Full text of Economic Review (Federal Reserve Bank of Cleveland) : 1995 Quarter 4, Vol. 31, No. 4

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1995 Quarter 4
A Conference on Liquidity,
Monetary Policy, and
Financial Intermediation

2

by David Altig and Charles T. Carlstrom

Marriage and Earnings

10

by Christopher Cornwell and Peter Rupert

Absolute Priority Rule
Violations in Bankruptcy
by Stanley D. Longhofer and Charles T. Carlstrom

FEDERAL RESERVE BANK
OF CLEVELAND

21

1

ECONOMIC REVIEW
1995 Quarter 4
Vol. 31, No. 4

A Conference on Liquidity,
Monetary Policy, and

2

Financial Intermediation
by David Altig and Charles T. Carlstrom
In September 1994, the Federal Reserve Bank of Cleveland and the Journal
of Money, Credit, and Banking sponsored a conference aimed at facilitating research on the structural context of U.S. monetary policy. The eight
papers covered three broad topics: the macroeconomic effects of price
rigidity and limited financial market participation by households, the interaction of inflation and financial intermediation, and the “deep structural”
generation of empirically useful money measures. This article provides an
overview of the conference.

Marriage and Earnings

10

by Christopher Cornwell and Peter Rupert
That married men earn more than unmarried men is now a fairly well
established fact. However, the source of this earnings premium remains
debatable. In this paper, the authors use various econometric techniques
to shed more light on the controversy, and find that much of the observed
differential can be traced to the correlation between marital status and
some unobservable individual effects. In other words, married men who
earn more on average than single men would have earned more even if
they were not married.

Absolute Priority Rule
Violations in Bankruptcy

21

by Stanley D. Longhofer and Charles T. Carlstrom
Violations of the absolute priority rule in both private workouts and Chapter 11 reorganizations have been enigmatic for financial economists. Why
do such violations exist? Do they promote or curtail economic efficiency?
This paper demonstrates that the answers depend on the specific contracting problem that a firm and its creditors face. As a result, an optimal bankruptcy institution should allow contract participants to decide ex ante
whether such violations will occur.

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ISSN 0013-0281

2

A Conference on Liquidity,
Monetary Policy, and
Financial Intermediation
by David Altig and
Charles T. Carlstrom

Introduction
In September 1994, the Federal Reserve Bank
of Cleveland and the Journal of Money, Credit,
and Banking sponsored a conference on
liquidity, monetary policy, and financial intermediation. This symposium was the fifth in a
jointly sponsored series aimed at promoting
research on basic issues in monetary policy,
financial markets, and the payments system.
This particular conference dealt with monetary policy issues. The papers included examinations of the macroeconomic effects of price
rigidity and “sluggish” savings decisions by
households (that is, the assumption of limited
participation in financial markets), the interaction of inflation and financial intermediation,
and the “deep structural’’ estimation of parameters in models with money and financial intermediation. The common thread in all of these
studies is the attempt to move us farther down
the road to understanding the fundamental
structures that ultimately determine the economic consequences of monetary policy. A
complete list of the papers, their authors, and
the discussants is provided in box 1.
This summary of the proceedings groups the

David Altig is an economist and
vice president and Charles T.
Carlstrom is an economist at the
Federal Reserve Bank of Cleveland.

papers (somewhat artificially) according to the
type of model presented. The first group examines the general equilibrium effects of sticky
prices, the second assumes that savings, rather
than prices, are sluggish, and the third represents models of deep structural intermediation.

I. Sticky Prices
In traditional static IS-LM models with sticky
prices, a monetary expansion leads to a fall in
both nominal interest rates (the so-called liquidity effect) and real interest rates, which in turn
stimulates investment spending and hence output. These types of models have come under
attack recently on both empirical and methodological grounds. The lessons of the 1970s
taught us that, contrary to the implications of
the simplest versions of these models, high
inflation concurrent with high unemployment is
possible. However, it is generally recognized
that such models were poorly specified and
that the dynamic general equilibrium implications of price inflexibility may be much different—and empirically more plausible—than
those of earlier static sticky-price models. For
these reasons, there is a great deal of interest in

3

B O X

1

Papers Presented at the Conference
on Liquidity, Monetary Policy,
and Financial Intermediation,
September 1994
“The Effects of Real and Monetary Shocks in a Business
Cycle Model with Some Sticky Prices,” by Lee E.
Ohanian, Alan C. Stockman, and Lutz Kilian. Comment
by Christian Gilles and John V. Leahy.
“The Quantitative Analytics of the Basic Neomonetarist
Model,” by Miles S. Kimball. Comment by Michael
Woodford.
“Financial Intermediation and Monetary Policy in a General Equilibrium Banking Model,” by Pamela Labadie.
Comment by Deborah J. Lucas and Stephen D.
Williamson.
“Monetary and Financial Interactions in the Business
Cycle,” by Timothy S. Fuerst. Comment by Charles L.
Evans and Mark Gertler.
“Inside Money, Outside Money, and Short-Term Interest
Rates,” by V.V. Chari, Lawrence J. Christiano, and Martin Eichenbaum. Comment by Wilbur John Coleman II
and Julio J. Rotemberg.
“Estimating Policy-Invariant Deep Parameters in the
Financial Sector When Risk and Growth Matter,” by
William A. Barnett, Milka Kirova, and Meenakshi Pasupathy. Comment by Stephen G. Cecchetti and David A.
Marshall.
“Liquidity Effects and Transactions Technologies,” by
Michael Dotsey and Peter Ireland. Comment by Finn E.
Kydland, Donald E. Schlagenhauf, and Jeffrey Wrase.
“Computable General Equilibrium Models and Monetary
Policy Advice,” by David E. Altig, Charles T. Carlstrom,
and Kevin J. Lansing. Comment by Eric M. Leeper and
Edward C. Prescott.
SOURCE: Journal of Money, Credit, and Banking, vol. 27, no. 4, part 2
(November 1995).

examining price rigidities in dynamic general
equilibrium frameworks.
In this vein, the papers by Miles Kimball and
by Lee Ohanian, Alan Stockman, and Lutz Kilian
take as their starting point this familiar position:
Monetary policy has real effects because some
or all goods in the economy have sticky prices.

Both papers represent an attempt to construct
explicitly dynamic macroeconomic models
with less-than-perfect price flexibility, incorporating elements typically associated with simple
Keynesian analysis into relatively standard realbusiness-cycle frameworks.
In “The Effects of Real and Monetary Shocks
in a Business Cycle Model with Some Sticky
Prices,” Ohanian, Stockman, and Kilian (OSK)
adopt a simple specification for price stickiness
(dating back at least to Phelps and Taylor
[1977]) in which firms that exhibit price rigidity
preset their prices one period in advance. However, unlike the few other papers that are similarly constructed, OSK allow for both a stickyand a flexible-price sector.1 Their novel finding
is that the cyclical behavior of aggregate variables is influenced only slightly by introducing
price rigidities, even when the sticky-price sector is relatively large and despite the important
distributional consequences associated with real
and monetary shocks.
This surprising conclusion—which does not
characterize one-sector sticky-price models—
appears to arise from the assumption that the
investment sector is not subject to price rigidities. The key insight into understanding this
result is that modeling investment as a stickyprice good induces both an intratemporal and
an intertemporal distortion, the latter of which
is not present when investment is the flexibleprice good. If investment were placed in the
sticky-price sector, OSK’s results would presumably change dramatically.
In “The Quantitative Analytics of the Basic
Neomonetarist Model,” Miles Kimball maintains
the simpler one-sector setup of earlier papers.
However, unlike OSK, who assume that all
sticky prices are preset one period in advance,
his introduction of less-than-perfect price flexibility is motivated by increasing returns to
scale and imperfect competition. Like Calvo’s
(1983) model, each firm gets the opportunity to
adjust its prices at intervals determined exogenously by a Poisson process.2 One interesting
implication of this setup is that the aggregate
rate of price adjustment in general equilibrium
differs from the rate at which prices adjust for
individual firms. In fact, given Kimball’s preferred parameter values, the rate of macroeconomic price adjustment is four times that of
an individual firm. This surprising degree of
s 1 See, for example, Cooley and Hansen (1994), Cho and Cooley
(1990), and King (1990).
s 2 The Poisson distribution specifies that the probability of an opportunity to adjust prices is the same for all time intervals of equal length,
and that these probabilities are independent across any two periods.

4

persistence is potentially important, given that
the persistence in most general equilibrium
business-cycle models is very weak. (We will
return to the issue of persistence below.)
The sticky prices at the heart of the OSK and
Kimball papers are, of course, central to the
typical textbook treatment of static Keynesian
IS-LM analysis. Interestingly, it is unclear
whether the liquidity effect survives the translation of price rigidity to dynamic general equilibrium contexts. In Kimball’s model, a monetary
injection stimulates investment spending, which,
in the absence of adjustment costs, will increase
the real interest rate. Because such policies also
raise inflation expectations when money is positively serially correlated, the nominal interest
rate rises unambiguously. This conclusion can
be overturned by the introduction of adjustment
costs if prices in the economy adjust quickly
enough. However, unless the half-life for
macroeconomic price adjustments is less than
two quarters—which Kimball argues is unrealistically brief—real interest rates will increase
with monetary injections, ruling out any hope
for generating liquidity effects.
In OSK, monetary injections do temporarily
lower the real rate of interest.3 However,
based on their chosen calibration, increases in
anticipated inflation dominate these real
effects, and the nominal rate rises following a
positive monetary shock.
In light of these results, it does not appear
straightforward to construct sticky-price models
that generate liquidity effects. The key difficulty
is that prices must adjust slowly to mitigate the
expected inflation component. However, we
know from Kimball’s paper that slower price
adjustment is precisely the condition that magnifies demand effects, thus increasing investment
demand and the real rate of interest.4

II. LimitedParticipation
Models
The difficulty in generating a liquidity effect
with sticky-price models leads Kimball to conclude that “it may be necessary to model any
real-world tendency for the real (and hence the
nominal) interest rate to fall in response to a
monetary stimulus as a result of output being
temporarily off the IS curve.” In some sense, this
is essentially the strategy of the so-called limitedparticipation framework pioneered by Lucas
(1990) and Fuerst (1992). The key insight of
these papers is embedded in the assumption

that agents must adjust their portfolios slowly.
Although investment equals saving ex post, limitations on financial market transactions break the
household’s ex post intertemporal linkage, at
least temporarily. Such a break would appear to
be a necessary condition for any model to simultaneously generate a liquidity effect and a humpshaped response of consumption following a
decline in the federal funds rate, both of which
seem to characterize post–World War II data.5
In fact, a central motivation for the limitedparticipation framework is to provide a model
in which monetary injections can generate both
a liquidity effect and a temporary expansion of
output. Four of the papers in this volume—
Chari, Christiano, and Eichenbaum; Altig, Carlstrom, and Lansing; Dotsey and Ireland; and
Fuerst—can be considered studies that flesh
out the properties of models incorporating the
limited-participation device.
“Inside Money, Outside Money, and ShortTerm Interest Rates,” by V.V. Chari, Lawrence
Christiano, and Martin Eichenbaum (CCE),
attempts to impose a theoretical structure on
key monetary business-cycle regularities identified in Christiano and Eichenbaum (1992) and
Christiano, Eichenbaum, and Evans (1995). Of
particular concern is what the authors refer to
as the “sign-switch” phenomenon: Nonborrowed reserves co-vary negatively with the federal funds rate, while broader measures of
money co-vary positively.
An essential element of CCE’s model is a
careful disentangling of exogenous monetary
shocks from endogenous responses of both
the monetary authority and private intermediaries. The key identifying assumptions with respect to the monetary authority’s behavior are
that innovations in nonborrowed reserves are
associated with exogenous policy shocks, and
innovations in borrowed reserves are endogenous policy reactions to output, or technology,
shocks. Because nonborrowed-reserve innovations represent unanticipated policy changes,
s 3 Because the OSK model presets prices for one period, this result
is consistent with Kimball’s conclusion that real rates decline when prices
adjust relatively quickly.
s 4 Sticky wages do not resolve this quandary. Wages that take sufficiently long to adjust also lead to the prediction that the real interest rate
is positively related to monetary surprises. Ohanian and Stockman (1995)
provide an example of a two-sector model with price rigidity in which liquidity effects arise. However, this variant of their model does not include
capital. Again, it appears that the treatment of investment is critical in
sticky-price models.
s

