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Discretionary Policy and
Multiple Equilibria
Robert G. King

S

ince the seminal work of Kydland and Prescott (1977), it has been
understood that policymaking under discretion can lead to a substantially worse outcome than policymaking under commitment. Many
economists believe that discretionary policymaking is important for understanding central issues in monetary policy1 and fiscal policy.2 Although there
are now many different models of discretionary policymaking, there are two
common and essential aspects in all models: (i) private agents make current
choices that affect the evolution of state variables on the basis of beliefs about
future policy, and (ii) future policymakers take these state variables as historically determined when choosing their optimal actions. Further, within the
models of this large literature, there is typically a cost arising from the fact
that the discretionary policymaker cannot manage expectations, so that the
resulting equilibrium is inefficient relative to that arising with a committed
policymaker.
Another potential impact of discretion, however, is that more than one
equilibrium may result from the central interaction between private sector
choice of state variables, private sector beliefs about future policy, and future
policy reaction to state variables. Some of these discretionary equilibria are
Boston University, National Bureau of Economic Research, and the Federal Reserve Bank of
Richmond. This article builds on work with Alexander Wolman, who also helped me develop
the example. I have also benefited from conversations with Alberto Alesina, Russ Cooper,
Huberto Ennis, Ed Green, Borys Grochulski, Per Krusell, Leo Martinez, and Ned Prescott.
The views expressed herein are the author’s and not necessarily those of the Federal Reserve
Bank of Richmond or the Federal Reserve System.
1 For example, a discretionary monetary policymaker may produce a positive rate of inflation
in an economy while a committed policymaker would produce a zero rate of inflation (see Kydland
and Prescott 1977 and Barro and Gordon 1983).
2 For example, a discretionary fiscal policymaker may eliminate private incentives for socially
beneficial accumulation by taxing all capital income every period (see Fischer 1980), while a
committed fiscal policy may provide ample incentives for accumulation by not taxing capital at
all (see Chamley 1986).

Federal Reserve Bank of Richmond Economic Quarterly Volume 92/1 Winter 2006

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Federal Reserve Bank of Richmond Economic Quarterly

better than others in terms of the welfare of the members of the society. An
economy may get stuck in a relatively bad equilibrium, so that there can be
even greater costs of policy discretion.
Recent work on discretionary monetary policy by King and Wolman
(2004) shows how dynamic multiple equilibria can arise in a simple “plain
vanilla” New Keynesian macroeconomic model of monopolistic competition
and sticky prices of the variety that is now standard in macroeconomic research
and policy analysis. In that context, a discretionary monetary authority adopts
a policy rule that fosters strategic complementarity between the actions of
pricesetters. In turn, that strategic complementarity makes for dynamic multiple equilibria, as in a large literature on the boundary of game theory and
macroeconomics concerning coordination games in aggregate economies.3
In the terminology of Cooper and John (1988), the standard New Keynesian
model can give rise to a “coordination failure.”
The objective of this article is to construct a very simple and transparent real model in which dynamic multiple equilibria are a consequence of
discretionary policymaking for the same economic reasons as in the monetary policy literature. The model is inspired by a brief discussion in Kydland
and Prescott (1977) about the interaction of individual location decisions and
policy response to disasters such as floods:
The issues [of time inconsistency arise] in many well-known problems
of public policy. For example, suppose the socially desirable outcome is
not to have houses built in a particular floodplain but, given that they are
there, to take certain costly flood-control measures. If the government’s
policy were not to build the dams and levees needed for flood protection
and agents knew this was the case, even if houses were built there,
rational agents would not live in the flood plains. But the rational agent
knows that, if he and others build houses there, the government will take
the necessary flood-control measures. Consequently, in the absence of a
law prohibiting the construction of houses in the floodplain, houses are
built there, and the army corps of engineers subsequently builds the dams
and levees. (Kydland and Prescott, “Rules Rather Than Discretion: The
Inconsistency of Optimal Plans,” Journal of Political Economy 85: 477)

3 Chari, Christiano, and Eichenbaum (2000) describe “expectation trap equilibria” within a
monetary policy setting. In these situations, a monetary authority optimally responds to the beliefs
of the private sector in ways that are self-confirming so that there is a thematic resemblance to the
discussion of the main text. However, the expectation trap equilibria studied by these authors are
members of a set of “sustainable plan equilibria” in which great latitude is given to expectation
formation and, in essence, a summary of beliefs operates as a state variable. For this class of
equilibria to exist, it is necessary that there be no known endpoint to the economy. By contrast,
the equilibria described in King and Wolman (2004) are multiple Markov-perfect equilibria in the
language of game theory, arising even when there is a fixed endpoint to the dynamic game (as
in the example in this article, where the game is essentially static).

R.G. King: Discretionary Policy and Multiple Equilibria

3

The essence of the situation just described is that there is a strategic interaction between the private sector and the government. Accordingly, following
much recent literature on policymaking under discretion and commitment, we
will make use of game-theoretic constructs to discuss the interaction between
private location decisions and the government dam-building decision.
In their analysis, Kydland and Prescott were concerned with understanding the nature of a single discretionary equilibrium and why it would be worse
than a single commitment equilibrium. By contrast, this article shows how
policy discretion fosters strategic complementarity among private sector decisionmakers in ways that lead to multiple equilibria. In the example studied
below, however, the mechanisms are exactly those highlighted in the quotation
from their work. An individual knows that the discretionary government will
choose not to build a dam if there are only a small number of residents on the
floodplain, so that one equilibrium involves the efficient outcome in which no
individuals live on the plain and no dam is built. Yet, an individual also knows
that the discretionary government will choose to build a dam if there are a
large number of floodplain residents, he thus finds it in his interest to locate
on the floodplain if a dam is built. Hence, there is another equilibrium that
involves a socially inefficient building of a dam and location of individuals
on the floodplain. In terms of game theory, it is well understood that multiple
equilibria arise when there is sufficient strategic complementarity in a coordination game (Schelling 1960 and Cooper 1999). In the example studied
in this article, the strategic complementarity is that an individual’s rewards
to locating on the plain are higher when other individuals choose to locate
there. But the strategic complementarity is present in this setting only when
policymaking is discretionary.

1. THE MODEL
There are two locations of economic activity: the floodplain and elsewhere.
There are two sets of actors: a government and a private sector. To highlight
aspects of the interactions between the government and the private sector, we
begin by studying a situation in which there is just one member of the private
sector (in Section 2) and then move to the more realistic case in which there
are many individuals (in Section 3).
The government and the members of the private sector each have a single
action. The private sector must decide to live on the floodplain (call this action
p = 1) or elsewhere (p = 0). The government must decide whether to build a
dam (d = 1) or not (d = 0). Despite the fact public and private decisionmakers
take different actions (d and p, respectively), the government’s objective is
to maximize the welfare of its citizens so that there is no intrinsic conflict
between the public sector and private sector. Further, if the government builds

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Federal Reserve Bank of Richmond Economic Quarterly

the dam, it finances construction via lump-sum taxation, with each member
of the private sector paying the same level of taxes.4
Individuals derive utility from their location and their consumption of
goods. Their utility function takes the form
u(c + bp)

(1)

with b > 0. That is, if an individual lives on the floodplain, then it is as if
his consumption is raised by an amount, b. Consumption is constrained by
after-tax income, which can take on several different values depending on the
actions of the government and private sector. The dependence of after-tax
income on private and public actions is displayed in Figure 1. The reference
level of income is y. If the government builds a dam at cost ψ and finances it
with lump-sum taxation, then after-tax income is y − ψ. If the government
does not build a dam and individuals choose to live on the plain then income
is f , which is assumed to be substantially less than y because of floods.
Next, consider the utility level that a single individual receives as it depends on his location decision and the dam-building decision of the government. The various possibilities are shown in Figure 2. We make the following
assumptions on the relative sizes of y, b, f, and ψ.
First, we assume that the best situation—the socially optimal situation—is
one where individuals do not live on the floodplain and the dam is not built,
which requires a pair of restrictions on the parameters of the model. First, it
requires that y > f + b, which is the idea that effective income is lower when
one lives on the plain. Second, it requires that y > y + b − ψ or, equivalently,
that ψ > b: the dam’s cost is higher than the value of living on the floodplain.
Second, we assume that the dam is productive in the sense that y −ψ > f .
That is, if all individuals are constrained to live on the plain, then there is an
economic benefit to building a dam to avoid the low output, f , which arises
because of floods.
These assumptions mean that it is easy to determine the optimal choice
for an individual. First, if he knows that the government will not build the
dam, then it is best for him not to locate on the floodplain since y > f + b.
Second, if he knows that the government will build the dam, then it is best for
him to locate on the floodplain because there are positive benefits from that
location choice (b > 0 implies that b + y − ψ > y − ψ).
Similarly, the optimal choice for the government is easy to describe. As
discussed above, the government seeks to maximize the welfare of the individual. If the government knows that the private agent will not locate on the
plain, then it is best not to build a dam since it is costly. If the government
knows that the private agent will locate on the plain, then it is best to build the
dam since it is a productive way of avoiding losses due to floods (y − ψ > f ).
4 The Appendix considers the sensitivity of the core results to some alternative financing rules.

R.G. King: Discretionary Policy and Multiple Equilibria

5

Figure 1 Dependence of Income on Individual and Government Actions
Government Action
d=0

y

p=1

f

Individual Action

p=0

d=1

y − ψ

y − ψ

Notes: The possible government actions are to build a dam (d=1) or not (d=0). The
possible individual actions are to locate on the floodplain (p=1) or not (p=0). The income
resulting from these actions is given by the entry in the relevant cell of the matrix. For
example, if the individual locates on the plain and the government does not build the
dam, then the individual receives income “f.”

2. A TWO-PERSON GAME
We start by exploring the strategic interactions between a single individual
and the government, considering three different cases. First, we assume that
the private sector and the government act simultaneously. Second, we suppose that the government acts first, which corresponds to policymaking under
commitment. Third, we suppose that the private individual acts first, which
corresponds to policymaking under discretion.

Simultaneous Actions
Nash (1951) proposed a definition of equilibrium in games such as the following: a pair of actions (p, d) is an equilibrium if p is the private sector’s best

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Federal Reserve Bank of Richmond Economic Quarterly

Figure 2 Dependence of Welfare on Individual and Government
Actions
Government Action
d=0

Individual Action

p=0

p=1

u(y)

u ( f + b)

d=1

u (y − ψ )

u (y + b − ψ )

Notes: The possible government actions are to build a dam (d=1) or not (d=0). The
possible individual actions are to locate on the floodplain (p=1) or not (p=0). The utility
resulting from these actions is given by the entry in the relevant cell of the matrix. For
example, if the individual locates on the plain and the government does not build the
dam, then the individual receives income “f” and utility u(f+b), with “b” measuring the
benefits to living on the floodplain.
The model assumes that the dam is costly ( >0); that there are benefits to living on
the plain (b>0); that there are costs of living on the plain if there is no dam (y>f+b);
and that the dam is productive if individuals must live on the plain (y+b- >f+b). These
assumptions imply that the diagonal elements of the matrix B are dominant.

response to the action, d, by the government and if d is the government’s best
response to the private sectors’s action, p.5
There are, therefore, two Nash equilibria when the private individual and
the government move simultaneously. One is that the individual does not
locate on the plain and no dam is built by the government (p = 0, d = 0).
The other is that the individual locates on the plain and a dam is built by the
government (p = 1, d = 1). Each of these outcomes is an equilibrium in the
5 Attention is restricted here to individuals choosing one action or the other. Mixed strategies
in which individuals choose one or the other with a specified probability are not considered.

R.G. King: Discretionary Policy and Multiple Equilibria

7

Nash sense since it is optimal for (a) the individual to choose p = 0 if d = 0
and to choose p = 1 if d = 1, and (b) the government to choose d = 0 if
p = 0 and d = 1 if p = 1. One can verify the first of these equilibria by
looking at Figure 2. For example, starting at the welfare level corresponding
to d = 0, p = 0, one can see that the individual gets lower welfare if he
chooses p = 1 (since f < y), and that the government’s outcome is worse
if it chooses d = 1 (since y − ψ < y). Proceeding similarly, one can also
confirm that both diagonal elements are equilibria and that the off-diagonal
elements are not.
The two equilibria yield different welfare levels for the individual: the
benefit from living on the floodplain is not as large as the cost of building
the dam, so that the p = 0, d = 0 equilibrium is unambiguously better than
the p = 1, d = 1 equilibrium. In terms of the literature on game theory,
this is an example of a coordination game, and at least since since Schilling
(1960), it has been known that coordination games can display more than one
equilibrium.

A Dominant Government
There is symmetry between the individual and the government in the situation
just discussed, with each agent deciding on an optimal action taking as given
the action of the other. An alternative situation is that the government is
dominant, choosing its best action knowing how the individual will respond
to government intervention. In our case, the government looks at the various
scenarios and recognizes that the individual will respond with p = 0 if the
government action is d = 0 and that the individual will respond with p = 1
if the government action is d = 1. Since welfare is higher when d = 0 and
p = 0 than when d = 1 and p = 1, the government will choose not to build
the dam.
This situation can be described in other ways. One is to say that the
government has a first mover advantage, selecting its action and seeing a
subsequent response from the private sector, which stresses the timing of
actions. The second is to say that the government can credibly commit to take
the action d = 0 even if the private sector chooses p = 1, which stresses
aspects of feasible government strategies. Either of these perspectives limits
the equilibrium solely to the optimal one.

A Dominant Individual
We next consider a setting in which the private sector is dominant. In the
current setting, the individual knows that if he chooses p = 0 then the government will choose d = 0. He also knows that if he chooses p = 1 then the
government will choose d = 1. Since the individual’s welfare is highest with

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Federal Reserve Bank of Richmond Economic Quarterly

p = 0 and d = 0, he will choose that action. Hence, a dominant individual
will also bring about a socially optimal outcome. That is, the fact that the government cannot commit does not lead to multiple equilibria or to inefficiency
when there is a single dominant individual.

3.

MANY INDIVIDUALS AND ONE GOVERNMENT

A more realistic situation is that there are many similar private agents and
only one government. We study this setting under the assumption that all
individuals are identical in their preferences and opportunities, restricting our
attention to analysis of symmetric equilibria (those in which all individuals
choose the same action).
Each individual makes his location action (p = 0 or p = 1), taking
as given the location decisions of all other individuals: we denote the action taken by all others as p; the restriction to symmetric equilibria is that
p is also 0 or 1.6

A Committed Government
Suppose that the government can commit to the action d = 0. Then, in view
of Figure 2, the individual agent will choose p = 0. Further, the individual
does not really care what other individuals are doing; it is enough for him to
know that the government will not be building the dam. The individual will
not want to live on the floodplain if there is no dam.

A Discretionary Government
Matters are more complicated when there is a discretionary government.
Based on our prior discussion and assuming that the government policy is
not influenced by the actions of an individual agent but only by those of the
average agent, the optimal decision for the government takes the form
d=0

if p = 0 and

d = 1 if p = 1.

(2)
(3)

That is, a dam is constructed if people choose to live on the floodplain, but
not otherwise. This is precisely the same behavior by the discretionary government as in Section 2.
However, the situation for the individual agent is quite different now. He
is playing a simultaneous game with his fellow agents in which the choice
6 Equilibria that are not symmetric are studied in the Appendix.

R.G. King: Discretionary Policy and Multiple Equilibria

9

variable is location. Although it continues to be the case that it is the actions of the government that are important for the individual’s location decisions, it is now the behavior of all other agents that determines how the
government acts. The individual has lost his power relative to the case
studied in Section 2.
We can again use Figure 2 to determine how the individual will make his
location decision. We can represent this as
p = 0 if p = 0 because d = 0, and

(4)

p = 1 if p = 1 because d = 1,

(5)

stressing that governmental response depends on the aggregate private sector
action. Hence, there are two symmetric equilibria under policy discretion.
In one, no individual chooses to locate on the floodplain and the dam is not
built. In the other, all individuals choose to locate on the floodplain and the
dam is built. As in Section 2, the equilibrium with floodplain location and
dambuilding results in lower utility.
Of course, it would be desirable for individuals to coordinate their actions
and for each person to choose p = 0. But, the p = 1, d = 1 example is one
that involves a “coordination failure” in the sense of Cooper and John (1988).
As in the monetary policy analysis of King and Wolman (2004), it is strategic
complementarity that leads to coordination failure, making it optimal for any
single individual to align his location action with those of his fellow citizens.
Further, it is discretionary policy that leads to this strategic complementarity,
as was also true in the monetary policy case.

4.

DISCUSSION AND CONCLUSIONS

Working with an example discussed by Kydland and Prescott (1977), this
article provides a simple model economy in which there is a single, efficient
equilibrium under commitment and multiple equilibria under discretionary
policymaking. In particular, there are two equilibria that can arise, and one is
clearly worse than the other.
As Kydland and Prescott (1977) suggest, it would be desirable for the
government to pass a law to restrict individual location choices. If no one
was allowed to live on the floodplain, then it would not matter whether a dam
would be built by the discretionary government if people did live there. Thus,
the model economy displays the property—stressed in the literature on the
Samaritan’s dilemma that begins with Buchanan (1975)—that limitations on
individual choice may be warranted in settings where policymakers lack the
ability to commit their future actions.
The analysis has focused on a government that maximizes the welfare
of the agent, as is natural when all agents are the same. Yet, the tendency
would also arise in more concretely political environments. For example, if

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Federal Reserve Bank of Richmond Economic Quarterly

agents are allowed to vote on whether a dam should be built after their location
decisions, then it is clear that there would be unanimous support for the dam
if p = 1 and unanimous opposition if p = 0. If individuals were allowed to
vote on a floodplain prohibition law (of the form suggested by Kydland and
Prescott) before location decisions, then there would be unanimous support for
that rule, even though it limited individual choice. That is, the detailed timing
of opportunities for political decisionmaking would be relevant for outcomes
in this economy.
We now understand that there is a potential for a multiplicity of equilibrium outcomes in many settings in economic analysis as diverse as monetary
policy and flood control. For positive studies of discretionary policymaking,
this means that there may be previously unstudied equilibrium outcomes. It
is possible, for example, that an extension of the analysis of King and Wolman
(2004) might be used to study “inflation scares,” as put forward by Goodfriend
(1993), in which informational events induce endogenous switches between
low-inflation and high-inflation equilibria. In terms of the design of institutions for policymaking in discretionary environments, it is necessary to guard
against adverse equilibrium outcomes.

R.G. King: Discretionary Policy and Multiple Equilibria

APPENDIX:

11

GOVERNMENT DECISIONMAKING

The focus of the main text is on a situation in which there are many private
agents and a government that acts in a discretionary manner (taking its dambuilding action after the private sector’s location decision). However, the
text restricts attention to situations in which there are symmetric equilibria
(those with 0 < p < 1) so that it is relatively simple to describe government
decisionmaking: it simply acts to maximize welfare as if there was a single
agent. Further, the government is restricted to financing the dam (if it builds
one) via lump-sum taxes that are common across all agents.
The purpose of this Appendix is to explore how the dam-building decision
for a discretionary government is altered when there is an intermediate fraction
of agents (0 < p < 1) that chooses to live on the plain and when there are
other financing schemes. In all settings, there is a continuum of agents indexed
by i, with 0 ≤ i ≤ 1 that are making the location decision between the plain
and elsewhere (which we will call the hill in this Appendix).

