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Reflections on
Monetary Policy
J. Alfred Broaddus, Jr.

I

t is a pleasure and indeed an honor to be with you this evening. I must
confess that when I recall the long line of distinguished economists who
have delivered the Sandridge lecture, I wonder whether I am really worthy
of this opportunity. But in any case I am grateful for it and will strive to make
the most of it.
I have worked at the Federal Reserve Bank of Richmond for just about a
quarter of a century, and for virtually all of that time I have been involved in
one way or another in the formation of monetary policy. For most of that period
I was an advisor to the president of the Richmond Fed, and for the last two
years I have served as president myself. Given this background, I believe the
most useful thing I can probably do this evening is to make a few remarks about
monetary policy and some of the major issues the Fed is facing in conducting
policy currently, in the context of my experience with the policymaking process
over the years.
The last 25 years have been extraordinarily eventful ones for monetary
policy in many ways. In this period there were fundamental changes in attitudes
among policymakers, financial market participants, and the public regarding the
appropriate role of monetary policy and also about some of the procedures used
by the Fed in implementing policy decisions. The major factor triggering this
reevaluation without any doubt was the inflation that began at the end of the
1960s and peaked at about 13 percent at the beginning of the 1980s. This rise
in inflation was unprecedented in recent peacetime American history; it was
largely unexpected by the public and the Fed; and it severely challenged widely
held assumptions about the economy and inflation prevailing at the time.
This article is adapted from the Sandridge Lecture delivered by J. Alfred Broaddus, Jr.,
president of the Federal Reserve Bank of Richmond, at the annual meeting of the Virginia
Association of Economists in Richmond on March 16, 1995. Mr. Broaddus wishes to thank
his long-time colleague, Timothy Cook, for substantial assistance in preparing the address.
The address also draws on several published and unpublished articles by other members of
the Bank’s staff. The views expressed are those of the author and not necessarily those of
the Federal Reserve System.

Federal Reserve Bank of Richmond Economic Quarterly Volume 81/2 Spring 1995

1

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Federal Reserve Bank of Richmond Economic Quarterly

The inflation in the 1970s was followed by a severe recession in the early
1980s and, subsequently, a sharp deceleration in the rate of inflation to approximately 4 to 5 percent. Most recently, as you know, inflation has been running
at about a 3 percent rate, which is the lowest rate since I began my career at the
Fed. If the 1970s taught us the necessity of containing inflation, I would say
that the major lesson of the 1980s was the importance of (1) having a long-run
strategy to achieve that goal and (2) maintaining the public’s confidence in that
strategy or, to use the currently popular jargon, maintaining the credibility of
the strategy.
Tonight I want to look back over my years at the Fed, explain to you
how developments over this period have influenced thinking about monetary
policy and how it should be conducted, and share some of my own views with
you. My purpose is not so much to convince you of the wisdom of my views,
although I certainly hope you find at least some of them persuasive, but to give
you perhaps a fuller appreciation of the fundamental issues facing monetary
policy today.

1.

THE ORIGIN OF THE FEDERAL RESERVE
AND ITS MANDATE

Let me begin with just a few introductory comments about the Fed. Most if
not all of you are probably familiar with the Fed; nonetheless, a brief review
may increase your appreciation of some of the points I will be making.
The Federal Reserve was established by Congress in 1914. Initially, the
Fed’s main purpose or “mandate” was to cushion short-term interest rates from
liquidity disturbances arising from banking panics or from seasonal changes in
the demand for credit. In later years, however, the Fed’s mandate was broadened
to include a wide range of macroeconomic goals. Currently, Section 2A of the
Federal Reserve Act instructs the Fed to “maintain long-run growth of the
monetary aggregates commensurate with the economy’s long-run potential to
increase production, so as to promote effectively the goals of maximum employment, stable prices, and moderate long-term interest rates.” Moreover, in
carrying out monetary policy, the Fed is to “[take] account of past and prospective developments in employment, unemployment, production, investment, real
income, productivity, international trade and payments, and prices.”
The Fed has a measure of independence within the government in that
it makes its month-to-month policy decisions without the direct involvement
of Congress, but it is fully accountable to Congress. Accordingly, the Fed
reports formally to Congress on monetary policy every six months, and the
chairman of the Fed’s Board of Governors and other System officials testify
before congressional committees on monetary policy issues as well as other
matters throughout the year. The body within the Fed that actually formulates
and carries out monetary policy is called the Federal Open Market Committee.

Alfred Broaddus: Reflections on Monetary Policy

3

It is made up of the seven members of the Board of Governors located in
Washington and, at any particular time, five of the twelve regional Federal
Reserve Bank presidents. I am a voting member of this committee every third
year. I voted last year and will vote again in 1997.
A final point I would make is that the Fed’s policy instrument—the particular variable it controls on a week-to-week basis to achieve its ultimate policy
objectives—is the interest rate on reserves that private banks lend to one another, generally referred to in financial markets as the “federal funds rate.”
Changes in this rate trigger adjustments in other interest rates, in money and
credit flows, and ultimately in broad macroeconomic variables—particularly
the aggregate level of prices in the economy.
So the key points about the Fed are (1) that it is a creature of Congress,
which has ultimate authority over it; (2) that, as such, it receives its “mandate”
from Congress, regarding what it should try to achieve with monetary policy;
(3) that the policymaking Federal Open Market Committee has some degree
of independence in making its short-run policy decisions, although over time
these decisions are subject to congressional review; and (4) that the Fed’s policy
instrument is the federal funds rate.

2.

PREVAILING VIEWS REGARDING MONETARY
POLICY IN THE 1960S

With these points about the Fed in mind, let me review policy over the last 25
years, obviously in a very summary fashion. When I began my career at the Fed
in 1970, there were three widely held views about the economy that strongly
influenced monetary policy and the procedures used to implement it. First,
most economists believed that there was a Phillips Curve trade-off between
unemployment and inflation in the long run as well as the short run. As you all
know, this famous curve summarizes the inverse empirical correlation between
unemployment and inflation especially evident in the 1950s and 1960s. The
implication for monetary policy, in the eyes of many, was that the Fed could
exploit the trade-off the curve seemed to indicate: that is, it could seek a lower
level of inflation at the cost of higher unemployment; conversely—and perhaps
more to the point—it could seek lower unemployment at the cost of higher
inflation.
The second widely held assumption was that economists knew enough
about the structure of the economy and the way businesses and consumers
behave to permit the Fed to make policy decisions that would eliminate, or
at least greatly diminish, the amplitudes of business cycles. This confidence
had been fostered by the relatively steady economic growth that had characterized the 1960s and by the neo-Keynesian macroeconomic theories dominant at
the time.

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Federal Reserve Bank of Richmond Economic Quarterly

The third important idea commonly held in the 1960s was that the welfare
costs of inflation were small and that, in any case, they were pretty much limited
to the “shoe-leather costs” associated with economizing on money balances in
moderately inflationary periods. Of course, there had not been much inflation
since the Korean War in the early 1950s, so this belief that inflation was a
relatively benign phenomenon probably reflected the absence of any significant
recent experience with inflation.

3.

INFLATION IN THE 1970S AND ITS EFFECTS

Each of these three views fell victim—largely, if not completely—to developments in the 1970s. During this period there were three major cycles of rising
inflation, each more severe than the one before. Each of these accelerations of
inflation, in turn, was followed by a sharp tightening in monetary policy and a
recession. The most memorable episode occurred in 1979 and 1980, when the
Consumer Price Index rose at an annual rate exceeding 12 percent. Confronted
with this situation, the Fed took actions that raised short-term interest rates to
unprecedented levels, and the worst recession in the postwar period followed,
lasting fully six quarters between mid-1981 and the end of 1982.
Sharp increases in oil prices in the mid- and late 1970s no doubt contributed
to inflation, but in the long run we know that monetary policy determines the
rate of inflation; consequently, inflation could not have risen so sharply over
this period without the Fed’s acquiescence. There are a number of explanations
for the Fed’s loss of control over inflation in this period, but in retrospect the
breakdown is not terribly surprising. If one combines the notions (1) that the
Fed can trade off higher inflation for lower unemployment, (2) that the costs
of inflation are small and, moreover, (3) that the Fed has sufficient knowledge
about the economy’s structure to fine-tune economic activity, it is not difficult
to see how the Fed could be led to make monetary policy decisions that had
an inflationary bias.
In any case, our experience in the 1970s had a profound impact on conventional thinking about inflation and monetary policy. Most obviously it provided
much new data that was, to put it mildly, inconsistent with the Phillips Curve
relationship observed in the 1960s. It was in the 1970s, of course, that the term
“stagflation” arose to describe a combination of high inflation and low growth.
In recent years substantial research has been done on the long-run relationship
between growth and inflation—much of it based on cross-country data—and I
think it is fair to say that on balance there is no compelling evidence that higher
inflation is associated with higher growth. Indeed, the research suggests that
the relationship may be inverse. The implication, of course, is that inflationary
monetary policy is not conducive to economic growth; indeed, the opposite
may be true.

Alfred Broaddus: Reflections on Monetary Policy

5

The 1970s inflation also made people realize that the costs of inflation are
much greater and more varied than had been thought earlier. We now understand much better than we did before that inflation creates arbitrary and unfair
redistributions of income and wealth that cause social tensions and weaken the
fabric of society. Inflation also distorts the signals that prices send in our market
economy, which produces serious inefficiencies in the allocation of resources
and reduces economic growth. Further, inflation needlessly causes people to
spend additional time and energy managing their personal finances. Finally,
the 1970s experience illustrated all too well that the public distress caused by
rising inflation is inevitably followed by corrective monetary policy actions that
depress economic activity, often—as in the early 1980s—severely.
The third consequence of our experience with inflation in the 1970s was a
healthy diminution in our confidence that we knew enough about the structure
of the economy and the way it functions to fine-tune economic activity and
eliminate recessions. As you know, this diminished confidence in our ability
to guide economic activity has been mirrored by important developments in
monetary theory over the last two decades. I cannot review these developments
here in any detail, but most monetary economists now believe that the economy
will inevitably be buffeted by various unexpected “shocks” from a variety of
directions—such as the energy sector or the stock market—and that it simply
is not feasible, and probably not desirable, for the Fed to try systematically to
offset the effects of these shocks on the economy. Indeed, we have to be very
careful that our efforts to cushion the effects of such shocks do not create rising
inflation and thereby exacerbate the economy’s problems. As in the practice of
medicine, our first responsibility is to do no harm.
I hasten to add that this recognition of the limitations of monetary policy
does not relieve the Fed from making short-run policy decisions. And inevitably
these decisions will be affected by current developments in the economy. My
main point here is that we now realize that these short-run decisions must
be consistent with a feasible and credible longer-term policy strategy and that
we should not compromise this strategy in a futile attempt to fine-tune the
economy.

4.

THE IMPACT OF THE 1970S EXPERIENCE ON
POLICY PROCEDURES

The 1970s inflation pointed to two fundamental weaknesses in the Fed’s overall
conduct of monetary policy—weaknesses that to some extent are still present
today. First, the System did not have a clear and unambiguous longer-run objective. As inflation accelerated in the mid- and late 1970s, it became apparent
that to contain inflation the Fed needed to set targets for some nominal variable
that it could control over time and that was clearly linked to inflation over time.

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Federal Reserve Bank of Richmond Economic Quarterly

It was in this period that the Federal Open Market Committee first began to
set numerical targets for growth rates of the money supply. Initially, the committee set short-run targets for internal use only. Subsequently, in response to a
congressional resolution in 1975, the committee began voluntarily to announce
quarterly targets for the growth rates of several definitions of the money supply.
Finally, the Humphrey-Hawkins Act of 1978 required the Fed to set moneygrowth targets on a fourth-quarter-to-fourth-quarter basis and to present them
formally to Congress. Unfortunately, there was a major flaw in the targeting
procedure—commonly referred to as “base drift”—which in fact remains to
this day. Base drift occurs because the base level of the money supply used
in calculating each new annual target is not the target level set for the fourth
quarter of the preceding year, but the actual level achieved in that period.
Therefore, target misses are forgiven when new targets are set, which allows
the base level to drift, either upward or downward. In the late 1970s persistent
upward base drift led to a prolonged period of unacceptably rapid growth in the
monetary aggregates, which in my judgment was a major factor contributing
to the subsequent double-digit inflation.
The second weakness in the conduct of policy highlighted by the inflation
of the 1970s was the tenuous link between the Fed’s month-to-month policy
decisions and the emerging longer-run money supply objectives. Under the
procedure in place through much of the decade, the Fed was supposed to
tighten policy if money growth exceeded the annual target ranges, but the response in any instance was entirely at the Open Market Committee’s discretion
and, in practice, responses were uncertain and unpredictable. Many economists
would agree that the Fed did not react aggressively enough to the persistent
above-target growth registered in the latter years of the decade. To deal with
this problem, in October 1979 the Fed instituted a new, so-called nonborrowed
reserve operating procedure. This procedure was quite complicated in its actual
implementation, and I will not try to explain it in any detail tonight. Suffice
it to say that the innovation was a monetary policy milestone because for the
first time in the Fed’s history, its operating procedure caused short-term interest
rates to rise automatically in response to excessive money growth.
The nonborrowed reserve procedure was abandoned in October 1982,
mainly because of increasingly significant practical problems in defining the
money supply accurately in a period of rapid technological and institutional
change and financial innovation—a problem that has continued to this day.
Since then, month-to-month operating decisions have become once again entirely discretionary. I am uncomfortable with this procedure, needless to say,
and I will return to this point in a few minutes.

Alfred Broaddus: Reflections on Monetary Policy

5.

7

DISINFLATION IN THE 1980S:
THE IMPORTANCE OF CREDIBILITY

The prolonged recession in the early 1980s was followed by a pronounced
disinflation, and by the end of 1983 the inflation rate had fallen to approximately 4 percent, where it remained for the next ten years. In recent years the
rate has fallen further to approximately 3 percent. Against the background of
these developments, one can say that the decade of the 1980s was a relatively
tranquil period for monetary policy—certainly by comparison to the preceding
decade. But the more recent period was not without its own lessons for policy.
If the 1970s taught the Fed that the costs of inflation are significant and that it
must commit itself clearly and fully to a low-inflation policy, the years since
have underlined the necessity of maintaining the credibility of this policy—by
which I mean maintaining the public’s confidence that controlling inflation is
not a sometime thing but a permanent feature of the Fed’s overall longer-term
monetary strategy.
We now understand more clearly than before the vital role credibility plays
in minimizing the cost of reducing inflation and eventually stabilizing the price
level. In practical terms, maintaining credibility means the Fed must react
promptly to rising inflation expectations. If the Fed’s policy actions suggest
an indifference to higher expected inflation, the public will lose confidence
in its strategy, and workers and firms will demand higher wages and charge
higher prices in a perfectly natural effort to protect wages and profits from
inflationary erosion. The longer the Fed waits to respond to deteriorating inflation expectations, the more likely it will need eventually to raise real short-term
interest rates sharply with potentially depressing effects on business activity. In
a nutshell, low credibility makes it more costly from an economic perspective
to pursue an anti-inflation strategy.
A few years ago one of my colleagues at the Richmond Fed, Marvin
Goodfriend, wrote a widely read article1 in which he referred to episodes of
sharply rising inflation expectations as “inflation scares,” and use of that term
has now become rather general. Inflation scares can be captured by a variety of
financial market indicators, but in my view the most reliable is the long-term
bond rate, and this is the indicator I watch most closely to gauge the credibility
of our anti-inflation strategy. A sharp rise in long-term rates—as occurred, for
example, in the first half of 1994—is a strong signal that inflation expectations
have risen and the credibility of our policy has declined, and it is a sign that
demands a response from the Fed. The Fed has, in fact, reacted to inflation
scares more promptly in recent years than earlier, and I believe that this has
been one of the hallmarks of recent monetary policy.
1 Marvin

Goodfriend, “Interest Rate Policy and the Inflation Scare Problem: 1979–1992,”
Federal Reserve Bank of Richmond Economic Quarterly, vol. 79 (Winter 1993), pp. 1–24.

8

6.

Federal Reserve Bank of Richmond Economic Quarterly

PRINCIPLES FOR MONETARY POLICY

This completes my review of monetary policy over the last quarter century. I
hope it has helped you appreciate why I believe so strongly that the Fed can
make its maximum contribution to the economy’s growth and productivity by
providing a stable price environment in which private individuals, households,
and business firms can thrive. For me, the broadest lesson of our experience
in the seventies and the eighties is that the overriding goal of monetary policy
should be the elimination of inflation, and by that I mean achieving a condition
where changes in the general price level are no longer a significant factor in
the economic decisions of individuals and businesses.
In this regard, it seems clear that we should not be satisfied with the current
3 to 4 percent inflation rate. One frequently hears the argument that the benefits
of achieving price-level stability do not justify the costs. I disagree strongly
with this assertion, because I do not believe that a 3 to 4 percent inflation rate
could ever be a credible monetary policy objective in the way that price-level
stability could. A Fed commitment to aim for 3 or 4 percent inflation—despite
its relatively moderate level by recent historical standards—would lack credibility because financial markets and the public quite understandably would
fear that eventually the Fed would tolerate higher inflation to achieve some
short-term objective. In technical terms, the “time inconsistency” problem in
conducting monetary policy, which is one of the most important elements in
the recent professional literature on policy, would be much more compelling in
a policy regime with a 3 to 4 percent inflation objective than in a regime firmly
committed to price stability. This suspicion, in turn, would create uncertainty
regarding future inflation, and the attendant increase in risk obviously could
harm the economy in a variety of ways.
So my first core belief about monetary policy is that the Fed should remain committed to a policy of eventually achieving true price-level stability and
strengthen that commitment in any way it can. My second core belief is that the
System needs to maintain the credibility of this policy, which implies—among
other things—that its policy procedures and short-run policy actions must be
consistent, to the greatest extent possible, with its long-term price stability objective. (I will make some specific points in this regard in a minute.) As I have
already noted, by maintaining credibility the Fed can make its anti-inflationary
strategy less costly in the transition to price stability and therefore more likely
to be successful.
If I have been persuasive this evening, you may think that the two monetary
policy principles I have put forward—a policy of price stability and maintenance of the credibility of that policy—are obvious and that there is little left
to say. Unfortunately, we still have a substantial distance to go in putting these
principles fully into practice. To see that our price stability objective lacks full
credibility, one has only to open the newspaper and look at the current level

Alfred Broaddus: Reflections on Monetary Policy

9

of the long-term U.S. Treasury bond rate, which is still well over 7 percent.
Since it is doubtful that real long-term bond rates ever rise above 4 percent,
this means that market participants, on average, currently expect a long-run
inflation rate of at least 3 percent.
What are the reasons for this lack of credibility? I think there are a number,
and I would like to close my remarks tonight by identifying some of them and
sharing some ideas about what might be done to deal with them.
As I have indicated before, I believe the most pressing problem the Fed
faces in conducting monetary policy currently is the lack of a clear policy mandate from Congress. As I explained earlier, the current mandate contained in the
1978 Humphrey-Hawkins law makes the Fed responsible for a laundry list of
economic outcomes having to do with employment, productivity, international
trade, and so forth, in addition to the price level. A revised mandate instructing
the Fed to focus squarely on achieving price stability almost certainly would
enhance the contribution of monetary policy to the nation’s long-run economic
growth and productivity—indeed, because it would do so, it would increase, not
reduce, the likelihood that the laudable objectives of the Humphrey-Hawkins
law will be achieved.
Five years ago Congressman Steve Neal of North Carolina introduced in
Congress an amendment to the Federal Reserve Act proposing just such a mandate. This resolution would have instructed the Federal Open Market Committee
to pursue a policy strategy that would “reduce inflation gradually in order to
eliminate inflation by not later than 5 years from the date of enactment of
[the] legislation and [to] then adopt and pursue monetary policies to maintain
price stability.” We at the Federal Reserve Bank of Richmond wholeheartedly
supported the Neal amendment, as did many others in the Federal Reserve
System, as an operationally feasible means of increasing the credibility of the
Fed’s anti-inflationary strategy. Unfortunately, the amendment did not pass.
Since Congress has not seen fit to pass the amendment, my personal view—
and I need to emphasize here that I am speaking strictly for myself—is that the
Fed should explicitly and publicly announce that it is adopting the language of
the amendment as its longer-term strategic policy goal. In my judgment this
step would put the Fed’s reputation clearly on the line, which would directly
increase the credibility of our strategy. Moreover, as I have already suggested,
such a step would be fully consistent with the present Humphrey-Hawkins
mandate since price stability would permit the economy to achieve maximum
growth in output and employment over time. In this regard, I might note that the
value of price stability as a primary monetary policy objective is increasingly
recognized around the world. In recent years the central banks in Canada, New
Zealand, and the United Kingdom have actually specified explicit numerical
inflation targets. Since the Neal amendment does not specify numerical targets, its adoption by the Fed would be a step short of these actions abroad.
Nonetheless, the amendment’s language is sufficiently clear to commit the Fed

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Federal Reserve Bank of Richmond Economic Quarterly

firmly to attaining price stability in a specific time frame and hence contains
all the ingredients necessary to enhance the System’s credibility. Moreover—
and this is an especially important point—adoption of the amendment language
as its long-term objective would increase the Fed’s flexibility in dealing with
short-term economic disturbances since appropriate short-term actions could be
taken without (or with much less) concern about the potential loss of long-term
credibility.
A second area requiring attention is our operating procedures. As I mentioned in my earlier historical review, only in the three-year period from October
1979 to October 1982 has the Fed used an operating procedure that automatically linked movements in our policy instrument—namely the federal funds
rate—to a longer-term policy goal, in this case growth rates of the monetary
aggregates. As I noted earlier, that procedure was abandoned, largely because
of the technical difficulties that arose in defining an operationally reliable measure of the money supply in a period of rapid technological and institutional
change—difficulties that unfortunately still confront us. Currently, we still set
annual targets for the money supply, but these targets have little effect on our
month-to-month policy decisions, which are made pretty much in the same
discretionary fashion that characterized the pre-1979 period. This is another
important reason why, in my judgment, our credibility is not as full as it could
be and should be.
What the Fed needs, in my view, is an operating procedure that clearly
links our short-run policy actions directly to our longer-run inflation goals
or to some other nominal variable such as nominal gross domestic product.
Regrettably, at this point no such procedure exists that commands sufficient
confidence to be used in practice. Many economists both inside and outside
the Fed are working actively on this problem, however, and I have confidence
that somewhere down the road we will come up with an acceptable operating procedure that more systematically and efficiently links our instrument to
our goals. In the meantime, the Fed must retain the independence to take the
short-run policy actions that it believes are most likely to be consistent with
its long-run objectives—recognizing, of course, that it is responsible for and
accountable for the consequences of these decisions.
A final and very important point I would make is that the Fed has a strong
obligation to educate the public about the cost of inflation and the limitations
of activist short-term monetary policies. In my review, I explained how the
inflation of the 1970s led me and many others to conclude that some of the
views regarding inflation and monetary policy in the 1960s were not valid.
Unfortunately, in my opinion, many people still believe that a long-run as well
as a short-run trade-off between inflation and unemployment exists, that the
costs of inflation are small, and that the Fed can fine-tune economic activity.
The persistence of these views—particularly when they are held by people
with political power—naturally diminishes the credibility of our anti-inflation

Alfred Broaddus: Reflections on Monetary Policy

11

strategy, especially given that our mandate is so imprecise. It would be a tragedy
if the lessons of the last 25 years were forgotten and the nation needlessly
experienced another devastating boom-bust cycle like the one in the 1979–82
period. So I think we in the Fed have an obligation to speak out on these issues.
My remarks here tonight have been an effort in that direction, and I hope that
I have added at least a bit to your appreciation of some of the fundamental
issues facing monetary policymakers today.

