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Business
Review
Federal Reserve Bank of Philadelphia
May • |une 1994

ISSN 0007-7011

Making More Out of Less:
The Recipe for Long-Term
Economic Growth
Satyajit Chatteijee




Business
Review

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Digitized for 2FRASER


MAY/JUNE 1994
MAKING MORE OUT OF LESS:
THE RECIPE FOR LONG-TERM
ECONOMIC GROWTH
Satyajit Chatterjee
From 1950 to 1991, the real value of output
produced by an hour's work rose steadily
in the United States. This increase in
productivity is the hallmark of economic
growth. But what factors caused this
growth in productivity? The answer to
that question must take into account the
increase in the amount of capital used by
each worker and technical progress. In
basic terms, however, Satyajit Chatterjee
shows that economic growth is the result
of the human ability to make more out of
less.
IS THE FOREIGN EXCHANGE MAR­
KET INEFFICIENT?
Gregory P. Hopper
If interest rates for government securities
in the Canadian market are at 5 percent,
but they're only 4 percent in the U.S.
market, does it make sense to invest in the
higher-rate securities? In other words, are
there exploitable profit opportunities in
the foreign exchange market? Some econ­
omists say yes; others say no. Greg Hop­
per looks at the arguments on both sides
and discusses factors such as statistical
problems, rational expectations, and risk
premia.

FEDERAL RESERVE BANK OF PHILADELPHIA

Making More Out of Less:
The Recipe for Long-Term
Economic Growth
Satyajit Chatterjee*

R

eferences to the pace of economic growth
in the United States and elsewhere are com­
monplace in the news media. However, it's
much less common to find informed discus­
sions of the forces that shape the economic
growth of nations. This article describes the
salient facts gathered by economists on the
sources of economic growth in the United States
and other countries. Although these facts do
not cover every aspect of this complex phenom­
enon, they do shed considerable light on the
mainsprings of economic growth and on the

* Satyajit Chatterjee is a senior economist in the Research
Department of the Philadelphia Fed.




kinds of growth-related government policies
that might prove beneficial to the economy.
The phenomenon of economic growth has
many aspects, but the central one is that the real
value of output produced by an hour's work in
the U.S. has risen over the years: in 1991, the
value of output for an hour of work was about
twice the value of output for an hour's work in
1950 (Figure 1). This increase in productivity or
in the economic worth of work-time is the
hallmark of economic growth. The question to
which we seek an answer is: what are the main
reasons for increases in productivity? The key
parts of the answer are an increase in the amount
of capital used by each worker and technical
progress.
3

BUSINESS REVIEW

MAY/JUNE 1994

FIGURE 1
SOURCES OF GROWTH
IN OUTPUT
Output per Hour Worked
PER HOUR WORKED
E con om ists ap p roach the
1950 -1991
question of the sources of eco­
1982 Dollars
nomic growth by relating the to­
24
tal value of output produced per
hour to variations in the use of
the two primary factors of pro­
duction: labor-time and the cap­
ital stock. Since these terms will
have specific meaning in this ar­
ticle, it's best to begin by defining
what they mean.
Labor-time means the total
amount of time, say, in a year,
that members of a nation spend
in the production of goods and
50
54
58
62
66
70
74
78
82
86
90
services valuable to households
and firms. In principle, it includes
the total time spent earning a living (through a nation means the monetary value of all the
honest means!) and also the total time spent buildings, structures, and machinery used in
doing chores around the house. Since measur­ conjunction with labor-time.
ing the time spent on housework is difficult, the
How, then, might variations in labor-time
practical definition of labor-time (and the one and the capital stock explain variations in out­
that we will use) is the time spent in the produc­ put per hour? As an extreme but illuminating
tion of goods and services for the marketplace example, consider how a building is construct­
and in the production of government services.1 ed in the United States versus how one is
Capital stock means the vast stock of every constructed in a country like India. In the
kind of building, structure, and machinery used United States, a construction worker has at his
in conjunction with labor-time. It includes all disposal a large array of sophisticated tools:
factories and office buildings and the equip­ pneumatic drills, jackhammers, electric screw­
ment therein, as well as infrastructure: facilities drivers, forklifts, cranes, and all kinds of heavy
such as roads, railroads, bridges, canals, har­ earth-moving equipment to help carry out the
bors, and docks. This enormously diverse building tasks. In contrast, a construction work­
collection of man-made things can be mea­ er in India works with nothing more than ordi­
sured only in terms of its total economic or nary hammers, chisels, and shovels. As a
monetary value. Therefore, the capital stock of result, if the construction of a similarly sized
building is to be completed in the same amount
of time, the number of construction workers
needed for the job in India will be many times
Sim ilarly, the measure of national output should, in
that needed in the United States. More gener­
principle, include the monetary value of the work done
ally,
the number of hours of work needed on a
around the house. However, because of the difficulty of
building will be much greater in India than in
constructing such a measure, the value of housework is
excluded from official estimates of national output.
the United States. If the economic value of the
4



FEDERAL RESERVE BANK OF PHILADELPHIA

Making More Out of Less: The Recipe for Long-Term Economic Groivth

Satyajit Chatterjee

building is the same in both countries, the value stock of tangible physical capital per hour
of output produced per hour of work will be worked to see if increases in the capital stock
much lower in India than in the United States, per hour worked were the dominant factor
i.e., the productivity of the Indian construction driving U.S. economic growth. In perhaps the
worker is a fraction of the productivity of the most well known of these studies, Robert Solow
calculated the annual percentage change in
American construction worker.
It should be clear why this is the case. An national output per hour worked and capital
American construction worker is assisted by stock per hour worked for the 1909-1949 peri­
more capital stock than an Indian construction od. To complete his calculations he needed to
worker: the dollar value of pneumatic drills, know how much a 1 percent increase in the
jackhammers, electric screwdrivers, forklifts, capital stock per hour worked would increase
cranes, and heavy earth-moving equipment output per hour. He observed that over this
used in the U.S. is many times larger than the period the owners of capital received about 36
dollar value of hammers, chisels, and shovels percent of national income (the rest being pay­
used in India. In other words, one important ment to labor), which suggested that, on aver­
reason why productivity in the American con­ age, the capital stock contributed 36 percent of
struction industry is so much higher than in the the total output of the economy. With this in
Indian construction industry is that the capital mind, Solow concluded that a 1 percent in­
stock used per hour of work (the capital-labor crease in the capital stock per hour worked
ratio, as economists call it) is much higher in the would raise output per hour by 0.36 percent.
Using this estimate of the contribution of cap­
United States than in India.
What is true of India and the United States ital stock to national output, Solow discovered
today is also true, in less extreme form, of the that growth in capital stock per hour worked
United States of 1950 and the United States of accounted for less than 15 percent of the in­
today. Measurements of the U.S. capital stock crease in national output per hour worked over
reveal that capital stock per hour
worked has risen over the years
(Figure 2). From this increase in
FIGURE 2
the capital stock per hour of work,
Capital Stock per Hour Worked
we should expect productivity to
be higher in 1991 than in 1950. A
1950 -1991
natural question is: is the increase
1982 Dollars
in capital stock per hour worked
the sole factor, or even the most
important factor, underlying the
economic growth of the United
States?
In the m id -1950s, several
American economists attempted
to answer this question for the
United States. Moses Abramovitz
(1956), John Kendrick (1956), and
Robert Solow (1957) examined
historical data on national out­
put per hour worked and the



5

BUSINESS REVIEW

this period. Moses Abramovitz, who used the
same methodology for the period 1870 to 1953,
found that increases in capital stock per hour
worked accounted for only 14 percent of the
increase in national output per hour worked
over this period. In other words, an astonishing
85 percent of the total economic growth over
the 80-odd years beginning in 1870 appeared to
be caused by factors other than an increase in
the capital stock per hour worked!
What else could be contributing to economic
growth? Let's go back to the comparison be­
tween the American and the Indian construc­
tion worker. While it's true that the dollar value
of the tools that the American worker has at his
disposal is much greater than the dollar value
of the tools at the disposal of the Indian worker,
it's not merely the case that the American
worker has more of the same tools than the
Indian worker. There's a clear qualitative dif­
ference between a bulldozer and a shovel, al­
though both are used to move soil. In other
words, the higher dollar value of capital stock
per hour worked in the United States is also
associated with a superior construction tech­
nology. Similarly, superior technology also
accompanies the larger capital stock per hour
worked in 1953 relative to 1870, and output per
hour worked would be higher in 1953 on this
count as well. Robert Solow made the bold
suggestion that technical progress explained
the remaining 85 percent of economic growth.
Technical progress makes any given dollarvalue increase in the capital stock per hour
worked more effective in generating additional
output, or, conversely, it allows any given in­
crease in national output to be attained with
less of an increase in capital stock per hour
worked (which might mean less capital or less
labor-time or both). This increase in output per
hour worked due to technical progress is called
an increase in total factor productivity (TFP).2
The quantitative importance of TFP growth
in accounting for U.S. economic growth over
the period 1870-1953 proved to be a phenome­
Digitized for 6FRASER