A1: The Basic Model With Lump-Sum Taxation
In this subsection, we maintain the text assumption that all agents receive a
tax bill equal to dψ. (Each agent pays a lump-sum tax equal to government
expenditure irrespective of his location decision.) In the main text, attention
is restricted to symmetric equilibria so that p = 0 or p = 1, but we now relax
that assumption.
Since we are studying discretionary equilibria, we assume that the government takes p as given and chooses the optimal d. Since agents are heterogeneous by location, we assume here that the government maximizes average
utility, pu(cp + b) + (1 − p)u(ch ), where cp and ch are the amounts of consumption by plain and hill residents, respectively. In particular, if d = 0, then
the welfare of private agents living on the hill is u(y) and that of those living
on the plain is u(f + b) so that average utility is
pu(f + b) + (1 − p)u(y).
By contrast, if d = 1, then average utility is
pu(y + b − ψ) + (1 − p)u(y − ψ).
To understand the optimal choice of the government, consider the function
(p), defined as the average utility with a dam less the average utility without
a dam. It is clear that is linear in p. It is also clear that (0) = u(y − ψ) −
u(y) < 0, and that (1) = u(y + b − ψ) − u(f + b) > 0, so that there is a
single value, p, such that (p) = 0.

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Federal Reserve Bank of Richmond Economic Quarterly

Hence, for all p < p, then, it is optimal for the government not to build
the dam and for all p > p, it is optimal for the government to build it.
Further, suppose that individual i takes d, p as given and chooses optimally. Then, his optimal strategy is
p = 0 if p < p
p = (0, 1) if p = p
p = 1 if p > p.
If p = p then agents can be viewed as playing mixed strategies, selecting
a probability of living on the plain of p = p. Alternatively, some agents
can simply choose to live on the plain while others don’t. But, in any event,
consideration of nonsymmetric equilibria indicates that there is a third equilibrium possibility not considered earlier. Since individuals are indifferent to
location when p = p and the government is indifferent about whether to build
the dam or not, then there is a third equilibrium at which p = p and we are
not able to say whether the dam is built. This particular equilibrium seems
less interesting, as it is “unstable” in a particular sense: if p = p ± ε, for a
small number ε then it is no longer optimal for an individual to choose the
action required by this equilibrium. It is for this reason that we ignore such
equilibria in the main text.
The consideration of nonsymmetric equilibria also makes it clear that the
Nash equilibria p = 0, d = 0 and p = 1, d = 1 are stable with respect
to changes in behavior by small fractions of the population. If p = ε, the
government would continue to choose d = 0, and if p = 1−ε, the government
would continue to choose d = 1.

A2: Taxation Just on Floodplain Residents
Suppose, alternatively, that it is possible to tax only residents of the floodplain,
but not the other residents of the community. This fiscal restriction can be
understood in two ways. A direct interpretation is that it is just a particular
posited fiscal policy. A more subtle implication is that the government chooses
this taxation so as to maximize social welfare (as in the next section) subject
to the requirement that it must not lower the welfare of any agent and the
recognition that individuals can always generate welfare of u(y) by staying
on the hill.
In this situation, then, the government maximizes the welfare of floodplain
residents:
ψ
du(y + b − d ) + (1 − d)u(f + b).
p
From the standpoint of these residents, the cost of the dam is now higher
because there is a smaller base of individuals subject to the lump-sum tax.

R.G. King: Discretionary Policy and Multiple Equilibria

13

Hence, the government will build the dam if
y+b−

ψ
> f + b,
p

or if
p>

ψ
=p
y−f

and it will not if p < p. (The value of p is positive because y > f and
it is less than 1 because y − f > ψ, which is the condition that the dam is
productive if discussed in the main text.) Hence, the government’s decision
rule is again to build a dam if there are many floodplain residents and to not
build it if there are few. However, relative to the prior case in A1, the “switch
point” for the government has changed.
Importantly, the individual private agent’s location decision is substantially changed by this alternative tax regime. If he remains on the hill, he
gets u(y) while if he moves to the plain he gets something less, irrespective
of whether the dam is built. Hence, no rational agent will ever move to the
floodplain.
Hence, under discretion with location-specific lump-sum taxes, the only
Nash equilibrium is the efficient one in which p = 0 and d = 0. That is, the
change in the structure of taxation has eliminated a “fiscal externality” that is
partly responsible for the results in the main text.

A3: Endogenous Taxation
We now consider a discretionary government that chooses the levels of lumpsum taxation so as to maximize the utility of the average agent in the economy,
taking as given that there is a fraction of agents, p, that lives on the plain. As
above, this average utility is
pu(cp + b) + (1 − p)u(ch ),
where cp and ch are the amounts of consumption goods that the government
allocates to residents of the plain and hill, respectively. The resource constraint
of the economy takes the form
pcp + (1 − p)(ch ) ≤ (1 − p)y + p{dy + (1 − d)f − dψ}.
That is, the total amount of consumption must be less than the income earned
by hill and plain residents, net of any cost of dam building.

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Federal Reserve Bank of Richmond Economic Quarterly

A Pareto-optimal allocation mandates that “full” consumption be equated
across plain and hill residents:7
(cp + b) = ch .
Hence, the amount of consumption available for hill residents is given by
ch = pb + y − ψ if d = 1 and
ch = pb + (1 − p)y + pf if d = 0
Accordingly, the government will maximize consumption and welfare by
choosing to build the dam if p > p and not to build the dam if p < p.
The associated taxes by location are
Tp = y − c h − b
Th = y − c h
with the amounts of consumption, ch , depending on the dam-building decision
in ways specified above.
Confronted with this government fiscal policy and dam-building decision
rule, the individual’s behavior is as in the basic model of A1 with lump-sum
taxation but with p replacing p: individuals find it desirable to locate on the
plain if p > p and to locate on the hill if p < p. Hence, the equilibria are
the same as in the main text.

A4: Comparing the Fiscal Regimes
Looking across the three fiscal regimes, we can see that the results of the main
text are broadly sustained, except when the government is required to levy
location-specific taxes in ways that fully discourage location on the plain. In
terms of the discussion of Kydland and Prescott (1977) quoted in the main
text, the critical point is that the fiscal policy cannot be equivalent to passing
a law “prohibiting construction of houses in the floodplain.” That is, the
fiscal regime must not fully punish individuals for the action of locating to the
floodplain.

7 Effectively, floodplain residents have consumption equal to c + b, with c being market consumption and b being the consumption value of living on the floodplain.

R.G. King: Discretionary Policy and Multiple Equilibria

15

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Chari, V.V., Lawrence J. Christiano, and Martin Eichenbaum. 1998.
“Expectation Traps and Discretion.” Journal of Economic Theory 81 (2):
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Cooper, Rusell. 1999. Coordination Games: Complementarities and
Macroeconomics. Cambridge: Cambridge University Press.
, and Andrew John. 1988. “Coordinating Coordination
Failures in Keynesian Models.” Quarterly Journal of Economics 103
(3): 441–63.
Fischer, Stanley. 1980. “Dynamic inconsistency, cooperation and the
benevolent dissembling government.” Journal of Economic Dynamics
and Control 2: 93–107.
Goodfriend, Marvin. 1993. “Interest Rate Policy and the Inflation Scare
Problem: 1979–92.” Federal Reserve Bank of Richmond Economic
Quarterly 79 (Winter): 1–24.
King, Robert G. and Alexander L. Wolman. 2004. “Monetary Discretion,
Pricing Complementarity, and Dynamic Multiple Equilibria.” Quarterly
Journal of Economics 119 (4): 1513–53.
Kydland, Finn E., and Edward C. Prescott. 1977. “Rules Rather Than
Discretion: The Inconsistency of Optimal Plans.” Journal of Political
Economy 85 (3): 473–91.
Lindbeck, Assar, and Jorgen Weibull. 1993. “A Model of Political
Equilibrium in a Representative Democracy.” Journal of Public
Economy 51 (2): 195–209.
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286–95.
Schelling, Thomas. 1960. The Strategy of Conflict. Cambridge, Mass.:
Harvard University Press.

Credit Exclusion in
Quantitative Models of
Bankruptcy: Does It
Matter?
Kartik B. Athreya and Hubert P. Janicki

W

hy is there unsecured lending? Given that borrowers seem to
have essentially no obvious incentive to repay under the generous
provisions afforded them by U.S. consumer bankruptcy law, why
would anyone make an unsecured loan? One answer is that borrowers are
actually providing a more intangible form of collateral, such as their reputation
or “good name.” Such an answer is problematic, however. In particular, can
households credibly bind themselves to agreements to which they may later
have little interest in keeping? What about lenders? In particular, notice that
lenders themselves have no incentive to act “punitively” after a bankruptcy
filing. This is because if there are gains from renewed trade, any lender that
“renegotiates” with borrowers will profit. In other words, in a competitive
setting, the only reasonable changes in credit terms are those warranted by a
change in assessing the likelihood of repayment.
Perhaps the most natural representation of the destruction of a reputational
form of capital in unsecured loan markets is the reduction in the “credit score”
that typically follows a bankruptcy filing. Thus, if neither borrowers nor
lenders can credibly promise to forgo mutually beneficial transactions after a
default, there would seem to be little hope for unsecured credit. And yet, a
great deal of such credit exists, in an amount that currently exceeds $1 trillion!
The thorny issues raised above have, in large measure, been avoided
by quantitatively oriented researchers. Instead, they typically assume that
a penalty for default is exclusion from future borrowing, at least temporarily.
The authors would like to thank Chris Herrington, John Walter, John Weinberg, and especially
Leonardo Martinez for helpful comments. The views expressed herein are not necessarily those
of the Federal Reserve Bank of Richmond or the Federal Reserve System.

Federal Reserve Bank of Richmond Economic Quarterly Volume 92/1 Winter 2006

17

18

Federal Reserve Bank of Richmond Economic Quarterly

However, for such analysis, the effects of exclusion on borrowing and lending
depend on the precise specification of the income paths facing households.
To understand why, assume first, as economists since Friedman (1957) have,
that households use credit markets to “smooth” consumption. That is, they
wish to shield consumption from changes in income. Smoothing occurs both
in response to predicted changes in income as well as to unforeseen ones. The
value of credit markets, in turn, depends on what households ask of them.
Notably, if income risk is large and extremely persistent, or permanent, the
household has little choice but to reduce consumption when hit with a negative
shock. In such a case, the value of access to the credit markets may be quite
low. If, instead, shocks are small or primarily transitory, borrowing will be an
effective bulwark. It is the latter case in which the assumption of exclusion
following bankruptcy would have the most bite. Thus, both households facing
large and possibly infrequent shocks, as well as those facing small but frequent
shocks may find the inability to borrow quite painful. Because the quantitative
role of exclusion following bankruptcy may depend on the precise specification of income risks faced by households, the relevant question is: In recent
quantitative models of bankruptcy, what role does credit exclusion play?
The two central contributions of this article are to (1) take a first step
in evaluating the commonly used (but rarely justified) assumption in recent
models of unsecured household borrowing of credit that defaulting borrowers
get exiled and (2) quantitatively examine the role of exclusion in affecting the
sharp rise of both debt and bankruptcy observed in the 1990s. We consider
a simple model of consumer borrowing and lending developed in Athreya
(2002, 2004). This model shares enough with other recent work to be useful
in gleaning insights about exclusion. We organize our results around three
experiments. In the first two, we investigate the extent to which reductions
in exclusion-related penalties matter for post-bankruptcy asset accumulation
under a variety of income processes. In the third experiment, we ask whether
these changes generate outcomes consistent with recent observations on aggregates, such as the bankruptcy rate and debt discharged in bankruptcy.
Specifically, we proceed in two steps. First, we simulate counterfactual
exclusionary periods precisely to understand the extent to which exclusion
matters. Second, we link the length of credit exclusion to the level of competition in the unsecured lending market. The experiments performed in the first
step will inform us as to the inherent “plausibility” of exclusion as a credible
phenomenon. That is, if exclusion is found to be a “binding” constraint, then
households value borrowing and would, in the absence of other constraints, be
able to renegotiate loans with lenders. It has been observed that a high level
of competition in the unsecured credit market makes purely punitive exclusion increasingly unlikely. This trend stems from a reduction in search and
switching costs for households. We employ the intuition that while punitive

K. B. Athreya and H. P. Janicki: Credit Exclusion

19

exclusion may be sustainable with a few lenders, it will not be with a large
number of them.
Our central findings are twofold. First, we find that exclusion from credit
markets alone seems insufficient to explain current repayment rates on unsecured debt. Second, we observe that a reduction in exclusion-related penalties
for bankruptcy arising from technological changes in the 1990s is consistent
with both growth in debt and personal bankruptcy.
One consideration that we address is the reason for borrowing. In particular, the nature of income shocks determines not only the usefulness of
borrowing, but also the misery inflicted by exclusion. Consider an example in
which a household faces minimal and transitory uncertainty nearly all of the
time, but is nonetheless prone to prolonged spells of relatively low income. In
such a world, the household may choose to borrow and may hold substantial
debt at the time that the “long-term” shock occurs. In this situation, the household may not value highly the option to borrow, simply because the shock is
expected to last a long time, thereby altering the present value of future earnings nontrivially. In this setting, the household will not care greatly that it
will be excluded if it defaults. More troubling is that we may not be able to
easily disentangle a reduced need to borrow after bankruptcy from a willful
imposition of exclusion by creditors. Both causes have similar symptoms.

What Is Exclusion?
The sanctions assumed in recent work range from infinitely long periods of
autarky for defaulters to relatively short periods where only borrowing is prohibited and saving is allowed. The former penalties have been used extensively
to evaluate the best possible risk-sharing arrangements that are sustainable
given a party’s ability to walk away from contracts at any time. In these settings, default does not occur in equilibrium. These studies dismiss the issue
of whether the penalties are credible. However, for their purposes, permanent
autarky may be appropriate as a harsh punishment that allows for a bound of
sorts on risk sharing under limited commitment. By contrast, when attempting
to capture costs of default in the U.S. credit market, exclusion appears less
plausible because of the coexistence of finite penalties and default.
Purely temporary exclusion has been an attractive modeling device for
recent quantitative work, such as Athreya (2002, 2004) and Chatterjee et al.
(2005) on unsecured consumer debt, and Yue (2005), Aguiar and Gopinath
(2005), and Sapriza and Cuadra (2005) on sovereign debt. Nonetheless, such
exclusion is not easily supported and deserves more justification than has
been provided. In particular, a key problem is that in choosing to punish
default ex post by exclusion, lenders and borrowers forgo opportunities for
mutually beneficial trade that exist after default. In other words, once default
has taken place, “bygones should be bygones”; the parties should recontract

20

Federal Reserve Bank of Richmond Economic Quarterly

and move on. However, the possibility of recontracting itself undermines
the initial obligation of the borrower to commit to repay. Unless the lender
can somehow credibly threaten to cut off the borrower from all creditors, the
problem is not easily circumvented.
One case where exclusion may be plausible occurs when a single, or small
number of, creditors may be able to coordinate to sustain ex post exclusion
as a credible threat. Furthermore, it is possible, even with a large number
of creditors and an infinite horizon, to construct systems of beliefs among
market participants such that exclusion becomes sensible ex post. These belief
systems are, however, not immune to criticism. In the subsequent section, we
discuss an example where assumptions regarding these beliefs rationalize, at
one level, the presence of unsecured debt. Nevertheless, the lack of discipline
imposed on “off-equilibrium” beliefs can make ex post exclusion inefficient.
There is a good deal at stake in understanding the nature of penalties for
default on unsecured debt. From an efficiency standpoint, limits to commitment, along with private information, are the prime suspects in the limited risk
sharing we observe in the world around us. Moreover, since exclusion does
not involve transfers of resources across parties, these penalties are socially
wasteful ex post. Thus, unless offset by their ability to sustain better risk
sharing, deadweight penalties should be regarded with concern. From a distributional standpoint, there is perhaps even more at stake; it is reasonable to
suspect that the income-poorest are often the young, who, in turn, are wealthpoor. Therefore, the inability to commit to repayment affects this subgroup
most profoundly, while leaving untouched those who may post collateral such
as home equity.

