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Vol. 30, No. 2
ECONOMIC REVIEW
1994 Quarter 2
U.S. Banking Sector Trends:
Assessing Disparities in
Industry Performance
2
by Katherine A. Samolyk
Competition for Scarce Inputs:
The Case of Airport Takeoff
and Landing Slots
18
by Ian Gale
Regional Wage Convergence and
Divergence: Adjusting Wages
for Cost-of-Living Differences
by Randall W. Eberts and Mark E. Schweitzer
FEDERAL RESERVE BANK
OF CLEVELAND
26
B U E E
MI C
REVIEW
1994 Quarter 2
Vol. 30, No. 2
U.S. Banking Sector Trends:
Assessing Disparities in
Industry Performance
2
by Katherine A. Samolyk
While the past decade appears to have been a difficult time for the U.S.
banking sector, performance within the industry varied widely. Using statelevel data, the author investigates the extent to which variations in banking
conditions were associated with differences in bank size and holding com
pany relationships. Controlling for local economic factors, very large banks
had more problems with loan quality and poor profitability over the period
than did smaller banks; the results, however, do not indicate an emerging
relationship between bank size and bank performance. At the same time,
smaller banks that affiliate with larger organizations in the form of holding
companies appear to benefit from the relationships.
Competition for Scarce Inputs:
The Case of Airport Takeoff
and Landing Slots
18
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Coordinating Economist:
William T. Gavin
Advisory Board:
Ian Gale
Jagadeesh Gokhale
Joseph G. Haubrich
by Ian Gale
Since 1986, airline carriers have exercised the right to buy and sell takeoff
and landing slots at airports. Questions remain, however, about the optimal
way to allocate these slots. This paper provides a framework for analyzing
competition for such scarce inputs, describing the outcome of an auction
of slots between two carriers, who may have existing slots, and the possi
ble outcomes from a merger or takeover wave. The author finds that the
equilibrium allocation of slots is typically asymmetric, but not monopo
listic, because as the allocation of slots becomes more concentrated, the
price that the leader must pay for the marginal slot rises. This suggests that
the concern over monopolization of airports may be misplaced.
Regional Wage Convergence and
Divergence: Adjusting Wages
for Cost-of-Living Differences
26
by Randall W. Eberts and Mark E. Schweitzer
After decades of convergence, the economic fortunes of U.S. regions appeared
to diverge in the early 1980s as measured by both per capita income and
wages. This study examines that phenomenon by looking at the effect of rela
tive price-level controls on the convergence/divergence of regional wages. The
authors find that once prices are factored in, relative wage rates continue to
converge across regions due to rising covariance between price and wage lev
els. The results also confirm that the trend in regional wage variation can be
traced to declining differences in labor market valuations of worker attributes
rather than to shifts in the regional composition of the workforce.
Editors: Tess Ferg
Robin Ratliff
Design: Michael Galka
Typography: Liz Hanna
Opinions stated in Economic Re
view are those of the authors and
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Material may be reprinted pro
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Please send copies of reprinted
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ISSN 0013-0281
U.S. Banking Sector Trends:
Assessing Disparities in
Industry Performance
by Katherine A. Sarnolyk
Introduction
The U.S. banking industry has a long tradition
of decentralization as measured by geographic
market structure. This feature largely reflects
the impact of both inter- and intrastate branch
ing restrictions as well as regulatory policies to
ward mergers and acquisitions. As a result of
these policies, the industry comprises many
small banks that operate in relatively localized
and stmcturally diverse markets. In states al
lowing branching, banks tend to be fewer but
larger than in unit banking states.
The phenomenon of bank holding companies
emerged in the 1950s and 1960s as a response
to restrictions on the scale and scope of bank
ing activities. By holding banks as affiliates, a
holding company can expand the geographic
scale of its banking operations and broaden the
scope of its nonbank activities to certain per
missible lines of financial services. During the
1970s and 1980s, both the number of bank
holding companies and the share of banks so
affiliated increased, partly as a response to
regulatory changes (Savage [1982], Amel and
Jacowski [19891). However, the trend also re
flects changes in the environment in which
http://fraser.stlouisfed.org/these organizations operate.
Federal Reserve Bank of St. Louis
Katherine A. Samolyk is an econo
mist at the Federal Reserve Bank
of Cleveland. The author thanks
Robert B. Avery, Richard Dreese,
Ian Gale, William Gavin, and
James Thomson for helpful
comments.
While the U.S. banking industry has been con
solidating into holding companies, it also appears
to be shrinking. Domestic nonfinancial-sector
debt grew substantially faster than GDP in the
past decade, but the share of intermediated
funds advanced by banks fell from 50 percent to
36 percent. The number of banks contracted by
nearly 21 percent, from more than 14,400 in 1982
to about 11,400 at the end of 1992. The decade
also witnessed a dramatic rise in bank failures
and a spate of asset quality problems that trans
lated into low industry profitability.
In assessing these trends, analysts have de
voted considerable attention to the regional na
ture of the banking industry. Disparities in bank
profitability over the past decade have been
widely attributed to differences in local economic
fortunes. Bank failures were largely concentrated
in states experiencing economic difficulties. More
recently, the poor performance of banks in New
England and California has been associated with
the so-called bicoastal recession.
Regional banking conditions also reflect the
structural diversity across state banking sectors.
Historically, bank failures have tended to occur
in unit banking states, whereas institutions in
branch banking states seem to have fared better
during periods of economic adversity.1 In the
past several years, however, the problems con
centrated in large banks have raised concerns
that a “too big to fail” regulatory policy is en
couraging excessive risk-taking.2
Differences in economic fortunes and in
bank structure across states complicate the as
sessment of industry performance. Are certain
types of banks performing poorly because
they are inherently different from other types
of banking organizations, or do they happen
to be concentrated in regions where the local
economy is faltering? In this paper, I exploit
the differences both within and across states in
an attempt to evaluate how these factors were
related to banking sector performance during
the past decade. Performance refers to stan
dard measures of banking conditions, including
bank profitability, asset quality, capitalization,
and lending. Data are compiled from individ
ual Federal Financial Institutions Examination
Council’s Reports o f Condition a n d Income
(call reports) for each year between 1984 and
1992. I disaggregate state-level balance sheets
and income statements to construct perform
ance measures for banks that differ in size as
well as in their holding company relationships.
Then, controlling for state-specific economic
factors, I examine the extent to which dispari
ties in performance have been associated with
differences in these bank characteristics.
The tone of this analysis is descriptive; the
parsimonious number of relationships examined
precludes a more causal interpretation. The find
ings reveal that the health of the local economy
is indeed important in assessing the performance
of the local banking sector. However, differences
in banking conditions also appear to be associ
ated with bank size and holding company affili
ation; moreover, the emergent relationships are
consistent with microeconomic studies that exam
ine individual bank performance (Berger, Hanweck, and Humphrey [1987]). The results indicate
that, controlling for local economic factors, rela
tively small banks (assets between $100 million
and $1 billion in 1987 dollars) turned in the best
performance over the past decade. In addition,
smaller institutions that were affiliated with
1 This trend is less true in recent years. With the exception of
Texas, failures during the past decade were not disproportionately located
in unit banking states. Moreover, Wheelock (1993) notes that the choice
of unit banking restrictions was popular in states with relatively cyclical
economies, such as agricultural states.
multibank holding companies had fewer prob
lems with asset quality than did other small
banks. Alternatively, the largest institutions —
almost all of which belong to multibank hold
ing companies — were less profitable. Hence,
although banking fortunes reflect those of the
local economy, performance also appears to
be related to local industry structure. Judging
at least by the experience of the 1980s, it
seems that banks can be too large.
I. Industry Structure
and Performance:
An Overview
Assessments of the banking industry frequently
describe it as a composite of banks that differ
in size and location. For example, the FDIC
Quarterly Bulletin presents industry data on
banks classified by size and geographic region.3
This focus reflects the view that such factors are
important determinants of banking conditions.
The term bank structure is frequently used
when referring to the characteristics of banking
markets as well as those of individual institu
tions. Individual bank characteristics, such as the
scale and scope of operations, can affect the
costs at which banks produce financial serv
ices; hence the rationale for the focus on bank
size. Market stmcture, measured by the relative
size and number of firms, can influence the de
gree of local competition and, by extension,
the quality, quantity, and price of financial serv
ices ultimately available to bank customers.
Researchers have studied how both market
structure and individual bank characteristics
are related to bank performance. One genre of
studies looks at how market concentration is
related to bank profitability and to the cus
tomer’s cost of banking services.4 Most find
ings reveal a positive relationship between
market concentration and bank profitability.
This result has been cited as evidence that
more concentrated markets are less competi
tive. However, it also has been interpreted as
an indication that more efficient firms tend to
dominate the marketplace. A second line of re
search looks at how the costs associated with
producing financial services are related to a
■
■ 2 See Boyd and Gertler (1993) for a recent evaluation of this
http://fraser.stlouisfed.org/
perspective.
Federal Reserve Bank of St. Louis
■
3 Similarly, assessments of changes in the structure of banking
markets focus on how the geographic distribution of banks and the atten
dant concentration of banking markets have evolved (Amel and Jacowski
[1989]).
■
4 For example, see Berger and Hannan (1989).
Structural Characteristics
of Bank Cohorts
Size Classes (1987 dollars)
Very small: Less than $100 million in assets.
Small: $100 million to $500 million in assets.
Medium: $500 million to $1 billion in assets.
Large: $1 billion to $10 billion in assets.
Very large: More than $10 billion in assets.
Holding Company Affiliations
MBHC: Bank holding company holding more than one bank.
SBHC: Bank holding company holding only a single bank.
Independent: Not affiliated with a bank holding company.
Performance Measures
of Industry Conditions
Lending and Capitalization
Capitalization: Bank equity capital as a percentage of total
assets.
C&I lending: Commercial and industrial loans as a percent
age of total assets.
CRE lending: Commercial real estate loans as a percentage
of total assets.
Total bank lending: Total loans (including C&I loans, CRE
loans, home mortgages, consumer loans, and other loans)
as a percentage of total assets.
Bank Profitability and Asset Quality
ROA: Return on assets as measured by the ratio of annual
net income to total assets.
Nonperforming assets: Past due loans (more than 90 days)
plus nonaccruing assets plus other real estate owned, as a
percentage of total assets.
Net loan charge-offs: The ratio of annual net charge-offs
for loan losses to total bank loans as defined above.
NOTE: All measures use fourth-quarter data from the Federal Financial Insti
tutions Examination Council’s Reports o f Condition and Income (call reports).
Each performance measure is constructed from the cohort-level balance sheet or
income statement. For example, ROA for each size class of banks is measured
as the ratio o f net income to total assets for each respective cohort o f banks.
bank’s structural characteristics.5 Although the
results are mixed, these cross-sectional assess
ments of bank efficiency have found evidence
of modest economies of scale; the costs of pro
viding banking services decline as firm size in
creases up to a relatively small size (Berger,
Hanweck, and Humphrey [1987]).
The potential for the characteristics of banks
and banking markets to affect industry perform
ance motivates our interest in the phenomenon
of bank holding companies. The importance of
viewing holding company affiliation as a struc
tural characteristic of banks depends on whether
a bank in a holding company behaves differently
than it would as an unaffiliated entity. At one
extreme, holding companies may be passive ve
hicles that diversify across a number of banks
and allow almost all decisions to be made at the
subsidiary level. In this case, holding company
affiliation might be unrelated to a bank’s perform
ance because it does not affect the bank’s behav
ior. At the other extreme, if a bank can draw on
its relationship with its holding company (for ex
ample, by reducing certain operating costs or
increasing portfolio diversification through inter
bank loan sales), it may perform more like a
larger institution.
Here, my focus on the link between the
structural characteristics of banks and industry
performance at the state level is more macroeconomic than microeconomic in nature. To
the extent that banking conditions may impact
credit availability, they may also affect eco
nomic activity. In a previous study using statelevel data from the past decade (Samolyk
[1992]), I found evidence suggesting that the
health of the local banking sector plays a role
in local economic fortunes. Banking conditions
were more strongly related to current real per
sonal income growth in states where the health
of the banking sector was poor than in states
where it was sound. Moreover, this relation
ship was not simply mirroring a correlation be
tween banking conditions and past income
growth. These findings suggest that if local
bank characteristics affect local industry per
formance, they may have important economic
consequences.
Both market factors and regulatory policies
determine the structural characteristics of
banks and banking markets. Here, I merely ex
amine whether these characteristics have been
associated with differences in banking sector
performance. For example, small, localized
banks may be more vulnerable to local eco
nomic distress, while larger banks are able to
diversify over regional or even national markets.
Thus, the state is not defined as the relevant
“market” for banks of all types. Nevertheless,
performance differentials across the various
types of banking institutions within a state may
provide evidence as to how bank characteris
tics can affect local banking conditions.
■ 5 The scale of a bank’s activities is usually defined in terms of bal
ance sheet stocks, such as the volume of lending. The scope of a bank’s
activities refers to the composition of financial services it provides (for ex
ample, making loans versus funding securities). See Clark (1988) for a
survey of these studies.
5
I
TA8L E 1
Banks and Banking Assets
Panel A
By Size of Largest
Banking Organization
By Individual
Bank Size
1992
1984
1992
1984
Number of Banks
Total
14,451
11,419
14,451
11,419
Very small
Small
Medium
Large
Very large
11,769
2,171
210
274
27
8,823
2,037
229
293
37
9,830
1,985
412
1,445
779
7,399
2,196
344
855
625
Percentage of Banking Assets
Total
Very small
Small
Medium
Large
Very large
Panel B
100.0
100.0
100.0
100.0
15.2
11.6
13.6
5.5
32.1
37.2
12.0
9.2
10.1
15.1
5.3
28.7
35.7
In Multibank
Holding
Company
1984
9.9
3.8
27.2
47.1
In Single Bank
Holding
Company
1992
1984
1992
3.3
18.8
58.6
Not in a Bank
Holding
Company
1984
1992
Number of Banks
Total
3,748
3,295
4,967
4,891
5,736
3,233
Very small
Small
Medium
Large
Very large
2,426
989
132
176
25
2,030
871
141
220
33
4,088
728
58
91
2
3,932
828
64
63
4
5,255
454
20
7
0
2,861
338
24
10
0
Percentage of Banking Assets
Total
67.0
72.7
Very small
Small
Medium
Large
Very large
3.7
7.4
3.3
18.7
33.9
3.0
6.2
3.4
26.2
33.9
23.2 • 20.7
5.5
4.8
1.5
9.6
1.8
5.3
5.3
1.5
5.3
3.3
9.8
6.6
6.0
2.9
0.5
0.4
0.0
3.3
2.1
0.6
0.6
0.0
o f single bank holding companies. Following
convention, I characterize a bank’s size in terms
of the dollar value of its assets. Banks are
placed in five size categories, which are ad
justed for inflation so that a bank’s classification
will change only if its asset size has changed
in real terms.6 The inflation-adjusted (constant
dollar) ranges for the five size cohorts are pre
sented in box 1. Between 1984 and 1992, the
unadjusted (current dollar) ranges of these size
classes rose by approximately one-third.
Panel A of table 1 shows the distributions of
banks and bank assets across the five categories.
