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Tom Humphrey: An
Appreciation
John A. Weinberg

This issue of the Economic Quarterly marks the end of Tom Humphrey’s
tenure as editor. Tom, who is retiring at the end of 2004, took on the role
of editor of the Monthly Review in 1975 and continued in that post as the
publication evolved, first into the bimonthly Economic Review, and eventually
into its current form as the Economic Quarterly. Over that time, Tom has
guided to publication hundreds of articles by Department economists and
visiting scholars. He has also found the time to write more than 70 articles
for this publication, its predecessors, and the Bank’s Annual Report, not to
mention numerous articles for external publications. His editorial gaze has
seen many changes in our publication, our department, and the economics
profession over the last 30 years. Despite these changes, Tom’s editorial
guidance has provided a constancy to the quality of our publications, just as
his own work has stressed a certain constancy to the ideas and debates that
have engaged economists throughout the history of our profession.
Tom came to this Bank in 1970, an opportune time for a young monetary
economist with an interest in the history of thought on the subject. Much
of the profession’s thinking on aggregate fluctuations and inflation was still
dominated by the Keynesian view that emphasized movements in aggregate
demand as the force driving real output. The taxonomy of “demand-pull”
and “cost-push” inflation allowed for a variety of causes, mostly unrelated
to the central bank’s monetary policy. Empirical evidence on the Phillips
curve trade-off seemed to suggest that price stability could only be had at an
unacceptable cost of long-lasting, high unemployment. In the Keynesian view,
money was just one part of a broad spectrum of liquid assets, the evolution of
which further limited the central bank’s ability to control inflation.
The Keynesian view, however, faced a challenge from the monetarist
school of thought that placed the quantity of money at the center of the determination of the price level and other nominal variables. This quantity theory
view, which presumed the long-run neutrality of money, allowed for short run
real effects when money growth and inflation deviated from their expected
rates. Indeed, under this view erratic monetary policy was seen as a primary
Federal Reserve Bank of Richmond Economic Quarterly Volume 90/4 Fall 2004

Federal Reserve Bank of Richmond Economic Quarterly

cause of economic fluctuations. Where the Keynesian school saw causation
running from prices to money, the monetarist view was the opposite; the central bank, through its control of the monetary base, could achieve price stability
without a long-run inflation-unemployment tradeoff.
Of course, the 1970s experience of high unemployment and high inflation presented a particular challenge to the traditional Keynesian view. It all
appeared to underscore the importance of expectations, a view that gave rise
ultimately to the rational expectations revolution. This evolution of thinking
played itself out in the profession throughout Tom’s career at the Richmond
Fed and in the Economic Quarterly and its predecessors under Tom’s editorial
eye. Along the way, he established himself as a leading scholar on the history
of monetary thought.
Tom’s notable contribution has been to make clear that the debates that
took place during his career as a Federal Reserve economist were in fact not
new to the 1970s, or even to the 20th century. Applying his knowledge of
the history of monetary thought, Tom traced the debate from the mercantilist
writers John Law and James Steuart to their classical quantity theory critics
David Hume and others in the 18th century, to the Bullionist-Antibullionist
controversy in the early 19th century, to the Currency School-Banking School
debate in the middle decades of that century, to the mid-19th / early 20th
century disputes between cost-pushers Thomas Tooke and James Laurence
Laughlin and their opponents Knut Wicksell and Irving Fisher, and finally to
the German hyperinflation debate of the early-to-mid-1920s. He showed that
the debate keeps recycling because people forget the lessons of the past and
because, for better or worse, politicians and the public have tended to believe
that central banks have the power to boost output, employment, and growth
permanently. The result is that Keynesian ideas and their antecedents gained
currency when unemployment was the main concern, just as monetarist ideas
tended to reign when price stability was the dominant problem.
This historical perspective makes it clear that the central dimensions along
which people have thought and debated about monetary policy and inflation
have always remained essentially the same, even as economic thinking and
methodology have evolved. It also shows that intellectual debate can be affected by political forces and the fluctuating degree of social concern for
different problems. This last point provides an important cautionary tale for
current and future economists and policymakers. Indeed, Tom’s article in
this issue shows that the recurrence of debates and the interaction of political
forces with intellectual discourse are not unique to monetary concerns. Similar patterns can be seen in the history of thinking on such questions as the
effects of technology on labor.
We at the Richmond Fed have gained much from our association with
Tom Humphrey. We have benefited both from the red pen he has wielded to
make our papers more readable and, more importantly, from the long-view

J.A. Weinberg: Tom Humphrey: An Appreciation

perspective he has brought to our thinking about economics and monetary
policy. For all this we thank him, and we offer him our best wishes. We won’t
say good-bye, though, as I’m sure we’ll be hearing from him again.

Ricardo versus Wicksell on
Job Losses and
Technological Change
Thomas M. Humphrey

re technological innovations net destroyers of jobs? Many think
so and point to the information technology (IT) revolution and its
progeny, the offshore outsourcing of service activities, as prime current examples. Here the simultaneous advent of (1) undersea installation of
mega-bandwidth fiber optic cable allowing virtually costless transmission and
storage of data, (2) global spread of personal computers, and (3) standardization of software applications allegedly have made it profitable to export
abroad service functions once performed in the United States, thereby throwing Americans out of work (Friedman 2004).
Others, however, disagree and contend that new technology, including
outsourcing, creates at least as many jobs as it destroys (Drezner 2004). It
lowers costs, cheapens prices, stimulates demand, boosts output, and provides
new employment opportunities. Historical experience, these observers contend, reveals such to be the case. Since the start of the industrial revolution,
the number of jobs has grown as fast as the level of technology. Were the opposite true and innovation continually to displace workers, firms employing
ever-advancing technology requiring ever-fewer hands to operate it eventually
would produce the entire GDP with a labor force of one person. That outcome,
the observers note, has not happened.
Concern with the jobs-versus-technology issue is hardly new—think of
Karel Capek’s famous 1920 play R.U.R. Its plot has factory automation permanently replacing human workers with robots, a possibility Paul Samuelson modeled mathematically in 1988. Samuelson and a few others aside,
For valuable comments and suggestions the author is grateful to his Richmond Fed colleagues
Yongsung Chang, Huberto Ennis, John Hejkal, Roy Webb, and John Weinberg. The views
expressed in this article are those of the author and not necessarily those of the Federal
Reserve Bank of Richmond or the Federal Reserve System.

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Federal Reserve Bank of Richmond Economic Quarterly

however, commentators all too often have addressed the jobs-innovation question in an ad hoc, anecdotal manner conducive to selective reasoning, ambiguous conclusions, and emotional rather than rational responses. Too rarely has
a coherent analytical framework capable of yielding dispassionate, clear-cut
answers disciplined the discussion.1 This article traces the first attempts to
overcome this deficiency and to resolve the issue of technology’s effect on
jobs theoretically with the aid of a rigorous analytical model.
The model in question is David Ricardo’s famous machinery example.
It has capital-embodied innovation converting the wage-fund stock of consumable goods that sustains workers over the production period into fixed
machinery that cannot sustain them. The result is to lower permanently the
demand for labor, the number of jobs, and the level of output. Reversing his
original position that innovation benefits all, Ricardo in 1821 constructed his
model to demonstrate that workers have much to fear from technical change.
“All I wish to prove,” he said, “is, that the discovery and use of machinery
may be attended with a diminution of gross produce: and whenever that is the
case, it will be injurious to the labouring class, as some of their number will be
thrown out of employment, and population will become redundant, compared
with the funds which are to employ it” (Ricardo [1821] 1951, 390). Almost
one hundred years later, Knut Wicksell deployed essentially the same model,
albeit with a different assumed coefficient of elasticity of labor supply and
a different theory of labor demand, to argue that Ricardo’s predictions were
flawed and that jobs and real output need not be lost to technological progress.
Wicksell’s contribution was to refurbish Ricardo’s model with new ideas
emerging from the celebrated marginal revolution in economic theory that
occurred in the 1870s, 80s, and 90s. He replaced Ricardo’s classical wagefund theory of labor demand with a neoclassical marginal productivity explanation. Likewise, he substituted a fixed-factor-endowment interpretation of
labor supply for Ricardo’s old-fashioned subsistence-wage approach. These
improvements rendered the machinery model amenable to marginal analysis,
thereby bringing it closer to modern theorizing on the jobs-innovation issue.
They enabled Wicksell to challenge Ricardo’s melancholy predictions within
the framework of his own rehabilitated model. In short, in their respective
readings of the model, Ricardo was the pessimist and Wicksell the optimist as
far as innovation’s impact on jobs and the well-being of labor were concerned.
Among the few who have commented extensively on these opposing outlooks is Paul Samuelson. In his 1989 Scandinavian Journal of Economics
article “Ricardo Was Right!” Samuelson writes that “in the famous suit K.
1 Exceptions include research on the jobs-innovations question recently initiated by Gali
(1999), Basu, Fernald, and Kimball (1998), and Francis and Ramey (2002). These studies use
formal modeling to conclude that technical progress reduces employment in the short run, but not
the long. Job loss is transitory, not permanent.

T. M. Humphrey: Ricardo versus Wicksell

Wicksell vs. D. Ricardo—in which Knut Wicksell denied that a viable invention could reduce aggregate output [and jobs],” a “modern judge must rule
. . . against the plaintiff. My title therefore could have been . . . Wicksell was
wrong!” (Samuelson 1989, 47–8).
What follows takes issue with Samuelson, arguing, contrary to him, that
while both men were right in theory—that is, within the context of their particular variants of the hypothetical machinery model—only Wicksell was right in
practice. Realizations match the predictions emerging from his reading of the
model, but not from Ricardo’s. True, with respect to theory, both economists
employed impeccable logic and valid reasoning in constructing and manipulating their versions of the model to grind out the solutions they did. Their
versions left nothing to be desired on internal consistency grounds. With respect to practice, however, only Wicksell’s optimistic predictions have stood
the test of time. He rightly foresaw that output and jobs would expand with
labor-saving technological progress. He likewise predicted that labor-neutral
and labor-using innovations would boost real wages as well. History has confirmed his predictions and falsified Ricardo’s. It has revealed his version of
the model to be the more realistic of the two.
Besides providing historical perspective on the outsourcing issue, the
Ricardo-Wicksell controversy is of interest for at least six other reasons. First,
it shows how the same analytical model can, with different assumptions about
the values of its coefficients and the shapes of its functions, yield opposite results. In Ricardo’s machinery model where labor demand is key, technology
essentially enters the labor demand function as a variable bearing a negative
sign. It thereby ensures that innovation harms, rather than helps, labor. A positively signed technology variable, Wicksell noted, would reverse that result.
So too would a negatively signed variable if offset or negated by compensating profit-sharing schemes. Another key is the assumed slope of the labor
supply curve. Depending on that slope, labor-saving innovation either shrinks
or expands real output just as it destroys or preserves jobs.
Second, in spotlighting these polar results, the controversy shows how a
single model under alternative parameter settings can, when used to organize
discussion, encompass the entire range of opinion on the issue of jobs and
innovations. Whether one believes innovations on balance are job destroyers, job creators, or merely job preservers, one’s stance on this issue (albeit
not necessarily one’s acceptance of the model) falls somewhere between the
extremes of Ricardo and Wicksell.
Third, the controversy shows that even the greatest economists’ most cherished beliefs are not fixed and immutable. Ricardo recanted his long-held position that technical progress is Pareto-improving (that is, benefits all parties
and harms none) only when he became convinced that he had been in error
and that innovation could hurt labor even while it profited capital.

Federal Reserve Bank of Richmond Economic Quarterly

Fourth, the controversy shows that mainstream economists, notwithstanding their theoretical differences and social sympathies, tend to favor, on
efficiency grounds, public policies conducive to technical progress. With
respect to innovation, both Ricardo and Wicksell recommended that governments refrain either from suppressing or discouraging it regardless of whether
it destroys jobs (Ricardo) or preserves them (Wicksell). Ricardo in particular argued that anti-innovation policy magnifies job destruction and intensifies
harm done to labor. That is to say, he thought that while innovation hurts workers, attempts to prevent it only make matters worse. And Wicksell, though a
redistributionist, welcomed pro-innovation policies. They would, he believed,
help maximize the size of the pie—gross product—to be shared.
Fifth, the controversy shows how the study of a practical social issue
such as technology’s effect on jobs spurs new concepts and ideas that advance
economic science. Here, in addition to the machinery model itself, the new
concepts include Wicksell’s distinction between labor-saving, labor-using, and
labor-neutral innovations, namely those that lower, raise, or leave unchanged,
respectively, labor’s marginal productivity relative to capital’s. Still another
novel idea was the compensation principle according to which winners in an
economic change compensate losers so as to make both groups better off.
Wicksell devised this concept to argue that capitalists could profitably bribe
workers to accept technological innovations that otherwise would hurt them.
Sixth and most of all, the controversy serves as a cautionary tale.
Economists (not to mention general observers) have been discussing the effects
of innovations on labor for a long time. The analysis has always been fraught
with pitfalls, so one should be careful in jumping to conclusions, especially
regarding policy responses. A common pitfall (albeit one largely avoided by
Ricardo and Wicksell) is failure to distinguish between immediate and longerrun effects of innovation. Initially, technical progress is quite likely to hurt
groups of workers possessing specific acquired skills and abilities. One must
weigh this short-run cost of innovation against potential long-run benefits. In
the long-run, workers will invest in acquiring a different set of skills that will
enable them to operate the new technology. But this adjustment process may
involve a painful transition period, and society may wish to ease the pain of
those adversely affected during the transition. Yet because pain provides an
incentive to undertake the necessary changes, too much assistance may delay
the adjustment for an inefficiently long time.

1. THE MACHINERY QUESTION
Fears of job destruction through new technology antedate both today’s outsourcing scare and David Ricardo. Think of the manuscript copyists whose
skills Johannes Gutenberg’s 1436 invention of the printing press rendered

T. M. Humphrey: Ricardo versus Wicksell

obsolete. Later, like their medieval counterparts, 18th- and 19th-century observers watching the mechanization of textile and other key manufactures
also saw machinery as the source of technological unemployment (Rashid
1987; Berg 1980). Workers and their advocates then posed the celebrated
machinery question: Could new machines embodying advanced technology
permanently destroy jobs? Like modern economists, 18th-century economists
generally answered in the negative, and with the same reasoning, too. New
machines lower production costs. Lower costs mean cheaper prices. Cheaper
prices extend the market. They stimulate demand for consumption goods and
make it profitable for firms to expand output to satisfy the demand. Since extra
output requires hands to produce it, increased production absorbs the initially
laid-off workers and other workers as well. Technical advance, in addition
to benefiting workers by giving them lower prices, begets more jobs than it
destroys. Josiah Tucker said it all in his 1757 explanation of the effects of
machinery:
What is the Consequence of this Abridgment of Labour, both regarding
the Price of the Goods, and the Number of Persons employed? The Answer
is very short and full, viz. That the Price of Goods is thereby prodigiously
lowered from what otherwise it must have been; and that a much greater
Number of Hands are employed. . . .
And the first Step is that Cheapness, ceteris paribus is an inducement
to buy—and that many Buyers cause a great Demand—and that a great
Demand brings on a great Consumption; which great Consumption must
necessarily employ a vast Variety of Hands, whether the original Material
is considered, or the Number and Repair of Machines, or the Materials out
of which those Machines are made, or the Persons necessarily employed in
tending upon and conducting them: Not to mention those Branches of the
Manufacture, Package, Porterage, Stationary Articles, and Book-keeping,
&c. &c. which must inevitably be performed by human Labour. . . .
That System of Machines, which so greatly reduces the Price of
Labour, as to enable the Generality of a People to become Purchasers of
the Goods, will in the End, though not immediately, employ more Hands
in the Manufacture, than could possibly have found Employment, had
no such machines been invented (Tucker [1757] 1931, 241–2, quoted in
Rashid 1987, 265).

Other classical economists, including Adam Smith, Jean Baptiste Say, and
most notably David Ricardo, echoed this optimistic view. Ricardo, for example, wrote that mechanization (“a general good”) benefits all social classes
including workers, capitalists, and landlords alike. Mechanization conserves
scarce resources, improves efficiency, increases output, and lowers production
costs. The resulting fall in prices gives all consumers more purchasing power
to spend on an augmented bundle of goods. In this way “the labouring class
. . . equally with the other classes, participate[s] in the . . . general cheapness of
commodities arising from the use of machinery” (Ricardo [1821] 1951, 388).

10
2.

Federal Reserve Bank of Richmond Economic Quarterly
LABOR UNREST AND RICARDO’S ABOUT-FACE

Ricardo, in other words, initially believed that mechanization benefited workers by giving them more and cheaper goods. And it did so without destroying
jobs or lowering money wages. “I thought that no reduction of wages would
take place,” he wrote, “because the capitalist would have the power of demanding and employing the same quantity of labour as before, although he might
be under the necessity of employing it in the production of a new, or at any
rate of a different commodity” (Ricardo [1821] 1951, 387). Cheaper prices
at accustomed money wages together with availability of jobs in the innovating and non-innovating sectors of the economy—what more could workers
want? They should welcome mechanization, not oppose it. That was certainly
Ricardo’s initial expectation.
Then came episodes of labor unrest—the violent strikes, riots, protests,
and machine-breaking of 1811–21—that overlapped with periods of high unemployment in the post-Napoleonic War years of 1815–30. Famous among
the rioters of this time were organized bands of English handicrafters know
as Luddites. Taking their name from Ned Ludd, an apocryphal 18th-century
Leicestershire handloom weaver who supposedly destroyed two stocking
frames in a fit of rage, the Luddites conspired to smash the textile and clothfinishing machines that they thought were threatening their jobs. Observing
these uprisings, Ricardo changed his views radically in the famous Chapter 31
“On Machinery,” which he added to the third (1821) edition of his Principles
of Political Economy and Taxation.
In that chapter, which Samuelson (1988, 274) calls the best in the book,
Ricardo took labor agitation seriously. He had always modeled agents as rational maximizers acting in their own self-interest (Maital and Haswell 1977,
365). Might not workers, as such agents, have a legitimate case against machines? Might not machines be inimical to their interests as they themselves
maintained? Answering in the positive, Ricardo proceeded to construct a formal model (with a numerical example as its core) to demonstrate that “the
opinion entertained by the labouring class, that the employment of machinery is frequently detrimental to their interests, is not founded on prejudice
and error, but is conformable to the correct principles of political economy”
(Ricardo, [1821] 1951, 392).

OVERVIEW OF THE MODEL

Ricardo’s general equilibrium model says that when a capitalist installs new
labor-saving technology in the form of a machine, that same capitalist permanently displaces labor and renders it superfluous. That is the initial effect.
The intermediate, or transition, effects come when the redundant workers, in
an effort to regain their lost jobs, bid down the wage rate. Since in Ricardo’s
model, as in the labor-market models of most classical economists, the initial

T. M. Humphrey: Ricardo versus Wicksell

wage rate already is at the equilibrium (or Malthusian minimum subsistence)
level where the work force barely maintains its size with neither increase nor
diminution, the fall in wages below that level means that fewer workers can
survive and indeed must die off (see Samuelson 1994, 621). They continue to
die off in sufficient numbers until the wage rate returns to its subsistence equilibrium. In that new, long-run equilibrium, the output-reducing effect of labor
force diminution dominates the output-raising effect of the machine’s greater
efficiency so that gross output falls. Final steady-state equilibrium features
these conditions: smaller output, fewer jobs, fewer workers to fill those jobs,
subsistence wages, and raised profits (a necessary condition for the capitalist
to install new machinery in the first place).2
It is hard to avoid noticing the model’s current relevance. Replace the
word “machinery” with “outsourcing” and downplay the Malthusian overtones. What you get is the typical current complaint that technical progress in
the form of offshore outsourcing hurts labor at the same time it helps capital.

RICARDO’S EXAMPLE

The model itself has a group of laborers working for a single capitalist farmer
who represents the entire productive sector of the economy. The capitalist
initially has a total capital stock of £ 20,000, of which £ 7,000 is fixed capital
(buildings, equipment, and the like), and £ 13,000 is circulating capital (stores
of food and necessaries used to provision, or grubstake, labor over the period
of production and thus the wherewithal to employ, or demand, workers). The
importance to the model of circulating capital cannot be overstressed. It
and it alone constitutes the capitalist’s ability to employ workers. Nothing
else, neither the lower prices and higher profits that innovation yields, nor the
increased spending spurred by them, can affect employment in the model. To
Ricardo, circulating capital, rather than demand for commodities, constitutes
demand for labor. Anything that shrinks the stock of such capital automatically
shrinks labor demand. No compensating mechanism such as the previously
mentioned price and profit effects leading to increased demand for goods can
offset, or negate, the resulting adverse employment effects of reductions in
the stock of circulating capital.
Ricardo makes the foregoing point exceedingly clear in his example. He
begins by assuming that year after year in stationary equilibrium the capitalist
and his workers produce annual output worth £ 15,000. Of this sum, £ 13,000
2 In his Chapter 31 Ricardo always speaks of the new machine as raising profit, or net
income. Yet in his model and numerical example, profit remains constant. There is no inconsistency
here. Ricardo recognized that profit must rise by some positive amount, however small, call it
epsilon, to motivate the capitalist to invest in the risky new machine. To simplify his model,
however, he let epsilon assume a limiting value of zero. Nothing would have changed if he had
assigned it a positive value. See Barkai 1986, 599-600, footnote 2.

