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Vol. 28, No. 2
ECONOMIC REVIEW
1992 Quarter 2
Intervention and the Bid-Ask
Spread in G-3 Foreign
Exchange Rates
2
by William P. Osterberg
An Ebbing Tide Lowers All
Boats: Monetary Policy,
Inflation, and Social Justice
14
by David Altig
Sluggish Deposit Rates:
Endogenous Institutions and
Aggregate Fluctuations
by Joseph G. Haubrich
FEDERAL RESERVE BANK
OF CLEVELAND
23
1992 Quarter 2
Vol. 28, No. 2
Intervention and the
Bid-Ask Spread in G-3
Foreign Exchange Rates
2
by William P. Osterberg
Recent research suggests that central-bank intervention may influence
the volatility of foreign exchange rates or impair the efficiency of such
markets. Using official daily intervention data for Germany, Japan, and
the United States, the author tests for whether the anticipation of inter
vention explains wider bid—ask spreads. No evidence is found for such
a relationship in the spot and forward rates of marks/dollars and yen/
dollars. Rather, it appears that narrower spreads are associated with
periods of purported intervention and that spreads are narrower if, con
ditional on the occurrence of intervention, the market is likely to have
expected intervention.
An Ebbing Tide Lowers
All Boats: Monetary Policy,
Inflation, and Social Justice
14
by David Altig
Some economists argue that, because low-income individuals are un
duly burdened by unemployment and not much affected by inflation in
the short run, fairness dictates expansionary monetary policy in times
of sluggish economic activity. However, individuals with low incomes
are likely to be hurt in the long run if such policies lead to higher infla
tion. This paper argues that the same social justice criterion that justi
fies the call for the Fed to “do something" during recessions supports
the case for a long-run anchor to the price level.
Sluggish Deposit
Rates: Endogenous
Institutions and
Aggregate Fluctuations
23
by Joseph G. Haubrich
This paper provides an equilibrium analysis of how endogenously aris
ing financial institutions alter the impact of macroeconomic shocks. It
explains the low volatility (sluggishness) of bank interest rates relative to
other short-term rates and illustrates a powerful principle: When aggre
gate disturbances also have distributional consequences, the shock can
change the pattern of prices specified by efficient contracts. Interest-rate
sluggishness arises because banks provide insurance against individual
uncertainty, which itself is affected by economic conditions.
Economic Review is published
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Opinions stated in Economic
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ISSN 0013-0281
Intervention and the Bid-Ask
Spread in G-3 Foreign
Exchange Rates
by W illiam P. Osterberg
W illiam P. Osterberg is an
economist at the Federal Reserve
Bank ot Cleveland. The author is
grateful to David Altig, Jeffrey
Hallman, Owen Humpage, Jacky
So, and James Thomson for use
ful comments and suggestions,
and to Rebecca Wetmore Humes
for research assistance.
Introduction
Tests of the efficiency of foreign exchange
markets continue to proliferate. Because these
markets have become worldwide in scope and
nonstop in operation, economists have been
able to test many hypotheses about how infor
mation becomes incorporated into prices and
transferred between markets in different loca
tions. However, the finding that forward rates
for foreign exchange are not unbiased predic
tors of future spot rates remains without a
coherent explanation.
It seems reasonable to speculate on the role
that central-bank intervention plays in such find
ings. After all, central banks may possess infor
mation not available to other traders. However,
since central banks usually have not made avail
able to the public accurate information about
their daily foreign exchange activities, it has
been difficult to determine if intervention influ
ences foreign exchange market efficiency.
Greater interest in central-bank intervention
has also been stimulated by an increase in the
frequency of intervention. During the period of
ostensibly floating rates, central-bank interven
tion policy has been, at various times, designed
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either to influence the level of the exchange
Federal Reserve Bank of St. Louis
rate or to reduce its volatility. Specifically, as dis
cussed by Funabashi (1989) and Dominguez
(1990), soon after the Plaza accord in September
1985, the finance ministers of the G-5 (France,
Germany, Japan, the United Kingdom, and the
United States) agreed to reduce the dollar’s ex
change value. Then, at the Louvre meeting in
1987, they decided to shift to a regime of stabili
zation. Thus, there is a clear interest in analyz
ing the impact of intervention on both the level
and volatility of exchange rates.
This paper examines the relationship between
G-3 (Germany, Japan, and the United States)
central-bank intervention and bid-ask spreads in
the German mark/U.S. dollar (DM/$) and yen/U.S.
dollar (yen/$) spot and forward foreign exchange
markets. Bid-ask spreads may be related to vola
tility and risk. The examination is stimulated by
the speculation of Bossaerts and Hillion (1991),
henceforth referred to as B/H, that an intraweekly
pattern in intervention explains the intraweekly
pattern in bid-ask spreads that they observed for
the currencies in the European Monetary System.
They determine that bid-ask spreads are higher
on Fridays and that taking account of such asym
metry alters conclusions regarding the efficiency
of forward markets. B/H surmise that the higher
Friday bid-ask spreads are related to market
participants’ anticipation that decisions about
intervention will be undertaken on weekends.
Here, I utilize official intervention data to see if
G-3 intervention influences G-3 spreads. To the
best of my knowledge, this is the first time that
such an investigation has been undertaken.
The organization of this paper is as follows.
Section I reviews selected literature on forward
market efficiency and the impact of central-bank
intervention. Section II discusses the data on inter
vention and the bid-ask spreads. In the third sec
tion, I examine 1) intraweekly patterns in bid-ask
spreads, 2) holiday effects, 3) intraweekly patterns
in intervention, 4) bid-ask spreads over periods
of nonintervention versus intervention, and 5)
Granger-causality tests for the intervention-spread
relations. Section IV concludes and summarizes.
I find that 1) bid-ask spreads are higher on
Fridays for both spot and forward G-3 exchange
rates, 2) intervention is no more likely to occur
on Mondays than on other days, 3) for both cur
rencies, periods of purported intervention are
associated with lower, rather than higher, bidask spreads, 4) conditional on whether or not
intervention occurred, expectations of interven
tion seem to be associated with lower spreads,
and 5) intervention generally does not Grangercause spreads. Overall, there appears to be little
evidence to support the view that spreads widen
in anticipation of intervention. A more plausible
view is that the expectation of intervention has
a negative impact on spreads. A structural model
of the relations among intervention, spreads,
and volatility would be necessary to address
these issues in more detail.
and asks from their books of orders. Flood sug
gests that adverse selection costs and inventory
holding costs are likely influences on marketmaker spreads. Adverse selection influences
spreads if market-makers confront traders who
have inside information and who are thus able
to speculate against the market-maker. Inven
tory holding costs are influenced by the possi
bility of unfavorable price changes during the
time that currencies are held.
Flood submits that models of brokers’ spreads
are less applicable to the foreign exchange mar
ket, where (unlike in securities markets) brokerage
and market-making are separated. One distinction
between the two activities is that brokerage main
tains the anonymity of the transacting parties. It is
worth noting that U.S. intervention operations util
ize both market-makers, who generally are com
mercial and investment banks, and brokers.
“Secret” intervention occurs via a broker. Interven
tion via a market-maker may increase spreads,
since a market-maker could view the intervening
central bank as having inside information. This is
the mechanism to which B/H refer.
Early empirical work by Fieleke (1975) and
Overturf (1982) shows that spreads are positively
related to foreign-domestic interest differentials and
exchange volatility. Allen (1977) provides a theoreti
cal rationale for the volatility-spread relation. Black
(1989), Boothe (1988), Glassman (1987), and Wei
(1991) find that spreads are positively related to
transactions volume. Although a lower rate of trans
actions could influence the risk component of the
spread by increasing the length of time an open
position would be held, it is also possible that vola
tility and volume are determined simultaneously.
I. Related Literature
Foreign Exchange
Bid-Ask Spreads
A small body of literature focuses on the determi
nation of foreign exchange bid-ask spreads. Flood
(1991) provides a summary of the theory and
points out the difficulties in applying to the foreign
exchange market the framework used to analyze
securities market spreads.1 A unique aspect of
spread determination in exchange markets is that
two trading structures coexist. There are marketmakers, who provide both bids and asks upon
demand, and brokers, who quote the best bids
1 George, Kaul, and Nimalendran (1991) provide a recent summary
of the findings regarding spreads in equity markets. They conclude that only
8 to 13 percent of the spreads can be explained by adverse selection and
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claim that the predominant influence on equity spreads is processing costs.
Intervention and
Risk Premia
Though B/H contend that intervention influences
the spread, most investigations have viewed inter
vention as influencing a risk premium defined in
other terms, as discussed below. However, it is not
at all clear that a significant risk premium exists
(see Hakkio and Sibert [1991]). The existence of a
time-varying risk premium is only one of the pos
sible explanations of the finding that the forward
rate is not an unbiased and efficient predictor of
future spot rates.
The unbiasedness and efficiency of forward
rates has been widely tested by analyzing varia
tions on equation ( l) .2
■
Federal Reserve Bank of St. Louis
■
2 Baillie and McMahon (1989) and Hodrick (1987) provide com
prehensive reviews of this literature.
(U
Et (SH i ) = FIH II,
where the left side is the expectation at time t
of the spot exchange rate k periods in the future
and the right side is the forward rate at time t
for a transaction at time t + k. In practice,
Et (St+k) is replaced by S[+k, S and F are often
replaced by their logarithms or by (St+ k—St)/St
and (.Ft—St)/St; and an equation such as (2) is
analyzed.3
G)
(5 ,+ * - 5 , ) / J ,
—oc + (3 (Ft t+k —St ) / St + ul+ k .
As summarized by Baillie (1989), a consensus
against unbiasedness has emerged— the hypoth
esis that a = 0 and that (3 = 1 is usually rejected.
One possible explanation is the presence of a risk
premium. Equation (1) could be expected to hold
purely as the outcome of arbitrage among riskneutral speculators who can take an open position
in the forward market based on their expectation
of the future spot rate at which positions would
have to be covered. On the other hand, the
portfolio-balance approach to exchange-rate de
termination considers risk-averse investors who
choose holdings of assets denominated in differ
ent currencies. If such assets are imperfect substi
tutes, then factors such as relative asset supplies
will influence exchange rates and imply rejection
of the unbiasedness hypothesis.
B/H suggest that the frequent use of the aver
age of the bids and asks in equations (1) and
(2) is inappropriate and claim that intervention
is responsible for an asymmetry of the true
price around the average of bids and asks. Other
possible theoretical explanations include the
inappropriateness of the rational expectations
assumption (Frankel and Froot [1987D, the pos
sibility that policy changes would lead to ex post
biasedness even if unbiasedness held ex ante
(Lewis [1988]), anticipation of real exchangerate changes (Levine [19891), and the existence
of liquidity premia (Engel [1990]).4
A variety of approaches, summarized by
Hodrick (1987), imply a time-varying risk pre
mium. Lucas (1978) relates the risk premium to
■ 3 These transformations ameliorate problems introduced by the nonstationarity of exchange rates (see Baillie and McMahon [1989] or Hodrick
[1987] for details) and Siegel’s paradox. Siegel's paradox states that if equa
tion (1) holds when S and F are expressed as units of currency A per unit
of currency B, then it cannot also hold for the inverse rates, because E(MK)
and 1/E(X) are not equal.
■
4 Other possibilities include Siegel's paradox and transactions
costs. Research has generally concluded, however, that these are not im
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portant empirically. See Baillie and McMahon (1989) for a summary.
Federal Reserve Bank of St. Louis
the conditional covariance between a long posi
tion in the forward market and the marginal rate
of substitution between future and current con
sumption. Hodrick (1989) shows how the risk
premium in the forward market can be more
directly related to the conditional variance of
market fundamentals, such as money supply
and government spending. Osterberg (1989)
modifies Hodrick’s paper to show how interven
tion can influence the risk premium in the for
ward market. In general, evidence in favor of
the existence of a risk premium in the forward
market is weak (see Engel and Rodrigues [1989],
Kaminsky and Peruga [1990], and Mark [1988]).
This may result in part from using data of no
higher than monthly frequency in analyzing the
relationship between the forward-rate forecast
error and either consumption or money.5 Vola
tility measures such as conditional variance ex
hibit less time variation when constructed from
data of lower frequency.
Measurement and testing issues are also in
volved with the controversy over the existence
of risk premia in forward rates 6 B/H determine
that the use of the average of bids and asks in
tests of forward market efficiency ignores the
information contained in the bid-ask spread,
biases the test results, and distorts the magnitude
of the implied risk premium. In this paper, I
focus on the authors’ contention that the bidask spread widens when the market anticipates
intervention, because the possibility of interven
tion induces an adverse selection problem for
market-makers or brokers. B/H conclude that
the spreads are wider on Fridays.
Other investigators have found evidence of
day-of-the-week effects in foreign exchange
markets. Glassman (1987) finds that bid-ask
spreads are higher on Fridays and on days
before market holidays. So (1987) confirms pre
vious findings that exchange rates on Monday
■
5 There are indirect approaches to testing for a risk premium using
daily data. One approach is that taken by Levine (1989), who tests the im
plication of many asset-pricing models that the risk premium embedded
in the forward rate is exactly equal to the risk premium in the differential
in real interest rates. Giovannini and Jorion (1987) test for the influence
of various proxies for a risk premium, such as lagged forward rates and
squared interest rates.
■
6 Bekaert and Hodrick (1991) discuss the impact on the measure
ment of risk premia of 1) matching forward and spot quotes so as to be
consistent with settlement conventions in the foreign exchange markets
and 2) the use of averages of bids and asks.
■ 7 Thaler (1987) summarizes the evidence regarding day-of-theweek effects in equity markets, but finds no consistent explanation of the
results. Negative returns from Friday to Monday are due to the change
from the Friday close to the Monday open. Highest returns are on Wed
nesday and Friday. Returns also tend to be lower on days before holidays.
and Wednesday tend to be higher than on Thurs
day and Friday. McFarland, Petit, and Sung (1982)
contend that these findings may be related to set
tlement conventions and to the fact that money
supply announcements are made on Thursday.
