the extent to which real
interest rates and expected inflation have changed.
The next section describes the relations among
*Senior Economist. Federal Reserve Bank of San
Francisco. Laura Leete and Mary-Ellen BurtonChristie provided valuable research assistance for
this article.
45
in Section II. One important finding is that the
variability oflong-term real interest rates has apparently increased dramatically since the change in
Federal Reserve operating procedures in 1979.
Another is that long-term real interest rates have
remained relatively high in 1982 and 1983, despite a
substantial fall in nominal interest rates.
real interest rates and· expected inflation and the
financial variables used as their indicators. An intuitive description of howthe indicators can be used to
measure real interest rates (and expectedinflation as
well) is also given. A more precise and technical
description of the approach is given in the Appendix. Our estimates of the actual variations in monthly real interest rates over 1976-mid-1983 are given
I. Indicators of Real Interest Rates
interest rates on the economy thus will depend upon
the extent to which they reflect changes in real rates
or in expected inflation. For this reason, real interest rates and inflation premia are generally more
useful to know than nominal rates alone.
Only nominal interest rates are actually quoted in
financial markets, however. Their real and expected
inflation components are not directly observable.
Plainly, there is no way to determine from changes
in nominal interest rates alone how much these
components have varied.
Thus to measure real interest and expected inflation rates requires some information in addition to
that provided by nominal interest rates. A common
approach to this problem is to use an independent
measure of expected inflation. For example, inflation over the near-term future is generally most
closely related to that experienced in the recent past.
The inflation premium on a short-term security can
often be approximated by the current trend in actual
inflation, providing a rough measure of the shortterm real interest rate. On this basis it seems fairly
clear that U.S. short-term real interest rates have
fluctuated considerably over the last several years,
much more so than during the 1970s. 3
Unfortunately, this approach isnotappropriateto
the measurement of medium and longer-term real
interest rates. Inflation expected over the coming
years depends critically .llpon the macroeconomie
policies authorities follow in the future. Public perceptions about these future policies-indeed. any
reasonable guess about them-need not be. related
in any obvious or dependable way to past trends,
and therefore are apt to be extrememly difficult to
gauge correctly. Who, after all, can pretend to know
with any confidence what the stance of monetary
and fiscal policies will be several years from now?
Any interest rate can be conceptually divided into
two parts: an inflation premium and a (before tax)
real interest rate. The inflation premium is equal to
the amount of inflation expected over the life of the
investment and serves to compensate for the erosion
of the purchasing power of the funds lent. For
example, an individual who lends $100 for one year
at a 10% rate is not really better off at the end of the
year if inflation during the year is also 10%; then the
$110 repaid at the end of the year buys the same
amount of goods and services as the amount lent
could have purchased a year earlier, and so no real
return on the investment is gained. 2
The rea. interest rate, which equals the nominal
rate less the inflation premium, thus measures the
amount of additional purchasing power an investment yields. So if the nominal interest rate were
12% while inflation was expected to be 10%, the
real interest rate would be 2%. This relation can be
written for reference as:
iu,(n) = ru,(n) + IIu,(n)
(I)
where iu(n) is the U.S. nominaHnterest rate on a
n~year security, ru(n) is the corresponding U. S. real
interest rate,· and IIu(n) is the expected inflation rate
overthe nextnyears, thatis, the inflation premium.
The real interest rate and the inflation premium
are likely to> have very different impacts on economic behavior. EconomiC theory implies tha.t individuals' and businesses' real spending decisions are
influenced by the real interest rate, but little, if at
all, by the inflation premium, Inflation expectations, as reflected in the inflation premium,are
likely to be important determinants of wages and
prices set in contracts, besides serving asa gauge of
the credibility of authorities' policies to ensure price
stability. The effects of fluctuations in nominal
46
Indicators
An alternative approach is to look for economic
variables whose movements provide clues about the
variations in real interest rates and/or expected inflation, and hence serve as indicators of their
values. In principle, any variable that is affected by
real interest rates or expected inflation rates could
serve as such an indicator. In this sense, nominal
interest rates are indicators of their real and expected inflation components.
Particularly helpful as indicators are financial
variables which react differently to real interest
rates than to expected inflation. Suppose that a
certain financial variable tended to increase when
real interest rates rose, but generally was unaffected
by fluctuations in expected inflation. Then a rise in
nominal interst rates that was accompanied by an
increase in this variable would suggest that real
interest rates had increased. A variable that was
affected by expected inflation but not by real interest ratescouldbe;\lsed in an analogous fashion.
Admittedly, no particular indicator is likely to
provide a completely accurate measure of either real
interest rates or expected inflation. Still, it ought to
be possible to use several such indicators to estimate, Or approximate, these components of nominalinterest rates. This approach, which attempts to
'read' the signals provided by financial markets, is
the one taken here.
inflation rates expected to prevail in the "longrun," that is, N years from now.
In the long-run though, the real interest rate is
mainly determined by the productivity of capital,
which in tum reflects the savings decisions of
households, businesses, and government, the
growth of the labor force, and the rate of progress of
technology. Generally these conditions change
slowly, so that the expected Long-run real interest
rate (as reflected in the forward interest rate) can be
regarded as essentially constant when considering a
period of several years. Variations in current real
interest rates can be viewed as resulting from non·
persistent imbalances in supply and demand in
money and credit markets. For example, economic
theory suggests that because of the lag' between
money and inflation, increases in money growth
temporarily lower real interest rates by raising real
balances; real interest rates return to their original
values once inflation "catches up," however. 5
This reasoning implies that changes iin the longterm forward interest rate mainly reflect shifts in
long-run expected inflation. So arise in the forw¥d
rate corresponding to ten years in the future would
measure the change in inflation expected to prevail
ten years from now, or
(2)
where EJlut+Nis inflation expected' to prevail
beginning N years in the future. The forward rate
also provides a more indirect indication of inflation
expected to prevail over the next ten years, that is of
the inflation premium in medium and long-term
nominal interest rates. The reason is that an increase
in inflation expected ten years from now suggests
that inflation over the next several years has also
increased. Thus it is more likely that an increase in,
say, the 5. year nominal interest rate reflects an
increase in expected inflation over the next five
years if the forward interest rate has also increased
than ifit has not.
Conversely, a rise in the nominal n-year interest
rate relative to the forward interest rate is more
likely to signal an increase in the real interest rate
than would an increase in the nominal interest rate
taken by itself. Hence, the change in the difference
between the rate on a n-period asset and the forward
rate,
ButWhat Indicators?
Changes' in interest rates expected to prevail in
the distant future ("long-run") are apt to be especially good indicators of expected Long-run inflation. Consider the nominal (say one-year) interest
rate now (at t) expected to prevail 'many,, or N,
years in the future. This will be referred to as the
forward· interest rate.' and..denoted .fiu t (it. being
understood that it is the forward rate corresponding
to many years in the future).
(Etiut+Nstandsfor the "expected value" of ill t+N
based on information available at t). This can be
approximated from the term structure of nominal
interest rates, since long-term rates are approximately averages of expected future shorter-term
rates. 4 As with any nominal interest rate, the
forward rate is composed of the real interest arid the
47
I I: Ildiu,(n) == Iliut(n) - Miu,
(4)
where e t is the current foreign currency price of the
dollar (expressed in logarithms) and Ete,+n is its
expected value n years from now.
This relation between nominal interest rates and
the nominal exchange rate is easily converted to one
between real interest rates and the real exchange
rate_ The real exchange rate, x" is simply the
nominal exchange rate 'deflated' by the ratio of the
foreign to the U.S. price level:
is apt to be a better indicator of variations in the
n-year real interest rate than changes in the nominal
interest rate itself. This indicator is composed of
changes in the real interest rate plus changes in the
difference between inflation anticipated over. the
next n years and that expected in the longrun.
Ildiu,(n) =Ilru,(n)+ Ildllu,(n),
where dIIu,(n)=IIu,(n)- E,IIu'+N.
(3)
Thus this new indicator effectively removes from
nominal interest variations that portion Of shifts in
expected n-year inflation that simply reflect movements in anticipated long-run inflation. Since inflation expected over the next several years is apt to be
closely related to long-run inflation. expectations,
this implies that real intere~ rates .are likely to
account for a larger proportion of the variationsin
the indicator II than those of the nominal interest
rate. This suggests that II will be the better indicator
of real interest rate movements (although by no
means an exact one). 6
x, = e, + (pf, ~ pu,)
where pf and pu are the logarithms of the foreign
and U. S. price levels.