It also presents the distributions of banks and
banking assets when each bank is classified by
the size of its largest related organization. For
example, in classifying a $100 million bank that
is a subsidiary of a holding company with as
sets of $5 billion, I include that bank’s data in
the larger size cohort. This classification illus
trates the distribution of banking assets by firm
size when multibank holding companies are
treated as branches of the holding company.7
Panel A shows the trend toward fewer, larger
banks in the industry: The number of very
small banks has declined markedly. It also indi
cates that at the holding company level, the
past decade has witnessed very large banking
organizations growing into even larger ones.
Panel B of table 1 presents the distribution
of banks and of banking assets classified by
both size and holding company affiliation as
defined in box 1. It indicates that the decline
in the number of small and very small banks
reflects decreases in both holding company
affiliates and unaffiliated (independent) institu
tions. These data also underscore the emer
gence of the bank holding company as a prom
inent organizational entity. However, inde
pendent banks continue to be well represented,
especially among smaller institutions.
Panel B of table 1 is also useful for under
standing the measures employed in assessing
banking conditions at both the national and
SOURCE: Author’s calculations.
■
II. Trends in
Industry Structure
At the end of 1992, 11,419 domestic commer
cial banks filed call reports. O f these institu
tions, 71.7 percent were affiliates of a bank
holding company. O f holding company affili
ates, 40.3 percent were part of multibank hold
ing companies and 59.7 percent were affiliates
6 Both the FDIC Quarterly Report and the Federal Reserve Bulletin
publish data on performance trends for banks classified by nonindexed size
cohorts. Empirical studies that use cross-sectional data in a given year do
not need to index nominal asset size classifications. However, studies that
pool data on banks across time should deflate asset values into real terms to
evaluate differences associated with bank size. For example, Avery and Ber
ger (1991) index their classification of large and small banks in assessing
the implications of risk-based capital on these segments of the industry.
■
7 The data on the number of banks require more clarification, as
this category refers to the number of banks affiliated with holding compa
nies of a given size, not the number of holding companies of that size.
This indicates the potential misclassification associated with ignoring
holding company affiliations.
TABLE
2
III. Trends in
Bank Lending
and Capitalization
Bank Balance Sheets:
Lending and Capitalization
(percentage of bank assets)
All
Banks
Very
Small
Small
Medium
Large
Very
Large
52.9
52.9
51.6
56.5
60.0
56.7
58.5
65.2
60.0
60.5
65.4
60.1
65.0
63.4
58.3
and industrial loans
22.6
16.8
13.1
10.7
18.8
13.9
8.8
15.3
10.5
18.9
16.9
12.2
21.0
18.8
14.8
30.9.
23.5
20.0
Bank lending
1984
60.2
1989
62.4
1992
58.0
Commercial
1984
1989
1992
Commercial real estate loans
7.3
11.3
10.4
6.9
9.2
10.2
10.1
13.5
14.1
9.4
14.8
14.5
8.3
13.2
11.4
5.2
8.8
7.5
Capitalization
1984
6.1
1989
6.2
1992
7.5
8.6
8.9
9.3
7.2
7.6
8.3
6.9
6.7
7.7
5.8
6.1
7.6
4.8
4.8
6.6
1984
1989
1992
SOURCE: Author’s calculations.
the state level. The focus here is on how per
formance differs across banks of various sizes
and holding company affiliations. I construct
national-level fourth-quarter performance meas
ures for each of the five size classes (and each
size class disaggregated by the three types of
holding company relationships) by first aggre
gating the call report data for U.S. commercial
banks in the size cohorts illustrated in panel B.
The aggregated balance sheet and income
statement of each cohort is then used to con
struct measures of capitalization, lending, bank
profitability, and asset quality. These measures
are defined in box 1. The state-level measures
analyzed in the study are also constructed in
this manner— albeit with the call report data
on the individual banks for a given state. As a
point of reference, I first examine the recent
trends in banking conditions evident at the
national level.
Table 2 illustrates bank lending and capitaliza
tion (as percentages of bank assets) for the
five size cohorts of commercial banks in se
lected years. Despite distinct differences in
both loan/asset and capital/asset ratios across
the size classes, these balance sheet measures
have moved somewhat in concert during the
past decade.
Larger banks appear to have invested a
greater percentage of assets in loans than did
smaller banks. While loan/asset ratios moved
procyclically in medium and large banks, very
small and very large banks did not exhibit this
portfolio shift.8 However, banks of all sizes
changed the types of loans they funded over the
period. The percentage of assets invested in
commercial and industrial (C&I) loans declined
and the percentage held as commercial real
estate (CRE) loans rose in all segments of the
industry. Large and very large banks moved
most aggressively into CRE lending in the mid1980s and have subsequently retrenched. For
smaller banks, the monotonic shift to funding
CRE loans is more indicative of a secular trend
than of a cyclical real estate boom (and subse
quent bust).
Larger banks also appear to have been less
capitalized than smaller banks. However, the
greatest disparities across the size classes oc
curred early in the 1980s, when industry capi
talization was below 6 percent. Until the late
1970s, smaller banks faced higher capital re
quirements: They were viewed as riskier be
cause they could not diversify as much as
larger institutions. Subsequently, regulatory
changes have eliminated differences in capital
ratios based on size in favor of requirements
associated with portfolio risk. The result has
been that capitalization has increased in the in
dustry as a whole, but by relatively more in
larger banks.
There also appear to be differences in bank
lending and capitalization across similar-sized
banks that vary in holding company affiliation.
The panels in figure 1 depict capitalization and
loan/asset ratios for very small banks sorted by
their holding company relationships. Multibank
holding company affiliates were less capital
ized than otherwise affiliated institutions and
made more loans than other very small banks,
■
8 See Boyd and Gertler (1993) for documentation of trends over
the postwar period.
FI GURE
although the differences in loan/asset ratios di
minished over the decade. Thus, in terms of
lending and capitalization, industry-level data
suggest that multibank holding company affili
ates behaved more like “larger” institutions
than did other very small banks. This also ap
pears to have been the case for small banks.
1
Capitalization and Loan/Asset
Ratios for Very Small Banks:
by Holding Company Affiliation
Percentage
11.0
A. Capitalization
10.5
Independent b a n k s ____ _
10.0
IV. Trends in Bank
Profitability and
Asset Quality
9.5
9.0
SBHC affiliates
8.5
8.0
MBHC affiliates
7.5
7.0
1984
1985
1986
1987
1988
1989
1990
1991
1992
Percentage
57
B. Total Lending
\ MBHC affiliates
^
SBHC affiliates"'“ '''■
50
*- *** ^ x * Independent banks
49 ______ i______ i----- 1----- 1----- 1----- 1----- 1----- 1-1984 1985 1986 1987 1988 1989 1990 1991 1992
Percentage
Percentage
13
12
D. CRE Lending
11
MBHC affiliates
10
9
SBHC affiliates
8
7
6
Independent banks
-------1-------------- 1--------------L.
1984
1985
1986
1987
SOURCE: Author’s calculations.
-I_________I_________ I_________L.
1988
1989
1990
1991
1992
Differences in loan/asset ratios and bank capi
talization are important factors in assessing the
relative profitability and risk of banks. How
ever, these variations do not inevitably trans
late into differences in risk or profitability.
Although loans are a relatively risky class of in
vestments (compared to securities), banks that
have higher loan/asset ratios do not necessar
ily have riskier portfolios. Larger banks (or
those affiliated with multibank holding compa
nies) may be able to diversify the risks in their
loan portfolios more successfully than smaller,
more localized institutions. Moreover, larger
banks may be profitable in spite of lower profit
margins because their higher leverage allows
them to pay a greater return to stockholders
for a given return on their assets.
As evidenced by capital requirements in the
past, smaller banks were viewed as riskier be
cause of their limited ability to diversify. In the
1980s, government policies may have changed
the relationship between bank size and bank
risk by reducing the incentives for banks to man
age losses prudently (Boyd and Graham [1991]).
Deregulation, in tandem with changes in the
treatment of problem institutions, may have in
creased the risks that uninsured investors allow
banks — especially larger ones — to assume.
The policy that banks can be too big to fail and
the usual method of resolving bank failures (via
purchase and assumption by healthy banks) shift
the cost of bank failure from these investors to
the Federal Deposit Insurance Corporation (and
ultimately to taxpayers).
Unfortunately, ex ante portfolio risk and ex
pected risk-adjusted yields are unobservable,
so I examine data on ex post performance to
infer indirectly how the risk-return relationship
may vary across types of banks. I employ stan
dard industry ratios used to measure bank profit
ability and asset quality (see box 1). Bank
profitability is measured by the return on assets
(ROA) for each class of banks. Problems with
asset quality are measured by nonperforming
FIGURE
2
Industry Performance
Measures by Bank Size
Percentage
A. Return on Assets
Ì
»
^
m• mè
^ —______
-1
•
•
;
1985
1986
„
--- Very small
—
Small
---Medium
— — Large
...... Very large
. . *.. -...... J..... ..... 1_--------........
1987 1988 1989 1990 1991
1992
\I*
1984
---- ----
assets as a percentage of total assets, and net
charge-offs for loan losses as a percentage of
total loans.
The panels in figure 2 illustrate how bank
profitability and problems with asset quality var
ied across the five size classes of banks between
1984 and 1992. These performance measures re
veal less of a discernible relationship to bank size
and holding company affiliation than do bank
lending and capitalization. Panel A indicates that
the ROA for very large banks was more volatile
than for smaller institutions. However, the differ
ences in ROA do not indict size per se as an indi
cator of profitability. This is especially true from
the perspective of bank stockholders; since larger
banks are more leveraged, stockholders can earn
a higher return on equity for a given ROA.
Panels B and C of figure 2 illustrate that
smaller (primarily agricultural) banks experienced
problems with asset quality in the mid-1980s.
These problems have been widely attributed to
the impact of local economic conditions. The dra
matic rise in both nonperforming assets and loan
charge-offs by larger institutions from 1988 to
1991 is commonly viewed as stemming from the
troubled commercial real estate markets on the
East and West coasts. These disparate economic
conditions make it difficult to identify a consis
tent relationship between bank size and asset
quality in the national-level data.
V. A Regional
Perspective on
Banking Sector
Performance
SOURCE: Author’s calculations.
Both banking sector performance and broader
economic conditions varied widely across states
during the past decade. At the same time, restric
tions on branching and on bank holding com
pany acquisitions were being eased in many
states. In spite of these regulatory changes, a
great deal of stmctural diversity remains both
within and across state banking sectors. This di
versity reflects the interaction of current regula
tory environments with inherent market factors
(such as size or population density).
Table 3 summarizes the differences in bank
ing sector conditions across states in 1984 and
1992 in terms of the maximum, median, and
minimum values of each measure as well as
their means and standard deviations. The data
mirror the trends evident at the national level,
yet the variation across states is striking.
TABLE
3
State-Level Commercial
Banking Industry Ratios
(percentage of total assets)
Capitalization
Maximum
Median
Minimum
Mean
Standard deviation
1984
1992
9.7
6.7
5.2
7.0
1.0
12.8
CRE
Lending
1984
1992
C&I
Lending
1984
7.9
6.5
8.2
22.0
8.2
1.6
8.4
22.5
11.0
2.4
11.0
30.3
17.5
7.2
18.0
1.3
3.5
3.9
4.5
Return
on Assets
1992
Net Loan
Charge-offs
1992
1984
1992
1984
1992
1.6
0.8
-0.1
0.8
3.0
1.1
0.0
1.1
7.0
1.4
0.6
2.0
5.1
0.8
0.3
0.5
3.6
1.6
0.4
1.8
0.8
1984
24.4
12.0
5.7
12.8
4.1
Nonperforming
Assets
1.9
1.3
0.5
0.2
0.7
0.3
1.2
0.5
1.0
NOTE: Net charge-offs are expressed as a percentage of total loans.
SOURCE: Author’s calculations.
Table 4 presents the distribution of banks
within and across states by their holding com
pany affiliation in 1984 and 1992. Each state is
ranked according to its total number of banks
in 1984. Industry consolidation has been the
rule rather than the exception in state banking
sectors. The number of banks fell in 42 states
during this period, and for 20 of these states
the numbers dropped by more than 20 percent,
although 38 states still had more than 50 banks
at the end of 1992. These declines were accom
panied by a decrease in the number of inde
pendent banks in 42 states. Overall, the
percentage of smaller holding company affili
ates also fell. This, however, is due to signifi
cant decreases in some states (most notably,
Texas), which outweigh the increases in these
affiliates in other states.
A trend toward one organizational type is
not evident at the state level. Savage (1993) ar
gues that the coexistence of holding company
affiliates and independent banks within states
indicates that there is not yet a dominant form
of banking organization. The distribution of
banks by size varies more substantially across
states. In states with a tradition of unit banking,
the industry tends to be populated by a large
number of smaller institutions. As of year-end
1992, only 10 states had banks in the largest
size cohort. Seven states had no banks with
more than $1 billion (1987 dollars) in assets.
However, except for very large banks, each
size class is fairly well represented within and
across states.
VI. Assessing
Disparities
in Industry
Conditions
The diversity in the types of banks within and
across states suggests a simple way of assess
ing the extent to which variance in bank per
formance can be attributed to differences in
bank characteristics versus local economic con
ditions. In the following analysis, each state is
treated as an individual sector composed of
banks that vary in size and holding company
affiliation. I then test for differences in industry
profitability and asset quality that can be attrib
uted to these structural characteristics, control
ling for local economic conditions and other
state-specific fixed effects.
The analysis features state-level data over the
nine-year sample period of 1984 to 1992. As with
the evaluation of national-level trends, I disaggre
gate state-level measures of industry conditions
into cohort-level measures for the five bank size
categories, crossed with the three types of hold
ing company relationships. Hence, the annual
data yield 15 potential observations in each year
on industry conditions within a state. Not all
states have banks in each class.9 The nine years
of data for 51 states (including the District of Co
lumbia) yielded a data set of 4,062 observations
on a given measure of bank performance.
The rationale for analyzing the performance
of a cohort of banks rather than that of each
■
9 For example, almost all very large banks are multibank holding
company affiliates (two are affiliates of single bank holding companies). The
distribution of the data is discussed in the final section.