5 See, for example, Christiano, Eichenbaum, and Evans (1995).

5

T A B L E 1
Correlation Properties of Money
and Output, 1954:IQ–1988:IIQ
xt + 2

xt + 1

xt

xt – 1

xt – 2

M1

0.33

0.34

0.29

0.18

0.10

Monetary base

0.37

0.39

0.34

0.26

0.20

Nonborrowed
reserves

0.10

–0.06

–0.22

–0.32

–0.34

NOTE: Entries represent the correlation of x t with outputt – k. All variables
are logged and Hodrick–Prescott filtered.
SOURCE: V.V. Chari, Lawrence J. Christiano, and Martin Eichenbaum,
“Inside Money, Outside Money, and Short-Term Interest Rates” (see box 1).

they interact with the limited-participation
assumption to generate liquidity effects.6
Broader aggregates, however, are dominated
by both the positive response of the discount
window and loan creation by financial intermediaries, thus accounting for the sign switch
that the authors wish to capture.7
The model also broadly captures some of the
simple dynamics of relationships between the
federal funds rate and various monetary aggregates found in U.S. data (see table 1). Specifically, consistent with the data, the CCE model
generates a positive correlation between the
short-term interest rate and lagged values of the
model’s analogue to M1 and the monetary base,
as well as a negative correlation with future
values. In addition, the model exhibits the observed symmetric negative correlation between
the interest rate and nonborrowed reserves.
However, the leading relationship of the funds
rate with the monetary variables is much
stronger in the data than in the model. The
authors attribute this to the offsetting influences
of real and monetary shocks, and suggest that
fully capturing these dynamics would require
either strengthening the dynamic effect of monetary shocks or reducing that of real shocks.
Contrasted with CCE, the paper by David
Altig, Charles Carlstrom, and Kevin Lansing
(ACL) maintains the less-rich intermediary
structure of earlier limited-participation models.
In “Computable General Equilibrium Models
and Monetary Policy Advice,” ACL’s innovation
involves examining the model’s short-run forecasting performance—an approach for “taking
the model to the data” that has been largely
unexplored in the context of quantitative general equilibrium analysis.8 In addition, the

setup in ACL incorporates a central-bank reaction function that involves operating on a
nominal interest-rate target, as opposed to the
standard strategy of expressing the reaction
function in terms of a monetary aggregate.
ACL’s goal is to investigate whether computable general equilibrium models have
reached the stage where they can be directly
useful to policymakers. The specific question
posed is whether variations and extensions of
fairly standard quantitative-theoretic models can
provide accurate real-time forecasts of both inflation and real GDP growth. The results of this
exercise are mixed. ACL argue that quantitativetheoretic models do appear to be capable of
delivering a reasonable degree of forecasting
accuracy: When mean-squared-error and meanabsolute-deviation metrics are used, the model’s
forecast errors with respect to inflation and output growth are comparable to those of the
internal Federal Reserve Board forecasts constructed for Federal Open Market Committee
briefings. However, to obtain inflation forecasts
that are at least as good as Board staff projections, ACL make an ad hoc, “judgmental” adjustment to their model.9
As in the CCE paper, the failures in ACL
provide some clues about the direction that
limited-participation models must take to deliver a fully satisfactory empirical performance.
For example, the problem with the nonjudgmental ACL model shows up clearly in its inflation forecasts for 1993. Over the course of that
year, the federal funds rate and inflation both

s 6 Some additional persistence is built into the model by assuming
that interperiod portfolio adjustment is costly, in contrast to the solely oneperiod sluggishness built into the Fuerst (1992) model.
s 7 The identifying assumptions in CCE are somewhat stronger than
those imposed in either Christiano and Eichenbaum (1992) or Christiano,
Eichenbaum, and Evans (1995), in that these papers do not assume that
nonborrowed-reserve innovations are entirely exogenous to current technology shocks. This difference is likely to be important: The CCE model
counterfactually predicts a positive contemporaneous correlation between
nonborrowed reserves and output. As the authors point out, the observed
negative correlation could presumably be generated by incorporating a
reaction function in which the monetary authority “leans against the wind.”
Whether such a model would continue to exhibit the sign-switch property
is an open question.
s 8 See, however, Rotemberg (1994), which measures model performance in terms of the correlations among long-run forecastable movements of prices, output, and the monetary aggregates.
s 9 The ACL model treats deviations of the federal funds rate as
exogenous inputs in simulating the path of inflation and output. Their
judgmental adjustment amounts to replacing the deviation of the nominal
federal funds rate from a constant mean (or the long-run value) with the
deviation from a “moving” mean, measured as a moving average of past
federal fund rates.

6

F I G U R E 1
Federal Funds Rate and Inflation,
1982:IVQ–1994:IQ

a. Average daily rate on overnight fed funds as reported by the Federal
Reserve Bank of New York.
b. Four-quarter percent change in the Consumer Price Index.
SOURCES: U.S. Department of Labor, Bureau of Labor Statistics; and Board
of Governors of the Federal Reserve System.

stabilized near 3 percent, implying inflationadjusted real rates near zero (see figure 1).
Given the calibration of the model, the ACL
framework delivers a long-run real interest rate
of 3 percent. In the absence of persistence in
real interest rates, or perhaps more extensive
monetary non-neutralities than those delivered
by a one-quarter limited-participation assumption, the only way to support a sustained 3 percent nominal funds rate is for monetary policy
to engineer an expected inflation of approximately zero. But such an outcome is clearly
inconsistent with the data, since it is unreasonable to believe that agents would have rationally expected zero inflation during that period.
ACL argue that the failure of their model is
actually a failure present in most general equilibrium models; that is, most existing frameworks do not deliver the type of persistence in
real variables that is found in the data.10 In
“Monetary and Financial Interactions in the
Business Cycle,” Timothy Fuerst examines this
issue by investigating whether adding more
extensive non-neutralities arising from financial
markets can generate more serial correlation in
real variables than does a standard model. In
particular, he looks at whether persistence can
be introduced by adding a financial structure
that gives rise to countercyclical endogenous
agency costs.
The basic idea of the Fuerst framework is to
build in frictions similar to those discussed by
Bernanke and Gertler (1989). Entrepreneurs
live for one period and work to receive a wage

income. They then use this income, along with
additional funds borrowed from households, to
produce capital. Individual entrepreneurs can
costlessly observe how much capital they produce, but other agents must expend a resource
cost to monitor the project’s outcome. This
agency problem leads to a standard debt contract and reduces the amount of investment
(and thus capital accumulation) in equilibrium.
The idea is that a positive technology shock
today will increase an entrepreneur’s net worth
or wage income, which will mitigate agency
costs and boost capital accumulation. The
hope is that this extra capital will lead to
greater persistence.
Fuerst finds that the amount of persistence
generated by his experiments is nearly identical
to that of standard quantitative business-cycle
models. The reason is that his method of introducing agency costs leaves capital as the only
method of propagating shocks across time. The
failure is thus another illustration that capital
adds little to the serial correlation properties of
the standard quantitative business-cycle model.
Although Fuerst’s model does exhibit a small
propagation effect on net worth through the
capital channel, his setup is fundamentally
unable to generate persistent movements in net
worth because entrepreneurs are assumed to
live for only one period. However, allowing
entrepreneurs to live for many periods opens
up the possibility of a repeated game between
households and entrepreneurs as well as an
immense amount of potential heterogeneity,
implying that straightforward extensions of
Fuerst’s model are nontrivial.11
A skeptical view of the limited-participation
framework is provided by Michael Dotsey and
Peter Ireland. In “Liquidity Effects and Transactions Technologies,” they note the ad hoc oneperiod adjustment cost formulation in both ACL
and Fuerst, and similarly criticize CCE’s use of
a more general adjustment cost formulation
without proper calibration of the magnitude of
these costs. Like CCE’s model, Dotsey and
Ireland’s considers a financial intermediation
structure that implies a spread between the

s 10 This idea is not new. For example, Cogley and Nason (1995)
argue that persistence in most quantitative business cycle models is
completely inherited from the exogenous shock process, which is
assumed to be serially correlated. See Boldrin, Christiano, and Fisher
(1995) for a recent attempt to build a framework that directly tackles this
issue in the context of resolving asset-pricing puzzles that arise in standard business cycle models.
s 11 See Carlstrom and Fuerst (1996) for an extension of Fuerst’s
model that includes entrepreneurs who live for multiple periods.

7

deposit rate paid to households and the loan
rate charged by intermediaries. Although less
rich in detail than the CCE model, the Dotsey/
Ireland framework expands the basic limitedparticipation setup by introducing explicit representations of the costs of adjusting both
household and intermediary portfolios. The
central question they address is whether the
liquidity effects generated by existing limitedparticipation models survive the introduction of
12
plausible specifications for such costs.
The challenging aspect of this exercise is to
calibrate the relevant adjustment cost functions. Dotsey and Ireland do so by capitalizing
on the fact that their model delivers a wedge
between loan and deposit rates that is dependent on the parameters of the representative
intermediary’s adjustment cost function.13 The
model is explicitly connected to the data by
associating loan rates with commercial paper
rates, and deposit rates with the return on
small time deposits.
Unfortunately, it is not possible to calibrate
directly to the spread itself, since generating the
observed average differential would require
introducing fixed marginal costs to loan production, which are themselves unobservable.
The authors’ provocative solution is to calibrate
to the standard deviation of the difference
between commercial-paper and time-deposit
rates. This does not, however, pin down the
key parameter in the household’s cost function.
Dotsey and Ireland proceed by assuming that
household costs are a simple multiple of the
costs to a financial intermediary.
The bottom line of the Dotsey/Ireland
experiments is that the liquidity effects which
motivate the limited-participation framework
are not easily preserved when the assumption
of infinite transaction costs is relaxed. Given
their parameterization, they find that liquidity
effects of the magnitude reported by, say,
Christiano and Eichenbaum (1992), require
household transaction costs that are roughly
seven times as large as intermediaries’ costs.
This corresponds to about 123 minutes of forgone leisure per quarter.

III. Deep
Structural
Intermediation
Dotsey and Ireland conclude that their results
militate for research efforts that return to “... the
more careful methodology of building financial
structure from microfoundations ....” Such
efforts are represented in the papers by Pamela

Labadie and by William Barnett, Milka Kirova,
and Meenakshi Pasupathy.
The Labadie study, “Financial Intermediation
and Monetary Policy in a General Equilibrium
Banking Model,” contains a detailed model
with many salient features of the U.S. financial
sector. Banks, for example, are subject to
reserve requirements, hold assets that consist of
loans (to both the private and public sectors)
and equity capital, and have access to deposit
insurance. Furthermore, the model contains a
government sector that operates much like the
Federal Reserve in that it sets reserve requirements, supplies deposit insurance, and conducts open-market operations that alter the
aggregate ratio of bonds to money.
The Labadie framework incorporates several
features typically associated with monetary nonneutrality. These include informational asymmetries that make intermediation costly, and
household assets (deposits) with fixed nominal
returns. Despite these elements, Labadie reports
the surprising result that monetary policy actions which alter the size and composition of
nominal assets are entirely neutral. Although
she finds that non-neutralities appear in cases
where monitoring costs are fixed in nominal
terms, it is unclear how such a device should
be interpreted.
It is apparent that some other special features of Labadie’s model contribute to this
result. Banks, for instance, write optimal statecontingent loan contracts that are expressed in
real terms. Also, household saving consists
solely of bank deposits and bank equity. Thus,
it appears that any redistribution of wealth
caused by the effects of unanticipated price
changes on real deposit returns are rechanneled to the affected agents via changes in the
market value of equity claims. Disentangling
this and the many other elements of her very
rich model could provide considerable insight
into how the regulatory environment and financial market structure interact and what the consequences are for the macroeconomy.

s 12 The standard model in this class assumes (at least implicitly)
that intraperiod adjustment costs are infinite.
s 13 The model’s cost functions — which depend on the ratio of
deposits to money — are quadratic, so that the spread is proportional to
the function’s sole parameter. Although both the CCE and Dotsey/Ireland
models generate deposit-to-loan-rate spreads, they arise from very different sources. The spread in CCE results from a combination of reserve
requirements and the contribution of excess reserves in the representative
intermediary’s production function.