Neighborhoods and Banking
Jeffrey M. Lacker

T

he economic condition of some of our low-income neighborhoods is
appalling. Are banks responsible? Critics blame the banking industry
for failing to meet the credit needs of poorer neighborhoods. Some
claim that bankers pass up worthwhile lending opportunities because of racial
or ethnic bias. Others argue that a market failure causes banks to restrain lending
in low-income neighborhoods. They claim that joint lending efforts by many
banks in such neighborhoods would be profitable, but no single bank is willing
to bear the cost of being the pioneer.
The central statute regulating the relationship between bank lending and
neighborhoods, the Community Reinvestment Act of 1977 (CRA, or “the Act”),
was inspired by the critics’ view that banks discriminate against low-income
communities.1 The Act directs the bank regulatory agencies to assess the extent
to which a bank meets “the credit needs of its entire community, including lowand moderate-income neighborhoods.” In a similar spirit, the Home Mortgage
Disclosure Act (HMDA) requires depository institutions to disclose mortgage
originations in metropolitan areas by census tract. The annual HMDA reports
routinely show large disparities in mortgage flows to minority and white neighborhoods, bolstering the critics’ case.
Defenders of the banking industry attribute the disparity in credit flows to
differences in the creditworthiness of potential borrowers, information that is
This article originally appeared in this Bank’s 1994 Annual Report. The author has benefited
from comments by Marvin Goodfriend, Tom Humphrey, Tony Kuprianov, Stacey Schreft,
and John Weinberg. The views expressed are the author’s alone and do not necessarily reflect
the views of the Federal Reserve Bank of Richmond or the Federal Reserve System.
1I

will use the term “banks” throughout to refer to commercial banks and thrifts. Credit
unions are currently exempt from the CRA.

Federal Reserve Bank of Richmond Economic Quarterly Volume 81/2 Spring 1995

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Federal Reserve Bank of Richmond Economic Quarterly

unavailable from the HMDA reports. They view the CRA as a burdensome
interference in otherwise well-functioning credit markets and as a regulatory
tax on banking activity. They argue that the decay of low-income neighborhoods, while deplorable, is beyond the capacity of the banking industry alone
to repair.2
The CRA is currently attracting renewed attention. Public release of expanded HMDA reports, along with widely publicized research suggesting bank
lending discrimination, has sparked complaints that banks neglect low-income
neighborhoods. Critics now assert that regulators have been too lax in implementing the CRA, and they press for regulations based on measures of bank
lending in low-income neighborhoods. In response, federal banking agencies
recently adopted revisions to the regulations implementing the CRA that would
base a bank’s assessment in part on quantitative measures of lending in lowincome neighborhoods (Board of Governors of the Federal Reserve System
1994). Banks’ defenders argue that the regulations were already too burdensome and that numerical measures inevitably will come to resemble lending
quotas. Banks will be induced to make loans to uncreditworthy borrowers,
risking losses to the deposit insurance funds and, ultimately, to taxpayers.
This essay reexamines the rationale for the CRA. A reconsideration seems
worthwhile in light of the dire condition of our poor neighborhoods on the one
hand, and the demonstrable risks to banks and taxpayers on the other. After
a review of the empirical literature relevant to critics’ claims, I will argue
that there is little conclusive evidence that banks fail to meet the credit needs
of low-income neighborhoods per se. Instead, the CRA regulations should be
understood as a transfer program, aimed at redistributing resources to lowincome neighborhoods. The basic goal of the CRA to improve conditions in
distressed neighborhoods is obviously a worthy one. But the lending and community investment obligations impose an implicit tax on the banking industry for which there is little justification. Nonprofit community development
organizations (CDOs) also redistribute resources through subsidized lending in
low-income neighborhoods and represent an alternative to imposing a potentially unsustainable burden on banks. Directing investment toward low-income
neighborhoods could be better accomplished by carefully subsidizing existing
institutions that specialize in community development, rather than by imposing
a burdensome and potentially risky implicit tax on the banking system.

2I

will use throughout the essay the less cumbersome term “low-income neighborhoods”
to refer to the low- and moderate-income neighborhoods that are the focus of the CRA. The
newly proposed CRA regulations define low-income neighborhoods as census tracts with median
household income less than 50 percent of the median household income of the metropolitan
statistical area (MSA). Moderate-income neighborhoods are defined as census tracts with median
household income between 50 and 80 percent of the median household income of the MSA.

J. M. Lacker: Neighborhoods and Banking

1.

15

DO BANKS REDLINE?

The legislative history of the Community Reinvestment Act makes clear that the
Act was based on the premise that banks engage in “redlining.” Senator William
Proxmire, principal sponsor of the CRA, defined redlining during debate on the
Senate floor:
By redlining . . . I am talking about the fact that banks and savings and loans
will take their deposits from a community and instead of reinvesting them in
that community, they will invest them elsewhere, and they will actually or
figuratively draw a red line on a map around the areas of their city, sometimes
in the inner city, sometimes in the older neighborhoods, sometimes ethnic and
sometimes black, but often encompassing a great area of their neighborhood.3

The term “redlining” dates back to the 1930s, when the Home Owners
Loan Corporation (HOLC) and the Federal Housing Administration (FHA)
used detailed demographic and survey analysis to classify city neighborhoods
for lending risk.4 The agencies adopted standardized appraisal and underwriting practices that embodied the common real estate practice of the time
of rating neighborhoods in part on the basis of their current and prospective racial and ethnic composition (Jackson 1985). Blocks with the lowest of
four grades were color-coded red on secret maps. A 1939 FHA Underwriting
Manual warned that “if a neighborhood is to retain stability, it is necessary
that properties shall continue to be occupied by the same social and racial
classes.”5 While government agencies retreated from explicitly racial policies
after the 1948 U.S. Supreme Court decision against racial deed covenants,
neighborhood racial composition apparently continued to affect appraisals into
the 1970s.6
As evidence of continuing redlining, legislators cited the results of numerous studies in the early 1970s by community groups and local governments.
The availability of HMDA data in the mid-1970s spurred further redlining
research in the academic and policy communities. Although critics often cite
discrimination against older or lower-income neighborhoods, research has addressed almost exclusively redlining on the basis of a neighborhood’s racial
composition. The studies documented large disparities in mortgage lending
activity, which led critics of banks to conclude that they had unfairly restricted
3 Congressional Record, daily ed., June 6, 1977, S. 8958, cited in Dennis (1978). Senator
Proxmire’s definition of redlining also reflects the doctrine of localism in banking—the idea that
the savings of a community should be invested locally rather than where returns are highest. See
Macey and Miller (1993) for a critique.
4 See Woelfel (1994) for a description of the HOLC and the FHA.
5 Quoted in Jackson (1985), p. 207.
6 In 1977 the American Institute of Real Estate Appraisers removed discriminatory racial
references from their textbook as part of an agreement settling a federal lawsuit. See Art (1987),
p. 1078.

16

Federal Reserve Bank of Richmond Economic Quarterly

loan supply in predominantly minority neighborhoods and thus had failed to
serve the credit needs of their communities.7
This first-generation research failed to show, however, that supply rather
than demand was responsible for the lending disparities. A basic premise of the
redlining hypothesis is that banks curtail the supply of credit to a neighborhood
for noneconomic reasons such as racial composition. Many factors that influence the demand for mortgage credit by qualified borrowers also vary across
neighborhoods: income and wealth levels, owner-occupancy rates, and housing
turnover rates, for example. Moreover, many of these factors are known to
be correlated with the racial composition of a neighborhood. Without controlling for differences in the demand for credit, there is little one can say about
constraints on the supply of credit to minority neighborhoods.
Subsequent redlining research sought to remedy this problem using information on the economic characteristics of neighborhoods and individual
loan applicants. When such information is taken into account, mortgage flows
and loan approval rates appear unrelated to neighborhood racial composition.
For example, Schill and Wachter (1993) estimate models of banks’ loan approval decisions. In their simplest model, the neighborhood racial composition
is significantly related to approval probability, but when neighborhood characteristics such as median income, vacancy rate, and age of the housing stock are
included, neighborhood racial composition is no longer important. Similarly,
Canner, Gabriel, and Woolley (1991) find that after controlling for individual
and neighborhood measures of default risk, there is no evidence of discrimination based on the racial composition of neighborhoods. Several other studies
confirm these findings.8 Research thus has failed to uncover any evidence that
banks discriminate against neighborhoods on the basis of racial composition.9

7 See

Canner (1982) and Benston (1979) for surveys.
Avery and Buynak (1981), Holmes and Horvitz (1994), King (1980), Munnell et al.
(undated), and Schill and Wachter (1994). Some studies have reported evidence of redlining, but in
these the controls for individual characteristics are limited or absent. Bradbury, Case, and Dunham
(1989) use data at the neighborhood level, but they employ a problematic credit flow variable
that includes commercial as well as residential transactions. They do not control for individual
economic characteristics. Calem and Stutzer (1994) also use neighborhood-level data, and so do
not control for individual economic characteristics. Avery, Beeson, and Sniderman (1993) rely on
HMDA data and census tract information, and so are unable to control for applicant wealth or
creditworthiness. Although it is conceivable that future research will turn up evidence of redlining,
it seems unlikely; the fact that studies with better controls for individual economic characteristics
obtain smaller or negligible estimates of the effect of racial composition on mortgage outcomes
suggests that the estimates we have are biased upward.
9 Critics also have charged that banks redline older and lower-income neighborhoods (see
Art [1987], for example), but age of the housing stock and borrower income are both plausibly
related to lending risk. As a result, statistical research of the type referred to above is unable
to distinguish between legitimate underwriting practices and redlining these neighborhoods. I am
unaware of any attempt to disentangle the two.
8 See

J. M. Lacker: Neighborhoods and Banking

2.

17

DO BANKS DISCRIMINATE AGAINST INDIVIDUALS?

Redlining is distinct from racial discrimination against individuals because not
all minority applicants live in redlined neighborhoods.10 Although research has
found little evidence of discrimination against minority neighborhoods, recent
research has uncovered evidence consistent with discrimination against individual minority loan applicants. The most widely publicized evidence comes from
the HMDA data. In 1989, Congress amended the Home Mortgage Disclosure
Act to require lenders to report the disposition of every mortgage loan application, along with the race or national origin, gender, and annual income of
each applicant. Numerous press reports have focused on the disparities between
whites and minorities in the fraction of applicants denied credit. For example,
the 1993 data show that for conventional home purchase loans, 34 percent of
African-American applicants and 25 percent of Hispanic applicants were denied
credit, while only 15 percent of white applicants were denied credit (Federal
Financial Institutions Examination Council 1994).
By themselves, however, simple tabulations of HMDA data are inconclusive for the same reason that raw mortgage flow data are misleading. The
HMDA data report applicant income, but not credit history or other economic
characteristics. Without controlling for applicant creditworthiness, the disparity
in mortgage loan denial rates in the HMDA data could reflect the disadvantaged economic status of minorities, rather than noneconomic discrimination
by banks. It is well known that racial and ethnic groups differ significantly
on many dimensions of creditworthiness. For example, the average minority
individual has lower income, lower net worth, and lower financial asset holdings than does the average white American. Furthermore, minority mortgage
applicants are more likely to have adverse credit histories and to request larger
loans relative to property value, factors associated with higher default risk.11
In short, differentiating between racial discrimination and racial disparities in
creditworthiness is difficult.

10 For example, in 1992, 39.2 percent of minority individuals lived outside of census tracts
in which over half of the population was minority (derived from Canner, Passmore, and Smith
[1994]).
11 On racial disparities in income and economic status, see, for example, Kennickell and
Shack-Marquez (1992), Jaynes and Williams (1989), or the Symposium in the Fall 1990
issue of the Journal of Economic Perspectives. Munnell et al. (1992) report that loan-to-value
ratios and adverse credit history variables are higher for minority applicants; see also Carr and
Megbolugbe (1993). Canner and Luckett (1990) report that households headed by a minority are
significantly more likely to have missed a debt payment, even after controlling for other household
characteristics.

18

3.

Federal Reserve Bank of Richmond Economic Quarterly

THE BOSTON FED STUDY

A recent study by economists at the Federal Reserve Bank of Boston has gone
the farthest toward solving this problem.12 They asked banks and mortgage
companies for detailed information from the loan applicant files for a sample
of Boston HMDA data for 1990. They obtained data on housing expenses, total
debt payments, net wealth, credit and mortgage payment histories, appraised
property values, whether properties were single- or multi-family dwellings,
whether applicants were self-employed, and whether applicants were denied
private mortgage insurance. Combining this information for a sample of 3,062
individual applicants with applicant race and the unemployment rate in the
applicant’s industry, they estimated the probability of a particular mortgage
loan application being denied.
The study’s major finding is that after controlling for the financial, employment and credit history variables they were able to observe, race still had
a highly significant effect on the probability of denial. The results imply that
minority individuals with the characteristics of an average white applicant have
a 17 percent denial rate compared to an 11 percent denial rate for white applicants with the same characteristics. Moreover, the Boston Fed study suggests
that whatever discrimination takes place is of a subtle form. Whereas applicants
of all races with unblemished credentials were almost certain to be approved,
the study found that the vast majority of applicants had some imperfection. As a
result, lenders have considerable discretion to consider compensating factors in
evaluating creditworthiness. The Boston Fed researchers suggest that “lenders
seem more willing to overlook flaws for white applicants than for minority
applicants” (Munnell et al. 1992, p. 3).
These findings are consistent with the widely held view that lending discrimination is common in housing markets. A recent survey found that 69
percent of African Americans and 33 percent of whites do not feel that African
Americans have an equal opportunity for credit loans and mortgages. Housing
discrimination also has been the focus of housing market audit studies, in which
matched pairs of testers, one white and one minority, respond to advertisements
for rental or sales properties. Such studies have found evidence of differential
treatment based on race, such as African Americans not being shown certain
available properties. The few pilot studies on home mortgage lending discrimination at the pre-application stage are too small to be conclusive. Anecdotal
reports of lending discrimination are sometimes cited as well.13

12 See

Munnell et al. (1992).
survey data are from National Conference (1994). On audit studies in housing, see
Fix and Struyk (1993), but particularly the critique by Heckman and Siegelman (1993). Cloud
and Galster (1993) survey home mortgage lending audit studies, along with anecdotal reports of
lending discrimination. The application of audit methodology to lending discrimination is inhibited
13 The

J. M. Lacker: Neighborhoods and Banking

4.

19

INTERPRETING THE BOSTON FED RESULTS

Although anecdotes and evidence from audit studies are suggestive, the Boston
Fed study remains the most rigorous evidence available of home mortgage
lending discrimination.14 Despite the study’s sophistication, however, considerable uncertainty remains concerning its interpretation. Some researchers have
questioned the reliability of the data and the empirical model underlying the
study.15 Although the critiques are far from definitive, replication of the study’s
results using different data sets obviously would increase confidence in its findings. Seldom is a single retrospective study taken as conclusive, particularly in
the social sciences, and the Boston Fed study is the only research on lending
discrimination that explicitly controls for individual applicants’ credit history.
Further research would be especially valuable in view of the plausible alternative hypotheses that are consistent with the Boston Fed results.
One such alternative view is that the variables in the study measuring
creditworthiness are imprecise or incomplete and fail to capture completely
the judgment of a hypothetical unbiased loan officer. If there is any random
discrepancy between applicants’ true creditworthiness and their creditworthiness as measured by model variables, there is likely to be a bias in measuring
discrimination. When true creditworthiness is inaccurately measured, it is very
difficult to distinguish racial discrimination from unmeasured racial disparities
by laws prohibiting applying for a mortgage under false pretenses. Audit methodology is thus
limited to the more subjective problem of differential treatment at the pre-application stage.
14 Several redlining studies examined data for outcomes of individual mortgage applications.
Some found that minority applicants were less likely than whites to obtain a mortgage loan, even
after controlling for neighborhood economic characteristics. See Avery, Beeson, and Sniderman
(1993), Shafer and Ladd (1981), Canner, Gabriel, and Woolley (1991), and Schill and Wachter
(1993, 1994). None of these studies controlled for applicant credit history, and so they suffer
from the same omitted-variable problem that plagues the analysis of the HMDA data. In related
research, Hawley and Fujii (1991), Gabriel and Rosenthal (1991), and Duca and Rosenthal (1993),
using data from the 1983 Survey of Consumer Finances, find that after controlling for individual
characteristics, minorities are more likely than whites to report having been turned down for
credit. Information on individual creditworthiness was quite limited, however, again leaving these
studies vulnerable to the omitted-variable problem.
15 Horne (1994) reports on reexaminations of some of the loan files at the FDIC institutions
participating in the study. Although he reports a large number of data errors, he does not reestimate the model, so no conclusion is possible about the effect of those errors. In addition, files
were selected for reexamination in a way that would bias any reestimation. Liebowitz (1993)
claims in an editorial page essay in The Wall Street Journal that correcting selected data-coding
errors eliminates the finding of discrimination, but Carr and Megbolugbe (1993) and Glennon and
Stengel (1994) document that the discrimination finding persists after systematic data-cleaning,
suggesting bias in the way Liebowitz corrects errors. See also Browne (1993a). Zandi (1993)
claims that omission of a variable assessing whether the institution reports that the applicant met
their credit guidelines was responsible for the estimated race effect. Carr and Megbolugbe (1993)
confirm that including this variable reduces the estimated race effect somewhat, but note that
this subjective assessment by the lending institution is significantly related to an applicant’s race,
even after controlling for the objective economic characteristics of the applicant. See also Browne
(1993b). Schill and Wachter (1994) also study the Boston Fed data set.

20

Federal Reserve Bank of Richmond Economic Quarterly

in creditworthiness. If true creditworthiness is associated with applicant race,
the model will indicate that race affects the probability of denial, even if race
plays no direct causal role. If true creditworthiness is lower on average for
minority applicants, then there will be a bias toward finding discrimination
against minorities.16
The fact that measured creditworthiness is statistically associated with race
suggests that this condition holds. Regulatory field examiners report that it is
often difficult to find matched pairs of loan files corroborating discrimination
detected by a statistical model or summary statistics. Examination of applicant
files often reveals explanatory considerations that are not captured by any model
variables. The credit history variables in the Boston Fed study are simple functions of the number of missed payments or whether the applicant ever declared
bankruptcy, and do not reflect the reasons for any delinquencies. Evaluating
explanations of past delinquencies is at the heart of credit underwriting; some
will indicate poor financial management skills or unstable earnings, while others
will reflect response to unusual one-time financial shocks or inaccurate credit
reports. It seems quite plausible, therefore, that the Boston Fed findings are
an artifact of our inability to capture complex credit history information in a
tractable quantitative representation.
Another hypothesis consistent with the evidence from the Boston Fed study
is that minority borrowers are more likely to default than equally qualified white
borrowers, so lenders implicitly use race as an indicator of creditworthiness in
marginal cases, above and beyond the information provided by income, balance
sheets, or credit history. Such behavior, often called “statistical discrimination,”
might be economically rational, though still illegal. The statistical discrimination and measurement error hypotheses are closely related because both assume
that the outside analyst does not observe true creditworthiness. The distinction
is that under the measurement error hypothesis the loan officer observes true
creditworthiness, while under the statistical discrimination hypothesis the loan
officer does not directly observe credit quality but uses race as a proxy.
A recent study of mortgage default data supports these alternative explanations. The study found that an African-American borrower is more likely to
default than a white borrower, even after controlling for income, wealth, and
other observable borrower characteristics.17 Why would a minority borrower

16 If a true explanatory variable is measured with noise, its regression coefficient will be
biased toward zero. In that case, any other variable correlated with the true explanatory variable
will be significant in the regression, even though it may play no direct causal role in explaining the
behavior in question. Thus, measurement error is a very serious problem in statistical inference.
See Johnston (1963) for a discussion of measurement error and Cain (1986) for a discussion of
the implications for detecting discrimination.
17 Berkovec et al. (1994) use data on more than a quarter of a million FHA mortgages
originated during 1987–1989. Their data do not include information on the borrower’s credit
history, but they estimate that including credit history would reduce the estimate of the race effect

J. M. Lacker: Neighborhoods and Banking

21

be more likely to default than an equally qualified white borrower? Mortgage
defaults often are attributable to “trigger events,” such as involuntary job loss or
large unexpected health care costs, that sharply reduce the borrower’s ability
to repay.18 Most people are poorly insured against such risks, and it seems
plausible that minorities experience these events more often than whites.19 For
example, unemployment rates are higher for minorities than for whites, but
more important, the probability of involuntary job loss is higher for minorities (Jackson and Montgomery 1986; Blau and Kahn 1981; Flanagan 1978).
Minority household holdings of financial assets are far smaller on average,
reducing their ability to withstand uninsured financial shocks (Kennickell and
Shack-Marquez 1992). Minorities tend to be less healthy on average and are
more likely to lack health insurance (National Center for Health Statistics
1994). There seems to be no research on whether these differences in the
likelihood of trigger events persist after controlling for income, wealth, credit
history, and other factors observable at the time of the application. But it seems
plausible that these risk factors can explain the disparity in mortgage default
rates and can thereby account for disparities in loan approval rates. This line
of reasoning suggests that disparities outside lending markets—in labor markets, for example—might well be responsible for what appears to be lending
discrimination.20
One other consideration that lends support to these alternative explanations
of the Boston Fed results is the presumption that competitive forces should act
to eliminate unprofitable discriminatory practices. If some lenders discriminate
on noneconomic grounds, they ought to systematically lose business over time
as long as there are some lenders that do not discriminate. The discriminatory
lenders may end up serving only part of the market, but nondiscriminatory
lenders would be eager to fill the void.21
To summarize, the empirical evidence on bank lending discrimination based
on an applicant’s race seems inconclusive. A skeptic with a strong prior belief
in the ability of market forces to restrain unprofitable discrimination could
easily remain unconvinced by the Boston Fed study. On the other hand, critics
by only 30 percent. Barth, Cordes, and Yezer (1979, 1983) and Evans, Maris, and Weinstein
(1985) also show that race is significantly related to default probabilities, but the omission of
important variables weakens the interpretation of their results.
18 See Quercia and Stegman (1992) for a review of recent literature on mortgage default.
19 Cochrane (1991) reports evidence that households are poorly insured against involuntary
job loss and long-term absences due to illness.
20 See Jaynes (1990) for a survey of the labor market status of African Americans.
21 Calomiris, Kahn, and Longhofer (1994) suggest that a lack of “cultural affinity” between
white loan officers and minority applicants may explain findings of discrimination. A lack of
affinity might reduce the reliability and accuracy of loan officers’ subjective evaluations, leading
to higher standards for African Americans at predominantly white banks. The cultural affinity
hypothesis, however, has trouble explaining the higher rejection rates found at minority-owned
banks.