MAY/JUNE 1994

non that cut across national boundaries and
particular histories. Edward Denison's wellknown study of the U.S. and eight European
countries for 1950-1962 shows that TFP growth
was by far the most important source of growth
in national output (Table). For these countries,
its contribution is never below 64 percent (U.S.)
and reaches as high as 86 percent (Germany).3
We can plot the advance of TFP in the United
States during 1950-1991 (Figure 3). The top line
is the level of output per hour worked in the U.S
and is the same line that appears in Figure 1.
The lower line shows the level of output per
hour worked that would have been attained if
TFP had remained at its 1950 level; its rise is
solely the result of the increase in capital stock
per hour worked. Thus, the gap between the
two lines is a measure of how much the level of
output per hour worked owes to increases in
TFP.
While the Table and Figure 3 display the
importance of TFP growth in accounting for
growth in national output, they understate its
importance as a causal factor. According to
Solow (1956), the reason is that capital stock per
hour worked grows partly in response to an

2The use of the term "TFP growth" rather than "technical
progress" partly reflects the controversy that followed
Solow's suggestion that technical progress accounted for
the unexplained growth in output. At that time, many
economists were unconvinced that technical progress was
the key to the unexplained growth in output per hour
worked. Hence, they adopted the more neutral term, TFP
growth. Since the 1950s, however, numerous authors have
shown that a large portion of the unexplained growth in
output can be accounted for by careful measurements of the
improvements in the quality of labor-time and capital stock
(see, for instance, Maddison, 1987). Since improvements in
the quality of inputs is an aspect of technical progress,
Solow's suggestion stands vindicated.
3Denison, unlike Solow, measured labor input by the
number of persons employed rather than total hours worked.
However, since he adjusted his figures for changes in the
average number of hours worked by a person, this differ­
ence is unimportant.

FEDERAL RESERVE BANK OF PHILADELPHIA

Making More Out of Less: The Recipe for Long-Term Economic Growtii

Satyajit Chatterjee

TABLE

stock per hour worked
rose in response to an
increase in TFP, the
The percentage contribution of
Country
Growth Rate of
capital-to-output ratio
National Output per
need not rise because
Person Employed
of the added effect of
(1950-62)
higher TFP on output
per hour worked. For
TFP Capital per Person Employed
the United States the
ratio of capital to out­
64
United States
2.15
36
put has rem ained
2.64
Belgium
75
25
Denmark
2.56
74
26
roughly constant, sug­
France
4.80
75
25
gesting that capital ac­
Germany
14
5.15
86
cumulation in the U.S.
Holland
3.65
75
25
has largely been in re­
Italy
5.36
80
20
sponse to increases in
3.27
74
26
Norway
TFP.4Also, capital-outUnited
put ratios are observed
Kingdom
74
1.63
26
to be roughly constant
as well for the Europe­
Source: Adapted from Tables 21-2 to 21-20 in Edward F. Denison: Why Growth Rates
Differ, Washington, D.C.: Brookings Institution, 1967.
an countries examined
by Denison. Thus, in­
creases in TFP have
increase in TFP: as advances in technology been the single most important factor driving
make labor and capital more productive, firms economic growth in these countries. In short,
exploit the increase in TFP by investing in the human ability to make more out of less is at
newer and better buildings, structures, and the heart of economic progress.
equipment. In other words, growth in capital
stock per hour worked is never an entirely DETERMINANTS OF TFP GROWTH
Inventions. Inventing new products or new
independent factor contributing to economic
growth: part of the growth in a nation's capital ways to make old products accounts for one of
stock per hour worked occurs to keep pace with the primary sources of TFP growth in industriincreases in its TFP.
Is there a way to tell how much of the
4T o state this point differently, if capital stock per hour
increase in capital stock per hour worked oc­
curs in response to increases in TFP and how worked rose without an accompanying increase in TFP,
much of it occurs for other reasons? Solow diminishing returns to capital would cause the outputcapital ratio to fall. For the United States, the fact that the
pointed out that if a nation's capital stock per capital-output ratio has remained constant in the face of
hour worked rose in response to factors other growing capital stock per hour means that a continuous rise
than an improvement in TFP, the percentage in TFP has offset the force of diminishing returns. In Solow's
increase in national output per hour worked growth model, a steady increase in TFP stimulates firms to
would be only 0.36 of the percentage increase in raise the capital stock per hour and, by simultaneously
increasing household income, also provides the resources
capital stock per hour worked, so that the ratio to finance this accumulation. Output and capital stock grow
of capital stock per hour worked to output per together at a rate equal to the growth rate of TFP, and thus
hour worked would rise. In contrast, if capital the capital-output ratio remains constant.



7

BUSINESS REVIEW

alized countries. Each of these
activities makes labor and capi­
tal more productive, although for
somewhat different reasons. An
improved process for making an
1982 D ollars
existing product directly enhanc­
es productivity by economizing
on labor and capital or on inter­
mediate inputs such as raw ma­
terials and energy. A new
product improves productivity
indirectly by drawing away la­
bor and capital from less valu­
able uses, thereby enhancing the
value of goods and services pro­
duced by existing amounts of la­
bor and capital.
In light of the international dif­
ferences in TFP growth evident
in the Table, an important issue is
whether the pace of inventions in a country is
related to the amount of resources it expends
on inventive activity.
Zvi Griliches and Ariel Pakes (1984) studied
the correlation between the research and devel­
opment (R&D) expenditures of large U.S. firms
and the number of patents issued to them each
year. They found that the quantity of patents
issued yearly to different firms was positively
and strongly related to the level of R&D expen­
ditures in that firm: firms that spent more on
R&D generated more patents, on average.
However, all patents are not equally valu­
able, and not all inventions are patented. To
make a more compelling case for the potency of
R&D expenditures, it's necessary to examine
its correlation with firm-performance measures
such as the market value of common stock.
Ariel Pakes (1985) documented a positive cor­
relation between companies' expenditures on
R&D and their stock value. Since many other
factors besides the outcome of R&D efforts
affect stock value, the correlation found is nat­
urally not as strong as that between R&D and
patents. Nevertheless, there's enough evidence
8 FRASER
Digitized for


MAY/JUNE 1994

FIGURE 3

Growth in TFP
1950 -1991

to suggest that R&D expenditures generate
valuable inventions for firms. Also, Saul Lach
and Mark Schankerman (1989) and Saul Lach
and Rafael Rob (1992) have shown that firms
and industries that spend more on R&D also
tend to spend more on equipment and machin­
ery in future periods, which suggests that spend­
ing on R&D does generate profitable invest­
ment projects.
Therefore, at least for the U.S., evidence
shows that the rate of TFP growth is influenced
by the level of R&D expenditures. Neverthe­
less, this influence is imperfect because the
outcome of R&D efforts involves a substantial
amount of randomness. Also, as John Bound
and associates (1984) document, many firms
that generate patents do not report any signif­
icant R&D expenditures, perhaps because many
inventions do not arise from directed R&D
efforts but happen simply because individuals
think up improvements in the course of doing
their jobs. The R&D expenses for such acciden­
tal inventions are probably minor.
The existence of patented inventions that
were apparently generated at little or no cost
FEDERAL RESERVE BANK OF PHILADELPHIA

Making More Out of Less: The Recipe for Long-Term Economic Growth

serves to remind us that firms do not explicitly
pay for some of the most critical inputs in the
R&D process. The worker who comes up with
an innovative suggestion is surely using the
basic skills and knowledge taught in schools
and the experience acquired in previous jobs.
Indeed, a portion of the worker's wage must be
compensation for the valuable knowledge and
experience brought to the job. Therefore, we
can be reasonably confident that the average
education level of the working population—
education conceived broadly as years of work
experience and formal schooling—also con­
tributes to a nation's TFP growth, although this
contribution may be difficult to quantify.
Recognizing that TFP growth may respond
to the level of R&D expenditure and the aver­
age level of education, economists have begun
to examine whether international differences in
R&D expenditures and education levels help
explain international differences in TFP growth.
Since data on productivity are hard to compile,
researchers have been content to study wheth­
er international differences in R&D expendi­
tures and education levels help explain interna­
tional differences in per capita GDP growth.
Two authors, Paul Romer (1989) and Frank
Lichtenberg (1992), concluded that international
differences in per capita GDP growth are influ­
enced by international differences in R&D ex­
penditures. However, a recent study by Nancy
Birdsall and Changyong Rhee (1993) found that
correcting the data set used by Romer and
Lichtenberg for possible measurement errors
eliminates this correlation. Therefore, the role
of R&D expenditures in the explanation of
international differences in TFP growth rates
remains an open issue.5With regard to educa-

5R&D expenditures may matter for growth, but differ­
ences in R&D spending across countries may not be large
enough to appreciably affect productivity growth. Alterna­
tively, a country that invents a new product or process may
not be the only one to benefit from it. If inventions are
patented and sold to producers in other countries, the