Baillie and Osterberg (1991) examine the forwardrate error with daily data and find that conditional
variances are higher on Fridays and before holi
days. Baillie and Bollerslev (1989) estimate a
generalized autoregressive conditional heteroscedasticity (GARCH) model for daily exchange rates
and determine that conditional variances are
higher on Mondays and lower on Thursdays.
Humpage and Osterberg (1992) estimate a
GARCH model for the risk premium implied by
the deviation from uncovered interest parity for
the G-3 currencies. They find that the risk pre
mium for the DM/$ is lower on Thursdays and
that the conditional variance of the deviation for
the yen/$ is higher on Fridays and around holi
days. Hsieh (1988) concludes that daily exchangerate distributions are not independently and
identically distributed across days and that there
are no day-of-the-week effects in the mean of the
exchange-rate change. However, he does find
that variances are larger when the trading period
spans a weekend or holiday.
Channels of
Influence for
Intervention
The linkage between intervention and bid-ask
spreads has not previously been examined. In
stead, studies of intervention view it as influencing
risk premia or conditional variances. Most analyses
have concentrated on sterilized intervention, partly
because there is interest in whether it can be
viewed as a policy lever in addition to monetary
and fiscal policies.8 Unsterilized intervention is
equivalent to monetary policy.
The two major channels through which steril
ized intervention can influence exchange rates
are the portfolio-balance channel and the signal
ing channel.9 Sterilized intervention alters the
■
8 A country sterilizes its intervention when it negates the initial
impact ol the intervention on its money supply through an offsetting
open-market transaction. For example, when U.S. authorities purchase
marks with dollars, the supply of dollars is increased. Selling U.S.
government securities in the same amount as the intervention removes
dollars and sterilizes the intervention.
■
9 Some authors have suggested other channels. Humpage (1988)
finds that intervention sometimes provides “news” other than about future
monetary policy. Dominguez (1988) discusses how intervention can have
an influence by misleading exchange market participants. The vast major
ity of theoretical and empirical research focuses on the portfolio-balance
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and signaling
channels.
Federal Reserve Bank
of St. Louis
relative supplies of domestic and foreign bonds
and, if investors are risk averse and if domestic
and foreign bonds are imperfect substitutes,
leads to a readjustment of rates of return via the
exchange rate; this is the portfolio-balance
mechanism. The impact of intervention operat
ing through the portfolio-balance channel can
be mitigated by three conditions: 1) perfect sub
stitutability, 2) Ricardian equivalence, under
which consumers perfectly anticipate future
taxes associated with the change in government
debt, and 3) the slight effect of intervention on
asset supplies.
The signaling channel is usually analyzed with
in the asset-market approach to exchange-rate
determination. Exchange rates equal the present
discounted value of future economic fundamen
tals. If monetary authorities have inside informa
tion, intervention may signal future monetary
policies. For example, a sterilized purchase of
marks by the United States may lead to an appre
ciation in marks (a decrease in the DM/$ rate) if
the purchase is believed to signal inside informa
tion (more expansionary U.S. monetary policy)
that increases the expected future exchange rate.
The question arises as to why intervention is
the type of signal chosen. One answer may be
that it gives authorities an incentive to follow
through with the expected policy. For example, if
authorities have just purchased foreign currency,
they may wish to see an appreciation in its value.
O n the other hand, since intervention does not re
quire an immediate change in the monetary base,
market participants may be misled. However, if
the subsequent monetary policy is not consistent
with that implied by the initial action, the effective
ness of future intervention may be reduced. This
has led some to suggest that intervention is an
effective signal only if followed by consistent mon
etary policy. If this is true, however, it is not clear
that intervention is independent of monetary pol
icy. Humpage (1991) discusses concerns asso
ciated with this point.
Empirical evidence suggests that the signal
ing channel is probably of more significance
than the portfolio-balance channel. Early stud
ies of the latter, summarized by Obstfeld (1988),
generally find that intervention has little impact
or that coefficients’ signs are inconsistent with
theory. One reason for the small estimated im
pact is that intervention is minute relative to the
outstanding stocks of assets. Another reason
may be that calculation of asset supplies pre
cludes the use of high-frequency data.
Studies that utilize relatively high-frequency
data have found signaling effects. Dominguez
(1988) examines weekly data on money surprises,
exchange rates, and intervention and concludes
that the effectiveness of intervention as a signal
depends on the credibility of the implied monetary
policy. In a later paper, Dominguez (1990) finds
the distinction between coordinated and unilateral
intervention to be important. If the mechanism
was portfolio balance, only the change in relative
asset supplies would matter.10
Few studies use both daily exchange-rate
data and official intervention data, as does this
paper. Dominguez (1990), Loopesko (1984),
and Humpage and Osterberg (1992) use official
data to examine the impact of intervention on
the risk premium implied by deviations from
uncovered interest parity. All three studies find
significant effects of intervention. Baillie and
Humpage (1992) estimate a simultaneous sys
tem in which intervention either “leans against
the w ind” or seeks to stabilize volatile markets.
They determine that intervention influences the
conditional variance of the exchange rate. Bail
lie and Osterberg (1991) examine intervention’s
impact on the conditional mean and variance of
the daily forward-rate forecast error, finding that
U.S. purchases of foreign currency influence the
conditional mean. If efficiency is assumed, the
mean is interpreted as a risk premium.
B/H and Hung (1991) both view intervention
as operating via the market microstructure of
heterogeneous traders. In B/H, traders face the
possibility that the central bank may decide to
push the rate down or up. As a result, traders
may find that they have offered to buy too high
or to sell too low. In either case, the dealer sets
a wider bid-ask spread.
Hung (1991) considers a signaling role for
intervention that differs from that discussed by
Dominguez. If doubts about credibility make
intervention an ineffective signal of monetary
policy, and if the market is without a strong di
rection, public intervention can influence the
trading strategies of chartists or other nonfunda
mental traders. A strong implication of this is
that the central bank must know the current
market trading strategies. In addition, the ability
of intervention to increase or decrease volatility
depends on market conditions. For example, if
the dollar is acknowledged to be overvalued but
is still moving upward, the Fed would prefer to
wait until a short-term downward movement
■
10 Dominguez and Frankel (1991) and Ghosh (1989) attempt to
distinguish between portfolio-balance and signaling channels. Using
monthly data, Ghosh finds that portfolio-balance variables add a small
but significant effect to exchange rates. With weekly data, Dominguez and
Frankel determine that the signaling mechanism enhances the portfolio
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effect.
Federal Reserve Bank ofbalance
St. Louis
began, which it could encourage through secret
intervention. Selling dollars with this downward
trend would increase volatility. However, if the
dollar is on a strong downward trend, the Fed
could help it move down and decrease volatility
by countering short-term upward movements.
II. Data
The exchange-rate data were provided by the
Federal Reserve Bank of New York. At 10:00
a.m. of each day on which the New York market
is open, the Bank obtains both bid and ask
quotes for the spot and forward rates for the
DM/$ and the yen/$. The intervention data were
provided by the Board of Governors of the
Federal Reserve System.11 I analyze four series:
U.S. purchases of dollars vis-à-vis the mark, Ger
man purchases of dollars (sales of marks), U.S.
purchases of dollars vis-à-vis the yen, and Jap
anese purchases of dollars (sales of yen).
The sample period is from August 6, 1985 to
September 6, 1991. However, because not all
Japanese and German holidays coincide, the num
ber of observations differs for the two exchange
rates under examination. The intervention data
are close-of-business (COB) net daily purchases,
measured in $1 million units. The following analy
sis attempts to account for the fact that the foreign
exchange quotes are not contemporaneous with
the intervention numbers. Unfortunately, the avail
able data do not permit discrimination between
interventions that occur via a broker and those
that occur via market-makers.
III. Results
Table 1 presents the bid-ask spreads for both
the spot and forward rates for the DM/$ and
yen/$ for each day of the week. Beneath the
spreads are the t-statistics for the hypothesis
that each day’s spread is equal to the Friday
spread. Except for the Tuesday numbers for
both the spot and forward spreads for the yen/$,
the two-tailed test indicates rejection of the null
at the 5 percent level. In all cases, the null is
rejected at 10 percent. The Friday versus nonFriday tests are consistent with these results.
Table 2 looks at holiday effects in the spreads.
This focus is motivated by three facts: First, mar
kets by definition are closed on holidays as well
as on weekends (although markets may be open
elsewhere in the world on U.S., Gennan, or
■
11 The data on U.S. intervention are now publicly available from
Publications Services, Board of Governors of the Federal Reserve System.
D
TABLE
1
Daily Patterns in Bid-Ask Spreads
DM/$
Spot
T-stat.
Forward
T-stat.
N
Yen/$
Spot
T-stat.
Forward
T-stat.
N
Monday
Tuesday
Wednesday
Thursday
Friday
Non-Friday
6.360E-4
5.l60a
7.6l6E^i
4.984a
6.465E-4
4.818a
7.687E-4
4.779a
304
6.796E-4
3.523a
8.034E-4
3.497a
302
7.774E-4
6.544E-4
5.985a
7.778E-4
266
6.534E-4
4.405a
7.754E^i
4.4lOa
311
6.123E-2
2.712a
7.316E-2
2.531a
263
6.384E-2
1.760b
7.52E-2
1.735b
304
6.222E-2
2.468a
7.370E-2
2.465a
303
6.186E-2
2.530a
7.378E-2
2.359a
298
9-065E-4
9 .6 6 0 a
304
1,183
6.872
6.233
3.324a
7.407E-2
3-181a
1,168
8.062E-2
298
a. Significant at the 5 percent level for a two-tailed test.
b. Significant at the 10 percent level for a two-tailed test.
NOTE: Entries for “spot” and “forward” are the average bid-ask spreads. The t-tests are for the differences from the Friday spreads. “N ” indi
cates the num ber o f observations.
SOURCE: Author’s calculations.
Japanese bank holidays). If spreads are higher
on Fridays because markets are going to be
closed and prices therefore cannot “reveal” in
formation, spreads may also be higher on days
before holidays. Second, an examination of the
intervention data shows that intervention does
not occur on weekends, although it does some
times occur on U.S., German, or Japanese
holidays in markets that are still open. If market
participants are aware of these facts, and if an
ticipated intervention widens spreads, then
spreads will indeed be wider on days before
holidays. Third, since more holidays are on
Mondays than on any other day, the “Friday
effect” could be a “holiday effect.” In order to
focus on the possible influence of intervention
on spreads, I isolate a pure holiday effect by
controlling for whether or not the day before a
holiday falls on a Friday. I also present the com
parisons necessary to detect a pure Friday effect.
The results show that spreads are higher on
days before holidays, but there is mixed evi
dence of a pure holiday effect. First, although
spreads are higher on Fridays before holidays
than on other Fridays, the difference is not sig
nificant for any of the four spreads. Second, for
other days before holidays, both spot and for
ward spreads are wider for the DM/$ rates, but
not for the yen/$ rates. There is also mixed evi
dence for a pure Friday effect. In terms of both
http://fraser.stlouisfed.org/
currencies
and spreads, Fridays not before
Federal Reserve Bank
of St. Louis
holidays are higher than non-Fridays not before
holidays. However, there are no significant dif
ferences between Fridays not before holidays
and non-Fridays not before holidays.
These comparisons provide no compelling
reason to think that higher spreads on Fridays
are due to the fact that many Fridays fall before
holidays on which intervention may occur. The
last column of table 2 compares spreads on
days before single holidays with spreads on
days before consecutive holidays. The spreads
on days before multiple holidays are lower
than, but not significantly different from, days
before single holidays.
The remaining tables present information
about the relationship between the daily and
holiday patterns in spreads and intervention.12
Ideally, data on expected intervention would be
used to test the hypotheses presented by B/H.
Newspapers regularly report intervention. Such
reports, however, often either mention inter
vention that did not occur or fail to note actual
intervention (see Klein [19921). Another consid
eration is that while the foreign exchange
quotes are as of 10:00 a.m., the intervention
data are as of COB.
■
12 Intervention rarely occurred on holidays. The United Slates and
Germany intervened five and nine times, respectively, in the DM/$ mar
ket. The United States and Japan intervened eight and 13 times, respec
tively, in the yen/$ market.
8
TABLE
2
Friday and Day-BeforeHoliday Effects in
Bid-Ask Spreads
DM/$
Spot
T-stat. (H)
T-stat. (F)
Forward
T-stat. (H)
T-stat. (F)
N
Yen/$
Spot
T-stat. (H)
T-stat. (F)
Forward
T-stat. (H)
T-stat. (F)
N
A
B
C
D
E
F
G
H
Before
~A
Fri., A
Fri., -A
-Fri., A
~Fri., ~A
Multiple
Single
8.015E-4
6.718E-4
3.694a
8.430E-4
7.664E-4
1.290
7.600E-4
6.502E-4
2.355a
6.250E-4
8.097E-4
-0.868
9.292E-4
7.961E-4
3.595a
7.733E-4
2.406a
7.500E-4
9.376E-4
-0.844
90
1,397
1,138
4
86
6.943E-2
6.320E-3
2.038a
6.210E-2
1.341
6.423E-2
7.020E-2
-0.672
8.223E-2
7.489E-2
2.253a
7.380E-2
1.488
7.577E-2
8.323E-2
-0.779
101
1,365
1,118
13
88
0.955
9.669E-4
0.820
45
7.147E-4
0.692
8.443E-2
0.678
51
8.960
1.130
259
6.815E-4
0.570
7.983E-2
0.744
247
5.408a
8.916E-4
5.390a
45
6.735E-2
2.905a
8.007E-2
2.708a
50
a. Significant at the 5 percent level for a two-tailed test.
NOTE: Entries for “spot” and “forward” are the average bid-ask spreads. “N ” indicates the number of observations.
Explanation o f columns:
A: Days before market holidays
B:
C:
D:
E:
F:
(~A) Days not before market holidays
(Fri., A) Fridays before market holidays
(Fri., ~A) Fridays not before market holidays
(~Fri., A) Non-Fridays before market holidays
(~Fri., ~A) Non-Fridays not before market holidays
G: Days before multiple, consecutive market holidays
H: Days before single market holidays
Explanation o f t-statistics:
(H), (F) distinguish tests designed to isolate pure day-before-holiday and Friday effects, respectively.