22

Federal Reserve Bank of Richmond Economic Quarterly

with a strong prior belief in the prevalence of lending discrimination will find
striking confirmation in the Boston Fed study. Between these two extremes lies
a range of reasonable assessments.22
What does the empirical evidence on discrimination, such as it is, imply
about appropriate public policy? Discrimination against mortgage applicants on
the basis of an individual’s race calls for vigorous enforcement of fair-lending
laws. However, the lack of evidence of discrimination against neighborhoods
per se raises questions about the need for a lending obligation aimed at neighborhoods. Not all minority applicants have low incomes or live in low-income
neighborhoods, so the connection between racial discrimination against individuals and lending to low-income neighborhoods is doubly obscure. The evidence
that we do have, which suggests the possibility of racial discrimination against
individuals but not neighborhoods, provides little reason for a law like the CRA
that targets lending to low-income neighborhoods.23

5.

IS THERE SOME OTHER SOURCE
OF MARKET FAILURE?

Lacking evidence of bank discrimination against neighborhoods, is there some
other rationale for a government-imposed lending obligation? Could CRAinduced lending be socially desirable even though banks would otherwise find
it unprofitable? In other words, is there a market failure affecting lending in
low-income neighborhoods?24
Many writers have pointed out that low-income housing markets are frequently characterized by “spillover effects” because the physical condition and
appearance of one property affects the desirability of nearby properties. This
leads to a strategic interaction among property owners; improvements to a
house in a well-maintained block are worthwhile but would have little value if
the rest of the block is poorly maintained or vacant. A run-down neighborhood
might be worth renovating from society’s point of view, yet no single property
owner has an incentive to invest. This strategic interaction extends to potential
lenders as well. Each bank judges an applicant in isolation, ignoring the effect
on nearby properties. Taking the poor condition of neighboring properties as
22 Public policy toward neighborhoods and banking could be aided greatly by research on
the root cause of mortgage defaults: Why is it that trigger events such as health problems or
involuntary job loss are so poorly insured? Such research might allow us to distinguish between
competing explanations of disparities in credit flows across neighborhoods and ethnic groups.
Furthermore, we might find that reducing disparities in the incidence of trigger events is more
effective than affirmative lending obligations that encourage banks to ignore such disparities.
23 For a similar view, see the Shadow Financial Regulatory Committee (1994).
24 Market failure can occur in situations with spillover effects, since one person does not
have to pay for the effect of their decision on the well-being of others, as when polluters do not
pay for the damage caused by their emissions.

J. M. Lacker: Neighborhoods and Banking

23

given, the loan might appear to be a poor risk, even though simultaneous loans
to improve all properties might be worthwhile. All would be better off if lenders
could coordinate their decisions and agree to lend, since those loans would be
profitable. But in the absence of coordination, each bank’s reluctance to lend
confirms other banks’ reluctance to lend and becomes a self-fulfilling prophecy
of neighborhood decline. In these circumstances, a genuine market failure could
be said to occur.25
Spillovers seem quite important in affluent residential and commercial markets as well. The preeminence of location in valuing suburban homes epitomizes
the importance many homebuyers place on the characteristics of the surrounding
neighborhood. Office buildings often are clustered to take advantage of common services or homogeneity of appearance. What is striking about spillovers
in more affluent real estate markets is that they do not seem to cause any serious
market failure; private market mechanisms seem quite capable of coordinating
investment decisions. For example, suburban housing is often developed in
large parcels of very similar homes, ensuring the first buyers that subsequent
investment will not blemish the neighborhood. The development is coordinated
by a single entity that either builds all the homes or enforces homogeneity
through building restrictions and deed covenants.
From this perspective, it is hard to see just what would impede similar
market mechanisms in low-income neighborhoods. A substantial part of the
economic role of a real estate developer is to coordinate investment decisions,
internalizing the spillovers inherent in closely neighboring investments. If a
coordinated investment in a low-income neighborhood is in society’s best interest, why wouldn’t a private developer assemble the capital to finance the
investment?
Several notable differences between the suburbs and low-income, inner-city
neighborhoods might explain why coordinating investments is more difficult or
costly in city neighborhoods. Low-income urban neighborhoods tend to be
older, higher-density areas, while development in the suburbs is often on virgin
tracts of undeveloped land. Assembling control of the requisite property rights
is arguably less costly for the latter. Another factor affecting the ease of assembling property rights is the higher incidence in the cities of governmental
encumbrances such as rent controls or tax liens. The greater incidence of crime
in urban areas also inhibits development by making it more costly to provide
residents with a given level of security.
Disparities between urban and suburban markets in the costs of coordinating investments, however, do not necessarily provide a rationale for government
stimulus of low-income community development. The expense of keeping
crime out of a neighborhood, for example, is a real social cost that deserves to

25 Guttentag

and Wachter (1980) present this externality argument.

24

Federal Reserve Bank of Richmond Economic Quarterly

be addressed directly, and there is no reason to encourage people to ignore it in
their investment decisions. Similarly, government restrictions on property rights
distort decisions, although usually with the aim of benefiting some particular
group. These distortions impose genuine costs, and it is hard to see why we
should encourage people, including lenders, to discount them. In sum, these
very real costs do not, by themselves, represent a market failure.
Lang and Nakamura (1993) describe a more subtle type of spillover. The
precision of appraisals, they argue, depends on the frequency of previous homesale transactions in the neighborhood. A low rate of transactions makes appraisals imprecise, which increases mortgage lending risk in the neighborhood,
reducing mortgage supply, and thereby reducing the frequency of transactions.
A neighborhood can get stuck in a self-reinforcing condition of restricted mortgage lending and low housing stock turnover. The key impediment to efficiency
in this story is the failure of lenders and homebuyers to account for the social
benefit of their transaction on others’ ability to make accurate appraisals in the
future.
While this argument seems theoretically plausible, some important problems remain. For example, it is not clear what limits this phenomenon to
low-income neighborhoods. Affluent housing markets are quite prone to transitory declines in transactions volume, but rarely seem to get stuck in a depressed
condition. And again, it is not clear why market mechanisms would be unable
to coordinate transactions in low-income neighborhoods as they do in many
other real estate markets. On the whole, then, it seems difficult to argue that
lending in low-income neighborhoods is any more beset by market failures
than lending in affluent neighborhoods.

6.

IS REDISTRIBUTION THE PURPOSE
OF THE CRA?

If the CRA cannot be rationalized as a corrective for lending discrimination
or some other identifiable market failure, then the CRA must be essentially a
redistributive program that should be justified by equity rather than efficiency
considerations. Indeed, the desire to simply transfer resources to low-income
neighborhoods is understandable in view of their appalling condition. But how
should such a transfer be carried out?
The CRA has been likened to a tax on conventional banking linked to
a subsidy to lending in low-income neighborhoods (White 1993; Macey and
Miller 1993). Although banks are examined regularly for compliance with CRA
regulations and receive public CRA ratings, enforcement relies on the power of
the regulatory agencies to delay or deny an application for permission to merge
with or acquire another bank or to open a new branch. The prospect of having
an application delayed or denied, along with the public relations value of a high

J. M. Lacker: Neighborhoods and Banking

25

CRA rating, provides banks with a tangible incentive for CRA compliance.26
According to this view, by tilting banks’ profit-loss calculations, the CRA regulations give banks an incentive to make loans they would not otherwise have
made. To the extent that banks are induced to make loans and investments
they would not otherwise have found profitable, the CRA regulations encourage banks to subsidize lending in low-income neighborhoods. Investments at
concessionary rates and CRA-related outlays, such as for marketing programs
and philanthropic contributions, directly reduce a bank’s net earnings. The gap
between the cost of these loans to borrowers and what they would have cost in
the absence of the CRA represents a transfer to the low-income neighborhood.
Two questions naturally arise, though, if the CRA is viewed as a redistributive program. First, why should we provide low-income neighborhoods with
an enhanced credit supply rather than unencumbered cash payments? Second,
why should the banking industry be the source for such transfers?

7.

WHY SUBSIDIZE LENDING IN
LOW-INCOME NEIGHBORHOODS?

If the goal is to make the residents of low-income neighborhoods better off,
why not provide unrestricted transfer payments? Economists generally argue
that unrestricted income transfers are more efficient than equally costly transfers
tied to particular goods or services. This efficiency arises from the expanded
choices available to recipients. Community development subsidies via enhanced
mortgage lending, in contrast, tie transfers to borrowing and homeownership.
Why encourage low-income households to take on more debt? And why should
subsidies to residents of low-income neighborhoods be tied to their ownership
of housing?
A plausible argument can be made for targeting subsidies to low-income
homeowners as a way to rectify the baneful housing and lending policies of
the past. A variety of explicit policies at both public and private institutions in
the first half of this century encouraged the flight of white middle-class residents from inner cities to the suburbs. Metropolitan real estate boards adopted
explicitly racial appraisal standards and attempted to prevent members from
integrating neighborhoods (Helper 1969). The FHA provided a significant stimulus to homeownership, but agency underwriting policies and housing standards
strongly favored newly constructed homes in all-white suburbs (Jackson 1985).
It recommended racially restrictive deed covenants on properties it insured until
the Supreme Court ruled them unenforceable in 1948. The banking industry
26 The recent proposed revision to the regulations implementing the CRA would allow regulators to seek enforcement action in cases of “substantial noncompliance,” the lowest possible
CRA rating.

26

Federal Reserve Bank of Richmond Economic Quarterly

apparently adopted similar underwriting policies (Jackson 1985, p. 203). Some
researchers cite these policies as important in the creation and persistence of
racial segregation and the concentration of poverty in the inner cities.27
This rationale for the CRA invokes the notion of corrective justice, the
normative idea that compensation should be made for past inequities.28 The
discriminatory practices of earlier times depressed the welfare of low-income
minority communities by raising the cost of home mortgages there relative to
more affluent suburban communities, although the lack of evidence of redlining in recent years suggests that noneconomic cost differentials have largely
been removed. Subsidies that lower the cost of home mortgage lending in
low-income minority communities—in contrast to unrestricted cash payments—
transfer resources to precisely the same groups that the earlier discriminatory
policies transferred resources from—nearly creditworthy low-income homeowners. As Peter Swire (1994) notes, “Only a very small subset of the effects
of discrimination [in housing markets] can be traced with enough specificity
to permit legal redress” (p. 95). Thus, it may be quite difficult to target unrestricted income transfers to individuals directly harmed by past discriminatory
practices. Mortgage lending subsidies that mirror the implicit tax of historic
home lending discrimination might be the most efficient way of compensating
those who were harmed.

8.

SHOULD BANKS SUBSIDIZE LENDING?

Why should depository institutions be singled out for the affirmative obligation imposed by CRA regulations? Why do other lending intermediaries such
as mortgage, finance, and life insurance companies escape obligation? More
broadly, why should financial intermediaries bear the burden rather than society
as a whole? Senator Proxmire provided a partial answer when introducing the
original Act by noting that a bank charter “conveys numerous benefits and it
is fair for the public to ask something in return.”29 The CRA, in this view, is
a quid pro quo for the special privileges conferred by a bank charter, which
incidentally explains why the Act links assessment to a bank’s “application for
a deposit facility.” To the extent that CRA obligations are unprofitable or are
equivalent to charitable contributions, apparently they are to be cross-subsidized
from the stream of excess profits otherwise generated by the bank charter.
27 See,

for example, Wilson (1987) or Massey and Denton (1993). Homeowner preferences
apparently play a role as well.
28 In a paper devoted to legal and economic analysis of the CRA, Swire (1994) discusses
corrective justice as a “noneconomic” rationale for the CRA. He also discusses “distributive
justice,” which would also rationalize transfers but would not necessarily suggest they take the
form of subsidized lending.
29 U.S. Congress (1977), p. 1. See also Fishbein (1993).

J. M. Lacker: Neighborhoods and Banking

27

The difficulty with this role for the CRA is that cross-subsidization may
be infeasible (White 1993). The competitive environment facing banks has
changed greatly since passage of the CRA in 1977. Over the last two decades
the legal and regulatory restrictions on competition among banks have been
substantially reduced, a trend that will continue with the implementation of
the Interstate Banking Efficiency Act of 1994. Perhaps more important, rapid
changes in financial technology are eroding the advantages of banks relative to
nonbank competitors. Consequently, imposing a unique burden on the banking
industry might only diminish banks’ share of intermediated lending. The regulatory burden ultimately would fall on bank-dependent borrowers in the form
of higher loan rates and on bank-dependent savers in the form of lower deposit
rates. And to the extent that lending induced by the CRA regulations increases
the risk exposure of the deposit insurance funds, taxpayers who ultimately back
those funds bear some of the burden as well.
Senator Proxmire suggested a practical reason banks are asked to shoulder the CRA burden when he remarked that “there is no way the Federal
Government can solve the problem [of revitalizing the inner cities] with its
resources.”30 From this perspective, the CRA imposes a tax on banks to avoid
an explicit general tax increase. But a general tax increase is usually less costly
to society than an equal-sized tax on a single industry because spreading the
burden over a wider base minimizes the resulting distortions in economic activity. From this perspective, imposing the CRA tax on banks rather than the
economy as a whole involves an excess social cost.
Compelling banks to provide subsidized lending in low-income neighborhoods might be warranted nevertheless if banks have a unique comparative
advantage in doing so. The cost savings from such a comparative advantage
might justify incurring the excess social cost of the CRA burden on banks. But
if no comparative advantage can be identified, we ought to consider alternative
means of providing subsidized lending that avoid the excess cost of a tax levied
solely on banks.

9.

COMMUNITY DEVELOPMENT ORGANIZATIONS
PROVIDE SUBSIDIZED LENDING

Community development organizations (CDOs) are institutions that promote
investment in target neighborhoods, working closely with homebuyers, private
lenders, businesses, government agencies, and private donors.31 They primarily
30 See

U.S. Congress (1988), p. 7.
Wells and Jackson (1993) for a survey of community development lending, and see
Board of Governors of the Federal Reserve System (1993) for a survey of community development
lending by banks.
31 See

28

Federal Reserve Bank of Richmond Economic Quarterly

arrange loans for development projects and homeowners, and their costs are
generally funded by grants and donations. Their goal of revitalizing decaying neighborhoods matches exactly the avowed purpose of the CRA. CDOs
represent an alternative to channeling subsidized lending through the banking
system.
Neighborhood Housing Services of Baltimore (NHSB) is one such organization.32 The main focus of the NHSB is promoting occupant homeownership,
improving the physical appearance of neighborhoods, and “stabilizing” the real
estate market. The NHSB has targeted four different Baltimore neighborhoods
since its inception in 1974. Within a neighborhood, it often targets particular
blocks by systematically searching for owner-occupants for each property on the
block. When it finds a suitable buyer for a property, NHSB often arranges for
extensive renovations, handles the design and bidding, and selects a contractor.
A great deal of the work of NHSB involves lending. It provides extensive education and counseling to help prospective borrowers qualify for loans.
This assistance can involve establishing bank accounts, repairing credit records,
documenting sources of income, learning about home purchase and mortgage
application procedures, and saving for a down payment. Qualification often requires a number of sessions lasting nearly a year or more. Counseling serves as
a screening process—NHSB officials often talk of seeking a “match” between a
property and a borrower. After the purchase, counselors provide advice to financially strapped borrowers and may help them renegotiate payment schedules.

10.

COMMUNITY DEVELOPMENT LENDING
IS DIFFERENT

The activities of NHSB are different in many ways from the usual for-profit
home mortgage lending that banks perform. NHSB coordinates a package of
home purchase financing for a borrower that is generally more complex than
typical arrangements. A first mortgage is obtained, sometimes from a conventional lender, often on conventional terms, but occasionally through a special
mortgage program tailored to low-income borrowers. NHSB also makes first
mortgages from its own loan fund. Some NHSB loans are sold in a secondary
market run by a national organization, Neighborhood Housing Services of
America. A second mortgage is usually crucial to the package since borrowers
generally have just a minimal amount of cash. NHSB arranges for the second
mortgage, usually from its own loan fund. Further funding may be available
32 Neighborhood

Housing Services of Baltimore, Inc., is a private nonprofit organization and
is affiliated with a network of over 200 Neighborhood Housing Services organizations nationwide.
NHSB also operates an affiliated organization, Neighborhood Rental Services, that renovates rental
property.

J. M. Lacker: Neighborhoods and Banking

29

from a “Closing Cost Loan Program” it administers. Loan terms often are
designed to retire the junior debt first before retiring principal on the first
mortgage. NHSB officials often refer to their supplemental financing as “soft
second” money, since they are sometimes willing to reschedule payments if the
borrower suffers an adverse financial shock.
The NHSB goes to great lengths to minimize the credit risks posed by its
clients. Extensive information about borrowers emerges in the early counseling
stage. Borrowers are carefully selected for the right “fit” with the property in
the sense that the payments will be affordable. Borrowers generally are required
to save a down payment of at least $1,000, which provides an equity interest
in the home and helps demonstrate the discipline required to manage mortgage
payments. NHSB also closely monitors the neighborhood and encourages close
connections between residents through community clean-up projects, neighborhood organizations, and crime patrols. This helps NHSB learn early on about
a borrower’s financial difficulty before a costly mortgage default, generally
the last stage of financial distress for a conventional borrower. In addition,
renovations are designed in part to minimize the chance of costly repairs—new
furnaces and appliances are often installed, even when existing units satisfy
city housing codes. Active post-purchase counseling helps minimize the ex
post costs of financial distress.
Second, the NHSB spends much time coordinating investment in targeted
neighborhoods. A primary goal of NHSB is to achieve a “generally good
physical appearance” in a neighborhood. It tries to develop vacant properties,
rehabilitate existing properties, and improve commercial areas. It encourages
owner occupancy in the belief that owners who occupy their own home spend
more on maintenance and improvements. It tries to influence local government
spending on amenities such as streets, sidewalks, and public lands. Sometimes
it helps arrange the departure of taverns or other “undesirable” businesses. In
short, much of NHSB’s activity involves trying to overcome just the sort of
neighborhood externalities discussed earlier in this essay.
Third, NHSB lending requires substantial subsidies. Its counseling, monitoring, and coordination activities are quite labor-intensive, and home purchase
transactions are often subsidized. Operating and program expenditures are
funded out of federal, state, and local grants and private donations. Officials
admit that they often “overimprove” a house, undertaking renovations that cost
more than the resulting increase in market value. NHSB officials also recognize
that their second-mortgage loans are not “bankable” in that no private lender
would lend on the same terms. In fact, loans sold to Neighborhood Housing
Services of America, a national umbrella group, are backing for notes sold to
institutional investors who agree to receive a below-market rate of return on
their “social investment.”

30

11.

Federal Reserve Bank of Richmond Economic Quarterly

SHOULD BANKS DO COMMUNITY
DEVELOPMENT LENDING?