8

As in almost all of the papers presented at
the conference, the Labadie model takes the
measurement of money as a given. In studies
where models are taken to the actual data,
money is assumed to correspond to some standard monetary aggregate. An exception is the
article by Barnett, Kirova, and Pasupathy
(BKP), who explore a methodology to construct money from the fundamental problems
solved by economic actors in a well-defined,
explicit economic environment.
In “Estimating Policy-Invariant Deep Parameters in the Financial Sector When Risk and
Growth Matter,” BKP start from the perspective
of the well-known Lucas critique; that is, sensible experiments involving policy simulations
require knowledge of the functions describing
private decision rules that are invariant to the
class of policy interventions being considered.
However, the authors, appealing to insights
from Barnett’s earlier work, take the argument
one step further: Experiments involving policy
simulations also require knowledge of the
policy-invariant aggregator functions describing
14
the theoretical monetary aggregates.
The strategy in BKP is to jointly estimate the
deep parameters of preferences and technologies—including the parameters of the relevant
aggregator functions—from Euler-equation representations of the optimization problems of
financial intermediaries, manufacturing firms,
and households. Upon obtaining these estimates, the authors compare the implied theoretical aggregates from the separate sectors with
the corresponding Divisia indexes and simplesum aggregates. They argue that the Divisia
indexes do a relatively good job of tracking
their theoretical money measures, and that
simple-sum aggregates—the class of which contains all the typical monetary aggregates used in
the other papers—do substantially worse.
BKP’s critique of the standard approach to
measuring monetary assets is a serious challenge to anyone interested in the empirical
relationship between money and the macroeconomy. In describing their methodology,
BKP write:
The purpose of all scientific research is to
reveal the truth, not to alter the data in a manner that may tend to justify some preconceived policy view. The purpose of data is to
measure something that exists, i.e., an aggregator function that is separable within the
structure of the economy. (p. 1405)

s

14 See Barnett (1987), Barnett, Fisher, and Serletis (1992),
and Barnett and Hahm (1994).

Contrast this view with the position taken by
Friedman and Schwartz (1970):
... the definition of money is to be sought for
not on the grounds of principle but on
grounds of usefulness in organizing our
knowledge of economic relationships.
“Money” is that to which we choose to assign
a number by specified operations; it is not
something in existence to be discovered, like
the American continent .... (p. 137)

Determining which of these views is correct
has fundamental implications for the organization and development of monetary facts and,
ultimately, for the conduct of monetary policy.

IV. Summary
Each paper presented at the conference investigates at least one piece of the puzzle that
must be solved if policymakers are to use
dynamic general equilibrium models for giving
policy advice. OSK and Kimball both provide a
cautionary note by showing that the implications of sticky prices may not be as apparent
as many economists think. For instance, it is
inherently very difficult for this assumption to
deliver a liquidity effect—something that most
policymakers take for granted. Although the
limited-participation (or sluggish-portfolio)
assumption was invented to specifically generate inverse movements in money shocks and
nominal interest rates, Dotsey and Ireland
question whether portfolio costs, when properly calibrated, are large enough to deliver the
desired effect.
Similarly, when a fairly standard computable
general equilibrium model is actually taken to
the data and used for forecasting purposes,
ACL conclude that existing models need either
more extensive monetary non-neutralities or
some other added friction in order to generate
the persistence in real variables that characterizes the data. Yet the message of Labadie’s
paper is that adding frictions is not always sufficient to generate monetary non-neutralities,
let alone ones that have lasting effects on the
real economy.
These unanswered questions clearly leave
researchers with much work to do before
dynamic general equilibrium models supplant
static IS-LM models for policymakers, as they
have for most academic economists.
NOTE: To order a copy of these conference
proceedings, see page 32.

9

Additional References
Barnett,W.A. “The Microeconomic Theory of
Monetary Aggregation,” in W.A. Barnett and
K.J. Singleton, eds., New Approaches to Monetary Economics. Cambridge: Cambridge
University Press, 1987, pp. 115–68.
_________, D. Fisher, and A. Serletis. “Consumer Theory and the Demand for Money,”
Journal of Economic Literature, vol. 30, no. 4
(December 1992), pp. 2086–119.
________, and J. H. Hahm. “Financial-Firm Production of Monetary Services: A Generalized
Symmetric Barnett Variable-Profit-Function
Approach,” Journal of Business and Economic Statistics, vol. 12, no. 1 (January
1994), pp. 33–46.
Bernanke, B., and M. Gertler. “Agency Costs,
Net Worth, and Business Fluctuations,”
American Economic Review, vol. 79, no. 1
(March 1989), pp. 14–31.
Boldrin, M., L.J. Christiano, and J.D.M. Fisher.
“Asset Pricing Lessons for Modeling Business
Cycles,” Federal Reserve Bank of Minneapolis, Working Paper 560, November 1995.
Calvo, G.A. “Staggered Prices in a UtilityMaximizing Framework,” Journal of Monetary Economics, vol. 12, no. 3 (September
1983), pp. 383–98.
Carlstrom, C.T., and T.S. Fuerst. “Agency Costs,
Net Worth, and Business Fluctuations: A
Computable General Equilibrium Analysis,”
Federal Reserve Bank of Cleveland, working
paper, 1996, forthcoming.
Cho, J-O., and T. Cooley. “The Business Cycle
with Nominal Contracts,” Rochester Center
for Economic Research, Working Paper No.
260, Rochester, N.Y., December 1990.
Christiano, L.J., and M. Eichenbaum. “Identification and the Liquidity Effects of a Monetary Shock,” in A. Cukierman, L.Z. Hercowitz, and L. Leiderman, eds., Political
Economy, Growth, and Business Cycles.
Cambridge, Mass.: MIT Press, 1992.
________ , ________ , and C. Evans. “What
Happens after a Monetary Policy Shock?”
Review of Economics and Statistics, 1995,
forthcoming.

Cogley,T., and J.M. Nason. “Output Dynamics
in Real-Business-Cycle Models,” American
Economic Review, vol. 85, no. 3 (June 1995),
pp. 492–511.
Cooley,T., and G. Hansen. “Money and the
Business Cycle,” in T.C. Cooley, ed., Frontiers of Business Cycle Research. Princeton
University Press, 1994, pp. 175–216.
Friedman, M., and A. Schwartz. Monetary Statistics of the United States. Cambridge, Mass.:
National Bureau of Economic Research,
1970.
Fuerst,T.S. “Liquidity, Loanable Funds, and
Real Activity,” Journal of Monetary Economics, vol. 29, no. 1 (February 1992), pp. 3–24.
King, R. “Money and Business Cycles,” University of Rochester, Working Paper, Rochester,
N.Y., October 1990.
Lucas, R.E., Jr. “Liquidity and Interest Rates,”
Journal of Economic Theory, vol. 50, no. 2
(April 1990), pp. 237–64.
Ohanian, L.E., and A.C. Stockman. “Theoretical
Issues of Liquidity Effects,” Federal Reserve
Bank of St. Louis, Review, vol. 77, no. 3
(May/June 1995), pp. 3–25.
Phelps, E.S., and J.B.Taylor. “Stabilizing Powers
of Monetary Policy under Rational Expectations,” Journal of Political Economy, vol. 85,
no. 1 (February 1977), pp. 163–90.
Rotemberg, J. J. “Prices, Output, and Hours: An
Empirical Analysis Based on a Sticky Price
Model,” Cambridge, Mass: MIT Press, 1994.

10

Marriage and Earnings
by Christopher Cornwell
and Peter Rupert

Introduction
Uncovering the determinants of earnings is an
important and well-researched area in labor
economics. In studies of race or sex discrimination, it is imperative to use statistical methods
that control for various factors so that the
researcher can obtain an unbiased measure of
discrimination. Another area that has attracted
interest is the interaction of wages and union
membership. Again, controlling for certain factors enhances our understanding of how unions
affect wages. Of course, knowing exactly what
to control for is at the heart of the problem. In
this paper, we examine one particular control
variable that is often used in earnings regressions—an indivdual’s marital status. In analyzing and interpreting the results obtained from
earnings regressions, we hope to develop a better measure of how any policy affects (or does
not affect) individual behavior.
The wage premium attributable to marriage
has been well documented in the literature and
is typically as large as that associated with union
status. The source of this premium, however,
remains debatable. Two common explanations
of why married men earn more than unmarried
men are 1) the division of labor in a married

Christopher Cornwell is an associate professor of economics at
the University of Georgia, Athens,
and Peter Rupert is an economic
advisor at the Federal Reserve
Bank of Cleveland.

household allocates more of the man’s time to
the market,1 and 2) married men have a lower
cost of human capital acquisition, since a
spouse may be working to help finance the
additional human capital.2 Both of these stories
imply that marriage enhances productivity, and
therefore wages, as a result of an increase in
human capital. We suggest an alternative explanation for the marriage premium, derived from
the job-matching literature, in which marriage
signals certain unobservable individual characteristics that are valued by employers—including ability, honesty, loyalty, dependability, and

s 1 As evidence that married men are relatively more market intensive,
it is often noted that they work more hours. For example, in the sample we
draw from the 1971 wave of the National Longitudinal Survey of Young
Men (NLSYM), mean hours per week for married men is 44.17, versus
41.28 for unmarried men. However, after age 22, the mean hours differential drops to less than one hour per week.
s 2 Some evidence that marriage facilitates human capital acquisition
is provided by Kenny (1983), but the potential endogeneity of an individual’s marital status is ignored. Furthermore, the argument that marriage
makes it cheaper to accumulate human capital is difficult to reconcile with
the fact that men who acquire more formal education tend to marry later
than those who acquire less (Bergstrom and Schoeni [1992]).

11

determination.3 Failure to control for the correlation of the fixed effects with marriage will lead
to a bias in the marital status coefficient. That is,
some of the returns attributable to marriage will
actually be returns to some unobserved qualities
correlated with marital status.
Under either of the above scenarios, marital
status should not be treated as an exogenous
determinant of the wage rate. However, it is
assumed to be exogenous in most wage regressions that control for marital status, resulting in an estimated marriage premium that is
biased upward.
In this paper, we reexamine the empirical
relationship between marriage and wages. Our
investigation proceeds along two lines. First, to
the extent we can model the process that determines marriage, our cross-section procedures
attempt to capture the kind of incentives that
the human capital stories imply for the marriage
premium. Second, we employ panel data estimation techniques that allow us to control for
unobservable individual-specific effects that
may be correlated with marital status. If we
interpret these individual effects as ability—
or as any of the qualities listed above that may
lead to better job matches — then panel data
estimation addresses a different source of endogeneity than that arising from the human capital arguments.
The clearest picture of the effects of marriage on wages emerges in our panel estimates.
In every case where we condition on unobserved individual effects, the estimated marital
status coefficient is essentially zero. We argue
that these results support the view of marriage
as a “signal’’ of some underlying characteristics.
Furthermore, specification tests confirm the
importance of unobserved heterogeneity and
reject the exogeneity of marital status.

I. Marriage,
Wages, and
Individual
Effects
Virtually all cross-section wage regressions that
control for marital status report a large, statistically significant wage premium for married
men. Some of the more prominent examples
are discussed by Reed and Harford (1989) and
Korenman and Neumark (1991). Our view is
that the marriage premium commonly reported
in cross-section wage regressions is largely a
statistical artifact, at least for young men. The
wage premium can be explained in terms of
unobservable individual characteristics that are

positively correlated with marriage and wages.
The characteristics that lead to “good’’ (long
and stable) marriages are the same characteristics that produce “good’’ (long and stable) jobs
and higher wages.
This view has some additional support from
another strand of the literature relating to the
returns to job tenure. Abraham and Farber
(1987) propose that workers in long-tenure jobs
earn more in every year on the job, and that
most of the cross-section return to tenure is due
to unobserved individual and job-match effects.
They test their proposition by estimating wage
equations conditional on predicted job duration. Interestingly, the results of their job duration model indicate that marriage has a large
and positive statistically significant effect.
Further evidence exists in the quit behavior
of married men. Consistent with the positive
relationship between marriage and job duration
is the depressing effect marriage has on quits.
Shaw (1987) reports that the quit rate for married men aged 25–54 is less than half that of
unmarried men. He also finds that marriage has
its strongest deterrent effect on the quit behavior of younger men.
Only Nakosteen and Zimmer (1987) argue
explicitly that marriage does not significantly
affect wages. However, the empirical support
for their argument is weak. Using a crosssection of 576 employed men between the ages
of 18 and 24, taken from the 1977 wave of the
Panel Study of Income Dynamics (PSID), they
estimate an earnings equation in which marriage is modeled as a treatment effect, thereby
making marital status endogenous.4 When they
restrict marital status to be exogenous and apply
ordinary least squares (OLS) to their wage equation, Nakosteen and Zimmer obtain a statistically significant marital status coefficient estimate
of 0.370. Relaxing the exogeneity restriction
actually causes this coefficient estimate to rise,
although it is no longer statistically significant.
Furthermore, specification tests of exogeneity
are inconclusive. Nevertheless, Nakosteen and
Zimmer find that the true marriage premium is
not significantly different from zero.

s 3 Reed and Harford (1989) provide another alternative—that the
marriage premium represents a compensating differential required to induce married men to accept “undesirable’’ working conditions. In their
view, marriage is related to the purchase of costly “family goods’’ such
as children.
s 4 See Barnow, Cain, and Goldberger (1980) for an explanation of
treatment effect models.

