Full text of Economic Review (Federal Reserve Bank of Cleveland) : 1989 Quarter 1

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The Determinants
of Direct Air Fares
to Cleveland:
How Competitive?
b y Paul W . Bauer
and T h o m a s J. Z la to p e r

Bank Capital Requirements
and the Riskiness
of Banks: A Review
b y W illia m P. O sterberg
and J a m e s B. T hom son

Turnover, Wages,
and Adverse Selection
b y C harles T. C arlstro m

FEDERAL RESERVE BANK
OF CLEVELAND

1989 Quarter 1
Vol. 25, No. 1

2

The Determinants
of Direct Air Fares

Economic Review

to Cleveland:
How Competitive?

is published

quarterly b y the Research
D ep a rtm e n t of the Federal

b y Paul W . Bauer

R eserve B an k o f C leve lan d.

and T h o m a s J. Z la to p e r

C opies of the

Review

are

available through our Public
A spate of recent fare increases has focused attention on the airline indus­

A ffa irs and B an k Relations
D e p a rtm e n t, 2 1 6 / 5 7 9 -2 1 5 7 .

try’s competitiveness. M an y analysts are concerned about continuing
changes in the industry in the wake of its consolidation in the last few years.
The authors examine the competitiveness issue by developing a model for

C oordin ating Ec o n o m is t:

the determinants of air fares. They find that, controlling for other important
factors, air fares are lower on routes that have more carriers offering service,

Randall W . E b e rts

although most of the decrease in fares is achieved once two or three carriers
Ed ito rs : W illia m G . M u rm a n n
offer service.

Robin Ratliff
D e s ig n : M ich ae l G a lk a
T y p e s e ttin g : L iz H a n n a

Bank Capital Requirements
and the Riskiness
of Banks: A Review

10
Op in ion s s ta te d in

Review

Economic

are those of the

b y W illia m P. O sterberg

au th o rs an d not n ecessarily

and J a m e s B. T hom son

th o s e o f the Federal Re s e rve
B a n k of C leve lan d or o f the

Previous studies of the impact of capital requirements on bank portfolio deci­
sions typically assume that the deposit rate paid by banks is not a function

B oard o f G o ve rn o rs o f the F e d ­
eral R e s e rve S y s te m .

of the riskiness of the bank's portfolio. Such studies conclude that stiffer cap­
ital requirements decrease portfolio risk, but m ay increase the probability of
bankruptcy. The authors show that the variance of earnings and the incentive

M aterial m a y be reprinted p ro­
vid e d th a t the s ource is credited.

to increase leverage are reduced with risk- and leverage-related deposit
rates. How ever, the impact of increased capital requirements on portfolio

Ple as e s en d copies o f reprinted
m aterial to the editor.

behavior is generally ambiguous.

I S S N 0 0 13 -0 2 8 1

Turnover, Wages,
and Adverse Selection

18

b y C harles T. C arlstrom
Empirical studies of turnover and wages have shown that frequent jobchangers have lower average wages and flatter age-earnings profiles than
workers who change jobs infrequently. This paper argues that adverse selec­
tion in the labor market can explain this phenomenon. Lower-productivity
workers are the frequent job-changers, according to Akerlof’s “ lemon" princi­
ple, giving rise to the observed relationship between turnover and wages.
Adverse selection also provides a basis for examining the welfare implica­
tions of low-productivity workers in the labor market.

The Determ inants
of Direct A ir Fares
to Cleveland:
H o w Com petitive?
b y Paul W . Bauer
a n d T h o m a s J . Z la t o p e r

Paul W . Bauer is an economist at
the Federal Reserve Bank of Cleve­
land. Thomas J . Zlatoper is a profes­
sor at John Carroll University and a
research associate at the Center for
Regional Economic Issues at Case
Western Reserve University. The
authors would like to thank John R.
Swinton and Paula J . Loboda for
their expert research assistance, and
thank Randall W . Eberts for his
comments.

Introduction

Eleven years ago, Congress decided in the form
of the Airline Deregulation Act of 1978 that the
operational decisions of airlines—where planes
can fly and what fares can be charged—would be
better left to the airlines than to the regulators.
This decision has caused numerous changes
in the industry: discount fares have become
widespread and traffic has boomed, new carriers
have come and gone, hub-and-spoke networks
have emerged, and frequent-flier plans have
become the rage. As long as the industry remains
competitive, many analysts assert that travelers
have little to fear from these continuing changes,
since competition ensures that fares are held
close to cost and that economically viable service
is provided.
With the consolidation of the airline industry
that started in 1986, many analysts have begun to
wonder about its competitiveness, both now and
in the future. The wave of mergers has resulted
in an increase in the number of airlines that offer
nationwide service, but this comes in the form of
“fortress hubs.” At such airports, the dominant
carrier typically offers about three-quarters of the
airport’s flights. In addition, the national carriers
now face less competition from regional and

local service carriers, many of whom have been
purchased by or signed operating agreements
with the national carriers. The impact of these
developments (and of possible future consolida
tions) on fares depends on the competitiveness
of the markets for air travel.
To gain insight into the competitiveness of the
airline industry, this paper examines the determi­
nants of air fares for first-class, coach, and dis­
count service to a particular destination: Cleve­
land, Ohio. We begin by examining two of the
market models that have been proposed for the
airline industry. The first is the traditional view
that market competitiveness is determined by the
number and concentration of firms in the market.
The second is the theory of contestable markets,
in which the number of actual competitors in
the market plays only a small role. According to
this theory, it is the number of carriers that could
potentially enter the market that constrains fares.
We then discuss the implications for appro­
priate public policy. A reduced-form equation for
air fares is constructed, and the data that were
collected to estimate its parameters are de­
scribed. Finally, we present and analyze the
empirical results and discuss the implications for
public policy.

Our results suggest that these markets (the air­
line routes) are not perfectly contestable. The
number of actual competitors does influence the
fares charged by the airlines, other things being
equal. Thus, policymakers should act where pos­
sible to ease entry- barriers in the industry in
order to preserve and enhance competition.

I. Economic Models
of Airline Competition

The traditional method of determining the
amount of competition in a market is to examine
the market shares of the largest firms operating
in that market. This measure is relevant because,
until recently, most economists thought that
competitiveness was determined by the number
and concentration of the actual participants in
the market.
The U.S. Department of Justice uses a
Hirschman-Herfindahl Index (HHI: the sum of the
squares of all of the firms’ market shares) as an
aid in assessing the impact of proposed mergers
on market competition. This index ranges from
close to zero in the case of a perfectly competi­
tive market to 10,000 (1002) in the case of a
monopoly.1 The Department ofjustice guidelines
recommend rejecting mergers that result in mar­
kets with an HHI greater than 1,800 unless the
resulting increase in the HHI is less than 50 or
there are some other special considerations. The
rationale is that fewer competitors reduce the
competitiveness of the market, since there will
be less pressure to hold down prices and costs
and since the firms will find it easier to collude.
The airline industry appears to be very
uncompetitive when one examines the HHIs of
various airline routes. According to a recent
Congressional Budget Office study, on a typical
route only 2.5 carriers offer service. Even if these
carriers each had an equal share of the market,
this would result in an HHI of over 4,000.
The U.S. Department of Transportation— the
agency charged with oversight of the airline
industry— has taken a different approach than
the Justice Department. Over the last few years, it
has allowed mergers to occur between carriers
even when many of their routes overlapped. For
example, TWA and Ozark competed on many
routes involving their joint hub of St. Louis, and
their merger in 1986 resulted in a large increase
in concentration on these routes. In 1983, the
HHI was about 3,100; just after the merger, the

HHI was about 5,800; and in 1988 the HHI had
risen to about 6,800, with TWA offering about 82
percent of the flights out of St. Louis. The TWAOzark merger was clearly outside the Depart­
ment of Justice’s guidelines discussed above
(however, there was the special consideration
that Ozark was in financial difficulty and might
have failed unless it was taken over).
In approving mergers such as this one, the
Department of Transportation relied heavily on
the relatively new theory7of contestable markets
developed primarily by Baumol, Panzar, and Willig (1982).2 This theory states that under certain
conditions, it is not necessary to have a large
number of firms actually operating in a market in
order for prices and output in that market to
approximate the ideal outcome of a perfectly
competitive market. If entry barriers into the
market are low, and if there are no irrecoverable
costs to exiting the market, then even markets
with only a few firms will be constrained to fol­
low the same marginal-cost pricing that perfect
competition with many firms would. If the firms
in the market tried to raise prices above marginal
cost (the extra cost of producing an additional
unit of output), then entrepreneurs could enter
the market and charge a slightly lower price than
the incumbent firms (taking away those firms’
customers) and could earn an above-average
profit. The ease of entry and exit from a perfectly
contestable industry means that potential com­
petitors also exercise competitive pressure on
the firms in the industry.
There were several reasons to believe that the
airline industry might approximate a perfectly con­
testable market after the Civil Aeronautics Board
stopped regulating routes and fares, a process
phased in over several years starting in the late
1970s. Planes now can quickly be shifted from
one route to another, and many of the airlines
rent a significant proportion of their aircraft fleets.
In addition, there is a ready secondary market for
used aircraft, so a major component of an air­
line’s capital stock is much easier to acquire and
dispose of than in most other industries.
Working against the idea that the airline indus­
try is perfectly contestable are the current con­
gestion problems in the air traffic control net­
work. Also, new entrants find it difficult to
acquire gate space and slots for takeoffs and
landings at the more congested airports. Compu­
ter reservation systems, travel agent commis­
sions, frequent-flier plans, and hub-and-spoke

■ 2
■

1 Since the market shares are squared before summing, the market

shares of the largest firms will influence the index the most.

The theory of contestable markets has been applied to a number of

other industries. Whalen (1988) finds evidence that the banking industry is per­
fectly contestable.

networks are also cited as characteristics of pro­
viding air service that make entry into new
markets difficult. Borenstein (1988) provides a
more detailed investigation of these issues.
If the market for air fares approximates a per­
fectly competitive market, then there is very little
need for government oversight of the economic
conditions in the airline industry, although there
still would be a role in the regulation of air
safety. Actual and potential competitors force the
airlines serving a market to provide the service
that passengers want at the lowest possible fares.
If the market is not perfectly contestable, then the
government can ensure that entry into the market
is as free as possible, and should enforce existing
antitrust laws to protect consumers by preserving
as much competition in the market as possible.