The community development lending performed by CDOs is the type of subsidized lending encouraged by CRA regulations. As suggested above, however,
the community development activities of CDOs like NHSB differ in many respects from traditional banking. Do banks have any comparative advantage in
providing community development lending? Furthermore, how many of these
activities are banks capable of performing safely?
First, the concessionary lending done by NHSB seems inappropriate for
insured depository institutions. Although CRA regulations require that lending be “sound,” the regulations also encourage concessionary investments and
charitable contributions toward community development. Banks get CRA credit
for offering higher loan-to-value ratios and other “more flexible” lending terms,
which can only mean more risky lending terms. In fact, in the newly adopted
CRA regulations, concessionary community development investments are included alongside low-income neighborhood lending in assessing CRA compliance. This approach threatens to blur the distinction between concessionary
and for-profit lending and could induce banks to make underpriced or excessively risky loans. In the absence of convincing evidence that banks pass up
economically viable lending opportunities in low-income neighborhoods, the
attempt to stimulate additional bank lending to these neighborhoods risks
saddling the banking industry with a large portfolio of poorly performing
mortgages if it has any effect at all. Since these debts would carry regulators’
implicit imprimatur, forbearance in the event of widespread losses would be
hard to avoid, as in the case of sovereign debt in the 1980s.
Maintaining a clear boundary at banks between concessionary and for-profit
lending is thus crucial to the clarity and integrity of regulatory supervision.
Examiners need to know whether a portfolio is intended to be profitable or philanthropic. Allowing government-insured banks to carry concessionary lending
on their books hides the cost, unless the subsidy is explicitly recognized up front
through higher loan loss reserves or discounting the value of the loan for interest
rate subsidies. Funding concessionary lending explicitly out of retained earnings or bank capital subjects transfers to at least minimal accounting safeguards,
ensures timely recognition of costs, and makes their redistributive nature clear.
Better yet, concessionary community development lending could be conducted
separately through a community development subsidiary of a bank’s holding
company. This would have the advantage of keeping such lending programs
separate from the bank’s conventional lending, making the evaluation of both
portfolios easier.
One impediment to community development lending by banks or bank
holding companies, however, is the extensive counseling that appears crucial
to lending by NHSB and other CDOs. Unlike CDO counselors, bank loan

J. M. Lacker: Neighborhoods and Banking

31

officers face regulatory constraints on their ability to communicate with borrowers; under the Equal Credit Opportunity Act, they cannot tell an applicant
what to do to qualify for a loan without triggering a formal application with
the required documentation and disclosures. As a result, NHSB counselors
learn far more about borrowers than would bank loan officers. Because the
screening inherent in these programs appears to be essential to the viability of
community development lending, banks often contract with community development groups to perform pre-application counseling. Thus, even bank holding
company subsidiaries may require external assistance to perform community
development lending.33
Would banks have any comparative advantage in community development
lending that would motivate a community development requirement for banks?
The experience of the NHSB suggests the answer is no. NHSB counselors have
extensive contact with local bank lending officers and appear well informed
about specialized loan programs available and the constraints associated with
conventional for-profit lending. In addition, NHSB has extensive contact with
residents through ongoing work with neighborhood associations, and thus sometimes has better information about borrowers than would a bank. If anything,
then, CDOs would seem to have a comparative advantage over banks in the
community development lending encouraged by the CRA regulations.
Banks have made substantial contributions of funds to community development, much of it under agreements negotiated with community groups.34 Do
banks have any special advantage at making such contributions? Perhaps their
working involvement with local community development groups helps them
compare and evaluate organizations. Bankers often speak of trying to select
“truly responsible” organizations.35 On the other hand, banks and other lenders
appear to be a minority among NHSB’s contributors. Most are corporations,
individuals, and foundations in the Baltimore area, and it seems unlikely that
they learned about NHSB through joint lending arrangements. Also, the national network of Neighborhood Housing Services organizations, along with
explicit certification programs, assures some uniformity, making evaluation

33 Other community development activities of the NHSB seem difficult for banks as well.
For example, much of the coordinating activity that seems vital to the CDO approach involves
finding owner-occupants that are viewed as beneficial to the neighborhood. Such discrimination
among buyers or borrowers would pose legal problems for a bank real estate subsidiary.
34 Allen Fishbein (1993) of the Center for Community Change estimates that around $35 billion has been “committed” by banks and savings and loans since the late 1970s under agreements
with community groups. The banking agencies officially view commitments for future action as
“largely inapplicable to an assessment of the applicant’s CRA performance” (Garwood and Smith
1993, p. 260).
35 “Our job, quite frankly, is to choose partnerships with organizations that do not have
hidden agendas, are truly responsible and have an appreciation of our limitations” (Milling 1994,
p. 7).

32

Federal Reserve Bank of Richmond Economic Quarterly

easier for outside investors and contributors. Thus, it is unclear why banks
would have any advantage in evaluating subsidy recipients.
To summarize, there does not seem to be a compelling rationale for imposing a costly lending obligation on banks. Ultimately such an obligation is a tax
on bank-dependent borrowers and depositors. Similarly, there seems to be scant
economic justification for looking to banks for the concessionary investments
encouraged by the CRA regulations.

12.

WHERE DO WE GO FROM HERE?

Our low-income neighborhoods nevertheless remain in appalling condition.
Community development lending seems to be a promising way of channeling
resources toward improving conditions in these neighborhoods. The evidence
summarized in this essay, however, suggests that the CRA is not an efficient
vehicle for revitalizing decayed neighborhoods, despite its laudable goals.
An alternative to the CRA is to fund community development subsidies
directly out of general tax revenues. The Community Development Banking Act
(CDBA), signed into law in September 1994, provides federal funding for community development. This Act creates a new government corporation, called the
Community Development Financial Institutions Fund, charged with providing
financial and technical assistance to specialized, limited-purpose community development financial institutions (CDFIs), and authorizes expenditures of $382
million over four years.36 Explicit appropriation for community development
has distinct advantages over drawing subsidies from banks. Removing the implicit tax burden on banks would reduce existing distortions in financial flows
and avoid the risks of concessionary lending. By directing assistance through
organizations that have community development as their sole mission, monitoring and evaluation of such assistance would become transparent.
The CDBA leaves considerable uncertainty, however, about important aspects of the Fund’s operation.37 For example, the CDBA requires that a CDFI
have “a primary mission of promoting community development,” without defining the latter term. Other key provisions depend on undefined concepts like
“significant unmet needs for loans or equity investments.” More fundamentally, distributing public money to a network of small, information-intensive
36 Funds can be provided in the form of grants, equity investments, loans, or deposits, and
must be matched dollar for dollar by private funds. The Fund is prohibited from holding over 50
percent of the equity of a CDFI and may not provide more than $5 million to any one CDFI during
any three-year period. Up to one-third of the appropriation may be applied toward a depository
institution’s deposit insurance premium. The appropriation covers administrative costs as well.
Many similar efforts have been funded in smaller amounts in the past. See Wells and Jackson
(1993). Macey and Miller (1993) also argue that direct funding of community development would
be superior to the CRA as it is currently implemented.
37 See Townsend (1994) for a critique of an earlier draft of the Community Development
Banking Act.

J. M. Lacker: Neighborhoods and Banking

33

lending organizations can create adverse incentives in much the same way
that deposit insurance can distort bank behavior. Moreover, the oversight and
reporting provisions in the CDBA are notably less detailed than current banking
legislation, and formal regulations have been left to the Fund to establish. Consequently, much will depend on the way in which the CDBA is implemented;
in particular, effective screening and monitoring is essential. Nevertheless, the
CDBA or something similar to it seems to be more promising than the CRA
for dealing with the plight of the nation’s low-income neighborhoods.

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Federal Reserve Bank of Richmond Economic Quarterly

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When Geometry
Emerged: Some Neglected
Early Contributions to
Offer-Curve Analysis
Thomas M. Humphrey

I

n his 1952 A Geometry of International Trade, Nobel Laureate James
Meade presented the definitive modern version of the celebrated reciprocaldemand, or offer-curve, diagram of the trade theorist. The diagram features
curves depicting alternative quantities of exports and imports countries are willing to trade at all possible prices (see Figure 1).
Let two countries, home and foreign, trade two goods, x and y. Measure
quantities of these goods along the horizontal and vertical axes, respectively.
Suppose the home country exports good x and imports good y while the foreign
country does the converse. The slope of any ray from the origin expresses the
relative price of x in terms of y. That is, it expresses the quantity of y exchanged
per unit of x, or y price of x. Curve H is the home country’s offer curve. Curve F
is the foreigner’s. Each curve shows alternative quantities of imports demanded
and exports supplied at all price ratios or terms of trade.
As drawn, the curves display declining elasticity, or price responsiveness,
throughout their length. They slope upward from left to right when the demand for imports in terms of exports is elastic—that is, when more exports
are offered for imports at successively lower import prices. They cease to
slope upward when import demand becomes unit-elastic. At such points, the
quantity of exports offered for total imports remains unchanged as import
prices fall. They bend backward (or downward) when import demand is inelastic. Along such segments, fewer exports are offered for total imports when
import prices fall.

The author thanks Bob Hetzel, Peter Ireland, Tony Kuprianov, Jeff Lacker, and Dawn
Spinozza for their helpful comments and suggestions. The views expressed are those of
the author and not necessarily those of the Federal Reserve Bank of Richmond or the Federal
Reserve System.

Federal Reserve Bank of Richmond Economic Quarterly Volume 81/2 Spring 1995

39

40

Federal Reserve Bank of Richmond Economic Quarterly

Figure 1 Offer-Curve Diagram

Foreign Exports
Home Imports
y

Curves H and F show alternative
quantities of exports offered and
imports demanded by each
country at all different price ratios.
Equilibrium occurs at intersection
point P. The slope of ray 0P is the
equilibrium price ratio or terms of
trade. The coordinates of point P
depict the equilibrium quantities
of goods traded.

H
P

•

F

0

x
Home Exports
Foreign Imports

+

World trade equilibrium occurs at point P, where the offer curves intersect.
At that point, the market-clearing price ratio, or terms of trade, given by the
slope of the ray 0P equates each nation’s import demand with the other’s export
supply. The supply of both commodities equals the demand for them, and the
coordinates of point P show the resulting equilibrium volume of world trade.
The foregoing diagram has proved indispensable in illuminating the central ideas of trade theory. Generations of professors and their students have
employed it to demonstrate how the strength and elasticity of each country’s
demand for the other’s product determine the equilibrium volume and terms
of world trade. Likewise, scores of textbooks use it to illustrate how tariffs,
technological advances, resource discoveries, taste changes, and other such
disturbances shift the offer curves and thereby alter world trade equilibrium.
That a simple geometrical diagram would prove so useful is hardly surprising. Other economic diagrams, including the Keynesian cross, Marshallian scissors, Hicksian IS-LM, Knightian circular flow, Vinerian cost envelope, FisherHaberler production possibility frontier, and expectations-augmented Phillips
Curve, or zero long-run trade-off between inflation and unemployment, have
proved equally indispensable. Indeed, as long ago as 1879, Alfred Marshall
insisted that diagrams are absolutely essential to exact reasoning in economics

T. M. Humphrey: Early Contributions to Offer-Curve Analysis

41

because they yield many of the same results as higher mathematics while being
accessible to the mathematically untrained.
What is surprising is how little has been written on the doctrinal history
of offer curves. Few systematic surveys of that topic exist. Textbooks scarcely
do it justice. Even history-of-thought treatises spotlight at best only a handful
of the chief contributions. Meade himself was largely silent on the diagram’s
history even though it was more than 100 years old when he published his
Geometry.
The development of offer-curve analysis involves some of the leading
names in classical and neoclassical economics. John Stuart Mill, Robert Torrens, Alfred Marshall, Francis Ysidro Edgeworth, and Abba Lerner all contributed to the diagram’s development and policy applications. Mill invented
reciprocal-demand schedules. He used them to determine precisely where,
within the limits set by comparative-cost ratios, the terms of trade, or quantity of
imports bought by a unit of exports, must fall. He used them also to estimate the
impact of tariffs and technology shocks on the terms of trade. Torrens likewise
employed such schedules to argue the merits of a policy of reciprocity in tariff
erection and removal. Marshall translated Mill into geometry and examined
the stability of offer-curve equilibria. Edgeworth combined offer curves with
indifference maps to derive the theory of the optimum tariff. Lerner corrected
Edgeworth’s error of alleging an asymmetry between export and import taxes
and also showed how the government’s disposal of the tax receipts influences
the position of the curves. Finally, Meade completed the analysis by deriving
offer curves from price vectors and trade indifference maps—themselves derived from underlying production possibility frontiers and consumption indifference curves. His demonstration was crucial. It proved once and for all that
domestic production as well as consumption conditions influence offer curves.
The paragraphs below attempt to trace this evolution and to identify specific
contributions to it. Besides exhuming lost or forgotten insights, such an exercise
serves as a partial corrective to the tendency of modern trade theory textbooks to
overemphasize Meade’s contribution at the expense of those of his predecessors.
By resurrecting pathbreaking earlier work, the exercise dispels misconceptions
concerning the origins of offer-curve analysis. It establishes that the diagram is
not a twentieth-century innovation. In this connection, it reveals that at least two
of Meade’s predecessors instinctively grasped the concept of offer curves long
before Marshall invented the diagram. It nevertheless indicates that the diagram
played a crucial role in advancing the analysis. By crystallizing, condensing,
and generalizing earlier insights into a powerful yet simple visual image, the diagram at once rendered them transparent and easy to comprehend. For evidence
of the diagram’s power to illuminate and enhance earlier work, one need only
refer to Mill’s and Torrens’ laborious verbal and numerical examples. Those
examples convey their full meaning only when translated into geometry. For
this reason, the following paragraphs take the liberty of interpreting Mill and

42

Federal Reserve Bank of Richmond Economic Quarterly

Torrens with the aid of offer-curve diagrams unavailable to them when they
wrote. Such anachronisms involve little distortion when, as is the case here,
they correspond faithfully to the original work.

1.

JOHN STUART MILL

Reciprocal-demand, or offer-curve, analysis originated to fill a gap in David
Ricardo’s theory of comparative advantage. Ricardo, in his 1817 volume On
the Principles of Political Economy and Taxation, demonstrated (1) that
comparative-cost ratios in each country determine pre-trade relative prices,
(2) that international differences in such prices render trade advantageous, and
(3) that countries therefore trade when their comparative-cost ratios differ, exporting their relatively cheap-to-produce goods and importing their relatively
dear-to-produce ones. Ricardo also indicated that the post-trade terms of trade
must fall somewhere between these limiting cost ratios. He did not, however,
explain what determines the terms of trade or where it would tend to settle. He
merely assumed it would fall roughly halfway between the cost ratios without
explaining why.
Priority for identifying the relative strength of each country’s demand for
the other’s product as the determinant of the terms of trade goes to James
Pennington, Robert Torrens, and, above all, John Stuart Mill. Pennington in
1840 was the first to state the point in print. His account, however, was marred
by the notion that volatile reciprocal demands cause the terms of trade to oscillate ceaselessly within the limiting cost ratios rather than to achieve a stable
determinate value. Torrens was the first to coin the phrase “reciprocal demand”
(see Viner [1937], p. 536). Because he used the concept to argue against unilateral tariff reduction, however, his analysis was condemned by his classical
contemporaries, most of whom were free-traders. Of the three originators of the
reciprocal-demand idea, John Stuart Mill exerted by far the greatest influence.
His conception of reciprocal demand as a schedule or function of price enabled
him to convey its importance more clearly, systematically, and convincingly
than had Pennington and Torrens. In any case, it was from Mill rather than
from the latter two writers that later economists took the idea.

Reciprocal-Demand Theory
Mill stated the idea first in his essay “On the Laws of Interchange Between
Nations,” which he wrote in 1829–30 but did not publish until 1844 in response
to Torrens’ (1841–42) The Budget. He presented it again in Chapter 18 of Book
III of his 1848 Principles of Political Economy. His statement is as modern as
the latest trade textbook.

T. M. Humphrey: Early Contributions to Offer-Curve Analysis

43

First comes the notion of comparative-cost ratios as limiting values for
the terms of trade.1 Next comes the argument that reciprocal-demand schedules express an inverse relationship between import relative price and quantity
demanded.2 There follows the idea that to each quantity of imports demanded
along a reciprocal-demand schedule there corresponds an associated amount of
exports supplied. This amount equals the product of import price and quantity.
It expresses the condition that a trading country’s export receipts constitute its
means of purchasing imports of the same value.3 In other words, reciprocaldemand schedules are at once demand-and-supply curves expressing import
demand in terms of export supply.4
Finally comes Mill’s requirement that reciprocal-demand schedules intersect at the equilibrium volume and terms of trade. The latter variable, the
equilibrium price ratio, clears the world goods market such that each country’s demand for imports equals the other’s export supply. Mill referred to this
equilibrium condition as the Law of International Values.5
Having shown how reciprocal-demand schedules intersect to determine
world trade equilibrium, Mill examined the stability of that equilibrium. In
language familiar to any modern economist, he argued that a displacement of
the terms of trade from its equilibrium value would invoke an excess world
demand for one good and corresponding world excess supply of the other.
These excess demands and supplies would exert corrective pressure on the
terms of trade until it returned to equilibrium.
Clearly, Mill had put his stamp on the diagram just as surely as if he had
drawn it himself. That much is evident from how easily his statements map
into offer-curve space (see Figure 2). Closest to the axes lie the comparativecost (CC) lines. Their slopes represent the production substitution, opportunity
cost, and domestic price ratios of the two goods in each country in the absence
of trade. The lines are drawn straight to correspond to the Ricardian or classical
1 “The limits within which the [relative price or exchange ratio between importables and
exportables] is confined, are the ratio between their costs of production in the one country, and
the ratio between their costs of production in the other” ([1844] 1968, p. 12).
2 “The higher the price, the fewer will be the purchasers, and the smaller the quantity sold.
The lower the price, the greater will in general be the number of purchasers, and the greater the
quantity disposed of” ([1844] 1968, p. 9).
3 Let X and M denote export and import quantities and p and p their money prices. Then,
x
m
at each point on a reciprocal-demand schedule, the value of exports supplied px X equals the value
of imports demanded pm M, or px X = pm M. Dividing both sides of this equation by px yields X =
(pm /px )M, which says that the amount of exports offered equals the product of import relative
price and quantity.
4 “The supply brought by the one constitutes his demand for what is brought by the other. So
that supply and demand are but another expression for reciprocal demand” ([1848] 1909, p. 593).
5 “The produce of a country exchanges for the produce of other countries, at such values as
are required in order that the whole of her exports may exactly pay for the whole of her imports.
This law of International Values is but an extension of the more general law of Value, which we
called the Equation of Supply and Demand” ([1848] 1909, p. 592).

44

Federal Reserve Bank of Richmond Economic Quarterly

Figure 2 Mill’s Reciprocal-Demand Schedules
Foreign Exports
Home Imports
y

CCF

The schedules H and F follow
the comparative-cost lines over
a range in which the countries
are indifferent to trade. Then
they bend toward equilibrium.
If the terms-of-trade ray lies
below the market-clearing ray
going through the point of offercurve intersection, the resulting
excess demands and supplies
restore it to equilibrium.

H
t

•
• excess

••D

C

t'

•

F
excess
supply of y

demand for x

CCH
B

0

•
•
A

x
Home Exports
Foreign imports

+

assumption of constant marginal and average costs. That the home country’s
line is the flatter of the two indicates that it (the home country) possesses a
comparative-cost advantage in producing the good measured along the horizontal axis. Conversely, the steep slope of the foreigner’s cost line signifies his
comparative-cost advantage in producing the good measured along the vertical
axis.
As for the offer curves, they follow the cost lines over a range in which
the countries are indifferent to trade. Thus if the home country faces world
terms of trade equal to its domestic opportunity cost ratio AB/0A, it cares not
whether it obtains AB units of good y through domestic production or through
foreign trade. Either way, the cost is the same, namely, 0A units of good x.
Likewise, when the terms-of-trade ray coincides with the foreigner’s cost line,
he is equally willing to obtain CD units of good x through trade or domestic
production. In each case, he sacrifices 0C units of good y.
At a certain point, however, the offer curves depart from the cost lines.
Thus, at point B, the home country’s curve begins to bend away from its cost
schedule. Precisely at this point, the home country specializes completely in
the production of its exportable, the excess of which it trades for importables to
reach its desired consumption bundle—the same bundle it would consume under

T. M. Humphrey: Early Contributions to Offer-Curve Analysis

45

self-sufficiency. Beyond this point, however, the offer curve bends upward in
response to better terms of trade. The resulting fall in the export price of imports
has a twofold effect. It increases the quantity of imports demanded. And, by
inducing the country to consume fewer exportables, it makes more of those
goods available for sale abroad and so raises the quantity of exports offered.
This latter step is necessary since the country already is at its specialization
point and can produce no more goods for export. A similar analysis holds for
the foreign offer curve, which at point D bends away from its cost line toward
equilibrium.
Equilibrium occurs where the curves intersect. Running through that intersection point is a ray from the origin whose slope represents the market-clearing
price ratio or terms of trade. A self-correcting mechanism ensures this equilibrium price ratio will prevail. Should a disequilibrium terms of trade such as
that indicated by the slope of the lower dashed ray occur, the result would
be an excess demand for the home country’s exports and an excess supply of
its imports. The resulting rise in export prices and fall in import prices would
restore the equilibrium terms of trade.
Applications
Having derived his reciprocal-demand apparatus, Mill put it to work in analyzing a variety of cases. He showed that where the terms of trade settle between
the autarkic cost lines depends on the relative strength and elasticities of the
reciprocal demands. The greater and more elastic one country’s demand relative
to the other’s, the more the terms of trade would move against the first country
and in favor of the second. And in the case of a large country trading with a
small one, he showed that the latter’s offer curve might cut the former’s in its
linear segment. If so, the terms of trade would coincide with the large country’s
cost ratio. All gains from trade would go to the small country, and the large
one would be incompletely specialized in production.
Technological Improvements and the Terms of Trade
He likewise applied his reciprocal-demand technique to predict the terms-oftrade effects of a cost-reducing improvement in the foreign country’s export
sector (see Figure 3). To do so, he distinguished between elastic, unit-elastic,
and inelastic home import demands. Such elasticities result in greater, unchanged, and smaller outlays of exports as import prices fall. Accordingly,
they give rise to upward-sloping, vertical, and backward-bending home offer
curves, respectively.
Mill concluded that the improvement would, by raising the supply of exports relative to the demand for them, turn the terms of trade against the
foreign country by an amount that depended on the home country’s importdemand elasticity. The improvement lowers the foreigner’s opportunity cost of

46

Federal Reserve Bank of Richmond Economic Quarterly

Figure 3 Technological Advance and Trade Taxes

Foreign Exports
Home Imports
y
H
unit
elastic
H
inelastic

•

H
elastic

•

F'

•
•

F

0

Technological advance shifts
the foreigner’s offer curve upward.
The extent of his terms-of-trade
deterioration depends on the
elasticity of the home country’s
curve. Conversely, the foreigner’s
trade taxes shift his curve
downward. His terms of trade
improve by an amount that
depends on the elasticity of the
home country’s curve.

x
Home Exports
Foreign Imports

+

producing exports. It thus enables him to offer more for any given quantity of
imports. In so doing, it shifts up his offer curve equiproportionally to the cost
reduction.6 The resulting counterclockwise rotation of the equilibrium price ray
constitutes the terms-of-trade deterioration. The deterioration is proportionally
greater than, equal to, or less than the cost reduction as the home offer curve
is inelastic (backward-bending), unitary-elastic (vertical), or elastic (upwardsloping). Mill’s inelastic case anticipated the modern concept of immiserising
growth in which the adverse terms-of-trade effects of improved productivity
swamp the beneficial output effects and so make the country worse off than
before.
Trade Taxes and the Terms of Trade
Mill also employed his reciprocal-demand apparatus to examine the terms-oftrade effects of a tax on exports or imports. Despite his aversion to all forms
of trade restriction, he demonstrated that such taxes could improve the levying
6 Mill

admitted that this result might not hold exactly if the cost reduction exerted an income
effect on the foreigner’s own demand for his exportable good.