B: Days before holidays compared to days not before holidays
C: Fridays before holidays compared to non-Fridays before holidays
D: Fridays before holidays compared to Fridays not before holidays
E: Fridays not before holidays compared to non-Fridays not before holidays
F: Non—Fridays before holidays compared to non-Fridays not before holidays
H: Days before multiple holidays compared to days before single holidays
SOURCE: Author’s calculations.
Table 3 presents the daily variation in fre
quency of intervention. B/H suggest that deci
sions about intervention took place over the
weekend for the currencies in the European
Monetary System. If this were true for the G-3,
we may expect to see more intervention occur
ring on Mondays. However, there is no signifi
cant evidence that this is the case.
Rather than define periods of intervention as
days on which intervention officially occurred
ex post, in table 4, I use two measures of ex
http://fraser.stlouisfed.org/
pected intervention. Panel A compares the bidFederal Reserve Bank of St. Louis
ask spreads over periods usually thought of as
times of intervention as opposed to “noninter
vention” periods. Ignored for the moment is the
issue of whether intervention actually occurred
at these times. The intervention periods are
defined as 9/1/85 to 12/31/85, 9/1/86 to 1/1/87,
2/1/87 to 6/1/87, and 10/1/87 to 12/31/87. The
most noteworthy dates are 9/22/85 (Plaza ac
cord), 2/23/87 (Louvre accord), and 10/19/87
(the U.S. stock market crash). Dominguez
(1990) presents reasons to focus on the wider
time frames utilized here. The nonintervention
9
T ABL E
3
Day-of-the-Week
Effects in Intervention
DM/$
U.S.
T-stat.
Germany
T-stat.
N
Monday
Tuesday
Wednesday
0.1312
0.1158
0.5759
0.1897
0.0614
311
0.1118
0.7198
0.1447
1.5022
304
0.1325
-0.0306
0.1523
1.245
302
0.1513
-0.6724
0.1809
0.3303
304
0.1278
0.1684
0.1671
0.9663
1,221
0.1151
0.7794
0.1875
1.4067
304
0.1089
1.0135
0.1848
1.4877
303
0.1342
0.0915
0.2114
0.6902
298
0.1174
0.6899
0.1946
1.1843
298
0.1189
0.8079
0.1945
1.5089
1,203
0.1917
266
Yen/$
U.S.
T-stat.
Japan
T-stat.
N
0.1367
0.2358
263
Thursday
Friday
Non-Mond
NOTE: Entries for each country are the proportion o f days on which intervention occurred. T-statistics are for the difference between the M on
day numbers and other days. “N” indicates the num ber o f observations.
SOURCE: Author’s calculations.
TABLE
4
Bid-Ask Spreads: Intervention
Periods vs. Nonintervention Periods
Panel A: Purported
Intervention?
Panel B: Two
Consecutive Days
Panel C: Expected vs. Unexpected,
Realized vs. Unrealized
1) Yes
2) No
1) Int.
2) Non.
A :l, B:1
A: 1, B:2
A:2, B:1
A:2, B:2
DM/$
Spot
T-stat.
Forward
T-stat.
N
8.342E-4
-1.308
9930E-4
-5.465a
339
8.744E-^t
6.670E-4
-0.472
7.987E^
-0.211
111
6.82 IE-4
7.707E-4
8.050E-4
9361E-4
1,145
41
8.323E-4
-1.011
9-883E-^
-0.832
229
9.455E-4
-1.576
1.084E-3
-1.300
11
8.856E-4
-1.973a
1.042E-3
-1.779b
222
Yen/$
Spot
T-stat.
Forward
T-stat.
N
7.799E-2
-2.099a
9.290E-2
-1.975a
339
8.41 IE-2
7.091E-2
3.855a
8.464E-2
4.524a
147
6.176E-2
7.393E-2
7.309E-2
8.907E-2
1,098
61
7.671E-2
-0.667
9.113E-2
-0.465
234
8.182E-2
-1.354
9.655E-2
-1.262
44
8.317E-2
-1.880b
9.820E-2
-1.818b
161
1.030E-3
246
9-890E-2
246
a. Significant at the 5 percent level for a two-tailed test.
b. Significant at the 10 percent level for a two-tailed test.
NOTE: T-statistics for panels A and B are for the intervention-nonintervention difference. T-statistics for panel C are for the differences from the
A :l, B:1 spreads. “N ” indicates the num ber o f observations.
Explanation o f panel C:
A: 1,
A: 1,
A:2,
A:2,
B: 1:
B:2:
B: 1:
B:2:
Days
Days
Days
Days
o n w hich intervention was expected and realized
o n which intervention was expected but not realized
o f “surprise” intervention
o n which intervention was neither expected nor realized
SOURCE: Author’s calculations.
10
■
13 I am grateful to Jacky So for suggesting this further refinement.
Because B/H claim that anticipation of intervention widens spreads, theirs
is a claim about weak-form market efficiency. Use of actual, confidential
http://fraser.stlouisfed.org/
intervention data is relevant for tests of strong-form efficiency.
Federal Reserve Bank of St. Louis
findings in panel B had for concluding that inter
vention lowers spreads. More important, how
ever, panel C is contrary to the B/H hypothesis
that expectations of intervention increase bidask spreads.
Causality should not be inferred from correla
tions such as those presented here. While B/H
contend that spreads widen in anticipation of in
tervention, at times intervention has been in
tended to counter volatility. Bid-ask spreads
may in part reflect volatility, and thus interven
tion and bid-ask spreads may be correlated be
cause of attempts to counter volatility reflected
in spreads.
In the absence of a fully specified model of
the determinants of the spreads and of the re
sponse of intervention to market movements, I
utilize the concept of Granger-causality to learn
more about the temporal relations between
spreads and intervention. Granger-causality util
izes equations of the form
<7
M
II
p
(3)
bSSi S t -
i= 1
/+ Xf
ii
yfe= 1
bS i j I t- j +
us n
7=1
r
(4)
M
period is defined as all other days. For purposes
of comparability, the panel A calculations leave
out the post-1987 subsample. Both DM/$ and
yen/$ spreads are significantly lower during
periods of purported intervention.
Panel B of table 4 compares spreads from days
within actual intervention periods with days from
periods when intervention did not occur. Specifi
cally, if either the United States or Germany was
intervening on day t- 1 and on day t, the 10:00
a.m. day t quote on the DM/$ is said to be from a
period of intervention. If both countries were not
intervening on either day, the quote is from a non
intervention period. In effect, this indicates that if
there was intervention on day t-\ (ex post) and
intervention as of COB on day t, it is likely that, at
10:00 a.m. on day t, traders perceived that they
were in the midst of a period of intervention. Table
4 shows that the yen/$ spreads were significantly
higher during these periods, while the DM/$ rates
were lower, though not significantly so.
Panel C further refines these measures of ex
pected intervention.13 The periods of purported
intervention analyzed in panel A might be better
thought of as periods when intervention was
likely to have been anticipated. The “two con
secutive days” criterion utilized in panel B may
better identify periods of actual intervention.
Thus, one possible explanation of the higher
spreads for the yen/S in panel B may be that
not all intervention that occurred during two
consecutive days was anticipated. Days that fell
into the first columns of both panels A and B
may more closely identify intervention that was
both expected and realized. Days that fell into
both of the second columns tell us when inter
vention neither occurred nor was expected. The
in-between cases are when days met only one
of the criteria. Panel C provides the results for
all four cases.
All four of the t-statistics imply significant dif
ferences at the 10 percent level, and the relative
magnitudes of the spreads are consistent with
my interpretation of panel A- Spreads are lower
when actual intervention was expected than when
intervention was neither expected nor realized.
Spreads when intervention was expected but not
realized lie between the “expected intervention”
and “neither” cases. In addition, conditional on
whether intervention occurred as defined by the
panel B criterion, spreads are lower when inter
vention was anticipated, as defined in panel A.
This weakens the qualification that the yen/$
S
^isk
^ n il t - 1
St- k +
+
uIt
1= l
Here, / and S are each regressed on past val
ues of themselves and on lagged values of the
other variable. / Granger-causes S if past values
of / improve upon the ability of past values of S
to predict S. Since the focus is on whether inter
vention Granger-causes spreads, I test for the
significance of the bSI's.14 However, before esti
mating these equations, I test for the presence of
unit roots in the spreads. The presence of such
effects would imply a type of nonstationarity that
would invalidate the results. I consistently reject
the null that such an effect existed.15 In addition,
the length of the autoregressions, p, q, r, and s,
must be chosen. I arrive at a lag length of 20 by
considering successively longer lag lengths (10,
15, 20, and 25) and by testing whether the addi
tional terms are significant.
■
14 Alternative concepts of, and tests for, causality are presented by
Granger and Newbold (1986).
■
15 These tests were performed with both the Dickey-Fuller and
Phillips—Perron procedures, both with and without deterministic trends.
The number of lagged first differences on the right side was the minimum
number to produce residuals that were free of serial correlation as meas
ured by Box—Ljung Q statistics. Baillie and McMahon (1989, pp. 105—
107) discuss these test procedures. The results of the unit root tests are
available from the author.
J T A B L E 5
| intervention. In this paper, I use official data on
Granger-Causality Tests: Intervention
to Spreads, Significance Levels
Full Sample
9/9/8512/31/86
1/1/8712/31/89
U.S.-Germany
Int.—»Spreads
0.4978
0.4260
0.3657
U.S.-Japan
Int.—»Spreads
0.9680
0.0001
0.6717
NOTE: Significance levels are for the likelihood ratio tests o f whether the vec
tor of intervention terms Granger-causes the vector o f spreads.
SOURCE: Author’s calculations.
Table 5 presents the results of the tests for
Granger-causality from intervention to
spreads.16This is done for each currency, so that
when DM/$ (yen/$) spreads are on the left side,
then lagged DM/$ (yen/$) spreads, lagged Ger
man (Japanese), and lagged U.S. intervention
are on the right side. For the full sample, there
is no evidence of Granger-causality from inter
vention at conventional levels of significance.
Table 5 also presents the results of the same
causality tests when the sample was split at the
end of 1985 and the second subperiod ends at
the close of 1986. Hung (1991) suggests that the
impact of U.S. intervention on unexpected vol
atility changed over these periods in response
to different market conditions, as discussed
above. U.S. and Japanese intervention Grangercauses yen/$ spreads for the first subperiod. No
such effect is found for the three other tests. It is
well known, however, that such tests should
not be interpreted in terms of structural models.
IV. Summary
In a recent article, Bossaerts and Hillion (1991)
present evidence that tests of forward market
efficiency that ignore variation in the bid-ask
spread are biased, at least for currencies in the
European Monetary System. They observe that
spreads are wider on Fridays and speculate that
this may be due to anticipation of central-bank
■
16 Tests of whether spreads Granger-cause intervention would
need to be strongly qualified due to the nature of the distribution of the in
tervention variables (many observations are clustered at zero). This prob
lem, however, does not invalidate the tests for Granger-causality from
http://fraser.stlouisfed.org/
intervention.
Federal Reserve Bank
of St. Louis
intervention to see if it can explain intraweekly
patterns in G-3 spreads.
The tests confirm the tendency for Friday
spreads to be higher than for other days of the
week and also find some evidence of holiday
effects. However, there is no evidence that intra
weekly patterns in intervention are related to
the patterns in spreads. In addition, I find no evi
dence to support the conclusion that anticipa
tion of intervention widened spreads. Last,
Granger-causality tests suggest that intervention
generally does not lead spreads.
Although I cannot interpret such results in
terms of a structural model, previous research
has documented that intervention influences
risk premia and that conditional variances ex
hibit intraweekly variation. Intervention policies
at times have been explicitly designed to
respond to volatility. Further investigation into
the relations among intervention, spreads, and
volatility would be greatly facilitated by a struc
tural model.
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Bl
An Ebbing Tide Lowers All Boats:
Monetary Policy, Inflation, and
Social Justice
by David Altig
David Altig is an economist at the
Federal Reserve Bank of Cleve
land. The author thanks Stephen
Cecchetti for useful comments.
It is essential that the direction o f public policy
be well targeted to the nature o f the problem it
is seeking to ameliorate.... But only in the con
text o f prudent, noninflationary expansion o f
money a n d credit are such improvements likely
to be lasting.
— Alan Greenspan, December 18, 1991
Introduction
During periods of slow growth and rising unem
ployment, the dynamics of the economic policy
debate inevitably reveal an almost irresistible sen
timent for stimulative monetary policies. To cite a
current example, the steady march of the unem
ployment rate from 5.3 percent in mid-1990 to 7.3
percent as of April 1,1992 has been matched on
the monetary policy front by persistent calls for
the Federal Reserve to take action that would
ensure an economic recovery regardless of any
longer-term price-level consequences. The dual
circumstances of lower-than-expected inflation
and slow growth of the M2 monetary aggregate
have reinforced this pressure. At the same time,
the reluctance of private-market participants to
fully incorporate recent inflation outcomes in their
http://fraser.stlouisfed.org/
inflation
expectations, coupled with the persistent
Federal Reserve Bank of
St. Louis
steepness of the yield curve, suggests that infla
tion fears are very real to the decision-makers
whose behavior ultimately determines the
course of the economy.1
Still, at times like this, there are always many
who feel that the inflationary risk inherent in an
aggressive monetary policy is worth taking if
such a policy can effectively stimulate economic
activity, especially since the costs of recessions
and slow-growth periods are unequally distrib
uted throughout the population. This sentiment
is forcefully expressed in the book H ard Minds,
Soft Hearts: Tough-Minded Economics fo r a Just
Society, written by economist Alan Blinder of
Princeton University (see Blinder [1987]). As the
evidence presented in the next section makes
■
1 The spread between three-month T-bill and 30-year Treasury
bond yields reached a record high of 436 basis points in the week ended
April 24,1992. With respect to inflation expectations, the following quote
is from the April 1992 issue of the Federal Reserve Bank of Cleveland's
Economic Trends: ‘‘The P-Star model, which links the trend in M2 growth
to future inflation, projects continued downward pressure on the inflation
rate through 1993.... Apparently, private forecasters are not as optimistic
about the near-term inflationary trends. The Blue Chip consensus forecast
shows the GDP im plicit price deflator edging up to slightly more than 3
percent next year.” The first-quarter 1992 number for the deflator indi
cates that these forecasts are well founded.