The real e~change rate measures the value of
foreign goods and services in terms of our own, or
the rate at which U.S. and foreign products can be
exchanged for one another. Suppose a 'basket'. of
U. S. goods sells for one dollar (our price level is
one) while a 'basket' of German goods sells for one
mark. Then. if the nominal exchange rate is 2 marks/
dollar, 2 baskets of German goods are needed to
obtain one basket of U. S. products. Hence, the real
exchange rate for the dollar is two.
As this suggests, the real exchange rate is . a reflection of the relative value of U.S. versus foreign
products. Ultimately, this rate will be determined
by supply and demand conditions in product and
factor markets. Furthermore, in the long-run, the
level of the real exchange rate should be largely
unaffected by inflation (since inflation's effect on
relative prices is neutral, at least approximately) or
by real interest variations (since these result from
temporary disturbances in financial markets).
Subtracting the U.S. minus the foreign expected
inflation rate from (2) and rearranging gives,
Exchange Rate Indicators
The foreign exchange value of the dollar is
closely related to U.S.-and foreign~interest
rates simply because in comparing· the yields on
investments in different currencies an individual
must take account of the expected change in the
exchange rate between them .. For example, if the
interest rate on a one-year German-mark denominated7security were.5 percent while the mark were
expected to appreciate by 3 percent over the year vis
a vis the dollar, its expected yield in dollars would
be 8 percent.
Because of the risk that exchange rates will not
change by exactly thearnolmtorigin.allyanticipated, the expected dollar yields on securities identical in all respects except the cllrrencie~they are
denomiriated in may differ. 7 However available
evidence suggests that in the absence of •capital
controls, such currency 'risk' premia are not very
large, at least among the US. and other major
industrial nations. 8 Thus the difference between
U .S.and foreign interest rates for a given maturity
can be viewed as a reasonable approximation of the
expected change in foreign currency value of the
dollar, expressed at an annual rate:
ru,(n) - rf,(n) = (l/n) [xt - Etx,+n]
or
(5)
where E,x'+n is the future real exchangerate expected to prevail after n years. The relation shows that
the n-year real interest differential effectively measures the divergence between the current real exchange rate. and that expected to prevail at maturity.
This relation also implies that increases in the
long-term U.S.-foreign real interest differential
48
tors of the real and expected inflation portions of the
long-tenn nominal interest rate, namely changes in:
the n-year nominal interest rate relative to the forward interest rate; the current real exchange rate;
and the (n-year) deflated forward exchange rate.
The relations between these indicators and real interest rates are summarized in Table 1. The likely
increase in the real interest rate accompanying· a
given rise in the nominal interest rate (iu) is greater:
(i) the larger the accompanying rise in the interest rate indicator II;
(ii) the larger the accompanying increase inthe
real exchange value of the dollar, 12;
(iii) the smaller the decline in the forward exchange rate indicator, 13 (since a decline in y
suggests a rise in expected U,S. inflation).
These observations suggest that movements in real
interest rates and expected inflation can be estimated from variations in the indicators. An obvious
course is to use weighted averages of the indicators
as these estimates, say:
raise the current real exchange rate, Xt. For
example, an increase of one percentage point in the
(annualized) 5 year U.S. real interest relative to
abroad, all other factors the same (that is, no change
in the expected 'long-run' real exchange rate) will
raise the real value of the dollar by five percent. In
this sense, variations in long-tenn real interest rates
cart have very substantial impacts on actual real
exchange rates. 9. It follows that variations in the
current real exchange rate are an indicator of the
U.S. (and foreign) long-tenn real interest rates; a
rise in x t suggests that our real interest rate may have
gone up. 10
12: Llx t= n[Llrut(n)~ Llrft(n)] + LlEtx t+n
Finally, the two indicators defined above can be
combined with the foreign interest rate to yield an
indicator of the change in our expected inflationagain· expressed relative to that anticipated for the
distant future. Define
Yt=xt+n[dift(n)-diut(n)]
Llrut(n)=WILldiut(n) + W2Llxt + W3LlYt. (6)
where the foreign interest rate indicator, dift(n), is
defined analogously to that for the U.S. Now using
the expressions for the real exchange and interest
rate indicators (see II and 12) gives:
Ideally the weights used should reflect the average
degree to which the real interest rate changes with
the indicators. For example, WI should reflect the
average change in the real interest rate corresponding to a given change in the interest rate indicator,
all other indicators being constant.
13: LlYt=n[:.:ldJ1ft(n)-LldIlu t(n)] + LlEtx t+n
where again dIlft(n) is analogous to the corresponding U~S. variable. The variable defined in 13 can be
regarded as a third indicator of the U.S. long-tenn
real interest rate. The reason is that its variations
provide infonnation about the expected inflation
component of the U.S. nominal interest rate indicator, II, and hence indirectly about its real interest
component. In particular, a rise in this indicator
suggests afall in U.S. expected inflation, and therefore an increase in the U.S. real interest rate for any
given value of the nominal interest rate indicator.
This third indicator will be referred to as the deflated 'forward exchange rate,' since it is effectively the n-year forward excha.nge value.of the dollar
(the currently quoted value of the dollar for delivery
n years from now) deflated by the current U.S.foreign price level ratio, and expressed relative to
the U.S.-foreign forward interest differential. 11
Table 1
The Indicators and Their Relations
Indicators
II: Lldiut(n)- - change ill the n-year U.S. nominal interestrat~. (expressed in ·logarithrns)
less the (log of) the forward interest rate, fiu t
12: Llx t - - change in the logarithm of the U.S.
real exchange rate, calculated as the spot foreign currency/$ ratetimes the ratio ofO.S. to
foreign price level (using consumer prices)
13: Llyt- ~ change in the deflated forward exchange value of the .dollar (relative to the
U.S.-foreign forward interest rate differential), again in logarithms. Yt=xt+n (dift(n)
-diut(n»
Relations
(i) Lldiut(n) = Llrut(n) + LldIlut(n)
(ii) Llxt=n [Llrut(n)-Llrft(n)]+LlEtxt+n
(iii) LlYt= n[LldIlf,(n)- LldIlut(n)] + LlEtx t+n
How Do We Use Them?
The analysis has identified three potential indica-
49
W=Cov[Lldru,(n),!,]Var(I,f l ,.
Of course such estimates of changes in the U. S.
rea~ interest rate cannot be expected to .beexact,
mamly because, as can be seen from Table 1, the
indicators are affected by other variables as well.
For example, the real exchange rate indicator is
affected by the foreign real interest rate and the
expected future real exchange rate, as well as the
U.S. real interest rate. In fact, there are five
"underlying" variables making upthe set of indica~
tors (the U.S. and foreign real interest rates, the
U.S. and foreign expected inflation rates, and the
expected future real exchange rate) none of which
are directly observable. Given thaUhereare only
three indicators, none of these underlying variables
can be determined exactly.
If direct observations of real interest rates were
available, the weights, W,could be estimated
simply by performing a regression of the form in
(6), that is of changes in the real interest rate on the
indicators. The problem then is, how can this.regression be performed without any direct measurements of the dependent variable, namely the
changes in the U.S. long-term real interest rate?
As explained in more detail below (and more
completely in the Appendix), this regression, that is
the estimation of the weights, can actually be Carried out indirectly given certain additional assumptions discussed below. In effect, the weights can be
inferred from c1uesprovidedbythe relations among
the indicators. Recall, for example, that an increase
in the U. S. nominal interest rate indicator due to a
rise in the real interest component, will, all other
factors held constant, be associated with an increase
in the real exchange rate indicator. This suggests
that the greater the extent to which U.S. nominal
interest rate. ~nd exchange. rate indicators . actually
tended to. move together,· the greater the weight,
W2, is apt to be.
(7)
where W=(WI,W2,W3), Cov( ) stands for the
covariance of changes in the U.S. real interest rate
with the three indicators, and Var( ) is the variance
matrix of those indicators.