T. M. Humphrey: Early Contributions to Offer-Curve Analysis

47

country’s terms of trade in proportion to the elasticity of the other’s reciprocal
demand.
Let the foreign government levy the tax and consume the proceeds (see
Figure 3 again). If the tax is on imports, it reduces the demand for them. If it
is on exports, it reduces their supply. Either tax, therefore, causes an equiproportionate downward shift in the foreigner’s offer curve and thus improves his
terms of trade. The improvement is in greater, equal, or lesser proportion than
the tax depending on whether the home country’s offer curve is backwardbending (inelastic), vertical (unit-elastic), or upward-sloping (elastic).
Theoretically, then, trade taxes could improve the terms of trade and thus
national welfare. Nevertheless, Mill opposed them on practical and moral
grounds. In his view, they invite retaliatory duties abroad that nullify the initial
terms-of-trade improvement. Worse still, they bring costly reductions in the volume of world trade. Even in the absence of retaliation, they are unjust because
they benefit the levying country at the expense of other countries. Since the rest
of the world’s loss exceeds the dutying country’s gain, such taxes are inimical
to global welfare and cannot be justified from a cosmopolitan standpoint.
Mill’s Failure
The bulk of Mill’s analysis remains as valid today as when he wrote it. Still,
he was not completely successful. He failed to resolve the problems that arise
when offer curves exhibit (1) multiple equilibria and (2) indeterminacy of equilibrium. The first problem arises when the curves intersect more than once; the
second when they coincide over certain ranges. Both phenomena require for
their occurrence inelastic offer curves. Unfortunately, however, Mill chose to
analyze them under the special assumption that the curves are unit-elastic. Neither Alfred Marshall ([1879] 1975, pp. 148–49) nor Francis Edgeworth (1894a,
pp. 609–14) let this slip pass unnoticed. They pointed out that unit-elastic
curves intersect only once and cannot coincide (see Figure 4). Accordingly,
they concluded that Mill’s choice of unit-elastic curves was useless in resolving
questions of indeterminacy and multiple equilibria.
Mill’s Paradox
Mill was successful, however, in using his unit-elastic schedules to demonstrate
what Akira Takayama (1972, pp. 144–45) calls “Mill’s paradox.” That paradox
states that a country’s gains from trade decline as its resource endowment
expands.
Let the offer curves be unit-elastic beyond the production-specialization
points on the comparative-cost lines (see Figure 5). Suppose that prior to resource expansion the foreign curve initially cuts the home curve at its kink.
The result is that the terms of trade coincide with the home country’s cost ratio
and the foreigner reaps all the gains from trade.

48

Federal Reserve Bank of Richmond Economic Quarterly

Figure 4 Unit-Elastic Reciprocal-Demand Curves

Foreign Exports
Home Imports
y

Unit-elastic curves are
horizontal and vertical in
the relevant range. They
intersect once. They display
no multiple equilibria or
indeterminacy.

H

•

0

F

x
Home Exports
Foreign Imports

+

Mill then assumes that resource expansion occurs in the foreign country.
Such expansion, provided it raises the output of exportables more than it raises
the foreigner’s own demand for them, shifts upward his production (exportcapacity) point and with it his offer curve. The resulting growth-augmented
curve cuts the unit-elastic segment of the home country’s curve, thus yielding
a terms-of-trade deterioration for the foreigner. In the limit, growth continues
until the terms of trade coincide with the foreigner’s cost ratio and all trade
gains accrue to the home country. Here is the rationale for Mill’s statement
that “the richest countries, ceteris paribus, gain the least by a given amount of
foreign commerce” ([1848] 1909, p. 604).
Assessment
Overall, Mill’s analysis must be judged one of the greatest contributions in
the history of economics. It generalized classical value theory by shifting the
emphasis from cost of production to equilibrium of demand and supply. True,
Mill’s predecessors occasionally acknowledged demand as a determinant of
price. But they did so only for the singular case of nonreproducible goods
in absolutely fixed supply. Mill now extended that analysis to cover laborproduced goods as well. He showed that even if cost determines the autarkic

T. M. Humphrey: Early Contributions to Offer-Curve Analysis

49

Figure 5 Mill’s Paradox

Foreign Exports
Home Imports

H

y

•
Z

•
•

•

F ''

•

F'

•

F

0

+

Growth of the foreigner’s resource
endowment shifts his offer curve
upward. His terms of trade
deteriorate until they eventually
coincide with his cost ratio. Beyond
point Z he ceases to specialize.

F '''

x
Home Exports
Foreign Imports

value of such goods, as Ricardo claimed, another principle, namely that of reciprocal demand, determines their international value. By distinguishing between
cost-determined domestic prices and international prices determined jointly by
supply and demand, he identified both blades of the Marshallian scissors. True,
it remained for the neoclassical school to elaborate his insight into a full microeconomic theory of price determination. But Mill clearly pointed the way.

2.

ROBERT TORRENS

Mill had shown that with unit-elastic home demand for imports, the foreigner’s
trade tax improves his terms of trade equiproportionally with the tax. Two
years before Mill published his analysis, Robert Torrens (1841–42) independently reached this same conclusion in a numerical example presented in his
Postscript to Letter IX of The Budget. There he showed that a 100 percent
import tariff, through its effect on reciprocal demands, improves the levying
country’s terms of trade by the same 100 percent. His example has the foreign
country, Cuba, imposing the tariff on imports of English cloth. His assumption
of unit-elastic reciprocal demands implies that Cuba’s offer curve is horizontal
and England’s curve is vertical in the relevant range (see Figure 6).

50

Federal Reserve Bank of Richmond Economic Quarterly

Figure 6 Torrens’ Tariff Model

Cuban Sugar

Cuba’s 100 percent tariff
shifts her offer curve down
from C to C'. Her terms of trade
improve equiproportionally such
that the slope of ray 0t' is half
that of ray 0t.

E

t

•

C

t'

•

0

C'

English Cloth

+

Start from the free-trade equilibrium. Cuba’s imposition of the 100 percent
tariff shifts her effective offer curve down to half its initial level. At the original
terms of trade, there occurs an excess world demand for Cuba’s export good,
sugar, and a corresponding excess world supply of her import good, English
cloth. To eliminate these excess demands and supplies, Cuba’s terms of trade
must improve—and England’s deteriorate—by 100 percent. In the new, tariffridden equilibrium, Cuba imports the same initial amount of cloth at the cost
of only half the initial amount of sugar given up. England, on the other hand,
receives only half the initial amount of sugar at the cost of the same amount of
cloth sacrificed. Torrens’ conclusion: Foreign governments can, by means of
tariffs, manipulate reciprocal demands to their advantage and thereby worsen
the other country’s terms of trade.
Having shown how the home country might lose from the foreigner’s tariff,
Torrens next used his reciprocal-demand schedules to argue for reciprocity in
tariff removal (see Figure 7). He pointed out that the home country’s unilateral
abolition of tariffs would, in the face of their existence abroad, only worsen
her terms of trade. He likewise noted that the home country’s retaliatory duties
would cancel the unfavorable terms-of-trade effects of foreign levies. Finally,
he observed that the simultaneous imposition or removal of duties by all countries tends to leave the terms of trade unchanged. Like today’s proponents of
“a level playing field,” he proposed that England counter foreign tariffs with

T. M. Humphrey: Early Contributions to Offer-Curve Analysis

51

Figure 7 Tariff-Policy Reciprocity

Cuban Sugar

E
E'

t

•1

C

Cuba’s unilateral tariff improves her
terms of trade. Equilibrium moves
from point 1 to point 2. England’s
reciprocal duty shifts her offer curve
leftward and corrects her terms-oftrade deterioration (point 2 to point 3).
Simultaneous tariff removal by both
parties restores initial equilibrium
without affecting the terms of trade
(point 3 to point 1).

t'

•3

0

+

•2

C'

English Cloth

equal duties of her own, that she trade freely only with countries admitting
her goods duty-free, and that she drop her tariffs only insofar as her trading
partners abolish theirs.
Torrens’ analysis was unsympathetically received by his classical contemporaries who feared it would undermine the case for free trade (see O’Brien
[1975], pp. 194–97). They noted that tariff removal would hardly worsen
England’s terms of trade to the extent Torrens claimed if reciprocal-demand
elasticities were, as they believed, greater than one.7 Furthermore, they contended that any adverse terms-of-trade effects of moving toward freer trade
would be more than offset by gains in productivity and competitiveness due to
enhanced international specialization and division of labor. Finally, they noted
that the gist of Torrens’ analysis implied that England should levy not equal but
higher retaliatory duties than those levied abroad to improve her terms of trade.
They saw such action as intensifying the danger of a trade war with all parties
7 To Torrens’ critics, high elasticities stemmed from the availability of numerous alternative
goods and markets in the world economy. Such availability meant that a country could avoid
tariffs levied by its trade partner. The country could divert production from taxed to nontaxed
exports. Or it could export to third, tariff-free countries, competition from which would limit
the tariff-imposing country’s power to manipulate the terms of trade. In short, access to multiple
export outlets and import sources rendered reciprocal demands extremely elastic with respect to
price changes emanating from any single source.

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Federal Reserve Bank of Richmond Economic Quarterly

losing. In response to the criticism that his analysis aided protectionists, Torrens
rather disingenuously protested that he was a free trader merely applying the
logic of the classical model.

3.

ALFRED MARSHALL

Without actually drawing the offer-curve diagram, Mill and Torrens had described the workings of its principal components. Indeed, Mill’s account, in
the words of Joseph A. Schumpeter (1954), “reads almost like a somewhat
clumsy instruction for choosing these curves rather than others” (p. 609). It
was Alfred Marshall who took the crucial step of translating Mill’s instructions
into geometry and thus invented the diagram that bears his name.
That Marshall was the first to draw the diagram is beyond dispute. What
is disputed is the originality of his contribution. Did his trade diagrams do no
more than merely “polish and develop Mill’s meaning,” as Schumpeter (1954,
p. 609) claimed? Or were they “of such a character in their grasp, comprehensiveness and scientific accuracy” as to put them “far beyond the ‘bright ideas’
of his predecessors,” as John Maynard Keynes ([1925] 1956, p. 24) thought?
Marshall himself disclaimed originality by stressing the Millian pedigree of his
diagrams. “As to International Trade curves,” he wrote, “mine were set to a
definite tune, that called by Mill” (Pigou [1925] 1956, p. 451). He dismissed
his curves as nothing more than “a diagrammatic treatment of Mill’s problem
of international values” (Pigou [1925] 1956, p. 416).
Of the fourteen diagrams Marshall presented in his Pure Theory of Foreign
Trade (1879), at least five appear to confirm Schumpeter’s and Marshall’s judgments. For they merely elaborate in elegant and compact geometry what Mill
had already expressed in words and numerical examples. Certainly Mill would
have found unexceptional the curves in Figure 8a just as he would Marshall’s
explanation of their convex (bowed in toward their respective axes) shapes and
their positive slopes. Their convexity, Marshall held, captures the inverse demand relationship between import price and quantity. And their positive slopes
indicate the normal case of elastic demands in which import-sales proceeds—
and thus the quantity of exports produced with the aid of those proceeds—rise
with import-quantity demanded.8
Nor would Mill have been surprised by Figure 8b. There Marshall depicts
a case of inelastic import demand as manifested in a backward-bending offer
curve. Mill would have agreed with Marshall that beyond point B, import-sales
proceeds, and so the export volume they finance, must fall as import-quantity
demanded rises. He had said much the same thing himself.

8 Marshall

always assumed that the price-times-quantity sales receipts of importers pay for
the cost of exports. Import receipts finance export production.

T. M. Humphrey: Early Contributions to Offer-Curve Analysis

53

Figure 8 Marshall’s Normal Class and Exceptional Class I Curves

a

b
Foreign Exports
Home Imports

Foreign Exports
Home Imports
y

y
H
H

F
F

•

0

x
Home Exports
Foreign Imports

B

0

x
Home Exports
Foreign Imports

In panel a, both curves are elastic. Import and export quantities rise as the
relative price of imports falls. In panel b, the home curve becomes inelastic
beyond point B. Import quantity rises but export quantity falls with decreases
in the relative price of imports.
+

Finally, Mill would have found Marshall’s diagrammatic treatment of trade
taxes totally unsurprising. Marshall showed that when both offer curves are
elastic (provided the foreigner’s is not infinitely so), tariffs and export taxes
always improve the levying country’s terms of trade. He also showed that
when the levying country’s curve cuts the foreigner’s curve in its inelastic
range, a trade tax yields a twofold gain (see Figure 9). The taxer’s terms of
trade improve. And, by obtaining a larger quantity of imports at the sacrifice
of a smaller quantity of exports, the taxer has more of both goods to consume
at home. A country lucky enough to face an inelastic foreign offer curve, said
Marshall, has nothing to lose and everything to gain by exploiting it.9 But Mill
had already arrived at these conclusions. Thus Marshall’s diagrammatic tax
analysis goes little beyond Mill’s work on that subject.
9 Marshall

assigned a low probability to this case. He thought that (1) international competition, (2) countries’ ability to shift production from taxed to nontaxed exports, and (3) the option
of trading with third, free-trade nations rendered offer curves highly elastic. Levying countries
were left with little scope for tariff-induced improvements in the terms of trade.

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Federal Reserve Bank of Richmond Economic Quarterly

Figure 9 Exploiting an Inelastic Foreign Offer Curve

Home Imports

H'
t'

y' •

•
H
t

y

•

•

The home country imposes a
trade tax that shifts her offer
curve counterclockwise. Her
terms of trade improve. And she
obtains more imports at the cost
of fewer exports given up and
so has more of both goods to
consume at home.

F

0

•

x'

•
x

Home Exports

+

Scale Economies and Offer Curves
Figures 10 through 13, on the other hand, go far beyond anything Mill or
Torrens had to offer. Figure 10 constitutes what John Chipman (1965) calls
“the first fairly rigorous approach to the treatment of scale economies in international trade” (p. 738). It depicts Marshall’s Exceptional Class II, in which
economies in the production of exportables render the offer curve nonconvex
and subject to irreversible downward shifts.
Let trade expansion move the home country from point R to point T on its
offer curve. The resulting increased export production invokes scale economies
associated with enhanced specialization and division of labor, with improved
know-how (learning by doing), and with use of advanced technology and large
machines. These economies in turn enable the larger quantity of exports to be
produced at lower unit cost than the original quantity. Since unit-cost reductions
pass through into product prices, it follows that scale economies cause export
prices to fall from RV/0V to TU/0U. Such economies account for the inflection
points on the offer curve.
Moreover, once the scale economies are put in place, they and their associated cost reductions cannot be reversed even if output drops back to its original
level. To capture such irreversible path-dependent effects, the offer curve shifts
downward toward the export axis (see dashed line). In short, scale economies

T. M. Humphrey: Early Contributions to Offer-Curve Analysis

55

Figure 10 Marshall on Scale Economies

Foreign Exports
Home Imports
y
H
F
R

•

0

+

V

•T

Because of irreversible
scale economies, movement
from point R to point T causes
a reduction in the unit cost of
producing exports and a
downward shift in the offer
curve.

x
U
Home Exports
Foreign Imports

constitute a form of technical progress that shifts the offer curve simultaneously
with movements along it. Here was a novel element in offer-curve analysis.
Uniqueness and Stability of Equilibrium
Further confirming Marshall’s originality was his analysis of uniqueness and
stability of offer-curve equilibrium. Indeed, Murray Kemp (1964) calls this
analysis one of “the most remarkable contributions ever made to theoretical
economics” (p. 66). Regarding uniqueness, Marshall noted that there can be
but one equilibrium when both curves are positively sloped and possess no
inflexion points (see Figure 11a). Equilibrium is likewise singular when one
curve is elastic and the other inelastic in a certain range (see Figure 11b).
If, however, both curves are inelastic (Figure 11c), or if at least one contains
inflexion points (Figure 11d), multiple equilibria may result. Such equilibria,
according to Marshall, are always odd in number. Moreover, they are alternately
stable and unstable, with the stable equilibria flanking the unstable ones (see
Figures 11c and d in which stable equilibrium points A and C flank the unstable
point B).
As for stability of equilibrium, Marshall analyzed it with phase diagrams
superimposed on his offer curves. His phase diagrams—the first ever used in
print by an economist—treat points off the curves as disequilibrium phenomena produced by random real shocks such as wars, harvest failures, and the
like. For any given disequilibrium trading point, Marshall sketched the dynamic

56

Federal Reserve Bank of Richmond Economic Quarterly

Figure 11 Single and Multiple Equilibria

a

b
y

y

H
H
F

A

•A

•

F

0

x

0

x

c

d

y

H

y
C

H

F

•

C

•

•

B

B
A

•

0

•

F
A

x

0

•

x

Panels a and b display cases of unique (singular) equilibrium. Panels c and d
display multiple equilibria, with the stable equilibria (A and C) bounding or
bracketing the unstable one (B).
+

adjustment mechanism that moves the point toward equilibrium. To him, the
propelling force consisted of the profitability of expanding production of exports
when they are in short supply.
Consider trading points to the left of the home country’s curve and below
the foreigner’s curve. Such points represent shortfalls of actual quantities of

T. M. Humphrey: Early Contributions to Offer-Curve Analysis

57

Figure 12 Marshall’s Disequilibrium Mechanism

Foreign Exports
y

The shortfall of actual below desired
exports at trading point P stimulates
production of exports and so moves
that point toward equilibrium.

H

•
R

•
•
P

0

•

•

A

•Q

F

•

x
Home Exports

+

exports below quantities the countries are willing to offer (see Figure 12). These
shortfalls render exports extraordinarily profitable and induce competitive producers to produce more. The resulting export expansion moves the trading point
toward the curves just as—to use Marshall’s analogy—the force of magnetic
attraction moves metal filings toward a rigid wire. The arrows point rightward
and upward to indicate the trading point’s movement.
Conversely, disequilibrium trading points to the right of the home country’s
curve and above the foreigner’s curve spell surpluses of actual over desired exports. The resulting losses bring declines in export production as shown by the
leftward and downward direction of the arrows.
In all cases, the directional arrows indicate whether trading points will
move away from or toward their neighboring equilibria (see Figure 13). On the
basis of such analysis, Marshall concluded that every equilibrium intersection
is stable except those in which (1) both curves slope in the same direction and
(2) the foreign curve is more nearly vertical than the domestic one (see Amano
[1968], pp. 327–28).
Surplus Analysis of Gains from Trade
Further proof of Marshall’s originality is his diagrammatic treatment of the
gains from trade. In a straightforward application of his concept of consumer
surplus, he expressed such gains as the excess of the maximum prices a country would be willing to pay for successive units of imports over the market
price, or terms of trade, it actually pays. Accordingly, he devised a technique

58

Federal Reserve Bank of Richmond Economic Quarterly

Figure 13 Marshall’s Phase Diagram

Foreign Exports
Home Imports
y

The directional arrows indicate
whether disequilibrium trading
points move toward their stable
or away from their unstable
neighboring equilibria.

H
W
•
•

•
A

•

T

B

•

U
S

Q

•

P•

F

•C

V

0

x
M L
Home Exports
Foreign Imports

+

for projecting from the offer curve a series of unit surpluses into a triangle
resembling the area lying between an ordinary Marshallian demand curve and
the price line (see Figure 14). Expressed in terms of export quantities, the
resulting triangular area UHA sums the excesses of the maximum unit prices
over the prevailing terms of trade shown by the slope of the ray through the
trade equilibrium point A. This was his measure of the net benefit a country
derives from trade.10
Assessment
It should be obvious by now that Keynes was right. Marshall’s diagrams were
more than a mere refinement of Mill’s analysis. They were a major innovation
and a powerful aid to theorizing. The mystery is why Marshall himself refused
to acknowledge as much. Perhaps a desire to stress the intellectual continuity
of trade theory led him to disguise his contribution modestly as part of the
accumulated wisdom of his classical predecessors. Or perhaps his reluctance to
claim originality for his diagrams stemmed from a puritanical sense of guilt over
the pleasure he derived from them. Jacob Viner (1941) writes that mathematics,
10 Actually, Marshall divided the surplus triangle by the distance 0D to correct for the
arbitrary choice of point D. That point fixes the location of the vertical line used in projecting
unit price surpluses onto the quasi-demand curve UP A .

T. M. Humphrey: Early Contributions to Offer-Curve Analysis

59

Figure 14 Surplus Measure of the Gain from Trade

Exportable
Good
U•

•R

P'

•T

•

A'

•

H

•K
Offer
curve

A

•

•P
0

+

•

M

Trade
equilibrium
point

•
B

•
D

The maximum price the
country is willing to pay for
successive units of imports
ranges from the slope of the
top ray to the slope of the
bottom one. A mapping of the
excess of these unit prices
over the equilibrium terms of
trade forms the surplus
triangle UHA'. The net gain
from trade is measured by the
triangle UHA' divided by the
distance 0D, which corrects
for the arbitrary choice of the
location of the projection
line DR.

Importable
Good

especially geometry, yielded Marshall “so much intellectual and aesthetic
delight that it for that reason alone became somewhat suspect to him as a worthwhile occupation. Mathematics, and especially graphs, were Marshall’s fleshpots, and if he frequently succumbed to their lure it was not without struggle
with his conscience. . . . [W]hen he did succumb he . . . warned his readers not
to take his mathematical adventures too seriously” (p. 231). Keynes agreed. He
pointed out that when Marshall’s “intellect chased diagrams and Foreign Trade
and Money, there was an evangelical moralizer of an imp somewhere inside
him, that was so ill-advised as to disapprove” ([1925] 1956, p. 37). But disapprove Marshall did and in so doing disclaimed originality for his invention.