II. Empirical Model
and Data

Although other researchers (for example, Bailey,
Graham, and Kaplan [1985], Borenstein [1988],
Butler and Huston [1987], and Call and Keeler
[1985]) have explored the extent of competition
in the airline industry by using models similar to
the one we develop, none of these studies
employs data as recent as ours (April 1987).
Thus, not only are our data further away from the
beginning of deregulation, but they also follow
the latest wave of mergers that occurred in 1986.
The following observations will be useful in
constructing the testable hypotheses. If the
market were perfectly contestable, then the
number of carriers serving a route would have
no relationship to passenger fares. If potential
competitors constrain the fare-setting abilities of
existing carriers, then the market is imperfectly
contestable and the effect of the number of car­
riers serving a route should have a significant,
although small, effect on the fares charged.
Lastly, if entry is so blocked that existing carriers
have little to fear from new entrants, then the
degree of competition on a route will be deter­
mined by the number of carriers currently serv­
ing the route, and the effect of an additional car­
rier on the route could cause a significant
reduction in fares. This is the more traditional
view of the relationship between the degree of
competition and the number of competitors.
In comparing the fares charged with the num ­
ber of carriers on the route across routes, one
must allow for other factors that influence fares.
In essence, we are estimating a reduced-form
equation for air fares, so that anything that influ­
ences the demand for, or the cost of, air travel

should be taken into account. The most impor­
tant of these factors are the length of the route,
the volume of traffic on the route, and whether
one or both of the airports involved are hubs or
are restricted in takeoff and landing slots.
The characteristics of a particular flight on a
given route can also influence both the supply
and the demand for the flight. The most impor­
tant of these are the number of stops on a par­
ticular flight, whether a meal is provided, and the
particular carrier offering the flight. Finally, the
demand for air service on a particular route will
depend in part on characteristics of the flight’s
origin and destination cities, such as their aver­
age per capita incomes and whether they are
business or tourist centers.
We estimate the following model using ordi­
nary least squares (OLS):

(1)

where

FARE

= Oq + ax CARRIERS
+ a2 CARRIERS2 + a} PASS
+ a4 MILES +
MILES2
+ a6 POP + a-, INC + aH CORP
+ a9 SLOT + aw STOP
+ au MEAL + a x2 HUB
+ tf,3 EA + a u CO + error,

FARE = one-way air fare;
CARRIERS = number of carriers;
CARRIERS2 = number of carriers
squared;
PASS = total number of pas­
sengers flown on route (all
carriers);
MILES = mileage from the origin
city to Cleveland;
MILES2 = the number of miles
squared;
POP = population of the origin city;
INC = per capita income of the
origin city;
CORP = proxy for potential busi­
ness traffic from the origin
city;
SLOT = dummy variable equaling
1 if the origin city has a slotrestricted airport,
0 otherwise;
STOP = number of on-flight stops;
MEAL = dummy variable equaling
1 if a meal is served,
0 otherwise;
HUB = dummy variable equaling
1 if the origin city has a hub
airline, 0 otherwise;

EA = dummy variable equaling
1 if the carrier is Eastern Air­
lines, 0 otherwise;
CO = dummy variable equaling
1 if the carrier is Continental
Airlines, 0 otherwise.

This model is estimated separately for each of
three classes of fares: first class, coach, and re­
stricted discount.
The data to estimate this model were com­
bined from a number of sources. The
(April 1987) was the source of the
fare information and the data on the flight char­
acteristics, such as CARRIERS, STOP, SLOT, MEAL,
EA, and CO. All of the data pertain to direct
domestic flights terminating in Cleveland. Unfor­
tunately, fares for connecting flights could not be
analyzed here because only direct fares are
reported in the
In future
research, we hope to obtain such data.

Official

Airline Guide

Official Airline Guide.

T A B L E

generated by each city. Information on whether
an origin city was considered to have a hub air­
line (HUB) was obtained from 1985 Department
of Transportation statistics. For each of the three
fare classes, summary7statistics on the variables
used in the analysis are provided in table 1.

III. Estimation
Results

Tables 2, 3, and 4 report OLS estimates of equa­
tion (1) for first-class, coach, and discount fares.
The amount of variation in fares explained in
each estimated equation (the adjusted R-square
statistics in tables 2 through 4) is generally high,
and is higher for the first-class and coach catego­
ries than for the discount category. This is prob­
ably the result of the discount fares being less
homogeneous than the other fare classes. For
our discount fare, we always selected the least
expensive restricted-discount fare reported in the

1

Summary Statistics of the Variables

Variable
FARE
CARRIERS
PASSENGERS
MILES
INCOME
CORP
SLOT
STOP
MEAL
HUB
CO
EA
POP

Mean

Standard
Deviation

330.17
2.77
18,458.00
744.19
13,996.00
10.63
0.22
0.46
0.60
0.71
0.16
0.16
4,046.30

123.63
1.33
22,802.00
535.18
1,766.00
16.67
0.42
0.60
0.49
0.46
0.37
0.37
4,668.20

Discount Fares

Coach Fares

First-Class Fares

Mean

Standard
Deviation

Mean

Standard
Deviation

201.78
2.89
15,260.00
537.27
13,709.00
8.76
0.19
0.41
0.44
0.66
0.08
0.07
3,497.60

89.60
1.25
21,414.00
465.43
1,643.60
15.17
0.39
0.63
0.50
0.47
0.27
0.26
4,184.90

62.65
2.88
15,273-00
541.25
13,727.00
8.75
0.19
0.42
0.44
0.66
0.08
0.08
3,493.40

29.85
1.25
21,406.00
466.32
1,656.10
15.17
0.39
0.63
0.50
0.47
0.27
0.27
4,187.80

SOURCE: Authors’ calculations.

Data on passengers (PASS) and nonstop
mileage from origin to destination (MILES) were
taken from the U.S. Department of Transporta­
tion’s
Data on per capita income (INC) of the
origin cities were obtained from the
(April 1986 issue). The number
of Standard & Poor’s companies headquartered in
each origin city (CORP) was compiled to be used
as a proxy7for the business traffic likely to be

mary’.

Origin and Destination City Pair Sum­

Current Business

Survey of

Official Airline Guide,

and these fares were not
always subject to exactly the same restrictions.3
In interpreting these results, recall that only
direct flights to Cleveland were included in the
data. Also note that since more than 90 percent of
passengers travel on some type of discount fare,

■ 3

It w as not possible to select one particular type of discount fare for all

of the routes because no type of discount fares were reported for all routes.

_............... ■

T A B L E

2

First-Class Fare Estimates

Variable
CARRIERS
CARRIERS2
MILES
MILES2
POP
INC
CORP
PASS
STOP
SLOT
HUB
MEAL
EA
CO
CONSTANT

Estimated
Coefficient

Standard
Error

-19.50
2.79
0.233
-0.974E-5
-0.598E-2
-0.195E-2
3-62
-0.818E-3
12.50

22.20
4.42
0.455E-1
0.197E-4
0.357E-2
0.285E-2
1.05
0.106E-2
9.18
23.90
12.60
10.50
11.40
11.60
40.60

7.13
11.30
11.20
-18.30
-66.40
212.00

T-Ratio
-0.878
0.632
5.13
-0.495
-1.67
-0.686
3.45
-0.771
1.36
0.299
0.900
1.07
-1.60
-5.72
5.21

NOTE: All values are authors’ calculations. Number of observations = 163;
R-squared = 0.863.

according to the Air Transport Association, this
class of service is probably the most important for
evaluating the competitiveness of the industry.4
The first issue is the effect of the number of
carriers on fares. The estimated values for CAR­
RIERS and CARRIERS2 have the expected signs
■

t

a

b

l

3

e

Coach Fare Estimates

Variable
CARRIERS
CARRIERS2
MILES
MILES2
POP
INC
CORP
PASS
STOP
SLOT
HUB
MEAL
EA
CO
CONSTANT

Estimated
Coefficient

Standard
Error

-23.00
4.00
0.277
-0.520E-4
-0.114E-2
-0.178E-2
1.22

11.60

-0.275E-3
7.64
-0.746
4.18
0.945
5.80
-56.50
126.00

2.19
0.231E-1
0.104E-4
0.200E-2
0.168E-2
0.487
0.522E-3
3.59
11.20
5.16
5.35
7.48
7.42
22.00

T-Ratio
-1.99
1.83
12.00
-4.98
-0.570
-1.06
2.51
-0.527
2.13
-0.667E-1
0.810
0.177
0.775
-7.61
5.75

for all three classes of fares. These results suggest
that as additional carriers begin service on a
route, fares are lowered, since CARRIERS is nega­
tive. But because the coefficient of CARRIERS2 is
positive, each additional carrier lowers fares on
the route less than the one before. After three or
four carriers are serving a route, fares no longer
appear to be affected by the number of carriers.
These coefficients are statistically significant
for coach and discount fares, but are not signifi­
cant for first-class fares. For discount fares, the
addition of one carrier to a monopoly route
would lower fares by about $11, other things
being equal. Adding a third carrier to the route
would again lower fares, but by only about $6.50.
With a fourth carrier, fares drop even less, by
about $2. Fares do not appear to fall any more
once about four carriers are serving the route. At
this point, discount fares are about $20 less than
they would be if only one carrier served the
route. Extrapolation beyond this point is not
warranted since the maximum number of carri­
ers on any route in our sample is only five.
The above result for first-class fares does not
mean that these fares are perfectly contestable,
however. If we estimate the same model as equa­
tion (1), but replace CARRIERS and CARRIERS2
with a dummy variable equal to one if there is
more than one carrier on the route and zero
otherwise, we find that the coefficient of this var­
iable is significant and negative for first-class
fares. First-class fares are about $21 lower on
routes with more than one carrier, other things
being equal. In other words, since fares are
cheaper on routes with more than one carrier,
these results do not support the notion that
these routes are perfectly contestable.
Earlier studies that investigated whether the
market for air fares was perfectly contestable also
found little support for perfect contestability. As
mentioned above, their data generally came from
the early 1980s and thus may have been estimated
too soon after deregulation for the airlines to
have adjusted to their new environment. Because
our study employs fare data from April 1987, it is
unlikely ,that the lack of contestability is a result
of the airlines’ having insufficient time to adjust
to the deregulated environment. This data set
also has the advantage of being gathered about a
year after the merger wave that peaked in 1986.
Not surprisingly, MILES has a positive and sig­
nificant estimated coefficient for each class of
fares. Coach and discount fares have a significant
amount of “fare taper”: as the flight distance
increases, the cost per mile falls. First-class fares

NOTE: All values are authors’ calculations. Number of observations = 323;
R-squared = 0.871.
■ 4

Cited in Kahn (1988).

do not exhibit this property to a significant
extent. For a flight of average length, first-class
and coach fares increase about $0.22 per mile
and discount fares increase about $0.06 per mile.
The PASS, SLOT, and HUB variables all measure
possible capacity constraints facing the airlines
serving a given route.5 HUB is not statistically sig­
nificant at the 5 percent level for any type of
fares. The density of traffic on a route as measured
by the PASS variable significantly increases dis­
count fares. Only discount-fare passengers pay the
expected premium for flying into slot-restricted
airports. Flying into a slot-restricted airport
increases the one-way fare by about $18 for these
passengers.

Discount Fare Estimates

Variable

Estimated

Standard

Coefficient

Error

-17.50
2.19
0.791E-1
-0.140E-4
-0.868E-3
-0.411E-2
-1.06
0.853
-3.85
17.70
-3-50
1.80
-10.60
-4.17
113.00

CARRIERS
CARRIERS2
MILES
MILES2
POP
INC
CORP
PASS
STOP
SLOT

HUB
MEAL

EA
CO
CONSTANT

4.76
0.905
0.96 IE-2
0.434E-5
0.829E-3
0.679E-3
0.203
0.217E-3
1.48
4.63
2.16
2.21
3.04
3.09
9.10

T-Ratio

-3.67
2.42
8.24
-3.23
-1.05
-6.05
-5.22
3.93
-2.60
3-82
-1.62
0.813
-3.49
-1.35
12.40

NOTE: All values are authors’ calculations. Number of observations = 323;
R-squared = 0.799.