Satyajit Chatterjee

tion levels, Robert Barro (1991) has document­
ed that countries that start out with low schoolenrollment rates grow at a discernably slower
rate.
Economies of Scale. A second important
determinant of TFP growth is economies of
scale. Economies of scale exist if unit costs fall
at higher levels of production. Increases in TFP
that result from increases in the size or capacity
of production facilities represent one type of
economies of scale. For instance, in the chem­
ical and petroleum industries the average cost
of production is much lower in bigger plants if
these plants operate near capacity.6
The increase in TFP resulting from econo­
mies of scale is distinct from that resulting from
a new industrial process. A firm may be aware
that a bigger plant, if operated near capacity,
lowers costs but may not build or buy a bigger
plant if the larger volume of output needed to
make it economical cannot be profitably sold.
However, with an expansion in market size,
bigger plants do become practical and are ac­
quired, thereby contributing to the increase in
the productivity of labor and capital.
A second example of economies of scale is
the increase in TFP that comes from specializa­
tion. Adam Smith in his Wealth o f Nations noted
that the division of labor constitutes a major
source of productivity increase. A group of
workers in which each worker concentrates on
a limited set of tasks produces much more than
an equally large group of workers in which
each worker performs every task. This gain
stems from several factors: less time is lost

purchasing country will also experience an increase in TFP.
Indeed, Robert Evenson (1984) documents a brisk interna­
tional trade in inventions. Therefore, it might be expected
that differences in the rate of economic growth due to
differences in R&D levels would be difficult to discern in the
data.
6See Alfred Chandler's book Scale and Scope: The Dynam­
ics o f Industrial Capitalism, for an in-depth discussion of the
role of increasing returns to scale in modern industries.

9

BUSINESS REVIEW

switching from one task to another; some work­
ers may be better at some tasks than other
workers; or simply performing a task many
times over entails a gain of efficiency.
The efficiency gain from specialization of
tasks within a firm extends to the specialization
of production across firms as well: if produc­
tion is organized so that a large number of firms
produce very specialized products (which are
then assembled to manufacture the final good),
the productivity of labor and capital will be
higher. Indeed, a proliferation of intermediate
goods used in the production of goods and
services always accompanies the industrial
development of any country, which suggests
that some of the increase in TFP must be due to
gains from specialization. Again, a firm may
not wish to incur the expenses involved in
buying or building more specialized plants if
the increased volume of its specialized output
cannot be profitably sold in the market.
The economic integration of geographically
dispersed markets is perhaps the most signifi­
cant channel through which economies of scale
contribute to the growth of TFP. When regions
that did not previously trade with each other
begin to do so, market size for producers in
both regions expands, making it possible for
more and more firms to profitably adopt bigger
plants and to profitably specialize.
The integration of markets can come about
for various reasons. For instance, the prolifer­
ation of railroads contributed to the higher pace
of adoption of large-scale production facilities
in the U.S. during the 1880s and 1890s. Similar­
ly, the development of the U.S. interstate high­
way system in the 1950s and 1960s integrated
markets even further. More generally, innova­
tions in the transportation sector that reduce
the costs of moving goods around have the
effect of expanding the geographic size of mar­
kets. Removal of trade barriers such as tariffs
promotes trade between regions and is another
channel through which the geographic size of
markets may increase. Edward Denison esti­
Digitized for
10 FRASER


MAY/JUNE 1994

mates that the portion of TFP growth that can
be accounted for by economies of scale ranges
between 23 to 36 percent.
Learning-by-Doing. Economists have iden­
tified a third source of TFP growth: learning on
the job, or learning-by-doing. As individuals
working together in a factory gain experience in
the production of a new product or process,
they learn to become more efficient, that is, they
waste less time and raw materials in producing
a given volume of output. Consequently, TFP
increases simply as a result of experience. The
existence of learning-by-doing is well docu­
mented for many manufacturing industries
(see the article by Linda Argote and Dennis
Epple). As one example, let's consider Alan
Searle's 1945 study of the manufacture of Lib­
erty Ships during World War II.
From December 1941 through December
1944,14 shipyards in the U.S. produced a total
of 2458 Liberty Ships, all to the same standard­
ized design. On average, with each doubling of
cumulative output, the reduction in manhours
required per ship ranged from 12 to 24 percent
across the 14 shipyards. Similar reductions in
unit manhour requirements were also seen in
the production of other ships as well. Leonard
Rapping (1965) showed that after accounting
for variations in labor hours and capital used in
each of the shipyards, the effect of learning was
to increase TFP between 11 and 29 percent over
the three-year period, i.e., to increase TFP at an
annual rate between 4 and 10 percent.
While learning effects can be quite substan­
tial over a two- to three-year period, industry
studies also show that TFP growth from learn­
ing ultimately stops. For instance, in the case of
Liberty Ships, the maximum productivity gain
had been achieved by the end of 1943, and
productivity was roughly constant over the last
year of production. This raises a natural ques­
tion: can learning-by-doing really be a source of
sustained increases in TFP? The answer may be
yes because, as already noted, new products
and new processes get added every year, so
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Making More Out of Less: The Recipe for Long-Term Economic Growth

that there are fresh opportunities for learning
effects to increase TFP.7
Indeed, some economists have recently con­
jectured that the effects of learning-by-doing
may be an important part of the explanation of
the fast economic growth of countries like Hong
Kong, Korea, and Taiwan since the mid-1960s.8*
These countries have not been technological
leaders, so their rapid economic growth cannot
be ascribed to a rapid pace of invention. Also,
although benefits from specialization exist, re­
searchers do not consider them a major factor
in the economic growth of these countries. On
the other hand, these countries have rapidly
added the production of more and more tech­
nologically advanced goods to their economy
and have certainly been in a position to reap the
TFP gains from learning-by-doing. In this they
have (somewhat paradoxically) been helped by
the fact that they are technological followers:
they haven't had to await the outcome of costly
R&D efforts to obtain "new " products.
To summarize the discussion so far, econo­
mists have identified three important determi­
nants of TFP growth. First, TFP increases
because of the invention of new products and
processes. Second, it increases because of econ­
omies of scale. Third, it increases because indi­
viduals in firms learn at their jobs. The degree
to which each of these sources contributes to
TFP growth depends on the choices that indi­
viduals, firms, and governments make: the
pace of innovation depends on the amount of
resources spent on R&D and education; the
importance of economies of scale depends on
the speed with which the transportation net­

7The gains from learning-by-doing may be limited for a
new product or process if the product or process is not
produced to the same specifications each time but is cus­
tomized to a significant degree.
8See, for instance, articles by Robert Lucas (1993), Nancy
Stokey (1988), and Alwyn Young (1991).




Satyajit Chatterjee

work of a country develops; the extent to which
a country benefits from learning-by-doing de­
pends on how quickly a country expands the
production of new goods. Thus, a country's
TFP growth is shaped by the choices that its
citizens make.
ECONOMIC POLICY AND TFP GROWTH
For an economist, the first and most impor­
tant issue about economic policy and TFP growth
is whether the government should attempt to
influence TFP growth at all. Is there reason to
believe that individuals and corporations act­
ing in their own interests in this regard do not
fulfill the broader interests of society? Is there
a serious mismatch between private gain and
social benefit in the generation of productivity
improvements? This section explores some of
the justifications for government intervention
with regard to the three sources of TFP growth
discussed in the previous section.
Economists recognized early on that the eco­
nomics of technical progress had some peculiar
features to it. Fundamentally, technical progress
depends on our understanding of the physical
universe; it draws upon the fruits of basic re­
search in the various sciences, including medi­
cine. However, basic research cannot be done
for profit because scientists do not have proper­
ty rights on the laws of nature. Once a scientific
discovery is communicated to the scientific
community, anyone can use it free of charge.
Therefore, the government should, by and large,
support basic research. Of course, this raises
very thorny issues about the kinds of basic
research to fund, whether the level of funding
in any year is too little or too much, and exactly
how to measure the benefits of past funding on
basic research. However, these largely unex­
plored issues are beyond the scope of this arti­
cle.
In contrast to basic research, the fruits of
applied research are new products that can be
sold for profit and new production processes
that can lower costs. Therefore, applied reli

BUSINESS REVIEW

search can, in principle, fund itself. However,
even here there may be a mismatch between
private return and social benefits. The mis­
match arises because, in many instances, the
discovery of a new product or production pro­
cess stimulates the discovery of other products
and processes elsewhere in the economy. If the
new discoveries are closely related to the first,
patent laws will allow the first discoverer to
benefit monetarily from these unexpected and
unintended consequences of his discovery pro­
vided the original invention was patented.
However, more often than not, the discoverer
cannot capitalize on these subsequent inven­
tions.
Scholars who have attempted to measure
these external benefits of research and develop­
ment have generally found them to be signifi­
cant and quite pervasive.9 Thus, corporations
and individuals, guided by the value of inven­
tions to themselves alone, will undertake less
R&D than is warranted by the true social ben­
efit of their R&D efforts. Therefore, a case can
be made for subsidizing applied commercial
research. Again, the issue of subsidies raises
difficult questions about which kinds of re­
search should be subsidized, how the benefits
from past subsidies should be evaluated, how
the incentives for R&D should be structured,
and how much subsidy should be provided.
The U.S. government subsidizes applied com­
mercial research through government grants
and tax breaks, but economists have only an
imperfect understanding of these issues.10
As noted earlier, the average level of educa­
tion of the working population is also likely to
be an important factor in promoting TFP growth.
The government has an obligation to support

9See, for instance, the articles by Adam Jaffe (1986) and
Ricardo Caballero and Adam Jaffe (1993).
10For an attempt to come to an understanding of this
knotty issue, see Linda Cohen and Roger Noll's book The
Technology Pork Barrel.