Recent Changes in the Unsecured Credit Market
Our interest in the potential implication of changes in the competitiveness of
the unsecured credit market is derived from the seminal studies of Ausubel
(1991) and Calem and Mester (1995). These studies confirmed the popular
view of many that, in the late 1980s and early 1990s, the U.S. market for
unsecured credit was an imperfectly competitive marketplace in which rational
lenders systematically earned supernormal profits. We now examine some
well-publicized changes in the structure of unsecured lending and assess its
role in driving the even more well-publicized increases in household debt and
bankruptcy. We divide our focus into two broad periods: the 1980s and the
1990s to the present.
The 1980s

The most important article in this relatively large body of literature might be
that of Ausubel (1991), who argues on empirical grounds that as of the late

K. B. Athreya and H. P. Janicki: Credit Exclusion

21

1980s, returns in unsecured credit markets were highly supernormal. Moreover, and more intriguing, was that the market seemed to offer a near textbook
case of perfect competition. In particular, Ausubel documents that there were
in excess of 4,000 lenders and that free entry seemed possible. In particular,
Ausubel (1991) notes that the ten largest lenders accounted for only two-fifths
of market share and therefore could not be said to monopolize the market.
The returns to credit card lending grow even more puzzling as it is difficult to
find any evidence of overt collusion or price fixing. One finding in particular
has spurred substantial analysis, namely, the feature that credit card interest
rates are remarkably insensitive to changes in the measured cost of funds. In
conclusion, Ausubel (1991) suggests three possibilities for the observed behavior of the credit card market. First, he allows for departures from standard
consumer rationality, and argues that in a setting with irrational households
that systematically underestimate their own likelihood of carrying credit card
balances, lenders may be able to earn supernormal profits. Second, Ausubel
allows for search and switching costs to reflect several hurdles that lie in
front of those wishing to switch credit cards. Lastly, Ausubel suggests that
asymmetric information regarding the default risk of borrowers could make it
difficult to control risk using interest rates. In particular, a fall in the rate offered by a lender might simply attract a disproportionate response from those
most likely to default, and would generate only indifference from low-risk
households that often did not carry balances on which they paid interest. In
this setting, one might reasonably expect retail interest rates to move far less
in response to changes in funding costs than when more was known about
cardholders.
An important article that pursues the conjectures of Ausubel (1991) in
explaining credit card interest-rate stickiness is that of Calem and Mester
(1994). These authors conclude that all three aspects of Ausubel’s reasoning
receive empirical support when data from individual consumers (from the
Survey of Consumer Finances) is used. Notably, Calem and Mester do find a
significant role for the effect of both search and switching costs. One of the
costs they note that is that while borrowers provide real-time information on
their financial situation through their repayment behavior, credit bureau data in
the 1980s was not updated as frequently. In turn, while lenders had measures
of the risk posed by their own cardholders, this risk was only partially revealed,
as it did not reveal the behavior of the same individual with respect to other
accounts, nor the risk posed by new account holders. More subtly, as noted
by Calem and Mester (1995), high switch costs can independently limit the
value of search, leading again to stickiness in interest rates.
The 1990s to the Present

The preceding work deals with a period immediately prior to a noticeable
change in technology for intermediation. As documented by Furletti (2003),

22

Federal Reserve Bank of Richmond Economic Quarterly

FDIC (2004), and Edelberg (2003), the use of large-scale credit scoring and
intensive data mining led to large changes in the growth of information available to lenders. In turn, search costs fell. Notably, to the extent that search
could be initiated by either buyer or seller, a major change in the 1990s was the
growth of massive preapproved, direct-mail solicitation. Figure 1 (all figures
appear at the end of this article) shows that even a casual viewing of the data
makes clear that an important “regime change” occurred in the early 1990s.
To the extent that technological advances mitigated adverse selection, pricebased completion grew more attractive. Indeed, Furletti (2003) and Edelberg
(2003) argue that these changes paved the way for much more detailed pricing
strategies according to cardholder risk.1 Perhaps the most interesting aspect
about the 1990s was the growth of debt and bankruptcy to unprecedented
levels.
The facts documented above for the 1990s can be expected to result in a
reduction or elimination of exclusion. Moreover, these changes may be expected to first generate a transitional period during which repayment rates on
credit contracts issued prior to the early 1990s did not reflect the intensifying
competition. Additionally, in the longer run, we might expect a “supply side”
response leading to a repricing of terms to accommodate this new reality. The
first period might well be associated with increased borrowing and default,
while in the longer run, the repricing of the riskier loans might led to a fall
in default rates (all else equal). Once again, the preceding experiment is only
partially a natural one because of the simultaneous change in the technology
of credit intermediation. Athreya (2004) explores the effects of a fall in transactions costs on borrowing and default and finds that it accounted well for the
period between 1991 and 1997. In this article, we abstract from technological
advances and focus exclusively on the aggregate consequences of reductions
in credit exclusion for debt, bankruptcy, and credit supply.
The article is organized as follows. In Section 1, we document some
recent empirical evidence on the consequences of bankruptcy. We also briefly
present a theoretical model and some quantitative theory to review the standard
approach to incorporating credibility of ex post punishment and use of assets
for consumption smoothing. Section 2 presents a simple model and evidence
from counterfactual experiments to examine the extent to which household
behavior is dictated by exclusion and income. In Section 3, we extend the
model to address the effects of exclusion on the aggregate unsecured credit
market. Section 4 concludes.
1 See Athreya (2004) for an account of these changes and the implication they have for
indebtedness and default.

K. B. Athreya and H. P. Janicki: Credit Exclusion
1.

23

BACKGROUND EMPIRICAL EVIDENCE AND THEORY

Consequences of Bankruptcy: Empirical Evidence
Several recent articles have gathered empirical evidence that argues that
bankruptcy blights a credit score. Stavins (2000) finds that having been
turned down for credit makes one substantially more likely to have filed for
bankruptcy in the past. Relatedly, and perhaps as a consequence, bankruptcy
filers are less likely to hold at least one credit card if they have filed for
bankruptcy in the past. These two observations are suggestive, but they do
not have an unambiguous interpretation of forcible “exclusion” from credit
markets. Ideally, what one would like to know is the probability of rejection given a past bankruptcy. Instead, what we know from Stavins (2000)
is the probability of having filed a bankruptcy given that one is rejected for
credit. The second observation is perhaps more informative, as the absence of
a credit card means that households have foregone the potential transactionsrelated benefits of convenience associated with credit cards. On the other
hand, the growth of debit cards allows for access to the payment network of
Visa, Mastercard, and others without the need for a credit card. Moreover,
the quantitative differences between those with a prior bankruptcy and those
without are not so large. In particular, Stavins (2000) finds that the mean number of credit cards held by those with a past bankruptcy was 2.91, while it was
3.58 for those without a bankruptcy. This also calls into question the extent to
which bankruptcy filers are truly “excluded.” Among the strongest findings in
Stavins (2000) is that a past bankruptcy was predictive of future delinquency.
This suggests that something systematic characterizes bankruptcy filers that
warrants differentially strict treatment, such as more frequent rejections in
credit application. Once again, the data do not speak with one voice, because
the interest rates faced by those having filed averaged only one percentage
point more than those who had not. Thus, conditional on obtaining an unsecured credit card loan, past bankruptcy filers appear not to be paying a great
premium.
In the United States, credit bureaus are important institutions that aggregate debt and repayment data across consumers and over time. In the scoring
models most commonly used, such as Fair Isaac & Co. (FICO), the leading
issuer of credit scores, repayment history is a major determinant of score.
In turn, scores are interpreted by lenders as measures of risk, implying that
the drop in credit score triggered by bankruptcy leads to at least temporary
repricing and possibly exclusion from unsecured borrowing.
In addition to Stavins, another important reference in the literature on postbankruptcy credit extension is that of Musto (2004), who exploits a natural
experiment created by laws limiting the length of time a bankruptcy may be
retained on a credit record to ten years. The main finding of the latter is
that for more “creditworthy” households, the removal of a past bankruptcy

24

Federal Reserve Bank of Richmond Economic Quarterly

from a credit record has an immediate and economically significant effect on
household indebtedness. When those with high and medium credit ratings
were studied, as measured by FICO, the average credit lines jumped in the
tenth year from $2,810 to $4,578.
Lastly, Fisher, Filer, and Lyons (2000) study a panel of households that
have filed for bankruptcy, and they argue that the consumption of this group
is somewhat more sensitive to income than in the period preceding the filing.
This is consistent with borrowing constraints binding in the post-bankruptcy
period. Furthermore, the authors find that after five years beyond the removal
of the bankruptcy from a credit record, consumption ceases to be excessively
sensitive to income. Again, this is consistent with bankruptcy leading to a
temporary cutoff from unsecured credit markets.

Exclusion in Theory: A Simple Example
Given the observation that sovereign debt and unsecured consumer debt markets both exist, work on supporting punishments as credible threats has occupied the time and imagination of theorists for some time. A textbook example
of such a system of beliefs is taken from Obstfeld and Rogoff (1995, Ch. 6,
376–77). In this example, there are a large number of a risk-averse nations
facing uncertain country-specific output. However, all shocks to output are
uncorrelated across countries, and there is, therefore, the possibility for complete insurance. However, it is also assumed that each nation may walk away
with its current income at any time. The only penalty is a permanent exclusion
from credit markets. The key question is whether such a punishment can be
credible. Below is a set of beliefs and strategies that generate credibility. If
country A is to be penalized by the others, (1) it must be that country A has
no reputation for repayment, and (2) all other countries lose their own reputations for repayment by dealing with country A. Note that without clause (2), a
country could default and then buy an insurance contract against income risk
by putting up money up front, thereby removing all credit risk. With clause
(2) in place, no defaulting country would dare send money to a country that
agreed to insure it. This is also beneficial because it confirms the beliefs held
by the nondefaulters about country A. Namely, since country A believes that
any insurer B will default at the first chance, country A will default on any
obligations it has to country B. In turn, country B would be optimizing by
seizing any payments by country A.
What is notable about this example is not so much that punishments may
be sustained, but that they depend intricately on the systems of beliefs held
by market participants. Moreover, to the extent that we do not have definitive
means of winnowing the sets of beliefs that are “plausible,” such resolutions
are somewhat troubling. There is also a more serious problem, namely that
of “renegotiation.” In particular, even though the threats specified above are

K. B. Athreya and H. P. Janicki: Credit Exclusion

25

credible in that they remain in the interest of countries to impose ex post,
they are not immune to renegotiations. We now examine a problem with
the belief system discussed above. In particular, all the gains from trade
that could be realized between the parties go unrealized. In the preceding
example, the problem arises because even though the specification of beliefs
makes it sensible for the borrower to take the threat of exclusion seriously,
the actual imposition of the threat ex post is inefficient for all parties. This
creates incentives for all parties, not just the ones that have experienced default,
to create other contractual arrangements beyond those rendered unworkable
given people’s beliefs. As a result, one might expect that ex ante, the threat of
exclusion will once again become ineffective to sustain risk sharing.

Value of Asset Markets in Quantitative Theory
To obtain an initial measure of the value of assets for smoothing, and thereby
the pressure not to impose exclusion ex post, we turn now to a canonical model
of savings and consumption taken from Deaton (1991). A broad lesson of this
work is that temporary shocks will generally be smoothed via borrowing and
savings, while persistent, or permanent, shocks will not.
To make things clearer, consider a household that maximizes the following
objective:
∞

βt

E0
t=0

ct1−κ − 1
.
1−κ

In the preceding, consumption in period t is given by ct , β is the discount
factor, and κ specifies risk aversion. The latter is a key parameter governing
the extent to which households borrow to keep consumption smooth in the
face of shocks. The objective function is maximized subject to the constraints
a
≤y+a
1+r

c+

a ≥ 0,
where y denotes income from sources other than wealth, a, and r denotes
the interest rate. Notice that there is a restriction that a ≥ 0, ruling out
borrowing. However, the exercise is still instructive because our primary goal
is to understand the effect of limits on the decumulation of wealth, with an
exclusion from borrowing being a special case. If we now specify a simple
AR(1) income process
yt − y = ϕ(yt−1 − y) +
where
t

∼ N (0, σ ),

t,

26

Federal Reserve Bank of Richmond Economic Quarterly
Table 1

Persistence (ϕ)

-0.40

0.00

0.30

0.50

0.70

0.90

1. s.d. y
2. estimated. s.d. y
3. estimated. s.d. c
s.d. c
ratio s.d. y

10.90
10.80
4.60
0.43

10.00
10.20
5.10
0.50

10.50
10.00
6.70
0.67

11.50
11.40
7.60
0.67

14.00
13.30
10.40
0.78

22.90
27.50
25.90
0.94

we obtain Table 1 from Deaton (1991).
Notice that as shocks become more persistent, households choose not to
smooth shocks. The ratio of the standard deviation of consumption to that of
income grows systematically with the persistence of shocks to income. The
intuition here is that highly persistent negative shocks, for example, have a
grave impact on lifetime income. To the extent that it is lifetime income that
determines in large part the long-run average level of consumption, a large
downward revision demands a reduction in average consumption. In other
words, households will generally be unwilling to borrow against a greatly
diminished future income just to avoid today the anticipated pain of a bad
event. By contrast, a highly persistent positive shock implies a relatively large
upward revision in future income prospects. In light of this, households will
reduce their indebtedness or increase their savings. Lastly, take the extreme
case where the shocks to income are permanent. An example of this is a “raise”
in salary that also resets the “base” at which future raises are computed. In this
case, the positive shock may lead to borrowing in anticipation of future good
times. At the other extreme, if a permanent bad shock occurs, households
may actually increase their savings to allow them to make the transition more
smoothly to a permanently lower level of income.
The implications of this example for a world with bankruptcy are noteworthy. In particular, it matters a great deal whether one lives in a world of
highly persistent income risk. If so, credit markets are not useful to households anyway, and credit exclusion is not painful. In short, the incentives
to default for any given debt level are relatively large when compared to
a world of less persistent income risk. On the other hand, the usefulness
of bankruptcy in such a setting is less obvious. After all, little smoothing
can be done via borrowing in such an environment. Ironically, exclusion
may be “sustainable” in this setting simply because there is not much at stake
for creditors in imposing it.
With more transitory shocks, however, the incentives to borrow for consumption smoothing are relatively large, and the threat carried by a credible
promise of exclusion following default is meaningful. Nonetheless, ex post
exclusion hurts the household precisely because it values borrowing and raises
the issue of the credibility of an exclusion. Credibility is even more implausi-

K. B. Athreya and H. P. Janicki: Credit Exclusion

27

ble when it is assumed to be imposed by a highly competitive industry where
consumers are well aware of competitors’ terms and rates.
As we will see in the following section, the presence of default makes the
results above less obvious. In particular, one’s willingness to smooth even
temporary disturbances may depend importantly on the presence of longerterm shocks and the ability to default should such shocks occur. Conversely,
even a persistent shock may be smoothed by a household that has access to
a default option. In particular, bankruptcy introduces an incentive to “gamble” that is not otherwise present. In the present context, the household may
gamble by borrowing more than it otherwise would just to ensure a smooth
consumption path, knowing that bankruptcy is a possibility should poor incomes continue. Of course, creditors will price such risk, and in the end,
households may choose not to borrow in equilibrium. Therefore, the net
effect of bankruptcy on the equilibrium willingness of households to smooth
shocks is not perfectly straightforward and remains a quantitative issue.

2. THE BASIC MODEL
To study the effects of exclusion and the dependence of the effects of exclusion
on income risk, we now turn to the following model, taken from Athreya
(2004). Let there be a large number of infinitely lived households with identical
preferences given by
∞

βt

E0
t=0

ct1−κ − 1
.
1−κ

(1)

Households save in risk-free claims to consumption that mature in the
next period. Savings earns an interest rate of (1 + r d ). Households have the
option of defaulting on debt. In each period, the household chooses whether
to file for bankruptcy. Bankruptcy is kept simple and is assumed to remove
all the debt of a household.
Bankruptcy generates two costs. Households must pay transactions costs
associated with legal proceedings, as well as have their utility lowered by any
stigma they may feel. Moreover, households are assumed to be temporarily
banned from borrowing. We denote the sum of all costs that did not arise from
credit exclusion by λ and the length of the average exclusionary period by γ .
The preceding structure leads to the following set of value functions.2
At any date, households are either solvent, which we denote by S, or
“borrowing constrained” while excluded because of a past bankruptcy, which
we denote by BC.
2 See Athreya (2004) for more details.

28

Federal Reserve Bank of Richmond Economic Quarterly
The value of being solvent, V S , must satisfy
V S (y, a) = max[W S (y, a), W B (y, a)].

(2)

The value of repaying debt in the current period satisfies
W S (e, a) = max{u(c) + βEV S (e , a )}

(3)

s.t.
a
≤ y + a.
(4)
1 + r l (a )
If a household files for bankruptcy, their debts are removed, and they pay the
transactions costs, λ.
In the period following a bankruptcy, the household is excluded from
borrowing, which means that the value, V BC , from beginning in this state is
c+

W B (e, a) = max{u(c) − λ + βEV BC (a )}

(5)

s.t.
a
≤ y.
(6)
1 + rd
The exclusion from credit markets ends each period with probability, γ , with
the average restriction from borrowing lasting 1/(1-γ ) periods. The value of
this state is therefore
c+

V BC (y, a) = max{u(c) + γ βEV S (y , a ) + (1 − γ )βEV BC (y , a )

(7)

s.t.
c+

a
≤ y + a.
1 + rd

(8)

Let the default probability for a debt of d units be denoted θ bk (a ). In equilibrium, economic profits must be zero. Therefore, given the cost of funds
for intermediaries, (1 + r d + τ ), where τ is a transactions cost that represents
recordkeeping and other operational expenses, the interest rate on loans will
be restricted to
(1 + r d + τ )
r l (a ) =
− 1.
(9)
(1 − θ bk (a ))

Parameterization
With this simple model of consumer borrowing and bankruptcy, we evaluate
the interplay between income persistence, the size of income shocks, the exclusionary period, and desired borrowing. We study five income processes,
which differ along two dimensions: the persistence of shocks, denoted by ϕ,
and their variance, denoted by σ 2 . The first process is our benchmark, taken

K. B. Athreya and H. P. Janicki: Credit Exclusion

29

Table 2
Income Process

μ

σ2

ϕ

YB
Y1
Y2
Y3
Y4

1
1
1
1
1

0.15
0.10
0.10
0.30
0.30

0.97
0.50
0.99
0.50
0.99

from Athreya (2004). It is an AR(1) process broadly consistent with panel
data on U.S. households and includes low income states that are interpretable
as “unemployment.” For brevity, the reader is referred to Athreya (2004) for
details on the (discretized) version of this process. The key parameters of that
process are the mean level of income, μ, which we fix at unity, the variance
among working households, set to 0.15, and the serial correlation of income,
set at 0.97. The remainder of the processes involve changes in the variability
persistence of income shocks relative to the benchmark, where we hold mean
income fixed. The processes are summarized in Table 2. One period in the
model represents one quarter. The remaining parameters are given as κ = 1
(which implies logarithmic utility), τ = 0.0085, β = 0.9865.
Using these processes, we simulate the income, consumption, savings,
and bankruptcy decisions of a large number of households. We then evaluate
household behavior immediately prior to, and following, a bankruptcy filing.
Specifically, we concentrate our attention to the 10 quarters preceding and
20 quarters following a bankruptcy. We study the behavior of cross-sectional
averages in each quarter of this 30-quarter window. Our goal is to evaluate
the extent that exclusion from credit markets is actually a binding restriction
that requires explanation. For example, if, for the benchmark income process, removing exclusion did not change post-bankruptcy debt accumulation,
we would know that exclusion cannot be an important deterrent to default.
By contrast, if removing exclusion did imply a substantial increase in postbankruptcy debt, we have evidence that exclusion matters.
For the remainder of this section, we focus on Figures 2–6. These figures display the path of average quantities in the window around the date of
bankruptcy, where date 0 on the x-axis is the period of the bankruptcy filing.
The top panel in Figures 2–6 presents the results where no post-bankruptcy
exclusion is assumed. The middle panel in Figures 2–6 contains results across
the income process when exclusion is set as in Athreya (2004) to an average
of four years. By contrast, in the bottom panel in Figures 2–6, we assume a
lengthy exclusion of 25 years. For reasonable discount factors, exclusions of
such high duration generate outcomes similar to a truly permanent exclusion.

30

Federal Reserve Bank of Richmond Economic Quarterly

Experiment 1: Effects of Income Risk, Given
Exclusion
We begin by holding exclusion, γ , and filing costs, λ, fixed. We vary the
income process in order to display the effects of income volatility and persistence on asset accumulation and decumulation before and after a bankruptcy.
In the top panel of Figures 2–6, we set γ = 0 (no exclusion). When comparing the top panel across Figures 2–6, we see immediately that asset holdings
are uniformly higher at all dates under processes Y 1 and Y 3 , both of which
display relatively low persistence, than under Y 2 or Y 4 , both of which display
high persistence. The intuition here is the same as presented earlier. Note first
that the average income preceding a bankruptcy is falling for the population.
Given the mean-reversion implicit in all the income processes under consideration, we see that on average, after a filing, incomes rise again and then
level off at their long-term average. The positive income shocks that occur
on average to bankruptcy filers after they file are treated as temporary under
processes Y 1 and Y 3 and treated as somewhat more permanent under the other
two processes. In turn, the former save some of the gains and accumulate
a “buffer stock” of savings. The relationship between persistence and asset
holdings is robust and survives in the middle and bottom panels of Figures
2–6 as well. However, the behavior of assets across the income process grows
more similar as exclusion becomes longer lasting.