Flight characteristics, such as the number of
intermediate stops on the flight, influence coach
and discount fares, but not first-class fares. Coach
passengers pay about $7.60 for each stop, whereas
discount-fare passengers actually get compen­
sated about $3.85 for each stop. The fare charged
does not seem to depend on whether the flight
includes a meal.

■ 5

The characteristics of the cities involved influ­
ence the fare charged to the various classes of
passengers. The larger the population of the
origin city, the lower the fare for all three classes
of service, although this result is statistically sig­
nificant at the 5 percent level only for first-class
fares. The per-capita income variable seems to
affect only discount fares significantly. Discount
fares fall as incomes rise, indicating that higherincome passengers expect compensation in the
form of lower fares for flying with discount
tickets, other things being equal. The more
important the city is as a business center (as
measured by CORP), the higher the first-class
and coach fares tend to be. Discount fares, on
the other hand, are lower.
Continental charges significantly less than
other carriers for first-class and coach service,
other things being equal. Conversely, Eastern
charges significantly less for discount service
than other airlines, other things being equal.6
Texas Air may own both of these carriers, but
they appear to follow different criteria in setting
fares. Keep in mind that these carrier-based fare
differentials reflect differing cost and demand
characteristics, including quality of service.

IV. Conclusion

An understanding of forces setting fares and the
level of competition in the airline industry is
crucial in order to formulate effective public pol­
icies for the industry. Some analysts have sug­
gested that the ease of entry into most airline
markets after deregulation increased the compe­
titiveness of fares, even though the actual number
of carriers is relatively small. We found that the
number of airlines serving a route does influ­
ence the fares charged for all classes of service.
Thus, the airline industry is not perfectly contestable even when very recent data are employed.
The benefits to passengers of adding an addi­
tional carrier on a typical route are still sizable,
with fares declining until about four carriers are
serving the route. This result is the strongest for
discount fares. Fares on routes with four to five
carriers are about $20 less than fares on routes
with only one carrier, other things being equal.
This is about a third of the average one-way dis­
count fare.

It is reasonable to consider whether both the number of carriers and

the number of passengers on a route should be treated as endogenous varia­

6

bles in equation (1). Hausman specification tests were performed and indicate

■

that in setting the fare on a given route, these variables can be treated as

lines, because only these two carriers appeared to behave differently from the

W e only report results that controlled for Continental and Eastern Air-

exogenous variables.

other carriers in setting fares.

Since deregulation, the airlines’ clear goal has
been to maximize their profits. Thus, they charge
the highest fare possible on all their routes, with
competition among existing carriers and the
ease of entry of new carriers limiting how high
those fares can be on a particular route. It is
important that policymakers look at both the
actual number of competitors and the ease of
entry for a particular route. Since the number of
carriers serving the typical route has risen since
1983— even if one allows for the recent merger
wave— this suggests that the market for air fares
remains fairly competitive, but that public poli­
cies to ease the entry of more carriers per route
could lead to increased benefits for consumers.
In short, these findings suggest that the tradi­
tional concepts of market concentration, such as
the number of competitors, are still relevant in
assessing the amount of competition on a given
route, even in the deregulated environment. Con­
sequently, the antitrust laws that are applied to
other industries are pertinent to the airline
industry.

References

Bailey, Elizabeth E., Graham, David R., and
Kaplan, Daniel P.,

Deregulating the Airlines,

Cambridge, MA: The MIT Press, 1985.

Baumol, William J., Panzar, John C., and Willig,
Robert D.,

Contestable Markets and the The­
ory of Industry Structure, New York: Har-

court Brace Jovanovich, Inc., 1982.

Borenstein, Severin, “Hubs and High Fares: Air­
port Dominance and Market Power in the U.S.
Airline Industry,” Institute of Public Policy
Studies Discussion Paper No. 278, University
of Michigan, March 1988.

Butler, Richard V. and Huston, John H., “Actual
Competition, Potential Competition, and the
Impact of Airline Mergers on Fares,” paper
presented at the Western Economic Associa­
tion Meetings, Vancouver, British Columbia,
July 1987.

Call, Gregory D. and Keeler, Theodore E., “Air
line Deregulation, Fares, and Market Behavior:
Some Empirical Evidence,” in Andrew F.
Daughety, ed.,
New York: Cambridge University
Press, 1985.

Analytical Studies in Transport

Economics,

Congressional Budget Office, “Policies for the
Deregulated Airline Industry,” July 1988.

Hausman, JA., “Specification Tests in Econo­

Econometrica,

metrics,”
1251-71.

46,

November 1978,

Kahn, Alfred E., “I Would Do It Again,”

tion,

1988,

2.

Regula­

Morrison, Steven and Winston, Clifford, “Empir­
ical Implications and Tests of the Contestabil­
ity Hypothesis,”
April 1987,
53-66.

nomics,

TheJournal of Law and Eco­
30,

Official Airline Guide:
North American Edition, April 1, 1987, 13-

Official Airline Guides,

Standard & Poor’s Corporation,

Security Price Index Record,

Statistical Service:
1986 Edition.

U.S. Department of Commerce, Bureau of the
Census,
1984.

State and Area Data Handbook,

U.S. Department of Commerce, Regional Eco­
nomic Measurement Division, “County and
Metropolitan Area Personal Income, 1982-84,”
April 1986.

Survey’ of Current Business,

U.S. Department of Transportation, Center for

Transportation Information,

nation City Pair Summary,

Origin and Desti­

Data Bank 6,

Computer Files.

Whalen, Gary, “Actual Competition, Potential
Competition, and Bank Profitability in Rural
Federal Reserve
Markets,”
Bank of Cleveland, Quarter 3, 1988, 14-20.

Economic Review,

Bank Capital
Requirem ents
and the Riskiness
of B anks: A Review
by William P. Osterberg
and James B. Thomson

William P. Osterberg is an economist
and Jam es B. Thomson is an assis­
tant vice president and economist at
the Federal Reserve Bank of
Cleveland.

Introduction

Banks are required to hold capital primarily as a
buffer against future losses and in order to
reduce the exposure of the deposit insurer.
However, as regulators and researchers have
recognized, changes in capital requirements also
affect bank portfolio behavior. It is possible that
increased capital requirements may lead banks
to increase their riskiness and thus increase their
expected losses or increase the potential expo­
sure of the deposit insurer.
The object of this article is to show that the
impact of increased capital requirements
depends on the extent to which deposit costs
reflect bank portfolio risk.1 In particular, we
show that with risk-based deposit insurance, the
incentives to increase leverage or portfolio risk
in response to an increase in bank capital
requirements are reduced.
The article is organized as follows. First, we
define bank capital and discuss the mechanisms

■

1

For uninsured deposits, deposit costs are the interest rate banks have

through which it is intended to affect bank
behavior. Next, we discuss the incentives for
banks to decrease their capital buffer (increase
their leverage). These incentives mainly stem
from conflicts between the interests of creditors
(depositors) and stockholders. We also show
how these incentives are influenced by pricing
deposit insurance. Previous research has shown
that deposit insurance that is not adjusted for risk
may encourage banks to increase their riskiness.
We discuss previous research on the impact of
increased capital requirements. We then present
a model in which deposit costs are allowed to
vary with risk, including the risk associated with
leverage and, thus, with the capital buffer. By
comparing our results with those of previous
studies where explicit deposit costs do not vary
with portfolio risk and leverage, we show that
risk-based deposit insurance reduces the incen­
tives to increase leverage or portfolio risk in
response to an increase in bank capital require­
ments.2 We also show that risk-based deposit

■ 2

Even though w e do not assume correctly priced deposit guarantees, we

to pay on the deposits. For insured deposits, the cost of a dollar of deposits is

do not get perverse effects from risk-based premiums (see Pyle [1983])

the interest rate paid on the deposits, plus the per-dollar deposit insurance

because we assume that the FD IC does not make relative pricing errors (that

premium.

is, that it can measure risk and price it consistently).

insurance reduces the variance of earnings and
the expected loss to the federal deposit guaran­
tor when banks fail.

Functions and Definitions
of Bank Capital

Regulators define bank capital in terms of book
values. The regulatory definition of bank capital
usually includes claims on bank profits (equity),
reserves on loans or securities, and long-term
subordinated debt. The primary function of bank
capital is to serve as a cushion against unantici­
pated losses on assets, thereby ensuring the sol­
vency of the bank. Bank capital is also used to
finance asset purchases and thus bank growth.
Minimum capital requirements (measured in
terms of capital-to-asset ratios) constrain bank
growth when it is costly to raise capital by issu­
ing stock. Otherwise, if the rate of return on
assets exceeds the cost of funds, banks would try
to increase size as much as possible. In this arti­
cle, we focus on how capital requirements affect
bank risk, rather than bank size.

Incentives for Banks to
Engage in Risky Behavior

While banks in some ways may be different from
other firms, banks’ incentives to engage in risky
behavior are in some ways similar to the incen­
tives of nonfinancial corporations. In particular,
in the absence of conflicts between stockholders
and bondholders (depositors), total bank value
maximization and bank equity value maximiza­
tion lead to identical results. However, as Jensen
and Meckling (1976) argue, conflicts arise
between stockholders and bondholders that
cause total bank value maximization and equity
value maximization to differ. By increasing the
risk of the bank’s portfolio or by increasing
financial leverage, stockholders may be able to
reduce the risk-adjusted value of the depositor’s
claim on the bank and thereby reallocate wealth
from depositors to the stockholders. Wealth is
reallocated if the reduction in the value of the
bank is less than the reduction in the value of
creditor claims on the bank. This type of conflict
is referred to as an agency problem in the
finance literature.
In most models of bank behavior, banks max­
imize the market value of equity and thus have
the incentive to increase the portfolio variance.
Because the value of equity cannot fall below
zero but can increase without limit, stockholders
will choose investments with a greater likelihood

of high profits, regardless of the chance of loss.
Unlike stockholders, bondholders receive only
the promised amount if returns are high, but
lose increasingly more as returns fall below the
total amount of their claim. Thus, creditors have
an incentive to control stockholder behavior.
Any analysis of the impact of capital require­
ments must also consider the banks’ incentives
to increase leverage (that is, to minimize their
capital holdings). If the cost of raising funds
from issuing stock exceeds the cost of raising
funds from deposits, stockholders will prefer to
increase their asset holdings via deposits and
thus lower their capital ratios. Lower capital
ratios (higher leverage) increase the probability
of bankruptcy7and thus of losses to creditors.
The cost of raising funds from deposits is influ­
enced by the pricing of deposit insurance. When
deposit insurance is not priced so as to reflect
bank risk, we refer to it as being “mispriced.” We
contend that it is the mispricing of deposit insur­
ance that is at least partially responsible for an
incentive for increased leverage. It is this incen­
tive that makes capital requirements binding.
At least for nonfinancial corporations, it is
common practice for bond covenants to contain
restrictions on stockholder/manager behavior
(see Smith and Warner [1979]). In fact, capital
requirements and restrictions on bank portfolios
can be viewed as bond covenants designed to
protect the creditors. On the other hand, credi­
tors may be protected if interest rates reflect
bank risk. Risk- or leverage-related deposit rates
could influence stockholders’ incentives to
increase portfolio risk or leverage.
It is an accepted conclusion that fixed-rate
deposit insurance encourages risky7behavior. Even
if the deposit insurance agency adjusts the depos­
it insurance premium so that banks on average
pay high enough premiums to cover expected
losses, safe banks subsidize risky banks. In the
absence of “correct” pricing of deposit insur­
ance, and given the unresolved agency conflict
between creditors and stockholders, banks will
attempt to maximize the subsidy provided by the
deposit insurance agency by increasing portfolio
variance and leverage.3 In this situation, there is
a rationale for restrictions on bank leverage.
However, if deposit costs reflect the increased
risk associated with higher leverage, capital re­
strictions may no longer be necessary or binding.

