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Transparency in the Practice
of Monetary Policy
J. Alfred Broaddus, Jr.


his has been a very useful conference in my view, and I am honored by
this opportunity to be a part of it. As some of you may know, I was the
second choice for this slot, but that doesn’t bother me at all because the
first choice was Don Brash, the Governor of the Reserve Bank of New Zealand
and a pathbreaker in bringing both transparency and accountability to central
banking in practice. I won’t be able to fill Don’s shoes completely, but I have
a strong interest in this topic, and I am very happy that Bill and Dan saw fit to
give me the opportunity to share some thoughts with this distinguished group.
Actually, it is hard to imagine that anyone interested in improving the
conduct of monetary policy would not be interested in this topic. There is a
growing consensus among monetary economists at this point that the impact
of monetary policy on expenditure is transmitted primarily through the effects
of policy actions on expectations regarding the future path of short-term interest rates rather than the current level of the overnight rate.1 Further, the
more financial markets know about the reasons for a central bank’s current
policy actions and its longer-run policy intentions, the more likely it is that
market reactions to policy actions will reinforce these actions and increase
the effectiveness of stabilization policy. It follows that central banks should
be highly transparent regarding both their long-term policy objectives and the
shorter-term tactical actions they take with policy instruments.
Against this background, it seems to me that the Fed, along with other
central banks, has made considerable progress in increasing transparency in
This article is the text of an address given by J. Alfred Broaddus, Jr., president of the Federal
Reserve Bank of Richmond, before the 26th Annual Economic Policy Conference sponsored
by the Federal Reserve Bank of St. Louis, Missouri, on October 12, 2001. The author thanks
his colleague Marvin Goodfriend for his assistance in preparing these remarks. The views
expressed here are the author’s and not necessarily those of the Federal Reserve Bank of
Richmond or the Federal Reserve System.
1 See Woodford (2001, p. 17).

Federal Reserve Bank of Richmond Economic Quarterly Volume 87/3 Summer 2001



Federal Reserve Bank of Richmond Economic Quarterly

recent years. When I first joined the Fed back in 1970, to the extent that
anyone thought explicitly about transparency issues at all, the idea seemed
to be that limited transparency—or even no transparency—was best. Central
banks in industrial democracies were thought to work most effectively behind
the scenes, away from the glare of public scrutiny, at least in part because they
could then quietly take appropriate actions that might be politically unpopular,
or, more broadly, difficult to explain to a public not well versed in the intricacies
of finance.2 There was also a belief in some quarters that central banks could
enhance the effects of certain policy actions—most notably foreign exchange
market intervention operations—if they kept market participants uncertain
about their intentions.
Attitudes toward transparency appeared to change in the 1980s, partly reflecting progress made by economists in understanding the monetary policy
transmission mechanism, and probably partly because of public demand, particularly in the United States, for greater openness in government and public
policy generally. (As you may recall, the most widely read popular book
about the Fed and Fed policy in the 1980s was somewhat derisively titled
Secrets of the Temple.) Further, in the early 1980s, Chairman Volcker publicly took responsibility for reducing inflation from its then high level, and
subsequently took strong and temporarily painful actions to accomplish the
reduction. Some public explanation of the need for these steps was required,
and this need probably facilitated the transition to viewing transparency more
favorably. In any case, given the normal resistance to change in bureaucratic
organizations, I believe the Fed has made remarkable progress over the last
decade or so in opening up its conduct of monetary policy to market and public
Since the Fed is now quite open regarding many important aspects of its
policy strategy and operations, and in view of the strong performance of the
U.S. economy in recent years, at least up until the last several quarters, one
might reasonably ask whether still greater transparency is necessary or even
desirable in U.S. monetary policy. I think it is, and I will try to make this
case in the next few minutes. Let me comment briefly on four points: (1) the
transparency of our long-term inflation objective, (2) what I’m going to refer
to as the “intermediate-term transparency problem,” (3) the transparency of
our policy directive, including its “tilt,” and (4) the role of testimony, speeches,
and other public statements by Fed officials in providing transparency.

2 See Goodfriend (1986).

J. Alfred Broaddus, Jr.: Transparency and Monetary Policy


Probably the most important thing the public wishes to know and needs to
know with some precision about Fed monetary policy is our long-term objective for inflation. Longer-term inflation expectations are obviously critical
to households and businesses in committing to long-term investments, home
purchases, insurance contracts, and wage and benefit agreements. Conversely,
the Fed needs the public to understand and trust its long-term commitment to
low inflation to achieve maximum benefit from this long-term strategy.
How to convey this objective credibly to the markets and the public has
been a major focus of our policy research at the Richmond Fed for a long
time. For many years I’ve personally been convinced that controlling inflation
should be the Fed’s overriding objective, that this objective should be explicit,
and that it should be supported by a congressional mandate. At one level,
abstracting, for example, from political obstacles, this seems obvious. We
know that the Fed has the ability to determine the long-run inflation rate with
monetary policy, and theoretical analysis and all of our practical experience
suggest we should use that power in the public interest to maintain low and
stable inflation over time.
An explicit long-term inflation objective supported by a congressional
mandate would be a substantially beneficial step, in my view, even if it were
limited to a verbal statement along the lines of the language in the proposed
Neal Amendment to the Federal Reserve Act.3 Quantifying the objective in
terms of an explicit numerical rate (say, 2 percent per annum using the core
PCE inflation index) would make the objective even more transparent and
probably more effective.
Committing to an explicit inflation objective would achieve at least three
things. First, it would help anchor longer-term inflation expectations and
therefore facilitate the longer-term transactions I noted earlier. Second, it
would help prevent inflation scares in financial markets, which would allow
the Fed to act more aggressively in response to downside risks in the economy
with less concern that rising long-term interest rates might neutralize the effect
of the action.
Third, and most importantly, an explicit inflation objective would discipline the Fed to explain and justify short-run actions designed to stabilize output and employment against our commitment to protect the purchasing power
of the currency over the long run. An explicit objective would force such
explanations and justifications to be more sharply focused than in the current
regime without such an objective. Routine, clear explanations of short-term
actions would build confidence in the Fed’s commitment to price stability and
3 See Black (1990) and Greenspan (1990).


Federal Reserve Bank of Richmond Economic Quarterly

over time help reinforce credibility for low inflation. If the explanations were
made in testimony before Congress, supplemented perhaps by a written inflation report along the lines of the Bank of England model, Congress would be
positioned to enforce an accountability for monetary policy that arguably is
now weaker in the United States than in the United Kingdom and the European
Monetary Union.
One final point here: The Fed’s long-term commitment to price stability is
now largely embodied in our current Chairman’s demonstrated commitment
to this objective, rather than being institutionally grounded in an explicit objective. It is therefore inherently tenuous since its continuance will depend on
the preferences of future Chairmen and their susceptibility to political pressure
to pursue other goals.
For all these reasons, it seems clear to me that the increased transparency
that would be provided by an explicit long-term inflation objective would
increase the probability that we will attain our goal over time. Some argue
strongly for a dual objective that refers explicitly to output or employment as
well as inflation. But both theory and experience indicate that the Fed cannot
control real variables directly with monetary policy, and in my view there are
reasonable grounds to presume that the Fed will optimize its contribution to the
economy’s overall performance by maintaining credibility for low inflation.4
A unitary goal focused on low inflation would strengthen credibility by making
the Fed’s commitment to this objective definite and unambiguous.
It is one thing to advocate an explicit inflation objective; it is another to
actually put one in place. I doubt seriously that an explicit objective set and
announced unilaterally by the Fed would be credible. Any explicit inflation
objective would need to be accepted by the government as a whole through
legislation or some other formal agreement, as such objectives are in countries
that employ them. With its public standing high, the Fed seems well positioned
currently to make the case for such a mandate.



Even if the Fed obtains a price stability mandate, transparency issues are
still likely to arise in practice—specifically, when current inflation or nearterm inflation projections deviate from the long-term objective. For example,
inflation may rise above its objective at a time when real output is below
potential and unemployment is rising. It would be difficult or impossible in
this situation for the Fed to ignore the weakness in the real economy and act
aggressively to bring inflation quickly back to target.
4 See Goodfriend and King (2001).

J. Alfred Broaddus, Jr.: Transparency and Monetary Policy


Some have argued that precisely this possibility makes an explicit inflation
objective for the United States impractical. I don’t find this objection particularly compelling. Especially if the Fed has previously established credibility,
inflation may remain above its objective for some time without undue damage
to the Fed’s credibility if the Fed is transparent regarding its medium-term
strategy for bringing inflation back to path. Even with established credibility, explaining this strategy clearly and convincingly to market participants
and the general public would be challenging. Strategies and the accompanying explanations will have to be tailored to each case. In particular, the Fed
may anticipate bringing inflation back to the objective more quickly in some
cases than in others. Consequently, it may be useful for the Fed to announce
intermediate-term inflation forecasts to assist the public in making financial
and business decisions during the transition back to the long-term objective.
Beyond this, even if inflation is stable at or near its long-term objective,
unanticipated shocks may push employment and output growth temporarily
away from their sustainable noninflationary rates. Here, too, Fed transparency
about its intentions will help the public gauge how production, employment,
and interest rates will evolve in the medium term as the economy adjusts to the
shock. Transparency is in the Fed’s interest as well since it can help build confidence that, first, monetary policy can be effective in dealing with temporary
departures of real activity from its long-term potential, and, second, that the
Fed has the competence to exploit this capability. More generally, I believe
that the Fed’s expertise regarding the functioning of the U.S. economy—while
far from perfect—is now of high enough quality that transparency of our thinking about the economy’s medium-term prospects can build public confidence
and trust in periods of economic stress. To be sure, actual developments may
deviate from our announced expectations in particular situations, but trust can
be maintained if the Fed provides reasonable explanations for the deviations.

Having dealt with longer-term and intermediate-term issues, let me now make
a few comments about transparency as it relates to short-term policy tactics:
specifically, transparency regarding the current Federal funds rate target, the
“tilt” of the directive language, and the statement released to the press after
each Federal Open Market Committee (FOMC) meeting. It is in this area that
the greatest progress has been made in increasing transparency over the last
decade. The funds rate target set at a particular FOMC meeting, previously
released only after the next FOMC meeting, since February 1994 has been


Federal Reserve Bank of Richmond Economic Quarterly

announced shortly after adjournment of the meeting where it is set. So, markets
now know the current target. And the Committee has released the tilt (or
absence of a tilt) in the directive language along with the current funds rate
target since its meeting on May 18, 1999. Previously, it too had been released
only after the next FOMC meeting.
This increased instrument transparency, in my view, is all to the good. I
believe the immediate release of the tilt language is especially useful. Again,
the effect of monetary policy is transmitted to the economy not only through
the current level of the funds rate target but also through market expectations
about the future level of the target, which are reflected in the short-term yield
curve. Market participants are going to form these expectations in any event.
By announcing the tilt immediately, the FOMC shares its best current estimate
of the most likely direction of any near-term change in the funds rate target,
which should increase the efficiency with which markets form their expectations, help prepare markets and the public for changes in the target, and reduce
short-term disruptions caused by leaks. In particular, since markets know the
current tilt, they are better positioned to interpret the likely policy implications of incoming current economic data. For example, the release of strong
data after disclosure of an upside tilt in the directive language should increase
the probability that long-term rates will be bid upward in response. Consequently, immediate disclosure of the tilt should enable long-term interest rate
adjustments to perform their stabilizing role in the economy more effectively.
While, again, considerable progress has been made in increasing the transparency of the Fed’s short-term instrument settings, and its short-term expectations regarding at least the direction of future settings, there is room for
further progress in my view. In particular, there may be different views about
the extent to which a tilt in the directive in one direction or the other commits
or obliges the Fed to a future funds rate change. To the degree that markets
interpret a tilt as committing the Fed to future action, failure to take action
may surprise or “whipsaw” markets. It should be possible for the Fed to mitigate this problem by emphasizing publicly that a tilt only implies a greater
likelihood that any near-term change in the funds rate will be in a particular
direction and is not a commitment to any action. It might seem tempting to
consider eliminating the tilt in the formulation of short-term policy to remove
any confusion it may produce. But such a reduction in transparency would deprive the FOMC of the benefits of announcing the tilt noted above. Moreover,
beyond these benefits, abandoning it would deprive the Committee of a useful way to keep in touch with the strength of its internal consensus regarding
policy at any point in time and of a valuable supplementary tool for reaching
agreement on a funds rate target when there is a significant divergence of views
regarding the appropriate level of the target.

J. Alfred Broaddus, Jr.: Transparency and Monetary Policy


Finally, it is important to recognize that the language of the press statement
announcing the funds rate target and any tilt after each meeting also influences
market expectations regarding future policy actions. This language is widely
reported and interpreted currently in media coverage of FOMC meetings. In
essence, the language in the statement, like the tilt language in the directive, is
viewed by market participants as an additional short-term policy instrument.

The role of the Fed’s explicit policy announcements in shaping market expectations of future policy actions is obviously important, but as anyone even
slightly interested in Fed policy is well aware, public statements by individual
FOMC members (including Reserve Bank presidents who are not currently
voting Committee members) are at times especially important. This is particularly so in today’s environment where media coverage of these utterances
by cable television financial news channels, instant e-mail transmission of
market analysis, and the like are much more extensive than even just a few
years ago. Obviously, the Fed Chairman’s remarks in congressional testimony
(including answers to questions as well as prepared testimony), his speeches,
and his interviews are followed more intensely than the comments of other
FOMC participants since the Chairman is clearly the most influential Committee member and only he speaks for the Committee as a whole. At times,
however, comments of other participants can affect market expectations, at
least in the short run, if, for example, a comment is the Fed’s first public reaction to a new economic report (particularly if the content of the report was
unanticipated by markets), or the comment comes at a time when markets
are especially uncertain about near-term policy prospects. Consequently, we
also receive our share of media attention. Bill Poole, I, and, I expect, all of
our colleagues at other Reserve Banks can tell stories about being covered
by several reporters even when making speeches in fairly remote parts of our
respective districts.
Some argue that this form of Fed transparency may be counterproductive,
at least at times, if the views expressed in these comments seem inconsistent—
particularly if they appear to conflict with a recent FOMC decision or a public
statement by the Chairman. On occasion I have personally received criticism
and complaints from market professionals and others when they have found
my statements at variance with other Fed statements or confusing in some
other way, and I will acknowledge that on a few occasions my remarks may
have briefly complicated the formation of market expectations.
Over time, however, speeches and other public statements by individual
FOMC participants provide markets and the public with a more robust and
complete understanding of thinking inside the Fed about current economic


Federal Reserve Bank of Richmond Economic Quarterly

and financial conditions and near-term prospects than that provided by the
policy announcements I discussed a minute ago alone. Also, it is important to
recognize that market analysts are adept at filtering and appropriately weighting press reports of individual FOMC participant remarks in the context of
the broad range of Fed public statements from all sources. In short, I believe
a convincing case can be made that the public remarks of individual Reserve
Bank presidents and other FOMC participants increase the efficiency with
which markets form short-term policy expectations.
I would offer one other—admittedly speculative—note on this point. It is
obvious, again, that the Fed Chairman speaks with by far the most influential
voice among FOMC participants. It might appear superficially that comments
by other participants that seem to be “off message” might create confusion
about the Fed’s intentions and undermine the force of the Chairman’s statements. As I just suggested, there might be a little of this from time to time, but I
doubt these instances are of much significance. Again, markets are well aware
of the much greater weight of the Chairman’s statements and discount the remarks of other FOMC participants accordingly. Perhaps more importantly,
public commentary by other participants reinforces the Chairman’s credibility in the eyes of informed observers of Fed policy since it demonstrates that
the Chairman leads, builds consensus among, and speaks for a thoughtful,
competent group of policy professionals who naturally have diverse views on
specific policy choices. If the public believed the Chairman was conducting
policy unilaterally, he or she would be more vulnerable to an abrupt loss of
public confidence. This might not be a risk for the current Chairman, who
justifiably enjoys exceptionally high public respect, but it could be a problem
for a future Chairman.



Again, I have enjoyed participating in this panel discussion. This conference
has addressed what is clearly a crucial topic in understanding how monetary
policy affects the economy and how it might be improved. The subject deserves continued research. Thanks to this conference, I am confident it will
get it.