4.

FRANCIS YSIDRO EDGEWORTH

As sophisticated as they were, Marshall’s offer curves lacked clear grounding
in the underlying utility functions. Credit for establishing these foundations and
for introducing utility considerations into the diagram goes to F. Y. Edgeworth,
Marshall’s colleague and the inventor of the indifference map and the contract
curve.
Edgeworth’s earliest work on the diagram appears on pages 113–14 of his
Mathematical Psychics (1881). There he derived offer curves for two representative price-taking individuals. Each possesses (1) a fixed endowment of

60

Federal Reserve Bank of Richmond Economic Quarterly

goods and (2) a utility function described by a consumption indifference map.
Like trade theorists today, Edgeworth defined each individual’s offer curve as
the locus of points of tangency of indifference curves and the price ray as it
pivots about the origin (see Figure 15). Each point represents an outcome of
constrained utility maximization in which the price ratio, or slope of the price
ray, equals the ratio of marginal utilities, or slope of the indifference curves.
In the same diagram, he demonstrated that the offer curves must intersect on
the contract curve, or locus of points at which one trader’s indifference curves
are tangent to the other’s. Along the contract curve, neither trader’s utility can
be increased without reducing the other’s. In demonstrating that offer curves
intersect on the contract curve, Edgeworth proved that price-taking equilibrium
is efficient in the sense that both traders together cannot be made better off by
another outcome. Moreover, since the equilibrium outcome lies between the
two indifference curves passing through the origin, or endowment point, where
no trade occurs, he also proved that free trade leaves each party at least as well
off as no trade.
He next extended this latter insight to measure a single country’s gain
from trade. In so doing he provided an alternative to Marshall’s measure of
the gain. In his 1889 Journal of the Royal Statistical Society article, “On the

Figure 15 Traders’ Price-Taking Equilibrium

Foreign Exports
Home Imports
y

Offer curves intersect on the
contract curve CC'. At freetrade equilibrium, both traders
occupy indifference curves
superior to those going through
the origin or endowment point
where no trade occurs.

i

0,F

H
C

t

i1,H

•

i1,F

•

F

i0,H

•C '
0

x
Home Exports
Foreign Imports

+

T. M. Humphrey: Early Contributions to Offer-Curve Analysis

61

Application of Mathematics to Political Economy,” he drew a community trade
indifference curve passing through the origin (see Figure 16). This curve, of
course, shows all combinations of exports and imports that leave the country no
better off than if it refrained from trade. The vertical distance between this “no
gain from trade” curve and the country’s offer curve—or rather the indifference
contour going through it—at free-trade equilibrium measures the utility gain
from trade.
Figure 16 Utility Gain from Trade

Foreign Exports
Home Imports
y
T

i

•

0, F

H

gains
from
trade

•
␶

0

The vertical distance between the
trade equilibrium point and the
foreigner’s “no gain from trade”
indifference curve–the particular
curve passing through the
origin–constitutes the foreigner’s
utility gain from trade.

F

x
Home Exports
Foreign Imports

+

Optimum-Tariff Analysis
The foregoing pathbreaking innovations were but a prelude to Edgeworth’s
crowning achievement—his geometrical demonstration of the optimum-tariff
argument. An optimum tariff, of course, maximizes the excess of the gains
from terms-of-trade improvement over the loss from lower trade volume and
reduced international specialization and division of labor. The idea itself goes
back to Mill and Torrens. They had argued that a large country caring only
for its own welfare and facing an imperfectly elastic foreign demand schedule
could exploit its monopoly power in world markets through such a tariff. But
rigorous diagrammatic illustration of the argument was lacking until Edgeworth
provided it in his 1894 Economic Journal article, “The Theory of International
Values, II.”

62

Federal Reserve Bank of Richmond Economic Quarterly

Figure 17 The Optimum Tariff

Foreign Exports
Home Imports

i2,H

y

i1,H

H

The optimum tariff puts the
levying country on the point
where its highest attainable
trade indifference curve is
tangent to the foreigner’s
offer curve.

H'
t
Q

i2,H

•

•

P
F

M
i1,H

0

•

x
Home Exports
Foreign Imports

+

His demonstration begins with the home country’s trade indifference curve
passing through the free-trade point where the offer curves intersect (see Figure
17). That particular indifference curve indicates the level of welfare or satisfaction the home country enjoys under free trade. It provides a benchmark against
which to compare alternative welfare levels produced by different degrees of
trade restriction.
It also, together with the foreign offer curve, specifies the range of tariff
rates beneficial to the home country. In this connection, Edgeworth noted that
the same indifference curve that passes through the free-trade point P also
cuts the foreign offer curve at point M. That latter point therefore yields the
same level of welfare as free trade. Since all points on the foreign offer curve
between these two extremes lie on higher indifference curves, it follows that
any movement to a position between points P and M will result in the home
country being better off than under free trade. In other words, points P and M
mark the range of tariff-induced terms-of-trade improvement beneficial to the
home country. Somewhere within this range, benefit is at a maximum.
Edgeworth identified this maximum with point Q, the point where the home
country reaches its highest possible trade indifference curve given the foreign
offer curve. The optimum tariff, he argued, is that which distorts the home

T. M. Humphrey: Early Contributions to Offer-Curve Analysis

63

country’s offer curve such that it intersects the foreign offer curve at this point
of tangency with the highest attainable indifference curve. Here is the famous
tangency solution to the determination of the optimum tariff.
Edgeworth then showed that if the tariff is too high, it reduces rather than
increases welfare. Suppose the country progressively raises its tariff from the
zero rate corresponding to point P to positive rates corresponding to points
Q and M. As it does so, it finds that its welfare first rises, then reaches a
maximum, and finally starts to fall. If it persists in raising the rate beyond that
corresponding to point M, it will discover that its welfare has fallen below the
level attained at the free-trade position P. It follows that the tariff must not be
too large if the nation is to benefit.
Finally, Edgeworth noted some pitfalls to the practical application of his
diagram. First, the optimum tariff, though precisely identified in theory, cannot
be ascertained with any accuracy in practice. Second, protectionists will exert
strong political pressure on policymakers to raise tariffs far beyond the optimum point, thereby reducing welfare. Third, retaliation by foreign countries
may erase any gains generated by the tariff. Fourth, viewed from a global
standpoint, tariffs are harmful since other countries lose more than the levying
country gains. For these reasons, free trade remains the best and most practical
policy for a country to pursue.
Alleged Asymmetry of Export and Import Taxes
No scholar is infallible, not even one of Edgeworth’s stature. In the very
same Economic Journal article containing his optimum-tariff demonstration,
Edgeworth (1894b) committed a celebrated error. He rejected the standard
proposition that export and import taxes are equivalent in the sense of having
identical real effects. Other leading classical and neoclassical theorists, including Mill, Marshall, A. C. Pigou, and C. F. Bastable, took such equivalence for
granted. But Edgeworth alleged that the two taxes shift the dutying country’s
offer curve differently and therefore have disparate real effects.
According to Edgeworth, export taxes shift the curve horizontally to the
left. But import taxes shift it vertically upward such that it lies everywhere
above the original curve. The result is that the tax-ridden curves intersect the
foreign offer curve at different points, especially when both foreign and domestic curves are in their inelastic ranges (see Figure 18). In such cases, the
export tax-ridden equilibrium lies to the northwest of the free-trade point so
that the levying country is on a higher indifference curve with better terms
of trade. By contrast, the import tax-ridden equilibrium lies to the southeast
of the free-trade point, putting the country on a lower indifference curve with
worsened terms of trade. Such was Edgeworth’s allegation.
It took 42 years to identify and correct Edgeworth’s error. Abba Lerner
finally did so in his classic 1936 paper, “The Symmetry Between Import and

64

Federal Reserve Bank of Richmond Economic Quarterly

Figure 18 Alleged Asymmetry of Export and Import Taxes

Export Tax

Import Tax
Foreign Exports
Home Imports
y
H
H'

Foreign Exports
Home Imports
y
H'
H
2

•

1

1

•

•
F

0

2

•

F

x
Home Exports
Foreign Imports

0

x
Home Exports
Foreign Imports

Edgeworth alleged that an export tax shifts the home country’s offer curve
horizontally to the left whereas an import tax shifts it vertically. As a result,
the export tax moves the home country to a superior position (better terms of
trade and a higher indifference curve), whereas the import tax moves her to
an inferior position.
+

Export Taxes.” There Lerner argued, contrary to Edgeworth, that export and
import taxes indeed affect the offer curve identically. They thus have symmetrical effects on the volume and the terms of trade. Differential effects stem not
from the taxes per se. Rather they stem from how the government disposes of
the revenue. The greater the proportion spent on the levying country’s export
good, the greater the improvement in its welfare and terms of trade. Conversely,
the greater the proportion spent on imports, the smaller the improvement. Edgeworth’s first result obtains when all the proceeds are spent on export goods;
his second when all are spent on imports. His error lay in confusing these
expenditure effects for tax effects. What he saw as differential results of trade
taxes were really outcomes of how the government spent the revenue.

T. M. Humphrey: Early Contributions to Offer-Curve Analysis

5.

65

ABBA LERNER

Lerner (1936) established the foregoing results by means of the ingenious
device of a geometrical pencil, or wedge, superimposed on the offer curves
(see Figure 19). Consisting of two price radiants, the pencil expresses the taxinduced divergence between world and domestic relative prices. Its width shows
the rate of the tax. Its location on the offer curves depicts the government’s
apportionment of the proceeds between exportable goods and imports. And its
position around the free-trade price ray shows how tax imposition and disposal
affects the terms of trade and domestic relative prices. Finally, the pencil embodies the symmetry notion that export taxes are equivalent to import taxes of
Figure 19 Trade-Tax Pencil
Foreign Exports
Home Imports

R'

y

H
C

F

•

T

0

•

R

•U

The pencil R' 0R represents
the tax wedge between world
and domestic relative prices.
The pencil’s dimensions are
the same whether the tax is
levied on imports or exports.
The arms of right angle CTU
correspond to the proportions
of the tax revenue that the
government spends on the
two goods.

x
Home Exports
Foreign Imports

+

the same percentage rate. Since both taxes produce the same divergence between world and domestic prices in a two-good model, the pencil’s dimensions
are the same measured in either tax.11 What matters is not which good is taxed
but how the government disposes of the tax proceeds.
11 A tax on imports renders them dearer at home than abroad. By contrast, a tax on exports
raises their foreign price, thus making them cheaper at home than abroad. But a fall in the relative
price of exports is equivalent to a rise in the relative price of imports in Lerner’s two-good model.
Hence, an export tax raises the domestic real price of imports above the world price just as does
an import tax. The two taxes are symmetrical.

66

Federal Reserve Bank of Richmond Economic Quarterly

Lerner’s demonstration of this point was at once seminal and definitive.
Inserting the pencil into the offer curves, he obtained a right angle CTU connecting the points of entry of the pencil’s radiants. This right angle has a special
meaning. Its vertical and horizontal arms measure the world excess supplies
of the two goods resulting from the tax. Market-clearing equilibrium requires
that the government eliminate these excess supplies by consuming them in the
proportion in which they occur. That is, world market equilibrium obtains when
the ratio of the lengths of the right angle’s arms matches the ratio in which the
government consumes the two goods.
Lerner took this latter ratio as given and known. Then he found equilibrium
by pivoting the pencil about the origin until the matching right angle appeared.
For example, suppose the government spends the tax proceeds equally on exports and imports. Then, following Lerner, swing the pencil until it yields a
right angle whose arms are of equal length (see lines CT and TU in all panels
of Figure 20). Alternatively, suppose the government spends all the proceeds
on exportables such that the right angle reduces to a horizontal line. Then rotate
the pencil counterclockwise until it yields a flat line traversing the pencil and
meeting the offer curves (see lines C1 U1 in all panels). Finally, suppose the
government spends all the proceeds on imports so that the right angle reduces
to a vertical line. Then swivel the pencil clockwise until it yields a vertical line
between the offer curves (see lines C2 U2 in all panels). In each case, Lerner
examined the resulting location of the pencil’s radiants relative to the free-trade
price ray passing through the point of offer-curve intersection. These indicate
how the disposition of the tax affects the terms of trade and domestic price
ratio, respectively. Radiants to the left of the free-trade ray represent a fall and
those to the right a rise in post-tax relative prices.
Standard Tariff Propositions
Employing this technique, Lerner derived four key propositions of standard
tariff theory. His derivation marks a turning point in the diagram’s history. Before him, the diagram was largely regarded as an esoteric tool employed by a
select circle of economists. After him, it was seen as a conventional instrument
and widely used. His work, more than any other, convinced the economics
profession of the diagram’s power and versatility as an analytical tool.
His standard propositions are as follows. First, provided both offer curves
are elastic but not infinitely so, a trade tax, no matter how spent, improves the
levying country’s terms of trade and raises the domestic relative price of its
imports (see Figure 20a). In other words, the radiants of the pencil encompass
the free-trade price ray.
Second, regardless of elasticities, a tariff improves the terms of trade more
(or worsens it less) the larger the fraction of the tax spent on the country’s
exportable good. Thus, the pencil’s upper radiant lies more to the left (or less

T. M. Humphrey: Early Contributions to Offer-Curve Analysis

67

Figure 20 Lerner’s Trade-Tax Analysis

a

b
H

y

C

C

y

C2

•
• • •U1
T• •U
•U2

•

F

1

H
C1

U

•1
•
C
C2
• U• •
T

F

•U2

0

x

0

c

x

d
H

y
C1

y

• • C•
C •2
•U
T•

H
C2

C1
• U1•
•
•
•
T• U
•U2
C

U1

F

F

•U2

0

x

0

x

The pairs of C-U points show where the upper and lower radiants of the pencil
enter the offer curves. Pairs C -U , C-U, and C -U correspond to tax proceeds
1 1
2 2
allocated all, some, and none, respectively, to exportables. Taxes and their
disposal improve the terms of trade when radiants through the C points lie to
the left of the free-trade ray (not shown) that passes through the point of offercurve intersection. Taxes and their disposal raise the domestic relative price of
imports when radiants through the U points lie to the right of the free-trade ray.
+

68

Federal Reserve Bank of Richmond Economic Quarterly

to the right) of the free-trade ray as it passes through points C1 , C, and C2 ,
representing export expenditure shares of one, half, and none, respectively (see
Figure 20, all panels).
Third, suppose the taxing country spends all the tax on imports and possesses an inelastic import demand, or backward-bending offer curve. In this
case, a trade tax actually worsens the terms of trade. Geometrically, the radiant
passing through point C2 lies to the right of the free-trade ray (see Figure 20b
and d). Indeed, one can relax the assumption that all the tax is allocated to
imports. Lerner’s result holds as long as the taxer’s import-demand elasticity
is less than the fraction of the proceeds spent on imports.12
Fourth, assume the home country faces an inelastic foreign offer curve and
spends its tariff proceeds largely on its exportable good. In this case, a tariff
may improve the terms of trade by more than the tariff such that the domestic
price of imports falls below its free-trade level. Geometrically, the radiant passing through point U1 lies to the left of the free-trade ray (see Figure 20b and
c). If so, the tariff achieves the opposite of its intended purpose. By lowering
the domestic price of imports, it harms rather than protects domestic importcompeting industries and the relatively scarce factors they employ intensively.
Today, textbooks attribute this paradoxical result to Lloyd Metzler. He proved,
in 1949, that it holds when the dutying country’s marginal propensity to spend
the tariff proceeds on its own export good exceeds the foreigner’s elasticity of
demand for that good.13 But it was Lerner, not Metzler, who first established
this proposition.

6.

CONTROVERSIES IN THE 1920S AND 1930S

Offer curves also constituted the focus of Frank Graham’s (1923, 1932) celebrated critique of Marshall’s work. Graham’s critique raised issues not fully
resolved until the 1950s.
The first issue concerned the effects of demand-induced shifts in the home
country’s curve. In Appendix J of his 1923 Money, Credit and Commerce,
Marshall analyzed such shifts stemming from autonomous increases in import
demand. He argued that the resulting extent of terms-of-trade deterioration
would vary directly with the home import-demand elasticity and inversely with
12 A high import-expenditure fraction augments the demand for imports and tends to raise
their relative price. But a low elasticity spells little offsetting fall in import-quantity demanded
in response to the higher price. The resulting excess demand for imports raises their price and
causes the terms of trade to deteriorate.
13 The government’s high propensity to spend on its exportable puts upward pressure on the
domestic (and world) price of that good. But the low foreign demand elasticity militates against
offsetting falls in quantity demanded abroad in response to the higher price. The net result is an
excess demand for exportables. This excess demand raises the relative price of exports and lowers
its inverse, the relative price of imports.

T. M. Humphrey: Early Contributions to Offer-Curve Analysis

69

the foreign one. Similarly, he thought the accompanying degree of expansion
in trade volume would vary directly with both elasticities.
Graham, however, disagreed. He thought that the extent of terms-of-trade
deterioration would vary inversely with both elasticities. He also thought tradevolume expansion would vary directly with the foreign elasticity but inversely
with the home elasticity.
How could two leading economists differ over something as elementary as
the effects of shifts of offer curves? Murray Kemp supplied the answer in 1956.
The disagreement stemmed from ambiguity of the phrase “increase in reciprocal
demand.” More precisely, it stemmed from Marshall’s failure to state explicitly
the type of shift postulated. It turns out that he implicitly posited horizontal
shifts due to increases in the quantity of exports offered against a given quantity
of imports. By contrast, Graham posited equiproportional or radial shifts due to
increases in the quantity of exports offered at given terms of trade. Both were
right in terms of their own implicit definitions. Still, the controversy taught the
economics profession a lesson. Elasticity affects the extent to which demand
shifts alter price and quantity. Exactly how it does so depends on the precise
definition of such shifts (see Bhagwati and Johnson [1960], p. 78).
The second issue concerned the link between offer curves and the underlying production conditions. Graham accused Marshall, Mill, and their followers
of neglecting these conditions and overemphasizing demand. But this accusation was hardly fair since Marshall and the others always viewed the offer curve
as embodying an exhaustive classification of all its determinants, supply as well
as demand. True, Edgeworth initially derived Marshallian curves for a pure exchange economy involving no production. But he later explicitly acknowledged
underlying changes in production in his famous analogy comparing Marshall’s
offer curves to the hands of a clock driven by the workings of a complex but
hidden machinery.
The full revelation of the machinery, however, had to wait for the famous
demonstrations of Leontief (1933) and Meade (1952). Both derived offer curves
from production transformation frontiers (expressing supply conditions) and
consumption indifference curves (expressing demand conditions).
Leontief’s derivation was the simplest. He superimposed a trading country’s consumption indifference curves directly on its transformation curve. He
then assumed alternative international price ratios represented by negatively
sloped lines. Tangency of such lines with the transformation and indifference
curves gave him the quantities of the two goods produced and consumed at
each price ratio. The excess of production over consumption of the one good
and of consumption over production of the other at each price ratio constituted
export-import bundles lying on the offer curve.
Meade, on the other hand, derived offer curves in two stages (see Figure
21). First, he slid a transformation curve, or production block, along a succession of consumption indifference curves. The origin of the block traced out a set

70

Federal Reserve Bank of Richmond Economic Quarterly

Figure 21 Meade’s Derivation of the Offer Curve

y

Consumption
indifference
curves
Trade
indifference
curves

Production
block

x

0

y

H

•
•
•
•
0

Meade slides
the production
block along each
consumption
indifference curve.
The block’s origin
traces out a set of
trade indifference
curves. He then
derives the offer
curve as the locus
of the points of
tangency of the
trade indifference
curves and the
price line as it
swivels about
the origin.

x

+

of trade indifference curves, each curve showing alternative export-import
bundles that yield the same level of collective satisfaction. From these trade
indifference curves he derived offer curves just as Edgeworth had done. He
found the locus of points of tangency of trade indifference curves and alternative price rays emanating from the origin. This locus constituted the offer curve.
In deriving the curves from the underlying production conditions, Leontief and
Meade vindicated Marshall and exonerated him from Graham’s charge.

7.

CONCLUSION

Historically, the offer-curve apparatus has been put to two uses. Modern analysts employ it as a pedagogical or expository device to illustrate established
truths. By contrast, the concept’s originators applied it as an analytical tool to
derive new propositions and postulates. They used it to generate key theorems
on the gains from trade, on the efficiency of free-trade equilibrium, on the
effects of tariffs and technological change on the terms of trade, and on the
specification of the optimum rate of a tariff. That they were able to do so using
nothing more sophisticated than numerical examples and geometrical diagrams
shows what keen minds can accomplish with the simplest of analytical tools.

T. M. Humphrey: Early Contributions to Offer-Curve Analysis

71

Their successive accomplishments typify the workings of normal science
wherein the drive to perfect an existing paradigm propels advances in theory. In
their case, the paradigm consisted of the Mill-Marshall model of terms-of-trade
determination. Perfecting it meant (1) making it more precise, (2) generalizing
it to cover the widest possible range of cases, and (3) purging it of errors and
inconsistencies.
Offer-curve pioneers were more than up to these tasks. Thus Mill’s and
Torrens’ concept of reciprocal demand expunged terms-of-trade indeterminacy
from Ricardo’s analysis. Mill generalized Torrens’ unit-elastic demand schedules to include elasticities ranging from zero to infinity. Marshall generalized
Mill’s model to cover cases of (1) multiple as well as singular equilibrium and
(2) nonconstant as well as constant costs. Edgeworth’s invention of indifference
maps and the contract curve lent precision to Marshall’s concept of the gains
from trade. Lerner’s innovation, the tax pencil, helped correct Edgeworth’s error
regarding the symmetry of trade taxes. Finally, Leontief and Meade extended
the entire apparatus to include production as well as preference functions.
The result was that offer curves became a fixture of trade theory and a commonplace of textbooks. The survival of the concept testifies to its continued
usefulness. Modern students owe the originators of this tool a debt of gratitude.
Even today, if one understands the diagram, one comprehends how various
disturbances—technology shocks, resource discoveries, taste shifts, erection
and removal of trade barriers, and the like—affect the volume and terms of
world trade.