Federal Reserve Bank of Richmond Economic Quarterly

goes to replace the circulating capital stocks of food and necessaries workers
have consumed over the year, and £ 2,000 goes to the capitalist as profit (a 10.0
percent profit rate) to reward him for the use of his capital. Ricardo assumes
that the capitalist consumes, rather than invests, his profit such that no capital
growth occurs.
Things change when the capitalist decides on profit grounds to divert half
his labor force from the production of food and necessaries to the fabrication of
a new machine. Since the workers reassigned to machine-building produce no
food and fiber, farm output is halved to £ 7,500 while fixed capital rises from
£ 7000 to £ 14,500 by the £ 7,500 value of the new machine. The machine, of
course, is counted in final output during the time of its construction. But it is
not so counted afterward when, its fabrication completed, it assumes its place
in the economy’s stock of fixed capital assets and production reverts to farm
product only. When the capitalist extracts his £ 2,000 profit (still 10.0 percent
of his capital stock) from the £ 7,500 value of farm output, barely £ 5,500
worth remains to provide for the maintenance of labor in the following year.
In other words, circulating capital, or means of employing labor, falls from
£ 13,000 to £ 5,500. Given that circulating capital constitutes demand for
labor in Ricardo’s model, the capitalist can now employ but 42.3 percent, or
5,500/13,000, of the labor he employed before to produce a gross output of
half its former size. In short, switching labor from food production to machine
installation permanently reduces the fund available to grubstake and therefore
to hire workers. “There will,” Ricardo gloomily concludes, “necessarily be
a diminution in the demand for labour, population will become redundant,
and the situation of the labouring class will be that of distress and poverty”
(Ricardo [1821] 1951, 390).
Attempting to regain their lost jobs, the redundant workers put downward
pressure on the real wage rate forcing it to drop below the minimum subsistence level, which the Malthusian iron law of wages—represented in Ricardo’s
model by a horizontal labor supply curve—dictates as the equilibrium wage.
The resulting starvation of workers shrinks the population, the labor force, and
with it the gross product until the real wage returns to its subsistence level.
Here then is the second crucial component of Ricardo’s machinery model,
namely the iron law of wages. Developed by Richard Cantillon, Adam Smith,
and above all by Thomas Malthus, it says that population and labor force numbers respond to gaps between actual and subsistence wages. Their response
together with diminishing returns to extra doses of labor applied to the fixed
factor land keeps wages gravitating to subsistence. Thus below-subsistence
wages lead to starvation, high death rates, low birth rates, and population and
labor force decline. With fewer workers tilling the fixed amount of land, the
land-to-man ratio rises, which means that each laborer has more land to work
with and so experiences a rise in his productivity. Real wages rise with productivity until both return to the subsistence level where population shrinkage

T. M. Humphrey: Ricardo versus Wicksell

ceases and the labor force stabilizes in size. Conversely, above-subsistence
wages encourage population growth and the crowding of more workers on the
fixed land. Each worker has less land to work with and so experiences a fall
in his productivity and real wage, both of which converge to the subsistence
equilibrium where population growth ceases and the labor force stabilizes.
In short, diminishing returns together with the feedback of wage deviations
from subsistence on population growth operate to keep wages at subsistence.
Operating through these channels, mechanization in Ricardo’s model not only
displaces workers but kills them off as well. Workers indeed have a legitimate
case against machinery, or more precisely, against the ultra labor-saving bias
of the technical progress embodied therein.

REACTION TO THE MODEL

Ricardo’s demonstration appalled his classical contemporaries who found it
incompatible with the rest of his work. Typical was the reaction of John Ramsay McCulloch who complained that Ricardo’s machinery chapter ruined the
book (see St. Clair [1957] 1965, 234, 237). How could Ricardo, creator of the
comparative-advantage theory of gains from trade, contend that technological
innovation, a key source of comparative advantage, hurts labor? How could
he be so inconsistent? “[N]othing can be more injurious,” wrote McCulloch
to Ricardo on June 5, 1821, “than to see an Economist of the highest reputation strenuously defending one set of opinions one day, and unconditionally
surrendering them the next” (McCulloch [1821] 1951, 382). “I will take my
stand,” declared McCulloch, “with the Mr. Ricardo of the first not of the third
edition [of the Principles]” (385).
Ricardo’s peers also feared his analysis might discredit the free-market
precepts of classical economics, not to mention the aid and comfort it would
provide to anti-market reformers. “[A]ll those who raise a yell against the extension of machinery,” wrote McCulloch to Ricardo, “will fortify themselves
by your authority” and claim that “the laws against the Luddites are a disgrace
to the Statute book” (384–5).

RICARDO’S QUALIFICATIONS

Ricardo himself seemed sufficiently uncomfortable with his theoretical demonstration to express reservations about its practical relevance. At the end of his
chapter he noted that capitalists often mechanize their operations gradually instead of suddenly, thus allowing time for smoother adjustment. He also noted
that machine installation may be a manifestation of saving-financed growth in
capital rather than of conversion of the circulating-into-fixed components of a
capital stock of constant size. With no conversion, or shrinkage, of circulating
capital there is no displacement of labor. Jobs are not destroyed.

Federal Reserve Bank of Richmond Economic Quarterly

Indeed, circulating capital (and jobs) conceivably might expand together
with fixed capital. Tracing a causal chain from mechanization to falling production costs to cheaper product prices to rises in the real purchasing power
of nominal profit incomes, Ricardo suggested that such increased real profit
incomes could generate the saving from which investment in circulating, as
well as fixed, capital would come. Alternatively, capitalists might spend their
profit increases on the hiring of menial servants or on the purchase of luxury
consumption goods. These expenditures would create new demands for labor. But such demands, Ricardo realized, could reabsorb but a fraction of the
workers displaced by wage-fund contractions that exceeded profit expansions
in size. He further pointed out that, in the context of an expanding population,
mechanization, far from occurring autonomously, is often induced by rising
money wage rates relative to the cost of machines. (The money wage hikes
are, of course, necessary to maintain real wages at subsistence in the face of
rising food prices caused by diminishing returns as the growing population resorts to more intensive cultivation of the fixed land). Capitalists then attempt
to economize on costly labor by substituting relatively cheap machines for
it. This point, however, refers to pure capital-labor substitution under given
technology. It does not refer to technological change and so hardly qualifies
as an exception to Ricardo’s example.
Most of all, Ricardo warned of the futility and harmfulness of limiting or
discouraging the introduction of new machines in a world where foreign competitors would introduce them anyway. By lowering the return on domestic
relative to foreign capital, such restrictions would spur the export of capital,
leading to even less demand for labor at home. In short, whereas conversion of
circulating capital into machinery lowers domestic labor demand, capital exported abroad annihilates the demand altogether (Ricardo [1821] 1951, 397).
Another point recognized by Ricardo is that the banning of machines makes a
nation less efficient than its trade partners so that it obtains fewer labor hours’
worth of imports per each labor hour’s worth of exports given up. In other
words, rejection of machinery turns the country’s double factoral terms of
trade against it (O’Brien 1975, 226).
The upshot of these considerations is that no restrictions should be placed
on the introduction and use of machines. As Ricardo put it, “he would not
tolerate any law to prevent the use of machinery. The question was,—if they
gave up a system which enabled them to undersell in the foreign market, would
other nations refrain from pursuing it? Certainly not. They were therefore
bound, for their own interest, to continue it” ([1823] 1951 303). Ricardo’s
disapproval of anti-machinery policies aimed at preserving jobs indicates that
were he alive today he would likewise oppose all restrictions on offshore
outsourcing.
Nevertheless, Ricardo’s reservations and doubts about his model evidently
were not so serious as to invalidate his conclusion that capital-embodied inno-

T. M. Humphrey: Ricardo versus Wicksell

vations may harm labor. Thus when speaking before the House of Commons
on May 30, 1823, he abandoned all mention of doubts and reservations and
instead firmly reiterated “his proposition . . . that the use of machinery was
prejudicial . . . to the working classes generally. It was the means of throwing
additional labour into the market, and thus the demand for labour, generally,
was diminished” (Ricardo [1823] 1951, 303).

MCCULLOCH ON THE MODEL

Ricardo’s model was a very special one with several curious features. Job
destruction results solely from the conversion of circulating into fixed capital. The introduction of machinery leaves the total stock of capital (albeit
not its composition) unchanged. Fixed capital bears no depreciation charges,
implying that it has infinite life. Wages cannot fall permanently below their
Malthusian minimum subsistence limit. Profits, too, cannot fall and indeed
must rise by some amount, however small—call it epsilon—to induce innovation. (Here Ricardo created unnecessary confusion by having epsilon assume
a limiting value of zero so that profits apparently remain unchanged.) Output
falls.
Classical economist John Ramsay McCulloch, who as we have seen
objected to Ricardo’s analysis, focused on some of these peculiarities (see
O’Brien 1975, 227–28). He argued that displaced workers would find jobs
in making machines, including new machines to replace worn-out ones. On
this point he disagreed with Ricardo who, thinking that replacement was of
little importance, modeled machines as lasting forever and so incurring no
depreciation.
Regarding profits, McCulloch claimed that the capitalist would require
a rise (rather than the apparent zero change) in them to compensate for the
uncertainty of investing in untried new technology. Without additional profits,
the capitalist would have no incentive to install the risky new machine. This
criticism, too, missed its mark because, as previously mentioned, Ricardo
agreed that profit rises were necessary. The zero rises in his model were but
a proxy for and lower limit to the required positive rises.
McCulloch concentrated the bulk of his attention on the model’s output
result. Machines, he said, raise, not lower, output. They do so through a causal
chain running from lower production cost to lower product prices to increased
consumer demand in response to cheaper prices, and thence to the profitability
of producing extra output (and hiring extra hands) to satisfy that demand.
Replacing Ricardo’s concept of circulating capital as demand for labor with
the alternative notion of demand for goods as demand for labor, McCulloch
argued as follows (see O’Brien 1975, 227–8): If product demand is unitary
elastic such that price falls induce proportionate rises in quantity demanded,
then labor re-absorption is complete. The machine-installing sector rehires

Federal Reserve Bank of Richmond Economic Quarterly

the displaced workers. Similarly, if product demand is elastic such that price
falls induce more-than-proportionate rises in quantity demanded, then labor
re-absorption is more than complete. The sector rehires more workers than it
laid off.
Conversely, if product demand is inelastic such that price falls induce a
less-than-proportionate rise in quantity demanded, then labor re-absorption is
incomplete. Even so, the price cuts in this last case still leave consumers with
more purchasing power to spend on other goods, leading to increased hiring
of workers to produce those other goods.
Of course, consumers may choose not to spend all the extra purchasing
power that price cuts bring. If so, those consumers save. The saving, upon
its deposit in banks, is loaned out to capitalists to finance investment in new
capital goods. Demand for those goods and the labor to produce them rise.
Finally, if capitalists fail to pass cost reductions on into price reductions,
the resulting extra profits they receive are used either to increase their own
consumption or their purchases of investment goods. Either way, demand for
goods and, in turn, for labor, rises, and displaced workers are reabsorbed. To
be sure, re-absorption implies that workers must acquire new skills to enable
them to adapt to the better technology. Likewise, it implies that they must
learn new trades so that they can occupy new jobs to replace the old ones lost
to mechanization. These adjustments may involve pain. But such distress is
a reasonable cost to pay considering the gains to be made. Here in a nutshell
was McCulloch’s elaboration of Tucker’s earlier analysis.

8. WICKSELL’S CRITIQUE
McCulloch’s 19th-century critique of the machinery model was quite perceptive. But it remained for the Swedish neoclassical economist Knut Wicksell,
writing a hundred years after Ricardo, to deliver the definitive critique. In
his 1901 Lectures on Political Economy and his 1923 manuscript “Ricardo
on Machinery and the Present Unemployment”—a manuscript that Economic
Journal editor John Maynard Keynes rejected for publication in 1923 and
that Lars Jonung shepherded into print in that same journal in March 1981—
Wicksell argued that Ricardo had it all wrong. The latter’s long-run steady
state equilibrium had no room for lower wages and the resulting re-absorption
of displaced labor. Nor did it have room for the increased output that the fully
employed labor force equipped with improved technology could produce. Using the classical assumption that the long run equilibrium wage rate is fixed
exogenously at minimum subsistence, Ricardo was denied the neoclassical
insight that the equilibrium wage rate is instead determined endogenously by
labor’s marginal productivity at full employment. Deprived of that understanding, he failed to see that innovations do not reduce production, but rather
augment it. In short, there is no floor to equilibrium wages. The labor supply

T. M. Humphrey: Ricardo versus Wicksell

curve is vertical rather than horizontal. The demand for labor determines the
wage rate rather than the level of employment. Labor’s marginal productivity,
not the stock of circulating capital, constitutes labor demand. Labor-saving
“machinery”—a word Wicksell uses to denote disembodied technical progress
rather than fixed-capital-embodied technical progress in Ricardo’s sense of the
word—drives that demand through its influence on worker marginal productivity. If innovation is biased against labor, marginal product falls although
gross product rises.
Incorporating these changes into Ricardo’s model ensures that neither
jobs nor output are lost to the machine, that is, to innovation. On the contrary,
Wicksell ([1923] 1981, 200, 203) thought that with a sufficient drop in wages,
all the workers displaced by the machine would be rehired and, with the aid
of the new technology, would produce more output than they did before. The
innovation-induced fall in wages, variously estimated by him ([1901] 1934,
138; [1923] 1981, 202) to be between 10.0 percent and 1.0 percent in size,
was absolutely crucial.3 It ensured continual equality between the wage rate
and labor’s lowered marginal productivity, this equality being a necessary
condition for output to reach its maximum allowed by the innovation.

REDISTRIBUTION SCHEMES, OR PARETO OPTIMAL
BRIBES

As for Ricardo’s claim that the lower wages would invariably decimate labor
through starvation, Wicksell ([1923] 1981, 204–5) denied it. True, Wicksell
recognized that the post-innovation reduction in wages necessary to clear the
labor market and to allow output to reach its maximum level makes workers
worse off. Their jobs are preserved, but at dwindled pay. And he also realized
that if the resulting reduced wage is below subsistence, the labor force would
have to undergo Malthusian shrinkage just as in Ricardo’s case. But Wicksell
insisted that this outcome was not inevitable. Distinguishing between technical conditions necessary for maximum production on the one hand versus
distributional requirements of maximum social welfare or satisfaction on the
other, he noted that lower wages (equaling as they do labor’s marginal product
at full employment) satisfy the first set of conditions but not necessarily the
second. Maximizing satisfaction requires that everyone’s welfare, notably labor’s, be improved. To obtain that maximum, the government, Wicksell said,
must supplement wages with welfare relief payments sufficient to maintain
workers at the subsistence standard of living or above.
3 These wage falls are relatively small. In later writings, however, Wicksell entertained the
notion that wages might have to fall to zero or close to it to clear the labor market following the
introduction of new labor-saving technology (see Boianovsky and Hagemann 2003, 24–5). But he
seems to have regarded such extreme wage falls as purely hypothetical. In his careful and detailed
1901 and 1923 critiques of Ricardo’s model, he posits small, not large, reductions in wages.

Federal Reserve Bank of Richmond Economic Quarterly

Of course these relief payments ultimately would come from taxes on
profits. Even so, profits net of tax would be higher with the machine than
without it, thanks to the machine’s capacity to raise the profit rate. Nor would
the profit tax itself discourage production and so dry up the very proceeds
that constitute the source of relief payments. No such disincentive effects
could wreck the scheme; for Wicksell ([1896] 1958, 256–7) elsewhere had
used a model of imperfect competition to prove that a lump sum profit tax,
being independent of the level of output, is like a fixed cost. It does not affect
producers’ marginal cost and marginal revenue schedules and so leaves the
profit-maximizing level of output unchanged. The tax, in other words, shifts
the hump- or inverted U-shaped profit function downward by the amount of the
levy. But it does not change the output level where the function reaches its peak
or maximum value. Desiring to reach that peak, maximizing capitalists might
complain about the tax. Still, they would be doing the best for themselves by
maintaining the level of production rather than by curtailing it.4
The upshot was that society could devise a post-innovation tax-transfer
scheme that would leave capitalists better off and workers at least no worse
off than before. In this way, the fruits of technical progress could be shared by
all. Via income transfers, capitalists could effectively bribe workers to accept
those innovations that threatened to lower labor’s marginal product and so real
wages.
Wicksell, of course, realized that not all innovations would lower labor’s
marginal productivity and real wages. On the contrary, he thought that some,
perhaps most, innovations would raise those productivity and real wage variables instead of lowering them. “[T]he great majority of inventions and technical improvements,” he wrote, “tend to increase the marginal productivity
of both labour and land, together with their share in the product” (Wicksell
[1901] 1934, 143). For such labor-using innovations, transfers and bribes
would be unnecessary since workers would benefit anyway.
And although he excluded capital accumulation from his disembodiedtechnical-change version of Ricardo’s model, he elsewhere stressed the modern view that such accumulation creates jobs while raising labor’s marginal
productivity and real wages. “[T]he capitalist saver,” he wrote, “is thus,
fundamentally, the friend of labour, though the technical inventor is not infrequently its enemy” (Wicksell [1901] 1934, 164). It follows that innovation
accompanied by, or embodied in, new capital requires no income transfers to
benefit labor.
4 Wicksell failed to note that, under certain circumstances, taxing the profit that innovation
yields may dry up the future supply of that activity. If profit includes a cost payment, or normal
rate of return, necessary to coax forth innovation, then removing that return would destroy the
incentive to innovate. In other words, if the supply of innovation is elastic with respect to profit,
taxing profit will reduce the quantity of innovation supplied.

T. M. Humphrey: Ricardo versus Wicksell

To summarize, Wicksell disputed Ricardo’s ideas of (1) a lower bound,
or floor, to wages, (2) a post-innovation decline in output, jobs, and the labor
force, and (3) the absence of tax-transfer profit-sharing schemes.5 Discarding
these notions, Wicksell showed that the freedom of wages to fall to marketclearing levels where labor receives its marginal product promotes the re-hiring
of displaced workers. Equipped with the improved technology, these workers
together with their already employed counterparts produce additional output.
Redistribution mechanisms then allow labor to share the extra output with
capital so that both parties enjoy higher incomes after the innovation than before it. In Wicksell’s own words, “the only completely rational way to achieve
the largest possible production [is] to allow all production factors, including
labour, to find their equilibrium positions unhindered, under free competition,
however low they may be, but at the same time to discard resolutely the principle that the worker’s only source of income is his wages. He, like every
other citizen, ought rather to be entitled to a certain share of the earnings of
the society’s natural resources, capital, and (where they cannot be avoided)
monopolies” ([1924] 1969, 257).

10.

DIAGRAMMATIC ANALYSIS

Geometrical diagrams illustrate Ricardo’s and Wicksell’s cases (see Figure 1,
suggested by Samuelson [1989], 53). Panel 1 shows how Ricardo’s capitalist—
when converting circulating (wage fund) capital into fixed capital via the installation of the machine—causes the labor demand curve to shift downward
and to the left. The shifted demand curve intersects the horizontal labor supply
curve, the height of which is fixed by the Malthusian minimum subsistence
wage rate, at new equilibrium B. There the labor force is halved. Despite the
machine’s effect in enhancing efficiency, shown by the upward shift in Panel
2’s aggregate production function, fewer workers spell less output so that gross
product falls. At the same time, the innovation, by shifting outward Panel 3’s
factor price frontier, or menu of alternative maximum wage rate-profit rate
combinations, reveals that the rate of profit rises from A to B. The end result
is that output is down, jobs are down, the labor force is down, the wage rate is
unchanged, labor income (wage rate times labor force) is down, and the profit
rate and profit income (profit rate times total capital, a constant) are both up.
5 Hansson (1983, 55) argues that Wicksell’s criticism of the lack of a tax-transfer redistribution
mechanism in Ricardo’s model is misguided for two reasons. First, no such mechanism existed in
Ricardo’s time when welfare aid to unemployed workers, such as it was, consisted of poor relief
and charity. Second, 19th-century English capitalists operated in a political system that catered
to their interests. Given this state of affairs, they would have no incentive to depart from the
Ricardian equilibrium and agree to income transfers. No pro-labor social and legal sanctions were
in place to make them to do so.

Federal Reserve Bank of Richmond Economic Quarterly

Figure 1 Wicksell vs. Ricardo on Technological Innovation and Job
Loss
Panel 3: Factor Price Frontier

Panel 1: Labor Demand and Supply
Wage
Rate

W sub

D'L

Wage
Rate

S L(Wicksell)
B

●

W sub

●

0
L1

●

S L(Ricardo)

●

FPF'
FPF

●

SL
L

D'L

DL
Labor

FPF'
FPF

0
1

Profit Rate

Panel 2: Production Function
Q'=f (L,T')
Q=f (L,T)

Output
Q2
Q
Q1

C
●
●

●

0
L1

Labor

Ricardo: Conversion of circulating into fixed capital via the installation of a machine
shifts down the labor demand curve in Panel 1. At the same time, the advanced technology embodied in the machine shifts up Panel 2’s production function and Panel 3’s
factor price frontier. The horizontal labor supply curve in Panel 1 dictates that equilibrium move from A to B in all panels. Output, jobs, and the labor force drop. Wages
remain at subsistence. Profits rise.
Wicksell: Panel 1’s vertical labor supply curve dictates that innovation moves equilibrium
from A to C in all panels. Jobs and the labor force remain unchanged. Output and profits
rise. But wages fall below subsistence. The remedy for reduced wages is a tax-financed
subsidy that redistributes profit income from capital to labor. Move from C to B along
Panel 3’s factor price frontier to restore labor’s subsistence standard. Move further from
B toward E to make both parties better off than they were at initial point A.