J. Alfred Broaddus, Jr.: Transparency and Monetary Policy


Black, Robert. “In Support of Price Stability,” Federal Reserve Bank of
Richmond Economic Review (January/February 1990), pp. 3–6,
Statement before the Subcommittee on Domestic Monetary Policy of the
U.S. House of Representatives Committee on Banking, Finance, and
Urban Affairs.
Goodfriend, Marvin. “Monetary Mystique: Secrecy and Central Banking,”
Journal of Monetary Economics (January 1986), pp. 63–92.
, and Robert King. “The Case for Price Stability,” in
European Central Bank, The First ECB Central Banking Conference,
Why Price Stability? 2001, pp. 53–94.
Greenspan, Alan. Statement before the U.S. Congress, House of
Representatives, Subcommittee on Banking, Finance, and Urban Affairs.
Zero Inflation. Hearing, 101 Cong. 1 Sess. Washington: Government
Printing Office, 1990.
Woodford, Michael. “Monetary Policy in an Information Economy,” Federal
Reserve Bank of Kansas City “Symposium on Economic Policy for the
Information Economy,” Jackson Hole, Wyoming, August 2001.

The Growth of Unsecured
Credit: Are We Better Off?
Kartik Athreya


he growth in unsecured credit over the past two decades has, because
of current bankruptcy law, reduced the average welfare of the poor.
This striking conclusion emerges from a model designed to maximize
the benefits of both plentiful unsecured credit and lax bankruptcy law. Even
exclusive concern for wealth redistribution does not provide self-evident justification for lax bankruptcy law in the face of the unprecedented expansion
in unsecured credit occurring over the past two decades. Specifically, according to the model, the welfare of low-income, low-asset households appears to
have fallen in response to the dramatic increase in the availability of unsecured
credit that has occurred since the Marquette Supreme Court ruling in 1978.
The driving forces behind this welfare decrease are, first, the role of lax personal bankruptcy law in thwarting debtors from credibly committing to repay
debts, second, the premium that the poor must pay to borrow on unsecured
credit markets, and third, the welfare loss from the imposition of deadweight
bankruptcy penalties. Before discussing the model in greater detail, I will turn
to a brief history of unsecured credit and personal bankruptcy in the United
The Supreme Court ruling in 1978 in the case of Marquette National
Bank of Minneapolis v. First of Omaha Service Corporation, 439 US 299
(1978) was a watershed. This ruling against Marquette National Bank allowed
a bank in nearby Nebraska, First of Omaha, to issue loans to residents of
Minnesota at rates higher than the ceiling in effect in Minnesota; the maximum
rate allowable in Nebraska was higher. Marquette argued that allowing First
of Omaha to export loans to Minnesota would undercut Minnesota’s usury
I thank Beth Anderson, Marvin Goodfriend, Tom Humphrey, John Walter, and John Weinberg
for very helpful comments and criticisms that have greatly improved this paper. I am particularly indebted to Jeff Lacker and Joseph Pomykala for their extremely thorough comments.
The opinions expressed in this article are those of the author and do not necessarily reflect
those of the Federal Reserve Bank of Richmond or the Federal Reserve System.

Federal Reserve Bank of Richmond Economic Quarterly Volume 87/3 Summer 2001



Federal Reserve Bank of Richmond Economic Quarterly

restrictions. The Supreme Court saw otherwise and ruled that First of Omaha
was within its rights to issue loans at rates exceeding Minnesota’s ceiling. This
ruling was critical to the growth of an organized unsecured credit industry in the
United States, as it suddenly made a relatively risky form of lending profitable.
Within two years, credit card lenders including Citibank and MBNA moved
to states with the highest interest rate ceilings, such as Delaware and South
Dakota, and began nationwide operations.
Since the 1978 ruling, low-income households in particular have seen
their access to uncollateralized credit grow dramatically, principally via credit
cards. The growth of this credit market enhanced the ability of U.S. households to deal with individual-specific and economywide risks by conveniently
allowing them to borrow more when times are bad. The credit card industry, in
particular, expanded enormously because lenders were given the opportunity
to offer uncollateralized loans and short-term credit to those with little tangible
wealth. This expansion of unsecured credit mainly affected borrowers with
low tangible wealth. Others could credibly commit to repaying loans via collateral, making usury laws a non-issue. Those who could not credibly commit
to repayment were most likely to be deemed unprofitable risks at interest rates
below the usury ceiling.
Personal bankruptcy law has a major impact on the ability of unsecured
borrowers to commit to repayment of loans. While intended to provide insurance against misfortune, these rules have the perverse effect of preventing
borrowers with little collateral from promising to repay a loan. Those who
hold collateral can and do avoid the constraints of bankruptcy protection and
face lower borrowing costs as a result. Those with collateralizable wealth also
obtain all the transactions benefits of credit cards without facing the annual
fees and relatively low credit limits typically imposed on low-income credit
card users. Therefore, the inability to commit to repayment even affects the
distribution of pure transactions cost benefits made possible by recent rapid
advances in payment card technology.1
The growth in unsecured credit has been accompanied by an unprecedented rise in personal bankruptcy, thereby making bankruptcy law relevant
to welfare. The level of recent filings, currently greater than 1 percent of all
U.S. households, has led to calls for more stringent law by some, but has been
defended by others. The proponents of strict bankruptcy law argue that plentiful unsecured credit and lax bankruptcy law give debtors an easy way out.2
Opponents argue that bankruptcy and easily available unsecured credit are like
insurance and are therefore part of a larger social safety net. Both arguments
1 Very recently, the advent of debit cards/check cards has helped high-risk borrowers obtain
transactions benefits without paying the fees intended to reveal their risk profile.
2 See, for example, the contrasting remarks of Senator Charles Grassley (R-Iowa) and Senator Paul Wellstone (D-Minn.) in congressional testimony on the Bankruptcy Reform Act of 2000.
The complete discussion is available at

K. Athreya: Unsecured Credit


contain some truth, and it is therefore certain that the welfare gains from the
increased availability of unsecured credit and additional implicit insurance
available through bankruptcy are tempered by a default premium.3
The question we must ask, then, is the following. What is the net benefit or
cost of the rapid expansion in unsecured lending that has taken place following
the Marquette ruling? This question, first posed over a decade ago in the
seminal and prescient work of Sullivan, Warren, and Westbrook (1989), has
since gone unanswered.
To the extent that bankruptcy provides additional all-purpose insurance
to American households, the rising rate of filings may simply represent a
wider group of borrowers cashing in an implicit insurance policy. This policy,
in turn, is priced appropriately by increased default premiums in loan rates.
From this perspective, the rising level of filings may not be anything to worry
about.4 Those arguing for tighter personal bankruptcy law must show that
the very option of easy bankruptcy retards the ability of households to tide
over fluctuations in their incomes by making borrowing excessively expensive,
or that easy bankruptcy lowers welfare by necessitating the frequent use of
socially costly “deadweight” penalties. In what follows, I demonstrate that
both of the preceding arguments can be made for U.S. households.
There has been no shortage of opinions on the impact of easy credit
and bankruptcy on the poor in recent times.5 Unfortunately, these views
are typically based on anecdotal evidence or static empirical approaches.
Such approaches typically cannot quantify the complex interactions between
the widespread availability of credit, the bankruptcy system, the behavior of
households trying to smooth temporary fluctuations in their income and employment, and the interest rates they pay to borrow. This article presents
a simple, unified analysis of how changes in unsecured credit interact with
bankruptcy law to affect consumer welfare. The framework provides a preliminary assessment of the net effects of the post-Marquette revolution in
unsecured credit and the attendant revolution in personal bankruptcy.
The expansion of credit to low-income households and bankruptcy protection is most often defended as helping to protect the poor against bad luck
and unscrupulous creditors. Therefore, this article stacks the deck in favor of
generating a positive role for expanded unsecured credit and lax bankruptcy.

3 By “default premium,” I am referring to the high interest rates paid by borrowers on the
unsecured market relative to those paid by secured borrowers, as with home equity loans.
4 An analogy can be seen as follows. In general, we do not question the appropriateness of
allowing people to purchase hurricane insurance when we see people collecting on their policies
after a hurricane. Perhaps the insurance feature embedded in bankruptcy is no different, but if
not, why?
5 See The Washington Monthly (March 1997), and, again, the testimony of Senator Charles
Grassley (R-Iowa) and Senator Paul Wellstone (D-Minn) at


Federal Reserve Bank of Richmond Economic Quarterly

To this end, I make three assumptions, discussed in detail later, that are designed to maximize the benefits of lax bankruptcy law as a means of wealth
redistribution from the rich to the poor.
Surprisingly, despite such assumptions, the existing combination of easily available unsecured credit and current bankruptcy law is found to reduce
welfare relative to the environment of tighter unsecured credit that prevailed
before 1978. The real welfare loss comes from a subset of low-income, lowwealth households being prevented by bankruptcy law from credibly committing to repaying loans. One possible remedy is therefore to allow individuals
to pre-commit to debt rescheduling instead of being forced into Chapter 7
liquidation.6 The model also strongly suggests that U.S. households are actually less inclined to file for bankruptcy, all else equal, since the increase in
filings is well accounted for by an increase in credit availability to low-income
households. Therefore, contrary to the popular view, the stigma associated
with bankruptcy appears to be as strong as ever.7

By making large-scale uncollateralized lending commercially feasible, at least
in principle, the Marquette ruling set the stage for overcoming a “chicken-andegg” problem facing payment cards in general and credit cards in particular.
That is, how could an industry establish a large, smoothly functioning payment system when consumers would only hold a card that was widely accepted
and merchants would bear the costs of entering the given payment network
only if they felt that cardholding would expand sufficiently? As Evans and
Schmalensee (1998, p. 72) argue, “less balkanization of state credit restraints
set the stage for the marketing of payment cards on a nationwide basis. . . [and]
by permitting a national market, Marquette probably enabled issuers to realize
scale economies in marketing and processing costs, and thus to make payment
cards more readily available to consumers across the country.”8 At the same
time that the construction of a payments network began, a revolution in credit
risk management in the form of “credit scoring” was underway. Credit scoring
enabled credit issuers to predict fairly precisely overall losses on a large nationwide portfolio of cardholders while remaining probabilistically uncertain
about the repayment behavior of any given cardholder. Credit scoring is an
6 Unfortunately, the difficulties associated with credible opt-out are daunting. In particular,
Section 362 in the bankruptcy code makes opt-out essentially unenforceable (personal communication with Professor Joseph Pomykala, July 27, 2001).
7 Bankruptcy stigma is defined as feelings of guilt and shame and dispproval from others.
8 Although I will maintain the assumption of competitive credit markets throughout, the following caveat is warranted. To the extent that Marquette removed the last vestiges of market
power by eliminating regional segmentation of credit market, the negative welfare consequences
presented here may be somewhat moderated.

K. Athreya: Unsecured Credit


instrumental feature of today’s credit market, and has allowed better pricing
and increased availability of credit for all consumers, including those as seen
as “risky.”9
The interest rate ceilings in place prior to Marquette appear to have greatly
limited the growth of this credit market. Canner and Fergus (1987) provide
a careful empirical analysis of the likely effects of Senate bills S.1603 and
S.1922. Each of these bills was aimed at imposing nationwide interest rate
ceilings. Canner and Fergus argue that existing interstate variation in interest rate ceilings indicates that consumers in states with low ceilings face
greater difficulty in obtaining loans and would suffer if nationwide ceilings
were implemented. Their arguments are further buttressed by Villegas (1989),
who cites evidence from the 1983 Survey of Consumer Finances that restrictive interest rate caps lower the availability of credit to high-risk borrowers,
often those who are poorest.10 Also suggestive is the dramatic increase in
the number of credit cards held by U.S. households beginning in the period
immediately following Marquette. In 1981, there were 572 million credit
cards outstanding, and by 1987, this number had risen to 841 million. Lastly,
the detailed empirical analyses of Evans and Schmalensee (1999), Black and
Morgan (1999), Moss and Johnson (2000), and Ellis (1998), provide clear accounts of the disproportionately rapid increase in unsecured credit availability
among those with low incomes. Given the preceding, a maintained hypothesis
of this article is that the increased availability of commercial unsecured consumer credit did not simply displace existing informal credit arrangements,
but substantially relaxed the liquidity constraints faced by poor households.



I will now briefly document the revolution in personal bankruptcy filing rates
that has accompanied the revolution in unsecured credit. While business filings
remained a negligible and steady fraction of the total number of bankruptcies,
non-business filings have increased dramatically. First, as seen in Figure 1,
total non-business filing rose from roughly 250,000 filings in 1980, just after
the Marquette ruling, to roughly 1.3 million in each year from 1997 to 2000.11
This is an increase in filing rate from roughly 1 in 400 households to more than
9 See Evans and Schmalensee (1998, pp. 95–97, 251).
10 See also The Economist (November 1998), which details the stark differences in credit

availibility on either side of the border town of Texarkana. On the Texas side, lending and purchases of consumer durables flourishes, while it stagnates on the Arkansas side.
11 2001 is already on pace to break all previous records, with the second highest number of
filings ever recorded in the first quarter. Source: American Bankruptcy Institute,


Federal Reserve Bank of Richmond Economic Quarterly

1 per 100 households.12 The volume of debt discharged in these bankruptcies
had grown to roughly $40 billion in 1997, 1998, 1999, and 2000.
The losses above arose primarily from what are known as Chapter 7
bankruptcies. A Chapter 7 filing removes all unsecured debt from the debtor’s
balance sheet in exchange for all “nonexempt” assets that are held by the
household. Of the 1.4 million bankruptcies in 1997, over 70 percent—nearly
one million filings—were Chapter 7 filings. The average debtor in a Chapter
7 bankruptcy defaulted on an average of $35,000 in 1997.13 Chapter 7 filings
alone led to losses of $36.4 billion. Although Chapter 13 bankruptcies essentially reschedule secured debts, and therefore result in very low losses of
secured debt relative to Chapter 7 bankruptcies, they still result in the discharge
of most unsecured debt. For example, in a study by Wharton Econometric
Forecasting Associates (WEFA), in 1997, approximately 90 percent of the
$6.5 billion in total unsecured debt in Chapter 13 bankruptcy was not repaid.
For the purposes of this article, my focus will be on unsecured debt; therefore,
I do not distinguish between Chapter 7 and Chapter 13 filings.
With respect to the identity of the filers described above, note first that
the income gap between bankruptcy filers and average households reflects a
systematic difference in occupational structure as well as education levels.
Luckett (1988) finds that bankruptcy occurs most often among low-income
individuals working in unskilled occupations.14 Empirically, the link between
low-mean income and high volatility is documented clearly in Kydland (1984)
and will be the basis for my parameterization of labor income risk.
A large portion of bankruptcies result from the disruption of labor income
due to job loss, sickness, or other factors.15 In their landmark study, Sullivan,
Warren, and Westbrook (1989) find that roughly 80 percent of bankruptcy filers
in their 1981 sample reported an income change in the two years previous to
filing. Of these, 62 percent had experienced a change in income of greater than
10 percent over the previous year, and of those whose income fell, the mean
decline was 37.2 percent!16 Additionally, Sullivan, Warren, and Westbrook
find that the median and mean incomes in their sample of bankruptcy filers
12 The median state in the United States had almost exactly one filing per 100 households
in 2000. Source: American Bankruptcy Institute.
13 Culhane and White (1999).
14 Interestingly, Sullivan, Warren, and Westbrook (1989) also find that while the mean incomes
of bankrupts are lower than average, the distribution of these workers by industry across the labor
force mirrors that of the general population.
15 See Sullivan, Warren, and Westbrook (1989, pp. 95–101, 187).
16 To quote Sullivan, Warren, and Westbrook (1989), “these figures portray highly volatile
income streams, making a mismatch between debts and income likely.”
To be more precise, what is true is that a “mismatch” between debts and income is more
likely conditional on a level of debt. However, the level of debt taken on by a household depends, among other things, on income volatility and bankruptcy law. Therefore, the unconditonal
likelihood of a mismatch may or may not be more likely.