REFERENCES
Amano, Akihiro. “Stability Conditions in the Pure Theory of International
Trade: A Rehabilitation of the Marshallian Approach,” Quarterly Journal
of Economics, vol. 82 (May 1968), pp. 326–39.
Bhagwati, Jagdish, and Harry G. Johnson. “Notes on Some Controversies in
the Theory of International Trade,” Economic Journal, vol. 70 (March
1960), pp. 74–93.
Chipman, John S. “A Survey of the Theory of International Trade: Part 2,
The Neo-classical Theory,” Econometrica, vol. 33 (October 1965),
pp. 685–760.
Edgeworth, Francis Y. “On the Application of Mathematics to Political
Economy,” Journal of the Royal Statistical Society, vol. 52 (December
1889), pp. 538–76, reprinted in Francis Y. Edgeworth, Papers Relating
to Political Economy, Vol. 2. London: Macmillan (for Royal Economic
Society), 1925.

72

Federal Reserve Bank of Richmond Economic Quarterly

. “The Theory of International Values, III,” Economic Journal,
vol. 4 (December 1894a), pp. 606–38.
. “The Theory of International Values, II,” Economic Journal,
vol. 4 (September 1894b), pp. 424–43.
. Mathematical Psychics: An Essay on the Application of
Mathematics to the Moral Sciences. London: Kegan Paul, 1881.
Graham, Frank D. “The Theory of International Values Re-examined,”
Quarterly Journal of Economics, vol. 28 (November 1923), pp. 54–86,
reprinted in Howard S. Ellis and Lloyd A. Metzler, eds., Readings in the
Theory of International Trade. Philadelphia: The Blakiston Co., 1949,
pp. 301–30.
. “The Theory of International Values,” Quarterly Journal of
Economics, vol. 46 (August 1932), pp. 581–616.
Kemp, Murray C. The Pure Theory of International Trade. Englewood Cliffs,
N.J.: Prentice-Hall, 1964.
. “The Relation Between Changes in International Demand and the
Terms of Trade,” Econometrica, vol. 24 (January 1956), pp. 41–46.
Keynes, John Maynard. “Alfred Marshall, 1842–1924,” in Arthur Cecil Pigou,
ed., Memorials of Alfred Marshall. London: Macmillan, 1925, reprinted,
New York: Kelley and Millman, 1956.
Leontief, Wassily W. “The Use of Indifference Curves in the Analysis of
Foreign Trade,” Quarterly Journal of Economics, vol. 47 (May 1933),
pp. 493–503, reprinted in Howard S. Ellis and Lloyd A. Metzler, eds.,
AEA Readings in the Theory of International Trade. Philadelphia: The
Blakiston Co., 1949, pp. 229–38.
Lerner, Abba P. “The Symmetry Between Import and Export Taxes,”
Economica, vol. 3 (August 1936), pp. 306–13, reprinted in Richard
E. Caves and Harry G. Johnson, eds., AEA Readings in International
Economics. Homewood, Ill.: Richard D. Irwin, 1968.
Marshall, Alfred. The Pure Theory of Foreign Trade. Privately printed, 1879,
reprinted in amplified form in John K. Whitaker, ed., The Early Economic
Writings of Alfred Marshall 1867–1890, Vol. 2. New York: Free Press,
1975.
. Money, Credit and Commerce. London: Macmillan, 1923,
reprinted, New York: Augustus M. Kelley, 1963.
Meade, James E. A Geometry of International Trade. London: George Allen
and Unwin, Ltd., 1952.
Metzler, Lloyd A. “Tariffs, the Terms of Trade, and the Distribution of
National Income,” Journal of Political Economy, vol. 57 (February 1949),
reprinted in Richard E. Caves and Harry G. Johnson, eds., AEA Readings
in International Economics. Homewood, Ill.: Richard D. Irwin, 1968.

T. M. Humphrey: Early Contributions to Offer-Curve Analysis

73

Mill, John Stuart. “On the Laws of Interchange Between Nations: and
the Distribution of the Gains of Commerce Among Countries of the
Commercial World,” in Essays on Some Unsettled Questions of Political
Economy. 1844. Reprinted, New York: Kelley, 1968.
. Principles of Political Economy, with Some of Their Applications
to Social Policy. 1848. Edited with an introduction by W. J. Ashley,
London: Longmans, Green and Co., 1909.
O’Brien, Denis P. The Classical Economists. London: Oxford University Press,
1975.
Pennington, James. “Letter to Kirkman Finlay Esq.” 1840. Reprinted in R. S.
Sayers, ed., Economic Writings of James Pennington. London: London
School of Economics, 1963.
Pigou, Arthur Cecil, ed. Memorials of Alfred Marshall. London: Macmillan,
1925, reprinted, New York: Kelley and Millman, 1956.
Ricardo, David. On the Principles of Political Economy and Taxation. London:
Murray, 1817, reprinted in Piero Sraffa, ed., The Works and Correspondence of David Ricardo, Vol. 1. Cambridge: Cambridge University Press
(for Royal Economic Society), 1951.
Schumpeter, Joseph A. History of Economic Analysis. London: George Allen
and Unwin, 1954.
Takayama, Akira. International Trade. New York: Holt, Rinehart & Winston,
1972.
Torrens, Robert. Postscript to Letter IX of The Budget: A Series of Letters
on Financial, Commercial, and Colonial Policy. London: Smith, Elder &
Co., 1841–42.
Viner, Jacob. “Marshall’s Economics, In Relation to the Man and to His
Times,” American Economic Review, vol. 31 (June 1941), pp. 223–35.
. Studies in the Theory of International Trade. New York: Harper,
1937.

An Index of Leading
Indicators for Inflation
Roy H. Webb and Tazewell S. Rowe

M

acroeconomic forecasts attempt to provide useful information on
aggregate economic conditions. A good forecast provides a user with
specific information that allows him or her to make better decisions.
A forecast, whether explicit or implicit, underlies a wide range of choices,
such as consumer decisions on whether to spend or save, business decisions on
investments in plant and equipment, and central bank actions affecting reserve
supply.
No single approach to macroeconomic forecasting has dominated the
others. Different users may require different types of information, leading to
different forecasting methods. For example, researchers have proposed substantially different strategies for predicting the timing of an event, such as a
recession, versus predicting the magnitude of a related statistic, such as the
rate of real GDP growth. Probably most important, even the best forecasts lack
precision. Macroeconomic forecasts usually have high average errors, but even
the average size of errors can change substantially over time. It can therefore
be difficult to distinguish a good forecasting method from a mediocre one.
One approach to forecasting is to construct a theoretical model, use it to
identify the shocks affecting economic activity, and then use it for forecasting. But forecasters of inflation must confront the difficulty in modeling the
interaction of real and nominal variables. No consensus has emerged among
economists on the best way to model that interaction. The large macroeconomic
models designed specifically for forecasting typically incorporate such ingredients as a Phillips Curve relationship between wage inflation and unemployment,
and a backward-looking method for modeling how individuals form expectations. Many macroeconomists, however, do not believe that such relationships

The authors gratefully acknowledge helpful comments from Mary Finn, Robert Hetzel,
Thomas Humphrey, Peter Ireland, Stephen McNees, and Michael Niemira. The views and
opinions expressed in this article are solely those of the authors and should not be attributed
to the Federal Reserve Bank of Richmond or the Federal Reserve System.

Federal Reserve Bank of Richmond Economic Quarterly Volume 81/2 Spring 1995

75

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Federal Reserve Bank of Richmond Economic Quarterly

accurately reflect actual behavior. In the 1970s those models had large errors
when predicting inflation, which is consistent with the critics’ concerns.1
Another approach to forecasting involves using an explicit statistical model
that requires little economic theory. A prime example of this “atheoretical”
approach is the vector autoregressive (VAR) model. While that strategy has
produced relatively accurate forecasts of real variables, it has also produced inflation forecasts that not only failed to be more accurate than the large models,
but also were worse than a naive no-change forecasting method.2
This article takes a different approach to forecasting inflation. Like VAR
models, it uses little explicit theory. Unlike the standard theoretical and atheoretical models, however, its primary contribution is not to predict the magnitude
of future inflation, but rather to help recognize and predict major swings in inflation, based on an index of leading indicators for inflation (ILII). The article first
presents background information on leading indicators, followed by a detailed
account of the ILII’s construction. The index’s performance is then evaluated.
Finally, that performance is related to the business cycle and the strategy of
monetary policy.

1.

WORK BY OTHER AUTHORS ON
LEADING INDICATORS

The study of leading indicators of cyclical change was an important part of
the pathbreaking studies of business cycles conducted by scholars associated
with the National Bureau of Economic Research (NBER). This classic NBER
approach is well represented by Burns and Mitchell (1946) and Moore (1961).
That work has inspired more recent work such as that by Stock and Watson
(1989).
The performance of traditional leading indicators has been mixed. The
same, of course, can be said about every macroeconomic forecasting method.
One problem is that the best-known index, the Commerce Department’s Composite Index of Leading Indicators (CLI), does not have a precise meaning
defined by economic or statistical theory. Any evaluation of that index must
therefore begin with two key considerations: the objective of the CLI and a
method for defining signals. The objective of predicting cyclical turning points
is usually taken for granted, and perhaps the most common definition is that
two or three successive declines signal an imminent recession.
Diebold and Rudebusch (1991) evaluated the three-decline rule and also
a newer technique proposed by Neftci (1982) for using the index of leading
1 Lucas

and Sargent (1979) give a forceful statement of that view.
(1986) documents the poor performance of Robert Litterman’s VAR inflation
forecasts versus other forecasters. Webb (1995) documents the poor performance of many VAR
forecasts of inflation in comparison to the naive no-change forecast.
2 McNees

R. H. Webb and T. S. Rowe: Leading Indicators for Inflation

77

indicators to predict cyclical changes. When using originally released data and
the Neftci approach, they found at best a slight improvement over a simple rule
of always predicting a constant probability of a turning point. They found no
improvement for the three-decline rule when compared to the simple prediction.
Their negative judgment was seconded by Koenig and Emery (1991). Niemira
and Fredman (1991) found a more positive value for the index, possibly because they used revised values of the CLI instead of originally released data.
Zarnowitz (1992a) presented another positive view of the leading index. Instead
of using the usual three-decline rule, he used a multi-step rule that yielded a
more complicated signal3 of an approaching cyclical turning point. Despite
their advocacy, this rule has not been widely used, although it continued to
work well after they proposed it.
Responding to the lack of specific meaning of the Commerce Department’s
leading index, Stock and Watson (1989) proposed an index of leading indicators
that has a well-defined meaning in a particular statistical model. First, they defined a coincident index as an estimate of the unobserved state of the economy,
that is, as a measure that summarizes the economy’s position in relation to the
business cycle. They then constructed a leading index by predicting the value
of the coincident index six months ahead. They were then able to calculate a
recession index as the probability that the coincident index would decline over
the next six months. In its first post-sample test, their index failed to predict or
recognize the 1990 recession (Stock and Watson 1993).
A few authors have constructed leading indicators for inflation. Roth (1991)
gives an initial assessment of their performance. Most prominent is a leading
series constructed by Geoffrey Moore and his associates at the Center for International Business Cycle Research (CIBCR).4 That series now includes seven
constituent series, including a commodity price measure, the growth rate of
total debt, and the ratio of employment to population. Roth found that the
Moore index anticipated turning points in CPI inflation “quite well.”
All of the leading indicator indexes mentioned above share an important
characteristic: they are constructed as a weighted average of a fixed set of indicators. The weights and components, however, are subject to change at irregular
intervals according to criteria that have not been specified in advance. An index
can therefore be constructed to do well in a particular period under study, but
when the economy changes, the index will need revision. Users are thus faced
with the necessity of deciding whether a signal may have been produced by
3 The complexity of the signal results from it having three parts at peaks and troughs. The
first indication of a peak, labeled P1, is a long-leading signal that has produced several false
positives. A first confirmation, labeled P2, has had only one false positive, in 1951, and has
correctly anticipated or confirmed the eight peaks since then. The median P2 signal arrives two
months following the peak. In addition, there is a second confirming signal labeled P3 that has
had no false positives.
4 See, for example, Klein (1986).

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Federal Reserve Bank of Richmond Economic Quarterly

an out-of-date index that will be substantially revised in the near future. This
is a particular problem for a leading indicator of inflation, since changes in
monetary regimes may well change previous historical relationships.5
Sims (1989) proposed a solution for the problem of adapting an index to
a changing economic environment. In his comments on the work of Stock and
Watson (1989), he advocated using a model with time-varying coefficients,
rather than the fixed coefficients they actually employed. In addition, he proposed performing their variable selection process annually. (Stock and Watson
examined 280 series in order to select the 7 in their leading index.) Sims argued that because of abnormal events in the 1970s, Stock and Watson’s index
overemphasized interest rates, which affected estimates for the whole sample
period. That large emphasis on interest rates did lead to the failure of their
index to capture the 1990 recession, which in turn led them to propose an
alternative leading index that omits the financial variables.
The index of leading indicators for inflation that we propose incorporates
one of Sims’s suggestions. Instead of relying on a fixed set of series that will
probably be changed at an unspecified future date, we propose a strategy for
each month selecting seven indicators from a much larger set of candidates.
The following section explains that strategy in detail.6

2.

CREATING AN INDEX OF LEADING INDICATORS
OF INFLATION

To create an index of leading indicators of inflation (ILII), we initially specified
a set of time series that might be included in the ILII. Potential indicators had to
meet two criteria. First, each series had to be related to inflation in some plausible manner since we did not want to include any series that had a completely
spurious correlation with inflation. Second, in order to construct an index that
would be available promptly, we studied only potential indicators that would
be available prior to the release of the monthly CPI figures. A notable example
of a series that failed to meet the latter requirement is the capacity utilization
rate.
Table A1 in the appendix lists the potential indicators used below. Series
can be grouped into several broad categories, including money supply data,
interest rates (studied as a leading indicator of inflation, for example, by Dasgupta and Lahiri [1991]), commodity prices (for example, see Boughton and
5 For example, Webb (1995) found that two changes in the monetary regime account for the
poor forecasting record for inflation rates of VAR models using postwar U.S. data.
6 Another strategy for handling a changing relationship between indicators and inflation is
sketched by Niemira and Klein (1994, pp. 383–88). Their prediction of inflation from seven
leading indicator series is based on a neural network method, which was designed to be able to
adapt over time to certain economic changes.

R. H. Webb and T. S. Rowe: Leading Indicators for Inflation

79

Branson [1991]), and labor market measures. Note that in some cases, one
series is simply a transformation of another series, such as an interest rate
and its difference over six months. Those cases resulted if we were unsure as
to whether to remove a trend or how best to transform a nonstationary variable to a stationary one. There are 30 potential indicators, including different
transformations of the same variable.
The second step was to create a strategy to select seven series for the
index.7 Rather than following the traditional approach and using a single set of
inflation indicators for the entire sample, we developed a method for creating
an index for which components could change frequently. The strategy was
designed to use only information that would have been available to a “real
time” user; that is, the index for January 1966 would be based only on data
released by the middle of that month.
For each month from January 1958 to December 1994, the strategy was
to select the seven candidate series that had the largest correlation coefficients
with inflation. We measured inflation by the percentage change in the monthly
level of the core CPI—that is, the CPI excluding food and energy prices—
from its value 12 months earlier. We used the core CPI in order to focus on
sustained inflation trends; the core CPI removes transitory changes in the CPI
caused by movements in volatile food and energy prices.8 In order to reflect
current economic conditions, each correlation coefficient was calculated over
the most recent 48-month period rather than using a longer sample. And to
examine correlations with future inflation, we lagged each candidate series 12
months. For example, in January 1995 the latest inflation reading would be
calculated from December 1993 to December 1994, and the latest observation
of a candidate series before that inflation occurred would be December 1993.
A correlation coefficient dated January 1995 would thus be computed between
(1) inflation rates calculated using price levels from December 1989 to December 1994 and (2) a candidate series from December 1989 to December 1993.
At each date the seven selected series were then combined into a leading
indicator index. First, each series was adjusted for differences in levels and
volatility by subtracting the mean (computed over the previous 48 months) and
dividing by its standard deviation (also calculated over the previous 48 months).
To avoid undue influences from highly unusual events, such as the government’s
freeing the price of gold, each observation had a maximum absolute value
of three (larger values were accordingly reduced). Unlike the procedure for

7 Why seven? That seems to be a popular number that works reasonably well. Stock and
Watson (1989) include seven series in their index of leading indicators for predicting the real
economy. The CICBR index of leading indicators for predicting inflation has seven components,
as does the index for predicting inflation described in Niemira and Klein (1994).
8 Official data on the CPI excluding food and energy prices only extend back to 1959. For
earlier data, we used the nonfood CPI.

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Federal Reserve Bank of Richmond Economic Quarterly

producing the CLI for most of its history, the strategy employed here was to
use equal weights for the series. Our index was simply the average of the seven
transformed series.9
The graph of the resulting series, along with the 12-month change in the
core CPI, is presented in Figure 1. The inflation series is dated so that an entry
at date t is the percentage change in the core CPI from t to t + 12. Table A2 in
the appendix shows how often the various series enter the index, and Table A3
contains the composition of the index at turning points of the inflation cycle.

3.

PERFORMANCE OF THE INDEX OF LEADING
INDICATORS OF INFLATION

Ex Post Qualitative Evaluation
We experimented with the possibility of following Stock and Watson (1989) and
constructing an index with an explicit statistical meaning, namely, the forecast
of the core CPI from a bivariate VAR of the core CPI and the ILII. When such
models are estimated for U.S. data over the last 30 years, however, the estimated
coefficient on the first lagged value of the inflation rate in the price equation is
always relatively large and tends to overshadow other terms. If one then uses
that estimated equation for forecasting, it therefore tends to place such a large
weight on recent inflation that the resulting forecasts are lagging indicators
around turning points. Since the goal of the ILII is to promptly recognize or
predict sustained and substantial changes in the inflation rate, the additional lag
introduced by stating the index as a VAR forecast is unacceptable.
The ILII therefore needs a well-defined signal before its performance can be
assessed. Figure 1 indicates that the ILII tends to promptly recognize substantial
changes in inflation, although inevitably there are a lot of small fluctuations in
the graph. In order to filter out small changes, we reduced to zero those values
that had absolute values of less than one, thereby producing the series shown
in Figure 2. A signal of rising inflation is thus a value greater than or equal to
one, and a signal of declining inflation is a value less than or equal to minus
one. An observation of at least one in absolute value will be referred to as a
main signal.
The interpretation of observations with absolute values less than one is
less obvious. We adopt the rule that a main signal is valid for up to 11 months
if followed by absolute values less than one. Twelve months of such small
readings, however, can be an early signal of a turning point. We define it as
a signal if the ILII in the twelfth month is positive for a signal of rising inflation
9 Although the weights on individual series are equal, it is possible for several closely related
series to be included. The effective weight on commodity prices, for example, could be quite high.
In Table A3, note that the index in November 1983 contained six commodity price series.

R. H. Webb and T. S. Rowe: Leading Indicators for Inflation

81

Figure 1 Core CPI and Leading Indicator Index

15.0
12.5

Inflation Rate
10.0

7.5
5.0

2.5

Leading Index

0.0

-2.5
Jan
1954

58

62

66

70

74

78

82

86

90

94

Note: The inflation rate is from t to t + 12.

(that is, in the neighborhood of a trough) or if the ILII is negative for a signal of
falling inflation. An early signal remains valid until a main signal is received.
As can be seen in Figure 2 or Table 1, in several instances there is no early
signal of a turning point.
There is also no official dating of periods of substantial and sustained
changes in the rate of inflation. Inspecting Figure 1 yields the following dates:
peaks in March 1956, November 1969, February 1974, June 1979, and February
1990, and troughs in January 1962, January 1972, October 1976, August 1982,
and possibly in December 1993. There is, of course, room for disagreement
about particular dates. The hardest call was whether to define another peak and
trough in the mid-1980s. Other authors, looking at slightly different data, have
taken opposing sides. Roth (1989) argued that “[t]he eleven-month upturn in
inflation beginning in March 1983 is most likely a statistical artifact” (p. 283).
Moore (1991), however, found a peak in early 1984 and a trough in 1986. By
looking at the 12-month forward rate of change of the core CPI, one can see
that inflation reached a local minimum in August 1982 at 3.1 percent. It then
rose to 5.3 percent in July 1983, which is a substantial change. However, it
then fell to 4.2 percent by July 1984 and to 3.8 percent in November 1985.
Thus the bulk of the increase was not sustained but rather was fairly quickly

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Federal Reserve Bank of Richmond Economic Quarterly

Figure 2 Core CPI and Filtered Leading Indicator Index

15.0

12.5

Inflation Rate
10.0
7.5

5.0
2.5

Leading Index

0.0
-2.5
Jan
1954

58

62

66

70

74

78

82

86

90

94

Note: The inflation rate is from t to t + 12.

reversed. Accordingly, the 11-month upswing is not counted as a substantial
and sustained increase in the rate of inflation.
Table 1 contains the resulting inflation signals from the ILII and compares
them with peaks and troughs. The index is helpful in recognizing major changes
in inflation rates, but often does not anticipate turning points; the median time
for receiving the first signal is five months after the turning point. The 1990
peak is the only one that is clearly predicted, although the turn is recognized
immediately at the November 1969 peak. If December 1993 or a nearby date
turns out to be a trough, the ILII will have given a prompt signal; it is possible,
however, that it will turn out to be a false signal. The worst performance is the
1982 trough, which is only recognized after 15 months. Other turning points
are recognized within a year. Importantly, no false signals are generated10 and
no turning points are missed. In addition, although the ILII appears to recognize, not anticipate, the dates of major changes in the rate of inflation, Table
2 presents evidence that it does anticipate the bulk of the change in the inflation rate. The change in the inflation rate before a signal is no greater than 0.5
10 A

false signal would be one that is later reversed before a predicted peak or trough occurs.