15
clear, unemployment disproportionately burdens
lower- and middle-class workers relative to more
affluent Americans, while inflation, to the extent
that it affects income distribution at all, appears to
do just the opposite. In Blinder’s words:
Sometimes inflation is piously attacked as the
“crudest tax,” meaning that it weighs most heavily
on the poor.... On close examination, the “crudest
tax” battle cry is seen for what it is: a subterfuge for
protecting inflation’s real victims, the rich.... [Elvery
bit of evidence I know of points in die same direc
tion: inflation does no special harm to die poor....
The meager costs that inflation poses on the poor
are dwarfed by the heavy price the poor are forced
to pay whenever the nadon embarks on an anti
inflation campaign.... (p. 54)
Two important features of the evidence to
which Blinder refers deserve further comment.
First, most of the evidence points to the distribu
tion of income rather than to the level of income.
The former is a somewhat strange measure of
welfare: I would gladly see you gain a zillion
dollars of real output if doing so would obtain a
billion for me, even if the distribution of our in
comes becomes more unequal in the process.
Second, and more critically, the evidence cited
by Blinder focuses on cyclical fluctuations in eco
nomic activity. Few economists believe that lower
unemployment can be “traded” for higher inflation
in the long run. Consequently, a more accurate
statement would be that the meager costs inflation
poses on the poor are dwarfed in the short run
by the heavy price this segment of the population
is forced to pay when the nation embarks on an
anti-inflation campaign.
Some empirical and theoretical arguments
for factoring the long-run costs of inflation into
calculations of the “fairness” of anti-inflation
policies are presented in section II. These argu
ments refer primarily to the resource cost to the
average individual and thus do not directly
address the fairness issue. However, the argu
ments do relate inflation to reductions in the
overall level of GDP and hence indirectly bear
on welfare considerations, to the extent that the
burden of falling income is in the long run
shared by the less-than-wealthy.
A more direct argument is presented in sec
tions III and IV, by way of a simple model that
illustrates how the long-run costs of inflation
arise due to distortions created by a tax system
based on nominal income. Although the world I
consider is highly stylized, it captures some key
elements of the real world: The tax system is im
perfectly indexed for inflation. There are “rich”
people and “poor” people. Rich people own
capital; poor people do not. The share of the
economic pie earned by rich people is larger
than the percentage of the total population they
represent. Also, inflation raises the tax burden
of the rich relatively more than that of the poor
and, consistent with empirical evidence, does lit
tle to change the distribution of income.
Within this model, inflation-induced tax in
creases on capital definitely hurt the poor.
Because inflation effectively raises the tax on
capital, a sustained increase in price-level
growth ultimately results in a lower capital
stock, reduced output, and lower productivity
for all workers. Declining output and productiv
ity can be expected to fall especially hard on
the poor because they start from a lower stan
dard of living to begin with.
The example given by this simple model is
not provided as an argument for eschewing dis
cretionary, short-run stabilization policies as
rationalized by variants of the Phillips curve
model that serve as the foundation of Keynesian
economics — even in its more recent incarna
tions.2 Although I am skeptical of the Keynesian
framework, neo or otherwise, as a useful guide
for policymaking, the purpose of this paper is
not to engage in a theoretical or philosophical
quarrel with the proponents of activist monetary
policy.3 Instead, I attempt to show that the “fair
ness” objectives that motivate people to urge the
Federal Reserve to “do something” when eco
nomic activity drags also dictate that the Fed
achieve a long-run goal of maintaining price
stability. In broad terms, I am arguing that, if we
adopt Blinder’s arguments as a guide to shortrun monetary policy, we should symmetrically
adopt procedures that provide a long-run
anchor to the price level in order to ensure
against the possibility of making the cure worse
than the illness.
I. Inflation,
Unemployment, and
the Size Distribution
of Income
The perception that inflation does no special
harm to the poor arises from studies that
■
2 The volumes edited by Mankiw and Romer (1991) are an excel
lent introduction to some of the important works in the “New Keynesian”
literature.
■
3 Those readers who are interested in such a quarrel are referred to
Barro (1989).
16
T A B L E
1
The Effect of U n e m p lo ym e n t
and Inflation on Incom e Shares
Quintile
Real
Per Capita
GNP
1
0.111
2
Post-1983
Trend
Lagged
Dependent
Variable
Inflation
Unemployment
0.016
(1.1)
0.012
(1.0)
-0.076
(3.3)
-0.082
(4.7)
-0.043
(1.0)
0.694
(6.7)
0.8034
(1.3)
-0.122
(1.8)
-0.052
(1.5)
0.610
(6.8)
0.9426
3
-0.088
(1.2)
0.014
(1.0)
-0.038
(2.0)
-0.018
(0.5)
0.669
(6.4)
0.8140
4
0.254
(2.8)
-0.022
(1.7)
-0.018
(1.0)
-0.070
(2.2)
0.396
0.8143
0.003
(0.01)
-0.041
(1.2)
0.175
(3.5)
0.123
(1.2)
0.700
(7.5)
5
Adjusted R 2
(2.9)
0.8501
NOTE: Standard errors are in parentheses.
SOURCES: U.S. Department of Commerce, Statistical Abstract o f the United States, 1990, and Economic Report o f the President, 1991.
examine the effects of macroeconomic variables
on the share of income received by distinct
population quintiles. These share data, col
lected and reported by the U.S. Department of
Commerce, are obtained by ranking the income
of all households from lowest to highest and
calculating the percentage of total income that
accrues to the first (lowest-income) one-fifth of
households, the second one-fifth of households,
and so on, up to the last one-fifth, who have the
highest incomes in the population.
The effect of macroeconomic activity on these
income shares can be seen by examining the re
sults of the regressions reported in table 1. The
regressions measure the effect of unemployment
and inflation on the income share of each popula
tion quintile after controlling for the level of per
capita income, lagged share values (essentially a
catchall for the effects of omitted variables), and a
shift in the income distribution that appears to
have occurred subsequent to 1983.4
The results in table 1 indicate that the burden
of unemployment clearly falls on the lowerincome quintiles. The jobless rate is negatively
related to the share of income received by the
three lowest-income quintiles and is positive for
the upper two.5 Inflation, on the other hand,
has no statistically significant effect on the dis
tribution of income.
As indicated by the Blinder quotation in the
introduction, these results are consistent with
http://fraser.stlouisfed.org/
the bulk of the evidence on income inequality
Federal Reserve Bank of St. Louis
in the United States.6 However, the information
provided by studies of this sort is of a very par
ticular type. Specifically, the regression results
indicate only that, on a year-to-year basis, infla
tion does not reduce the relative share of in
come received by the lower-income quintiles.
They do not tell us anything about the long-run
effects of sustained inflation on the level of in
come for any particular income class.
In fact, if inflation has adverse effects on the
long-run level of income, the poor may indeed
be hurt — and perhaps hurt disproportionately
in utility terms — even though their relative
■
4 This regression model follows that reported in a recent paper by
Cutler and Katz (1991). Although I use a different sample period than they
do, the results in table 1 are qualitatively sim ilar to their findings. The
post-1983 shift toward greater inequality in income distribution is an
interesting phenomenon that appears to have resulted from a significant
structural shift in the employment patterns of skilled versus unskilled
labor. I recommend the Cutler—Katz paper to those readers interested in a
thorough discussion of this change.
■ 5 Note that, by construction, the income shares over all five quin
tiles must sum to one. Thus, a significant negative effect of some variable
on the income share of one group must be offset by positive effects on
one or more other quintiles.
■
6 Buse (1982) finds a sim ilar resultfor Canada. Specifically, he
discovers that inflation does not significantly affect the share of income
received by different income quintiles. Interestingly, neither does he find
a significant effect arising from unemployment rates. However, other
labor market variables, specifically the employment and labor participa
tion rates, are found to influence income distribution, with greater em
ployment and participation related to less income inequality.
income shares are not reduced. I turn now to a
brief overview of the empirical evidence on the
relationship between inflation and the long-run
level of output.
II. Is Inflation
Harmful to the
Economy in
the Long Run?
A recent study by Charles T. Carlstrom and William
T. Gavin of the Federal Reserve Bank of Cleveland
attempts a direct comparison of the welfare impli
cations of the effects of disinflationary policies in
both the short and long run (see Carlstrom and
Gavin [1991])- The authors argue that, in terms of
forgone output for the average individual, the
long-run “shoe-leather” costs of a steady 4 percent
inflation rate are similar in magnitude to the shortrun costs that would typically be attributed to a
tight-money policy that reduced the rate of infla
tion from 4 percent to zero.7
More generally, simple correlations do suggest
that economic growth is negatively related to infla
tion. Using data from the International Financial
Statistics, Gomme (1991) reports that “...62 of 82
countries exhibit a negative correlation between
inflation and per capita real output growth.” More
complicated statistical examinations — essentially
regressions of cross-country growth rates on a
variety of political and economic variables— yield
mixed conclusions. But, as convincingly argued by
Levin and Renalt (1991), nonrobustness appears
to be a generic weakness of the methodology
employed in such studies.
Two features of these cross-country studies
may help to explain this nonrobustness. First,
there is a subtle point to be made here about
the correlations between growth and inflation.
In standard neoclassical growth models, the
growth rate of the economy is exogenous and
constant. In particular, the growth rate of in
come is not affected by inflation even though
the level of income is.8 Thus, the absence of a
significant correlation between inflation and the
long-run growth rate of the economy does not
necessarily imply that a particular level of infla
tion will fail to reduce per capita income below
the level attainable at lower inflation rates.
Second, the relationship between inflation and
long-run economic performance may operate
through indirect and complicated channels. One
such possibility is the interaction between infla
tion and the tax system. Although indexing has
been partially implemented in many countries, in
cluding the United States, extant indexing schemes
are generally insufficient to remove the distortions
created by inflation/tax interactions.9 Although it
is true that such interactions provide revenue that
might be channeled to productive uses by funding
desirable government expenditures or by reducing
the level of government debt, research in progress
by Charles Carlstrom and me suggests that allow
ing inflation to interact with the structural tax sys
tem is not an efficient way to raise revenue.10
In the next section, I examine a simple model
economy in which inflation distortions arise
through exactly this channel. Specifically, inflation
is allowed to interact with a tax system based on
nominal wage and capital income. The model is
chosen to illustrate a rather straightforward point
— that inflation can have deleterious long-run
effects on the economic well-being of both the
rich and poor, without affecting either the growth
rate of the economy or the distribution of income.
■
■ 7
Shoe-leather costs are defined as the value of real money balances
that would be held by individuals if the inflation rate were zero instead of 4
percent. An even more dramatic comparison of the welfare costs of short-run
versus long-run changes in economic resources, although one not directly
related to inflation, was given by Robert E. Lucas, Jr. in his 1985 Vrjo
Jahnsson Lectures (see Lucas [1987], section III). He posed the following
question: What is the maximum percentage of per-period consumption a rep
resentative individual would willingly give up in exchange for 1) a complete
smoothing of short-run (or cyclical) fluctuations in consumption or 2) an in
crease in the long-run (or trend) growth rate of consumption from 2 to 3 per
cent? Using plausible values for individual risk preferences, volatility in
consumption, and so on, Lucas argues that the amount of consumption that
would be forgone in exchange for higher long-run consumption growth is
several hundred times the amount that would be given up to eliminate shorthttp://fraser.stlouisfed.org/
run fluctuations.
Federal Reserve Bank of St. Louis
8 The assumption of exogenous, or policy-invariant, growth rates
typical of the neoclassical growth framework presented here has recently
been challenged by proponents of so-called endogenous growth models.
Good overviews of the neoclassical and endogenous growth frameworks
can be found in two papers by Sala-i-Martin (1990a, 1990b). A short and
informal presentation of the issue is provided in an article entitled “Eco
nomic Growth: Explaining the Mystery," published in the January 4,1992
edition of The Economist. See also Mankiw, Romer, and Weil (1990) for
a skeptical empirical assessment of the endogenous growth framework.
■ 9
■ 10
See Altig and Carlstrom (1991b).
This message is implicit in Altig and Carlstrom (1991a). Bear
in mind that we are not referring to issues related to seigniorage, or the
“ inflation tax,“ per se. See Cooley and Hansen (1989,1991) and Gomme
(1991) for recent analyses of the welfare implications of revenue collec
tion through seigniorage.
U
III. A Simple
Model11
To illustrate the argument, I present a simple
general-equilibrium framework that admits two
types of individuals: those who earn income
solely through wages and those w ho earn both
labor and capital income. Each of the groups
arises endogenously as a result of its preferences.
Members of the first group, who earn only labor
income in equilibrium, allocate their earnings
according to their own life-cycle consumption
needs. Those in the second group care not only
about their own life-cycle consumption, but
also about their children’s consumption. These
altruistic impulses effectively make the planning
horizon of this group infinite. They therefore
have a much stronger motive for saving than
the first group and, in equilibrium, end up
owning the entirety of the economy’s capital
stock. For simplicity, and with obvious motiva
tion, the first group will be referred to as “poor”
and the second will be referred to as “rich.”12
Each generation in this model lives, with abso
lute certainty, for two periods, which I refer to as
the young and old phases of life. Labor is inelastically supplied in each period, and the productivity
of labor, identical for rich and poor, is the same
when young and old. I assume that a fraction £ of
each generation is rich and 1-e is poor.13 The
population growth rate is assumed to be zero, and
the aggregate capital stock, wages, and the interest
rate are determined by 1) the aggregate production
■
11 The model developed in this section is similar to that presented
in section V(b) of Altig and Davis (1992).
■ 12 Some readers may be uncomfortable with the model's implica
tion that rich people “care” about their children but poor people do not.