12

Korenman and Neumark, whose results are
based on the 1976, 1978, and 1980 waves of
the NLSYM, take the opposite stance. They
claim that the gains to marriage are large for
young (white) men, even after controlling for
unobserved heterogeneity. In their preferred
specification, years married and its square are
included in the wage equation, along with the
marital status dummy. Marriage premiums are
derived from both cross-section and fixed
effects (“within’’) estimates. The marriage premium at mean years married, calculated from
the fixed effects estimates, is 15 percent, which
is about 20 percent smaller than the premium
yielded by their cross-section estimates.
However, the large gains to marriage reported by Korenman and Neumark may be misleading. First, only the estimated years-married
coefficients are statistically significant. This is
true in both their cross-section and fixed effects
regressions. Thus, more than one-fifth of these
premiums are due to shift-parameter estimates
that are not significantly different from zero.
Second, when we include years married and
its square along with tenure and its square in
our sample, the former never enters statistically
significantly, while the latter always does.
Because married men hold longer jobs (experience less turnover), years married may be playing a role similar to tenure in the Korenman/
Neumark regressions.
Third, Korenman and Neumark’s results
suggest that each additional year of marriage
translates into a 1 to 2 percent wage gain. As
indicated by Bergstrom and Schoeni (1992),
this implies that men who married at age 17
should earn 10 to 20 percent more at age 40
than men who married at age 27, all else equal.
However, their results show that, controlling
for current age, men who married at 17 make
25 percent less on average than men who married at 27.5 Finally, Cornwell and Rupert (1996)
demonstrate that adding another year (1971) to
the Korenman/Neumark sample changes the
results substantially. This change can be attributed to the fact that most of the marital status
changes in their sample represent individuals
who are either leaving or entering marriage for
the second time.6

to derive a consensus regarding the contribution of marital status to earnings.
We begin with a general model of wage
determination for married (M ) and single (S )
men, where the wage-generating process is initially assumed to be different for each type:7
(1)

M
M
y it ϭ ␦ M ϩ X M´ ␤M ϩ u it
it

(2)

S
S´
S
y it ϭ ␦ S ϩ X it ␤S ϩ u it ,

where i indexes individuals (i = 1, ... , N ) and
t indexes time periods (t = 1, ... T ), y it is the
natural logarithm of the real wage, X it is a vector of explanatory variables, and the u it ’s are
disturbances with time-invariant and timevarying components, expressed as
(3)

M
u it ϭ ␣ M ϩ ⑀ M
i
it

(4)

S
S
u it ϭ ␣iS ϩ ⑀ it .

The ␣i ’s, which vary over individuals but not
over time, capture unobserved, individualspecific attributes that may be valued in both
the labor and marriage markets. The ⑀it ’s,
which vary over individuals and time, reflect
aspects of the wage-determining process that
can be represented as statistical noise.
In our sample, we cannot reject the null
hypothesis that ␤ M = ␤ S.8 Thus, we express the
model given in equations (1)–(4) in terms of a
single wage equation,
(5)

yit ϭ ␦ S ϩ Xit ␤ ϩ (␦ M – ␦ S ) Mit ϩ ␩it ,
¢

where
(6)

S
M
S
␩it ϭ uit ϩ (u it – u it ) Mit

and Mit is a dummy variable indicating marital
status.
s 5 Bergstrom and Schoeni point out that to reconcile these results,
one would have to argue that if men who married at 27 had married at 17,
they would have earned 35 to 40 percent more per year than men who
actually did marry at 17.

II. Econometric
Framework

s 6 By appending the additional (earlier) year to the Korenman/
Neumark data set, we can look at the earnings of younger men or, more
specifically, at the earnings of men who have never been married. The evidence suggests that to the extent there is a gain to marital status, it is purely
an intercept shift, with no additional effect attributed to the number of years
married.

Our econometric methodology addresses the

s 7 Our approach is similar to that employed by Robinson (1989) in
his analysis of union wage effects.

possibility of marital status endogeneity in a
variety of ways. Each of the techniques has
shortcomings as well as merits. Therefore, we
cover a wide range of procedures and attempt

s 8 The value of the F -statistic from a comparison of regressions of
married and single men over the two periods covered in our data set is
only 0.75, and the 95 percent critical value is about 2.8.

13

If the correlation between marriage and the
error term is zero (that is, E [M it h it ] = 0), then
treating (5) as a standard cross-section wage
regression and estimating by OLS produces a
consistent estimate of the marriage premium,
(dM – dS ). However, for reasons outlined in the
previous section, this is not likely to be the
case. Thus, in general, the marriage premium
cannot be identified by OLS.
Since Mit is unlikely to be orthogonal to
hit , identification of the marriage premium is
problematic. The difficulty is that the wage differential comprises two terms: (dM – dS ) and
S
(u M – u it ). The first term is fixed and the same
it
for all men. If men are randomly distributed
across married and single states, then this term
represents the true wage premium. Even if
assignment across married and single states is
random, however, standard cross-section estimation may still be inappropriate. If the source
of endogeneity of Mit is unobserved individual
attributes that are valued by employers as well
as potential marriage partners, then consistent
estimation would imply conditioning on the
ai ’s. Panel data are important in this regard, a
point that we elaborate on below.
If assignment to the married and single states
is not random, then identification of the true
wage premium is complicated by the second
term, (u M – u S ). In this case, the expected
it
it
increase in the wage rate as a result of marriage
M
is (dM – dS ) + E [(u it – u S )|Mit = 1]. Separate
it
identification of (dM – dS ) requires additional
restrictions on our model so that the process
generating marital status can be parameterized.
The restrictions may involve orthogonality conditions that define a set of exogenous variables
for marital status, or distributional assumptions
like bivariate normality of yit and Mit . The validity of such restrictions is an empirical question.
Imposing them when they are empirically invalid is a misspecification, the statistical consequences of which may be less acceptable than
the failure to control for nonrandom assignment.

Alternative
Estimators and
Specification Tests
We consider three different approaches to estimating the effect of marriage on wages: instrumental variables (IV), the inverse Mills ratio
(IMR) method, and methods that exploit the
availability of panel data. Each approach
imposes a different set of restrictions on the

model. The choice of which approach to use is
determined largely by whether the restrictions
can be justified.
The appeal of both the IV and IMR methods
hinges on the ability to specify the process governing marital status.9 Let the reduced form for
this process be expressed as
(7)

Mit ϭ Zit ␥ ϩ vit ,
*
¢

*
where M it is a latent index representing the
net gain to marriage, Zit is a vector of explanatory variables that includes Xit, and vit is a zero
mean disturbance with variance s 2 . We obv
*
serve only a discrete realization of M it, which
we define as the dummy variable Mit . Note that
*
*
Mit = 1 if Mit Ͼ 0, and Mit = 0 if Mit Յ 0.

Instrumental
Variables
The IV procedure exploits the orthogonality
condition
(8)

E [g(Zit )␩it ] ϭ 0,

where Zit contains at least one regressor not in
Xit, and g is some known transformation of Zit.
The set of restrictions in (8) are used in (7) to
construct an instrumental variable for Mit that
has been purged of correlation with hit . No
distributional assumption about the vit ’s is necessary, although one may be imposed. For example, if the vit ’s are independently and identically distributed (i.i.d.) standard normal and are
independent of Zit, then (7) can be estimated
by probit maximum likelihood. The resulting
ˆ
instrument for Mit would be M it = F (–Zit g),
¢ˆ
where F is the standard normal cumulative distribution function. In any case, the instrumental
variable is inserted in a least squares regression
ˆ
of yit on (Xit, Mit ), and the estimated coefficient
ˆ
of Mit is taken to be the measure of the effect
of marriage on wages. However, if the condition
in (8) is violated, the IV estimate of the marriage
premium will not be consistent. Assuming (8)
holds, the IV estimator provides a natural contrast to OLS, thereby providing a Wu–Hausmantype test of the exogeneity of marital status (see
Wu [1973] and Hausman [1978]).

s 9 A detailed discussion of these methods is provided by Heckman
and Robb (1985).

14

Inverse
Mills Ratio

same impact on wages regardless of whether
an individual is married or single (Robinson
[1989]). Then, (6) becomes

The IMR method addresses the endogeneity of
marital status in the context of the nonlinear
regression function
(9)

E (yit |Zit , Mit ) ϭ dS ϩ Xit¢ ␤ ϩ (d M – dS )Mit
ϩ ␰h(Zit , Mit ; g),

where
(10) h (Z it , M it ; g) ϭ Mit E(hit|Zit , Mit ϭ 1)
ϩ (1 – Mit )E(hit|Zit , Mit ϭ 0),
2
␰ = s h v /sv , and shv = cov(h, v). Note that h
comprises the relevant inverse Mills ratios. If
the vit ’s are assumed to be i.i.d. standard normal, then the inverse Mills ratios are, respectively, j/F and –j/(1 – F), where j is the standard normal probability density function, and
both j and F are evaluated at –Z it g.
¢
This method is designed to correct for the
self-selection of individuals into marriage; that
is, it accounts for whether there is something
different about individuals who marry versus
those who do not. Estimation of (9) can be accomplished through a simple two-step procedure. First, probit maximum likelihood is applied to (7) to obtain an estimate of g, which is
ˆ
ˆ
used to construct h (Zit,Mit ; g). Then, h is subˆ
stituted for h in (9), and the resulting regression
is estimated by least squares.10 The statistical
ˆ
significance of h in this regression provides
another test of the exogeneity of marital status.
Consistency of the IMR method also depends on whether (8) is satisfied, as well as on
knowledge of the functional form of h. In
a given empirical application, the IMR method
may not be robust to departure from the
functional-form assumption (say, normality).
Another problem is that the inverse Mills ratios
may simply be proxying for omitted nonlinearities, in which case interpretation as a correction for self-selection becomes difficult.

(11) yit ϭ dS ϩ Xit ␤ ϩ (d M – dS )Mit ϩ ai ϩ eit .
¢
Finally, assume that the ai ’s and eit ’s are i.i.d.
random variables, uncorrelated with each
other, with zero means and constant variances
2
2
␴ a and ␴e.
In a standard human capital wage equation,
it is likely that E (X it ai ) 0, since X it typically
¢
contains measures of education, work experience, and job tenure that are correlated with
unobserved ability reflected in the ai ’s. Furthermore, because men with large amounts of
human capital are more attractive as potential
spouses, it is likely that Xit and Mit are correlated. Hence, attempts to estimate the effect of
marriage on wages should go beyond correction for self-selection per se.

The “Within”
Estimator
The simplest procedure for consistently estimating (11) is the so-called within estimator, which
is calculated by applying least squares to data
that have been transformed into deviations
from individual means. Since the a i ’s are
treated as fixed parameters, the within estimator is consistent regardless of the relationship
between (X it , Mit ) and ai. Alternatively, the
¢
within estimator can be viewed as an instrumental variables estimator, with the instruments
being the deviations from the means, which are
orthogonal to the ai ’s by construction.
Of course, if the ai ’s are uncorrelated with
(X it , Mit ), more efficient estimation of (11) is
¢
possible via generalized least squares (GLS).
Like the within estimator, GLS can also be computed from a least squares regression on transformed data. In this case, the transformation is
to “whiten’’ the errors.11 Another advantage of
panel data is that this proposition can be tested.
The efficiency of GLS under the null hypothesis

Panel Data
With panel data, alternative estimators to the
cross-section approaches of IV and IMR exist.
M
S
For convenience, assume that u it = u it
i.
This will have no adverse statistical consequences if 1) men have only the same knowledge as the econometrician regarding their eit ’s,
but have exclusive knowledge of their ai ’s, and
2) men’s unobservable characteristics have the

s 10 Other estimation strategies include direct nonlinear least squares
estimation of (9) and maximum likelihood. To estimate by maximum likelihood, one must be willing to assume that (␩, ␯) is distributed bivariate
normal. See Barnow, Cain, and Goldberger (1980) and Heckman and Robb
(1985) for details.
s 11 This transformation follows from Fuller and Battese (1973) and
amounts to a “(1 – ␪) differencing’’ of the data, where
2
2
2
␪ = [␴ ⑀ / (␴ ⑀ + T␴ ␣ )] 1/2.