Here is Ricardo’s conclusion that machine-embodied technical progress hurts
labor and helps capital.
Wicksell’s case, by contrast, replaces Ricardo’s horizontal labor supply
curve with a vertical supply curve corresponding to the assumption of fixed
factor endowments fully employed. As before, the labor-saving innovation
shifts down Panel 1’s labor demand curve at the same time it shifts up Panel

T. M. Humphrey: Ricardo versus Wicksell

2’s production function and Panel 3’s factor price frontier. To ensure that
the post-innovation production function is consistent with the downwardly
shifted labor-demand curve, the former has been drawn in the relevant range
with a flatter slope that its pre-innovation counterpart. Since the slope of the
production function represents labor’s marginal productivity—which, in turn,
constitutes the demand-for-labor curve in Wicksell’s analysis—it follows that
a flatter post-innovation production function signifies a lower marginal product
of labor and so corresponds to the lower labor demand curve.
Now, however, because the labor supply curve is vertical, labor demand
determines the wage rate rather than the level of employment. Equilibrium
moves from A to C rather than from A to B, as in Ricardo’s analysis. The
wage rate is allowed to fall to its new market-clearing level where all workers,
including those temporarily displaced by the machine, are (re)hired. The
wage fall is crucial. It keeps the wage rate equal to labor’s lowered marginal
productivity and allows output to rise to C, the maximum permitted by the
unchanged labor force working with the new technology. Most of all, the
wage fall permits the rise in the profit rate that spurs capitalists to expand
production and re-hire labor.
Of course the new equilibrium wage rate is below subsistence. But workers need not starve. The government can compensate—indeed more than
compensate—labor for below-subsistence wages by taxing profits and redistributing the proceeds to workers in the form of relief payments. The resulting
move from C to B and thence toward E on the new factor price frontier is
equivalent to restoring wages to and then raising them above their subsistence
level. While helping labor, such redistribution hardly hurts capital. On the
contrary, the transfer leaves both parties, capital and labor, better off than they
were at initial point A. With extra output to share, everybody gains.

11. WICKSELL ON OUTSOURCING
Wicksell’s analysis can be applied to the current offshore outsourcing problem. His advice to labor and the policymakers would go something like this:
Don’t discourage outsourcing. Like Ricardo’s machine, it has the potential to
benefit all parties through the extra output it permits. Instead, prevent domestic job losses by letting wages fall to market-clearing levels where it becomes
profitable to re-hire laid-off workers. Offset the wage reductions if you must
with compensatory profit-sharing or tax-transfer schemes. Such schemes, designed in cooperation with employers and/or the government, can spread the
gains from outsourcing over all parties, labor as well as capital. In this way,
outsourcing will prove to be unanimously beneficial despite being sharply
labor saving.

22
12.

Federal Reserve Bank of Richmond Economic Quarterly
CONCLUSION

Innovation destroys jobs in Ricardo’s model. But that model, the first rigorous
treatment of the machinery question, is too sparsely specified and idiosyncratic to support the generalizations he drew from it. His assumptions of a
horizontal supply-of-labor curve, a minimum bound to wages, and a wagefund-determined demand-for-labor curve—all essential to his contention that
technological change decimates jobs, output, and the labor force—already
were becoming anachronistic descriptions of the English labor markets of his
day. Certainly his assumptions are unrealistic characterizations of labor markets in developed nations now. Drop the assumptions, and you get Wicksell’s
optimistic results.
Labor-saving innovations, Wicksell often noted, represent the worst-case
scenario as far as job losses are concerned. And if such innovations cannot hurt labor under flexible wages and compensatory profit-sharing schemes,
how much less do workers have to fear from labor-neutral and labor-using
innovations? Indeed, Wicksell considered labor-saving innovations of the
kind depicted in his rendition of the machinery model to be the outliers, and
labor-neutral and labor-using innovations the norm. Counting on future technical progress to raise, not lower, labor’s marginal productivity, he expected
such advances to boost the demand for labor so much that the resulting wage
increases would render profit-sharing schemes unnecessary. Historical evidence, showing that innovation, employment, and real wages have advanced
together for centuries, supports his view and contradicts Ricardo’s.
As an economic theorist, Ricardo was in a class by himself. Arguably
the best pure theorist who ever lived, he was at least Wicksell’s equal and
head and shoulders above Tucker and McCulloch. But on the machinery
question, their vision of the job-creating power of technical change seems far
more convincing than his pessimistic view. President Richard Nixon in 1972
famously said, “We are all Keynesians now.” Similarly, most economists today
are Tucker/McCulloch/Wicksellians when it comes to technological progress.
They would say with some assurance that innovation and its offspring, offshore
outsourcing, are beneficial for the overall American economy and promise to
create more jobs in the long run than they destroy in the short.

REFERENCES
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Economy 94 (June): 595–613.
Basu, S., J. Fernald, and M. Kimball. 2004. “Are Technology Improvements

T. M. Humphrey: Ricardo versus Wicksell

Contractionary?” NBER Working Paper 10592.
Berg, Maxine. 1980. The Machinery Question and the Making of Political
Economy, 1815–1848. Cambridge: Cambridge University Press.
Boianovsky, M., and H. Hagemann. 2003. “Wicksell on Technical Change,
Real Wages and Employment.” Economics Department/University of
Brasilia Working Paper 274 (January 17).
Drezner, Daniel W. 2004. “The Outsourcing Bogeyman.” Foreign Affairs
83(3) (May/June): 22–34.
Francis, Neville, and Valerie Ramey. 2003. “Is the Technology-Driven Real
Business Cycle Hypothesis Dead? Shocks and Aggregate Fluctuations
Revisited.” Unpublished manuscript.
Friedman, Thomas L. 2004. “Small and Smaller.” The New York Times. Late
Edition. 4 (March): 29.
Gali, Jordi. 1999. “Technology, Employment, and the Business Cycle: Do
Technology Shocks Explain Aggregate Fluctuations?” American
Economic Review 89 (March): 249–71.
Hansson, Bjorn. 1983. “Wicksell’s Critique of Ricardo’s Chapter ‘On
Machinery.’ ” Journal of Economic Studies 10 (Winter): 49–55.
Jonung, Lars. 1981. “Ricardo on Machinery and the Present [1923]
Unemployment: An Unpublished Manuscript by Knut Wicksell.”
Economic Journal 91 (March): 195–8.
Maital, S., and P. Haswell. 1977. “Why Did Ricardo (Not) Change His
Mind? On Money and Machinery.” Economica 44 (November): 359–68.
McCulloch, John R. [1821] 1951. Letter to Ricardo, 21 June. In Letters,
1819–1821. The Works and Correspondence of David Ricardo, vol. 8.
Ed. Piero Sraffa and Maurice H. Dobb. Cambridge: Cambridge
University Press.
O’Brien, D. P. 1975. The Classical Economists. New York: Oxford
University Press.
Rashid, S. 1987. “Machinery Question.” In The New Palgrave: A Dictionary
of Economics, vol. 3. Ed. J. Eatwell, M. Milgate, and P. Newman. New
York: Stockton Press: 264–67.
Ricardo, David. [1821] 1951. On the Principles of Political Economy and
Taxation, 3rd edition. Vol. 1 of The Works and Correspondence of David
Ricardo. Ed. Piero Sraffa and Maurice H. Dobb. Cambridge: Cambridge
University Press.
. [1823] 1951. Speech of 30 May 1823 on Wages of
Manufactures—Use of Machinery. In Speeches and Evidence; vol. 5 of

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The Works and Correspondence of David Ricardo. Ed. P. Sraffa,
Cambridge: Cambridge University Press.
. [1819–1821] 1951. Letters, 1819–1821. Vol. 8 of The
Works and Correspondence of David Ricardo. Ed. Piero Sraffa and
Maurice H. Dobb. Cambridge: Cambridge University Press.

Samuelson, Paul. 1988. “Mathematical Vindication of Ricardo on
Machinery.” Journal of Political Economy 96 (April): 274–82.
. 1989. “Ricardo Was Right!” Scandinavian Journal of
Economics 91(1) (March): 47–62.
. 1994. “The Classical Classical Fallacy.” Journal of
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St. Clair, Oswald. [1957] 1965. A Key to Ricardo. London: Routledge &
Kegan Paul. Reprinted New York: A. M. Kelley.
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Schuyler’s Josiah Tucker. New York: Columbia University Press.
Wicksell, Knut. [1901] 1934. Lectures on Political Economy. Vol. 1. 1915
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. [1923] 1981. “Ricardo on Machinery and the Present
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Richard D. Irwin, Inc.

(Un)Balanced Growth
Andreas Hornstein

ince the late 1800s, real output in the United States has been growing
at a steady rate of about 3.5 percent per year (see Figure 1).1 With the
exception of the 20 years between 1930 and 1950, the real aggregate
capital stock of the United States has also been growing at that same steady
rate. Thus, although output tripled and capital increased by a factor of 2.5 over
this time period, the capital-output ratio remained roughly constant before
1930 and after 1950. Available data also indicate that the relative price of
capital in terms of consumption goods has not changed much since the 1950s.
In this article I review to what extent the stability of the aggregate capital
accumulation pattern actually masks substantial changes in the composition
of the aggregate capital stock—namely, changes in the relative importance of
equipment and structures.
The observed stability of output and capital growth rates and the capitaloutput ratio are part of the “stylized facts” of growth (Kaldor 1957, 1961). The
stylized facts also include the observations that the rate of return on capital and
factor income shares have remained stable over long time periods in the United
States and other industrialized countries.2 These observed regularities suggest
that a common theoretical framework might be able to account for the output
and capital accumulation path of the U.S. economy and other industrialized
economies over the last 100 years. Indeed, neoclassical growth theory was
built around the stylized facts of growth.
I would like to thank Kartik Athreya, Yongsung Chang, Jason Cummings, and Marvin Goodfriend for helpful comments. I also would like to thank Jason Cummings for making his data
available to me, and Jon Petersen for excellent research assistance. The views expressed in
this article are those of the author and not necessarily those of the Federal Reserve Bank of
Richmond or the Federal Reserve System.
1 Detailed descriptions of the data used in this paper are in the Appendix.
2 The rate of return on capital as measured by the real return on equity in the United States

has not changed much over time. Siegel (1998) calculates an average rate of return on equity of
7.0 percent for the time period 1802–1870, 6.6 percent for 1871–1925, and 7.2 percent for 1926–
1997. Using BEA figures on nonfarm private business factor incomes, I calculate wage income
shares for the time period 1929–2001. The average wage income share is 0.66 and varies between
0.63 and 0.72 with no discernible trend. If I exclude the housing sector, the average wage income
share is 0.75 and varies between 0.71 and 0.84, again with no discernible trend.

Federal Reserve Bank of Richmond Economic Quarterly Volume 90/4 Fall 2004

Federal Reserve Bank of Richmond Economic Quarterly

Figure 1 Real Output and Capital in the Private Business Sector,
1889–2001
2.50

Log Level, 1929=1

2.00

1.50

1.00

0.50

0.00
90

Capital Stock, Log
GDP, Log

Capital-GDP Ratio
Relative Price of Capital, Log

Notes: A detailed description of the data is in the Appendix.

Neoclassical growth theory assumes that there are two inputs to production: non-reproducible labor and reproducible capital. For a given level of
technology, production is constant returns to scale in all inputs, and there are
diminishing marginal returns for individual inputs. Technical change is taken
as exogenous and is assumed to increase the marginal products of capital and
labor for given amounts of inputs. Both inputs are assumed to be paid their
marginal product, and the higher marginal product of capital induces more
capital accumulation. In an equilibrium, capital accumulation proceeds at a
rate such that the return on capital remains constant. Since the labor endowment is fixed, higher productivity and more capital increases payments to labor
over time.
Within the framework of neoclassical growth theory, the stylized facts are
interrelated. The rate of return on capital, r, is the gross rental rate, u, minus
the value of depreciation, δp, plus any capital gains due to changes in the

A. Hornstein: (Un)Balanced Growth

Figure 2 The Relative Price of New Capital Goods, 1929–2001
2.00

1.80

Log Level, 1996=1

1.60

1.40

1.20

1.00

0.80
30

Equipment & Software (BEA)

Structures (BEA)

Equipment & Software (C&V)

Notes: A detailed description of the data is in the Appendix.

price of capital, p, divided by the price of capital:
r=

u − δp + p
uk y
p
=
−δ+
.
p
y pk
p

(1)

Conditional on a constant depreciation rate, δ, and a constant price of capital,
p = 0, the stability of either two of the three time series—capital-output
ratio, capital income share, and rate of return on capital—implies the stability
of the third time series.
In neoclassical growth theory, growth is driven by technological change,
and capital accumulation responds to technical change, but the source of technical change is not explored. Greenwood, Hercowitz, and Krusell (1997) have
argued that technical change in the sector that produces equipment capital is a
major source of growth. Their argument for relatively faster technical change
in this sector is based on the long-run decline of the relative price of equipment
capital. Since the 1960s, the price of equipment capital relative to the price of
consumption goods has been falling by about 40 percent, whereas the relative

Federal Reserve Bank of Richmond Economic Quarterly

price of structures has been increasing by about 10 percent (see Figure 2).3 If
the relative price of equipment capital has been declining, then the producers
of equipment capital must have become relatively more efficient.
Greenwood et al. (1997) evaluate the long-run contribution of different
sources of technical change, including the response of capital accumulation
to technical change. This is a reasonable procedure since long-run growth
depends not only on exogenous technical change, but also on the endogenous
capital accumulation response to technical change. But in order to determine the capital accumulation response to hypothetical time paths of technical change, one needs a theory of growth. Greenwood et al. (1997) use a
straightforward extension of the aggregate neoclassical growth model to their
multi-sector view of the economy, and they use a standard characterization
of long-run growth. In particular, they assume that the long-run equilibrium
growth path is balanced; that is, all variables grow at constant but possibly
different rates. The stylized growth facts represent a balanced growth path
(BGP) for the aggregate economy.
In order to obtain a balanced growth path, Greenwood et al. (1997) have
to assume that the elasticity of substitution between inputs is unitary; that
is, production is Cobb-Douglas (CD) in all sectors of the economy. I argue
that the accumulation of equipment and structures in the second half of the
20th-century United States is not characterized by balanced growth. In particular, I argue that equipment capital has become relatively more important
over time. This means that the stylized facts of growth do not apply to a
more disaggregate view of the economy.4 It also means that one cannot argue
for a unitary elasticity of substitution between inputs based on growth path
properties alone.
The changing composition of the aggregate capital stock does have implications for the implicit aggregate depreciation rate. Because the relative
share of equipment capital has increased and equipment capital depreciates
relatively faster than structures, the implicit aggregate depreciation rate has
increased substantially since the 1980s. With a constant return on capital and
a constant capital income share, neoclassical growth theory would then imply
that the economy should move towards a new BGP with a lower aggregate
capital-output ratio, which we have not observed. Thus, growth theory now
appears to be at odds with the stylized facts of growth, at least for the last 20
years.
3 Alternative measures of the relative price of equipment and software that try to account
better for changes in product quality (Cummins and Violante 2002) indicate an even bigger decline,
about 90 percent, over the same time period.
4 This observation alone should not be too surprising since we have known for a long time
about the extent of structural change in the U.S. economy and its limited impact on the growth
path of the aggregate economy. See, for example, Kuznets’ (1971) work on the secular decline of
the agricultural sector and the corresponding increase of the service sector.

A. Hornstein: (Un)Balanced Growth

In Section 1, I describe a balanced growth path for a simple growth model
where the relative price of capital is changing on the BGP. In the model are two
types of capital: equipment and structures. I show that the capital-output value
ratios are constant over time on the BGP but that the capital-output quantity
ratios are not constant. In Section 2, I first review the long-run evidence on
the ratio of the real capital stock to output. I find that from the late 1800s to
the present, the ratio of structures to GDP has been steadily declining, and the
ratio of equipment capital to GDP has been steadily increasing since 1950. I
then review the evidence on the ratio of the capital value to output value for
equipment and structures for the United States from 1950 on and find that these
ratios also do not remain constant. It thus appears that we can find evidence
for BGP properties of the U.S. economy at the level of aggregate capital only.
I then return to the evidence of stable aggregate capital-output ratios and argue
that this in fact appears to be evidence against, rather than for, balanced growth
since the 1980s because the depreciation rate of the aggregate capital stock
has increased substantially since the 1980s. In Section 3, I discuss some
implications for modeling long-run growth and economic policy.

BALANCED GROWTH WITH MULTIPLE CAPITAL GOODS

I now describe a simple three-sector growth model with two types of capital
and a fixed labor supply based on Greenwood, Hercowitz, and Krusell (1997).
Technical change is labor-augmenting and sector specific. I will discuss under
what restrictions balanced growth can occur—all variables grow at constant
but not necessarily equal rates. In particular, I am interested in BGPs where
the relative price of capital changes over time. I will focus on the production
structure of the economy and disregard any restrictions on preferences necessary for a BGP. I will assume that, for the implied time paths of prices, a
constant labor supply and the implied constant consumption growth rate are
consistent with an equilibrium.

A Three-Sector Economy
Consider an economy that produces three goods: a consumption good, c, and
two investment goods—equipment, xe , and structures, xs . Inputs to the production of any of the three goods are labor, n, and the stocks of the two capital
goods—equipment, ke, and structures, ks . Assume that there is perfect mobility of labor and capital between the production sectors. Let ρ i ≥ 0 denote the
fraction of labor allocated toward the production of the type i = c, e, s good.
Analogously, let φ i ≥ 0 and µi ≥ 0 denote the fraction of the equipment
capital stock and the structures stock allocated toward the production of type
i goods. Capital stocks and labor allocated to each sector are limited by the

Federal Reserve Bank of Richmond Economic Quarterly

total endowment of each input:
φ c + φ e + φ s ≤ 1, µc + µe + µs ≤ 1, and ρ c + ρ e + ρ s ≤ 1.

(2)

Production is constant returns to scale (CRS), and technical change is laboraugmenting:

(3)
c = C φ c ke , µc ks , Ac ρ c n ,

(4)
xe = E φ e ke , µe ks , Ae ρ e n , and

(5)
xs = S φ s ke , µs ks , As ρ s n .
The effective labor input in a sector equals employment times labor-specific
productivity, Ai . Labor-specific productivity may differ across sectors and
may change at different but constant rates. Time is continuous, and the rate of
change of labor-specific productivity is Âi = γ i .5 Investment augments the
existing capital stock after depreciation, δ i > 0:
k̇e = xe − δ e ke , and

(6)

k̇s = xs − δ s ks .

(7)

Balanced Growth with Constant Returns to Scale
On a BGP, all variables change at constant rates.6 Since total employment is
fixed by assumption, this means that, on a BGP, employment in each sector is
constant. Thus, the fraction of labor allocated to each sector, ρ i , is constant.
Given the resource constraint for equipment capital, the rate at which the use
of equipment capital grows in each sector must be the same as the growth rate
of total equipment capital. Therefore, the fraction of equipment capital, φ i ,
allocated to each sector remains constant on a BGP. By the same argument,
the fraction of structures, µi , allocated to each sector remains constant.
The equations for capital accumulation, (6) and (7), imply that on a BGP,
the investment-capital stock ratio is constant for each capital type:
k̂e =

xe
xs
− δ e , and k̂s =
− δs .
ke
ks

(8)

Thus, investment in new capital goods grows at the same rate as does the stock
of capital:
k̂e = x̂e , and k̂s = x̂s .

(9)

5 In the following, a dot represents the time derivative of the variable, ẏ = dy/dt, and a hat
denotes the growth rate of the variable, ŷ = ẏ/y.
6 Variables may remain constant on a BGP; that is, their rate of change is zero.

A. Hornstein: (Un)Balanced Growth
Since production is CRS, we can rewrite the production functions as

c/ke = C φ c , µc ks /ke , nρ c Ac /ke ,

xe /ke = E φ e , µe ks /ke , nρ e Ae /ke , and

xs /ks = S φ s ke /ks , µs , nρ s As /ks .

(10)
(11)
(12)

A sufficient condition for a BGP to exist is then that each argument in the
rescaled production functions, (10) to (12), is constant; that is,
k̂s = k̂e = Âc = Âe = Âs .