Such an implication, however, is more apparent than real. First, the group
I have designated as poor (because they have no capital income) is pre
sented as nonaltruistic for convenience only. As long as the degree of al
truism is lower for one group than the other, the equilibrium outcome will
be such that the group with the higher degree of altruism will own the en
tire capital stock, even if it is more altruistic by an infinitesimally small
amount. Second, a more general model than the one I use here could
allow the effective degree of altruism to be related to an individual’s level
of wealth. Thus, a framework in which bequest levels depend on the
serendipitous mortality history of a given family line could result in the
same type of sorting I exploit here, even though the utility functions of all
individuals are identical.
13 Mankiwand Zeldes (1991) reportthat, in 1984, some portion of
wealth was held as stock for approximately 25 percent of the families sur
veyed in the University of Michigan’s Panel Study of Income Dynamics. (This
figure does not include equity implicitly held through pension plans.) These
families accounted for approximately 40 percent of total disposable income.
As described below, our model will be parameterized such that 25 percent of
the population holds capital, with the shares of income accruing to the rich
http://fraser.stlouisfed.org/
and poor according fairly closely with this evidence.
technology, 2) the government’s tax and expen
diture policy, and 3) the saving and consump
tion decisions of the two groups.
The government raises revenue by applying
a uniform flat tax rate, p , to nom inal labor and
capital income. In other words, the tax code is
not indexed for inflation. Although the actual
U.S. personal tax code is partially indexed, ad
justments for inflation are far from perfect. In
particular, the indexing provisions in the current
tax code would not vitiate the overstatement of
capital income that is critical for the results
reported here.14
Denoting variables associated with the rich by
superscript R and those for the poor by super
script P, the government’s budget constraint is
(1)
c,+ r f + r f
= p [ (r i +7ii M ,+ ( l + 7Tr) U’tLt\,
where Gt represents government purchases of
output, Tf and T f are transfer payments to
the rich and poor, respectively, rt is the real
return to capital (the interest rate), wt is the real
wage, n, is the exogenously determined infla
tion rate, At is aggregate capital holdings, and
Lt is aggregate labor supply.1’ Government
spending is not productive, nor does it substitute
for private consumption.
In what follows, I examine the steady-state, or
long-run, effects of a change in the inflation rate
on the level of income and lifetime consumption
of the rich and poor. Subscripts indicating time
periods will therefore be dropped. To further
streamline the presentation, superscripts denoting
rich and poor will be suppressed except when
necessary. Readers who have no special interest
in the details of the model can, without loss of
continuity, skip to the next section, which presents
the numerical results.
The utility function of each individual who,
in equilibrium, is rich is given by
(2)
U (c v c2, Uk ) = In (q ) + p/rc (c2) + y U\,
where cx and c2 denote own consumption in
the first and second period of life, (3 is a subjec
tive time-discount factor, U*k is the maximum
attainable utility of the individual’s child, and y
is the rate at wrhich a parent discounts his or her
■
Federal Reserve Bank of St. Louis
■
14 See Altig and Carlstrom (1991b) for a more detailed discussion
of inflation indexing in the U.S. personal tax code. The corporate tax code
contains no indexing provisions.
■
15 There is no “money” in the model. Inflation is introduced as the
exogenous rate of depreciation of an arbitrary unit of account.
child’s utility. If y = 1 , parents weight their child’s
utility equally to their own. Using analogous
notation, the utility function of each individual
who, in equilibrium, is poor is
For both groups, the intertemporal first-order
condition for utility maximization is given by
(3)
For the group with preferences given by equa
tion (2), the first-order condition governing
intergenerational transfers, g, is
U (c v c2) = /«(Cj) + $ ln (c 2) .
Equations (2) and (3) are maximized subject
to the budget constraints
(11)
(12)
(4)
q + g + Tx= w [1 —p (1 + 7t) ] + a
and
(5)
c2 + T2 + b = w\l - p (1 + 7i) ]
+ { 1 + r[l - p (1 + 7t) ]} « ,
where g represents transfers received by children,
b represents transfers given by parents, and a
represents asset holdings. Note that b = g = 0
for individuals with preferences given by equation
(3). Also, recall that a p = 0 in equilibrium.
Production is undertaken by profit-maximizing,
competitive firms that apply competitively ob
tained capital and labor inputs to a CobbDouglas technology, given by
(6)
y - Ke,
where y and k are, respectively, per capita out
put and the per capita capital stock, and 0 is a
parameter that measures capital’s share of total
output. The profit-maximizing conditions of
firms imply that the aggregate wage and interest
rate are given by
(7 )
r - 6k0-1
and
(8 )
w
= ( 1 - Q )
k
*.
Along with the government’s budget constraint
given in equation (1), the specification of the
model is completed by the goods-market and
capital-market clearing conditions. Because capi
tal does not depreciate and the population is sta
tionary, government purchases and aggregate
consumption, C, exhaust total output. The capital
stock is simply the sum of asset holdings by the
rich and poor, with the latter, once again, being
zero in equilibrium. The two market-clearing con
ditions are thus given by
(9)
y = G+ C
and
http://fraser.stlouisfed.org/
(1 0 ) k = eaR+ (1 - e) ap .
Federal Reserve Bank of St. Louis
c2 = (3 (1 + r) cx .
c2 = y c l k ,
where c]k is the children’s first-period consump
tion. Because every generation’s consumption is
the same in a steady-state equilibrium, clk = cv
Equations (12) and (13) thus imply that (3 (1 + r)
= y when the transfer motive is operative for the
group with preferences indicated by (2). Com
bined with equation (7), this condition implies that
the per capita capital stock is given by
(13)
K = r i= J L r ± llf iJ E le ^
L e p y ( l- p )
-I
IV. How Inflation
Hurts the Poor
The model is constructed so that the effects of
inflation work through interactions with the tax
system. Thus, as is clear from equation (1), an
increase in the inflation rate (it) raises the amount
of revenue collected by the government even when
real income (r A + w) is unchanged. Because the
model does not incorporate government debt,
satisfaction of the government budget constraint
requires either an increase in government expen
ditures, an increase in transfer payments, or some
combination of the two. Aggregate and individual
consumption levels thus depend on the nature of
the fiscal policy regime.
The results of three distinct fiscal policy ex
periments are presented in this section. In the
“benchmark” model, tax revenues and govern
ment purchases of real output are endogenously
determined. A second case, which I refer to as
the “progressive-transfer” model, maintains a
constant, exogenous level of government pur
chases, transferring all surplus revenues to the
poor. Results in the third case, which I call the
“revenue-neutral” model, are obtained by
assuming a constant level of government pur
chases, with all surplus revenues used to in
crease transfer payments such that the net tax
payments of each cohort remain constant. Equa
tions (4) to (13) can be combined to obtain con
sumption levels under each of the fiscal regimes.
The solutions are given in the appendix.
T A B L E
2
Simulated Steady-State Effects
of Inflation/Tax Interactions
Income Share
Consumption Loss
from Inflation (percent)
Model
Rich
Poor
Rich
Poor
Benchmark model,
zero inflation
0.44
0.56
__
__
Benchmark model,
4 percent inflation
0.44
0.56
3.1
2.2
Progressive transfer,
4 percent inflation
0.43
0.57
3.1
0.0
Revenue neutral,
4 percent inflation
0.44
0.56
1.5
1.3
SOURCE: Author’s calculations.
invariant to the rate of inflation. Despite this,
the lifetime consumption opportunities of the
poor fall by as much as 2.6 percent. Only when
all surplus revenues from inflation are trans
ferred to the poor is this group unharmed by in
flation. And even in this case, their lot is not
improved. It is clear, then, that evidence regard
ing income distribution is of limited value as a
measure of the welfare consequences of infla
tion on the poor.1
More directly, the poor are decidedly hurt by
inflation, even though these adverse conse
quences do not manifest themselves in lost in
come shares. It is possible that in a more fully
articulated model, the poor might actually gain
in the short run. However, if the effects of infla
tion emphasized here capture some important
part of economic reality, such a gain would be
transitory. If inflation is harmful in the long run,
the less affluent will not be exempt.
V. The Moral
of the Story
The results of the three distinct fiscal policy
experiments, presented in table 2, are obtained as
suming that capital’s share of output is 25 percent
(0 = 0.25), the productivity factor in each period
of life ( a ^ , a / , a 2p, and a / ) equals 0.25, the
subjective discount factor ((3) equals 0.778, the in
come tax rate is 20 percent (p = 0.20), 75 percent
of the population is poor and 25 percent is rich
(e = 0.25), and the rich weight the utility of their
children equally to their own (y = l ).16
For each of the experiments, I calculate the
relative share of income received by the rich
and poor populations, as well as the change in
lifetime consumption for each group in a steady
state as the rate of inflation is increased to 4 per
cent from the benchmark case with zero infla
tion. The results in the second row of table 2 are
obtained from the benchmark model (with 4
percent inflation), the results in the third row
correspond to the progressive-transfer model,
and the results in the fourth row are obtained
from the revenue-neutral model.
Table 2 conveys the central message of this
paper: The distribution of income, as measured
by relative shares of personal income (total out
put less government purchases), is virtually
This paper is a cautionary tale for the “soft
hearted”: Attempts to alleviate the burden of
unemployment on the less well-to-do through
expansionary monetary policy may hurt the clien
tele it is supposed to serve if, ultimately, the policy
leads to higher long-run rates of inflation. This study
is not, however, a criticism of fine-tuning attempts
per se. Current Fed policy may or may not fall vic
tim to the “too much, too late” syndrome (that is,
too rapid an expansion of the money supply at too
late a stage in the slowdown to prevent upward
pressure on the price level once the recovery begins
in earnest). But if policy mistakes do occur, shortrnn monetary medicine could further harm those
who are most affected by recession, slow growth,
and diminished income levels.
Fortunately, the presumed trade-off between a
monetary policy that responds to short-run eco
nomic circumstances and one that maintains price
stability in the long run is a false exchange. By set
ting long-run price-level targets collateralized with
credible and clearly articulated enforcement mech
anisms, the Fed would be free to pursue stabiliza
tion efforts aggressively without destabilizing
inflation expectations or ultimately risking higher-
■
■
16 Although the results are sensitive to the choice of e, this
value accords fairly well with evidence concerning the actual distribu
tion of income. The poor segment of the model population receives a
higher share of total personal income than the rich, but the poor repre
sent three-quarters of the population. The rich, who make up only one quarter of the population, receive almost 44 percent of personal income.
http://fraser.stlouisfed.org/
See footnote 13.
Federal Reserve Bank of St. Louis
17 A 2.6 percent reduction may not seem like much, especially
when stacked against the potential costs of unemployment. But 2.6 per
cent of lifetime consumption may be larger than you think. With a sus
tainable real consumption level of $20,000 per year, a 55-year planning
horizon, and a 5 percent real rate of return, a loss of this magnitude
would be equivalent to a current lump-sum tax on the order of $10,000,
or half a year’s consumption.
21
than-desired inflation paths that are difficult to
reverse after the fact.
Creating such a policy environment is, of
course, easier said than done, but certainly no
more difficult than determining an effective way
to exploit notoriously slippery Phillips curve
trade-offs. Furthermore, institutional rules that
advance price stability while maintaining flexi
bility over monetary policy choices in the short
run do exist. William Gavin, of the Federal
Reserve Bank of Cleveland, and Alan Stockman,
of the University of Rochester, have recently
presented such a proposal (see Gavin and
Stockman [1992]). This, and related work, de
serves the attention of anyone interested in the
long-run welfare of rich and poor alike.
where xNtT is all tax revenues net of capital in
come taxes paid by the rich, C p is the total con
sumption by the poor, and Z is the (exogenous)
aggregate labor supply. Note that C R is obtained
by first solving for consumption by the poor.
ProgressiveTransfer Model
For the poor:
f e t + p Z k (r+
„
,l
n)
2 ( 1 —e)
Appendix
~ T|
+ P <p r 2
Consumption
Solutions for
the Alternative
Fiscal Regimes
„
p (r+7i)
r\
(oCj + oc2) [1 - ( 1 +
an exogenous lump-sum tax payment of the
poor when young, and x2 is an exogenous
lump-sum tax payment of the poor when old.
Consumption by the rich is
k0 -
(1 - e) C p - G]
e (l+ y )
RevenueNeutral Model
n ) p] w
For the poor:
<ptt + P)
1+
where (p = l + r ( l - p ) - p 7 t .
The consumption solution for the rich is
f ( 1 - (p) [ Z
k
8 - (1 - e )
Cp]
^ l e ( 1 + y ) [ 1 - c p - p ( r + ju) ]
e p (p ( a ] + q 2) ( p + 7i)
p (r+7i)
= ( l + r) ---- --- , r 2= l + ------ , X j is
c, =
In the benchmark model, government expendi
tures are endogenous. The poor’s first-period
consumption is
,
2(1 -e)
r , + p <pr 2
where
y [Z
Benchmark Model
cn =■
r £T + p Z K ( r + 7 t )
^
This appendix presents steady-state consump
tion solutions for the rich and poor when young
(that is, for q ^ a n d q * ). Solutions for old-age
consumption are given by these expressions and
equation (11). Asset levels are then given by
equations (4) and (5). Superscripts indicating
rich and poor are suppressed except where
absolutely necessary.
q
w
(fj a , + a 7 T ,)
c, =
- xNHT
£ ( l + y ) [ l — cp — p ( r + 7 t ) ]
.
1 +P
a.
(« ii + T—
\+ -r ) w ~ (h1 + 71 T
+ "r )
Given the consumption solutions for the poor,
the consumption solutions for the rich have the
same form as in the progressive-transfer model.
References
Altig, David, and Charles T. Carlstrom. “Inflation,
Personal Taxes, and Real Output: A Dynamic
A n a ly s is Jo u rn a l o f Money, Credit, a n d
Banking, vol. 23, no. 3, part 2 (August
1991a), pp. 547-71.
______ , a n d _______ . “Bracket Creep in the Age
of Indexing: Have We Solved the Problem?”