15

T A B L E

1

Means and Standard Deviations
by Year, and Percent of Sample
Changing Marital Status
1971
Cross
Section

1971
Panel

1976
Panel

1.122
(0.438)
0.718
(0.450)
23.96
(3.18)
3.209
(2.532)
0.314
(0.464)
0.360
(0.480)
0.679
(0.467)
12.738
(2.519)
0.141
(0.348)
1,073

1.179
(0.437)
0.716
(0.451)
24.00
(3.18)
3.321
(2.551)
0.326
(0.469)
0.367
(0.482)
0.687
(0.464)
12.802
(2.467)
0.149
(0.356)
860

1.399
(0.414)
0.895
(0.306)
29.00
(3.18)
6.197
(4.032)
0.342
(0.475)
0.379
(0.485)
0.688
(0.463)
13.321
(2.620)
0.149
(0.356)
860

Variable

LOG REAL WAGE
MARITAL STATUS
AGE
TENURE
UNION
SOUTH
SMSA
EDUCATION
RACE
No. of observations
Marital Status Changers
Frequency
Percent of observations

Never Married
to Married

Married to
Not Married

197
22.9

43
5.0

NOTE: Standard errors are in parentheses.
SOURCE: National Longitudinal Survey of Young Men.

that E [(X i t , M it )ai ] = 0, along with the robust¢
ness of the within estimator to departures from
the null, form the basis of a Wu–Hausman test
of the difference between the GLS and within
estimates of (11).

The Hausman–
Taylor Estimator
A consistent and potentially more efficient alternative to the within estimator is Hausman and
Taylor’s (1981) efficient instrumental variables
procedure (HT-IV).12 HT-IV exploits knowledge of the uncorrelatedness of certain columns of X¢ with ai to increase the instrument
it
set beyond that of the within estimator.13 Computation involves an IV regression on the same
data transformation required for GLS. Thus,
the efficiency gains to HT-IV come from an expanded instrument set and whitened errors.

More efficient estimation of the parameters
of (11) is one motivation for considering HT-IV.
Another is that HT-IV permits a direct test of
the uncorrelatedness of M it with a i . The GLS/
within contrast does not indicate which explanatory variables are correlated with the effects if
the null is rejected. However, using a Wu–
Hausman test of the difference between HT-IV
estimates that maintain a legitimate set of overidentifying restrictions with HT-IV estimates that
take M it to be exogenous, we can determine
whether marital status is in fact exogenous.
Note that both the within and HT-IV estimators are distinguished from the cross-section procedures, which depend on over-identifying
restrictions like those defined in (8) and/or on
special distributional assumptions. In addition,
within and HT-IV allow consideration of another
source of nonidentifiability of the marriage premium that is not addressed by the cross-section
approaches, namely, correlation between
Xit and the effects. Consistent estimation of
(dM – dS ) is not possible if E (X i¢t ai ) 0, unless
Xit is orthogonal to Mit, even if E (Mit ai ) = 0.

III. Estimation of the
Marriage Premium
Data
Our data are drawn from the 1971 and 1976
waves of the NLSYM. The primary advantage of
the NLSYM is that it allows us to follow individuals moving from the single (and not previously married) to the married state. Between
1971 and 1976, roughly 23 percent of the
young men in our sample went from never
married to married, while only about 5 percent
were divorced or separated. The 1971 crosssection data set consists of 1,073 young men
who were between the ages of 19 and 29 in
1971 and who worked more than 40 weeks
during the year. Our panel is constructed from
the individuals in the cross-section data set who
are also observed in 1976. Attrition reduces the
number of observations in both periods to 860,
of which about 15 percent are black.
In addition to marital status, we observe (in
both years) each man’s wage, age (AGE), years
s 12 Extensions of this procedure to broader classes of instrument
sets can be found in Amemiya and MaCurdy (1986) and Breusch, Mizon,
and Schmidt (1989).
s 13 HT-IV uses the individual means and deviations from means of
each time-varying exogenous variable in Xit as separate instruments (see
Breusch, Mizon, and Schmidt [1989]).

16

T A B L E

2

Cross-Section Marital Status
Premiums from the 1971 NLSYM
OLS

CONSTANT

–2.156
(0.697)
MARITAL STATUS 0.054
(0.025)
AGE
0.188
(0.059)
AGE2
–0.003
(0.001)
UNION
0.214
(0.023)
SOUTH
–0.122
(0.024)
SMSA
0.157
(0.023)
EDUCATION
0.032
(0.004)
RACE
–0.169
(0.033)
h

IV1

IV2

IMR

–5.381
(2.721)
–0.691
(0.554)
0.471
(0.238)
–0.008
(0.004)
0.223
(0.032)
–0.095
(0.038)
0.156
(0.030)
0.027
(0.007)
–0.287
(0.103)

–4.858
(2.278)
–0.570
(0.488)
0.425
(0.199)
–0.007
(0.004)
0.221
(0.030)
–0.100
(0.035)
0.156
(0.028)
0.028
(0.007)
–0.268
(0.087)

–3.835
(1.330)
–0.334
(0.253)
0.335
(0.115)
–0.006
(0.002)
0.219
(0.026)
–0.108
(0.028)
0.156
(0.025)
0.029
(0.005)
–0.231
(0.053)
0.196
(0.149)

NOTE: Standard errors are in parentheses.
SOURCE: National Longitudinal Survey of Young Men.

of tenure with his employer (TENURE), years of
education (EDUCATION), union status (UNION
= 1 if a union member), race (RACE = 1 if
black), and residence (SOUTH = 1 if resident of
the South; SMSA = 1 if resident of a Standard
Metropolitan Statistical Area).14 The variable
MARITAL STATUS has a value of 1 if the individual is married and living with his spouse, and
zero otherwise. Table 1 provides the means and
standard deviations for the variables in our samples, and documents the percentage of men
who change their marital status.

Results
First, we estimate our model using purely crosssectional methods. In each case, X it contains
the explanatory variables AGE, AGE2, UNION,
SOUTH, SMSA, EDUCATION, and RACE. The
dependent variable in every regression is the
natural logarithm of the real wage. The results
of cross-section estimation are presented in
table 2. The OLS estimates, given in the first
column, serve as a baseline for comparing esti-

mates obtained from procedures that allow for
marital status endogeneity.
In general, the results of our OLS regressions
are typical of those found elsewhere in the literature. Of interest here is the coefficient of marital status, which is estimated to be 0.054 with a
standard error of 0.025 (statistically significant at
the 5 percent level). We have argued that the
marriage premium estimated by OLS is biased
upward due to the endogeneity of marital status. A Wu–Hausman test of the exogeneity of
marital status can be performed by comparing
OLS and IV estimates of our model.
To construct an instrument for M it , we need
an empirical specification of the decision rule
that determines marriage (equation [7]); that is,
a regressor (or set of regressors) that is not included in X it . From the NLSYM, we obtain two
family-background variables for this purpose:
number of siblings (NSIB) and years of education of the father (FED). The Wu–Hausman test
ˆ
amounts to a test of significance of Mit in a
ˆ
regression of y it on (X i¢t , Mit , Mit ). We conduct
ˆ
the test using a Mit calculated from both OLS
and probit maximum likelihood estimates of g.
The p-values of the test statistics for the null
ˆ
hypothesis that the coefficient of Mit equals
zero are 0.089 and 0.108, respectively. Taken
together, these tests provide weak evidence
against the exogeneity of marital status.

Instrumental
Variables
Assuming that marital status is endogenous, we
turn to the IV estimates of our model, which are
presented in the second and third columns of
table 2. The results in the IV1 column are based
ˆ
on a Mit obtained by OLS, while those in the
ˆ
IV2 column are based on a Mit derived from
probit maximum likelihood. In both cases, we
fail to reject, even at a 10 percent level of significance, the null hypothesis that the estimated
marital status coefficient is zero. Moreover, both
IV marital status coefficient estimates are less
than zero and are large in absolute value.
Consistency of these IV estimates depends
on the validity of the over-identifying restricˆ
tions exploited in the construction of Mit. A
test of the over-identifying restrictions examines whether (NSIB, FED) jointly adds to the
s 14 The wage-rate variable provided by the NLSYM is the hourly
wage for hourly workers and salary/usual hours for salaried workers. Our
wage-rate variable is deflated by the Consumer Price Index and is
expressed in 1970 dollars.

17

predictive power of our model. The value of
the test statistic, which is distributed as F 3,992,
is 2.337. Hence, the restrictions cannot be rejected at the 5 percent level of significance. On
the other hand, the p-value of the F-statistic is
only 0.949, and only NSIB (aside from certain
variables in X it ) enters (7) statistically significantly. This may be part of the reason that,
using our IV procedures, we are unable to
arrive at any stronger conclusions about the
impact of marital status endogeneity on the
estimated marriage premium.15

Inverse
Mills Ratio
As an alternative to IV, we estimate our model
using the two-step IMR procedure. First, we
estimate (7) by probit maximum likelihood to
obtain an estimate of g. This estimate is then
used to form the estimates of the relevant IMR
terms that comprise h in (10). Second, we
ˆ
apply OLS to (9), where h is substituted for h.
The results of this two-step procedure are given
in the fourth column of table 2. The marital status coefficient estimate is –0.334 and, like the
IV estimates, is not statistically significant. Furˆ
thermore, the “selection term,’’ h, does not
enter the regression statistically significantly,
thereby providing no (additional) evidence of
the endogeneity of marital status.16
In sum, cross-sectional approaches to the
identification of the marriage premium yield no
definitive conclusions. The evidence against the
exogeneity of marital status is relatively weak.
When marital status is treated as endogenous,
the resulting coefficient estimates are large and
negative. Moreover, when the estimated marital
status coefficient is large in absolute value, the
fact that it is not statistically different from zero
may have little meaning.
Next, we consider estimation techniques that
exploit the availability of panel data.

Panel Data
We proceed under the assumptions of (11) and
focus on the role of unobservable individualspecific characteristics in estimating the return
to marriage. The advantage of panel data is the
ability to control for such characteristics, which
may be correlated with (X it , M it ). Consequently,
¢
we can address another likely source of nonidentifiability of the marriage premium, namely,
the potential correlation of X it with the effects.
Furthermore, our panel data procedures do not

require the data to satisfy orthogonality conditions such as those in (8), or to meet any special distributional assumptions. This is important, since the cross-section estimates appear to
be sensitive to these kinds of restrictions.
Under the null hypothesis that the explanatory variables are uncorrelated with the effects,
OLS applied to the individual means of the
variables (the so-called between estimator)
yields consistent estimates of all the coefficients
in our model. Conditional on X it as defined
above, we estimate our model with our panel
data set using the between estimator as a basis
for comparison with procedures that are consistent under the alternative hypothesis.
The between estimates, which exploit only
the cross-section dimension of the panel, are
presented in the first two columns of table 3.
Like the OLS estimates in table 2, they are typical of cross-section estimates derived from
human capital wage equations.
Focusing on the returns to marriage, the first
column reports a statistically significant marriage premium of 7 percent. However, the
regression associated with the first column does
not condition on tenure. When TENURE and
TENURE2 are included, the estimated MARITAL
STATUS coefficient declines by one-third and is
no longer statistically significant. At the same
time, the estimated returns to tenure are sizable.
This pattern is repeated in Korenman and
Neumark when they introduce years married to
their regressions. But if Abraham and Farber
are correct, tenure and years married simply
capture individual characteristics that lead to
longer-lasting and higher-wage jobs.
This might be expected given the evidence
cited in Abraham and Farber (1987) on the
relationship between marital status and job
duration (completed tenure). Table 4 presents
further evidence on this relationship from our
cross-section data set. Here, we report the
results obtained from estimating an exponential hazard of job duration (correcting for rightcensoring) conditional on MARITAL STATUS,
AGE, AGE2, UNION, BLUE COLLAR (= 1 if the
individual is employed in a blue-collar occupation), EDUCATION, and RACE. Other than the
effect of union membership, marriage has the
largest positive impact on job duration.
s 15 The instrument set (NSIB, FED) represents our best attempt,
using our 1971 NLSYM cross-section sample, at a specification of (7).
s 16 We also estimated (9) by maximum likelihood, which assumes
(␩i t , ␯it ) to be bivariate normal. The maximum likelihood estimate of
(␦ M – ␦ S ) is 0.032 with a standard error of 0.033, so it is not statistically
significant. In addition, the correlation coefficient ␳␩v is only –0.117 and
is also not statistically significant.