Experiment 2: Effects of Exclusion, Given Income
Risk
We now turn to the experiment of central interest: the effect of varying exclusion under a fixed income process. A comparison across panels of each
of Figures 2–6 shows that increased exclusion is met after bankruptcy by increased asset accumulation. Preceding a bankruptcy, asset paths are quite
similar across exclusionary periods. What is perhaps more important to see
is that even when exclusion is eliminated (top panel in Figures 2–6), households simply do not borrow much after bankruptcy. This is true across all four
income processes considered here. It suggests that a valid interpretation of
the observation is that households are not simply excluded from borrowing;
rather they do not wish to borrow after bankruptcy.
One consideration worth mentioning is that our experiments consider the
equilibrium effect of changes in exclusion. Namely, households are assumed
to know, understand, and respond to the changes. In turn, note that our results
focus on the behavior of those in and around a bankruptcy filing. Therefore,
when exclusion becomes strict, it is possible that we observe bankruptcy only
in those circumstances when ex post exclusion would be least painful, all else
equal. For example, consider a world with long exclusionary periods and both
transitory and long-lasting income shocks, such as the processes used here. In

K. B. Athreya and H. P. Janicki: Credit Exclusion

31

such a setting, one might expect that bankruptcy becomes used predominantly
when debts are large and a persistent shock strikes, rather than when a more
transitory shock occurs. Our findings suggest that this effect is unimportant,
as average incomes at the time of filing are very similar across Figures 2–6.
In the discretized income process we employ, the income level “triggering”
bankruptcy is always the state we associate with prolonged unemployment at
a time when unemployment insurance benefits no longer are provided.
A second issue is that even if the circumstances at the time of filing are
not affected strongly by bankruptcy, the rate at which people file may be
materially altered by credit exclusion. This happens in part because debt
accumulation overall may change significantly, making exclusion important
as a deterrent even when it leaves the proximate “cause” (i.e., the state of
the household at the time of filing) of bankruptcy unchanged. We address
this issue next by evaluating the effects of exclusion on aggregate unsecured
credit-market activity in terms of debt accumulation, bankruptcy rates, and
loan pricing. We also provide a first look at studying a narrative that addresses
recent technological changes that have reduced search and switching costs for
households and have led to greater effective competition across lenders.

3.

COMPETITION IN UNSECURED CREDIT MARKETS

Athreya (2004) proposes an explanation for events detailed above by modeling
technological advances by reductions in transactions costs and finds that such
changes produce outcomes broadly consistent with the data. In the current
work, we propose a different approach. Namely, we emphasize in this article
that while reductions in transactions costs are part of the story, the fact that
search and switching costs in particular have fallen may resurrect the credibility problem faced by unsecured lenders. In other words, a borrower who
has defaulted now has an easier time communicating his risk to prospective
lenders, as better credit bureau data are available to lenders. Moreover, a borrower may more easily evaluate the quality of offers from a very wide range of
solicitors both because he receives roughly five times as many offers in the late
1990s as he did in the late 1980s, and also because disclosure regulations such
as the “Schumer Box” allow for easy comparisons of rates and terms. These
changes, in turn, must begin to force lenders to “treat bygones as bygones.”
Therefore, the only remaining rationale for treating bankruptcy filers like “hot
potatoes” is that they must have revealed something about themselves that
makes them undesirable.
A key issue here is the following: To what extent does bankruptcy differentiate households into persistently different risk categories? Answering
this question requires answering the question of “who” bankruptcy filers are.
Athreya (2004) summarizes work by Sullivan, Warren, and Westbrook (1989,
2000), and others, reaching the conclusions that along many relevant dimen-

32

Federal Reserve Bank of Richmond Economic Quarterly

sions such as age, education, and income, bankruptcy filers appear to be “middle class” people who have gotten unlucky. While some of this poor luck was
persistent, much of the immediate history preceding bankruptcy filings was not
atypical. Once again, there in an inherent conflict in arguing that bankruptcy
leads to credit embargoes that filers are mainstream households. After all,
mainstream households would not be treated as pariahs unless they were truly
different from the remainder of the population.

Experiment 3: Are Rising Indebtedness and Default
Rates Consistent With Reduced Search and Switching
Costs?
We now assume that the improvements in informational flows between borrowers and lenders have led to competitive behavior, especially in terms of
lenders no longer being able to sustain the credit exclusion of bankruptcy filers. Athreya (2004) investigates the role of reducing the cost of intermediation
itself and finds that such changes imply more indebtedness and default. In this
article, we focus solely on discerning the effects of reduced credit exclusion,
while fully acknowledging that both processes may (and indeed seem likely
to) have occurred together. To generate the quantitative implications of such
a change, we ask whether the total elimination of any means of ex post credit
exclusion, whereby γ = 0, produces increases in bankruptcy and debt broadly
consistent with the data since the early 1990s.
We proceed in two steps. We first allow for the removal of exclusion in a
way that creditors are not fully aware of the change. This allows us to capture
the initial effects of reductions in search costs that facilitated more switching
among debtors. In particular, we study this “transitional” period by holding
the loan pricing function fixed at its initial steady state level. We then allow for
prices to adjust as lenders learn their environment and compute a new steady
state equilibrium.3 Our first finding is seen in column one of Table 3. We
study the effects of setting γ = 0 under the benchmark income process.

3 A natural criticism could be that we allow borrowers to learn about the new environment
before creditors do. Note, however, that we assume that the technological change (i.e., reduced
search and switching costs) was unanticipated. Therefore, loans made just prior to adopting the
technological change turn out to be mispriced ex post.

YB =(0.97, 0.15)

Y1 =(0.5, 0.1)

Y2 =(0.995, 0.1)

Table 3
Y3 =(0.5, 0.3)

Y4 =(0.995, 0.3)

Exclusion Length
0
0.9375 0.99
0
0.9375 0.99
0
0.9375 0.99
0
0.9375 0.99
0
0.9375 0.99
Bankruptcy Rate
0.0018 0.0012 0.0010 0.0025 0.0014 0.0011 0.0023 0.0012 0.0010 0.0015 0.0009 0.0008 0.0020 0.0012 0.0009
E(a|a<0)
−0.443 −0.472 −0.505 −0.280 −0.318 −0.353 −0.227 −0.356 −0.380 −0.417 −0.453 −0.483 −0.332 −0.303 −0.195
Consumption Coefficient
of Variation
0.142 0.142 0.140 0.084 0.077 0.075 0.123 0.121 0.120 0.104 0.101 0.100 0.296 0.295 0.294
Fraction Borrowing
0.369 0.344 0.324 0.337 0.309 0.301 0.465 0.311 0.295 0.232 0.225 0.235 0.419 0.366 0.329
Transition Pricing
qy=0.9375
qy=0.9375
qy=0.9375
qy=0.9375
qy=0.9375
Bankruptcy Rate
0.0101
0.0006 0.0145
0.0006 0.0060
0.0006 0.0136
0.0006 0.0016
0.0005
E(a|a<0)
−0.505
−0.342 −0.539
−0.341 −0.496
−0.300 −0.515
−0.322 −0.348
−0.214
Consumption Coefficient
of Variation
0.131
0.139 0.127
0.139 0.137
0.139 0.128
0.139 0.142
0.139
Fraction Borrowing
0.415
0.247 0.449
0.248 0.405
0.241 0.427
0.245 0.252
0.130

Income Process

K. B. Athreya and H. P. Janicki: Credit Exclusion
33

34

Federal Reserve Bank of Richmond Economic Quarterly

As in Athreya (2004), the initial steady state assumes an exclusionary period averaging 16 quarters (four years), and thereby sets γ = 0.9375, and
under the benchmark income process, matches several aggregate U.S. unsecured credit and default facts. When exclusion is eliminated, the initial
transition period is quite striking. Notably, the quarterly aggregate default
rate rises sharply from 0.12 percent to 0.18 percent, a 50 percent increase in
quarterly filing rates! The increase in filings is in part driven by the temporary
mispricing of credit risk, which households use to their advantage. This is
seen along both the “extensive” margin of borrowing, whereby more people
borrow, and the “intensive” margin, whereby borrowers are more indebted
than before. In terms of the fraction of borrowers, there is a very large 7.1 percentage point, or roughly a 20 percent increase in the fraction of households
that borrow. Overall indebtedness, as measured by the conditional mean of
debt among those who borrow, also grows substantially, from approximately
$3,400 in the benchmark to $5,050 in the transition. These facts are all qualitatively consistent with the observations over the early 1990s, during which
margins fell while debt and bankruptcies both grew. As lenders adjust pricing
to a world in which exclusion is simply unsustainable, credit supply effectively shrinks, reducing indebtedness and default along with it. This is seen
in the top block of column one in Table 3. The fraction of borrowers falls
back from its transitional maximum to a lower level that is very close to the
initial steady state. Conversely, to get a measure of the deterrent power of
exclusion, we present results for the case where exclusion is increased so as to
average 25 years. In essence, this represents nearly permanent exclusion. In
this case, the previous intuition goes through in reverse, whereby borrowing
and default initially fall very sharply, but then result in long-run loan terms
that make borrowing attractive again, as seen in Figure 7. These features can
also be seen in Figure 8. In the long run, bankruptcy nearly disappears, but
borrowing increases to the point where roughly one-third (32.4 percent) of all
households borrow, and when they do, they actually borrow more than under
benchmark exclusion, at $5,050. These results are largely robust across the
entire set of income processes we consider, and for brevity, we refer the reader
to Table 3 and Figures 9–12 for details.

4.

CONCLUDING REMARKS

Our finding that the removal of ex post exclusion leads to greatly increased
bankruptcy rates and indebtedness is striking. A corollary is that the other
costs of bankruptcy—namely, fees, time costs, and ultimately, the shame or
“stigma” felt by filers—must be very acute indeed. After all, even in the
absence of exclusion, the credit market in our model continues to exist rather
than collapse, even though stigma-related costs were held fixed throughout.

K. B. Athreya and H. P. Janicki: Credit Exclusion

35

In other words, stigma is arguably even more important, and might be all there
is, in keeping unsecured credit markets in existence.
Filing-related costs are important and worrisome, because they indicate
that unless monetary policymakers act to provide repayment commitment, attitudes may be all that lie between the current setting and a setting in which the
young and the wealth-poor generally cannot obtain credit. In particular, one
institutional impediment to the commitment to repay is the U.S. bankruptcy
code. Even after currently enacted reforms take hold, it is still unconstitutional to write contracts waiving the right to bankruptcy. At present, only the
wealthy, who might post collateral, can do so. One alternative is that exemptions be stricter, as they implicitly will make much of the borrowing of even
the wealth-poor collateralized. On the other hand, the benefits arising from
an increase in strictness of exemptions must be weighed against the costs imposed by facing a rigid repayment schedule in an environment of nontrivial
income risk.
The results presented here are simple and suggestive, but by no means
definitive. Yet, they point to several directions for future research, all of
which seem essential if we are to explain the rich array of unsecured credit
products in a world where penalties appear nebulous and even unavailable.

36

Federal Reserve Bank of Richmond Economic Quarterly

Figure 1 Annual Credit Card Solicitations
6

Annual Credit Card Mailings (in billions)

5

4

3

2

1

0
1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004
year

K. B. Athreya and H. P. Janicki: Credit Exclusion

37

Figure 2 Mean Household Behavior Before and After Bankruptcy
(Y=YB )=(0.97, 0.15)
γ=0.00
10

-6

5

-7

0

-8

-5

-9

-10

-10
-5

0

5

10

15

20

γ=0.9375
-6

10

-7

5

-8
0
-9
-5
-10
-10

-11

-15

-12
-10

-5

0

5

10

15

20

γ=0.99
-4

10

-6

5

-8
0
-10
-5

Assets
Consumption
Value Function
Income

-10

-12
-14

-15

-16
-10

-5

0

5
quarters

10

15

20

Value Function

Asset Holdings, Consumption, Income (`000 dollars)

-10

38

Federal Reserve Bank of Richmond Economic Quarterly

Figure 3 Mean Household Behavior Before and After Bankruptcy
Y1 =(0.5, 0.1)
γ=0.00
10

-4

5

-5

0

-6

-5

-7

-10

-8
-5

0

5

10

15

20

γ=0.9375
-4

10

-5

5

-6
0
-7
-5
-8
-10

-9

-15

-10
-10

-5

0

5

10

15

20

γ=0.99
15
0
10
-2
5
-4

0

-6

Assets
Consumption
Income
Value Function

-5
-10

-8

-15

-10
-10

-5

0

5

quarters

10

15

20

Value Function

Asset Holdings, Consumption, Income (`000 dollars)

-10

K. B. Athreya and H. P. Janicki: Credit Exclusion

39

Figure 4 Mean Household Behavior Before and After Bankruptcy
Y2 =(0.995, 0.1)
γ=0.00
-8

10

5
-9
0
-10
-5

-10

-11
-5

0

5

10

15

20

γ=0.9375
-8

15

-9
5
-10
-5
-11

-15
-10

-5

0

5

10

15

20

γ=0.99

15

-8

10
-9
5
0

-10
Assets
Consumption
Value Function
Income

-5
-10

-11

-15

-12
-10

-5

0

5
quarters

10

15

20

Value Function

Asset Holdings, Consumption, Income (`000 dollars)

-10

40

Federal Reserve Bank of Richmond Economic Quarterly

Figure 5 Mean Household Behavior Before and After Bankruptcy
Y3 =(0.5, 0.3)
γ=0.00
-4

10

-5

-6

0

-7

-10

-8
-5

0

5

10

15

20

γ=0.9375

15

0

10

-2

5
-4
0
-6
-5
-8

-10
-15

-10
-10

-5

0

5

10

15

20

γ=0.99
15

0

10

-2

5
-4
0
-6

Assets
Consumption
Value Function
Income

-5
-10

-8
-10

-15
-10

-5

0

5
quarters

10

15

20

Value Function

Asset Holdings, Consumption, Income (`000 dollars)

-10

K. B. Athreya and H. P. Janicki: Credit Exclusion

41

Figure 6 Mean Household Behavior Before and After Bankruptcy
Y4 =(0.995, 0.3)
γ=0.00
-15

10

-17

5

-19
0
-21
-5
-23
-10

-25
-5

0

5

10

15

20

γ=0.9375

10

-18
-19

5

-20
0

-21
-22

-5

-23
-10
-24
-10

-5

0

5

10

15

20

γ=0.99

10

-18
-19

5

-20
0

-21
Assets
Consumption
Value Function
Income

-5

-22
-23

-10
-24
-10

-5

0

5
quarters

10

15

20

Value Function

Asset Holdings, Consumption, Income (`000 dollars)

-10

42

Federal Reserve Bank of Richmond Economic Quarterly

Figure 7 Loan Pricing By Income and Exclusion
γ=0.0

5.0
4.5
4.0
3.5
3.0
2.5
2.0
1.5
1.0
0.5
-5.5

-4.5

-4.0

-4.5

-5.0

-4.0

γ=0.9375

5.0
4.5

Interest Rate

4.0
3.5
3.0
2.5
2.0
1.5
1.0
0.5
-5.5

-5.0

γ=0.99

5.0
4.0

Benchmark
Y1=(0.5,0.1)

3.0

Y3=(0.5,0.3)

Y =(0.995,0.1)
2

Y4=(0.995,0.3)

2.0
1.0

-5.5

-4.5

-5.0
Assets

-4.0

K. B. Athreya and H. P. Janicki: Credit Exclusion

43

Figure 8 Transitional Effect of Change in γ with Unadjusted Pricing
Income Process: YB
γ=0.00
2

Assets ('000 dollars)

0
-2
-4
-6
-8
No Exclusion Post-BK|qγ=0.9375

-10

No Exclusion|qγ=0.0
Exclusion γ=0.9375|qγ=0.9375

-12

-10

-5

0

5

10

15

20

quarters

γ=0.99

Assets ('000 dollars)

5

0

-5

Exclusion γ=0.99|qγ=0.9375

-10

Exclusion γ=0.99|qγ=0.99

Exclusion γ=0.9375|qγ=0.9375

-10

-5

0

5

quarters

10

15

20

44

Federal Reserve Bank of Richmond Economic Quarterly

Figure 9 Transitional Effect of Change in γ with Unadjusted Pricing
Income Process: Y1
γ=0.00
4
2

Assets ('000 dollars)

0
-2
-4
-6
-8
-10

No Exclusion Post-BK|qγ=0.937
No Exclusion|qγ=0.0

-12

Exclusion γ=0.9375|qγ=0.9375

-14
-10

-5

0

5

10

15

20

quarters

γ=0.99
8
6

Assets ('000 dollars)

4
2
0
-2
-4
-6
-8

Exclusion γ=0.99|qγ=0.9375

-10

Exclusion γ=0.99|qγ=0.99

Exclusion γ=0.9375|qγ=0.9375

-12

-10

-5

0

5

quarters

10

15

20

K. B. Athreya and H. P. Janicki: Credit Exclusion

45

Figure 10 Transitional Effect of Change in γ with Unadjusted Pricing
Income Process: Y2
γ=0.0
2
0

Assets ('000 dollars)

-2
-4

-6
-8
-10

No Exclusion Post-BK|qγ=0.9375

-12

Exclusion γ=0.9375|qγ=0.9375

No Exclusion|qγ=0.0

-10

-5

0

5

10

15

20

quarters

γ=0.99
6
4

Assets ('000 dollars)

2
0
-2
-4
-6
-8
Exclusion γ=0.99|qγ=0.9375

-10

Exclusion γ=0.99|qγ=0.99

-12

Exclusion γ=0.9375|qγ=0.9375

-14
-10

-5

0

5

quarters

10

15

20

46

Federal Reserve Bank of Richmond Economic Quarterly

Figure 11 Transitional Effect of Change in γ with Unadjusted Pricing
Income Process: Y3
γ=0.00
6
4

Assets ('000 dollars)

2
0
-2
-4
-6
-8

No Exclusion Post-BK|qγ=0.9375

-10

No Exclusion|qγ=0.0
Exclusion γ=0.9375|qγ=0.9375

-12
-14
-10

-5

0

5

10

15

20

quarters

γ=0.99
10

Assets ('000 dollars)

5

0

-5
Exclusion γ=0.99|qγ=0.9375
Exclusion γ=0.99|qγ=0.99

-10

Exclusion γ=0.9375|qγ=0.9375

-10

-5

0

5

quarters

10

15

20

K. B. Athreya and H. P. Janicki: Credit Exclusion

47

Figure 12 Transitional Effect of Change in γ with Unadjusted Pricing
Income Process: Y4
γ=0.00
0

Assets ('000 dollars)

-2

-4

-6

No Exclusion Post-BK|qγ=0.9375

-8

No Exclusion|qγ=0.0
Exclusion γ=0.9375|qγ=0.9375

-10
-10

-5

0

5

10

15

20

quarters

γ=0.99
6
4

Assets ('000 dollars)

2
0
-2
-4
-6

Exclusion γ=0.99|qγ=0.9375
Exclusion γ=0.99|qγ=0.99

-8

Exclusion gamma=0.9375|qγ=0.9375

-10
-10

-5

0

5

quarters

10

15

20

48

Federal Reserve Bank of Richmond Economic Quarterly

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. 2000. The Fragile Middle Class. New Haven, Conn.: Yale
University Press.
Yue, Vivian Z. “Sovereign Debt and Default with Renegotiation.” Mimeo,
University of Pennsylvania.

