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Economic Quarterly— Volume 99, Number 4— Fourth Quarter 2013— Pages 251–
285

Evaluating Executive
Compensation Packages
Arantxa Jarque and John Muth

E

xecutive compensation is a topic that has received attention
both in the media and the academic literature. This article
discusses issues relevant to the construction and interpretation
of compensation …gures typically reported in both sources. First, it is
not clear what precisely should be included within a measure of the
chief executive o¢ cer’ (CEO’ income tied to his …rm. Second, the
s
s)
study of executive compensation remains constrained by the availability
of data. We discuss the main source of data used in most studies on
the topic: Execucomp. We highlight where the lack of data requires a
deviation between a theoretical “ideal” measure of compensation and
that which the researcher must use as an approximation. In this way,
we hope our article will be a useful …rst introduction for those looking
to do further research on the topic.
We propose a measure of realized annual pay, compare it to other
measures used in the literature, and illustrate the di¢ culties in calculating it. Using data in Execucomp, we provide our pay measure
for CEOs of large U.S. …rms in the period 1993–
2012 and use it to
estimate sensitivity of pay to …rm performance. The main di¢ culties
in this exercise lie in the fact that compensation packages of most executives include stock and option grants on their own …rm’ shares,
s
which typically come with requirements that they be held by the executive for at least three or four years.1 This implies two important
We thank the editor, Ned Prescott, and the referees, Kartik Athreya, Zhu Wang,
and Peter Debbaut, as well as Huberto Ennis and Todd Keister, for helpful comments. The views expressed in this article are those of the authors and do not
necessarily represent the views of the Federal Reserve Bank of Richmond or those
of the Federal Reserve System. E-mail: arantxa.jarque@rich.frb.org.

1
Moreover, it is a fact that most CEOs hold on to stock for which selling restrictions have expired, or to options that are exercisable and in the money. The reasons
for these “voluntary” holdings are not entirely clear, since CEOs are risk averse and

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Federal Reserve Bank of Richmond Economic Quarterly

things. First, the compensation …gures that are reported by …rms (and
are readily available to the press and researchers) are a combination
of both expected value of compensation (for deferred compensation in
the form of restricted stock and option grants that are not convertible
into cash right away) and realized value (salaries, bonus payments, and
perks). Second, a given year’ compensation package provides income
s
for several years to follow, since the CEO will be able to realize gains
from selling and exercising stock and option grants once their vesting
restrictions expire. That is, an important part of the annual realized
pay of a CEO in any given year comes from his net gains from trading
stock that he received in a past grant. Due to the fact that stock price
realizations may di¤er from ex-ante expectations of those prices, the
ex-post realized gains from those trades will typically di¤er from the
valuation made at the time of the grant.
A measure of what is sometimes called direct compensation (the
sum of salary, bonus, other compensation such as pension plans or
perks, and the value of new stock and option grants during the year)
is readily available in Execucomp (variable TDC1).2 As we just discussed, grants included in this measure are valued in expectation. Our
objective in this article is to provide a measure of realized pay instead.
We de…ne realized pay as the sum of salaries, bonuses, and other compensation, plus the gains from trades that the CEO realizes in a given
year. We will argue that this measure is close to the one …rst proposed
by Antle and Smith (1985) and used later by important contributions
such as Hall and Liebman (1998) and Gayle and Miller (2009). Total
yearly compensation is de…ned in these studies as the change in the
wealth of the CEO that is tied to his employment in the …rm, and it
is calculated in practice as direct compensation plus the year-on-year
change in the market value of stock and option holdings of the CEO
from past grants. This measure is, hence, still a measure of expected
pay, although more sophisticated than TDC1. The main departure of
our measure of realized pay with respect to this total yearly compensation is that it does not attribute changes in the value of grants that
are not yet exercised to the realized pay in the year when they occur;
rather, the …nal realized value is captured in gains from trades and
attributed to the period of exercise of the grants. This simpli…cation is
useful in terms of the calculation of the measure— we need to rely less
heavily on assumptions about the unavailable details of grants.
standard economic theory would suggest that they would value a diversi…ed portfolio of
assets more. Overcon…dence, privileged information, or personal tax considerations have
been proposed in the literature as potential explanations (Jin and Kothari 2008).
2
This measure has been studied, for example, in Gabaix and Landier (2008) and
Frydman and Saks (2010).

A. Jarque and J. Muth: Executive Compensation Packages

253

Figure 1 Median Realized Pay, and Mean Expected Pay as
Measured by Execucomp in the Variable TDC1, as
well as Measured in Total Yearly Compensation
(TYC)

Still, only part of the information that we need for our measure
(about trades or vesting restrictions and exercise prices of past grants)
is available in Execucomp. When approximating the gains from trades,
in particular, we follow closely the algorithm used in Clementi and
Cooley (2009) to recover the executive’ holdings of stocks and options
s
of his …rm.3 In the Appendix, we walk the reader through the step-bystep construction of the portfolio, discussing the shortcomings of the
available data in Execucomp and how di¤erent assumptions about the
unknowns may a¤ect the compensation numbers.
We use our measure of realized pay to provide an updated account
of CEO compensation through the year 2012. Figure 1 presents a comparison of our measure of realized pay versus two measures of expected
pay used in the literature: “direct compensation,” the variable TDC1
in Execucomp, and “total yearly compensation,” as calculated by us
following the implementation in Clementi and Cooley (2009) of the
3
For another recent application of the algorithm …rst developed in Antle and Smith
(1985), see Gayle and Miller (2009).

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Federal Reserve Bank of Richmond Economic Quarterly

concept introduced by Antle and Smith (1985). Median realized pay
is mostly below median direct compensation. The main di¤erence observable with total yearly compensation is that it is a lot more variable
than either of the other two measures. This …gure suggests that di¤erent measures of pay present di¤erent pictures of CEO compensation,
and it is important to understand what is behind the measurements
before using them to evaluate pay practices.
We use our realized pay measure to perform a sensitivity analysis
of annual realized pay to performance, with a special focus on the …nance sector throughout the recent crisis in 2008. We simplify some
of the di¢ culties of the analysis by assuming that the choice of selling and buying stock is invariant to the stock price movements in our
counterfactual exercises; i.e., only the pro…ts from the trades change,
not the quantities. We …nd that in the aftermath of the crisis the realized pay of CEOs of …nance …rms has decreased in level relative to
other industries. Moreover, the sensitivity exercise suggests that, during the whole sample period, mean realized pay for CEOs in …nance
…rms changes with the performance of the …rm in similar magnitudes
than that of the average CEO.
We proceed as follows. In Section 1, we introduce compensation
instruments included in most CEO pay packages and discuss data availability and measurement challenges. In Section 2, we present a simpli…ed model of compensation accounting to illustrate the di¤erences
between three di¤erent measurement alternatives: the measure of realized pay that we construct in this article, and two measures of expected
pay— the simple measure of expected pay readily available in Execucomp, direct compensation, and the one based on the concept of total
yearly compensation introduced by Antle and Smith (1985). Section 3
presents the results on the implied measure of realized pay over time,
with a special focus on pay sensitivity, as well as a detailed look at
the …nancial sector before and after the recent …nancial crises. Section
4 concludes. The Appendix provides the technical details on how we
construct our realized pay measure from the data available.

1.

UNDERSTANDING COMPENSATION PACKAGES

Nowadays, companies pay their top executives mainly through di¤erent
combinations of the following instruments: a salary, a bonus program,
a signing bonus, stock grants (also referred to as “restricted stock,”
since they are usually granted with restrictions on the ability to sell
them), grants of options on the stock of the …rm, and perks and longterm incentive plans that specify severance payments, as well as pension
plans.

A. Jarque and J. Muth: Executive Compensation Packages

255

Table 1 Summary of Annual Compensation Information
Available in Execucomp
Instrument (Average % of TDC1)
Salary (32%)
Bonus and Incentive Compensation (23%)
Perks and Other Compensation (6%)
Restricted Stock Grants (11%)
Stock Option Grants (28%)

Information in Execucomp
Value
Value, some details on targets
(after 2006)
Value
Value (stock price times number
of shares)
Value (Black and Scholes), number
of shares underlying options

Notes: Information available in Execucomp about the components of CEO compensation packages. For the percent calculations, the sample includes the CEOs
of the largest 1,500 public …rms in the United States in the period 1993–
2010.

The publicly available information on CEO compensation comes
from the compensation tables included by …rms in their annual reports,
as mandated by the Securities and Exchange Commission (SEC). This
is the same data that Execucomp has compiled since 1992 and has
been used in numerous empirical studies of CEO compensation, including this article. When the press publicizes information on CEO
pay, it usually reports a summary measure of total or “direct compensation,” which is also readily available in Execucomp as the variable
TDC1. Direct compensation is the sum of cash compensation (wage,
bonus, and incentive compensation), pension contribution and other
perks, plus the expected value of new stock and option grants given
to the CEO within a given year. Execucomp also reports separately
the di¤erent components of total compensation, and it includes some
limited information on stock ownership and the portfolio of unvested
restricted stock and option grants of the executives. A brief description of each of the instruments and further details on the information
available about them in Execucomp follows. Table 1 presents statistics
for their relative importance as a share of total pay using data from
1993 to 2010 and summarizes the information on availability.
Salaries are the simplest compensation instrument: They are not
contingent on performance and information on their level is readily
available on the proxy statements of …rms.4 Bonus plans and incentive
pay typically depend on yearly accounting results. Information is available mainly on payouts and more recently on some limited details of
4
The source for the shares of compensation that are reported come from Jarque
and Gaines (2012). See the article for details on sample selection.

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Federal Reserve Bank of Richmond Economic Quarterly

Table 2 Classi cation of Compensation Instruments

Non-Contingent
Contingent

Current (within year)
Salary, perks,
signing bonus
Bonus plan

Deferred
Pension plan
Options, stock, severance,
future pay

the bonus plans. Information on perks and other compensation is also
available, although not to a great level of detail. Grants of restricted
stock of the …rm make pay depend on the results of the …rm over a
longer time horizon, since the CEO is restricted from selling them until
their vesting period expires. Execucomp compiles information on their
expected value at the time of the grant (number of shares times market price of stock), but it does not have separate information on the
number of shares granted. Grants of stock options allow the executive
to purchase stock of the …rm at a pre-established price (the “exercise
price” and are also typically granted with restrictions as to how soon
)
they can be exercised. These also provide incentives for longer-term
performance, but they only pay o¤ if the stock price of the …rm is
above the exercise price. For option grants, Execucomp has information on both the number and the Black and Scholes value of the total
grants during the year. Typically, both stock and option grants come
with a clause that forces the executive to forfeit them in the event of
employment termination. Information on the vesting periods is not
generally available in Execucomp for either stock or option grants.5
It should be apparent that compensation instruments can be classi…ed according to two criteria: whether or not they are contingent on the
performance of the …rm, and whether or not they are deferred.6 Table
2 summarizes this classi…cation of the main compensation instruments.
Given that executives are risk averse, paying them with contingent
instruments, such as bonuses, stocks, and options, comes at a cost, since
they will demand higher expected payments to compensate them for the
risk. The most accepted explanation for the inclusion of compensation
instruments that are contingent on the performance of the …rm is the
existence of a moral hazard problem: The separation of ownership
and control of the …rm implies the need to provide incentives to the
5
A commonly cited length of this restriction period is four years, with vesting taking place proportionally over this period— see Hall and Liebman (1998).
6
Firm performance is typically proxied by accounting measures such as return on
equity, sales, and pro…t, or on market-based measures such as the stock price.

A. Jarque and J. Muth: Executive Compensation Packages

257

CEO that align his interests with those of the …rm owners.7;8 Within
this context of incentive provision, it is also commonly accepted that
expectations over future wages or jobs (career concerns), as well as the
threat of dismissal, are also important compensation instruments—
although less easy to study due to the lack of hard information on
them.9
Deferral of pay also comes at a cost if CEOs are more impatient (i.e.,
they discount the future more) than the shareholders of the …rms they
manage. Several reasons may explain the use of deferred instruments.
Perhaps the most accepted one is that, despite the cost of waiting,
deferral is valuable— in combination with commitment to long-term
contracts— because it allows to smooth incentives over time, making
(costly) exposure to risk less necessary.10 Other reasons include retention purposes in the face of lack of commitment to long-term contracts
or provision of incentives for hidden actions with long-term e¤ects.11
In most cases, instruments that are “cashed” within the year (labeled “current” in the table) are straightforward to value. In contrast, for contingent deferred instruments an expected value needs to
be calculated, which presents some challenges. For example, the actual amount of compensation that the CEO will receive from stock and
options granted to him in a given …scal year will depend on the stock
price of the …rm at the moment he sells or exercises them. Similarly,
the value of future compensation will depend on the performance of
the …rm during the tenure of the CEO. The value of pension payments
will be contingent on the …rm being solvent once the CEO retires. The
value of severance payments is typically pre-set at the time of contracting, but a full list of the contingencies that may lead to termination is
not written in the employment contract of the CEO. Hence, in order to
calculate the expected value of compensation, one needs to know both
the set of contingencies that trigger each payment (for example, the circumstances that trigger …ring of the CEO or the performance targets
for granting salary increases), as well as the probability attached to
each of these performance contingencies (for example, the probability
7
See Prescott (1999) and Jarque (2010) for an introduction to static and dynamic moral hazard problems, respectively. Classical references in the literature include
Grossman and Hart (1983), as well as Spear and Srivastava (1987).
8
Bebchuck and Fried (2004) argue that captive boards may use stock and option
grants as a less obvious instrument to transfer excessive amounts of pay to their CEOs.
9
See Jensen and Murphy (1990); Gibbons and Murphy (1992); and Jenter and
Kanaan (forthcoming).
10
Wang (1997) ‡eshes out this explanation using a repeated moral hazard model.
11
See Bolton, Sheinkman, and Xiong (2006); Clementi, Cooley, and Wang (2006);
and Edmans and Liu (2011).

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Federal Reserve Bank of Richmond Economic Quarterly

distribution over future stock prices of the …rm). These di¢ culties are
important when choosing a measure of CEO pay.

Measurement of Pay: Expected versus
Realized Value
There are two main approaches to measuring CEO pay:
1. Expected value of pay: The expected value of compensation
granted in a given year, which includes the cash (realized value)
he receives in salary and bonus, plus the expected value of the
deferred contingent instruments such as stock and options;
2. Realized pay: The actual amount of money received in a given
year, which includes the cash he receives in salary and bonus,
plus the proceeds from selling past stock and option grants for
which selling restrictions have expired (all realized).
Any attempt at valuing contingent deferred compensation, either in
expectation or its realized value, will be constrained by the availability
of data. Table 3 summarizes the data available in proxy statements
and compiled by Execucomp about CEO holdings of stock and options
of his own …rm, the evolution of which is key to measurements in both
categories. For stock holdings, we have the number of shares held by
the CEO at the end of the …scal year, as well as the number and value
of both stock that remains restricted and of stock that vested during
the year. For option holdings, we know the number of options exercised during the year, as well as their value. We also know the number
and value of options exercisable (but still unexercised) and those whose
vesting restrictions did not yet expire. These values, however, are calculated using the “intrinsic” valuation (stock price at the end of the
year minus exercise price, times number of options, if positive), hence
ignoring the options that are currently out of the money, and provide
a simplistic evaluation (Black and Scholes would be a more accurate
choice).
We choose our measure of realized pay (presented in the next section) in light of these data availability issues. Our choice tries to minimize the sensitivity of our measurements to assumptions about the
unknown details of compensation packages, while still exploiting the
information we have available on the portfolio of stock and options of
the CEO.
Before we present our measure, it is important to note that we
view expected and realized measures of pay as complements rather than
substitutes when trying to understand incentives for CEOs. Expected

A. Jarque and J. Muth: Executive Compensation Packages

259

Table 3 Summary of Information Available in Execucomp
about Stock and Option Holdings

Stock Holdings

Option Holdings

Information in Execucomp
Number of unrestricted
Number of restricted
Value of restricted
Number vested during the year
Value of vested during the year
Number exercised during the year
Value of exercised during the year
Number of all unexercised vested
Value of in-the-money unexercised
vested (intrinsic)
Number of all restricted
Value of restricted in-the-money
(intrinsic)

pay is a forward-looking measure, which gives important information
about the value of the current compensation package given to the CEO.
However, it is a di¢ cult task to get a realistic valuation of stock or
options for the CEO, especially because of selling restrictions and risk
aversion considerations. In practice, the data in Execucomp re‡
ects the
…rm’ estimate of that value for CEOs. For options, usually a pricing
s
model based on arbitrage conditions, such as Black and Scholes’option
valuation model, is used to provide a value in the company’ report
s
with the SEC. Ad hoc modi…cations are often used to accommodate
the fact that CEOs are risk averse and there are selling restrictions on
the option grants.12
Realized pay, instead, is a backward-looking measure: Given past
performance, we can calculate how much payo¤ the CEO actually got
in the given period. In contract theory terms, we can view this measure
as a description of the contract payo¤s on the equilibrium path. That
is, we observe what the CEO gets for the actual performance that
materialized, but we do not have information on what the payo¤s would
have been for better or worse performances. For an estimate of these
o¤-the-equilibrium-path payo¤s, in Section 3 we perform sensitivity
analyses that exploit the fact that we have some information on the
number of stocks and options the executive sold or exercised.
12
See Hall and Murphy (2002) for a quantitative evaluation of the di¤erence between the executive’ value of options and the cost to the …rm in providing them.
s

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Federal Reserve Bank of Richmond Economic Quarterly

One advantage of our realized pay measure is that we do not need
to take expectations over the value of deferred contingent pay. Hence,
we will be able to use the publicly available information on compensation packages without resorting to assumptions about the future value
of contingent compensation. Still, even for the purposes of measuring realized pay, we are missing some important information on these
deferred contingent instruments. As re‡
ected in Table 3, Execucomp
records the value of stock and the value and number of stock underlying
options at the time when they are granted to the CEO. The values are
approximations to the expected income that the CEO will realize in the
future, when their restrictions expire. However, we do not have explicit
information on the vesting schedules of these grants, or the exact date
when the vested stocks are sold or the options exercised, or the market
price of the stock at those times. This information is key to compute
the actual cash the CEO receives as a result of the original grant. Our
construction of a realized pay measure will necessarily involve assumptions on these unknown characteristics of the compensation, which we
discuss in detail in the Appendix.
Larcker, McCall, and Tayan (2011) have a short and interesting
essay in which they also point out the di¤erences in measuring expected
and realized pay.13 The authors include illustrative examples of the
di¤erence between expected and realized compensation based on data
for a handful of …rms in the year 2010. In this article we will use a larger
number of …rms and a longer period of time to illustrate quantitatively
the di¤erence between the two measures.

2.

CONSTRUCTING A MEASURE OF
REALIZED PAY

In this section, we provide a framework for comparing di¤erent measures of compensation. For this, we describe the types and timing of
the di¤erent components in a typical compensation package. Using this
framework, we introduce our proposed measure of realized contingent
pay, denoted It ; which is de…ned as the sum of salary, bonus, and gains
from selling stock and exercising options in the current year. To construct it, we use information on the several components of pay packages
that is publicly available, along with some assumptions. We refer to
the model to illustrate the need for these assumptions and to justify
13
Larcker, McCall, and Tayan (2011) also present a third measure that they call
earned pay (the value of pay at the moment when all selling restrictions are lifted, which
does not necessarily coincide with the value at the time the CEO decides to sell). We
do not have enough information in Execucomp to calculate this measure.

