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Economic
•
eview
Federal Reserve Bank
of San Francisco
Fall 1988

Number 4

Ramon Moreno

Saving, Investment, and the
U.S. External Balance

Carl E. Walsh and
Peter R. Hartley

Financial Intermediation, Monetary Policy,
and Equilibrium Business Cycles

Randall Johnston Pozdena

Banks Affiliated with Bank Holding Companies:
A New Look at their Performance

Ronald H. Schmidt

Hotelling's Rule Repealed?
An Examination of Exhaustible Resource Pricing

Table o f Contents

Saving, Investment, and the
UoSo Externa! Balance „»0.„0..

0„„.... 0<0„«.».00»..«, ©< e»»o•», •» , . . .... „ 3
,
. ,•„
«

Ramon Moreno

Financial Intermediation, Monetary Policy,
and Equilibrium Business Cycles 0. . . . . 0. . „. . „. . « . . . . „ . . . . . . » » • . . . . . . . • . . • 19
CarS E. Walsh and
Peter R„ Hartley

Banks Affiliated with Bank Holding Companies:
A New Look at their Performance . . . . . . • . . . . . «, . „ . . . . . . . . . . . 00„ . . . . . . « . . . . 29
Randall Johnston Pozdena

Hotelling’s Rule Repealed?
An Examination of Exhaustible Resource Pricing 0. „• .. 0. „. • • .. „0„ . . • . . . , . . . . 41
Ronald H. Schmidt

Federal Reserve Bank of San Francisco

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(415) 974-2163.

Saving, Investment, and the
u. S. External Balance

Ramon Moreno
Economist, Federal Reserve Bank of San Francisco.
Editorial committee members were Michael Keeley, Reuven Glick, and Ronald Schmidt.

The unprecedented rise in the US. external deficit in the
1980s was not only the result of large government budget
deficits. A significant decline in the extent to which the
private saving-investment balance adjusted to finance
government budget deficits also contributed to the U.S.
external deficit. It is hypothesized that the shift in US.
monetary policy after 1979 reduced domestic financing of
us. budget deficits in the 1980s by encouraging foreign
capital inflows.

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The size and persistence of the U.S. external deficit in
recent years is unprecedented in this century, and has
prompted extensive discussion and research on its underlying causes. Many observers have argued that large government budget deficits are primarily responsible for the U.S.
external deficits. However, external deficits depend not
only on government budget deficits, but on the private
saving-investment balance, as well. This paper discusses
the role of the private saving-investment balance in the
growth of U.S. external deficits of the 1980s.
Prior to the 1980s, the private saving-investment balance
varied negatively with the government budget balance,
almost fully offsetting budget deficits. Thus, until the
1980s, budget deficits largely were not associated with
external deficits. The extent of this offset decreased significantly in the eighties, thereby increasing the impact of
budget deficits on the U.S. external position. This change
in the behavior of the private saving-investment balance
helps to explain why in the 1980s the external deficit rose in
response to the increase in the government budget deficit.
This study argues that the change in the behavior of the
private saving-investment balance may have been caused
by the change in inflationary expectations associated with
the shift in monetary policy that took place at the end of
1979. Specifically, after 1979, the change in monetary
policy meant that higher budget deficits no longer would
cause money growth, inflation, and inflationary expectations to rise automatically, thereby increasing the willingness of foreigners to finance such deficits.
The paper is organized as follows. Section I discusses the
behavior of budget deficits, the private saving-investment
balance, and the external balance between 1960 and 1987. It
reviews the findings of recent empirical and simulation
studies on the response of the private saving-investment
balance to fiscal and monetary policy and identifies certain
developments that may have changed this response over
time. Section II investigates the empirical relationship
between fiscal and monetary policy and the private savinginvestment balance, and tests for changes in this relationship after 1974 and after 1980. Section III discusses some
factors that may have contributed to the change in the
response of the private saving-investment balance to fiscal
policy. Section IV summarizes the findings of this paper
and highlights some policy implications.

I. Saving, Investment, and the External Deficit-An Overview
Internal and External Balances
To set the context for the discussion that follows, consider the national income accounting identity:
Y=C+I+G+B=C+S+T

(1)

where all variables are real and:

gross national product;

C = domestic consumption;
I
G
B

S
T

domestic gross private investment:
domestic government expenditure;
exports minus imports of goods and services
external balance;
private domestic saving; and
government receipts.

Dropping C from both sides, and re-arranging yields the
following:
(S - 1) + (T - G) = B = Net capital flow

(2)

where the net capital flow is the difference between U.S.
investment abroad and foreign investment in the United
States.
Equation (2) describes the external balance of an economy as the sum of the saving of its private sector, or the
private saving-investment balance (the difference between
gross private saving and gross private investment), and of
its public sector, or the government budget balance. The
left hand side corresponds to the internal balance of the
economy, the right hand side to the external balance.
Equation (2) also illustrates why the external balance
may be interpreted as the saving of the economy as a whole.
A country experiencing an external surplus is producing
more than it spends, and its saving is used to finance excess
foreign spending. Conversely, a country experiencing an
external deficit is purchasing more goods than it produces,
and foreign capital inflows finance excess domestic spending. There must be a correspondence between a country's
external balance and the balance in its capital account.
Chart 1 illustrates the path of the U.S. external balance
since 1960. 1 The series is nominal (not adjusted for inflation), and shown as a proportion of the middle expansion
trend of GNP. 2 As a net exporter of capital, the U.S.
maintained a trade surplus averaging over two-fifths of a
percent of GNP up to 1980. However, the U.S. external
balance began falling sharply at the end of 1982. Between
the last quarter of 1982 and the last quarter of 1987, the

nominal U.S. external deficit averaged 2.5 percent of GNP,
and peaked at 3.7 percent of GNP in the last quarter of
1987. The magnitude of the U.S. external deficit since
1982 is unprecedented in the twentieth century.
The duration of this external deficit also is unprecedented. Over five years have passed since the U.S. external
balance went into deficit in the third quarter of 1982. In
contrast, from the end of World War II until 1980, the U.S.
experienced external deficits for more than one quarter on
only four occasions, and the average duration was less than
a year and a half.
Chart 1 also illustrates the two components of internal
balance that together equal the external balance-the
government balance and the private saving-investment
balance, both as proportions of the middle expansion trend
of GNP.3 The chart shows that during contractions, the
government balance tends to fall as tax revenues fall, and
the private saving-investment balance tends to rise as
investment declines. The reverse is true during expansions."
However, the most recent economic expansion, which
began in 1982, has not been accompanied by the typical
reduction in the government deficit that has characterized
earlier expansions. Given the typical cyclical reduction in

Chart 1
U.S. External and Internal Balance*
Percent

9
6
3

o
-3
-6

63 65 67

69 71

73 75 77 79 81

83 85 87

*Shaded areas indicate recessions as defined by the National Bureau
of Economic Research.

Economic Review / Fall 1988

the private saving-investment surplus as the recovery progressed, analysts point to these budget deficits as the
primary cause of the unprecedented external deficits observed to date.
But a closer examination of Chart 1 also suggests that
prior to the 1980s, the private saving-investment balance
tended to vary opposite to budget deficits even apartfrom
cyclical influences, thereby producing no discernible cyclical or secular trend in the trade balance until the 1980s.
'Thus a change in the behavior of the private savinginvestment balance, as well as rising budget deficits,
apparently has contributed to the external deficits of the
1980s.
'The question whether external deficits in the 1980s are
the result of budget deficits, a change in the behavior of the
private saving-investment balance, and/or other factors
cannot be resolved simply by looking at the accounting
relationships embodied in Equation 2. 'These variables
respond to exogenous changes in fiscal and monetary
policy as well as to other autonomous factors. Thus, to
determine the effect of any of these variables on the
external balance of the U.S., it is important to examine
how they have behaved in response to exogenous changes
in policy. Because changes in the private saving-investment balance have received relatively less attention, this
article focuses on the implications of this relationship for
the U.S. external deficit.
Abstracting from cyclical effects, the response of the
private saving-investment balance to fiscal and monetary
policy may be expressed as follows:

s -[ = ao + a J (T -

+ a2M

(3)

Where (T - G) and M now refer to the exogenous behavior
of the budget balance and the money supply, and 30
contains all other factors." (Note that the observed budget
balance in Chart 1 is the sum of the exogenous budget
balance and the endogenous response of the budget balance to all exogenous disturbances.) Equation (3) may be
interpreted as a reduced form. 'The underlying structure
may be motivated in terms of a standard Keynesian macroeconomic model of an open economy.
With this framework in mind, consider first the effects of
an expansionary fiscal policy. Such a policy tends to raise
income and interest rates; the rise in income tends to
increase domestic saving, and the rise in interest rates
tends to discourage domestic investment. Consequently,
budget deficits tend to produce an offsetting rise in the
private saving-investment balance, suggesting that a, is
likely to be negative.

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An expansionary monetary policy tends to lower interest
rates, stimulating investment and income. The increase in
income, in turn, stimulates saving. (In an open economy
with floating exchange rates, lower interest rates tend to
cause the currency to depreciate, stimulating net exports
and causing a further increase in income.) Since both
saving and investment tend to rise, the net impact of an
expansionary monetary policy on the private savinginvestment balance (the sign of a 2 ) is ambiguous.

The Response of Private Saving-Investment
Equations (2) and (3) imply that it is the interaction of
fiscal and monetary policy and the private saving-investment balance that determines the external balance. 'Thus,
the magnitude of the response of the private savinginvestment balance to fiscal policy-that is, the magnitude
of aI-determines whether fiscal policy affects the trade
balance. If a l = - 1, fiscal deficits generally will not be
associated with external deficits; however, fiscal deficits
will be reflected in external deficits if a.> -1. 6 Unfortunately, the literature provides conflicting evidence on the
magnitude of a 1•
Two well-known structural simulation models (Taylor,
and Sachs and Roubini), and a recent study by Benjamin
Friedman that estimates a reduced form model suggest that
the private saving-investment balance does not fully offset
budget deficits (that is, a.> -1). Taylor (1987) estimates a
multi-country version of the Mundell-Fleming model? and
finds that five years after the start of a simulated cut in
government purchases "virtually all of the cut generates a
rise in [national] saving, and about 3/4 of this rise in saving
[is reflected in] an increase in net exports."8 This suggests
that a cut in the government deficit does not produce a fully
offsetting reduction in the private saving-investment balance and is thus reflected largely in a reduction in the
external deficit.
Similarly, using a dynamic general equilibrium simulation model of a six-region world economy, Sachs and
Roubini (1987) argue that the combination of sharply
higher budget deficits in the U.S. and sharply reduced
deficits in Japan goes far to explain the movements of the
external balance and exchange rates of the two economies.? Friedman's (1986) reduced-form estimates also
suggest that budget deficits largely are reflected in external
deficits.
In contrast to these three studies, a well-known study by
Feldstein and Horioka (1980) found that national saving
(T -G + S) was positively associated with gross private
investment (full crowding out) in a cross-section sample of
industrial countries. Subsequent time series analysis by

Obtsfeld (1986) and Frankel (1985) found a similar positive correlation between national saving and gross private
investment in the U.S. 10 The results of the studies by
Feldstein and Horioka, Obtsfeld, and Frankel suggest that
at = -1, or close to it.
There is also no agreement on the direct impact of
changes in the money supply on the private saving-investment balance. Friedman finds that an increase in the ratio
of money to GNP increases the ratio of private saving to
GNP more than it increases the ratio of private investment
to GNP, II thus reducing the external deficit (this suggests
that a z >0). In contrast, Darby, Gillingham, and Greenless
(1987) find that a rise in the real money supply in the 1980s
has tended to increase the external deficit'? through its
negative impact on private saving (that is, az <0). Similarly,
Taylor finds that in the short run, an expansionary monetary policy tends to increase the external deficit, and, by
implication, to reduce the private saving-investment bal-

ance.P
Several reasons may be offered for the conflicting results, including different specifications for models, variables, and econometric methods. Omitted variables may
explain the differences in some cases and simultaneous
equations bias in others. An alternative explanation is a
change in the response of the private saving-investment
balance to fiscal and monetary policy. This possibility has
received relatively little attention, although studies reported by Darby (1987) and Darby, Gillingham, and
Greenless (1987) suggest that changes in the behavior of
the private saving-investment balance may have contributed to the external deficits of the 1980s.14
A change in the relationship between the private savinginvestment balance and budget deficits might be expected,

in view of two major developments that occurred in the
1970s. First, industrial countries shifted to floating exchange rates'> and liberalized capital controls'< in the first
half of the 1970s. This process largely was completed by
1974, although restrictions on capital movements in the
U.K. and Japan were not removed until 1979. As discussed
more fully below, increased capital mobility and floating
exchange rates could
expected to lower the offsetting
response of the private saving-investment balance to budget deficits.
The second major development was the decision by the
Federal Reserve in October 1979 to change its operating
procedures for implementing monetary policy from reliance on an interest-rate instrument to the use of an
aggregates instrument. Dewald (1982) finds evidence that
during the earlier period, monetary
tended to "accommodate" fiscal policy, in the sense that there was a
positive relationship between money growth and fiscal
deficits in the U.S. In particular, the acceleration in money
growth and inflation in the 1970s appears to have been
directly related to the near tripling of fiscal deficits to over
one percent of GNP in the 1970s. 17
As a result, rising budget deficits in the 1970s may have
produced rising inflationary expectations. As discussed
below, this may have discouraged foreign capital inflows
and raised the offsetting response of the private savinginvestment balance to budget deficits in the 1970s. However, once monetary policy changed and money growth
and inflation apparently ceased to respond to budget
deficits in the 1980s, foreign capital was more likely to
flow in, thereby lowering the offsetting response of the
private saving-investment balance to budget deficits in the
1980s.

II. The Response of the Private Saving-Investment Balance
to Fiscal and Monetary Policy
To determine whether the response of the private savinginvestment balance to fiscal and monetary policy has
changed, regressions of the following form were run using
seasonally-adjusted quarterly data:
8

I=bo+b]'(T-G)t+

l2: o bz +

' M 2/-

+ b 13 • DUM· (T-G)t +
. DUM· M2 t -

.2:

1=0

b]4+i

+ b 23 • DUM· GAP t

(4)

where S - I is the private saving-investment balance,
T - G is the government budget balance, GNPGAP is the
gap between the middle expansion trend of GNP and actual
GNP (a negative gap indicates a strong economy) as
defined by the Department of Commerce, 18 and
is the reciprocal of the middle expansion trend of GNP. All
variables are scaled by the middle expansion trend of
GNP. 19 The variables prefaced by DUM are slope dummy
variables, and they correspond to values ofT - G, M2, and
the GNPGAP. Significant coefficients for biZ' b l4 + i' and
b 22 would indicate a change in the response of the private
saving-investment balance to fiscal policy, monetary policy, and cyclical fluctuations, respectively.

Economic Review / Fall 1988

M2 was selected as the proxy for monetary policy
because of the severe instability characterizing the demand
for Ml in the 1980s. In view of possible simultaneous
equation bias, an instrumental variable was used for contemporaneous M2 as well as for the contemporaneous
budget balance.P? A correction for serial correlation also
was performed. 21

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A regression first was run over the period 1963:31979:4,22 with slope dummies beginning in the first quarter of 1974, to ascertain whether there was any change in
the relationship between the budget balance and the private
saving-investment balance following the liberalization of
capital controls and the shift to floating exchange rates.
The results are reported in the first column of Table I.

A second regression then was run over the period
1963:3-1987:4, with slope dummies beginning in the first
quarter of 1980, to examine whether the response of the
private saving-investment balance changed with the shift
in monetary policy in the last quarter of 1979 and the
further liberalization of capital controls in the U.K. and
Japan. (The slope dummies for 1974-1979 were not included in this regression.) The results are reported in the
second column of Table I. Four and eight quarter lags on
M2 were tested in both the first and second regressions. To
select the best specification, Amemiya's prediction criterion (PC) was used.P
As can be seen in Table 1, both the fiscal and monetary
policy variables are significant. The extent to which the
private saving-investment balance offsets fiscal deficits did
not decline following the liberalization of capital flows in
1974, but did decline after 1980. In addition, the slope
dummies on M2 are significant after 1974, but not after
1980. To improve the fit of the second regression, the slope
dummies for M2 after 1980 were eliminated, and the
second regression was re-run. The results are reported in
the third column of Table 1.
One potential objection to all these regressions is that
there may be a lag in the response of the private savinginvestment balance to the government budget balance as
well as to monetary policy. The regressions were therefore
re-run over the period 1963:3-1987:4, with four and eight
quarter lags on M2 and on the government budget balance,
respectively. However, in all cases, the third regression of
Table 1 was superior to the alternative regressions according to the PC criterion.
The results of the third regression in Table 1suggest that
a one point increase in the budget balance brings about a
0.88 decline in the private saving-investment balance. In
addition, the hypothesis that the private saving-investment
balance fully offset the government budget balance up to
1980 cannot be rejected. There was no change in this
relationship after 1974, and exogenous increases in the
fiscal deficit apparently did not translate into external
deficits up to the 1980s. The extent of the private savinginvestment offset weakened by nearly 50 percent after
1980, and budget deficits came to be reflected in external
deficits. Since changes in the response of the private
saving-investment balance to fiscal policy appear to account for a significant part of the deterioration of the
external balance in the 1980s, these results are interpreted
more fully in the next section.
While these results assign a major role to the behavior of
the private saving-investment balance in explaining the
external deficits of the 1980s, they nevertheless imply that

a reduction in budget deficits now would reduce the U.S.
external deficit substantially, as long as the relation between the saving-investment and budget balance remains
unchanged.
The results also indicate that cyclical effects were amplified in the 1980s. The private saving-investment balance
appeared to be higher in the recessions of the 1980s and
lower in the most recent expansion, which began in 1982,
than was characteristic of earlier cycles. The stronger
cyclical response is not easy to explain. It could reflect a
stronger response of investment to income (a stronger
accelerator effect) in the 1980s or the tendency for wealth
effects to reduce private saving in the current expansion.
Financial wealth has risen due to the accumulating government debt and the stock market boom of recent years. 24
Finally, money exerts an independent influence on the
private saving-investment balance. The sum of the coefficients on M2 consistently is negative and the t-statistic on
this sum is significantly different from zero, indicating that
an increase in the money-to-GNP ratio lowers the private
saving-investment balance-and by this channel, the external balance. In particular, a rise in the M2/GNP ratio
after 1982 has contributed to a lower private savinginvestment balance, and therefore has tended to increase
the external deficit.
As demonstrated in the Appendix, the significant and
positive slope dummies on M2 after 1974 are consistent
with the liberalization of capital flows in the early 1970s,
although the net effect of the positive shift is apparently
very small.P A greater degree of capital mobility will
bring about a positive shift in the response of the private

Chart 2
Private Saving-Investment Balance:
Percent
Actual and Predicted

Actual
Predicted: Pre-80s
Coefficients

o
Predicted: Post-80s
Coefficients

- 2 +--..,.--..,.--.,.---.,.....-.,..---.,..---.,..------,
80

Economic Review / Fall 1988

saving-investment balance to monetary policy because it
reduces the responsiveness of interest rates and investment
to changes in the money supply, and increases the responsiveness of exchange rates, income, and therefore, saving
to such changes.
To illustrate the implications of these results, Chart 2
compares the predicted path of the U.S. private savinginvestment balance in the 1980s using the pre- and post-