■ 3

Correct pricing means that the deposit guarantor charges a deposit

insurance premium equal to the risk premium the market would charge for
uninsured deposits (see Thomson [1987]).

□
Mathematical Models
of the Impacts
of Increased Capital
Requirements

Most mathematical models of the impacts of
increased capital requirements assume that the
bank is run for the benefit of the owners or
stockholders. The creditors (depositors and
deposit guarantors) are viewed as passive, per­
haps being protected somewhat by bank portfo­
lio restrictions designed to limit the ability of
banks to engage in risky activities and the covari­
ation of deposit costs with portfolio risk. Without
an explicit model of either the creditors’ position
(for example, the market value of their claim) or
the exact nature of the agency conflict, these anal­
yses cannot explain the financial structure or
capital position of the bank. The unresolved
agency conflict pushes the capital-asset ratio
towards its minimum.
The impact of capital regulation also depends
on the overall regulatory structure. Both the dif­
ficulty of monitoring banks and uncertainty
about the willingness of the guarantors to honor
explicit and implicit guarantees play a role (see
Kane [1986]). Pyle (1986) and Merton (1977)
show how the value of deposit insurance
depends on the closure policy and auditing fre­
quency. Pennacchi (1987) shows how banks’
preferences for greater leverage depend on the
regulator’s closure policy.
In our model, as well as in the mcxiels we
survey below, the bank is closed at the end of a
finite period of time. If the gross return on assets
is insufficient to pay off depositors, the insurer
provides the difference. In effect, these studies
simplify the analysis by assuming that insolvent
banks are closed and that there are no monitor­
ing difficulties or uncertainties about closure.
A relatively early study by Koehn and Santomero (1980) viewed banks as utilitymaximizers. They concluded that increased capi­
tal requirements would lead to increased asset
risk, and possibly to increased risk of bank fail­
ure. However, interest rates did not reflect
increased riskiness, as we would expect if depos­
its were uninsured. Neither was there an explicit
treatment of deposit insurance. Keeley and Fur
long (1987) emphasize the problems with the
utility-maximization approach.
Karenken and Wallace (1978) utilize the statepreference framework and assume that the de­
posit rate is fixed. However, due to the presence
of the deposit-insurance subsidy, the net deposit
cost varies with asset risk and leverage. Lower

leverage or lower asset risk decreases the proba­
bility of bankruptcy and hence the value of the
subsidy.
A third approach utilizes the cash flow version
of the Capital Asset Pricing Model ( Lam and
Chen [1985]). Deposit interest rates vary but do
not necessarily reflect asset risk or leverage.
Hence, there may still be a subsidy provided by
deposit insurance. Nonetheless, the covariation
between deposit rates and the rate of return on
assets plays a role in the bank’s portfolio deci­
sions. When deposit interest rates covary with
the return on the bank’s portfolio, the marginal
return associated with increased asset risk or lev­
erage is reduced. Therefore, the impact of
increased capital requirements on bank risk and
the probability of bankruptcy depends on
whether interest rates are held fixed or whether
they covary with the rates earned on assets.

Deposit Insurance Pricing
A separate body of research shows how deposit

insurance should be priced. Merton (1977)
models deposit insurance as a put option, show­
ing how the value of the put option, and thus
the position of the insurer, varies with the bank’s
leverage and portfolio risk.4 Since increased
leverage implies greater expected costs to the
insurer, with correctly priced deposit insurance
the premium charged each bank increases with
bank leverage and portfolio risk, where the port­
folio risk is measured as the variance of the earn­
ings on assets. With correct pricing, there is no
subsidy to the banks. Higher leverage results in
higher insurance premiums, ameliorates the
incentives to increase leverage, and modifies the
impact of increased capital requirements.

I. The Joint Effects
of Capital Requirements
and Risk-Based Deposit
Insurance on Optimal
Bank Portfolios
The Model

In Osterberg and Thomson (1988) the cash flow
version of the Capital Asset Pricing Model
(CAPM) used by Lam and Chen was modified to
allow for an endogenously determined cost of
deposits. The cost of deposits varies in a manner

■ 4

A put option is a contract that gives its holder the right to sell an asset

at a predetermined price to the issuer of the option on or before a specified
date. It represents a right but not an obligation to sell the asset.

similar to that suggested by the literature discuss­
ing the “correct pricing” of deposit insurance
(for example, Merton [1977]). By comparing the
results of our paper with those of previous stud­
ies where explicit deposit costs do not vary with
portfolio risk and leverage (Lam and Chen
[1985], and Koehn and Santomero [1980]), we
show how risk-based deposit insurance changes
the incentives to increase leverage or portfolio
risk (as measured by the variance of earnings) in
response to an increase in bank capital
requirements.
The organization of the model and the basic
results are presented below. As in our earlier
paper, we make the usual assumptions necessary
for the CAPM to hold. Furthermore, we assume
that bankruptcy costs and taxes are zero and that
the bank is operated by its owners.5 The owners
seek to maximize the value of bank equity,
which has three components:

V,

(1)

V= —1\ [E (n) - AC V (jf,W )
- \C V (n ,7r )], with
CV(n,W)

%

--

j

CV ( 7T,7T)

=

and

j =1

E( ) =

W -

W)
the aggregate cash flows M into n and W ,
where W is the aggregate cash flows in the

)

market, excluding the bank. This allows us to iso­
late the risk of the asset portfolio (internal risk)
from market risk in the maximization problem.
The owner-manager assumption is used to resolve the agency problem

that m ay exist between outside stockholders and managers (see Jensen and
Meckling [1976]).

g,

The deposit insurance premium,
varies
with the bank’s leverage and asset portfolio deci­
sions (internal risk). We assume that the bank
knows how its choices influence
and thus
what results from its asset portfolio and capital
structure decisions.
We can view the minimum ratio of deposits to
capital,
as a covenant imposed on the
bank by the FDIC in exchange for its deposit
guarantees. A second restriction is the balancesheet constraint that sources of funds must equal
uses of funds. Thus, the problem facing the bank
is to maximize
with respect to
and
sub­
ject to

g,

g

C = D/K,

A

D,

X Aj - D + K and
=i

D

(4)

the market;
tv = cash profit of the bank;
tt
expected value of cash profit;
A = market price of risk-bearing services;
aggregate cash flow in the market,
excluding the bank.
As in Lam and Chen (1985), the covariance
between the cash profit of the bank and the

■ 5

y=i

j

Ai - amount invested asset i,
o ij = covariance between rates of return
on asset i and j ;
o/ w - covariance between rates of return
on asset j and cash flows of all other firms;
R - one plus the risk-free rate;
M - aggregate cash flow of all firms in

CV

g

n
E (n ) = % r A - (R+g)D .

(2)

(3)

X X A i A, Oi

CV (n ,M)
CV (

D,

K.

V

AjOj,,,,

aggregate cash flow of all firms,
is
partitioned into internal portfolio risk
ttjt
and external risk
(5r,
by separating

7

j.

=i

i=l

N

Suppose that there are
risky assets in which
the bank can invest. Let . be the uncertain
return on asset Furthermore, the bank issues
only insured deposits,
and a fixed amount of
capital,
The bank pays its deposit guarantor
(henceforth, the FDIC) a premium of per dol­
lar of deposits. Its expected cash profits at the
end of the period are

CK (D

CK when the capital con­

<
=
straint is binding).

The solution to this problem is a series of opti­
mality conditions describing the bank’s choices
(see Osterberg and Thomson [1988] ). We
assume that the capital constraint is binding and
thus that equity value could be increased with a
looser capital requirement. The bank will choose
its asset mix so that marginal expected returns of
all assets are equal. The marginal increase in
equity value from a lower capital requirement,
7 , is just equal to the risk-adjusted return on
assets less the cost of deposits. Changes in lever­
age and portfolio composition affect
We utilize Merton’s (1977) put option formu­
lation of FDIC deposit insurance, which indicates
how varies with portfolio variance ( p ) and
leverage
and
are nonnegative func­
tions of portfolio variance and leverage, respec­
tively. We do not assume, however, that the
deposit guarantor correctly prices the insurance
and drives the net value of the FDIC’s claim to
zero (see Osterberg and Thomson [1987]). As a
result, the agency problem is not completely
resolved, and the stockholders still have incen­
tives to increase leverage and portfolio risk
(hence the binding capital constraint).

y.

g

(8). p

8

Bank stockholders seek to maximize equation
( 1 ) subject to ( 3 ) (the balance-sheet constraint)
and (4) (the capital constraint). The optimality
conditions, from the constrained maximization
problem, for the
assets can be written as (see
Lam and Chen [1985] or Osterberg and Thom­
son [1988])

n

(5)

2[A +

pCK] %Afa ik + R y

+

i =1

= a k - R - g,

(k

CK8

= 1,2,....,«).

The right side of (5) represents the expected
spread associated with investing in asset
is
the return on asset adjusted for external risk.
7
is the Lagrangian multiplier associated with a
binding capital constraint. Note that the riskbased deposit insurance premium affects portfo­
lio decisions by affecting the spread of return
over cost and by affecting the risk adjustment
associated with changes in leverage and variance.

k. a k

k

Portfolio Composition

As in Osterberg and Thomson (1988), the solu­
tions for the multiplier, 7 , and the optimal port­
folio shares,
, are

A*k

( 6)

7

= {[2(A+ «„)]-! X Xt,,,}-'
i=l7=1 ’

+ cKp)]-1 2

{[20

R - g - CK8}

-

Ak =

(7)

*=1./ =1 '

- (1 +

Note that 7 is smaller under risk-based deposit
insurance than under fixed-rate deposit insurance
because by definition
and p are posi­
tive. 6 7 can be interpreted as the cost to the
bank of a more restrictive capital constraint. In
this model, the 7 is positive because of agency
problems. By tying deposit costs to bank-asset risk
and leverage, the risk-based deposit-insurance
premiums in this model partially resolve the
agency conflict and, hence, lower the cost of the
capital constraint. 7 Intuitively, deposit rates that
do not vary with risk or leverage provide a sub­
sidy to the stockholders. The subsidy increases
with the risk and leverage of the bank. Riskbased deposit rates reduce the risk- and
leverage-related subsidy and therefore the cost to
stockholders of increasing the capital constraint.
Equation (7) shows that the optimal portfolio
share for asset is a function of 7 . Since 7 is
smaller for banks paying risk-based deposit rates
than for banks paying fixed-rate deposit rates, the
impact of the capital requirements has less
impact on portfolio composition for banks pay­
ing risk-based premiums than for banks paying
fixed-rate premiums. Equation (7a) gives the
relationship between the optimal portfolio share
for asset under fixed- and variable-rate premi­
ums. From (7a) it is clear that adjusting depositinsurance premiums for asset risk and leverage
has an uncertain impact on portfolio composi­
tion. To see more clearly the effects of risk-based
premiums on portfolio composition, we substi­
tute ( 6 ) into (7),

C, K, 8,

k

k

(7b)

C)K}.

n

[2(A

+ pCK)]-l {% vk jak

vt

R - g - CK8

-

7

}

7

(k =

( 6 a)

=

(1 +

A -.