A. Jarque and J. Muth: Executive Compensation Packages

261

our choices. Then we illustrate in the context of the model what the
di¤erences are between our measure and two alternative ones: (1) direct compensation, which is de…ned as the sum of salary, bonus, perks,
and other compensation, and the value of stock and options at the time
of grant, and (2) total yearly compensation, which is de…ned as direct
compensation plus dividends, plus the change in the value of stock and
options in the portfolio of the CEO.
Consider a CEO who lives for T years. He starts his tenure with
a …rm at year t = 1. He receives compensation for all the years he
is working, and after he retires he consumes out of his accumulated
wealth and pension payments. We assume he has no sources of income
other than what he receives as payments for his job as CEO, which we
denote as It . The value he attaches to his employment at the beginning
of period 1, denoted V0 ; is equal to the expected stream of income that
he expects to receive in exchange for his work in each of the periods of
his life:14
#
" T
X It (p1 ; : : : ; pt )
je ;
(1)
V0 (e ) = E
(1 + r)t 1
t=1
where the expectation is with respect to stock price realizations (which
summarize the performance of the …rm in this simple model), conditional on the sequence of e¤ort choices by the CEO (denoted e ) given
the optimal contract. We denote the market interest as r:
In this article, we want to measure the realized value of It : A more
ambitious objective, which would relate more directly to theoretical
models of CEO compensation based on repeated moral hazard models
(Wang 1997), would be to try to measure Vt (e ). We discuss some of
the added di¢ culties of this measurement at the end of this section.
Realized pay It will not all be delivered directly in cash. Rather, the
executive will receive an annual compensation, Ct ; that will consist of
two elements: a cash-based portion, or current liquid payment, denoted
Lt ; and a grant-based portion, denoted Gt : We assume compensation
is received only once per year, at the end of the …scal year. We have
that
Ct = Lt + Gt 8t;

(2)

where
Lt = Wt + Bt + Dt + Kt

8t:

14
Note that the utility the CEO may get from a given value of employment will
also depend on his wealth from sources other than the executive’ employment. There is
s
typically no information on this outside wealth to be used in empirical studies of CEO
compensation.

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Federal Reserve Bank of Richmond Economic Quarterly

That is, Lt is the sum of annual salary Wt ; bonus payment Bt ; which
usually will depend on the annual results of the …rm, dividends Dt ; and
perks and contributions to pension plans Kt :15 Grants consist of both
restricted stock of the …rm, sr ; and options to buy stock, or , and are
t
t
valued at any t0 t as16
0

Gt
t

= EV (sr ; pt0 ) + EV (or ; xt ; pt0 )
t
t
r
r
0 + EV (o ; xt ; pt0 ) :
= st pt
t

In this expression, EV (sr ; pt0 ) is the estimated value of restricted stock,
t
i.e., the amount of stock, sr ; valued at the stock price at the time of
t
valuation, pt0 . The estimated value of options, EV (or ; xt ; pt0 ) ; stands
t
for some version of the Black and Scholes (1973) option valuation formula and depends both on the market price at the time of valuation,
pt0 ; and the exercise price, xt .

Our Measure of Realized Pay
The stream of realized pay It that the CEO will receive from the …rm
while working will be equal to the cash part of his compensation, Lt ;
plus whatever net gains from trade he gets from buying and selling
unrestricted stock (or vested exercising options). To compute these
gains from trade, it will be important to keep track of the accumulated
number of stock and option grants that have vested, what we will refer
to as the “portfolio” of the CEO.17 Let St 1 denote his holdings of
unrestricted stock at the beginning of period t; and Ot 1 denote his
holdings of vested options. Let Tt (St 1 ; Ot 1 ) denote the gains from
the sales of stock and exercises of options at period t: Then, we can
write realized pay as
It = Lt + Tt (St

1 ; Ot 1 ) :

Tracking the holdings St and Ot involves understanding the law of
motion of the quantities of vested stock and options available to the
CEO. Under the assumption that the CEO did not own any stock or
options of the …rm before his employment as CEO started, we have
15

Note that dividends are not included in Execucomp’ TDC1 (which we will coms
pare later to our own proposed measure of income). We include them because they are
attached to the grants given to the CEO, and hence they are income that he receives
because of his association with the …rm.
16
Here and in the rest of the model description, we use capital letters to denote
values and lowercase letters to denote quantities.
17
Note that option grants also come with expiration dates; we are abstracting from
those in this discussion, since the information we have on expirations is limited.

A. Jarque and J. Muth: Executive Compensation Packages

263

that his holdings in the beginning of year 1 are equal to zero:
S0 = 0;
O0 = 0:
Any subsequent year, the quantities available to trade will change for
two main reasons:
1. some of the past grants will have vested, or the CEO may choose
to buy unrestricted stock; these actions will increase his holdings;
2. some of the past grants in his holdings will be sold or exercised,
decreasing his holdings.
It is worth noting here that accurately evaluating the evolution
of the holdings of the CEO would necessitate a large amount of information. For example, the CEO may choose to buy or sell stock,
or exercise options, at di¤erent times during the year— with di¤erent
market prices for each transaction. Also, he may choose to exercise
options and hold on to the stock that he obtains with this transaction.
Moreover, he may inherit or donate stock at any time. Unfortunately,
the only data we have for the holdings of stock and options is their
quantities and value at the end of each …scal year (see Table 3), and
we are lacking the details on the speci…c transactions that determine
their evolution. Hence, we make the following important simplifying
assumptions. First, we assume each of the possible trades happens only
once in the …scal year. Note that this still accommodates for a given
sale of options to include options from di¤erent past grants, which implies di¤erent exercise prices. Second, we assume that the executive
never purchases options, and that he exercises options only if he plans
to sell the stock immediately. Third, we ignore any inheritances or
donations.
We can summarize the above discussion in a formal law of motion
for the holdings of stock and options by introducing some notation.
The vesting restrictions on the stock and option grants determine the
available St and Ot in each period. Typically, only a portion of the previous years’restricted stock vests every t. Denoting the vested shares
in year t by sv and vested options in year t by ov , the accumulated
t
t
number of shares and options available for selling in year t is
St = S t 1
ss sb + sv ;
t
t
t
X
e
v
Ot =
og og;t + ot ;
og 2Ot

(3)

1

where we are denoting the three types of trades that can happen at
time t as follows:

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Federal Reserve Bank of Richmond Economic Quarterly
1. selling stock ss of the unrestricted stock available at period t,
t
St 1 , at price pst ;
2. buying an amount sb of stock from the market, at price pbt ;
t
3. buying stock through the exercise of oe of any vested option
g;t
grant g (with corresponding exercise xg ) at price pet .

With this notation, we can write an expression for the gains from
trade:
X
Tt (St 1 ; Ot 1 ) = ss pst sb pbt +
max 0; oe (pet xg ) : (4)
t
t
g;t
og 2Ot

1

This completes the description of our measure of realized pay, It :
Next, before moving on to the estimates of It using data, we use the
model in this section to compare our measure of realized pay with
alternative measures used in the literature.

Alternative Measures: Expected Pay
As we discussed in Section 1, the literature has used compensation measures based on the expected value of pay. The theoretical measure of
expected pay is described by (1). The employment value, Vt ; is the sum
of the expected stream of realized pay. For the measurement of Vt (e )
in the data, however, one would have to make assumptions about the
terms of the contract o¤ered to the CEO regarding compensation in
future periods (i.e., what would trigger a wage increase, or what is the
schedule of future grants contingent on realized performance). One
would also need to understand the CEO’ expectations about stock
s
prices in the future, which will determine his future realized gains from
trade. One would also need to understand his expectations regarding
his transitions to other …rms and their consequences for his realized
pay. Moreover, one would need to model how performance during the
CEO’ working life will a¤ect his pension payments. To the best of our
s
knowledge, no study has provided a reliable measure of Vt . Instead, two
di¤erent approximations to Vt have been widely used: “direct compensation” (TDC1) and “total yearly compensation” (TYC). We de…ne
each of these using our notation, in turn, and compare them to our
measure of realized pay.
The Execucomp variable TDC1 can be written in terms of our
notation as
T DC1t = Wt + Bt + Kt + Gt :
t
This measure of expected pay does not closely correspond to the theoretical Vt ; since it does not include any estimation of future wages,

A. Jarque and J. Muth: Executive Compensation Packages

265

bonuses, and new grants. It includes an estimate of the expected future value of the grants given to the CEO in the current year, Gt =
t
sr pt + EV (or ; xt ; pt ) ; but it ignores the changes in the value of past
t
t
grants, or the realized gains from exercising them once they are vested,
as well as the dividends that correspond to the CEO from holding stock.
The main di¤erence between our I measure and TDC1 is that we do
not include the value of grants, Gt ; but rather the realized net gains
from trade, Tt . Also, dividends are included in It but not in TDC1t :
A second alternative measure of expected pay, TYC, has been used
in the literature since Antle and Smith (1985) proposed it. The idea
behind it is to calculate the expected value that the CEO attaches to
working in his …rm, every period, as the current expected value of stock
and option holdings plus the expected future compensation; then one
can interpret the annual change in this expected value from one period
to the next as the TYC of the executive.18 Because the expected value
of grants is updated every year, this measure presents a more accurate
picture of the incentive value of the CEO’ contract. However, the
s
measure is not without problems. For example, a common simplifying
assumption when computing this measure is to assume that salary and
bonus payments remain constant in future years and that the expected
value of future grants is zero.19
We follow the description in the Appendix of Clementi and Cooley
(2009) to replicate their measure of TYC, assuming wages, bonuses,
and perks remain constant throughout the work life of the CEO, and
no turnover. We graph it for comparison purposes in Figures 1, 2, and
5. In terms of our notation, TYC can be written as
T Y Ct = Wt + Bt + Kt + Dt +

t
X

Gt

Gt

1

;

=1

where Gt in this case denotes the updated expected value during period
t of stock and (unexpired) option grants that were given at period
t
20
and are still unexercised.
The measure TYC attributes initial grants as compensation in the
year when they are granted, and then subsequent appreciations and
18
Examples of di¤erent implementations of this concept of expected pay include
Jensen and Murphy (1990); Garen (1994); Haubrich (1994); Hall and Liebman (1998);
Haubrich and Popova (1998); Schaefer (1998); Aggarwal and Samwick (1999); Baker
and Hall (2004); Clementi and Cooley (2009); Edmans, Gabaix, and Landier (2009);
and Gayle and Miller (2009).
19
See, for example, Clementi and Cooley (2009; 2, 29).
20
Note that Gt 1 = 0 whenever > t: Also, note that this re-evaluation of grants
coincides conceptually with our measure of gains from trade, for the portion of the
vested portfolio that is converted to cash in period t: That is, if, for example, only
grants given at t 4 are exercised at t; then Tt (St 1 ; Ot 1 ) = Gt 4 :
t

266

Federal Reserve Bank of Richmond Economic Quarterly

depreciations of the grants to the periods when they happen— even if
they do not translate into realized pay in that particular period. In
comparison, our measure I of realized pay records only the realized
value of grants when they get exercised, and it attributes the gains
from trade to the particular period when they happen. It is easy to see
P
P
that the simple sum of T It = T T Y Ct ; however, the individual
t=1
t=1
year entries will di¤er, and hence the properly discounted sum will
di¤er as well.

3.

MEASUREMENTS

In this section, we present the empirical measurement of pay according
to the methodology described above. In the Appendix, we provide the
details on how to map the elements of pay described in the previous
section to the data available in Execucomp.
In this article, we work with the August 2013 release of Execucomp,
which includes annual observations through the …scal year 2012. We
drop CEOs who own 50 percent or more of the shares of their company,
since we want to focus on measuring incentives in relationships for
which there is an agency problem. Our …nal sample includes 3,345
di¤erent …rms, for a total 34,497 …rm-CEO-year observations.21;22
Figure 1 presented the median of our measure of realized pay from
1993 to 2012. We compare it to the two measures of expected pay
discussed earlier in this article: “total compensation”reported in Execucomp as the variable TDC1 and our own calculation of TYC following
Clementi and Cooley (2009).23
Two features emerge from Figure 2. First, averages are much larger
than medians. This is well known for the measure TDC1, and it is con…rmed for our measure of realized pay, I. Second, average realized pay
is more volatile over time than average total compensation, and it is
typically above TDC1t , while it was typically below it when we looked
at the medians in Figure 1. However, TYCt is more volatile than either
of the other two measures. This is true both when looking at medians, in Figure 1, or when looking at means, here. Our analysis of the
21
The database includes up to …ve executives of a …rm per year, but we restrict
our sample to those designated as the CEO by the Execucomp variable CEOANN.
22
We also exclude from our analysis Warren Bu¤ett, the CEO of Berkshire
Hathaway, and Larry Ellison, the CEO of Oracle Corporation, because their values of
trades are extreme outliers.
23
We replicate Clementi and Cooley’ simpler calculation of TYC, which uses ins
trinsic valuations for options when their value is updated with new stock prices at the
end of the …scal year. Clementi and Cooley report in their manuscript that their results do not change substantially when they use Black and Scholes to produce those
revaluations.

A. Jarque and J. Muth: Executive Compensation Packages

267

Figure 2 Mean Realized Pay and Mean Expected Pay as
Measured by TDC1 and TYC

di¤erent components of pay shows that the estimated gains from trading stock are causing the volatility in realized pay. Also, every year
there are a few CEOs who realize very large gains from trading stock,
making the averages of the two measures of compensation di¤er more
than the medians. Moreover, the large revaluations of the portfolio
of the CEOs with changes in the stock price do not seem to translate into gains from trades, causing the large deviation of the measure
TYC from the measure I: One potential explanation would be that
CEOs have in their portfolios a large fraction of restricted stock and
options, so even if their value increases they are not able to realize
those gains. However, the information available in Execucomp about
restricted stock and options does not seem to support this hypothesis
(the restricted grants are a small part of the portfolio of the CEO at
any point in time). However, it is still plausible that implicit selling
restrictions are in place even after the explicit vesting period expires,
presumably with the objective of strengthening the market perception
about the con…dence of the CEO in the performance of his own …rm.

268

Federal Reserve Bank of Richmond Economic Quarterly

Figure 3 Liquid Portion of Compensation

Notes: The blue line presents mean total realized pay, It , and its liquid component, Lt (wage, bonus, perks, and dividends). The di¤erence equals mean trades,
Tt : The red line presents mean total expected pay as measured in TDC1t and its
liquid component (wage, bonus, and perks). The di¤erence equals grants, Gt .

In Figure 3, we display the liquid portion of compensation for mean
realized pay, It ; and for mean total expected pay as measured in TDC1t .
We see that the higher volatility of mean It compared to that of mean
TDC1t is mainly driven by the volatility of trades. Figure 4 plots separately the medians of the di¤erent components of realized pay, Lt and
Tt ; and the median of It : (Figure 4 plots also these statistics for …nance
…rms, which we will discuss in the next subsection.) Both components,
as well as the total It ; are increasing over time. For comparison, the
median value of grants, Gt ; is included as well. The value of grants is
also increasing over time.
As a robustness check, we replicate Figure 2 in Figure 5 for a subsample of the …rms including only the CEOs that own less than 1
percent of the shares of their company.24 The level of TYCt is much
24
This subsample includes 2,169 out of our 3,345 …rms, and 16,302 out of our
34,497 observations.

A. Jarque and J. Muth: Executive Compensation Packages

269

Figure 4 All CEOs versus Finance CEOs

Notes: A comparison of the medians of liquid compensation, Lt , net gains from
trading and stock options, Tt , the expected liquid value of stock and option
grants, Gt , and total realized pay, It . Note that although It = Lt + Tt ; the sum
of the median of Lt and Tt is not equal to the median of It .

lower, and mean realized pay is sometimes above TDC1t . The main
di¤erence for this sample continues to be the higher volatility of TYCt .

Finance Firms
In Figure 4, we include statistics for …rms in the …nance sector with the
statistics for …rms in all sectors.25 Note that …rms in the …nance sector
are, on average, larger (in the sample, the average size in …nance is between …ve and six times larger than the average size for all …rms, year
by year, with a decreasing trend between 2004 and 2009). Because the
level of total compensation (TDC1) has been shown to be positively
25
Firms in the …nance sector are those with SIC classi…cation in the 6,000–
6,300
range. There are 144 …rms per year, on average, in our subsample of …nance. We
performed the same analysis with a broader category including real estate …rms as well
as insurance, and the plots looked qualitatively similar.

270

Federal Reserve Bank of Richmond Economic Quarterly

Figure 5 Mean Realized Pay and Expected Pay, as Measured
both by TDC1 and TYC, for CEOs Who Own Less
Than 1 Percent of the Stock of Their Firm

correlated with size, we expect a higher realized pay for CEOs in …nance. This is con…rmed in the data up to the …nancial crisis of 2008.
Figure 4 shows that the composition of realized pay is slightly di¤erent
among …nance …rms, with higher liquid compensation and higher value
of trades (which are also more volatile, although this could be due to
the smaller number of …rms).
When looking in detail at the period since the 2008 …nancial crisis,
it is apparent in the graphs that there has been a steeper decline in
median realized pay— both for liquid compensation and trades— for
…rms in …nance than for the full sample of …rms. It is worth noting
that the median value of grants is, for both groups of …rms, well above
the median value of trades. The adjustment pattern of median grants
during the crisis is similar to that of realized pay, i.e., we see a steeper
decline for …rms in …nance.

Sensitivity of Realized Pay to Performance
Hall and Liebman (1998) provide a measure of sensitivity of pay to performance by using information on stock holdings to construct

A. Jarque and J. Muth: Executive Compensation Packages

271

Figure 6 Stock Returns by Percentile

Notes: Evolution of the 5th percentile, median, and 95th percentile stock returns
for the largest 1,500 …rms in our sample. For comparison, the same percentiles of
returns for all …rms in …nance are included as well.

counterfactuals.26 First, they construct a measure of the portfolio of
the CEOs, similar to our St and Ot holdings of stock and options.
Then, using the realized distribution of performances (stock returns),
they evaluate the holdings of each CEO in the data for di¤erent performance scenarios corresponding to di¤erent percentiles of the distribution of returns: We follow this methodology and provide a similar
counterfactual for our measure of annual realized pay. An important
caveat of this measure is that the quantities of stock traded and of options exercised are assumed to remain constant when stock prices vary
in the counterfactual. A model of how these trades would vary in a
more realistic setup is beyond the scope of this article.
For our performance counterfactuals, we need to propose the support and distribution of stock returns. For this, we use the observed
distribution of stock returns in each given year. We denote the annual
26
Given the limited quantitative importance of bonuses in total compensation, we
will ignore changes in bonus payments in our sensitivity analyses.

272

Federal Reserve Bank of Richmond Economic Quarterly

stock price return as
rt =

pt

pt
pt

1

:

(5)

1

This measure has the advantage of being comparable across …rms, as
opposed to the stock price itself. In Figure 6, we summarize the evolution of these distributions of returns rt of the 1,500 largest …rms in
our sample over time by plotting the return value for the median, and
the 5th and 95th percentiles.
Each realization of returns in the support of the distribution can be
translated into a stock price for each individual …rm using (5). That
is, when calculating the counterfactual value of Tt for an individual
executive working for …rm j; we will construct a counterfactual stock
price for various percentiles of the return distribution. We use a hat
to denote a variable’ counterfactual value, and a superscript nth to
s
indicate the percentile to which we are setting the performance of the
…rm. For the nth percentile, the counterfactual price for …rm j at time
t is
nth
pnth = 1 + rt
^j;t
pj;t

1:

With this price pnth , a new valuation of Tj;t can be produced, assuming
^j;t
nth
the return of the …rm was equal to the nth percentile return, rt .
Recall that we approximate the gains from trade coming from stock
purchases and sales as max[0; pt qt ]; where pt is the average price within
the year. We will set the counterfactual for this average price to
pt
d
pnth = pnth ;
^
t
pt t

(6)

that is, we assume that the proportionality between the average price
and the end-of-the-year price is maintained in the counterfactual.
For the portion of the gains from trade that comes from exercising
options, we will need several pieces of information. First, in order
to compute the net bene…t per option exercised, (^et xg ), we would
p
need to construct the counterfactual for the stock price at the time of
exercise, pet ; possibly using pet ; and we would need to know the exercise
^
price, xg , corresponding to each option exercised. Unfortunately, as
discussed earlier, we do not know pet or xg (we do not know which
particular past grant g was used to purchase the shares). The value of
exercised options is recorded in Execucomp:
X
oe (pet xg ) OP T _EXER_V ALt 8t:
g;t
og 2O0

A. Jarque and J. Muth: Executive Compensation Packages

273

Figure 7 Mean Counterfactual Income

Notes: Average percentage change in income for three di¤erent performance counterfactuals, for all …rms and for …rms in …nance only.