Federal Reserve Bank of Cleveland, unpub
lished manuscript, 1991b.
Altig, David, and Steve J. Davis. “The Timing of
Intergenerational Transfers, Tax Policy, and
Aggregate Savings,” Am erican Economic
Review, forthcoming, 1992.
Barro, Robert J. “New Classicals and Keynesians,
or the Good Guys and the Bad Guys,” Na
tional Bureau of Economic Research,
Working Paper No. 2982, May 1989Blinder, Alan S. H ard Heads, Soft Hearts: ToughM inded Economicsfo r a Just Society. Reading,
Mass.: Addison-Wesley Publishing Co., 1987.
Buse, Adolf. “The Cyclical Behaviour of the Size
Distribution of Income in Canada: 1947-78,”
C anadian Jo u rn a l o f Economics, vol. 15,
no. 2 (May 1982), pp. 189-204.
Carlstrom, Charles T., and William T. Gavin. “Zero
Inflation: Transition Costs and Shoe-Leather
Benefits,” Federal Reserve Bank of Cleveland,
Working Paper 9113, October 1991.
Cooley, Thomas F., and Gary D. Hansen. “The
Inflation Tax in a Real Business Cycle Model,”
Am erican Economic Review, vol. 79, no. 4
(September 1989), pp. 733-48.
______ , a n d _______ . “The Welfare Costs of
Moderate Inflations,” Jo u rn a l o f Money,
Credit, a n d Banking, vol. 23, no. 3, part 2
(August 1991), pp. 483-503.
Cutler, David M., and Lawrence F. Katz. “Macroeconomic Performance and the Disadvan
taged,” Harvard University, unpublished
manuscript, September 1991.
Gavin, William T., and Alan C. Stockman. “A
Price Objective for Monetary Policy,” Federal
Reserve Bank of Cleveland, Economic Com
mentary, April 1, 1992.
Gomme, Paul. “Money and Growth Revisited,”
University of Western Ontario, unpublished
manuscript, November 1991.
Levin, Ross, and David Renalt. “A Sensitivity
Analysis of Cross-Country Growth Regres
sions,” World Bank, unpublished manuscript,
March 1991.
Lucas, Robert E., Jr. Models o f Business Cycles.
New York: Basil Blackwell, 1987.
Mankiw, N. Gregory, and David Romer, eds.
New Keynesian Economics, vols. 1 and 2.
Cambridge, Mass.: MIT Press, 1991.
______ , _______ , and David N. Weil. “A Contri
bution to the Empires of Economic Growth,”
Harvard University, unpublished manuscript,
September 1990.
Mankiw, N. Gregory, and Stephen P. Zeldes.
“The Consumption of Stockholders and Non
stockholders, vJo u rn a l o f F in an cial Econom
ics, vol. 29, no. 1 (March 1991), pp. 97-112.
Sala-i-Martin, Xavier. “Lecture Notes on Econom
ic Growth (I): Introduction to the Literature
and Neoclassical Models,” National Bureau
of Economic Research, Working Paper No.
3563, December 1990a.
______ . “Lecture Notes on Economic Growth
(II): Five Prototype Models of Endogenous
Growth,” National Bureau of Economic Re
search, Working Paper No. 3564, December
1990b.
23
Sluggish Deposit Rates:
Endogenous Institutions
and Aggregate Fluctuations
by Joseph G. Haubrich
Introduction
The interest rates that banks pay on deposits
move more slowly than money-market interest
rates, a phenomenon documented in several
recent studies (Flannery [1982], Hannan and
Berger [1991], and Neumark and Sharpe [1992]).
Understanding deposit-rate sluggishness has im
portant direct consequences for comprehending
money demand and bank profitability, as well as
indirect consequences for understanding almost
all industrial pricing.
However, even when this recent work takes an
explicitly microeconomic approach, it does not
consider market conditions that lead to the exis
tence of banks. It may therefore distort the lessons
of sluggishness both for macroeconomics and for
industrial structure. This paper approaches the
Issue in terms of the microfoundations of banking.
Although this theory may not be all-inclusive and
may work in combination with other effects,
ignoring it may mean that previous explanations
of interest-rate sluggishness are misleading and
that attempts to draw parallels with other indus
tries regarding price rigidities could be biased.
The sluggish adjustment of bank interest rates
relative to prevailing market rates, as shown in
http://fraser.stlouisfed.org/
figures
1 and 2, has puzzled economists since at
Federal Reserve Bank
of St. Louis
Joseph G. Haubrich is an
economic advisor at the Federal
Reserve Bank of Cleveland. The
author thanks Peter Garber,
Robert King, Jeremy Siegel, and
James Thomson for helpful
criticism.
least the mid-nineteenth century. Figure 1 com
pares the savings bond deposit rate with the
commercial paper rate from 1840 to 1899. Figure
2 compares the same rate paid on savings bank
deposits with the interest rate charged on call
money from 1857 to 1899- In both cases, the
bank rate shows substantially less movement
than the market rate.1 In fact, bank interest rates
appear to be even more rigid than predicted by
this paper. The stability of nominal rates, even
in the face of the inflation of the 1850s and the
deflation preceding resumption of the gold
standard in 1879, suggests that for some reason,
interest rates did not index to the inflation rate
or to the money supply.
Many of the price and nonprice constraints
producing macroeconomic behavior originate
not from an auction market, but from an organi
zation. Banks, labor contracts, and corporations
set interest rates, wages, and prices. I contend
that such institutions arise to solve problems of
risk and private information— precisely those
problems associated with a recession, which
■
1 For evidence on twentieth-century inflexibility, as well as explana
tions based on exogenously motivated banks, see Flannery (1982), Klein
(1972), Weber (1966), and the references cited therein.
24
F I G U R E
1
Regular Deposit Rate and Commercial
Paper Rate, Yearly Averages
Percent
io
14 12 -
I
10 -
Commercial
A paper rate
I
8 -A
6-
f
\
1
/ -- \
\ / \ J
420
1840
/
Savings bank
deposit rate
1845
1850
1855
1860
1865
1870
1875
1880
1885
1890
1895
1900
1855
I860
1865
1870
1875
1880
1885
1890
1895
1900
SOURCE: Homer (1977).
F I G U R E
2
Regular Deposit Rate and Call
Money Rate, Yearly Averages
Percent
16
14
12
10
8
6
4
2
0
1840
1845
1850
a. Data were unavailable prior to 1857.
SOURCE: Homer (1977).
changes the uncertainty that is the very basis of the
institution. Thus, the equilibrium prices faced by
agents adjust in a way that no market could mimic.
Individual agents respond to a macroeconomic
shock only after it has been filtered through an
organization. Derivative markets then react and
alter individuals’ response to disturbances.
This paper builds on the recent informationbased banking models of Diamond and Dybvig
(1983), Smith (1984), and Haubrich and King
(1990). As in those papers, banks in this model
arise endogenously in response to a demand for
insurance against private risk. Banks are the
optimal contract arising from uncertainty. The
macroeconomic approach leads to some modi
fications, however. These changes should pro
vide a picture of banks that can be more easily
and realistically integrated with aggregate fluc
tuations. Diamond and Dybvig introduce a basic
insurance-theoretic banking model in which the
bank insures individuals facing a privately
observable preference risk: Some individuals die
25
early and therefore need to consume early. Be
cause it is costly to remove goods from storage
early, such individuals face a liquidity problem.
A deposit bank, by setting proper interest rates,
can pool the risk between those who die and
those who survive.
The present paper makes several changes in
that basic structure. First, the uncertainty generat
ing the bank is somewhat different. The privately
observed shock alters endowments, not prefer
ences, which seems to capture more realistically
what actually constrains agents' liquidity. It also
seems more plausible that these endowment
shocks are correlated with aggregate disturbances.
Also, the shock is a continuous random variable.
The continuum, in combination with the endow
ment risk, allows use of the optimal taxation litera
ture deriving from Mirrlees (1971) to provide a
clearer picture of the insurance role of banks. This
in turn sets the stage for the second and main
innovation of the paper: the interaction between
the aggregate shock and individual uncertainty.
This interaction takes a particular fonn. In
creases in the underlying productivity of the
economy, leading to higher market interest
rates, induce greater individual uncertainty. This
assumption has previously been presented in
various forms, but it is by no means obviously
true. Analysis along these lines produced the
neo-Keynesian concept of autonomous invest
ment, which is investment driven not by de
mand or savings, but by technological advances
and the introduction of new products. It plays a
prominent role in the business cycle theories of
such diverse authors as Robertson (1915) and
Hicks (1950), and also shares the property that
low values imply a small, uniform advance
while high levels mean a divergence of growth
across industries and firms.3 The assumption
also suggests the effects of aggregate disturbances,
such as business cycles, on the distribution of in
come. For example, Dooley and Gottschalk (1984)
■ 2 In Diamond and Dybvig (1983), insurance against private preference
shocks is complete due to restrictions on preferences. Haubrich and King
(1990) analyze a richer environment, in which insurance against privately
observable income shocks is desirable. But in the Haubrich—King setup, in
surance is incomplete because there is a trade-off between insurance and
intertemporal efficiency. Both papers concentrate on the form of the banking
contract, not on its interaction with macroeconomic shocks.
■ 3 For applied work justifying the stylized fact of a positive relation
between the level of autonomous investment and its dispersion, see the
historical section of Schumpeter (1939) or Safarian (1959, chapter 6).
For a different view, see Sheffrin (1984).
http://fraser.stlouisfed.org/
Federal Reserve Bank of St. Louis
find the variance of weekly earnings to be nega
tively correlated with the unemployment rate.4
Some macroeconomic work based on con
tract theory' makes similar assumptions. Gross
man, Hart, and Maskin (1983) consider shocks
that increase the dispersion of the value of mar
ginal product. Haubrich and King (1991) posit a
link between the size and dispersion of mone
tary shocks as an incentive for sticky nominal
price contracts.
This paper differs in the sense that it intro
duces endogenously arising financial institutions
as a response to the uncertainty and traces the
consequences of those institutions. In section I,
the economic environment is specified and the
standard representative-agent solution is dis
cussed. The forces motivating the endogenous
formation of banks are then presented in sec
tion II, under the assumption that there are no
aggregate shocks. With that analysis in hand,
the mutual interaction of banks, private risks,
and aggregate shocks is explored in section III.
A final section summarizes and concludes.
I. The Economic
Environment
This investigation begins by specifying a hypo
thetical stochastic economy with three basic ele
ments central to the problem at hand. First,
agents face an intertemporal decision problem
concerning the correct amounts of storage and
consumption. Second, the aggregate opportuni
ties vary in a stochastic fashion; that is, there
exist shocks common across all individuals. Third,
agents face idiosyncratic, privately observable
risks concerning their income (endowment). This
paper examines the simplest hypothetical econ
omy that incorporates these features. The econ
omy lasts for three periods, T= 0,1,2. The two
consumption periods allow intertemporal choice,
and the stochastic intertemporal terms of trade pro
vide the aggregate disturbance. There is also uncer
tainty due to environmental randomness in T= 1,
which is private information.
■ 4 The data show a positive correlation between unemployment and
variance of annual earnings, however. More generally, income disper
sion across agents appears to be positively associated with growth (see
Danziger and Gottschalk [1986]). Robinson (1972) also emphasizes the
macroeconomic consequences of the increased dispersion of incomes
resulting from growth and technological progress.
26
T A B L E 1
! Intertemporal
Technology
The Storage Technology
for Three Periods
T= 0
Return
-1
T= 1
T= 2
1
0
0
R
SOURCE: Author.
Tastes
Agents are identical, with the following constant
elasticity of substitution (CES) utility function:
(1)
U — G (u ) ,
where u (cp c2) = (c1 1~'/o + (3c2 1~>/a) 07(G_
and G (u ) = 1/(1 - y) w1_Y.
Three important parameters specify prefer
ences: (3, the discount factor; o, the intertemporal
elasticity of substitution; and y , the rate of relative
risk aversion toward variation in lifetime wealth.
In the economies studied below, agents face un
certainty about lifetime wealth, so that we can
meaningfully separate attitudes about risk aversion
from those concerning the time pattern of con
sumption. Once individuals enter period 1, they
face neither uncertain income nor risky assets.
Thus, agents formulate consumption plans contin
gent on the level of lifetime wealth. Lifetime utility,
but not the consumption strategy, depends on the
risk-aversion parameter y .
Endowments
Each individual has an endowment of a single
good in each period. At periods 0 and 2, all
agents have identical endowments
and y2 . At
period 1, each individual receives a privately ob
servable income level ^(0 ) =
+ 0, where y 1
is the level of per capita income. Consumers
know yx at T= 0, and they leam 0 at T = 1. The
idiosyncratic component of income, 0, is con
tinuously distributed on (0, 0) with density
function / ( 0 , x) having E (0) = 0 and E (0 |x) =
0 (x is an aggregate shock discussed later). I
assume a continuum of traders indexed at
period 1 by the realized value of 0. Thus, the
analysis proceeds as if each value of the distri
bution is realized (see Judd [1985]).
Along with preferences and endowments, the
actors in the model have a storage technology,
that is, an intertemporal production function
that rewards long-term storage. Goods stored in
T- 0 pay no net interest if removed in period 1,
but pay a gross return R > 1 if left until T= 2, as
shown in table 1.
This provides a tractable case in which the time
paths of investment projects are somewhat irre
versible. An alternative motivation Ls that individ
uals (banks) cannot costlessly liquidate assets
before their maturity. Economywide movements
are captured by introducing randomness into the
intertemporal technology.