The weights, W, are those that would be estimated if the regression (6) could actually be performed directly. Estimates of the change in the real
interest rate using these weights are 'optimal' inthe
s~nse that they -minimize the average (squared)
dIvergence between the estimated and actual values
of Llru,(n) (in comparison with any other weighted
average of the indicators). 12
With no direct observations of the real interest
rate, the technical problem becomes that of estimating the covariance of real interest rate changes with
the indicators. (Clearly, the variance matrix of the
indicators can be estimated directly), However it
can be seen from Table I that these are determined
by the relations-that is the variances and covariances-among the underlying variables that make
up the indicators, the U.S. and foreign real interest
and expected inflation changes, and changes inthe
expected future real exchange rate. For example,
ih~ covariance of the U. S. real interest rate change
wIth the nominal interest rate indicator is determined by the variance of fluctuations in the real
interest rate and its covariance with changes in U. S.
expected inflation.
As suggested earlier, the relations among the
indicators provide the primary source of information about the relations among the variables underlying them. A simplified example illustrates this.
Suppose that changes in the U.S. real interest rate
were independent of (uncorrelated with) the other
underlying variables. Then the observed covariance
between the interest rate and real. exchange rate
indicators is:
Cov[Lldiu,(n), Llx,] = nVar[Llru,(n)]
Obtaining the Weights
To see more precisely what is involved inestimating these weights, let It stand for the vector of the
indicators at '1.' (The following discusionis a bit
technical; readers interested mainly in the results
can skip to Section II: Empirical Results.)
In short, under these assumptions, the variance of
the real interest rate, and hence its covariance with
the nominal interest rate indicator, couldbecalculated from the observed relation between the U.S.
nominal interest rate and the real exchange rate.
Proceeding in this way, it would appear possible
to estimate the relations among all the underlying
variables (their variances and covariances) from the
I t= [Lldiut(n), Llx"Lly,]
Then the weights given in (5) are defined by:
50
relations among the indicators, This in tum would
define the relation of real interest rate changes to the
indicators, allowing the weights, W, to be estimated. This is the sense in which the approach taken
here amounts to an 'indirect' regression.
The complication is that it cannot plausibly be
assumed that real interest rates are independent of
all other underlying variables. More generally, the
relations among these variables could befairIyqomplex; for example, there might be complex interactions between U.S .• and foreign real interest.rates
and expected inflation, and, if so, these would
aff~ct the way in which the relations b~tween the
interest rate and exchange rate indicators~;are interpreted. Once these possibilities are alloweg for, the
information provided by the relations among the
indicators is no longer sufficientto determine those
among the variables underlying them. The reason is
that there are five underlying variables, and hence
more relations. among them than for the. three indicators. Thus while. the relations aIIlong the indicators Will continue to be the primary basis for the
estimation of weights, some additional assumptions, suggested by economic theory or other data,
must be made. 13
ted inflation changes have no direct impact on U. S.
real interest rates, and similarly for U.S. expected
inflation and. the foreign real interest rate. This can
be stated as:
(A2) Foreign expected inflatiol1affects. the D,S.
real interest rate only to theextel1t·to which
it affects U.S. expected inflation.. Similarly, U.S. expected inflation affects the foreign real interest rate only via its impacton
foreign expected inflation. 15
Finally, the estimation also requires some assurnption, that is, prior estimates,concerning the
average response of U. S. and foreign real interest
rates to' their respective changes in expected inflation. These responses are measured by the 'coefficients' bu and bf defined as:
bu = average change in rut(n) given a one percent change in dIIut(n)
bf = average change in rft(n) given a one percent
change in dTIft(n)
Sirnilarly, some prior assumption must also be
made· about the average response of variations in
foreign real interest rates tochanges in the US. real
interest rate, measured by the coefficient g defined
as:
Assumptions
One' assumption is suggested by the earlier discussion, where it was argued thatthe real exchange
rate is unaffected in the long-run by inflation or real
interest fluctuations. This implies (assuming that
n-years is sufficient for this long-run condition to
hold): 14
(AI) Changes in the expected. future (n~years
from now) real exchange rate, aEtx t+ n , are
uncorrelated with\changes in the n-year
U.S. and foreign real interest and expected
inflation components.
It is also reasonable (and necessary) to restrict the
cross-country relations among real interest rates and
expected inflation by assuming thatforeignexpec-
\(" g = average change in rfln) given aone percent
(
change in ruin).
Given these assumptions, the relations (covariances) among the five underlying variables can be
expressed in terms of (see Appendix): their (5)
variances; and .the relation (covariance) between
U.S. and foreign expected inflation. These parameters can then be calculated from the six .independent variables provided by the covariance matrix of
the indicators-once, that is, the values of bu, bf
and garespecified; The way in which these coeffic
cients are estimated is described briefly in the next
section and in more detail in the Appendix.
II. Empirical Results
nominal interest rates. The forward interest rates
correspond to 7 years in the future for the U.S., and
five years for Germany, while the exchange rate
indicators are based on the foreign exchange value
of the dollar vis avis the German mark. 16 Separate
estimates are calculated for the sub-periods before
Theanalysis of the previous section will now be
appliedto estimate actual changes in U.S. real interest rates and expected inflation for the period
1976-mid-1983. These estimates will be based on
the five year U.S. and German government bond
rates (n=5), which are taken to be the 'long-term'
51
in the U. S. nominal interest rate indicator, that
indicator could be expected to be associated with
more than proportionate changes in the real exchange rate in the same direction.
In fact, during the earlier period, a one percentage point rise in the nominal U. S. interest rate
indicator was, on average, associated with only a
0.9 percent increase in the real exchange rate. This
suggests· that changes in expected inflation, rather
than in real interestrates, were the main sources of
variations in U. S. nominal interest rates during this
period-a conclusion supported by a number of
previous studies of short-term interest rates. 18 Similar reasoning suggests that the variability ofreal
interest rates rose substantially from the first to the
second period: on average the real exchange rate
increased by about 3 percent for each I percentage
point rise in the U.S. interest rate indicator after
mid-1979.
Second, the data suggest that the variability of
(changes in) expected inflation may also have risen
substantially from the first to the second period.
This is suggested by the fact that the variability of
the forward exchange rate indicator (which helps
measure foreign relative to U.S. expected inflation)
rose dramatically. (In addition, the U.S. forward
interest rate variability also increased sharply after
mid-1979).
Third, the data also suggest that there may be
considerable variability in the expected future real
and after June 1979. The reason is that the variability of nominal interest rates changed dramatically in
1979(especially after the change in Federal Reserve
operating procedures in October ofthat year), as did
their relation to exchange rates. This suggests that
the behavior of real interest rates, and their relation
to the indicators, also changed, and that the appropriate weights prior to mid-1979 are not the same as
those applying after that date. 17
A First Look
Its useful to begin by examining relations among
the indicators to see what they tentatively suggest
about the extent of fluctuations in real interest rates
and expected inflation. For this purpose, Table 2
lists measures of the actual extent to which a given
indicator tended to vary with a given change in each
of the others (these are based on the variances of the
indicators and correlations among them).
Several tentative conclusions are suggested by
the figures in the table. First, the very weak relation
between changes inthe U.S. interest rate indicator
and the real exchange rate for the earlier period
suggests that the real interest rate's variability was
low.in comparison with that of the nominal interest
rate itself. The analysis of the last section implies
that a one-percent increase in the 5-year real interest
rate will, all other factors held constant, raise the
real exchange rate by 5 percentage points. Thus if
real interest rates were the main source of changes
Table 2
Relations Among The Indicators 1
Standard Deviation
(Basis Points)
Average response to 1 percentage point change in:
Adiu t(5)
AXt
AYt
2
I.
First Period
(1976.01-1979.06)
a. Adiu t (5)
b. Ax,
C.dYt
Memo: Adift(5)
II.
.01
37.3
.92
-2.50
-.37
40.3
300.7
342.9
3.06
-2.48
26.0
.11
~.07
.42
1.24
.06
.10
.05
.03
-.05
.65
.04
.03
.04
Second Period
(1979.07-1982.12)
a. Adiu,(5)
b.Ax,
c. .s.Yt
Memo: 4dif t (5)
I
17.3
177.9
306.3
For variable definitions, see Table I.
~ This is the coefficient in a bivariate regression of the column variable on the row variable; for example, the response of Adiu,(5) to AX t
is: Cov(Adiu,(5), Ax,) / Var(Ax,) = .01 for the first period.