Digitized for
12 FRASER


MAY/JUNE 1994

education for reasons similar to those for sup­
porting R&D. While most individuals value
education and are willing to devote time and
money to acquire it (or make sure that their
family members do), they consider only their
private gain. However, education confers in­
numerable benefits on society as a whole (faster
TFP growth is one), so there is a case for subsi­
dizing it. However, as in the case of R&D
subsidies, many unresolved issues remain con­
cerning the details of government support for
education.11
For developing countries, the possibility of
achieving TFP growth through economies of
scale suggests a special rationale for govern­
ment intervention. In a nutshell, the rationale
stems from the fact that cost-effective largescale production of one product typically hing­
es on the cost-effective large-scale production
of constituent inputs, and these inputs in turn
require large-scale production of other inputs
and so on. If a developing country is to replicate
this interlocking pattern of large-scale industri­
al production within a short period of time, it
has to advance simultaneously across a broad
industrial front. Therefore, an individual firm
contemplating investment in a large-scale tech­
nology must be reasonably confident that sup­
porting investments in large-scale technologies
will occur in other industries.12 In such a situa­
tion, the government can play a vital coordinat­
ing role by assisting firms in different sectors of
the economy to commit to a common industrial
plan. Virtually all developing countries have
relied on such coordination of economic activ­

11For a discussion of the benefits of education, with
explicit reference to economic growth and some of the
related policy issues, see the article by T. Paul Schultz
(1988).
12Another option for the firm is to buy the necessary
inputs from abroad. However, developing countries often
find the domestic price of imported inputs to be prohibitive­
ly high so that this option may not be practical.

FEDERAL RESERVE BANK OF PHILADELPHIA

Making More Out of Less: The Recipe for Long-Term Economic Growth

ity, although its extent and scope have varied
greatly.
Other than financing the transportation net­
work, there are no U.S. policies designed to
directly affect the advance of TFP through
economies of scale. However, some policies
inadvertently do so, for example, anti-trust
laws and international trade rules. To reap the
TFP benefits of economies of scale, firms must
enlarge the scope of their operations, which, in
many instances, means that a few large firms
will have a major share of the market being
served.13 However, economic theory suggests
that firms (or groups of firms) that are so big as
to have no effective competition from their
rivals tend to cut back on the supply of their
product so that the artificial scarcity can gener­
ate hefty profits for the firm or the group. For
this reason, the U.S. legislated anti-trust laws
(the Sherman Act of 1890) that prohibit price­
fixing agreements and mergers and acquisi­
tions whose main intent is to gouge customers.
However, while these laws protect consumers
from errant firms, they also slow down the rate
of adoption of large-scale technologies because
expansions in firm size that typically accompa­
ny such adoptions need to be cleared by regu­
latory authorities. There are no estimates of the
adverse impact of anti-trust regulation on TFP
growth, but such an impact surely exists.14 On
the other hand, policies to break down barriers
to international trade promote larger markets,
thus allowing greater economies of scale and
TFP growth.

Satyajit Chatterjee

The phenomenon of learning-by-doing per se
does not suggest a role for government policy.
While it is true that uncertainties and setbacks
faced during the learning phase might mean
that a firm doesn't survive to reap the benefit
from learning-by-doing, it does not follow that
governments should step in to help out failing
firms. If private investors are not willing to risk
their money in the venture, why should the
government risk the taxpayers' money? Gov­
ernment help is justified only if surviving firms
provide benefits (to the economy) for which
private investors are not compensated, thereby
causing private investment in new ventures to
be too low. However, learning-by-doing pre­
sumably invests workers and entrepreneurs
with skills that are also valuable outside of their
existing firm, so that uncompensated benefits
from learning-by-doing may well exist. For
instance, a worker who breaks away and pio­
neers a valuable innovation after acquiring
useful training in a firm is not obligated to share
his newfound wealth with his former employ­
ers. If this kind of phenomenon is pervasive, it
may be beneficial for governments to subsidize
firms during the costly learning-by-doing
phase.15

13Indeed, as Chandler's book cited earlier documents,
the adoption of large-scale technologies in the last two
decades of the nineteenth century went hand in hand with
the emergence of monopolies, trusts, and combines.

CONCLUSIONS
This article makes several important points
about econom ic growth. First, technical
progress, which economists call total factor
productivity (TFP) growth, has been a major
factor underlying increases in output per hour
worked in the United States and Europe. In
fact, it has been more important than the rising
amount of capital available to each worker,
although this, too, has contributed.
Second, the constancy of capital-output ra­
tios in the United States and many European

14See Crandall (1980) for a general discussion of govern­
ment regulations on U.S. productivity growth. Denison
(1979) estimates that 13 percent of the decline in productiv­
ity growth over the 1965-1978 period was due to increased
government regulations.

15At least one astute observer of economic life believes
that innovators are frequently breakaways. See Jane Jacobs'
The Economy o f Cities.




13

BUSINESS REVIEW

MAY/JUNE 1994

countries suggests that accumulation of capital
stock in these countries has been mostly in
response to their TFP growth. Thus, it is rea­
sonable to think that differences in growth of
output per hour worked across these countries
are mostly the result of differences in TFP growth.
Third, the TFP growth experienced by a
country is a result of the pace of innovations
and inventions, the extent of the economies of
scale experienced by the country, and the ex­
tent of productivity improvements from learn­
ing-by-doing. These sources of TFP growth in

turn depend on profit calculations of individu­
als and firms and the wisdom of government
policies. Therefore, there is a potential econom­
ic explanation for the differences in TFP growth
across countries and for the same country over
time. However, despite these advances in our
understanding of economic growth, there's a
great deal still to be learned, especially in the
area of designing economic policies to promote
productivity growth.

REFERENCES
Abramovitz, Moses. "Resource and Output Trends in the United States Since 1870," American Economic
Review, Papers and Proceedings (1956), pp. 5-23.
Argote, Linda, and Dennis Epple. "Learning Curves in Manufacturing," Science, 247 (1990), pp. 920-24.
Barro, Robert. "Economic Growth in a Cross Section of Countries," Quarterly Journal o f Economics, 106
(1991), pp. 407-43.
Birdsall, Nancy, and Changyong Rhee. "Does R&D Contribute to Economic Growth in Developing
Countries?" Rochester Center for Economic Research, Working Paper 359 (1993).
Bound, John, and others. "Who Does R&D and Who Patents?" in Zvi Griliches, ed., R&D, Patents and
Productivity. National Bureau of Economic Research Conference Report, University of Chicago Press,
1984.
Caballero, Ricardo, and Adam Jaffe. "How High Are the Giants' Shoulders: An Empirical Assessment of
Knowledge Spillovers and Creative Destruction in a Model of Economic Growth," in Olivier Blanchard
and Stanley Fischer, ed., NBER Macroeconomics Annual. Cambridge, MA: The MIT Press, 1993.
Chandler, Alfred D. Scale and Scope: The Dynamics o f Industrial Capitalism. Cambridge, MA: Harvard
University Press, 1990.
Cohen, Linda, and Roger Noll. The Technology Pork Barrel. Washington D.C.: The Brookings Institution,
1991.
Crandall, Robert. "Regulation and Productivity Growth," in The Decline in Productivity Growth. Boston, MA:
The Federal Reserve Bank of Boston, 1980.
Denison, Edward F. Why Growth Rates Differ, Washington, D.C.: The Brookings Institution, 1967.
Denison, Edward F. "Explanations of Declining Productivity Growth," Survey o f Current Business, 59 (1979),
pp. 1-24.
Evenson, Robert. "International Inventions: Implications for Technology Market Analysis," in Zvi Griliches,
ed., R&D, Patents and Productivity. National Bureau of Economic Research Conference Report, Univer­
sity of Chicago Press, 1984.
Griliches, Zvi, and Ariel Pakes. "Patents and R&D at the Firm Level: A First Look," in Zvi Griliches, ed.,
R&D, Patents and Productivity. National Bureau of Economic Research Conference Report, University of
Chicago Press, 1984.
Jacobs, Jane. The Economy o f Cities. New York: Random House, 1969.