K. Athreya: Unsecured Credit


were both roughly two-thirds that of the average household. It is clear therefore
that unsecured debt and bankruptcy protection together form an all-purpose
insurance policy against the hardships caused by volatile and low incomes.17
Bankruptcy is not, however, an insurance policy given to households for
free. Beyond increased interest rates on unsecured loans, there are four types
of costs to the debtor associated with bankruptcy. First, and most importantly,
bankruptcy results in at least some exclusion from credit markets. Second,
there are costs associated with the surrender of nonexempt assets, and, more
rarely, with possible future wage garnishments. Third, stigma appears to play
a role (see Fay, Hurst, and White [1996] and Gross and Souleles [2000]).
Finally, although they are usually small, there are explicit costs, such as those
such as those arising from court dates or lawyer’s fees.
In practice, bankruptcy almost never involves the transfer of assets or
income from debtor to creditor. Over 95 percent of Chapter 7 bankruptcies
are “no-asset” cases.18 Almost all bankruptcy penalties levied on debtors filing
for bankruptcy therefore constitute deadweight losses. Deadweight costs are
important for two reasons. First, by construction, bankruptcy is typically used
only by those who do not have a great deal of material wealth. Second, even
when debtors have wealth at the time of filing, it is often difficult to seize it
in the presence of various exemptions. Therefore, the only remaining route
to arrange transfers from borrowers to lenders is via wage garnishing, which
is rarely used.19 The inability to seize future income further requires that the
vast majority of penalties for bankruptcy be those involving punishment of the
borrower without wealth transfers to the lender. The reliance on deadweight
penalties clearly hinders the ability of bankruptcy to function as a welfareimproving, risk-bearing institution. This is an important part of the arguments
for stricter, but finite, penalties for bankruptcy (see Dubey, Geanakoplos, and
Shubik [2000]).
I turn now to a description of formal economic environments in order
to study the consequences of alternative credit market arrangements, with
specific reference to the growth of unsecured credit availability among lowerincome households.

17 Such volatility may understate the full risk faced by the uninsured, as illness can cause
shocks to expenses as well as income.
18 See Sullivan, Warren, and Westbrook (1989, pp. 201–18).
19 See again Sullivan, Warren, and Westbrook (1989, pp. 22–24). In particular, bankruptcy
also stops garnishments.


Federal Reserve Bank of Richmond Economic Quarterly

My model is specifically aimed at understanding the welfare, price, and quantity consequences of the dramatic change in the distribution of unsecured
consumer credit over the past two decades.

There is a continuum of infinitely-lived agents with constant relative riskaversion (CRRA) preferences. This standard formulation captures risk aversion, the desire for smooth consumption, and the concern households have for
future generations. The parameter β ∈ (0, 1) indicates the rate at which future
consumption is discounted, and the parameter α indicates the risk aversion, as
well the desire for smooth consumption over time. Expected lifetime utility
is given by




where ct is consumption at time t.

Labor Income
There are two types of agents who will receive systematically different incomes
over time. These differences are meant to capture the higher average income
and lower income risk faced by skilled individuals. I further assume that the
type of a household is unobservable to a lender. This assumption is plausible
because credit reports do not contain labor income, other than self-reported
measures at the time of application.20 The type of household is denoted by
i ∈ I , where i = h indicates high average income households and i = l
indicates low-income households. The proportion of high-income agents in
the population is denoted by ω, and low-income agents represent the remaining
fraction (1 − ω) in the population. Labor income i is denoted by Y i and can
take on two values, Yg and Yb . The subscripts g and b denote income in the
good and bad states respectively, and Yg > Yg and Yb > Yb . Let mean income


for type-l and type-h households be given by Y and Y , respectively. Labor
income also evolves smoothly over time in the sense that current (annual)
income is helpful to an individual for estimating future income. I denote by
pgg the probability that income next period is good if income this period is
20 While it is true that a borrower may reveal some information on his or her type via
serious deliquency behavior, this is typically too late for risk managment purposes. See Sullivan,
Warren, and Westbrook (1989, p. 187) for more.

K. Athreya: Unsecured Credit


good. The probability of staying in the bad income state is given by pbb . The
forecastability of future income allows agents to plan savings or borrowing to
keep consumption smooth.

Consumer Debt, Savings, and Intermediaries
Despite the large levels of default, the market for unsecured credit in the
United States does function smoothly, and it is well characterized as a large
competitive marketplace where price-taking lenders issue credit through the
purchase of securities backed by repayments from those who borrow.21 These
transactions are intermediated principally by credit card issuers. The interest rates charged by credit card issuers are not individually tailored for each
account but instead cover the aggregate default rate. The typical credit card
contract is described by a fixed interest rate and credit line. Interest rates are
typically rather insensitive to changes in individual debt levels, even though
the marginal likelihood of default may change.
Given the preceding, I assume that in order to smooth consumption, agents
have access to competitive markets wherein they may borrow or save assets.
An agent’s financial wealth is denoted at , where at > 0 represents saving and
at < 0 represents borrowing. Agents may borrow at the going interest rate
on loans (1 + r l ) or save by holding deposits at the interest rate (1 + r d ).
Note that the interest rate on loans does not vary with an agent’s type, income,
or current wealth level. This invariance reflects an assumption that lenders
are unable to differentiate between households. Each agent of type i faces a
borrowing limit Ai .22 Borrowing limits play a central role in the model, and
I will study outcomes arising from a variety of values for them.

Bankruptcy in the Model
Bankruptcy works in the model as follows. When an individual files, his or
her debts are removed and he or she is then penalized in two ways. First,
an agent is prevented from borrowing (i.e., is borrowing constrained) for an
uncertain length of time, although the average length of this period, ρ, is
known to the agent. During this period of exile from loan markets, agents
may still save to meet contingencies. After this time, they may borrow freely
21 A strong case can be made for the appropriateness of this characterization. See Evans
and Schmalensee (1999) and the references therein. Lest one think that lax bankruptcy would
be obviously desirable if the credit card industry were monopolistic, note that the brunt of high
borrowing costs for unsecured credit are borne not by the wealthy, who have cheaper secured
borrowing available to them, but by the poor and those with low collateralizable wealth. Therefore,
the competitive assumption may actually make lax bankruptcy law easier to defend.
22 As with incomplete insurance contracts, borrowing limits (the rationing of credit) can be
derived from more primitive assumptions on the structure of information possessed by lenders and
borrowers. We avoid this complication here and directly assume credit limits.


Federal Reserve Bank of Richmond Economic Quarterly

and are considered solvent. Agents in the borrowing constrained state are
probabilistically returned to credit markets, whereby with probability 1/ρ
they are returned to solvency (i.e., they are free to borrow and default in the
following period), and with probability (1 − 1/ρ) they are still restricted from
borrowing or defaulting.
The second feature of bankruptcy in the model is that the filer is penalized
in the ways discussed earlier. However, given that these penalties do not
involve resource transfers, and given that the sum of these various penalties
governs behavior, I employ a penalty levied directly on utility. I use λi to
denote all costs of bankruptcy, in terms of utility, to a type-i household beyond
those costs accruing directly from credit market exclusion; this includes legal
fees and the psychic costs of stigma.
The combination of easily available unsecured credit and lax personal
bankruptcy law is often seen as beneficial for the unlucky poor against the
ravages of bad luck and greedy creditors. In order to give this view its best
day in court, I proceed as follows.
Assumption 1 Only low-mean income agents will choose to file for bankruptcy.
Assumption 1 simply assumes that the cost of bankruptcy to high-mean
income households is so high that they never declare bankruptcy. As was
argued earlier, this assumption is supported by the evidence that filers have
systematically lower paying occupations than non-filers (see again Sullivan,
Warren, and Westbrook [1989]). Assumption 1 blunts the argument that we
should tighten bankruptcy law to defend the poor from the excesses of the rich;
this argument is frequently heard from proponents of tougher law whenever a
high-profile case of bankruptcy surfaces.23

The Consumer’s Choice Problem24
The consumer’s choice problem is most naturally expressed recursively. Specifically, at a point in time an agent can be solvent (denoted S ), bankrupt
(denoted B ), or borrowing constrained (denoted BC ). The value to an agent
of having a given level of current income, asset holdings, and credit market
status (borrowing constrained or solvent) can be expressed in terms of utility
from choices over current consumption/savings and credit market status (if
solvent) and the expected future value of those choices. I restrict borrowing
according to an agent’s credit status as follows. For solvent agents of type
23 As in the cases of the actor Burt Reynolds and former Commissioner of Major League
Baseball Bowie Kuhn.
24 This section and the following section defining equilibrium may be skipped by those
primarily interested in the results.

K. Athreya: Unsecured Credit


i, net assets must be greater than the borrowing limit, Ai , and for borrowing
constrained agents, Ai . There are no restrictions on savings.
Each period, given their current income and beginning-of-period assets,
agents must choose consumption, c, and asset holdings, denoted a , to carry
forward into the next period. Depending on whether they choose to be net
borrowers or lenders, they face either the net rate of interest on loans r l or on
deposits r d , where r l > r d .
When an agent is solvent and qualifies for bankruptcy protection, he or
she must first choose whether or not to file and then choose assets subject
to the constraints for solvent or borrowing constrained agents, depending on
their default decision. I now introduce two pieces of notation. First, the vector
(a, y) is an agent’s current period state conditional on credit status. With this
notation, the value of being solvent VSi is given as follows.
VSi (a, y) = max[WS (a, y), WB (a, y)],


where WS denotes the value of not filing for bankruptcy in the current period,
and satisfies

WS (a, y) = max{u(c) + βEVSi (a , y )}



a ≥ Ai ,



where r is understood to be the interest rate on loans r l if assets are negative
and the rate on deposits r d if assets are positive.
Bankruptcy is relevant to only those with debts, i.e., to households with
assets a < 0. When the agent files for bankruptcy, he or she has his or her
debt removed, pays the cost of bankruptcy, λi , and is sent with probability
one to the borrowing constrained state, where he or she obtains value VBC .
Therefore, the value of filing for bankruptcy, denoted WB , satisfies
WB (a, y) = max{u(c) − λi + βEVBC (a , y )}


1 + rd


a ≥ 0.



Federal Reserve Bank of Richmond Economic Quarterly

To define VBC above, note that agents in the borrowing constrained state
are probabilistically returned to credit markets, whereby with probability 1/ρ,
they are returned to solvency (i.e., they are free to borrow and default in the
following period), and with probability (1 − 1/ρ), they are still restricted from
borrowing or defaulting. Let ψ ≡ 1/ρ. Thus,
VBC (a, y) = max{u(c) + ψβEVSi (a , y ) + (1 − ψ)βEVBC (a , y )}


≤ y i + a,
1 + rd
a ≥ Ai .



I turn now to the definition of equilibrium in the model.

The consumer choice problem above captures the decisions of a very large
number of households. However, given the absence of perfect income insurance, households who have received many bad income shocks are likely to
find themselves in debt, while those who have been lucky will hold perhaps
large levels of savings. Their choices are governed by a decision rule, which,
for a household of type i, specifies asset holdings as a function of interest
rates, income, current assets, and borrowing constraints.
An equilibrium consists of a decision rule for each type of agent and
interest rates r l and r d such that four requirements are met. First, given
these interest rates, decision roles are optimal and feasible. Second, total
economywide borrowing by households equals total economywide saving.
Third, I restrict attention to steady state equilibria where the bankruptcy rate
and fraction of agents in the population with a given level of assets are
stationary, i.e., the same at every date. Fourth, I require that the spread between
loan and deposit rates is such that financial intermediaries exactly cover their
costs, given the observed bankruptcy rate.

The assumption of stationarity implies that the analysis here is appropriate as
a study of two different long-run situations, one in the pre-Marquette era and
one currently prevailing. The relatively flat bankruptcy rate over the past four
years suggests that at this point in the post-Marquette era we may have attained
a new steady state. Given the preceding, the overall strategy is as follows. I
will first choose a set of parameters such that the equilibrium outcomes match

K. Athreya: Unsecured Credit


salient features of the pre-Marquette environment. In particular, I will set
the parameters to match bankruptcy filing rates in the pre-Marquette era. I
will then choose alternative values for the nonpecuniary costs of bankruptcy,
credit limits, and the parameter governing the average period that bankrupt
borrowers are excluded from the credit market, such that the model matches
outcomes in the post-Marquette world.
I am assuming that the post-Marquette expansion in bankruptcy rates
resulted from the increased ease with which borrowers who declare bankruptcy
are able to borrow again, along with an increase in borrowing limits and a
reduction in the costs of filing for bankruptcy, notably in terms of stigma.
All other parameters will remain fixed in both the pre- and post-Marquette
eras and are set to match certain statistics concerning income risk in the United
States. Specifically, the income processes are set to match observed persistence and volatility by skill level, along with the observed skill-premium, and
are summarized in Table 1. For brevity, I do not give exhaustive details on
these parameters, but rather refer the interested reader to the detailed discussions in Athreya (2000a,b), as well as to Kydland (1984), Heaton and Lucas
(1997), and Autor, Katz, and Kreuger (1998).
The welfare criterion used here measures the percentage change in consumption, at all dates, that would make a household indifferent between the
pre- and post-Marquette eras. This increment /decrement to consumption is
denoted by φ. A negative value for φ implies that households are worse off in
the post-Marquette era, and a positive value implies the reverse. With respect
to the policies chosen by a society, if it turns out that the welfare of low-income
agents improves significantly under lax bankruptcy law, even if that of highincome people worsens significantly, such a law may still be chosen. Given
this, Assumption 2 is the following.
Assumption 2 Low-mean agents matter at least as much as high-mean agents
in measuring welfare.
I also assume that even though only low-mean income agents go bankrupt,
creditors are unable to distinguish them from high-mean income borrowers.
That is:
Assumption 3 Creditors are not able to price-discriminate between highand low-mean agents.
This assumption implies the spreading of default costs not just across the
low-mean, high-volatility group, but across all high-mean agents as well. It is
in exactly this way that bankruptcy can redistribute wealth from rich to poor.25
25 See Sullivan, Warren, and Westbrook (1989, p. 187) for evidence that this is an appropriate


Federal Reserve Bank of Richmond Economic Quarterly

By combining Assumptions 2 and 3 with Assumption 1, I effectively allow
for the most generous possible redistribution from high-mean income people
to low-mean income people.
Credit Market Exclusion

An important parameter in the model with respect to bankruptcy is the period of
credit market exclusion, ρ. While ρ is not easily observable, an upper bound is
ten years—the length of time for which bankruptcy remains on a credit record.
In current times (the post-Marquette era), the restriction on future borrowing,
denoted ρ post , is certainly less than ten years, as evidenced by the growth of
sub-prime lending. Lenders in this market, while typically more expensive
than credit card lenders, still allow agents access to loan markets following
default or bankruptcy within a year or two. I err on the side of strictness in the
penalty and set ρ post such that the average period of exile from credit markets
is four years. However, in the pre-Marquette era, exile for a period of ten
years may have been a reasonable estimate for the restriction on borrowing. I
therefore fix the pre-Marquette exile parameter ρ pre to imply an average exile
period of ten years.
Nonpecuniary Costs and the Bankruptcy Rate

The parameters λi will be inferred by the level that it must take in order to
match observed bankruptcy filing rates in the pre- and post-Marquette eras,
given the applicable credit market penalties and credit limits. Assumption 1
simply requires that λh be set such that no high-mean income households files
for bankruptcy. The cost for low-mean income households, λl , is set to match
pre-Marquette filing rates and is then used in the post-Marquette era, where
it will be denoted λlf ixed . When λl is reestimated in order to match the filing
rate in the post-Marquette era, it will be denoted λlendog .
In terms of bankruptcy rates, in 1978, the year of the Marquette ruling,
roughly 300,000 filings occurred in a 76 million household economy, which
implies a national filing rate of 0.4 percent.26 In contrast, in 1998, total nonbusiness bankruptcy filings hit 1.4 million. Thus, of the roughly 100 million
households in America, 1.4 percent filed for bankruptcy, a nearly four-fold
increase since Marquette.
Credit Limits

Credit limits, while at the heart of this article, are not easily observed, and tests
for the presence of binding credit constraints are rarely definitive. For example,
26 Source: and

K. Athreya: Unsecured Credit


observed credit lines do not tell us how much additional credit lenders may
be willing to extend to households. We also observe true limits only for those
who are denied further credit, a group that may not represent the majority
of borrowers. However, that credit limits do bind for a subset of households
is well established (see Jappelli [1989]). I therefore study outcomes under
a variety of credit limits. Mean amounts discharged in personal bankruptcy
in recent years have remained close to twice annual income, which motivates
setting Als−post = −2Y . With respect to high-income households, the model
here assumes that they do not file for bankruptcy, so their credit limits are less
important. For simplicity, I set Ah
s−post ≈ −2Y .
To be consistent with the evidence discussed earlier, credit limits in the
pre-Marquette era will be kept at least as strict as those in the post-Marquette
era. Mean amounts discharged in bankruptcy were much smaller in the period immediately following Marquette, at close to annual income, than in
current times. However, as hard data on credit limits is not available, I explore
three levels, ranging from one-half of annual income in the benchmark case
(Als−pre = −0.5Y ), to three-fourths annual income (Als−pre = −0.75Y ),

and lastly to annual income (Als−pre = −Y ). The pre-Marquette limit for
high-mean income households is also smaller than in the post-Marquette era,
and is set such that Ah
s−pre is roughly one-and-a-half times (high) annual mean

income. By setting Als−pre = −0.5Y , the benchmark case considers the most
generous increase in credit availability to low-mean income households. The
set of fixed parameters is given in Table 1.