KO
TABLE
4
Distribution of Banks by
Holding Company Affiliation
In Multibank
Holding C o m p a n y
In Single Bank
Holding C o m p a n y
Not in a Bank
Holding C o m p a n y
Percent
Percent
Percent
Total N u m b e r
1984
1992
1984
1992
1984
1992
1984
1992
13
15
16
19
21
25
26
27
32
46
50
59
60
12
8
18
22
17
20
22
21
40
38
48
28
54
7.7
20.0
18.8
5.3
23.8
20.0
34.6
22.2
46.9
2.2
16.0
35.6
18.3
16.7
37.5
38.9
40.9
23.5
45.0
22.7
28.6
50.0
42.1
18.8
25.0
13.0
69.2
33.3
18.8
52.6
4.8
32.0
15.4
33.3
15.6
32.6
20.0
18.6
38.3
41.7
37.5
27.8
31.8
11.8
15.0
50.0
42.9
25.0
31.6
29.2
50.0
25.9
23.1
46.7
62.5
42.1
71.4
48.0
50.0
44.4
37.5
65.2
64.0
45.8
43.3
41.7
25.0
33.3
27.3
64.7
40.0
27.3
28.6
25.0
26.3
52.1
25.0
61.1
North Carolina
Oregon
South Carolina
Maryland
New Mexico
Washington
Wyoming
Massachusetts
New Jersey
South Dakota
Mississippi
Montana
Virginia
63
72
73
88
95
102
116
124
125
140
153
167
176
78
48
81
96
84
94
63
63
106
121
121
120
170
1.6
13.9
1.4
30.7
41.1
16.7
56.0
48.4
38.4
23.6
0.0
44.9
26.1
21.8
20.8
18.5
38.5
44.0
14.9
36.5
19.0
23.6
28.9
5.0
35.8
27.1
28.6
20.8
28.8
11.4
32.6
21.6
24.1
23.4
20.8
32.9
46.4
29.3
10.2
25.6
27.1
38.3
26.0
38.1
21.3
41.3
46.0
37.7
47.1
53.7
40.8
22.4
69.8
65.3
69.9
58.0
26.3
61.8
19.8
28.2
40.8
43.6
53.6
25.7
63.6
52.6
52.1
43.2
35.4
17.9
63.8
22.2
34.9
38.7
24.0
41.3
23.3
50.6
North Dakota
New York
West Virginia
Arkansas
Alabama
Tennessee
Louisiana
Ohio
Pennsylvania
Kentucky
Michigan
Indiana
Georgia
177
190
227
258
269
293
302
320
326
336
365
378
383
143
177
164
259
215
248
221
271
281
311
215
270
397
24.9
30.0
18.5
16.7
26.0
17.1
0.0
31.3
15.3
4.5
54.5
2.1
25.6
21.7
19.8
59.8
34.0
25.1
27.4
7.2
32.1
33.1
37.3
42.3
43.3
30.0
46.3
21.1
16.3
39.9
25.3
38.6
52.0
12.2
22.7
49.7
8.5
46.3
26.9
64.3
46.9
18.9
44.4
49.3
54.0
60.2
26.6
40.6
46.9
38.1
39.3
39.5
28.8
48.9
65.2
43.4
48.7
44.4
48.0
56.6
62.0
45.8
37.0
51.6
47.5
14.0
33.3
21.3
21.6
25.6
18.5
32.6
41.3
26.3
15.8
19.5
17.4
30.5
427
446
449
472
538
590
628
629
713
738
1,241
1,853
394
349
451
374
393
445
508
542
510
593
1,006
1,089
44.0
49-6
6.9
10.0
8.7
32.0
3.3
21.8
45.4
24.4
25.9
40.9
29.9
47.6
8.9
26.5
15.0
40.2
17.7
29.7
36.9
- 27.2
37.0
20.7
23.4
30.3
34.7
61.4
57.6
28.3
66.6
49.4
28.5
47.8
33.1
23.0
32.0
29.5
31.9
52.9
59.3
35.7
61.8
54.8
42.7
54.3
40.6
40.8
32.6
20.2
58.4
28.6
33.6
39.7
30.1
28.8
26.1
27.8
41.0
36.0
38.1
22.9
59.2
20.6
25.7
24.0
20.5
15.5
20.4
18.5
22.5
38.6
Rhode Island
Alaska
Nevada
Washington, D.C.
Hawaii
Idaho
Maine
Vermont
Delaware
Arizona
Connecticut
New Hampshire
Utah
Florida
Colorado
California
Nebraska
Oklahoma
Wisconsin
Kansas
Iowa
Missouri
Minnesota
Illinois
Texas
SOURCE: Federal Financial Institutions Examination Council, Reports o f Condition and Income, 1984 fourth quarter and 1992 fourth quarter.
individual bank is to mitigate the effects of out
liers and bank mergers. The cohort measures
are averages of the individual banking data,
where each bank is effectively weighted by its
share of the cohort.10 However, the findings
should be similar to those obtained using indi
vidual bank data to assess differences across
these classes of banks. Moreover, in examining
the performance of classes of institutions, I can
construct estimates of the performance differen
tials associated with bank size and holding
company affiliation. These adjusted measures
are directly comparable to the national-level
data presented in figures 1 and 2.
Data on banks sorted by size and holding
company affiliation within each state are used as
cross-sectional observations on banking condi
tions in each year of the sample period. I then
pool the data for each year to estimate reducedform regressions for six measures of bank per
formance. To identify variance in performance
that may be attributed to differences in bank size
and holding company affiliation, I control for
other factors that affect banking conditions both
within each state and over time. In each regres
sion, the following control variables are included:
D a dummy variable identifying the state of an ob
servation to control for state-specific differences in
banking conditions during the sample period; 2) a
dummy variable indicating the year of an observa
tion to control for economywide variation in bank
ing conditions over time; 3) the contemporaneous
and lagged values of both the growth rate of state
personal income and the volume of per capita
failed business liabilities to control for the effect of
local business conditions on banking sector per
formance; and 4) the ratio of state banking assets
to state personal income in each year to control
for variation in banking sector activity relative to
that of the broader state economy.
Finally, to test whether bank size and hold
ing company affiliation can explain differences
in bank performance, I include dummy vari
ables in each regression that measure intercept
shifts for all classes of banks. Two different
specifications for each measure of industry con
ditions are estimated; these vary the ways in
which the dummy variables are interacted with
■ 10 This method mitigates the effects of outliers within a class of
banks. Outliers, in terms of a performance measure, will affect the measure
only to the extent of their relative importance in the cohort. For example, to
measure the ROA of small independent banks in each state (and each year), I
take the ratio of their aggregated net income to their aggregated assets. A
$50 million bank will, on average, contribute less to each term in the ratio
than a $100 million bank. Of course, this is also the case for the data gener
ally used in industry analyses.
http://fraser.stlouisfed.org/
Federal Reserve Bank of St. Louis
time to examine whether performance differ
entials changed over the sample period. Both
regression specifications include the same
control variables and differ only in their treat
ment of the dummy variables.
VII. Evidence on
Banking Sector
Performance
Specification 1 includes an intercept shift for
each size class (Size) and type of bank holding
company affiliation (HCA) as well as the set of
control variables. This specification takes the form
+X
W Ec°n,nj+ ZnXsA
i= 1
where Ration t, h is an observation of a bank
performance measure, in the nth state and i th
year, of banks in Size class 5 and HCA class h.
Econi „ t( i= 1,
5) is the set of state-level
economic variables that includes current and
lagged personal income growth, current and
lagged per capita failed business liabilities, and
the ratio of bank assets to personal income.
Here, the intercept shifts associated with Size
and HCA will measure how the average per
formance of banks with these characteristics
varies. It is possible to estimate performance
differentials only relative to a base group in
each class. Very small banks are the Size base
group and multibank holding company affili
ates are the HCA base group.
Table 5 presents selected results of the re
gressions on six measures of banking condi
tions (summarized in table 3) obtained using
specification 1. For brevity, the individual coef
ficient estimates of the intercept shifts for each
state are not reported. However, they suggest
that significant differences in banking condi
tions across states can be attributed to statespecific factors (other than current economic
conditions) during the sample period. These
may reflect average differences in local indus
try structure, including the structure of the
banking sector. Similarly, the estimated inter
cept shifts for each year of the sample (relative
to the base year, 1992) indicate that in evaluat
ing bank performance over time, it is impor
tant to control for economywide trends that
affect banks in all states. These coefficient esti
mates mirror the trends in banking conditions
evident in the national-level data shown in
Regressions Explaining
Cohort-Level Performance
Capitalization
CRE
Lending
C&I
Lending
Return
on Assets
Nonperforming
Assets
Net Loan
Charge-offs
0.146
0.407
0.397
0.164
0.285
0.188
State Dummies
(a)
(a)
(a)
(a)
(a)
(a)
Year Dummies
(a)
(a)
(a)
(a)
(a)
(a)
-0.0155
(-0.37)
0.0038
(0.09)
-0.0010
(-1.06)
-0.0018
(- 1.99)b
-0.0027
(-1.10)
-0.1816
(—3.4l)a
-0.1464
(-2.72)a
0.0787
(1.49)
-0.0003
(-1.16)
-0.2622
(—15.69)a
-0.1780
(-8.42)a
-0.0931
(-7.21)3
0.1043
(1.99)b
-0.0025
(- 2.09)b
-0.0027
(-2.34)a
-0.0081
(-2.66)a
0.07447
(6.65)a
0.0661
(5.99)a
-0.0017
(-0.66)
-0.0009
(-2.81)a
-0.0056
(-1.81)
-0.0009
(-2.85)a
0.0053
(8.25)a
0.0029
(7.59)a
0.001
(1.00)
0.0070
(3.33)a
-0.0062
(—3.33)a
—
-0.0258
(-9.78)a
-0.0084
(-3.69)a
-0.0272
(- 10.20)a
0.0026
(1.13)
0.0031
(5.65)a
0.0012
(2.53)a
0.0022
(2.51)a
0.0016
(2,l6)b
0.0013
(1.99)b
0.0005
(0.89)
—
—
—
—
—
—
Small
-0.0173
(-10.37)3
0.0222
(10.54)a
0.0150
(7.04)a
-0.0229
(- 10.71)3
-0.0304
(- 14.42)3
0.0188
(6.99)a
0.0087
(3.28)a
-0.0276
(-5.60)3
0.0340
(12.47)3
0.0432
(16.10)3
0.0856
(17.20)3
0.0003
(0.50)
0.0016
(1.80)
0.0021
(2.38)a
0.0066
(3.99)a
-0.0009
(-1.77)
Medium
0.0020
(4.49)a
0.0008
(1.34)
0.0011
(1.98)b
-0.0008
(-0.77)
Dependent Variable
R2
Explanatory Variables
Economic Controls
Personal income growth
Lagged personal income growth
Failed business liabilities
Lagged failed business liabilities
Bank assets to personal income
0.0009
(2.24)b
-0.1071
(-8.41)3
0.0010
(3.33)a
0.0014
(4.97)a
0.003
(4. I I ) 3
Holding Company Affiliation Dummies
Not in a bank holding company
In single bank holding company
In multibank holding company
Size Dummies
Very small
Large
Very large
-0.0389
(-9.93)a
0.0009
(1.34)
0.0012
(1.83)
0.0039
(3.23)a
a. Significant at the 1 percent level.
b. Significant at the 5 percent level.
NOTE: T-statistics are in parentheses. Coefficients o f dum m y variables indicate the intercept shift relative to the omitted category, as
indicated by dashed lines.
SOURCE: Author’s calculations.
13
FIGURE
3
Adjusted and Unadjusted Performance
Differentials in Return on Assets by
Bank Size (Relative to Very Small Banks)
Percentage
Percentage
Percentage
Percentage
SOURCE: Author’s calculations.
table 2 and figure 3 (again, for brevity, the indi
vidual coefficients are not reported).
Bank performance does appear to reflect lo
cal economic conditions, particularly in regard
to bank profitability and asset quality. Both in
come growth and failed business liabilities
help explain ROA, nonperforming assets, and
loan charge-offs in the expected ways. Profit
ability as measured by bank ROA is positively
related to income growth and negatively re
lated to failed business liabilities. Symmetrically,
asset problems measured in terms of both
nonperforming assets and loan charge-offs are
negatively related to income growth and posi
tively related to failed business liabilities. C&I
lending— and to a lesser extent CRE lending—
is negatively related to failed business liabilities;
banks appear to fund fewer loans when the
credit quality of the local business sector dete
riorates. However, the coefficients on state in
come growth suggest that end-of-year lending
as a share of assets is also lower when recent
income growth has been higher. The coeffi
cients on the ratio of banking assets to state
personal income are positive in the regressions
explaining both ROA and loan charge-offs.
Hence, when banking activity is high relative
to economic activity, both bank profitability
and problems with asset quality are higher as
well. Finally, bank capitalization is relatively
unrelated to the economic control variables.
These findings, then, reveal that the profit
ability and asset quality of different segments
of the industry to a large degree reflect the
economic conditions impacting these institu
tions: W hen the local economy has been far
ing poorly, it is likely that the banking sector
will follow suit. This analysis is consistent with
most interpretations of banking trends. How
ever, the results also hint that differences in
bank performance can be attributed to differ
ences in bank characteristics.
The results for specification 1 yield signifi
cant variations in banking conditions among
institutions having different holding company
relationships. Both single bank holding com
pany affiliates and independent banks had a
smaller share of assets invested in CRE loans
than did multibank holding companies, while
only independent banks held a significantly
smaller share of C&I loans. Controlling for size,
independent banks were, on average, more
capitalized than multibank holding company
affiliates, while single bank holding company
affiliates were less capitalized. All else equal,
both independent banks and single bank hold
ing company affiliates earned a higher ROA
14
FIGURE
4
Adjusted and Unadjusted Performance
Differentials in Nonperforming Assets by
Bank Size (Relative to Very Small Banks)
Percentage
3.0
2.5
2.0
1.5
1.0
0.5
0.0
1984
1985
1986
1987
1988
1989
1990
1991
1992
1986
1987
1988
1989
1990
1991
1992
1986
1987
1988
1989
1990
1991
1992
1986
1987
1988
1989
1990
1991
1992
Percentage
2.0
1.5
1.0
0.5
0.0
-0.5
-
1.0
1984
1985
Percentage
1.5
1.2
0.9
0.6
0.3
0.0
-0.3
-
0.6
1984
1985
Percentage
0.6
0.4
0.2
0.0
-
0.2
-0.4
-
0.6
1984
1985
SOURCE: Author’s calculations.
than banks in multibank holding companies.
However, independent banks and single bank
holding company affiliates also had more prob
lems on average with asset quality, as reflected
in nonperforming assets and loan charge-offs.
Thus, controlling for size, the performance
of banks in multibank holding companies dif
fered from otherwise affiliated institutions; the
former earned a lower average ROA, but also
had fewer problems with asset quality. These
affiliates invested a larger share of their portfo
lios in loans, but they appear to have been
better risks than both single bank holding com
pany affiliates and independent banks in terms
of their performance during the past decade.
Bank performance also varied significantly
across the five size classes. As illustrated in
table 5, the differences in capitalization and in
lending mirror those evident in the nationallevel data. The coefficients measuring the aver
age differences in capitalization for each size
class indicate that controlling for other factors,
capitalization is inversely related to bank size.
These coefficients imply that on average, the
capital/asset ratio of very large banks was 3.9
percentage points lower than that of very small
banks. C&I lending as a share of assets is posi
tively related to bank size. Alternatively, while
the middle three size classes of banks invested
a higher percentage of assets in CRE loans
than did very small banks, very large banks
held a significantly smaller share.
Perhaps not surprisingly, I find a less consis
tent relationship between bank size and bank
performance in terms of profitability and asset
quality. All else equal, small and large banks
earned significantly higher ROAs than did
either very small or very large banks. Large
and very large banks had higher loan chargeoffs and lower nonperforming asset ratios than
did very small banks. Relatively small banks
($100 million to $500 million in assets, 1987
dollars) seem to have turned in the best per
formance in terms of profitability and asset
quality. Interestingly, these banks are about
the size that some studies have shown to maxi
mize economies of scale (Berger, Hanweck,
and Humphrey [1987]).
In summary, specification 1 estimates the
average differences in bank performance that
can be attributed to bank size and holding
company relationships, controlling for local
economic factors and aggregate trends that
affect banking conditions. Thus, the results
measure the extent to which the variation in
bank performance w ithin states is related to
these structural characteristics. I find systematic
19
F I G U R E
differences in capitalization and lending across
banks that vary in their size and holding com
pany relationships. Indeed, the disparities in
capitalization and lending observed at the na
tional level appear to largely reflect these struc
tural differences. The results also indicate some
variation in bank profitability and asset quality
across the different types of banks during the
past decade.
5
Adjusted and U nadjusted Perform ance
D ifferentials in N et Lo a n C harge-offs by
Bank S ize (R e la tive to V e ry S m a ll Banks)
V III. W ill
Performance
Differentials
Continue?