R, the technological rate of return, varies
positively with the aggregate shock x. Individ
uals observe x costlessly and perfectly at T= 0,
so that they know R(x) from the beginning. Fur
thermore, the distribution of 0 depends on the
aggregate shock. A higher value of x induces a
mean-preserving spread on the distribution of
0 ,/ (0 ), subjecting agents to more risk. This
assumption is designed to capture the view that
progress benefits some individuals more than
others. Schumpeter (1939) assigns this view a
major role:
Industrial change is never harmonious advance
with all elements o f the system actually moving, or
tending to move, in step. At any given time, some
industries move on, others stay behind; and the dis
crepancies arising from this are an essential element
in the situations that develop, (pp. 101-102)
Thus, I separate the effects of an aggregate
shock into two components. One is an increase in
the productivity of long-term storage, whereby a
positive x increases R. The other is an increase in
the dispersion of the random variable 0. Follow
ing Rothschild and Stiglitz (1970), I let the shift put
more weight in the tails of the distribution. ’ These
effects cause /(0 , x) to become riskier (in the
sense of a mean-preserving spread) with increases
in x and cause R (x) to increase in x. That is, the
shock raises market (or technological) interest
rates. Conversely, a negative shock decreases R
and reduces the dispersion of 0.
This connection between a macroeconomic
variable (R ) and a microeconomic variable (the
■
5 As the authors point out, this sort of mean-preserving spread
corresponds to natural economic measures of increasing dispersion. Any
risk-averse individual w ill prefer the old distribution, and the new dis
tribution w ill equal the old distribution plus a noise term.
27
T A B L E
2
Observation of Shocks
for Three Periods
T =
T =
O
x realized
1
0 realized
T = 2
R Cr) paid off
/ ( 0, x) known
agents' diversifiable risk by exploiting the pro
duction structure of the economy. This section
abstracts from aggregate shocks in order to
examine the nature of the emergent institutions
more clearly.
Demand for
Insurance
SOURCE: Author.
individual’s endowment risk) is critical in study
ing the behavior of optimal bank contracts in
this economy. Because individuals can observe
jc at 7’= 0, knowledge of R (x) a n d / ( 0 , x) sim
plifies the analysis by reducing the problem to
comparative statics on the distribution of 0. Addi
tionally, this specification abstracts from the uncer
tainty about aggregate shocks and instead empha
sizes their distributional consequences. I thus con
centrate on the direct effects of the aggregate
shocks, not on uncertainty about them. To recapit
ulate, then, agents observe x, and thus /(0 , x) in
period 0, and 0 obtains in period 1 (see table 2).
As a benchmark for comparison with later
results, consider the macroeconomic effects of
an aggregate shock in this economy without
contracts. The individual uncertainty about the
distribution of income has no effect on aggre
gate variables, so it makes sense to examine
only the average individual. The increased dis
persion caused by the impulse has no effect on
aggregate variables: The per capita change in con
sumption and savings is the same as if the distribu
tion of income had been entirely ignored.
The simplicity of this macro model underscores
a point generic to models of this class; namely, this
simple economy can be understood in an aggre
gate sense by ignoring individual differences and
by focusing on the average agent.
II. Economic
Institutions and the
Exchange of Risk
When facing diversifiable risk, however, agents
in this economy will not accept the market struc
ture imposed above. The ability to write con
tracts at T= 0 means that they can improve upon
their initial position by creating a richer institu
tional structure. In the simple world considered
here, banks arise endogenously to meet that
demand for insurance. The bank is able to pool
Whether the market system produces a bank, an
insurance company, or a security market depends
on the information structure of the economy. If 0
were public information, a regular insurance con
tract with premiums and payoffs could protect
people against the diversifiable income risk. The
private character of 0 gives rise to adverse selec
tion, however, and mles out such insurance. Still,
since I assume that individuals may write con
tracts on any observable quantity, there may be
some other way to trade risk.
In one case, individuals might exchange claims
on long-term storage maturing in T= 2 after re
ceiving their random income. Unfortunately, this
ex post security market provides no improvement
over autarky. In equilibrium, arbitrage opportuni
ties between production and securities imply that
the price of such securities must be one. If a claim
on one unit in storage (R tomorrow) sold for
more than one, no one would buy it, preferring
instead to place one unit in productive storage. If
the price were below one, no one would sell (see
Diamond and Dybvig [1983] for a more detailed
discussion of this point). Selling these bonds is
thus equivalent to taking goods out of production.
As we have seen, the ability to draw down storage
stocks does not eliminate the possibility of low
first-period income.6 There is still room for an
institution that can provide insurance and pool risk
even if private income shocks are unobservable.
The Organization
of Banking
I define a bank as a coalition of individuals, per
haps brought together by an entrepreneur, that
receives a deposit <5 in T= 0 and pays interest
rates r0 from T= 0 to T= 1, and r, from T= 1 to
T= 2. Agents can withdraw any fraction of the
account in any period. A bank is linear if the
■
6 I assume that <t> is sufficiently large relative to y 1 and y 2 so that
market equilibrium takes place “off the corner" at the aggregate level.
That is, individuals w ill want to store some of 0>. Also, O is not so large
relative to lifetime wealth that agents wish to deposit in T=1.
28
interest rate paid is independent of the amount
in the account. A bank provides agents with a
higher level of expected utility than a situation
of autarky because the bank partially insures
agents against income risk. The provision of in
surance is typically incomplete, because the
bank faces a trade-off between risk-pooling and
the incentives for saving.
Relative to the technological return (or, equiv
alently, to ex post security markets), banks offer
higher short-term yields (rQ> 1) and lower long
term yields (r{ < R). This is how banks provide
insurance. To determine the interest rates that
actually occur, take the analysis one step further
and consider the optimal linear bank.7 This
bank sets rQand rxto maximize the expected util
ity of agents given the total resources of the bank
and the decision rules of the individuals. The
analysis closely follows the optimal income taxa
tion investigations of Mirrlees (1971).
An individual must choose consumption and
savings withdrawal given the bank’s interest
rates r0 (from T= 0 to T= 1) and rx (from T = 1
to T= 2). If r0 > 1, the problem for a rational in
dividual begins in period 1:
(2)
dw *
dw *
dw *
--— > 0, -r— < 0, and - _ < 0 . Recall the
drQ
dr,
d0
assumption (footnote 6) that the initial endow
ment is large enough so that the withdrawal will
be positive for all 0.
The bank, as a coalition of individuals, wishes
to maximize the depositors’ expected utility
EG [u (0, r0 , rj)] subject to a resource con
straint. This constraint, written as equation (3),
states that the period 0 present value of assets,
, must equal the present value of the liabilities
both in period 1, Ew* (0, r0 , r2), and in period 2,
rx[r0 O - Ew* (0, r0 , ra)l .
(3)
O = E w *(Q , rQ, rj)
+ R~' { r} [r0O - Ew * (0, r0, rx) ] 1.
In other words, the bank must be able to cover
all withdrawals. Notice that the bank views total
withdrawals as certain. Thus, Ew* involves
simply “summing” across all depositors. In addi
tion to the resource constraint (3), the bank is
constrained by the individuals’ decision rules,
such as the withdrawal function, which is a
function of bank actions r0 and rxas well as 0.
max w(cj,c2)
Banking and
Insurance
subject to
(i) j / O ) + w =
(ii)
cv
y 2 + r ^ r ^ - iv )
=
c 2.
The solution to this problem provides four func
tions of the income shock and interest rates: an
indirect utility function, v (0, rQ, ra); two con
sumption functions, c* (0, r0, rx) and c* (0, r0, rx);
and an optimal withdrawal function w* (0, rQ, rx).
With a CES utility function, indirect utility is linear
in wealth, v= CL(r^) a (r0, r-,0). Since w* =
What are the characteristics of an optimal bank
ing structure? First, consider a small increase in
r0 from its initial position of one and a small
decrease in rx. The bank must respect its budget
constraint, that is,
(4)
0 = drQ[ O - (1 / rx - 1 / R ) E(dc*2/d r Q) ]
- drx { ( y2-E c2)
+ (1 / rx - 1 / R ) E [dc2 / a (1 / rx) 11/r\ .
c*\~Ti(0), one can straightforwardly show that
When evaluated at r, = R, expression (4) be
comes simply drQO = drl(y 2 - E c * ) / r * . Since
■
7 Haubrich and King (1990) examine such a bank, but with an o nreversible storage technology. Consideration of linear institutions un
doubtedly simplifies the analysis, but more important, it prevents the
formation of depositor coalitions that could arbitrage across nonlinearities
in the rate structure. In other words, an interest-rate structure that is non
linear in the size of withdrawals would be subject to raiding by coalitions
of depositors at 7"= 1. For example, small depositors might combine
funds and act as a syndicate to obtain the better rates received by large
depositors. This would change the distribution (especially the expected
value) of withdrawals and ruin the bank. A budget just balanced, with
some individuals obtaining low interest rates, has no room for everyone
to receive high rates. A competitive bank simply could not give everyone a
http://fraser.stlouisfed.org/
higher interest rate.
Federal Reserve Bank of St. Louis
2> Vi ’ a smaH increase in r0 requires a
decrease in rv
The effects on expected utility can similarly
be calculated by differentiation.
(5)
d U = E ( G 'd v / d r 0 ) drQ
+ E ( G ' d v/d rx ) drx
= E ( G ' a ) O dr0
- E { G ' a [ y 2- c^(0)]} drx/ r x .
29
Expression (5) indicates that increases in r0 have
an identical wealth effect on all consumers, a is
the marginal utility of a unit of period 1 wealth.
As discussed above, a is invariant to 0 under
CES utility. By contrast, the wealth effect of an
increase in rx is greatest for the largest lenders
in period 1, for whom y2 < c* ( 0 ) . Requiring
feasibility of d r0 and d rxand rearranging the
resulting expression,
(6)
dU = a E[G'(c*2-Ec*2 )] drx / r\.
With risk aversion, G " > 0 , so that the covari
ance term is unambiguously negative and a
small decline in rx raises welfare. Intuitively, by
raising r0 and lowering rx, the bank has shifted
wealth from those with high 0 ’s to the average
individual. The lucky people with high 0 ’s will
attempt to smooth consumption and save the
windfall, withdrawing relatively little. The lower
rxpenalizes them. The unlucky people with a
low 0 withdraw a lot, benefiting from the high
r0. This redistribution provides insurance in T=
0, when 0 is unknown. In effect, in period 0, the
bank offers an individual a security that 1) has a
certain period 1 expected return (Oi/r0), 2) pays
negative returns when high 0’s occur, and 3)
reduces individual risks.
The Optimal
Linear Bank
The economic intuition behind these results
(small changes in r0 and rxfrom the initial posi
tion r0 = 1 and rx = R) extends to interpretation
of the optimal banking structure. Again, follow
ing Mirrlees (1971) and Atkinson and Stiglitz
(1980), I derive the result that for the CES case,
the optimal level of rxsatisfies the following
condition:
3c(7)
dc*
r1 = S ( E 2 + 82 ~ ) / ( e 2 + 82- j j + /?82 )
3a
dc*,
- R - z ( e 2 , 52 , da ),
where e2 is the compensated semi-elasticity of
second-period consumption with respect to its
price, p 2 = — . e2 is a constant because utility is
C E S , e2 = ( 1 / c*), and
> 0.
ap2
dp2
is the effect
of a wealth increment on second-period consump
tion, and 82 is the risk premium of a private agent
for a consumption bet of the form c2 / Ec\ . Such
a bet has expected utility of one but covaries
negatively with lifetime marginal utility:
§2 = - { cov [<?', c2 (0) 1 /E G ' Ec2 }.
Notice that risk aversion implies r, < R and
thus r0 > 1, both of which preserve the flavor
of the local results above.
Banks and
Other Structures
It is worth comparing this bank with the other
institutions already discussed. In autarky, each
individual agent is subject to income risk. Be
cause the technology is reversible, no one bene
fits from being able to sell shares in an ex post
security market, that is, by transferring goods
from T= 2 to r = 1. A simple ex post equity
market, then, does not improve upon autarky,
because it cannot remove any of the income
risk faced by agents.
However, the optimal linear banking structure
provides agents with a higher level of expected
utility than an ex post market does, because it par
tially insures agents against income risks. The
provision of such insurance is incomplete because
the bank pays for insurance by distorting the inter
temporal trade-ofif facing consumers. Relative to
ex post security markets, banks offer higher short
term yields (r0 > 1) and lower long-term yields
(rx< R). Without income uncertainty, or with full
insurance from another source, the optimal bank
would set r0 = 1 and rx= R, and would serve no
economic purpose.
Notice this classic relation between the bank
and asset markets: The bank creates long-term
assets from short-term liabilities. Though agents
may withdraw money from their account at any
time, the bank balances these withdrawals and
invests partly in long-term production. A nonclassical restriction is the requirement of a choice
of institution. As in other models of this sort
(Diamond and Dybvig [19831, Haubrich and
King [1990], andjacklin and Bhattacharya [1988]),
a bank and an equity market cannot coexist.
A more detailed analysis of these questions
would proceed by initially characterizing Paretooptimal allocations— subject to resource and
incentive constraints— and then asking whether
particular market arrangements can effectively
decentralize these allocations or yield Paretooptimal quantities as the outcomes of individual
choices in a specified market. Because this paper
concentrates on the effects of aggregate shocks,
and not on the banking contract per se, it will
not formalize the mechanism-theoretic approach
to this problem. Additionally, a digression here
30
could not do justice to the many interesting
issues that arise, and would be redundant in
light of the fuller treatment of the banking con
tract found in Haubrich (1988) and Haubrich
and King (1990). Still, an informal discussion
summarizing results from the other papers can
clarify several related issues.
A key question is which institutions can sup
port the optimal allocations arising from the
planning problem. A bank contract supports
such allocations, as do some other institutions.
The main difference concerns the possibility of
bank runs. Adding a sequential service con
straint, as in Diamond and Dybvig (1983), will
create panics. However, banks without this fea
ture (and indeed mutual funds issuing derivative
securities) can support the optimal allocations
and remain immune to panics. I consider only
such stable institutions.
An equity market does not support the opti
mal allocation. Once a bank exists, there are
individual incentives to create a stock market.
This would ruin the bank, however, so the plan
ner does not allow that market to open. This
exclusivity seems to be a generic defect of this
type of banking model. Haubrich (1988) exam
ines the informational assumptions allowing
such exclusion. Jacklin and Bhattacharya (1988)
interpret banking regulation as a means of pre
venting the arbitrage that would destroy banks.
Gorton and Haubrich (1987) explore coexis
tence using a somewhat different model.