1980coefficients. For reference, the actual path of the U.S.
private saving-investment balance also is shown. Given
the actual fiscal deficit, which averaged 3.1 percent of
GNP between 1982:4 and 1987:4, the model predicts that
the private saving-investment balance would have averaged two percent, rather than the 0.7 percent actually
observed, had the pre-1980s' relationships prevailed. As a
result, the external deficit would have averaged 1.3 percent
of GNP over the period, rather than 2.5 percent. 26

III. Interpreting the Results
The finding that the private saving-investment balance
adjusted to fully offset changes in the budget balance until
1980 suggests a very limited degree of net international
capital flows, which is in line with the results of the
literature inspired by Feldstein and Horioka cited earlier.
The absence of net international capital flows up to the
early 1970s might be explained by restrictions on international capital movements, since such restrictions require
the private saving-investment balance to adjust fully to
cover the financing requirements of the public sector. 27
However, it is surprising that there was no change in the
relationship between the private saving-investment balance and the budget balance after 1974 (that is, the slope
dummy on the budget balance variable was not positive and
statistically significant between 1974 and 1979).28
Theory suggests that liberalization of capital flows as
well as the shift to floating exchange rates in the early
1970s should have reduced the offsetting response of the
private saving-investment balance to fiscal policy. The
reason is that in an open economy where capital flows
freely and exchange rates float, the rise in domestic interest
rates associated with government budget deficits should
tend to attract foreign capital and limit the required adjustment in the domestic private saving-investment balance.
The adjustment in the private saving-investment balance
should be muted by capital mobility for two reasons. First,
foreign financing directly limits the extent to which government deficits reduce or "crowd out" investment Second, under floating exchange rates, capital inflows cause
the currency to appreciate. This increases the external
deficit, which in turn reduces the stimulus budget deficits
provide to income, thereby limiting the rise in saving. With
capital mobility and floating rates, the limited response of
the private saving-investment balance to budget deficits
should ensure that the latter are reflected in external
deficits.
However, if budget deficits raise inflationary expectations and thus increase uncertainty about the investment

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environment, increased capital mobility will not necessarily diminish the response of the private saving-investment balance to budget deficits. The positive correlation
between money growth and budget deficits in the 1970s
suggests that there also may have been a positive link
between inflationary expectations and budget deficits. As
demonstrated more formally in the Appendix, such a link
has two effects that could influence the response of the
private saving-investment balance to budget deficits.
First, an increase in inflationary expectations reduces
money demand and could lower real interest rates even as
budget deficits increase. In the standard analysis, such
lower interest rates would discourage capital inflows and
cause the dollar to depreciate. Huizinga and Mishkin
(1986) provide evidence that rising inflationary expectations were in fact associated with falling e\" ante real
interest rates in the 1970s. The real trade-weighted value of
the dollar also depreciated almost continuously between
1971 and 1980.
As in the case of a direct increase in the money supply,
however, the currency depreciation stimulates income and
saving, while the interest rate decline stimulates investment, so the net impact of excess money demand on the
private saving-investment balance must be determined
empirically. The negative coefficients for monetary policy
in the previous regression suggest that the stimulus to
investment from an excess demand for money is stronger
than the stimulus to saving. Thus, the tendency for rising
inflationary expectations to lower money demand apparently does not explain why the behavior of the private
saving-investment balance did not change in the 1970s.29
However, rising inflationary expectations could have an
additional effect on the behavior of the private savinginvestment balance. Specifically, rising inflationary expectations may increase uncertainty about the investment
environment, and thus raise the risk premium demanded
on U.S. dollar assets. A rise in the risk premium, in turn,
would discourage capital inflows, and cause the currency

to depreciate, even if domestic real interest rates do not fall.
The currency depreciation would stimulate saving, but not
investment spending in this case. Thus, a rise in the risk
premium unambiguously would raise the offsetting response of the private saving-investment balance to budget
deficits.
This analysis suggests that if inflationary expectations
had not been rising in the 1970s, the impact of the liberalization of capital controls and the shift to floating exchange
rates on the behavior of the private saving-investment

balance would have been felt earlier. Instead, the impact of
the liberalization of capital controls and the shift to floating
exchange rates was felt only after 1979, when monetary
policy changed and budget deficits no longer had the same
influence on inflationary expectations. This break in the
link between budget deficits and inflationary expectations
led to capital inflows and an appreciating currency in the
1980s, as would have been expected, given enhanced
international capital mobility.

IV. Conclusions
The unprecedented rise in the U.S. external deficit in the
1980s mainly is the result of the interplay of two factors.
First, government deficits remained large in the expansion
of the 1980s, rather than tending towards zero as they had
during previous expansions. Second, the private savinginvestment balance failed to offset the rising budget deficits as it had in the past.
The liberalization of capital movements in industrial
countries and the shift to floating exchange rates in the first
half of the 1970s had no perceptible effect on the offsetting
response of the private saving-investment balance to fiscal
policy until a major shift in monetary policy and a further
liberalization of international capital movements occurred
in 1979.
This paper offers a hypothesis that is theoretically
consistent with the timing of the changes in the response of
the private saving-investment balance to fiscal policy. By
feeding back into inflationary expectations and increasing
uncertainty about the investment environment, the tendency toward monetary accommodation of fiscal policy
until 1979 (found by Dewald) reduced the willingness of
foreigners to finance U.S.deficits and caused a continuing

currency depreciation which stimulated a strong offsetting
response of the private-saving investment balance to the
budget balance. This curtailed the tendency for the external deficit to increase in response to rising budget deficits
in the 1970s, notwithstanding the liberalization of capital
restrictions and the shift to floating exchange rates in the
early 1970s. Once monetary accommodation of fiscal
policy ceased in the 1980s, the external balance deteriorated significantly. As the reduced-form specification used
in this paper does not permit a direct test of this hypothesis,
further research is needed.
If this interpretation is valid, the results presented here
have important policy implications. Budget deficits pose a
dilemma-a decline in the external balance can be averted
by accommodating budget deficits with monetary policy
and currency depreciation, but at the cost of high inflation
and greater crowding out of domestic investment. Conversely, policymakers can avoid high inflation and reduce
crowding out by refusing to accommodate budget deficits,
but with a rising external deficit. Thus, if efforts to reduce
the U.S. external deficit are to succeed without a resurgence of inflation, they must be accompanied by a
reduction in budget deficits.

Economic Review / Fall 1988

APPENDIX
The purpose of this Appendix is to demonstrate how the
balance to policy
response of the private
may be affected by inflationary expectations, as this mechanism is not usually discussed in the literature. It also
shows that the direct response of the private savinginvestment balance to monetary policy is more likely to be
positive if capital mobility is high.
Rewrite equation (2) in the text as follows:
S(Y)

l(r, Y)

(A-I)

T - G = B(E. Y. Y*)

*
f

Equation (A-I) represents equilibrium in the goods market.
The money market equilibrium equates real money supply
to demand by domestic residents (assume foreign residents
hold no domestic money):
M = L(Y, i)

(A-2)

+
where M is the real money supply, L is the demand for
money. The nominal interest rate, i, is defined as the sum of
the real interest rate and inflationary expectations:
i

= r

(A-3)

The domestic bond market is in equilibrium when the real
supply of domestic bonds equals the demand by domestic
and foreign residents:
Ie'

key. i, i*

+ +

kf(Y* .i

<1>. i*)

(A-4)

where k s is the supply of domestic bonds, k(.) and k f ( . ) ,
respectively, are the domestic and foreign demand for
domestic bonds, and <\> is the risk premium. It is assumed
that inflationary expectations, Il, also correspond with the
expected rate of depreciation. For similar specifications up
to this point see Dornbusch (1980) or Marston (1985).

Federal Reserve Bank of San Francisco

(A-5)

+
Assume further that monetary authorities respond to
changes in fiscal policy by changing the rate of growth in
the money supply. * If agents are aware of this, they will
form inflationary expectations as follows:
(A-6)

(-)

mcome
real domestic interest rate
domestic currency price of a unit of foreign
currency (e.g. dollars per yen)
superscript for foreign variables
superscript for holdings by foreign residents

<1> = <1>(11)

IT = l1(T - G)

The signs refer to the partial derivatives and:
y

Assume that the risk premium on dollar assets responds
to rising inflationary expectations, that is:

The extent to which inflationary expectations respond to
fiscal deficits will depend on the degree of monetary
accommodation to fiscal policy.
The above is a Mundell-Fleming model that allows for
imperfect asset substitutability and includes specific assumptions about monetary policy and expectations formation. The following simplifying assumptions have been
made in obtaining a solution:
a. The country is small, which means that the ramifications of domestic policies on foreign income and world
interest rates are ignored. The impact of these foreign
effects on the U.S. economy apparently is small (see Sachs
and Roubini and Taylor).
b. Short-term price rigidity is assumed. Except for
specifying inflationary expectations, the dynamics of price
adjustment are not spelled out.
c. The effect of exchange rate changes on the domestic
price level is ignored. This implies that two effects of an
exchange rate appreciation are ignored in the present
analysis. These are: the improvement in the terms of trade
and real income, which tends to raise saving; and the
increase in real wealth brought about by an exchange rate
appreciation, which tends to reduce saving. Wealth effects
are important in principle, specifically in portfolio demand, but they are ignored to simplify notation. This does
not affect our main conclusions.
d. The implications of a country's net creditor or debtor
position similarly are ignored. As discussed in Frenkel and
Razin (1987), if a country is a net debtor, the slopes of the
LM and IS curves may change (the LM curve may slope
downward, the IS curve becomes steeper), reversing a
number of standard conclusions. For example, a tax increase may be expansionary, rather than contractionary.
Discussion of this type of model usually focuses on the
implications of capital mobility and the exchange rate

regime for the ability of fiscal and monetary policy to affect
income. Here we will focus instead on how inflationary
expectations affect the responsiveness of the private saving-investment balance to fiscal and monetary policies.
The Solution
Substituting (6) into (3) and totally differentiating (2) to
(4), we obtain:

s+m-i,.

-lr

-L y

-L;

(kj + 10~lI-<I»

Ljll(T-dd(T - G)

-d(T - G)

- dM

k,.

where

s = marginal propensity to save
m = marginal propensity to import

and subscripts refer to partial derivatives.
The solution to the system is

- d(T - G)

d,
dE

I- A '

- dM

LJI(T_dd(T - G)

(k;* + n + <I> -10-11-<1> )<l>nIIT_cd(T- G)

where:

under plausible conditions, and

o
- (s+m-i,,)(k j +

A' =

~-n-<I»

- I.k;

(s+m-iy)L; + l L;

Fiscal Policy:

d(T - G)

Economic Review / Fall 1988

dE
d(T - G)

d(T - G)

Where, to simplify notation, the following relation is used:
ki * + II + <I>

ki: [J -

<I>

Inflationary expectations (reflected in the term ITC -G ))
T
expand income by making it more likely that the currency
will depreciate in response to fiscal deficits (that is,
dE/d(T - G)<O). Two effects are at work here. First, the
rising inflationary expectations in response to fiscal deficits lower real money demand. The resulting excess demand for money lowers real rates in the short run, tending
to depreciate the currency, and stimulate net exports and
income. Second, in addition to the effect of lower interest
rates, the currency depreciates further because inflationary
expectations raise the risk premium demanded by foreigners, thereby stimulating net exports and income even
more.
d(S

----=s
d(T -- G)2

dy
- - - - - Ir
d(T

(A-7)
d(T -

The effect of inflationary expectations on money demand tends to lower real interest rates, while the effect of
inflationary expectations on the risk premium tends to raise
real interest rates. Ifthe impact of inflationary expectations
on the risk premium is sufficiently strong, the currency
may depreciate even when domestic real interest rates are
not falling, or perhaps even when they are rising. In a large
economy such as the United States, it is likely that the
effects of variations in the risk premium will be reflected
largely in the exchange rate rather than in the interest rate.
The effect of an increase in the government surplus on
the private saving-investment balance is therefore:

In the absence of international capital mobility, deS - 1)/
d(T - G) = I, because domestic saving must fully finance government deficits. However, in the presence of
capital mobility and floating exchange rates, as assumed
here, deS - I)/d(T - G) = 0 if n C G) = O. This is because
T
neither income nor interest rates will increase in response
to fiscal deficits, in the case where fiscal deficits do not
affect inflationary expectations. Thus, in the absence of

Federal Reserve Bank of San Francisco

changes in inflationary expectations, capital mobility and
floating rates imply that the offsetting response of the
private saving-investment balance to budget deficits will
decline. The intuition is discussed in the text.
Equation (A-7) shows that if n C G) is negative, the
T
response of the private saving-investment balance to fiscal
deficits will not necessarily fall to zero even with capital
mobility and floating exchange rates. The sign of the first

right hand side term, which reflects the impact of inflationary expectations on money demand, is ambiguous; the
private saving-investment balance may rise or fall. In
contrast, the second right-hand side term (multiplied by
<D n ) is unambiguously negative. Thus, deS - I)/(T - G)
will remain negative if the second right-hand side term.is
sufficiently large.
The text argues implicitly that the response of inflationary expectations, and particularly its impact on the
risk premium in the 1970s, may have risen by enough to
prevent deS - I)/d(T - G) from falling in absolute value in
the 1970s. In the 1980s, deS l)/d(T - G) fell because
II(T G) fell to zero.
In the next section, it is shown that the conditions that
determine the sign of the impact of monetary policy on the
private saving-investment balance determine the sign of
the first right hand side term of equation (A-7).
Monetary Policy

> 0
dM

m - iJ(ki

In the text the impact of an expansionary monetary policy
on the private saving-investment balance, and therefore the
external balance, is ambiguous. For example, if the interest
sensitivity of investment demand (L) is large, an expansionary monetary policy will lower the private savinginvestment balance.
An increase in capital mobility [(kj + kf i n <1» increases in absolute value] means the term (BeI~/ Ll)
becomes smaller, which implies that a monetary expansion
is more likely to improve the external balance. ** The
reason is that a greater degree of capital mobility will tend
to weaken the ability of monetary policy to influence
domestic interest rates, and therefore, investment demand
and the external balance. The finding that there was an
increase in the impact of monetary policy on the private
saving-investment balance after 1974 is consistent with the
expected effect of liberalization of capital controls.
It has been assumed that an increase in the stock of
money does not directly affect inflationary expectations;
instead, expectations respond to the growth in the money
supply associated with fiscal deficits. Inspection of equations (A-7) and (A-8) also confirms that if deS - 1)/
d(T - G) in equation (A-8) is negative, as found in the
regressions in the text, the impact of inflationary expectations on money demand cannot explain why deS - 1)/
(T - G) did not fall in the 1970s.

kllI_<l» - Irk,

> 0
dM

< 0
dM

The effect of an increase in the money supply on the private
saving-investment balance is

d(S - I)

dr
1r
dM

(A-8)

Notes to Appendix

See Dewald (1982), who finds evidence of this type of accommodation between 1948 and 1980.

The effect of a tax cut may differ from that of an increase in government spending in two ways: first, a tax cut will raise disposable
income directly as well as indirectly. Second, a tax cut may increase money demandfor any level ofpretax income. This tends to reduce
the expansionary impact of a tax cut on income. These effects are ignored in order to simplify the present discussion.

Economic Review / Fall 1988

ENDNOTES
1. The external balance measure used here is U.S. net
foreign investment abroad, the measure which is conceptually most consistent with the use of equation 2. This
measure is approximately equal to net exports of goods
and services as measured in the national income-and
product accounts.
2. The middle-expansion trend of GNP is calculated by
classifying each quarter into one of four cyclical phases:
recession, recovery, middle expansion, and late expansion. The geometric mean of GNP during each middle
expansion phase provides one observation of the trend
GNP. The middle expansion begins when the level of real
GNP passes its pre-recession peak and lasts 12 quarters
unless a downturn occurs before 12 quarters have passed. In the latter case, the middle expansion ends at the
cyclical peak just before the downturn. The advantage of
this approach is that it reflects the path of actual GNP
purged of cyclical movements and requires no assumption about potential GNP. See De Leeuw and Holloway
(1983).
3. The statistical discrepancy between internal and external balances has been added to gross private saving. It
is therefore reflected in the private saving-investment
balance.
4. The cyclical patterns disguise certain trends in these
variables and may provide a misleading picture of the
relationships among the variables. For example, the unadjusted U.S. government budget deficit, illustrated in
Chart 1, averaged 0.7 percent between 1976:1 and 1979:4
and turned into a surplus for a brief period. On a cyclically
adjusted basis, however, the government budget was
consistently in deficit, averaging nearly 2 percent of the
middle expansion trend of GNP. The empirical analysis
reported later controls for cyclical effects.
5. The observed budget balance, and by the accounting
identity of (2), the external balance, are also the consequence of these same exogenous disturbances to fiscal
and monetary policy.
6. A coefficient for a, of -1 could mean that an expansionary fiscal policy will produce a trade surplus because
such an expansionary policy will tend to create an offsetting improvement in the fiscal balance.
7. The model assumes perfect capital mobility and perfect asset substitutability. Careful attention is paid to
dynamics, and rational expectations in asset and labor
markets is assumed. Sticky wages are modelled by staggered wagesetting. An earlier example of a structural
analysis of the U.S. external balance as determined by
internal balances is provided by Von Furtensberg (1980),
who examines the domestic price and quantity determinants of three components of the net national saving rate
(government saving, personal saving, and corporate saving) and two components of net domestic investment
(fixed domestic investment and the rate of inventory
change). A similar approach, which focuses on interna-