The observed differences between large and
small banks may have changed during the past
decade. Estimating how the average perform
ance of one type of bank (over a number of
years) compares to that of another may ob
scure emerging differences in performance.
For example, because of greater asset diversifi
cation, the asset quality of larger banks could
have been significantly better than that of
smaller banks early in the 1980s. If, indeed,
these institutions have increased the relative
risk of their investments (because they are too
big to fail), they may still be on par with small
banks in terms of average performance al
though their asset quality has been declining.
To examine the possibility that structural dis
parities in bank performance have changed in
the past decade, I estimate a second set of
regressions:
Percentage
(2)
Ratio n tsh = a + $ *ate +
*Year +
*Year
5
+X
1984
1985
1986
1987
SOURCE: Author’s calculations.
1988
1989
1990
1991
1992
i=
W ECOnt,rU+E>Us,h-
1
Specification 2 includes an intercept shift for
each Size and HCA class for each year in the
sample period, as well as the control variables
included in specification 1. Again, it is possible
to estimate differences only relative to a base
group in each class; hence the choice of very
small banks as the Size base group and multi
bank holding company affiliates as the HCA
base group. In these regressions, each inter
cept shift associated with a class of banks
measures the estimated difference between the
performance of that class and its respective
base group in a p articular year. Therefore, the
estimated performance differentials associated
with bank size and holding company relation
ships are allowed to vary over time.
16
Here, I present the evidence of performance
differentials in ROA, nonperforming assets, and
loan charge-offs obtained using specification 2.
The results for the control variables in these re
gressions are similar to those presented in table 5.
Thus, I focus on patterns in the time-varying in
tercept shifts associated with bank size and hold
ing company affiliation. The intercept shifts can
be interpreted as annual bank performance differ
entials that have been adjusted for state-specific
factors, local economic conditions, and economywide trends. These adjusted performance differ
entials are therefore estimates of the within-state
variations in bank performance attributable to
structural characteristics.
In figures 3, 4, and 5, the green lines illustrate
the adjusted performance differentials in ROA,
nonperforming assets, and loan charge-offs for
each Size class of banks. It is instructive to com
pare these estimates to measured differences in
performance that have not been adjusted for
other economic factors. The national-level per
formance measures presented in table 2 are used
to construct unadjusted performance differentials
of this sort for each Size class of banks. For exam
ple, the unadjusted differential in the ROA of
very large banks in each year is simply the ROA
for this cohort of banks minus the ROA for very
small banks (as illustrated in figure 2). The unad
justed performance differentials in ROA, nonper
forming assets, and loan charge-offs are depicted
by the blue lines in figures 3, 4, and 5.
The panels in figure 3 illustrate both the
adjusted and unadjusted differences in ROA for
each Size class of banks (relative to very small
banks). A comparison of these series indicates
that controlling for other economic factors miti
gates the relatively poor performance of larger
banks in recent years. The adjusted differentials in
ROA for small banks suggest that, all else equal,
they were more profitable than very small banks
during the entire sample period. However, the
adjusted differentials for the three largest classes
reveal no emerging trends in profitability differen
tials that can be attributed to bank size per se.
The panels in figure 4 depict the unadjusted
and adjusted differentials in nonperforming as
sets by Size class. The adjusted series do not ex
hibit the increasing disparities between sizes that
are evident in the unadjusted data. Panels A and
B do indicate that, all else equal, larger banks
had significantly higher nonperforming asset ra
tios than did smaller banks in the late 1980s. Sub
sequently, however, the differences attributable
to size decreased.
Finally, the panels in figure 5 illustrate both
the adjusted and unadjusted differences in loan
charge-offs for various-sized banks. The ad
justed differentials are measurably smaller than
the unadjusted ones. As in the case of nonper
forming assets, controlling for other economic
factors mitigates the emerging relationship be
tween size and asset quality problems sug
gested by the unadjusted measures. However,
again, it does appear that larger banks showed
more asset quality problems than did smaller
banks during the late 1980s.
The key result yielded by these series is that,
controlling for economic factors, there is no
evidence of a trend toward increasing dispari
ties in bank performance that can be attributed
to bank size as a structural characteristic. Simi
larly, the estimated performance differentials for
the HCA classes do not suggest emerging dis
parities in bank profitability and asset quality
associated with holding company relationships.
IX. Banking Sector
Performance:
Assessing the Trends
One interpretation of observed bank perform
ance in the past decade is that the disparities be
tween larger and smaller banks may indicate that
increasing risks are being borne by the largest
players (Boyd and Gertler [19931)■Accordingly,
the trend toward larger banks has been viewed
with some concern. This paper investigates the
merits of this perception by descriptively assess
ing the extent to which differences in banking
conditions can be attributed to variations in bank
size and holding company affiliation.
Taking local economic factors into considera
tion reduces the disparities in bank performance
attributable to these structural characteristics.
There is some evidence that, after controlling for
state-specific fixed effects, local economic condi
tions, and national-level trends, larger banks perfonned worse during the 1980s than did smaller
institutions. However, the trend appears to have
since reversed. In addition, the results indicate
that, all else equal, banks that are associated with
larger organizations through multibank holding
company affiliations tended to perform better
than otherwise-affiliated institutions.11
■
11 In interpreting these findings, it is important to note that I am
evaluating cohort-level banking conditions. Smaller banks that grow
large because they are profitable are allowed to be reclassified into larger
size cohorts. On the other hand, banks that are poor performers also may
leave their cohorts as they are either closed or merged into larger institu
tions. Although beyond the scope of this study, it would be interesting to
examine the extent to which trends in banking sector performance have
been associated with changes in the population of banks across size
classes and holding company affiliations.
One potential explanation for the finding
that large banks performed relatively poorly is
that these institutions may be more likely to
make loans outside their locality. To the extent
that this is true, I do not control for economic
conditions where they made loans. An obvious
example is the case of the huge write-offs asso
ciated with loans to developing countries. The
rationale for controlling for local economic con
ditions is that certain institutions are more sub
ject to these conditions. Thus, evidence that
less constrained firms are riskier may suggest
that they could and did take on more risk dur
ing the past decade.
In assessing the performance of large banks,
it is also important to note that most of these in
stitutions are part of multibank holding compa
nies. Thus, a study of the behavior of large banks
is effectively a study of the joint effects of both
large size and this form of banking organization.
O n the other hand, the evidence indicates that,
all else equal, multibank holding company affili
ations appear to benefit banks. This suggests that
smaller affiliates have not experienced the same
problems with asset quality as have larger institu
tions. Thus, it seems that the performance of
larger banks reflects the effects of size rather
than holding company status per se. Indeed, risk
ier loans may have been channeled to larger
banks in the holding companies.
The results of this analysis indicate that the
U.S. banking industry during the 1980s may have
been characterized by a duality related to bank
size. Although reregulation in the past several
years has attempted to address this possibility,
the evolving role of banks indicates that the link
between bank size and bank performance mer
its further study from a regulatory perspective.
References
Amel, Dean F., and Michael J.Jacowski. “Trends
in Banking Structure since the Mid-1970s,”
Federal Reserve Bulletin, vol. 75, no. 3 (March
1989), pp. 120-33.
Avery, Robert B., and Allen N. Berger. “Riskbased Capital and Deposit Insurance Re
form,” Jo u rn a l o f Banking a n d Finance, vol.
15, nos. 4/5 (September 1991), pp. 847-74.
Berger, Allen N., Gerald A. Hanweck, and David
B. Humphrey. “Competitive Viability in Bank
ing: Scale, Scope, and Product Mix Econo
mies,” Journal o f Monetary Economics, vol.
20, no. 3 (December 1987), pp. 501 —20.
Berger, Allen N., and Timothy H. Hannan. “The
Price-Concentration Relationship in Bank
ing,” Review o f Economics a n d Statistics,
vol. 71, no. 2 (May 1989), pp. 291-99.
Boyd, John H., and Mark Gertler. “U.S. Commer
cial Banking: Trends, Cycles, and Policy,”
National Bureau of Economic Research
Working Paper No. 4404, July 1993Boyd, John H., and Stanley L. Graham. “Investi
gating the Banking Consolidation Trend,”
Federal Reserve Bank of Minneapolis, Q uar
terly Review, vol. 15, no. 2 (Spring 1991),
pp. 3-15.
Clark, Jeffrey A. “Economies of Scale and Scope
at Depository Financial Institutions: A Re
view of the Literature,” Federal Reserve Bank
of Kansas City, Economic Review, vol. 73,
no. 8 (September/October 1988), pp. 16-33.
Samolyk, Katherine A. “Bank Performance and
Regional Economic Growth: Evidence of a
Regional Credit Channel,” Federal Reserve
Bank of Cleveland, Working Paper 9204,
February 1992.
Savage, Donald T. “Developments in Banking
Structure, 1970-81,” Federal Reserve Bulletin,
vol. 68, no. 2 (February 1982), pp. 77-85.
________ . “Interstate Banking: A Status Report,”
Federal Reserve Bulletin, vol. 79, no. 12 (De
cember 1993), pp. 1075-89.
Wheelock, David C. “Is the Banking Industry in
Decline? Recent Trends and Future Prospects
from a Historical Perspective,” Federal Re
serve Bank of St. Louis, Review, vol. 75, no.
5 (September/October 1993), pp. 3-22.
Competition for Scarce Inputs
The Case of Airport Takeoff
and Landing Slots
by Ian Gale
Ian Gale is an economic advisor
at the Federal Reserve Bank of
Cleveland. The author thanks
Mark Stegeman for helpful
discussions.
Introduction
The process of deregulating airlines in the
United States began in earnest with the passage
of the Airline Deregulation Act of 1978. The Act
set in place a timetable for removing govern
ment controls on fares and entry into routes.
However, airline access to airports has not
been fully deregulated. In 1968, the Federal
Aviation Administration (FAA) adopted the socalled “high-density rule” to combat congestion
at four airports. Specifically, limits were placed
on the number of operations per hour at Ken
nedy, La Guardia, O'Hare, and Washington
National. More and more airports are becoming
crowded, given the difficulties in securing per
mission from local authorities to expand exist
ing facilities or to build new ones, so this prob
lem will persist.1
For many years, the right to take off and
land at the four crowded airports was deter
mined by a committee system. Multilateral ne
gotiations took place among the incumbent
carriers and prospective entrants, with the FAA
stepping in if an impasse occurred. Since 1986,
■ 1 Only one major airport has been built in the United States since
http://fraser.stlouisfed.org/1974, that being the new Denver facility.
Federal Reserve Bank of St. Louis
incumbents have had property rights called
“takeoff and landing slots” or simply “slots.” A
slot permits the owner to make one operation
(a takeoff or landing) during a specified time
period. Carriers now have the right to buy and
sell slots.2 Questions remain about the optimal
way to allocate existing or new slots. The first
question asks why the incumbents should be
given valuable property rights.3 The second
asks whether allowing carriers to buy and sell
slots will lead to monopolization of airports,
with resulting higher fares. Repossessing slots
and then selling them back to carriers would
raise revenue and would ensure that those car
riers willing to pay the most would acquire the
slots. This has positive welfare implications in
a perfectly competitive environment, but the
impact is less clear if there is the potential for
wielding market power.
This Economic Review analyzes competition
for scarce inputs such as airport takeoff and
landing slots. It describes the outcome of an
auction of slots between two carriers, w ho may
■
■
2 For further discussion, see Grether, Isaac, and Plott (1989).
3 A slot at O’Hare recently rented for $66,000 per month. See
“United Wins TWA Lease," New York Times, March 20,1992.
have existing slots. This allows us to evaluate
the welfare implications of selling slots. It like
wise describes the outcome of a merger or
takeover battle in which two large incumbents
seek to buy up the slots of small competitors,
if not the competitors themselves."4
The objects for sale (the slots) are sold in a
sequence of auctions. The aggregate value of
the slots, and each bidder’s valuation of the
marginal slot, increase as slots become more
concentrated in the hands of one bidder. These
conditions arise naturally in market games,
since control of slots can confer market power
by limiting the competitiveness of one’s rivals.
I focus primarily on the case of two bidders
who start with no slots. The final allocation is
typically unequal, and many different interme
diate allocations lead to the same final alloca
tion. In addition, if bidders start with nonzero
holdings of slots, a bidder who holds the en
tire initial allocation of slots often does not
block new entry. I then discuss the extension
to more than two bidders, starting with three
bidders, and then with more bidders than slots.
While the focus here is on the allocation of
scarce inputs, the analysis contributes to the
general theory of auctions as well.'’ Most theo
retical studies of auctions have considered
“one-shot” auctions in which a single object is
sold or several objects are sold simultaneously.
In reality, related objects are often sold sequen
tially, either because sellers enter the market
one at a time, or because it is practical for an
individual seller to sell related objects as an on
going process. (Goods auctioned sequentially
include art, wine, procurement contracts, tim
ber rights, and mineral rights.) McAfee and
McMillan (1987) note that all levels of govern
ments of western nations procure goods and
services equal to 10 percent of gross national
product annually, much of it by competitive
bidding. Given the economic importance of
these markets, further study is warranted.
A common feature of many of these settings
is that the value of the object for sale, be it a
contract to produce or a scarce input, depends
on the other objects obtained. If the objects
are identical, then this observation implies that
the total value of the objects obtained is a non
linear function of the quantity obtained, which
is the case here.
■
4 For an example, see “American Deal W ill End Britt O’Hare Opera
tion,” Chicago Tribune, December 20,1988.
■
5 See McAfee and McMillan (1987) tor a survey of the literature on
sequential auctions.
I. The Model
Suppose that N identical objects called slots
are offered for sale by one or more sellers.6
Assume that N > 2 and N is an even number.
The sellers could be a government agency
wishing to allocate some or all of the takeoff
and landing slots at an airport, or they could
be carriers with small holdings of slots. (Large
carriers may wish to take over the small carriers
outright or they may simply wish to purchase
their slots.) Two bidders compete for the slots.
I denote a typical allocation of slots by the
ordered pair (x, y), where x denotes the num
ber of slots currently held by bidder X, y de
notes the number of slots currently held by
bidder Y, and 0 < x + y < N. If x +y = N,
then (x, y) is a final allocation. At each nonfinal
allocation, an auction allocates the next slot. Af
ter all slots are allocated, each bidder receives
a “final payoff’ that depends on the final allo
cation. This payoff can be thought of as the
profit from production.
The specific auction format used is the
second-price sealed-bid auction. In this auction,
the high bid wins, and the winner pays the
amount bid by the losing bidder. This format is
used for ease of exposition because its outcome
mimics that of the standard oral ascending-bid
auction. Suppose, for example, that bidder X
was willing to pay up to $100 for a slot, where
as bidder Y was willing to pay up to $80. In
an oral ascending-bid auction, where the auc
tioneer raises the price, bidder Y should not
drop out until the price hits $80 exactly. Thus,
bidder X will win the auction and pay a price
of (approximately) $80. If, instead, the bidders
were asked to write down how much they
were willing to bid, with the understanding
that the bidder who submitted the higher fig
ure would receive the slot at a price equal to
the loser’s figure, then the outcome should be
the same. The latter scheme is the secondprice sealed-bid auction.
A minimal requirement for an equilibrium
of this game is that each bidder’s strategy be
optimal, given the strategy of the other bidder.