AFk

g ~g

7

If we set p equal to zero in (7b) we get
bank paying fixed-rate deposit-insurance
premiums.

,

„

A*k =

A*k for a

y F - CK8 - CKp( 1 + C)K,
■

x
(7a)

I

' ' ■1

C)K% vkj
+ ----- n n~~---- (k=
t M j
i = l j =l

1,2,...,«).

ijth.

8

2 'V ,

i= 1 7 =1

Here
. is the
element of the inverse
variance-covariance matrix of the asset shares
Let
and
be the multiplier and the
optimal asset share for the fixed-rate deposit
, p = 0,
insurance case (that is, =
and
= 0). Equations ( 6 ) and (7) can be re­
written as

yF

[2(k + p C K )V '{X vkJak
j =l
X~! vki
n n
- — TH --2 S

=

2

7=1

-

Al

AFk + pCK(l C)K
pCK)

2A
+
-------------------- •
2(A +

6

This differs from Lam and Chen's stochastic interest-rate case where

the capital constraint multiplier m ay be larger or smaller than the capital con­
straint multiplier in the deterministic deposit case.

■ 7

The risk-based deposit-insurance premiums only partially resolve the

agency conflict because we do not assume the FD IC charges the bank the full
value of the insurance. That is, we do not impose correct pricing on the model.

From (7b) the optimal asset share is a func­
tion of the expected asset returns adjusted for
outside risk weighted by the elements of the
inverse of the variance-covariance matrix. The
fixed-rate deposit insurance result is identical to
Lam and Chen’s result when Regulation Q pre­
vails and is equivalent to Koehn and Santomero’s
results. For both fixed-rate and risk-based deposit
insurance,
is also a function of the capital
constraint. When variable-rate deposit insurance
is introduced into the model,
is also a func­
tion of the change in the cost of deposit insur­
ance due to a change in the risk of the bank’s
portfolio, p. It is interesting to note that
is
not a function of <5 or
The impact of increased capital requirements
on asset portfolio composition is uncertain for
banks facing both the fixed-rate and risk-based
deposit insurance. The indeterminate sign on

(9)

E(ff)
=

n n

i=\

2^<
7=1 '

is consistent with the findings of Lam and

Chen.8 That is, although the purpose of an
increase in the capital requirement is to reduce
overall bank risk, it may cause the bank to
choose a riskier portfolio and may increase over­
all bank risk.

Portfolio Risk and
Expected Profits

For investors and bank regulators, it is not the
risk or return of the individual activities (or
assets) that matters, it is the risk-adjusted return
on the bank’s portfolio. Therefore we are inter­
ested in the effects of risk-based deposit insur­
ance and changes in capital requirements on
internal risk (portfolio risk),
), and
on expected profits,
From Osterberg
and Thomson (1988), the portfolio risk and the
expected profits of the optimal bank portfolio are

CV ( n , n

CV(tt,tt)
= ( 2 [A + pC K ]y2 { 2 2 vij0iiaj
„ „
*=U=1 ’

„

{ J 2 v i j ri oti
i= l7=1 '
.

22

2= 1 7 = 1

n n
(1 + 0 * 2

2 v>

________i‘=iy=i
n n

(R+ g)CK.

2 2 vi:j

A*k

g.

(8 )

% vu ri

2

A*k

E (n ).

2

i - 1 7 =1

A\

dAl
dC

(2[\ + pC K])~l

i = 1 7 =1

If we set p = 0, equation (8) is the variance of
earnings in the fixed-rate deposit case. Note that
( , tt is not a function of <5org.
like ^4^,
Furthermore, because p is positive, the variance
of portfolio earnings for a bank with fixed-rate
deposit insurance is greater than the variance of
earnings for a bank with risk-based deposit insur­
ance. In other words, banks that have to pay
depositors (or the FDIC) for risk-bearing services
will hold less-risky portfolios than banks that do
not have to pay for those risk-bearing services.
This result holds for all values of
As in Lam and Chen, an increase in the
capital requirement leads to a reduction in
portfolio risk under fixed-rate deposit
insurance. That is,
)
---------- is positive when p = 0. However,

CV n

)

C.

d C V (n ,n
dC

the sign of

dCV (n ,n
oC

)
---------- is ambiguous for

banks facing risk-based premiums. Therefore, the
joint effect of a more restrictive capital constraint
and of risk-based insurance premiums may be to
increase bank portfolio risk.9 However, because
the value of (8) is greater when banks face fixedrate premiums than when they face risk-based
premiums for all
risk-based premiums result
in less internal risk than do fixed-rate premiums.
Therefore, so long as the FDIC does not make
relative errors in pricing its guarantees, riskbased deposit-insurance premiums do not intro­
duce any new perverse effects into the analysis.

C,

g ~g

2 M

j

i= l =1 '
1(1 +

C)K]2

n n

t t vi:j

i=U=i

If we set =
and p = 0, equation (9) is
the expected profits for a bank with fixed-rate
deposit insurance. As anticipated, when the risk

■

6

Lam and Chen also get an indeterminate result for the net effect of

more stringent capital requirements on overall bank risk in their stochastic
deposit case.

■ 9

Separation between capital structure and portfolio decisions m ay not

hold in our model because we do not assume that the deposit guarantor
charges banks a premium equal to the fair value of the deposit guarantees.

E3
profile of the bank results in a risk-based pre­
mium,
equal to the fixed-rate premium,
profits are lower for the bank paying risk-based
premiums than for the bank paying fixed-rate
premiums. This result holds because, as we
know from equation (8), banks paying fixed-rate
premiums will hold riskier portfolios than banks
paying risk-based premiums, and there is a posi­
tive relationship between risk and return
(expected profits).
For both fixed-rate and risk-based insurance,
the effect of a change in
on expected profits is
ambiguous. Since expected profits are not
adjusted for risk, it is possible for a relaxation of
the capital constraint to increase the value of the
firm and to reduce profits. This result was also
found by Lam and Chen (1985).

g,

C

Bankruptcy Risk

The only time the FDIC must honor its guaran­
tees is when a bank fails. So, the impact of
changing the capital requirement on the risk of
bankruptcy is an important issue for the FDIC. A
bank’s bankruptcy risk is a function of asset port­
folio risk and leverage. Since an increase in the
capital requirement reduces leverage, an
increase in internal risk in response to increased
capital requirements does not necessarily
increase bankruptcy risk. Koehn and Santomero
(1980) show that the probability of failure,
is

P,

(10)

P = P r{n < K }<

CV (n ,7T )
-

K]2

C

Holding
constant, the impact of risk-based
deposit insurance is to reduce both the numera­
tor and denominator of
Therefore, the impact
of risk-based insurance on default risk is uncer­
tain. O n the other hand, a reduction in the vari­
ance of earnings should reduce the expected
loss to the FDIC when a bank fails. From this
standpoint, risk-based deposit insurance pro­
duces a desirable result.
Lam and Chen (1985) show that the impact of
changing the capital requirement on P is inde­
terminate for fixed-rate deposit insurance. It is
also indeterminate when risk-based deposit insur­

P.

ance is introduced. Our inability to s ig n __

QP.—
dC

for banks with risk-based deposit insurance is at
least partially due to our assumption that the
FDIC does not charge banks for the fair value of
their insurance.

II. Conclusion

Studies of the impact of changes in capital
requirements on bank portfolio behavior and
risk are extremely sensitive to the assumptions of
how deposit insurance is priced. Previous
mathematical analyses of the impact of increased
capital requirements on bank portfolio behavior
implicitly or explicitly assume that deposit insur­
ance is mispriced. This introduces an agency
problem into the analysis that causes the capital
constraint to be binding and generates the con­
clusions of these studies. We contend that with
correct pricing of deposit insurance the capital
constraint is no longer binding. Using a m odi­
fied version of the cash flow CAPM, which incor­
porates a put option formulation for deposit
insurance, we compare the results of our earlier
study (Osterberg and Thomson [1988]), where
deposit rates vary with portfolio risk and lever­
age, to the general results of previous studies
where explicit deposit costs are independent of
portfolio risk and leverage.
We find that, with risk- and leverage-related
deposit rates, the incentive to increase leverage
is smaller than when the deposit rate and insur­
ance premium are fixed. Allowing explicit de­
posit costs to vary with risk and leverage also
reduces the portfolio variance. In addition, asset
choice is influenced by the response of the risk
premium to increases in portfolio variance.
As in the case where explicit deposit costs do
not vary with risk and leverage, the impact of
increased capital requirements on portfolio
behavior for banks paying risk-based deposit
insurance premiums is generally ambiguous. In
both cases, the impact of increased capital
requirements on asset choice is indeterminate,
as are the responses of portfolio variance,
expected profits, and the probability of bank­
ruptcy. However, our failure to impose correct
pricing may be responsible for these indeterminacies. Nonetheless, allowing deposit rates to
vary with portfolio risk and leverage results in
reductions in portfolio variance and in the incen­
tive to increase leverage. These would seem to
be desirable results from a regulator’s viewpoint.

Pyle, David H., “Pricing Deposit Insurance: The

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Jensen, Michael C. and Meckling, William H.,
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Effects of Mismeasurement,”
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_________, “Capital Regulation and Deposit
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189-201.

foum al of Banking and Finance,
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posit Insurance: The Case for Reform,”
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175-88.

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Financial Contracting: An Analysis of Bond
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July 1978,
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51,

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Koehn, Michael and Santomero, Anthony, “Reg
ulation of Bank Capital and Portfolio Risk,”
December 1980,
1235-44.

Journal of Finance,

35,

Lam, Chun H. and Chen, Andrew H., “Joint
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June 1985,
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40,

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Merton, Robert C., “An Analytic Derivation of
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June 1977,
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1,

Osterberg, William P. and Thomson, James B.,
“Deposit Insurance and the Cost of Capital,”
8714, Federal Reserve Bank
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_________ , “Capital Requirements and Optimal
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Proceedings:
A Conference on Bank Structure and Compe­
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Pennacchi, George G., “A Reexamination of the
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August 1987,
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Thomson, James B., “The Use of Market Informa­

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tion in Pricing Deposit Insurance,”
November 1987,
528-37.

Money, Credit and Banking
19,

Tu rn o ve r, W ages, and
A d ve rs e Selection
by Charles T. Carlstrom

Charles T . Carlstrom is an economist
at the Federal Reserve Bank ot
Cleveland. This paper is based on
the author's Ph .D . dissertation at the
University of Rochester. The author
wishes to thank Randall Eberts, Wil­
liam Gavin, Erica Groshen, Jam es
Hoehn, Kenneth McLaughlin, Walter
Oi, and Richard Rogerson, all of
whom provided helpful comments on
earlier drafts of the paper.