Federal Reserve Bank of San Francisco

tional as well as domestic determinants, is followed by
Turner (1986) for the seven major OECD countries.
8. Taylor (1987) p. 15. Taylor performs a counterfactual
experiment in which U.S. government spending grows
less rapidly than it actually did starting in the first quarter of
1982, so that by 1986:1 real government purchases are
lower than they actually were by an amount equal to 3
percent of real GNP. This roughly would balance the fiscal
deficit, and result in a reduction in the outstanding stock of
government bonds.
9. The model is related to intertemporal dynamic models
of fiscal policy and solves for a full intertemporal equilibrium in which agents have rational expectations of
future variables. Attention is given to intertemporal optimization and intertemporal budget constraints. In this
respect, it differs from the simple Mundell-Fleming framework utilized in this paper. Obstfeld (1987) provides an
analytic (as opposed to simulation) solution to this type of
optimization problem.
10. For a study that includes developing countries see
Dooley, Frankel, and Mathieson (1987). For a similar approach that treats investment as the exogenous, rather
than the endogenous variable, see Sachs (1981).
11. This is consistent with the standard trade literature,
recently summarized by Hooper and Mann (1987), who
suggest that by bringing about a currency depreciation, a
monetary expansion would tend to improve the external
balance, presumably by increasing the private savinginvestment balance as well as the budget balance. Friedman uses the detrended logarithm of the ratio of M1 to
GNP as the monetary policy variable.
12. They argue that four years of erratic upward movements in real per capita M1, which reversed a secular
decline, contributed significantly to a decline in saving.
13. To see this, recall equation (2), S -I + T - G = B. An
expansionary monetary policy will always tend to increase
T - G, because as income rises, tax revenue increases. If
an expansionary monetary policy lowers B, it must be
because S - I has fallen. Note that given the neutrality of
money in Taylor's model, in the long-run money has no
effect on the external balance in his simulations (a2 = 0).
Sachs and Roubini also find that monetary policy is of little
importance in influencing the external balance.
14. Darby, Gillingham, and Greenless argue that the reduction in the U.S. national saving rate in the 1980s, and
the associated deterioration in the U.S. external balance,
were caused in large measure by a decline in the personal
saving rate. Darby reports preliminary studies that find a
significant increase in investment demand in the U.S. over
the period 1981-85. In Darby's view, such an increase in
demand permitted investment to flourish in the 1980s,
even though negative real U.S. interest rates in the 1970s
turned positive in the 1980s. Darby argues that this upward shift in investment demand was due to reductions

in anticipated business taxes and greater confidence
that the regulatory environment would not arbitrarily turn
against business. Note, however, that the empirical approach of the present paper is closer to that of Friedman
than that of Darby et. et. The theoretical interpretation of
the results also differs from those in the studies conducted
by Darby.
15. The U.S. shifted to floating exchange rates in March
1973. Except for a brief effort to strengthen a rapidly falling
dollar in November 1978, the behavior of exchange rates
apparently had little influence on U.S. monetary policy
from March 1973 until the Louvre agreement of February
1987.
16. Capital controls, which were widely used in OECD
countries after World War II, were liberalized in the first half
of the 1970s following the adoption of generalized floating
exchange rates and in response to the rapid growth of the
Euromarkets in the 1960s, which tended to limit the effectiveness of such controls. Capital mobility probably
had increased after the convertibility of European currencies was restored in 1958, but restrictions on capital flows
largely remained effective throughout the 1960s. See
OECD (1982).
In the case of the U.S., restrictions that were designed to
prevent capital outflows largely were eliminated in January 1974. These were the Interest Equalization Tax (lET),
the Voluntary Foreign Credit Restraint Program, and controls on direct foreign investment More stringent controls
on capital flows had been imposed from time to time in the
1960s. For example, at the beginning of 1968, President
Johnson announced controls on outflows of capital by
American businesses, banks, and other financial institutions. This included a requirement that no U.S. capital
finance direct investment in other industrial countries. This
action was taken in response to the deterioration in the
U.S. external position.
17. Dewald finds evidence that money growth was positively related to fiscal deficits between 1948 and 1980. He
estimates that over the period a unit rise in the ratio of the
fiscal deficit to high employment output was associated
with a rise in the growth of M2 of 0.4 percent
18. See De Leeuw and Holloway (1983).
19. Because the variables are expressed in ratios, a
significant constant term (b o) indicates that the level (not
the ratio) of the private saving-investment balance is
related to the middle expansion trend of GNP. Furthermore, a significant coefficient on INVMET indicates that if
the relationship between the private saving-investment
balance and the budget deficit were expressed in levels
rather than ratios, the constant term would be significant
To see this, assume 8 lags on M2. Suppose the true
relationship in levels (not ratios to the middle expansion
trend of GNP) is
8

S-I=co+C1'(T-G)t+.k

1=0

c2 + i ' M2t -

+ C11 . GNPGAP t + C12 ' GNPMETt

(5)

+ C 13 ' DUM· (T . DUM· M2t

G),

+ C2 3

+ 1=0 C 14
k

DUM· GAP t

where GNPMET is the middle expansion trend of GNP.
Then the relationship expressed as ratios will be the
equation shown in the text Note that Co = b 1 and C 1 = bo
2
2
in equation (4) in the text
20. The first stage regression to construct an instrumental
variable for the budget balance included the budget
balance lagged 1 to 3 quarters and contemporaneous
department of defense spending. It produced an adjusted R2 coefficient of .81 and a D.W statistic of 1.93, The
first stage regression for M2 included a constant, the
short-term nominal interest rate in the U,S, lagged 1 to 8
quarters and M2 lagged 1 quarter, The adjusted Rsquared was ,967, the Durbin-Watson statistic 1.4. Equation (4) in the text resembles one of the reduced form
regressions performed by Friedman (1986), However,
Friedman did not use an instrumental variables procedure,
21, The correction was implemented by running a regression with quasi-differenced data, The data were quasidifferenced with the rho coefficient estimated from the
instrumental variables regression.
22, The sample begins in the first quarter of 1959, However, degrees of freedom were used up by various lag
lengths tried in the second stage regressions, Lagged
variables were also used in creating instrumental variables,
23, The PC criterion is a better indicator than the adjusted
R-squared because it considers the losses associated
with choosing an incorrect model. It thus imposes a
higher penalty for adding variables than does Theil's
adjusted R-squared, See Judge et. el. (1985), pp 865866,868,
24, However, attempts to introduce a stock market variable as an explanatory variable were not fruitful. The
absence of a slowdown in the economy after the stock
market decline of October 1987 also suggests that wealth
effects are not very strong.
25, The marginal significance level is 10 percent, which is
a weak basis for not rejecting the hypothesis that there
was a shift
26. The external balance is estimated by adding the
actual government deficit and the predicted private saving-investment balance, Note that the actual government
deficit may be seen as the sum of the exogenous contemporaneous government deficit used on the right hand side
of the regressions and of the endogenous response of the
budget balance to fiscal and monetary policy,
27, In terms of equation (3), a, = -1 or close to it, as there
is no foreign financing of fiscal deficits,
28, It also should have increased the positive response of

Economic Review I Fall 1988

the private saving-investment balance to monetary policy,
which did occur, as there is a statistically significant and
positive slope dummy variable for M2 for 1974-79.
29. This interpretation needs to be qualified because the
regression allows for lags in the impact of the M2/GNP

ratio. Furthermore, although the demand for M2 has been
more stable than the demand for M1 in the 1980s, it is still
not perfectly stable. The rise in the M2/GNP ratio may in
some cases reflect a rise in money demand, particularly in
the most recent expansion.

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Towers: The Current Account Deficit, Capital Account
Surplus, and National Investment and Saving." Manuscript, October 2, 1987.
Darby, Michael R., Robert Gillingham and John S. Greenless. "The Impact of Government Deficits on Personal
and National Saving Rates." U.S. Treasury Department. The Office of the Assistant Secretary for Economic Policy. Research Paper No. 8702. August 1987.
De Leeuw, Frank and Thomas M. Holloway. "Cyclical
Adjustment of the Federal Budget and Federal Debt,"
Survey of Current Business, December 1983.
Dewald, William G. "Disentangling Monetary and Fiscal
Policy," Economic Review, Federal Reserve Bank of
San Francisco, Winter 1982.
Dooley, Michael, Jeffrey Frankel and Donald J. Mathieson.
"International Capital Mobility: What Do Saving-Investment Correlations Tell Us?" Staff Papers, International Monetary Fund, V. 34, No.3, September 1987.
Eichengreen, Barry. "Trade Deficits in the Long Run."
Prepared forthe Conference The U.S. Trade DeficitCauses, Consequences and Cures. Federal Reserve
Bank of St. Louis, October 23-24, 1987.
Evans, Paul. "Do Deficits Raise Interest Rates?" Journal of
Monetary Economics, September 1987.
Feldstein, Martin. "Domestic Saving and International
Capital Movements in the Long Run and the Short
Run", European Economic Review, 21, 1983.
Feldstein, Martin and Charles Horioka. "Domestic Saving
and International Capital Flows," Economic Journal,
90, 1980.
Feldstein, Martin and Douglas W Elmendorf. "Taxes,
Budget Deficits and Consumer Spending: Some New
Evidence." National Bureau of Economic Research
Working Paper No. 2355, August 1987.
Frankel, Jeffrey. "International Capital Mobility and
Crowding Out in the U.S. Economy: Imperfect Integration of Financial Markets or of Goods Markets?" National Bureau of Economic Research Working Paper
No. 1773, December 1985.
_ _ _ _.The Yen Dollar Agreement: Liberalizing Japanese Capital Markets. Policy Analyses in International Economics, NO.9. Washington D.C., Institute for
International Economics, 1984.
Frenkel, Jacob A. and Assaf Razin. "The Mundell Fleming
Model A Quarter of a Century Later: A Unified Exposition." IMF Staff Papers. Vol 34, No.4, December 1987.
Friedman, Benjamin. "Implications of the U.S. Net Capital
Inflow," National Bureau of Economic Research Working Paper No. 1804, January 1986.

FederalReserve Bank of San Francisco

Hooper, Peter and Catherine L. Mann. "The U.S. External
Deficit: Its Causes and Persistence." Prepared for the
Conference The U.S. Trade Deficit-Causes, Consequences and Cures." Federal Reserve Bank of St.
Louis, October 23-24, 1987. Also, International Finance, Discussion Papers No. 316, Board of Governors of the Federal Reserve System, November 1987.
Huizinga, John and Frederic S. Mishkin. "Monetary Policy
Regime Shifts and the Unusual Behavior of Reallnterest Rates." Carnegie Rochester Conference Series on
Public Policy, Volume 24, pp. 231-274. Amsterdam:
Elsevier Science Publishers, 1986.
Judge, George, WE. Griffiths, R. Carter Hill, Helmut Lutkepohl and Tsoung-Chao Lee. The Theory and Practice
of Econometrics (2nd edition). New York: John Wiley
and Sons, 1985.
McKinnon, Ronald I. "The Exchange Rate and Macroeconomic Policy: Changing Postwar Perceptions,"
The Journal of Economic Literature, Vol XIX. (June
1981).
Marston, Richard C. "Stabilization Policies in Open Economies," in Ronald W Jones and Peter B. Kenen (eds.)
Handbook of International Economics, v. 2. Amsterdam: Elsevier Science Publishers, 1985.
Obstfeld, Maurice. "Capital Mobility in the World Economy: Theory and Measurement," Carnegie Rochester
Conference Series on Public Policy, 24, 55-104. Amsterdam: Elsevier Science Publishers, 1986.
Obstfeld, Maurice. "Fiscal Deficits and Relative Prices in a
Growing World Economy." Manuscript. May 1987.
OECD. Controls on International Capital Movements.
Paris, 1982.
Sachs, Jeffrey. "The Current Account and Macroeconomic Adjustment in the 1970s," Brookings Papers on
Economic Activity. 1, 1981.
Sachs, Jeffrey and Nouriel Roubini. "Sources of Macroeconomic Imbalances in the World Economy: A
Simulation Approach," National Bureau of Economic
Research Working Paper No. 2339. August 1987.
Taylor, John B. "The U.S. Trade Deficit, Saving-Investment
Imbalance and Macroeconomic Policy: 1982-87."
September 1987. Prepared for the Conference The
U.S. Trade Deficit-Causes, Consequences and
Cures." Federal Reserve Bank of St. Louis, October
23-34,1987.
Turner, Philip P. "Savings, Investment and the Current
Account: An Empirical Study of Seven Major Countries 1965-84," Bank of Japan Monetary and Economic Studies, Vol. 4., No.2, October 1986.
Von Furtensberg, George M. "Domestic Determinants of
Net U.S. Foreign Investment," IMF Staff Papers, December 1980.

Economic Review / Fall 1988

Financial Intermediation, Monetary Policy,
and Equilibrium Business Cycles

Carl E. Walsh and
Peter R. Hartley
Wide disagreement exists over the exact role that money
plays in the economy and why money seems to matter.
There is a related disagreement concerning the roleplayed
by financial intermediaries. This paper provides a disc~s
sion of alternative views of the role played by financial
intermediaries in determining the impact of monetary
policy. The emphasis is on the macroeconomic impact of
intermediaries and the discussion is limited to equilibrium
models of the business cycle.

University of California, Santa Cruz, and Federal Reserve Bank of San Francisco; and Rice University and the
Centre for Policy Studies, Monash University. Editorial
committee members were Ramon Moreno, Fred Furlong,
and Ronald Schmidt.

Federal Reserve Bank of San Francisco

Policymakers charged with responsibility for monetary
policy take it as self evident that their policy actions have
an impact on the real economy in the short-run. Professional economics journals, on the other hand, are filled
with models of equilibrium business cycles that imply
systematic monetary policies have no real effects. While
most economists would agree that monetary actions canand do-have real effects on the macro-economy, they
disagree on the exact role that money plays in the economy
and why money seems to matter.
Business cycle theories in the Keynesian tradition assume that monetary disturbances affect real output because
wages and prices adjust slowly in the face of economic
shocks. Changes in the nominal quantity of money generate changes in the real quantity of money-the nominal
quantity adjusted for the level of prices-since prices are
sticky. Fluctuations in the real supply of money then affect
interest rates and aggregate spending.
In sharp contrast, equilibrium business cycle theories
assume wages and prices adjust continually to ensure that
markets are in equilibrium. In most equilibrium models,
the real effects of monetary fluctuations are typically either
nonexistent or arise only when individuals have incorrect
information about the current stock of money.
Economists also disagree on the role played by financial
intermediaries. Some economists incline to the view that
financial intermediaries are a "veil" in the sense that they
re-package financial assets but do not affect real savings or
investment behavior. Others emphasize that financial intermediaries can have real effects on economic resource
allocation. This divergence of opinion is significant for the
bearing it has on the debate about the role of monetary
policy. An understanding of the roles of both money and
financial intermediaries is necessary for evaluating and
designing both macroeconomic monetary policy and bank
regulatory policy.
In this article, we discuss how the behavior of financial
intermediaries-and that of banks, in particular-may
have an influence on real economic activity and how,
through its impact on banks, monetary policy influences
economic activity! The objective of this article is not to
present a complete survey of recent developments in the
economics of financial intermediaries. Rather, the article
focuses on developments that promise to advance our

understanding of the roles played by both financial intermediaries and monetary policy. The emphasis is almost
exclusively on the macroeconomic impact of intermediaries, and the discussion is limited to equilibrium models
of the business cycle." Specifically, this article examines
some of the channels through which systematic monetary
policy will have real effects even when prices adjust
quickly.
Sections I and II examine the role played by the liability
side of the banking sector's balance sheet. Bank deposits
are an important component of the medium of exchange,
and variations in the quantity of bank deposits may affect
economic activity. Section I discusses one recent approach
in the economics literature that allows some role for major

disruptions in the banking sector to affect the economy, but
in which monetary policy itself has no effect. on real
activity. Section II discusses other recent work that examines more closely the determinants of the demand for bank
deposits and concludes that monetary policy actions may
have real effects via their impact on bank liabilities.
Section III turns to the asset side of the banking sector's
balance sheet. Recent work that attempts to account for the
economic role played by financial intermediaries is reviewed. One conclusion from this work is that variations in
the supply of intermediated credit can affect the level of
economic activity. The effect of monetary policy on
supply of bank-intermediated credit is then discussed.
Conclusions are summarized in Section IV.

I. Transactions Services in Real Business Cycle Models
Charts I and 2 show that fluctuations in the money
supply and fluctuations in the general level of real economic activity exhibit a high degree of association. In
Chart I, deviations of real GNP and MI around trend are
plotted using quarterly data for the period 1960.1 to
1987.4. Chart 2 plots the growth rates of Ml and real GNP.
It is easy to see why monetary disturbances have played a
major role in theories of the business cycle. Disagreements
arise over whether this close association should be interpreted as evidence that monetary fluctuations have helped
to cause business cycles, or whether both output and
money supply movements are caused by nonmonetary
economic disturbances.

The economics profession recently has seen the development of a body of work that employs stochastic growth
models of competitive economies as a stylistic framework
within which to study business cycles. For example,
Kydland and Prescott (1982) and Long and Plosser (1983)
studied business cycles as induced responses to real productivity shocks in models of economies that exclude any
role for money. Because they ignore monetary factors as
possible sources of cycles, these "real business cycle
models" contrast strongly with models that focus on monetary disturbances as the major cause of cyclical fluctuations (for example, Lucas, 1975).

Chart 1
Deviations of Real GNP
and M1 from Trend
Percent

.08
.06
.04

.02
.00

-.02
-.04
-.06
1963

1967

1971

1975

1979

1983

1987

Economic Review / Fall 1988

In an important paper, King and Plosser (1984) introduce money into a real business cycle model. In their
model, the sources of business cycles are entirely nonmonetary. Money does not cause cycles. But their model
does predict a positive correlation between real output and
monetary aggregates, like Ml , that incorporate both outside money (the liabilities of the central bank) and inside
money (the liabilities of the banking sector).
King and Plosser focus on the financial sector as a
producer of transaction services that are used by firms and
consumers in the process of production and the purchase of
goods and services. Variations in the total output of goods
and services generate positively correlated movements in
the demand for transactions services. These changes in
demand then induce similar movements in the actual supply of transaction services, leading to a positive correlation
between measures of transaction services and real output
during the course of a business cycle.
To account for the observed co-movements of real
output and the stock of deposits at banks, it is necessary to
provide some link between deposits and the quantity of
transactions services produced by the financial industry.
An economic rationale for such a tie is not straightforward,
as Fama (1980) points out. King and Plosser skirt this issue
by assuming that transaction services are linked directly to
the stock of deposits held by the banking sector. Thus, by
construction, the positive co-movement of output and
transaction services translates into a positive co-movement
between output and bank deposits. Inside money and out-

put move together even though monetary factors have no
causal role in generating business cycles.
This reverse causality argument-s-output causes money
and money does not cause output-is not new. See, for
example, Tobin (1971). But
and Plosser extend the
argument by showing that their model implies measures of
inside money, such as real bank deposits, should be more
highly correlated with measures of real economic activity
than are measures of outside money, and they present some
evidence that such is the case in the U. S.
In the King and Plosser model, both individuals and
banks care only about the real value of their asset holdings
and the real value of the transaction services produced by
the payments system. There is no money illusion; individuals do not care about nominal values. Consequently,
changes in the nominal quantity
outside money simply
result in proportional variations in the aggregate price
level, leaving all real variables unaffected. Monetary policy, which varies the path of outside money, has importance
only for the price level. Thus, a change in the stock of
outside money does not affect the real value of bank assets
or liabilities.
The neutrality of money holds in their model even if the
variations in the path of outside money induce changes in
the expected rate of inflation. An increase in the money
supply that is viewed as only temporary, for example,
would raise the current price level relative to future prices
and generate expectations of future deflation. Such changes
will cause nominal interest rates to adjust, but in the model

Chart :2
Growth Rates of
Real GNP and 1\1I1
Growth Rate (%)