14 FRASER
Digitized for


FEDERAL RESERVE BANK OF PHILADELPHIA

Making More Out of Less: The Recipe for Long-Term Economic Growth

Satyajit Chatterjee

REFERENCES (continued)
Jaffe, Adam B. "Technological Opportunity and Spillovers of R&D: Evidence From Firms'Patent, Profits,
and Market Value," American Economic Review, 76 (1986), pp. 984-1001.
Kendrick, John W. "Productivity Trends: Capital and Labor," National Bureau of Economic Research,
Occasional Paper 53 (1956).
Lach, Saul, and Mark Schankerman. "Dynamics of R&D and Investment in the Scientific Sector," Journal of
Political Economy, 97 (1989), pp. 880-904.
Lach, Saul, and Rafael Rob. "R&D, Investment and Industry Dynamics," National Bureau of Economic
Research, Working Paper 4060 (1992).
Lichtenberg, Frank L. "R&D Investment and International Productivity Differences," National Bureau of
Economic Research, Working Paper 4161 (1992).
Lucas, Robert E. Jr. "Making a Miracle," Econometrica, 61 (1993), pp. 251-72.
Maddison, Angus. "Growth and Slowdown in Advanced Capitalist Economies: Techniques of
Quantitative Assessment," Journal of Economic Literature, 25 (1987), pp. 649-98.
Pakes, Ariel. "O n Patents, R&D, and the Stock Market Rate of Return," Journal of Political Economy, 93 (1985),
pp. 390-409.
Rapping, Leonard. "Learning and World War II Production Functions," Review of Economic and Statistics,
47 (1965), pp. 81-86.
Romer, Paul. "W hat Determines the Rate of Growth and Technological Change?" The World Bank,
Working Paper 279 (1989).
Searle, Alan D. "Productivity Changes in Selected Wartime Shipbuilding Programs," Monthly Labor Review,
61 (1945), pp . 1132-47.

Schultz, T. P. "Education Investments and Returns," in Hollis Chenery and T.N. Srinivasan eds., Handbook
of Development Economics, Vol. 1. Amsterdam: North Holland Publishers, 1988.
Solow, Robert M. "A Contribution to the Theory of Economic Growth," Quarterly Journal of Economics, 70
(1956), 65-94.
Solow, Robert M. "Technical Change and the Aggregate Production Function," Review of Economics and
Statistics, 39 (1957), pp. 312-20.
Stokey, Nancy L. "Learning by Doing and the Introduction of New Goods," Journal of Political Economy, 96
(1988), 701-17.
Young, Alwyn. "Learning by Doing and the Dynamic Effects of International Trade," Quarterly Journal of
Economics, 106 (1991), 396-406




15




Is the Foreign Exchange
Market Inefficient?
Gregory P. Hopper*
s

uppose you are in charge of investments
for your company and you have 1 million U.S.
dollars to invest for one month. You want to
obtain the highest return possible for the month
while assuming minimal risk, so you decide to
invest in short-term government securities:
Treasury bills. The rate of interest paid on U.S.
Treasury bills maturing in one month is cur­
rently 4 percent annually. However, while
reading the newspaper, you notice that Cana­
dian Treasury bills maturing in one month are

* Gregory Hopper is an economist in the Research Depart­
ment of the Philadelphia Fed.




currently paying 5 percent annually. Why not
sell the 1 million U.S. dollars for Canadian
dollars at the present exchange rate, invest the
proceeds in Canadian bills, and earn the 5
percent interest rate? Then, at the end of the
month, convert the Canadian dollars back to
U.S. dollars.
You tell your broker about your strategy, but
he objects. "The foreign exchange market is
efficient," he argues. "That means that inves­
tors eliminate exploitable profit opportunities.
Interest rates are always different between coun­
tries. If higher interest rates in a foreign country
really meant higher returns after taking expect­
ed exchange rate movements into account, in­
17

BUSINESS REVIEW

vestors would have recognized that years ago.
They would have moved funds from one coun­
try to another to capture those higher extra
returns, making interest rates converge in the
process. So, this extra return cannot really be
available."
"But I can earn an extra 1 percent interest in
the Canadian Treasury bill market," you pro­
test. "Why isn't that an extra 1 percent return?"
"Simple," replies your broker. "You have to
convert the Canadian dollars back to U.S. dol­
lars in a month, right? Given the current level
of interest rates and the exchange rate, the
market must expect that during the coming
month, the Canadian dollar will lose value in
terms of U.S. dollars at a 1 percent annual rate.
That way, you lose the extra 1 percent return
when you convert the Canadian dollars back
into U.S. dollars. Besides, you can't be sure
what the exchange rate will be when you con­
vert back to dollars; so you will assume a lot of
exchange rate risk."
Unconvinced, you decide to see what would
have happened had you followed this strategy
in the past. To do this, you look at monthly U.S.Canadian interest and exchange rate data over
the period June 1973 to April 1993. For each
month, you would have invested $1 million in
one-month U.S. T-bills whenever their interest
rate was higher than that on one-month Cana­
dian T-bills. However, in the months when the
Canadian T-bill interest rate exceeded the U.S.
T-bill interest rate, you would have converted
$1 million into Canadian dollars and invested
the sum in Canadian T-bills; at the end of the
month, you would have converted the accumu­
lated Canadian dollars back into U.S. dollars.
Over this period, there were 170 months in
which you would have made a Canadian T-bill
investment. Surprisingly, you find that this
strategy would have made an average $1072
per month in excess returns during the months
you invested in Canadian T-bills. The broker is
right about the exchange rate risk, though.
Because of the volatility of the U.S.-Canadian



MAY/JUNE 1994

dollar exchange rate, 26 percent of the time you
would have lost more than $5000 per month
during the months in which you invested in the
Canadian T-bill (Figure l) .1Sometimes, the risk
would have been quite large: during some
months you would have lost approximately
$40,000 per month, and in one particularly bad
month, you would have lost almost $60,000.
Thus, the average $1072 per month in extra
returns involves substantial risk. Even though
the risk-return tradeoff is not very good, do the
extra returns mean that the foreign exchange
market is inefficient?
In this article, we will consider this question.
Some economists argue that statistical prob­
lems falsely make it look like the extra returns
are there. Other economists do not deny that
the extra returns exist: one group claims the
extra returns are available because the market's
expectation of the worth of future currencies is
irrational; another group maintains that the
extra returns can be explained as compensation
to the investor for taking on the risk of losing
money. Ultimately, as we will see, economists
have not yet reached agreement; thus, we may
not rule out the possibility that opportunities
for extra returns do exist in the foreign ex­
change market.
EVIDENCE AGAINST
MARKET EFFICIENCY
If markets are efficient, then when the annu­
al foreign interest rate is x percentage points
above the domestic interest rate, the foreign
currency is expected to decline in value at an
annualized rate of x percent. If these expecta­
tions are borne out on average, over time the
extra x percent interest will be offset by the
currency's fall in value. But historically, these
expectations are not upheld: when foreign
interest rates rise above U.S. rates, the foreign

Sim ilar results arise for the short-term debt issued by
the governments of other major industrial countries.

FEDERAL RESERVE BANK OF PHILADELPHIA

Gregory P. Hopper

Is the Foreign Exchange Market Inefficient?

currency tends to rise in value rather than fall.
Moreover, when the U.S. interest rate rises
above the foreign interest rate, the U.S. dollar
tends, on average, to rise rather than fall in
terms of the foreign currency.2 These results
suggest a profit-making strategy for the inves­
tor: if the investor always puts his funds into the
short-term government securities of the major
industrial country that pays the highest interest
rate, he should make extra returns over time,
calling into question the efficiency of the for­
eign exchange market.3
Spot and Forward Exchange Rates. The
behavior of the forward exchange rate also
challenges foreign exchange market efficiency.
Before proceeding with this claim, however, a

2This result has been shown empirically to be generally
true for the currencies of the major industrial countries. See
for example Froot (1990).
3For a summary of the evidence against foreign ex­
change market efficiency, see Hodrick (1987).

description of the forward and spot exchange
rate markets is in order.4 Suppose the date is
September 1. If the spot exchange rate is 1
Canadian dollar per U.S. dollar, on September
1 the investor could exchange 1 Canadian dol­
lar for 1 U.S. dollar. Similarly, on September 1
an investor can lock into an exchange rate,
called the one-month forward exchange rate,
for a transaction that will occur one month from
that day. For example, an investor might be
able to buy the Canadian dollar in the forward
market at the forward exchange rate of 2 Cana­
dian dollars per U.S. dollar on September 1.
The forward exchange rate is agreed to and
known on September 1, but no money changes
hands. One month from that day, however, the
investor is obligated to trade 1 U.S. dollar for 2
Canadian dollars.

4For exposition, the description of the spot and forward
exchange rate markets has been simplified. The actual rules
governing these markets are slightly more complicated. For
a more detailed description, see Grabbe (1991).