This is the requirement that the strategies form
a Nash equilibrium. A Nash equilibrium is selfenforcing in the sense that neither bidder has
an incentive to change her strategy, given the
strategy of the other bidder.
Unfortunately, there can be many Nash
equilibria, so we must be more discerning.
■
6 The model and the analysis borrow extensively from Gale and Stegeman (1993).
Suppose, for example, that bidder X values a
slot at $10 while bidder Y values it at $8. In a
second-price auction, it is a Nash equilibrium
for X to bid $10 and for Y to bid any amount
strictly below $10. Neither bidder has an incen
tive to change her bid. If bidder X submits a
bid above Y ’s bid, then she receives a surplus
equal to the difference between her valuation
($10) and Y ’s bid. This holds regardless of X ’s
exact bid, as long as she wins. Bidder Y has
no incentive to change since he loses and re
ceives zero surplus currently, whereas if he
were to outbid X, then he would lose $2, since
he would pay $10 for a slot that he values at
$8. Thus, any pair of bids ($10, bY) with bY <
$10 constitutes a Nash equilibrium, as does any
pair of bids ( bx , $8) with bx > $8.
While there are many Nash equilibria, only
one is “robust” in a certain sense. Once we
consider the possibility that bidders might
make a mistake and submit the wrong bid,
then bidder X should bid $10 and bidder Y
should bid $8. If, for example, Y bids $9.50, ex
pecting that X will bid $10, but X makes a mis
take and bids only $9, then Y wins and pays
$9, yielding a net surplus of -$1. Likewise, if X
bids $9, thinking that Y will bid $8, but Y
makes a mistake and bids $9.50, then bidder X
has lost $.50 in surplus that would have ac
crued had she bid $10. The bids bx = $10 and
bY- $8 are referred to as “dominant strategies,”
since they are optimal regardless of the other
bidder’s bid. I restrict attention to dominant
strategies, which leaves each bidder with a
unique bidding strategy.7
I study the equilibrium sequences of winners
and the associated prices. (Tie bids produce mul
tiple sequences of winners.) The bidders know
the initial allocation of slots, the auction rules,
and the final payoffs (the profits from produc
tion, given the final allocation of slots). I focus on
the case in which both bidders start the auction
with no slots, but consider other initial allocations
as the analysis progresses.
A numerical example illustrates the work
ings of the sequential auction. Suppose that
there are two slots for sale. The two firms re
ceive a profit from production of $2 apiece if
each of them owns one slot. A firm receives a
profit of $5 if it controls both slots, in which
case the other bidder receives zero. The slots
are sold in a sequence of two second-price
auctions. Suppose that bidder X wins the first
auction. She will be willing to pay up to $3 for
■
7 Strictly speaking, I eliminate, iteratively, all strategies that are
http://fraser.stlouisfed.org/dominated by some other strategy.
Federal Reserve Bank of St. Louis
the second slot, which is her marginal valua
tion. Bidder Y is willing to pay up to $2, which
is his marginal valuation. Bidder X will win the
second auction and pay a price of $2. Given
this behavior in the second auction, both bid
ders are willing to bid exactly $3 in the first
auction. Therefore, the price of the first slot is
$3 and the price of the second is $2. One bid
der wins both, but both bidders receive net
profits of zero.
Now suppose that owning one slot is worth
$3 instead, all else equal. After the first auc
tion, the winner has a marginal valuation of
$2, whereas the loser has a marginal valuation
of $3. The loser of the first auction will win the
second and pay a price of $2 for that slot.
Thus, neither bidder will be willing to pay
more than $2 to win the first slot, since by los
ing he or she will win the second slot. Simi
larly, each bidder will be willing to pay up to
$2 for the first slot. Since winning the first auc
tion at any price strictly less than $2 is better
than winning the second auction at a price of
$2, it follows that both bidders will bid $2 for
the first slot. This process generalizes to N
slots. The equilibrium bids are determined by
backwards recursion, as outlined below.
At any point during the sequence of auctions,
the current allocation of slots is an ordered
pair (x; y), where bidder X owns x slots and
bidder Y owns y slots. The allocation (x, y) is
followed by (x + 1, y) or (x, y + 1), depending
on who wins at (x; y). For each number of
slots, x = 0, 1, ..., N and each bidder i = X, Y,
f t (x) denotes the final payoff given to bidder i
if the final allocation is (x, N - x). Since the
slots are assets,^ is increasing in x and f Y is
decreasing. Each bidder i seeks to maximize
the difference between her final payoff (x)
and her total expenditure for slots purchased
in auctions.
Let Vi (x, y), i = X, Y, denote bidder i ’s valu
ation of allocation (x, y). In other words, Vj
(x, y) is bidder i’s equilibrium payoff in the
game commencing at (x, y). The valuation of a
final allocation is the final payoff:
(1)
Vi (x ,N - x ') = f {(x ),
x =0, 1, 2, ...,N; i= X, Y.
The valuation of an intermediate allocation
(x, y) depends on the valuations of its sequels
(x + 1, y) and (x, y + 1). There is a unique val
uation of (x, y ) if each bidder adopts the strat
egy in auction (x, y ) and in all subsequent
auctions of bidding the increment to value re
sulting from obtaining the next slot. (As noted
above, any auction in which the resulting bids
are unequal has many Nash equilibria, but the
possibility of mistakes justifies the assumption
that bidders will play dominant strategies.)
Consider first the penultimate allocations
(x, y), where 0 < x, 0 < y, and x +y = N - 1.
The value of that next slot to bidder X, say, is
the difference between her final payoff when
she wins and when she loses: Vx (x + 1, y) Vx (x, y + 1). It is a dominant strategy for bid
der i to bid Bi (x, y) in auction (x, y), where
slots increases, while assumption (3d) means
that aggregate final payoffs increase with the
final concentration of slots. (Note that 13c] says
that bidder Y ’s final payoff is increasing and con
cave in his own number of slots.) Finally, assump
tions (3e) and (30 are invoked for concreteness.
The example discussed below satisfies these
conditions, but the results of Theorem 1 do not
require them.
(2a)
Bx (x ,y ) = Vx (x + l,y ) - Vx(x, y+ 1) ;
(3b) fx (x) is strictly increasing and convex,
(2b)
By(x, y) = VY(x, y+ 1) - VY (x + l,y ).
(3a)
/ x (x ) = f Y (N - x ) for all x.
for x > N / 2.
If B x(x, y) > B Y(x, y), then bidder X wins the
next slot and pays bidder Y ’s bid. If B x(x ,y)
< B y ( x , y), then bidder Y wins the next slot. If
Bx (x, y) = B Y(x, y), then the tie-breaking rule
determines the winner.
The valuations at each penultimate allocation
can now be calculated, given these equilibrium
bids. This allows bids to be determined one auc
tion earlier, at the antepenultimate allocations,
and so on. Bids at any earlier allocation also take
the form of (2). The bidders’ valuations of each
allocation can be calculated recursively. The price
paid in auction (x, y) is min [Bx (x, y), BY(x, y)].
The tie-breaking rule, which I leave unspecified
for now, cannot affect bids or valuations in
any given auction.
The equilibrium of the auction game com
prises the bidding functions Bx (x, y) and B v
(x, y ), for all (x, y). Henceforth, I assume that
the bidders are symmetric with respect to their
final payoffs. The outcomes will typically not
be symmetric, however.
II. Competition for
Scarce Inputs
I now put some additional structure on the
model. First, symmetry of bidders is imposed
in (3a). Second, aggregate final payoffs, and
each bidder’s valuation of the marginal slot,
are assumed to rise as the final concentration
of slots increases (that is, as the allocation of
slots between bidders becomes more un
equal). These conditions arise naturally for
scarce inputs because higher concentration
typically leads to higher output prices, increas
ing both aggregate profits and the value of
marginal output. Assumptions (3b) and (3c)
mean that each bidder’s valuation of the mar
ginal slot rises as the final concentration of
(3c)
f Y (x) is strictly decreasing and concave,
for x > N /2.
(3d) f ( x ) = fx(x ) +fY (x) is strictly increasing,
for x > N /2.
(3e)
fx (x) = a x + (3x x+ d x x 2/2 , and
(30
fy (x ) = a y + P Kx - 8}.x 2/2,
where d Y > 5X >0.
Assumptions (3a) - (3d) place additional restric
tions on the parameters, which I leave unspeci
fied for now.
W inning a particular slot affects a bidder di
rectly by increasing her current holdings of
slots, but it also affects the competition for the
remaining slots. Two countervailing effects de
termine the number of slots won by, say, bid
der X. The first effect argues for one bidder to
acquire all slots, since that outcome maximizes
the sum of the final payoffs. This effect is coun
tered by the fact that the more slots bidder X
wins, the higher is the marginal valuation of
another slot to bidder Y (presuming that y < x),
and the fiercer is the competition for the mar
ginal slot. If bidder Y ends up with very few
slots, then bidder X is a near-monopolist. Bid
der Y benefits from X ’s relative passivity in the
production game, so marginal capacity is most
valuable to bidder Y when he has very little.
(Empirically, airlines that dominate airports tend
to have the highest fares. See Borenstein [1992].)
This trade-off leads to an equilibrium alloca
tion of slots that is typically neither symmetric
nor monopolistic.
A heuristic argument provides some intuition
for the determinants of the equilibrium alloca
tion of slots. I proceed by conjecturing the form
of the equilibrium. I then show that it is optimal
in each auction for bidders to bid in the way
prescribed. The heuristic argument for deter
mining the equilibrium allocation is now given.
Consider an allocation (x, y) such that, in
equilibrium, bidder X wins any auction (x ', y ')
> (x, y) such that y ' < y + 2. In other words, if
bidder X has at least x slots and bidder Y has
y, y + 1, or y + 2 slots, then bidder X will win
all remaining slots in equilibrium. If a deviation
at (x, y) causes bidder Y to win one more slot,
then any additional slot that bidder Y wins will,
in equilibrium, be his last slot. Therefore, fol
lowing the deviation, bidder Y bids the value
of that last slot, B y (N - y - 2, y + 1), in every
remaining auction. If the deviation did not oc
cur, bidder Y would bid B Y(N - y - I, y) in
every remaining auction. Since bidder X wins
all remaining slots, even if a deviation causes
her to lose one of those slots, the marginal con
tribution to her final payoff of winning auction
(x, y) is equal to the marginal value of winning
the last auction, BX (N - y - 1, y).
By winning auction (x, y ), bidder X in
creases the price that she must pay upon win
ning the remaining N - x - y - 1 auctions by
ABY(N - y - 2, y+ 1) = B Y(N - y - 1, y )- B Y
(N - y - 2, y + 1). Therefore, bidder X wins
auction (x, y) if and only if BX(N - y - 1, y) >
(N - x - y - 1 )ABY(N - y - 2 , y+ 1) +
BY(N - y - 1, y). Recalling that /(x ) = f x (x) +
/ y-(x), the condition can be rewritten:
(4 )
f ( N - y) - fC N - y -1 ) >
(N - x - y - 1) AB Y CN - y - 2, y+ 1).
In other words, bidder X wins auction (x, y)
only if the increment to aggregate final payoffs
(the left-hand side) exceeds the increment to
total prices paid (the right-hand side).
Define p to be the smallest integer such that
(y + 2, y) satisfies (4) for y = p, p + 1, N/2 - 2.
The equilibrium allocation will be (N - p, p),
which I call the “modal allocation,” or its sym
metric counterpart.
Theorem 1. When (3) holds, either bidder X
wins N - p slots and bidder Y wins p, or the re
verse holds.
The equilibria of the original game and the
game starting from any intermediate allocation
have a regular form. From here on, I assume
that ties are won by bidder X if the allocation is
even. This tie-breaking rule ensures that bidder
X always has at least as many slots as bidder
Y, so the equilibrium allocation in this case is
(TV- p, p). If x = y, then there will be a tie in
the next auction, which buyer X wins by the tie-
breaking rule. Buyer X also wins the next auc
tion to maintain her lead. Thereafter, different
patterns are possible. If I assume that bidder Y
wins all ties when he is behind, then the bidders
alternate victories until buyer X commences
her final string of victories, and the modal allo
cation is reached. If x > y, then buyer Y wins a
string of auctions first, but not enough to catch
up. Either buyer Y catches up to within one slot,
and then a pattern of alternation persists until
the modal allocation is reached, or else he
never catches up to within one, in which case
buyer X wins all auctions after Y ’s string of vic
tories. The point at which buyer X commences
her string of victories is determined by (4).
The theorem is illustrated by the following
numerical example. Suppose that each slot repre
sents one unit of capacity in a subsequent pro
duction game, where the inverse demand is P =
24 - Q and average cost is zero, up to capacity.
If bidder X has x slots, then she is able to pro
duce up to x units of output. For quantities
strictly less than x, marginal and average cost
both equal zero, but for quantities strictly above
x, marginal and average cost are infinite.8
Suppose that the firms behave like Cournot
duopolists in the production game. In a Cour
not duopoly, each firm chooses the optimal
quantity to produce, given the level produced
by its competitor. In the absence of capacity
constraints, each duopolist produces eight units
of output in the Cournot equilibrium. To see
this, note that if bidder X produces q x units of
output, then bidder Y ’s profit from producing
q units is (24 - qx - q) q, a concave function
that takes its maximum at q = (24 - qx )/2. Like
wise, if Y produces qY, bidder X ’s optimal
strategy is to produce q = (24 - qy)/2. If both
bidders are unconstrained, then the unique
Cournot equilibrium has qx = qY = 8.
Assume, however, that exactly N = 16 slots
are available, and x > 8. Concavity of the profit
function ensures that the best responses for
the two bidders are
(5a)
qx = min{(24 - qY)/2, x I
(5b)
qY = min {(24 - qx ) / 2 ,16 - x }.
There are now four possibilities, depending on
whether the bidders are constrained. The bid
ders cannot both be unconstrained, since that
would require that bidder Y produce eight units,
which exceeds his capacity. It is also immediate
■
8 In reality, the capacity constraint is not absolute, since more seats
can be put on an airplane, but the qualitative properties need not change
when this possibility is permitted.
FIGURE
1
Possible Sequences
of Equilibrium Victories
wins and (3,0) is reached or whether Y wins
and (2,1) is reached.
The modal allocation is (10,6) here. Straight
forward calculations confirm that (4) amounts to
(7)
x
SOURCE: Author’s calculations.
that the bidders cannot both be constrained. If
Y produced 16 - x units, X would wish to
produce only [24 - (16 - x W 2 = 4 + (x/2),
whereas he has available x units of capacity.
Because x > 8, 4 + (x /2 ) < x. Now suppose
that X is constrained and Y is unconstrained. If
qx = x, qY = min {(24 - x)/2, 16 - x } = 16 - x,
which is a contradiction. The only remaining
possibility is that bidder X is unconstrained and
bidder Y is constrained. It is straightforward to
confirm that qx = 4 + (x /2) and qY = 16 - x are
the unique equilibrium outputs. Total output is
20 - (x/2). The price of output is (8 + x)/2,
so the final payoffs (that is, the profits in the
Cournot production game) are
(6a)
f x (x) = (8 + x)2/4,
(6b) f Y(x) = (8 + x)(l6 - x)/2.
Note that these final payoffs are consistent
with (3a) - (30.