.16

.13
.10

.07

1963

Federal Reserve Bank of San Francisco

1967

1971

1975

1979

1983

1987

of King and Plosser these nominal rate adjustments leave
all real rates of return on interest bearing instruments
unchanged. Since outside money is non-interest bearing, a
rise in the expected rate of inflation reduces its real return.
The resulting fall in the demand for outside money would
be eliminated by an immediate rise in the price level, thereby reducing the real supply of outside money.3
Unfortunately, the empirical evidence that King and
Plosser present to support their model is weak. For example, correlations between outside money, inside money,
and real economic activity are very dependent on the way
has been conducted.
money has
never been used as a policy target by the Federal IIp,,pnrp
but instead has been allowed to fluctuate in a manner
consistent with the Fed's interest rate or monetary aggregate targets. Thus, the relative strength of the correlation
of outside money with measures of real activity does not
necessarily provide much information on King and Plosser's hypothesis. In fact, King and Plosser actually demonstrate that the exact relationship between the monetary
base, the stock of currency, the stock of inside money, and
the price level will depend on the presence or absence of
reserve requirements and the particular aggregate targeted
by the central bank.
Moreover, King and Plosser choose to ignore one channel in their model by which monetary variables could have
effects on real economic activity. Because transaction serv-

ices-the banking sector's output-are used as inputs into
the production of other goods and services, a real shock to
the banking sector can have real effects on production in
other sectors. Thus, a major disruption of the payments
system, such as occurred during the
of massive
bank failures in the early 1930s, would contribute to a fall
in real output by lowering the quantity of an important input into production." Bernanke's 1983 study of the impact
of intermediation during the Great Depression provides
some empirical evidence relevant to this issue. Bernanke
showed that measures of the liabilities of failing banks
enter
in real
estimated
the 1920s
1930s, even when measures of the money
supply also are included. 5
If the transaction services provided by bank deposits are
an important determinant of the general level of economic
activity, then more mild fluctuations in the stock of bank
deposits than those accompanying major bank failures also
may produce general economic fluctuations. Substitution
between bank deposits and other financial assets might
then affect economic activity. King and Plosser ignore this
channel from monetary variables to real variables on the
grounds that it is likely to be unimportant empirically.
Whether, in fact, such an effect is small enough to neglect
will depend on the nonbank sector's demand for liquid
assets.

n. Bank Liabilities and the Medium of Exchange
Until recently, economists studying the microeconomic
foundations of the demand for transaction services concentrated on the demand for outside money (the liabilities of
the central bank). In some of the earlier literature, such as
the Baumol and Tobin transactions costs models, there was
an explicit recognition that interest bearing assets were an
alternative to non-interest bearing money as a store of
value so that the interest yield on those assets represented
the opportunity cost of using money to fund transactions.
models did not
to explain
noninterest bearing money was used to effect transactions, and
in that sense,
the microeconomic foundations of the
demand for money partly unexplained.
In any event, changes in expected inflation induced by
monetary policy will lead market interest rates to adjust
and cause substitution between interest bearing bank deposits (inside money) and non-interest bearing outside
money. Consequently, the real impact of monetary disturbances may depend on the properties of bank liabilities as
medium of exchange substitutes for outside money. This
suggests that the liability side of the banking sector's bal-

ance sheet may be important in determining the impact of
monetary policy.
In recent years, the overlapping generations model of
Samuelson (1958) has been the most popular way of explaining the role of money in intermediating transactions.
This model suggests that money is needed to facilitate spatially or temporally-separated transactions since anyone
generation is unable to arrange trades with all successive
generations without the use of some "money-like" asset. 6
A difficulty with these models is that
leave unexplained the use of non-interest bearing outside money to finance transactions when interest bearing inside money
also is available.
Bryant and Wallace (1984) appeal to legal restrictions on
private intermediation to explain the co-existence of currency and interest bearing default-free bonds. Interest
bearing default-free bonds are unsuitable for financing
many transactions because of the bonds' large denominations. Legal restrictions prevent intermediaries from creating a better medium of exchange by issuing default-free
small denomination claims to such bonds.

Economic Review / Summer 1988

Bryant and Wallace use their model to examine the
interactions between such legal restrictions and monetary
policy. In effect, the legal restrictions and the use of both
currency and bonds to fund transactions permit the government to levy a non-linear inflation tax. The real equilibrium their model achieves is not independent of either
monetary policy or the institutional factors explaining the
demand for currency and intermediary liabilities. However, these effects depend solely upon the nature of the legal
restrictions on intermediary behavior and may not be
intrinsic to all economies in which financial intermediaries
issue inside money.
Another strand of the recent literature on the demand for
monetary assets has focused on the cash-in-advance constraint model of liquidity. Drawing on a suggestion of
Clower (1967), Lucas
developed a formal model
the transaction services provided by money by assuming
money balances were required to finance purchases of consumption goods. Goods could be exchanged for money and
money for goods, but goods could not be exchanged for
goods. Also, purchases were limited by the cash in hand at
the time of purchase and could not be paid for by a subsequent exchange of interest bearing assets. In Lucas and
Stokey (1983), the model was further elaborated to allow
for two categories of goods. Some goods could only be purchased with cash, while other goods could be paid for with
a subsequent exchange of interest bearing assets. In Lucas
(1984), consumers can hold interest bearing state-contingent "securities" in addition to money. While the securities bear interest, they can be exchanged only at
infrequent intervals and therefore are not very useful for
financing consumption.
These ideas are developed further in Svensson (1985)
and Hartley (1988). In Hartley's model, consumers can use
either cash or interest-bearing "deposits" to purchase
some goods, while other goods can only be purchased with
cash. Consumers also can hold interest-bearing statecontingent securities. Cash and deposits are more liquid
than securities in that only the former can be used at any
to effect
. Cash is more
than deposits
because it can effect a wider range of purchases. While the
liquidity return is highest for cash and absent for securities,
the explicit interest payments are highest on securities and
absent for cash. This inverse relationship between liquidity
and interest yield suggests that changes in the nominal
interest payments on deposits or securities will affect the
demand for all three assets. As a result, monetary policy,
by changing the anticipated rate of growth of base money,
will have real effects by altering the demands for the different categories of financial assets.
Englund and Svensson (1986) examine banking in a

Federal Reserve Bank of San Francisco

general equilibrium
to
Lucas, Svensson,
and Hartley models. They
that changes in the credit
multiplier, or "banking sector shocks," will have real
effects, but one-time changes in the level of base money
will affect only prices. In the macroeconomic model examined in Hartley and Walsh (1986), one-time changes in the
level of the base money supply also are neutral, whereas
temporary changes in the level of the base, or changes in its
rate of growth, will have real effects by inducing substitution between holdings of inside and outside money.
Economists typically rule out the real effects of inflation-induced portfolio substitution (Tobin effects) on the
grounds that they are likely to be unimportant empirically.
For example, this is the position taken by King and Plosser.
This is a reasonable assumption concerning direct substitution between money
on the part of the
economy's wealth holders. However, the real effects of
monetary shocks in Hartley and Walsh are driven by
substitution among monetary assets such as currency and
bank deposits. The elasticity of substitution among different monetary assets is likely to be large, even if the
elasticity of substitution between portfolio holdings of
capital and liquid assets as a whole is esentially zero.
While the microeconomic models that allow roles for
both outside and inside money as mediums of exchange are
far from complete, they all suggest that monetary policy
could have significant aggregate real effects in equilibrium
models of the business cycle. In general, these effects arise
by altering the relative demands for different liquid assets.
As consumers substitute between different liquid assets as
mediums of exchange, interest rates are affected and the
flow of "savings" to
investment may be altered.
business CVC:le-Thus, even inequilbrium models of
models in which prices
move in response to perceived monetary disturbances-the role of bank liabilities
in the payments system, and their substitutability for
outside money plays a role in determining the impact of
monetary policy on the real economy.
This discussion has focused on the liability side of the
banking sector's balance
and on banks as producers
of transaction services. Banks, however, also provide
portfolio management services.
hold deposits
in order to gain access to the
system and the
transaction services banks provide, and these deposits
represent claims against the assets held by the bank. Thus,
it makes sense to consider the asset side of the banking
sector's balance sheet and banks' role as suppliers of credit
as a key channel of the impact of monetary policy. To
understand this potential channel
monetary policy
actions, it is necessary to understand the role of banks as
suppliers of credit.

III. Increasing Returns, Financial Intermediaries, and Credit
Variations in the demand for currency and bank deposits
may affect the total volume of bank liabilities and, as a
result, lead to variations in the volume of bank lending. An
increased demand for currency, for example, may produce
a decline in bank lending. But while banks are distinguished by the transaction accounts they offer, banks are
not the only intermediaries that supply credit, and the
impact on the total supply of credit due to a reduction in
bank lending will depend on how easily borrowers can
replace bank loans with credit from nonbank sources.
Changes in
volume of bank loans will have the greatest
impact on economic activity when there is something
"special" about bank credit.
This section begins with a discussion of an environment
in which bank credit has no special characteristics that distinguish it from other sources of credit and in which financial intermediaries are unimportant for the determination
of real economic activity. Then, some recent work that focuses on the role played by intermediaries is discussed.
This work suggests there may be something special about
bank credit. If this is the case, monetary policy is likely to
affect economic activity through its impact on bank
lending.
Suppose, as in the real business cycle model of King and
Plosser, that banks face constant returns to scale as providers of portfolio management services. In this case,
banks will care only about the management fees they earn,
and not about the composition of the portfolio of assets
they hold. Banks "simply cater to the tastes and opportunities of suppliers of securities and demanders of deposits. Thus, the real activity that takes place, the way it is
financed, and the prices of securities and goods are not
controlled either by individual banks or by the banking
sector." (Fama 1980, pA8)
The size of the intermediation industry can undergo
proportional expansions and/or contractions without having any effect on the relative prices of different assets.
Asset prices and the financing of real economic activity are
determined by the behavior of the economy's savers. They
ultimately hold the economy's assets, whether they do so
directly or indirectly by holding the liabilities of the
financial intermediaries. When returns to scale are constant, shifts in the public's demand for the liabilities of
intermediaries have no real effects; a reduced demand for
these liabilities shrinks the assets held by intermediaries,
but the affected assets can instead simply be held directly
in the public's portfolio.
Reserve requirements present a potential problem in this
framework. Reserve requirements force institutions subject

to such regulations to hold some of their assets in the form
of non-interest bearing assets or, in some countries, in the
form of low interest rate government securities. Reserve
requirements impose a tax on the banking sector, and drive
a wedge between the return on banks' portfolio of assets
and the return paid to depositors. With constant returns to
scale, the demand for the portfolio management services of
intermediaries subject to a reserve requirement would fall
to zero. Individuals would prefer to hold assets directly
rather than use the portfolio services of the intermediary.
Banks would not be able to pass this reserve requirement
tax on to the consumers of their portfolio management
services.
King and Plosser argue that such a reserve requirement
tax will lead to higher deposit service fees-that is, fees for
access to the payments system will rise. As a result, the
demand for bank deposits will fall, and the banking sector
will contract. However, in the model of King and Plosser,
variations in the size of the banking sector have no effect on
the real allocation of credit or the financing of real economic activity. Either financial intermediaries not subject
to reserve requirements will expand to offset the shrinkage
of the banking sector or individuals will hold the liabilities
of the economy's ultimate borrowers directly.
Fama (1985) recently has argued, however, that the
reserve tax seems to be borne by bank borrowers, not by
bank depositors. This implies that there is something
"special" about bank loans [see also James (1988)]. Borrowers are willing to pay more to obtain a loan from a bank
than from a nonbank source of credit. But this uniqueness
of bank loans seems at odds with the view that intermediation is simply a veil behind which real activity is conducted, or that variations in bank-intermediated credit can
be offset by the actions of nonbank intermediaries.
If bank credit is special, monetary policy actions that
affect the size of the banking sector will have an impact on
real economic activity. Thus, an increase in reserve requirements, for example, would shrink bank credit and
force firms to switch to less attractive sources of funds.
This would raise the net cost of funds in the economy and
lead to a fall in aggregate investment activity.
To understand fully the role of banks in determining the
effectiveness of monetary policy, it is necessary to examine
more closely why bank loans might be special. In King and
Plosser's model, asset choices of banks play no real
economic role. A very different view of financial intermediaries emerges from another body of recent reserarch
which includes papers by Boyd and Prescott (1986), Bernanke (1983), Bernanke and Gertler (1986), Stiglitz and

Economic Review / Fall 1988

Weiss (1981), and Williamson (1986a, 1986b). These papers all attempt to provide economic explanations for the
endogenous development of such institutions as financial
intermediaries (both bank and nonbank).
Two characteristics of economic transactions are sufficient to generate the presence of intermediaries: asymmetric information and increasing returns to scale. The
exact manner in which these two characteristics interact
has been modelled differently by different authors. For
example,Williamson (1986b) develops a model in which
entrepreneurs have access to a technology that requires a
fixed investment and yields a random real return, the
expected value of which is known by both borrowers and
lenders. The actual realization of the random return is
known (ex post) to the entrepreneur, but other individuals
can obtain information on the realized return only by
incurring a fixed cost to monitor each project. The presence of fixed monitoring costs makes it costly for individual investors to attempt to diversify by lending to many
different borrowers. Moreover, the projects are assumed to
be sufficiently large relative to individual wealth that entrepreneurs must gain access to the savings of several individuals in order to carry out their investment projects.
This rudimentary framework is sufficient to generate a
role for intermediaries. Since the project's actual return is
known only by the entrepreneur, in the absence of monitoring, the entrepreneur always has an incentive to report a
low return to his creditors and abscond with the profits. To
prevent this behavior, each of the individual investors who
finances a project must incur the monitoring cost. A large
intermediary, on the other hand, can finance a large number of projects and incur the fixed cost of monitoring only
once for each project. The intermediary is able to exploit
the increasing returns to scale implicit in the fixed-cost
monitoring technology. In addition, the intermediary's
ability to fund a large number of projects permits diversification of nonsystematic risks. If there is no systematic
risk, a large intermediary can offer a certain return to its
depositors. 7
Information asymmetries also give rise to debt contracts between lenders and entrepreneurs. In Williamson's
model, the optimal contract can be shown to involve a
fixed payment to the lender if the project return exceeds
some critical value R *. If the actual return is less than R *,
the lender receives the entire return. In other words, the
borrower pays a fixed rate of interest on the loan if the
return exceeds R *; otherwise the entrepreneur declares
bankruptcy and the intermediary recovers the entrepreneur's assets, which will be worth less than R*. This
contract minimizes monitoring costs since the entrepre-

Federal Reserve Bank of San Francisco

neur has no incentive to lie if the actual return is greater
than R*.
The introduction of financial intermediaries in the presence of asymmetric information and monitoring costs
leads to increasing returns to scale from intermediation. In
contrast to the view of intermediation as a constant-returnto-scale industry, increasing returns imply that the level of
intermediation has an impact on real activity, the way that
activity is financed, and the prices of securities and goods.
This is particularly apparent if the equilibrium involves
credit rationing (Williamson, 1986a).
Although these models help to explain why intermediation matters, they do not explain why banks might be
special and therefore, why monetary policy might have real
effects. One reason is that banks are both lenders and
providers of transaction services. Banks have informational advantages that result in lower monitoring costs
because they simultaneously lend to and maintain the
transaction accounts of firms. The firm's transactions account provides the bank with low cost information about
the firm. A nonbank intermediary lacking this source of
information faces higher monitoring costs. In this case,
banks are able to supply credit more efficiently than can
other intermediaries. Consequently, if monetary policy
affects the size of the banking sector, it also will affect the
level of real economic activity.
While the economic role of intermediaries seems more
fully developed in the asymmetric information literature,
the real business cycle research has, somewhat paradoxically, provided a much more detailed analysis of the
impact of monetary policy.8 One attempt to bridge this gap.
is developed in Hartley and Walsh (1986), which supplements a conventional ad hoc macroeconomic model with a
banking sector that makes loans to finance real investment
spending. This framework permits the study of the macro
implications of intermediation when intermediation matters. They show that monetary policy has real effects when
changes in expected inflation induce substitution between
bank liabilities and non-interest bearing outside money.
Equal changes in all nominal interest rates (in order to
restore expected real rates) alter the relative demands for
non-interest bearing outside money and interest bearing
inside money. Both the market for bank deposits and the
market for outside money are affected, and adjustments in
the price level cannot restore equilibrium to both markets
simultaneously. As a result, real interest rates must adjust.
Movements in the rate on bank deposits then lead to
changes in the supply of bank loans and bank loan rates
that affect the level of real economic activity. Unlike the
case considered by King and Plosser in which returns to

scale in intermediation are constant, changes in the quantity of bank credit are not fully offset by changes in credit
supplied by nonbank intermediaries or by changes in direct
lending by lnnnl1,ill51d"
Additional
which monetary policy can
affect real activity arise when bank liabilities are subject to
reserve requirements.
reducing the nonbank sector's
demand for outside money, an increase in expected inflation increases the supply
reserves available to the
bankmg sector. Since reserves can be viewed as an input in
the intermediation process under a fractional reserve system, an increase in expected inflation allows the banking
sector to
the
of loans. This reduces the
equilibrium loan rate and leads to a rise in real investment.
Shocks to the banking sector have effects on the level of
real economic activity,
because they affect the supply
of loans. In Williamson's model of intermediation, for
example, disturbances work through the asset side of the
banking sector's balance sheet. In contrast, disturbances to
banks in King and Plosser's model can have real effects
only if they influence the provision of transaction services.
Real effects arise, not because of variations on the asset
side of banks' balance sheets, but because of variations on
the liability side
to the role bank deposits as a means
of payment.
Several recent
have been made to determine

whether it is bank credit (the asset side) or money (bank
liabilities) that matters for real economic activity. Bernanke (1983) found that for the 1920s and 1930s money had
effects on real output even after controlling for credit.
Empirical evidence from post-war data is reported by King
(1986) and Bernanke (1986). King finds little support for
the role of credit as the transmission mechanism for
monetary policy. In vector autoregressions (VARs) that
include real GNP, demand deposits, and various measures
of bank loans, demand
account for a
much higher fraction of the variance of GNP forecasts
errors than do any of the loan variables. Since King's
measure of money-demand deposits-is a measure of
inside money, these results seem most consistent with the
real business cycle view.
Bernanke (1986) obtained somewhat
results
when he used a structural model to identify underlying
money and credit shocks in a VAR that included, in
addition to Ml and a measure of credit, real GNP, real
defense spending, and the monetary base. Based on a
decomposition of the output forecast error variance, credit
shocks appeared to be much more important than shocks to
the monetary base (outside money). Ml and credit shocks
were of roughly equal importance. These results make it
clear that few generally agreed upon empirical regulantres
exist in this area,

IV. Conclusions
Recent research in monetary economics that has focused
on the role of information asymmetries and the costs of
monitoring provide an improved understanding of the role
of financial intermediaries.
research highlights three
characteristics
intermediaries that seem of special importance from the
of understanding the role
played by monetary policy in equilibrium models of business cycles.
when intermediation is modeled as a
constant-returns-to-scale
(as in the real business
the asset side of the
cycle model of King and
banking sector's
is irrelevant for real economic activity. Variations in bank-intermediated credit are
offset by other
or
portfolio adjustments on the
of lnrlnl1,rlllClI"
Second, the
bank liabilities as a means
of payment
the impact of
monetary policy.
policy can induce individuals
to substitute between bank deposits and outside money.
These portfolio
will
relative rates of return and
real economic
of the portfolio
adjustments caused
in the relative yields of
bank deposits and outside money
depend on the

transaction properties of currency and bank deposits, and
the characteristics of the payments system.
Third, if bank loans are special, perhaps due to the
information efficiencies attributed to the banking sector's
role as a provider of both credit and transaction services,
then variations in the banking sector's aggregate lending
will have an impact on real economic activity. Monetary
policy will influence the real economy through its influence
on the supply of bank
. Variations in the path
inflaof outside money that induce changes in
tion will result in nominal
rate adjustments,
such adjustments generally will affect real rates and will
thereby affect the supply of bank
If financial intermediaries
form a veil behind
which real activity takes place, the resolution of many of
the issues faced by economic policy makers is quite simple.
If real activity, and the way it is financed, is independent of
the actions of financial intermediaries as Fama (1980) and
King and Plosser (1984) assume, then there would appear
to be no justification on monetary policy grounds for any
special regulation of the banking sector." The appropriate
conduct of monetary policy in
an environment also is

Economic Review I Fall 1988

straightforward. Since variations in the monetary base have
no effect on real variables, the monetary authority need
concern itself only with achieving price stability.
However, if bank loans or deposits are in some sense
special, then the optimal design policy becomes a more
complicated task. From both sides of the banking sector's
balance sheet there seem to be good theoretical reasons to

believe monetary policy disturbances will not be neutral,
even in equilibrium models of the business cycle. Policy
analysis requires a better understanding of the role of both
bank lending and bank provision of the medium of exchange. Without such an understanding, we are unable to
evaluate alternative policy proposals.