Introduction

Worker mobility is necessary for the efficient
operation of the labor market, so that the best
matches can be found between workers and
employers. Employers have only limited infor­
mation about the abilities of each prospective
worker, however. When making hiring decisions,
they take the chance of employing a worker who
does not have the skills (and thus the productiv­
ity) that was originally expected.
Both high- and low-productivity workers seek
higher-paying jobs at any given time. The prob­
lem facing the employer is how to distinguish
between the two. Low-productivity job searchers,
of course, try to pass themselves off as highproductivity workers. The employer can discern
a worker’s true abilities only after the hiring
decision has been made, however. Because of
this asymmetrical information, workers’ ability to
change jobs and find the best match may be
seriously impaired. Consequently, the labor
market may not work efficiently.
This paper suggests that asymmetrical informa­
tion can result in adverse selection. Adverse
selection is a term coined by Akerlof (1970) to
explain why the used-car market is dominated
by “lemons.” Car owners, he argues, often sell

their vehicles because of poor performance or
unreliability. Potential buyers realize the owner’s
motivation and pay less for a used car because of
the likelihood of purchasing a lemon. The ten­
dency is then reinforced for new-car owners to
sell their vehicles only if they are unreliable.
Thus, adverse selection can explain why a new
automobile sells for considerably less as soon as
it is driven off the showroom floor. In the case of
the labor market, adverse selection comes about
because low-productivity workers may change
jobs in order to be confused with highproductivity job-changers.
A model of worker mobility based on adverse
selection can help to explain several stylized
facts of the labor market, particularly in regard to
job turnover and wages. First, as Mincer (1984)
shows, frequent job mobility among older
workers results in lower wages. Second, while
earnings for all workers tend to increase over
time, older workers who quit generally experi­
ence zero or negative wage growth (Bartel and
Borjas [1981]). Adverse selection can also help
to explain why workers who have had a history
of frequent job moves are more likely to move
in the future.
For the same reason that lemons may dom i­
nate the used-car market, lower-productivity

workers tend to be frequent job-changers. These
workers will then have lower wages, on average,
compared to infrequent job-changers. This can
explain why mobility among older workers
results in lower wages and why prior mobility
can predict future mobility.
These empirical regularities are frequently
explained by combining the concept of “firmspecific” human capital with the assumption that
workers differ in their propensities to change
jobs. Firm-specific human capital is knowledge
that increases workers’ productivity at their pres­
ent firm, but that cannot be transferred to other
firms. Thus, as a worker’s tenure with the same
firm increases, his or her firm-specific knowl­
edge grows, pushing up his or her productivity.
Frequent job-movers would invest in less firmspecific human capital, since the knowledge they
gain on the job would be forfeited after each job
change. The argument is then that frequent jobmovers would have lower average wages and
flatter age-earnings profiles than infrequent jobchangers. Consequently, infrequent job-movers
would have a steeper age-earnings profile than
would the frequent job-movers.
Arguments based on firm-specific human capi­
tal have some problems explaining these obser­
vations of the labor market, however. First, no
reasons are given for the assumed difference in
propensities among workers to change jobs.
Second, the firm-specific human capital model
cannot explain the relationship between wages
and turnover in light of work by Salop and Salop
(1976). They show that if a worker’s propensity
to move is not public information, then the
infrequent job-changers would post bonds at
firms in order to separate themselves from the
frequent job-movers. The implication is that the
wage rates for job-movers should be higher than
those of job-stayers in the early part of their
careers— an observation that is inconsistent with
the findings of Bartel and Borjas.
Third, if a substantial number of firms require
general rather than firm-specific human capital,
then frequent movers would sort themselves
into these firms. They thus would have steeper
age-earnings profiles because they would bear
the full cost of acquiring the general human cap­
ital. In firms with primarily firm-specific human
capital, the costs would be shared by both the
worker and the employer.
The adverse-selection model of labor mobility
can help explain these empirical anomalies with­
out relying on firm-specific human capital. More­
over, it provides a basis for examining the wel­
fare implications of “lemons” (low-productivity
workers) in the labor market. The model predicts
that mobility is hampered because frequent

moves can brand a person as a low-productivity
worker. However, it is shown that government sub­
sidies to increase mobility would be ineffective.
The model is developed in several steps. The
basic assumptions are presented in section I.
The first version of the model incorporates con­
tingent wage contracting, which in effect allows
firms to sort among workers according to pro­
ductivity. In this case, it is shown that adverse
selection is not a problem, since all workers are
paid their expected output.
The remaining versions of the model exclude
contingent wage contracts, which introduces the
situation in which all workers receive the same
wage, ex ante. This pooling of low- and highproductivity workers creates adverse selection,
where the low-productivity workers are the fre­
quent job-changers.
Example 2 of the model assumes that workers
post no bonds, in which case the worker’s wage
in every period is the firm’s estimate of his or
her productivity. Next, example 3 allows bond­
ing, which benefits high-productivity workers
(the infrequent job-changers) and hurts lowproductivity workers (the frequent job-changers).
Bonds arise in order for firms to compete for the
high-productivity workers. Finally, example 4 is a
two-period model with bonding. This example is
useful for discussing the welfare implications of
the model, which are presented in section II.

I. Job Mobility
and Adverse Selection

In the following model of the labor market,
workers are assumed to live and work for three
periods indexed by 1, 2, and 3. A three-period
horizon allows the model to explain why
workers who moved frequently in the past are
more likely to move in the future. At the end of
periods one and two, workers decide whether to
continue working at their present job or to
change jobs. Workers change jobs if the change
raises the expected value of their future wages.
Productivity at a firm consists of a jobmatching component, 6 and an individualspecific component,
The labor contribution to
production is represented by the simple linear
relation
A worker’s base productivity
level,
is assumed to be constant across firms.
The matching component, 6 varies across firms,
so workers shop around in order to improve
their job match. However, since only the workers
know their own base productivity,
firms can­
not immediately observe whether a new worker
changed jobs because he was a high-productivity
worker with a bad job match or because he was

p.

p,

,

y - p+ 0.

,

p,

a low-productivity worker wishing to be con­
fused with a high-productivity job-changer.
The following restrictions are placed on the
distributions of and 0:
is assumed to be dis­
tributed on the interval ' ,
with a cumula­
tive distribution function of
and a density
function of /
0 is assumed to be distributed
on the interval 6 6
with a cumulative dis­
tribution function of (0) and a density func­
tion of (0) with (0) = 0. In addition, it is
assumed that 0 is independent both across indi­
viduals and across different jobs, and that and
0 are independently distributed random varia­
bles. Thus, a worker’s current job match— or the
quality of another worker’s match— does not
provide the worker with any information regard­
ing his match at another firm. Similarly, a worker’s
productivity does not indicate which job or task
he will be most productive in performing.
Prior to production, neither firms nor workers
know what 0 will be, although workers know
their own productivity type,
After one period,
a worker’s output at the firm,
is assumed to be
perfectly observable by both the worker and the
firm. Furthermore, it is assumed that a worker’s
output at a firm is constant over time but cannot
be observed by other firms.1
For simplicity, it is assumed that firms cannot
observe an applicant’s past wage rates. This
ensures that workers who did not move after the
initial period will not move in subsequent peri­
ods. The only reason a worker would want to
move after the second period would be to find a
better job match. He would not move after
period two, however, because the incentive to
search for a better match declines with age.

p

g

(p)\
[- ', "]
G
E

p
[p p"]
F (p )

p

p.
y,

Example 1 : Mobility
and Wages With Contingent
Wage Contracts

This section examines the model’s properties in
an economy with no restrictions on types of
wage contracts offered, in order to show that the
stylized facts of the labor market cannot be
explained without adverse selection. The model
predicts that workers will be paid their realized
output,
at the end of each period. This is
called a contingent wage contract, because a
worker’s pay is contingent on his or her realized
output in that period.

y

Since workers are risk-neutral, they are indif­
ferent between accepting a wage equal to their
base productivity level,
or accepting a wage
equal to their realized output,
Contingent
wage contracts in effect allow firms to sort
among workers according to productivity. If
workers are paid based on their output, the
model collapses to a Simple version of a stan­
dard job-matching model, in which workers
move only to seek better matches.
Define
to be the value of future wage
payments at the beginning of the first period for a
worker with a base productivity level of
define
) to be the value of future wage payments at
the beginning of period two for a worker who
produced
+ 0i in the first period and
decided not to move; and define X2
6 2 to be
the value of future wage payments for a worker
who moved after the first period.

p,

y.

W\(p)

p;

Vziy

y =p

(p, )

Wiip)
= p+Oi + Ei max[X2(p, ), V (y)]

(1)

62

where

^(pyfh) = p + O + £ 2max[p + 03 ,p + # ]
2

V (y) = 2(p+

00

2

and

2

i

0 f. = match at th firm,
expectation given the information at
the end of period

Et =

t.

(p

) consists of the worker’s first-period
wage (the value of his productivity +0i) and
either A2 or 2 depending on whether he
switches jobs after the first period. A worker
switches jobs if X2 >
but stays at his job if
A2 <
If a worker does not move after period
one, he earns his output,
0lt in both
periods two and three. A worker who moves
after period one will earn + 02 in the second
period and then either his output, + 02, if he
stays and works at this firm again in period three,
or if he switches jobs once more. A worker
who changes jobs after the first period will do so
again if his output, + 02 , is less than
(his
expected wage if he moves). Thus, a worker
who changes jobs after the first period does so
again if 0 < 0. Figure 1 depicts a worker’s wage
based on whether he moves or stays at his firm
after periods one and two.
The reservation output level for a
productivity worker,
is defined to be the
wage at which the worker is indifferent between
staying and leaving, 2
=
2
02)
= A2(p). A worker stays at his present job if
0i >
This definition implies the following

p

V,

V2,

V2.

y - p+
p

■

1 This assumption is not crucial because observing a worker’s output at

base productivity level.

p

p

p

p

y r(p),

a previous firm would give a potential employer a "noisy” signal of a worker's

2

V (y r(p))

y r(p).

p-

E \\ (p,

p+

F I G U R E

1

Possible Moves and Wages
With Contingent Contracts

SOURCE: Author.

W, V,

expressions for the expected values of
and
A (where
denotes the expectations operator):

E

(2)

EWx(p) = p + G (y r (p Y p )\i(p )
-G (y r(p)-p)) x
E(V (p+ d 2\ 02 > y r(p)-p)

+ (1

2

(3)

(4)

EX (p) = p

2
+ G (0 )p
+ (1-C7(0))(p + £ ( 0 2l0 > 0))

EV (y) = 2p.
2

The probability that a worker leaves after the
first period, 0i <
is given by
since
is the cumulative distri­
bution function of 0. Similarly,
(0) is the
probability that 0 2 < 0 and is the probability
that a worker will move after period two if he
moved after the first period. The expected value
of future wages for a worker who moved after
the first period, 2
is his expected wage in
the second period,
plus the product of his
probability of moving again,
(0), and his aver­
age wage if he moves again,
plus the proba­
bility that he does not move, (1
(0)), multi­
plied by his expected wage if he stays,
+ £ ( 0 2 102 > 0).
If we further assume that the 0s are uniformly
distributed over the interval (-0', 0'), then the res­
ervation output for a risk-neutral -productivity
worker with no search costs is
= +0'/8.
The probability that a worker moves after period
zero would then be
9/16, and
the probability that a worker moves after period
two, given he moved after period one, would be
(0) = 1/2. These separation probabilities are

G (y r(p)-p),

y r (p) - p,
G

X (p),
p,

G

G
p,

G

p

p
y r (p) p

G (yr(p)-p) -

G

constant across workers, implying that adverse
selection is not a problem. The reason is that, on
average, workers are paid their expected output,/).
The example predicts that job-movers— those
with the worst matches— earn lower wages. How­
ever, it cannot explain why these same workers
have less future wage growth. Similarly, the driving
force behind this result is the matching character­
istic, which can explain the mobility of younger
workers. However, it cannot explain the empirical
evidence which suggests that older workers, but
not younger workers, are hurt when moving.
Because most wage contracts are not contin­
gent on a worker’s future output, the remaining
examples in this paper exclude contingent wage
contracts. This introduces a pooling equilibrium,
where, ex ante, all workers receive the same
wage. The result is adverse selection, where the
low-productivity workers are the frequent
job-changers.
Adverse selection can explain why older work­
ers are seemingly worse off after they move.
Although a job-matching model is not realistic
when considering the mobility of older workers,
the assumption is maintained in order to ensure
that some workers always change jobs. The
matching component is not necessary7for the fol­
lowing examples.2 The next example examines
the implications of the model excluding both
contingent wage contracts and bonds, so that a
worker’s wage in every period is his expected
output in that period.