The two main results of this article are as follows.
Result 1 The stigma-related costs of bankruptcy have risen over the postMarquette period, not fallen, as has often been suggested.
Result 2 The post-Marquette expansion in unsecured credit and current bankruptcy law have together actually lowered the welfare of low-mean income
I begin by providing intuition for the first result. It has by all accounts
become distinctly easier to borrow following a bankruptcy in the past decade,
as seen in the growth of sub-prime lending, i.e., average credit market exclusion times have fallen. Given the fall in credit exclusion, the model may or
may not be able to capture observed filing rates. Subsequently, I relax this
assumption and compare welfare under states in a setting that allows for timevarying levels of these difficult-to-observe costs. When λl is reestimated in the
post-Marquette period, it will be set to reproduce observed filing rates, given


Federal Reserve Bank of Richmond Economic Quarterly

Table 1 Fixed Parameters





Aiyagari (1994)



Heaton and Lucas (1997)



Kydland (1984); Aiyagari (1994)


Y /Y











Huggett (1993); Sullivan et al.
(1989); Culhane and White (1999)
Autor, Katz, and Kreuger (1998)

the post-Marquette term of exclusion from credit markets. This reestimation
will allow for the possibility that stigma effects may have changed in recent
years, as recent work by Gross and Souleles (1998) suggests. In particular,
the assertion that stigma has fallen over time can and will be directly tested by
the reestimation of λl in the post-Marquette era. It turns out that even under
the assumption that credit market exclusion continues for ten years, the estimated nonpecuniary cost for the pre-Marquette period implies substantially
higher bankruptcy rates than have been observed. This result is displayed in
Table 2 and is obtained by recomputing the implied penalties, beyond credit
market exclusion, that are required to generate the observed filing rate in the
post-Marquette period. I find that these penalties, when estimated in the preMarquette era and applied to the post-Marquette era, produce far too many
filings given the current availability of unsecured credit.
The preceding is a surprising implication of the model, and it suggests that
stigma effects haven’t fallen in the manner often suggested. For an example
of such a suggestion, see Senator Charles Grassley, who states in a May
17, 1997, PBS interview, “There is no shame anymore with bankruptcy” (in
“Going for Broke,” A News Hour with Jim Lehrer transcript, May 17, 1999).
For a contrasting view, note the remarks of U.S. Bankruptcy Judge Joe Lee,
who states, “I don’t see many people cavalier about bankruptcy. The reason
for so many bankruptcies is because consumer credit is so overwhelming”
(“No More Stigma in Being Broke?” July 25, 2001, Cincinnati Enquirer).
Anecdotal evidence suggesting that credit market exclusion may not be that

K. Athreya: Unsecured Credit


severe can be seen in the explosion of “no credit, bad credit, . . . no problem”
advertising populating late-night television.
To understand the second result, I now turn to the results of a quantitative
exercise. The benchmark case evaluates the effects of increasing unsecured
credit availability when the pre-Marquette credit limit for low-mean income
agents is set at Als−pre = −0.5. The results are presented in Table 2. In
the first column of Table 2, I report outcomes for bankruptcy rates, interest
rates, consumption, and asset volatility for the pre-Marquette era. In the
second column, I present the outcomes obtained from the post-Marquette
environment, when the nonpecuniary costs of bankruptcy are held at their
calibrated value from the pre-Marquette era. The third column also presents
the results after the move to a post-Marquette environment; however, in this
case the nonpecuniary costs are recalibrated such that the model matches the
post-Marquette bankruptcy rate of 1.4 percent.27
I find that the interest rate on unsecured loans is 9.0 percent, close to its true
value in 1980 (see Evans and Schmalensee [1999], p. 239). The coefficient of
variation in consumption, denoted cv(cl ) and cv(ch ) for low- and high-mean
income households respectively, is roughly one-third that of income for both
high- and low-income households. The relatively low ratio of consumptionto-income volatility suggests that even with low bankruptcy rates, households
do a good job of smoothing their consumption using asset markets, such as
savings accounts and credit cards.
Turning to specifics, note first that as we move from the pre-Marquette
era to the present, holding λ fixed, bankruptcy rates skyrocket, along with
interest rates on unsecured loans. The bankruptcy rate reaches a counterfactually high level of 4.8 percent. The interest rate on unsecured loans is 18.6
percent, also higher than the observed rate of approximately 12.5 percent. The
volatility of consumption rises for two reasons. First, as the loan rate rises,
borrowing becomes less useful in smoothing. Second, and perhaps more important, is the discrete jump upward of consumption in the periods following
a bankruptcy. That is, bankruptcy is an immediate discharge of debts, and
thus net wealth rises sharply when a household files for bankruptcy, thereby
inducing a concurrent rise in consumption.
The immediate impact on welfare is large. Under a welfare criterion where
only low-mean income households matter, denoted φ low , the welfare of the
poor agent is reduced by an amount equivalent to taking away 3.51 percent of
the household’s consumption at all dates, regardless of income. Alternatively,
the median household would experience a loss equal to an income reduction
27 Note that I model high-income households as having seen their access to unsecured credit
grow. However, given the reliance of this group on secured debt, and the low incidence of
bankruptcy in this group, it is not important that its ability to borrow in the unsecured market
change across the pre– and post-Marquette eras.


Federal Reserve Bank of Richmond Economic Quarterly

Table 2 Results

λl ixed





















cv(cl )
cv(ch )
φ low
φ equal








of roughly $900. When the welfare criterion weights all households equally,
welfare losses still fall, but by less, as seen in the row headed by φ equal .
Consumption is much less smooth than before, and interest rates are far
higher than the 9.0 percent level of the pre-Marquette era. Additionally, each of
the large number of filings induces the imposition of nonpecuniary penalties,
which, ex-post, imply substantial deadweight loss for society. When nonpecuniary costs are recalibrated, however, these welfare losses shrink somewhat,
to −2.83 percent when the welfare of only low-mean income households is
taken into account. Thus, although the recalibrated cost λlendog is larger, at
1.48 relative to 0.60, the reduction in bankruptcy rates from 4.8 percent to
1.4 percent reduces deadweight loss substantially. In turn, interest rates on
loans fall, from 18.6 percent under the pre-Marquette nonpecuniary cost of
0.60 to 11.6 percent. The consumption of high-mean income agents is much
smoother in all cases, at 0.051.
Thus, with respect to the question of whether households are better off
with the increased credit available today, even if it has brought with it more
bankruptcy, the answer is “no.” This result obtains even though three strong
assumptions were made in an attempt to enhance the role of easily available
unsecured credit and easy bankruptcy. Even when lenders are forced to price
loans according to average behavior in the population as a whole, when only
low-mean income households file for bankruptcy, I find that bankruptcy lowers
welfare. Furthermore, this result holds even when all welfare weight is placed

K. Athreya: Unsecured Credit


on the poor. The first reason for the fall in welfare is that households appear to
smooth consumption fairly well without bankruptcy, so forcing them to buy the
option to file is wasteful. Secondly, easy bankruptcy implies frequent use of
deadweight penalties such as credit market exclusion and stigma. Such penalties reduce welfare when imposed after the fact. A third reason is that interest
rates on loans rise dramatically, and when credit limits are increased, each
bankruptcy discharges more debt than before. Therefore, similar bankruptcy
rates may imply a substantially higher interest rate on loans.
The results above are quite robust to credit limits for the poor in the preMarquette period. As credit limits are relaxed, consumption becomes only
slightly smoother, suggesting that even small amounts of credit are sufficient
for patient consumers to effectively smooth temporary shocks. For conciseness, these results are not presented in detail here.
Stigma, Individual Debts, and Welfare

Interestingly, because it is hard to argue that credit limits are stricter now
than in the pre-Marquette era, and equally hard to argue that exclusion from
credit markets is greater now than before, we arrive at a somewhat contrarian
position. The United States is far from being a country where stigma and personal shame have fallen and where everyone is out to exploit the bankruptcy
system; instead, I find that increased nonpecuniary penalties, unrelated to
statutory or creditor-imposed penalties, are necessary in order to explain observed bankruptcy rates. In particular, given the slow growth rate of real
income among the unskilled, the rapid income growth of the skilled, and the
rapid increase in unsecured credit, it is puzzling why more households, especially high-income ones, did not file over the past two decades. This strongly
suggests that rumors of the demise of stigma and conscience are greatly exaggerated.28
A final point concerns mapping from individual circumstances at the time
of a bankruptcy filing to inferences about the desirability of a bankruptcy
system as a whole. In all of the cases considered in this article, households only
filed for bankruptcy when they held the maximum allowable debt and were
then hit by the low income shock. Despite the fact the only the “desperate”
filed for bankruptcy in this model, bankruptcy protection was still found to
be a welfare-reducing insurance system. Consider then the debate between
Senators Charles Grassley and Paul Wellstone referenced in footnote 2. In their
debate, much was made of the attitudes and circumstances of individuals in
bankruptcy, as if these considerations immediately made clear the desirability
or lack thereof, of bankruptcy. To the extent that the inability to opt out
28 As noted earlier, this result survives even if the credit market exclusion period is fixed in
both eras at ten years.


Federal Reserve Bank of Richmond Economic Quarterly

of bankruptcy protection lowers welfare, seeing people in dire straits at the
time of filing may simply suggest that deadweight and nonpecuniary costs
of bankruptcy are so large that the institution of bankruptcy may well reduce
aggregate welfare.



The results presented here should be interpreted as a first estimate of the welfare
consequences of the post-Marquette expansion in unsecured credit. The results
demonstrate that the interaction of the post-Marquette expansion in unsecured
credit with current bankruptcy law has led to a decrease in aggregate welfare.
That is, expanded unsecured credit, when combined with lax bankruptcy law,
helps some poor people at the expense of other poor people in a manner
that reduces overall welfare. Strikingly, the results presented here may even
understate the welfare costs of bankruptcy.
Perhaps a more subtle point is that in each of the experiments considered here, the households that filed had hit their borrowing constraint. However, while households are almost always in desperate straits at the time of
bankruptcy, which might suggest that bankruptcy is being used wisely, this
circumstance in no way implies that the system overall is welfare-improving.
The penalties for bankruptcy are not definitively connected with the level of
debt defaulted on. Therefore, rational households have incentives to carry
large debts, although these incentives are balanced here by the possibility of
having to service them. That is, the position of households at the time of filing
may say precious little about overall desirability of the bankruptcy system.
The latter has been a point of confusion in recent public debate.
The model developed here also strongly suggests that U.S. households are
actually less inclined to file for bankruptcy, all else equal, than they were in
the pre-Marquette era. That is, the increase in filing rates is well accounted
for by an increase in credit available to low-income households. This result
echoes the work of Ellis (1998) and Moss and Johnson (2000).
The results presented here are perhaps a lower bound on the welfare loss
from easy unsecured credit and lax bankruptcy. Of the three assumptions used
above, Assumption 1, that high-income households do not file for bankruptcy,
is particularly important. While the assumption can be rationalized by supposing that high-income agents face large nonpecuniary penalties for filing, it is
not statutorily accurate. High-income people can, if anything, file more easily
than low-income people. The rich have smoother incomes, making exclusion
from credit markets less painful for them. At present, the rich can get more
credit, which will allow them to consume more prior to default. Therefore,
there is something very intangible keeping bankruptcy rates from being much
higher than they are.

K. Athreya: Unsecured Credit


In terms of the desirability of returning to a pre-Marquette world, the
present-day environment is advantageous in that a large efficient payments
network exists alongside substantially better credit risk management. The latter allows lending to a group that found borrowing difficult before Marquette.
The downside of the current environment is that the mean level of consumption
volatility is still higher than it would be in a world where individuals could
credibly commit to repaying loans. Thus, the real welfare loss comes from a
subset of low-income, low-wealth households being prevented by bankruptcy
law from credibly committing to repaying loans. Additionally, the inability to
impose penalties that transfer resources from borrower to lender necessitates
high interest rates on unsecured credit and the frequent use of socially costly
bankruptcy penalties. These latter penalties appear to render bankruptcy a fundamentally inefficient system for risk bearing. One possible remedy here is to
allow individuals to pre-commit to debt rescheduling, rather than to let them
be forced into Chapter 7 liquidation.29 If pre-commitment to debt rescheduling in lieu of outright liquidation were allowed, those who wanted to retain
the option to file for a Chapter 7 bankruptcy could be charged a higher price
for the option, while others could opt out of Chapter 7 bankruptcy rather than
being forced to pay for it as they are now.

Aiyagari, S. R. “Uninsured Idiosyncratic Risk and Aggregate Saving.”
Quarterly Journal of Economics, vol. 109 (August 1994), pp. 659–84.
Athreya, K. B. “Welfare Implications of The Bankruptcy Reform Act of
1998.” Manuscript, Federal Reserve Bank of Richmond, 2001a.
. “Fresh Start or Head Start? Uniform Bankruptcy
Exemptions and Welfare.” Manuscript, Federal Reserve Bank of
Richmond, 2001b.
Autor, D., L. Katz, and A. Kreuger. “Computing Inequality: Have Computers
Changed the Labor Market?” The Quarterly Journal of Economics,
vol. 113 (November 1998), pp. 1169–213.
Ausubel, L. M. “The Failure of Competition in the Credit Card Industry,”
American Economic Review, vol. 81 (1991), pp. 50–80.

29 However, see Jackson (1985) for an argument in defense of disallowing pre-commitment.


Federal Reserve Bank of Richmond Economic Quarterly

Bankruptcy Reform Act of 1998. Hearing Before the Subcommittee on
Commercial and Administrative Law of the Committee on the Judiciary,
House of Representatives. 105 Cong. 1 Sess., June 1998. Washington:
Government Printing Office, 1999.
Black, Sandra, and Donald P. Morgan. “The Democratization of Bank Credit
Cards and the Rise in Charge-Offs.” Handout prepared for Federal
Reserve Bank of Chicago Conference on Bank Structure and
Competition, May 6–8, 1999.
Canner, Glenn, and James T. Fergus, “The Effects on Consumers and
Creditors of Proposed Ceilings on Credit Card Interest Rates.” Staff
Study 54, Board of Governors of the Federal Reserve System, October
Congressional Budget Office. “Personal Bankruptcy: A Literature Review.”
CBO paper. Washington: Government Printing Office, September 2000.
Culhane, Marianne B., and Michaela M. White. “Taking the New Consumer
Bankruptcy Model for a Test Drive: Means-Testing Real Chapter 7
Debtors,” American Bankruptcy Institute Law Review, vol. 7 (Spring
Dubey, Pradeep, J. Geanakoplos, and M. Shubik. “Default in a General
Equilibrium Model with Incomplete Markets,” Yale Cowles Foundation
Discussion Paper 1247, 2000.
Ellis, Diane. “The Effect of Consumer Interest Rate Deregulation on Credit
Card Volumes, Charge-Offs, and the Personal Bankruptcy Rate,” Bank
Trends (98-05), Federal Deposit Insurance Corporation, February 1998.
Evans, David, and Richard Schmalensee. Paying With Plastic: The Digital
Revolution in Buying and Borrowing. Cambridge, Mass.: MIT Press,
Fay, Scott, Erik Hurst, and Michelle White. “The Bankruptcy Decision,”
American Economic Review (forthcoming).
Gropp, Reint, White, Michelle J., and John Karl Scholz, “Personal
Bankruptcy and Credit Supply and Demand,” Quarterly Journal of
Economics, vol. 112 (1997), pp. 217–51.
Gross, David B., and Nicholas Souleles. “Explaining the Increase in
Bankruptcy and Delinquency: Stigma vs. Risk Composition,” Wharton
Financial Institutions Center, 98-28-B. University of Pennsylvania.
Heaton, John, and Deborah Lucas. “Market Frictions, Savings Behavior, and
Portfolio Choice,” Macroeconomic Dynamics, vol. 1 (1997), pp. 76–101.