ENDNOTES
1. By "banks," we mean financial intermediaries whose
liabilities provide transaction services.
2. For a more general summary of the real effects of
monetary policy, see Blanchard (1987).
3. This superneutrality result does not strictly hold in a
model like King and Plosser's which incorporates an
endogenous labor supply decision unless the labor supply decision also depends only on ex-ante real interest
rates. However, King and Plosser ignore this potential
effect as empirically unimportant.
4. For a model of bank runs, see Diamond and Dybvig
(1983).
5. As will be discussed in Section III, Bernanke's evidence also is consistent with the view that it is bank
lending that is the key channel through which banking

disturbances affect real economic activity.
6. Assets used to carry out intergenerational trades need
not, however, bear much resemblance to money For
some examples from nonmonetary economies, see Walsh
(1983).
7. Since the large intermediary can earn a certain rate of
return through diversification, the type of asymmetric information problem between bank and depositors analyzed by Leland and Pyle (1977) does not arise.
8. A recent paper by Williamson (1987) attempts to incorporate his earlier work on intermediaries into a real business cycle model.
9. For a discussion of banks and regulatory policy, see
Furlong and Keeley (1988)

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Federal Reserve Bank of San Francisco

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Kydland, Finn E. and Edward C Prescott. "Time to Build
and Aggregate Fluctuations," Econometrica, 50 (6),
November 1982, 1345-1370.
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Long, John B., Jr. and Charles I. Plosser. "Real Business
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1983, 39-69.
Lucas, Robert E., Jr. "An Equilibrium Model of the Business Cycle," Journal of Political Economy, 83 (6),
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_ _ _ _ ."Equilibrium in a Pure Currency Economy,"
Economic Inquiry, 18, April 1980, 203-220.
_ _ _ _ ."Money in a Theory of Finance," CarnegieRochester Conference Series on Public Policy, 21,
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and Monetary Policy in an Economy Without Capital,"
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1958,467-482.
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Economic Review /Fall 1988

Banks Affiliated with Bank Holding Companies:
A New Look at their Performance

Randall Johnston

The bank holding company (BHC) form oforganization
has a number ofadvantagesfor banking firms. It also is the
form that many are recommending be used to enforce
corporate separation of traditional banking from expanded banking activities. This paper examines the influence ofBHC affiliation on bank behavior. The literature on
this subject is large, but has ignored an important potential
source of bias. The measured effects of BHC affiliation
generally are larger when this bias is treated statistically
using a technique described in the paper. BHC-affiliated
banks do appear to behave differently than their nonaffiliated counterparts, a finding that does not augur well
for using this organizational form to isolate a bank from
the effects of nonbank activities.

Assistant Vice President, Banking and Regional Studies, Federal Reserve Bank of San Francisco, The author
wishes to thank William M. Robertson and Rachel A.
Long for their excellent research assistance. Editorial
committee members were Michael Keeley, Reuven Glick,
and Ronald Schmidt.

Federal Reserve Bank of San Francisco

The bank holding company (BHC) form of organization
has a number advantages
banking
but analysts
have argued that such an organizational form also may lead
to changes in the behavior of banks affiliated with BHCs. In
the 1960s and 1970s, the rate of formation
was very
rapid, leading to increased concern that this organizational
form would have adverse effects on bank performance.
This interest in the effects of BHC affiliation on bank
performance has been revived recently as part of the debate
over the expansion of bank powers. Many are recommending that expanded powers be placed in nonbank subsidiaries of bank holding companies as a means of insulating
the bank from any risks arising from those new activities.
The assumption is that if the new, nonbanking activities are
"corporately" separate from banking activities, the behavior and financial soundness of the bank will be unaffected. An examination of the effect of BHC affiliation
on the performance of banks may shed some light on this
debate. To the extent that affiliation with a bank holding
company affects bank behavior, expectations about the
effectiveness of the BHC structure in insulating banks
from other activities in the BHC may be too sanguine.
The methodology for examining the influence of BHC
affiliation has been quite straightforward. Analysts have
compared the income and portfolio characteristics of affiliated banks with those of banks that are not affiliated with a
BHC. To ensure that other characteristics of the banking
organizations do not bias the comparisons, various statistical control methods have been used. Most commonly, each
affiliated bank is "matched" with an unaffiliated bank in
size, location, or other attributes. Any differences in
performance are then attributed to the affiliation status of
the banks. Alternatively, econometric techniques have
been employed to control for the diverse characteristics of
affiliated and non-affiliated banks. Both types of studies
have found important differences in the behavior of BHCaffiliated and non-affiliated banks.
These analyses implicitly assume that, except for their
organizational form, affiliated and non-affiliated banks are
identical. If they really are identical, however, why are
some banks part of BHCs and others
It seems likely
that there is some tendency for self-selection processes to
bias simple comparisons of the behavior of affiliated and

non-affiliated banks. Banks that choose to become part of
holding companies may have more aggressive management, for example. This may influence observed performance, and simple comparisons with non-affiliated banks
will detect the differences. In this case, it may be incorrect
to attribute the cause of these differences to the affiliation
status. With the renewed importance of understanding how
banks behave in different organizational contexts, it would
be useful to reexamine the behavior of affiliated banks and
to correct, if possible, for the effects of serr-seiecnon
processes.
The purpose of this paper is to explore the possible
influence of self-selection bias on the typical findings
regarding the behavior of BRC-affiliated banks. By using
simple techniques to control for self-selection in the affiliation decision, I obtain results that differ
many tradi-

tional findings. Some of my nndmgs are more consistent
with the theory of why banks
with BRCs
the
first place.
In the first section, the reasons
affiliate
a
and the theoretical implications
bank behavior are
briefly.
conventional techniques
affiliation are examined,
studies have produced.
methods to control for such a
In
statistical control technique is applied to data
a
sample of western banking organizations
paper conof the
eludes with a summary and
implications of this research.

I. Bank Holding Company Amnauon:
The Economic Implications
To understand why affiliation of a bank with a
might affect the bank's behavior, it is important to discuss
the motivations for BRC affiliation. These motivations
involve both operational and tax advantages of the BRC
form of organization and explain formations of both onebank and multi-bank holding companies.

Motives for BHC Formation
The numerous operational advantages of BRC affiliation derive largely from distortions introduced by regulation and law. First, the activities of non-affiliated banks
traditionally have been restricted by regulation to endeavors related to conventional banking business. One way a
banking organization may expand its range of activities is
to affiliate with a bank holding company. I A bank holding
company may engage in a variety of activities through the
nonbank affiliates of the bank; the affiliated bank thus may
gain advantages from joint marketing or production of
services with these subsidiaries.
Second, banking organizations structured as holding
companies also can avoid some of the laws that restrict
branching in certain states. By acquiring individual banks
and maintaining them as separate subsidiaries of a BRC,
such a banking organization and its bank subsidiaries may
be able to enjoy geographical portfolio diversification,
economies of scale, and other benefits that accrue to branch
bank structures. In fact, the multi-bank holding company
structure is common in states with laws that restrict
branching by individual banks.
Third, bank holding company affiliation affords a banking organization greater flexibility in financing its activ-

ities. For example, shares of
are more liquid than shares in ,nrl1u,rI,,·, I
generally may not repurchase their own
BRC may.
forming a one-bank
therefore, the shareholders
obtain increased marketability
securities of the BRC also enjoy favorable
ment compared to the same securities
cally,
non-deposit debt is not Cllf,ip,~t
requirements, whereas similar obligations
Affiliation with a
was used as a mechanism to avoid
bank level. Specifically,
(vs.
used to
a
assets is ~"5I.HU'''U
means of limiting bankruptcy risk in
Through means of a bank holding company structure,
affiliate bank's
(capital) can be nrrnruipr!
the BRC. To the extent that
investment in
bank
level, the
is
in
constraints imposed at the bank
as "double leverage,
the ratio
the equity in the
equity investments in a bank thus is
form of orgamzanon.
Since 1982, bankregulators
practice by coordinating
BHCs.
the bank
the bank, the parent
with their interorganization obligations

Economic Review / Fall 1988

maintain the same ratio of capital to total assets. This does
not completely eliminate opportunities for double leverage
of the bank's capital,
capital in nonbank
subsidiaries can be manipulated to create the appearance
of more capital in the
(although regulators try to
monitor nonbank capital}? In addition, there are differences in the treatment of goodwill and certain types of
debt on the books of the
versus those of the bank that
tend to have the effect of creating double leverage opportunities.
in assets,
to
300 percent double leverage is permitted by regulation.
Thus, the BHC form of organization still may be perceived
as
to
bank capital
regulation.
Double leverage also creates a tax-related incentive for
using the bank holding company
of organization. It
involves the tax treatment of dividends generated by a
banking organization. If the bank is owned directly by
private shareholders, dividends paid to these shareholders
are non-deductible expenses of the bank, taxable to the
shareholder at his personal tax rate. If the bank, instead, is
owned by a bank holding company, 85 to 100percent of the
dividends are deductible at the bank level (that is, they may
be passed essentially tax-free to the parent BHC). To the
extent that the parent BHC can use debt to finance its
activities, these "upstrearned" dividends can be converted, in effect, to deductible interest expenses. Thus, an
investor desiring to finance banking activities with a given
proportion of debt and equity enjoys better tax treatment if
he does so through a holding company rather than through
direct, private ownership the bank.
There are potential disadvantages to
affiliation as
well, since
holding company
of organization is
more complex in a legal sense, and regulation of
affiliated banks differs from that
non-affiliated banks.
Specifically,
affiliation brings the banking organization under the regulatory aegis of the Federal Reserve
System, which is charged with
bank holding
company law. In general, the range of
permitted
BHCs by federal law and regulation is not as broad as that
permitted by some state bank charters. Nonetheless, the
advantages appear to have
the disadvantages
historically, as
proportion
with
BHCs has increased steadily.

Implications
The advantages of
affiliation discussed above have
fairly straightforward implications for the consolidated
organization. Since shareholders have an interest in financing and operating the banking organization as a whole in
a value-maximizing manner,
of affiliation

Federal Reserve Bank of San Francisco

should be reflected in enhancement of aggregate shareholder wealth and in the superior ability of BHC organizations to compete in providing financial services. There is
some evidence for this. For example, the BHC organizational form does seem to be competitively superior because
it has come to dominate American banking market structure." Nonetheless, it would be desirable to observe the
improved (or degraded) value of the affected entity directly. Most research on the effects of BHC affiliation has
not focussed on the consolidated entities, however, but
rather on the affiliate banks. There are two reasons.
First, studies of the consolidated enterprises are inherently difficult to conduct. To study directly the effects of
affiliation on shareholder wealth, good estimates of the
market value of equity must be available. Since most
banking organizations are relatively small, closely held
companies, estimates of the market value of equity (with or
without affiliation) are not easily derived. It is possible to
narrow one's focus to the larger banking organizations
whose shares are actively traded, but the number of such
institutions is small and the effective sample size in such
studies compromises these efforts. 4
The second reason that research has not focussed on the
consolidated entity also is a pragmatic one. Policy interest
in the bank holding company movement has been focussed
on the implications of affiliation on bank affiliate behavior.
This is natural, since lawmakers and regulators view the
subsidiary bank as the entity delivering banking services; a
different corporate structure and method of corporate
control might well influence such an affiliate's behavior.
However, the link between the motives for BHC formation
and the likely behavior of bank affiliates generally does not
follow in an obvious way from the motives for BHC
formation.
Consider, for example, the potential influence of BHC
affiliation on the profitability of the subsidiary bank. The
underlying motivations for affiliation suggest only that
the profitability of the consolidated enterprise would be
higher with affiliation. The profits of the affiliated bank
may be higher if the affiliation produces scale or scope
economies for the bank affiliate. These may not appear at
the bank level, however, if the way in which the bank funds
or compensates other units in the holding company is
through payment of fees (implicitly or explicitly) rather
than through upstreaming of dividends to the parent
holding company. Indeed, if inter-affiliate fees are high
enough, it would be consistent with theory to find measured net bank income lower in affiliated banks (even
though consolidated company earnings are improved by
affiliation).
Similarly, the effects of affiliation on the capital position

of the bank also are ambiguous. If, for example, the desired
use of debt is greater than is permitted at the bank level and
the parent funds subsidiary bank equity with debt to relieve
the regulatory constraint, then affiliation might result in
increased capital at the bank level. If, on the other hand,
regulatory capital constraints are not binding, a bank
affiliated with a BHC might reduce its capital-redeploying it to fund the sister affiliates of the bank. This would be
consistent with a view that the benefits of affiliation flow
not from the double leverage opportunities afforded the
BHC, but rather from the economies offered by the expanded scope of activities.
The influence of affiliation on the portfolio composition
of banks also has been a concern of policy makers. One

likely possibility is that bank portfolios become less diversified or otherwise riskier because diversification opportunities exist elsewhere in the holding company. On the
other hand, the BHC form of organization avoids branching constraints and thus permits greater geographical
diversification of lending activity and reduced portfolio
risk.
These theoretical ambiguities, coupled with the focus of
policy-makers on banks, rather than on consolidated banking organizations, makes the effect of BHC affiliation on
bank behavior an empirical matter of some importance. It
is a matter of increasing policy relevance, too, as lawmakers debate the appropriate organizational form in which to
vest expanded powers.

II. Studying the Impact of Affiliation
The effect of BHC affiliation on bank behavior has
received considerable attention from banking analysts.
Over 50 studies published since the late 1960s have examined the effect of BHC affiliation on the performance of the
subsidiary bank.>
Both simple means and frequency comparisons, as well
as more sophisticated econometric techniques, are employed in this type of BHC research. Both types of studies
employ techniques to control at least partially for the wide
variation observed in bank characteristics and market
conditions. In the simple statistical studies, the variation in
bank characteristics is controlled by comparing the behavior of a bank after affiliation with its own behavior
before affiliation. To control for changes in overall banking
market conditions, the changes in the affected banks'
performance are compared with the changes in performance observed in a "paired" sample of unaffiliated banks.
The "pairing" involves identification of a non-affiliated
bank of approximately the same size as the affiliated bank,
located in the same (or a similar) banking market. 6
In other studies, variation in bank characteristics and
market conditions is controlled partially by entering attributes of the bank and the banking market as independent
variables in regressions on bank performance measures.
An estimate of the effect of BHC affiliation in a crosssection of affiliated and non-affiliated banks can then be
observed with a dummy variable indexing the affiliation
status of the banks in the sample.
Both types of studies have obtained similar estimates of
the effect ofBHC affiliation on bank behavior. Specifically,
affiliation is found to (1) increase the proportion of loan
assets in bank portfolios; (2) increase the proportion of
state and local obligations; (3) increase loan fees and

interest charges; (4) reduce holdings of cash and U.S.
Treasury securities; and (5) with less regularity, increase
deposit rates." There has been variation in all of these
findings across studies, as might be expected given the
variation in models, samples, and statistical techniques.
But the BHC affiliation studies have been striking in their
tendency to find significant differences in the behavior of
affiliated and non-affiliated banks.
In general, however, the findings have been particularly
weak regarding the effects of affiliation on profitability and
capital ratios-effects crucial to formulating regulatory
implications. By using either paired comparisons or econometric models, little change is found in regulatory capital
measures or profitability measures such as return on equity
(ROE) or return on assets (ROA).8

Problems with BHC Studies
Bank holding company research has been subject to a
variety of criticisms. One is that available statistical controls are insufficient to correct for the great variation in
circumstances that contribute to differences in bank behavior observed in the real world. In theory, there should
not be much, if any, variation in the performance of
affiliated and non-affiliated banks in a competitive market.
If sufficient statistical control for variation in market
conditions peculiar to individual banks were possible, the
observed variation in behavior would vanish. Research on
BHC affiliation, therefore, like most bank research, implicitly relies on the existence of disequilibrium, adjustment lags, or imperfections in the extent of competition to
introduce durable variations in observed performance and
the decision to affiliate.

Economic Review / Fall 1988

In addition to this general criticism, specific criticisms
of BHC studies concern the particular methods of control.
Univariate studies, for example, have been criticized for
the bias they introduce in limiting the comparisons to
banks of a size that permits "pairing" of observations.
Most independent banks tend to be small; using pairing as
a control technique thus tends to bias sampling toward
smaller institutions. 9 If scale economies or other sizerelated considerations are determinants of bank behavior,
as seems likely, such a sampling bias may be important.
The univariate studies also have tended to use pre- and
post-affiliation comparisons of bank behavior. This technique has been criticized for failing to control for the time
that elapses between independence and affiliation.t?
Econometric studies have received less fundamental
criticism. Most criticisms have been directed at alleged
errors of omission or commission in selection of control
variables and in the stress placed on simple cross-sectional
comparison, rather than the pre- and post-affiliation comparison technique used in the univariate studies.

Self-Selection Bias
A more important criticism of traditional bank holding
company research-both in its univariate and econometric
manifestations-is that it has ignored the potential problem of self-selection bias.'! Self-selection bias arises because the decision to affiliate with a BHC is not random;
rather, it is an outcome of the same organizational forces
that determine other aspects of bank behavior.
To see how self-selection processes may bias the estimation of the influence of BHC affiliation, consider the
typical cross-section regression employed in econometric
studies:
(1)

where Y, is a performance measure, such as bank ROE, or
a portfolio measure, H is a dummy variable indicating the
bank's affiliation status (H = 1, if affiliated, and =
otherwise), X, is a vector of other bank or market characteristics suspected of influencing performance, and a, b,
and c are coefficients.
The influence of BHC affiliation is measured by the
coefficient, c, on the affiliation variable. For the estimate
of c to be unbiased, however, it must be uncorrelated with
the error term, e" in the performance equation. This will
be the case if holding company affiliation is assigned
independently of the X variables, but not otherwise.
For example, suppose that a bank chooses to become
affiliated with a BHC on the basis of another (unobserved)

Federal Reserve Bank of San Francisco

factor (such as expectations of future profits) not included
in X" which we might call Y 2' Specifically, if
(2a)

and if
Y2

< 0, thenH

= 0.

(2b)

That is, if expected profits exceed a certain level, then
the bank chooses affiliation; if they are equal to or below
that level, then it does not choose affiliation. The value that
Y 2 takes depends upon other conditions that prevail in the
market or at the bank, X 2 , and a random disturbance term,
e 2 . That is,
(3)

The relationships (1), (2), and (3) make up a simple,
simultaneous equations system. Thus, if the covariance of
e, and e 2 is not zero, ordinary regression analysis of
equation (1) will not produce unbiased estimates of its
coefficients. This is because any disturbance to e 2 will
translate into a disturbance in H, which would then be
correlated with the covarying e,. Thus, H is a stochastic
variable correlated with e,.
As a practical matter, self-selection bias seems likely.
That is, it seems likely that factors that disturb the bank's
perception of its expected profits, for example, are likely
also to disturb its performance. Therefore, it is likely that
the disturbance terms of equations (1) and (3) do have nonzero covariance, and that simple regression analyses of
BHC impact will produce biased estimates of the effects of
BHC affiliation.