Example 2: Mobility and
Wages Without Contingent
Wage Contracts and Bonds

The examples given in tables 1-4 assume that
there are two types of workers, who can have
three possible outputs at a firm. Half of the
workers are high-productivity with
2; the
rest are low-productivity with
1. The jobmatching component is assumed to take on
three values (-1, 0, or 1), each of which occurs
with a one-third probability.
This example considers an equilibrium where
no bonds are posted, that is, where a worker’s
wage in every period is the firm’s estimate of his
or her productivity. This implies that there will
be a pooling equilibrium and that all workers
will receive the same wage in the first period.
With these assumptions, the solution given in
tables 1 and 2 can be verified.

p-

■ 2

See Greenwald (1986).

p=

T A B L E

1

yr

Mobility and Wages
for a Low-Productivity

y r(

Worker Without Bonding

Period

Period
1
Output at which a
low-productivity
worker is indifferent
between moving and
staying

y r (1) = 1.4 u

Period

__ 2 ____

3

= 6/5

—

'3

Example 3: Mobility
and Wages Without
Contingent Contracts,
Bonding Allowed

Fraction of workers
who move at end
of period

2/3

2/3

Wages for a lowproductivity worker
who never moves

3/2

y =2

Wages for a lowproductivity worker
who moves only after
period one

3/2

W

Wages for a lowproductivity worker
who moves after both
periods one and two

3/2

w 2 = 4/3

2

= 4/3

y

= 2

y

- 2

w 3 = 6/5

NOTE: w2 = the second-period wage for workers who changed jobs after
period one; W3 = the third-period wage for workers who changed jobs after
periods one and two.
SOURCE: Author.

The transition probabilities and wages given
in tables 1 and 2 can be shown to solve the
preceding problem. First assume that the separa­
tion rates in the tables are correct. They can then
be used to verify the wages, 2 and 3 . Given
that the wages are consistent with the separation
rates, it is then necessary to show that these
wages imply the separation rates posited.
For example, if the reservation output for a
high-productivity worker is 1.7, then he will leave
his original firm if < 1.7 or equivalently if
1 = 1 , which occurs one-third of the time.
High-productivity workers who stay will earn their
output, which is either = 2 or
3. If a highproductivity worker moved after period one, he
would move again if
<
= 6/5. This
occurs one-third of the time, or when 2 = 1 .
Similarly, low-productivity workers will move
two-thirds of the time given their reservation
outputs. With these transition probabilities, we
can calculate the wages of job-movers. Then, X2
and
can be calculated with these wages to

w

w

y

y

y

y%

V (y)

verify that the reservation output for a lowproductivity worker,
( 1 ), is 1.4, while the res­
ervation output for a high-productivity worker,
2), is 1.7.
Notice that the low-productivity workers move
twice as often as the high-productivity workers:
two-thirds (one-third) of the low- (high ) pro­
ductivity workers move after period one, while
two-thirds (one-third) of those who moved pre­
viously move again after period two. This is a
result of adverse selection.

y=

wz

y

Because of the difference in mobility between
high- and low-productivity workers, example 2
cannot be an equilibrium once bonding is
allowed. Firms could earn positive profits by try­
ing to compete for the high-productivity workers,
since firms make money by employing these
workers and lose money by employing lowproductivity workers.
Because high-productivity workers move only
half as often as low-productivity workers, firms
try to attract the high-productivity workers by
requiring incoming workers to post bonds that
are paid according to their future mobility. Those
who change jobs forfeit their bonds, while the
job-stayers split the proceeds of the bonds.
Bonding implies that workers no longer earn
their expected productivity every period: instead,
they are paid less than their expected productivity
in the first period of an employment contract,
and make up for this loss in later periods. The
amount of the bond is the difference between a
worker’s expected productivity and his wage dur­
ing the first period of an employment contract. In
later periods, a worker is paid more than his mar­
ginal productivity, the bonus being the difference
between his wage and his expected productivity.
Bonding benefits the high-productivity
workers— those who move infrequently— and
hurts the low-productivity workers— the frequent
job-movers. Because bonds offset some of the
income gained by the low-productivity workers
as a result of adverse selection, they redistribute
income from the low-productivity workers to the
high-productivity workers. Competition for highproductivity workers ensures that workers post
bonds, although in equilibrium, bonding may
not be sufficient to separate workers according
to their respective productivities.

b\

T A B L E

b%

Mobility and Wages
for a High-Productivity
Worker Without Bonding

Period
1
Output at which a
high-productivity
worker is indifferent
between moving
and staying

Define
to be the bonus paid to workers
who did not change jobs after period one, and
define
to be the bonus paid to workers who
switched jobs after period one and stayed after
period two. Figure 2 depicts a worker’s wage
based on whether he moves or stays at his firm
after periods one and two. Given the structure of
bonding as described above, tables 3 and 4 illus­
trate the solution for this example.3
Tables 3 and 4 are an equilibrium for this
example, since a potential firm could never suc­
cessfully compete for either a low-productivity or
a high-productivity worker. The low-productivity
workers are still being confused with the highproductivity workers and thus do better than
they would if they admitted that they were lowproductivity workers and were paid their
expected output, 1, every time they moved and
did not post any bonds.
It can also be shown that if the amount of the
bond posted by workers changed, the highproductivity workers would be made worse off.4
This is because the bonuses,
and fo, are the
largest possible so that the high-productivity
workers still move. (That is,
and 2 are
chosen such that a high-productivity worker who
produces an output of 1 would be indifferent
between moving and staying.) If
were
increased, high-productivity workers would
never move, even if they have a bad match,
0 = -1. If 2 were increased, high-productivity
workers would never move after period two and
would be made worse off.
This example illustrates that adverse selection
is present in the model, since two-thirds (onethird) of the low- (high ) productivity workers

y r (1 )=

Fraction of workers
who move at end
of period

1/3

Wages for a highproductivity worker
who never moves

3/2

Wages for a highproductivity worker
who moves only after
period one

3/2

Wages for a highproductivity worker
who moves after both
periods one and two

3/2

1.7

Period

Period

2

3

w

3

= 6/5

1/3

y = 2 or 3 y = 2 or 3
W

2

= 4/3

y = 2 or 3

b\

b\

W

2

W

= 4/3

3

= 6/5

b\

NOTE: w2 = the second-period wage for workers who changed jobs after
period one; w3 = the third-period wage for workers who changed jobs after
periods one and two.
SOURCE: Author.

U

R

E

b

b

2

Possible Moves and Wages
Without Contingent Contracts

■ 3

Since two-thirds (one-third) of the (low-) high-productivity workers

move after period zero and again after period one, the expected productivity of
a worker who changes jobs after the first period is [(2/3 x 1/2 x 1) + (1/3 x
1/2 x 2)] / [(2/3 x 1/2) + (1/3 x 1 / 2 ) ] « 4/3; the expected productivity of a
worker who changes jobs after both periods is [(2/3 x 2/3 x 1/2 x 1) + (1/3 x

+ 0:---- Stay-----

- p + d + b\
1

1/3 x 1/2 x 2)] / [(2/3 x 2/3 x 1/2) ♦ (1/3 x 1/3 x 1/2)] - 6/5; and the
expected productivity of a worker in the initial period is simply [(1/2 x 1) +
( 1 / 2 x 2 ) ] = 3/2. The wages reported in the text can be obtained as follows. In

Stay

the first period, the probability that a worker stays at his present job is 1/2,

p
Move

+ 02 +

t

>2

therefore

w\

= 3/2 - ( 1 / 2 ) ib 2 = 10/9; similarly, the conditional probability that

a worker changes jobs after the second period given that he changed jobs after
the first period is 4/9, therefore

w2 = 4/3

- (4/9) 0b 2 = 56/45; and the wage

for a worker who changes jobs twice is his expected productivity, w3 = 7/6.

■ 4

Under the assumptions of this model, bonds cannot be made contin­

gent on a worker’s realized output. Bonds are allowed to be made contingent
only on a worker’s decision either to move or to stay at the firm. The more
general case, when the bond can depend on y , has proven intractable. Intui­
tion suggests that including this more general case would make it more likely

SOURCE: Author.

that a separating equilibrium will exist, but if there is enough variability in the
job-matching component, 0 , then there will be groups of workers in which a
pooling equilibrium will still result. The remainder of the paper maintains the
assumption that the return on bonds cannot depend on y.

T

A

B

L

E

3

Mobility and Wages
for a Low-Productivity
Worker With Bonding

Period

Period

Period

1

2

3

W3

b2

Output at which a
low-productivity
worker is indifferent
between moving
and staying

y ( i ) = i .o

Fraction of workers
who move at end
of period

2/3

Wages for a lowproductivity worker
who never moves

3/2 - 7/18
= 10/9

y=

Wages for a lowproductivity worker
who moves only after
period one

3/2 - 7/18
= 10/9

W2

56/45

Wages for a lowproductivity worker
who moves after both
periods one and two

3/2 - 7/18

W2 =

=10/9

56/45

-

= 1.0

2/3

2

=

that he changed jobs in the first period, is fiveninths. In contrast, workers who did not move
after the initial period will choose never to
change jobs. The presence of movers and stayers
results because low-productivity workers move
more often than high-productivity workers.
The next example illustrates this result by a
two-period example. The cost of using a twoperiod model is that the model can no longer
explain why prior mobility is a good indicator of
future mobility. The example helps illustrate
how these results apply when workers have a
continuum of different productivity7types.

Example 4 : Mobility and

y=
y=

Wages in a Two-Period
Example With Bonding
2

+7/9

2 + 1/5

The following example is a two-period version of
the model presented in example 3. Using the
notation defined above,
is the bonus paid in
the second period to job-stayers, while
is the
first-period wage for all workers and
is the
second-period wage for job-changers. In this
is allowed to vary continuously with
example,
the distribution function, /
Thus, each
worker has a different productivity level. In addi­
tion, we define A to be the fraction of workers
who change jobs after the first period. Remem­
bering that a worker will change jobs only if
6 <
)2
A is determined as follows:

b

wz

W3

=

6/5

NOTE: w2 - the second-period wage for workers who changed jobs after
period one; w3 = the third-period wage for workers who changed jobs after
periods one and two.
SOURCE: Author.

p

w\

(p).

u - p - b,

(5)

= $G (u - p - b )f (p)dp.