52
exchange rate, E t xt +5 • The analysis in the last section (see Table l) showed that movements in the
actual real exchange rate reflect changes in the
U.S.-foreign rell! interest differential, or shifts in
the expected future real exchange rate, or both. The
actual real exchange rate indicator was in fact highly variable in both periods. Yet, as argued above,
the Table 2 figures do not point to much variability
of the U.S. real interest rate, or indeed (similar
reasoning would show) to much variability in the
foreign real interest rate, over the first period. This
suggests that much of the variability of the actual
re,al exchange rate was due to changesjn its expected future value. The same conclusion i~ suggested
by the fact that the actual real exchange rate and
deflated forward exchange rate indicators are very
positively correlated. The expected future real exchange rate is the factor common to variations in
these two indicators, and so iftluctuations in E t xt + 5
were substantial, the real and deflated forward exc:hange .rates could. be expected to move closely
together-as in fact they did. 19
Variability of Real Interest Rate Changes
Table III lists estimates of the variabilityof the
U.S. five year real interest and expected inflation
changes obtained using the procedures outlined in
the previous section. (The 'memo' lines in the Table
are. intended to provide an indication of how the
estimates are affected .by alternative choices of the
prior-estimated parameters, bu, bf, and g.)
For the first period, the estimates are based on
measures of the average response of U.S. al1d foreign real interest rates to their respective expected
inflation rates estimated from observed short-term
interest rates and expected inflation (see Appendix
for details). This amountsto assuming thatJhe average response of longer-teon reaUnterest rates to
expected inflation (that is, bu and bf as· defined
earlier) is essentially the same as that for~bort-tenn
rates and is plainly only an approximatio~.}O It was
also assumed for the period prior to mid-i,~79 that
U.S. real interest rates had no direct irr{ t . on
foreign real interest rates, which is consistelth
previous studies suggesting that authoritiesabroad~
did not systematically vary their domestic • interest
rates in response to variations in U.S. (real) interest
rates. 21
The second period results are based on the assurnption that. the. variability of changes in the
expected future real exchange rate is the same as
that estimated for the first-period. '(This leads to
estimates that-seem more plausible thanthose based
on bu and bfestimates from short-teon interest
rates). This amounts in effect to assuming that all of
the increased variability in the actual real exchange
rate from the first to the second period is due to
Table 3
Estimates of the Variability of Real Interest Rates and Expected Inflation
~ Standard
1. 1976.01-1979.06
Estimates:
Memo: estimates with
alternativ~ bu,bf,
g1
gl
Aru(S) Adllu(S) Allu(S)
Deviation (Basis Points) ~
Arf(S)
Adnt(S)
23.6
22.3
51.1
26.0
128.1
16.8
17.2
22.9
50.5
25.3
113.1
47.0
47.4
95.4
41.1
62.2
99.0
123.0
39.6
20,8
76.6
10.5
30,7
65.4
253.3
bu
bf
0
-.33
0
10.0
14.1
-.30
-.33
-.10
13.4
-.63
-.63
.20
-.44
-.20
.20
Ant(S) AE t x l+5
II. 1979.07-1982.12
Estimates:
Memo: estimates with
alternative.bu, bf,
i
Notes:
I
'g' is the average change in the foreign real interest rate for a given change in the U. S. real interest rate;
g = Cov [ATU,(5), Arft (5»)/Var[Aru,(5»)
2
See Appendix for details on how the estimated variance of the 5-yearexpected inflation change, Allu t (5) and Allf,(5), is obtained.
3
The 'memo' estimate for bu forthe first period is taken from Mishkin's (1981) estimates; the 'memo' buand bffor the second period are
taken from Appendix Table AI, using short-term nominal interest rates and inflation.
53
Chart 1
Nominal and Estimated Real Interest Rates
increased variations in real interest rates. In addi~
tion, the. average response of foreign real interest
rotes to those in the U.S. is estimated from shortterm interest rates for this period. The reason is that
therei~ at least casual •evidence to suggest that
foreign authorities may at times have 'reacted' to
interest rate changes in the U .S.after 1979. 22
The results in Table 3 have three major implications. First, as suggested earlier, the variability of
the U. S. real interest rate in the first period was
relativt:;IY<;!B\V compared to. that of expected infla~
tion'4\~~~eptly, movements in expected inflation
~?1U'in.~t~df1uctuations in nominallong-tenn interest~a,~$,.~~ previous studies have suggested is the
case 'for short-term rates. This conclusion seems to
be reasonably robust, in the sense that it remains
even if U.S. real interest rates and expectedinfla~
tion are assumed to be substantially negatively
correlated.
Second, the variability of U. S. real interestrates
rose dramatically afterthe Federal Reserve stoppeq
,smoothing' nominal interest rates in' 1979. This
conclusion too is very robust, since it holds even if
the prior-estimated parameters (bu, bf, g) are as-,
sumed the same as for the first period. More surprising, perhaps, isthat the variabilityofU.S. expected
inflation has also increased and apparentlycontinues to be greater than that of the real interest rate.
Finally, the results imply that variations in real
interest rates have not accounted for all the variations in the 'long-run' real exchange rate. For th~
first period, variations in the long-run real exchange
rate accounted for about half of the variations in the
current real exchange rate. This result is of interest,
since it suggests that purchasing power parity, that
Percent
16
14
12
10
8
6
4
2
--"C:*tI-------
OI-~...
-2
,c.
*
**
1976~~{i1978
'.' 1.980
U.S. 5-ye~?vernmentbondrate.
Real inten~~;rate measured as the cumulative change since
Decemberi~75,
is U. S. versus foreign inflation, is not the sale
determinant of nominal exchange rates in the longrun, as is often asserted tobethe case}3
Estimates of Real Interest Rates
It is now straightforward to estimate the actual
variations in U. S. long-term real interestrate.The
weights on the indicators corresponding to theesti~
mates in Table 3 are given in Table 4. In some cases,
these weights are more easily interpreted byrewriting the eStimating relations in tenus of the U.S.
i~~~f?st rate, the real exchange rate, andthejoreign
inteI"~~trate, as is done in the last three columns of
Table 4 (see the relations in Table 1). Note that in
this rewritten form the coefficients of the U.S.
nominalinterest rate indiCator are all positive, as are
those on the real exchange rate. 24
Chart I plots the estimates of the cumulative
change in the U.S. real interest rate for January
1976 through July 1983 obtained from these weights
Ta~le4
Relati()ns F()rEstirnating Real Interest Variations
Coefficient of ~rUt on:
Period I
hTlplied Coefficients of: 2
~Yt
(1976.01-1979.06)
.335
.012
.001
.39
.330
.013
.005
-.583
.275
-.164
.60
.237
.111
-.816
Period II
(1979.07-1983.07)
Notes:
1
Estimate of the fraction of variance of changes in the real interest rate accounted for by the indicators:
V(Mu,) is the variance of the estimates of ~ru'Clllculatedfrom the above relations.
2
Obtained using the expression for ~ y, in Table ·1 .
54
V(~ru,) /V(~ru,) where
Chart 3
and the indicators.25 As expected, the estimates
imply that real interest rates fluctuated little before
1979, but considerably more after then. Apparent
ly, real interest rates rose from mid-1979 through
April 1980, fell back through the following June,
and then generally rose over the next several years.
A particularly interesting implication of these
results is that U.S. long-term real interest rates
remained quite high over August 1981 through Dec
ember 1982 even as our nominal interest rates de
clined sharply. The nominal 5-year interest rate fell
by nearly 5 percentage points over this period, yet
the estimates suggest that the real interest rate ac
tually increased, by nearly one percent. This sug
gests that the decline in U.S. nominal interest rates
during this period reflected a very sharp drop in
expected inflation, rather than any substantial de
cline in real interest rates. Note also that the esti
mates of the long-term real interest rate generally
Industrial Production Growth
and Estimated Real Interest Rate
Year-over-year
Percentage Change
Percent
* Real interest rate measured as the cumulative change (percen
tage points) since December 1975.
moved with short-term real interest rates until mid1982, when the latter fell sharply.
That the U.S. real interest rate remained very
high during 1982 is strongly suggested by the fact
that both the real exchange rate and forward ex
change rate indicators rose substantially during the
period (the U.S. forward interest rate also fell by
nearly as much as the 5 year nominal interest rate—
see Chart 2.) Recall that increases in the real ex
change rate suggest a rise in our real interest rate,
while increases in the forward exchange rate signal
a drop in our expected inflation. It is also interesting
to note that the rise in the U.S. real interest rate from
August 1981 through mid-1982—despite a nearly
200 basis point fall in the nominal rate—nearly
coincided with a sharp drop in U.S. growth (Chart
3).