(13)

Note that, without imposing any additional restrictions on the form of the
production functions, a BGP exists only if labor-augmenting technical change
proceeds at the same rate in each sector.
Relative goods prices do not change on the BGP of a competitive equilibrium if technical change proceeds at the same rate in each sector. In a
competitive equilibrium, profit maximizing firms take prices as given and hire
inputs until an input’s rental rate is equalized with the value of the marginal
product of that input. Because inputs are perfectly mobile across sectors,
they are paid the same rental rate no matter where they are employed. The
conditions for optimal input use are then:7

ue = pe Ee φ e ke , µe ks , Ae ρ e n
(14)

= ps Se φ s ke , µs ks , As ρ s n = Ce φ c ke , µc ks , Ac ρ c n ,

(15)
us = ps Ss φ s ke , µs ks , As ρ s n

= pe Es φ e ke , µe ks , Ae ρ e n = Cs φ c ke , µc ks , Ac ρ c n , and

(16)
w = Cn φ c ke , µc ks , Ac ρ c n Ac

= pe En φ e ke , µe ks , Ae ρ e n Ae = ps Sn φ s ke , µs ks , As ρ s n As .
Normalize the price of the consumption good to one, and let pe (ps ) denote
the price of new equipment (structures) in terms of consumption goods. Let w
denote the real wage, that is, the price of labor in terms of consumption goods,
and let ue (us ) denote the rental rate of equipment (structures) capital. The
rate of return on investment in either of the capital goods is also equalized:
r=

us − δ s ps + ṗs
ue − δ e pe + ṗe
=
.
pe
ps

(17)

We now see that if labor-augmenting technical change proceeds at the
same rate in each sector, the relative price of capital will be constant on a BGP.
Because production is CRS—that is, homogeneous of degree one—the first
derivatives of the production function (marginal products) are homogeneous
7 The notation, I for I = C, E, S and i = e, s, n, denotes the partial derivative of the function
i
I with respect to the input i.

Federal Reserve Bank of Richmond Economic Quarterly

of degree zero. We can therefore rewrite equation (14) as

Ce φ c , µc ks /ke , nρ c Ac /ke

,
pe =
Ee φ e , µe ks /ke , nρ e Ae /ke

(18)

and, on a BGP, all ratios on the right-hand side are constant. The same argument applies to the relative price of structures.

Balanced Growth With Unitary Elasticity
of Substitution
We can construct a BGP where relative goods prices change at a constant rate
if production in each sector is of the Cobb-Douglas variety. On a BGP, the
total derivative of consumption (3) with respect to time is8
ċ = Ce φ e k̇e + Cs µs k̇s + Cn Ȧc ρ c n.

(19)

This expression gives us the growth rate of consumption goods in terms of the
growth rates of inputs and labor-augmenting technical change:
ċ
Ce φ e ke k̇e
Cs µs ks k̇s
Cn Ac ρ c nc Ȧc
=
+
+
.
(20)
c
C ke
C ks
C
Ac

Let ηIj ≡ ∂I /∂kj kj /I denote the input elasticity of type I production
with respect to the type j capital good. Then we can write the BGP growth
rates for outputs as9

ĉ = ηC,e k̂e + ηC,s k̂s + 1 − ηC,e − ηC,s Âc ,
(21)

(22)
x̂e = ηE,e k̂e + ηE,s k̂s + 1 − ηE,e − ηE,s Âe , and

(23)
x̂s = ηS,e k̂e + ηS,s k̂s + 1 − ηS,e − ηS,s Âs .
On a BGP, investment grows at the same rate as the capital stock (9), implying
the following system of equations for the growth rates of consumption and
capital goods:

ĉ = ηC,e k̂e + ηC,s k̂s + 1 − ηC,e − ηC,s Âc , (24)

(25)
1 − ηE,e k̂e − ηE,s k̂s = 1 − ηE,e − ηE,s Âe, and

(26)
−ηS,e k̂e + 1 − ηS,s k̂s = 1 − ηS,e − ηS,s Âs .
Thus, a BGP with potentially different rates of labor-augmenting technical
change exists if the input elasticities are constant. That is, the production
functions are of the Cobb-Douglas (CD) variety. For example, the production
8 I have used the fact that the total labor endowment is constant, and, on a BGP, the fraction
of resources allocated to each sector remains constant.
9 Because of constant returns to scale, the input elasticities sum to one.

A. Hornstein: (Un)Balanced Growth
function for consumption goods is
1−ηC,e −ηC,s
η
η

,
c = φ c ke C,e µc ks C,s Ac ρ c n

(27)

with ηC,e , ηC,s , 1 − ηC,e − ηC,s ≥ 0. Analogous expressions hold for the
production of new equipment and structures. For CD production functions,
the elasticity of substitution between inputs is unitary. That is, cost minimizing
firms respond to a 1 percent increase in the relative price of an input with a
corresponding 1 percent reduction in the relative usage of that input such that
the cost share of the input remains constant at the input elasticity.10
We can now derive expressions for the rate of change of relative capital
goods prices. Using the CD production structure, we can rewrite the condition
for the profit maximizing use of equipment capital (14) as
ηC,e c
ηE,e xe
ηS,e xs
= pe
= ps
.
(28)
ue =
φ c ke
φ e ke
φ s ke
Given the constant input elasticities and the constant allocation shares of total
equipment capital, this expression implies that the rates of change for relative
prices are given by
p̂e = ĉ − k̂e and p̂s = ĉ − k̂s

(29)

Thus, the relative price of capital in terms of consumption goods will change
if capital accumulation proceeds at a different pace than does consumption
growth. On the other hand, even if capital accumulation proceeds at a different
pace than does consumption growth, the value of the capital stock relative to
the value of consumption will remain constant. Finally, equation (28) for
equipment and the corresponding expression for structures also imply that the
rate of return on investment in either of the capital goods is constant.
The implications of the CD production structure for a BGP are most easily seen if we further simplify the production structure and assume that input
elasticities (income shares) are equal in all industries, ηI,j = ηj (see, for example, Greenwood, Hercowitz, and Krusell 1997). In this case, consumption
and capital growth rates on the BGP are

ĉ = ηe Âe + ηs Âs + 1 − ηe − ηs Âc ,
(30)

(31)
k̂e = 1 − ηs Âe + ηs Âs, and

(32)
k̂s = ηe Âe + 1 − ηe Âs .
The rates of change for relative prices are

p̂e = 1 − ηe − ηs Âc − Âe , and p̂s = 1 − ηe − ηs Âc − Âs .
(33)
10 This fact is immediate from equations (14) to (16) and the constant input elasticities.

Federal Reserve Bank of Richmond Economic Quarterly

Note that the relative price changes directly reflect differences in the rates of
labor-augmenting technical change.
Finally, we can define real output as total output in terms of consumption
goods:
y = c + p e xe + p s xs .
Since capital investment grows at the same rate as capital stocks and since the
value of capital grows at the same rate as consumption, real output grows at
the same rate as consumption.

OBSERVATIONS ON CAPITAL ACCUMULATION
IN THE UNITED STATES, 1869–2001

The fact that the relative price of equipment capital declined substantially,
whereas the relative price of structures increased somewhat, suggests a differential productivity growth rate in the two broadly defined capital goodsproducing sectors. An economy with productivity growth rates that are
constant but different across capital goods-producing sectors can still achieve
a BGP. Note that, however, on the BGP, the capital-output value ratios remain
constant but that the capital-output quantity ratios do not. I now argue that
there is no evidence for balanced growth in the United States economy at this
more disaggregate level. Over the long run, capital-output quantity ratios do
not appear to be stationary, and, for the post-WWII period, the equipment
capital-output value ratio does not appear to be stationary either. Finally, I
argue that one of the conditioning assumptions for balanced growth at the
aggregate level—namely, constant depreciation rates—also does not hold for
the late 20th century. Some of the changes in depreciation rates have to be
attributed to the changing composition of the aggregate capital stock.
The structure of the U.S. economy changed drastically over the time period
I consider. For example, government accounted for between 4 and 5 percent
of GDP in the late 1800s, but since the 1930s, government’s share in GDP has
increased to about 10 percent. Within the private business sector, the share of
value added that originated in agriculture declined from 30 percent in 1889
to 10 percent in 1930. It then stayed there until the mid-1940s and since then
has declined to less than 1 percent.11 These changes in GDP shares are also
reflected in the changed employment shares of government and agriculture,
but they are not the focus of this article.12 In an attempt to limit the potential
impact of this structural change on the BGP properties of capital-output ratios,
I limit my analysis to output and capital in the nonfarm private business sector.
11 The shares for the pre-1929 period are calculated from Kendrick’s (1961) constant dollar
estimates, and the shares for the post-1929 period are from BEA’s current dollar estimates. In
1930, the shares based on constant and current dollar estimates are both roughly the same.
12 See, for example, Kuznets (1971).

A. Hornstein: (Un)Balanced Growth

Figure 3 Real Capital and Output in the Nonfarm Private Business
Sector, 1889-2001
Panel A: Equipment

2.50

1929=1

2.00
1.50
1.00
0.50
0.00
90

Panel B: Structures

2.50

1929=1

2.00
1.50
1.00
0.50
0.00
90

Capital-GDP Ratio

GDP, Log

Capital Stock, Log

Notes: A detailed description of the data is in the Appendix.

Capital-Output Ratios for Equipment and Structures
Over the long run, capital-output quantity ratios for either equipment or structures do not appear to be stable. Figure 3 displays real nonfarm private GDP,
nonfarm private equipment and structures, and the relevant capital-output ratios from 1889 to 2001. The stock of structures includes residential structures.
There is a clear downward trend in the capital-output ratio for structures—the
ratio has been falling steadily since the late 1800s, from 1.4 to 0.6 today. The
behavior of the equipment capital-output ratio is more ambiguous. This ratio
appears to be quite stable before 1929, then declines substantially until the
1950s and from then on shows a clear upward trend.
We now study the capital-output quantity and value ratios for the nonfarm
private business sector, excluding housing. A big component of the housing
sector output in National Income and Product Accounts (NIPA) consists of

Federal Reserve Bank of Richmond Economic Quarterly

Figure 4 Capital-Output Ratios in the Nonfarm Private Business
Sector Excluding Housing, 1950–2001
Panel A: Real Capital-Output Ratios

Panel B: Nominal Capital-Output Ratios

Notes: A detailed description of the data is in the Appendix.

imputed rental income for owner-occupied housing. One could argue that
NIPA data that includes residential housing is less reliable and that one should
therefore focus on the non-residential business sector. Figure 4 graphs the
capital-output quantity and value ratios for this sector. Even though residential
structures are now excluded, the structures-output quantity ratio continues to
decline for the period from 1.3 in 1950 to 0.8 in 2000. The structures-output
value ratio, however, remains relatively stable over this time period. For
equipment capital, we see that both the quantity and the value capital-output
ratio increase from 0.4 in 1950 to 0.6 in 2000.
Figure 4 also includes real and nominal equipment-output ratios based on
updated data from Cummins and Violante (2003). Cummins and Violante
(2003) argue that the official NIPA figures overestimate the inflation rate
for equipment capital because they do not appropriately account for quality
change. Based on Cummins and Violante (2003), the real equipment-output
ratio increased drastically from 0.2 in 1960 to 0.7 in 2000. On the other hand,

A. Hornstein: (Un)Balanced Growth

according to their numbers, the nominal equipment-output ratio actually fell
from 1.6 to 0.5.13

Other Related Work
Maddison (1991) also argues that real capital-output ratios are not stationary, in
particular, that the ratio of nonresidential capital to GDP changed substantially
for some countries other than the United States. According to Maddison (1991,
67), from 1890 to 1987 the capital-GDP ratio doubled for the UK (from 0.95
to 2.02) and almost tripled for Japan (from 0.9 to 2.8). Maddison (1991)
also calculates big increases for France and Germany from 1913 to 1987.
Finally for the 19th-century United States, Gallman (1986, 192) argues that
the real equipment capital-GDP ratios actually increased from 0.15 in 1840 to
0.91 in 1900 and that the corresponding nominal capital-GDP ratios increased
from 0.23 in 1840 to 0.40 in 1900. Related to the stability of capital-output
ratios on a BGP is the stability of expenditure shares in GDP. Along these lines
King, Plosser, Stock, and Watson (1991) argue that the behavior of real private
GDP, consumption, and investment in the United States satisfies the balanced
growth conditions from 1949 to 1988. Their statistical tests indicate that
output and consumption, as well as output and investment, are cointegrated
and that the consumption-output and investment-output ratios are stationary.
Whelan (2003) reviews the evidence for balanced growth of two expenditure
components: consumption and investment. He also emphasizes that in the
face of drastically changing relative prices of investment in producer-durable
equipment and investment in structures, one should not expect that the ratios of
real consumption to real investment in either of the two types remain constant,
but rather that the ratios of nominal expenditures remain constant. Whelan
shows that for an extended sample—the United States from 1949 to 2000—
one can reject the null hypothesis of cointegration for real investment and real
consumption, but one cannot reject the null hypothesis of cointegration for
nominal consumption and nominal investment.

Depreciation
Depreciation rates for equipment capital have been increasing significantly
since the 1980s (see Figure 5). This increase reflects mainly an aggregation
13 At first, one might be surprised that the capital-output value ratios for Cummins and Vi-

olante (2003) are so different from the corresponding NIPA ratios. After all, we usually observe
values, and the problem is one of obtaining a quantity index by deflating values with an appropriate price index. The problem with capital is that most capital is not traded, so we do not observe
values. The NIPA procedure to obtain current values of the capital stock is to evaluate the estimated real capital stock at the current prices of capital stocks. I have used the same procedure
to obtain capital stock values for Cummins and Violante (2003), and there is no reason to expect
that the two estimates should agree on their values.

Federal Reserve Bank of Richmond Economic Quarterly

Figure 5 Depreciation Rates, 1926–2001
30
25

Percent

20
15

10
5
0
30

Information Technologies and Software
Equipment and Software

Aggregate Capital Stock
Nonresidential Structures

Notes: A detailed description of the data is in the Appendix.

effect since information technology (IT) equipment has higher depreciation
rates than other equipment capital types, and the relative share of IT in total
equipment has been increasing as part of the IT revolution. Assuming a stable
real rate of return on capital, higher depreciation rates require a higher rental
rate of capital to satisfy the optimal capital accumulation condition (1). This,
in turn, implies that the aggregate capital-output ratio should have declined
significantly, since the capital income share has remained stable for this time
period. Thus, the stability of the aggregate capital-output ratio since the 1980s
suggests that the behavior of the U.S. economy has not been well approximated
by a BGP.
The aggregate depreciation rate on private nonfarm capital increased from
about 4 percent before the 1970s to about 10 percent in the year 2000 (see
Figure 5). Based on the neoclassical growth model, this increase in the depreciation rate should have resulted in a significant decline of the capital-output
ratio. Before 1970, the capital-output ratio for the nonfarm private business
sector was about 2.5 (1.5, excluding housing), and the capital income share
was about 0.33 (0.25, excluding housing) (cf. footnote 2). Assuming a con-

A. Hornstein: (Un)Balanced Growth

stant price index for the aggregate capital stock and use of the optimal capital
accumulation condition (1) implies a 9.3 (12.5, excluding housing) percent
rate of return on capital.14 An increase of the depreciation rate to 10 percent
would then imply that the capital-output ratio should decline to 1.7 (1.1, excluding housing), conditional on a constant return on capital and a constant
capital income share. We have not observed such a decline in the capital-output
ratios.15
I interpret the depreciation rates constructed from the BEA depreciation
and capital stock series as physical depreciation of the capital stock. Whelan
(2002) argues that this is not a valid interpretation of the BEA depreciation
rates since the BEA frequently applies depreciation schedules in its procedures
that include both physical and economic depreciation. While this is a valid
concern, it does not necessarily affect our conclusions. First, to the extent
that the BEA data overestimate the depreciation of the capital stock, they also
underestimate the size of the capital stock. This means that the equipment
capital-GDP ratio should have increased even faster over the last 20 years,
implying that the aggregate capital-output ratio would have increased rather
than remained stable. Second, it is not clear that the higher depreciation
rate observed for the BEA data can only be attributed to faster economic
depreciation. IT equipment depreciates at a rate of more than 20 percent,
which is substantially higher than the 10 to 20 percent rates of other equipment
capital.16 Thus, the composition effect induced by an increase of the relative
share of IT equipment alone increases the aggregate depreciation rate.

CONCLUSION

Does it matter whether the time path of the economy is characterized by
balanced growth? Yes. Observed empirical regularities are important for
the development of our understanding of how the economy works, and a
breakdown in one of these empirical regularities might be viewed as a setback.
The perceived stylized facts of growth certainly stimulated research on growth,
and the neoclassical growth theory provided a simple interpretation of the facts
that added to the appeal of that theory. On the other hand, since the behavior
of the capital-output ratio over the last 20 years apparently no longer conforms
14 Note that these estimates for the return on capital are significantly higher than other estimates, such as Siegel’s (1998) estimate of 7 percent for the long-run rate of return on equity.
15 One can argue that it takes some time for the economy to converge to the new BGP, given

the new higher depreciation rates. Note, however, that for the observed capital income shares and
depreciation rates, convergence—as predicted by the growth model—tends to be fast, and a higher
depreciation rate speeds up the convergence process.
16 In a recent reevaluation of the BEA depreciation scheme for PCs, Doms et al. (2003)
have found annual depreciation rates of up to 35 percent, even accounting for quality change and
economic depreciation. The work of Doms et al. (2003) has already been incorporated in the
2003 NIPA revisions.

Federal Reserve Bank of Richmond Economic Quarterly

to the stylized facts, it may just point to some structural break. After all, there
was also a structural break in the aggregate capital-output ratio between 1930
and 1950, and the ratio was quite stable before 1930 and after 1950. We
would then have to come up with some explanation for this structural break.
The behavior of the aggregate capital-output ratio is also of some interest
for the evaluation of monetary policy. Some observers have argued that the
investment boom in the late 1990s was in part due to monetary policy that
did not raise interest rates fast enough. The collapse of the investment boom
and the ensuing 2001 recession are then attributed to having too much capital
around, that is, overcapacities. In order to talk about whether the capital stock
is too high, one needs an estimate of the “normal” capital stock. If the long-run
capital-output ratio is quite stable, we might use this ratio to construct a good
first indicator of the “normal” capital stock. Since the aggregate capital-output
ratio at the end of the 1990s was not much out of line with its long-run average,
we would therefore conclude that the investment boom of the 1990s did not
result in any overcapacities. Thus, it did not contribute to the 2001 recession.
On the other hand, taking into account the substantial increase of aggregate
depreciation rates, we should conclude that the “normal” capital-output ratio
was much lower than the observed capital-output ratio. Thus, the investment
boom did result in “excess” capital.

APPENDIX
Economic time series are usually reported in current prices—nominal terms.
For much of our analysis, we want to eliminate the effect of price level changes
and use time series in “real” terms. These real time series are supposed to reflect quantity rather than price movements. Given the level of aggregation
we usually deal with, the construction of aggregate quantity indexes is neither easy nor unambiguous. Most data on historical “real” series calculate
constant-dollar base period quantity indexes. That is, aggregate quantities are
constructed by weighting individual quantity series with a fixed set of base
period prices. For the most part, aggregation procedures are a matter of convention, but based on economic theory, some indexes are better than others.
One can make an argument that quantity indexes from constant base period
prices are not very reliable indicators for quantity movements when large
changes of relative prices occur during the period of interest. In response to
these concerns, the Bureau of Economic Analysis (BEA), which provides the
National Income Accounts for the United States, has shifted from quantity
indexes that are based on constant base period prices to chain-weighted quantity indexes that deal better with relative price changes. The BEA constructs
Fisher-Ideal quantity indexes that, for most applications, are well approxi-

A. Hornstein: (Un)Balanced Growth

mated by Divisia-quantity indexes. For a more detailed description of the
BEA procedures, see Seskin and Parker (1998) or USBEA (1997).

Output
The GDP series used in this article are from Kendrick (1961) and the official
NIPA series published by the BEA. Output in Figure 1 is real private business
GDP; in Figure 3, output is real nonfarm private business GDP, and in Figure
4, output is real (nominal) nonfarm private business GDP, excluding the contributions of the housing sector. For the long-time series in Figures 1 and 3,
I splice the constant 1929 dollar GDP series from Kendrick (1961) with the
chained 1996 dollar GDP series from the BEA in 1929 at the level of 1929
BEA GDP. Obviously, there are potential problems since the two series use
different methods to obtain estimates of real activity. Nevertheless the average growth rates of real private business GDP for the pre-1929 and post-1929
periods are remarkably similar—3.8 percent before 1929 and 3.7 percent after
1929. For the time series in Panel A of Figure 4, I construct real nonfarm
private business GDP excluding housing as a Divisia index using the series on
nonfarm private business GDP and housing GDP.
In this article I rely on the work of Kendrick (1961) for the time period
before 1929. Balke and Gordon (1989) provide a useful survey on the different
sources for GNP data in the United States before 1929, the most important
source being Kuznets (1961). Kendrick (1961) essentially restates Kuznets’
estimates of GNP for the definitions used by the Department of Commerce
in its construction of the NIPAs. Balke and Gordon (1989) update this early
work, but their concern is with the relative volatility of GNP in the period
before and after WWII. Since they consider the work of Kuznets (1961) and
Kendrick (1961) as providing acceptable estimates of trends, they construct
their own GNP estimates around the Kuznets and Kendrick trend estimates.
Thus Balke and Gordon’s (1989) updates do not affect the information in
Kendrick (1961) that is relevant for this article.
Cummins and Violante (2002), discussed below, have recently provided
alternative estimates of the price deflator for producer-durable equipment investment. Using this alternative deflator affects the measure of real investment
and, in turn, the measure of the real capital stock and real GDP. In Figure 4,
Panel A, I also display an equipment capital-GDP ratio that is based on Cummins and Violante’s (2002) measure of real nonfarm private business GDP,
excluding housing, and their estimate of the real capital stock.