18

T A B L E

Within Estimates

3

Estimated Marital Status
Premiums from the 1971
and 1976 NLSYM

The between estimates are consistent only if

Between

Between

–1.908
(0.809)
MARITAL STATUS 0.070
(0.037)
AGE
0.150
(0.062)
AGE2
0.002
(0.001)
TENURE

–1.851
(0.794)
0.0461
(0.036)
0.141
(0.061)
–0.002
(0.001)
0.055
(0.012)
–0.003
(0.001)
0.142
(0.025)
–0.084
(0.023)
0.197
(0.023)
0.041
(0.004)
–0.202
(0.030)

CONSTANT

TENURE2
UNION
SOUTH
SMSA
EDUCATION
RACE

0.162
(0.025)
–0.093
(0.023)
0.198
(0.023)
0.040
(0.004)
–0.203
(0.031)

␹2

Within

–0.012
(0.025)
0.118
(0.022)
–0.002
(0.000)
0.015
(0.007)
–0.001
(0.000)
0.190
(0.027)
–0.058
(0.056)
0.070
(0.041)
0.045
(0.014)

34.770

HT–IV

–0.968
(0.161)
–0.017
(0.024)
0.124
(0.021)
–0.002
(0.000)
0.013
(0.007)
–0.001
(0.000)
0.181
(0.020)
–0.082
(0.022)
0.158
(0.021)
0.054
(0.012)
–0.193
(0.035)
8.030

NOTE: Standard errors are in parentheses.
SOURCE: National Longitudinal Survey of Young Men.

T A B L E

4

Exponential Hazard
of Job Duration

Hausman–Taylor
Estimates
Coefficient
Estimate

CONSTANT
MARITAL STATUS
AGE
AGE2
UNION
BLUE COLLAR
EDUCATION
RACE
Log-likelihood
No. of observations

(X¢i t , Mit ) is orthogonal to the effects. The within
estimates, given in the third column of table 3,
are consistent regardless of whether the effects
are correlated with the explanatory variables.
Our within regression yields an estimated marriage premium that is essentially zero. The MARITAL STATUS coefficient estimate is –0.012 with
a standard error of 0.025. Conditioning on unobserved heterogeneity has a similar effect on
the return to tenure, as the estimated TENURE
coefficient declines from 0.055 to 0.015. One
interpretation of these results, consistent with
Abraham and Farber, is that the cross-section
gains to marriage and tenure largely reflect
unobserved individual characteristics that are
valued by the firm.
The outcomes of two specification tests support this interpretation. First, the assumption of
the between regressions that (X it , M it ) is
¢
orthogonal to the effects is soundly rejected. A
Hausman test of the difference in the between
and within estimates yields a test statistic that is
asymptotically distributed as c2 and that has a
9
value of 34.770. The interpretation of the test
statistic is as follows: The within estimates are
consistent under the null or alternative hypothesis, while the between estimates are consistent
only if there is no correlation between (X i¢t , M it )
and ai , implying that the estimates should be
somewhat close if no correlation exists. However, the statistic reported above shows that the
estimates are quite far apart, leading us to reject
the assumption of no correlation.

Standard
Error

1.526
0.284
–0.076
0.004
0.512
–0.012
–0.008
0.125
–1,597
1,073

2.412
0.086
0.205
0.004
0.083
0.087
0.018
0.107

SOURCE: National Longitudinal Survey of Young Men.

While the Hausman test demonstrates the general importance of unobserved heterogeneity in
our model, it does not specifically address the
uncorrelatedness of M it with ai. This is accomplished by appealing to the HT-IV estimator of
Hausman and Taylor (1981). Efficiency gains
over the within estimator are obtained by exploiting information about the uncorrelatedness
of certain columns of X it with ai and account¢
ing for the variance components. The null
hypothesis that M it is orthogonal to ai can be
tested by comparing HT-IV estimates derived
from a legitimate set of over-identifying restrictions with HT-IV estimates computed assuming
M it is exogenous.
Hausman tests contrasting HT-IV and within
estimates reveal that a legitimate instrument can

19

be constructed by assuming that AGE, AGE2,
UNION, SOUTH, SMSA, and RACE are uncorrelated with the ai ’s. This result comes from the
fact that the within estimator is consistent
regardless of the correlation of the ai ’s with the
above variables, while the HT-IV’s are not.
Therefore, if the results are close in some sense
(as defined by a Hausman test, for example),
that would lead to the acceptance of the variables being uncorrelated with the ai ’s. The test
statistic, which is asymptotically distributed as
c2, has a value of 8.03, which is well within the
5
95 percent statistic of 12.8. The HT-IV estimates
based on this instrument set are presented in
the last column of table 3. In general, they corroborate the results from within estimation. The
estimated marital status coefficient is again very
small and statistically insignificant. The HT-IV
tenure coefficient estimate is 0.013, quite close
to the within estimate.
A Hausman test of the difference between
the HT-IV estimates in the last column of table
3 and those obtained from HT-IV estimation
with marital status added to the instrument set
rejects the exogeneity of marital status. The test
statistic equals 3.89 and is asymptotically distributed as c2 with a p-value of 0.048.
1

IV. Conclusion
We use cross-section and panel data estimation
procedures to determine the effect of marriage
on the wages of a sample of young men drawn
from the NLSYM. Whenever we control for
unobservable individual effects, the estimated
returns to marriage are virtually zero. In addition, specification tests reject the hypothesis that
marital status is uncorrelated with the effects.
We conclude that the usual cross-section marriage premium is essentially a statistical artifact,
at least for young men. Within the job-matching
literature, this conclusion has a reasonable interpretation: As an explanatory variable in human
capital wage equations, marital status appears to
fulfill a role similar to that of tenure, namely,
proxying for unobservable individual-specific
characteristics that are valued by the firm.

References
Abraham, K.G., and H.S. Farber. “Job Duration,
Seniority, and Earnings,” American Economic Review, vol. 77, no. 3 (June 1987),
pp. 278–97.
Amemiya, T., and T.E. MaCurdy. “InstrumentalVariable Estimation of an Error Components
Model,” Econometrica, vol. 54, no. 4 (July
1986), pp. 869–80.
Barnow, B.S., G.G. Cain, and A.S. Goldberger.
“Issues in the Analysis of Selectivity Bias,”
Evaluation Studies Review Annual, vol. 5
(1980), pp. 43–59.
Bergstrom, T., and R. Schoeni. “Income Prospects and Age at Marriage,” University of
Michigan, Center for Research and Economic
Social Theory, Working Paper 92-10, March
1992.
Breusch, T.S., G.E. Mizon, and P. Schmidt.
“Efficient Estimation Using Panel Data,”
Econometrica, vol. 57, no. 3 (May 1989),
pp. 695–700.
Cornwell, C., and P. Rupert. “Unobservable
Individual Effects, Marriage, and the Earnings of Young Men,” Economic Inquiry,
1996, forthcoming.
Fuller, W., and G. Battese. “Transformations for
Estimation of Linear Models with NestedError Structure,” Journal of the American
Statistical Association, vol. 68, no. 343
(September 1973), pp. 626–32.
Hausman, J.A. “Specification Tests in Econometrics,” Econometrica, vol. 46, no. 6
(November 1978), pp. 1251–72.
_________ , and W. Taylor. “Panel Data and
Unobservable Individual Effects,” Econometrica, vol. 49, no. 6 (November 1981),
pp. 1377–98.
Heckman, J., and R. Robb. “Alternative
Methods for Evaluating the Impact of Interventions: An Overview,” Journal of Econometrics, vol. 30, nos. 1 and 2 (October/
November 1985), pp. 239–67.

20

Kenny, L.W. “The Accumulation of Human
Capital during Marriage by Males,” Economic Inquiry, vol. 21, no. 2 (April 1983),
pp. 223–31.
Korenman, S., and D. Neumark. “Does Marriage Really Make Men More Productive?”
Journal of Human Resources, vol. 26, no. 2
(Spring 1991), pp. 282–307.
Nakosteen, R.A., and M.A. Zimmer. “Marital
Status and Earnings of Young Men: A Model
with Endogenous Selection,” Journal of
Human Resources, vol. 22, no. 2 (Spring
1987), pp. 248–68.
Reed, W., and K. Harford. “The Marriage Premium and Compensating Wage Differentials,” Journal of Population Economics,
vol. 2, no. 4 (1989), pp. 237–65.
Robinson, C. “The Joint Determination of
Union Status and Union Wage Effects: Some
Tests of Alternative Models,” Journal of Political Economy, vol. 97, no. 3 (June 1989),
pp. 639–67.
Shaw, K. “The Quit Propensity of Married Men,”
Journal of Labor Economics, vol. 5, no. 4,
part 1 (October 1987), pp. 533–60.
Wu, D. “Alternative Tests of Independence
between Stochastic Regressors and Disturbances,” Econometrica, vol. 41, no. 4
(July 1973), pp. 733–50.

21

Absolute Priority Rule
Violations in Bankruptcy
by Stanley D. Longhofer and
Charles T. Carlstrom

Introduction
Any transaction involving a continuing relationship over time depends on a mechanism by
which parties can commit themselves to some
future behavior. This often involves writing contracts. In most cases, we depend on government to enforce these contracts through a court
system. Indeed, one of government’s most important roles in any economy is defining and
enforcing private property rights. Since contracts
are simply a means of transferring private property, the use of courts to enforce them has a
certain logical appeal.
Loan agreements are one of the most common types of contracts in our economy. Lenders
agree to invest in a business and the owners of
that business agree to repay the loan, with interest, at some future date. If the borrower fails to
repay the loan, his creditors may force him into
bankruptcy and seize his assets. By definition,
debt contracts require that creditors be paid
before the firm’s owners receive any value. In
other words, creditors are assumed to have
“priority” over a firm’s equity holders.
This principle is known as the absolute priority rule (APR). Simply stated, this rule requires
that the debtor receive no value from his assets

Stanley D. Longhofer and Charles
T. Carlstrom are economists at the
Federal Reserve Bank of Cleveland.

until all of his creditors have been repaid in
full.1 While this rule would seem quite simple
to implement, it is routinely circumvented in
practice. In fact, bankruptcy courts themselves
play a major role in abrogating this feature of
debt contracts. If private loan contracts are
entered into voluntarily, why do courts allow
(and even encourage) their terms to be violated
on a regular basis? More important, what impact
do these violations have on the cost of financial
contracting and, hence, economic efficiency?
This article addresses these questions by
analyzing the impact of APR violations on
financial contracts. We begin in the next section
by reviewing the magnitude of these violations
and the frequency with which they occur. In
section II, we develop a simple model to analyze the efficiency of APR violations. We complicate this model with several market frictions
to show how the impact of these violations
depends on which friction is present. Section
III discusses the model’s implications for the
proper role of bankruptcy law in enforcing
these contracts. Section IV concludes.
s 1 The APR also states that senior creditors should be paid before
junior creditors. In this paper, we consider only APR violations between the
borrower and a (single) lender.

22

T A B L E

1

Empirical Research
on APR Violations
Article

Data

Dates

Frequency

Magnitude

Franks and Torous (1989)

30 firms with publicly traded
debt filing for bankruptcy

1970–84

66.67%

LoPucki and Whitford
(1990)

43 firms with more than
$100 million in assets and
at least one publicly traded
security under Chapter 11

1979–88

48.84%

Eberhart, Moore, and
Roenfeldt (1990)

30 firms with publicly traded
stock under Chapter 11

1979–86

76.67%

Weiss (1990)

37 NYSE and AMEX firms
under Chapter 11

1980–86

72.97%

Franks and Torous (1994)

82 firms with publicly traded
debt under Chapter 11 or an
informal workout

1983–90

Tashjian, Lease, and
McConnell (1996)

48 firms with a publicly traded
1980–93
security or more than $95 million
in assets, reorganizing with a
prepackaged bankruptcy

72.92%

1.59%

Betker (1995)

75 firms with publicly traded
securities under Chapter 11

72.00%

2.86%

1982–90

7.57%

9.51% workouts
2.28% Chapter 11

SOURCE: Authors’ review of the literature.