K. Athreya: Unsecured Credit


Huggett, M. “The Risk-Free Rate in Heterogeneous-Agent IncompleteInsurance Economies,” Journal of Economic Dynamics and Control,
vol. 17 (1993), pp. 953–69.
Jackson, Thomas H. “The Fresh-Start Policy in Bankruptcy Law,” Harvard
Law Review, vol. 98 (1985), pp. 1393–440.
Jappelli, Tullio. “Who Is Credit Constrained in the U.S. Economy?”
Quarterly Journal of Economics, vol. 105 (February 1990), pp. 219–34.
, S. Pischke, and N. Souleles. “Testing for Liquidity
Constraints in Euler Equations with Complementary Data Source,”
Review of Economics and Statistics, vol. 80 (1998), pp. 251–62.
Kydland, F. E. “Labor Force Heterogeneity and the Business Cycle,”
Carnegie-Rochester Series on Public Policy, vol. 21 (Autumn 1984),
pp. 173–208.
Luckett, Charles. “Personal Bankruptcies,” Federal Reserve Bulletin, vol. 74
(September 1988), pp. 591–603.
Moss, David A., and Gibbs Johnson. “The Rise of Consumer Bankruptcy:
Evolution, Revolution, or Both?,” American Bankruptcy Law Journal
Storesletten, Kjetil, C. Telmer, and A. Yaron. “Asset Pricing with
Idiosyncratic Risk and Overlapping Generations.” Mimeo, July 1999.
Sullivan, Teresa A., Elizabeth Warren, and Jay Lawrence Westbrook. As We
Forgive Our Debtors: Bankruptcy and Consumer Credit in America.
New York: Oxford University Press, 1989.
Villegas, Daniel. “The Impact of Usury Ceilings on Consumer Credit,”
Southern Economic Journal, vol. 56 (1989), pp.126–41.
WEFA Group. “The Financial Costs of Personal Bankruptcy,” GAO
B-279802 GAO/GGD-98-116R (Feb. 1998).
White, Michelle. “Why Don’t More Households File for Bankruptcy?”
Journal of Law, Economics, and Organization, vol. 14. (October 1998),
pp. 205–31.
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Markets Are Incomplete,” American Economic Review, vol. 83 (1993),
pp. 1142–64.

Regulating Bank Capital
Structure to Control Risk
Edward S. Prescott


he most important recent developments in bank regulation are based on
capital requirements. For example, the Basle Accord of 1988 specifies
that bank capital must be at least 8 percent of a bank’s risk-weighted
assets.1 Also, the Federal Deposit Insurance Corporation Improvement Act
of 1991 (FDICIA) requires regulators to shut down a bank whose capital has
dropped below a cutoff level.
While these regulations are important, their focus is too narrow in that they
concentrate solely on equity. There are other types of financial instruments
available, and these can be even more effective than capital requirements
at controlling risk. Proposals to require banks to issue subordinated debt
recognize this, but even those proposals do not make full use of the possibilities
available. This article argues that capital regulation can be improved by using
financial instruments like convertible debt and warrants with high strike prices.
Furthermore, some of the improvement brought about by these instruments
would allow a reduction in the traditional capital requirements.
Any economic study of bank capital regulation requires a theory of capital
structure. Modern theories of corporate financial structure start with the celebrated result of Modigliani and Miller (1958): that in a world without taxes or
bankruptcy costs, the value of a firm does not depend on its capital structure.
These theories then consider departures from the world of Modigliani and
Miller—departures that cause the capital structure to matter. The particular
departure studied in this article is agency theory. In the agency theory of capital structure, limited liability creates an incentive for highly leveraged firms
to take excessive risk. These incentives are made worse in banking because
The author would like to thank Kartik Athreya, Tom Humphrey, David Marshall, Roy Webb,
and John Weinberg for helpful comments. The views expressed in this article do not necessarily represent the views of the Federal Reserve Bank of Richmond or the Federal Reserve
1 Recent proposals by the Basle Committee on Banking Supervision are still based on capital
requirements even though they change the way the requirements are calculated.

Federal Reserve Bank of Richmond Economic Quarterly Volume 87/3 Summer 2001



Federal Reserve Bank of Richmond Economic Quarterly

of deposit insurance. This idea was developed by Merton (1977) and Kareken
and Wallace (1978) in the context of deposit insurance and is related to the
agency theory of capital structure developed by Jensen and Meckling (1976).2
The analysis presented in this article is a simplified exposition of the
analysis contained in Marshall and Prescott (2001). They examine the value
of augmenting capital regulations with securities that fine-tune the payoff
received by a bank. In the Marshall and Prescott model, a bank chooses the
risk and mean characteristics of its loan portfolio. For reasons described later,
limited liability and government insured bank debt gives banks an incentive
to take risk. They find that capital requirements are much more effective at
controlling risk taking if they are augmented with securities like warrants or
convertible debt. As in Green (1984), these latter instruments control risk
taking because they lower the net return to a bank when it performs extremely
The present article’s focus on controlling risk taking is particularly relevant
to banking. The most striking example of a failure to control risk-taking
incentives is the savings and loan crisis of the 1980s. The standard story told
about this event is that the inflation of the 1970s lowered the value of the
savings and loans’ fixed rate mortgages to the point that many had a negative
net worth. Because of this negative net worth, the savings and loans had
nothing to lose by taking on lots of risk. The deregulation of the early 1980s
gave the savings and loans the opportunity to take on the risk, and many
failures throughout the 1980s resulted.3
There is additional evidence of excessive risk taking. Boyd and Gertler
(1994) argue that large banks, who had stronger deposit insurance protection
due to the “too big to fail” doctrine, took more risk than smaller banks during
the late 1980s, which was a period of widespread banking problems. Other
studies have found a connection between low capital levels and bank risk.
The survey in Berger, Herring, and Szego (1995) lists studies that imply that a
higher capital ratio is associated with lower bank risk, though this relationship
is sometimes weak. On a related point, several researchers have found that
franchise value is negatively correlated with risk. Franchise value is the value
of continued operations by the bank and can represent organizational capital
or the present value of future lending opportunities. Failure of the bank would
mean a loss of its franchise value, which implies that high-franchise-value

2 For a survey on non-tax-driven theories of capital structure, see Harris and Raviv (1992).
3 Another important part of this story is why so few banks failed from World War II until

the early 1980s. Keeley (1990) argues that in this period, banking was heavily regulated with
numerous protections that reduced competition. These protections included restricted entry by limiting charters and branching, and limited price competition by interest rates controls. Because of
these protections, banks received a flow of monopoly profits that would be lost if the bank went
bankrupt. For this reason, banks behaved prudently.

E. S. Prescott: Regulating Bank Capital Structure


banks would behave more prudently than low-franchise-value banks. Evidence that in the 1990s U.S. banks with low franchise value took more risk
than those with high franchise value is contained in Demsetz, Saidenberg, and
Strahan (1996). In an international sample of banks, De Nicolo (2000) finds
that franchise value decreases and risk increases with bank size.

This section analyzes bank capital regulation when a bank is restricted to
issuing only debt and equity. This simple environment is useful for reviewing
corporate finance theory and for discussing bank regulation. It will also be
valuable in assessing the gain from introducing instruments like warrants into
bank capital regulation, as is done in Section 2.
A bank’s financing problem is considered under three different sets of
assumptions. The first set illustrates the Modigliani-Miller Theorem. The
second set of assumptions is based on the agency cost theory of Jensen and
Meckling (1976). The present article, however, restricts its focus to the agency
cost of debt; agency costs of equity are ignored because the focus on debt costs
is all that is needed to illustrate the risk-control properties of warrants and
convertible debt.4 The final set of assumptions adds deposit insurance to the
agency cost story; this set illustrates how deposit insurance creates additional
risk-taking incentives and how it shuts down the market’s incentive to control
the bank’s risk taking. Recent subordinated debt proposals are discussed.
Consider a bank with an investment project that requires exactly one dollar
of investment. The risk-neutral owner or manager of the bank also has one
dollar of funds that he or she can either invest outside the bank at the risk-free
rate of zero or hold as equity in the bank.5 Any investment not funded by equity
must be funded by debt that is raised from the market. For the purposes of this
article, the terms debt and deposits will be used interchangeably. Because of
limited liability, debtholders cannot be repaid out of the returns to the banker’s
market investments. Instead, if the face value of the debt cannot be repaid out
of the bank’s investment project, then the bank is liquidated and whatever is
left is used to pay the debtholders. Finally, since the exogenous risk-free rate
is zero, debtors must receive an expected gross return of 1.0 on their debt.
After raising the investment funds, the bank chooses one of two investment
strategies. It can choose a high-mean, low-risk strategy or a low-mean, highrisk one. The high-mean strategy has a one-half probability of paying 0.5
4 Marshall and Prescott (2001) contains additional features that generate an agency cost for

5 The treatment of equity owners and managers as the same entity is common in the corporate
finance literature. This assumption, however, is not without consequences. Even so, the analysis
in this article should still apply to managerial pay.


Federal Reserve Bank of Richmond Economic Quarterly

and a one-half probability of paying 1.5. In expectation this strategy pays
1.0, which is the risk-free gross return. The low-mean strategy has a one-half
probability of paying 0.25 and a one-half probability of paying 1.6. It pays
0.925 in expectation. The high-mean strategy is the socially desirable option.6

The Modigliani-Miller Theorem
For the first set of assumptions, the bank can commit to the investment strategy
that it will take. Let D be the amount of debt raised and let F be the face
value of the debt, or the amount the bank repays if it has the available funds.
Also, let I be the amount of funds invested in the market by the banker. Of
course, for each dollar of own funds invested in the market, the banker has to
raise one dollar in debt; therefore, D = I in this environment.
If the bank commits to the safe, high-mean investment strategy, then for
debt D ≤ 0.5 the bank always has enough funds to pay back debtholders. In
this case, F = D and the banker’s expected payoff is
0.5(0.5 − D) + 0.5(1.5 − D) + I = 1.


For debt in the range 0.5 < D ≤ 1.0, the bank cannot fully pay back the
depositors if it produces the low return. To compensate for this loss, the face
value of debt needs to reflect a risk premium. The risk premium depends on
the amount of debt issued. In particular, the face value of debt must satisfy
(0.5)(0.5) + (0.5)F = D, which implies that F = 2D − 0.5. Therefore, if the
bank’s investment project is entirely financed with debt, that is, if D = 1.0,
then the face value of the debt would be 1.5. If the bank fails the debtholders
receive 0.5, and if it succeeds they receive 1.5, which in expectation is 1.0, the
risk-free rate.
For 0.5 < D ≤ 1.0, the bank’s expected payoff is
0.5(0.0) + 0.5(1.5 − 2D + 0.5) + I = 1,


which is the same level as if it issued debt such that it never defaulted.
Similar calculations for the risky investment strategy reveal that the bank’s
expected payoff of committing to that strategy is also independent of the debt
and equity structure, though the bank’s expected payoff is at the lower value
of 0.925. The value of the firm depends only on its investment decision, and
its capital structure has no effect on its investment decision. This invariance of
the value of the firm to its financing decision is an example of the ModiglianiMiller theorem (Modigliani and Miller 1958).
6 Implicit in the analysis is the assumption that the bank must make an investment decision;
that is, it cannot simply invest its funds in the market and not operate. This assumption prevents
the trivial regulatory solution of shutting the bank down, and it is only necessary because the
bank’s return under the high-mean strategy is the same as that of the market and this is a linear
partial equilibrium model. In a general equilibrium model with some diminishing returns, the
expected returns would be equal in equilibrium and the banking sector would still operate.

E. S. Prescott: Regulating Bank Capital Structure


Jensen and Meckling
For the second set of assumptions, I assume that a bank’s investment decision
is private information, that is, known only to the bank. Jensen and Meckling
(1976) use this assumption to establish a connection between the investment
and financing decisions of a bank.7 Under private information, a bank cannot
commit to its investment strategy. Instead, given its capital structure, an
investment strategy must be in the best interest of the bank, that is, incentive
compatible. Of course, the market anticipates the bank’s inability to commit
and the price of debt will reflect whichever strategy the bank is expected to
choose given its debt structure.
There are three distinct ranges of debt to analyze. If D ≤ 0.25, then the
bank can always honor its obligations no matter which investment strategy it
chooses. For this case, the analysis is the same as that in the Modigliani-Miller
case. The face value of debt is F = D. The bank owner receives a payoff
of 1.0 by taking the high-mean strategy and 0.925 by taking the low-mean
strategy, so he or she takes the safe strategy.
For the second debt range, of 0.25 < D ≤ 0.5, there is no failure if the
bank takes the safe, high-mean strategy. In this case F = D and the bank’s
return is 1.0 as before; however, because of the private information assumption,
it must now be verified that this strategy is incentive compatible. We therefore
need to calculate the bank’s expected payoff from issuing this debt contract
and taking the low-mean, risky investment strategy. If this number is less than
or equal to 1.0, then the safe strategy is incentive compatible; if it is greater
than 1.0, then it is not. In this case, the market will recognize that under
this debt structure the bank takes the risky strategy and it will price the debt
When the market thinks the bank is taking the safe strategy but it is really
taking the risky strategy, the bank’s return is
0.5(0) + 0.5(1.6 − F ) + I = 0.8 − 0.5F + I = 0.8 + 0.5D.


For D ≤ 0.4, the value of equation (3) is less than or equal to 1.0 (what the
bank receives from taking the safe strategy), so the safe strategy is incentive
compatible. Above 0.4, however, the value of equation (3) is greater than 1.0,
so at these debt levels the safe strategy is not incentive compatible.
Figure 1 illustrates the risk-taking incentives created by limited liability.
The solid line is the bank’s payoff as a function of the return given that the
bank has raised D = 0.50 and that the market assumes that the bank is taking
the safe strategy, that is, F = D. The payoff function is piecewise linear and
convex because of limited liability. This convex shape generates a taste for
risk on the part of the bank. If the bank takes the safe strategy, its payoffs range
7 Jensen and Meckling’s (1976) analysis applies to all firms, not just to banks.


Federal Reserve Bank of Richmond Economic Quarterly

Figure 1 Risk-Taking Incentives Created by High Levels of Debt

The solid line is the bank’s payoff as a function of the return given that D = 0.5. It is
horizontal over the range 0.0 to 0.5 because of limited liability. Above 0.5, the slope of
the line is 1.0 because once the debt is repaid all returns above 0.5 accrue to the bank.
The dashed line connects the two possible returns (0.25 and 1.6) if the risky investment
is taken. The first coordinate of x (0.925) is the expected return if the risky strategy is
taken. The second coordinate of x (1.05) is the bank’s expected payoff. The first and
second coordinates of * are the corresponding values if the bank takes the safe strategy.

over a linear portion of the returns (over 0.5 and 1.5) and the bank’s expected
payoff is 1.0, just like that of the investment project. In contrast, if the bank
takes the risky strategy, it gains from the convexity. Consider the dashed line
in Figure 1, which connects the payoff from the two returns produced by the
risky strategy (0.25 and 1.6). Because of limited liability, a return of 0.25
gives the bank a payoff of 0.5 (the return on its market investment). The
convex payoff function rewards a bank on the upside without punishing it
on the downside, and this payoff structure is reflected in its higher expected
payoff of 1.05, despite producing a socially inefficient investment return of
only 0.925, as indicated by the x in Figure 1.
Of course, for 0.4 < D ≤ 0.5, the market realizes that the safe strategy
is not incentive compatible, and it prices the bank’s debt as if it has taken the
risky strategy. Thus, if the bank takes the risky strategy, the face value of the
debt is F = 2D − 0.25 and the bank’s expected payoff is 0.925.