Treating Self-Selection Bias
The statistical solutions to the problems of self-selection
bias belong to a class of econometric methods known as
simultaneous equations techniques.F The general approach of these techniques is to "purge" the stochastic
explanatory variable (H, in this case) of the influence of e 2 .
This is achieved by estimating H using only non-stochastic
variables in a separate, "first-stage" regression. The predicted values of H are then mathematical combinations of
non-stochastic variables and would be uncorrelated with
e,_ If these predicted values are used instead of the actual
values of H in regression (1) (the second stage), then the
estimates of c would be unbiased.
Two problems arise in applying this technique to the
model described by equations (1), (2), and (3). First, if all

of the non-stochastic variables in the first stage also
logically belong in the second stage regression, then the
predicted values of H are simply a linear combination of
the Xl' and the second stage regression will not be
estimable. (Of course, it need not be the case that all of the
X variables in equation 0) belong in equation (3) and vice
versa. In such a case, the exclusion of certain X variables
will permit identification of the influence of BHC affiliation on the performance measure, Y].)
Second, H (the stochastic variable that introduces the
simultaneous equations bias) is a dichotomous variable; it
takes on values only of 0 or 1.
of a
regression equation with a dichotomous dependent
able (such as the first stage regression above) poses
difficulties.
Both the identification problem and the dichotomous
dependent variable can be addressed by estimating the first
stage using a model known as a probit model. Specifically,
a probit relationship can be used to estimate the first stage,

producing
values of H. The probit model is
nonlinear, and permits identification of the coefficient on
H even ifexclusion is not possible. The probit model also is
intended specifically
use with dichotomous dependent
variables.
Equation
would then be
in the form

(4)
where H is the predicted probability of being affiliated
with a BHC
the
and
It can
that the
be unbiased, though the
standard error
will not be precisely correct
unless
maximum-likelihood estimation technique is
used. As a practical
the standard error estimates
tend to change little with maximum likelihood estimation.P

III. Application to a BUC Performance Study
In this section, the probit technique for controlling
sample selection bias is applied to an econometric study of
the performance of affiliated and non-affiliated banks.
Results from conventional econometric techniques for
identifying the effects of affiliation are compared to those
obtained from a two-stage estimation procedure using a
probit model to explain the BHC affiliation selection
process.

The Sample
The study examines the performance of a cross-section
of commercial banks in the Twelfth Federal Reserve District in 1985.]4 Because the circumstances of the banks in
the sample in previous years were expected to be relevant
to both the affiliation status of the banks and their performance, data were collected
these banks for the years

Economic Review I Fan 1988

and 1985. The only selection criterion
constructing the sample was that the banks have
k'p'....rvr-t c of Condition and Income Statecontinuously during the sample period. There were
Not all
all varisome of the analyses presented below using
performance measures or other variables result in
correspondingly smaller samples.
notcmg company affiliation grew steadily in the
20 percent of the banks in
By 1985, the proporthe 324
in
affiliation status at some
The growth in «UIHUl.IUll
small-bank phenomenon, however.
proporassets in
was already 87
and grew to 95 percent in 1985.
sample means are presented in Table I. From a
comparison of sample means, affiliated banks tend
with more loans and higher loan rates, fewer
lower returns than non-affiliated
of leverage appears to be approximately
of organizations.

econometric model described by equaeffect of affiliation with a BHC can be
ordinary least squares regression techHl'!I"''"'" The effects of affiliation in the current period are
estimated in
manner for current measures of leverage,
profitability,
composition, and pricing.
In
to
dummy variable representing current
variables to control for crosssectional variation in
and market attributes were
regressions. Lagged bank size is used to
potential influence of size on the behavior of
age of the institution is included, on
the
mature financial
may
behave
than start-up organizations. The length
the bank has
affiliated with the
also is
affiliation status-to capture
of affiliation on bank performdummy vananies are included to control for
ance.
variation in
conditions, variations in bank
branching, state charter powers, or other regulations that
might be expected to vary by state. J5
estimated impacts of affiliation using this simple
regression
are summarized in the first column of
2. Not all of the coefficients on the affiliation
variable
in this column are statistically significant.
however, that affiliation with a

Federal Reserve Bank of San Francisco

BHC appears to (1) increase the proportion ofloans in total
bank assets, (2) increase municipal bond holdings by the
affiliated bank, (3) increase average loan income and
deposit rates, (4) reduce holdings of cash and Treasury
securities, and (5) reduce return on equity or assets. The
effects on leverage are mixed; the use of equity is lower
relative to total assets, but higher relative to risk-assets.
These findings generally are consistent with the findings of
other studies that have used other samples at other points in
time.

Correcting for Self-Selection
As
the process for
correction
self-selection bias involves a two-stage estimation procedure. The first stage involves estimation of the "Affiliation Choice" relationship. The current affiliation status of
the banks in the sample is modelled using probit representations. The selection of variables for inclusion in the
probit regression is constrained somewhat by the availability of historical data on the study sample. The variables
selected are intended to capture the influence of prior
performance, prior affiliation status, and state location on
the affiliation choice. The estimated parameters of the
probit model of the affiliation choice relationship are
presented in Table 3.
It appears from this regression that, in addition to prior
affiliation status, prior performance of the banking organization bears importantly on whether it was affiliated in
1985. The probability of being affiliated with a BHC in
1985 appears to be positively related to the capital/asset
ratio and the loan rate, and negatively related to the return
on equity, the deposit rate, and total assets. The latter effect
is consistent with the availability of more favorable doubleleverage opportunities to smaller (less than $150 million in
assets) banks. The state dummies are consistently insignificant, an observation in keeping with the notion that
variations in state branching or charter powers are not
important in determining BHC affiliation status-at least
in the states that comprise the Twelfth District.
The
are
Ineluded in two alternative representations of the performance relationships. The first, called the "Exclusion
Model," excludes from the performance relationship some
of the explanatory variables that were included in the
affiliation choice relationship. The excluded variables are
various bank performance measures from the year 1976. 16
This may help to identify the effects of the affiliation
decision by excluding these variables from the performance relationships. In the second representation, called the
"Non-Exclusion Model," these variables for 1976 are

included in the performance regressions as well. Identification of the influence of BHC affiliation on performance
is achieved exclusively by virtue of the nonlinearity of the
probit relationship.
Identification by exclusion mayor may not be justified.
One must be willing to assume that some variables that
influenced holding company affiliation can be excluded as
influences on current bank performance. There is no a
priori way of telling, however, whether that assumption is
more reasonable than the alternative approach, which
relies exclusively on the nonlinearity of the affiliation
choice
17
In the
column
2,
effects of
affiliation are reported for an exclusion model with no
correction for self-selection bias. In the second and fourth
columns, the impact of affiliation is presented for the twostage model that corrects for self-selection bias. The second column presents the results from the exclusion model
and the fourth column presents the non-exclusion results.
For comparison, the third column reports the results of a
simple regression which does not exclude any performance
variables and does not correct for self-selection bias.

Economic Review / Fall 1988

Findings
The results of these simple tests of the effects of bank
holding company affiliation differ qualitatively between
the models that treat self-selection bias and those that do
not. The low levels of significance of some of the estimated
coefficients permit few strong statistical statements. How
ever, qualitatively at least, treatment of self-selection bias
appears to reverse the estimated direction of the effect of
BHC affiliation or change the point estimate of its magni
tude in virtually all cases.
The effects are most easily seen in the two panels of
Chart 1. The conventional finding that equity is lower in an
affiliated bank is reversed in both of the models that treat
self-selection bias. After correcting for self-selection, eq
uity relative to risk assets and equity to total assets both
appear to be higher at affiliated banks, although the finding
for the equity/risk asset ratio is statistically significant only
for the self-selection model that employs the exclusion
assumption to identify BHC impact.
The models with self-selection corrections find that
measured capital ratios are higher at BHC-affiliated
banks. This is consistent with the view that affiliation is

C h a rt 1A
E f f e c t s @ B H C A ffiliatio n
1
om B ank Peirf@™ar8©@
bhc

Coefficient

E x c lu s io n

H@ dei

*These effects have been multiplied by a factor of ten to make them
more visible on the chart.

Federal Reserve Bank o f San Francisco

attractive because it allows BHCs to downstream debt as
equity to the subsidiary bank. Indeed, the failure of earlier
studies to find this impact consistently has been puzzling.
As the table and charts indicate, the self-selection cor
rection models also change the findings regarding the
impact of BHC affiliation on portfolio composition. The
measured impact of affiliation on the share of loans in total
assets is two times larger after correction for self-selection
than before. Failing to correct for self-selection bias may
underestimate the impact because banks choosing to affili
ate with BHCs may tend to be those that, for other reasons,
may wish to take on more risky assets and see the BHC
vehicle as a convenient means of financing such a portfo
lio.
A larger impact on the average loan rate (measured as
the ratio of average loan income and fees to total loans) also
is found with the models using a self-selection correction.
The impact of BHC affiliation on the measured loan rate is
six to seven times higher in the corrected versus the
uncorrected models. This finding is consistent with the
argument that those seeking BHC affiliation may be seek
ing more risk if the higher rates reflect a risk-compensated
return.

BHC
coefficient

@Biart 1IB
E ffe e te ©f BH© A ffiliatio n
©n Bainlc P©rf@rmaiti©©
N on-ExoSysion M odel

*These effects have been multiplied by a factor of ten to make them
more visible on the chart.

Other impacts of BHC affiliation are less notably altered
by employing the two-stage model for self-selection bias.
The holding of Treasury securities appears to be reduced
by BHC affiliation in the corrected models. The influence
of affiliation on the holding of cash assets remains of low
statistical significance. The measured negative impact on
the return on equity is larger, but of low statistical significance. The measured impact on the return on assets is
about the same, but of lower statistical significance. Difficulty in measuring impacts on earnings and returns is
typical in banking research, due to the problems in using
accounting measures of the components of these statistics.
Traditional models have tended to find a significant,
positive effect of BHC affiliation on a bank's willingness to
hold municipal bonds. This is not the case in my sample,
perhaps because of the relatively recent data used. The tax
treatment of municipal bonds held by banks changed with
tax legislation in the 1980s and may have changed the
direction of the effect of BHC affiliation. Both corrected
models appear to amplify this effect.

Most of the other coefficients of the regression are not of
policy interest and, for brevity, are not discussed here.
However, it is interesting to note that the variable designed
to capture the effect of the time elapsed since BHC
formation-the age of the BHC interacted with affiliation
status-is insignificant in all performance regressions.
Hence, all of the effects of BHC affiliation appear to be
captured by the affiliation status variable alone. (This is the
measure reported in Table 2.) This suggests that, whatever
the influence ofBHC affiliation, the effects do not grow or
fade with time. It also is interesting to note that the dummy
variables for the various states in the region generally are
not significant in the affiliation choice probit regression.
There is considerable variation in the powers afforded
banking organizations in the various states of the region. If
state chartering was a viable alternative to obtaining some
of the flexibility ofBHC affiliation, presumably the affiliation choice regression would have been influenced accordingly by the state dummies.

IV. Conclusion and Policy Implications
The measured effects of BHC affiliation on subsidiary
banks are sensitive to attempts to correct for self-selection
bias. This suggests that the behavior of a bank and its
decision to affiliate with a BHC are statistically related.
This, in turn,implies that the findings of the large number
of earlier BHC impact studies should be reconsidered in
light of their failure to recognize and address this statistical
problem directly.
In the specific population of banks examined here,
several important measured effects of BHC affiliation are
changed when self-selection correction procedures are
employed. As important as the direction and magnitude of
the changes, however, is the fact that BHC affiliation

continues to be associated with significant differences in
bank behavior even when self-selection bias is treated. This
suggests that the behavior of a bank is not independent of
the nonbank and holding company affiliations it forms,
and contradicts the notion that banks can be "corporately"
separated from the activities of their sister or parent
organizations. Such separation often forms the basis of
proposals that would give banking organizations additional nonbanking powers. My findings suggest that corporate separation cannot fully insulate the bank from the
expanded risk-taking opportunities that such an expansion
might imply.

Economic Review / Fall 1988

ENDNOTES
1 In some states, a banking organization is allowed to
engage in a wide variety of activities under a state charter.
Thus, obtaining a state charter is one way to obtain broad
banking powers. The fact that the BHC movement has
dominated state chartering may suggest that other aspects of the BHC form of organization may be more
important than the powers issue.
2. Specifically, if a BHC has substantial nonbank subsidiaries, its consolidated capital/asset ratio may appear high
(and compatible with the subsidiary bank standard), but
be lower than it would be if the bank truly had to be
financed with equity. In addition, Regulation Y permits
banks smaller than $150 million in assets to form a BHC
and use as much as three times the debt in the parent as
would be permitted in the bank affiliate.
3. In the population employed in this study, for example,
fully 92 percent of bank assets are represented by BHC
affiliated banks.
4. A good example of a market valuation approach that
suffers from sample size problems is Varvel (1975).
Frieder and Apilado use share price evidence in the 1982
study, and a synthetic valuation scheme in their 1983
study.
5. The paper by Frieder and Apilado (1982) provides a
useful summary and synthesis of bank holding company
research.
6. Frequently cited "matched pair" studies include Smith
(1971), Talley (1972), and Hobson, Masten and Severiens
(1978). The econometric studies cited are those by
Johnson and Meinster (1975), Rose (1975), Mingo (1976),
Mayne (1977), and Rhoades and Rutz (1982).
7. See Frieder and Apilado (1982).
8. See the study by Fraas (1974) summarizing the ambiguous findings of earlier studies.
9. This criticism is mentioned by Jessup (1974) and
Frieder and Apilado (1982).
10. The Hobson, Masten and Severiens (1978) study was
one of the first to emphasize the effects of the time elapsed
since acquisition.
11. The author is not aware of any direct reference to the

problems of self-selection bias in previous bank holding
company research.
12. The literature on self-selection bias in economics
arose out of studies of government program impact. See,
for example, Barnow (1975) and Barnow and Cain (1977).
The statistical properties of estimators of program impact
in an environment of self-selection bias were studied by a
number of authors, including Heckman (1976 and 1979)
and Olsen (1979).
13. See Hausman and Wise (1977).
14. The cross-sectional design has been employed in
most earlier studies of the effects of BHC affiliation. Other
designs, such as a pooled time-series cross section, pose
a number of difficulties for the analyst. Banking regulation
and law changed significantly in the early 1980s, first with
deposit deregulation in 1980, and then with changes in
capital regulation in 1982. Also, the format of the Reports
of Condition and Income changed several times during
this period, making comparisons of certain financial
measures suspect over time.
15. The use of variables lagged prior to change to BHC
status also was examined. This modification turns out not
to have significant effects on the regression analyses.
More importantly, however, since any bank could conceivably change its status at any time-albeit with some
implementation lag-a fixed lag in the explanatory variables across all observations is more appropriate.
16. For the regressions reported in the paper, the excluded independent variable set includes leverage, ROE,
loan rate, deposit rate, affiliation status, and total asset
size measures from the year 1976.
17. In the results presented here, the probit formulation of
the choice regression is used to correct for self-selection
bias in both the exclusion and non-exclusion models. This
is not strictly necessary to achieve identification with an
exclusion assumption. The choice regression used to
produce predictions of affiliation status can be linear and
identification still achieved. A linear formulation of the
choice regression, however, has a number of undesirable
properties, including the propensity to predict choice
probabilities outside the range of zero to one.

REFERENCES
Barnow, B.S. "The Effect of Head Start and Socioeconomic
Status on Cognitive Development of Disadvantaged
Children," Ph.D. Dissertation, University of Wisconsin,
1975.
Barnow, B.S. and G.G. Cain. "A Reanalysis of the Effect
of Head Start on Cognitive Development Methodology and Empirical Findings," Journal of Human Resources, 1977.

Federal Reserve Bank of San Francisco

Bedingfield, J.P., P.M. Reckers, and AJ. Stagliano. "Distributions of Financial Ratios in the Commercial Banking Industry," Journal of Financial Research, Volume
8, Spring 1985.
Boyd, J.H., GA Hanweck and P. Pithyachariyakul. "Bank
Holding Company Diversification," Proceedings of a
Conference on Bank Structure and Competition, Federal Reserve Bank of Chicago, 1984.

Brewer, Virgil and William Dukes. "Empirical Evidence on
the Risk Return Relationships Between Banks and
Related Bank Holding Companies," Review of Business and Economic Research, Volume II, Spring
1986.
Curry, Timothy J. and John T Rose. "Bank Holding Company Presence and Banking Market Performance,"
Journal of Bank Research, Winter 1984.
Fraas, Arthur G. "The Performance of Individual Bank
Holding Companies," Staff Economic Study, #84,
Board of Governors of the Federal Reserve System,
1984.
Frieder, Larry A and Vincent P. Apilado. "Bank Holding
Company Expansion: A Refocus on its Financial Rationale," The Journal of Financial Research, Volume
VI, Spring 1983.
Heckman, James J. "The Common Structure of Statistical
Models of Truncation, Sample Selection and Limited
Dependent Variables and a Simple Estimator for Such
Models," Annals of Economic and Social Measurement, 1976.
_ _ _ _ . "Sample Selection Bias as a Specification
Error," Econometrica, Volume 47, January 1979.
Hobson, Hugh A, John T Masten, and Jacobus T Severiens. "Holding Company Acquisitions and Bank Performance: A Comparative Study," Journal of Bank
Research, Summer 1978.
Jessup, Paul and Roger Upson. "Return from Bank Holding Companies," The Bankers Magazine, Volume
155, Spring 1972.
Johnson, Rodney D. and David R. Meinster. "An Analysis
of Bank Holding Company Acquisition: Some Methodological Issues," Journal of Bank Research, Volume 4, Spring 1973.
Lawrence, Robert J. "The Performance of Bank Holding
Companies," Staff Economic Study, #55, Board of
Governors of the Federal Reserve System, June 1967.
Lawrence, Robert J. and Samuel H. Talley. "An Assessment of Bank Holding Companies," Federal Reserve
Bulletin, Board of Governors of the Federal Reserve
System, January 1976.
Lee, Warren F. and Alan K. Reichert. "Effects of Multibank
Holding Company Acquisitions on Rural Community
Banks," Proceedings of a Conference on Bank Structure and Competition, Federal Reserve Bank of Chicago, May 1975.
Light, Jack S. "Effects of Holding Company Affiliation on
De Novo Banks," Proceedings of a Conference on
Bank Structure and Competition, Federal Reserve
Bank of Chicago, 1976.
Maddala, G.S. and Lung-Fei Lee. "Recursive Models with
Qualitative Endogenous Variables," Annals of Economic and Social Measurement, 1976.
Mayne, Lucille S. "A Comparative Study of Bank Holding
Company Affiliates and Independent Banks, 19691972," Journal of Finance, Volume 32, March 1977.