Capital Stock
The capital stock series in this article is based on Kendrick (1961) and on the
official fixed durable asset series published by the BEA. Capital in Figure 1
is real total private capital; in Figure 3, it is real nonfarm private capital; and

Federal Reserve Bank of Richmond Economic Quarterly

in Figure 4, it is real (nominal) nonfarm private capital excluding residential
structures. From 1889 to 1953, Kendrick (1961) provides constant 1929 dollar
estimates of farm structures and land, nonresidential structures and equipment,
and residential structures.
Total capital is the sum of all these capital stocks. From 1929 to 2001,
the BEA provides data on current and chained 1996 dollar estimates of capital
stocks and depreciation for agricultural equipment (tractors and other farm
machinery) and structures, nonresidential equipment (information technology
and software, transportation equipment, etc.) and structures, and residential
equipment and structures. The quantity index for individual asset classes is
constructed based on the perpetual inventory method using deflated investment
expenditures and estimates of the depreciation pattern for that class. The
current dollar estimate is then calculated as the quantity index for the stock
evaluated at current prices. To the extent that I have to construct quantity
indexes from the BEA data, I construct them as Divisia indexes from the
available current dollar and chained dollar estimates.
Real capital stock estimates by Kendrick (1961) and the BEA are quantity
indexes of the real value of capital. That is, the components of the aggregate
quantity index are weighted using their asset values. For the nominal capitalGDP ratios in Figure 4, Panel B, the nominal asset value series for capital
are appropriate. From the point of view of production theory, one would
prefer a quantity index that uses factor rental weights for the different assets
in the aggregation procedure for the real capital-GDP ratios in Figures 1,
3, and 4 (Panel A).17 A capital stock index that is based on factor rentals
better reflects the role of capital as an input to production and is used in total
factor productivity studies (see, for example, Jorgenson, Gollop, and Fraumeni
1987). A problem with this approach is that we do not have observations on
the average factor rentals of individual asset categories. The usual procedure
is then to impute factor rentals based on required returns on capital using a
version of equation (17) (Hall and Jorgenson 1967).
For the long time series in Figures 1 and 3, I splice the constant 1929
dollar capital stock series from Kendrick (1961) with the chained 1996 dollar
capital stock series from the BEA in 1929 at the level of 1929 capital stock.
From 1929 to 1954, the Kendrick and BEA series overlap and do not behave
very differently.
I also display in Figure 4 the equipment capital-GDP ratio based on Cummins and Violante’s (2002) estimates of the real equipment capital stock. For
the nominal capital-GDP ratio in Figure 4, Panel B, I evaluate Cummins and
Violante’s (2003) estimate of the real equipment capital stock using their price
deflator for new equipment capital.
17 For a discussion, see Whelan (2002).

A. Hornstein: (Un)Balanced Growth

Depreciation
The depreciation rates are based on official fixed durable asset series published by the BEA. The depreciation rates in Figure 5 are the ratio of nominal
depreciation to nominal capital stock. The alternative calculation of depreciation rates as the ratio of constant-dollar depreciation to constant-dollar capital
stocks yields slightly lower depreciation rates, but they are also increasing
from the mid-1980s on.
Prices
For the period 1929 to 2001, the BEA provides current and chained 1996
estimates of personal consumption expenditures (PCE) for nondurable goods
and services separately. I aggregate these to a nondurable goods and services
index—consumption price index for short. For the same time period the BEA
also provides price indexes for new investment in equipment and software
and nonresidential structures. We can compare these price indexes with the
capital price indexes implied by the current value and quantity indexes for
the capital stock. Although the new investment price index and the implied
capital price index are not the same, they follow each other closely, more so for
structures than for equipment. The relative price of capital in Figure 1 is the
implied capital price index for total private capital relative to the consumption
price index. The relative capital prices in Figure 2 are the implied capital
price indexes of nonfarm equipment and software and structures relative to
the consumption price index. Figure 2 also displays an alternative relative
price index for equipment and software constructed by Cummins and Violante
(2002). Following the work of Greenwood, Hercowitz, and Krusell (1997),
Cummins and Violante (2002) essentially extrapolate the quality adjustments
of Gordon (1990) for producer-durable equipment prices from the time period
1947–1983 to the period 1983–2001.

REFERENCES
Balke, Nathan S., and Robert J. Gordon. 1989. “The Estimation of Prewar
Gross National Product: Methodology and New Evidence.” The Journal
of Political Economy 97 (February): 38–92.
Cummins, Jason G., and Violante, Giovanni L. 2002. “Investment-Specific
Technical Change in the United States (1947–2000): Measurement and
Macroeconomic Consequences.” Review of Economic Dynamics 5
(April): 243–84.

Federal Reserve Bank of Richmond Economic Quarterly

Doms, Mark E., Wendy E. Dunn, Stephen D. Oliner, and Daniel E. Sichel.
2003. “How Fast Do Personal Computers Depreciate? Concepts and
New Estimates.” Federal Reserve Bank of San Francisco Working Paper
2003–20.
Gallman, Robert E. 1986. “The United States Capital Stock in the
Nineteenth Century.” In Stanley L. Engerman and Robert E. Gallman,
Long-Term Factors in American Economic Growth. (Studies in Income
and Wealth 51): 65–206. Chicago: University of Chicago Press.
Gordon, Robert J. 1990. The Measurement of Durable Goods Prices. The
University of Chicago Press: Chicago.
Greenwood, Jeremy, Hercowitz, Zvi, and Krusell, Per. 1997. “Long-Run
Implications of Investment-Specific Technological Change.” The
American Economic Review 87(3): 342–62.
Hall, Robert E., and Dale W. Jorgenson. 1967. “Tax Policy and Investment
Behavior.” The American Economic Review 57 (June): 391–414.
Jorgenson, Dale W., Frank Gollop, and Barbara Fraumeni. 1987. Productivity
and U.S. Economic Growth. Cambridge: Harvard University Press.
Kaldor, Nicholas. 1957. “A Model of Economic Growth.” The Economic
Journal 67 (December): 591–624.
. 1961. Ed. F.A. Lutz and D.C. Hague. “Capital
Accumulation and Economic Growth.” The Theory of Capital. London:
Macmillan:177–222.
King, Robert G., Charles I. Plosser, James H. Stock, and Mark W. Watson.
1991. “Stochastic Trends and Economic Fluctuations.” The American
Economic Review 81 (September): 819–40.
Kendrick, John W. 1961. Productivity Trends in the United States. Princeton:
Princeton University Press.
Kongsamut, Piyabha, Sergio Rebelo, and Danyang Xie. 2001. “Beyond
Balanced Growth.” Review of Economic Studies 60 (October): 869–82.
Kuznets, Simon S. 1961. Capital in the American Economy: Its Formation
and Financing. Princeton: Princeton University Press.
. 1971. Economic Growth of Nations—Total Output and
Production Structure. Cambridge: Harvard University Press.
Maddison, Angus. 1991. Dynamic Forces in Capitalist Development—A
Long-Run Comparative View. Oxford: Oxford University Press.
Seskin, Eugene P. and Robert P. Parker. 1998. “A Guide to the NIPA’s.”
Survey of Current Business (March): 26–48.

A. Hornstein: (Un)Balanced Growth

Siegel, Jeremy L. 1998. Stocks for the Long Run. 2nd ed. New York:
McGraw-Hill.
U.S. Department of Commerce, Bureau of Economic Analysis. National
Income and Product Accounts of the United States, 1927–1997. At
http://www.bea.doc.gov/bea/an/nipaguid.pdf
U.S. Department of Commerce, Bureau of Economic Analysis. Fixed Assets
and Consumer Durables in the United States, 1925–97 (2003). At
http://www.bea.doc.gov/bea/dn/Fixed Assets 1925 97.pdf
Whelan, Karl. 2002. “Computers, Obsolescence, and Productivity.” Review
of Economics and Statistics 84 (August): 445–61.
. 2003. “A Two-Sector Approach to Modeling U.S. NIPA
Data.” Journal of Money, Credit and Banking 35 (August): 627–56.

Auditing and Bank Capital
Regulation
Edward Simpson Prescott

apital regulations for banks are based on the idea that the riskier a
bank’s assets are, the more capital it should hold. The international
1988 Basel Accord among bank regulators set bank capital requirements to be a fixed percentage of the face value of assets. The only risk
variation between assets was based on easily identifiable characteristics, such
as whether it was a commercial loan or a government debt.
The proposed revision to the Accord, commonly called Basel II, is an
attempt to improve upon the crude risk measures of the 1988 Accord. Under
Basel II, banks use their internal information systems to determine the risk of
an asset and report this number to regulators.1 In an ideal sense, the proposal
is eminently sensible. After all, who knows the risks of a bank’s asset better
than the bank itself? But a serious problem exists in implementation. What
incentive does a bank have to report the true risks of its assets? Without
adequate supervision and appropriate penalties, the answer is, “Not much.”
Analysis of Basel II has been primarily focused on setting the capital
requirements, commonly referred to as Pillar One of the proposal. But good
capital requirements mean little if they cannot be enforced. For this reason,
more attention needs to be focused on Pillar Two of the proposal, that is,
supervisory review.2 This pillar gives supervisors the authority to enforce
compliance with the Pillar One capital requirements, and while not usually
the focus of Basel II, it is fundamental to the success of the project.
I would like to thank Rafael Repullo, Pierre Sarte, Javier Suarez, John Walter, John Weinberg,
and seminar participants at CEMFI for helpful comments. This article was prepared while I
was visiting CEMFI. The views expressed in this article do not necessarily represent the views
of the Federal Reserve Bank of Richmond or the Federal Reserve System.
1 Technically, in the proposed U.S. implementation, banks will use their internal systems to

estimate several key numbers—like the probability of default and the loss given default. Banks
then enter these numbers into a regulatory formula to determine capital requirements.
2 The third and final pillar of Basel II is concerned with market supervision.

Federal Reserve Bank of Richmond Economic Quarterly Volume 90/4 Fall 2004

Federal Reserve Bank of Richmond Economic Quarterly

These issues are examined in models where regulatory audits affect the
incentives for banks to send accurate reports. By the term “audit” we mean
the process of determining if the reported number is accurate. In practice, our
use of the term “audit” refers more to a supervisory exam than to an external
audit, though our models are broad enough to incorporate this activity, too.
The models have strong implications for how supervisors should deploy
their limited resources when examining banks. We find that stochastic auditing strategies are more effective than deterministic ones. Furthermore, the
frequency of an audit should depend on the amount of capital held. The less
capital a bank holds, the more frequent the audits need to be, even though the
safest banks hold the least amount of capital. The reason for this counterintuitive result is that audits prevent risky banks from declaring that they are safe
banks. Therefore, the safer a bank claims to be, the more prevention is needed
and the more frequently it is audited.

1. THE MODEL
Verifying the risk of a bank’s investment requires a model that illustrates
the role of examinations and monitoring. The simplest model sufficient for
the purposes of this study is the costly state verification model of Townsend
(1979). In his model, a firm’s cash flow is the information to be verified. Here,
it will be the risk of a bank’s investment. We study capital regulations in four
variants of the basic model: an idealized one where the regulator observes
the bank’s risk characteristics; one where the regulator does not observe the
risk characteristics; another where the regulator can audit deterministically to
find out the risk characteristics; and a final model where the regulator may
randomly audit, that is, conduct an audit with a probability anywhere between
zero and one.
The Basic Model
In the model, there is one regulator and many small banks. Each bank has
one investment of size one. Investments either succeed or fail. All successful
investments return the same amount, and all failed investments produce zero.
Banks’ investment projects differ only in their probability of failure. The
probability of a bank’s investment failing is p, which lies in the range, [p, p̄],
with 0 ≤ p < p̄ ≤ 1. This probability is random to the bank and drawn from
the density function, h(p). The cumulative distribution function is H (p).
Shocks are independent across banks.
A bank’s investment can be financed with either deposits or capital. Banks
prefer less capital to more. For the moment, there is no need to be specific
about the details of this preference. We only need banks to desire to hold
less capital than the regulator wants them to. Such a desire by banks could

E.S. Prescott: Auditing and Bank Capital Regulation

come out of a model with a deposit insurance safety net or any model in which
equity capital is costlier to raise than deposits. Let K(p) be the amount of
capital held by a bank with investment opportunity, p. Because each bank is
of size one, 1 − K(p) is the amount in deposits each bank holds as well as
being its utility.3
The regulator cares about losses from failure and the cost of capital. We
assume that the failure losses depend on the amount of deposits that the regulator needs to cover in case there is failure. This function is V (K(p)) with
V increasing and concave (V > 0 and V < 0). Because V measures losses,
we assume that V (K(p)) ≤ 0 for all values of capital, with V (1) = 0 (see
Figure 1). The regulator suffers no losses from a failed bank if it has 100
percent capital. The purpose of this function is to generate a desire on the part
of the regulator for banks with riskier portfolios to hold more capital.
The regulator also cares about the cost of capital. Assuming that the per
unit cost is q, this cost represents the foregone loss of liquidity services from
a bank’s use of capital rather than deposits.4
The problem for the regulator is to choose a risk-based capital requirement, K(p), that balances the regulatory benefit of reducing losses of failure
with the costs to banks of issuing capital. This problem is the maximization
problem:
p̄
max
(pV (K(p)) − qK(p))dH (p).
K(p)∈[0,1]

The term pV (K(p)) is the expected failure loss to the regulator from a bank
with risk p, while qK(p) is the cost to the bank of raising capital.
It is straightforward to solve this problem. We assume that the solution is
interior, so the first-order conditions are
∀p, pV (K(p)) = q.

(1)

The expected marginal benefit of capital is set equal to the marginal cost of
capital. Equation (1) implies that K(p) increases with p. As the probability
of failure grows, the regulator increases the capital requirement. For example,
if V (K) = −(1 − K)α with α > 1, then (1) takes the simple form,
q
K(p) = 1 − ( )1/(α−1) ,
αp
assuming q and the range of p are such that 0 ≤ K(p) ≤ 1 (see Figure 2).
The positive relationship between default probability, p, and capital, K, is the
goal of both the Basel I and II regulations.
3 A bank’s preferences over K are independent of its risk, p. Banks always prefer less capital
to more. This assumption is strong, but it simplifies the analysis in several advantageous ways.
4 We decided to model bank’s preferences over capital by 1−K rather than formally including
the cost of capital because it simplifies the algebra. This modeling decision has no impact on the
article’s results because the important feature is that the bank prefers less capital to more.

Federal Reserve Bank of Richmond Economic Quarterly

Figure 1 Example of V (k) Function
0.0
-0.1
-0.2

Regulator's utility

-0.3
-0.4
-0.5
-0.6
-0.7
-0.8
-0.9
-1.0
0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

Capital

Notes: Figure 1 illustrates an example of the regulator’s utility from failure losses as a
function of a bank’s capital given p, that is, V (K). The more capital a bank holds, the
less the loss to the regulator. The function is non-positive, increasing, and concave.

Private Information
The fundamental problem for Basel I and II is to determine the risk of a
bank’s assets. The premise of the Basel II reform is that a bank has the best
information on its own assets so that by using its internal models and data, a
regulator can get a better estimate of its risks than from the crude measures
underlying Basel I. The problem for Basel II is that a bank has an incentive to
understate the risk as long as it wants to save on capital costs.
For illustrative purposes, we start with the extreme assumption that the
regulator knows almost nothing about the riskiness of a bank’s investment
opportunities except that the distribution of these risks is H (p). Each bank,
however, knows its own risk; that is, it has private information. Now, how
should the regulator set capital requirements? The regulator would like to use
the capital requirements illustrated in Figure 2, but that would be a disaster.
Each bank would say that it was the safest bank; that is, report p to get the
low capital of K(p). All banks would do this, and there would be nothing

E.S. Prescott: Auditing and Bank Capital Regulation

Figure 2 Full-Information Regulatory Capital Schedule
0.8

0.7

Capital requirement

0.6
0.5

0.4

0.3

0.2

0.1

0.0
0.1

0.2

0.3

0.5
0.6
Probability of failure

0.4

0.7

0.8

0.9

1.0

Notes: Figure 2 illustrates optimal regulatory capital as a function of bank risk when the
regulation knows the bank’s risk.

the regulator could do afterwards. The result for the regulator would be huge
losses.
Instead, the regulator should design a capital schedule that takes into
account each bank’s private information. The effect of private information
is modeled with an incentive constraint that says a capital schedule is only
feasible if it is in the interest of a bank to report its risk truthfully.5 Formally,
the incentive constraint is
∀p, p̂, 1 − K(p) ≥ 1 − K(p̂),
or, equivalently,
∀p, p̂, K(p) ≤ K(p̂).
5 The Revelation Principle is being used here.

(2)

Federal Reserve Bank of Richmond Economic Quarterly

This constraint says that the utility a bank with failure risk, p, receives from
K(p) is at least as much as it would receive if it claimed to have any other
failure risk, p̂.

The 1988 Basel Accord
The incentive constraint, (2), is very stringent, eliminating most capital schedules. The only schedules that satisfy it are those where K(p) is a constant.
If K(p) varies with p at all, a bank assigned a higher K(p) would simply
claim that its assets are a risk that receives the lowest capital charge under
the capital schedule. Consequently, all bank investments must face the same
capital charge, regardless of how risky their portfolios are. Indeed, this lack of
responsiveness of capital charges to risk looks exactly like the Basel Accord
of 1988 as applied to assets within a particular risk class. For example, a
commercial and industrial loan with a 10 percent chance of default is treated
the same as one with a 2 percent chance of default.
It is precisely this equal treatment of different risks that has led to the development of Basel II. Basel II distinguishes between the riskiness of loans—the
ps in the model—by allowing banks to report the risk characteristics of their
loans. This is an admirable goal, as represented by (1), but in light of the
incentive constraint (2), it is not attainable. That constraint says there can be
no risk variation in capital requirements.
Something else is needed to make Basel II work. As will be discussed in
the next section, that “something else” is audits and penalties. Unfortunately,
these critical features are not usually discussed in the context of Basel II.

2. A ROLE FOR AUDITS
Risk-sensitive capital requirements could be implemented if the regulator
could gather some information about the true risk of the investments. We
assume that the regulator, devoting m units of resources, can observe a bank’s
risk characteristics. Other cost functions are possible. Indeed, some activities
pose greater difficulty in gathering information than others do. Still, the fixed
cost function is the simplest to study and illustrates the main points, so we
will use it.
Audits are performed after the bank reports to the regulator on the risk
characteristics of its investments. For the moment, we assume that auditing
is deterministic; that is, in response to a particular report the regulator must
either audit or not audit. Later, we will extend the model to allow the regulator
to audit with some probability.
If an audit is performed and the bank is found to have misrepresented its
asset risk, the regulator may impose a penalty. We model this penalty as a

E.S. Prescott: Auditing and Bank Capital Regulation

fixed utility amount, u. The utility of an audited bank found to have lied is
1 − K(p) − u.
The addition of audits requires a slight modification to the regulator’s
decision problem and to the incentive constraints. Now the regulator must
decide which reports of p to verify with an audit and which not to. Let A be
the region of [p, p̄] for which the regulator audits and N the region for which
it does not. There are two sets of incentive constraints. The first set concerns
misrepresentations in the no-audit region. These incentive constraints are
∀p, 1 − K(p) ≥ 1 − K(p̂), ∀p̂ ∈ N
or, equivalently,
∀p, K(p) ≤ K(p̂), ∀p̂ ∈ N.

(3)

Incentive constraints (3) state that a bank’s capital must be less than it would
receive if it claimed to have a p in the no-audit region, N . Like the earlier
incentive constraints (2), these incentive constraints strongly restrict feasible
allocations. However, the restriction only applies to p in the non-auditing
region, N, so capital must be a constant only over this region. We refer to this
amount of capital as KN .
The second set of incentive constraints prevents misrepresentations in the
audit region. These incentive constraints are
∀p, 1 − K(p) ≥ 1 − K(p̂) − u, ∀p̂ ∈ A,
or, equivalently,
∀p, K(p) ≤ K(p̂) + u, ∀p̂ ∈ A.

(4)

These incentive constraints are usually less important than (3). As long as u
is high enough, they will be automatically satisfied.
To summarize, the main difference between the earlier model and the
deterministic auditing model is the severity of the incentive constraints. In the
earlier model, (2) forces the capital requirement to be the same for all risks
while in the deterministic auditing model, (3) forces the capital requirement
to be the same only for risks in the non-auditing region.
Even before writing out the program, two properties of optimal capital
requirements can be derived. The first follows from (3). Because banks can
always claim that their failure probability is some p in the non-auditing region,
we know that
Proposition 1 K(p) ≤ KN .
The second proposition that we can prove is that the non-auditing region
is convex and consists of the highest risk banks. This proposition will let us
formalize the regulator’s problem in a simple way.
Proposition 2 The non-auditing region, N , is convex and consists of the
highest risk banks.