E. S. Prescott: Regulating Bank Capital Structure


The final range of debt levels is D > 0.5. For this range, there is a chance
of default even if the safe strategy is taken. This changes the formula for
the face value of the debt, but the high-mean strategy is still not incentive
compatible for the same reasons described earlier in relation to the second
range of debt levels. Consequently, the bank will choose the risky strategy so
the face value of debt is F = 2D − 0.25 and the bank’s expected payoff is

Market Responses

Given these expected payoffs, the bank will choose a capital structure with
D ≤ 0.4 and then take the safe, high-mean strategy. The value of the firm
is 1.0, the expected payoff of the safe, high-mean strategy. For higher levels
of debt, the market realizes that the bank cannot commit to the safe strategy.
Consequently, it prices the debt as if it were taking the risky strategy. The
value of the bank for these debt levels is 0.925, the expected payoff of the
risky, low-mean strategy. In the world of Jensen and Meckling (1976), the
value of a firm is not invariant to its capital structure.
Debt prices are not the only area in which a market may respond to capital
structure. For example, debt contracts often include covenants that restrict
borrower activities or trigger call options. The market also may decide to
spend resources monitoring the borrower. All of these activities can be viewed
as costly methods for reducing the adverse effects of private information. In
the present article, with no costs to equity these unmodeled additional features
are not needed, but in more general environments they very well may be. I
will return to this issue below in the discussion of bank regulation.

Deposit Insurance
The final set of assumptions I consider is the addition of deposit insurance to
the agency theory of Jensen and Meckling (1976). In practice, deposits (up
to a limit) are the only debt explicitly insured. But bailouts may implicitly
insure other types of bank debt. To keep the analysis simple, I assume that
all bank debt is insured in one way or another. Insurance in this context
means that if the bank does not have enough funds to pay back debtholders,
the government insurer will make them whole. More specifically, insurance
means that debtholders always receive a payment of D, so the face value
of the debt is F = D. I also assume that the government provides deposit
insurance for free. This assumption is a reasonable approximation of present
FDIC policies. My analysis in this section is quite similar to that done under
the second set of assumptions, which had no deposit insurance, but now the
government insurance also leads to transfers to the bank via underpriced debt.


Federal Reserve Bank of Richmond Economic Quarterly

For D ≤ 0.25 the bank can always pay back debtholders, so there is no
incentive problem and the analysis is the same as under the first two sets of
assumptions. The bank’s expected payoff is 1.0 if it takes the safe strategy
and 0.925 if it takes the risky strategy. Consequently, it will choose the safe
For 0.25 < D ≤ 0.5 most of the analysis is the same as that under the
previous set of assumptions. At or below 0.4, the safe investment is incentive
compatible and since F < 0.5, there is no default; that is, F = D. For
D > 0.4, the safe investment is no longer incentive compatible, so the bank
takes the risky investment, just as it did without deposit insurance. What
changes, however, is the face value of the debt and the bank’s expected payoff.
Deposit insurance always makes debtors whole, so there is no longer a need
for a risk premium. Consequently, F = D and the bank’s expected payoff
increases because it has to pay out less when it does well. For D > 0.4, the
bank’s expected payoff is
0.5(0.0) + 0.5(1.6 − F ) + I = 0.8 + 0.5D.


Figure 2 describes the bank’s expected payoff as a function of its investment strategy and debt level. The higher expected payoff level indicates which
investment strategy is incentive compatible at a particular level of debt. For
debt levels below 0.4, the bank chooses the safe investment, but for debt levels
above 0.4, it chooses the risky investment. The bank’s choice of investment
strategies is identical to the previous case without deposit insurance. However, as can be seen in Figure 2, the bank’s expected payoff exceeds 1.0 for
debt levels exceeding 0.4 and it increases with leverage. The value of the
bank increases with leverage because expected transfers from the government
increase. These expected transfers are considered by the market as part of the
return generated by investment in the bank’s debt. These additional transfers
are sometimes referred to as the value of the deposit insurance put option
(Merton 1977). A put option is the right to sell something at a fixed price. In
this case, the bank has the right to sell its losses at a strike price of zero to
the deposit insurance fund. Because the bank is able to dump its losses on
the insurance fund, the value of its investments increases and, in this example,
this increase accrues entirely to the banker.
In contrast with the second set of assumptions, risk is not reflected in the
face value of bank debt, which shuts down the market’s desire to control risk.
The problem is so severe in this example (i.e., with deposit insurance) that
without any restriction on its capital structure, the bank would choose D = 1
and the risky investment strategy. In this example, the loss in output is the
only social cost from deposit insurance. There are, however, additional unmodeled costs of deposit insurance. For example, deposit insurance payments
could require some potentially distorting taxes, while the high returns would
encourage too much entry into banking.

E. S. Prescott: Regulating Bank Capital Structure


Figure 2 Bank’s Expected Payoff as a Function of Debt under Deposit

The solid line lists the bank’s expected payoff as a function of the debt level and given
that it takes the safe investment strategy. The dashed line corresponds to the risky investment strategy. Both lines are horizontal over lower levels of debt. In these ranges there
is no default and the bank’s expected payoff depends only on the return to its investment.
This is not true at higher levels of debt because of deposit insurance. The price of debt
does not reflect the true risk of the bank’s investment. Instead, debt is priced as if it
is risk free because the deposit insurer makes debtors whole by transferring resources to
them in the case of failure. These expected transfers increase with the size of the debt.
Furthermore, from the perspective of the bank and its investors, these transfers are simply
additional returns generated by the bank’s investment strategy. Consequently, the bank’s
expected payoff increases in leverage.

Bank Regulation

Without deposit insurance, the market prices debt to accurately reflect risk
and monitors or imposes debt covenants to control risk. These measures align
the bank’s interests with those of society. With deposit insurance, however,
the market has no reason to properly price the risk, to impose limitations on
bank capital structure, or to place restrictive covenants in debt contracts, so
the bank’s interests are not aligned with society’s.
Much of safety and soundness regulation can be viewed as an attempt
by the government to replicate what the market would do in the absence
of government deposit insurance. Capital requirements are the most striking


Federal Reserve Bank of Richmond Economic Quarterly

example of this. In the numerical example, a capital requirement of 60 percent
would eliminate any risk-taking incentives and generate the social optimum.
It would also prevent banks from maximizing their leverage in order to exploit
the deposit insurance put option. FDICIA seems to acknowledge the dangers
of high leverage when it allows regulators to shut down or limit the activities
of undercapitalized banks.
The parallels between market measures and governmental regulations extend to other regulations as well. For example, the activities in which banks
may engage are limited. There are prohibitions on the amount of lending a
bank can do to a single entity. Examiners audit and assess bank practices.
Recent proposals that require banks to issue subordinated debt can be
viewed as an attempt to return some of the monitoring role to markets. Unfortunately, much of the discussion about the merits of these proposals focuses
on the signal about risk revealed by prices, as in the example. But as was
discussed in the section about market responses, debtholders not only price
risk but may require covenants or changes such as increased transparency
of investment. For an excellent discussion of the parallels between market
measures and bank regulation, see Black, Miller, and Posner (1978).



The analysis in Section 1 limited the available financial instruments to debt
and equity (the latter is really the banker’s own funds). This limitation illustrated the corporate finance principles at work and demonstrated how capital
requirements can work. For some purposes, restricting the analysis to debt
and equity is not limiting. For example, in a Modigliani and Miller world, the
invariance of firm value to capital structure still holds for more general capital
structures. In the Jensen and Meckling world, however, additional financial
instruments can be quite effective at controlling risk, and by extension, these
same financial instruments can be effective regulatory tools.
Section 2 builds on the previous analysis by adding a richer return structure, which brings us a step closer to the full model in Marshall and Prescott
(2001). The new example is first studied in the case in which the bank regulatory capital requirements can only take the form of minimum equity requirements, as under present regulations. Next, the example is studied in the case
in which capital requirements can restrict the entire capital structure; that is,
regulations can require issue of securities other than debt and equity. As will
be shown, much more debt can be issued in the latter case.
As before, there is deposit insurance and the bank can choose a high-mean,
safe investment strategy or a low-mean, risky one.8 Now, however, a multitude
8 The example posits a reverse mean-variance tradeoff in investment returns. Marshall and
Prescott (2001) study a more general set of possible investment strategies where the bank chooses

E. S. Prescott: Regulating Bank Capital Structure


Figure 3 Probability Distribution of Returns

The two lines list the probability distribution of returns for each investment strategy. Both
distributions are approximately normal, though truncated from above and below. The safe
investment strategy has a mean of 1.0 and a low variance. The risky investment strategy
has a mean of 0.95 and a higher variance. If the risky strategy is taken, the return is
much more likely to be very low or high than if the safe strategy is taken.

of returns can be generated. Figure 3 shows the probability distribution of
the returns for each investment strategy. The solid line is the return for the
risky strategy and the dashed line is the return for the safe strategy. The
mean of the risky strategy is 0.95 while the mean of the safe strategy is 1.0.
Both distributions are approximately normal but with differing means and
The other difference from the previous section is that the bank is allowed
to lower its return without cost if it so desires. This assumption is reasonable
both the mean and variance of its investment strategy. In that setup, the incentive constraint that
matters the most is the one where the agent deviates to the high-risk, low-mean strategy. The
formulation adopted herein is designed to capture this feature.
9 The distributions were generated in the following way. The set of returns was divided into
an equally spaced grid of 21 points over the range 0.6 to 1.4. The risky investment strategy
probability distribution was created by evaluating each return with a normal distribution of mean
0.95 and standard deviation 0.3. These numbers were then normalized to sum to one in order
to generate a probability distribution. The safe investment strategy was created in the same way
except that the mean is 1.0 and the standard deviation is 0.2.


Federal Reserve Bank of Richmond Economic Quarterly

because it is easy enough to raise costs in order to lower profits. It is also
appealing to make the assumption because it guarantees that the net payoff to
the bank is monotonically increasing in its return, otherwise, the bank would
destroy returns to a point where its net return was highest.10
For each case, we find the regulatory policy that is best from society’s
perspective. Because the example leaves out any costs of equity finance, an
all equity financed firm would face no incentive problem and would receive
no transfers in expectation from the deposit insurer. To avoid this result, I
use as society’s criterion the maximum amount of debt the bank could raise
while keeping the high-mean, safe investment strategy incentive compatible.
This social objective function is sufficient for the purpose of illustrating the
risk-control features of warrants and subordinated debt. Marshall and Prescott
(2001) contains additional features such as liquidity services from bank deposits and franchise value that lead to additional factors in determining optimal
capital regulation.
The most debt that can be supported in the minimal equity requirement
case is D = 0.94 with equity equal to 0.06. The bank provides 0.06 of its own
funds to satisfy the capital requirement and raises the rest in deposits. This
quantity is the most highly leveraged capital structure that the bank can have
while still providing an incentive for it to take the safe, high-mean investment.
The expected payoff of the bank is 1.0466, which is greater than 1.0 because
in expectation some transfers are made to the bank from the deposit insurance
fund when the bank fails. Under the assumptions in this example, these extra
funds accrue to the bank’s owner as additional expected profits.
Under more general capital requirements, much more debt can be supported while keeping the high-mean strategy incentive compatible. The solution to the general capital structure problem contains much more debt. In this
example, the bank can fund its investment entirely with debt, that is, D = 1.0.
The bank’s expected payoff is 1.0729, reflecting the increased transfers from
the government.11 Despite the high leverage, the safe investment is incentive
compatible because of the way payoffs to the bank are structured.
Figure 4 reports the payoff to the bank as a function of the return for both
the minimal equity requirement problem and the general capital regulation
problem. The dashed line lists the payoff for the pure debt and equity case.
It is horizontal at a level of 0.94 from 0.6 to 0.94. For this range of returns,
the bank’s entire payoff comes from its own funds that it invested with the
market at the risk-free rate. Everything produced by the investment project
goes to debtholders. Above 0.94, the investment project begins to pay off for
10 This assumption has no effect on the pure debt and equity case because equity is intrinsically monotonically increasing.
11 Since there is nothing that resembles equity when D = 1.0, the return to the bank should
be viewed as payments to the banker for supplying investment services.

E. S. Prescott: Regulating Bank Capital Structure


Figure 4 Bank’s Payoff as a Function of the Return

The dashed line lists the payoff to the bank if a minimal equity requirement of 0.06 is
imposed on it. For returns above 0.94, the bank’s payoff increases because it has paid off
its debt and keeps the remainder. The solid line lists the payoffs to the bank generated
by the best set of general capital requirements that can be imposed. Under these capital
requirements, the bank issues 1.0 units of debt but cannot keep returns in excess of 1.26.
These returns must be paid to outside investors. By limiting the payoff from high returns,
this payoff structure makes the high-variance investment strategy unappealing.

the bank. All additional returns accrue to the equity holders (the banker) so
their payoff is linear in the return with a slope of one. This payoff structure
is convex, but the 6 percent capital requirement is enough to prevent the bank
from taking the risky investment. However, if the bank issued more debt the
payoff structure would shift to the right, making the payoff structure even
more convex and making the safe strategy no longer incentive compatible.
The solid line lists the payoff structure to the bank that general capital
regulations should try to duplicate. At this point, I only discuss the payoffs,
but later I describe how specific financial instruments can be used to generate
this payoff structure. Over the range of 0.6 to 1.26, the payoff for the general
capital structure case has a similar shape to that of the pure debt and equity
case. Above this range, however, the bank’s payoff is horizontal in the return.
This feature reduces the range of returns over which the bank’s payoff is
convex, which helps to control risk taking. Furthermore, an examination of


Federal Reserve Bank of Richmond Economic Quarterly

Figure 3 reveals that low and high returns are much more likely under the risky
strategy than under the safe strategy. The ratio of the probability of a given
return under the risky strategy to the probability of that return under the safe
strategy is called the likelihood ratio for that return.12 The goal of the capital
structure is to keep payoffs to the bank low when the ratio is high, and to keep
it high when the ratio is low. This payoff structure rewards the safe strategy
relatively more than it rewards the risky strategy if the bank indeed followed
that strategy.
The role of likelihood ratios can be seen more formally. For simplicity,
assume there is a finite number of returns. Let ps (R) be the probability
of return R if the safe investment strategy is chosen, and let pr (R) be the
corresponding probability if the risky investment is chosen. Also, let u(R) be
what the bank receives, net of payments to all security holders. The incentive
constraint is
ps (R)u(R) ≥

pr (R)u(R).

This constraint says that the expected payoff the bank receives from the safe
strategy must be at least as much as it would receive if it took the risky strategy.
If ps (R) is low and pr (R) is high, then it is desirable to set a low u(R).
Conversely, if ps (R) is high and pr (R) is low, then it is desirable to set a high
In this example, the likelihood ratio is at its highest level for low returns.
The regulator would like to prevent the bank from taking the risky investment by lowering the bank’s payoff for these returns as much as possible.
Because of limited liability, however, these payoffs cannot be lowered below
zero. (Recall that the bank still receives payments from its risk-free investment. This accounts for its positive payoff.) At high returns, this ratio is also
high, but limited liability does not bind so payoffs to the bank are lowered.
Interestingly, it would be desirable to lower payoffs in these returns to zero,
but because of the monotonicity requirement (from the costless destruction of
returns assumption) there are limits to which these returns can be lowered.13

A Capital Structure That Replicates the Payoffs
Figure 4 describes the optimal payoff structure. But can this structure be replicated with a combination of financial instruments that regulators can require
banks to hold? The answer is yes. One way to do this is for the bank to issue
warrants with a strike price of 1.26. A warrant is an option that gives the
12 See Hart and Holmstrom (1987) for more analysis of likelihood ratios in moral hazard
13 For more details see Marshall and Prescott (2001), who compare solutions with and without
the monotonicity constraint.

