Reprinted with Permission
Gibson's Paradox Revisited: Professor Summers Analyzes Gold Prices
Due in no small measure to articles he wrote as a young economist,
especially his 1966 essay "Gold and Economic Freedom"
(reprinted in A. Rand, Capitalism: The Unknown Ideal),
Fed chairman Alan Greenspan is widely recognized as quite an
authority on gold. Far less widely known are professional articles
on gold by another young economist who also went on to serve
until quite recently in some of the nation's top economic policy
Not long before joining the new Clinton administration as
undersecretary of the treasury for international affairs, Harvard
president and former treasury secretary Lawrence H. Summers,
then Nathaniel Ropes professor of political economy at Harvard,
co-authored with Robert B. Barsky an article entitled "Gibson's
Paradox and the Gold Standard" published in the Journal
of Political Economy (vol. 96, June 1988, pp. 528-550). The
article, which appears to draw heavily on a 1985 working paper
of the same title by the same authors, is an excellent technical
piece, revealing a high level of expertise regarding gold, gold
mining, and the interconnections among gold prices, interest
rates, and inflation.
Indeed, for any administration concerned that the bond vigilantes
on Wall Street might thwart its economic policies by pushing
up long-term rates at inopportune times, the article is must
reading and qualifies its authors as attractive candidates for
government service. Of even more interest looking at the Clinton
administration retrospectively, the article provides strong theoretical
evidence that since 1995 gold prices have not acted as would
normally be expected in a genuine free market, but instead have
behaved as if subject to what the authors describe as "government
Lord Keynes gave the name "Gibson's paradox" to
the correlation between interest rates and the general price
level observed during the period of the classical gold standard.
It was, he said, "one of the most completely established
empirical facts in the whole field of quantitative economics."
J.M. Keynes, A Treatise on Money (Macmillan, 1930), vol.
2, p.198. And it was a paradox because contemporary monetary
theory, largely associated with Irving Fisher, suggested that
interest rates should move with the rate of change in prices,
i.e., the inflation rate or expected inflation rate, rather
than the price level itself. Yet when Keynes wrote, data for
the prior two centuries showed that the yield on British consols
(government securities issued at a fixed rate of interest but
with no redemption date) had moved in close correlation with
wholesale prices but almost no correlation to the inflation rate.
Economists have long tried to find a theoretical explanation
for Gibson's paradox. Professors Summers and Barsky provide the
following executive summary of their contribution to this debate
A shock that raises the underlying real rate of return in
the economy reduces the equilibrium relative price of gold and,
with the nominal price of gold pegged by the authorities, must
raise the price level. The mechanism involves the allocation
of gold between monetary and nonmonetary uses. Our explanation
helps to resolve some important anomalies in previous work and
is supported by empirical evidence along a number of dimensions.
They begin their article with an examination (at 530-539)
of the data supporting the existence of Gibson's paradox, concluding
that it was "primarily a gold standard phenomenon"
(at 530) that applies to real rates of return. Regression analysis
of the classical gold standard period, 1821-1913, shows a close
correlation between long-term interest rates and the general
price level. The correlation is not as strong for the pre-Napoleonic
era, 1730-1796, when Britain effectively adhered to the gold
standard but many other nations did not, and "completely
breaks down during the Napoleonic war period of 1797-1820, when
the gold standard was abandoned" (at 534).
Nor is the evidence of Gibson's paradox as strong for the
period of the interwar gold exchange standard, 1921-1938, which
was marked by active central bank management and restrictions
on gold convertibility. Following World War II, the correlation
weakened substantially under the Bretton Woods system, and "[t]he
complete disappearance of Gibson's paradox by the early 1970s
coincides with the final break with gold at that time" (at
With the nominal price of gold fixed, Barsky and Summers note
(at 529) that "the general price level is the reciprocal
of the price of gold in terms of goods. Determination of the
general price level then amounts to the microeconomic problem
of determining the relative price of gold." For this, they
develop a simple model (at 539-543) that assumes full convertibility
between gold and dollars at a fixed parity, fully flexible prices
for goods and services, and fixed exchange rates.
Next, they examine the response of the model to changes in
the available real rate of return. In this connection, they observe
(at 539): "Gold is a highly durable asset, and thus ...
it is the demand for the existing stock, as opposed to the new
flow, that must be modeled. The willingness to hold the stock
of gold depends on the rate of return available on alternative
assets." With respect to the gold stock, the model distinguishes
between bank reserves (monetary gold under the gold standard)
and nonmonetary gold, principally jewelry.
Summarizing the mathematical formulas of the model, Barsky
and Summers make two key points. The first (at 540):
The price level may rise or fall over time depending on how
the stock of gold, the dividend function [formulaic abbreviation
omitted] and the demand for money [formulaic abbreviation omitted]
evolve over time. Secular increases in the demand for monetary
and nonmonetary gold caused by rising income levels tend to create
an upward drift in the real price of gold, that is secular deflation.
Tending to offset this effect would be gold discoveries and technological
innovations in mining such as the cyanide process.
And the second (at 542):
The economic mechanism is clear. Increases in real interest
rates raise the carrying cost of nonmonetary gold, reducing the
demand for it. They also reduce the demand for monetary gold
as long as money demand is interest elastic. The resulting reduction
in the real price of gold is equivalent to an increase in the
general price level.