Federal Reserve Bank of Richmond Economic Quarterly

We do not provide a formal proof. Conceptually, the idea is simple.
Assume that there is an audited bank that is riskier than some non-audited
bank (and for simplicity both are equal fractions of the bank population). By
Proposition 1, the non-audited bank holds more capital. Now, switching their
regulatory requirements—switching the amount of capital each holds—and
auditing the safe bank but not auditing the riskier bank satisfies the incentive
constraints. It also increases the utility of the regulator since the capital is more
effective when deployed against the risky bank rather than the safer bank.
These properties can be incorporated when formulating the regulator’s
problem. Let a be the cutoff between audited and non-audited banks. The
regulator’s program is:

Regulator’s Program with Deterministic Auditing

max

a,KN ,K(p)

(pV (K(p))−m−qK(p))dH (p)+

p̄
a

(pV (KN )−qKN )dH (p),

subject to the incentive constraints
∀p < a, K(p) ≤ KN

(5)

and (4).
For the purpose of our analysis, we are going to assume that the penalty
u is high enough so that (4) does not bind. Furthermore, when we take the
first-order conditions, we are going to ignore the incentive constraint (5) and
show that the solution to the program without it still satisfies it. This property
does not mean that the private information does not matter in this problem.
Instead, it means that setting up the problem with a cutoff between the auditing
and non-auditing regions and with constant capital in the non-auditing region
is enough for incentive compatibility to hold.
The derivative with respect to KN is
p̄
p̄
pdH (p) = q
dH (p).
(6)
V (KN )
a

The first-order conditions with respect to K(p) are
∀p < a, pV (K(p)) = q.

(7)

Again, we assume that the solutions are interior.
Two properties of a solution follow from these two constraints. First,
from (7), we know that K(p) is increasing in p for p ∈ A. Second, there is a
discontinuity in K(p) at the cutoff a. Let K̃(a) = limp→a K(p). Taking the
limit of (7) at p = a and substituting for q in (6) delivers
V (KN )E(p|p ≥ a) = aV (K̃(a)),

(8)

E.S. Prescott: Auditing and Bank Capital Regulation

Figure 3 Optimal Regulatory Capital with Deterministic Auditing
0.8

0.7

Capital requirement

0.6
0.5

0.4

0.3

0.2

0.1

0.0
0.1

0.2

0.3

0.5
0.4
0.6
Probability of failure

0.7

0.8

0.9

1.0

Notes: Figure 3 illustrates optimal regulatory capital when banks have private information
about their true risks and the regulator may undertake deterministic audits. The schedule
is discontinuous at the point where the regulator stops auditing banks. The horizontal
portion corresponds to the capital holdings of the risky banks, that is, KN , none of which
are audited.

where
p̄

pdH (p)
.
E(p|p ≥ a) = a p̄
a dH (p)
Because a is less than the average probability of failure in N , that is, over the
range a to p̄, (8) implies that V (K̃(a)) > V (KN ), which, in turn, implies
that K̃(a) < KN . Thus, K(p) is discontinuous at a. Furthermore, this result
proves that constraint (5) is redundant.
The intuition for the discontinuity is that for p ∈ A, K(p) is set as in the
full-information problem, where (7) is satisfied when the marginal benefit of
capital equals its marginal cost. But for p ∈ N, K(p) is a constant, so KN is
set to equalize the expected marginal benefit of capital with its marginal cost.
Figure 3 illustrates what a capital schedule might look like.

Federal Reserve Bank of Richmond Economic Quarterly
The final first-order condition is taken with respect to the cutoff point, a.

It is
(aV (KN ) − (aV (K(a)) − m)) − q(aKN − aK(a)) = 0.
Canceling terms and rearranging gives
aV (KN ) + qK(a) + m = aV (K(a)) + qKN .

(9)

The left-hand side of equation (9) is the marginal cost of increasing the cutoff
point, and the right-hand side is the marginal benefit.

Back to Basel
The model’s implications for capital regulation are very strong and, at first
glance, counterintuitive. The highest risk banks do not need to be audited.
Only banks that want to hold less capital than the maximal amount are audited.
This result, however, should not be surprising since, for incentive reasons,
there is no need to audit a bank willing to hold the maximal amount of capital.
Indeed, if regulators have a maximum amount of risk, p, they are willing to
allow banks to take, and assuming they have the power to shut down banks,
they would have to audit every bank in operation.
The model demonstrates just how fundamental auditing and the penalties
are to regulatory policy. Risk-sensitive regulation requires auditing of any
bank holding less than the largest amount of capital. Presumably, this result
would include most banks and likely would cause high auditing costs, which
seems problematic. Fortunately, other regulatory policies may still implement
risk-sensitive capital requirements at a lower cost. In the next section, we
consider such policies in a model with stochastic auditing.
Still, the point remains that auditing and penalties cannot be avoided.
Basel II contains many details on how a bank should justify its capital ratio,
but these procedures can never be perfect. If they were, we could turn over
investment decisions to regulators. Basel II is premised on the belief that
banks know their risks better than regulators, and while regulators can gather
some information on these risks, they can never know as much as the bank.
For this reason, the incentive concerns detailed above are unavoidable.

STOCHASTIC AUDITING

In this section, we modify the model so that the decision to audit by the
regulators can be stochastic. By stochastic we mean that in response to a
bank’s risk report, the regulator may audit with some probability. As we will
see, this policy saves on supervisory resources. As before, we will assume
that these audits fully reveal the information. Alternatives can be studied. For
example, the regulator could observe only a signal correlated with the true
risk, or the quality of the signal could depend on the intensity of the audit.

E.S. Prescott: Auditing and Bank Capital Regulation

Stochastic auditing requires making a few changes to the model. First,
we drop the distinction between the auditing and non-auditing regions. Let
π (p) be the probability of an audit, given that p is reported. As before, m is
the cost of an audit, and u is the utility penalty that is imposed if a bank is
found to have lied. The regulator’s program is:

Regulator’s Program with Stochastic Auditing

max

K(p)∈[0,1],π(p)≥0

p̄

(pV (K(p)) − π (p)m − qK(p))dH (p)

subject to the incentive constraint
1 − K(p) ≥ 1 − K(p̂) − π (p̂)u, ∀p, p̂.

(10)

Incentive constraint (10) differs from the deterministic case incentive constraints (3) and (4) in that π (p) can take on any value from zero to one.
There are many incentive constraints in (10), but, fortunately, most of
them are redundant. Notice that utility is decreasing in K(p), and utility from
reporting the wrong p does not depend on a bank’s risk type. Therefore, if
the incentive constraint holds for the type with the highest capital charge—for
now, assume that it is the highest risk bank p̄—then the incentive constraint
holds for all other risk types. Formally, (10) can be replaced by
K(p̄) ≤ K(p) + π (p)u, ∀p.

(11)

Another simplification is possible. Audits are a deadweight cost, so it
is best to minimize their probability. For a given capital schedule, the audit
probabilities are minimized when (11) holds at equality. Therefore,
K(p̄) − K(p)
π (p) =
.
(12)
u
We hinted above that the highest risk bank would be the type to hold the
greatest amount of capital. This is intuitive, but it can be proven. Imagine that
the bank assigned the highest amount of capital is not the highest risk one.
For simplicity, assume that all types of banks occur with equal probability.
Then, simply switch the capital requirement faced by the highest risk bank
and the one holding the most capital. Incentive compatibility still holds and
the regulator’s objective function is higher since the highest risk bank holds
more capital.
We could substitute (12) directly into the objective function, but for optimization purposes it is more convenient to consider
K̄ − K(p)
(13)
u
and require that K(p) ≤ K̄, for all value of p. Equation (13) will be substituted into the objective function, and we will make K̄ a choice variable.
π (p) =

Federal Reserve Bank of Richmond Economic Quarterly

As long as the solution has K(p) ≤ K(p̄), auditing probabilities will be nonnegative. Furthermore, because auditing is a deadweight cost, any solution
will necessarily set K̄ = K(p̄). With these changes, the program is:

Simplified Regulator’s Program with Stochastic
Auditing

max

K(p)∈[0,1],K̄

p̄

pV (K(p)) −

K̄ − K(p)
m − qK(p) dH (p)
u

subject to
∀p, K(p) ≤ K̄.

(14)

Even before studying the first-order condition, the solution has the following properties from (13) and the desire to lower K̄. First, the probability of an
audit is zero for any bank that holds the highest amount of capital. Second,
the audit probability increases as capital declines.
The first set of first-order conditions for this problem is
∀p, (pV (K(p)) + m/u − q) = λ(p),

(15)

where λ(p)h(p) ≥ 0 is the Lagrangian multiplier on (14) for p. The remaining
first-order condition is
p̄
m/u =
λ(p)dH (p).
(16)
p

We already demonstrated that only the highest risk banks hold the greatest
amount of capital. Therefore, K(p) ≤ K(p̄). For any bank with K(p) <
K(p̄), λ(p) = 0, so (15) implies that capital is increasing in risk in this range.
The first-order conditions can be used to derive two additional properties
of a solution:
Proposition 3 A range of banks at the upper tail of the distribution (more
formally a range with positive measure) holds K(p̄).
This proposition is equivalent to showing that there is a range of p for
which constraint (14) binds. A proof is contained in the Appendix.
The second result is differs from that of the deterministic auditing case.
Proposition 4 The capital schedule K(p) is continuous.
This proof is also in the Appendix.
The properties of the stochastic auditing model are illustrated with an
example. We also calculated the optimal deterministic auditing contract to
compare the two. The example used the following parameter values: h(p)

E.S. Prescott: Auditing and Bank Capital Regulation

is a uniform distribution over the range p = 0.1, and p̄ = 0.5, V (K) =
−1.5(1 − K)2 , m = 0.01, u = 1.0, and q = 0.5.
Figure 4 illustrates optimal capital requirements under deterministic and
stochastic auditing. The schedule for the deterministic case has a discrete jump
at the non-audit point. The schedule for the stochastic case is continuous. In
the deterministic case, there is a much bigger range of p for which capital is
flat. Capital requirements are, necessarily, less finely tuned in this case. Also,
for p in the audit range (roughly between 1.0 and 1.5), K(p) is slightly smaller
under deterministic auditing than under stochastic auditing. This difference
comes from comparing the two problems’ first-order conditions. Condition
(15) has an additional term m/u that is not in (7). This term makes K(p)
higher in this range.
Figure 5 illustrates the audit probabilities for both models. Of course, the
deterministic case probabilities are either zero or one. Probabilities for the
stochastic case move smoothly and hit zero for the risk types that hold the
highest amount of capital. As capital declines, audit probabilities increase.
Finally, the stochastic auditing case saves on auditing resources. In the deterministic case, banks are audited 15.5 percent of the time and 13.7 percent of
the time in the stochastic case.
The differences in the two types of arrangement are evident in the figures.
Stochastic auditing is, of course, more efficient. Here it allows for more finely
tuned capital requirements and uses less auditing resources.

CONCLUSION

Banks know their own risks better than regulators. Basel II is based on the
premise that these risks can be communicated by banks to regulators and then
used to determine regulatory capital. But with this informational advantage,
banks can control precisely what is communicated. For this reason, it is
necessary to consider the incentives banks have for truthfully reporting their
risks. This article argues that the penalties or sanctions imposed for noncompliance are critical for determining these incentives. Basel II is, unfortunately,
relatively silent on this issue. As Basel II is adopted and implemented, these
issues will have to be addressed.
The models developed in this article not only illustrate the role of penalties,
but also illustrate various supervisory strategies for gathering information and
imposing sanctions. Supervisory resources are scarce and costly. Therefore,
finding the best way to deploy them is valuable. The stochastic auditing model
demonstrates that randomized audits, or exams, could improve upon regularly
planned audits.6
6 Audits may be made to depend on other signals. Marshall and Prescott (2001) analyze a
model where regulatory sanctions depend on the realization of bank returns.

Federal Reserve Bank of Richmond Economic Quarterly

Figure 4 Capital Requirements

1.0

Stochastic auditing
Deterministic auditing

Capital requirement

0.8

0.6

0.4

0.2

0.0

0.1

0.2

0.3

0.4

0.5

0.6

Probability of failure

Notes: Figure 4 describes optimal capital requirements for both the deterministic and
stochastic auditing cases. Where the discrete jump for the deterministic auditing case
occurs is the point where the regulator stops auditing. Where the regulator audits in the
deterministic case, the capital schedule is slightly lower for the deterministic case than
in the stochastic case.

In the models, audit frequencies and capital requirements are inversely
related. Less capital requires more frequent auditing for incentive reasons,
implying, counterintuitively, that the safest banks are audited the most. The
reason for this regulatory behavior is that the role of audits is to prevent risky
banks from claiming to be safer than they really are. Because no one wants to
claim to be riskier than they actually are, auditing a bank that claims it is the
highest risk is unnecessary. This bank has agreed to hold more capital, and
that is all the regulators desire.
The precise relationship between audit frequencies and capital requirements depends on parameters such as available penalties, auditing costs, the
costs of capital, and the distribution of bank risk types. If these parameters
differ between countries, then there should be different capital schedules in
each country. Harmonization of regulations is not without its costs.

E.S. Prescott: Auditing and Bank Capital Regulation

Figure 5 Audit Probabilities

1.0

Stochastic auditing
Deterministic auditing

Audit probability

0.8

0.6

0.4

0.2

0.0

0.1

0.2

0.3

0.4

0.5

0.6

Probability of failure

Notes: Figure 5 describes optimal audit probabilities as a function of bank risk type for
both the deterministic and stochastic cases. By necessity, the deterministic case probabilities are either zero or one. The probabilities vary smoothly for the stochastic case.

The models developed in this article omit other relevant dimensions to
the problem. For example, audits are not perfect. Sometimes the information
gathered is incorrect. One way to incorporate these important factors is to
allow regulators to observe only a signal correlated with the true state. Other
possibilities include making it costly for banks to hide information, e.g., Lacker
and Weinberg (1989). Another important extension is to consider dynamic
capital schedules. Supervisors interact over time with banks and may have
latitude to generate the equivalent of penalties through their future treatment
of the bank. The literature on dynamic costly state verification models should
be relevant here and includes Chang (1990), Smith and Wang (1998), Monnet
and Quintin (2003), and Wang (2003).

Federal Reserve Bank of Richmond Economic Quarterly

APPENDIX
Proposition 3 There is a range of banks at the upper tail of the distribution
(more formally a range with positive measure) that hold K(p̄).
If only the highest risk bank, p̄, holds the greatest amount of capital, then
p̄
λ(p) = 0 for all p < p̄. But then p λ(p)h(p) = 0, which contradicts
(16). Therefore, λ(p) > 0 for a range of p with positive measure. These
values of p have to be the highest risk values. If not, consider p1 < p2 with
K(p1 ) = K(p̄) and K(p2 ) < K(p̄). We know that λ(p1 ) ≥ 0 and λ(p2 ) = 0.
Using (15), we have
p1 V (K(p̄)) + m/u − q = λ(p1 ) ≥ λ(p2 ) = p2 V (K(p2 )) + m/u − q,
which implies that p1 V (K(p̄)) ≥ p2 V (K(p2 )). But V (K(p̄)) < V (K(p2 )),
so p1 > p2 , which is a contradiction.
Proposition 4 The capital schedule K(p) is continuous.
Let p̂ be the lowest value of p at which K(p) = K(p̄). The capital
schedule is clearly continuous above and below this point. Take the limit of
K(p) as p approaches p̂ from below. Call this limit K̃(p̂). Evaluating (15)
at the limit gives
(p̂V (K̃(p̂)) + m/u − q) = 0.
If K(p) is not continuous at p̂, then K(p̂) = K(p̄) > K̃(p̂), which implies
that
λ(p̂) = (p̂V (K(p̄)) + m/u − q) < 0.
But λ(p̂) < 0 is a contradiction, so K(p) is continuous at p̂ as well.

REFERENCES
Chang, Chun. 1990. “The Dynamic Structure of Optimal Debt Contracts.”
Journal of Economic Theory 52 (October): 68–86.
Lacker, Jeffrey M., and John A.Weinberg. 1989. “Optimal Contracts Under
Costly State Falsification.” Journal of Political Economy 97
(December): 1345–63.

E.S. Prescott: Auditing and Bank Capital Regulation

Marshall, David A., and Edward Simpson Prescott. 2001. “Bank Capital
Regulation with and without State-Contingent Penalties.”
Carnegie-Rochester Conference on Public Policy 54 (June): 139–84.
Monnet, Cyril, and Erwan Quintin. 2003. “Optimal Contracts in a Dynamic
Costly State Verification Model.” Manuscript, July.
Mookherjee, Dilip, and Ivan Png. 1989. “Optimal Auditing, Insurance, and
Redistribution.” Quarterly Journal of Economics 104 (May): 399–415.
Rochet, Jean-Charles. 1999. “Solvency Regulations and the Management of
Banking Risks.” European Economic Review 43 (April): 981–90.
Smith, Bruce D., and ChengWang. 1998. “Repeated Insurance Relationships
in a Costly State Verification Model: With an Application to Deposit
Insurance.” Journal of Monetary Economics 42 (July): 207–40.
Townsend, Robert M. 1979. “Optimal Contracts and Competitive Markets
with Costly State Verification.” Journal of Economic Theory 21
(October): 265–93.
Wang, Cheng. 2005. “Dynamic Costly State Verification.” Economic Theory
25 (June): 887–916.

Using Manufacturing
Surveys to Assess Economic
Conditions
Matthew Harris, Raymond E. Owens, and Pierre-Daniel G. Sarte

tarting in the 1980s, the Richmond Fed began surveying District manufacturers as input into the Bank’s Beige Book reports. The effort, which
mimics the Institute of Supply Management’s (ISM) national survey,
was undertaken because little timely information on regional manufacturing
activity was available. Surveys such as the ISM’s are generally used because
they are thought to provide a good balance between collection effort and the
information obtained. While the earliest Richmond Fed Surveys appeared to
be useful gauges of activity, they had an important shortcoming. They were
conducted approximately every six to seven weeks—prior to the Fed’s Beige
Book reports, so that the results did not coincide with the regular monthly or
quarterly findings from other surveys or economic reports. This irregular timing meant that Richmond Survey results could not be easily verified against
other “benchmark” data, leaving unanswered the appropriate weight to assign
the information. To overcome this shortcoming, the Richmond Survey was
redesigned and conducted on a monthly basis starting in November 1993.
To address this question, we examine why surveys are conducted, and
what information is collected. We also examine how the Richmond Fed Survey specifically compares to other benchmarks, including the ISM and the
Philadelphia Fed Business Conditions Survey, how well it gauges regional
economic activity, and what improvements may be made to the Survey going
forward to increase its value.
We find that the ISM is a very good gauge of national economic activity
as measured by GDP. Its accuracy is highly valued by analysts because it is
We thank Andreas Hornstein, Yash Mehra, and Roy Webb for their helpful comments. In
addition, we thank Judy Cox for her assistance and help. The views expressed in this article
do not necessarily represent those of the Federal Reserve Bank of Richmond or the Federal
Reserve System. Any errors are our own.

Federal Reserve Bank of Richmond Economic Quarterly Volume 90/4 Fall 2004

Federal Reserve Bank of Richmond Economic Quarterly

available up to three months before final GDP data. We also find that the Richmond Manufacturing Survey—alone and when used in conjunction with the
Philadelphia Fed Survey of Business Conditions—is highly correlated with
the ISM. In addition, we find the Richmond Survey to be a good predictor
of several important measures of Fifth District Federal Reserve regional economic activity. It follows, therefore, that the value of the Richmond Survey
would increase if it were released sooner and contained an overall measure of
economic activity.

1. WHY SURVEY?
Prior to the Richmond Survey, information on Fifth District manufacturing
activity was available primarily from the annual Gross State Product (GSP)
reports of District states as well as manufacturing employment. But the GSP
data are typically released one to two years after the period covered by the
report. Other information, such as manufacturing employment, is received
in a more timely manner, though still with a one- to two-month lag. Since
manufacturing activity has historically shown cyclical behavior, the long lag
in the GSP data is problematic. With lags, the cyclical nature of manufacturing
activity raises the likelihood that current conditions in manufacturing activity
differ from those described in the GSP report, rendering the data useful as
a historical benchmark, but sharply reducing their value in assessing current
conditions.
A second alternative was the monthly survey of manufacturing conditions
provided by the National Association of Purchasing Management (NAPM),
now called the ISM. Although timely, the ISM Survey gauges manufacturing
activity at the national level rather than at the regional level. This broad
geographic coverage raises questions about the NAPM’s ability to represent
accurately Fifth District manufacturing activity. The Richmond Fed’s Survey
was undertaken to fill this gap. The information gathered is timely, but has
it been accurate? To address this question, an examination of the Richmond
Survey and its results follows.