I. The Prevalence
of APR Violations
A growing body of empirical evidence supports
the conclusion that APR violations are commonplace both in Chapter 11 reorganizations and in
informal workouts. Using different samples of
large corporations with publicly traded securities, numerous researchers have found that
equity holders receive value from financially
distressed firms in violation of the APR in nearly
75 percent of all reorganizations.2 This appears
to be true whether one looks at private, informal workouts, conventional reorganizations, or
“prepackaged bankruptcies” in which the details
of the reorganization are negotiated before the
bankruptcy petition has been filed.
The frequency with which APR violations
occur might be misleading if the magnitude of
these deviations as a percentage of the firm’s
value were relatively small. Indeed, some commentators have suggested that value paid to
equity is simply a token to speed up the process

and has little economic significance: “Shareholders were tossed a bone, crumbs off the table, to
get the deal done...” 3 Existing evidence, however, suggests that this is not generally the case.
Estimates of the magnitude of APR violations in
favor of equity vary, but in reorganizations in
which such violations occur, equity holders
appear to receive between 4 and 10 percent of
the firm’s value.4 And although the evidence is
limited, some have suggested that these deviations are larger for small firms whose owners
s 2 See Franks and Torous (1989), LoPucki and Whitford (1990),
Weiss (1990), Eberhart, Moore, and Roenfeldt (1990), and Betker (1995).
s

3 Quoted in Weiss (1990), p. 294.

s 4 See Eberhart, Moore, and Roenfeldt (1990), Franks and Torous
(1994), Tashjian, Lease, and McConnell (1996), and Betker (1995). Franks
and Torous note that the larger deviations found by Eberhart, Moore, and
Roenfeldt may be a consequence of the latter’s older sample of distressed
firms: “With the growth in the market for distressed debt securities and the
greater involvement of institutional investors such as ‘vulture funds,’
debtholders may have increased their bargaining power at the expense of
equity holders” (Franks and Torous [1994], p. 364).

23

also manage the company.5 Table 1 summarizes
recent empirical research on APR violations.
One major caveat should be kept in mind
when considering these findings: All the studies of bankruptcy resolution cited here have
focused on firms with publicly traded stock
and/or debt.6 However, such firms comprise
only a small subset of those filing for Chapter 11
bankruptcy or initiating out-of-court debt workouts. As a result, the number of firms included
in these studies averages less than 50. In contrast, there were over 176,000 Chapter 11 cases
filed nationwide in the first 10 years after the
new Bankruptcy Code was implemented in
1979 (Flynn [1989]). Even after eliminating
single-asset real estate partnerships and “house”
filings to focus on what might reasonably be
considered true “business” reorganizations,
these studies have depressingly small and
biased samples of “average” reorganizations.7
Indeed, bankruptcy judge Lisa Fenning notes
that only five out of more than 600 Chapter 11
cases on her docket involve publicly traded
companies.8 Clearly, we must be cautious and
avoid overinterpreting these empirical studies.

II. APR Violations
and Efficiency
Many have argued that APR violations occur because they are privately optimal for bankruptcy
participants. If strict adherence to the APR creates perverse investment incentives once the
firm is in bankruptcy, it may be privately optimal (ex post) for everyone involved to abrogate
such rules and renegotiate their contracts.9
Under this view, APR violations—both inside
Chapter 11 and in out-of-court workouts—are
a desirable consequence of renegotiation between the firm and its creditors; APR violations
are essentially payoffs by lenders to encourage
the firm’s shareholders to make good investment decisions once the firm is in financial distress. Unfortunately, this view fails to take into
account how such behavior affects ex ante efficiency through the terms of the original financial contract, which is ultimately the only way to
evaluate the efficiency of APR violations fully.
To focus on this problem, we develop a simple model of financial contracting. Consider an
entrepreneur who wants to open a firm and invest in a project, but needs to borrow I dollars
from an outside investor to do so. In return for
this loan, the entrepreneur agrees to repay his
lender R dollars from his firm’s future profit.
For ease of exposition, we will often refer to
R as “the interest rate.”10 Of course, the firm’s

profit is not guaranteed. Let x denote the firm’s
realized profit, which can take values on the
interval [ Ϫ, Ϫ]. Let f (x) be the probability that
x x
any given x is realized (that is, its probability
density function) and, as is standard, let F (x) be
the associated distribution function. To model
APR violations, let ␦ represent the fraction of
the firm’s profit retained by the entrepreneur in
bankruptcy.
The entrepreneur will default whenever doing so gives him a higher return (that is, whenˆ
ever x – R < ␦x). Define x = R /(1– ␦) as the
critical level of profit below which default
occurs. The entrepreneur’s expected return
from his business, E, is then:
ˆ
x

x

x

(1)

ˆ
x

E = ͵␦xf (x)dx + ͵ (x – R)f (x)dx.

When bankruptcy occurs, the entrepreneur
receives only fraction ␦ of the firm’s profit x;
by weighting this by f (x) and integrating over
all levels of profit for which default occurs, we
obtain the first term in E. On the other hand,
ˆ
when the firm’s profit exceeds x , the entrepreneur uses it to repay his loan and keeps the
rest. Weighting this by f (x) and integrating over
ˆ
all x > x gives us the second term in E.
In a competitive lending market, the equilibrium interest rate, R *, is set to ensure that the
lender is just willing to make the loan:11
ˆ
x*

(2)

–
x

L = ͵ (1 – ␦ )xf (x)dx + ͵R *f (x)dx – I = 0.
x

ˆ
x*

As above, the first term in this expression
represents the lender’s expected return when

s

5 See LoPucki (1983) and LoPucki and Whitford (1990).

s

6 LoPucki (1983) is an exception.

s 7 House filings are Chapter 11 filings by individuals whose home
mortgages exceed the Chapter 13 debt limit. The 1994 changes to the
Bankruptcy Code should make such filings less common.
s

8 Fenning (1993).

s 9 See Bulow and Shoven (1978), White (1980, 1983), Gertner and
Scharfstein (1991), and Berkovitch and Israel (1991) for models that promote this idea.
s

10 Technically, R is the “face value” of the debt and is equal to
(1 + r ) I , where r is the nominal interest rate on the loan.

s 11 Implicit in this specification is the assumption that the competitive return on riskless assets is 1, so that the lender’s cost of funds is only I.

24

default occurs, and is the firm’s profit in these
states minus the APR violation. The second
term in L follows from the fact that the lender
is simply paid R * in all nondefault states.
In this simple model, APR violations have no
impact on the firm’s cost of financing. While it is
true that once the firm is in bankruptcy the entrepreneur is “better off” with large APR violations, these gains are entirely offset by increases
in the interest rate the firm is forced to pay. To
see this, we substitute the equilibrium solution
for R into (1) to get
–
x

(3)

͵ xf (x)dx – I.

E=

x

The fact that ␦ does not appear in this expression shows us that the firm’s profit is unaffected by the size of the APR violation.12
In this simple model, the magnitude of APR
violations has no impact on the cost of the initial financial contract. Of course, this analysis
ignores many of the problems that plague realworld financial contracting. Throughout the rest
of this section, we extend this model with several standard complications and show how the
effect of APR violations depends on which
problem is present.

Costly Bankruptcy

ˆ
cF (x *), lower the entrepreneur’s ex ante
expected return.
In this environment, APR violations may create an additional problem. Although the lender’s
expected return is generally increasing in the interest rate, eventually the added expected bankruptcy costs associated with higher interest rates
outweigh their benefits; that is, L will eventually
be decreasing in R. Williamson (1986) shows
that this effect can lead to credit rationing, since
changes in the interest rate may be insufficient
to clear the loan market.
Increases in the magnitude of APR violations
have the same impact: By reducing the lender’s
payoff in default states and increasing the probability that bankruptcy will occur, a point
comes at which the lender can no longer be
compensated for additional violations of the
APR through increases in the interest rate. In
other words, APR violations exacerbate creditrationing problems.
Thus, when bankruptcy is costly, there are
strong reasons to avoid APR violations. First,
these violations raise the interest rate the entrepreneur must pay, increasing the chance that
default—and its corresponding costs—will
occur. Furthermore, violations make credit
rationing more likely, thereby limiting the
entrepreneur’s investment opportunities. Why,
then, do they occur with such frequency? We
next turn to one possible reason.

One of the most basic problems in financial
contracting is the fact that bankruptcy is costly.
Let c denote the cost paid by the lender whenever he forces the entrepreneur into bankruptcy
(for simplicity, assume c < Ϫ).13 As before, the
x
equilibrium interest rate, R *, must be set to ensure that the lender earns a competitive return:
ˆ
x*

(4)

L = ͵ [(1 – ␦ )x – c ]f (x)dx
x

–
x

+ ͵R *f (x)dx – I = 0.
ˆ*
x

In the appendix, we verify that, as before, increases in the magnitude of the APR violation
make default more likely (that is, dx ␦ > 0).
ˆ*/d
Substituting (4) into the entrepreneur’s
expected profit (1), we get
–
x

(5)

E=

͵ xf (x)dx – I – cF (x *).
ˆ

x

This expression demonstrates how APR violations affect the terms of the loan agreement.
ˆ
Since x * increases with ␦, larger APR violations
make bankruptcy occur more frequently. As a
result, the added expected bankruptcy costs,

Asymmetric
Liquidation
Value
The model presented above assumes that the
firm had no capital assets once the project was
completed or, alternatively, that the firm had no
“going-concern” value. But much of the justification for a reorganization procedure derives
from the belief that many firms in financial distress are in fact economically viable and should
be reorganized rather than liquidated.14
To focus on this idea, we return to our original model (in which bankruptcy is costless) and
simplify it by assuming that only two levels of

s 12 On the other hand, APR violations can lead to credit-rationing
problems, even in this simple model, since they make default occur more
frequently. We discuss this problem in the subsection that follows.
s 13 This, then, is the costly state verification environment developed
by Townsend (1979) and Gale and Hellwig (1985).
s 14 Harris and Raviv (1993) develop a model based on this issue
and come to similar conclusions.

25

profit are possible. In good states of the world,
which occur with probability ␲, the entrepreneur’s business earns x H . In contrast, when
business is bad, the firm earns only x L ; this occurs with probability (1 – ␲). Furthermore,
assume that when business is good the entrepreneur can repay his debt, but in bad states he
cannot; that is, x H > R > x L .
In addition to its profit, x, the firm has capital assets worth A once its project is completed;
these can be thought of as the value of the
firm’s expected future profit. If this value is the
same regardless of who owns the firm, our
results remain unchanged: APR violations have
no impact on the terms of the financial contract. On the other hand, if the firm’s assets are
worth more in the hands of the entrepreneur,
there will be an incentive to modify the financial contract to allow him to retain control of
the firm even after filing for bankruptcy.
Let ␣ represent the fraction of the firm’s
assets (and hence future profit) retained by the
entrepreneur during bankruptcy. In this case,
the entrepreneur’s expected profit15 is
(6)

E = (1 – ␲)(␦x L + ␣ A) + ␲ (xH – R + A).

Let ␥ be the fraction of the firm’s ongoing
value that is lost by transferring these assets to
the lender. Once again, the equilibrium interest
rate must be set to guarantee the lender a competitive return:
(7)

L = (1 – ␲)[(1 – ␦)xL + (1 – ␣)␥A]
+ ␲R * – I = 0.

Substituting this into the entrepreneur’s
expected profit gives us
(8)

E = (1 – ␲)(xL + A) + ␲ (xH + A)
+ (1 – ␲)(1 – ␥) (␣ – 1)A – I.

As before, it is irrelevant whether the entrepreneur is allowed to keep some of the profit
(the size of ␦ ) when the firm defaults; the interest rate adjusts so as to keep the entrepreneur’s
expected return unchanged. Likewise, when
␥ = 1 and the firm’s capital assets have the same
value regardless of who controls them, the size
of ␣ does not matter; that is, APR violations
involving the firm’s capital assets are irrelevant.
In this case, we are back to our original model.
Notice, however, that the same is not true
when ␥ is less than one. Differentiating (8)
with respect to ␣ gives us
(9)

dE
ᎏᎏ = (1 – ␲ )(1 – ␥ ) A > 0;
d␣

since these assets are worth less to the lender
than they are to the entrepreneur, APR violations of this sort are beneficial.
Why are both ␣ and ␥ necessary to analyze
the impact of APR violations in this environment? The intuition is clear: APR violations are
beneficial only when they are applied to A,
since this is the only part of the firm’s value
that is worth more in the hands of the entrepreneur. If allowing the lender to keep some
of xL has any detrimental impact (such as
costly bankruptcy), the desirability of distinguishing between these two types of APR violations is obvious.
One might wonder whether there is a practical distinction between xL and A. For large,
publicly traded firms, this distinction may be
irrelevant. After all, the going-concern value of
Johnson & Johnson is likely to be unaffected by
the identity of its stockholders (that is, their ␥ is
equal to one). On the other hand, firms that are
owned and managed by an entrepreneur who
brings specialized skills to his company are
likely to have small ␥ ’s. In this case, it might be
reasonable to allow the entrepreneur to keep
control of his firm after bankruptcy, but all of
the firm’s liquid assets should be transferred to
its creditors.