Less plausible, perhaps, is the results’ implica
tion that the long-term U.S. real interest rate
increased by nearly two percentage points from
mid-1982 to mid-1983. This result is a reflection of
the sharp increase in the real value of the dollar
during this period, as the other two indicators were
essentially unchanged. Some increase in the U.S.
real interest rate during 1983 is not implausible as
nominal interest rates (and proxies for short-term
real interest rates) did rise. However in view of the
robust real growth during this period, it seems less
reasonable to suppose that the real interest rate
increased as much as the results here imply.26
Consider now the implications of these estimates
for the behavior of expected inflation over the last
several years. The estimates suggest that inflation
Chart 2A
Real Exchange Rate and Interest Rate Indicators
* Both variables measured as the cumulative percentage change
since December 1975.
Chart 2B
The Forward Exchange Rate Indicator
Percent
* Cumulative percentage change in the indicator since Decem
ber 1975.
55
fall in expected inflation since the end of 1981, and a
substantial fall in real interest rates as well).
anticipated for the next five years actually increased
during 1980 and 1981, even though actual inflation
began to decline in mid-1979. Is this pattern plausible? While inflation began to fall in 1980, actual
inflation over 1980-1981 was actually higher than
during the two previous years. Hence, the drop in
actual inflation beginning in mid-1980 may not
have. affected longer-term inflation expectations
much by the end of 1981.
Furthermore, actual and prospective U.S. government budget deficits rose substantially during
1980-1981, as the Administration's "supply-side"
fiscal package was put in place. Many market
~ommentators (although certainly not all) have
/argued that these developments substantially increased the risk that the Federal Reserve would have
to raise money growth to accommodate huge deficits, and as a result raise inflation in the future. Uso,
inflation expected several years in the future could
have been rising even as actual inflation was comingdown. That expected future inflation did rise
substantially over this period is also suggested by
thefact that the forward U. S. interest rate increased
by nearly 3 percentage points during this period.
However these results do conflict with survey
evidence gathered by Richard Hoey that suggests a
fa.ll in the public's expected 5 year future inflation
rate of about 1:5 percentage points during 1980~
1981. 27 If the Hoey data is correct, the results here
underestimate both the fall in expected inflation and
the rise in real interest rates over this period.
The results also suggest a very dramatic decline
in the expected inflation rate over the last eighteen
months, indeed by nearly as much as the fall in the
nominal U.S. interest rate. According to the estimates, expected inflation in mid-1983 was about 2
percentage points below its level in mid-1979. The
downward trend in expected inflation (although
not, perhaps, the implied magnitude of the decline)
is very plausible in view of the dramatic drop in
actual inflation during 1982. In addition, the substantial slowing of money growth from mid-1981 to
mid, 1982 may well have raised the credibility of the
Federal Reserve's anti-inflation resolve, and so
contributed to a further easing of market expectations of inflation. (Again, however, the Hoey survey suggests a milder-although still substantial~
Assessment
Overall, the results point to two conclusions
about the 'indicator' approach to measuring real
long-term interest rates taken here. First, the general pattern traced by the estimates for U. S. real
interest rates and expected inflation seems generally
plausible. The results suggest a substantial decline
in expected five-year inflation over the last several
years, as seems reasonable in view of the sharp drop
in actuaLihflation and the course Of Federal Reserve
policy.~heestimates also suggest that our longerterm re~J interest rates have remained very high
over th~14asteighteenmonths in comparison to their
level pri~r to the initiation of the Fed's anti-inflation
drive in 1979. This too is very plausible since nominallonger-term interest rates are now much higher
than in 1979, while, again, expected inflation almost certainly has fallen greatly.
Second, it is evident that the use of exchange rate
indicators can greatly alter the impression of movements in longer-term real interest rates that would
be conveyed by variations in nominal interest rates
alone. The fall in long-term nominal interest rates
here between August 1981 and March 1982 would,
of itself, have suggested a substantial decline
in longer-term real interest rates. The behavior of
exchange rates, though, suggests a very different
pattern, one which seems more plausible given the
behavior of other economic variables. Thus .exchange rate indicators do appear to provide useful
information about long-term real interest variations
in addition to that conveyed by nominal interest
rates.
Needless to say, these results are highly experimental, and subject to substantial error in measurement. More accurate estimates may well be obtainable by using several exchange rates (rather than
one), and by adding proxies for short-term real
interest rates (or other variables related to long-term
real interest rates) or expected inflation to the set of
indicators. Nonetheless, the results do suggest that
an indicator approach to measuring long-term real
interest rate movements is practical and of potential
use for policy-guidance.
56
III. Conclusion
The last several years have providedamplereminders· that there are many factors that critically
affect economic behavior that cannot be measured
or observed directly. Economists and business ana"
Iysts have long known that 'business confidence' is
an important influence on investment, butthey still
have not found a way to measure this confidence
withan.yprecision. More recently, wehave come to
appreciate the impact of real interest rates and expectedinflationon.oureconomy, and thus to·regret
evenmore our inability.toobservethem.
In measuring longer-term real interest rates and
expected inflation, this paper has attempted to apply
systematically an approach long used implicitly by
economists and others. That is, movements in variables that cannot be observed directly-in this case
real interest rates and expected inflation-have
been inferred from variations in other variables to
Which they are related, and which are directly measurable. Tht main basis. for this analysis is economic theory,. which specifies the relations that are
likely to hold between the unobservable variables of
interest and the indicators which are usedto measure them. This process amounts to abit ofeconomic 'detective work,' with the observable. indicators
providing th~ 'clues' and economic analysis providing the rules by which they areused,The resulting
estimates of real interest rates and expected inflation are, in effect the most likely explanations for
the observed movements in the indicators, given the
assumptions supplied by economic theory.
Here it has been arguedthat exchangerates, spot
and forward, are likely to be especially good sources
of 'clues' about movementsinlonger-tenn real interest rates and expected inflation. The main reason
is that real spot exchange rates are directly affected
only by the real interest component of nominal
interest rates, while (long"term) forward exchange
rates are directly affected by expected inflation, but
not by real interest rates. For this reaSon, movements in exchange rates provide information about
how to separate changes in real interest and expec-
ted inflation rates that underlie observed movementSinnominal interest rates. Similarly; theterm
structure of interest rates has been used to provide
information about the source of changes. in nominal
interest rates, in the sense that when currentnominal interest rates vary with long-term forward interest rates, the most likely cause is a change in expected inflation.
The analysis has also illustrated some oftheprac'"
. tical difficulties of-implementingwhat is; in theory;
a fairly simple and straightforward idea. Of necessity, the estimates are based on certain assumptions
which are not easily tested, and on parameters about
which· neither economic theory nor available·evidence supply much definite information. This is one
reason why the results must be regarded as provisional. Another is that more information, supplied
by exchange rates vis a vis other countries, measures of short-term real interest rates, orothervariabIes might well be added to thesetof indicators to
obtain more accurate and reliable estimates.
Nonetheless, the estimates are both plausible and
surprising in. ways that suggest that useful information can indeed be extracted from foreign exchange
and other financial markets. Viewed by itself, the
sharp fall in nominal interest rates overlate 1981
and early 1982 would have suggested a·significant
drop in long-term real interest rates. Yet a very
different impression, that real interest rates remained high and did not drop much, if at all, was
suggested by the c?ntinued strength of the dollar. in
the foreign exchange markets, a conclusion supported by this paper's formal analysis based on both
sets of indicators. And again, the actual behavior of
the real sector of the U.S. economy during this
period (although not that later in 1982 and during
1983) supports this latter impression more than that
conveyed by nominal interest rates alone. This experience suggests that while using economic knowledge to 'read' the signals from financial markets is
not an exact science, it is still of considerable potential use for policy guidance and worth further study.