2. THE RICHMOND SURVEY
The Richmond Survey is distributed to approximately 200 manufacturers in
the Fifth Federal Reserve District during the second week of each month,
with approximately 40 of those manufacturers also receiving the Survey by
e-mail. Responses are delivered to us by mail, fax, or via the Internet where
respondents can directly input their data by the deadline. Responses must be
received by the cutoff date—usually the first day of the following month—and
typically number about 90 to 100. After compiling the results, the Richmond

M. Harris, R. Owens, and P.D. Sarte: Manufacturing Surveys

Fed places them on the bank’s Web site at 10:00 a.m. on the second Tuesday
of the month following the survey month.
The survey sample is designed to approximate the distribution of manufacturing output by state, industry type, and firm size. Firms possessing
the desired characteristics are typically identified through industry listings or
other means. Once chosen, each manufacturer is invited by mail, e-mail, or by
telephone to participate. Periodically, new names are added to the sample to
improve the distribution’s characteristics, to replace or to enlarge the sample,
or to take advantage of a particular manufacturer’s offer to participate.
The first portion of the Survey asks about business activity. Each survey
includes questions on shipments, new orders, backlogs, finished goods inventories, employment, average workweek, vendor lead time, capacity utilization,
and capital expenditures. Manufacturers are asked whether their firms experienced an increase, decrease, or no change in a variety of activity measures
in each variable over the preceding month. They are also asked whether they
expect an increase, decrease, or no change in the next six months. Raw data
are combined to create diffusion indexes equal to the percentage of respondents reporting increases minus the percentage reporting decreases. Diffusion
indexes are a standard survey tool and are used by many agencies, including
the Philadelphia and Kansas City Feds.1
The diffusion index used for the Richmond Survey is centered on 0, meaning that 0 infers that the level of activity is unchanged from the prior month’s
level. A positive reading indicates a higher level, and a negative reading infers
a lower level. Greater or lesser readings compared to the prior month are
interpreted as faster or slower rates of change in activity, respectively. The
diffusion index is computed according to the standard form,
Index Value = 100(I − D)/(I + N + D),

(1)

where I is the number of respondents reporting increases, N is the number of
respondents reporting no change, and D is the number of respondents reporting
decreases.
Once the raw diffusion indexes are derived, seasonal adjustment factors
are applied. The factors are determined from the last five years of data using
the Census X-12 program.2
The second portion of the Survey focuses on inventory levels. Manufacturers are asked how their current inventory levels compare to their desired
1 For a recent detailed description of the Kansas City Fed Survey, see Keeton and Verba
(2004).
2 The Richmond Survey’s results are bounded between -100 and 100 by construction. It
has been suggested that the results could be transformed into an unbounded series using a logit
transformation procedure before being seasonally adjusted. However, a comparison of this method
with the simple add-on method reveals no substantial difference in the results.

Federal Reserve Bank of Richmond Economic Quarterly

levels. They may respond too low, too high, or correct. The manufacturers
are also asked a similar question about their customers’ inventories.
The third portion of the Survey covers price trends. We ask manufacturers
to estimate recent annualized changes in raw materials and finished goods
prices and price changes expected in the next six months. We report the
simple means of their responses; no seasonal adjustment factors are applied.
The most recent survey form and the most recent press release are shown
in Appendixes A and B. Unlike the ISM and the Federal Reserve Bank of
Philadelphia, Richmond does not publish an overall or composite business
index.3 The construction is straightforward, however, and to allow for comparability, we construct a regional business index similar to that of the ISM.
Our index differs from the ISM’s in two respects. First the Richmond Survey
asks only three questions similar to the five asked by the ISM. Given this, our
weights on the questions differ from those of the ISM. The composite index,
defined by the following components and weights, is used in the next section:
shipments (0.33), new orders (0.40), and employment (0.27).
Before analyzing the usefulness of the Richmond Survey specifically, we
first address the design and ability of the overall ISM to capture changes in
economic activity at the national level.

3. THE ISM
The ISM Survey’s indexes are highly regarded by business analysts because
they have proven to be a reliable gauge of economic activity over a long period.
The ISM’s extensive history is a result of purchasing managers’ long-standing
desire to obtain industry-level information. The earliest purchasing manager
survey was the local NewYork City’s association poll of its members regarding
the availability of specific commodities. The survey began in the 1920s and,
by the 1930s, was broadened to capture a wider range of business activity
measures. Following World War II, the report assumed a format similar to the
current survey instrument, asking about production, new orders, inventories,
employment, and commodity prices. Beginning in the 1970s, other series
were added, including supplier deliveries and new export orders, and, in the
1980s, the Purchasing Manager’s Index (PMI) was developed. The PMI is a
weighted average of several of the seasonally adjusted series in the ISM survey
and will be referred to as the ISM index in this article. The components and
their weights are production (0.25), new orders (0.30), employment (0.20),
supplier deliveries (0.15), and inventories (0.10).
At present, the Survey is sent to approximately 400 purchasing managers
at industrial companies across the country each month. The sample is stratified
3 The Federal Reserve Bank of Philadelphia does not construct an index from a weighted
average of several questions. Rather, the survey directly asks about business conditions.

M. Harris, R. Owens, and P.D. Sarte: Manufacturing Surveys

Figure 1 GDP Growth Rate
... and the Composite ISM Index
23.5

GDP

18.5

ISM

80.0
70.0

GDP, SAAR

8.5

60.0

3.5

50.0

-1.5

40.0

-6.5

Index Levels

13.5

30.0

-11.5

20.0

-16.5

49 53

57 61 65 69

73 77 81 85 89 93 97 01

... and the New Orders Component of the ISM
23.5

GDP

18.5

New Orders

80.0
70.0

GDP, SAAR

8.5

60.0

3.5

50.0

-1.5

40.0

-6.5

Index Levels

13.5

30.0

-11.5

20.0

-16.5

49 53

57 61 65 69

73 77 81 85 89 93 97 01

... and the Production Component of the ISM
23.5

GDP

Production

18.5

70.0

GDP, SAAR

60.0

8.5

50.0

3.5
-1.5

40.0

-6.5

Index Levels

13.5

30.0

-11.5
-16.5

80.0

20.0

49 53

61 65 69

73 77 81 85 89 93 97 01

... and the Employment Component of the ISM
23.5

Employment

GDP

80.0
70.0

13.5
8.5

60.0

3.5

50.0

-1.5

40.0

-6.5

30.0

-11.5

20.0

-16.5

49 53 57 61 65 69

73 77 81 85 89 93 97 01

(Recessions are shaded)

Index Levels

GDP, SAAR

18.5

Federal Reserve Bank of Richmond Economic Quarterly

Figure 2 U.S. Personal Income Growth
... and the Composite ISM Index
23.5

ISM

80.0
70.0

13.5
8.5

60.0

3.5

50.0

-1.5

40.0

-6.5

Index Levels

PI, SAAR

18.5

30.0

-11.5

20.0

-16.5

49 53 57 61 65 69 73 77 81 85 89 93 97 01
... and the New Orders Component of the ISM
23.5

New Orders

80.0
70.0

13.5
8.5

60.0

3.5

50.0

-1.5

40.0

-6.5
30.0

-11.5
-16.5

Index Levels

PI, SAAR

18.5

20.0

49 53 57 61 65 69 73 77 81 85 89 93 97 01
... and the Production Component of the ISM
23.5

80.0

Production
70.0

13.5
8.5

60.0

3.5

50.0

-1.5

40.0

-6.5

Index Levels

PI, SAAR

18.5

30.0

-11.5

20.0

-16.5

49 53 57 61 65 69 73 77 81 85 89 93 97 01
23.5

80.0

Employment
70.0

13.5
8.5

60.0

3.5

50.0

-1.5

40.0

-6.5
30.0

-11.5
-16.5

20.0

49 53 57 61 65 69 73 77 81 85 89 93 97 01
(Recessions are shaded)

Index Levels

PI, SAAR

18.5

... and the Employment Component of the ISM

M. Harris, R. Owens, and P.D. Sarte: Manufacturing Surveys

to represent proportionally the 20 two-digit SIC manufacturing categories by
their relative contribution to GDP. In addition, the Survey is structured to
include a broad geographic distribution of companies (Kauffman 1999).
The ISM survey questions are not released by the organization, so we
do not know precisely what questions respondents answer or whether the
questions changed over time. In addition, the number of respondents is not
revealed by the organization, making variations in response rates impossible
to determine.
Despite a lack of detailed information on the survey instrument and response size, the purchasing manager’s report has an enviable track record as
an indicator of both national manufacturing and general economic conditions.
A review of the ISM as an indicator of broader economic conditions follows.

4. THE ISM AND THE BUSINESS CYCLE
Figures 1 and 2 illustrate how various components of the ISM have moved
with GDP and personal income, respectively, over the post-war period. The
ISM appears to track movements in GDP closely. Note also that both the
volatility of GDP growth and that of the ISM seem to have fallen together
beginning in the early 1980s. Over the period from 1949 to 1984, the standard
deviation of GDP growth was 5.0 percent, as compared to just 2.2 percent
from 1984 to the present. This represents a decline of more than 50 percent
between the two sample periods. Similarly, the standard deviation of the
ISM fell from 8.8 percent over the 1949–1984 period to 4.6 percent since
1984. McConnell and Quiros (2000) argue that much of the reduction in
output fluctuations over the last two decades can be attributed to a discrete
fall in the volatility of durables output around 1984. Khan et al. (1999) then
make the case that the fall in durables volatility itself reflects technological
innovations in inventory management. To the degree that this explanation is
an important factor driving the fall in output volatility starting in the early
1980s, one would expect the ISM to show precisely the kind of corresponding
decrease in standard deviation it has experienced over the same period. In
fact, all components of the ISM display a significant decrease in volatility
after 1984.
Figures 3 and 4 show the cross-correlations between primary components
of the ISM and GDP as well as personal income. Leads and lags in Figures 3
and 4 are measured in quarters. In both cases, the ISM correlates quite well
with those measures, although the cross-correlations with personal income
are generally smaller. Observe also that the cross-correlations are highest
contemporaneously (i.e., k = 0) across components of the ISM, seemingly
suggesting that the ISM offers no advance information on the state of the
business cycle. However, the cross-correlations depicted in Figures 3 and 4
relate to revised GDP releases. Since GDP numbers for a given quarter are

Federal Reserve Bank of Richmond Economic Quarterly

released in preliminary form with a one-month lag, and in revised form with
up to a four-month lag, the ISM appears to provide surprisingly accurate realtime information on the business cycle, essentially one quarter or more ahead
of the release of the final GDP report.
Interestingly, the cross-correlations with both GDP and personal income
are highest not for the overall ISM but for its production component (as much
as 70 percent contemporaneously in the case of GDP), which is not surprising. The production component of manufacturing most directly represents the
sector’s contribution to the value of real GDP in a contemporaneous setting.
In contrast, new orders represent demand for some future period, and though
they can offer insight about future production, they can also be canceled or
altered.
The notion that the individual components of the ISM are not equally
useful in terms of assessing current economic conditions is best reflected in its
employment component. In the case of personal income, for instance, Figure
4 shows that the correlogram peaks at k = 1, indicating a one-quarter lag with
respect to the business cycle. This lag is consistent with the idea that, once
layoffs have taken place in a downturn and the economy subsequently begins
to pick up, manufacturing firms at first are reluctant to hire new workers and
would rather induce their current labor force to work longer hours. In other
words, firms may adjust first along the intensive, rather than the extensive,
margin.
While Figures 3 and 4 show that the ISM is highly correlated with GDP,
the following rolling regressions show that it also generally improves the
forecast performance of both GDP and personal income, as measured by the
mean-squared forecast error. The regressions are run against two lags of the
dependent variable and each of the ISM components, in turn, over the period
1949:Q1 to 1994:Q1, using a ten-year rolling window.
In Table 1, MSEy,x and MSEy denote the mean-squared error of the y
forecast with and without the ISM, or one of its components, respectively.
Here, y refers to the cyclical component of GDP obtained from a HodrickPrescott (HP) filter decomposition.4 Observe that the ratio of the MSEs is
significantly less than one. This value demonstrates that including lags, either
of the ISM or one of its components, always improves upon the current-quarter
forecast of either GDP or personal income, relative to using their own lags
alone.5 Moreover, the ISM series performs better a quarter ahead for both GDP
and personal income. The production series most improves the forecastibility
4 GDP growth can be used in place of cyclical movements without substantial changes in the
findings.
5 Forecasting current-quarter GDP is a useful exercise because advance, preliminary, and final
GDP data are released approximately one, two, and three months, respectively, after the quarter
ends. In contrast, the ISM data are available one business day after the quarter ends.

M. Harris, R. Owens, and P.D. Sarte: Manufacturing Surveys

Figure 3
Correlation between the Composite ISM and GDP Growth
0.8
0.7
0.6
0.5
0.4

0.65

0.59
0.41

0.41

0.3
0.2
0.1
0.0
-0.1
-0.2

0.19
0.12

-0.08
-3

-2

-1

Correlation between the Production Component of the ISM and GDP Growth
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
-0.1

0.70
0.57
0.46
0.32
0.19
0.10
-0.01
-3

-2

-1

Correlation between New Orders Component of the ISM and GDP Growth
0.8
0.7

0.67

0.6
0.5

0.5

0.49

0.4
0.3

0.24

0.2
0.1

0.03

0.02

0.0
-3

-2

-1

Correlation between the Employment Component of the ISM and GDP Growth
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
-0.1
-0.2

0.63

0.64
0.5
0.33

0.32

0.04

-0.16
-3

-2

-1

(3-quarter lead to 3-quarter lag)

Federal Reserve Bank of Richmond Economic Quarterly

Figure 4
Correlation between the Composite ISM Index
and the U.S. Personal Income Growth
0.6
0.49

0.5
0.4

0.50

0.35

0.33

0.3
0.2

0.18
0.12

0.1
0.0

0.02

-3

-2

-1

Correlation between the Production Component
and the U.S. Personal Income Growth
0.6
0.52

0.5

0.46

0.4

0.37

0.3

0.25

0.23

0.2
0.1

0.09
0.04

0.0
-3

-2

-1

Correlation between the New Orders Component
and the U.S. Personal Income Growth
0.5

0.47
0.40

0.39

0.4
0.3

0.27

0.2

0.18
0.13

0.1
-0.04

0.0
-0.1

-3

-2

-1

Correlation between the Employment Component
and the U.S. Personal Income Growth
0.6

0.55

0.5

0.49
0.42

0.4
0.31

0.3

0.24

0.2

0.14

0.1
0.0
-0.1

-0.04
-3

-2

-1

(3-quarter lead to 3-quarter lag)

M. Harris, R. Owens, and P.D. Sarte: Manufacturing Surveys

Table 1 Results from Rolling Regressions
yt =

j =1 α j yt−j +

j =0 β j xt−j

A: y denotes detrended GDP
Predictor, x:
ISM
ISM - Production
ISM - New Orders
ISM - Employment

Current Quarter
MSEy,x /MSEy

1 Quarter Ahead
MSEy,x /MSEy

0.78
0.74
0.78
0.75

0.69
0.64
0.71
0.64

Current Quarter
MSEy,x /MSEy

1 Quarter Ahead
MSEy,x /MSEy

0.86
0.86
0.87
0.87

0.84
0.83
0.85
0.85

B: y denotes Personal Income
Predictor, x:
ISM
ISM - Production
ISM - New Orders
ISM - Employment

of both GDP and personal income in the current quarter and one quarter
ahead. This result is not surprising, as production most closely matches GDP
conceptually and would be expected to perform well compared to personal
income. In addition, the new orders component of the ISM generally improves
both the current and one-quarter-ahead forecasts of GDP, although to a slightly
lesser degree than the other components of the ISM one quarter ahead. This
underscores the notion that new orders may not translate into shipments at a
later date.
Although the ISM and its components improve the ability to forecast
personal income in both the current quarter and one quarter ahead, Table 2
indicates that this improvement is somewhat reduced relative to GDP in Table
1. While personal income tends to track GDP over the long run, there are often
substantial deviations between the two in the short run because of measurement
error in personal income as well as differences in its definition. For example,
personal income includes income from interest and rental sources which do
not closely track movements in GDP.
While we have shown that the survey of purchasing managers is effective
in tracking movements in GDP in real time (i.e., considerably ahead of the
GDP release for the corresponding time period) and forecasting real growth, a
more central question concerns its ability to alert us of impending recessions.
Figure 1 shows that the ISM and its individual series tend to fall prior to
recessions. As in Dotsey (1998), we can establish whether this behavior
contains any predictive power most simply by assessing the signal value of

Federal Reserve Bank of Richmond Economic Quarterly

Table 2 Signal Value of the ISM and its Components One Quarter
Ahead
x < µ − σ2

x <µ−σ

(%)

42
61.90

21
71.43

11
90.91

(%)

29
68.97

14
78.57

5
80.00

(%)

21
66.67

12
83.33

3
66.67

(%)

78
38.46

31
67.74

18
72.22

Predictor, x:
ISM
Total Signals
Frequency of True Signals
Production
Total Signals
Frequency of True Signals
New Orders
Total Signals
Frequency of True Signals
Employment
Total Signals
Frequency of True Signals

x < µ − 3σ
2

the ISM series at different thresholds. Accordingly, let us define a signal as
true if the ISM or one of its components falls below its mean (µ) by at least
φ standard deviations (σ ), where φ is alternatively 1/2, 1, and 3/2, and a
recession occurs in the following quarter. We define a signal as false if no
recession takes place in the quarter following one of the above signals. We
can also carry out this exercise with respect to two-quarter-ahead predictions.
In general, examining the relative frequency of true signals gives us a sense of
how reliably the purchasing managers’ survey anticipates recessions. Note,
however, that this procedure says nothing about potential Type 2 errors—that
is, situations in which a recession takes place without a signal occurring. As in
Dotsey (1998), “this exercise lets us determine if” the ISM series “are like the
boy who cried wolf or, in other words, if they correctly predict a weakening
economy.” The results from this non-parametric exercise are shown in Tables
2 and 3.
The results from Table 2 confirm the graphical intuition obtained from
Figure 1 in that the ISM and its individual components generally represent a
reliable, albeit imperfect, signal of future recessions. These results explain
why both market participants and policymakers place so much emphasis on
the monthly ISM release. For comparison, the unconditional likelihood of
a recession over the period 1948:Q1 to 2004:Q1, as defined by the relative
frequency of recession quarters, is just 20 percent. In contrast, conditioning
on the ISM being one standard deviation below its mean, Table 1 indicates
that the likelihood of being in a recession next quarter jumps to 71 percent.
As expected, the weakest signal of an impending recession associated with
the survey of purchasing managers stems from the employment series. For
that series, the majority of false signals distinctly occurs towards the end of

M. Harris, R. Owens, and P.D. Sarte: Manufacturing Surveys

Table 3 Signal Value of the ISM and its Components Two Quarters
Ahead
x < µ − σ2

x <µ−σ

(%)

42
42.86

21
42.86

11
54.55

(%)

29
51.72

14
50.00

5
40.00

(%)

21
42.87

12
50.00

3
33.33

(%)

78
26.94

31
38.72

18
44.44

x < µ − 3σ
2

recessions where the employment index remains low despite the end of the
recession. As discussed earlier, this feature reflects firms’ reluctance to hire
new workers until they are convinced that the recession has come to an end.
Table 3 indicates that the signal value of the ISM and its components in terms
of foretelling recessions falls significantly two quarters ahead, although the
frequency of true signals still hovers around 40 to 50 percent for most series.
Again, the one exception is the employment series of which the signal value
becomes barely more than the unconditional likelihood of a recession.
The above analysis can be refined by adding more structure to the way
the likelihood of a recession is modeled conditional on observing the ISM or
one of its components. In particular, one approach would be to model the
probability of a recession as depending continuously on both the observed
predictor, x (i.e., the ISM or one of its series), and some parameter, β, that
translates the effect of the predictor on the likelihood of a recession. The
probit model, for instance, expresses the likelihood of a recession as
βx
Pr(recession) =
φ(ω)dω
(2)
−∞

= (βx),
where φ(ω) is the normal density function that corresponds to the cumulative
distribution, 0 ≤ (ω) ≤ 1. It follows that the likelihood of not being in a
recession at a given date is simply 1 − (βx). Moreover, from (2), we can
immediately see that the probability of a recession now increases continuously
with the predictor, x.
Figure 5 shows the results from having estimated equation (2) using the
ISM or one of its individual series as the conditioning variable. Observe that

Federal Reserve Bank of Richmond Economic Quarterly

Figure 5 Probability of Recession

Probability of Recession

... as Indicated by the Composite ISM Index
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
48 52

Probability of Recession

... as Indicated by the New Orders Component of the ISM Index
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0

48 52

00 04

Probability of Recession

... as Indicated by the Production Component of the ISM Index
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
48 52

00 04

Probability of Recession

... as Indicated by the Employment Component of the ISM Index
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0

48 52

(Recessions are shaded)

00 04

M. Harris, R. Owens, and P.D. Sarte: Manufacturing Surveys

actual recessions, shaded in gray, are generally associated with spikes in the
estimated probability of a recession at those dates. This is especially true for
the production series where many of the spikes are very near 1. Furthermore,
consistent with the signal value analysis exercise carried out above, Figure
5 generally shows few cases of spikes taking place without a recession. In
that sense, the ISM is typically not “a boy who cries wolf.” Recall that
our signal analysis had nothing to say about potential Type 2 errors—that
is, situations where a recession took place without a signal from the survey
of purchasing managers. In fact, Figure 5 suggests that these situations are
seldom the case. One obvious exception concerns the 1960–1961 period
where, despite a recession having taken place, the ISM, as well as all of its
components, nevertheless implied a relatively low recession probability. This
implication suggests that factors outside of manufacturing may have played
an unusually large role in generating that specific downturn.

DO THE PHILADELPHIA AND RICHMOND SURVEYS
HELP FORECAST THE ISM?