Date of Turning Point
Peak, March 1956
(April 1957)
Trough, January 1962
(January 1963)
Peak, November 1969
(April 1970)
Trough, January 1972
(January 1973)
Peak, February 1974
(October 1974)
Trough, October 1976
(December 1976)
Peak, June 1979
(April 1980)
Trough, August 1982
(March 1983)
Peak, February 1990
(August 1990)
Trough? December 1993

Early Signal

Main Signal

Lead (+) or Lag (−)
from First Signal

Recognition Rule

Down, January 1958
Up, June 1959

na

Up, September 1964

+31

January 1964

0

August 1971

Down, November 1969
Up, June 1972

Up, March 1973
Down, January 1975

−5
−11

November 1958

November 1973
June 1975

Up, November 1983

−7

October 1978

Down, June 1980

Up, May 1977

−12

January 1981

Up, May 1987

−15

March 1984

Up, May 1978

Down, August 1989
Up, December 1993

6

Up, June 1994

February 1992

0?

83

Notes: The leading indicator series begins in January 1958 and ends in December 1994. Peaks and troughs correspond to the 12-month percentage change in
the CPI excluding food and energy, as shown in Figures 1 and 2. (The dates in parentheses are peaks and troughs in the “6-month smoothed inflation rate”
discussed in the text and footnote 11.) The inflation series begins in January 1954 and ends in December 1993 and represents the inflation rate from each date
to 12 months ahead. The last trough, identified by the question mark, is tentative. The rightmost column presents the first date that a two percentage point
change in the inflation rate from a previous turning point could have been observed.

R. H. Webb and T. S. Rowe: Leading Indicators for Inflation

Table 1 Turning-Point Signals from the Index of Leading Indicators of Inflation

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Federal Reserve Bank of Richmond Economic Quarterly

Table 2 Inflation Rates Before and After Lagging Signals of
Turning Points

Turning-Point
Date

Inflation Rate,
Previous
Turning Point
to First Signal

Inflation Rate
at Next
Turning Point

Anticipated
Change

Unanticipated
Change

January 1972
February 1974
October 1976
June 1979
August 1982

2.8
11.8
6.2
13.6
3.6

11.9
6.0
13.6
3.1
5.7

9.1
5.8
7.4
10.5
2.1

0.3
0.1
0.2
0.0
0.5

Notes: The table presents turning-point dates for which the first signal from the leading index
occurred after a turning point. The first column lists turning-point dates at which a lagging signal
of a turning point was given. The second column gives the annualized rate of change in the
core CPI from the turning-point date to the date of the first signal given by the ILII. The third
column gives the rate of inflation at the next turning point. The fourth column represents the
change in inflation after a signal is received, calculated as the difference between column three
and column two. The last column represents the change in inflation before a signal is received
and is calculated as the difference between the inflation rate at the previous turning point and the
value listed in column two.

percent, whereas the change after the signal is received ranges from 2.1 to
10.5 percent.
Although the format of Table 1 and Figure 2 may at first glance resemble
those used by others who have evaluated leading indicators, such as Klein
(1986), Moore (1991), and Roth (1991), there is a key difference. The other
authors compare the value of a leading indicator with inflation calculated as the
contemporaneous value’s change from lagged values. Thus they are comparing
an indicator with lagging inflation, a comparison that may not be relevant for
actual use of a leading index. Our analysis compares the leading indicator with
future inflation. The difference can be seen in Table 1, in which inflation is also
calculated in the manner used by the other authors, and the resulting dates of
turning points are displayed in parentheses. From those dates it would appear
that the index has more predictive power than originally indicated, even though
the ILII is unchanged. What has changed is the method of calculating inflation,
which shifts the dates of turning points forward by a little over eight months,
on average.11
Recognizing major swings in inflation is not always a simple exercise, as
Cullison (1988) demonstrates. An example is 1972: inflation’s low point was
11 The

alternative method of calculating inflation is referred to as the “6-month smoothed
annual rate.” It is calculated as the ratio of the current month’s price index to the average index
of the preceding 12 months and is converted to an annual rate by raising the ratio to the 12/6.5
power.

R. H. Webb and T. S. Rowe: Leading Indicators for Inflation

85

in January, and the ILII gives an early signal in June, lagging the change by
five months. The following commentary on a well-regarded model’s forecasts
is recorded by Cullison:
April, 1972: “The rate of price increase is expected to slow. . . . The anticipated slowing . . . reflects the large projected rise in real product and associated
productivity gains.”
June, 1972: “The rise in the [GNP implicit price] deflator is expected to . . .
moderate. . . . The expected moderation reflects a moderation in the rise in
unit labor costs.”
May, 1973: “The projected slowdown in the rise in the private GNP fixed
weight price index reflects primarily the anticipation that food price increases
will slow sharply.”12

As this example illustrates, having leading indicators that began to signal
rising inflation in June 1972 could have been valuable to forecasters. Another
comparison can be seen by using the rightmost column of Table 1, in which
each entry denotes the first date at which one could observe a 200 basis point
change in the inflation rate after a turning point. The ILII signals turning points
much sooner than that simple rule.
While the index appears to perform well, that judgment is based on the
same data that were used to construct the index; its actual performance will
be revealed by new data. The apparent performance of the index undoubtedly
could have been improved by a systematic search over parameters such as
the number of series, the weights on each series, the magnitude of the main
signal, or the number of months required for either a main signal or an early
signal. The future performance of an index so constructed undoubtedly would
deteriorate, however. We therefore picked obvious values that seemed to work
well, but a caveat remains. Any choice that we made would have been rejected
if it conflicted with the data. The proof of how well the index works must
await new data that were not used to construct it. An additional caveat is that
we used the latest revisions of data, not data as originally released. That fact
should be less important for this index than for the Commerce Department’s
CLI, however, since most of the individual series employed in this paper are
not revised by substantial amounts.
Simulated Forecasts
Another check on whether the ILII contains useful information is to test whether
it adds predictive power to lagged values of inflation. To test for additional
12 Cullison’s quotations are from the Greenbook, prepared by the staff of the Board of Governors of the Federal Reserve System prior to meetings of the Federal Open Market Committee.
Karamouzis and Lombra (1989) have conducted a thorough examination of the quality of these
forecasts and have concluded that the forecasts were “state of the art” in comparison with other
macroeconomic forecasts.

86

Federal Reserve Bank of Richmond Economic Quarterly

predictive power, we constructed a bivariate VAR for monthly percentage
changes in the core CPI and the level of the ILII. We first set lag lengths
in the VAR by minimizing the Akaike Information Criterion over each lag
length in each equation, resulting in the following equations:
9

Pt = β10 +

β11,i Pt−i + β12 ILIIt + e1,t ,

(1)

i=1
2

ILIIt = β20 +

3

β21,i Pt−i +
i=1

β22,i ILIIt−i + e2,t ,

(2)

i=1

where P is the percentage change in the core CPI from the previous month, ILII
is the index of leading indicators of inflation, β is the model’s coefficients, and
e is the error term. For comparison we also estimated a univariate autoregression for the core CPI, using nine lagged values. The equations were estimated
starting in 1958:1 and ending in 1969:12, and out-of-sample forecasts were
made up to 12 months ahead. One month was then added to the period, the
equations were reestimated, and new forecasts were made. We repeated this
process to create series of 12-month inflation forecasts for the period 1970:12
to 1994:12.
Forecast errors were calculated as the difference between actual inflation
and forecasted values, and summary statistics were calculated. The root mean
squared error for the univariate forecasts was 2.19; it fell to 1.96 for the bivariate
forecasts. Comparing the two series of squared errors, we found the difference
to be significant at the 1 percent level according to a test proposed by Diebold
and Mariano (1991). We conclude that the index does contain information with
significant predictive value beyond that contained in the inflation series itself.
The size of the forecast error, however, is a reminder of substantial remaining
uncertainty in forecasts from this method. For perspective, consider that in the
post-1983 period the average 12-month change in the core CPI was 4.2 percent. Taking the root mean squared error as an approximation of the anticipated
standard error of current forecasts, even a 70 percent confidence interval, ±2
percent, includes a wide range of outcomes.
We also estimated equation (1) over the entire sample period. The average
error was again significantly lower when the ILII was included, indicating that
it significantly improved one-month forecasts of inflation.

4.

WHY THE INDEX APPEARS TO WORK,
AND WHAT COULD CHANGE

On the basis of experience in the United States and other industrial countries
before 1913, Wesley Mitchell (1941) presented an account that describes a

R. H. Webb and T. S. Rowe: Leading Indicators for Inflation

87

stylized business cycle. The behavior of prices played a key role in that account,
as the following passages illustrate.
A revival of activity, then, starts with this legacy from depression: a level
of prices low in comparison with the prices of prosperity, drastic reductions
in the cost of doing business [p. 150]. While the price level is often sagging
slowly when a revival begins, the cumulative expansion in the physical volume
of trade presently stops the fall and starts a rise [p. 151]. Like the increase
in the physical volume of business, the rise in prices spreads rapidly; for
every advance of quotations puts pressure upon someone to recoup himself
by making a compensatory advance in the prices of what he has to sell. . . .
Retail prices lag behind wholesale . . . and the prices of finished products
[lag] behind the prices of their raw materials [p. 152]. [O]ptimism and rising
prices both support each other and stimulate the growth of trade [p. 153].
Among the threatening stresses that gradually accumulate within the system
of business during seasons of high prosperity is the slow but sure increase in
the costs of doing business [p. 29]. The price of labor rises. . . . The prices
of raw materials continue to rise faster on the average than the selling prices
of products [p. 154]. [T]he advance of selling prices cannot be continued
indefinitely . . . [because] the advance in the price level would ultimately
be checked by the inadequacy of the quantity of money [p. 54]. [Once a
downturn begins] with the contraction in trade goes a fall in prices [p. 160].
[T]he trend of fluctuations [in prices] continues downward for a considerable
period. . . . [T]he lowest level of commodity prices is reached, not during the
crisis, but toward the close of the subsequent depression, or even early in the
final revival of business activity. The chief cause of this fall is the shrinkage
in the demand for consumers’ goods, raw materials, producers’ supplies, and
construction work [p. 134]. [E]very reduction in price facilitates, if it does not
force, reductions in other prices [p. 160]. Once these various forces have set
trade to expanding again, the increase proves cumulative, though for a time
the pace of growth is kept slow by the continued sagging of prices [p. 162].

Zarnowitz (1992b) reviewed the literature and found that much of
Mitchell’s account has been consistent with cyclical data generated after he
wrote it. There has been an important change, however. Under the gold standard there was little, if any, trend to the price level, and prices could fall in one
phase of the business cycle and rise in another. In contrast, American monetary
policy in the last 50 years has put in place an upward trend in prices. Thus,
where Mitchell observed prices declining when cyclical contractions ended and
expansions began, one now observes inflation being relatively low. Similarly,
toward the end of expansions Mitchell saw price increases, but one now would
see relatively high inflation.
Table 3 presents some evidence on this last point by looking at the behavior
of inflation and other statistics over the business cycle. Expansions are divided
into four segments of equal length, and contractions are divided into two equal
segments. The inflation rate is calculated for each cycle, measured on a troughto-trough basis. For each segment of the cycle, the average inflation rate for

88

Federal Reserve Bank of Richmond Economic Quarterly

the cycle is subtracted from the inflation rate for that segment; the result is
a relative inflation rate for each cyclical segment. The relative rates can then
be averaged over the last seven business cycles in order to depict the average
cyclical behavior of inflation. The picture is clear: inflation is low early in a
cyclical expansion, is relatively high in the last quarter of expansion, and peaks
in the first half of recessions. Inflation is therefore procyclical in the sense that
its rate increases during expansions and declines during contractions. It is also
a lagging indicator in the sense that its highest rate usually occurs after the
cyclical peak and its lowest rate usually occurs after the cyclical trough.13 The
leading indicator series anticipates that behavior by peaking in the third quarter
of a typical expansion and hitting its low point in the last half of recessions.
It therefore appears that the leading indicator index is capturing a regular
feature of the business cycle. High-frequency changes in inflation, which are
clearly not sustained, are ignored by design. Changes in inflation rates between
business cycles are also excluded from the picture. What is left are cyclical
movements that have been reliable and predictable. An individual indicator can
be a useful predictor if it has a definite place in the sequence of events of a
typical business cycle.
Consequently, this index has a reason for working and does not simply
reflect a spurious correlation. It is designed to continue to work under certain
changing conditions. If any particular indicator were to change its cyclical
behavior, its correlation with inflation would diminish and it would not be included in the index. Similarly, adding new indicators would be straightforward.
The one event that could drastically change the role of the index would be a
substantial change in the strategy of monetary policy. After all, the shift from
the gold standard to a fiat money system that involved a particular central bank
strategy changed the cyclical behavior of prices to the cyclical behavior of
inflation. A different monetary strategy might cause another dramatic change
that could change the role of this index.
For example, imagine a monetary strategy that eliminated the trend in
prices by keeping inflation rates small in magnitude and centered on zero.
Without sustained and substantial changes in inflation, would the index have
any purpose? Certainly the strategy of choosing indicators by past correlations
with inflation would need replacing. For a closely related example, imagine
a monetary strategy that eliminated large fluctuations in inflation by keeping
it relatively low but positive. In that case, the index would be much more
13 Some authors, such as Cooley and Ohanian (1991), have asserted that prices are countercyclical. By their definition, prices are countercyclical if there is a negative correlation between
the level of prices and the level of output when the same statistical transformation is applied to
both series. For example, in Table 3 there is a negative comovement between real GDP growth and
inflation: during the segment of the business cycle where one series peaks, the other series reaches
its lowest value. Their finding does not contradict the statement that inflation is procyclical, using
the usual NBER definition for procyclical.

Table 3 Cyclical Behavior of Inflation and Other Series

Statistic

Expansion
First Quarter

Expansion
Second Quarter

Expansion
Third Quarter

Core CPI

−0.40

−0.45

−0.53

1.66

2.09

0.90

CPI

−1.28

−0.90

0.15

2.14

2.21

0.91

PPI, Finished Goods

−1.57

−1.44

0.95

1.75

3.22

0.34

ILII

−0.21

0.02

0.51

0.28

−0.11

−0.85

3.55

2.42

0.43

−0.61

−6.10

−3.52

Real GDP

Expansion
Fourth Quarter

Recession
First Half

Recession
Second Half

Notes: Entries for all statistics except the ILII are relative rates of change. Each is calculated by subtracting the average rate of change over each business
cycle from the rate of change during each segment of the business cycle, and then averaging over all post-Korean War cycles (the core CPI begins with the
business cycle trough of 1958). The ILII is the relative value, calculated by subtracting the average value over each business cycle from the average value in
each segment and then averaging over the post-1960 business cycles.

90

Federal Reserve Bank of Richmond Economic Quarterly

valuable if it could give a third signal, stable inflation, in addition to signals of
inflationary increases and decreases.
This latter possibility can be illustrated with the ILII. The following rule
for a stable price signal is added in order to identify periods in which the index
is low and stable. If the level of the index, the 12-month change in the index,
and the 12-month average value of the index are all less than 0.3, then a stable
inflation period is signaled. This signal overrides the early signal of a turning
point and, in turn, is overridden by a main signal.
That rule gave two signals that identify the two major periods of stable
inflation in the sample period. The first signal was in May 1960; the inflation rate was within a two percentage point range from April 1957 until June
1965, with the low point in February 1960 and the first main signal of an
upswing occurring in September 1964. The second was in March, 1984; the inflation rate was within a two percentage point range from September 1982 until
July 1989, with the first main signal of an upswing occurring in May 1987.
Based on those two observations, it appears that the index can be adapted to
recognizing periods of stable inflation as well as signaling major changes in
the inflation rate.

5.

CONCLUSION

We have proposed a strategy for constructing an index of leading indicators for
inflation. The goal is to recognize or predict sustained and substantial changes
in the rate of inflation. A notable feature of our strategy is that it allows the
composition of the index to change over time in response to changing economic
conditions.
Our evaluation of the index emphasized its link to future inflation rates.
In contrast, other evaluations of inflation indicators have often looked at less
relevant lagging inflation rates. Our index appears to have value recognizing,
and sometimes predicting, major swings in inflation. Important to its possible
use is the fact that no false signals were generated and no turning points were
missed. In each case, the index allowed the bulk of the change in inflation
rates to be anticipated. And although the index was not designed to forecast
the magnitude of inflation, it did help lower the forecast error for inflation rates
in a simple model.
The performance of the index was related to typical movements of inflation
over the business cycle. Whereas inflation is a procyclical but lagging indicator, the leading index typically peaks in the middle of expansions and has its
lowest value in the first half of recessions. While this cyclical behavior should
be robust in many environments, a major change in the strategy of monetary
policy could substantially change the value of such an index. We illustrated the
possibility of using the index to recognize periods of stable inflation.

R. H. Webb and T. S. Rowe: Leading Indicators for Inflation

91

It should be emphasized that the same data were used to construct the
index and evaluate its performance. Since out-of-sample data will give the best
test of the index’s usefulness, the performance of the index outside the sample
period will be studied in future research.

APPENDIX :

SERIES USED IN THE INDEX OF
LEADING INDICATORS FOR INFLATION

The appendix lists the series used to create the index of leading indicators
for inflation. Table A1 contains series originally provided by the following
sources: the Bureau of Labor Statistics (BLS), the Board of Governors of the
Federal Reserve System (FRB), the Federal Reserve Bank of St. Louis (FSL),
the National Association of Purchasing Management (NAPM), The Wall Street
Journal (WSJ), the Journal of Commerce (JOC), the Commodity Research
Bureau (CRB), and the Treasury Bulletin (TB). Data used in this article were
obtained from secondary sources. The starting date, either January 1954 or the
first month for which the transformed series is available, is affected by data
availability and the particular method used for detrending data. Detrending
methods are denoted by superscripts.
Table A2 provides further information on the series, as well as how often
the individual series are included in the seven-series index. All three labor
utilization measures are included more frequently than any other series. The
NAPM price index is the only other series included more than half the time.
Table A3 gives the composition of the leading index at times of inflation
turning-point signals. Again, the three labor utilization measures and the NAPM
price index are included more frequently than other series.

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Federal Reserve Bank of Richmond Economic Quarterly

Table A1 Candidates for the Index of Leading Indicators for Inflation

Source

Series
Start

BLS
BLS
BLS

1954:1
1954:1
1954:1

FRB
FRB
FSL
FRB
FRB

1954:1
1954:1
1954:1
1954:8
1954:1
1954:8

Commodity price diffusion index
Price of gold, London fix
Producer price index, crude oil
Price index of industrial commodities
Spot price index
Futures price index
Producer price index—finished goods
Producer price index—intermediate goods
Producer price index—crude goods

NAPM
WSJ
BLS
JOC
CRB
CRB
BLS
BLS
BLS

1954:1
1967:12
1960:1
1954:1
1981:12
1970:7
1974:7
1974:7
1974:7

Supplier deliveries diffusion index
Lead time for orders and materials
Trade-weighted value of the dollar
Average hourly earnings
Federal government debt

NAPM
NAPM
FRB
BLS
TB

1960:1
1977:1
1960:1
1968:7
1958:7

Mnemonic

Definition

Labor Utilization
Ua
EPa
HRa

Civilian unemployment rate
Employment to population ratio
Index of aggregate weekly hours

Money and Interest Rates
M1b
M2b
MBb
RFFc
RT10c
RSP

M1 money supply
M2 money supply
Monetary base
Federal funds rate
Ten-year Treasury bond rate
RT10−RFF

Commodity Prices
PN
PAUd
POd
PJCd
PCSe
PCFd
PPIFb
PPIIb
PPICb
Other Indicators
SUP
LD
XD
Wb
FDb

a Each value is the ratio of the current month to the five-year average ending in the previous
month.
b Each value is the six-month difference of logarithms of the variable.
c The series is used both in level form and in the difference over six months.
d The series is used in two forms; one is detrended by the method described in footnote a, and
the other is detrended by the method described in footnote b.
e Each value is the ratio of the current month to the one-year average ending in the previous
month.

R. H. Webb and T. S. Rowe: Leading Indicators for Inflation

93

Table A2 Candidate Series Selected for Leading Indicator Index
Candidate
Series

Number of
Months Available

Number of
Months Included

Percent

U
EP
HR

444
444
444

275
307
247

62
69
56

M1
M2
MB
RFF, level
RFF, difference
RT10, level
RT10, difference
RSP

444
444
444
437
431
444
444
437

86
118
93
191
64
64
103
60

19
27
21
44
15
14
23
14

PN
PAU∗
PAU, difference
PO∗
PO, difference
PJC∗
PJC, difference
PCS∗
PCS, difference
PCF∗
PCF, difference
PPIF
PPII
PPIC

444
318
372
372
372
444
444
104
109
193
246
198
198
198

226
87
55
55
91
193
132
45
34
58
51
11
82
39

51
27
15
15
24
43
30
43
31
30
21
6
42
20

SUP
LD
XD
W
FD

372
168
372
337
390

120
47
67
50
57

32
28
18
15
15

∗

Ratio of the value of the variable divided by a trailing five-year average (one-year average
for PCS).
Notes: The first column lists each candidate series (see Table A1 for more complete descriptions).
The second column lists the maximum number of months each series could enter the ILII. The
third column lists the number of months the mechanical method outlined in the text selected each
series to enter the index. The fourth column shows the ratio of column 3 to column 2.

94

Federal Reserve Bank of Richmond Economic Quarterly

Table A3 Composition of Index of Leading Indicators of Inflation at
Dates of Turning-Point Signals

Series
U
EP
HR
M1
M2
MB
RFF
∆RFF
RT10
∆RT10
RSP
PN
PAU
∆PAU
PO
∆PO
PJC
∆PJC
PCS
∆PCS
PCF
∆PCF
PPIF
PPII
PPIC
SUP
LD
XD
W
FD

Jan
58

June
59

+
+
+

Nov
69

+
+
+

June
72

Jan
75

May
77

June
80

Nov
83

Aug
89

Dec
93

Total

+
+
+

+
+
+

+
+
+

+
+
+

+

+

+
+
+

9
7
7

+
+

+

+

+
+

+
+

+

+
+

+

+

+

+

+

+
+

+

+
+

+
+

+
+

+
+

+

+

+

+
+
+
+

+

+

+

+
+

+
+

+

+

+
+

+

+

1
2
0
2
1
1
3
1
7
4
1
0
1
5
2
1
0
2
2
0
2
2
5
0
0
1
1

R. H. Webb and T. S. Rowe: Leading Indicators for Inflation

95

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