We also have the number of options exercised within the year:
X
oe =
oe
OP T _EXER_N U Mt 8t:
t
g;t
og 2O0

To produce an estimate for the counterfactual value of exercising options, we assume pet = p; the average price during the year, and we
solve for an “e¤ective” exercise price x using
e
X
oe (p x) =
e
oe (pet xg ) :
t
g;t
og 2O0

Finally, we also assume that CEOs do not exercise options in the
d
counterfactual if they are “out of the money” (that is, if pnth < x):
e
t
With these assumptions, we have that our counterfactual for gains of
trade is
h
d
d
^nth
Tj;t (Sj;t ; Oj;t ) = max[0; pnth qt ] + max 0; oe pnth
t
t
t

x
e

i

:

274

Federal Reserve Bank of Richmond Economic Quarterly

This, together with the actual liquid compensation for the executive
in the data, Lt ; which is not contingent on stock price realizations,
^nth
amounts to a calculation of a counterfactual Ij;t :
The numerical results are listed in Tables 4 (levels) and 5 (percentage changes). We display the percentage changes for the 5th, median,
and 95th percentile counterfactuals graphically in Figure 7. Keeping
in mind that percentage changes are bounded below by 100 percent,
we see that there is an obvious asymmetry in changes when the …rm
performs better rather than worse. This responds to the uncontingent
nature of the wage and the bonus in our calculations. Also, we see in
Figure 7 that the gains for the 95th percentile (i.e., outstanding stock
return performance) is very extreme in particular years. Two things
can lead to high net gains from trade: particularly good stock returns
in the given year (i.e., the 95th percentile stock return is an outlier
when compared to the other 95th percentile returns in other years) or
particularly generous past grants that imply a large number of stock or
options are available for trade. We can use the distribution of stock returns, plotted in Figure 5, to track which of the two explanations seems
more plausible. The years 2000, 2003, and 2009 represent examples of
outlier stock return performance in the 95th percentile; however, only
in the year 2000 does this translate into a very large counterfactual
mean realized pay in the 95th percentile. The spikes in income for the
years 2005 and, to a lesser extent, 2008– may correspond instead to
09
particularly large net quantities traded, as computed by us from the
portfolios of the CEOs.
Sensitivity for Finance Firms
We observed a sharper decrease in median realized pay for …rms in
…nance during the recent …nancial crisis (see Figure 4). However, this
does not seem to correspond to a very di¤erent sensitivity of realized
pay to performance for …nancial …rms during the crisis. Tables 5 and 7
replicate the sensitivity analysis of Tables 4 and 6 for …rms in …nance.
That is, using the stock and option holdings of …nancial …rms, we feed
in the same percentile stock returns used in Tables 4 and 6 (i.e., those
from the distribution of stock for the overall population of …rms) to
calculate their counterfactual realized pays. We …nd that the sensitivity
estimates align with those of the general sample for the whole sample
period.27 It is worth referring back to Figure 4 and noting that the
median liquid (uncontingent) compensation of CEOs in …nance is
27
Given the way we construct the counterfactuals, any di¤erences in level between
Tables 1 and 3 is due to the original di¤erences in the level of actual compensation
between the average …nance …rm and the average …rm in the sample.

Year
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
2011
2012

5th
4,301
3,438
3,694
5,291
5,246
4,775
10,618
6,859
4,439
9,840
7,917
10,266
8,883
6,991
5,076
8,078
6,899
6,443
7,996

25th
5,630
4,296
4,923
7,231
9,150
7,060
27,698
11,909
6,956
12,994
11,463
14,414
11,849
10,090
8,934
11,230
8,447
8,809
10,718

Median
6,378
4,926
5,734
9,083
12,397
8,668
41,383
14,968
8,910
14,718
13,211
17,072
13,802
12,326
12,177
13,450
9,459
10,325
12,080

75th
7,203
5,562
6,554
10,809
15,911
11,217
55,636
18,089
10,472
17,314
15,242
20,330
15,503
14,769
15,324
17,288
10,749
11,913
13,623

95th
8,821
6,832
8,157
14,289
24,021
20,479
87,588
27,074
13,455
26,321
20,491
26,911
19,754
19,817
20,812
28,866
13,825
15,215
18,149

Actual
6,182
4,659
5,286
8,243
9,364
8,460
11,268
11,022
7,448
14,156
13,023
16,382
13,200
12,531
9,636
14,474
9,640
11,270
12,747

A. Jarque and J. Muth: Executive Compensation Packages

Table 4 Counterfactual Income: Mean Level of Income if
Certain Percentile Stock Return Had Been
Achieved|All Firms

275

276

Year
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
2011
2012

5th
3,687
5,256
6,515
6,656
5,664
6,341
6,189
8,507
6,345
8,898
8,933
11,591
9,153
10,455
4,957
5,600
5,291
4,314
5,535

25th
3,987
5,700
9,468
8,323
8,173
8,800
10,105
13,528
9,544
11,051
13,099
15,828
12,596
14,958
8,523
7,378
6,322
5,350
7,174

Median
4,190
6,072
11,628
11,956
10,442
10,453
16,523
16,610
12,237
12,293
15,118
18,226
14,916
18,105
11,570
8,645
7,025
6,024
8,023

75th
4,414
6,488
13,792
15,389
12,902
12,996
24,242
19,757
14,405
14,159
17,452
21,159
16,925
21,476
14,561
10,847
7,910
6,719
8,983

95th
4,851
7,679
18,017
22,304
18,538
22,127
41,568
28,852
18,536
20,626
23,474
27,077
21,937
28,427
19,803
17,502
10,125
8,152
11,791

Actual
4,228
7,047
9,881
12,473
9,452
9,485
12,604
14,333
10,947
12,467
13,744
17,473
13,284
14,184
7,918
8,275
6,621
8,980
7,594

Federal Reserve Bank of Richmond Economic Quarterly

Table 5 Counterfactual Income: Mean Level of Income if
Certain Percentile Stock Return Had Been
Achieved|Finance Firms Only

A. Jarque and J. Muth: Executive Compensation Packages

277

Table 6 Counterfactual Income: Mean Percent Change in
Income if Certain Percentile Stock Return Had
Been Achieved|All Firms
Year
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
2011
2012

5th
9.2
11.5
12.1
15.0
16.4
16.6
16.5
17.6
17.2
13.8
18.6
18.7
18.4
20.8
19.7
15.3
14.8
18.6
18.2

25th
2.2
3.5
1.6
3.7
1.7
5.0
13.7
1.4
1.5
4.3
3.7
4.3
6.4
8.2
1.9
6.1
6.2
5.8
2.8

Median
2.1
2.7
5.4
6.6
11.2
3.4
38.8
13.7
11.5
1.1
4.2
31.8
1.7
1.3
14.0
0.8
0.4
2.8
5.5

75th
6.8
9.0
12.5
16.3
25.5
16.8
65.3
26.5
22.1
9.4
13.4
65.6
8.9
11.8
29.9
13.1
7.1
12.0
14.8

95th
16.4
21.4
26.5
35.9
62.6
66.1
125.3
63.6
42.4
38.3
37.5
133.9
26.9
33.5
57.8
50.8
25.2
31.3
42.1

particularly large compared to the entire sample, up until the recent
crisis. This, together with the fact that sensitivity estimates are similar
to those of the overall sample, suggests that the quantities of stock and
options held by …nance CEOs are larger than those in other industries,
hence implementing a similar risk in their realized pay in spite of larger
uncontingent compensation levels.

4.

CONCLUSION

Information on CEO pay is typically obtained from the mandatory disclosure of compensation required by the SEC for large public …rms.
A good measure of realized pay for CEOs, which includes the actual
gains from trading stock rather than their expected value at the time
when the …rm awards them to the CEO, is not readily in this source.
This article discusses how to construct an approximation to the value
of realized pay using the partial information compiled in the database
Execucomp on the stock owned, bought, and sold by CEOs each year.
We present our estimates for the period 1993–
2012 and compare them
to two alternative measures of expected annual total compensation that
are frequently used in the media and the academic literature: direct
compensation (the sum of salary, bonus, other compensation, and the

278

Federal Reserve Bank of Richmond Economic Quarterly

Table 7 Counterfactual Income: Mean Percent Change in
Income if Certain Percentile Stock Return Had
Been Achieved|Finance Firms Only
Year
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
2011
2012

5th
7.7
13.3
17.8
22.1
21.9
16.0
21.0
20.4
21.8
13.7
18.3
13.6
18.9
13.7
12.7
7.8
10.2
13.5
11.1

25th
2.6
8.9
8.2
11.9
1.6
0.5
3.2
0.6
8.1
5.0
1.1
1.9
7.8
0.2
6.8
2.6
3.4
4.9
0.9

Median
0.9
5.2
1.2
2.2
15.6
10.1
13.5
14.4
5.7
0.1
7.9
5.4
0.2
10.0
24.3
10.4
1.2
1.1
7.6

75th
4.8
1.1
6.3
7.2
34.2
26.6
31.6
29.0
17.0
7.9
18.3
14.5
6.4
20.9
42.5
24.1
7.1
7.3
15.2

95th
12.5
7.5
21.0
26.1
76.9
85.6
72.8
71.9
38.5
34.8
45.1
32.9
22.8
43.4
75.4
65.5
23.8
20.2
37.5

market value of new grants) and total yearly compensation (which includes the year-on-year change in the value of the stock holdings of the
CEO). Our measure of realized pay tends to be more volatile over time
than direct compensation, mainly due to the volatility of the gains that
CEOs realize from trading stock. However, total yearly compensation
is markedly more volatile than the other two measures. We …nd that,
while the average realized pay level has historically been at or above
that of direct compensation, its median has consistently been lower.
We provide descriptive statistics of realized pay for …rms in the …nance
sector. In the aftermath of the crisis the realized pay of CEOs of …nance …rms seems to have decreased in level relative to the realized
pay of CEOs in all industries. Our calculations suggest, however, that
realized pay of …nance CEOs changes with the performance of their
…rm in similar magnitudes to that of the average CEO for the whole
1993–
2012 period.

A. Jarque and J. Muth: Executive Compensation Packages

279

APPENDIX
In this Appendix, we show how to map the variables de…ned in Section 2 to the Execucomp database. We discuss the elements of our
ideal measure of compensation that are missing in the data, and what
assumptions we make to go around these di¢ culties.
As we list the objects needed to calculate It ; we will note how
the change in reporting requirements of the SEC in 2006 changes the
availability of data (or, sometimes, simply the name of the Execucomp
variable that corresponds to a given concept). For this purpose, we will
refer to the reporting period before 2006 as P1 ; and the one after as
P2 :

Measuring Liquid Compensation, Lt
Our measure of liquid or cash-based compensation, Lt ; is the sum of
the executives’annual salary, bonus, dividends, and any perks received
within the year, such as contributions to pension plans. Data on annual
salary Wt is directly available in Execucomp:
Wt

SALARYt ; 8t:

Our measure of bonus, Bt ; is the sum of the Execucomp variable
BONUS and two variables that capture payments received from hitting
“objective” performance targets such as sales growth or stock price
performance:28
Bt

BON U St + LT IPt
BON U St + N ON EQ_IN CEN Tt

if t 2 P1
if t 2 P2 :

We also have information in the data about the dividend yield (dividends per share, divided by pt ; times 100) that the executive receives
from his stock ownership of the company. We back out the total dividend payments as follows:
DIV _Y IELDt
P RCCFt SHROW N _EXCL_OP T St 8t;
Dt
100
28

Speci…cally, after 2005 Execucomp’ BONUS variable was modi…ed to only
s
include discretionary or guaranteed bonuses.
So to include payments from objective targets, we sum BONUS with NONEQ_INCENT, the amount of income received in the year pursuant to non-equity incentive plans being satis…ed. Whenever
NONEQ_INCENT is missing (i.e., prior to 2006), we add BONUS with LTIP, the
amount of income received in the year pursuant to long-term incentive plans that measure performance over more than one year.

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Federal Reserve Bank of Richmond Economic Quarterly

where P RCCFt is Execucomp’ record of the stock price at the closing
s
of the …scal year:
pt = P RCCFt 8t:
Finally, our measure of perks and pension payments Kt is the sum
of Execucomp variables related to “other compensation”
:
Kt

ALLOT HT OTt + OT HAN Nt
if t 2 P1
DEF ER_RP T _AS_COM Pt + OT HCOM Pt if t 2 P2 :

Tracking Grants, Gt
Our measure of grant-based compensation Gt is the sum of the value
of restricted stock grants and options in the period. We have data on
the value of the stock component of that sum, EV (sr ; pt ), with the
t
following variables:29
EV (sr ; pt )
t

RST KGRN Tt
if t 2 P1
ST OCK_AW ARDS_F Vt if t 2 P2 :

In reality, there may be N grants within the year, each with a quantity
st;n and a market price at the time of granting of pt;n ; for n = 1 : N:
The variables above that we observe in Execucomp will not have the
disaggregated information grant by grant, but rather they correspond
to
EV (sr ; pt ) =
t

N
P

st;n pt;n :

n=1

The value of options awarded in the period is recorded in the data
as follows:30
EV (or ; xt ; pt )
t

OP T ION _AW ARDS_BLK_V ALU Et if t 2 P1
OP T ION _AW ARDS_F Vt
if t 2 P2 :

29
Both variables measure the value of stock awards as of the grant date. RSTKGRNT was reported by the companies themselves in the Summary Compensation Table,
while STOCK_AWARDS_FV is calculated by Execucomp. Strictly speaking, each also
contains restricted stock units and phantom stocks.
30
OPTION_AWARDS_BLK_VALUE is calculated by Compustat, during that period of time when— prior to FAS 123R— companies typically expensed options using the
“instrinsic value” method, i.e., the di¤erence between grant date stock price and exercise price of the option, which nearly always led to no expensing of options. OPTION_AWARDS_FV is the grant date fair value of option awards in the year, reported
by the company per FAS 123R using some version of Black and Scholes (1973) or a similarly accepted calculation.

A. Jarque and J. Muth: Executive Compensation Packages

281

Again, these variables aggregate all grants within a year, so e¤ectively
we will set
M
P
EV (or ; xt ; pt ) =
EV or ; xtg; ; pg;t ;
t
g;t
g=1

where M is the total number of option grants in the year. There is
some partial information in Execucomp about the date and exercise
price of the di¤erent grants for an executive in a given year. However,
we do not have their vesting schedule or the date of their exercise (that
is, we do not know what the stock market price was at the time when
the executive exercised the options). See the related discussion in the
realized pay sensitivity analysis in Section 3.

Computing Net Gains from Trading Stock, Tt
We will now de…ne the components of our net gains from trade measure,
Tt . To begin, recall that we assume each of these trades happens only
once in the …scal year, and if the executive exercises options, he sells
the acquired shares immediately.
The portion of Tt that comes from exercising options is captured
by the Execucomp variable OPT_EXER_VAL:31
X
oe (pe;t xg ) OP T _EXER_V ALt ; 8t:
g;t
oe 2Ot
g;t

1

The portion of Tt that comes instead from buying and selling stock on
the open market, ss ps1 sb pb1 ; must be estimated, because we cannot
1
1
observe in the data the quantities ss or sb (and, correspondingly, the
t
t
prices ps or pb ). We use an algorithm similar to Clementi and Cooley
t
t
(2009) to estimate this di¤erence, with slightly di¤erent assumptions
that we discuss later in this section. From the law of motion for vested
stock in (3), we have that the di¤erence between last year’ unrestricted
s
stock holdings and this year’ is either coming from the newly vested
s
stock this year, sv ; or net purchases. We denote the net quantity of
t
shares sold in t as qt ss sb : Rearranging (3) and substituting qt , we
t
t
have
qt = St 1 St + sv ; 8t:
(7)
t
Typically, qt will be positive in the data, i.e., the CEO will sell more
shares than he buys in a given year. Occasionally, however, qt
31

OPT_EXER_VAL is the total value realized from option exercises in the year,
and is measured (for each g award, in our notation) as the di¤erence between the exercise price and stock price on the date of exercise.

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Federal Reserve Bank of Richmond Economic Quarterly

calculated as in (7) will be negative. This could be due to violations of
our assumption that the CEO immediately sells stock acquired through
the exercise of options.32 Because we would rather bias our measure of
realized pay upward, we set qt in our calculations equal to the maximum
of qt from (7) and 0.
To calculate qt using (7) we need St 1 and St ; which correspond
to the CEO’ holdings of unrestricted stock. We observe this variable
s
directly in Execucomp:33
St

SHROW N _EXCL_OP T St ; 8t:

We also need the variable sv ; the stock vested within the year. This
t
variable maps directly into Execucomp’ SHRS_VEST_NUM in the
s
reporting period P2 : For observations in P1 ; when it is missing, we
estimate it by examining annual changes in aggregate restricted stock
holdings and annual grants. Speci…cally:
8
ST OCK_U N V EST _N U Mt 1
<
if t 2 P1 ;
ST OCK_U N V EST _N U Mt + sr
sv
;
t
t
:
SHRS_V EST _N U Mt
if t 2 P2 :

where our measurement of the number of stocks granted within the
year, sr ; is an approximation to the real total number of stock (unt
available in the data) that we recover from EV (sr ) by assuming all
t
grants are valued at the average price within the year, denoted pt :34
EV (sr )
t
sr =
:
t
pt
Note that pt is not in Execucomp. We match the …rms in Execucomp
to a di¤erent database from the Center for Research in Security Prices
(CRSP) containing daily stock prices, and we construct the average
price ourselves. For this, we take the 12-month window of each …rm’
s
…scal year. To summarize, in our notation, our estimate for the amount
of stock vested within t is
r
sv = St
t

1

r
St + sr :
t

Once we get qt from (7), we estimate the value ss ps1 sb pb1 by
t
t
assuming the qt shares were traded at the average market price over
32
In addition to what we have described, there are two other types of transactions
that will change CEO holdings: stock inheritances and stock donations. We abstract
from them, as these transactions will typically be small, if non-zero. However, these
could also be behind some of the negative qt in the data.
33
SHROWN_EXCL_OPTS reports shares of the …rm owned by the CEO, excluding options that are exercisable or will become so within 60 days.
This amount is
reported as of some date between the …scal year-end and proxy publication.
34
Clementi and Cooley (2009) use the end-of-the-…scal-year price for this calculation. We choose average price hoping to avoid some of the idiosyncrasy of pt due to
volatility of stocks.

A. Jarque and J. Muth: Executive Compensation Packages

283

the year, i.e., ps1 = pb1 = pt . Given our assumption of non-negative
net quantities traded, this amounts to stating
ss ps;t
t

sb pb;t
t

max[0; pt qt ]:

Thus, adding the stock and option portions of Tt , we get
Tt (St

1 ; Ot 1 )

max[0; pt qt ] + OP T _EXER_V ALt ; 8t:

Note that there are two di¤erences between our estimation of net
revenue from trade and the calculations in Clementi and Cooley (2009).
First, we use average instead of end-of-year prices to recover the quantity of shares granted in a given year, sr ; from the value of the grants;
t
this in‡
uences our estimate of the net quantities traded, qt : Second, we
use OPT_EXER_VAL directly to account for the proceeds of options
sales during the year: This variable is the true value of option exercises
collected in Execucomp and hence uses actual exercise prices and actual
stock prices on date of exercise. Clementi and Cooley (2009) instead
choose to lump the stock purchases resulting from option exercises in
with other stock sales, and they assume that they are acquired at the
average price.

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Bebchuk, Lucian, and Jesse Fried. 2004. Pay without Performance:
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Bolton, Patrick, Jose Sheinkman, and Wei Xiong. 2006. “Executive
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Clementi, Gian Luca, and Thomas F. Cooley. 2010. “Executive
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Clementi, Gian Luca, Thomas F. Cooley, and Cheng Wang. 2006.
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Gabaix, Xavier, and Augustin Landier. 2008. “Why Has CEO Pay
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Gayle, George-Levi, and Robert A. Miller. 2009. “Has Moral Hazard
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Haubrich, Joseph G. 1994. “Risk Aversion, Performance Pay, and the
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Haubrich, Joseph G., and Ivilina Popova. 1998. “Executive
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Composition of CEO Pay.” Federal Reserve Bank of Richmond
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Jensen, Michael C., and Kevin J. Murphy. 1990. “Performance Pay
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Jenter, Dirk, and Fadi Kanaan. Forthcoming. “CEO Turnover and
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Jin, Li, and S. P. Kothari. 2008. “E¤ect of Personal Taxes on
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Economic Quarterly— Volume 99, Number 4— Fourth Quarter 2013— Pages 287–
303

The Business Cycle Behavior
of Working Capital
Felipe Schwartzman

F

irms require short-term assets or liabilities in order to facilitate
production and sales. Those “working capital”requirements are
often incorporated in macroeconomic models designed to study
the impact of monetary or …nancial shocks.1 They are important for the
propagation of those shocks since they a¤ect the marginal cost of funds
faced by some set of agents in the economy. If …rms require working
capital in order to acquire variable inputs, a change in the cost of funds
faced by …rms translates into immediate changes in macroeconomic
activity.2 This article investigates the cyclical properties of the three
main components of working capital— inventories (raw materials, workin-process, and …nished goods), cash and short-term investments, and
trade credit— aggregated across all …rms and with special attention
to their correlations across time with output. The key objective is
to obtain stylized facts. While theory informs what kind of facts are
worth examining, the uncovering of stylized facts also serves as an input
for the development of new theories. The discussion above provides a
couple of examples of existing theoretical models that motivate the
exploration that follows, but the results stand on their own as useful
The views expressed in this article are those of the author and do not necessarily
represent the views of the Federal Reserve Bank of Richmond or those of the Federal
Reserve System. E-mail: felipe.schwartzman@rich.frb.org.
1
Technically, the accounting de…nition of working capital is the di¤erence between
the sum of short-term assets and the sum of short-term liabilities. In the article, as
in the literature, I use the term more broadly to refer to the collection of short-term
assets and short-term liabilities rather than the aggregate accounting concept.
2
Examples of articles that model working capital requirements explicitly are
Christiano and Eichenbaum (1992) and Fuerst (1992), who develop the canonical model
of working capital in monetary economics, and Jermann and Quadrini (2012), who advance working capital as a key part of the transmission mechanism for …nancial shocks.
Working capital also plays a prominent role in the emerging markets business cycles literature, much of which emphasizes the aggregate impact of shocks a¤ecting the supply
of foreign funds. Neumeyer and Perri (2004) is a primary example of the latter.