E. S. Prescott: Regulating Bank Capital Structure


owner the right to buy shares at the strike price. If the bank produces a return
of more than 1.26, a warrant holder collects the difference between the return
and the strike price by exercising his or her warrant, and the bank receives
just 1.26. This accounts for the flat payoff to the bank for returns above 1.26.
But, more generally, if the exercised warrants make up only a fraction of the
equity, then the bank’s payoffs for returns above 1.26 will increase (though at
a slope less than one).
Selling a warrant is equivalent to selling a portion of the bank’s return
above the strike price; the exact portion depends on the relative share of warrants and existing equity. In this example, selling the warrant is valuable
because it allows the bank to be more highly leveraged than in the pure equity case, while keeping the safe, high-mean strategy incentive compatible.
Furthermore, because the bank can finance its entire investment with debt,
the income received from selling the warrants is reinvested at the market rate
along with the banker’s own 1.0 units of funds. For this reason, the bank’s
payoff slightly exceeds 1.0 for the range of returns between 0.6 and 1.0.
The analysis contains a clear message about capital regulation. Capital
requirements that control risk by lowering the upper-tail payoff to banks can
improve upon the existing capital regulations. Warrants with a high strike
price are not the only financial instruments that can do this. For example,
convertible debt is debt that can be converted into equity at some agreed-upon
price. For a high enough strike price, convertible debt could substitute for
warrants. Alternatively, equity swaps might be possible.
Some Caveats

In assessing different financial instruments, it may be important to consider
additional features of financial instruments like control features or ability to
trade. If the banker sold warrants at a strike price of 1.26, he or she would
be turning the bank over to the warrant holders whenever the warrants were
exercised. Managers rarely want to give up control. The static analysis in
this article is inappropriate for an analysis of control; however, if control
was indeed an issue, then other financial instruments like swaps that separate
control from cash flow might be valuable.
Another point is that in this analysis, it matters who holds the warrants.
In the example, there is an anonymous market that purchases them, but if the
banker bought them, it would undo his or her incentives since his or her payoff
structure would then look convex again. In practice it would be necessary to
ensure that owners of the warrants are not the same people who own the equity
of the firm.


Federal Reserve Bank of Richmond Economic Quarterly

This article argues that financial instruments, such as warrants or convertible
debt, should be considered as part of capital regulations. They are effective at
controlling risk-taking incentives because they lower the payoff to a bank that
engages in risky activities without adversely affecting a bank engaged in safe
activities. Furthermore, at least in the example in Section 2, imposing these
requirements would allow a reduction in the traditional capital requirement of
an equity minimum.
While the example necessarily leaves things out, the analysis in Marshall
and Prescott (2001) includes several additional features and still finds that financial instruments like warrants and convertible debt are potentially valuable
regulatory tools. They include franchise value and disutility to managers from
screening the quality of its loans. These two features give equity some value
in their environment. They also include a utility value of deposits, which is
designed to capture the payment and liquidity services that deposits provide
but other kinds of debt do not. Furthermore, they allow banks to choose from
a richer set of investment strategies. Banks are allowed to choose the variance
and by screening, the mean, of its investment portfolio.
They find that the most binding incentive constraint is the one on the bank
taking the low-mean, high-variance investment. The regulator sets its capital
requirements mainly to prevent the bank from taking this investment strategy.
This reverse mean-variance tradeoff is the justification for the simple two
distribution choice faced by banks in this article. For low franchise values,
they find results qualitatively very similar to those in this article. Equity
minimums are higher under standard capital requirements than under a capital
requirement that also uses instruments like warrants with a high strike price.
For higher franchise values, they find that capital requirements are not that
important and that the banks will choose high levels of capital, in order to
reduce the chance of bankruptcy.
One important feature that Marshall and Prescott (2001) do not study is
that warrants and convertible debt may punish banks whose high returns are
generated by innovation or just simply better management. The investment
choices in their paper, as well as in this article, do not capture this phenomenon.
Future research should be concerned with determining the efficacy of payoff
structures for these kinds of situations.

E. S. Prescott: Regulating Bank Capital Structure


Berger, Allen N. “The Relationship between Capital and Earnings in
Banking,” Journal of Money, Credit, and Banking, vol. 27 (May 1995),
pp. 432–56.
, R. J. Herring, and G. P. Szego. “The Role of Capital in
Financial Institutions,” Journal of Banking and Finance, vol. 19 (June
1995), pp. 393–430.
Black, Fisher, Merton H. Miller, and Richard A. Posner. “An Approach to the
Regulation of Bank Holding Companies,” Journal of Business, vol. 51
(July 1978), pp. 379–412.
Demsetz, R. S., M. R. Saidenberg, and P. E. Strahan. “Banks with Something
to Lose: The Disciplinary Role of Franchise Value,” Federal Reserve
Bank of New York Economic Policy Review, vol. 2 (October 1996),
pp. 1–14.
De Nicolo, Gianni. “Size, Charter Value and Risk in Banking: An
International Perspective,” International Financial Discussion Paper 689.
Board of Governors of the Federal Reserve System, December 2000.
Green, Richard C. “Investment Incentives, Debt, and Warrants,” Journal of
Financial Economics, vol. 13 (March 1984), pp. 115–36.
Harris, Milton, and Artur Raviv. “Financial Contracting Theory,” in
Jean-Jacques Laffont, ed., Advances in Economic Theory: Sixth World
Congress. Cambridge: Cambridge University Press, 1992, pp. 64–150.
Hart, Oliver D., and Bengt Holmstrom. “The Theory of Contracts,” in
Truman F. Bewley, ed., Advances in Economic Theory: Fifth World
Congress. Cambridge: Cambridge University Press, 1987, pp. 71–155.
Kareken, John H., and Neil Wallace. “Deposit Insurance and Bank
Regulation: A Partial-Equilibrium Exposition,” Journal of Business,
vol. 51 (July 1978), pp. 413–38.
Keeley, M. C. “Deposit Insurance, Risk, and Market Power in Banking,”
American Economic Review, vol. 80 (December 1990), pp. 1183–200.
Marshall, David A., and Edward S. Prescott. “Bank Capital Regulation With
and Without State-Contingent Penalties,” Carnegie-Rochester
Conference on Public Policy, 2001 (forthcoming).
Merton, Robert C. “An Analytic Derivation of the Cost of Deposit Insurance
Guarantees,” Journal of Banking and Finance, vol. 1 (1977), pp. 3–11.


Federal Reserve Bank of Richmond Economic Quarterly

Modigliani, Franco, and Merton H. Miller. “The Cost of Capital, Corporate
Finance, and the Theory of Investment,” American Economic Review,
vol. 48 (June 1958), pp. 261–97.

Consumption, Savings, and
the Meaning of the Wealth
Effect in General
Carl D. Lantz and Pierre-Daniel G. Sarte


ver the latter half of the 1990s, the U.S. economy experienced both
a substantial decrease in the savings rate and a significant run-up
in household net worth. Between 1994 and 2000, the gross private
savings rate fell from 17 to 12 percent, while the personal savings rate declined
from above 6 percent to less than zero. Over the same period, the value
of household sector equity holdings (including those owned by nonprofits,
pensions, and other fiduciaries) increased nearly 150 percent for a dollar gain
in excess of $6 trillion.
At some level, the decline in savings and the rise in household equity value
during that period appeared to point towards a strengthening of the economy.
According to the Permanent Income Hypothesis (PIH), households save less
in a given period if they expect future increases in their income. Along these
lines, the dramatic gain in stock market wealth was thought to partly reflect
future opportunities made available to firms by rapid advances in information
technology. Both the fall in savings and the rise in net wealth seemed consistent
with the rapid growth of consumption during that period.
Despite the rosy outlook implied by the PIH at the close of the decade, the
U.S. economy slowed down considerably in 2000. Specifically, the growth
rate of per capita consumption fell to 2 percent in the first quarter of 2001 from
nearly 7 percent in the same quarter of the previous year. Between the first
quarter of 2000 and that of 2001, household net worth fell by 8 percent, or
The views expressed in this article are the authors’ and do not necessarily represent those
of the Federal Reserve Bank of Richmond or the Federal Reserve System. We wish to thank
Michael Dotsey, Margarida Duarte, Thomas Humphrey, and Yash Mehra for helpful suggestions. All errors are our own.

Federal Reserve Bank of Richmond Economic Quarterly Volume 87/3 Summer 2001



Federal Reserve Bank of Richmond Economic Quarterly

$3.5 trillion. In light of these developments, it seems only natural to question
the significance of the data in the late 1990s. With this question in mind, this
article seeks to emphasize the following points.
First, the PIH notwithstanding, a fall in savings today may not necessarily
reflect expected future gains in income, but rather the current realization of a
negative economic shock. Within the context of a simple neoclassical growth
model with investment adjustment costs, we show that an unanticipated permanent fall in productivity leads to a contemporaneous fall in both consumption
and savings. The fall in savings continues several periods into the future and a
lower steady-state level of savings ultimately emerges. It remains true, in this
model, that a fully anticipated increase in future productivity also leads to a
contemporaneous fall in savings as households seek to smooth consumption.
In the latter case, however, the savings rate eventually reaches a higher steady
state level as the shock is realized.
Second, it is important to recognize that discussions of the wealth effect,
such as those in Ludvigson and Steindel (1999) or Mehra (2001), are often
carried out in a partial equilibrium setting. In such a setting, both the rate of interest and the level of wealth are exogenous with respect to contemporaneous
consumption (i.e., wealth is a state variable). In contrast, general equilibrium
considerations imply that wealth, the rate of interest, and consumption all
contemporaneously react to the various disturbances affecting the economy.
Thus, an unanticipated permanent increase in productivity leads to a simultaneous rise in both consumption and household net worth. Note, however, that
consumption does not respond directly to wealth. Rather, both variables react
simultaneously to the higher level of productivity. The implication of this dual
reaction is that the measured marginal propensity to consume out of wealth is
unlikely to be constant, as is often assumed. Indeed, empirical studies such as
those in Mehra (2001) and Ludvigson and Steindel (1999) have found that the
magnitude of the wealth effect is dependent on the sample period in question.
This lack of time consistency in the wealth parameter would be expected if
the nature of the shocks impacting the economy was changing over different
sample periods.
In general, it can be misleading to think in terms of households’ marginal
propensity to consume out of wealth. Such thinking presumes that important
movements in wealth exist that are independent of economic fundamentals.
However, the value of corporate equity reflects the present discounted value
of future firm dividends and, in a general equilibrium framework, both the
discount rate and dividends respond to changes in the economic environment.
To make matters concrete, we show that consumption and wealth can move
in opposite directions in some cases. When a future increase in productivity

C. D. Lantz and P.-D. G. Sarte: Consumption, Savings, and Wealth


is fully anticipated, at the time of anticipation consumption rises while the
value of household equity falls. Although households eventually hold more
wealth in the new steady state, the initial fall in equity value reflects higher
future discount rates consistent with the anticipated increase in productivity. A
partial equilibrium framework prohibits this finding from ever arising because
the rate of interest is held fixed.1
In this article, we first present some basic empirical facts regarding consumption, savings, and wealth in U.S. data. We next outline a simple theoretical framework that allows us to simultaneously explore the price of corporate
equity and households’ consumption-savings decisions. Finally, we analyze
the results from several numerical experiments related to both anticipated and
unanticipated shocks to total factor productivity.



Figure 1 shows the behavior of two alternate measures of the U.S. savings
rate over the past 41 years. Panel a of Figure 1 captures the most basic
National Income and Product Accounts (NIPA) measure of savings, Personal
Disposable Income less Personal Consumption Expenditures in 1996 dollars.
The savings rate in panel b is computed using Gross Private Savings which,
in addition to Personal Savings, includes retained earnings by firms. We can
see that both measures of the savings rate fell drastically over the 1990s and,
by early 2001, had reached their lowest recorded levels.
We suggested earlier that a desire to smooth consumption may lead households to save less today if they expect future gains in their income or, alternatively, to save more if they expect future declines in their income. In particular,
Hall (1978) argued that the consumption behavior of a household at a given
date was based on all of that household’s future discounted earnings. Milton
Friedman (1957) was perhaps the first to draw a distinction between changes in
permanent and transitory income. Figure 2 illustrates (normalized) movements
in the savings rate four quarters prior to each of the past five U.S. recessions.
In panel a, we can see that the personal savings rate generally rises during the
year prior to a recession. However, this tendency is not clear-cut. Moreover,
it is much less pronounced for the gross private savings rate in panel b. In
this case, in the four quarters preceding two of five recessions, the savings
rate either falls or remains the same. Figure 3 plots the cross-correlations
between our two measures of the savings rate and output at different leads and
lags. Both the personal savings rate and the gross private savings rate show a
negative correlation with future values of GDP. Hence, there seems to be some
evidence to support the PIH. However, the magnitude of the cross-correlations
1 See Kiley (2000) for a more detailed description of stock price behavior in a production
economy versus a partial equilibrium setting.


Federal Reserve Bank of Richmond Economic Quarterly

Figure 1 Measures of Savings

shown in Figure 3 is relatively low, and it is possible that factors other than
expectations of future changes in income help drive the behavior of the savings

In order to explore some of the issues introduced above, we now describe a
model that can be simultaneously used to price corporate equity and address
household consumption-savings decisions. For simplicity, we abstract from
the inclusion of a noncorporate sector and intangible assets, as well as several
aspects of the U.S. tax system. McGrattan and Prescott (2000), however,
suggest that these considerations are important in calibration exercises meant

C. D. Lantz and P.-D. G. Sarte: Consumption, Savings, and Wealth


Figure 2 Savings Rate and Equity Price Behavior Prior to Various U.S.

to match data from the NIPA and the Statistics of Income (SOI). In particular,
the authors argue that the historical behavior of asset prices and returns can
be largely explained by changes in tax and regulatory policies as well as by
the evolution of the institutions affecting asset markets.
In this model, the economic environment consists of a large number of
identical households and firms. Each firm has access to a constant returns
yt = zt ktα n1−α , 0 < α < 1,


where yt is the firm’s output at a given date t, nt denotes labor input, zt is
a random technological shift parameter, and kt represents the firm’s capital
stock. In this article, we shall think of firms as owning their capital stock
instead of renting it from households. Households will be thought of as owning
claims on firms’ net cash flows, e.g., equity shares.


Federal Reserve Bank of Richmond Economic Quarterly

Figure 3 HP Filtered Cross-Correlations with Output corr[xt , yt+k ]

Barro and Sala-i-Martin (1995) suggest that if the stock of capital includes
a human component, then one will anticipate substantial adjustment costs
in investment. According to the authors, “the learning process takes time,
and attempts to accelerate the training process are likely to encounter rapidly
diminishing rates of return” (p. 119). Hence, we model the evolution of a
firm’s capital stock as
kt+1 = (1 − δ)kt + φ


kt ,


where 0 < δ < 1 is the capital depreciation rate and it represents the firm’s
investment decision at date t. The function φ(·), with φ (·) > 0, captures the
idea of adjustment costs in investment. Thus, the higher the level of investment
relative to the current capital stock, the more costly it becomes to increase next
period’s capital. Observe that the function φ (·) < 0 indexes the degree to
which adding to the capital stock becomes costly.2 In addition, note also that
the book value of capital at date t, kt , reflects investment decisions made at
date t − 1. Therefore, kt cannot respond contemporaneously to changes in the
economic environment. In contrast, if we think of the firm as having a fixed
number of equity shares outstanding, the value of these shares can contemporaneously react to disturbances affecting the economy. Put another way, we
expect both household net worth and consumption to move simultaneously in
response to various shocks.
2 For an early discussion of this formulation of investment adjustment costs, see Abel and
Blanchard (1983).

C. D. Lantz and P.-D. G. Sarte: Consumption, Savings, and Wealth


Firms pay each unit of labor the wage rate wt , and their net cash flow at t
is consequently given by
zt ktα n1−α − it − wt nt .


We assume that this cash flow is paid to households in the form of dividends,
Dt . Each firm attempts to maximize the present discounted value of future
profits. The representative firm’s problem, therefore, can be summarized as


τ −1
i=−1 Qt+i

zt+τ kt+τ n1−α − it+τ − wt+τ nt+τ ,


τ =0

subject to the sequence of constraints given by (2). In (P1), Qt−1 denotes the
price of a security that pays one unit of the consumption good at date t.
The solution to the firm’s problem must satisfy the following first-order
wt = (1 − α)zt ktα n−α ,




λt φ

= 1,

Qt αzt+1 kt+1 n1−α

= λt − Qt λt+1 (1 − δ) + φ






where λt ≥ 0 is the Lagrange multiplier associated with (2). Equation (4)
simply equates the wage rate to the marginal product of labor. Equation (5)
suggests that it is optimal for the firm to invest up to the point where the cost of
one additional unit of investment (in terms of foregone profits) exactly offsets
the marginal gain from increasing next period’s capital stock.
As mentioned earlier, the representative household owns all firms and
receives their profits, Dt , as dividends. At date t, the typical household’s net
worth, At , consists of stock market wealth and bonds. Specifically, we denote
the market value of household equity by Vt Xt , where Vt represents the price
of firms’ outstanding equity shares and Xt is the number of shares held by the
household. Agents also own one-period bonds, Bt , where a bond purchased at
date t pays one unit of the consumption good at time t + 1. The representative
household maximizes its lifetime utility and solves


τ =0

ct+τ − 1
, σ > 0,


subject to the sequence of constraints
ct + Vt Xt+1 + Qt Bt+1 = (Vt + Dt )Xt + Bt + wt nt .