Meinster, D.R. and RD. Johnson. "Bank Holding Company Diversification and the Risk of Capital Impairment,"
The Bell Journal of Economics, Volume 10, Autumn
1979.
Mingo, John J. "Capital Management and Profitability of
Prospective Holding Company Banks," Journal of
Financial and Quantitative Analysis, Volume 10, June
1975.
_ _ _ _ . "Capital Management by Holding Company
Banks," Journal of Business, Volume 48, October
1975.
_ _ _ _ . "Managerial Motives, Market Structures and
the Performance of Holding Company Banks," Economic Inquiry, Volume 14, September 1976.
_ _ _ _ . "More on the Performance Characteristics of
Holding Company Acquisitions," Proceedings of a
Conference on Bank Structure and Competition, Federal Reserve Bank of Chicago, June 1973.
Olsen, R.J. "A Least Squares Correction for Selectivity
Bias," Econometrica, Forthcoming.
_ _ _ _ ."Tests for the Presence of Selectivity Bias and
their Relation to Specification of Functional Form and
Error Distribution," Working Paper 812, Yale University,
Institution for Social and Policy Studies, 1979.
Piper, Thomas R. "The Economics of Bank Acquisitions by
Registered Bank Holding Companies," Research Report No. 48, Federal Reserve Bank of Boston, March
1971.
Piper, Thomas R. and Steven J. Weiss. "The Profitability of
BankAcquisitions by Multibank Holding Companies,"
New England Economic Review, Federal Reserve
Bank of Boston, September-October 1971.
Rhoades, Stephen A and Roger D. Rutz. "The Impact of
Bank Holding Companies on Local Market Rivalry and
Performance," Journal of Economics and Business,
1982.
Rose, John 1. and Donald 1. Savage. "Bank Holding
Company De Novo Entry, Bank Performance, and
Holding Company Size," Quarterly Review of Economics and Business, Volume 23, Winter 1983.
Rose, Peter S. and Donald R. Fraser. "The Impact of
Holding Company Acquisitions on Individual Banks,"
The Bankers Magazine, Volume 156, Spring 1973.
Smith, David, "The Performance of Merging Banks," Journal of Business, Volume 44, April 1971.
Talley, Samuel H. "The Effect of Holding Company Acquisitions on Bank Performance," Staff Economic
Study, #69, Board of Governors of the Federal Reserve System, 1972.
Varvel, Walter A "A Valuation Approach to Bank Holding
Company Acquisitions," Economic Review, Federal
Reserve Bank of Richmond, July-August 1975.
Wall, Larry D. "Has Bank Holding Companies' Diversification Affected Their Risk of Failure?" Journal of Economics and Business, Volume 39,1987.

Economic Review / Fall 1988

Hotelling's Rule Repealed?
An Examination of Exhaustible Resource Pricing

Ronald H. Schmidt
Contrary to the predictions of economic theory, prices
ofimportant exhaustible resources have not appreciated in
real terms during the past century. Possible explanations
for the lack of a trend in prices, such as changes in
demand, discoveries of new reserves, and technological
change are explored in this article. Based on the evidence,
it appears that theoretical models consistently have underestimated the price elasticity of supply of and demand for
exhaustible resources. Despite increasing consumption,
resource availability has increased as well, suggesting
that pressure for rising real resource prices will continue
to be suppressed.

Economist, Federal Reserve Bank of San Francisco. The
author would like to thank Steve Dean for his excellent
assistance. Editorial committee members were Michael
Keeley, Barbara Bennett, and Randall Pozdena.

Federal Reserve Bank of San Francisco

An important contribution of economics to public
policy is in the area of intertemporal resource allocation-particularly in the case of the optimal depletion of
exhaustible resources. Models ranging from very simple to
highly-sophisticated treatments of the topic have provided
important insights into how market forces often can address problems of growing scarcity without intervention
by centralized authorities.
One illustration of this role was provided in the early
1970s with the publication of Limits to Growth (LTG).I
Using computer simulations of trends in consumption,
output, resources, and population growth, LTG projected
growing shortages of key raw materials and a declining
standard of living in the world economy. Those projections,
however, ignored the endogeneity of prices. Rebuttals to
LTG based on dynamic optimization models were able to
evaluate the likelihood of the LTG outcomes and suggest a
far more adaptive environment. Prices would rise as commodities become scarce, they argued, causing automatic
shifts in consumption patterns.
The predictions generated by the dynamic optimization
models have become increasingly important in economic
policy formation. Growing familiarity with dynamic optimization techniques led to the widespread adoption in
economic and forecasting models of many of the "arbitrage equations" that are generated in the intertemporal
optimization literature. For example, following the oil
price spikes in 1973-74 and 1979-80, predictions of future
oil prices routinely have been based on the intuitively
appealing arbitrage relationship often referred to as "Hotelling's rule," which states that prices of exhaustible
resources should rise at the same rate as other financial
assets. That is, the rate of price increase should equal the
interest rate. Otherwise, commodity holders would not be
indifferent between current and future sales, and hence,
would withhold or accelerate current sales until the present
value of the future price equaled the current price.
This assumption that oil prices would be determined by
Hotelling's rule continues to be embedded in most dynamic economic forecasting models. Especially in longterm forecasting models, oil prices are assumed to rise
faster than the general level of inflation because the real
interest rate is positive.

This assumption, however, fails to correspond to experience. As discussed in this article, oil prices, as well as most
other major mineral prices, have not followed the predicted
path. Since the 1870s, these real resource prices have not
had a noticeable trend, in contrast to the rising trend
predicted by Hotelling's rule. Moreover, prices have been
highly volatile, rather than stable as arbitrage relationships
would suggest.
In both the LTG and HoteHing scenarios, the explicit
exhaustibility of the resource is a central assumption. New
discoveries and innovations can alter the period over which
extraction and consumption occur, but the resource eventually is fully consumed. Consequently, both theories
predict declining per capita wealth unless the economy can
substitute other factors of production for the resource.
Historical data contradict this view, however. As discussed in this article, the issue of scarcity and exhaustibility of natural resources is questioned by the evidence:
prices have not appreciated in real terms, consumption has
risen, and known reserves have risen sharply for nearly all
resources examined here.
The thrust of this article is to suggest that neither the
LTG nor the Hotelling scenarios, as commonly expressed,
are likely. Because of a consistent tendency to underestimate the response of technological progress and innovations to perceptions of scarcity, the models using Hotelling

arbitrage equations will tend to underpredict resource
availability and overpredict price increases. Moreover, the
LTG predictions are unlikely because technological progress appears to occur at a sufficiently rapid pace to
prevent growing scarcity.
In Section I, the simple Hotelling model and the resulting arbitrage equations are derived. Empirical evidence
testing the arbitrage condition for copper, lead, iron, zinc,
and petroleum is then presented in Section II. The evidence
generally provides poor support for a Hotelling price path,
indicating the absence of a trend and the presence of large
unexplained errors. Several explanations for this failure are presented in Section III. Some of the most important causes-uncertainty about reserves and the rate of
technological change, the properties of the extraction cost
function, shifts in
changes in market structure,
and problems caused by imperfect information-are discussed.
Concluding remarks are presented in Section IV. Based
on the information problems, uncertainty, and the empirical evidence presented in this article, Hotelling's rule
appears to be a poor guide for projecting prices of exhaustible resources, and the LTG model provides a poor prediction of resource scarcity. Rather, the lack of a trend in real
resource prices suggests that economic forces are working
to encourage expanding resource availability.

I. Hotelling's Rule
Exhaustible resources have received special attention in
the economics literature. A resource is said to be exhaustible if its current use in some way reduces a finite stock of
future uses:
If we ignore the act of extraction as a production
activity, such a resource is among the class of nonproduced goods (i.e., it is a primary commodity). But
then, so is agricultural land, and we do not usually regard
land as being exhaustible in the same way as fossil fuels
are. The distinguishing feature of an exhaustible resource
is that it is used up as an input in production and at the
same time its undisturbed rate of growth is nil. In short,
the intertemporal sum of the services provided by a given
stock of an exhaustible resource is finite. Land, if carefully
tilled, can in principle provide an unbounded sum of
services over time. This is the difference. 2

Exhaustible resources, therefore, can command a scarcity premium that grows over time, and unlike land, this
growth does not depend on the growth of demand for the
service, but rather, on the diminishing availability of the
stock of services because of previous consumption. Any
consumption of the resource should increase the scarcity of

the resource and, hence, affect the value of future scarcity
rents. Optimal depletion of an exhaustible resource, therefore, is a problem of intertemporal allocation.
The most influential approach to modeling intertemporal depletion of exhaustible resources is generally attributed to Hotelling (1931). Hotelling derived the path of
optimal prices and consumption in a model that assumes
that the objective of society is to maximize the present
discounted value of consumption of a resource that has a
fixed stock. In its simplest form, the Hotelling problem can
be stated as follows:

maximize
c

subject to:

(1)

R(t)
R(O) ?

c (t)
): c(t)dt

R(t), c(t) ? 0. 3

(2)
(3)

(4)

Economic Review I Fall 1988

where R is the level of remaining reserves, c is the
consumption of the resource at time t, U(c) is the utility
associated with consumption of the resource at time t
(which is assumed equal to production, for simplicity), 0 is
the discount rate, and T is the (finite) date at which the
resource is depleted. The problem is one of choosing an
optimal consumption path, c(t), to yield the highest value
to the agent subject to the constraints that production must
always be positive and cumulative production cannot exceed the resource stock.
The fixed supply of the resource is the critical difference
between exhaustible resources and other commodities produced at constant cost. Because the initial stock of resources is in fixed supply, a scarcity premium can be
captured by the resource owner. Hence, as long as the
scarcity is sufficiently
prices can exceed production costs throughout the period of its consumption.
The mathematical solution of (I) - (4) involves straightforward application of the calculus of variations, and
is available in a variety of sources [Hotelling (1931),
Dasgupta and Heal (1974), Stiglitz (1974), and Schmidt
(1984)]. It can be demonstrated that the arbitrage equation
determining intertemporal allocations is:
U

= o.

current production, because the returns to sales in the
future would have a higher present value. This response
would reduce the rate of price appreciation.
The solution to the problem can be seen graphically in
Figure 1, a four-quadrant depiction of the optimal depletion
problem [Herfindahl (1967)]. As demonstrated in Figure 1,
an optimal price path can be determined by using the
arbitrage equation to define the rate of change between
periods, in conjunction with the resource constraint, which
makes it possible to determine the starting price level.
The first quadrant depicts the demand curve for the
resource at a point in time. For simplicity, it is assumed that
demand is stationary; that is, the demand curve does not
shift over time. The second quadrant simply maps the
consumption at a particular point in time from the demand
curve in quadrant I to its cumulative consumption in
quadrant III. Quadrant III keeps track of resource use over
time. The area bounded by the consumption path and the
axes determines whether the chosen price and consumption paths violate the resource constraint. This area equals
total consumption over time, and cannot exceed the available reserves of the resource. The fourth quadrant maps the
price path described by Hotelling's rule.

(5)

The solution affirms that resource use is optimal when
the marginal utility of consumption rises at the agent's
discount rate. When this occurs, the present value of the
marginal utility of the last unit is the same in each time
period, and because the marginal utility of consumption is
assumed to be inversely related to consumption, no opportunity for arbitrage would remain.
In a competitive system, the marginal utility of consumption is proportional with the observed price for the
commodity. Substituting the resource price for U' (t), the
marginal utility of consumption, yields what has come to
be known as "Hotelling's rule":

P
Equation
predicts that real prices will rise at the rate
of time preference, which is often proxied by the observed
rate interest. 4
The logic behind this rule is difficult to contest. Producers with perfect foresight and no holding or production
costs should be indifferent between current and future
production as long as the resource appreciates at the same
rate that the proceeds from current production would earn
if invested in other assets. If prices grow at a faster rate,
arbitrage opportunities exist that would encourage reduced

Federal Reserve Bank of San Francisco

Figure 1
The Optimal Depletion
of an Exhaustible Resource
Price
IV

Demand for
Resource

Price of
Exhaustible
Resource
Over Time

Quantity

Time

Consumption
Over Time

III

II
Quantity

To determine the optimal path, an initial starting price is
chosen in quadrant IV. Then, given the resulting price path
in IV and the demand curve in quadrant I, it is possible to
trace out the implied consumption path in quadrant III. The
cumulative consumption resulting from the price path can
be compared to the resource stock available. If the implied
consumption exceeds the available stock, the starting price
is raised in quadrant I and the exercise is repeated. When
the starting price and resulting price path exactly exhaust
the available resource at the time when the price reaches a
level at which demand is choked off, the path is optimal.
The particular resource model developed above uses

highly restrictive
In particular, it assumes
constant demand, no extraction
known reserves, and
no technological change. As discussed later in this article,
more complicated depletion models have relaxed some of
these assumptions. These enhancements modify the optimal price path and make the relationship expressed in
equation (6) more
, but the results continue to
predict a positive
between price appreciation
and interest rates. In other words, the model described in
(1)-( 4) is an
central prediction-s-that
real prices
rise over time-is independent of many
of these assumptions.

II. Empirical Evidence
In contrast to the theoretical predictions, however,
Charts la-Ie show that the real prices of copper, lead, iron,
zinc, and petroleum have been highly volatile, but have not
exhibited a significant trend over the period from 1870 to
1986. Current real prices for many of these minerals are at
the levels of 100 years ago. None of the minerals has
exhibited the real appreciation that would be predicted by a
simple model.
Interestingly, the only mineral that visually demonstrates a rising real price is iron, which has little scarcity
rent attributed to the resource. Also, the commodities that
demonstrated some significant trend in the early 1980s
have seen a sharp reversal. Copper is shown with a
declining price since 1970, but the recent surge in copper
prices (not shown) has raised the price close to the historical average price. Similarly, the explosion in oil prices in
1979-80 now has been reversed, although the current level
remains above the historical average of $12.81 (in 1985
dollars).

One test
the
between prices
and the rate of interest follows directly from equation (6).
As shown by
and
a simple test of the
relationship is to estimate the
equation:
(7)

where r is the rate of return on alternative investments and
P is the price
the resource. The Hotelling model would
imply that 01
0
~ = I.
A joint test of this
for copper, iron, lead,
zinc, and petroleum is
in Table J.5 The annual
data cover the period 1870 to 1986.6 As shown in the table,
there is little support
the
model. Interest rate
coefficients are
and in all cases not significantly
different from zero.
as shown in Table 1, the
Durbin- Watson statistic
that there is little autocor-

Economic Review / Fan 1988

Chart 1A
Real Copper Prices
(1985 Dollars)

Cents/Pound

Chart 18
Real Iron Prices

Cents/Pound

250

(1985 Dollars)

12
10

200
8

150

61 \1\ A
4

100
2

50
1870

1890

1910

1950

1930

1970

1870

1990

1890

Chart 1C
Real Lead Prices
Cents/Pound

1950

1970

1990

1970

1990

(1985 Dollars)

1930

Chart 1D
Real Oil Prices

$/Barr,'

(1985 Dollars)

1910

50
30
40
20
30
10

10
1870

1890

1910

1950

1930

1970

1990

1870

1890

1910

1930

1950

Chart 1E
Real Zinc Prices
(1985 Dollars)

Cents/Pound

140
120
100
80
60
40
20
0
1870

Federal Reserve Bank of San Francisco

1890

1910

1930

1950

1970

1990

relation in the errors for commodities other than zinc,
indicating a lack of even short-term price trends. The lack
of a significant constant term in the regressions also is
consistent with a trendless process.
Similar to Feige and Geweke's findings, however, the
joint hypothesis Q( = 0 and f3 = I cannot be rejected.
Given the theoretically incorrect signs on the coefficients,
this evidence provides extremely
support for the
hypothesis. A more likely interpretation of the results
would point to the low signal-to-noise ratio. The hypothesis cannot be rejected simply because the unexplained
error swamps the explained variation. In fact, as shown by
the second F statistic in the table, which tests the hypothesis that both coefficients are not significantly different
from zero, those restrictions also cannot be rejected.
Consequently, little
can
in the model's reliability.
Because of the naive specification of the model, it is not
surprising that the data fail to confirm the Hotelling model.
Clearly, other factors are important in shaping and explaining short-term movements. Smith (1981) and Heal and
Barrow (1980), for example, have presented evidence
demonstrating that arbitrage-based models that include
several lagged price and interest rate terms have lower

forecast errors than a simple univariate time series
sentation for some minerals (copper and lead in the Smith
study)." However, the "best" specification was not COI1SI:,tent among models, and the best specification often was
rejected as unacceptable because the
on the
interest rate term was negative. 8
With more sophisticated versions of the
framework, optimal price paths need not be exponential
For example, as discussed in greater detail
the next
can
shown to have Usection, optimal price
shaped structures, given certain extraction cost "'vlJ'\-'UUl'v".
In virtually all of these models, however, an
trend
would have been predicted in recent data.
Some have argued that the trendless nature of real
model
resource prices does not violate the
ex
rates
been
to zero
over much of the period under study. However, even with
zero real interest rates, the coefficient on the interest rate
variable should not be negative in these models. Moreover,
estimates of a model with ex post real interest rates and the
ex post inflation rate as the explanatory variables (along
with a constant) yielded similar results. Only in the case of
lead was the inflation or interest rate variable significant,
and in that case, the coefficients were both negative.

III. Factors Preventing Price Appreciation
The failure of Hotelling's rule to predict price behavior
has been attributed to the restrictiveness of many of its
underlying assumptions and may not reflect any inconsistency with intertemporal optimization." In this section,
several of these assumptions-no extraction costs, known
reserves, no technological change, and
examined. This analysis suggests that the reason prices
have failed to follow Hotelling's path is that technological
innovations affecting both supply and demand consistently
have made resource constraints less binding. At the same
time, changes in market structure, along with these unexpected and abrupt changes in supply and demand, have
contributed to the
resource

Extraction costs
A number of researchers have attempted to provide
deterministic explanations for deviations from the Hotelling price path based on the properties of the extraction
cost function [Solow and Wan (1976), Hanson (1980), and
Roumasset, Isaak, and Fesharaki (1983)]. They argue that,
holding technology and knowledge of the stock of the
resource constant, the most easily accessible sources of the
resource will be exploited first. This suggests that extraction costs should rise over time, and
will affect the

resource price path [Dasgupta and Heal
1979)].
However, as demonstrated in this
extraction costs
alone-unless changed unexpectedly-do not
why prices have not risen.
Inclusion of extraction costs in the optimal depletion
problem results in a
that
net
of marginal extraction costs to rise at the rate of interest:

P(t)

= r

(8)

[P(t) - b(t)]

where b is the marginal extraction cost at time t, and r is the
discount rate [Hanson (1980)]. Rearranging terms, (8) can
be
as tAI!lnUi'C·

P (t)/P(t)

[1 - b(t)/P(t)].