288

Federal Reserve Bank of Richmond Economic Quarterly

for potentially any theory in which working capital plays a signi…cant
role.
In the simplest models, working capital is needed in advance of production. This requirement implies that, so long as data is available at
a high enough frequency, the relevant components of working capital
ought to be more strongly correlated with future values of cash ‡
ows
than with current values. This, however, need not be generally the
case. In an environment with credit frictions, working capital could
also lag production. Credit frictions commonly imply that …rms have a
borrowing capacity that is increasing in the size of their balance sheet.
In particular, interest rates can increase with leverage, as in Bernanke
and Gertler (1989), or there might be outright leverage limits, as in
Kiyotaki and Moore (1997).3 Models with credit frictions generate
endogenous propagation, since pro…ts retained in a given period increase the size of …rms’ balance sheets, which in turn allow …rms to
subsequently expand their borrowing and their acquisition of working
capital.
To evaluate the lead-lag relationships, I use data from the Financial
Accounts of the United States.4 The data set is put together by the
Federal Reserve Board and distributed online four times per year. The
accounts are constructed based on a variety of data sources to provide
a comprehensive view of how di¤erent sectors of the economy (households and di¤erent types of corporations) interact with one another, as
well as providing a breakdown of the assets and liabilities held in each
one of those sectors. The time series span most of the post-WWII period, from 1952 onward, and I use all of the data in my analysis. The
advantage of using this data set over …rm-level data, such as COMPUSTAT, is that it provides a comprehensive view of the economy,
including noncorporate businesses, whereas COMPUSTAT data only
include the largest …rms. For all the time series, I compare correlations
before and after 1984. This marks the end of the 1981 recession and the
beginning of the “Great Moderation.”The motivation for splitting the
sample follows Lubik, Sarte, and Schwartzman (2014), who …nd that
around the same time as the onset of the Great Moderation there was
a marked change in key business cycle properties of the U.S. economy.
Strikingly, these changes in correlations survive the end of the Great
Moderation after 2008. Since the focus of the article is on correlations
3
These two articles also correspond to the two most widely used microfoundations for credit frictions, which are costly state veri…cation and imperfect commitment,
respectively
4
These data were previously called the “Flow of Funds Accounts of the United
States.”

Schwartzman: The Business Cycle Behavior of Working Capital

289

and not on volatilities, I treat the whole period from 1984 onward as a
single one.
The …ndings are as follows: First, inventories lag business cycles in
the years before 1984 by about three quarters but by only one or two
quarters in the more recent period. This is consistent with the view that
before 1984 inventory accumulation was determined by previous cash
‡ accumulation by …rms but less so afterward. The second …nding
ow
is that cash holdings broadly de…ned to include short-term investments
commonly lead the business cycle, consistent with the cash-in-advance
model for short-term production decisions. This echoes classic results
by Sims (1972) and updated in Stock and Watson (1999) showing that
monetary aggregates are a good leading indicator of output. However,
and in contrast to monetary aggregates, the lead-lag relationship between cash holdings and output is considerably more robust, remaining
in place in the past 30 years, a period in which the relationship between
conventional monetary aggregates and output has broken down. Finally, I …nd that trade credit lags output, although less markedly than
inventories.
This article has a very simple structure. I …rst discuss in more detail how decisions made by a …rm over time can give rise to the various
components of working capital. The following three sections examine
in turn each of the three major components of working capital (inventories, cash and short-term investments, and trade credit). I provide
for each component additional background information about existing
theories explaining why …rms are willing to hold them, as well as some
broad descriptive statistics about how relevant those components are
on …rms’balance sheets, the long-run trends in those holdings, if any,
and the cyclical properties of those di¤erent components. The last
section concludes.

1.

WORKING CAPITAL DEMAND

In models, working capital requirements often arise out of timing restrictions. As an example of such restrictions, consider a …rm whose
production and sales process follows a seasonal ‡
ow, so that cash ‡
ows
are only realized every four periods f:::; t 4; t; t + 4; :::g. As an example of a real activity, one could think of this as a Christmas decorations
producer that only sells its products in the last quarter of the year.
However, in order to receive a cash ‡ at t, the …rm needs to perow
form several activities throughout the year that result in accumulating
working capital between t 3 and t. If one were to look at the balance
sheet of this …rm, one would see working capital peaking in the quarters

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Federal Reserve Bank of Richmond Economic Quarterly

Figure 1 Timeline

between cash ‡ accumulation periods and the cash ‡
ow
ows peaking in
periods f:::; t 4; t; t + 4; :::g.
Figure 1 shows a detailed breakdown of the production cycle, depicting the di¤erent components of working capital. The ‡
ows are
depicted by the vertical lines and stocks are described by the arrows.
In the example, the …rm starts the year with some cash ‡ that it
ow
receives in t 4. It may choose to distribute some of this cash ‡
ow
to shareholders as dividends, to use it to pay outstanding debts or to
dedicate it to long-term investments. It may also choose to retain some
of the cash for future use, an option that is attractive if external funds
are costly to acquire.
The production cycle starts in the spring, in t 3, with the acquisition and use of inputs, including materials and labor. These can be
paid for using the cash that the …rm has on its balance sheet or with
credit. The typical “cash-in-advance” assumption is that a subset of
the inputs that …rms acquire in t 3 require it to have cash available
from the previous period, t 4, onward. The required cash may be
a leftover of period t 4 cash ‡
ows that were not put to alternative
uses, raised through …nancial intermediaries, or acquired by issuing new
shares. Alternatively, the …rm might choose to defer payment for inputs to which the cash-in-advance constraint does not apply, acquiring
an account payable. In the example, those accounts payable remain on
the …rm’ balance sheet until it receives new cash ‡
s
ows in t and uses
those to pay the accounts payable out.
The raw materials that the …rm purchases in the spring, in t 3, are
incorporated into raw materials inventories. Some part of it is processed
right away, and the combination of the cost of those materials with

Schwartzman: The Business Cycle Behavior of Working Capital

291

labor and overhead costs involved in the processing are incorporated
into work-in-process inventories. Raw materials and work-in-process
inventories remain on the …rm’ balance sheet until production is …nals
ized in the summer, in t 2. At that point, all the inventories become
…nished goods inventories, which remain on the balance sheet until the
fall in t 1, when the Christmas decorations producer sells the goods
to wholesalers. However, since wholesalers will only sell those goods to
…nal customers in the last quarter of the year, the producer may agree
to let them delay the payment, acquiring an account receivable, which
is canceled at t. Firms can then use the associated cash ‡
ows to cancel
outstanding accounts payable and restart the production cycle.
The assumption of a seasonal pattern may be appropriate for certain …rms and industries but not for others. Some models of working
capital requirements such as in Christiano and Eichenbaum (1992) incorporate a seasonal-like pattern. However, instead of taking place over
the year, the seasonality takes place within each period, with working
capital being required in the beginning of the period so that cash ‡
ows
can be realized in the end of the period. Since model periods are chosen
to correspond to periods in the data, the seasonality is not observable
to an econometrician. A perhaps more natural case (although not usually explicitly modeled in the literature) is for …rms to run multiple
production processes simultaneously, with working capital being accumulated in any point in time for the sake of production in the following
period.
The di¤erent forms of working capital assets require the …rm to
commit funds ahead of cash ‡
ows. The marginal cost of those funds
can be determined in di¤erent ways depending on the details of the
environment in which the …rms …nd themselves. In the simplest case in
which there are no credit market frictions, the marginal cost of funds
dedicated to working capital assets is given simply by the interest rate
on …nancial assets of similar maturity. If, however, credit frictions
impose a wedge between the interest rate on borrowing and the return
on …nancial assets, the marginal cost of funds will depend on whether
the …rm is a borrower. More generally, if the …rm faces credit rationing,
the marginal cost of funds is given by the return on alternative uses of
those funds, for example in illiquid, long-term investment projects.
Finally, note that the demand for di¤erent components of working
capital emerges for very di¤erent reasons. The demand for inventories
arises because of a discrepancy between the timing of purchase and
use of inputs, production, and sales that is likely to arise largely for
technological reasons. However, the demand for cash and trade credit
is largely a function of the type of access that the …rm and its trading

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Federal Reserve Bank of Richmond Economic Quarterly

partners have to payment and credit institutions. We will examine each
component of working capital in the following sections.

2.

INVENTORIES

There is a large literature on inventories, some of it summarized in
Ramey and West (1999), but it is still evolving. Hornstein (1998) also
provides a detailed overview of stylized facts associated with inventory
investment. Holding inventories is inherently costly, because by dedicating funds to the purchase of inputs that will only result in cash ‡
ows
in the future, …rms forgo the return on …nancial investments. Furthermore, they might have to incur storage costs. Given those costs, there
are two dominant views of why …rms hold inventories. One emphasizes
…rms’desire to avoid stockouts, i.e., situations in which customers desire to purchase some good or the …rm desires to use some input but
cannot because it is not available at that moment.5;6 The second view
points to …xed costs of moving goods between locations, which leads
…rms to purchase inputs or deliver output to retailers in batches.7
In both views, inventories are a pre-condition for sales and, to
the extent that these theories also explain the holding of raw materials inventories, they are a pre-condition for production. Given either stockout avoidance or …xed delivery costs, …rms choose the inventory/sales ratio to balance out the costs associated with very low
inventories against the opportunity cost of funds and storage costs associated with holding those inventories. For a given target inventory/sales
ratio, changes in the economic environment that lead …rms to increase
their prospective sales are, therefore, likely to be accompanied by a
prior buildup of inventories. Likewise, changes in the opportunity cost
of holding inventories due to less expensive bank credit or lower return on …nancial investments might also lead …rms to build up inventories and, subsequently, increase their cash ‡
ow. In both cases, a
buildup in inventories precedes increases in cash ‡
ows. Alternatively,
to the extent that reduced cash holdings are associated with a higher
5

For a recent article analyzing the implications of this view for the macroeconomy,
see Wen (2011).
6
A closely related view is that …rms hold inventories in order to smooth production
in the face of erratic demand shocks. While still an important building block of inventory models, production smoothing is, by itself, at odds with the fact that production
is generally more volatile than sales (Ramey and West 1999).
7
See Khan and Thomas (2007) for an analysis of the implications of this view for
macroeconomic dynamics.

Schwartzman: The Business Cycle Behavior of Working Capital

293

Figure 2 Components of Working Capital/GDP

Notes: Share of GDP averages are in parentheses.

opportunity cost of funds for the …rm, a reduction in output or sales
may precede reductions in inventories holdings.8
Figure 2 shows the evolution of the di¤erent components of working capital, as calculated using the Financial Accounts of the United
States all normalized by gross domestic product (GDP). The normalization is chosen to control for underlying trends, and to give a sense
of the importance of inventories in production. In the speci…c case of
inventories, we can see that between 1952 and 2013 non…nancial businesses have held an amount of inventories equal to around 19 percent
of GDP. Furthermore, from the early 1980s onward there is a welldocumented secular decline in the inventories/GDP ratio (Ramey and
West 1999).9
Figure 3 shows the cyclical component of inventories together with
the cyclical component of GDP, where both GDP and inventories were
8
More complicated dynamics are certainly possible. For example, if demand for
products increases unexpectedly and …rms need time to ramp up production, …nal goods
inventories might decline momentarily with an increase in output and sales following that
decline.
9
When calculating ratios, I use nominal values in both the numerator and the
denominator.

294

Federal Reserve Bank of Richmond Economic Quarterly

Figure 3 Cyclical Components of GDP and Inventories

de‡
ated using the GDP de‡
ator. The cyclical component of the de‡
ated series is extracted using the band-pass …lter to isolate variation
in the data corresponding to cycles with amplitude between four and
32 quarters. Thus, it excludes seasonal variation (which have an amplitude of four quarters) and ‡
uctuations at lower than what is typically
considered business cycle frequencies (which have amplitudes of eight
years or fewer), including long-run trends. From the …gure, it is almost
immediate that inventories have lagged business cycles before the mid1980s, but that the lead-lag relationship becomes less salient afterward.
Table 1 con…rms the visual impression. For each column, the …rst
line of the table shows the correlation of the cyclical component of
GDP at t with the cyclical component of inventories in some t + k;
with each column corresponding to a di¤erent value of k. We say that
inventories lead output if the peak correlation occurs for k < 0 and
that it lags output if it occurs for k > 0. The table omits standard
errors for simplicity, but as a rule of thumb correlations above 0.2
in absolute value are statistically signi…cant. The table shows that
before 1984 GDP correlated most with inventories three quarters in
the future. After 1984, the peak of the lead-lag di¤erence shortens
from three quarters to one quarter, and the di¤erence between the peak
and the contemporaneous correlation becomes less salient. The result
provides a di¤erent perspective on the stylized facts pointed out by
Lubik, Sarte, and Schwartzman (2014), who show that inventory/sales

Schwartzman: The Business Cycle Behavior of Working Capital

295

Table 1 Correlations Between Inventories and Measures of
Economic Activity
t

4

t

3

t

2

t

GDP
Final Sales
Cash Flow 1
Cash Flow 2

0.48
0.50
0.56
0.52

0.31
0.32
0.53
0.43

0.11
0.11
0.44
0.29

1
t
t+1
1952–
1983
0.13
0.39
0.61
0.13
0.38
0.61
0.29
0.09
0.15
0.11
0.11
0.35

GDP
Final Sales
Cash Flow 1
Cash Flow 2

0.06
0.23
0.36
0.11

0.22
0.40
0.23
0.05

0.40
0.55
0.09
0.23

1984–
2013
0.57
0.70
0.67
0.73
0.03
0.11
0.38
0.47

0.78
0.77
0.21
0.51

t+2

t+3

t+4

0.76
0.78
0.37
0.55

0.81
0.84
0.53
0.66

0.77
0.82
0.60
0.66

0.77
0.75
0.36
0.54

0.63
0.60
0.50
0.52

0.40
0.37
0.58
0.48

ratios were strongly countercyclical prior to 1984 but became acyclical
or even somewhat pro-cyclical afterward.
As Figure 1 suggests, production begets inventories, thus implying mechanically the possibility of a lead-lag relationship. The bottom rows of each of the panels in Table 1 examine this possibility by
investigating whether the lead-lag relationship uncovered for GDP is
also present for …nal sales and cash ‡
ows. Final sales are de…ned as
being equal to GDP with inventory investment excluded from it. For
cash ‡
ow, I use two alternative de…nitions. The …rst one de…nes cash
‡
ows to be equal to net income plus the consumption of capital of both
corporate and noncorporate …rms. Adding the consumption of capital
back to net income is necessary in order to obtain a sensible measure
of cash ‡ since the consumption of capital (which is closely related
ow
to depreciation) does not reduce …rm cash ‡
ows even if it reduces the
economic income. The second one adds interest payments, thus separating the ability of the …rm to generate cash ‡ from the …nancial
ow
position of the …rm and the timing of interest payments. These de…nitions of cash ‡ are imperfect in that net income is recognized at
ow
the time of sale, not at the time in which trade receivables are paid
out. Thus, in terms of the diagram in Figure 1, the measured cash ‡
ow
might be recognized closer to time t 1 than to t. In all cases, inventories lag the particular ‡
ows considered, demonstrating that the lead-lag
relationship with output is not an artifact of timing restrictions.

3.

CASH AND SHORT-TERM INVESTMENTS

Cash and short-term investments represent cash and all securities readily transferable to cash. This includes, apart from cash on hand,

296

Federal Reserve Bank of Richmond Economic Quarterly

certi…cates of deposits, commercial paper, government and other marketable securities, demand deposits, etc. Firms hold cash and shortterm investments for many reasons, including to facilitate day-to-day
payments of variable inputs (Christiano and Eichenbaum 1992), to
serve
as
cushions to allow …rms to insure against negative cash ‡ shocks
ow
(Bates, Kahle, and Stulz 2009), to help …rms take advantage of ‡
eeting
investment opportunities (Kiyotaki and Moore 2012), or to help them
with their tax management (Foley et al. 2007). Of those motives,
business cycle models in which …rms demand cash typically focus on
the …rst, which is the payments for variable inputs. These models are
normally posited as “cash-in-advance” models, in which …rms need to
have cash at hand for a nontrivial period of time before the time in
which they use the cash.
For cash-in-advance constraints to play a meaningful economic role,
it must be the case that cash pays a rate of return below the opportunity
cost of funds for …rms. This is trivially the case if cash is understood
to include only currency, which pays no interest rate and the value
of which declines with in‡
ation. In that case, the opportunity cost of
holding cash is given by the nominal rate of interest on bonds. However,
…rms also hold a variety of assets that are “as good as cash,”in the sense
that they either mature very quickly or can be converted into cash at
very short notice. The opportunity cost of holding these “short-term”
investments is given by their liquidity premia, that is, by the di¤erence
between the rate of return on those securities and the rate of return on
alternative, illiquid investments.
Using the Financial Accounts of the United States data, I calculate
cash and short-term investments for both corporate and noncorporate
non…nancial businesses. For noncorporate businesses, these are the
sum of checkable deposits and currency, time and savings deposits,
money market fund shares, Treasury securities, and municipal securities. For non…nancial corporate businesses, cash includes, in addition
to those just listed, foreign deposits and agency and GSE-backed securities. From Figure 2, we can see that between 1952 and 2013 corporate
businesses have held on average 11 percent worth of GDP in cash. Furthermore, in the last few decades there has been a secular increase in
the shares of cash and short-term investments, a fact pointed out in articles by Foley et al. (2007) and Bates, Kahle, and Stulz (2009), among
others, who have found …rms holding increasing amounts of cash in the
last three decades.
Figure 4 shows the cyclical component of cash and short-term investments held by corporate businesses together with the cyclical component of GDP, with both series de‡
ated by the GDP de‡
ator, and

Schwartzman: The Business Cycle Behavior of Working Capital

297

Figure 4 Cyclical Components of GDP and Cash and
Short-Term Investments

…ltered using the band-pass …lter for variations at cycles with amplitudes between four and 32 quarters. As Table 2 makes clear, cash leads
business cycles throughout the period under analysis, although the relationship weakens after 1984. The relationship is only hard to discern
when cash ‡ 1 (incoming pro…ts plus depreciation, net of interest
ow
expenses) is used as a measure of economic activity, but it is again
apparent with cash ‡ 2 (incoming pro…ts plus depreciation, gross of
ow
interest expenses). Such a lead-lag relationship echoes the old monetarist view that money is a good leading indicator for business conditions, as well as formal analysis by Sims (1972), updated by Stock and
Watson (1999). Table 3 revisits these results by showing the lead-lag
relationship between M2 (which includes currency, demand deposits,
money market mutual funds, and other time deposits) and GDP, both
de‡
ated by the GDP de‡
ator and band-pass …ltered, for the whole sample and broken down before and after 1984. The lead-lag relationship
of M2 with GDP is very strong before 1984, but disappears afterward.
Given the comparison with the behavior of M2, it is remarkable that
the lead-lag relationship between cash and short-term investments held
by …rms with output is as robust as it is.
The …nding goes along with the assertion by Lucas and Nicolini
(2013) and Belongia and Ireland (2014) that traditional monetary aggregates do not measure adequately the amount of liquidity in the
economy, and that more carefully constructed measures of aggregate

298

Federal Reserve Bank of Richmond Economic Quarterly

Table 2 Correlations Between Cash and Short-Term
Investments and Measures of Economic Activity
t

4

t

3

t

2

t

GDP
Final Sales
Cash Flow 1
Cash Flow 2

0.46
0.47
0.17
0.35

0.60
0.60
0.34
0.48

0.69
0.68
0.48
0.55

1
t
t+1
1952–
1983
0.70 0.61
0.42
0.70 0.62
0.44
0.57 0.61
0.56
0.59 0.56
0.44

GDP
Final Sales
Cash Flow 1
Cash Flow 2

0.25
0.33
0.08
0.20

0.41
0.42
0.08
0.26

0.54
0.48
0.07
0.28

1984–
2013
0.57 0.51
0.49 0.46
0.08 0.12
0.24 0.20

0.43
0.41
0.20
0.18

t+2

t+3

t+4

0.18
0.21
0.40
0.24

0.09
0.04
0.19
0.02

0.32
0.28
0.01
0.17

0.31
0.33
0.28
0.17

0.19
0.22
0.33
0.16

0.09
0.11
0.34
0.17

liquidity have retained the ability to forecast output. Of course, a
measure of liquidity based on cash and short-term investments held by
…rms is distinct from measures such as M2 or others in that it does
not include cash held by households. A closer investigation of whether
liquid assets held by …rms are specially correlated with future output
as compared to those held by households is an interesting avenue for
future work.