FIGURE 1

Excess Dollar Returns

170 Canadian T-Bill Investments
From 6/73 to 4/93

40,000

20,000

0

-

20,000

-40,000

-60,000
10

20




30

40

50

60

70

80

90

100 110 120 130 140 150 160 170 180

19

BUSINESS REVIEW

In an efficient market, risk-neutral investors
should set the one-month forward exchange
rate equal to what they expect the spot ex­
change rate to be one month in the future.5
Otherwise, the market would be allowing ex­
ploitable profit opportunities. For example,
suppose on September 1 that investors expect­
ed the one-month-ahead spot exchange rate to
be 1 Canadian dollar per U.S. dollar, but the
market set the one-month forward exchange
rate to be 2 Canadian dollars per U.S. dollar.
Then, the market would be allowing an obvious
profit opportunity. On September 1, an inves­
tor could enter a one-month forward contract
to sell U.S. dollars in exchange for Canadian
dollars. One month later, the investor could
execute the forward contract by delivering 1
U.S. dollar in exchange for 2 Canadian dollars.
Then, if the spot exchange rate on October 1
turned out to be 1 Canadian dollar per U.S.
dollar as expected, the investor could sell his 2
Canadian dollars for 2 U.S. dollars in the spot
market. The investor would then have made a
$1 return, since he turned $1 into $2. However,
if the market had set the one-month forward
rate to be 1 Canadian dollar per U.S. dollar, and
the spot exchange rate on October 1 turned out
to be 1 Canadian dollar per U.S. dollar as
expected, no return would have been possible.
Since expectations about a specific event
usually prove incorrect, we cannot rule out
extra returns in any particular month, even if
the foreign exchange market is efficient. Sup­
pose that on September 1 the one-month for­
ward exchange rate is set to equal the expected
one-month-ahead spot exchange rate of 1 Ca­
nadian dollar per U.S. dollar. But on October 1,
expectations are proved wrong: the Canadian

5A risk-neutral investor does not need to be compensat­
ed for bearing the risk that the one-month-ahead spot ex­
change rate may turn out to be different from expectations.
Risk will be more fully discussed in the section "TimeVarying Risk Premia."

Digitized for20
FRASER


MAY/JUNE 1994

dollar exchanges for 1.25 U.S. dollars. Had an
investor bought the Canadian dollar in the
forward exchange market on September 1, he
would have made a $0.25 return on October 1.
So, in months when the Canadian dollar turned
out to be worth more than expected in terms of
the U.S. dollar, investors would earn extra
returns. In months when the Canadian dollar
turned out to be worth less than expected in
terms of the U.S. dollar, investors would incur
losses. As long as expectations were correct on
average, over many months the positive extra
returns would cancel out the negative ones and
no net extra return would be earned. The
market would be efficient even though extra
returns appeared randomly in some months.
Biased or Unbiased Predictor? The distinct
notions that the market is efficient and that
expectations are correct on average can be
combined in a single idea: the one-month for­
ward exchange rate should be an unbiased
predictor of the one-month-ahead spot exchange
rate. In any month, the forward exchange rate
in an efficient market will be the same as the
market's estimation of the one-month-ahead
spot exchange rate. Thus, the forward ex­
change rate will predict the one-month-ahead
spot exchange rate. If expectations are correct
on average, the forward rate prediction may
not be correct in any particular month but, on
average, ought to be correct. In some months,
the forward exchange rate will predict a onemonth-ahead spot exchange rate that is too
high, and in other months, one that is too low.
If the predictions are correct on average, the
high predictions should cancel out the low
predictions, so that the prediction will not be
biased either on the high side or on the low side.
Consequently, economists claim that the for­
ward exchange rate will be an unbiased predic­
tor of the one-month-ahead spot exchange rate
when markets are efficient and expectations
are correct on average.
Looking at the data on forward and spot
exchange rates, however, casts some doubt on
FEDERAL RESERVE BANK OF PHILADELPHIA

Is the Foreign Exchange Market Inefficient?

Gregory P. Hopper

FIGURE 2
the joint hypothesis that the market is
efficient and expectations are correct
One-Month Forward Rate
on average. It turns out that the for­
ward exchange rate is not an unbi­
vs. One-Month-Ahead Spot Rate
ased predictor of the one-monthahead spot exchange rate, a fact illus­
trated by looking at the historical re­
lationship between the one-month
forward and one-month-ahead spot
Canadian dollar-U.S. dollar exchange
rates for the period June 1973 to April
1993 (Figure 2). If the forward ex­
change rate were an unbiased predic­
tor of the one-month-ahead spot ex­
change rate, the forward exchange
rate should flu ctu ate random ly
around the one-month-ahead spot ex­
73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93
change rate. In that way, the forward
exchange rate would overpredict the
FIGURE 3
one-month-ahead spot exchange rate
as often as it underpredicts it. How­
One-Month Forward Rate
ever, the forward exchange rate for
vs. One-Month-Ahead Spot Rate
Canadian vs. U.S. dollars does not
tend to fluctuate randomly around
the one-month-ahead spot exchange
rate, but rather tends to stay below
the spot rate for extended periods
when the spot rate is rising and to stay
above the spot rate for extended peri­
ods when the spot rate is falling (Fig­
ure 2). The one-month forward ex­
change rate is therefore a biased pre­
dictor of the one-month-ahead spot
exchange rate.
Contrast this behavior with an
73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93
unbiased predictor I have construct­
ed (Figure 3).6 Notice that sometimes
the forward rate underpredicts and other times But it does not sy stem atically over- or
it overpredicts the future spot exchange rate. underpredict the future exchange rate as a
biased predictor would.
That the forward exchange rate is a biased
6The artificial one-month-ahead spot exchange rate se­
predictor of the one-period-ahead future spot
ries was constructed by adding to each actual U.S. dollarexchange rate suggests that the foreign ex­
Canadian dollar forward exchange rate in the series the
change market may not be efficient and that it
realization of an independent and identically distributed
may be possible to earn extra returns. Howev­
standard normal random variable.



21

BUSINESS REVIEW

er, economists are not convinced that forward
exchange rate bias proves that the foreign ex­
change market is inefficient. Consequently,
they have constructed explanations that allow
for the bias of the forward exchange rate while
at the same time maintaining market efficiency.
SOME EXPLANATIONS FOR SEEMING
MARKET INEFFICIENCY
Statistical Problems. A problem that plagues
the study of foreign exchange market efficiency
is that the one-month forward exchange rate
may be a biased predictor of the one-monthahead spot exchange rate, even though the
market is efficient. This can happen when
investors expect an event that has not yet oc­
curred to affect future exchange rates.
A real-world example of this problem con­
cerned the behavior of the Mexican peso in the
early 1970s. At that time, the Mexican govern­
ment fixed the spot dollar-peso exchange rate
at a constant value; however, it was widely
expected that sometime in the near future the
government would devalue the peso— that is,
change the rate so that the peso would be worth
less in terms of the dollar. Consider the situa­
tion before the government changes the fixed
exchange rate. When investors form expecta­
tions of the one-month-ahead spot exchange
rate, they have to take into account the chance
that the government might devalue the peso.
Thus, investors expect the peso to be worth less
in one month than it is today, even though the
spot exchange rate is currently fixed. In an
efficient market, then, risk-neutral investors
will set the peso in the one-month forward
market to be worth less in terms of the dollar
than it would be at the current fixed rate.
Therefore, until the government changes the
fixed exchange rate, the one-month forward
exchange rate will be a biased predictor of the
one-month-ahead spot exchange rate, even if
the market is efficient.
It would be a mistake, then, to conclude that
because the forward exchange rate is a biased
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predictor of the one-month-ahead spot exchange
rate, the market must be inefficient. This may
merely indicate that investors expect an event
that has not yet occurred to affect the future
exchange rate. International economists—quite
naturally—call this kind of statistical problem
a peso problem.
Failure of Rational Expectations. The prop­
osition that expectations are correct on average
is called rational expectations by economists.
The assumption of rational expectations per­
vades not only international finance but also
most branches of economics. Although it has
been described implicitly both in the bill-in­
vesting example and in our discussion of the
forward exchange rate market, it may be useful
to explain it in a simple context.
Suppose you play a game in which you flip
a fair coin. If heads comes up, you win $3. If
tails comes up, you lose $1. Clearly, the average
value you would win over time is $1, since half
the time you win $3, and half the time you lose
$1 [ ( $ 3 x l / 2 ) - ( $ l x l / 2 ) = $l]. So, if you expect
to win $1 on average, you have rational expec­
tations, since your estimate of the average val­
ue of the winnings is indeed its actual average
value. But if you expect to win $2 on average,
you do not have rational expectations.
The assumption of rational expectations
seems plausible. However, verification of ra­
tional expectations is difficult, since people's
expectations are not directly observable. Typ­
ically, researchers have attacked this problem
indirectly by using surveys of expectations to
represent true market expectations. For exam­
ple, in a 1987 study, Jeffrey Frankel and Ken
Froot provided evidence indicating that inves­
tors in the foreign exchange market may not
have rational expectations. Using survey data
of predictions made by private exchange-rate
forecasters, they found that forecasters make
biased predictions of future exchange rates.7

7This may also indicate a peso problem.