I
now return to the auction. The different
possible sequences of equilibrium victories are
noted in figure 1. Arrows indicate which alloca
tions can follow a given allocation. For exam
ple, starting from the allocation (2,0), where
bidder X currently has two slots and bidder Y
currently has none, the allocations (3,0) and
(2,1) can both be reached. This means that the
two bidders submit the same bid at (2,0), and
the tie-breaking rule determines whether X
(2y+ 1)/4 > (13 - 2y),
or y >5.1. Thus, jj. = 6. Price drops occur be
tween auctions separated by double cross
marks. O n any path from the origin, the price
is 10.5 in the first auction, 6.25 in the next 12
auctions, and 5.5 in the last three auctions. The
equilibrium paths in the example have several
other properties.
1. While the leader may ultimately win con
siderably more slots than the follower, the
leader strictly outbids the follower only when
his lead is reduced to one or after the follower
has already won all of her slots. A consequence
is that there is an equilibrium path in which
bidder X wins the first two slots, then bidder Y
wins one, and then they alternate victories un
til the allocation (fi +1, |i) is reached. At that
point, bidder X wins all remaining slots.
2. The trade-off that determines the num
ber of slots that the leader wants to win, along
with the preceding observation, ensures that
many intermediate allocations lead to the same
final allocation. Any initial allocation (x, y) at
which 0 < jy < x < | i + 1 and (x, y) # (|i + 1,
|a + 1) leads to the same final allocation. In the
example, the modal allocation is (10,6), and any
initial allocation (x, y ) with 0 < y < 7, except
ing only (7, 7), leads to the modal allocation.
Thus, many different histories lead to the same
equilibrium allocation of slots. This implies that a
sizable initial advantage need not be maintained.
3. If the initial allocation is (0,0), then the
price drops either once or twice. It drops im
mediately after the leader is established (which
equalizes net profits). It also declines immedi
ately after the follower wins his last slot if a de
viation causing him to lose that slot would have
caused him to lose all subsequent slots as well.
Since the follower loses some surplus in that
case, he bids more than he would bid if a loss
would be compensated by his winning another
auction subsequently. The existence of at most
three distinct prices depends on the precise
functional form assumed.
4. An incumbent monopolist typically does
not block entry if new slots become available.
For instance, suppose that the initial allocation
of slots is (12,0), which effectively makes firm
X an unconstrained monopolist. Calculations
show that if four new slots become available,
then the prospective entrant, firm Y, wins the
first two slots before firm X wins the last two.
The reason for this is simply that it is often too
costly to preempt an entrant completely, since
the incumbent monopolist would leave the ca
pacity idle whereas the entrant would find the
capacity very valuable because the incumbent
would still be a near-monopolist after entry.
III. More Bidders
In many markets, there are exactly two com
petitors of consequence. This is particularly
true at many airports and in many airline mar
kets, so the assumption of two bidders is realis
tic in such contexts. I now consider the impact
of having more than two bidders. The exten
sion is qualitatively different because the value
of winning a slot typically depends on which
rival would otherwise win it.9 Hence, a bidder
often has no dominant strategy, so I focus on
the equilibria in which each bidder bids the
value of the next slot to her, assuming that the
rival making the highest bid would otherwise
win the auction.
Multiple equilibria are common when produc
tive capacity is sold, because keeping capacity
away from constrained bidders is a public good
that the unconstrained bidders may individually
prefer not to provide. Thus, at an airport with
two dominant incumbents, if new capacity be
comes available, each incumbent may prefer that
the other buy the new capacity and keep the en
trant out. The following example illustrates the
public good aspect in a case where all bidders
start with no capacity.
Suppose that three firms bid for three slots.
Each slot represents one unit of capacity, where
inverse demand is P = 8 (4 - Q ) and production
is again costless up to the capacity constraint.
In the post-auction production game, the firms
again act as Cournot competitors. The final al
location (3,0,0) returns final payoffs of 32, zero,
and zero, respectively. The allocation (2,1,0)
returns payments of 18, 12, and zero. The allo
cation (1,1,1) returns a payment of 8 to each
bidder. The payments from the other final allo
cations are determined symmetrically.
Equilibria are computed through backwards
recursion. (The price paid in the second-price
sealed-bid auction is the larger of the two losing
bids here.) Consider the allocation (2,0,0). The
last slot is worth 14 to the leader and bidder X,
■
9 This is reminiscent of the situation in baseball pennant races,
where contending teams attempt to trade for a player whose team is out of
the race. How much a team is willing to pay depends on whether the other
http://fraser.stlouisfed.org/
team vying for that player’s services is in the same division.
Federal Reserve Bank of St. Louis
and 12 to the others. Therefore, the leader pays
12 for the last slot. The payoff to entering this
“subgame” (the game that takes place when the
initial allocation is (2,0,0)) is 32 - 12 = 20 for
the leader and zero for the followers.
Consider next the allocation (1,1,0). The last
slot is worth 10 to a leader if it would other
wise go to the follower, bidder Z, but it is
worth only 6 if it would otherwise go to the
other leader. It is worth 8 to the follower. If tie
bids are broken fairly, then there are three
equilibria of interest. The follower bids 8 in all
three equilibria. In one equilibrium, one leader
bids 10 and the other 6; in another, their roles
are reversed; in the last, they both bid 8. In the
first two equilibria, the payoff to entering this
subgame is 10 for the leader who wins, 12 for
the other leader, and zero for the follower.
Both leaders are willing to bid enough to shut
out the follower, but each prefers that the other
do it. If we assume that the leaders randomly
coordinate on one of the two equilibria, the
average payoff to entering this subgame is thus
11 for each leader and zero for the follower.
At the allocation (1,0,0), the next slot is
worth (32 - 1 2 )- 1 1 = 9 to the leader and 11
to each follower. (If the leader wins, he goes
on to win the third slot at a price of 12.) One
of the followers wins, and the payoffs to enter
ing this subgame are 11 for the leader and
zero for the followers. At the initial allocation
(0,0,0), each firm bids 11.
Summarizing, the assumption that firms ran
domly coordinate among equilibria at the time of
the auction generates an equilibrium allocation
that is a permutation of (2,1,0). The final payoffs
to the firms are 18, 12, and zero, and the equi
librium prices are p x= 11, p~, = 11, and p 5 = 8.
It is possible for three firms to earn higher
profits if they coordinate on an equilibrium be
fore the auctions begin. In particular, suppose
that they coordinate on the equilibrium in
which firm X wins auctions (1,1,0) and (1,0,1)
and firm Y wins auction (0,1,1). Then the
leader’s payoffs in these subgames are either
10 or 12, instead of 11. In auction (1,0,0) the
equilibrium price is 12, and in auctions (0,1,0)
and (0,0,1) the equilibrium price is 10. The pay
offs in these three subgames are now 10 for
the leader and zero for the followers, except
that firm Z’s payoff in subgame (0,1,0) is 2 in
stead of zero, and its payoff in subgame (0,0,1)
is 12 instead of 10. If tie bids are broken fairly,
then firm Z wins the initial auction (0,0,0) with
a bid of 11 and pays a price of 10. Since the
payoff to winning is 12, firm Z earns profits of
2, unlike the zero profits earned without advance
coordination. The price sequence is p x= 10,
p 2 = 10, p 3 = 8. Profits appear because advance
coordination creates an asymmetry that gives
firm Z an advantage from the start. This holds
because firm Z is never put in the position of
purchasing capacity that will not be fully util
ized, since the other leader is assumed to win
at (1,0,1) and at (0,1,1). In those cases, the
other leader produces only 1.5 units even
though it purchases 2.
Finally, consider the possibility of there be
ing more bidders than slots available. In
Krishna (1993), an incumbent monopolist and
potential entrants bid for new capacity. The
monopolist wins only the last unit of new ca
pacity, assuming that marginal costs are con
stant, market demand is concave, and entrants
always produce to capacity. The presence of
potential entrants, each of whom will produce
up to capacity, means that the bid from an en
trant is always the equilibrium price of output
should the entrant win. With two or three bid
ders, all bidders may have some slots, in which
case they all internalize the impact of increased
(aggregate) production on the value of their
current holdings. This makes the potential en
trants less competitive in the small numbers
case, so an incumbent monopolist will win
more slots.
IV. Concluding
Remarks
This paper has provided a framework for ana
lyzing competition for scarce inputs such as air
port takeoff and landing slots. The analysis
describes the outcome of an auction of slots
between two carriers, who may have existing
slots, and it also depicts the outcome of a
merger or takeover wave. The equilibrium allo
cation of slots is typically asymmetric, even
though firms are ex ante identical. It is not typi
cally monopolistic, however, since the more
concentrated the allocation of slots becomes,
the higher is the price that the leader must pay
for the marginal slot.
Many different histories, and many different al
locations of slots, lead to the same equilibrium
allocation of slots, implying that an initial advan
tage need not be maintained. Thus, the concern
with monopolization may be misplaced. Future
work will consider risk aversion, capital con
straints, and matching of slots between airports.
References
Borenstein, Severin. “The Evolution of U.S.
Airline Competition,” Jo u rn a l o f Economic
Perspectives, vol. 6, no. 2 (Spring 1992),
pp. 45-73.
Gale, Ian, and Mark Stegeman. “Sequential Auc
tions of Endogenously Valued Objects,”
University of Wisconsin, Social Systems Re
search Institute working paper, 1993Grether, David M., R. Mark Isaac, and Charles R.
Plott. The Allocation o f Scarce Resources-.
Experimental Economics a n d the Problem
o f Allocating Airport Slots. Boulder, Colo.:
Westview Press, 1989.
Krishna, Kala. “Auctions with Endogenous
Valuations: The Persistence of Monopoly Re
visited,” Am erican Economic Review, vol.
83, no. 1 (March 1993), pp. 147-160.
McAfee, R. Preston, and John McMillan. “Auc
tions and Bidding,” Jo u rn a l o f Economic Lit
erature, vol. 25, no. 2 (June 1987), pp.
699-738.
Regional Wage Convergence
and Divergence: Adjusting Wages
for Cost-of-Living Differences
by Randal IW . Eberts and Mark E. Schweitzer
Introduction
One of the basic tenets of economics is that
the mobility of labor and capital tends to equal
ize prices across markets. This tendency to
ward price convergence is particularly notable
across regional markets in the United States.
For as long as regional income data have been
collected, per capita income and wage rates
have generally become more alike.1
In light of this long-run trend, a surprising
reversal has occurred in several regional price
measures. Since the early 1980s, the regional
dispersion of wages, housing prices, and the
general cost-of-living indexes has been on the
rise. Browne (1989) provides evidence that re
gional disparities in per capita income have
been widening, while Eberts (1989) finds an in
crease in regional wage dispersion. In addition,
we demonstrate below that housing costs and
regional price indexes have been following a
similar pattern. Curiously, however, wages ad
justed for regional cost-of-living differences
■
1 Eberts (1989) demonstrates this trend. Unfortunately, the regional
wage series is relatively short, beginning only in the 1950s. However, the
same general pattern is found in regional per capita income, which is
http://fraser.stlouisfed.org/
largely composed of wages and which extends well into the 1800s.
Federal Reserve Bank of St. Louis
Randan w . Eberts is the director of
the W.E. Upjohn Institute for Em
ployment Research in Kalamazoo,
Michigan, and Mark E. Schweitzer
is an economist at the Federal
Reserve Bank of Cleveland.
(which for brevity we refer to as locally a d
justed wages) have continued to converge.
Temporary deviations from the tendency
toward convergence are not unexpected, as
localized shocks can result in significant adjust
ments to regional prices. Eberts and Stone (1992)
and Blanchard and Katz (1992) show that nega
tive localized employment shocks to a metro
politan area can depress wages there by as
much as 40 percent of their original level for
up to six years before equilibrium returns. Even
so, a significant period of increasing dispersion,
as observed in the 1980s, is rare. In the last
century, regional per capita income diverged
only one other time, between 1920 and 1940.
This paper focuses on the details of regional
convergence or divergence in goods prices, na
tionally adjusted wages (wages deflated accord
ing to the national price level), and locally
adjusted wages. Our goal is to identify and de
scribe these obviously related phenomena. The
characterization of this relationship follows Roback’s (1982) model of equilibrium in local la
bor and land markets in the presence of local
quality-of-life and production differences.
The dispersion in locally adjusted wages
depends on the dispersion of its components:
nationally adjusted wages and local prices. We
demonstrate the linkage between wages and
prices by showing how the comovements of
nationally adjusted wages and regional prices
affect locally adjusted wages. Given that the two
components of locally adjusted wage variation
have followed similar paths, it is the growing
covariance of these measures that results in con
tinued convergence of locally adjusted wages
between census regions.
We also show that trends in the two wage
dispersion series primarily reflect regional differ
ences in market valuations of worker characteris
tics rather than shifts in the levels of workforce
characteristics. We modify the decomposition
used by Eberts (1989) in examining the U-turn
in nominal wage dispersion. He identifies two
factors: 1) regional differences in the return on
various worker attributes and in wage differen
tials among industries and occupations, and 2)
regional differences in the level of worker at
tributes and in the distribution of workers among
industries and occupations. Basically, these two
factors distinguish between wage dispersion
caused by regional markets placing different
values on identical attributes, and dispersion
caused by regions having different composi
tions of attributes, even though regional mar
kets value these attributes similarly.
The analysis supports previous studies show
ing that changes in regional wage differentials
over time result from varying valuations of work
er attributes, not from shifts in the regional com
position of the workforce. The additional insight
offered by this paper is that market forces pro
duce different patterns of regional dispersion of
nationally and locally adjusted wages. While not
directly explained here, these differences are con
sistent with the view that workers and businesses
pursue separate objectives or place unequal
weights on local prices and amenities.
I. Explaining
Regional Wage and
Price Differentials
The key to understanding potentially perma
nent regional wage differentials is to recognize
that not all factors are mobile across regions.
Workers and firms interact in regional labor
markets, determining wages and prices. Al
though firms and their employees may respond
quickly to changes in local market conditions,
some factors that are unique to a region, such
as geographic and climatic characteristics, re
main the same. Even for those areas that share
common features, the quality and quantity of
site-specific characteristics may differ. There
fore, firms and households may be willing to
pay or accept different levels of compensation
depending on the value they place on those at
tributes. These immobile, site-specific features
are referred to here as amenities: consumptive
amenities apply to households and productive
amenities apply to firms.
A few examples of potential sources of con
sumptive and productive amenities indicate
their conceptual breadth and complexity. The
prototypical consumptive amenity is a weather
advantage. California and Florida attract people
who prefer a warm climate and who are will
ing to accept the higher costs of living there.
Other potential consumptive amenities include
familial or historical ties to an area, regionspecific recreational activities (skiing or surfing,
for example), community spirit, and the quality
and age of the housing stock. Despite the posi
tive connotation of the term amenities, in our
usage it also encompasses the negative features
of an area, such as high crime rates or a combi
nation of high local taxes and poor local gov
ernment services.2
Port facilities are an excellent example of
a productive amenity, since they can lower
transportation costs for firms located nearby.
Productive amenities also include low-cost dis
tribution channels, informational advantages
provided by firms’ proximity to other similar
producers or suppliers, and state or local gov
ernment protections or restrictions pertaining
to local businesses.
Interpreting Wage
and Price Dispersion
Interpreting regional wage and price conver
gence in this framework is difficult. House
holds and businesses can and will move to
locations where they can better prosper. If both
labor and capital are mobile, factor prices could
converge or diverge in response to shifts in
either firms’ and workers’ valuation of local
amenities or changes in the availability of
amenities in various locales.