4.

TRADE CREDIT

The third major component of working capital is trade credit, with
trade receivables as part of the assets and trade payables as part of the
liabilities. Trade receivables represent amounts owed by customers for
goods and services sold in the ordinary course of business. Conversely,
trade payables represent trade obligations due within one year, or the
normal operating cycle of the company.
Trade credit is an active area of research in corporate …nance, with
an abundant theoretical and empirical literature. To a large degree,
theories of trade credit emphasize the fact that, relative to …nancial institutions, suppliers often have advantages in securing repayment from
their customers. Among other reasons for that advantage, the literature
mentions information advantages for suppliers (Mian and Smith 1992),
incentives for customers to preserve their relationship with suppliers
(Cuñat 2007), and the fact that, since goods are harder to divert than
cash, borrowers have less incentive to default (Burkart and Ellingsen
2004).
The opportunity cost of holding trade receivables is given by the
di¤erence between the rate of return on alternative investments and

Schwartzman: The Business Cycle Behavior of Working Capital

299

Table 3 Correlations Between M2 and Short-Term
Investments and Measures of Economic Activity
t

4

t

3

t

2

t

GDP
Final Sales
Cash Flow 1
Cash Flow 2

0.66
0.66
0.24
0.45

0.77
0.76
0.44
0.60

0.82
0.80
0.62
0.71

1
t
1952–
1983
0.78 0.65
0.78 0.67
0.75 0.80
0.77 0.74

GDP
Final Sales
Cash Flow 1
Cash Flow 2

0.02
0.14
0.06
0.07

0.08
0.20
0.01
0.13

0.14
0.23
0.08
0.21

1984–
2013
0.22 0.29
0.26 0.29
0.19 0.31
0.31 0.38

t+1

t+2

t+3

t+4

0.46
0.47
0.74
0.62

0.23
0.22
0.61
0.43

0.01
0.02
0.43
0.22

0.22
0.23
0.23
0.02

0.32
0.30
0.42
0.41

0.27
0.25
0.49
0.38

0.15
0.14
0.52
0.30

0.01
0.01
0.50
0.20

the interest rate paid by customers. If the latter is smaller than the
former, it will be costly for …rms to hold trade receivables. Conversely,
there is a cost associated with issuing trade payables if the interest rate
on trade payables is higher than the rate of return on real or …nancial
investments.
When analyzing trade credit, I focus on trade receivables, which
I de…ne to include consumer credit held by corporate and noncorporate non…nancial …rms. Including consumer credit follows the spirit of
including in trade receivables all short-term credit conceded by the …rm
to other parties in order to facilitate production and sales. I focus only
on receivables rather than payables since, in a closed economy, whenever a …rm issues a trade payable, the counterpart acquires a trade
receivable. Because the U.S. economy is not closed, the two numbers do not exactly coincide. Furthermore, even after accounting for
foreign holdings and issuance of trade credit, the di¢ culties in collecting accurate data are signi…cant enough that there exists a nontrivial
discrepancy between aggregate trade payables and aggregate trade receivables. Finally, trade payables do not include consumer credit. In
spite of those di¤erences, both measures of trade credit behave very
similarly, so that for brevity I will only discuss trade receivables.
From Figure 2 we can see that between 1952 and 2013 corporate
businesses hold a value of trade receivables equal to 19 percent of GDP.
Furthermore, unlike inventories and cash, there is no clear trend in the
ratio of trade receivables to GDP. Figure 5 shows the cyclical component of receivables together with the cyclical component of GDP, both
de‡
ated using the GDP de‡
ator and extracted using a band-pass …lter for frequencies between four and 32 quarters. Table 4 presents the
cross-time correlation. Trade receivables lag output by a quarter both

300

Federal Reserve Bank of Richmond Economic Quarterly

Figure 5 Cyclical Components of GDP and Trade Receivables

before and after 1984. This is in line with the diagram depicted in
Figure 1, which predicts that …rms accumulate trade receivables after
production and sales have taken place. A comparison with …nal sales
and the di¤erent measures of cash ‡ shows a similar pattern. This
ow
is still in line with the diagram, since net income is recognized at the
time of sale, not at the time in which …nal payment is received. Thus,
to the extent that …rms tend to provide …nancing for their customers,
one would expect trade receivables to lag cash ‡
ows de…ned using data
from income.

5.

CONCLUSION

Working capital is an important part of many macroeconomic models
that emphasize the impact of ‡
uctuations in the cost of capital on …rm
decisions. I …nd that the cyclical properties of the di¤erent components are quite di¤erent. In particular, cash holdings consistently lead
the business cycle, whereas inventories and trade receivables are lagging. Interestingly, the lead-lag relationships for inventories appear to
weaken after 1984. To the extent that those relationships are indicators of payment and …nancial frictions, the reductions in the lead-lag
relationships between inventories and economic activity are consistent
with the view, argued by Jermann and Quadrini (2006), that …nancial markets became more e¢ cient after the early 1980s. A second
set of interesting facts concerns cash holdings, which are particularly

Schwartzman: The Business Cycle Behavior of Working Capital

301

Table 4 Correlation of Trade Receivables with Di erent
Measures of Economic Activity
t

4

t

3

t

2

t

GDP
Final Sales
Cash Flow 1
Cash Flow 2

0.25
0.22
0.55
0.40

0.03
0.03
0.49
0.29

0.25
0.23
0.32
0.08

1
t
1952–
1983
0.53 0.73
0.50 0.73
0.04 0.25
0.18 0.45

GDP
Final Sales
Cash Flow 1
Cash Flow 2

0.04
0.08
0.47
0.14

0.13
0.25
0.35
0.04

0.32
0.41
0.22
0.19

1984–
2013
0.50 0.64
0.56 0.67
0.07 0.09
0.31 0.40

t+1

t+2

t+3

t+4

0.81
0.84
0.47
0.64

0.78
0.83
0.59
0.70

0.68
0.74
0.63
0.62

0.52
0.58
0.60
0.48

0.71
0.72
0.25
0.45

0.71
0.71
0.38
0.47

0.64
0.65
0.47
0.47

0.54
0.53
0.50
0.45

noteworthy because the facts are robust over time. This is in contrast
to the lead-lag relationship between M2 and GDP, which broke down
after the 1980s. The results suggest that availability of cash is an important precursor of economic activity, giving some credence to models
that emphasize cash-in-advance type constraints.

REFERENCES
Bates, Thomas W., Kathleen M. Kahle, and René M. Stulz. 2009.
“Why Do U.S. Firms Hold So Much More Cash Than They Used
To?” The Journal of Finance 64 (October): 1,985–
2,021.
Belongia, Michael T., and Peter N. Ireland. 2014. “Interest Rates and
Money in the Measurement of Monetary Policy.” Working Paper
20134. Cambridge, Mass.: National Bureau of Economic Research
(May).
Bernanke, Ben, and Mark Gertler. 1989. “Agency Costs, Net Worth,
and Business Fluctuations.” The American Economic Review 79
(March): 14–
31.
Burkart, Mike, and Tore Ellingsen. 2004. “In-Kind Finance: A Theory
of Trade Credit.” The American Economic Review 94 (June):
569–
90.

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Christiano, Lawrence J., and Martin Eichenbaum. 1992. “Liquidity
E¤ects and the Monetary Transmission Mechanism.” Working
Paper 3974. Cambridge, Mass.: National Bureau of Economic
Research (January).
Cuñat, Vicente. 2007. “Trade Credit: Suppliers as Debt Collectors
and Insurance Providers.” Review of Financial Studies 20
(March): 491–
527.
Foley, C. Fritz, Jay C. Hartzell, Sheridan Titman, and Garry Twite.
2007. “Why Do Firms Hold So Much Cash? A Tax-Based
Explanation.” Journal of Financial Economics 86 (December):
579–
607.
Fuerst, Timothy S. 1992. “Liquidity, Loanable Funds, and Real
Activity.” Journal of Monetary Economics 29 (February): 3–
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Hornstein, Andreas. 1998. “Inventory Investment and the Business
Cycle.” Federal Reserve Bank of Richmond Economic Quarterly
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Jermann, Urban, and Vincenzo Quadrini. 2006. “Financial
Innovations and Macroeconomic Volatility.”Working Paper 12308.
Cambridge, Mass.: National Bureau of Economic Research (June).
Jermann, Urban, and Vincenzo Quadrini. 2012. “Macroeconomic
E¤ects of Financial Shocks.” The American Economic Review 102
(February): 238–
71.
Khan, Aubhik, and Julia K. Thomas. 2007. “Inventories and the
Business Cycle: An Equilibrium Analysis of (S; s) Policies.” The
American Economic Review 97 (September): 1,165–
88.
Kiyotaki, Nobuhiro, and John Moore. 1997. “Credit Cycles.” The
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Kiyotaki, Nobuhiro, and John Moore. 2012. “Liquidity, Business
Cycles, and Monetary Policy.” Working Paper 17934. Cambridge,
Mass.: National Bureau of Economic Research (March).
Lubik, Thomas, Pierre-Daniel Sarte, and Felipe Schwartzman. 2014.
“What Inventories Tell Us About How Business Cycles Have
Changed.” Manuscript.
Lucas, Jr., Robert E., and Juan Pablo Nicolini. 2013. “On the
Stability of Money Demand.” Manuscript, University of Chicago.
Mian, Shehzad L., and Cli¤ord W. Smith, Jr. 1992. “Accounts
Receivable Management Policy: Theory and Evidence.” The
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Neumeyer, Pablo A., and Fabrizio Perri. 2005. “Business Cycles in
Emerging Economies: The Role of Interest Rates.” Journal of
Monetary Economics 52 (March): 345–
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Ramey, Valerie A., and Kenneth D. West. 1999. “Inventories.” In
Handbook of Macroeconomics, Vol. 1, edited by J. B. Taylor and
M. Woodford. Philadelphia: Elsevier, 863–
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Sims, Christopher A. 1972. “Money, Income, and Causality.” The
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Stock, James H., and Mark W. Watson. 1999. “Business Cycle
Fluctuations in U.S. Macroeconomic Time Series.” In Handbook of
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Economic Quarterly— Volume 99, Number 4— Fourth Quarter 2013— Pages 305–
340

Pecuniary Externalities,
Segregated Exchanges, and
Market Liquidity in a
Diamond-Dybvig Economy
with Retrade
Borys Grochulski

P

rice changes a¤ect economic agents primarily by altering their
budget constraints. In many economic environments, however,
price changes additionally impact the agents by altering other
constraints agents face. Those additional ways in which prices a¤ect
agents, other than through budget constraints, are known as pecuniary externalities.1 Examples of the additional constraints that can
be a¤ected by prices include incentive compatibility, participation, and
collateral constraints.
Numerous recent macroeconomic studies have shown that pecuniary externalities can lead to market failure.2 The intuition behind
this failure is as follows. In standard Arrow-Debreu economies, where
The author would like to thank Tee Kilenthong, Sam Marshall, Wendy Morrison,
Pierre Sarte, Felipe Schwartzman, and Ned Prescott for their helpful comments. The
views expressed in this article are those of the author and not necessarily those of
the Federal Reserve Bank of Richmond or the Federal Reserve System. E-mail:
borys.grochulski@rich.frb.org.
1
The term pecuniary externality has been used more broadly than this de…nition. Viner (1932) uses it to describe the impact of a change in the price of an input
on the production cost curve of a …rm. Greenwald and Stiglitz (1986) and, more recently, Bianchi (2011) and Dávila et al. (2012) among others, use it in reference to the
generic constrained-ine¢ ciency of competitive equilibria in economies with exogenously
imposed market incompleteness (studied in, e.g., Stiglitz [1982] and Geanakoplos and
Polemarchakis [1986]). In the language of Prescott and Townsend (1984), the de…nition we use corresponds to prices having a direct impact on the agents’ consumption
possibility set, in addition to the budget constraint.
2
See, e.g., Kehoe and Levine (1993), Golosov and Tsyvinski (2007), Lorenzoni
(2008), and Di Tella (2014).

306

Federal Reserve Bank of Richmond Economic Quarterly

prices only a¤ect budget constraints, equilibrium allocations are e¢ cient. It is therefore impossible to alter equilibrium prices (perhaps
by imposing taxes) and obtain a Pareto improvement (i.e., make an
agent better o¤ without making someone else worse o¤). An increase
in the price of good x, for example, will relax budget constraints of
some agents, loosely speaking the sellers of x, making them better o¤,
but it will tighten budget constraints of others, the buyers of x, making
this group worse o¤. The equilibrium price of good x cannot therefore
be improved upon in Pareto sense.
The same may no longer hold true when prices a¤ect not only
budget but also some other constraints that can be tightened or relaxed
for all agents simultaneously. If an increase in the price of x relaxes
everyone’ incentive compatibility constraint, for example, then not
s
only the sellers of x but also the buyers of x can bene…t from a higher
price of x, as long as the relaxed incentive constraint helps them more
than the tightened budget constraint hurts them. The benevolent social
planner— a stand-in concept we use to calculate optimal allocations—
will take this e¤ect into account. In a market economy, however, agents
take prices as independent of their individual actions. By ignoring
the general equilibrium impact of their actions on prices, agents also
ignore the indirect e¤ect they have on how tight their own incentive
constraints are. The planner’ and the agents’ costs-bene…t calculus
s
are thus di¤erent, which leads to suboptimal equilibrium outcomes.
By relaxing a constraint that all agents face, a high price of good x
has in the preceding example a positive “external”e¤ect similar to, e.g.,
a clean environment or a good public highway system. Agents’inability
to coordinate on a su¢ ciently high price for good x in equilibrium is
therefore similar to the failure to internalize an external e¤ect, which
has led to the name pecuniary externality.
In this article, we discuss the pecuniary externality that leads to underprovision of liquidity in the banking model of Diamond and
Dybvig (1983) (hereafter, DD). We introduce the DD economy in Section 1. In this economy, agents have access to two assets: a short-term,
liquid asset with net return normalized to zero and a long-term, illiquid
^
asset with positive net return R 1 > 0. Agents face random liquidity
shocks: They may become impatient, i.e., …nd themselves having to
consume before the illiquid asset matures, or remain patient, in which
case they can postpone consumption until the illiquid asset pays o¤. By
investing a part of their initial endowment/wealth in the low-yielding
liquid asset, agents purchase insurance against the liquidity shock.
In Section 2, we derive the e¢ cient allocation of liquidity in this
economy, i.e., the optimal levels of investment in the two assets along
with the resulting amounts of consumption for the agents who do and

B. Grochulski: Pecuniary Externalities and Segregated Exchanges 307
do not experience the need for liquidity. At the optimum, the liquidity
shock is partially insured: The impatient agents are able to capture
a part of the return on the long-term asset despite the fact that they
have to consume before this asset matures.
There are several variants of the DD model in the literature. The
variant we consider follows closely Jacklin (1987) and Farhi, Golosov,
and Tsyvinski (2009). It has been designed to focus on market provision
of liquidity and not on the possibility of bank runs.3 In particular, we
assume that liquidity shocks are agents’ private information, but we
do not assume a sequential service constraint: Trade can be organized
after all agents have received their realizations of the liquidity shock. To
study pecuniary externalities, we follow Farhi, Golosov, and Tsyvinski
(2009) in giving the agents access to an anonymous, hidden market in
which they can borrow and lend at the market-determined gross rate
of return R. As this rate of return (the price of credit) a¤ects incentive
compatibility constraints, it gives rise to a pecuniary externality. This
pecuniary externality makes competitive equilibria ine¢ cient.
To show this ine¢ ciency, we analyze in Section 3 a simple model of
trade with incomplete markets. In this model, agents invest directly in
the two assets ex ante and trade the long-term asset for cash ex post,
i.e., after they …nd out their liquidity needs. Diamond and Dybvig
(1983) showed that competitive equilibrium in this simple, incompletemarkets model is ine¢ cient. In this model, a no-arbitrage condition
determines how the return on the long-term asset is allocated in equi^
librium: The whole net return R 1 is captured by the patient agents,
leaving the impatient agents with zero net return on their investment,
which is too low relative to the optimal allocation. In this incompletemarkets equilibrium, thus, agents do not obtain su¢ cient liquidity
insurance.
This ine¢ ciency prevails even when markets for state-contingent
contracts are introduced. Jacklin (1987) and Farhi, Golosov, and
Tsyvinski (2009) show that when agents can borrow and lend privately
in a hidden retrade market, liquidity is underprovided in competitive
equilibrium with complete markets and fully state-contingent contracts
(or banks). The ine¢ ciency is caused by a pecuniary externality that,
as we mentioned, enters the model through the agents’incentive compatibility constraints that depend on the retrade interest rate R. In
equilibrium, this interest rate is too high, which, by arbitrage, forces
the secondary-market price for the long-term asset to be too low. The
impatient agents, thus, re-sell their holdings of the long-term asset
3
See Ennis and Keister (2010) for a review of the literature on bank runs in the
DD model.

308

Federal Reserve Bank of Richmond Economic Quarterly

in the secondary market for too little. As in the incomplete-markets
model, they are unable to capture any part of the long-run net return
^
R 1, which again is ine¢ cient. We review this result in detail in
Section 4.
As is the case with standard externalities like pollution, the market
failure caused by the pecuniary externality creates a role for government
intervention. Farhi, Golosov, and Tsyvinski (2009) consider direct government intervention imposing a minimum requirement on the level of
liquid investment. They show that this intervention decreases the retrade interest rate R and increases the return on the initial investment
in the liquid asset. This allows the impatient agents to capture a part
^
of R and eliminates the e¤ect of the pecuniary externality.4
If the extent of an externality can be costlessly and veri…ably quanti…ed, the problem of excessive externality can also be addressed with
a more decentralized approach that can be implemented through the
so-called cap-and-trade mechanism. An explicit assignment of property
rights over the extent of the externality lets markets for these rights
emerge. In these markets, agents face prices for generating the externality, which makes them take into account the full impact of the
externality and thus restores the e¢ ciency of the equilibrium outcome.5
Pollution is a textbook example of a negative external e¤ect. Currently,
emission of greenhouse gasses is regulated through the cap-and-trade
mechanism in many countries.6
In a recent article, Kilenthong and Townsend (2011) (hereafter,
KT) study a market solution to the pecuniary externality problem
analogous to cap-and-trade.7 In addition to a class of moral hazard
environments, they consider a DD economy with retrade.8 In their
model, the impact of one’ liquidity demand on the retrade interest
s
rate is priced, which results in e¢ cient ex ante investment, su¢ cient
liquidity, and an optimal amount of retrade in competitive equilibrium.
Clearly, this approach is interesting because it implies no need for direct
government intervention into markets. Similar to the cap-and-trade
4
In this article, we do not present details of the implementation of this intervention.
The interested reader is referred directly to Farhi, Golosov, and Tsyvinski (2009).
5
See Chapter 11 of Mas-Colell, Whinston, and Green (1995).
6
The …rst and to-date largest implementation of this mechanism is the European
Union Emission Trading Scheme; see Ellerman and Buchner (2007).
7
Bisin and Gottardi (2006) use a similar approach in the Rothschild-Stiglitz adverse
selection economy.
8
Kilenthong and Townsend (2014a) study the model with segregated exchanges in
a class of environments with collateral constraints. Kilenthong and Townsend (2014b)
extend the analysis of segregated exchanges to a generalized framework nesting collateral
and liquidity constraints, incentive constraints with retrade, and exogenously incomplete
markets.