57
Appendix
The following explains in more detail how the
estimates of the real interest and expected inflation
rates can be calculated from the variance-covariancerelations among. the indicators; In addition,
Section C below explains how the estimates of bu,
bf,and g are obtained fromshort-tenn interest rates
and inflation.
cators, .:ldiu,(n), .:lx" and .:ldift(n) (or, alternatively, .:lyt, as<defined in the text) and those of the
underlying variables:
i) Var(.:ldiu,) = Var(&u,) + (1 +2bu) Var(.:ldflu t)
ii) Var(.:ldif,) = Var(.:lrf,) + (1+2bf) Var(.:ldDf,)
iii) Cov(.:ldiu" .:lx,)/n = Var (.:lru,) - Cov(.:lru"
.:lrf,) - bfCov(.:ldflu".:ldflf,) + buVar(.:ldflu,)
A. As in the text define:
iv) Cov(.:ldift, .:lxt)/n =--Var (.:lrft) +Cov(Llru"
.:lrf,) + buCov(.:ldflu" AdDf,) ~ btvar(.:ldflf,)
diuln) = iU,(n) - fiu t = rut (n) + dDu,(n)
dift(n) = if,(n) - fif, = rf, (n) + dDft(n)
v) Cov(.:ldiu".:ldif,) = Cov(Aru t, .:lrf,) +(1 + bu
+ bf) Cov(.:ldflu" .:ldDf,)
where dflu and dflf refer to the difference between
the inflation premium on an n year asset and the forward interest rate. The results in the text are based
on n= 5.
The basic assumptions discussed in Section III
can be stated fonnally as:
vi) Var(.:lx,)/n 2 = Var(.:lru,) + Var(.:lrf,)2Cov(.:lru t, .:lrf,) + Var(st)/n 2
•
where the '(n)' have been dropped to simplify notation. These six relations-whose left hand sides are
observable and come from the variance-covariance
relations among the thfee indicators-ar~. in terms
of 7 variables, given estimates of bu and bf: the
variances of the real interest and expected inflation
rates (4); the varianCe of the change in the expected
long-run realexchange tate (I); the covariance of
U.S. and foreign real interest rates, and the covariance of U.S. and foreign expected inflation (2) .
To close the model for their first period, it is
assumed that zu and zf are uncorrelated, which
implies:
(AIJLet..:lE,x,+n be denoted's,'. Thens"which
refers to the: change in the:long-run expected real
exchange rate ('long-run' being n years), is uncorrelated with changes in expected inflation or the real
interest rates (including the zu and zf components of
the latter).
(A2) .:lru,(n)= bu.:ldflu,(n) + zu t;
.:lrf.(n) =bf.:ldDf,(n) + zf,
where zU t and zf, are both uncorrelated with .:ldDu,
and .:ldflf..
The relation (A2) expresses the text assumption
that any correlation rehveen the u.S. real interest
rate and foreign expected inflation be indirect, and
similarly for the foreign real interest rate and u.s.
expected inflation. In particular it implies:
vii) Cov(.:lru".:lrf,)= bubfCov(.:ldflu" .:ldDf,)
that is, the correlation between real interest rates
entirely reflects the correlation between expected
inflation rates across countries.
For the second period estimates, it is assumed
that:
viii) Cov(.:lru" .:lrf,) = gVar(Adflu,)
Cov(.:lru,(n), .:ldDf,(n» =
buCov (.:ldflut(n), .:ldDft(n»
COy (.:lrft(n), .:ldflu,(n» =
bfCov (.:ldflut(n), .:ldDf,(n»
where g is independently estimated. To obtain the
bu and bf estimates for the second period; let rd and
dfld refer to the U.S.-Gennan real interest and
expected inflation differentials, and did for the
nominal interest differential. Then the relations
(i)-(vi) can be combined to obtain:
The definitions of bu and bf in the text also imply
that:
COy (.:lru,(n), .:ldflut(n» = buVar(.:ldflut(n»;
COy (.:lrf,(n), .:ldDf.(n» = btvar(.:ldDf,(n».
ix) Var(.:ldid,)= Var(.:lrd,)+ Var(.:ldfld,)+
2Cov(.:lrd" .:ldfld t) = al
x) Var(.:lx t)/n 2 - Var(s,)/n 2 = Var(.:lrd,)=a2
B. The following relations are easily shown to hold
among the variance-covariances of the three indi58
C. As indicated inthe< text, one way to derive
estimates of buandbf,and.g,is to.exaJ)1ine the
relations between shorHerm interest rates andproxies for short-term expected inflation-the. latter
being much easier to obtain than proxies forIongerterm expected infl(ltion.
Let iu, standforthe one-monthU.S. interestrate,
IIu t forthe actualone-month U. S. inflation rate for
the month ending at t (at an annual rate),and
E,IIu,+, for the inflation rate Jlnticipated to Prevail
over thenextmonth, Then bucould be estimated
fiQiiitneregression,· .
xi) Cov(L\did" L\x,)/5= Var(4rd,)+
Coy(L\rd" L\dIld,) =a3
Forthe second period estimates, Var(s,) is taken
equal tothe estimated value for the first period. This
allows a2 to be c<tlculated,$o tbat:
Var(L\rd,) = a2;Cov(L\rd" L\dIId,)=a3 ---a2;
Var(L\dIld,) =al+ a2-2a3
The .ratio of Cov(4rdt,L\dIld,)/Var(L\dIld,) provides therefore an estimate of the 'average' yaJueof
huand hf,. and this average value is used for bqth
countries for the estimates for the second period.
Finally, the variance of the actual expected five
yearinfla.tion rate,L\Ilu,(n) and. L\Ilf,(n), can be
obtained as follows. Assume that changesin the
forwardinterestrates (which measure changes in
inflation anticipated many years from. now, or
changes in 'longcrun' inflation) are related to
changes in the n-year real interest rates only to the
extent th<tt they.· affect the expected inflation components, L\dIlu,(n) and L\dIlf,(n). This means, in
effect, that changes in 'long-run 'inflation areindependentof thezu, and zf,components of the real
interest rate defined earlier. This implies:
rut=ju, ---IIu,+] =C +bu[E,Ilu,+, - fiu,]
(recallthatfiu, equals the expected 'long-run' nominalinterest rate, which consists of a constant'longrun' real interest rate and the expected 'long-run'
inflationrate). Them, is the ex-post,Qr re<tlized,
real interest rate and is an unbiased measure of the
TableA.1.
Estimates ofReaI. Interest-Expected
Inflation Relation
.
Using as Expected IrdlatiorfProxy:
Cov[L\ru,(n),L\fiu,J = buCov(L\dIIu,(n), L\fiu,)
1-Month
Inflation
6-Month AVlJrage
Inflation
bu
.04
.32
bf
-.33
EarlierPeriod:
or,
Cov(L\dIlu,(n), L\fiu t ).
=( 1+ bu) -]Cov(L\diu.(n),Miu,)
.33
(.04).1
Later Period:
where the covariance on the right~hand-side of the
latter expression is directly measurable. This allows
the covariance of L\dIlu,(n) with changes in·. the
forward interest rate, and hence its covariance with
shifts in expected 'long-run' inflation, to be estimated. This, given that the .observable variance of
changesinfiu'.lTIeasuresthe variance of expected
'long-run' inflation, allowsthevariance ofL\Ilu,(n)
givenin Table 3 to be computed. The corresponding
values for Germany are calculated similarly.
Note thatthese latter estimates·doflotaffect·the
estimates ofthe weights, andhenceth.e estimates.of
actual real interestvariations.•The reason is that the
weights. depend • only upon the estimated. variances
and.. covariancesof. the .variables underlying the
indicators, that is L\dIlu,(n) and L\drIf,(n), as well as
of the real interest and expected future real exchange ratecha.nges.
bu
-.44
-.78
bf
-.20
-.80
g2
.17
.20
'bu (bt) estimated from regression:
iu,- nuH
]
=
C +. bu [E,Uu,+ , - fiu,] (similarly forbO
where iu, is the. one-month eurodolIar deposit rate.Il~,+, is the
actual (consumer price )inflation rate from month tto t + I (atan
annual rate). and E,Ou,+] is a proxy for the e~pectedvalueof
that inflation rate as ofLThis expectationis approximated as
either the one month actual inflation. for the period ending in
montht. ortheaverage of the sixmonths inflation for the period
ending 1. Thus. the dependent variable is the 'ex-post" real
ihterestmte.
2g estiInated from regression:
if, - E,Of,+]. = C
+ g[iu, -
E,nu H
,1
Variable definitions are as in note I.
.1Recall that this value is not used for the first period estimates in
the text. Neither value is significantly different· from zero.
however.