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Is the Foreign Exchange Market Inefficient?

Of course, not all economists accept their re­
sults, since they rely on survey data that may
not properly reflect true market expectations.
Whether the lack of rational expectations
explains the seeming failure of market efficien­
cy is certainly controversial. Many economists
find it hard to believe that people do not pos­
sess rational expectations, since this implies
that investors do not learn from their mistakes
but continue to make them systematically. To
illustrate the point, let us return to our coin­
flipping game. Imagine the following invest­
ment. A broker offers investors the chance to
play a game in which the investor can win $3 or
lose $1. The investor may play the game as
often as he likes, but he is not permitted to know
that the broker is flipping a coin to decide
whether he wins $3 or loses $1. At this point, the
investor cannot have rational expectations, since
he does not know about the coin. However, if
the investor played the game many times and
saw the pattern, he would then be able to
estimate the average winnings even if he never
saw the coin. He may misestimate the average
winnings at first, but he would not likely con­
tinue to do so.
Many economists believe that investors in
the foreign exchange market develop rational
expectations in the same way. Investors have a
great incentive not to make systematic mis­
takes in estimating future exchange rates, since
failure to do so can lead to large losses. The
absence of rational expectations could well
explain the seeming failure of foreign exchange
market efficiency, but many economists are
reluctant to discard the notion of rational ex­
pectations given its inherent plausibility.
Time-Varying Risk Premia. A third poten­
tial explanation for the seeming failure of effi­
ciency in the foreign exchange market is the
possibility of time-varying risk premia. Since
the one-month forward exchange rate is a bi­
ased predictor of the one-month-ahead spot
exchange rate, extra returns seem to be avail­
able in the foreign exchange market. But these



Gregory P. Hopper

extra returns may simply be compensation for
bearing risk. In the discussion of the billinvestment example and of the forward ex­
change rate market, we made a crucial assump­
tion: the investor is risk-neutral, which means
he does not need to be compensated for taking
risk. However, any exchange rate investment
in which future exchange rates are uncertain
involves exchange rate risk, risk for which a
risk-averse investor must be compensated.
Before returning to our example of the Trea­
sury-bill investment, it may be useful to explain
the concepts of risk neutrality and risk aversion
in the context of our coin-flipping game. Recall
that if heads turns up, the investor wins $3. If
tails comes up, the investor loses $1. On aver­
age, the investor wins $1 playing this game.
What is the most an investor would pay each
time to play this game? The answer depends on
his attitude toward risk. On average the inves­
tor stands to win $1 per coin toss, but for any
p articu lar toss of the coin , he b ears the risk of
losing $1. Even if the investor tosses the coin 10
times, he cannot be sure of winning the $1
average return; he may have a run of bad luck.
If the investor is risk neutral, he does not need
to be compensated for bearing risk. In this case,
he would be willing to pay up to $1 to play this
game, since that is the average winnings. If he
is risk-averse, he must be compensated for
bearing risk. Therefore, he would pay, at most,
something less than $1 to play this game. The
risk premium is the amount that the investor
must be compensated for bearing risk.
Suppose the risk-averse investor paid $.75 to
play this game. Since the average winnings ($1)
in this game exceed the cost to play ($.75), it
would seem that a return of $.25 is available.
But it would be wrong to conclude that the
market for coin-flipping games is inefficient;
rather, the $.25 is not a profit opportunity, but
compensation for bearing risk.
The situation is much the same in our billinvestment example. A Treasury bill denomi­
nated in U.S. dollars represents a claim on the
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BUSINESS REVIEW

consumption of U.S. goods, since it is ultimate­
ly worth a certain amount of U.S. dollars upon
maturity. Similarly, a bill denominated in Ca­
nadian dollars represents a claim on consump­
tion of Canadian goods. Since Canadian dol­
lars can be converted to U.S. dollars, and vice
versa, a U.S. bill is also a claim on Canadian
consumption, and a Canadian bill is a claim on
U .S. con su m p tion . B u t the m ag n itu d e of these

claims is uncertain: when a U.S. bill is re­
deemed for U.S. dollars, how much U.S. or
Canadian goods these U.S. dollars will buy
cannot be predicted with certainty. That de­
pends on the exchange rate, which is uncertain,
and the prices of U.S. and Canadian goods
when the bills are redeemed. Thus, U.S. and
Canadian bills are risky assets, even though
there's no risk that the governments that issued
them will fail to pay investors when the bills
mature.
If an investor is risk-averse, he will require a
risk premium to compensate him for holding
the riskier bill. If Canadian Treasury bills are
judged riskier than U.S. bills, Canadian bills
must pay a higher return than U.S. bills. Con­
versely, if U.S. bills are the riskier assets, they
must pay a higher return than Canadian bills.
Let's go back to our first example: suppose the
annual interest rate on the Canadian bill is 1
percentage point higher than that on the U.S.
bill. If risk were not compensated, on average
the Canadian dollar should turn out to be
worth 1 percent less on an annual basis in terms
of the U.S. dollar. In that way, the return to
holding U.S. bills or Canadian bills is the same.
However, suppose we discover that the Cana­
dian dollar turns out on average to be worth 1
percent more in terms of the U.S. dollar on an
annual basis. According to the risk premium
hypothesis, one interpretation of this situation
is that investors are risk-averse. Since the
Canadian dollar turns out, on average, to be
worth 1 percent more in terms of the U.S. dollar
on average, the investor is being paid a 2 per­
cent premium for holding the Canadian bill: he
24 FRASER
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MAY/JUNE 1994

receives a 1 percent capital gain on the Canadi­
an dollar, and he also receives an interest rate 1
percentage point higher than that on the U.S.
Treasury bill. Therefore, under the risk premi­
um hypothesis, our interpretation is that Cana­
dian Treasury bills are riskier than U.S. bills,
and investors are being paid a 2 percent risk
premium to induce them to hold Canadian
bills.
The risk premium on Canadian Treasury
bills can also be negative. Suppose annual
interest rates on U.S. Treasury bills are 1 per­
centage point higher than those on Canadian
bills, and we observe that the U.S. dollar turns
out on average to be worth 1 percent more on
an annual basis. Then the investor is giving up
2 percent in additional returns to hold the
Canadian T-bill: the 1 percent in interest he
would have earned on the U.S. T-bill and the 1
percent capital appreciation of the dollar. Un­
der the risk premium hypothesis, the Canadian
T-bill is seen as safer than the U.S. T-bill. Be­
cause Canadian T-bills are less risky, investors
must give up 2 percent in returns in order to
hold them. In this case, the risk premium on the
Canadian T-bill equals -2 percent.
The risk premium on the Canadian T-bill,
then, tends to be positive when Canadian T-bill
interest rates exceed those on U.S. T-bills and
tends to be negative when interest rates on U.S.
T-bills exceed those on Canadian T-bills. Since
the interest rate on U.S. T-bills frequently moves
above and below the Canadian T-bill rate, the
risk premium, if one exists, must frequently
vary between positive and negative values. It
is in this sense that economists speak of timevarying risk premia.
Risk premium explanations, although plau­
sible, are hard to square with recent economic
history. For example, during the mid-1980s,
U.S. interest rates were consistently above the
interest rates of many foreign countries. Over
the same period, the dollar gained in value at a
rapid rate against these countries' currencies.
Thus, the risk premium in U.S. dollar terms
FEDERAL RESERVE BANK OF PHILADELPHIA

Gregory P. Hopper

Is the Foreign Exchange Market Inefficient?

seemed to be large and positive. If the risk
premium explanation is true, U.S. dollar assets
were seen as much riskier than foreign assets
precisely at a time when common opinion held
that the dollar was strong because the U.S. was
a safe haven for investment. After 1985, despite
the fact that U.S. interest rates remained above
the interest rates of some foreign countries, the
dollar lost value at a rapid rate against these
countries' currencies. Thus, the risk premium
seemed to become negative, meaning U.S. as­
sets were seen as safer than foreign assets.
What produced such a dramatic change? Look­
ing back on the history of the 1980s, it's difficult
to point to specific events that may account for
these swings in the riskiness of U.S. or foreign
bills. (See Testing fo r a Time-Varying Risk Premi­
um for more about risk premia.)
FILTER RULE STUDIES
Another strategy for earning extra returns in
the foreign exchange market recommended by
some economists is a so-called filter rule. The
idea is simple. Whenever a foreign currency is
worth a certain percent more (like 1 percent) in
U.S. dollar terms than its previous low, invest

in foreign assets. Stay invested in those foreign
assets until the foreign currency is worth a
certain percent less than its previous high, then
switch back into dollar assets.8 In 1983, two
economists, Michael Dooley and Jeffrey Shafer,
showed that had an investor followed a 1 per­
cent filter rule, he could have earned a fairly
consistent return speculating in the major cur­
rencies.
Since these returns may have occurred by
chance, Richard Sweeney, in 1986, tested wheth­
er filter rule profitability can reasonably be
attributed to chance. He found that the returns
made in filter rule strategies cannot be ascribed
to luck and argues that filter rules indeed may
provide excess returns, even when transac­
tions costs are accounted for. Sweeney's tests,
however, assume that the risk premium is con­
stant. If the risk premium is time-varying, then
even if the returns do not occur by chance, they
may not be evidence against market efficiency.
With time-varying risk premia, the filter rule

8The reader who is familiar with the investment litera­
ture may recognize this as a form of technical analysis.