B. Grochulski: Pecuniary Externalities and Segregated Exchanges 309
mechanism, this approach requires that agents’ activities generating
the externality— in this case retrade— be observable. We discuss the
KT model in Section 5.
In the KT market model, retrade is allowed but only within accesscontrolled ex-post markets called segregated exchanges. Agents are
admitted to membership in an exchange upon payment of an entry fee.
The size of the entry fee depends on the composition of the agent’
s
investment portfolio. The de…ning characteristic of a segregated exchange is the price at which agents expect to be able to (re)trade the
long-term asset ex post. In equilibrium, these expectations must be correct. This market structure is free of pecuniary externalities because
agents can no longer take retrade prices as independent of their actions. The portfolio-contingent exchange entry fee, similar to the price
for greenhouse gas emissions in the cap-and-trade mechanism, creates
an explicit connection between the investment decisions an agent makes
ex ante and the price at which he is able to trade ex post. Consequently,
equilibrium with segregated exchanges does not su¤er from the problem
of underprovision of liquidity, and the market outcome is e¢ cient.
Our exposition of the KT mechanism in Section 5 extends the exposition in Kilenthong and Townsend (2011). We explicitly solve for
equilibrium entry fees associated with each segregated exchange and
show how with these prices the agent’ ex ante utility maximization
s
problem becomes aligned with the planner’ problem of maximization
s
of ex ante welfare.
In Section 6, we conclude the article with a discussion of the question of whether the possibility of retrade in the DD model implies the
need for government intervention. The literature we review makes it
clear that the answer depends on the agents’ability to commit themselves to restrict retrade to access-controlled venues with priced entry.
This means that retrade itself does not imply the existence of a pecuniary externality requiring government intervention, only hidden retrade without commitment does. Which of these two kinds of retrade
possibilities …nancial …rms face in reality is an important empirical
question.
The Appendix contains proofs of two auxiliary results and a precise de…nition of the incomplete-markets equilibrium studied in Section
3. Table 1 summarizes the frictions and outcomes associated with all
allocation mechanisms we discuss in this article.

310
1.

Federal Reserve Bank of Richmond Economic Quarterly

A DIAMOND-DYBVIG ECONOMY
WITH RETRADE

The version of the Diamond-Dybvig economy that we consider here is
close to those studied in Jacklin (1987); Allen and Gale (2004); Farhi,
Golosov, and Tsyvinski (2009); and Kilenthong and Townsend (2011).
There is a continuum of ex ante identical agents. There are three
dates: t = 0; 1; 2. There is a single consumption good at each date.
Each agent is endowed with resources e at date 0. These resources can
be invested in two available technologies/assets. The short-term asset
pays the return of 1 unit of the consumption good at date 1 per unit
of resources invested at date 0. We will often refer to this asset as the
^
cash asset. The long-term asset pays nothing at date 1 and R > 1 at
date 2 per unit invested at date 0. Note that the long-term asset is
technologically illiquid at date 1, i.e., it cannot be physically turned
into the consumption good.
Agents do not consume at date 0. Their preferences over consumption at dates 1 and 2 are represented by a DD utility function
u(c1 + c2 );
where 2 f0; 1g is an idiosyncratic shock with Prf = 0g = > 0.
Note that if = 0, the agent is extremely impatient: He only values
consumption at date 1. The standard interpretation of this shock is
that with = 0 the agent experiences at date 1 a critical need for
liquidity. If = 1, however, the agent is extremely patient: He is in
fact indi¤erent to the timing of consumption between dates 1 and 2.9
We follow DD in assuming that relative risk aversion is larger than 1,
i.e., cu00 (c)=u0 (c) > 1 for all c. As we will see, this assumption implies
that the impatient agents will be allocated consumption with present
value larger than the value of their initial endowment e.
A consumption allocation c consists of fc1 (0); c2 (0); c1 (1); c2 (1)g;
where ct ( ) 0 denotes date-t consumption for an agent with shock .
Associated with allocation c are initial asset investment s
0 in the
liquid asset and x
0 in the illiquid asset. To ensure that resources
at date 1 and 2 are su¢ cient to provide consumption as speci…ed in c,
initial investment (s; x) associated with allocation c must satisfy
s

c1 (0) + (1

)c1 (1);

(1)

9
Note that with these preferences the DD economy violates standard smoothness
and convexity assumptions. In particular, the shadow interest rate (i.e., the rate at
which an agent is willing to refrain from borrowing or saving) is plus in…nity for the
impatient type and one for the patient type regardless of the allocation of consumption.

B. Grochulski: Pecuniary Externalities and Segregated Exchanges 311
and
^
Rx

c2 (0) + (1

)c2 (1):

(2)

The amounts s and x that can be invested in the two technologies are
constrained by the amount e of resources available at date 0:
s+x

e:

(3)

Substituting (1) and (2) into (3), we can express the economy’ aggres
gate resource constraint in terms of just the consumption allocation
c:
c1 (0) +

c2 (0)
^
R

+ (1

) c1 (1) +

c2 (1)
^
R

e:

(4)

Allocation c gives an agent an expected utility value of
E[u(c1 + c2 )] = u(c1 (0)) + (1

)u(c1 (1) + c2 (1)):

(5)

Since all agents are ex ante identical, the expected utility of the representative agent measures total utility, or social welfare, attained in this
economy.
We follow DD in assuming that realizations of are private information. That is, given an allocation c = fc1 (0); c2 (0); c1 (1); c2 (1)g; an
agent can obtain either fc1 (0); c2 (0)g or fc1 (1); c2 (1)g depending on
what realization of he reports.
In addition, we follow Farhi, Golosov, and Tsyvinski (2009) and
Kilenthong and Townsend (2011) in assuming that individual …nal consumption is also private and that agents have access to a hidden retrade
market where they can lend and borrow from one another “behind the
back” of the planner, i.e., with all trades in this market being hidden
from everyone but the parties directly involved. More precisely, at date
1 agents have access to a perfectly competitive market for one-period
IOUs. Given an allocation c = fc1 (0); c2 (0); c1 (1); c2 (1)g, an agent reporting shock realization ~ obtains the bundle (c1 (~); c2 (~)). But this
bundle does not have to be his actual consumption. Rather, this bundle becomes his endowment of goods in the hidden retrade market.
The agent’ …nal consumption is determined by his retrade activity.
s
At the hidden-market interest rate R, the agent can either save some
of his c1 (~) for consumption at date 2, or borrow against c2 (~) for
consumption at date 1. Speci…cally, given an allocation c and a gross
interest rate R in the hidden retrade market, an agent of type selects
a report ~ 2 f0; 1g, IOU purchases b, and a …nal consumption bundle

312

Federal Reserve Bank of Richmond Economic Quarterly

(~1 ; c2 )
c ~

(0; 0) that solve
~
V (c; R; )

=

c
~
max u(~1 + c2 )

~;~1 ;~2 ;b
c c

s:t:
c1 + b c1 (~);
~
c2 Rb + c2 (~):
~

(6)

~
The value V (c; R; ), thus, is determined by the agent’ best strategy
s
with respect to reporting his realization of the shock as well as saving/borrowing in the hidden market.
Allocation c is incentive compatible (IC) if agents prefer to reveal
their type truthfully and not use the retrade market. That is, c is IC
if it satis…es
~
u(c1 ( ) + c2 ( )) V (c; R; )
(7)
for both , with R being an equilibrium gross interest rate in the hidden
retrade market.

2.

OPTIMAL ALLOCATION

In this section, we …rst provide a result of DD characterizing the best
allocation with no frictions (i.e., without private information or hidden
retrade), which is often referred to as the …rst-best allocation. This allocation provides the highest social welfare among all allocations that are
resource feasible, i.e., it maximizes (5) subject to (4). Next, we present
a result of Farhi, Golosov, and Tsyvinski (2009) showing that the …rstbest allocation remains feasible even with the frictions of private and
hidden retrade. The …rst-best allocation thus remains optimal in this
environment, even with these two frictions present.

Optimal Allocation with no Frictions
Let us start out by noting that given the in…nite impatience of the
agents of type = 0, it is never e¢ cient in this economy to have the
impatient types consume a positive amount at date 2. Likewise, given
^
the complete patience of type = 1 and R > 1, it is never e¢ cient to
have the patient types consume a positive amount at date 1.
Lemma 1 If c = fc1 (0); c2 (0); c1 (1); c2 (1)g maximizes (5) subject to
(4), then c2 (0) = c1 (1) = 0.
Proof. In the Appendix.
Below, we will often write c1 for c1 (0) and c2 for c2 (1), silently
assuming c2 (0) = c1 (1) = 0, and refer to (c1 ; c2 ) as an allocation. With

B. Grochulski: Pecuniary Externalities and Segregated Exchanges 313
these notational shortcuts, the social welfare function (5) can be written
simply as
u(c1 ) + (1

)u(c2 );

the aggregate resource constraint (4) as
c2
c1 + (1
)
^
R

(8)

e;

(9)

and …rst-best allocation can be de…ned as a maximizer of (8) subject
to just (3), i.e., ignoring the incentive constraint (7). Further, from (1)
^
and (2) we have c1 = s and c2 = 1 x R. If no initial wealth is to be
wasted, we must have x = e s. We can thus express any resourcefeasible allocation (c1 ; c2 ) as a function of the initial liquid investment
s alone:
s e
;
1

(c1 ; c2 ) =

s ^
R

with s 2 [0; e]. The social welfare function (8) can thus be written as
u

s

+ (1

)u

e
1

s ^
R :

(10)

Denote this function by W (s). The …rst-best planning problem is reduced here to …nding a level of liquid investment s in [0; e] that maximizes W (s). Denote such a level by s . The corresponding level of
illiquid investment is x = e s and the …rst-best optimal allocation
^
is (c1 ; c2 ) = s ; e s R .
1
Proposition 1 (Diamond and Dybvig) The social welfare function
W (s) has a unique maximizer s in [0; e]. The maximizer satis…es
^
R

e<s <

^
R+1

e:

(11)

Proof. In the Appendix.
The two inequalities in (11) imply that the …rst-best consumption
allocation (c1 ; c2 ) satis…es
e < c1 <
^
Re > c2 >

^
Re
^
R+1
^
Re

;

(12)

:
(13)
^
R+1
The right inequalities above show that the …rst-best allocation does
^
not provide full insurance, c1 < ^ Re
< c2 . The reason for this is
R+1

314

Federal Reserve Bank of Richmond Economic Quarterly

that …rst-period consumption is more expensive to provide than secondperiod consumption. At the full-insurance allocation
c1 = c2 =

^
Re
^
R+1

;

(14)

marginal utility of consumption is the same at both dates, but by giving
^
up " > 0 units of consumption at date 1 the planner can deliver R" > "
units of consumption at date 2. Such a reallocation would therefore
increase overall expected welfare, and so full insurance is not optimal.
The left inequality in (11) implies that the …rst-best allocation gives
a larger present value of consumption to impatient agents than to patient ones. Indeed, discounting consumption at date 1 and 2 at, respectively, the rate of return of the short- and long-term asset, and using
the left inequalities in (12) and (13), shows
c1
c
> e > 2:
^
1
R

(15)

The optimality of this unequal allocation of the present value of consumption follows because relative risk aversion of the utility function
u(c) larger than 1 means that as consumption c increases, marginal
utility of consumption u0 (c) drops fast (faster than 1=c). Liquid in^
vestment s = e gives a …nal consumption allocation (c1 ; c2 ) = (e; Re),
where the present value of both types’consumption is the same (and
equal to the per capita initial endowment):
c2
c1
=e= :
^
1
R

(16)

^
At this allocation, however, c2 = Re > e = c1 , so the marginal utility of
c2 is low and the marginal utility of c1 is high. By increasing the liquid
investment s at date 0 above s = e, say by " > 0, the planner gives up
^
the return R" but is able to increase consumption in the high marginal
utility state, i.e., at date 1. On balance, this is an improvement because
^
u0 (c1 ) is su¢ ciently high relative to u0 (c2 ) and R [that is, "u0 (e) >
0 (Re)].
^
R"u ^
Alternatively, we can express this intuition using the elasticity of
substitution of the utility function u. With zero elasticity of substitution (Leontief preferences), the full insurance allocation (14) would be
optimal. With unit elasticity of substitution (logarithmic preferences),
the allocation (16) spending the same amount on each good would be
optimal. Under the DD assumption of the elasticity of substitution
larger than zero but smaller than one, it is optimal to make c1 and c2
closer to one another than under logarithmic preferences, but not go
all the way to full insurance.

B. Grochulski: Pecuniary Externalities and Segregated Exchanges 315
Optimal Allocation with Private Shocks
and Retrade
Having characterized the optimal allocation in the …rst-best version of
the DD environment, we now ask what the optimal allocation is with
private information and a hidden retrade market, i.e., with the addition
of the IC constraint (7).
With realizations of being private information and with agents
having access to retrade, Farhi, Golosov, and Tsyvinski (2009) show
that the …rst-best allocation is incentive compatible, i.e., remains feasible and thus optimal. This result is obtained as follows. The retrade
interest rate R associated with the optimum (i.e., the shadow interest
rate at the …rst-best), denoted by R , is
R =

c2
:
c1

(17)

First, let us check that with “endowments” (c1 ; c2 ), the interest
rate R = R is an equilibrium interest rate in the hidden market.
c1
c2
Note that from c2 > c1 we get R > 1 and from 1 > e > ^ we get
R
^
^
R < R, so 1 < R < R. Suppose the impatient types enter the hidden
market with an endowment vector (c1 ; 0) and patient types enter with
(0; c2 ). The impatient agent has no income at t = 2, so he cannot
borrow in this hidden market (for there is nothing he could pay back
with). Also, this agent wants to consume his income c1 irrespective
of the interest rate. Thus, the impatient type’ utility is maximized
s
with the quantity of zero traded at the interest rate R . A patient
agent could borrow against his date-2 endowment c2 and consume at
date 1, but R > 1 implies he would not want to do it, as his marginal
utility of consumption is the same at either date and he can consume
c
only R2 < c2 if he decides to use the hidden market and consume at
date 1. This con…rms that consumption (c1 ; c2 ) and interest rate R
are an equilibrium in the retrade market (with zero quantity traded in
equilibrium).
Now consider potential deviations in the revelation of combined
with retrade. The …rst-best allocation is immune to these deviations
because at the interest rate R the present value of each type’ endows
ment is the same. Indeed, the impatient types could claim endowment
(0; c2 ) and borrow against c2 in order to consume at date 1, but doing
c
so would give them R2 = c1 units of consumption, so there is no gain
for them from doing so. As well, the patient types could claim endowment (c1 ; 0) and save at the market interest rate R . But doing so gives
them …nal consumption R c1 = c2 so, again, no gain. This con…rms

316

Federal Reserve Bank of Richmond Economic Quarterly

that the …rst-best allocation is incentive compatible in the model with
private information and hidden retrade.
Note that although the possibility of hidden retrade does not change
the optimal allocation, it does change the IC constraint. With just
private information about the liquidity shock (without retrade), the
IC constraint would be c2 c1 . The …rst-best allocation satis…es this
constraint as a strict inequality simply because c2 > c1 . With the
hidden retrade market, however, the IC constraint holds only as an
c
equality because R2 = c1 .
Next, we move on to discuss market provision of liquidity in this
environment.

3.

COMPETITIVE EQUILIBRIUM WITH
INCOMPLETE MARKETS

The remainder of this article is devoted to studying competitive equilibrium outcomes under three di¤erent market arrangements, and comparing these outcomes with the optimal allocation (c1 ; c2 ).
In this section, we discuss a simple incomplete-markets model of
trade, in which agents invest directly in the two assets and subsequently
trade them (i.e., there are no intermediaries, no state-contingent contracts). This natural model of trade is a point of departure for Diamond
and Dybvig (1983). DD start their analysis of market provision of liquidity by considering this incomplete market structure. They conclude
that the equilibrium level of liquidity is too low, i.e., there is a market failure. We brie‡ review this result in this section and move on
y
to showing in the next section that with hidden retrade this conclusion generalizes to any market structure (even when state-contingent
contracts and/or intermediaries are taken into consideration).
The simple market structure is as follows. At date 0, each agent
invests directly in the two assets subject to s + x e. At date 1, after
agents …nd out their type , they trade the long-term asset for cash at a
market-determined price p. In addition to the market for the long-term
asset, agents have access at date 1 to a market for one-period IOUs.10 A
formal statement of the agents’optimization problem and competitive
equilibrium in this economy is given in the Appendix. Note that this
market structure is incomplete: There are no contracts for provision of
consumption conditional on .
A simple arbitrage argument shows that in any equilibrium of this
trading arrangement the date-1 cash price p of a unit of the long-term
10
As we will see, however, the (hidden) IOU market will not be active here, nor
imposing any binding constraints on the equilibrium allocation.

B. Grochulski: Pecuniary Externalities and Segregated Exchanges 317
asset must be 1. This argument is as follows. The fact that a market for
the long-term asset exists at date 1 makes the long-term asset de facto
liquid and thus a perfect substitute, at date 0, for the short-term asset.
The return from holding the long-term asset for one period, therefore,
must be the same as the return from investing in the short-term asset.
The date-1 price of the long-term asset must therefore be p = 1, or else
there is an arbitrage.
Indeed, if p > 1, all agents want to invest their initial resources
in the long-term asset only, as investing a unit of resources in that
asset and selling it at date 1 yields p, while investing in the shortterm asset yields 1. In this case, however, nobody has cash at date 1
and thus aggregate demand for the long-term asset is zero. This level
of demand is inconsistent with the equilibrium price p being positive.
Similarly, if p < 1, all agents want to invest exclusively in the shortterm asset at date 0, as investing a unit of resources in the long-term
asset is dominated by investing this unit in the short-term asset and
then buying the long-term asset at date 1 at price p < 1. This, however,
means that supply of the long-term asset at date 1 is zero while demand
is positive, as the patient types are willing to buy at p < 1. Thus, p < 1
cannot be an equilibrium price, either.11
The only price p consistent with equilibrium, therefore, is p = 1. At
this price, the return from holding the short- and the long-term asset
from date 0 to date 1 is the same, so agents are indi¤erent between
investments s and x. At date 1, the impatient agents want to sell their
holdings x of the illiquid asset. With p = 1, the patient agents want
to hold on to their x and spend their cash s to purchase additional
^
^
units of the long-term asset, as the return on this investment, R = R,
p
exceeds their required rate of return, 1. Aggregate supply of the longterm asset to the market at date 1 is therefore x and the supply of
cash is (1
)s. The market-clearing condition, thus, is
xp = (1

)s;

where, by the arbitrage argument given above, p = 1. The date-0
budget constraint implies
x=e

s:

Solving the above two conditions, we obtain
s = e; x = (1
11

)e:

(18)

Strictly speaking, these corner investment strategies are not arbitrages because
they are not self-…nancing. But they could be turned into arbitrages if agents could
short the expensive asset at date 0.

318

Federal Reserve Bank of Richmond Economic Quarterly

This solution is unique, so there exists only one equilibrium. In equilibrium, consumption of the impatient types is c1 = s + px = e +
s
^
1(1
)e = e; while the patient types consume c2 = x + p R =
^
^
(1
)e + 1e R = eR. Let us denote the unique equilibrium consumption bundle by (^1 ; c2 ). We have just shown that
c ^

^
(^1 ; c2 ) = (e; Re):
c ^

(19)

In the hidden retrade market, there is no active trade. The equi^
librium retrade interest rate is R = R. At this rate, agents choose not
to alter their consumption allocation (^1 ; c2 ) by either borrowing or
c ^
lending. The hidden retrade market has no impact on the equilibrium
outcome here because the (regular, “non-hidden” date-1 market for
)
^
^
the long-term asset already o¤ers a riskless return R = R = R. The
p
hidden IOU retrade market is thus redundant.
A key property of the DD environment is that the equilibrium allocation of consumption, (^1 ; c2 ), is ine¢ cient. That is, this allocation
c ^
yields lower ex ante welfare than the optimal allocation c . Clearly,
^
^
the right inequalities in (12) and (13) tell us that c1 > c1 and c2 < c2 .
Since, by Proposition 1, the optimum (c1 ; c2 ) is a unique welfare maximizer, equilibrium allocation (^1 ; c2 ) is indeed ine¢ cient.
c ^
As we saw in Section 2, optimal allocation calls for a present-value
transfer from the patient types to the impatient types. In equilibrium
with incomplete markets, however, each agent consumes the worth of
his own initial endowment, e, i.e., there are no present value transfers
between types, and insurance markets are missing. Moreover, it is easy
to see that an intervention by a benevolent planner/government can
improve welfare without introducing any new markets. If the planner forces each agent to invest (s; x) = (s ; x ) at date 0 and allows
free trade at date 1, the market price for the long-term asset will be
p = p , the retrade market rate will be R = R , and the equilibrium
consumption allocation will be (c1 ; c2 ).12
In sum, the equilibrium investment in the liquid asset is too low
relative to the optimum, s = e < s , i.e., free trade leads to underprovision of liquidity.
12
In the language of the incomplete-markets literature, equilibrium (^1 ; c2 ) is
c ^
constrained-ine¢ cient.