59
if, - E,I1f,+ I = C+ g(iu, - Etflu,+ ,)
actual real interest rate, assuming that market expectationsare ratiofial.This. form is used. because
the bl.l ifi the textrefers to the relation between the
long·term real interest rate and the difference between the n-year expected inflation rate. and that in
the. 'long-run'. Estimates ofthe value of bu, using
one and three month past inflation rates (consumer
price) as proxies for the next period's rate, are given
ifi Table A. 1.:1<
The fact that the German interest rate> indicatOr
(that·· is, Lldif,(n) .). and real exchange rate changes
·areposiiively· C()rrelated(seeTable2)strbl1gl)isug::··
gests that variations. in real interest and expected
inflation rates are negatively correlated for that
country, that is that bf must be negative for both
periods.:I<:I< The estimates in Table A.I. also suggest
a negative correlation between expected inflation
and real interest rates for the U.S. for the second
period. On this basis, the estimates in the first
column, using last month's inflation rate as the
proxy. for that expected thene",t month, are most
plausible, since these leadto negative estimates of
bf, and since the second column estimates for the
second period,while negative, give a negative estimate of the variance of the expected future real
exchange rate change (this means that they are too
large in absolute value). The actual (bu, bf) values
used in the text estimates for period two lie between
the first afid second column estimates.
Finally, the value of 'g' for the second period is
estimated from a similar regression of the form:
where the dependent and independent variables are
proxies for the foreign and U.S. real interest rates.
Asbefore,<one and six months past inflation are
used as proxies for that expected over· the next
month. Note again that the value of g estimated in
this way is used in the text estimates for the second
period only (where I have taken the column two
value). However, the estimates for the first period
are reasonably close to the zero value assumed in
thetexhc
:l<Admittedly, the relation should, ideally, be estimated in first-differenced form to be stricly consistent with the text analysis. However, the
estimates ofbu and bf (and g) obtained with a first
differenced fohn of the above yield implausible
estimates for the variances of the ufiderlying variables (that is, one or more are negative).
**Recall that, ceteris paribus, a rise in the German
real interest rate lowers the real exchange rate
indicator. The positive correlation between the
German nominal· interest rate and real exchange
rate changes thus implies a negative correlation
between German nominal and real interest rate
variations. This is most likely to occurifGerman
real interest and •expected inflation rate changes
are strongly negatively correlated.
FOOTNOTES
1. See, for. example, Cornel.1 (1982) and the article by
Joseph Bisignano in the Fall 1983 .issue of this Review.
ThiS mustbe regarded as anapproximatio~ for two
reasons. First,longer-term interest rates may well deviate
from an average of expected future shorter-term rates by a
"risk" premium that c<>mpensates for uncertainties about
the future. There ismuch evidence forthe existence ofsuch
a premium, although there remains considerable dispute as
to its. size. SeCOnd,even in the absence ofthis premium,the
f(mnul~ holdsexactly.only for pure discount (zero coupon)
bonds and can be regarded as only an approximationSbmetimes a rough one-'-when there are coupons.
2. As defined here, the real interest rate simply refers to the
expectedreal return of the investment. IUhus includes any
allo~ance.for. risk-from inflation, future interest rate
changes,or default-investors demand, since these help
determine that real rate.
3.. For example, the standard deviation of the one-month
U.S. interest rate less the average of the past six months
inflation increased more than three-fold from the period
1976-mid 1979 to the period mid-1979 through 1982.
4. That is, we can suppose that apprOXimately,
5. For an illustration, and the effect on exchange rates, see
Dornbusch (1976).
N
6. Frankel (1979a) used the difference between the shortterm and long-term nominal interestrates as a proxy for the
real interest rate. This is, however, equal to the difference
iUt(N+ 1) =(1/N+1) ~Eliut+j
j=O
so, again approximately,
60
between the short and long-term real interest rates pius the
short-term-Iong-terminflation differential,and is unlikely to
be avery good measure of the long-term real interest rate.
the long-run level in all subsequent months. The current
long-run real interest rate is thus unaffected,and hence, the,
current real exchange rate will not change. However. it is
easy to see that the real exchange rate expected to prevail
a month from now mustfaU, and that the actual real exchange rate a month fromnowwill fall from its current leveL
It is very important to note that in no sens~ can changes in
diut(n) be regarded as exact measures of variations in the
n-year real interest rate. This would only be the case if
changes. in. expected. inflation were, the same for all horizons, that is if shifts in the term-structure of expected inflation were "flat." Thiswill not always be the case, as numerC
ous past instances of temporaryinc:reasesin inflation due
tosupply"demandimbalariCeSinprimaryc:orhmoditYrharketssugges1. However,' if inflation increases tend. to be
fairlypersistent,.much·ofthevarianceintheexpectedinflation component· of the nominal" interest, iut(n), will be
"removed" by the transformation to diut(n).The expeCted
inflation component of this latter indicator will generally be
correlated with shifts in expected "long-run" inflation,
however.
10. Of course, inc:reasesin xtmayalsoreflect declines in
foreign realinterst rates, or an increase in the expected
future'real exchange rate.
11. Alternatively, thethird indicator can bethought ,Ofas
the foreign, interest rate'indicator, dift(n). Movements in
foreign interest rates provide informationaboutVariatioris in
"outJealinterestrate;in ··'part 'by\helpingto"interpret"
changes in the actual real exchange rate: the U.S" real
interest rate is more likely to haveincreased, given arise in
the real value ofthedollar, iftheforeigninteresfrate .has
remained unchanged than if it has fallen.
12. More precisely, relation (6) with the weights giVenin (7)
gives the conditional expectation of changes in the real
interest rate, giventheobserved changes in the indicators.
The statement that the estimates 'are "optimal" 'is strictly
true only when we have an exact, or correct, measure of
COV(arut, It). In practice, we have to estimate it.
7. The circumstances under which such premia Will exist
(and whatthey depend on) are described in Frankel (1979b).
8.' See, for example, Frankel, (1982).
9., In effect, the expected real depreciation of the doll!ir,
which is the percentage difference between its currentle"el
and that expected in the long-run, compensates for the real
difference in the totaLiqterest earned on theU.S.versus a
foreign asset over tJieentireli~e,of that investment For
example, anincr~a~e relative,to abroad inthe U.S. real ten
year rate of one percentage point ~nnualized implies that
the, U.S. instrume~tnow ,earns tenpercent more in real
terms that its forefgn co~nterpart over ,its ten-year life;
hence the real value of the dollar must rise abo"e its value
expected ten years {rom now by 10perc~nt. If in a(jdition the
real valueqf the, 9?"ar eXPected ten years from now is
unaffected-whiCh' means at the, least that, realintere,st
fluctuations are expected to have ceased by then-then the
current real dollar itself rises by ten percent. Note however
thatthe above (and text) relations between exchange rates
and the maturitY of an asset's yield are strictly true only for
pure discount instruments; for coupon instruments, the
'scale' factor is proportional to the duration.
13. The procedure for estimating the variances and covarianCes of the 'indicators from those of the underlying'vari.
abies is described in detail in the Appendix.
14. Note thatthis assumption is strictly valid 0ply for nlong
enough for real interest rates to have returned to their
(constant) long-run values. Real interest rates on shorterterm assets generally will be correlated with the real ex"
Change rate expected at maturitY. MOreover,permanent
shifts in the real interest rate, caused by changes in capital
productivity or other factors, generally willlead.tochanges
in long-run relative commoditY prices, and hence will be
correlated with the long-run real exchange rate. Therefore,
theassurnption that real interest rate fluctuations are the
result of temporary financial market distutbancesisclosely
related to (A1).
15. This does not necessarily imply that, say,changes in
U.S. expected inflation are uncorrelated with changes in
foreign real interest rates. An "indirect" correlation could
arise if U.S. and foreign changes in expected inflation were
correlated, and changes in foreign expected inflation and
realinterest rates werealsorelated.
As this suggests, only changes in long-term real interest
rates are likely to have unambiguous impacts on the current
real exchange rate. For any given term, the corresponding
real interest differential measures the deviation of the currentreaFexchange rate frorn the value expectedto prevail
at maturity. However it is ,only for longerctermmaturities,
that is for periods far ~nough into the futurethatrealinterest
fluctuations and other temporary influences on exchange
rates have ceased,thatthe value expected at maturity can
be expected to be unaffected.
16. All exchange rate and interest rate data refer to
monthly averages. The forward interest rate forthe U.S. is
effectively the 3-year bond rate expected to prevail seven
years from now, while for Germany!t islhe 2-year rate
expected to prevail five years from now. For example, for
the U.S.
fiut = 1/3[Log [(1 +iut(10))10J - Log [(Hiutll))7JJ
where the iUt are expressed in deCimal!).