Risk Shifting
Perhaps the most common problem in financial
contracting is the borrower’s incentive to undertake actions that affect the riskiness of his business.16 Suppose that, by exerting effort, the
entrepreneur can affect the likelihood that the
firm will be successful. If the entrepreneur
works hard, the firm will earn xH with probability ␲1; without effort, it will earn xH with
probability ␲2 < ␲1. In addition, assume that the
amount of effort required (or alternatively, the
cost of this effort) is not discovered until after
the loan is made; let e represent the effort ultimately required. Finally, suppose that the lender
cannot observe whether effort is exerted.
After learning the effort required, the entrepreneur’s expected return from the “good”
project is (1 – ␲1)␦xL + ␲1(xH – R) – e, while
his expected return from the “bad” project is
(1 – ␲2)␦xL + ␲2(xH – R). Ultimately, whether
s 15 This expression is analogous to equation (1); note that we have
assumed only two possible states of the world.
s 16 Bebchuk (1991) develops a different model of risk shifting and
comes to similar conclusions. See also Innes (1990).

26

the entrepreneur chooses to undertake the
good project (that is, exert effort) will depend
on how much effort is required. He will select
the good project as long as his realized e is less
than e*, where
(10) e* = (␲1 – ␲2)(xH – R – ␦xL ).
In what follows, it will be useful to know
how often the entrepreneur will select the
good project, which requires us to know the
distribution of e. Assume for simplicity that
e is distributed uniformly on the interval [0,1].
In this case, the probability that the entrepreneur will choose the good project (that is, that
e < e*) is simply e *.
The lender, knowing that the entrepreneur
will choose the good project with probability e *
and the bad project with probability 1– e *, will
demand an interest rate that guarantees him
zero expected profit:
(11) L = [e *(1 – ␲1) + (1 – e *)(1 – ␲2 )](1 – ␦)xL
+ [e *␲1 + (1 – e *)␲ 2 ]R * – I = 0.
Before he takes the loan, the entrepreneur’s
expected return is simply his expected profit
from each of the projects, weighted by the
probability that he will choose each, minus his
expected effort conditional on the good project
being chosen:
(12) E = (1 – e *)[␲2(xH – R) + (1 – ␲2 )␦xL ]
e *2
+ e *[␲1(xH – R) + (1 – ␲1)␦xL ] – ᎏᎏ .
2
Substituting R* into this expression gives us:
(13) E = e *(␲1 – ␲2 )(xH – xL ) + ␲2 xH
e 2
+ (1 – ␲2 )xL – ᎏ* – I.
ᎏ
2
As in our original problem, ␦ has no direct
effect on the entrepreneur’s ex ante expected
return; the interest rate simply adjusts to ensure
that the lender makes a competitive return. On
the other hand, such APR violations do have an
indirect effect through their impact on the
probability that the entrepreneur will exert
effort and choose the good project. Differentiating (13) with respect to ␦ yields
dE d
(14) ᎏᎏ = ᎏe * [(␲1 – ␲2)(xH – xL ) – e *]
ᎏ
d␦
d␦
d
= ᎏe * (␲1 – ␲2)[R – (1 – ␦)xL ].
ᎏ
d␦

Now, R > (1 – ␦)xL by assumption. In the
appendix, we demonstrate that de */d ␦ Յ 0,
that is, that the presence of large APR violations
makes the entrepreneur less likely to choose
the good project.17 Combining these results
shows that the entrepreneur’s expected profit is
decreasing in ␦. Hence, when risk shifting is a
problem, APR violations are ex ante inefficient.
The intuition behind this is straightforward.
As before, the direct benefit to the entrepreneur
of receiving compensation when the firm fails
is exactly offset by the higher interest rate he
must pay.18 On the other hand, APR violations
reduce the entrepreneur’s incentive to undertake the good project. Why is this the case?
Since effort is costly for the entrepreneur, he
would like to avoid it whenever possible. Nevertheless, he is willing to exert some effort,
since doing so makes it more likely that the
firm will be successful, reaping him a higher
return. The presence of these violations, however, reduces the pain of bankruptcy and hence
the relative benefits of this effort. After all, why
should the entrepreneur work hard if he can be
assured of a sizable payoff even when his business bombs? As a result, the entrepreneur
exerts less effort than he would if there were
no APR violations.

III. Policy Implications
The results of the last section suggest that an
optimal bankruptcy institution would allow
debtors and creditors to decide ex ante
whether APR violations will occur. In other
words, the parties to the loan agreement should
be allowed to write a contract that specifies
under what conditions APR violations will and
will not occur.
Although the desirability of such a system
might seem obvious, current bankruptcy law
does not enforce agreements like these. Once a
firm enters bankruptcy, it must follow the rules
and procedures set out in the Bankruptcy
Code, and no one is allowed to forfeit his
future right to file for bankruptcy when he
signs a loan agreement. This might not be a
problem if it weren’t for the fact that current
bankruptcy law strongly encourages APR violations, regardless of whether they are efficient.
17 For small ␦, de */d ␦ may be zero; in this range, the payments
that the entrepreneur receives in bankruptcy are not large enough to discourage him from choosing the good project, regardless of the level of
effort required.

s

s

18 Once again, however, a credit-rationing problem is possible.

27

Several features of the code make this true.
First, the debtor retains control of the firm
throughout the process, except in extraordinary
circumstances. Second, the debtor is allowed to
obtain “debtor-in-possession financing” to continue operation of the business; this financing is
automatically given priority over all of the
firm’s unsecured claims. Third, the debtor is
granted 120 days to propose a plan of reorganization; during this time, no other parties may
propose alternative plans.19 Finally, if the
debtor’s reorganization plan is not approved by
its creditors, it may attempt to enforce a “cramdown,” getting the judge to impose the plan
against the creditors’ wishes.20 Each of these
factors gives the debtor leverage in the reorganization, increasing the likelihood (and magnitude) of APR violations.
Although one might appeal to asymmetric
liquidation values as a justification for APR violations, a formal bankruptcy procedure that
mandates them seems unwarranted, especially
in light of other problems that make APR violations inefficient. After all, nothing prevents the
firm and its creditors from writing a loan agreement that would keep the firm’s capital assets
in the entrepreneur’s hands, even in default.
This points out an additional complication
that must be present to justify a special bankruptcy law: incomplete contracting. If the future
value of the firm’s capital assets is uncertain, and
the entrepreneur and the lender cannot agree
on a way to measure its value, some outside
arbiter may be useful. While bankruptcy courts
can certainly fill this role, the implicit assumption
that the contract participants cannot designate
such an arbiter in their agreement seems extreme. On the other hand, bankruptcy law may
be able to provide a useful baseline to reduce
the costs of contracting on improbable events.
Potential conflicts among different creditors
might provide another justification for bankruptcy laws.21 In their rush to retrieve some
value from a financially distressed firm, the
theory goes, lenders may inadvertently reduce
the total value of the firm’s assets that are available for distribution. This might happen if the
firm’s assets are worth more undivided, but
individual creditors have liens on specific
assets. Worse yet, this rush might cause financially viable firms to be liquidated. Setting aside
the question of why the firm and its creditors
cannot foresee these problems and write their
contracts so as to prevent them, this rationale
for bankruptcy law does not necessarily mandate that it violate contractual priorities that are
determined ex ante.

Nonetheless, many firms may feel that the
fact-finding and mediation services provided by
a formal bankruptcy institution provide a costeffective way of writing financial contracts. Similarly, conflicts among creditors may be sufficiently severe to justify the use of such an
institution. As a result, one would be overzealous in recommending total repeal of the Bankruptcy Code.
It is clear, however, that any bankruptcy procedure should merely provide an optional starting point for private contracts. If everyone involved finds it convenient to use this institution,
they may. But if they find the procedure unnecessarily restrictive, they should have the opportunity, when they write their financial contract,
to opt out of it entirely. That is, the parties to
the loan agreement should be allowed to decide
up front, when they write their agreement,
whether a formal bankruptcy procedure will
be used in the event of financial distress.
On the one hand, small entrepreneurial
firms with highly uncertain markets and products may find Chapter 11 protection beneficial.
As discussed above, Chapter 11 gives equity
substantial bargaining power in the renegotiation process. Since these firms are more likely
to benefit from the ability to recontract when
new information is available, and their managers are more likely to possess special skills
that affect the firm’s going-concern value, this
added bargaining power and the resulting violations in the APR are more likely to be beneficial. Firms in this situation would typically
include the right to seek Chapter 11 protection
in their debt contracts.
In contrast, firms that have greater opportunities to adjust their activities to the detriment
of their creditors would generally choose to opt
out of this protection. Formally forfeiting their
right to Chapter 11 protection would clearly
signal their creditors of their intention to avoid
high-risk projects. Likewise, large, publicly

s 19 This exclusivity period is often extended indefinitely (Franks and
Torous [1989] and LoPucki and Whitford [1990]).
s 20 Cram-downs are rather uncommon, and are allowed only in
cases in which all dissenting creditors receive at least what they are due
under the APR when the firm is liquidated. A cram-down may nonetheless
impose an APR violation if the firm would be worth more if it continued
than if it were liquidated, or if the face value of the securities offered to dissenting creditors is substantially above their true market value. Furthermore, the threat of a cram-down, which is costly to fight, may cause some
creditors to accept lower payouts than they might otherwise.
s

21 See Jackson (1986) for a complete discussion of this argument.

28

traded firms whose going-concern value is
unaffected by their ownership would benefit
from such an option.

IV. Conclusion
This paper has demonstrated how the efficiency
of APR violations depends on the nature of the
contracting problem present. When the firm’s
future profit will be higher if it is controlled by
the entrepreneur, it makes sense for him to retain the firm’s capital assets—if not its past
profits—after bankruptcy. On the other hand,
APR violations of any sort have the detrimental
effect of raising interest rates, thereby increasing expected bankruptcy costs and worsening
credit-rationing problems. Furthermore, APR
violations can reduce the entrepreneur’s incentive to work hard in order to ensure his
firm’s profitability.
The diversity of these implications suggests
that an optimal bankruptcy law would allow
firms and their creditors to decide ex ante
whether (and what type of) APR violations will
occur in the event of financial distress. While
such decisions could reasonably be left to private contracts, a formal bankruptcy law may be
desirable for other reasons. If this law de facto
encourages APR violations, it is clear that it
should also include an “opt-out” provision that
allows private agents to determine whether its
structure will be beneficial to them. This is not
allowed under current U.S. bankruptcy law.
In such a world, we might expect owneroperators of small firms to include APR violations in their contracts, since these firms are the
most likely to lose value from transferring their
capital assets. In contrast, the value of large,
publicly traded companies is less likely to be
affected by their ownership, and we would
therefore expect such companies to avoid APR
violations of any type, as would firms of any
size whose profit streams are easily affected by
managerial effort.

Appendix
In this appendix, we prove some of the more
technical results required in the text. The first is
the fact that, in the model with costly bankˆ
ruptcy, x * is increasing in ␦. Totally differentiating (4) shows that
x *[1 – F (x ϩ ͵x xf (x)dx
ˆ
ˆ*)]
dx *
ˆ
.
(15) ᎏᎏ ϭ
d␦
(1 – ␦)[1 – F (x – cf (x
ˆ*)]
ˆ*)
x*
ˆ

Ϫ

The numerator of this expression is clearly positive, as is the denominator whenever
c
1 – F (x
ˆ*)
(16) ᎏᎏ < ᎏ .
1–␦
f (x
ˆ*)
Longhofer (1995) shows that whenever this
condition does not hold, no lending occurs in
equilibrium. That is, when c or ␦ is too large,
credit rationing results.
The second fact we must prove is that
de*/d ␦ Յ 0 in the model with risk shifting.
Solving (11) for R *, substituting into (10), and
simplifying shows that e* is defined by
(17) e *2␮2 ϩ e*␮1 ϩ ␮0 ϭ 0,
where ␮0 = I – ␲2xH – (1 – ␲2 )xL + ␦xL,
␮1 = ␲2 – (␲1 – ␲2 ) 2 (xH – xL ), and
␮2 = (␲1 – ␲2 ).
Although two roots will solve this equation,
differentiation of (13) with respect to e * shows
that the larger root will always be the one chosen in equilibrium. Using the quadratic formula
to solve for e*, it is straightforward to verify that
(18)

de*
2
ᎏ ϭ – x L (␮1 – 4␮2␮0) – ½ ,
d␦

which must be nonpositive whenever a real
solution for e * exists.
It is worth asking what happens when the
optimal e *, as given by the quadratic formula,
is greater than one. This would imply that the
entrepreneur will always choose the good project, regardless of the level of effort ultimately
required. In this case, small APR violations will
have no impact on the firm’s ex ante profit.
Larger violations, however, will still reduce the
chance that the entrepreneur will choose the
good project.

29

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