B. Grochulski: Pecuniary Externalities and Segregated Exchanges 319
4.

COMPETITIVE EQUILIBRIUM WITH
CONTINGENT CONTRACTS

In this section, we allow for state-contingent contracts. We review
the following important result. Jacklin (1987) points out that when
retrade is allowed, an arbitrage argument similar to the one used in
the previous section implies that markets will underprovide liquidity,
even when fully state-contingent contracts are allowed. With retrade,
thus, the market failure shown in the previous section for the simple
incomplete-markets model continues to hold for all feasible models of
trade in the DD environment, including the intermediation economy of
Diamond and Dybvig (1983).
Consider the following general model of trade with fully statecontingent contracts, direct investment, and retrade.13 In addition to
directly investing in the two assets, agents can contract with intermediaries and access the hidden IOU market. Intermediaries, or banks,
make available to agents at date 0 a state-contingent contract ( 1 ; 2 ).
Under this contract, which can be thought of as a deposit contract,
the agent can obtain from the intermediary, at the agent’ discretion,
s
either 1 at date 1 or 2 at date 2 (but not both). Let us normalize
the price of this contract to e, i.e., an agent who accepts a contract
deposits his whole initial wealth with a bank. Also, as before, agents
can borrow from and lend to each other privately in the hidden retrade
market at date 1.
Under this market structure, an agent has the following choices to
make. At date 0, he decides whether to deposit his wealth e with a
bank or to invest directly in assets s and x. If he deposits, after he
learns his type , he chooses whether to withdraw at date 1 or 2, and
how much, if at all, to borrow or lend in the hidden retrade market
at the market rate R. If the agent chooses not to deposit at date 0
but rather to invest directly, he selects a portfolio (s; x). At date 1,
after he learns his type and his cash investment s matures, the agent
decides how much to borrow or lend in the retrade market at the market
rate R.
Competition among banks (existing or potential entrants) drives
banks’ pro…ts to zero and forces each active bank to o¤er the same
contract (namely, the contract that maximizes the ex ante expected
utility of the representative agent, for otherwise agents would deposit
with a di¤erent bank). Since intermediation is an activity with constant
returns to scale in this model, it is without loss of generality to assume
13
For a formal statement a version of this economy see Section 3.1 of Farhi,
Golosov, and Tsyvinski (2009) or Allen and Gale (2004).

320

Federal Reserve Bank of Richmond Economic Quarterly

that a single large bank operates in equilibrium (the market, however,
is perfectly contestable).
The bank’ contract design problem is similar to the social planning
s
problem in that in both cases the objective is to maximize the agent’
s
expected utility. There is, however, a key di¤erence. The planner
can control date-0 investment, which enables her to have an (indirect)
impact on the retrade market interest rate R. The bank cannot force
the agents to deposit, which means it must act competitively, i.e., take
prices as given. In particular, the bank takes as given the retrade
market interest rate R.
Given this di¤erence, it is not hard to see that the optimal allocation (c1 ; c2 ) cannot be an equilibrium allocation. If (c1 ; c2 ) were to
be an equilibrium allocation, the interest rate R in the hidden retrade
market would have to be equal to the shadow rate R given in (17),
for otherwise agents would use that market to trade away from this
allocation. But R cannot be an equilibrium retrade interest rate be^
cause the fact that R is strictly smaller than R creates an arbitrage
opportunity. This arbitrage opportunity is similar to the one that in
the incomplete-markets model discussed in the previous section pinned
down the secondary-market asset price p at 1.
The arbitrage strategy, described in Jacklin (1987), calls for investment x = e at date 0. If the agent executing this arbitrage is patient,
^
i.e., his = 1, he consumes nothing at date 1 and Re > c2 at date 2. If
he turns out impatient, i.e., his = 0, he can access the retrade market
^
Re
and borrow at rate R , which gives him date-1 consumption R > c1 .
In either case, thus, he consumes more than (c1 ; c2 ), which shows that
(c1 ; c2 ), with its shadow interest rate R , cannot be an equilibrium
allocation of consumption.
What allocation can be a market equilibrium allocation in this
model? The Jacklin arbitrage strategy pins down the interest rate
^
in the retrade market at R = R. With this interest rate, it is easy
to check (or consult Allen and Gale [2004] or Farhi, Golosov, and
Tsyvinski [2009]) that the equilibrium allocation (19) from the
incomplete-markets model discussed in the previous section is a unique
equilibrium allocation, also here in the richer model with fully statecontingent contracts.14
Why is the planner able to do better than the market in this model?
The planner makes the Jacklin arbitrage strategy infeasible for the
14
This conclusion applies to all conceivable market structures in which the Jacklin
arbitrage strategy remains feasible. In particular, when the hidden retrade market is
included, it applies to the general competitive private information model of Prescott
and Townsend (1984) in which agents trade lotteries over allocations subject to incentive
compatibility constraints.

B. Grochulski: Pecuniary Externalities and Segregated Exchanges 321
agent by controlling initial investment (s; x). In the planning problem,
although the agent has unfettered access to the retrade market, the
agent does not have private control over his initial investment. The
initial investment choice is publicly observable and therefore can be
controlled by the planner/government. The Jacklin arbitrage strategy
calls for the all-long investment (s; x) = (0; e) at date 0. By forcing/choosing investment (s; x) = (s ; e s ), the planner eliminates
this arbitrage. Moreover, this choice of date-0 investment pins down
the amount of resources available at dates 1 and 2 and, thus, also the
interest rate in the hidden retrade market, which with liquid investment
s is R = R . In a competitive market economy, by contrast, …rms have
to respect the agents’freedom to not contract with them but instead
to invest directly (or set up another …rm that will do the investing for
them, as in Farhi, Golosov, and Tsyvinski [2009]). Intermediaries thus
cannot make the Jacklin arbitrage strategy infeasible for the agents.
Having to respect this arbitrage condition, the best allocation they can
^
provide is (^1 ; c2 ) = (e; Re) with the associated retrade market interest
c ^
^
rate R = R.
To recap, the planner internalizes the fact that her control of the
initial investment changes the price in the equilibrium of the retrade
market. Firms, in contrast, take all prices as given, including those in
the retrade market. The discrepancy constitutes a pecuniary externality in this model and the equilibrium allocation is ine¢ cient.

E ciency Without Retrade
The Jacklin arbitrage strategy is clearly impossible to execute if arbitrageurs do not have access to the hidden retrade market. Absent
retrade, competitive equilibrium with state-contingent contracts would
be e¢ cient. Indeed, if the retrade market is shut down, the value func~
~
tion V (c; R; ) de…ned in (6) reduces to V (c; R; ) = max~ u(c1 (~) +
~)), which no longer depends on R. The incentive constraint (7),
c2 (
therefore, no longer depends on a price.15 This means that there is no
pecuniary externality. The welfare theorems of Prescott and Townsend
(1984) apply, and competitive equilibrium is e¢ cient. In particular, it
can be implemented as a banking equilibrium of Diamond and Dybvig
(1983) with the equilibrium deposit contract ( 1 ; 2 ) = (c1 ; c2 ).
The theoretical results we reviewed in this section suggest that retrade generates a pecuniary externality and leads to equilibrium
15
In particular, given Lemma 1, the impatient types will never misrepresent their
type and the patient types’ incentive constraint reduces to c2 c1 .

322

Federal Reserve Bank of Richmond Economic Quarterly

underprovision of liquidity. In practice, banks and other …nancial intermediaries have ample access to various retrade markets. Therefore,
one might be tempted to take as an implication of this theory the prediction that markets will fail to provide su¢ cient liquidity. In the next
section, we present a simple version of the analysis of Kilenthong and
Townsend (2011) showing that this conclusion would be premature:
If harnessed inside appropriate venues, retrade can be consistent with
e¢ cient functioning of markets in the provision of liquidity.

5.

COMPETITIVE EQUILIBRIUM WITH
SEGREGATED EXCHANGES

In this section, we consider the model of Kilenthong and Townsend
(2011), in which a market-maker eliminates the Jacklin arbitrage by
segmenting the retrade market and pricing entry into market segments
as a function of the investment portfolio held by agents entering a
given segment. With the Jacklin arbitrage eliminated, the pecuniary
externality causing market failure is eliminated as well. The resulting
equilibrium is e¢ cient. We supplement the analysis of Kilenthong and
Townsend (2011) by characterizing explicitly how the equilibrium exchange entry fees depend on the fundamentals of the exchange and on
the portfolio of the agent (equation [27] and Figure 2). We conclude
with a discussion of an important di¤erence between the environment
with pecuniary externality studied in the previous sections and the environment without it that we study here. The segregated-exchanges
equilibrium is e¢ cient, but, e¤ectively, it requires that agents commit
ex ante to not using the hidden retrade market ex post. Whether or
not retrade leads to a pecuniary externality and ine¢ ciency of market outcomes, therefore, depends on the practical feasibility of such a
commitment.

Trade Inside Segregated Exchanges at Date 1
Before we de…ne the general equilibrium concept with segregated
exchanges proposed by KT, we describe in this subsection segregated
exchanges, their fundamentals, and internal prices.
A segregated exchange is a competitive market for the long-term
asset that opens at date 1 after types are realized. A de…ning characteristic of such an exchange is a set of fundamentals determining the
market price p at which the long-term assets will be traded. The fundamentals and the price must be consistent: Given the fundamentals
in an exchange, the price p must indeed be a competitive equilibrium
price in that exchange. In the DD economy at hand, the level of the

B. Grochulski: Pecuniary Externalities and Segregated Exchanges 323
cash asset investment s held by each member of an exchange is a suf…cient description of the fundamentals in the exchange. Thus, we will
index exchanges by S 2 [0; e], where S represents the level of liquid
investment held by each agent entering the exchange. Note that this
de…nition assumes identical asset holdings by all exchange members.
We will see later that this assumption is without loss of generality in
the present environment.
Equilibrium price in exchange S
Let us derive an equilibrium consistency condition between fundamentals S and price p in the exchange S 2 [0; e]. It is a simple equilibrium
pricing condition in a competitive market with all agents holding the
same portfolio of assets (s; x) = (S; e S) and experiencing shocks
drawn from the same distribution. We will denote the equilibrium price
in exchange S by p(S).
The equilibrium condition for consistency between S and p is
(1
(e

p(S) = min

)S ^
;R :
S)

(20)

This condition is derived as follows. The equilibrium price of the illiquid
asset is determined by supply and demand in exchange S in the same
way as it was determined in the incomplete-markets model of Section 3.
At date 1, the impatient agents want to sell their long-term asset in the
market at any price. They supply (e S) units of the long-term asset
to the market. The behavior of the patient agents depends on the price
^
p. If p > R, a short position in the asset gives them a positive return,
so patient agents want to sell their holdings of the asset, just like the
impatient ones. This cannot be an equilibrium, as demand for the asset
^
is zero and supply is positive. Thus, in any equilibrium, p R. With
^ a long position in the asset gives patient agents a non-negative
p R,
^
return (strictly positive if p < R). With any such price, the patient
agents are willing to buy the long-term asset. They demand (1
)S
p
S
units. Thus, the equilibrium price p(S) solves (e S) = (1
) p(S) ,
which gives us
(1
(e

)S
;
S)

(21)

^
^
R. Solving R =

(1 )S
(e S)

for S, we get a threshold

p(S) =
provided that p(S)

S=

^
Re
^
R+1

:

(22)

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Federal Reserve Bank of Richmond Economic Quarterly

Figure 1 Equilibrium Asset Price p in Exchange S

^
For all S
S, the equilibrium price is ‡ at R.16 Combining this
at
restriction with (21) gives us the consistency condition (20).
Figure 1 illustrates the derivation of the consistency condition (20)
graphically. When S is small and e S is large, there is a large quantity
of the illiquid asset in the market, supplied by the impatient agents,
and very few units of the consumption good (cash), supplied by the
patient agents, and so the price of the asset is low.17 In exchanges with
higher S, the proportion of cash to units of the asset in the market is
higher, so the price p(S) is higher. This is true up to the threshold S.
^
In exchanges with S larger than S, the price p(S) remains ‡ at R and
at
the patient types are indi¤erent between buying and selling the asset.
^
^
The price of the asset cannot exceed R, as at a price higher than R the
patient agents would switch from buying to selling the asset. As we
see, the range of prices that can be consistent with some fundamentals
S 2 (0; e] is
0<p

^
R:

(23)

16
Note that S is the same threshold that in Proposition 1 results with the fullinsurance allocation (an upper bound on s ).
17
We will exclude the exchange S = 0 from our analysis. In this exchange, the
supply of resources at date 1 would be zero and thus welfare of the impatient agents
would be extremely low. No agent would want to enter this exchange at date 0.

B. Grochulski: Pecuniary Externalities and Segregated Exchanges 325
Markets at Date 0 and Equilibrium De nition
In this subsection, we use the segregated exchanges to de…ne the KT
notion of competitive equilibrium with segregated retrade.
At date 0, agents choose their investments s and x and join segregated exchanges. Each agent can physically join one exchange. Exchanges are de…ned by their fundamental level of liquid investment S.
Associated with each exchange is an entry fee pricing any deviations of
the investment portfolio of an agent wishing to join a given exchange
from that exchange’ fundamentals. If an agent joins an exchange S
s
with liquid investment s, the amount of shortage of his liquid asset
relative to the exchange fundamentals is S s. Upon entry, the agent
is charged a fee proportional to the amount of shortage of liquid investment in his portfolio. The price per unit of shortage in exchange S
is (S). Thus, an agent entering exchange S with liquid investment s
is charged an entry fee of (S)(S s). This charge is assessed by the
exchange as of the time of entry, i.e., at date 0. The unit price (S)
can be positive or negative. Note that if (S) > 0 and an agent joins
exchange S with liquid investment s > S, the entry fee is negative, so
the exchange makes a payment to the agent.
In sum, at date 0 agents choose investment portfolios (s; x) and
exchange membership S subject to the budget constraint
s + x + (S)(S

s)

e:

(24)

If, for example, an agent decides to join exchange S and go all-long, i.e.,
invest s = 0 and x = e, then the price for this shortage would be (S)S.
Clearly, public observability of the agent’ portfolio is important for the
s
assessment of fees. In particular, agents cannot avoid fees by “window
dressing” or changing the composition of their portfolio after the fees
are assessed but before the shock is realized and exchanges open for
business.
What if an agent chooses not to join an exchange? The decision not
to join is equivalent to joining an exchange in which the price of any
“deviation”or “shortage”relative to the “fundamentals”is zero. Thus,
not joining a segregated exchange is equivalent to maintaining access to
the free exchange in which = 0. As we will see shortly, the exchange
S = e will have = 0. This exchange corresponds to the incompletemarkets model of Section 3, where, as we saw earlier, all agents choose
investment s = e at date 0. It is natural to default all agents who do
not join a di¤erent exchange into this one. The model with segregated
exchanges, therefore, nests the simple incomplete-markets model as a
special case in which there is only one secondary market for the longterm asset, and access to this market is free.

326

Federal Reserve Bank of Richmond Economic Quarterly

Let us now discuss the agents’ objective function as of date 0.
Agents maximize
E[V1 (s; x; S; )];

(25)

where V1 (s; x; S; ) is the indirect utility function as of date 1, i.e., the
value the agent can get in exchange S with an asset portfolio (s; x) and
a liquidity shock realization . The indirect utility function
V (s; x; S; ) = max u(c1 + c2 );
s:t:
c1 + p(S)n s;
n
x;
^
c2 (x + n)R;

(26)

where n is the agent’ net demand at date 1 in the market for the
s
illiquid asset inside exchange S.
Next, we de…ne competitive equilibrium with segregated exchanges.
De…nition 1 (Kilenthong and Townsend) A price system (p( ); ( )),
ex ante investment and exchange membership choices s, x, S, value
functions V1 ( ; ; ; ) for 2 f0; 1g, and a consumption allocation (c1 ; c2 )
are an equilibrium with segregated exchanges if
1. expectations are correct: For each S, price p(S) satis…es the consistency condition (20) and value functions V1 ( ; ; ; ) solve (26);
2. agents optimize ex ante: Taking prices ( ( ); p( )) and value functions V1 ( ; ; ; ) as given, agents’choices s, x, S maximize their
ex ante utility (25) subject to the budget constraint (24);
3. market clearing: Consumption allocation (c1 ; c2 ) is an equilibrium allocation of consumption in the exchange S.
Note that this de…nition does not allow for mixed strategies. In
general, mixed strategies may be useful, as agents face a discrete choice
of exchange membership. As the theorem presented next makes clear,
in the environment at hand it is without loss of generality to restrict
attention to equilibria in pure strategies, where all agents, being ex
ante identical, join the same exchange.18
18
In excluding random exchange assignments, this de…nition follows De…nition 4 in
Kilenthong and Townsend (2014a).

B. Grochulski: Pecuniary Externalities and Segregated Exchanges 327
E cient Equilibrium with Segregated Exchanges
Theorem 1 Prices p(S) as in (20) and
(S) = min 1

1

e
S

^
R

1 ;1

1

;

(27)

ex ante investment and membership choices s = s , x = e s , S = s ,
and consumption allocation (c1 ; c2 ) = (c1 ; c2 ) are a competitive equilibrium with segregated exchanges.
The rest of this subsection is devoted to proving this theorem. We
need to check the three equilibrium conditions in De…nition 1.
We start by characterizing value functions (26). For = 0, the
optimized value of (26) is
V1 (s; x; S; 0) = u (s + p(S)x) :

(28)

Clearly, the impatient agents want to sell their holdings x of the longterm asset at any price p(S) and consume all their wealth at date 1, as
they have no use for consumption at date 2. At price p(S), an impatient
agent can a¤ord consumption c1 = s + p(S)x, which gives us (28).
The patient type’ value as of date 1 is
s
V1 (s; x; S; 1) = u

x+

s
p(S)

^
R :

(29)

To see that this is the case, note that in each exchange S patient
agents are happy to buy the long-term asset at date 1 because, by (23),
^
p(S)
R in all exchanges S. This means that the rate of return on
^
R
this investment, p(S) , exceeds the patient type’ rate of time preference,
s
s
which is 1. A patient agent’ demand for the long-term asset is n = p(S) ,
s
his consumption at date 1 is c1 = 0, and consumption at date 2 is
s
^
c2 = (x + p(S) )R. These quantities substituted to (26) with = 1 give
us (29).
We can now con…rm that with value functions (28) and (29) the …rst
equilibrium condition (correct expectations) is satis…ed, as these value
functions and prices p(S) de…ned in (20) are consistent with agents’
optimization at date 1. Note that the general pattern of behavior at
date 1 is the same in all exchanges. The impatient types sell and the
patient types buy the long-term asset. The exchanges are di¤erent only
in the composition of demand and supply, which gives rise to di¤erent
equilibrium prices at which the asset is traded in each exchange.
In order to check the second equilibrium condition (agents’ optimization ex ante), we now study the agents’ behavior at date 0.
Substituting the indirect utility functions (28) and (29) into the objective (25), we express the ex ante expected utility function of the

328

Federal Reserve Bank of Richmond Economic Quarterly

Figure 2 Unit Liquidity Shortage Price

in Exchange S

representative agent as
u (s + p(S)x) + (1

)u

x+

s
p(S)

^
R :

This expression gives the agent’ expected value of being in exchange
s
S with assets s and x. The representative agent chooses investment
portfolio (s; x) and exchange membership S to maximize this value
subject to the date-0 budget constraint (24).
The structure of the portfolio fees (S) charged upon exchange
entry is a key part of the budget constraint. Figure 2 graphs against
S the unit liquid asset shortage price (S) given in (27). As we argue,
these prices support the e¢ cient equilibrium.
e
^
It is easy to check directly in (27) that 1
1 <1 R 1
1

S

for all S < S, where S is, as before, given in (22). Thus,
(S) =

1

1

1

e
S
1
^
R

1

for S
for S

S;
S:

Note that (S) is increasing. This means that the portfolio charge
per unit of liquidity shortage is higher in exchanges with higher fundamental liquidity S. Substituting in (27) S = e < S, we check that
( e) = 0. Thus, the exchange with S = e is a (unique) free-entry
exchange, where portfolio charges are zero for all portfolios (s; x). In
exchanges with S > e, (S) > 0, i.e., agents are subject to a positive charge for shortage of liquidity in their portfolio. For all S < e,

B. Grochulski: Pecuniary Externalities and Segregated Exchanges 329
(S) < 0, i.e., portfolio charges are positive if the long-term investment
x is less than e S.
We now can study the agents’ date-0 problem of choice of investment (s; x) and exchange membership S. For each exchange S, we
need to determine the investment portfolio (s; x) the agent will choose
conditional on joining S and the consumption pair (c1 ; c2 ) he will be
able to a¤ord inside S. This will give us the ex ante expected value
of joining S, which we will then use to determine the agent’ most
s
preferred exchange membership decision and thus the solution to his
utility maximization problem.
We start by examining the exchanges with S
S. What ex ante
value can the representative agent obtain if he plans on joining one of
these exchanges? All exchanges S
S have the same entry fees and
long-term asset prices:
^
(S) = 1 R
^
p(S) = R:

1

;
(30)

Given a portfolio (s; x), an agent in exchange S
consumption

S can a¤ord

^
c1 = s + Rx
if impatient, or
c2 =

x+

s
^
R

^
^
R = s + Rx

if patient. As we see, the agent is fully insured against the liquidity
shock in any exchange S
S, as his optimal consumption in any
such exchange is independent of the realization of the liquidity shock
. His ex ante expected utility is therefore simply
^
u s + Rx :

(31)

^
With the entry fee of (S) = 1 R 1 per unit of liquidity shortage, the
agent’ ex ante budget constraint (24) can be written as
s
^
s + Rx

^
Re

^
(R

1)S:

(32)

Comparing the agent’ objective (31) and his budget constraint (32),
s
we see that the agent is indi¤erent between all portfolios (s; x) on the
^
^
^
budget line s + Rx = Re (R 1)S. This is because any such portfolio
^
^
gives the agent the same ex ante utility of u Re (R 1)S . Since
^
R > 1, this value is decreasing in S. Thus, among all exchanges S S,
exchange S is the best one for the agent.