The 3-6-3 Rule: An Urban
Myth?
John R. Walter

O

bservers often describe the banking industry of the 1950s, 1960s,
and 1970s as operating according to a 3-6-3 rule: Bankers gathered
deposits at 3 percent, lent them at 6 percent, and were on the golf
course by 3 o’clock in the afternoon. The implication is that the industry was
a sleepy one, marked by a lack of aggressive competition. Further, the often
heard phrase “bankers’ hours” also seems to point to a lack of competitive
zeal. Tight regulation is thought to have limited competition and allowed the
3-6-3 rule and the concept of bankers’ hours to survive.
The banking industry was indeed subject to a raft of regulations that were
introduced during the Great Depression and only began to be removed in the
early 1980s. Included were restrictions that limited the formation of banks
and the location of bank branches. These regulations also limited the interest
rates they could pay depositors and charge borrowers.
In today’s banking environment, one can hardly imagine bankers operating by anything close to a 3-6-3 rule because the market is clearly quite
competitive and is likely more competitive than during the 1950s, 1960s, and
1970s. Consider an example of today’s competitive setting: A visit to the
Internet allows a mortgage borrower the choice of hundreds of mortgage
lenders from around the country, any of whom are happy to lend. Price comparisons are fairly simple since all of these mortgage lenders openly advertise
their interest rates and, to a lesser degree, their fees. Further, with numerous
offers of home equity loans and an average of 4 billion credit card solicitations
mailed per year, consumers have ample options for financing non-real-estate
consumption (Lazarus 2003). Last, most shopping areas contain several bank
branches (including those from out-of-state banks) and consequently provide
The author benefited greatly from comments from Kartik Athreya, Hubert Janicki, Yash Mehra,
and Ned Prescott. Able research assistance was provided by Andrea Waddle and Chris Herrington. The views expressed herein are not necessarily those of the Federal Reserve Bank
of Richmond or the Federal Reserve System.

Federal Reserve Bank of Richmond Economic Quarterly Volume 92/1 Winter 2006

51

52

Federal Reserve Bank of Richmond Economic Quarterly

consumers with a wide choice of deposit facilities, as well as ATMs from
banks not located in the shopping area. Much of this type of competition was
not in place before the 1980s, in part because delivery technology had not
matured. Undoubtedly, restrictions on banks prior to the 1980s also played a
role.
There is a good deal of evidence that restrictions in place before the 1980s
limited the competitiveness of banking markets and thereby granted some
banks monopoly power. For example, Flannery (1984) presents evidence that
banks in unit banking states (i.e., states that largely prohibited branches) were
less efficient than those in states allowing less restrictive branching. Flannery
also indicates that branching restrictions reduced competition, allowing banks
in unit branching states to earn above-normal profits. Similarly, Keeley (1990,
1192) finds that branching restrictions “provide a degree of protection from
competition.” Others also have found evidence that branching restrictions
were anti-competitive, allowing banks to charge higher interest rates on loans
and pay lower rates on deposits.1
Nevertheless, how widespread was the influence of these restrictions on the
banking industry and its customers? When the restrictions were binding, they
likely had significant effects; however, a review of the regulations indicates
that they were often not binding or were at times sidestepped. Limits on the
formation of new banks, while fairly strict from the Depression through the
1950s, were loosened afterward. As a result, bank formation in the 1960s and
1970s was not very different from that in the 1980s and 1990s. While a number
of states maintained stringent restrictions on branching, aggregated across the
United States, the number of bank branches grew quite rapidly well before
branching restrictions were removed in the 1980s. Interest rate restrictions
were binding for only part of the period. Further, even if the restrictions had
been consistently binding, the opportunity for banks to exercise monopoly
power was checked to some degree by intense competition from nonbank
providers of most of the same products offered by banks. Also, some aggregate
measures of bank profits and costs do not indicate that banks held significant
monopoly power.
Evidence produced by Flannery (1984) and Keeley (1990) and others
clearly indicates that restrictions limited competition and allowed some
monopoly profits. Yet, the ability of financial market competitors (banks and
nonbanks) to sidestep the restrictions may have offset some of the negative
effects of the restriction.
1 Keeley (1990, 1192) cites a number of studies on the effect of branching on pricing.

J. R. Walter: The 3-6-3 Rule
1.

53

RESTRICTIONS AND EFFICIENCY

One can expect that the three types of restrictive banking regulations mentioned earlier—new bank entry, branching, and pricing—would have led to
a staid and inefficient banking industry. On the one hand, if the banking industry faced no restrictions, incumbent banks could not operate inefficiently
for long. Other banks or entrepreneurs, observing an inefficient bank or one
charging above-market prices, will perceive a profit opportunity by grabbing
the customers of the inefficient bank and forming a bank or opening a branch
in competition with the incumbent bank. Faced with this threat of entry,
incumbent banks have strong incentive to remain efficient.
On the other hand, entry restrictions (on the formation of new banks) and
branching restrictions remove the threat of entry, allowing inefficient banks
to remain. An investor, who might be tempted to form a new bank, will be
prevented by binding entry restrictions. Branching restrictions would preclude
incumbents from entering one another’s markets to vie for these profits.
Interest rate restrictions, or ceilings on deposits or loans, also remove
the incentive to compete aggressively. Interest rate ceilings on deposits, if
binding, remove the opportunity to compete since a new entrant cannot attract
the inefficient incumbent’s customers by offering a better interest rate. A
ceiling on loan interest rates likewise implies a reduced incentive to compete
aggressively. Incentives are reduced because, as discussed below, with a
ceiling, the bank does not wish to make as many loans as customers would
seek.

2.

ENTRY RESTRICTIONS

Restrictions on entry were a prominent feature of the American banking environment throughout its history that continues today.2 Their intensity varied
from extremely strict to fairly liberal. Entry restrictions were inaugurated
in America as a means of enhancing the flow of government revenues from
banks. After the formation of the national banking system in the 1860s, entry restrictions seem intended to protect from failure the banks for which the
chartering agency was responsible. Similarly, following the widespread bank
failures of the 1920s and the early years of the Depression, and with the 1934
creation of federal deposit insurance, the clear goal of these restrictions was
to protect incumbent banks from a repetition of the earlier failures.
From 1934 through the early 1980s, restrictions were tighter than they
are today, though the rate of entry was not significantly different for much of
the pre-1980 period. Bank entry was slow during much of the 1930s, 1940s,
2 In the next section, I discuss another type of entry restriction—limiting existing banks’
ability to open branches.

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Federal Reserve Bank of Richmond Economic Quarterly

and 1950s. In contrast, entry was more rapid in the late 1960s and 1970s,
occurring at rates similar to those of the 1980s and 1990s. Consequently,
entry restrictions, at least in the 1960s and 1970s, may have had only a small
negative effect on competition.

The Origin of the Tradition of Government-Granted
Banking Charters
Just prior to the Revolutionary War, American banking services, which at the
time mostly consisted of issuing notes to circulate as money, were largely
provided by colonial governments (McCarthy 1984, 4). The issue of such
notes in exchange for specie and other assets provided an inexpensive source
of funding for the colonial governments. Private attempts to form note-issuing
banks were quelled by colonial government rulings.
By the end of this period, government ownership of banks, or at least government authorization to operate a bank, was firmly established by 100 years
of American banking tradition. The U.S. Constitution (in Article 1, Section 10,
Clause 1) made state government ownership of note-issuing banks impossible
by denying states the power to issue paper money (called bills of credit in the
Constitution). As a result, the tradition was carried forward through government charter of private banks once the United States was formed. For the next
50 years, in order to form a bank, organizers were typically required to convince their state legislature to pass a law granting a bank charter (Robertson
1995, 21–22; McCarthy 1984, 5–8). While the colonial governments benefited directly from the seigniorage revenues earned from government bank
note issues, the constitutional prohibition meant that state governments had
to acquire the seigniorage earnings indirectly. States granted only a limited
number of charters and extracted compensation from these banks in exchange
for the valuable note-issue privilege (McCarthy 1984, 6–7). Such compensation included fees paid to states when charters were issued, shares in the new
banks issued to the state at below-market prices, and requirements that banks
finance various government services such as schools (Sylla, 4).
Starting with Michigan in 1837, states began to move away from requiring
legislative action to form banks. States formed administrative agencies empowered to charter banks that met minimum requirements. States continued
to derive extensive revenues from these banks by requiring them to purchase
state bonds as security for bank note issues.
In 1863, the opportunity to form banks with federal charters was created.
The charter-granting agency was a newly created bureau of the U.S. Treasury
called the Comptroller of the Currency and was headed by an appointee known
as the Comptroller. Following 1863, when investors decided to form a bank,
they had a choice of either a national charter or a state charter so that both
types of banks were extant, a situation that continues today. When the national

J. R. Walter: The 3-6-3 Rule

55

banking system was created by the National Currency Act of 1863, national
banks, chartered by the Comptroller, were granted the right to issue notes in
exchange for purchasing U.S. bonds as security for their note issues (McCarthy
1984, 11).
One reason for creating the national bank charter was to establish a market
for issues of government debt needed to finance the prosecution of the Civil
War. In 1865, state bank issues of notes were effectively restricted by a
10 percent tax on all banks issuing notes, and national bank notes became
the national currency (hence the title Comptroller of the Currency). The
replacement of state bank notes (backed by state government bonds) with
national bank notes (backed by U.S. government bonds) meant a source of
revenue was stripped from state governments and was shifted to the federal
government. This expropriation of government revenues was made politically
feasible only because the Civil War placed the federal government under severe
financial pressure (McCarthy 1984, 10).

Chartering Restrictions Tightened After
Depresssion-Era Bank Failures
While the first several Comptrollers held to a fairly strict policy of new national
bank charters, subsequent Comptrollers loosened the policy for a more liberal
one. State-chartering agencies followed suit.3 As seen in Figure 1, the number
of banks began growing rapidly in the late 1880s, and growth was especially
rapid after the turn of the 20th century until 1921.
An important explanation for the brisk growth in the number of banks
from 1900 to 1921 was that the minimum capital required to form a bank
was reduced (Mengle 1990; Wheelock 1993). But banks failed in growing
numbers starting in 1921, and the failure rate grew even higher with the advent
of the Depression and continued until 1934.4 Failures in the 1920s were tied
to agricultural problems and were concentrated in the agricultural regions of
the United States. Failures during the early years of the Depression were more
widespread.
By 1934, half of all banks had failed. The widespread banking failures
convinced many policymakers that the liberal chartering rules of the past 50
years had negative consequences and that entry should be restricted in the
future. In his January 1935 report to Congress, Comptroller J. F. T. O’Connor
expressed his view that future entry should be restricted:
3 Sources of historical information on chartering standards of state banking agencies are quite
limited. Consequently, my discussion of chartering policy is largely restricted to the policy of the
Comptroller of the Currency for which more information is available.
4 See Walter (2005) for a review of the causes of bank failures in the 1920s and 1930s.

56

Federal Reserve Bank of Richmond Economic Quarterly

Figure 1 Number of U.S. Banks: 1834–2004
35,000

30,000

25,000

20,000

15,000

10,000

5,000

20
04

19
94

19
84

19
74

19
64

19
54

19
44

19
34

19
24

19
14

19
04

18
94

18
84

18
74

18
64

18
54

18
44

18
34

0

Sources: U.S. Department of Commerce, Bureau of the Census; Federal Deposit Insurance Corporation.

Great caution should be exercised in the future in the establishment of
either State or national banks, or branches of either, in order to prevent a
repetition of the failures of a few years ago.... The Comptroller’s Office,
under existing law, is in a position to require national banks to maintain
adequate, sound capital, and also to prevent the organization of a new
national bank unless it has adequate, sound capital, and unless there is
a need for additional banking facilities in the location chosen.... (OCC
1934, 14)

O’Connor’s restrictive attitude toward chartering new banks, whereby the
agency approved relatively few new bank charters, continued until the early
1960s, overlapping the tenure of his two successors, Preston Delano and Ray
M. Gidney. Figure 2 shows a fairly low level of new bank entries from 1935
until the end of World War II, with some increase thereafter, mostly because
of new state charters.
As required by the BankingAct of 1935, the Comptroller analyzed applications for bank charters to review the character of the prospective management

J. R. Walter: The 3-6-3 Rule

57

Figure 2 Number of New Charters Per Year: 1935–2002
450
400
350
300
250
200
150
100
50

19
99
20
02

19
95

19
91

19
87

19
83

19
79

19
75

19
71

19
67

19
63

19
59

19
55

19
51

19
47

19
43

19
39

19
35

0

Source: Figure created from FDIC data.

and the “convenience and needs of the community” in which the bank would
operate. The Act did not specify the parameters of these analyses, but instead left that responsibility to supervisors. As part of the convenience and
needs analysis, the Comptroller carefully reviewed the market in which the
applicants intended to enter.

Variations in the Severity of Chartering Restrictions
The policy for chartering national banks was relaxed with the appointment
of James J. Saxon by President Kennedy in November 1961. Saxon made
clear to the banking community his willingness to approve more charters than
his predecessors. As a result, the Office of the Comptroller for the Currency
(OCC) received more applications in Saxon’s first three years in office than in
the past 20 years (Robertson 1995, 153). However, this increase was not so
far-reaching. Robertson (1995, 154) notes that the OCC remained “concerned
to prevent overinvestment in banking by trade areas, and the economists on
the staff were continually on the alert for signs of such overinvestment.” In his

58

Federal Reserve Bank of Richmond Economic Quarterly

1965 testimony on the OCC chartering policy before a Senate subcommittee,
Saxon indicated that the change was one of tone, not policy:
I would not characterize... our policy [as] being more liberal. Our policy
was clearly to minimize, to reduce the image of the national banking
system as being one of a closed industry. (White 1992, 11)

Further, in February 1965, Comptroller Saxon announced that new charters would not be granted in some states or portions of others, plus Washington,
D.C. (White 1992, 11). For the remainder of Saxon’s tenure (Saxon left the
OCC in 1966) and throughout the rest of the 1960s, the OCC approved fewer
new charters. The number of state bank charters per year declined in the late
1960s as well; Figure 2 shows a significant decline in the number of new banks
during this period.
Starting in the early 1970s, national bank charters began to increase again.
Still, the long-standing OCC policy of limited entry persisted to a degree.
The OCC continued to approve new banks only when the agency deemed it
necessary.

Analysis of Needs
How did the OCC determine the need for a new bank? The Senate Banking Committee investigated the question in the late 1970s. The Committee
reported that when OCC examiners reviewed the needs of a community in
which investors wished to open a bank, they were to answer the following
questions:
Is there a public need for the proposed bank, or do existing banks and
branches serve the area reasonably well?
Is it reasonable to expect that the available banking business will be
adequate to support the proposed bank, together with existing competitive
banks and branches, or will an overbanked situation be created? (The
Senate Banking Committee, U.S. Senate 1980)

The OCC often denied charters because it decided that there was little
need for a new bank; for example, a community might already be served
“reasonably well.” Need was measured by a number of factors including per
capita income, residential growth, deposit growth, loan-to-deposit ratios at
existing banks, population per banking office, hours of operation of existing
banks, and interest rates paid on deposits by existing banks. The Committee
notes, however, that the OCC could offer no clear benchmarks for any of these
measures used to determine whether a need existed and that various measures
were used either to justify or deny an application.

J. R. Walter: The 3-6-3 Rule

59

Need was the major reason for rejected applications during the years covered in the study (1970 through 1977 [U.S. Senate 1980, 31]). Inadequate need
accounted for, either in part or in whole, 62 percent of denials. In addition,
28 percent of denials were issued to protect “a newly approved or recently
opened bank.”
The negative findings of this Committee report sparked a policy shift at
the OCC. In October 1980, John Heimann, Comptroller from 1977 to 1981,
announced that the OCC would de-emphasize the analysis of need and focus instead on the proposed bank’s organizing group and operating plan (White 1992,
54). Following the announcement, new national bank charters increased, from
41 in 1979 to 268 in 1983 (White 1992, 54). The large increase in new charters
during the early 1980s was not only attributable to OCC actions, however. At
the same time, state agencies were chartering new banks fairly quickly (for
example, 171 in 1983) so that the total increase in bank charters in 1983 was
about 370 (see Figure 2).
The Heimann policy was reversed, however, in the mid-1980s. Falling
banking industry profitability led to a decline in new bank formations. In the
face of weakened bank profits, the OCC clamped down on new bank charters
in order to protect newly formed banks, an apparent return to the policies of
the late 1970s (White 1992, 54).
Needs analysis endures today. The OCC continues to consider the need for
a bank when reviewing an application (OCC 2005, 32). When reviewing a new
bank’s application for membership, the Federal Reserve also reviews market
need. State banking agencies often regard need as an important factor as well.
Still, supervisors report that needs analysis today receives less emphasis than
in the past.

Entry Restrictions Since 1934
Entry restrictions in the form of needs analysis almost certainly limited competitive pressure on banks. An existing bank knew that as long as it was
serving its market “adequately,” it had nothing to fear from new entrants.
Consequently, it was under less pressure to innovate or seek improvement
than if there had been no restrictions in place.
But how binding were these entry restrictions for new bank formation?
While the OCC as well as state agencies emphasized limiting bank entry to
only those banks that were, in the regulator’s determination, needed, how
many new bank formations were prevented? Figure 2 shows that during
the 1930s, 1940s, and 1950s, entry was slow compared to that during the
1980s and 1990s. On average, from 1934 through 1959, the annual rate of
new bank entry was 0.8 percent (the annual new bank formations divided
by the outstanding number of banks), compared to 1.6 percent during the
1980s and 1990s. Figure 2 implies that during the 1960s and 1970s, entry

60

Federal Reserve Bank of Richmond Economic Quarterly

was fairly rapid and not much different than in the 1980s and 1990s when
entry restrictions were less binding. On average, the rate of entry during
the 1960s and 1970s was 1.4 percent, just below the rate of entry in the
1980s and 1990s, but not greatly so.

3.