Testing for a Time-Varying Risk Premium
Economists have tried to find statistical evidence for the existence of time-varying risk premia, but they
have reached no firm conclusions. Typically, they have specified and tested an economic model of
investment in the foreign exchange market. A popular economic model, much used by academics and
practitioners alike, is the capital asset pricing model (CAPM). The CAPM relates the risk premium to the
difference between expected return on the market portfolio of securities and the risk-free rate of interest.
Mark (1988) and Hopper (1993) tested the CAPM to see if time-varying risk premia explained the fact that
the one-month forward exchange rate is a biased predictor of the one-month-ahead spot exchange rate.
Mark (1988) found results favorable to the risk premium hypothesis, but Hopper (1993) found evidence
against it.
A related model, popular among economists, is the consumption CAPM. Unlike the standard CAPM,
where investors are postulated as making only investment decisions, under a consumption CAPM,
investors are also hypothesized as making consumption decisions too. Mark (1985) and Kaminsky and
Peruga (1990) tested the consumption CAPM and reported results somewhat favorable to the risk premium
hypothesis, but not conclusively so. Hopper (1993) tested a version of the consumption CAPM, but found
evidence against the model. In general, most international financial economists believe that more evidence
must be accumulated before the risk premium hypothesis can be fully accepted.



25

BUSINESS REVIEW

could merely be putting the investor into the
foreign asset when the risk is high and taking
him out when the risk is low. Thus, if there are
time-varying risk premia, the returns found in
filter rule studies would be compensation for
bearing risk and would not be excessive on a
risk-adjusted basis.
IMPLICATIONS OF THE ANALYSIS
The reader who has progressed this far might
well feel somewhat disappointed with the anal­
ysis. The investor or corporate treasurer wants
to know whether extra returns can be made if
the foreign exchange market is inefficient. Is
the foreign exchange market inefficient? On
the one hand, excess returns seem to result
from following simple rules. On the other
hand, the returns may be explained by a peso
problem, the failure of rational expectations, or
time-varying risk premia. It's possible that
these phenomena may be present in the foreign
exchange market, but the evidence is far from
conclusive. Thus, at present, the best answer
economists can give to the question of market
inefficiency is— maybe.
How can this help the investor or corporate
treasurer? Economists may not be able to show
investors how to make money in the foreign
exchange market, but they do know enough to
help investors avoid losing money. The in­
sights gained by economists who study foreign
exchange market efficiency can be used to as­
sess proposed investment strategies. To see
how, let us consider a final example.
Suppose once again you are responsible for
managing investments for your company. An
investment consulting company approaches
you with a proposition. The proposition in­
volves not a simple filter rule, but rather a
complex rule involving arcane mathematics.
The consulting company shows that had their
rule been followed during the past 10 years, a 20
percent average annual rate of return would
have resulted. Moreover, clients who have
actually used the rule over the past year have
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MAY/JUNE 1994

continued to earn a 20 percent annual rate of
return. Should you use the rule? The analysis
in this article suggests some questions that can
guide your decision.
First, what is the time-varying risk in follow­
ing the strategy? After all, the complicated
mathematics in the rule might merely be in­
structing the investor to invest in very risky
assets at each point in time. If this were the case,
it would not be surprising to find a large aver­
age return. But the return would be at the
expense of assuming higher risk. Thus, the rule
is valuable only if it earns returns above what it
should earn when risk is accounted for. It's not
enough, then, for the consulting company to
claim a 20 percent average annual rate of re­
turn. The consulting company must show that
the returns are above normal on a risk-adjusted
basis, that is, the consulting company must
have a plausible model of time-varying risk
premia.
Second, could a peso problem account for
the rule's profitability? As we have seen, re­
turns may appear to be available if investors
expect an event that has not yet occurred. If a
peso problem exists, an investor following a
rule may make money before the event occurs
but would lose it after the event occurs. Thus,
if the market widely expects an event that has
not yet occurred (such as a country withdraw­
ing its currency from the European Exchange
Rate Mechanism), a peso problem must be
suspected when a technical trading rule seems
to offer excess returns.
CONCLUSION
An investor can earn extra returns by always
investing in the short-term government securi­
ties of the major industrial country that pays
the highest interest rate, although the risk to
such a strategy will be high; moreover, the
forward exchange rate is a biased predictor of
the future spot exchange rate. Economists are
at present undecided whether these facts should
be interpreted to mean that the foreign ex­
FEDERAL RESERVE BANK OF PHILADELPHIA

Gregory P. Hopper

Is the Foreign Exchange Market Inefficient?

change market is inefficient. A peso problem
might explain why the forward exchange rate is
a biased predictor of the future spot exchange
rate. Alternatively, if investors do not have
rational expectations or if there are time-vary­
ing risk premia, the foreign exchange market
may still be efficient. Some survey evidence
supports the claim that investors do not have
rational expectations, but such evidence is not
convincing to many economists, since surveys
may not reflect true expectations of investors in
the market. There is also some favorable evi­
dence on the existence of time-varying risk
premia, but the models are open to statistical
dispute.
Because the foreign exchange market may
well be inefficient, extra returns that cannot be
explained by the assumption of greater risk

might be earned in the foreign exchange mar­
kets. By employing filter rule strategies, the
investor can earn above normal returns that do
not appear to be attributable to chance. Wheth­
er these returns are truly evidence of market
inefficiency or are merely compensation for
bearing risk remains an open question.
Answering this question is important not
only for economists but also for practitioners in
the foreign exchange markets. Given the incon­
clusive nature of the literature and the possibil­
ity that the foreign exchange market is ineffi­
cient, investors cannot be sure whether they are
forgoing extra returns in the foreign exchange
market. How the literature on foreign ex­
change market efficiency will progress cannot
be predicted, but investors have a practical
incentive to follow its development.

REFERENCES
Dooley, Michael P., and Jeffrey Shafer. "Analysis of Short-Run Exchange Rate Behavior: March 1973 to
November 1981," in D. Bigman and T. Taya, eds., Exchange Rate and Trade Instability: Causes, Consequenc­
es, and Remedies. Cambridge, MA: Ballinger, 1983.
Frankel, Jeffrey A., and Kenneth A. Froot. "Using Survey Data to Test Standard Propositions on Exchange
Rate Expectations," American Economic Review (1987), pp. 133-53.
Froot, Kenneth A. "Short Rates and Expected Asset Returns," NBER Working Paper No. 3247 (January
1990).
Froot, Kenneth A., and Richard FI. Thaler. "Anomalies: Foreign Exchange," Journal o f Economic Perspectives
(1990), pp. 179-92.
Grabbe, J. Orlin. International Financial Markets. New York, NY: Elsevier Science Publishing Co., 1991.
Hodrick, Robert J. The Empirical Evidence on the Efficiency o f the Fonvard and Futures Foreign Exchange Markets.
New York, NY: Harwood Academic Publishers, 1987.
Hopper, Gregory P. "Can A Time-Varying Risk Premium Explain the Failure of Uncovered Interest Parity
in the Market for Foreign Exchange?" Working Paper 92-25, Federal Reserve Bank of Philadelphia (De­
cember 1992).
Hopper, Gregory P. "Time-Varying Consumption Betas and the Market for Foreign Exchange," mimeo,
Federal Reserve Bank of Philadelphia (November 1993).
Kaminsky, Graciela, and Rodrigo Peruga. "Can a Time-Varying Risk Premium Explain Excess Returns in
the Forward Market for Foreign Exchange?" Journal o f International Economics (1990), pp. 47-70.
Mark, Nelson C. "O n Time-Varying Risk Premia in the Foreign Exchange Market: An Econometric
Analysis," Journal o f Monetary Economics (1985), pp. 3-18.
Mark, Nelson C. "Time-Varying Betas and Risk Premia in the Pricing of Forward Foreign Exchange
Contracts," Journal o f Financial Economics (1988), pp. 335-54.
Sharpe, William F. "Capital Asset Prices: A Theory of Market Equilibrium under Conditions of Risk,"
Journal o f Finance (September 1964), pp. 425-42.
Sweeney, Richard J. "Beating the Foreign Exchange Market," Journal o f Finance (1986), pp. 163-82.



27

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PHILADELPHIA
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