330

Federal Reserve Bank of Richmond Economic Quarterly

Next, let us consider the choices of an agent who plans on joining
one of the exchanges with S S. The prices this agent faces are
(S) = 1
p(S) =

e
S

1

(1
(e

1 ;

)S
:
S)

(33)

Thus, given a portfolio (s; x), in exchange S the agent can a¤ord consumption
c1 = s +
if impatient, or
0

c2 = @x +

s
(1 )S
(e S)

1

^
AR =

(1
(e

s+

)S
x
S)

(1
(e

)S
x
S)

(e
(1

S) ^
R
)S

if patient. Unlike in the previous case, these consumptions are not
)S
identical. They are, however, directly proportional to s + (1 S) x.
(e
Substituting these consumption values into the ex ante expected utility
function, we have
S) ^
R :
)S
(34)
With the entry fee (S) given in (33), the agent’ ex ante budget cons
straint (24) can be rewritten, after some algebra, as
u s+

(1
(e

)S
x + (1
S)

)u

s+

(1
(e

s+

(1
(e

S

)S
x
S)

)S
x
S)

(e
(1

:

Comparing this budget constraint and the agent’ objective (34) we
s
see that here, as in the previous case, the agent is indi¤erent between
)S
all portfolios (s; x) on the budget line s + (1 S) x = S as any such
(e
portfolio gives him the same expected utility value of
u

S

+ (1

)u

e
1

S^
R :

Finally, we observe that this objective function, representing the agent’
s
utility from joining exchange S, is mathematically the same as the objective function (10) in the social welfare maximization problem studied
in Proposition 1. As we saw there, this objective is maximized by a
unique s < S. Thus, exchange S = s is a unique maximizer in the

B. Grochulski: Pecuniary Externalities and Segregated Exchanges 331
agent’ utility maximization problem we study here.19 To simplify the
s
notation, we will use S to denote the exchange S = s .
The last equilibrium condition that we need to check is to con…rm
that (c1 ; c2 ) is an equilibrium allocation of consumption in exchange S
with the asset price p(S ). For the pair (c1 ; c2 ) to be resource-feasible in
exchange S , agents must enter this exchange carrying the investment
portfolio (s ; e s ). Portfolio (s ; e s ) is (weakly) optimal for an
agent joining exchange S because, as we saw earlier, conditional on
joining an exchange, agents are indi¤erent among all portfolios (s; x)
on the budget line. Finally, since the asset price p(S ) satis…es the
consistency condition (20), the market for the long-term asset inside
the exchange S does clear.
We conclude that the prices and quantities speci…ed in Theorem 1
are indeed a competitive equilibrium with segregated exchanges. This
equilibrium is e¢ cient, as the equilibrium consumption bundle is exactly the optimal consumption bundle (c1 ; c2 ).

Discussion
In the two equilibrium concepts without segregated exchanges that we
discussed in Sections 3 and 4, arbitrage pinned at p = 1 the equilibrium
price in the secondary market for the long-term asset or, equivalently,
^
the retrade market interest rate at R = R. In the model with segregated
exchanges, agents trade the long-term asset in the secondary market
inside the exchange S at the equilibrium price
^
(1
) c1
R
(1
)s
^c
=R 1 =
=
> 1:
p(S ) =
c
(e s )
c2
R
(1
) 2
^
R

Why does arbitrage not force p(S ) down to 1 in the segregated exchanges model?
The Jacklin arbitrage strategy is infeasible in the segregated exchange model because of the entry fees ex ante and the separation of
agents in di¤erent exchanges ex post. The Jacklin arbitrage strategy
calls for the all-long initial investment (s; x) = (0; e) and a subsequent
sale of the long-term asset, or borrowing against it, in case the agent
attempting arbitrage turns out needing funds at date 1. But which
exchange should the arbitrageur join at date 0? If he defaults to the
entry-fee-free market S = e, he does not receive the favorable asset
price p(S ) > 1 but only the arbitrage-free price p( e) = 1, so no arbitrage pro…t can be made in this exchange. If the arbitrageur joins
19
Note in particular that the right inequality in (11) implies that exchange S =
s dominates the exchange S = S and thus also all exchanges S S.

332

Federal Reserve Bank of Richmond Economic Quarterly

exchange S , he must pay the entry fee of (S )S . This fee o¤sets
exactly the pro…t he makes selling the long-term asset at the high price
p(S ); thus eliminating the overall pro…tability of this attempt at arbitrage. The entry fee o¤sets exactly the asset sale pro…t because, conditional on joining an exchange, agents are indi¤erent between all feasible
portfolio choices. In particular, the arbitrageur joining exchange S
with the all-long portfolio (0; e) does no better than an agent entering
this exchange with the equilibrium portfolio (s ; e s ). Similarly, if the
arbitrageur with portfolio (0; e) joins any other exchange S, he is exactly as well o¤ as an agent joining S with the fundamentals-consistent
portfolio (S; e S). Thus, the arbitrageur joining S obtains the ex
ante expected utility value of W (S). As we saw in Proposition 1, this
value is maximized at S = S . No arbitrage attempt therefore can be
successful.
The agents’ ability to commit to not trading across exchanges ex
post is key in eliminating the Jacklin arbitrage. The segregated exchanges mechanism lets each agent join only one exchange. In addition, it requires that agents sign o¤ their right to trade freely with the
counterparty of their choice. Instead, it requires that agents commit
to trading only with other members of the exchange they belong to. If
agents do not have the ability to contractually give away their freedom
to trade without counterparty restrictions, an impatient arbitrageur
residing in the entry-fee-free exchange S = e can easily convince a patient agent in exchange S to buy the long-term asset from him rather
than in exchange S because he can sell for less than p(S ) and still
make a pro…t. As agents anticipate this at date 0, price expectations
embedded in p(S) are not credible and the equilibrium breaks down.
Thus, the restriction of participation to one exchange only and the
assumption of the agents’ ability to commit to not step out of their
exchanges ex post are crucial.
In the KT equilibrium, segregated exchanges can therefore be
thought of as a commitment device allowing the agents to promise credibly to not access the hidden IOU market. Clearly, if in the KT model
agents could access the hidden IOU retrade market after they trade in
segregated exchanges, the equilibrium with segregated exchanges supporting the optimal asset price p(S ) would collapse. The argument
for it is the same as in Section 4. The optimal allocation (c1 ; c2 ) is
consistent with free access to the retrade market only if the interest
rate in this market equals R = c2 =c1 . But with this interest rate, the
Jacklin arbitrage can again be executed by investing all long, joining
the entry-fee-free exchange S = e, and not trading in this exchange

B. Grochulski: Pecuniary Externalities and Segregated Exchanges 333
but rather borrowing in the IOU market if liquidity is needed at date
1.20
In the banking model discussed in Section 4, the intermediary designing the state-contingent deposit contract cannot put any restrictions on retrade between depositors and non-depositors. The marketmaking …rm in the segregated exchanges model, in contrast, can. In
particular, an agent who did not join exchange S and subject his portfolio to the entry fee (S) cannot retrade with agents who did join
exchange S. This additional power given to the market-maker in the
segregated exchanges model makes her equally as e¤ective as the social planner in Section 4 in controlling agents’ investment at date 0.
Unlike the planner, the market-maker does not control this investment
directly but rather sets up prices (i.e., exchange entry fees) to induce
e¢ cient investment.
As we see, the model with segregated exchanges, where retrade
does not lead to a pecuniary externality, requires a di¤erent economic
environment than the models in Sections 3 and 4, where access to
hidden retrade causes an externality. The segregated exchanges model
requires that agents have the ability to commit themselves to refrain
from trading in the hidden retrade market, which e¤ectively makes this
model equivalent to the model with observable trades that we discussed
in Section 4.21 If such commitment can be made credible, e.g., by
physically separating agents ex post, then all agents would choose to
extend it ex ante. If, however, it is a feature of the environment that
such a commitment cannot be made credible, as in Farhi, Golosov, and
Tsyvinski (2009), access to hidden retrade makes the Jacklin arbitrage
strategy feasible, the pecuniary externality exists, and markets fail to
provide su¢ cient liquidity in equilibrium.
Clearly, the cap-and-trade mechanism will not be successful at
limiting greenhouse gas emissions if …rms can emit completely privately/anonymously, i.e., without anyone observing it. If they can,
the price of the right to emit one tonne of CO2 will be zero. In the
KT model, retrade is analogous to observable emissions that can be
priced. In the pecuniary externality model, hidden retrade is analogous to anonymous emissions that cannot be priced or internalized
with a cap-and-trade scheme.
Are then segregated exchanges a solution to the pecuniary externality problem caused by retrade? Segregated exchanges do not solve
20
Better yet, the arbitrageur could join one of the exchanges S < e, where (S) <
0, which means with s = 0 he would get a payment from the exchange upon entry.
21
That the segregated exchanges model requires a di¤erent environment than the
unfettered hidden retrade model is clear from Table 1 on page 1,046 in Kilenthong and
Townsend (2011).

334

Federal Reserve Bank of Richmond Economic Quarterly

the pecuniary externality problem, but they show that retrade does not
have to lead to one. The literature on pecuniary externalities with complete markets and retrade assumes that agents have unfettered access
to an anonymous, hidden retrade market and cannot do anything to
make credible an ex ante promise to refrain from accessing this market
ex post. The segregated exchanges model assumes that such a commitment is possible. The segregated exchanges model, therefore, does not
solve the pecuniary externality problem associated with anonymous,
hidden retrade. Instead, it points out that retrade by itself does not
imply the existence of a pecuniary externality. The model shows that
retrade can be accounted for within the competitive market framework
without violating e¢ ciency, provided that a su¢ ciently rich market
structure, including markets for exchange membership, is allowed for.
In addition, the KT model shows that exclusivity and ex post trade
restrictions can be socially valuable. Their role can be to serve as a
commitment device that agents may be able to use to help them refrain
from the “harmful,”hidden retrade activity and still be able to engage
in e¢ cient, priced retrade.

6.

CONCLUSION

The literature we review makes it clear that in the Diamond-Dybvig
economy, the agents’access to retrade is key in understanding whether
markets are e¢ cient or require government intervention. The theory
makes a distinction between two kinds of retrade: the “priced” kind
and the “hidden” kind. Hidden, anonymous retrade leads to a pecuniary externality and market failure. Priced retrade, harnessed into
access-controlled segregated exchanges with exchange- and portfoliodependent entry fees does not cause market failure.
The observation of retrade itself in present-day …nancial markets
does not therefore imply that markets are ine¢ cient or e¢ cient in providing liquidity. To answer the question of e¢ ciency, one must assess
which of the two kinds of retrade discussed in the model is a better re‡
ection of reality. Kilenthong and Townsend (2014a) suggest that the
assumption of restricted retrade is a good one in …nancial markets. In
other applications, for example in the problem studied in Kehoe and
Levine (1993) where pecuniary externalities result from workers’ unrestricted access to spot labor markets, this assumption may be more
problematic, as …rms may lack the commitment to deny employment
to workers who have defaulted on some …nancial obligations in the
past. Given these theoretical predictions and their implications for
the e¢ cacy of government intervention, empirical research identifying

B. Grochulski: Pecuniary Externalities and Segregated Exchanges 335
the nature of retrade and the existence or nonexistence of pecuniary
externalities is needed.

APPENDIX
Proof of Lemma 1
Suppose allocation c is optimal with c2 (0) > 0 and de…ne an allocation
c = f^1 (0); c2 (0); c1 (1); c2 (1)g as follows:
^
c
^
^
^
c1 (0) = c1 (0); c1 (1) = c1 (1);
^
^
c2 (0) = 0;
^
c2 (1) = c2 (1) +
^

1

c2 (0):

Allocation c is feasible because at each date t = 1; 2 it uses the same
^
amount of resources as allocation c. Indeed:
c2 (1)
^
c2 (0)
^
+ (1
) c1 (1) +
^
c1 (0) +
^
^
^
R
R
c2 (1) + 1 c2 (0)
=
c1 (0) + (1
)
^
R
c2 (0)
c2 (1)
=
c1 (0) +
+ (1
) c1 (1) +
^
^
R
R
e:
Allocation c, however, attains a higher value of the objective (5) be^
cause it provides the same utility u(c1 (0)) to the impatient type and
a higher utility u(c1 (1) + c2 (1) + 1 c2 (0)) > u(c1 (1) + c2 (1)) to the
patient type. This contradicts the supposed optimality of c.
To prove that c1 (1) = 0, suppose that c is optimal with c1 (1) > 0
and de…ne an allocation c = f^1 (0); c2 (0); c1 (1); c2 (1)g as follows:
^
c
^
^
^
c1 (0) = c1 (0); c1 (1) = 0;
^
^
^
c2 (0) = c2 (0); c2 (1) = c2 (1) + Rc1 (1):
^
^

Allocation c is feasible because it costs the same in present value terms
^
as the feasible allocation c. Indeed:
c2 (0)
^
c2 (1)
^
c1 (0) +
^
+ (1
) c1 (1) +
^
^
^
R
R
^
c2 (0)
c2 (1) + Rc1 (1)
=
c1 (0) +
+ (1
)
^
^
R
R
c2 (0)
c2 (1)
=
c1 (0) +
+ (1
) c1 (1) +
^
^
R
R
e:

336

Table 1 Allocation Mechanisms, Frictions, and Outcomes
Allocation Mechanism

Hidden IOU
Retrade Market

Market Structure

Allocation

Page

First-best planning problem

Absent

Absent

No markets–
planner
chooses allocation

(c1 ; c2 )

313

Planning problem with
private

Present

Absent

No markets–
planner
chooses allocation

(c1 ; c2 )

321

Planning problem with
private and hidden retrade

Present

Present

No markets–
planner
chooses allocation

(c1 ; c2 )

315

Incomplete markets model

Present

Present

Ex ante: direct investment (s; x)
Ex post: market for the
long-term asset and the hidden
IOU market

Market model with statecontingent contracts, no
hidden IOU retrade markets

Present

Market model with statecontingent contracts and
hidden IOU retrade markets

Present

Market model with
segregated exchanges

Present

Absent

Present

Absent

Ex ante: deposit contract
( 1 ; 2 ) with price e
Ex post: no markets
Ex ante: deposit contract
( 1 ; 2 ) with price e
Ex post: hidden IOU
retrade market
Ex ante: continuum of
segregated exchanges
Ex post: retrade inside
exchanges, but not across

316
(^1 ; c2 )
c ^

321
(c1 ; c2 )
319
(^1 ; c2 )
c ^

(c1 ; c2 )

322

Federal Reserve Bank of Richmond Economic Quarterly

Private
Shocks

B. Grochulski: Pecuniary Externalities and Segregated Exchanges 337
Allocation c , however, attains a higher value of the objective (5)
^
than c, because it provides the same utility u(c1 (0)) to the impatient
^
type and a higher utility u(c2 (1) + Rc1 (1)) > u(c1 (1) + c2 (1)) to the
patient type. This contradicts the supposed optimality of c. QED

Proof of Proposition 1
Since W 00 (s) = 1 u00
u0

s

^
Ru0

s

e s ^
R
1

^
+ 1 1 R2 u00

e s ^
R
1

< 0, we have that W 0 (s) =

is continuous and strictly decreasing. The exis-

tence of a unique solution to W 0 (s) = 0 in (0; e) thus follows from the
fact that lims!0 W 0 (s) ! 1 and lims!e W 0 (s) ! 1.
For the two bounds on s , it is su¢ cient to show that W 0 ( e) > 0
^
< 0. We …rst note that relative risk aversion
and W 0 e ^ R
R+1
everywhere strictly greater than one implies that the function f ( ) =
u0 ( e) is strictly decreasing. Indeed, with f 0 ( ) = u0 ( e) + eu00 ( e)
00 (
we have that f 0 ( ) < 0 follows from 1 < ueu e) e) . Now, evaluating
0(
^
^
^
W 0 at s = e, we have W 0 ( e) = u0 (e) Ru0 (eR) = f (1) f (R) > 0,
^
where the strict inequality follows from f strictly decreasing and R > 1.
To show W 0
s

e s ^
R
1

=
W

0

=

^
R
^
R+1
^
Re
.
^
R+1

^
Re
^
R+1

!

^
Re
^
R+1

< 0; note that with s =

e

we have

Therefore,
= u
=

0

1

^
Re
^
R+1
^
R u0

!
^
Re
^
R+1

^
Re

^
Ru0
!

^
R+1

!

< 0;
^
where the inequality follows from u0 > 0 and R > 1. QED

Formal De nition of Incomplete-Markets
Equilibrium in Section 3
At date 0, each agent chooses an investment portfolio (s; x). Agents
solve
max

(s;x) (0;0)

s:t:
s+x

E[V1 (s; x; )]

e;

(35)

338

Federal Reserve Bank of Richmond Economic Quarterly

where V1 (s; x; ) is the indirect utility function representing the value
the agent can obtain at date 1 if he holds investments (s; x) and receives
realization of the liquidity shock. This indirect utility function is
de…ned as follows:
V1 (s; x; ) =

max

(c1 ;c2 ) (0;0);n;b

u(c1 + c2 );

s:t:
c1 + pn + b s;
n
x;
^
c2 (x + n)R + bR;

(36)

where n represents net purchases of the long-term asset in the asset
market at date 1 and b represents expenditures on the IOUs in the
hidden retrade market. Let n( ; s; x; p) denote net demand for the
long-term asset of a type- agent.
Competitive equilibrium consists of initial investments s and x,
value functions V (s; x; ), a date-1 price p for the long-term asset, and
a gross interest rate R in the hidden retrade market such that (i) given
p and R, value functions solve (36); (ii) given V , investment choices s
and x solve (35); and (iii) the date-1 market for the long-term asset
clears, E[n( ; s; x; p)] = 0, and R is an equilibrium interest rate on the
hidden retrade market.

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