The impact ofshorter-term real interest fluctuations on the
current real exchange tate thus depends upon how real
interest rates expected in the future are affect~d.As an
example, suppose that the current1-month U.S. real interest rate increases by one percentage point(annualizeq)
above its long-run level, butisexpected to fall one percentage point below that level next month, and then return to
Ideally, in calculating theS-year. forward exchange rate
from the current exchange rate,interest rates on assetsthat
are identical except for their currency of denomination
should be used. Since the government bOnds used here are
not strictly identical in this sense (their tax treatment, for
61
example,will differ), the Jorward exchange rate as calculated from the bond rates will differ from the 'true' value
somewhat. The analysis. in the text implicitly assumes that
the. difference is constant over time, so that it does not
affect the calculated changes in the forward exchange
rate.
tioniSoHhe nominal exchange rate reflects error in predicting the real exchange rate. Besides being applied to shortterm interest-exchange rate. relations, their analysis is
somev.'lJatmorerestrictive than that here. In particular, it
assumes that real interest and expected inflation variations
areuncorrelated;
17. The break is made in mid-1979, ratherthan in October
of that year, since the Fed began slowing money growth
somewhat before its official change in monetary targeting
24.•• JI1 interpreting the individual coefficients, it is very importanUClnote tlJata change in one indicator will typically
imply a change' insomeotlJer variable related to the. U.S.
real interest rate. For.example, a rise in the U.S. nominal
interestrate withnc:)changeln·thecurrent. real·or·forward
exchange JatE1 ',indi.cators--whose .implied. impact on the
. estimate Qfthe.·.U.S.·· re.al interest··rateclJangl;}··.is·.·given···qy
VV1-canonly occur if the foreign interest rate has also
risen.ThusW1 can, in effect, be interpreted as the, increase
intheU.S,realintE1rest rate given an equal change in the
U.S. and foreign nominal interest rates. The U.S. real and
foreign nominal interest rates apparently are negatively
aSiSociatedfor the second period, WhiCh iswhy W1 appears
to have .the "wrong" sign. (This negative association reflects the apparent negative correlation between the foreign
nominal and real interest rates, combined with the positive
assOciati?nof U.S. and foreign real interest rates). The fact
th~tthe.coefficient of the foreign interest r~te indicator i~
gener~llynegative in the "rewritten" eq~ation given in the
right porti?notthe table has an analogpus interpretatipn.
proc~dures.inqctober.1979.
18. See, for example, Mishkin(1981), Fama and Gibbons
(1982), and Cornell (1982).
f9TThisTpositilitFassbciatibncoUld·. alsbi"eflect a strong
negative relation between the U.S.-German real interest
differentiatial and their expected inflation differential (see
Table 1). This illustrates that a negative real interest!
expected inflation relation has many of the same implications fOr the behavior of •the indicators as does a high
degree of variability in the expected future real exchange
rate. This is the reason that the more. negative theestimated relation of real interestrates and expected inflation,
generallythe .lower the estimated variability of theexpected fuMe realexchangerate, and the higher the estimated
vari,aqility of real. interest rates,
20. See Appendix for more details on how bu and bfare
estimated.
25, 9~ta onthe5-yearand Z-year GeITl1anllond rates
were ~ot !ivailableafter 1982. Thechangein.the 5-year
Gerrnanbondratewasthentakento equal the change in
thE!5~y~areuro-DMdeppsit rateduri l1{J 1983.To'extrapolat~'thE!7-ye~rGerf11.anbond rate (to estimatefif,), this rate
w~s r~gressf3d on t~~ <;3ermanJong-termgovernment bond
rate.(v.thichcorr~spondstpa~averageof severaIJong-term
maturities) ()verthe period1979.07-1982,The reh:ltio n was
then used to estimate the seven year rate. for 1983,
The effect otestimating bu and bf from shorter term interest
rates can be seen from the "memo" item for the second
period in Table 3. Since the alternative (bu, bf)are lower in
absolute value, the, estimates ofthe variation .in U.s. and
foreign real interest rates are also lower. The resu lting
estimate al.so implies a very large increase in the variance
oftlJeexpectedfuture real exchange rate over the first
Period. Indeed, the "memo" estimates imply that the variance otchanges ill Etxf+n is about twice as great as that of
the actual real exchange rate during the first period__which
doesnotseem very plausible.
26.. Interestingly,jf the forward exchange rate indicator is
dropped,the resulting .estimates of the real interest rate
bl;}have veryiSimiiarly to those shown .inChart 1for 1982, but
increase by considerably less during 1983.(about 60 basis
points).
The "memo" for the first period uses a value for bu suggestedbya study by Mishkin (1981) of U.S. shortercterm
realinterest rates during the 1960's and 1970's. This suggests that the slJort-term real rate increased by about 30
basis pointsJor a 100 basis pointincrease in short-term
inflation.
The "[TIemo" estimates for the second period (using bu and
bt estimated from short,term interest rates) imply a some,what different pattern forthe U.S. real interestrate during
1982 and 1983. These suggest that real interest rates fell
nearly 1 percentage point during 1982, ending tlJeyear at
abouplJe level of mid-1979;the same estimates suggest
thatth~reaLinterest rate fell further during 1983. However
theesti[TIates also imply that expected future. inflation.in
mid-1.983 was. actually. several. percentage points. higher
than it was in mid-1979, a period overlNhich .theactual
inflation rate declined by nearly half. This is another reason
Why these el;timates donot seem soplausible.
21. See Throop (1980) and Bisignano (1983). The Appendix again explains how the relation between U.S. and foreign real interest rates is estimated for the two periods.
22.. Again, see Bisignano (1983).
23." Strictly speaking, of course, the results suggest only
that the rea.1 exchange rate expected to prevail five years
from now. varies substantially; it does not rule out' the
possibility that' purchasing power parity might hold· over
some longer period. However,examination of correlations
among longer-term interest rates and exchange rates suggest that the baSic conclusion would not be substantially
altered by considering, say, 10 year interest rates. Meyer
and Startz(1982) use an inference approach analogous to
that here and find that most oftheerror in short-term predic-
27. Foracompilation of Hoey's estimates., see Peter Isard,
"What's\IVrong with Empirical Exchange Rate Models... ,"
Discussion Paper #2?6 (August 1983) of The International
Finance Division of The Board of Governors of the Federal
Reserve.
62
REFERENCES
Bisignano, Joseph, "Monetary Policy Regimes and International Term Structures of Interest Rates," Economic
Review, of the FElderal Reserve Bank of San Francisco, Fall 1983, No.4.
Cornell, Bradford,. "Money Supply Announcements ·and
Interest Rates: Another View," Working Paper, UCLA,
1982.
Dornbusch, R., "Expectations and Exchange Rate
Dynamics," Journal of Political Economy, December1976.
Engel, Charles and Jeffrey Frankel, "Why Money Announcements Move interest Rates: An Answer ·from
the Foreign Exchange Markets," Conference Supplement: Sixth West Coast Academic/Federal Reserve
Economic Research Seminar, November 1982.
(November 1983).
Fama,Eugene and Michael R. Gibbons, "Inflation, Real
Returns, and Investment," Journal of Monetary
Economics, Volume 9, No.3 (May 1982).
Frankel, Jeffrey, "On the Mark: A Theory of Floating Exchange Rates Based on Real Interest Differentials,"
American Economic Review, September 1979a.
_ _ _ _ _ _ _ _, "The DiversifiabHity of Exchange
Risk," Journal of International Economics, September 1979b.
_ _ _~
, "In Search of the Exchange Risk
Premium: A Six-Currency Test Assuming Mean-VarianceOptimization," Journal of International Money
and Finance, Volume 1, No.3, December 1982.
Judd, John and Rose McElhatten,"The Behavior of Money
and the Economy in 1982-1983," FRBSF Economic
Review, Summer 1983, No.3.
Meyer, Stephen &nd Richard Startz, "Real Versus Nominal
Forecast Errors in the Prediction of Foreign Exchange
Rates," Journal of International Money and Finance, Volume 1, No.2, August 1982.
Mishkin, Frederic, "The Real Interest Rate: An Empirical
Investigation," Carnegie-Rochester Conference on
Public Policy, 15 (1981).
Throop, Adrian, "Managed Floating and the Independence
Interest Rates," Economic Review of the Federal Reserve Bank of San Francisco, Summer 1980.
63
@FedFRASER