Finally, support for the full optimum men
tioned above requires a nonlinear bank— one
that pays contingent on withdrawal size. The
general form of the contract remains the same,
and the same techniques can be used to charac
terize the interest-rate schedule, but comparative
statics become intractable. The linear bank
results from the arbitrage conditions discussed
above, which in the planning problem take the
form of "multilateral incentive compatibility con
straints” (see Haubrich [1988]). The nonlineari
ties that exist in the real world may result from
the inability to arbitrage the bank— perhaps due
to transactions costs or to the inability of group
members to monitor one another. Still, the linear
bank seems a useful approximation.
III. Banking with
Aggregate Shocks
This section reintroduces fluctuations into the
economy by integrating the banking sector into
the basic macro model. It explores how the
aggregate random variable x influences bank
interest rates and in turn affects savings and con
sumption. This section illustrates the importance
of contracts in economies with connections
between a macroeconomic variable, R, and a
microeconomic variable, individuals’ endow
ment risk. Recall that a positive x increases R
and induces a mean-preserving spread in /(0 ),
while a negative draw lowers R and reduces
the dispersion of 0. In the presence of banks,
this interaction has important consequences.
Individuals can observe x in T= 0, so that
knowledge of R(x) a n d /(0 , x) allows calcula
tion of the interest rates r0 and rx. This reduces
the problem to comparative statics on the dis
tribution of 0 and suggests that it is not uncer
tainty about aggregate shocks that drives banks’
effects on interest rates, but rather the distribu
tional consequences of such shocks.
It will be easier to examine these effects in
three steps. First, I examine how rx changes with
R if the distribution of 0 remains fixed. Next, I
keep R fixed and note how rx changes with the
dispersion of 0. Finally, I put the two together.
Pure Aggregate
Shocks
The case of an aggregate shock— with no effect
on the uncertainty of income— serves as a
benchmark for comparison with more compli
cated scenarios. With a “pure” aggregate shock,
if the underlying technological rate of return R
increases, the economy is richer and should be
able to support a higher interest rate on bank
deposits. This is indeed what happens, since
drx/ dR = z ( 5 2 , dc*2 /da, e2)
- r, 8 2(e2 + 8 2d c/d a + R 8 ) > 0 .
Thus, the direct or “pure” effect of an aggregate
shock moves both bank and market interest
rates in the same direction. The second term in
the equation is model specific: Because the
utility function exhibits constant relative risk
aversion, the increased income leads consumers
to demand less insurance for a given absolute
risk. This term would be absent with constant
absolute risk aversion. A short calculation re
veals that r0 rises with R\economically, because
of a higher payoff to storage, the bank can
afford to distribute more goods, and both bank
and market interest rates increase.
ta
Pure Distribution
Effects
The next determination is how banks’ interest rates
move when individuals are subject to greater
uncertainty. I wish to sign d z / d x ; that is, to hold
R fixed, but to allow x to change/(0). Equation
(7) tells us rx= z ( 8 2, dc2/ d a ,£ ,)/ ? .
Notice that the CES specification makes £2
constant, and the homotheticity of indifference
curves implies that dc2/d a is independent of
the distribution of 0. This means that the only
term changed by a mean-preserving shift in
/(0 ) is 82. Not surprisingly, the movement in the
interest rate depends on the movement of the
risk premium on period 2 consumption. Recall
that a greater risk premium indicates a greater
demand for insurance, which is provided
by a lower interest rate. Notice that 3 r, /0 5 , =
—£2R / (£ , + 8 2 + dc*2/d a ) 2 < 0. Thus, a meanpreserving spread will decrease rx if it increases
8^ Since 8, measures the risk premium on
c2/E c2 , we expect it to rise with a risker c2 ,
which in turn is a linear function of 0. Intuitively,
a positive shock, say a good harvest, will increase
the uncertainty of individual incomes. This drives
up 8 ,, the risk premium on the lifetime consump
tion gamble, and sends rx down. The bank pools
some of the increased risk by pushing rxand r()
closer together, hence further redistributing in
come from the lucky to the unlucky.
The clear intuition on the effects of a meanpreserving spread belies the complexity of the
actual calculation. The multiperiod, multiplechoice problem does not fit the one-variable
techniques of Rothschild and Stiglitz (1970,
1971). In a closely related problem, calculating
the change in the optimal linear income tax
with a change in the ability distribution, Stern
(1976) resorts to numerical examples even after
specifying both utility and distribution func
tions. With problems in such a simple case, it is
not surprising that more general specifications
prove intractable.
Calculating the change in 82 is straightforward
when G takes the form of log utility.8 This is
the only case for which an intertemporal inves
tor facing a changing investment opportunity
set will act as if he were a one-period maximizer
(Merton 11982]). With log utility, changes in the
interest rate alone do not alter consumption or
savings decisions, and the result is a one-period
problem on which standard comparative static
■
8 The dynamic asset pricing literature often exploits this tractability,
http://fraser.stlouisfed.org/
which stems from the offsetting income and substitution effects.
Federal Reserve Bank of St. Louis
techniques can be used. In this paper, because
interest rates differ across periods, individuals
face a changing investment opportunity set.
With that problem simplified, comparative statics
on the bank problem become feasible. The ap
pendix carries out the calculation for log utility and
examines the robustness of the result. A meanpreserving spread also increases the risk premium
in another tractable case, quadratic utility.
Another way to obtain results is to restrict the
distribution function. The appendix shows that
for arbitrary utility functions, a two-point dis
tribution yields the required result, as do certain
changes related to the martingale measure of
risk. Thus, although the general case seems in
tractable, a number of specific results support
the intuitive conclusion.
Micro and Macro
Shocks Together
The pure aggregate shock moves the underly
ing interest rate. The pure distribution effect, on
the other hand, increases individual uncertainty
and induces people to pool more risk by accept
ing a lower interest rate. The combination of
both effects means that a macroeconomic distur
bance will increase bank interest rates, but by
less than the underlying rate. In other words, the
aggregate shock x moves R directly, increasing
both rx and rQ. In fact, without changes in in
dividual uncertainty, an efficient bank would
raise rx proportionately with R. The distribution
effect by itself lowers rx when x rises. Both
effects together imply that rx moves by less than
R. Further, we expect that the direct effect dom
inates the distributional (indirect) effect, and
both rxand R increase (that is, bank rates move
less than one-to-one with the underlying inter
est rates). Similarly, a negative x decreases R,
and the distribution effect raises rx. Again, slug
gishness results. Since the two effects of x — an
increase in R and a greater dispersion of 0 —
are mathematically distinct, we must simply as
sume the dominance of the direct effect. This
assumption accords with the macroeconomic
evidence and theories mentioned in section I.
This distribution effect also influences r0. The
bank’s budget constraint, (3), implies that a
decrease in rx requires an increase in r0. When
the dispersion of 0 rises, the bank provides more
insurance by increasing r0 and decreasing rx.
This affects consumption and savings in two ways:
The higher r0 augments the wealth of all agents as
of T= 1, and the lower rx makes current con
sumption more attractive. These distributional
consequences counteract the intertemporal
effects of the pure gain in R, which induces
people to consume more later.
The effect on interest rates is an immediate
illustration of how contracts change the qualita
tive macroeconomic behavior of this economy.
As the intertemporal price, the interest rate has
additional effects. In general, comparing the
path of aggregate disturbances will be compli
cated, but in the case of log utility, simple results
emerge. The sluggish adjustment of interest
rates dampens the effect of aggregate shocks on
consumption and savings. Some lengthy but
straightforward calculations show that
(8)
(9)
dc*
dc*
0>—
zr ~ (bank) > -r-^- (no b a n k ), and
ox
dx
dc*
ox
(no bank) >
dc*
ox
(bank) > 0.
Thus, though idiosyncratic risk “washes out”
across all agents, it affects the economy because
agents form institutions and write contracts to
protect against that risk. Even if interest rates
adjust one-to-one, the deviation of the bank rate
from the technological rate alters behavior. More
significant, however, is that the bank filters the
effect of the shock by changing the underlying
risk. Hence, ignoring or simply exogenously im
posing institutions on a macro model seriously
distorts conclusions. Figures 1 and 2 give a
flavor of possible applications of this model and
show that there are useful and tractable exten
sions of the representative-agent framework.
IV. Conclusion
This paper illustrates how institutions play a cen
tral role in aggregate phenomena. In this section, I
argue that the results hold in a very general con
text and that the general study of institutions aris
ing from competition is essential for adequate
macroeconomics.
The analysis presented above extends beyond
bank rates. Other financial institutions play a part
in macroeconomic disturbances, and although
this paper argues in terms of risk-pooling, the
underlying ideas pertain to risk-shifting as well.
The institution studied here is termed a bank, but
as a pure financial intermediary, its functions may
be duplicated by an appropriate derivative secu
rity market.
For example, consider dividend payments.
When individuals face private risks, dividend
payments may set the return on equity to pro
vide insurance. An interaction between macroand microeconomic shocks leads to dividends
that adjust slowly (Copeland and Weston
[1979D.
In fact, the analysis is not limited to financial
institutions: Some recent work on labor con
tracts also discusses the role of aggregate shocks
as signals about unobservable individual distur
bances. Haubrich and King (1991) examine a
case in which the money supply signals individ
ual dispersion, leading to the non-neutrality of
perceived money. Grossman, Hart, and Maskin
(1983) focus on economies where asymmetric
information between firms and workers pro
duces cyclical unemployment.
These new markets and institutions attempt
to avoid the problems of adverse selection aris
ing from private information. In this sense, de
rivative security markets or institutions occupy
niches similar to other schemes discussed in the
literature. In order for the institution to survive,
the incentive structures must force agents to
reveal themselves at least partially. Markets can
not always completely exploit this information,
because to do so would distort the incentives
that allowed revelation in the first place.
This paper provides an equilibrium analysis
of how endogenously arising financial institu
tions alter the impact of macroeconomic shocks.
It explains the modifications in consumption
and investment decisions as reactions to prices
that react sluggishly to the underlying economic
disturbances. This suggests that income distribu
tion plays a major role in aggregate disturbances,
such as business cycles. It also suggests that a
relevant business cycle theory eventually must
explicitly model why banks exist and why they
take their present form. This explanation of
bank rate sluggishness illustrates a powerful
principle: When aggregate disturbances also
have distributional consequences, the pattern of
efficient contract-specified prices can change.
Appendix
In this appendix, I calculate the change in the
risk premium 5 , caused by an increase in indi
vidual uncertainty. First, recall that indirect util
ity and optimal second-period consumption are
(A l)
v= a ( r ) 1^(0) ] and
(A2)
c* = r[ 1 - h (p 2) ] [w(Q) ] = q (r) [*¿>(0) ] .
8? can be written as
(A3)
8 2 = - [E(v~v c2) - Ec2 Ev~y}/ E c2Ev~y
that in some cases (A4) is positive. Additionally,
(A4) is always positive with a discrete, symmet
ric, two-point distribution. To see this, write the
numerator of (A5) as
Ew~ yEw~ y0
+ y {Ew '~yEw~y- 'Q - E w ~ yEq~y§ ) .
The first term is always negative. I can use the
linearity of wealth to express w as (a ± k),
where the distribution is the two-point discrete
distribution with probability 1/2 on k. and -k.
The sign of (A5) is then the opposite of
= 1 - E{irlc2)/E c2Ev~'i.
(a - k )x~y {a + k )1~y(-4 a) , which is always
negative. Thus, the risk premium moves positively
Using (A l) and (A2), I rearrange (A3) to obtain
with x.
When G is quadratic, G (x ) = x - Vi bx2, the
(A4) 1 - 8 2 = E [w ($)l -y]/ E[w{$)} E[w{$)~y] . result also holds. Substitute into (A4) to obtain
(A 6)
To discuss how 5, changes with increases in the
dispersion of 0 ,1employ the techniques of
Sandmo (1970) and Rothschild and Stiglitz (1970,
1971) and stretch the distribution by replacing 0
with x 0 in order to sign d 8 , / d x . First, take the
derivative:
d 8 ?/d x =
- [Ew(xQ) Ew (xd)~ y(d/dx) Ew (x0 1~y)
- E w (x6) 1_Y Ew(xO) ■(d/dx) Ew (x6~ y)] /
(EwEu~y) 2.
Without loss of generality, I evaluate this expres
sion at x = 1.
(A5)
-{Ew (d)Ew (Q )-yE[( 1 -y) w(Q)~yQ]
- Ew (0) - -iEw(6) E[- y w (0)" y~ 10 ]} /
(EwEw-y)2.
Notice that the first and second terms of this ex
pression are positive, as are all the terms after
the minus sign (fourth, fifth, and sixth terms).
The third term is negative when y < 1, making
the entire derivative unambiguously positive.
Thus, an increase in x increases 5, and de
creases rv When y < 1, the sign of expression
(A4) becomes ambiguous. Without explicitly
determining its sign, though, we can gain some
idea of its properties. Simple numerical exam
ples involving uniform distributions indicate
1 - 8 2=
e
\i - b{ a[ a (a + 0)]} [q(a + 0) ]]
E[1 - b (a a + a 0)1 E[q(a + 0)]
With a mean-preserving spread on 0, only the
numerator of (A6) changes, becoming
E\q(1 + 0) ] - b a q E (a 2 + 2aQ) - baqE(Q 2) .
The MPS on 0 increases the variance, proving
the result.
For general utility functions, 1 - 81can be ex
pressed as a “martingale measure of risk” as in
Nachman (1979, section 4.1). Then, i f / is the dis
tribution for c2,
G’
G'
----- A c).
f* (c ) - — 7 ’ / =
EG
J G A c) dc
Defining E t (c) - \cf* (c) d c , Nachman extends
Rothschild and Stiglitz’s arguments to show
Ej (c) < E(c). The assumption on the movement
from f to g implies E*^(c) < E (c ). Similarly, if g
is riskier th a n /* , it is also risker than/ The
new expression for 1 - 8 , is £* (c) < E^ (c) <
E*/ (c) < Ef(c) . Again, the desired result follows.
Here, the function G is general, but a large shift
in dispersion is required.
E a
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