BRANCHING RESTRICTIONS

Like entry restrictions, branching restrictions are considered a major factor that
limited the level of competition in the U.S. banking market until they were
removed in the 1980s. Federal and state restrictions on banks’ability to branch
were an important feature of the U.S. banking environment throughout the 20th
century and certainly from the 1930s until the 1980s. Many states maintained
restrictions on branching within their home state, and the combination of
state and federal laws worked to prevent interstate branching until the 1990s.
Surprisingly, given that numerous states maintained restrictive branching laws,
the number of branches grew fairly rapidly during the 1950s, 1960s, and
1970s, as detailed below. In turn, population per branch declined significantly.
Further, even though today in-state and interstate restrictions on branching are
no longer significant, local banking market concentration is no lower now
than it was before the restrictions were lifted. Even without branches, banks
were able to compete for loans by locating loan production offices around the
country since in-state and interstate branching restrictions did not apply to
these offices. So branching restrictions may have imposed less of a burden on
competition than one might imagine.

Early History of Branching Restrictions
Branching was not a significant feature of the banking landscape until just
before the turn of the 20th century. It was not specifically prohibited before
this time but simply unused (Mengle 1990, 5). Early discussions of allowing
national banks to branch occurred in the late 1890s, but brought opposition
from bankers. Large money center banks opposed branching, fearing a loss of
revenues from services provided by country banks, but smaller banks opposed
branching as well (Mengle 1990, 6). By 1929, a number of states had enacted
laws restricting state-chartered banks’ ability to branch within their home
states. The law for national banks was unclear and from the late 19th century
until early in the 20th century, the views of the OCC concerning branching by
national banks changed with each new Comptroller.
Shifting views of the Comptroller became irrelevant when, in 1927, the
McFadden Act was enacted. The Act authorized national banks to branch
within their headquarter city, but no further, in states that allowed bank branching (Mengle 1990, 7). The McFadden Act was amended by the Banking Act
of 1933 to allow national banks to branch to the same extent as state banks in

J. R. Walter: The 3-6-3 Rule

61

their home state. This meant that in states that did not grant branching privileges, national banks could not branch either. Interstate branching was de
facto prohibited because the McFadden Act allowed national banks to branch
only within their home state; additionally, state laws prohibited branches of
out-of-state banks from forming (Mengle 1990, 3).

Branching Restrictions, Post-Depression
While many unit (nonbranching) banks failed during the Depression, branch
banks survived, encouraging some states to liberalize their branching laws.
Nine states allowed statewide branching in 1929 (Mengle 1990, 6). By 1939,
this number had doubled to 18. Likewise, the number of states prohibiting
branching fell from 22 to 14. In addition, in 1939, 11 states allowed limited
branching (for example, branching within a certain number of miles of the
bank’s headquarters).
These numbers changed between 1939 and 1979, but not by much. Only
three additional states allowed statewide branching during these 40 years, and
the number prohibiting any branching declined by one.
Between states that prohibited branching and those that allowed statewide
branching were a number of states with limited branching. In several such
states, limits were gradually removed before 1979. For example, in Virginia,
banks were only allowed to branch within their home county and contiguous
counties or cities. However, a 1962 amendment relaxed this rule. The amendment allowed bank holding companies (BHCs) to acquire banks throughout
the state while retaining the branching rights of the acquired banks. A BHC
could acquire small banks throughout Virginia and then add branches in all
contiguous counties, bringing new competitors to banks already in these counties or opening branches in communities that previously had no headquarter
or branch banks (Mengle 1989, 3–5).
Soon enough, in Virginia large BHCs formed that owned banks throughout
the state, all essentially sharing the same name and back-office processing. So,
after 1962, statewide branching was possible, though it was through the vehicle of bank holding company ownership. Still, multibank holding companies
faced some disadvantages as compared to banking organizations composed
of one bank with many branches. Each bank within a holding company had a
board of directors and a somewhat independent corporate structure, imposing
some additional costs. In 1978, the Virginia state legislature further liberalized branching laws by allowing banks to merge and keep their branching
privileges, still without moving to full statewide branching. At this point the
statewide multibank BHCs could merge their banks into one and produce a
bank with branches throughout the state. Finally, in 1986, Virginia allowed
de jure statewide branching so that banks could open branches anywhere in
the state without first acquiring a bank in a contiguous county.

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Federal Reserve Bank of Richmond Economic Quarterly

In the late 1970s and the 1980s, pressure was brought on state legislatures
throughout the country to further liberalize branching laws. An important
reason banks wanted to expand branching was that communications and information technologies improved, which lowered the cost of running large,
far-flung branch networks. In turn, large banks gained a relative advantage
in efficiency over smaller banks, encouraging bankers to argue for liberalization of branching laws so that the efficiencies might be captured. Banking
companies first took advantage of these efficiencies through holding company
acquisitions of banks within states and across state lines. As it became clearer
that branching banks and multistate banking companies enjoyed cost advantages that allowed them to predominate, unit banking states liberalized in-state
branching laws to give their home state banks the opportunity to compete with
larger banks from other states. By 1990, only two states prohibited branching. Ultimately, full interstate branching was authorized by the Riegle-Neal
Interstate Banking Act of 1994.

Branching Restrictions Sidestepped
When branching restrictions were in place prior to the 1980s, they may have
provided local banks competitive advantages in gathering deposits, and to
some degree, in making loans to their deposit customers. One important
reason is that most retail and small business customers tend to hold deposits
with nearby banks or branches. If bank customers have a strong preference for
local providers and outside banks are prevented from opening local branches,
then local banks may enjoy some degree of monopoly power in deposit-taking.
Further, there can be cost advantages to borrowing from the same institution
that holds the borrower’s deposits. As noted earlier, various studies have found
evidence that the restrictions had negative effects on competition.
Nevertheless, competition was not impossible. Banks were (and still are)
free to make loans to borrowers, regardless of the borrower’s location. Accordingly, they can make loans in locations where they do not have branches, either
by choice or because of regulatory restrictions. In other words, while in-state
and interstate branching restrictions may have limited a bank’s branches to
one state, or to one portion of a state, the bank could make loans to borrowers
anywhere in the country.
In order to lend more easily to borrowers distant from bank headquarters or branches, loan production offices (LPOs) were opened. Such offices,
which could be located throughout the United States, could not accept deposits but typically housed bank loan officers who prospected for commercial
and retail loan customers in a territory surrounding the office. Of course,
as mentioned earlier, the inability to accept deposits placed LPOs at a cost
disadvantage compared to incumbent banks. Still, LPOs were important
enough competitors to small local banks that the Independent Bankers As-

J. R. Walter: The 3-6-3 Rule

63

sociation of America argued strongly against continuing them when hearings were held in 1968 after the Federal Reserve first authorized them for
state member banks (U.S. Congress 1968, 2–12). The OCC had authorized LPOs for national banks at an earlier date (U.S. Congress 1968, 13).
A White House study estimated that in 1981 there were at least 350 LPOs
operating in 20 states (Golembe 1988, 92).

Branching Grew Regardless of
Restrictions—Concentration Was Low
The number of banking offices (including both head offices and branches) grew
fairly rapidly relative to population, despite branching restrictions. Branching
restrictions remained largely unchanged between the 1930s and 1980, except
as noted in states such as Virginia, which allowed widespread de facto branching while retaining de jure prohibitions on statewide branching. Fewer than
half of all states allowed statewide branching and about one-quarter prohibited
any branching. In 1950, the number of persons per bank office was 8,300.
This figure had fallen to 4,300 by 1980. Following the broad liberalization
of branching laws that began in 1980, population per banking office fell only
a little more to 3,800 in 2004. So while branching laws in restrictive states
clearly restrained competition, on average, the number of competing offices
appears to have grown rapidly despite the restrictions. Still, expansion in the
number of branches per person is not a completely definitive indication of
enlarged competition, since some of this growth may have been driven by the
growth of suburbs. If so, the number of branches might decline, while the
number of competitors near one another might change little or even fall.
Data on local market concentration provide a more complete measure of
market competition than the number of branches per person. Had branching restrictions severely limited competition, one might expect loosened branching
regulations to have produced significant declines in local market concentration once nonlocal banks were allowed to place branches in communities that
previously limited competition. Instead, average local concentration, as measured by local deposit shares, was almost completely unchanged from 1980
to the present (Moore and Siems 1998, 4).5

4.

INTEREST RATE RESTRICTIONS

Just as chartering restrictions were heightened immediately following the Depression, other types of limitations were placed on banks, which tended to
5 The measure used by Moore and Siems is the Hirshman-Herfindahl Index (HHI), which is

the sum of the squares of every bank’s deposit shares in the measured market. They create a
nationwide weighted-average HHI for each year from U.S. local market HHIs.

64

Federal Reserve Bank of Richmond Economic Quarterly

reduce competition beginning at about the same time.6 One important type
of restriction, ceilings on interest rates, constrained banks’ ability to compete
with one another in pricing. Nevertheless, the competitive effects of these
caps were limited.

Interest Rate Ceilings on Deposits
The Banking Act of 1933 prohibited the payment of interest on checking accounts for national banks and state-chartered Federal Reserve member banks.
It also required the Federal Reserve to regulate interest rates on time and savings deposits (Board of Governors 1933, 286). The same rules applied to
nonmember banks (i.e., state-chartered banks that were not members of the
Federal Reserve System) by the Banking Act of 1935. The Fed’s rule that
implemented these Acts was Regulation Q.
The history of theseActs indicates that legislators had several goals in mind
when imposing restrictions on interest rates (Gilbert 1986, 22–23). First, some
members of Congress expressed the view that interest rate competition among
banks was excessive, perhaps contributing to bank failures in the 1920s and
1930s, and should be curtailed in the future. Second, the prohibition of interest
on demand deposits was meant to prevent banks from sending funds gathered
in their local communities on to larger city banks. Prior to these Acts, country banks often deposited their excess funds into larger correspondent banks
that, of course, paid them interest on the deposits. Legislators claimed that
prohibiting such interest payments would encourage country banks to reinvest
the funds gathered from depositors in loans made in the local community,
presaging the Community Reinvestment Act of 1977 by 40 years.7
The third goal of the restrictions was to prevent the liquidity problems that
often accompanied seasonal funds demands of smaller banks. The agricultural
cycle often meant that many country banks in agricultural regions needed
funds for loans around the same time each year. In turn, these banks would
attempt to withdraw funds from city banks, creating liquidity problems for the
latter. Consequently, city banks necessarily curtailed lending to their nonbank
customers.
The fourth goal was to lower the interest expenses of banks by enough
to pay their deposit insurance premia. This was intended to overcome bank
6 Another type of restriction that arose at the same time limited the types of products banks
could offer. The Banking Act of 1933 prohibited banks from underwriting securities (Walter 1996,
19). Later, the Bank Holding Company Act of 1956 prohibited banking companies from underwriting insurance. This article does not discuss these product restrictions because there is no reason
to think that such restrictions reduced the competitiveness of the banking industry. Instead, they
would tend to reduce the competitiveness of the securities and insurance markets by eliminating
the competition that banks would have brought to these markets.
7 The Community Reinvestment Act is intended to encourage depository institutions to make
loans in their local communities.

J. R. Walter: The 3-6-3 Rule

65

objection to the cost of FDIC premia, which were newly imposed by the
Banking Act of 1933.
Regardless of Congress’ intentions, these ceilings had little effect until
the mid-1960s. Gilbert, who provides a careful review of the experience of
banks under the ceilings on demand deposits and time and savings deposits,
concludes that
for the first 30 or so years of their existence, ceiling interest rates on
time and savings deposits were above interest rates on Treasury securities
in all but a few months, and the average interest rates paid by member
banks on all time and savings deposits were below the lowest ceiling rate
in effect, the rate on savings deposits. (Gilbert 1986, 25)

Under Regulation Q, the Federal Reserve set ceilings on time and savings
deposits at 3 percent in late 1933. In 1934, the average rate paid by banks
on time deposits was 2.4 percent (Gilbert 1986, 25). So the ceilings were
25 percent (0.6/2.4) above the rates that banks were paying. A similar spread
was evident from the 1930s through the mid-1960s, indicating that the ceilings
were not a binding constraint on bank competition, except perhaps for the most
aggressive competition. When market rates rose for short intervals during this
30-year period such that customers demanded rates above the ceilings, the Fed
raised the Regulation Q ceilings.
In the mid-1960s, as rising inflation caused market interest rates to increase
significantly, Regulation Q interest ceilings did become binding. In 1966,
legislation extended ceilings to thrifts—savings banks and savings and loans
(Board of Governors, 1966, 1451–52). In order to encourage the flow of funds
into home mortgages, the ceiling was set higher at thrifts than at banks. The
hope was that the binding ceilings and the interest rate advantage afforded
thrifts would encourage consumers to deposit with thrifts, and because thrifts
primarily made mortgage loans, the additional thrift deposits would lead to
increased mortgage lending (Gilbert 1986, 26).8 Ceilings remained below
market interest rates; in other words, they were binding from 1966 until they
were removed in 1986 (Gilbert 1986, 29).
For much of this time, the spread between ceilings and market rates was
small enough that the difference could be offset with noninterest payments in
the form of free services and gifts, such as small home appliances (toasters,
for example) and kitchenware. Essentially, banks and thrifts were using barter
instead of cash interest payments. Consequently, even when binding, interest
8 Gilbert (1986, 29–30) concludes that the diffential between the ceiling on thrifts and banks
did not achieve the goal of encouraging mortgage lending. The differential was small enough so
that banks could sidestep it by offering free services. Further, at times, market rates were well
above the ceiling on thrift deposits. As a result, thrifts made fewer mortgage loans as growth in
deposits declined.

66

Federal Reserve Bank of Richmond Economic Quarterly

rate restrictions may not have been anti-competitive. While banks and thrifts
may have competed aggressively using services and gifts, such competition
likely meant a less efficient allocation of resources. Banks and thrifts likely
offered more of these services and gifts than they would have had they been
free to pay market rates of interest.
Nonetheless, when inflation rose quite high in the late 1970s, barter was
no longer sufficient and deposits began to move out of banks and thrifts to
competitors’ deposit-like accounts. The most important competitor for bank
customers’ funds was that of money market mutual funds, which grew from
$3 billion in 1977 to $75 billion in 1980 (Board of Governors 2005a).
In response to the disintermediation, Congress passed legislation in 1980
to remove ceilings on time and savings deposits, phasing them out through
1986. With the Depository Institutions Deregulation and Monetary Control
Act, Congress not only phased out all interest ceilings on time and savings
deposits, but also authorized banks nationwide to pay interest on a new type
of checking account available to retail customers, the Negotiable Order of
Withdrawal (NOW) account. NOW accounts had previously been available
only in certain states.
The zero ceiling on demand deposits, imposed in 1933, continues today.
Large banks sidestepped the restriction on their ability to pay interest on deposits that smaller banks held with them by paying implicit interest in the form
of services that were free of charge or below cost. Similarly, until the inflation of the late 1970s, free checking was probably sufficient to compensate
retail customers. However, when inflation rose, legislation allowed banks to
pay retail customers interest on checking accounts. Business customers were
likewise compensated with free services, at least until inflation drove up market interest rates. Since then, banks have developed means to sidestep interest
restrictions on business demand deposits using such arrangements as sweep
accounts.

Interest Rate Ceilings on Loans—Usury Ceilings
As with ceilings on deposits, government-imposed interest rate ceilings on
loans can also limit competition. Of course, if loan rate ceilings are not
binding, i.e., the government’s maximum interest rate is set above the market
interest rate, then they have no effect on the market. But, if binding, ceilings
on loans mean that borrowers wish to borrow more than lenders are willing to
lend at the ceiling rate. Borrowers will compete with one another to get the
few loans that banks are willing to make at the ceiling rate.
Banks could even be forced to ration loans at the ceiling rate. In such an
instance, banks would encounter the same excess demand as gas stations did
during the gasoline crisis of the 1970s, with far more cars lined up for gas
than there was available fuel. At the time, stations had little reason to compete

J. R. Walter: The 3-6-3 Rule

67

with one another to draw customers, because they had more than they could
handle. So with ceilings in force in banking, one can imagine the 3-6-3 rule
surviving, since banks had little reason to work hard to make loans.
Interest rate ceilings on loans, in the form of state-imposed usury laws,
were widespread in the post-Depression period. Usury laws set the maximum interest rates that lenders could charge borrowers domiciled in the state
imposing the law.
Still, usury ceilings seem unlikely to have propagated a low level of competition in banking. As noted in Bowsher (1974, 18), for most of the period
from the 1920s to the mid-1960s, “usury laws [were] ineffective because the
interest ceilings were at levels above prevailing market rates.” In the late 1960s
and to an even greater extent in the high inflation period of the 1970s, market
interest rates increased in response to rising inflation and the ceilings began
to bind. For example, in 1973, usury ceilings in 22 states were at 9 percent or
lower (Conference of State Bank Supervisors 1973, 109–12). With average
inflation that year at 6.2 percent (measured by the consumer price index) and
an average auto loan interest rate of 10.21 percent, the ceilings were clearly
significant (Board of Governors, 2005b).
In the early 1970s, there is evidence that lending declined in states with
binding ceilings (Bowsher 1974, 19–22), while lending increased for loans
not subject to the ceilings and in states with higher ceilings. So for a period of
time, banks in some states may have had little reason to compete aggressively
for loan customers.
Some states with binding ceilings enacted exemptions for the loans most
significantly affected by them, allowing banks and borrowers to sidestep the
ceilings (Bowsher 1974, 22). States also raised the ceilings in some cases
(Bowsher 1974, 19).
With double-digit inflation in 1979 and 1980, banks found a more effective
means of sidestepping the ceilings. They began to move operations to states
with no usury ceilings and export the higher rates allowed in those states to
low-ceiling states. Specifically, banks moved to South Dakota and Delaware,
both of which eliminated their usury ceiling in 1980. While typically the
usury law of the borrower’s home state prevails, a Supreme Court ruling allowed a loophole. In the December 1978 case of Marquette National Bank
of Minneapolis v. First Omaha Service Corporation, the U.S. Supreme Court
ruled that the National Bank Act granted national banks the power to export
their home usury ceiling when lending to a borrower located in another state,
regardless of the ceiling in the borrower’s state (Athreya 2001, 11–12; Furletti
2004, 7–8). For example, soon after South Dakota eliminated its ceiling, one
of the leading credit card lenders, Citibank, established a limited purpose national bank in South Dakota in which to house its credit card operation (Stein
2004). From there it could make credit card loans to a borrower in any state.

68

Federal Reserve Bank of Richmond Economic Quarterly

Soon after credit card banks began to export rates, many states, fearing the
loss of banking business, raised or eliminated their usury ceilings. In 1975,
only 3 states had no usury ceilings, and another 10 had ceilings above 15
percent on loans to individuals. By December 1981, there were 14 states with
no ceiling and another 17 with a ceiling above 15 percent.
So interest rate ceilings on deposits probably had a limited effect on competition, since most of the time they were not binding. When they became
binding, banks were able to compete with noninterest means of compensation,
though in an inefficient manner. When noninterest means of competing for
deposits failed, the ceilings were removed. Similarly, usury ceilings were not
binding until the middle of the 1960s. Exemptions allowed banks to avoid
them in some cases; ultimately, these ceilings either were removed or raised
high enough so they were no longer binding.