Another source of apparent convergence or
divergence in regional wages and prices is the
economy’s constant adjustment to a stream of
shocks. The demand for and supply of labor in
■
2 Local taxes are potential negative amenities to the extent that they
are not included in prices. However, property taxes are essentially incor
porated into the Consumer Price Index under the “rental equivalence
measure" of housing costs.
an area may be radically altered by technological
changes or shifts in consumption preferences.
Although households and businesses are mobile,
adjustment delays may result in temporary peri
ods of divergence. Studies by Eberts and Stone
(1992) and Blanchard and Katz (1992) suggest
that the adjustment period to a local labor-market
shock may be as long as 10 years.
Since housing and locally produced goods
and services represent a major portion of a
household’s budget, these prices become an
important component of household utility and
thus of household decisions. If local goods ac
counted for the entire household budget, then
consumption would equal household wages de
flated by local prices. On this basis, we assume
that given a stable value for local amenities, lo
cally adjusted wages represent the primary moti
vator of household mobility.
By contrast, the price of local goods and
services, including land, plays a smaller role in
business decisions. Wages are generally a larger
fraction of most firms’ costs than are local goods.
Furthermore, for producers of local goods, an
increase in local prices would affect both reve
nues and costs. The marginal firm most likely to
relocate would be a producer of national goods
for whom any rise in local wages (or prices)
relative to those faced by its competitors would
immediately lower profits. For these firms, local
wages (nationally adjusted), with little regard for
local prices, should be the determining factor in
their location once amenities and previous capi
tal investments have been accounted for.
It is important to compare observationally
equivalent workers if we are to measure regional
wage differentials accurately. Firms consider the
skill level of their workforce as well as the size
of their payrolls when making location decisions.
Similarly, workers must evaluate the marketabil
ity of their skills in various regions when compar
ing locally adjusted wages. Therefore, regional
shifts in factors associated with worker productiv
ity, such as average educational attainment or
workforce experience, should be controlled for
in any analysis of factor-price adjustments. Shift
ing patterns of employment by industry or occu
pation, which may be related to compensating
differentials associated with features of those
jobs, should also be considered.
II. Wage and
Price Trends
Wages
Wages of individual workers are obtained from
the March Current Population Survey’s (CPS)
wage supplements for the years 1973 through
1991. The March survey reports annual wage
and salary data and weeks worked from the
previous year. Dividing annual earnings by
weeks worked yields average weekly earnings
for the years 1972 and 1990. For purposes of
the respondents’ confidentiality, these data are
coded by the Bureau of Labor Statistics (BLS)
with a maximum salary for individuals whose
pay exceeds the top-code value (for example,
$199,998 after 1989). Average weekly earnings
are computed after correcting for top-coding
by assigning these individuals the mean of the
appropriate Pareto distribution.3 The sample is
limited to full-time workers who were em
ployed all year or who, if unemployed for part
of the year, spent that time actively seeking
work. Because only full-time workers are in
cluded, average weekly wages closely approxi
mate average hourly wages.
Two definitions of regions are used in this
paper: Metropolitan Statistical Areas (MSAs)
and census regions. Since cost-of-living indexes
are available only for metropolitan areas, the
basic unit of analysis is the MSA. The CPS iden
tifies 44 MSAs, but the limited availability of
price data for some of them reduces the usable
number to 21. The small number of respon
dents in most MSAs lowers the efficiency of
estimation for that section of the analysis deal
ing with the sources of wage convergence and
divergence. To increase the number of indi
viduals sampled in a given period, we pool to
gether three years of individual responses for
each MSA, resulting in a much broader cover
age of worker characteristics and wages. Each
of our six periods is identified by the middle
year of the pooled three-year sample.4 For
example, the first period, which consists of
earnings in 1972, 1973, and 1974, is referenced
as 1973 in the figures and tables.
To provide another means of increasing the
sample size for geographic comparisons, as
■
3 See Shryock and Siegel (1971) for details on how a Pareto distri
bution may be applied to truncated wage data. The Pareto distribution as
sumes an exponential decline in the number of individuals with incomes
above a certain amount, which is a reasonable characterization of higher
income levels.
■ 4 The final period covers 1987 to 1990.
F I G U R E
1
Variance of Regional Log Wage
Differentials: Single vs. Grouped Years
Variance of logs
0.012
0.010
0.008
Single years
_
/r
j/
-
Grouped
years
0.006
0.004 0.002 L
1972
J—
1974
_i_
1976
„
i_
1978
_
L „
i .
1980 1982
FIGURE
I , , L ......
1
1984
1986
1988
2
Variance of Regional Log
Wage Differentials: Regions
vs. Weighted MSAs
Variance of logs
Variance of logs
0.0035
0.012
/
0.010
'v. Regions
0.008
_
Jr
~
0.0020
0.006
0.0015
0.004 Weighted
MSAs
0.000
>
1973
I
1976
1
1979
1982
FIGURE
Variance of Local Price Indexes
Variance of logs
SOURCE: Authors’ calculations.
1985
1988
0.0010
_
_ 0.0005
0.0000
1990
well as to be consistent with earlier work by
Eberts (1989) and Browne (1989), MSAs are
aggregated by proportional population weight
ing to represent the nine census regions. Each
of these regions contains at least one of the 21
MSAs, except for the East South Central states
(Kentucky, Tennessee, Alabama, and Mississip
pi). As shown below, the patterns of wage and
price dispersion for MSAs and the constructed
census regions are quite similar. To adjust for
the effects of inflation, wages are deflated to
1982 levels by the GDP implicit price deflator.
Wage variance across regions exhibits a
marked U-shaped pattern between 1972 and
1990, with wages converging during the first
half of the period and then diverging thereafter
(figure 1). From 1972 to the trough, the vari
ance of wages is cut roughly in half. By the
end of the period, the variance surpasses the
level at which it started in the early 1970s. This
convergence and subsequent divergence is ap
parent for single and grouped years.
The same basic pattern of wage dispersion is
found in the MSAs aggregated to simulate the
census regions (figure 2). The level is generally
lower for the weighted MSA results because
metropolitan wages are more alike across re
gions — even though major MSA wages gener
ally reflect their region’s differential. The differ
ences between the two variances, shown in
figure 2, reflect the degree to which regional
wage differentials are altered by including
smaller MSAs and mral areas. These patterns
are generally consistent with the convergence/
divergence phenomenon reported by Eberts
(1989) using the May CPS, and by Browne (1989)
using per capita income (of which wages ac
count for a large portion).
3
Prices
Indexes that measure regional cost-of-living dif
ferences as well as price changes over an ex
tended period are not readily available. The BLS
releases a Consumer Price Index for selected
MSAs that records price changes for each area
over time. However, the index is constructed
to ignore price differences across these MSAs
by benchmarking the series to 100 on the basis
of 1982 to 1984 prices within each area. In order
to include this component in a regional price in
dex, we rebenchmarked these indexes using
the relative metropolitan cost-of-living index
from the 1981 BLS Report on Family Budgets.
(The report has not been updated because
funding for the project was eliminated.) The
F I G U R E
gated to the nine census regions exhibits a
similar pattern.
The largest component of the regional price
index — and the one that accounts for most of
the difference in prices across MSAs — is the
cost of housing services. This measure is closely
linked to the general price index, as indicated by
correlations between the MSAs’ relative prices and
housing costs of greater than 0.95 in each period.
Thus, locally adjusted wages can be viewed as
wages adjusted for local housing prices.
4
Locally Adjusted W age Variation
Variance of logs
0.012
0.010
0.008
0.006
0.004
Locally Adjusted
Wages
0.002
0.000
1972
1974
1976
1978
1980
F I G U R E
1982
1984
1986
1988
1982
1984
1986
1988
5
Factors in the Convergence
of Locally Adjusted W ages
Logs
0.016
0.014
0.012
0.010
0.008
0.006
0.004
0.002
0.000
-
0.002
1972
1974
1976
1978
1980
Locally adjusted wages refer to wages divided
by local prices (including cost-of-living differ
ences between localities). For comparisons
between census regions, these wages are ag
gregated in the same fashion as regional wages
and prices Locally adjusted wages do not con
form to the marked pattern of regional conver
gence/divergence found in nationally adjusted
wages and prices. Rather, the measure gener
ally converges throughout the entire period.
This is most pronounced for MSAs aggregated
to the nine census regions, as shown in figure
4. From peak to trough, the variance of locally
adjusted wages declines by almost 50 percent.
This tendency toward convergence is confirmed
at the metropolitan level for locally adjusted
wages, except for a slight increase in the last pe
riod. In order to be consistent with the previous
literature, we focus on census regions below.
a. Covariance o f nationally adjusted wages, local prices.
SOURCE: Authors' calculations.
metropolitan cost-of-living differences are based
on a consumption basket appropriate for a fourperson family with an intermediate income. The
index that we construct identifies metropolitan
price differences over time, which we use as
our deflator instead of relying on a national
price deflator.5
Figure 3 tracks the variance in the log of the
metropolitan price index over the same period
as wages. We use the log form to be consistent
with the use of log wages to measure wage dis
persion. Note that the dispersion of local prices
follows a similar U-shaped path, declining dur
ing the first half of the period, reaching its na
dir in the early 1980s, and then returning to
previous levels. The dispersion of prices aggre
■ 5 As already noted, wages are deflated by the GDP implicit price
http://fraser.stlouisfed.org/deflator to eliminate the effects of inflation.
Federal Reserve Bank of St. Louis
III. The
Relationship
between Wages,
Prices, and Locally
Adjusted Wages
Figure 5 offers a complete picture of locally
adjusted wages and its two components. As dis
cussed earlier, the variance of the log of nation
ally adjusted wages is considerably smaller than
both the variance of log prices and the variance
of the log of locally adjusted wages. The covari
ance of the log of nationally adjusted wages and
prices is positive, but smaller than the individual
variances. This positive but weak covariance sug
gests that MSAs with above-average rents also
pay above-average wages, which is consistent
with Gabriel, Shack-Marquez, and Wascher’s
(1988) finding that higher rents are only weakly
associated with higher wages. The relationship
of the dispersion of wages, prices, and locally
adjusted wages can be seen by decomposing
the variance of the log of locally adjusted
wages.
(1)
var[\n(wr/pr)] = var[\n(wr)]
+ var 1ln( p r ) ]
sex. The dispersion of regional wage differen
tials over time is decomposed into two compo
nents: changes in worker characteristics and
changes in labor market implicit valuations of
worker characteristics (as measured by regres
sion coefficients). Because we are not the first
to attempt to account for workforce differences,
we start by reviewing the existing literature.
-2 cov[ In(wr), ln(p r) ],
where r refers to the region, wr is the average
wage in region r, and p r is the relative price
level in region r. The variances are calculated
independently for each year. Thus, the change
in the variance of price-adjusted wages between
two time periods (0 and 1) can be decomposed
for each region as follows, dropping the redun
dant r subscripts:
( 2)
var[\n(wx/px)]~ var[\n(wQ/pQ)]
= [var[\r\(u\ )] - var[ ln (^ 0) l }
,+ {var[ ln(/?j )] - var[ ln(/>0) l }
- 2 {cov[ l n ( ^ ), ln(pj ) ]
- cov[\n(ivQ), ln (p 0) l }.
Note that price-adjusted wages can converge,
while nominal wages and prices diverge only if
the difference in the covariances is at least half
the magnitude of the two differences in vari
ances. Local amenities, whether the benefits are
accmed by firms or workers, provide a link be
tween wages and prices. Thus, there are substan
tial grounds for the existence of non-negligible
covariances between relative wages and prices.
Figure 5 does identify a significant covariance,
the rise of which is coincident with the increase
in wage variation among regions.
IV. Does Regional
Wage Convergence/
Divergence Represent
Shifting Incentives?
In order to explore regional wage differences,
observationally equivalent workers must be
compared. The role of regional workforce dif
ferences in the relative wages of regions should
be isolated from pay differentials that compara
ble workers would receive in other regions.
We account for most sources of wage disparity
by evaluating the typical differences in returns
associated with worker characteristics, including
education levels, experience, industry, race, and
Previous Studies
Previous studies examining the relative size of
the two components of wage differentials have
focused primarily on explaining differences be
tween the South and other regions of the United
States. Sahling and Smith (1983), for example,
compare the southern states with four other re
gions of the country: the Northeast, the West,
the North Central states, and the New York
metropolitan area. They estimate separate priceadjusted and nominal wage equations using a
sample of residents from 29 of the largest MSAs
in these five regions. Worker-attribute variables
include measures of schooling, experience,
race, occupation, sex, industry, job status, and
union membership. Using two cross sections
of data from the May 1973 and May 1978 CPS,
the authors conclude that cost-of-living adjust
ments dramatically increased the wages of
southern workers relative to their counterparts
across the United States.
Farber and Newman (1987) extend Sahling
and Smith’s analysis to look explicitly at changes
in characteristic prices over time. In addition to
analyzing regional wage differentials in two
separate years (1973 and 1979), they estimate
the changes in differentials between the two
years for various pairs of regions. Their results
show that more than half of the predicted
shifts in South/non-South wage ratios can be
accounted for by changing relative returns to
worker characteristics.
Using the same framework adopted in the
current paper, Eberts (1989) examines the
sources of nominal regional wage convergence
and divergence on a full sample of workers
from the May CPS. He finds that differences in
the returns to worker characteristics account for
both the convergence in regional wages from
1973 until 1982 and the divergence thereafter.
Other studies, using similar techniques but
more detailed data, do not necessarily agree with
the conclusion that characteristic prices explain
regional wage differentials. Bellante (1979) and
Gerking and Weirick (1983), for example, find
that regional wage differences result primarily
from variations in the level of worker character
istics. These findings leave open the possibility
that both characteristic prices and levels are
likely sources of regional wage differentials.6
Defining Sources of
Wage Differentials
Following the human capital specification of
Hanoch (1967) and Mincer (1974), we specify
the logarithm of individual wages — expressed
in either nominal or price-adjusted terms — as
a function of various worker attributes, includ
ing education level (entered as dummy variables
for the completion of four levels of schooling,
from high school to graduate studies), and po
tential experience (age, minus years of educa
tion, minus six, entered as a quadratic). Dummy
variables indicating race, gender, occupation,
and industry are also included as recognized
factors in individual earnings. Time dummies
are incorporated to account for aggregate fluc
tuations, including the business cycle, within
each of the pooled three-year periods.7
We estimate hedonic wage equations sepa
rately for each period and for each of the 21
MSAs. Prior to the estimation, individual wages
are deflated by either the national or local price
index, as described previously. We weight re
gional wages and estimated wage components
by their respective population shares in order
to construct a regional measure. The East South
Central region is excluded from the analysis be
cause no metropolitan area price data were
available for cities in these states. We then
compare the regional wage estimates to na
tional estimates based on the same regression
and the sample of workers from all 21 MSAs.
The technique used to account for the two
sources of wage differentials follows the ap
proach of Oaxaca (1973), with modifications by
Sahling and Smith (1983). The decomposition
assumes that y, the logarithm of wages, can be
appropriately described as a function of the
worker and industry characteristics discussed
earlier ( X and the hedonic labor market val
uation of each characteristic ( b ):
(3)
y = bXi + ui .
■
6 Dickie and Gerking (1988) provide a comprehensive and insight
ful critique of the literature.
■
7 If business cycle fluctuations alter general earning levels, then ignor
ing that variation would result in inconsistent estimates. Dummy variables
http://fraser.stlouisfed.org/
account for the mean aggregate differences between the two periods.