Because the model is "essentially a theory of the relative
price of gold," Barsky and Summers postulate (at 543) that
"an important test of the model is to see how well it accounts
for movements in the relative price of gold (and other metals)
outside the context of the gold standard." They continue
The properties of the inverse relative prices of metals today
ought to be similar to the properties of the general price level
during the gold standard years. We focus on the period from 1973
to the present, after the gold market was sufficiently free from
government pegging operations and from limitations on private
trading for there to be a genuine "market" price of
And they conclude (at 548):
The price level under the gold standard behaved in a fashion
very similar to the way the reciprocal of the relative price
of gold evolves today. Data from recent years indicate that changes
in long-term real interest rates are indeed associated with movements
in the relative price of gold in the opposite direction and that
this effect is a dominant feature of gold price fluctuations.
In other words, the bottom line of their analysis is that
gold prices in a free market should move inversely to real interest
rates. Under the gold standard, higher prices meant that an ounce
of gold purchased fewer goods, i.e., the relative price
of gold fell. Since under the Gibson paradox long-term interest
rates moved with the general price level, the relative price
of gold moved inversely to long-term rates. Assuming, as Barsky
and Summers assert, that the Gibson paradox operates in a truly
free gold market as it did under the gold standard, gold prices
will move inversely to real long-term rates, falling when rates
rise and rising when they fall.
To test this proposition, particularly for the period after
1984 not covered by Barsky and Summers in their 1988 article,
Nick Laird has constructed the following chart at my request.
Nick is the proprietor of www.sharelynx.net,
which offers an excellent collection of charts relating to gold
and financial matters, and I am most grateful for his assistance.
The chart plots average monthly gold prices on the inverted right
scale, i.e., higher prices at the bottom. Real long-term
rates are plotted on the left scale. They are defined as the
30-year U.S. Treasury bond yield minus the annualized increase
in the Consumer Price Index (calculated as the sum of the monthly
CPI increases for the preceding twelve months).
As the chart shows, Gibson's paradox continued to operate
for another decade after the period covered by Barsky and Summers.
But sometime around 1995, real long-term interest rates and inverted
gold prices began a period of sharp and increasing divergence
that has continued to the present time. During this period, as
real rates have declined from the 4% level to near 2%, gold prices
have fallen from $400/oz. to around $270 rather than rising toward
the $500 level as Gibson's paradox and the model of it constructed
by Barsky and Summers indicates they should have.
The historical evidence adduced by Barsky and Summers leaves
but one explanation for this breakdown in the operation of Gibson's
paradox: what they call "government pegging operations"
working on the price of gold. What is more, this same evidence
also demonstrates that absent this governmental interference
in the free market for gold, falling real rates would have led
to rising gold prices which, in today's world of unlimited fiat
money, would have been taken as a warning of future inflation
and likely triggered an early reversal of the decline in real
Other analysts have noted the inverse relationship between
real rates and gold prices. An interesting and informative recent
article along these lines is Adam Hamilton's Real
Rates and Gold, which makes reference to a 1993 Federal Reserve
study containing the following statement: "The Fed's attempts
to stimulate the economy during the 1970s through what amounted
to a policy of extremely low real interest rates led to steadily
rising inflation that was finally checked at great cost during
The low real long-term interest rates of the past few years
may have been engineered with far more sophistication than those
of a generation ago, including the coordinated and heavy use
of both gold and interest rate derivatives. By demonstrating
that falling real long-term rates will lead to rising gold prices
absent government interference in the gold market, Barsky and
Summers underscore the futility of trying to control the former
without also controlling the latter. But they do not provide
a model for successful long-term suppression of gold prices in
the face of continued low real rates.
What they do indicate (at 548), however, is that their model
of Gibson's paradox accords only a "minimal role [to] new
gold discoveries" and fails to account fully for shifts
between monetary and nonmonetary gold. As they note (at 546-548),
the fraction of the total gold stock held in nonmonetary form
during the gold standard era was substantial, perhaps exceeding
one-half, and the fraction varied over time. Also (at 548), "the
post-1896 rise in prices, after more than two decades of deflation,
is usually attributed to gold discoveries in combination with
the development of the cyanide process for extraction."
Accordingly, they conclude (at 548-549) that their "proposed
resolution of the Gibson paradox cannot be the whole answer"
and that determination of "the quantitative importance of
the mechanism in this paper would require better methods for
proxying movements in the stocks of monetary and nonmonetary
gold, and this might be an appropriate topic for further research."
The unusual and sharp divergence of real long-term interest rates
from inverted gold prices that began in 1995 suggests that Mr.
Summers found an opportunity to do some further applied research
on these matters during his tenure at the Treasury.
Both the heavy use of forward selling by mining companies
and the World Gold Council's obsession with promoting gold as
jewelry to the near exclusion of its historic monetary role appear
designed to exploit the conceded points of vulnerability in the
operation of the model. Viewed in this light, these two novel
and distinguishing features of the post-1995 gold market appear
less accidental and more as the handmaidens of the government
price-fixing operations that the model reveals.
At the time of his appointment, Professor Summers was the
youngest tenured professor in Harvard's modern history. On Friday,
October 12, 2001, in outdoor ceremonies in Tercentenary Theatre,
he will be formally installed as its 27th president, entrusted
with the job of leading the nation's oldest university -- where
"Veritas" is the motto -- into the new millennium.
Three days earlier, in Courtroom No. 11 of the new U.S. Courthouse
on Boston Harbor, the search for the truth about his interim
service in the highest positions at the U.S. Treasury will resume.
Judge Lindsay has scheduled a hearing on the defendants' motions
to dismiss for Tuesday, October 9, at 3:30 p.m. The underlying
issue in that proceeding is whether the Constitution and laws
of the United States may be enforced in a federal court action
challenging the authority of Mr. Summers and other American officials,
working at least in part through the Bank for International Settlements,
to conduct the surreptitious and illegal gold price-fixing operations
exposed even by his own academic research.
Aug 22, 2001