A

'2

The intuition behind this equation is simple.

move after period one, and two-thirds (onethird) of these workers move again after the
second period. Wages for both job-movers and
job-stayers increase over the life cycle, although
at a slower rate for job-movers.
Notice also that the increase in wages for
movers is not monotonic over time: it reaches a
maximum in period one and drops off slightly in
the last period. Workers who move twice con
tinue to earn more in the last period of their
working life than they did in the first period;
however, their wages decrease with their last job
move. This is consistent with the findings of Bar
tel and Borjas (1981), who determine that for
older men a quit can have either a zero or a
negative effect on wage growth.
The example also explains why prior mobility
is an indicator of future mobility. The probability
that a worker changes jobs in the first period is
one-half, while the conditional probability that a
worker changes jobs in the second period, given

G ( W - p - b) is the fraction of the p 2

productivity workers who change jobs after the
first period. This fraction is then multiplied by
/ (/>), the proportion of all workers who have a
productivity of
Summing this product over all
productivity types gives the average mobility rate
of workers.
The second-period wage for job-movers is
determined similarly:

p.

(6)

il - JpG (u - p - b )f(p )d p/A .
'2

>2

The intuition behind this equation is similar to
that given above.
'2 (/0 /A is the
fraction of job-movers who have a productivity of
. Multiplying by and summing over all
workers gives the average productivity, or the
average output, of a job-changer.
The following example assumes that the
matching component, 6 and the individual pro­
ductivity component,
are both uniformly dis­
tributed: 6 ~ [-0', 0'] and ~
', />"]. Fol-

G (u

p

p - b )f

p

p,

,

p

[p

Carlstrom (1989) shows that the problem
satisfies
Mobility and Wages
for a High-Productivity
Worker With Bonding

b =

p

Period
1
Output at which a
high-productivity
worker is indifferent
between moving
and staying

y (D =

Period

Period

2

3

W3

1 .7

-

b = (30'-2)/(60'-3),
wi = 3/2 -(1-A)b,
w = (90'-5)/(60'-3),
G (u - p -b ) = 1/2 - (p - 1)/20', and

= 1.0

2

’2

1/3

Wages for a highproductivity worker
who never moves

3/2 - 7/18

Wages for a highproductivity worker
who moves only after
period one
Wages for a highproductivity worker
who moves after both
periods one and two

3/2 - 7/18

U =

= 10/9

56/45

A = 1/2 -1/40'.

1/3

y=

y=

3/2 - 7/18

U =

y=

= 10/9

56/45

= 10/9

2 or 3

’2

2 + 7/9
or 3 + 7/9

2 + 1/5
or 3 + 1/5

w

’2

3=

6/5

lowing example 3, a candidate equilibrium for
this example is a pooling equilibrium (where all
workers are treated identically ex ante), which
maximizes the returns to the highest-productivity
worker. Competition for the high-productivity
workers, whom firms earn profits by employing,
ensures that a pooling equilibrium is obtained
by choosing a wage-bonus package (
to
maximize the expected return of the highestproductivity worker.

wi, b)

max {w\
w i, b

+ £ m a x [ //' + 0 +

b, u

>2

such that

w\

+ (1-A

(2) A = J g (
(3)

The above equations indicate that the more
disperse 0 is (with respect to ), the less impor­
tant adverse selection is. Increasing 0' raises the
wage rate of job-changers and workers’ mobility.
The reason is straightforward: increasing the var­
iance of 0 diminishes the impact of adverse
selection, since it increases the incentives for all
workers to change jobs. When more workers
change jobs, the probability that job-changers are
“lemons” is reduced.
Carlstrom also shows that an equilibrium for
this example exists if there is enough adverse
selection in the labor market, that is, if 6 > 1. If
we restrict 0' = 1, the corresponding prices and
quantities are

p

'

NOTE: w2 = the second-period wage for workers who changed jobs after
period one; wa = the third-period wage for workers who changed jobs after
periods one and two.
SOURCE: Author.

(1)

If we further assume that
is uniformly dis­
tributed between 1 and 2, the corresponding
prices and quantities are
A = 1/2 - 1/40',

b2

Fraction of workers
who move at end
of period

(7)

U’2 - p '

)b < E (p )

W -p -b )f(p )d p
2

u = fpG ( u’ -p -b)f(p)dp/A .
>2

2

]}

A = 1/4,
= 1/3,
5/4,
2
4/3, and

b
w\ w G ( W -p - b) = 1 - p /2 .
2

Notice that the example is consistent with the
stylized facts; workers experience a wage
increase when they change jobs, yet they earn
less over time than job-stayers who earn their
output,
plus their bonus, one-third.
The following section uses this example to
discuss questions of optimality.

y,

II. Welfare Implications

Example 4 illustrates another aspect of the
model: in equilibrium there is less job mobility
than occurs in a world with perfect information.
This is not true for all workers, however. Highproductivity workers move less often than they
would in a world without adverse selection, while
low-productivity workers may or may not move
less often. There are two reasons for this effect,
both of which are due to adverse selection. The

first is identical to that in Akerlof s “lemon”
model: adverse selection reduces the future
wages for workers when they move and thus
reduces the incentive to move. The second effect
is due to the posting of bonds in equilibrium,
which further reduces the incentives for mobility.
The results of this section are shown with a
two-period model, assuming that 6 is uniformly
distributed. For most of the results, these assump­
tions can be relaxed. Without bonds, the probabil­
ity that a worker with a productivity,
will
change jobs is
the average probabil­
ity that a worker changes jobs is { ( 2 - ) }
=
( 2
( )) <
(0), where
(0) is the
probability that a worker would change jobs in a
model without adverse selection. The posting of
bonds accentuates this effect. In example 4, the
unconditional probability that a worker moved
was one-fourth, with the lowest-productivity
worker moving half of the time, and the highestproductivity worker never moving.
Since mobility is lower in this example than in
a model with complete information, it is natural
to ask whether a government could increase wel­
fare by subsidizing mobility. An example of such
a government subsidy is unemployment insur­
ance. However, since there is no unemployment
in the model, unemployment insurance cannot
be analyzed. Instead, this paper models unem­
ployment insurance, which decreases the costs
of moving, as a subsidy to the wage of jobmovers. It therefore asks whether a government
can achieve a Pareto improvement by subsidiz­
ing the wages of job-movers. Because a govern­
ment does not have superior information about
a worker’s productivity, the answer is no.
Subsidizing mobility would not benefit the
highest-productivity workers, so taxing them to
pay for this subsidy would make them worse off.
However, a stronger welfare result can be proven
in this model. That is, a government cannot tax
first-period wage income to subsidize the wages
of job-changers in order to increase aggregate
welfare.5 In fact, it is shown that if a government
subsidized the wages of job-movers, there would
be no effect on the equilibrium allocations. With
a subsidy of 5, the equilibrium prices and alloca­
tions from the second example are

G ( wi - p);

G W -E p

■ 5

G

p,

E G W p
G

This is in contrast to the welfare implications of Akerlofs model, where

a government could subsidize the trading of cars and increase aggregate wel­
fare in the sense that owners of the low-quality cars would gain more than
owners of the high-quality cars would lose.

(8)

b- W

-

(9)

A = Jg

(p ' - p)f(p)dp,

(10)

u

(11)

2

>2

=

p ',

tpG (p ' - p ) f( p )d p /A

w\ = E ( p ) - (1 -A )b
= E (p ) - (1 —A )( w - p
2

, and

')•

W

To verify that subsidizing 2 by 5 and taxing
first-period income by
has no real effect,
consider the above equations. Assuming the
wage paid to job-movers by firms, 2 did not
change, then from (8) the equilibrium amount
of the bonus would increase
(or bonds
would increase by (1 - A )s). In other words,
the amount of the bonus paid to the job-stayers
would change one-for-one with the subsidy on
2 leaving mobility the same and thus implying
(and verifying the assumption) that the wage
paid to job-movers, 2 , remains the same. There­
fore, second-period income would increase by 5
for both movers and stayers, and first-period
income would decrease by s. The following are
the new equilibrium allocations:

As

w,

by s

W,

w

(8 ')
(9')

(10')

b' = W +s- p
2

J G (u - p - b )J(p)dp
f G ( p ' - p ) f ( p )dp,

A =
=

>2

W = J p G( u - p - b ) f ( p) dp /A
fpG (p ' - p ) f ( p)dp /A, and
2

>2

=
(IT)

w\ = E (p ) - (1 -A )b '
= E (p ) - (1 -A )b - .
5

Quick inspection of equations (8 ) - ( ll) and
(8’) - ( l l ’) shows that subsidizing mobility affects
neither mobility, (A), nor total wages over time.
Mobility stays the same, while wages in the first
period for all workers decrease by the subsidy,
and net wages in the second period increase by
the subsidy. The intuition behind this result is
straightforward. Subsidizing mobility benefits the
frequent job-movers— the low-productivity
workers. In a pooling equilibrium, however, the
returns to the highest-productivity workers are
maximized. The amount of the bond that would
be posted in equilibrium would change one-forone with the amount of the taxes to eliminate
the effects of the government’s action.

III. Conclusion

Adverse selection is thought to be prevalent in
many markets. This paper argues that adverse
selection may also be important in the labor
market. It can explain why wages tend to
increase as workers get older, except for fre­
quent job-movers, whose wages may actually
decrease in later years. It also can explain why
older workers who move frequently have lower
average wages than do infrequent job-changers.
Job-movers earn low wages because frequent
mobility brands them as low-productivity
workers. This effect then decreases the incen­
tives for workers to change jobs.
Thus, adverse selection may seriously impair
the ability of workers to change jobs and can
interfere with the efficient operation of the labor
market. Because of this market failure, it is natural
to ask whether a government action to subsidize
mobility can reduce the severity of adverse selec­
tion and improve the functioning of the labor
market. However, it is shown that such a govern­
ment action will have no real consequences. The
reason is that bonds arise in the model in order
for firms to compete for the high-productivity
workers. Subsidizing mobility hurts the infre­
quent job-movers (the high-productivity workers),
leading firms to increase the amount of bonds
required by incoming workers. This increase in
bonding offsets the subsidy given to job-movers,
leaving the government action ineffective.
The paper also suggests that adverse selection
will not be a problem for job-changers if they are
paid a piece rate or with a contingent wage con­
tract. Recent actions by firms to pay their workers
bonuses and stock options may ease the impact
of adverse selection. Future work is needed to
address whether these types of contracts are aris­
ing as a result of adverse selection and whether
these contracts may lead to a more fluid and
efficient labor market.

Leighton, Linda and Mincer, Jacob, “Labor Turn­

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Economic Theory>,

Econom ic Com m entary
Has Manufacturing’s Presence
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A User’s Guide to CapacityUtilization Measures

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by Paul W. Bauer
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July 1, 1988

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January 15, 1988

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July 15, 1988

Bank Runs, Deposit Insurance,
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February 1, 1988

by William T. Gavin
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August 1, 1988

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February 15, 1988

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The Bank Credit-Card Boom:
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Federal Budget Deficits:
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December 15, 1988

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an Evaluation, and New Directions
by Alan C. Stockman

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