As can be seen by inspecting (9), if b(t) is zero, the
arbitrage equation reverts to that
in equation
assuming that r = o. If b is a positive constant, on the
other hand, prices will grow at a slower rate than if
extraction costs were zero, but the rate will rise over
and eventually will approach the growth rate observed in
(6).10 Furthermore, if marginal extraction costs rise over
time, the growth rate of prices remains below that in the

Economic Review I Fall 1988

zero extraction case, and the rate of growth in prices can
slow to nearly zero if costs rise faster than prices. Finally, if
bet) is discontinuous, involving discrete changes in extraction costs as the extractor moves to a lower grade of the
resource, it is possible for the price path to exhibit periods
of accelerating increase and periods of slowing growth. 11
Most importantly in these models, however, prices
should rise monotonically if the stock of reserves is known
and fixed. As shown in (9), the only time prices fall (that is,
grow at a negative rate) is when resource prices fall below
marginal extraction costs, at which time production should
not occur.
The price path can be U-shaped, however, if the model is
further expanded to treat exploration and production costs
separately, and if the initial reserve stock is small [Pindyck
(1978)]. If production costs of the resource depend on both
the exploration and the development of a resource, marginal costs could fall in initial stages as the resource is
discovered and stocks of proven reserves grow. In this
case, the decline in production costs exceeds the rise in
exploration costs. In later stages, if costs of exploration
continue to increase, costs would rise, forcing the price to
rise as well.
Empirically, the impact of changes in extraction costs is
especially difficult to isolate because of the lack of cost
data. Evidence taken from various mineral census years is
presented in Table 2. As can be seen in the table, real
extraction costs of all minerals experienced step changes
following World War II and in the 1970s. 12 Furthermore,

Federal Reserve Bank of San Francisco

the breakdown of costs between labor, on the one hand,
and supplies and machinery, on the other, indicate a rapidly
growing capital component to the cost function, suggesting exploitation of grades that are more difficult to extract.
However, these data reflect average unit costs, and do
not indicate the path of marginal extraction costs. Furthermore, in the case of oil, the post-1973 observations include
the effect of the rapid increase in oil prices and resulting development of high-cost energy supplies outside of
OPEC. This high-cost development could not be construed
as optimal development from a global standpoint, however,
given that marginal extraction costs in the Middle East
remained far below the marginal cost of the high-cost
sources, and the Middle East had surplus capacity.
Similarly, rising commodity prices toward the end of the
1970s led to a sharp increase in exploration for other
minerals, such as copper. Because of the high prices,
marginal extraction costs rose significantly. When prices
fell, the industry retrenched and closed down or modernized the higher-cost facilities. In recent years, prices again
have risen, but unit costs are considerably lower because of
the efficiency gains achieved when prices fell. Consequently, when examining extraction costs, it is important to
distinguish temporarily high costs during periods of rapid
price appreciation-when cost control is less apparentand equilibrium situations where costs are closer to longrun equilibrium levels.
Other evidence by researchers finds limited support at
best to indicate that rising extraction costs explain the

trends in resource prices. Roumasset, et. al (1983) provide
some evidence relating the oil price increases of the 1970s
to rising extraction costs. Unfortunately, the marginal
extraction costs they use are for U.S. producers, while the
appropriate marginal extraction cost may be OPEC producers. Moreover, their results also fail to explain the
pattern of prices over a longer period of time.
Rather, the absence of a rising trend in resource prices
suggests two factors may be at work. First, technological
change has offset rising extraction costs by developing
more efficient extraction methods. Consequently, costs
have been held down by productivity gains. Second,
unexpected discoveries of reserves or technological progress in exploration have provided lower marginal cost
extraction opportunities. Examples of discoveries of oil in
Alaska, Mexico, and Columbia in the past 20 years suggest
that this phenomenon is important.
lJncertain reserves

Changes in extraction and exploration technology all
affect the size of the stock of proven, or extractible,
reserves. This uncertainty about the reserve base contrasts with another underlying assumption in the Hotelling
model. Constant real appreciation in exhaustible resource
prices is derived in this model because the reserve stock is
known with certainty (as are the demand function and
extraction costs). In practice, however, reserves are not
known with certainty and have increased dramatically over
time, often in large, discrete leaps.
Table 3 presents estimates of reserves for several minerals for 1950 and 1974. Despite continued extraction and
production of the minerals, reserves in 1974 were several
times larger. In the case of asbestos and bauxite, for
example, additions to reserves (new discoveries and extension of previously discovered reserves) were 11 to 17 times
the known reserve bases in 1950. A similar pattern is found
in petroleum and natural gas reserves, where additions to
world reserves have tended to outstrip production.
The effect of uncertain reserves on the optimal depletion path has been examined in a number of studies [Arrow
and Chang (1982), Pindyck (1980), Dasgupta and Heal
(1979)]. An unanticipated shock to reserves can cause a
shift among optimal paths. A sudden, unanticipated increase in proven reserves causes the price trajectory to fall
to assure full resource exhaustion. Observed prices in these
models fall sharply when the discovery is made.
In addition to unanticipated shocks to the reserve base, a
number of these models address the impact of endogenous
exploration behavior on the resource price path. As shown
by Arrow and Chang (1982), exploration tends to accelerate as the stock of known reserves declines and the price of

the resource rises. With major new discoveries, exploration tends to slow until scarcity again becomes important.
The implied price path, therefore, is one that rises and falls,
with little apparent trend.
As pointed out by Pindyck (1980), uncertainty about the
stock of reserves is consistent with observed price behavior, although such uncertainty does not fully explain
that behavior. Clearly, reserve shocks have played an
important role in preventing the LTG scenario from occurring by consistently raising the size of the resource stock.
The timing of reserve discoveries and shifts in price
trajectories, however, do not coincide precisely as the
theory would predict. Announcements of large new deposits have sometimes caused prices to move, but often there is
little immediate response. For example, the major oil
discoveries by Mexico in the mid-I970s may have contributed to pressure on OPEC in the mid-1980s, but those
discoveries seemingly had little effect on prices in the
mid-1970s.
In any case, the frequency with which shocks to the
reserve base have occurred-either because of luck or
because of the endogenous response of enhanced exploration activity-raises an important issue regarding the

Economic Review / Fall 1988

degree to which these resources really are exhaustible. The
steady rise in reserves, despite growing demand (see
Charts 2a-2e, which depict a steady upward trend in
consumption), may argue for decreasing scarcity value of
the resource over time. If these resources are not exhaustible in practice, the failure of Hotelling's rule to predict
trends in resource prices would not be surprising.

Uncertainty in demand
Technical change affecting the demand for a resource
also may be an important factor in the observed failure of
the Hotelling model. A key assumption of the model is that
demand for the resource is known and predictable. In
reality, however, dramatic changes in use patterns, the
availability of alternatives, and variations in resource use
intensity have caused frequent shifts in the demand for the
resources. For example, the discovery of semiconductors
and silicon chips significantly reduced the demand for
copper wiring. Increased energy efficiency in automobiles, including substitution of aluminum and plastic for
steel, had a direct impact on iron and petroleum demand.
These technological shocks result, in part, from a direct response to perceived shortages-reflected in rising
prices-and from spin-off discoveries in other applications. In the short-run, most resource demand is highly
inelastic: Over the longer-term, however, substitutes tend
to develop that allow much greater substitutability. Often,
the emergence of the substitutes leads to relatively sudden
shifts in demand when the product appears, typically
exceeding expectations of resource producers. 13 When
these shifts occur, the expected consumption path is altered, and the optimal depletion path changes.
Such changes in demand can lead to consistent errors in
the estimation of demand. Adjustments by producers to
those errors then can affect the observed price path for
resources. (See the accompanying Box.)
Relatively simple models of resource depletion have
been developed for the case where alternative technologies
exist. In the simplest form [Dasgupta and Heal (1979)], a
"backstop" technology is assumed to exist in perfectly
elastic. supply at some price. The only effect of this
modification is to affect the starting value of the arbitrage
equation.
A more complicated version of the process [Kamien and
Schwartz (1978)] considers the optimal depletion problem
when the alternative technology is endogenously determined. The extractor must then choose a price and production schedule that maximizes profits taking into account
the effect that the price level will have on encouraging
alternatives. This approach, however, continues to predict
monotonically rising resource prices.

Federal Reserve Bank of San Francisco

A model of endogenous alternative production can generate observed price declines, however, if the assumption
of complete information is relaxed. As is the case with
unanticipated additions to reserves and sudden changes in
technology or final demand, information limitations can
lead to unstable price paths. If, for example, development
of an alternative is characterized by high initial investment
and low marginal costs, a sudden increase in resource
prices can cause a large increase in the availability of the
alternative. This increase, in turn, can force prices to fall.
Models in which prices can fall depend on the existence
of uncertainty. Prices fall because supply or demand conditions change in a way the resource producer cannot anticipate. Presumably, if the producer could anticipate all
responses to a given price path, the producer would follow
an extraction path that would avoid these price declines.
Otherwise, the arbitrage condition would be violated.
The fact that prices do fall suggests that these information problems are significant. Furthermore, the information problems are not merely the result of luck, but also
because information is not often fully disseminated to the
affected parties. If the supply of and demand for the
resource depends on the actions of many agents, and the
involved agents do not have all the information on how the
other agents will react, this imperfect information can lead
to unstable prices.
Consider, for example, the case of alternative production
[Schmidt (1988)]. If the extractor and the alternative
producer are different agents, and information is proprietary, so that: a) the extractor does not know the nature of the
relationship between resource price levels and changes in
the price level on the future supply of alternatives; and b)
the alternative producer does not know with certainty the
desired price path of the extractor, unstable pricing can be
generated.
Consider the simplest case: no extraction costs, known
reserves, and constant total demand for the resource and
the alternative, which is a perfect substitute. The resource
extractor will seek to find the price path that maximizes the
present value of extraction rents, taking into account the
expected effect of the selected price path on the supply of
the alternative.
The alternative producer is assumed to choose current
investment in research and development to bring the substitute on line at some future period. The optimal investment level is determined, among other factors, by
the substitute producer's expectations of resource price
appreciation.
In both cases, expectations are based on imperfect
information. Furthermore, it is typically the case that the
gestation period of an alternative product is considerable.

Chart 2A
Copper Consumption

Thousands
of Tons

Chart 28
Iron Consumption

Millions
of Tons

2,500

150

2,000

125
100

1,500
75
1,000
50
500

o im'm"""""""'l"""ITImm'"""'1"TITImm''''''''''1'rmmmrmmml''''''''''''''''''''T''''''''"''''''"''l

O-i-~.-""'l""rmmm"""l"'rmmm"""'l""""""'''''''''l'rmmm''''''''''l
1870

1890

1910

1930

1950

1970

1990

1870

1910

1930

1950

1970

1990

Chart 2D

Chart 2C
Lead Consumption

Thousands
of Tons

1890

on Consumption

Millions
of Barrels

1,600

7,000
6,000

1,200

5,000
4,000

800
3,000
2,000

400

1,000
0

O;mmmmm""l"" rmmrrlTl11lTJTnnmnmmm'l"""""!IYI'I1tm"'T"'"'rnrrnTr"'"l"'"nmmr"""'1
1870

1890

1910

1950

1930

1970

1990

1870

1890

1910

1930

1950

1970

1990

Chart 2E
Zinc Consumption

Thousands
of Tons

1,500
1,200
900
600
300
Oi'fl\'iimmm""'f""mmmlTl11lTJTnmmrmmm,,""",mmm"'T"'"'mmm"'"l"'"nmmr"""'1
1870

1890

1910

1930

1950

1970

1990

Economic Review / Fall 1988

Consequently, it is possible for the extractor to underestimate the response of the alternative producer, and choose a
higher initial price. 14 In this case, the response of alternative production will exceed that expected by the extractor
in
forcing the extractor to shift to a lower
optimal price path. This shift to a lower price path would
appear as a sudden drop in observed prices.
Similarly, sudden price declines might convince the
alternative producer that prices will remain low, and lead to
sharp cutbacks in development activities. Such a cutback
would
result in lower
production in the
future than would be expected by the extractor, possibly
leading the extractor to shift to a higher price path in the
future.
Unless the agents learn the true nature of each othmay entail acquiring proprietary information-the process of observed

Federal Reserve Bank of San Francisco

price shocks can continue indefinitely. This phenomenon
explains, in part, why extractive industries also frequently are major investors in the development of substitute products in order to internalize these informational
externalities. For example, synfuels are developed by
oil companies. Nevertheless, some substitutes inevitably
emerge from non-extractive sources, surprising the market
(for example, the replacement of copper by fiber optics).
Moreover, miscalculations of demand elasticities may
cause extractors to raise prices so rapidly as to encourage
the development of alternatives that have high fixed costs,
but competitive marginal costs. The sharp increase in oil
prices led to major new investments in production capability outside OPEC, where marginal production costs
after drilling were low enough to continue production even
Furthermore, the price spike was sufficiently dramatic to encourage enormous investments

in energy-efficient equipment and structure-investments
that were not reversed when oil prices fell.
Consequently, the lack of perfect information among
agents and the slow nature of adjustment can lead to a
series of price fluctuations. Moreover, elimination of these
shocks through learning often is not possible because the
technology changes over time, resulting in new substitute
producers with different production functions.

Market Power
Finally, a number of researchers have suggested that
changes in the institutional structure of resource markets
help to explain short-term movements in resource prices.
Many important exhaustible resources are not sold in
competitive markets. In particular, tin and petroleum are
produced in cartelized market environments, and other
minerals largely are owned and produced by state-owned
enterprises that may have different objectives than those
embedded in the Hotelling model.
Beginning with Hotelling (1931), economists have compared the implications for extraction and prices in competitive and monopolistic markets [Dasgupta and Heal (1974,
1979), Stiglitz (1974), Hnyilicza and Pindyck (1976), and
Pindyck (1978)]. Researchers have found the production
and price paths under the two market structures to be quite
different. If marginal extraction costs are constant, monopolists will choose a price path that allows marginal
revenues, rather than prices, to rise at the discount rate.
Such a price path will tend to have higher initial prices and
slower appreciation, leading to depletion over a longer
period of time compared to the price path of a competitive
producer.
This difference in optimal pricing patterns may explain
part of the observed price behavior for some of the resources. For example, oil extraction has been characterized
by major institutional changes. In the pre-World War II
period, oil production was highly competitive in the

United States-so much so, that the Governor of Texas
called out the national guard to halt "cutthroat" competition in 1933, which had driven prices as low as ten cents
per barrel. Beginning in 1933, prices were stabilized (and
held virtually constant over long periods of time) by the
prorationing policies of the Texas Railroad Commission.
Production levels of Texas producers were set so as to meet
refiner demand at prices then prevalent. This power waned
in 1973 as imports became the marginal supply, and
pricing since 1973 has reflected frequent shifts in the cartel
unity of OPEC.
Similarly, a buyer's cartel has dominated the tin market
for decades. Prices have risen and fallen over time with
the cohesiveness of the cartel. Other industries also have
had important structural changes as the market shares of
government-controlled production have changed. In the
case of copper, market shares have fluctuated sharply be
tween U.S.producers (which produce in accordance with
profit maximization goals) and Latin American producers
(which produce to maximize foreign exchange). As the
market shares change, the different objectives of the producing groups force changes in the optimal price path.
Furthermore, competition for market share has at times
forced production capacity to be idled as excessive supplies are dumped on the market, reducing world prices.
In cases such as these, where market institutions shift
frequently, the price path can be expected to be discontinuous. Shifts in institutions reflect changes in underlying
goals, changes in discount rates as different players become market-makers, and differing degrees of monopoly
power. At each transition point, optimal price paths (optimal from the perspective of the dominant market participants) shift, and prices shift abruptly from the old path to
the new path. In the cases of oil and copper, shifts in cartel
cohesion have had immediate short-term effects on the
direction of prices.

IV. Conclusions
Examination of exhaustible resource price data over the
past century leads to a simple conclusion. Even with the
enormous sociological, political, technological, and economic changes of the past 115 years, real prices of important exhaustible resources have not increased significantly.
Certainly, those prices have at times risen or fallen sharply.
But if one were attempting to forecast prices in the future,
this historical behavior would nudge the forecaster toward
a prediction of little future appreciation in real prices.
Does this mean that the dire consequences of resource
exhaustion spelled out in LTG will occur? After all, one

argument against the LTG model was the economic rationale that prices would rise and allow a gradual shift away
from the resource, avoiding major disruptions. If prices do
not rise, what forces are available to shift production and
consumption patterns prior to the emergence of shortages?
Results of this study suggest that the corrective forces
attributed to the pricing mechanism remain viable and have
allowed consumption patterns to change in a nondisruptive
fashion. Rather than projecting a gloomy decline in standards of living as we run out of resources, the interpretation in this article argues for the best of both worlds. Not

Economic Review I Fall 1988

only is the LTG scenario unlikely, but so are the price
increases associated with the Hotelling scenario.
Rather, the trendless nature of real resource prices over
the past 115 years suggests that the Hotelling and LTG
approaches seriously underestimated the ability of agents
to substitute other resources and develop alternatives.
Shifts in consumption, changes in reserves caused by
new discoveries or gains in extractive technology, technological change that affects the output mix and production function of the economy, and shifting market power of
cartels all have the effect of changing the optimal depletion

trajectory. Moreover, growing reserves even with rising
consumption, also brings into question the degree of
scarcity that truly should be attributed to these resources.
The Hotelling model predicts a rising price path when
reserves do not grow, alternative technologies do not exist,
and demand does not change. But history would suggest
that these conditions always will change. Moreover, rising
prices in the short run seem to have a larger effect on the
supply of alternatives than we generally expect, given our
current state of knowledge and technology.

ENDNOTES
1. Meadows, Meadows, Randers, and Behrens (1972).
2. Dasgupta and Heal (1979), p. 153
3. A "dot" above a variable indicates the rate of change.
4. Prices and interest rates are usually expressed in real
terms in the theory. A similar relationship (including that
tested in Section III) exists between nominal prices and
nominal interest rates.
5. Similar results can be demonstrated for a wide variety
of other minerals.
6. Data for the estimation for 1870-1973 were taken from
Natural Resource Commodities-A Century of Statistics,
Robert S. Manthy, Johns Hopkins University Press (1978).
Data for 1973-1986 were constructed using the methodology described by Manthy from more recent publications
of the original sources. The interest rate is based on
railroad bonds for the early part of the series, and based
on Moody's Aaa corporate bonds in more recent years.
7. Smith, in particular, experimented with interest rates of
differing maturities, but found that the term of the interest
rate had little impact on the general relationship to price
appreciation.
8. Smith (1981), p. 110.
9. Other studies that have attempted less direct tests of
the theory have found mixed results for some implications
of the Hotelling model in the data. Farrow (1985), using
data from mining firms, found that the in situ value of the

Federal Reserve Bank of San Francisco

resource did not follow a time path consistent with the
theory. On the other hand, Miller and Upton (1985) found
some support for the theory by examining cross-sectional
evidence of the stock market value of U.S. domestic oil
and gas firms. Schmidt (1984) also found evidence that
exploration activity was consistent with a Hotelling model,
with drilling responding to expected real price appreciation.
10. Note that the limit of b(t)/P(t) is zero as t -+ 00, if r > 0.
11. See Hanson (1980) for a proof of this property.
12. The more recent data contrast with the findings of
Barnett and Morse (1963), who found that extraction costs
fell for almost all extractive products between 1870 and
1957.
13. This sequence of events characterized the pattern of
oil prices in the 1979-86 period. Prices rose sharply in
1979-80, causing major investments in energy-saving
technologies and the development of other sources
of energy. As these sources emerged, the demand for
OPEC oil diminished rapidly, leading to a sharp price
decline over the 1982-86 period.
14. The producer also might choose this path if the gestation period is long and the producer's discount rate is
high. In that case, the producer might attempt to capture
short-term higher profits by exploiting the inelastic shortrun demand, even though that action reduces future
profits.

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