5.

NONBANK COMPETITION

While banks faced restrictions from the Depression until the 1980s, nonbanks
were much less limited. These nonbanks brought strong competition by selling
many of the same products as banks did. Such competition is likely to have
limited banks’ opportunity to earn monopoly profits or to operate inefficiently
prior to the period the restrictions were removed.
During the 1970s, nonbank providers of financial products were significant
competitors with banks. For example, in 1978, commercial banks held 60
percent of auto loans outstanding. Yet, finance companies (GMAC, Ford
Motor Credit, and Chrysler Financial) held 21 percent of the market, and
other nonbank firms, 19 percent (Rosenblum and Siegel 1983, 9). In credit
card lending, the credit card issuers owned by banks, Visa and MasterCard,
together accounted for $5.1 billion in outstanding balances as of 1972. At
the same time, outstanding balances on Sears’ credit cards alone were $4.3
billion (Rosenblum and Siegel 1983, 11). In commercial lending, banks faced
stiff competition from a number of financial and nonfinancial firms, so that in
1981, 32 of the largest nonbank commercial lenders accounted for 18 percent
of these firms’ combined lending, plus all bank lending.
Commercial paper (unsecured debt issued by the largest corporations)
proved to be another significant form of competition for banks. It offers an
alternative to bank loans. Its growth was facilitated by the expanded availability of information on corporate creditworthiness made available because
of improvements in information technology in the 1960s and 1970s. Between
1970 and 1980, the market grew from $33 billion in outstanding commercial
paper loans to $124 billion (Board of Governors 1976, 1984).
Nonbank competition, however, preceded the 1970s. Commercial banks
faced major competition for consumers’ savings from insurance companies,
savings and loans, the Treasury with regard to U.S. savings bonds, mutual

J. R. Walter: The 3-6-3 Rule

69

savings banks, investment companies, and credit unions (Hodges 1966, 931).
In 1947, commercial banks held 22 percent of all savings, the remainder of
which was held largely by these nonbank competitors. By 1964, banks were
responsible for 35 percent. Clearly, in terms of savings deposits, banks faced
significant competition.
In consumer installment lending, banks have long faced strong competitors. In 1941, banks accounted for about 28 percent of consumer installment
lending. By the early 1960s, this figure had grown to 40 percent. The major
competitors for banks during this period were consumer finance companies,
sales finance companies, credit unions, finance subsidiaries of manufacturers, savings banks, savings and loans, and insurance companies (Nadler 1966,
1129).
In the broadest terms, out of all financial intermediation, banks accounted
for between 40 and 50 percent from 1957 to 1975, and between 30 and 40
percent from 1975 to 1990 (Boyd and Gertler 1990, Chart 1). Insurance companies, thrifts, brokers, dealers, investment companies, and finance companies
accounted for the remainder.
The one area in which nonbank firms cannot compete is in checking accounts. Only banks, and since the late 1970s, thrifts, can offer them. Banks
are protected from competition with nonbanks by state and federal laws that
require a bank charter in order to offer checking accounts. Nevertheless, in
the case of most deposits and all lending, banks face significant competition.

6. AGGREGATE DATA ON BANK COMPETITION
The previous discussion indicates that regulatory restrictions on new bank
entry, on branching, and on interest rates were less than completely binding
so that their effect on competition may have been modest. As a number of
studies (such as Flannery 1984 and Keeley 1990) have shown, the effect was
not negligible, at least of branching restrictions.
Using regression analysis, Keeley (1990, 1192) examined 85 of the largest
U.S. banking companies from 1970 through 1986 and found that the liberalization of branching laws in a state is “associated with a statistically significant
lower market-to-book ratio” for banks in that state. The implication of this
finding is that branching restrictions protected the profits of banks operating
in states with such restrictions. If a bank is earning above-normal profits, then
the market value of its stock is likely to be above the book (or accounting)
value of the bank, because investors, aware of this profit advantage, will bid
up the stock value of such banks.
Flannery (1984, 245–47), using data from 1978, compares profits of unit
banks (those with no branches) in branching states with unit banks in nonbranching states. He finds that the unit banks in nonbranching states earned
20 percent higher profits than such banks in branching states. This result

70

Federal Reserve Bank of Richmond Economic Quarterly

supports Keeley’s finding that branching restrictions protected banks from
competition and allowed them to earn above-normal profits. On the other
hand, Flannery finds only marginal evidence of cost differences between the
two groups of unit banks, indicating that branching restrictions had less effect
on bank efficiency.
If the effects of branching and other restrictions were large, one would
expect some sign in aggregate bank profitability or cost data. Specifically, if
restrictions were an important limit on competition, bank profits should have
been higher when the restrictions were in place. Alternatively, bank profits
might not have been any higher because monopoly earnings were directed toward excessive staffing, high salaries, and lavish perquisites. The analysis that
follows examines bank profits, numbers of employees, and bank expenses.9
Little evidence is found to support a hypothesis that banks had more monopoly
power during the 1950s, 1960s, and 1970s when the regulations were in place
than during the 1980s, 1990s, and early 2000s following their removal.
A standard measure of bank profitability is return on equity (ROE), which
is net income divided by the book value of bank equity, in percentage terms.
Figure 3 shows U.S. aggregate bank ROE (total net income for all banks
divided by total equity—in book value terms—for all banks). By this measure,
bank profits were higher in the 1950s, 1960s, and 1970s than they had been
in the 1930s and 1940s. But profits were higher still in the 1990s and in the
early 2000s.10 If the tight regulations of the 1950s through the 1970s limited
competition, one possible result would be high bank profits during the period,
as banks took advantage of the market power the regulations granted them.
Then, when the regulations were eased starting in the early to mid-1980s,
one would expect profits to decline. Instead, for the period after the mid1980s, bank profits were higher on average than in the earlier period. From
1986 through 2004, average ROE was 11.81 percent, considerably above the
average return of 10.66 percent produced by banks between 1950 and 1985.11
Therefore, these aggregate data provide no evidence that the banking industry
was earning extraordinary profits during the 1950s, 1960s, and 1970s.
9 If regulatory restrictions on banks had a significant negative effect on competition, one
would expect the effect to appear as reduced banking industry productivity. Yet, productivity data
are largely unavailable for the banking industry, so the following analysis focuses on profits and
expenses.
10 The difference is even greater when measuring profits by return on assets (ROA)—net
income divided by assets. From 1950 to 1985, average ROA was .72 percent, and from 1986
through 2004, it was .95 percent. But this difference may be somewhat overstated. During the
last 20 years, banks have increased their reliance on income from off-balance-sheet activities. As
a result, present day asset growth relative to income tends to be biased downward and ROA,
biased upward. ROE suffers less from this bias because banks are required to hold equity to
cover off-balance-sheet exposures.
11 Note that the highly variable ROE observations between 1987 and 1991 were largely the
result of losses suffered by large banks on their emerging country lending and commercial real
estate lending losses by a broader group of banks.

J. R. Walter: The 3-6-3 Rule

71

Figure 3 Return on Equity—All U.S. Banks
20

15

Percent

10

5

0

-5

20
02

19
98

19
90
19
94

19
86

19
82

19
78

19
74

19
70

19
66

19
62

19
58

19
54

19
50

19
46

19
42

19
38

19
34

-10

Source: Figure created from FDIC data.

Still, one might imagine that the increase in bank ROE in the 1980s and
1990s as compared to that in earlier years was simply the result of a broader
trend in ROE for all corporations. If so, after adjusting for such a trend,
bank profits might have been higher in the pre-1980 period, providing some
evidence of monopoly profits when banking restrictions were tighter. A review
of the data indicates otherwise, however. ROE for all U.S. corporations was
higher in the 1980s and 1990s than in the 1960s and 1970s. Figure 4 shows
bank ROE adjusted for the broad trend in ROE for all U.S. corporations by
subtracting ROE for all corporations from the same ratio for banks. The figure
shows that adjusted ROE for banks is as high or higher in the 1980s and 1990s
than earlier. On average, adjusted ROE was 3.43 percent from 1960 through
1985 and 6.03 percent from 1986 through 2002.
Limited competition resulting from tight regulatory restrictions might
have allowed banks to hire excess employees. Such excess would have allowed bank employees more leisure time, say, to be on the golf course by
3 o’clock. Figure 5 shows the ratio of number of employees to total assets.
Indeed, the ratio was higher in the 1950s, 1960s, and 1970s. But the post-

72

Federal Reserve Bank of Richmond Economic Quarterly

Figure 4 Bank Return on Equity Minus Return on Equity—All
Corporations
14
12
10

Percent

8
6
4
2
0
-2
-4

19
60
19
62
19
64
19
66
19
68
19
70
19
72
19
74
19
76
19
78
19
80
19
82
19
84
19
86
19
88
19
90
19
92
19
94
19
96
19
98
20
00
20
02

-6

Sources: U.S. Department of Commerce, Bureau of the Census; Federal Deposit Insurance Corporation.

World War II downward trend started in 1960, well before the deregulation
of banking in the mid-1980s. Certainly, this decline must have been driven
largely by the growing use of computer equipment, making the average bank
employee much more productive and allowing banks to reduce their staffs
while increasing lending and deposit-taking. This technological trend probably far exceeded any monopoly-power-driven factor, but the bottom line here
is that the data on aggregate banking employment provide no evidence of the
exercise of monopoly power.
Limited competition might also have allowed banks to allocate an unusually large portion of expenses toward employees. A bank subject to limited
competition would be able to pay its employees above-market salaries. Alternatively, the bank might use some of its monopoly earnings to provide
excessive perquisites to its staff. Such perquisites might include providing
employees with opulent offices, large expense accounts, and the latest equipment. Such practices would tend to show up as high noninterest expenses.

J. R. Walter: The 3-6-3 Rule

73

Figure 5 Employees to Assets—All U.S. Banks
0.006

0.005

0.004

0.003

0.002

0.001

20
02

19
98

19
86
19
90
19
94

19
82

19
78

19
74

19
70

19
66

19
58
19
62

19
54

19
50

19
46

19
42

19
34
19
38

0.000

Notes: Number of employees divided by assets (thousands).
Source: Figure created from FDIC data.

Figure 6 displays the aggregate of all U.S. bank noninterest expense (which
includes salaries and benefits) relative to assets. As in the previous cases (Figures 3 through 5), this figure provides no evidence to support a hypothesis that
banks had unusually high expenses in the 1950s, 1960s, and 1970s. Instead,
these expenses grew fairly consistently from the end of World War II until
1993, and especially rapidly from the mid-1970s until 1993.
In contrast to these other items of aggregate data, Figure 1 illustrates
some data that imply an important competitive effect of regulatory restrictions.
The figure shows that between 1934 and 1986, the number of U.S. banks
fluctuated very little, remaining close to 14,000 banks for all of the period. This
period of stability was an unusual one when compared to most of the past 200
years. The stability also coincides with the period of tight regulatory restriction
of the banking industry. One could easily imagine that entry restrictions
and monopoly profits were, at least in part, responsible for the stability. As

74

Federal Reserve Bank of Richmond Economic Quarterly

Figure 6 Noninterest Expenses (Including Salaries and Benefits) to
Assets—All U.S. Banks
4.0
3.5

3.0

Percent

2.5
2.0

1.5
1.0
0.5

20
02

19
98

19
86
19
90
19
94

19
82

19
78

19
74

19
70

19
66

19
58
19
62

19
54

19
50

19
46

19
42

19
34
19
38

0.0

Source: Figure created from FDIC data.

discussed earlier, new bank entry, branching, and interest rate restrictions
might have protected profits, thus reducing the incidence of bank failure and
preventing the number of banks from declining. In fact, failures were minimal
from the end of World War II until the mid-1980s. Still, as illustrated in Figure
2, entry was not unusually low, at least from the early 1960s forward, and
mergers were occurring at a healthy pace, just offsetting entry. Therefore,
while the number of banks was fairly stable, entry and merger was producing
change.

7. SUMMARY
Observers often consider the period from 1950 through 1980 as one of weak
competition in banking due to heavy regulatory restrictions. Indeed, a number of studies have produced evidence of monopoly profits and inefficiencies
during the period and have tied these to such restrictions, most importantly to
limits on branching.

J. R. Walter: The 3-6-3 Rule

75

Still, entry, branching, and interest rate restrictions may have had a somewhat limited effect on competition. For at least some of the period, such
restrictions were either nonbinding or were sidestepped when binding. While
from the 1930s through the 1950s entry restrictions may well have limited new
bank formation, during the 1960s and 1970s, rates of entry were only slightly
below those of the 1980s and 1990s when entry restrictions were notably
loosened.
Branching prohibitions, though binding in some states, were liberal enough
so that branch numbers grew fairly rapidly throughout most of the postDepression period. Interest rate restrictions, both on deposits and loans, were
not binding for much of the period during which they were in force. When
they became binding, banks often found means of bypassing them, albeit
inefficiently.
Finally, nonbank competitors were always present. This presence ensured that even if restrictions had limited banks’ ability to compete with one
another, they faced strong competition from financial institutions not subject
to restriction.
Likewise, aggregate measures of bank profits and costs show little sign of
the monopoly profits or the outsized expenses one might expect if the restrictions were tightly binding. Had the restrictions been more strictly enforced,
the competitive impact would have been more severe. As it is, the regulatory
restrictions probably had a limited effect on competition in the 1950s, 1960s,
or 1970s.

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Washington, D.C.

Are We Working Too Hard
or Should We Be Working
Harder? A Simple Model of
Career Concerns
Andrew Foerster and Leonardo Martinez

I

n modern corporations, ownership is typically separate from control.
Holderness et al. (1999) find that executives and directors, as a group,
owned an average of only 21 percent of the stock in corporations they ran
in 1995. Typically, employees in lower levels of the hierarchy do not have
any ownership. Moreover, employees are motivated by self-interest and not
necessarily by the interest of the owners. Therefore, incentive problems arise
in most corporations. The financiers cannot assure that employees will not
expropriate funds or waste them on unattractive projects. (For a discussion of
these corporate governance issues, see Shleifer and Vishny [1997] and Weinberg [2003].) The flows of enormous amounts of capital to firms indicate that,
at least in most advanced market economies, the problems of corporate governance have been solved reasonably well. However, problems still arise, as
illustrated by the scandals caused by the misreporting of corporate earnings;
Shleifer and Vishny (1997) discuss evidence of managerial behavior that does
not serve the interest of investors.
In this article, we study how an employee is disciplined by career concerns. Fama (1980) suggests that employees are disciplined by the opportunities provided by the labor market for their services, both within and outside
the firm. This is the case when the market does not know the employee’s future
productivity and learns about it by observing his performance. In general, the
employer has to pay more to the employee when the employee is believed to
The authors would like to thank Juan Carlos Hatchondo, Andreas Hornstein, and Roy Webb for
helpful comments. E-mails: Andrew.Foerster@rich.frb.org and Leonardo.Martinez@rich.frb.org.
The views expressed herein are those of the authors 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 92/1 Winter 2006

79

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be more productive; otherwise another firm in the market would offer more to
him. Thus, the employee’s compensation depends on the labor market’s belief
about his future productivity. Therefore, when the employee decides his actions, he cares about his performance (and, consequently, the performance of
the firm) because his performance influences his reputation—i.e., the beliefs
about the employee’s future productivity.
Consider a salesperson who knows that if the labor market believes that
he has high ability (for example, he has a good sales strategy and knowledge
of the market), he will more likely be offered a position as a sales manager.
The salesperson’s sales depends both on his ability and the number of hours
worked. Because the market cannot directly observe the hours worked, it does
not know if an increase in sales is the result of more hours or greater ability.
However, we assume that the market believes that the salesperson works the
typical number of hours (we require that the market expectation is confirmed
in equilibrium) and interprets the amount sold as a signal of his ability. For
example, suppose that the market believes that the salesperson works 40 hours
per week. Also, suppose the market observes that the salesperson sells 100
units per week. Then, the market considers the salesperson’s ability to be that of
someone who sells 100 units in 40 hours. In this situation, the salesperson has
incentives to work more hours in order to sell more, to appear more talented,
and consequently, to increase the probability of being offered a better job.
A complementary approach to the study of career concerns is one that
looks at how to pay employees in order to motivate them to act in the best
interest of the employer. Surveys of the literature on optimal contracts can be
found in Rosen (1992) and Murphy (1999).1 In this case, the salesperson’s
employer could offer a contract that commits to pay more when the salesperson
sells more. Such a contract also would provide incentives to work longer hours.
Compensation contracts are not discussed in this article.2
Incentives derived from career concerns are not only important for the top
executives of a firm, but also for other employees. Moreover, career-concern
incentives matter in many lines of work. For example, an assistant professor
writes papers for publication in part because the decision regarding his tenure
and future salary depends on the beliefs about his future productivity, which is
determined by his past production. Another example involves athletes. Stiroh
1 For a discussion of other mechanisms that discipline employees’ behavior, see Shleifer and

Vishny (1997).
2 In many jobs, compensation contracts are not observed. Moreover, understanding careerconcern incentives is also a step toward the study of compensation contracts that complement
these incentives. Gibbons and Murphy (1992) study optimal contracts in a framework with career
concerns and find that employers would choose to provide stronger incentives through contracts
when career-concern incentives are weaker (later in the employee’s career). They also present
empirical evidence of their findings.

A. Foerster and L. Martinez: Career Concerns

81

(2003) and Wilczynski (2004) present empirical evidence of the presence of
career concerns for basketball players.
There is a large literature on the effects of career concerns on policymakers’ decisions. We can think about policymakers as voters’ employees. Voters
learn about a policymaker’s ability through his performance. Their decision
to reelect him depends on the expectations about the policymaker’s future
performance (determined by the policymaker’s past performance).3 Policymakers want to be reelected, and therefore, consider how their decisions
affect their performance.4
Following Holmstrom’s (1999) seminal work, we present career-concern
incentives in a simple model in which the employee decides how much effort
to exert on the job.5 The labor market does not know the employee’s exact
productive ability, and his ability is inferred from his output. Effort can neither
be observed nor perfectly inferred from the output produced by the employee—
there is no one-to-one relationship between effort and output. Thus, after
observing output, the market still does not know the effort level exerted by
the employee. Even though it is costly for the employee to exert effort, he
does so because his future compensation depends on his performance. By
exerting more effort, the employee produces more, and therefore, makes the
market believe that he has more ability. When the market perceives that the
employee has more ability, it assigns a higher compensation. We show that the
employee exerts more effort when his future compensation is more sensitive
to his reputation, and when he believes it is more likely that he can affect his
compensation with his effort level.
To what extent do career-concern incentives eliminate the inefficiencies
originated by the separation of ownership and control? Does the employee
work as hard as he would if he owned the firm? In the model examined in
this article, the effort the employee would exert if he owned the firm is the
socially efficient effort level. This is the effort level a benevolent social planner
would choose if he could observe the effort exerted by the employee. It can be
defined as the effort level at which the social marginal cost of exerting effort
3 Empirical studies on economic voting show that voting behavior depends on economic performance (for a review, see Lewis-Beck and Stegmaier 2000). For example, Brender (2003) finds
that “the incremental student success rate during the mayor’s term had a significant positive effect
on his reelection chances.”
4 Barro (1973) starts the literature on political agency discussed by Persson and Tabellini
(2000) and Besley (2005). Besley and Case (1995) and Hess and Orphanides (1995, 2001) present
empirical evidence supporting this theory. There are many applications of political agency models
of career concerns. Besley and Case (1995) study the more typical effort-choice decisions. Persson
and Tabellini (2000) present models of rent-seeking. Shi and Svensson (2002) study the cyclical
manipulation of fiscal policy. Eggertsson and Le Borgne (2005) study the effects of career concerns
for monetary policy.
5 Discussions on the effect of career concerns on investment decisions are presented by Holmstrom (1999), Prendergast and Stole (1996), and Dasgupta and Prat (2005). Ahmad and Martinez
(2005) study how career concerns may discipline recipients in donor-recipient relationships.