Federal Reserve Bank of Richmond Economic Quarterly

Household income on the right-hand side of equation (7) stems from the ownership of firms, with dividend earnings given by Dt Xt , earnings from bonds,
Bt , and labor income, wt nt . These earnings can be used to purchase consumption goods, new equity shares, and bonds. The first-order conditions
associated with the household problem are
ct−σ = ψ t ,
Qt = β


ψ t+1


Vt = β

ψ t+1

Vt+1 + Dt+1



where ψ t is the multiplier associated with the household budget constraint
(7). Note that equations (9) and (10) can be used together to yield

Vt =

τ −1
i=1 Qt+i Dt+τ .


τ =1

In other words, the price of a firm’s outstanding equity shares reflects the
expected present discounted value of its future dividends. In this model,
therefore, even shocks that affect only future profit opportunities and discount
rates will lead to changes in today’s household wealth.
Observe that the multiplier λt in (5) can be interpreted as the shadow price
of installed capital. In particular, the Appendix shows that equations (6) and
(11) can be used to derive
Vt = λt kt+1 .


Since φ (.) < 0, an increase in investment leads to a rise in λt by equation
(5), as well as a rise in kt+1 . Hence, in thinking about the effects of various
shocks below, we need only keep track of the investment response in order to
understand movements in the value of corporate equity.3
An equilibrium for the economy we have just presented must satisfy firms’
optimality conditions (4) through (6), as well as households’ optimality conditions (8) through (10). In addition, the goods market clearing condition,
ct + it = yt ,


must hold. In equilibrium, we further have that Xt = Xt−1 = 1 for all t and,
since households are identical, bonds are in zero net supply, Bt = 0 for all t.
Equation (13) implies that savings equals investment, st = yt − ct = it .
3 Hayashi (1982) shows that equation (12) always holds when the production technology is
constant returns to scale.

C. D. Lantz and P.-D. G. Sarte: Consumption, Savings, and Wealth


Before investigating the joint response of consumption, savings, and wealth
to different changes in the economic environment, we must first assign values
to the exogenous parameters of our model. Each period represents a quarter,
and we set δ and σ to 0.025 and 2 respectively. These values for δ and σ
are standard in quantitative studies of business cycles. In the steady state,
equations (9) and (11) imply that the price-earnings ratio, V /D, is given by
β/(1−β). Hence, we set β to 0.983 in order to generate a long-run annualized
price-earnings ratio of 14.5.4 We set α to 1/3 which leads to an investment
share in output of 20 percent in the steady state. Finally, we set the parameter
that governs the degree of adjustment costs, φ , to −10. This calibration implies that the elasticity of the investment:capital ratio with respect to Tobin’s
q is approximately 5. Baxter and Crucini (1993) explore a variety of possible calibrations for this elasticity parameter, ranging from 1 to 15, without
substantially altering their results. This remains true in our framework.

On the Significance of the Wealth Effect in General
The solution to the model above implies a law of motion for the vector of state
variables, st+1 as a function of st , where st consists of the capital stock, kt , and
the random technological shift parameter, zt . This solution also links control
variables, such as consumption, ct , and the market capitalization of firms, Vt ,
to the state variables. Therefore, in a linearized form, we have
ct = c0 + ck kt + cz zt


Vt = v0 + vk kt + vz zt ,



where c0 , v0 , . . . are functions of the deep parameters of the model capturing
preferences and technology. Solving for kt in equation (15) and substituting
the resulting expression in (14) yields
ct = (c0 − v0 ) + ( ) Vt + (cz − vz )zt .



This last equation often forms the basis of regression equations that are meant
to uncover the size of the wealth effect, ∂ct /∂Vt = ck /vk = β. Observe that
the only source of random disturbances in equation (16) stems from movements in productivity, zt . Moreover, because changes in equity Vt are necessarily correlated with changes in fundamentals, zt , it will be important to make
4 Until recently, this value has been approximately the average implied by the S&P 500 index
since 1949.


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use of instrumental variables to properly estimate the coefficient β. That being
said, since all movements in both ct and Vt are generated from changes in economic fundamentals, estimates of the marginal propensity to consume out of
wealth are of little use in this environment. More to the point, the expression
∂ct /∂Vt is meaningful only to the degree that there exist significant exogenous
movements in net worth, ∂Vt , that are unrelated to changes in underlying economic conditions. Such movements may reflect, for example, the existence
of stock market bubbles. In our environment, however, changes in consumption and wealth are necessarily linked through movements in productivity and
given by


= cz .

+ cz − vz



We will now explore the behavior of our economy when the underlying source
of uncertainty lies in total factor productivity, zt . We shall examine the effects
of both unanticipated and anticipated changes in productivity, and outline
significant differences in the way the economy reacts to these shocks. To
emphasize these differences, we shall also compute the cross-correlations of
consumption and the savings rate with stock market wealth under both these
parameterizations of productivity shocks.

The Effects of Unanticipated Shocks in Productivity
Figure 4, panel a, depicts an unanticipated and permanent 1 percent fall in
productivity. As a result of this shock, output falls immediately as depicted
in Figure 4, panel d, and continues falling towards a lower steady state value.
Observe that both consumption and savings mimic the output response. Both
variables fall at the time of the shock and eventually reach a lower steady state
level. In this case, therefore, a fall in savings does not indicate better times
ahead, as a naive interpretation of the PIH suggests. Instead, by allowing
households to consume some of their capital, diminished savings behavior
softens the fall in consumption. It remains true, of course, that the economy
is unambiguously worse off in the long run.
In this numerical experiment, the savings rate decreases dramatically on
impact and then rises on its way to the final steady state. This is shown in
Figure 5, panel b. In the new long-run equilibrium, however, the savings rate
is ultimately lower relative to its level in the period prior to the shock. This
example suggests that it may be difficult to identify the source of a given
decline in the savings rate in the data. In particular, we shall see below that
one version of the PIH continues to hold in general equilibrium. That is,

C. D. Lantz and P.-D. G. Sarte: Consumption, Savings, and Wealth


Figure 4

an anticipated increase in future productivity also leads to a decrease in the
savings rate today, followed by a gradually increasing path. In the case of
this anticipated increase, however, the savings rate eventually increases all the
way to a higher steady state level.
Figure 5 also shows that the interest rate, firms’ dividends, and the market
value of equity all decrease when the negative productivity shock is realized.
Given equation (12), the fall in equity is relatively easy to follow. Because
the level of savings falls in response to the shock, firms are forced to cut back
on investment, which directly leads to a decrease in the value of corporate
equity. Note that this decline in equity is consistent with the fall in aggregate
dividends in Figure 5, panel c, but is mitigated by the decrease in interest
rates during the transition to the new steady state. Since the rate of interest
is simply the inverse of Qt in equation (9), the steady fall in consumption
in Figure 4, panel b, indeed implies a decline in interest rates until the new
long-run equilibrium is reached.
Finally, in this example, Figures 4b and 5d show that consumption and
wealth respond to the shock in the same direction. As we have already pointed
out, however, it should be clear that there is no sense in which consumption
responds directly to movements in wealth. Furthermore, the nonlinearity of the
impulse responses implies that the measured marginal propensity to consume
out of wealth will not be constant in this case. This implication is at variance


Federal Reserve Bank of Richmond Economic Quarterly

Figure 5

with studies, such as Davis and Palumbo (2001) and Poterba and Samwick
(1995), that have attempted to measure the additional increase in consumption
stemming from a rise in household equity.

The Effects of Anticipated Changes in Productivity
We now study the model economy’s response to an anticipated permanent
positive shock to total factor productivity. One interpretation of such a shock
may involve the conception of a new technology whose actual implementation
is likely to take time. We shall see that in the short run, there exist similarities in
the way savings respond to an anticipated positive shock and an unanticipated
negative shock. These similarities, while they can make the interpretation of
savings data ambiguous at times, eventually dissipate in the long run.
Figure 6, panel a, depicts a 1 percent positive shock in total factor productivity that takes place four periods in the future. This shock, however, is
fully anticipated by both households and firms in the current period. Because
productivity, and thus output, is expected to increase, household consumption immediately rises in Figure 6, panel b. This response reflects a desire
to smooth consumption that is implicit in the household problem. However,
since the capital stock, kt , is fixed at time zero, output cannot change at the

C. D. Lantz and P.-D. G. Sarte: Consumption, Savings, and Wealth


Figure 6

time of the shock. It must be the case, therefore, that savings initially fall in
a way consistent with the PIH, as shown in Figure 6c.
Observe that because the initial increase in consumption is sustained until
the productivity shock takes place, the level of savings continues to fall in the
short run. Therefore, as households find it optimal to temporarily consume
part of the capital stock, output declines between period 0 and period 4. Once
the positive productivity shock occurs in period 4, consumption, savings, and
output all increase and begin converging towards their new steady state. In
our context, adjustment costs limit the extent to which households wish to
increase consumption initially. To be specific, since firms will find it optimal
to increase investment once the shock occurs, and the marginal product of
capital will consequently rise, it will be important that the capital stock not
be too low at the point of the shock. Recall that the nature of investment
adjustment costs is such that the higher the level of investment relative to the
current capital stock, the more costly it becomes to increase the next period’s


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Figure 7

Figure 7, panel d, shows that the value of corporate equity actually falls
when the productivity shock is anticipated at time zero. This result can be most
easily understood in terms of the fall in savings in Figure 6c and the resulting
decline in investment. More importantly, this finding clearly indicates that
consumption, as shown in Figure 6b, and wealth do not have to move in the
same direction. This result is at odds with many empirical studies in which
consumption always responds positively to wealth within the assumed theoretical framework. On a related note, the impulse responses depicted in Figures 6
and 7 suggest that the data in the late 1990s were not necessarily indicative of
a future strengthening of the economy. As we pointed out in our introduction,
both consumption and wealth rose during that period while savings fell. Our
numerical experiment suggests that an anticipated positive shock to productivity, while leading to a fall in savings and a rise in consumption during the
current period, generates a fall in wealth initially.
Finally, Figure 7, panel a, illustrates a remarkable increase in the interest
rate in the period prior to the realization of the shock. This noticeable increase
is consistent with the jump in consumption that occurs in the next period
when the shock takes place. In particular, the high rate of interest prevents
consumption from rising too dramatically in anticipation of the productivity
increase. Moreover, observe that the interest rate spike is also consistent with

C. D. Lantz and P.-D. G. Sarte: Consumption, Savings, and Wealth


Figure 8 Model-Generated Cross-Correlations with Wealth
corr[xt , Vt+k ]

the initial fall in wealth in Figure 7c. Once the shock has occurred, the high rate
of interest depicted in Figure 7a is no longer part of the present discounted
value calculation with respect to future earnings. As a result, the value of
corporate equity increases markedly.

Implied Cross-Correlations between Consumption,
Savings, and Wealth
Thus far, we have seen that the nature of productivity shocks, whether they are
anticipated or unanticipated, has significant implications for the reactions of


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key economic variables. In particular, we have seen that wealth and consumption do not always have to respond in the same direction to a given productivity
shock. We will emphasize this point below by showing important differences
in the cross-correlation pattern of the data generated under each type of shock.
Figure 8 presents the cross-correlations of consumption and the savings
rate with stock market wealth generated by the model. As in the real-businesscycle literature, we first assume (in Figures 8a and 8b) that the dominant source
of uncertainty lies in productivity shocks, which we calibrate as
ln zt = ρ z ln zt−1 + ε zt ,


where ρ z = 0.95 and εzt is an i.i.d. normal random variable with mean zero and
standard deviation 0.01. The model statistics depicted in Figure 8 are the mean
values calculated from 200 simulations of samples with 216 observations each,
the number of quarterly observations in postwar U.S. data. Figures 8c and 8d
present the same cross-correlations under the assumption that all productivity
shocks are anticipated four periods in advance.
As we can see from the simulations in Figure 8, the cross-correlation patterns of consumption and savings with wealth are quite different depending on
the nature of productivity shocks. When shocks are unanticipated, the contemporaneous correlation between consumption and wealth is very near 1. This
contemporaneous correlation, however, is much lower at 0.25 when productivity shocks are anticipated. Therefore, to the degree that the U.S. economy
is continuously hit by a variety of shocks that are both unanticipated and
anticipated—to technology, preferences, or even public expenditures—and
whose processes may have changed over time, it is unlikely that a regression
of consumption on wealth would uncover a stable coefficient over different
sample periods.
Finally, it is important to recognize that the cross-correlation patterns
depicted in Figure 8 may change significantly with the particular model at
hand. For instance, Constantinides (1990) and Abel (1990) suggest that habit
formation is an important factor in explaining consumption behavior. When
subject to habit formation, consumption reacts to various shocks only with a
lag, and this lag may be essential in helping us understand U.S. consumption
data. In addition, the model we have examined does not allow for the presence
of credit-constrained households. For these households, consumption may be
more tied to current income and wealth than is suggested by permanent income

C. D. Lantz and P.-D. G. Sarte: Consumption, Savings, and Wealth



At the close of the 1990s, the U.S. economy experienced declining savings,
a rise in household equity value, and rapidly growing consumption. At some
level, this data appeared indicative of a strengthening economy going forward.
The Permanent Income Hypothesis (PIH) indeed suggests that savings should
fall in the current period if increases in income are expected in the future
and that the fall in savings would simply reflect households’ desire to smooth
Contrary to this optimistic scenario, the U.S. economy slowed down considerably in 2000. Consequently, it seems natural to reevaluate the significance of the data in the late 1990s. With this task in mind, we have stressed
the following points.
First, the PIH notwithstanding, a fall in savings does not necessarily reflect
the expectation of future gains in income but can instead reflect the current
realization of an unanticipated, negative economic shock. In the case of an
unanticipated decline in productivity, the level of savings continues to fall until
it reaches a lower steady state level. In contrast, in response to an anticipated
positive shock to future productivity, savings eventually rise to a higher steady
state level even if they fall initially.
Second, we have attempted to make clear that consumption and wealth
simultaneously react to fundamental changes in the economic environment. In
a general equilibrium context, there is no sense in which consumption responds
directly and positively to changes in wealth. The latter notion has, in fact, been
the starting point for many empirical studies, but we have shown that when
a future increase in productivity is fully anticipated, consumption and wealth
may initially move in opposite directions. Furthermore, because both the
consumption and wealth responses to productivity disturbances are nonlinear,
the measured marginal propensity to consume out of wealth is unlikely to be
constant. In light of these results, the data on consumption, savings, and wealth
in the late 1990s should not necessarily have been interpreted as presaging a
future strengthening of the economy. Our numerical experiments suggest that
an anticipated rise in productivity, while leading to a fall in savings and an
increase in consumption in the current period, initially generates a short-run
decline in wealth. The last response is at odds with the behavior of wealth at
the end of the last decade.


Federal Reserve Bank of Richmond Economic Quarterly



This appendix describes the derivation of equation (12) in the text. Specifically,
multiplying both sides of equation (6) by kt+1 ≥ 0 yields
λt kt+1 = Qt αyt+1 + Qt λt+1 (1 − δ)kt+1 + φ
−Qt λt+1 φ


it+1 .

In this last expression, (1 − δ)kt+1 + φ (it+1 /kt+1 ) kt+1 is simply kt+2 while
λt+1 φ (it+1 /kt+1 ) = 1 by equation (5). Therefore,
λt kt+1 = Qt yt+1 − wt+1 nt+1 − it+1 + Qt (st+1 )λt+1 kt+2

since αyt+1 = yt+1 − wt+1 nt+1 . By repeatedly substituting for λt+j kt+j +1 ,
j ≥ 1, we have

τ −1
i=0 Qt+i Dt+τ

= λt kt+1 ,

τ =1
τ −1
where ∞
i=0 Qt+i Dt+τ is simply Vt by equation (11) in the text. Thus,
τ =1
λt has the interpretation of Tobin’s q.

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