Among the regional Fed Surveys, Philadelphia has the longest running effort—
stretching back to May 1968—and Richmond has the second oldest with
monthly data beginning in November 1993. More recent surveys are those
by Kansas City (quarterly, dating to late 1994) and New York (monthly, first
released in 2002). In addition, Dallas is currently developing a manufacturing
survey.
While the Philadelphia and Richmond Surveys are designed to gauge
manufacturing conditions in their Districts, their results—seasonally adjusted
and released monthly—also generally track the national ISM. It is noteworthy,
however, that the regional Fed Banks collect and analyze their survey results
prior to the release of the ISM data. The Philadelphia Survey, for example,
is released on the third Thursday of the survey month compared to the first
business day of the following month for the national ISM release. Similarly,
while Richmond currently releases its index results to the public after the
purchasing managers’ index is made public, the Bank has preliminary results
available internally well before the public release date. In any case, in the
remainder of this analysis, the Richmond Survey information will be treated
as if it is available to the public prior to the release of the ISM results.
A second issue related to the gathering of regional information has to do
with the limits of the ISM. Ultimately, as with the Beige Book, dispersion matters. Although the current state of manufacturing nationally can be assessed
with the ISM, information may also be gained by gauging manufacturing activity in regions. To see why, imagine a manufacturing sector composed of
two industries, one stable and one volatile. If overall activity declines, but
the source cannot be identified, the question of whether or not the decline is

Federal Reserve Bank of Richmond Economic Quarterly

Figure 6
Correlation between the ISM Composite Index
and the Philadelphia Business Outlook Survey Index
0.8

0.74

0.7
0.6

0.76

0.73

0.68
0.62

0.58

0.5

0.5
0.4
0.3
0.2

-3

-2

-1
k
1
(3-quarter lead to 3-quarter lag)

Correlation between the ISM Composite Index
and the Richmond Survey of Manufacturing
0.8

0.766

0.7

0.720
0.636

0.580

0.6
0.5

0.767

0.690

0.440

0.4
0.3
0.2
-3

-2

-1

(3-quarter lead to 3-quarter lag)

a likely trend decline (if the stable industry declines) or a more temporary
change (if the volatile sector declines) remains unanswered. But if the source
of the decline can be identified, the question may be partially addressed. To
the extent that more detailed information can be gathered by surveying regions
with different manufacturing structures, insights may be gained by comparing
their relative performances.
Figure 6 shows the cross-correlations of the ISM with the regional indexes
constructed by the Federal Reserve Banks of Philadelphia and Richmond. Because these two Banks’ Surveys are monthly and have long histories—like the
ISM—they can be easily compared. From the figure, it is apparent that both
regional indexes correlate very well with the ISM, over the period analyzed,
although the Richmond index seems to lag the ISM slightly, relative to the
Philadelphia regional index. Both Surveys display virtually identical contemporaneous correlations at 0.76. However, while these contemporaneous
correlations with the ISM are very similar, they nevertheless stem from different regional information sets. Put another way, while the Philadelphia and

M. Harris, R. Owens, and P.D. Sarte: Manufacturing Surveys

Richmond indexes correlate with the national survey to the same degree, we
now show that they capture slightly different aspects of the ISM behavior.
In the following discussion, let P , R, and N denote, respectively, the
survey indexes computed by Philadelphia, Richmond, and the national survey
of purchasing managers. We assume that P , R, and N are random variables
such that
E(N |P ) = α + βp

(3)

for all values p taken on by P . In other words, the expectation of the ISM
number conditional on having observed the Philadelphia Survey index number
is simply a linear function of that regional number. Under this assumption,
one can show that
(N, P )σ N
(N, P )σ N
α = µ N − µP
, and β =
,
(4)
σP
σp
where µ and σ denote means and standard deviations, respectively, while (.)
represents the correlation between two variables. In addition, we can interpret
assumption (3) as deriving from the following equation,
N = α + βP + ε, E(ε|P ) = 0,

(5)

where ε denotes movements in the ISM that are not related to regional information captured by the Philadelphia Survey. Using equations (4) and (5), it is
straightforward to show that
(ε, R)σ ε
(N, R) = (N, P )(P , R) +
.
(6)
σN
Put simply, the degree to which regional information gathered in the Richmond
Survey correlates with the ISM, (N, R), can be split into two parts. The first
term on the right-hand side of equation (6) tells us that the degree to which the
Richmond Survey co-moves with the ISM is driven in part by the Richmond
and Philadelphia Surveys sharing a common component, (P , R), and the fact
that the Philadelphia Survey itself moves with the ISM, (N, P ). Put another
way, the correlation between the Richmond Survey and the ISM is explained by
regional information common to both Philadelphia and Richmond. In contrast,
the second term on the right-hand side of (6) depicts the co-movement between
the Richmond Survey Index and variations in the ISM that are not captured
by the Philadelphia Survey.
We know from Figure 6 that both (N, R) and (N, P ) are around 0.77.
Additional calculations yield that (P , R) = 0.64, so that approximately 64
percent of the correlation between the Richmond regional index and the ISM
is accounted for by regional information common to Richmond and Philadelphia. This means that roughly 36 percent of the co-movement between the
Richmond and purchasing managers indexes derives from the component of
ISM movements, ε, orthogonal to the Philadelphia Survey index. The fact
that the Richmond index is correlated with ε appears clearly in Figure 7.

Federal Reserve Bank of Richmond Economic Quarterly

Figure 7
Relationship between Richmond Manufacturing Survey Index and Residuals
from Regressing the Composite ISM Index on the Philadelphia Business Outlook Survey Index
Richmond Manufacturing Survey Index
Residuals from Regressing ISM on
Philadelphia Business Outlook Survey Index

8
6
4
2
0
-30.0

-20.0

-10.0

0.0

10.0

20.0

30.0

-2
-4
-6
y = 0.1245x-0.4362
R 2 = 0.1863

-8
-10

As mentioned earlier, the Philadelphia business outlook survey is typically
released approximately ten or more days prior to the ISM. Therefore, given the
ISM’s ability to convey changes in business conditions outlined in the previous section, the exercise we have just carried out suggests that Philadelphia’s
regional index constitutes one of the earliest available gauges of the business
cycle. Moreover, because the Richmond Manufacturing Survey captures variations in the ISM that are unexplained by Philadelphia’s business outlook,
we expect a simultaneous release of the two Surveys to convey most of the
ISM’s information in real time. Put another way, once regional information
is gathered across the Third and Fifth Federal Reserve Districts, we already
have a relatively accurate reading of what the national survey might indicate.
But this reading cannot be fully exploited at present because the Richmond
Survey results are released after the ISM results. As was mentioned earlier,
though, we treat the Richmond results as if they were available in advance of
the ISM. Tables 4 and 5 illustrate this point.
Analogous to the previous section, the first column of Table 4 tells us that
when the Philadelphia business outlook index falls more than 0.5 standard
deviations below its mean, the ISM behaves likewise almost 81 percent of
the time within the same month. This number increases to 84 percent in the
second column when both the Philadelphia and Richmond indexes fall below
their respective means by at least 0.5 standard deviations. On the up side, the
last column of Table 4 indicates that the ISM is above its mean by more than
0.5 standard deviations 88 percent of the time when both the Philadelphia and

M. Harris, R. Owens, and P.D. Sarte: Manufacturing Surveys

Figure 8
Correlation between 3rd District Personal Income Growth
and the Philadelphia Business Outlook Survey Index
0.40

0.35

0.37

0.30
0.20

0.25
0.18

0.10

0.08
0.02

0.00
-0.10
-0.20

-0.22

-0.30
-3

-2

-1

Correlation between 3rd District Personal Income Growth
and the Philadelphia Business Outlook Survey Index, New Orders Component

0.30
0.25

0.24

0.26

0.28

0.20
0.15

0.15

0.16
0.11

0.10
0.05
0.00
-0.05

-0.01
-3

-2

-1

Correlation between 3rd District Personal Income Growth
and the Philadelphia Business Outlook Survey Index, Production Component

0.30

0.26

0.25
0.20

0.21

0.23

0.18

0.16

0.15

0.15
0.10
0.05
0.00

-0.009

-0.05
-3

-2

-1

Correlation between 3rd District Personal Income Growth
and the Philadelphia Business Outlook Survey Index, Employment Component
0.45

0.41
0.34

0.34

0.35

0.35
0.28

0.25

0.21

0.15
0.08
0.05
-3

-2

-1

(3-quarter lead to 3-quarter lag)

Richmond Surveys behave likewise within the same month. Note that this
finding represents an increase from 68 percent in the third column when the
Philadelphia Regional Survey alone is considered.
Having established that the Richmond Survey—along with the Philadelphia Survey—is a good indicator of the ISM, the question of whether it also is

Federal Reserve Bank of Richmond Economic Quarterly

Table 4 Signal Value of the Philadelphia and Richmond Regional
Surveys
ISM, z:
Philadelphia, x:

z < µz − σ2x
x < µx − σ2x

Richmond, y:
Total Signals
Freq. of True Signals

31
80.65%

x < µx −
and
y < µy −
25
84.00%

z > µx + σ2x
σx
2

x > µx + σ2x

σy
2

44
68.18%

x > µx +
and
y > µy +

σx
2
σy
2

25
88.00%

a good indicator of Fifth District economic conditions remains. We now turn
our attention to that question.

6. THE RICHMOND SURVEY AND FIFTH DISTRICT
ECONOMIC ACTIVITY
The Richmond Survey is useful in assessing some—though not all—aspects of
regional economic activity. It is not, for example, a good gauge of gross state
product (GSP) data. GSP data are only released on an annual basis, which, in
terms of the Richmond Manufacturing Survey and the Fifth Federal Reserve
District, represent only 13 data points. In contrast, personal income at the state
level is available quarterly, and Figure 9 depicts the cross-correlations of the
Richmond business surveys with Fifth District personal income. These crosscorrelations are computed over the sample period for which the Richmond
Manufacturing Survey numbers are available, 1994–2004.
Although the Richmond manufacturing index shows a generally high correlation with Fifth District personal income, it lags personal income by approximately one quarter. However, because state-level personal income data are
released with a one-quarter lag, the Richmond results provide a more timely
gauge of movements in Fifth District personal income.
More encouraging, as shown in Figure 11, the Richmond employment
index distinctly leads changes in manufacturing employment by one quarter.
This is noteworthy because changes in manufacturing employment are among
the most timely and closely watched regional economic data.

CONCLUDING REMARKS

Given the strong interest in timely information on both national and regional
economic conditions, the Richmond Survey of Manufacturing performs a useful role. In a national economic setting, the Survey appears capable of adding

M. Harris, R. Owens, and P.D. Sarte: Manufacturing Surveys

Figure 9
Correlation between 5th District Personal Income Growth
and the Richmond Manufacturing Survey Index
0.39

0.40
0.30

0.28

0.31
0.25

0.20
0.12
0.10

0.04

0.00
-0.04

-0.10
-3

-2

-1

Correlation between 5th District Personal Income Growth
and the Richmond Manufacturing Survey Index, New Orders Component
0.50
0.39
0.40
0.31
0.30
0.30
0.23
0.20
0.1
0.10
0.02
0.00
-0.10

-0.11

-0.20
-3

-2

-1

Correlation between 5th District Personal Income Growth
and the Richmond Manufacturing Survey Index, Production Component
0.31
0.30

0.24

0.25

0.20
0.10

0.16
0.07

0.00
-0.02
-0.06

-0.10
-3

-2

-1

Correlation between 5th District Personal Income Growth
and the Richmond Manufacturing Survey Index, Employment Component
0.42

0.45

0.37
0.35
0.25

0.32
0.22

0.24
0.20
0.16

0.15
0.05
-3

-2

-1

(3-quarter lead to 3-quarter lag)

Federal Reserve Bank of Richmond Economic Quarterly

Figure 10
Correlation between the Composite ISM Index
and U.S. Personal Income Growth
0.5

0.42

0.4
0.3

0.31

0.27

0.31
0.21

0.2
0.1

0.04

0.0
-0.1
-0.2

-0.16
-3

-2

-1

Correlation between the ISM New Orders Component
and U.S. Personal Income Growth
0.5
0.38

0.4
0.3

0.28

0.26

0.22

0.2
0.10

0.1
0.0
-0.1

-0.09

-0.2
-0.26

-0.3
-3

-2

-1

Correlation between the ISM Production Component
and U.S. Personal Income Growth
0.4
0.3

0.37
0.31

0.29

0.25

0.2

0.17

0.1
0.02

0.0
-0.1
-0.2

-0.19

-0.3
-3

-2

-1

Correlation between the ISM Employment Component
and U.S. Personal Income Growth
0.6
0.53
0.5
0.42

0.49
0.44

0.4
0.3

0.30

0.26

0.2
0.10

0.1
0.0
-3

-2

-1
t
1
(3-quarter lead to 3-quarter lag)

M. Harris, R. Owens, and P.D. Sarte: Manufacturing Surveys

Table 5 Signal Value of the Philadelphia and Richmond Regional
Surveys
ISM, z :
Philadelphia, x:

z < µz − σ z
x < µx − σ x

x < µx − σ x
and
y < µy − σ y

x > µx + σ x

22
68.18%

15
86.67%

16
62.50%

Richmond, y:
Total Signals
Freq. of True Signals

z > µz + σ z
x > µx + σ x
and
y > µy + σ y
6
66.67%

to the ability to forecast the PMI component of the ISM index, especially when
combined with the results of the Philadelphia Fed’s Survey results. This is
important because the ISM has been a very good gauge historically. The ISM
is released well ahead of GDP data, and it provides relatively accurate signals
of both substantial changes in the growth rate of GDP and turning points in
the economy.
Both the Philadelphia and Richmond Federal Reserve Banks produce
monthly indexes that are highly correlated with the ISM. The Philadelphia
Index is currently released well in advance of the ISM and serves as a valuable predictor of the ISM.
The Richmond Survey results are less useful at present. The results are reported as components only rather than in the format of an ISM-style weighted
index. Moreover, the Richmond results are released after the ISM. But this
memo suggests that some modification of the Richmond Manufacturing Survey could add substantial value to forecasters. First, as was done in this
analysis, existing questions in the Survey could be combined and weighted in
a manner similar to the construction of the ISM. One such construction, considered in the memo, is shown to correlate very well with the ISM. A second
change would be to advance the release date of the Richmond Survey results.
Because the information is currently available internally to the Richmond Fed
well before it is released to the public, moving up the release date would provide the same advantage to the public. A second important finding is that the
Richmond Survey is a good indicator of economic activity in the Fifth District.
It provides a timely view of economic activity in the Fifth Federal Reserve
District. While the Richmond Survey tends to lag its Federal Reserve District’s personal income measure by around a quarter, the Survey’s information
is made available well in advance of the District personal income data and
so effectively provides an advance look at Fifth District personal income. In
addition, the Richmond Survey Index distinctly leads changes in Fifth District

Federal Reserve Bank of Richmond Economic Quarterly

Figure 11
Correlation between 3rd District Manufacturing Employment
and the Philadelphia Business Outlook Survey, Employment Component
0.7
0.6

0.63

0.59

0.54
0.47

0.5
0.4

0.41
0.35

0.3

0.29

0.2
0.1
0.0
-3

-2

-1

Correlation between 5th District Manufacturing Employment
and the Richmond Manufacturing Survey, Employment Component
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0

0.74

-3

0.71

-2

0.67

-1

0.63

0.58

0.52

0.47

Correlation between U.S. Manufacturing Employment
and the ISM, Employment Component
0.7
0.6

0.66

0.60
0.53

0.5
0.4

0.44
0.36
0.28

0.3

0.22

0.2
0.1
0.0

-3

-2

-1

(3-month lead to 3-month lag)

employment, giving an advance indication of changes in the region’s labor
market.

M. Harris, R. Owens, and P.D. Sarte: Manufacturing Surveys

APPENDIX A:

SURVEY OF FIFTH DISTRICT
MANUFACTURING ACTIVITY

Business Activity Indexes
Compared to the previous month
Shipments
Volume of new orders
Backlog of orders
Capacity utilization
Vendor lead time
Number of employees
Average workweek
Wages
Six months from now
Shipments
Volume of new orders
Backlog of orders
Capacity utilization
Vendor lead time
Number of employees
Average workweek
Wages
Capital expenditures
Inventory levels
Finished good inventories
Raw materials inventories

September
22
8
-6
13
14
5
1
10

August
18
13
1
9
21
-2
-1
10

July
6
13
-3
5
15
6
6
12

3-month avg.
5
11
-3
9
16
3
2
11

23
24
5
10
11
3
7
34
9

28
24
11
16
6
7
-4
42
19

33
31
14
17
4
9
0
46
17

28
26
10
15
7
6
1
41
15

16
11

16
7

19
7

17
8

Price trends
(percent change, annualized)
Current trends
Prices paid
Prices received
Expected trends during next 6 months
Prices paid
Prices received

September

August

July

1.71
1.25

2.28
2.17

2.33
3.20

1.25
0.08

2.17
1.37

3.20
2.59

Notes: Each index equals the percentage of responding firms reporting increase minus
the percentage reporting decrease. Data are seasonally adjusted. Results are based on
responses from 94 of 201 firms surveyed
All firms surveyed are located in the Fifth Federal Reserve District, which includes the
District of Columbia, Maryland, North Carolina, South Carolina, Virginia, and most of
West Virginia.

Federal Reserve Bank of Richmond Economic Quarterly

APPENDIX B:

FIFTH DISTRICT MANUFACTURING
ACTIVITY PRESS RELEASE

Manufacturing Output Strengthens in September;
Employment Improves; Average Workweek Flat
On balance, manufacturing activity continued to generally strengthen in
September, according to the latest survey by the Richmond Fed.6 Factory
shipments advanced at a quicker pace although the growth of new orders
edged lower. Backlogs retreated into negative territory while capacity utilization inched slightly higher. Vendor lead-time grew more slowly than last
month while raw materials inventories grew at a slightly faster rate. On the
job front, manufacturers reported that worker numbers were higher at District
plants; the average workweek was flat and wage growth stayed on pace of
recent months.
Looking ahead, respondents’ expectations were generally less optimistic
than those of a month ago—producers looked for shipments and capital expenditures to grow at a somewhat slower pace during the next six months.
Price increases at District manufacturing firms continued to increase at a
modest pace in September. Raw materials prices grew at a marginally slower
rate, while finished goods prices grew at a slightly quicker rate. For the coming
six months, respondents expected raw materials goods prices to increase only
modestly and finished goods prices to be nearly flat.
Current Activity

In September, the seasonally adjusted shipments index inched up four points
to 22, and the new orders index inched down five points to 8. In addition,
the order backlogs index moved into negative territory, losing seven points to
end at -6. The capacity utilization index advanced four points to 13 while the
vendor lead-time index shed seven points to 14. The level of finished goods
inventories was unchanged in September when compared to August, while
the level of raw materials inventories increased. The finished goods inventory
index held steady at 16, while the raw materials inventory index added four
points to finish at 11.
Employment

Employment at District plants showed signs of improvement in September.
The employment index posted a seven-point gain to 5 from -2; the average
6 Released 12 October 2004.

M. Harris, R. Owens, and P.D. Sarte: Manufacturing Surveys

workweek index picked up two points to 1 from -1. Wage growth remained
modest, matching August’s reading of 10.
Expectations

In September, contacts were slightly less optimistic about demand for their
products during the next six months. The index of expected shipments moved
down five points to 23, while the expected orders index stayed at 24. The
expected orders backlogs index dropped six points to end at 5 and the expected
capacity utilization index shed six points to 10. The index for future vendor
lead-time inched up five points to 11. In contrast, planned capital expenditures
registered a ten-point loss to 9.
Manufacturers’ plans to add labor in coming months were mixed. The
index for expected manufacturing employment inched down four points to 3,
while the expected average workweek index advanced eleven points to 7. The
expected wage index posted a ten-point loss to 9.
Prices

Price changes remained modest in September. Manufacturers reported that the
prices they paid increased at an average annual rate of 1.71 percent compared
to August’s reading of 2.28 percent. Finished goods prices rose at an average
annual rate of 1.25 percent in September compared to 0.79 percent reported last
month. Looking ahead to the next six months, respondents expected supplier
prices to increase at a 1.25 percent annual rate compared to the previous
month’s 2.17 percent pace. In addition, they looked for finished goods prices
to nearly match the pace of last month’s expected 1.37 percent rate.
Shipments Index
50.0
40.0
30.0
20.0
10.0
0.0
-10.0
-20.0
-30.0
1996

1997

1998

1999

seasonally adjusted

2000

2001

2002

2003

2004

3-month moving average

Federal Reserve Bank of Richmond Economic Quarterly

REFERENCES
Dotsey, Michael. 1998. “True Predictive Content of the Internet Rate Term
Spread for Future Economic Growth.” Federal Reserve Bank of
Richmond Economic Quarterly 84 (May): 31–51.
Keeton, William R., and Michael Verba. 2004. “What Can Regional
Manufacturing Surveys Tell Us?—Lessons from the Tenth District.”
Federal Reserve Bank of Kansas City Economic Review 89 (Third
Quarter): 39–69.
Lacy, Robert L. 1999. “Gauging Manufacturing Activity: The Federal
Reserve Bank of Richmond’s Survey of Manufacturers.” Federal
Reserve Bank of Richmond Economic Quarterly 85 (Winter): 79–98.
Kaufmann, Ralph G. 1999. “Indicator Qualities of the NAPM Report on
Business.” Journal of Supply Chain Management (Spring): 29–37.
Khan, James, Connell, Margaret, and Gabriel Quiros. 1999. “Inventories and
the Information Revolution: Implications for Output Volatility.” Mimeo,
Federal Reserve Bank of New York.
McConnell, Margaret, and Gabriel Quiros. 2000. “Output Fluctuations in the
United States: What Has Changed Since the Early 1980s?” American
Economic Review 90 (December): 1464–76.

Full text of Economic Quarterly (Federal Reserve Bank of Richmond) : Fall 2004, Vol. 90, No. 4

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