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Federal Reserve Bank of Richmond Economic Quarterly

equals the social marginal benefit of exerting effort. From a social standpoint,
is the employee working too hard or should he be working harder? In the
simple model we present, the social cost of effort is given by the employee’s
cost. On the other hand, the social benefit of effort is given by the value
of the output produced by the employee with his effort (this would be the
employee’s benefit if he owned the firm). In general, the social benefit does
not coincide with the employee’s private benefit of exerting effort, given by
the expected increase in his future compensation. Consequently, there is no
reason to expect that the employee would exert the efficient effort level. In
general, we cannot expect that career-concern incentives will eliminate the
inefficiencies originated by the separation of ownership and control. Similarly,
we cannot expect an employee’s decisions to be socially efficient because of
career concerns.
The remainder of this article is organized as follows. In Section 1, we
present a simple model of career concerns. In Section 2, we study the equilibrium effort decision for this model. In Section 3, we conclude.

1. A SIMPLE MODEL OF CAREER CONCERNS
We study a one-period version of the main model in Holmstrom’s (1999)
seminal article, but, following Martinez (2005a), we consider a discontinuous
compensation scheme, which is reasonable and will allow us to show that
the employee may work too hard in the simple framework presented in this
article. Thus, we present a game played by the employee and the market for
his services.

The Environment
At the beginning of the game, both the market and the employee are ignorant
of the employee’s ability. An employee may be ignorant of his ability when
met with new tasks. Further, this assumption represents situations where an
employee’s success does not only depend on his individual ability but also
on the ability of others working with him.6 The employee and the market
both share the same beliefs about the employee’s ability. These beliefs are
given by a probability distribution with a differentiable cumulative density
function, F .
6 As explained below, the assumption that the employee does not know his ability implies
that the effort exerted by the employee is the effort expected by the employer. This assumption
simplifies the exposition of the employer’s learning, and, in the simple model presented in this
article, implies that the employer learns the employee’s ability after observing output.

A. Foerster and L. Martinez: Career Concerns

83

First, the employee decides the effort he exerts on the job, a ≥ 0.7 The employee produces output, y. Output is a function of the employee’s productive
ability, η, and his effort. In particular,
y = a + η.

(1)

After the employee chooses his effort, η is realized. That is, when the employee
decides his effort, he does not know exactly how much he will produce, but
he knows that with increased effort he will produce more.
We do not consider the employee’s current-period compensation because
it has already been determined and does not affect the employee’s decision
problem.8 The employee exerts effort in order to influence his future compensation (for a multi-period version of this model, see Holmstrom [1999] or
Martinez [2005a]). At the end of the game, the employee’s future compensation, w, is determined (see discussion below).
There is a cost to exerting effort, c (a), with c (a) ≥ 0, c (a) > 0,
and c (0) = 0. With w, the employee buys w units of output for his own
consumption. We assume that the employee’s utility is linear in consumption.
In particular, if the employee consumes w, we assume that his utility equals
u (w, a) = w − c(a).

(2)

Players (the employee and the market) observe y, while η is not directly
observed. The market does not observe the employee’s exact effort, while the
employee does.9

The Equilibrium Concept
The equilibrium effort is given by a ∗ if when the market believes that the employee chooses a ∗ , it is optimal for him to do so. When the market determines
the employee’s compensation, it does not know the employee’s effort level.
Thus, the market’s belief about the exerted effort needs to be defined. We
assume that the market believes that the employee chooses the equilibrium
effort.

Equilibrium Learning
As explained above, in equilibrium, the market assigns probability one to
the employee exerting the equilibrium effort. The market is rational and
7 We assume that the employee plays a pure strategy.
8 Recall that we assume that there are no compensation contracts, and incentives come only

from career concerns. Gibbons and Murphy (1992) present a model with both compensation contracts and career concerns.
9 Alternatively, in agency models of career concern, we assume that the agent’s action is
observable but the principal is uninformed (see, for example, Shi’s and Svensson’s [2002] political
budget cycle model).

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understands the game. In particular, it can infer the employee’s equilibrium
strategy, a ∗ . Loosely speaking, the market knows how hard an employee with
certain characteristics works in certain situations.
Observing y allows the market to learn η by using its knowledge about
the effort exerted by the employee, a ∗ , and the production function. Thus, the
ability inferred by the market is given by
ηm ≡ y − a ∗ = η + a − a ∗ .

(3)

The employee can manipulate the ability inferred by the market with his
effort decision. In particular, if the employee exerts more effort, the market
believes that he has more ability: ηm is increasing with respect to a. Consequently, if the employee’s compensation is higher when the market believes
he has more productive ability, the employee has career-concern incentives to
exert effort.
On the equilibrium path, the effort expected by the market is the effort
exerted by the employee, and therefore, the ability inferred by the market is
equal to the true ability. The inference of the market is wrong, however, when
the employee deviates from equilibrium behavior.

The Compensation Scheme
In models of career concerns, the employee’s compensation depends on the
market’s belief about his future productivity.10 As illustrated in equation (1),
the employee’s productivity depends on his ability and on the effort he exerts. Martinez (2005a) shows that, in general, the market’s belief about the
employee’s ability is sufficient for determining the effort it expects the employee to exert (the equilibrium effort). Consequently, its belief about the
employee’s ability is sufficient for determining its belief about his future productivity, and therefore, for determining his compensation. Thus, we assume
that compensation is a function of the ability inferred by the market.
Furthermore, following Martinez (2005a), we consider a discontinuous
compensation scheme. That is, we assume that a small change in the employee’s reputation may imply a large change in his compensation. In particular, we assume that
w ηm =

wH , if ηm ≥ ηG
wL , otherwise,

(4)

10 The exact relationship between the market’s belief about the employee’s future productivity
and compensation depends on the labor market structure considered (see MacDonald 1982, Bernhardt 1995; Gibbons and Waldman 1999; Persson and Tabellini 2000; Prescott 2003). The analysis
of this relationship is beyond the scope of this article. We focus on the incentives generated when
the agent’s compensation depends on his future productivity.

A. Foerster and L. Martinez: Career Concerns

85

where wH > wL .11 This compensation scheme may be interpreted as the
employee being assigned to a high-compensation occupation if his reputation
is good enough, and to a low-compensation occupation otherwise.12 For
example, suppose that there are two tasks. One task has a low return, wL > 0.
The other task has a high return, wH , if assigned to a high-ability employee,
η ≥ ηG , and a negative return if assigned to a low-ability employee, η < ηG .
With this technology, the employee would be assigned to the high-return task
if and only if ηm ≥ ηG .13

2. THE EQUILIBRIUM EFFORT DECISION
At the beginning of the game, the employee’s expected utility is given by
wL + (wH − wL ) P ηm ≥ ηG − c (a) ,
where P [x] denotes the probability of x.
Recall that ηm ≥ ηG if and only if η ≥ ηG − a + a ∗ . Thus, by exerting a
higher effort, the employee decreases the minimum realization of ability that
would allow him to enjoy the high compensation. The employee’s maximization problem is given by
max (wH − wL ) 1 − F ηG − a + a ∗
a

− c (a) .

(5)

We shall proceed by characterizing the employee’s equilibrium effort decision through the first-order condition of his problem.14 Let a (a ∗ ) denote
ˆ
11 The results presented here do not change much if w and w depend on the employee’s
H
L
reputation. The assumption that wH and wL do not depend on reputation simplifies the analysis
and allows us to focus on the incentives generated by a discontinuity in the compensation scheme.
12 Employees’ abilities may be occupation-specific. However, as long as there is a positive
correlation between employees’ abilities in different occupations, employees with better performance
in one occupation are more likely to perform well in other occupations. We can interpret the model
presented in this article as one in which the employee tries to manipulate the signal that is relevant
in order to be assigned to the high-compensation occupation.
13 Discontinuous compensation schemes are widely observed in various occupations. First,
as documented by the empirical literature, the employee may be assigned to different levels in a
hierarchy according to his reputation, and these reassignments often imply a discontinuous change
in the employee’s compensation (see Murphy 1985; Kwon 2005). The span-of-control literature
presents theories of why employees with higher ability are assigned to higher levels in hierarchies (see Prescott 2003). There is a theoretical literature explaining why a firm would choose
this compensation structure (see Bernhardt 1995). Furthermore, capacity constraints imply that the
employer replaces the incumbent employee when the employer expects to be better off with the
replacement. In general, the employee is not indifferent about losing his position.
14 The first term in problem (5) may not be globally concave. Thus, the employee’s maximization problem may not be globally concave. However, we can assure the global concavity
of the employee’s problem by assuming that the cost of exerting effort is convex enough. For
example, one could find an upper bound for the slope of the marginal benefit curve and assume
that the slope of the marginal cost curve is always higher. Another alternative is to assume that
c(a) = a n , and n is high enough. Consequently, the marginal cost is very low for a low a and,
for a high enough a, it starts increasing rapidly, assuring that the marginal cost curve crosses the
marginal benefit curve only once (from below) and, therefore, the problem is globally concave (see
Martinez 2005b).

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Federal Reserve Bank of Richmond Economic Quarterly

the employee’s optimal effort choice when the market expects the employee
to choose a ∗ . Let f denote the density function corresponding to F . The
optimal effort, a (a ∗ ), is given by
ˆ
c a a∗
ˆ

ˆ
= (wH − wL ) f ηG − a a ∗ + a ∗ .

(6)

In order to find the equilibrium effort, we have to solve a fixed-point
problem. We need to find an a ∗ such that when the market expects a ∗ , it is
optimal for the employee to choose a ∗ . In equilibrium, the effort expected by
the market has to be equal to the effort the employee chooses to exert given
the market’s expectations. That is, a ∗ is the equilibrium effort exerted by the
employee if and only if a (a ∗ ) = a ∗ .
ˆ
Assuming that problem (5) is strictly concave assures that for a given effort
expected by the market, a ∗ , there exists a unique optimal effort level, a (a ∗ ) ,
ˆ
given by the first-order condition in equation (6). This does not mean that the
equilibrium effort, a ∗ , exists and is unique. There could be more than one a ∗
such that when the market expects a ∗ , the employee’s optimal effort level is
given by a ∗ , that is, there could be more than one a ∗ such that a (a ∗ ) = a ∗ . It
ˆ
could also be that there is no equilibrium effort level, a ∗ , such that when the
market expects a ∗ , it is optimal for the employee to choose a ∗ .
In our framework, a unique equilibrium effort exists.15 In order to find
the equilibrium effort, the fixed-point condition, a (a ∗ ) = a ∗ , is imposed in
ˆ
the first-order condition in equation (6). Thus, the equilibrium effort, a ∗ , is
defined by
c a ∗ = (wH − wL ) f ηG .

(7)

The right-hand side of equation (7) is positive. The marginal cost of exerting
effort is strictly increasing, and c (0) = 0. Consequently, there exists a unique
equilibrium effort, a ∗ > 0, satisfying equation (7). The intuition behind
uniqueness is clear. The effort expected by the market affects the marginal
benefit of exerting effort through the ability inferred by the market, ηm . In
equilibrium, the effort exerted by the employee is that which is expected by the
market, and therefore, ηm = η, which does not depend on that effort. Thus,
equilibrium effort does not depend on the effort expected by the market.

Discussion
In this section, we discuss the results presented above through a simple example. Let us consider a salesperson who sells products from store to store. The
15 Martinez (2004) discusses a firing model of career concerns in which the convexity of
the agent’s problem implies that the agent’s equilibrium strategy does not exist even though an
optimal effort level exists for each effort expected by the principal. He also shows that, in a more
general framework, if the agent’s problem is strictly concave, the agent’s equilibrium action exists
and is unique.

A. Foerster and L. Martinez: Career Concerns

87

market may not be able to observe how many hours the salesperson is working,
but it knows how many a salesperson typically works. We assume that the market believes that the salesperson works the typical number of hours. Suppose
that the market believes the salesperson works 40 hours per week (a ∗ = 40)
and observes that the salesperson sells 100 units per week (y = 100). Based
on this information, the market considers that the salesperson’s ability is that
of someone who sells 100 units in 40 hours.
We show that in our framework, a unique equilibrium effort exists, as
defined by equation (7). For any number of hours that the market expects the
salesperson to work, a ∗ , it is optimal for the salesperson to work a (a ∗ ) hours.
ˆ
We require that in an equilibrium, a (a ∗ ) = a ∗ . In general, it may be that such
ˆ
an equilibrium does not exist. It may also be that multiple equilibria exist.
For example, if the salesperson is expected to work 50 hours per week, it is
optimal for him to do so. On the other hand, if he is expected to work 40 hours
per week, it is optimal for him to do that.
The right-hand side of equation (7) represents the salesperson’s benefit from working an extra hour. This benefit is given by the change in the
probability of receiving the high compensation implied by an extra hour of
work, f ηG , multiplied by the gain from receiving the high compensation,
wH −wL . As intuition suggests, the model predicts that the salesperson would
work more hours because of career concerns when his future compensation is
more sensitive to his reputation (i.e., wH −wL is higher), and when he believes
it is more likely that he can affect his compensation with the hours he works
(i.e., f ηG is higher).16 Holmstrom (1999) shows that we can expect the
employee to exert less effort later in his career. Martinez (2005a) shows that
the relationship between the employee’s decisions and his current reputation
is typically nonmonotonic; equilibrium effort is hump-shaped over reputation.
Furthermore, Martinez (2005b) shows that there is a renegotiation cycle—if
the employee’s compensation is decided infrequently, he would typically exert
more effort (for the same reputation level) closer to the compensation period.
Recall that the uncertainty about the salesperson’s ability is crucial for
the existence of career-concern incentives. For example, suppose that in our
model, the market knows the salesperson’s ability at the beginning of the
game. Consequently, w ηm is determined at the beginning of the game,
and the salesperson knows that his compensation does not depend on sales.17
16 In a multi-period version of the model, the employee considers that exerting effort affects
the probability of receiving wH in every future period. In this situation, the employee makes
an intertemporal decision as well. In order to affect his future compensation, the employee could
decide to exert more effort in the current period or in the future. The employee compares the
cost and the effectiveness of exerting effort in each period (see Martinez 2005a, 2005b).
17 In general, in models of career concerns, the employee’s compensation depends on the
market’s belief about his future productivity. Therefore, compensation depends on output only
because output affects the market’s inference about the employee’s future productivity.

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Federal Reserve Bank of Richmond Economic Quarterly

Thus, the salesperson works the minimum number of hours. (Recall that in
our model there are no output-contingent compensation contracts.)
Similarly, in a multi-period version of the simple model we present in this
article, the salesperson would only work more than the minimum number of
hours in the first period. In this environment, the market completely learns
the salesperson’s productive ability after one observation of sales. When the
market knows his ability, the salesperson has no career-concern incentives to
work more than the minimum number of hours. This is not the case when
sales are a stochastic function of hours and ability, and therefore, ability is not
completely learned after one observation (see Holmstrom 1999). The units
sold may not only depend on the salesperson’s effort and ability but also,
for example, on his luck in finding customers who are more likely to buy.
Furthermore, if his ability varies over time, the salesperson would work more
than the minimum number of hours every period (see Holmstrom 1999). For
example, the products the salesperson offers or the type of customers he faces
may change over time, and his ability may depend on each of these factors.

Efficiency
Does the employee choose to work too hard or should he choose to work
harder? More specifically, is the effort decided by the employee higher or
lower than the efficient effort level? Would the employee exert a higher or
a lower effort if he owned the firm? The socially efficient effort level can be
defined as the level at which the social marginal cost of exerting effort equals
the social marginal benefit of exerting effort. In our model, this is the effort
level a social planner would ask the employee to exert if the planner could
observe the exerted effort. The social cost of effort is given by the employee’s
cost. On the other hand, the social benefit of effort is given by the value of
the output produced by the employee through his effort. The value of the
output is also the benefit the employee would consider if he owned the firm.
Consequently, the socially efficient effort level is also that which the employee
would exert if he owned the firm.
The linear production function in equation (1) implies that with an extra unit of effort, the employee produces an extra unit of output. The utility
function in equation (2) implies that the value of an extra unit of output (consumption) is 1. Thus, the efficient effort level, a, is given by c (a) = 1.
¯
¯
In general, the right-hand side of equation (7) is not equal to 1. That is, the
social benefit of exerting effort does not coincide with the employee’s private
benefit of exerting effort. Specifically, the employee will exert the efficient
level of effort if and only if f ηG (wH − wL ) = 1. This situation is fairly
restrictive, so there is no reason to expect that the employee would exert the
efficient effort level. Most likely, the employee works too hard or not hard
enough.

A. Foerster and L. Martinez: Career Concerns

89

If the employee believes that an increase in effort is very likely to affect
his future compensation (i.e., f ηG is high), or if the compensation structure
is very sensitive to reputation (i.e., wH − wL is high), the employee works
too hard. On the other hand, if he believes that increasing effort will have
negligible effect on his chances of higher future earnings (i.e., f ηG is low),
or if the increase in earnings from a better reputation is small (i.e., wH − wL
is low), then he will exert less than the efficient level. We cannot expect an
employee’s decisions to be socially efficient because of career concerns.

3.

CONCLUSION

This article presents a simple model of career concerns. An employee with
career concerns wants to establish a reputation for high productivity, as the
labor market’s expectations of high productivity allow the employee to receive
better compensation. These career concerns do not necessarily lead to socially
efficient decisions by the employee. For example, if the employee believes
exerting additional effort will drastically increase his chances for better compensation, or if the payoff for having a better reputation is significant, then
he will work too hard (from a social efficiency standpoint). Alternatively, if
exerting additional effort has a low impact on increasing the probability of
better compensation, and if the increase in compensation from having a better
reputation is low, the employee will not work hard enough. Getting employees to make socially efficient decisions would require additional incentives
beyond those created by career concerns.

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