Federal Reserve Bank of St. Louis
Estimating a well-specified earnings equation
for each region accounts for the value associated
with regional concentrations of particular work
force traits by identifying the^average valuation
of these traits in the region ( bSt for region S at
time 0- Using y for ln (^ ), we can decompose
the percentage difference in wages between
the regions during one time period as follows:
(4 )
( yst ~ y N t) = ( ^st ~ bN t) XNt
+ ( XSt - X Nt) bNt+ ( bSt - bNt) (x st - XNt).
The first term on the right side accounts for the
difference in labor market valuations of worker
attributes between a region and the base. The
second term denotes the difference in levels of
worker and industry characteristics. The third
term, a remainder, is generally assumed to be
small and in fact proved trivial in our analysis.
Below, we examine the relative contribution of
the first two right-side components of equation
(4) over time for both wage series.
Decomposing
the Variance of
Regional Wages
Having decomposed the regional wage differen
tials into separate factors, a number of variance
decompositions are possible. The traditional
decomposition focuses on the variance of the
first two terms of equation (4), neglecting the
third term (the interaction term):
(5)
v a r{ y st - yNt ) = v a r[ (b st- b Nt) XNt ]
+ var[ ( X SI- X NI) bNt]
+ 2 cov [ ( bSt- bNt) X Nt, ( x 5i - XNt) bNt ]
+ interaction term.
This approach generally yields the correct inter
pretation of the sources, although it is incom
plete due to exclusion of the interaction term.
If the covariance is significant but is not re
ported, then the decomposition is even less
complete. We report the results of this decom
position for purposes of comparison with the
existing literature.
The focus of our paper, however, is on re
gional wage differences when local prices are
factored in, so it is valuable to consider how
33
price-level corrections affect the variance de
compositions. The adjustment for local prices
is applied to individual earnings as follows:
6
( )
y*it = yit / Pst’
where p St is constant within the locality at time
t and y*t and yit are the vectors of individuallevel wage observations for region S at time t.
Given that each MSA’s wage equation is esti
mated independently for every three-year block
of time, we can expect that the transformation
of the dependent variable will adjust the bSt
estimates proportionally. This follows from the
normal equations for annual estimates:
(7)
b l = ( X ' X ) - ' X ' j - = j - t sr
With pooling over three years of data, the adjust
ment would be a weighted average of the rele
vant p St’s. Thus, in terms of the decomposition
of regional wage differentials shown in equa
tion (4), only the price term [(bSt- bNt) XNt\
and the interaction term reflect the adjustment
of wages for the local cost of living.
Consequently, only the valuation compo
nent of the variance decomposition (equation
151) would be altered, perhaps indicating that
cost-of-living adjustments affect the variance of
regional wages through the valuation of skills
alone. These variance terms, however, are not
a complete decomposition of the sources of re
gional wage differentials unless the covariance
between the valuation and workforce charac
teristic terms is zero. The covariance term rep
resents the correlations between regional
concentrations of labor skills (or other charac
teristics) and differentials paid to those skills. A
simple supply and demand model without per
fectly elastic or inelastic demand or supply
would predict non-zero correlations. The co
variance would then be reduced to the extent
that labor or firm mobility eliminated either re
gional skill concentrations or the wage differen
tials paid to specific skills. However, regional
production and consumption amenities should
ensure that this covariance is non-zero.
The problems with the commonly applied
decomposition in this context suggest the need
for an alternative decomposition that accounts
for the covariance term in a meaningful way.
A more complete decomposition that satisfies
this requirement is provided by the covariances
between the dependent variable and the addi
tive factors.8 To simplify the notation of the price
and quantity equation (4), let y be regional
differentials, b be the valuation term, 5c be the
workforce characteristics term, and i be the in
teraction term. The interaction term, which we
still expect to be small, is included so that the
definition of the decomposition is complete. In
place of equation (5), applying a covariance
decomposition to the factors shown in equa
tion (4) results in
(8)
v a r (y ) = co v (y ,b ) + co v (y ,x ) + c o v { y ,i).
The three decomposition terms in equation (8)
are easily interpreted as the effect of a factor on
the dependent variable after covariances with
all other factors have been accounted for. The
first term represents the effect of labor market
valuations, the second represents the effect of
labor force differences, and the third is the ef
fect of the small interaction term. Factors can
be either positive or negative, depending on
whether they augment or offset the sum of the
other factors contributing to the variation. If the
factors are fully independent, then the decom
position simplifies to the basic variance decom
position for the independent variables shown in
equation (5), with a covariance equal to zero.
Splitting the parenthetical terms in equation
(8) distinguishes the components of the three
terms. Equation (9) shows that each term of
this decomposition includes an expression for
the relationship between valuations and work
force characteristics.
(9)
var( y ) = [var(b) + cov(b,x) + cov(b, i ) 1
+ 1v a r(x ) + cov(b,x) + cov(x ,i) ]
+ [var(i) + cov(b ,i) + co v (x ,i)].
Adjusting wages by a local deflator alters these
correlations. Beyond this simple statistical rela
tionship, factors are adjusted for the degree to
which higher locally adjusted wages for skills
correspond to concentrations of those skills.
Regional skill concentrations are fundamentally
linked to the mobility decisions of workers
and firms. Locally and nationally adjusted
wages should result in different decomposi
tions due to the reactions of firms and workers
to wage differentials.
■
8 A similar decomposition is applied in Schweitzer (1993) to iden
tify sources of earnings inequality.
F I G U R E
Sources of
Nationally Adjusted
Wage Differentials
6
Decomposition of Nationally
Adjusted Wage Variation
Variance of logs
SOURCE: Authors’ calculations.
TABLE
1
Decomposition of Nationally Adjusted
Regional Wage Variation
Total Variation
Characteristics
Valuations
Covariance Decomposition
1972
1975
1978
1981
1984
1987
to
to
to
to
to
to
1974
1977
1980
1983
1986
1990
0.0022
0.0017
0.0014
0.0009
0.0011
0.0034
0.0002
0.0003
0.0007
0.0004
0.0008
0.0015
0.0020
0.0016
0.0008
0.0004
0.0003
0.0020
Variances of Factors
1972 to 1974
0.0022
1975
1978
1981
1984
1987
0.0017
0.0014
to
to
to
to
to
1977
1980
1983
1986
1990
0.0009
0.0011
0.0034
0.0006
0.0002
0.0006
0.0005
0.0008
0.0014
0.0026
0.0016
0.0007
0.0005
0.0004
0.0020
SOURCE: Authors’ calculations based on data from the U.S. Department of
Labor, Bureau of Labor Statistics.
Figure 6 addresses the question of whether the
convergence/divergence pattern of regional
wage differences results more from variations
in labor market valuations or from variations in
attribute levels (for example, the decomposition
of regional wage differentials in equation [7]).
The shaded area under the curve represents
the portion of the variance of log wages ac
counted for by differences in labor market valu
ations. The remainder of the area under the
curve is the portion of the variance explained
by differences in attribute levels. In some
years, the covariance decomposition terms for
valuations and attributes do not add up to the
total variance because of the interaction term,
which is not reported. It is evident from the fig
ure that differences in valuations follow the
same U-shaped pattern as total wage variance.
O n the other hand, differences in workforce at
tributes follow a generally upward trend. This
suggests that the pattern of convergence and
then divergence of nationally adjusted wages
results more from regional labor markets’ valu
ing attributes differently than from an increas
ing dissimilarity of workers within regions.
Nonetheless, regional differences associated
with workforce attributes have been playing a
growing role in regional wage differentials.
Table 1 compares the covariance decompo
sition results with the variances of the two
significant components. In this case, the covari
ance between the quantity and characteristic
price component is small; thus, the variances
sum to approximately the total variation and
are similar to the covariance decomposition
terms. This confirms Eberts’ (1989) results for
nationally adjusted wages in a sample of the
full-time metropolitan workforce.
The results in table 1 and figure 6 can be in
terpreted in two ways: Either incentives for
firms to move toward lower-wage areas are
growing, or local productive amenities are on
the rise. Both conclusions hinge on our having
captured the majority of worker productivity
differences between regions with the worker
attributes included in the wage equations. If
significant productivity differences are not cap
tured by the wage equations, and if the unob
served productivity factors have been growing
nationally in value, then we could mistakenly
identify productivity differentials between re
gions as price differences. Along these lines,
Juhn, Murphy, and Pierce (1993) argue that
35
FI GURE 7
higher wage payments to unobserved skills ex
plain the rise in total earnings inequality dur
ing the 1980s. A final caveat to our results is
that the analysis does not account for fringe
benefit costs. Differences in these costs be
tween regions would of course result in a dif
ferent distribution of total compensation.
Decomposition of Locally
Adjusted Wage Variation
Variance of logs
Sources of Locally
Adjusted Wage
Differentials
SOURCE: Authors’ calculations.
TABLE
2
Decomposition of Locally Adjusted
Regional Wage Variation
Total Variation
Characteristics
Valuations
Covariance Decomposition
1972
1975
1978
1981
1984
1987
to
to
to
to
to
to
1974
1977
1980
1983
1986
1990
0.0119
0.0107
0.0072
0.0062
0.0047
0.0040
0.0005
- 0.0002
- 0.0001
- 0.0002
0.0000
0.0002
0.0120
0.0110
0.0075
0.0065
0.0048
0.0039
Variances of Factors
1972
1975
1978
1981
1984
1987
to
to
to
to
to
to
1974
1977
1980
1983
1986
1990
0.0119
0.0107
0.0072
0.0062
0.0047
0.0040
0.0006
0.0002
0.0006
0.0005
0.0008
0.0014
0.0129
0.0116
0.0083
0.0075
0.0058
0.0052
SOURCE: Authors’ calculations based on data from the U.S. Department of
Labor, Bureau o f Labor Statistics.
While firms m ight be adjusting to these wage
differentials, households should react to wages
that reflect their cost of living. The pattern in
the variance of locally adjusted wages is quite
different from that of nationally adjusted wages.
Instead of exhibiting a U-shaped pattern, locally
adjusted wages steadily converge over the sample
period (figure 7). Moreover, the dispersion of lo
cally adjusted wages is roughly five times greater
than the dispersion of nationally adjusted wages.
Significantly, it is differences in labor market valu
ations that explain most of the total wage vari
ance. While the dispersion in labor costs relevant
to firms (nationally adjusted wages) has increased
in recent years, the dispersion of regional differ
ences in workers’ returns to labor has declined.
Comparing the covariance decomposition re
sults with simple variances indicates, in this
case, that accounting for covariance between
factors alters our interpretation of the compo
nents of the decline in locally adjusted wage
dispersion between regions. Table 2 reveals
that, unlike the nationally adjusted wage case,
a significant negative covariance exists between
the characteristic price component of regional
wage differences and the regional distribution
of attributes. This is evident both in the fre
quently negative quantities component and in
the fact that the simple variances of the compo
nents substantially overshoot the total variances
of locally adjusted wages.
Evaluating these results in terms of worker
location decisions, we find that the declining
differences in factor returns between regions is
consistent with workers’ moving to equalize
labor market differences. A larger impetus for
mobility is indicated by the greater wage varia
tion between regions when cost-of-living differ
ences are factored in. The mobility of house
holds responding to significant, but declining,
consumptive amenities in the high-price MSAs
could explain this reduction in locally adjusted
wage differentials between MSAs. Furthermore,
the differences between locally adjusted wage
differentials appear to be almost purely the re
sult of differences in valuations of labor rather
than differences in labor force characteristics.
These differentials could encourage significant
worker movement, which could lead to rising na
tionally adjusted wage differences as wages are
driven up in high-price areas and down in lowprice areas. But it could just as well be that firms
have moved to more costly areas, driving up
wages, in pursuit of an amenity that has been ris
ing in value. The unobservability of the full set of
amenities, either consumptive or productive, pre
cludes a direct test of these explanations.
V. Conclusion
The theoretically surprising fact that regional
wages appeared to diverge in the 1980s does
not hold up when cost-of-living differences are
taken into account. Our decompositions con
firm that wage differences are driven by vary
ing returns to worker attributes rather than by
regional differences in workforce charac
teristics. Further, the possibility is raised that
workers and firms are optimizing over differ
ent value functions (nationally versus locally
adjusted wages) or different local amenities. In
particular, local prices, and therefore locally ad
justed wages, may be more important for work
ers. The difference in the patterns of nationally
versus locally adjusted wage differentials is
consistent with a story of competing adjust
ments rather than of slowing adjustments.
However, other explanations are not elimi
nated by these results, because neither the ad
justment processes nor the values of amenities
have been explicitly incorporated. These short
comings provide an obvious direction for fu
ture research. Given the limited observability
of amenities, a sensible strategy would be to
estimate the adjustment processes of firms and
workers. This would make more explicit the
link between convergence rates and differen
tials in the two wage series. Although our con
clusion is largely descriptive, the diverse
patterns in nationally versus locally adjusted
wages clearly support analyzing regional wage
differentials from the perspective of both em
ployees and firms.
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Economic Review
M
1993 Quarter 2
H
Using Bracket Creep to Raise Revenue:
A Bad Idea Whose Time Has Passed
by David Altig and
Charles T. Carlstrom
Required Clearing Balances
by EJ. Stevens
The CPI as a Measure of Inflation
by Michael F. Bryan and
Stephen G. Cecchetti
Cyclical Movements of the Labor Input
and Its Implicit Real Wage
by Finn E. Kydland and
Edward C. Prescott
Money and Interest Rates under
a Reserves Operating Target
by Robert B. Avery and
Myron L. Kwast
M
1993 Quarter 3
Capital Requirements and Shifts
in Commercial Bank Portfolios
by Joseph G. Haubrich and
Paul Wachtel
FDICIA’s Emergency Liquidity Provisions
by Walker F. Todd
Efficiency and Technical Progress
in Check Processing
by Paul W. Bauer
1993 Quarter 4
The Inaccuracy of Newspaper Reports
of U.S. Foreign Exchange Intervention
by William P. Osterberg and
Rebecca Wetmore Humes
H
1994 Quarter 1
Institutional Aspects of U.S. Intervention
by Owen F. Humpage
The 1995 Budget and Health Care Reform:
A Generational Perspective
by Alan J. Auerbach,
Jagadeesh Gokhale, and
Laurence J. Kotlikoff
On Disinflation since 1982:
An Application of Change-Point Tests
by Edward Bryden and
John B. Carlson
Second Quarter
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■ 9405
The Federal Reserve
Board before
Marriner Eccles
■ 9406
Optimal Fiscal Policy
when Public Capital Is
Productive: A Business
Cycle Perspective
■ 9407
Anticipating Bailouts:
The Incentive—Conflict
Model and the Collapse
of the Ohio Deposit
Guarantee Fund
by Walker F. Todd
by Kevin J. Lansing
by Ramon P. DeGennaro and
James B. Thomson
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Economic Commentary
Enterprise Liability: A Prescription
for Health Care Reform?
by Charles T. Carlstrom
July 1, 1993
Making the SAIF Safe for Taxpayers
by William P. Osterberg and
James B. T h o m s o n
N o v e m b e r 1, 1993
T h e Evolving Loan Sales Market
by Joseph G. Haubrich and
James B. T h o m s o n
July 15, 1993
C o m m u n i t y Lending and
Economic Development
by Jerry L. Jordan
N o v e m b e r 15, 1993
Free Markets and Price Stability:
Opportunities for Mexico
by Jerry L. Jordan
August 1, 1993
Replacing Reserve Requirements
by E.J. Stevens
D e c e m b e r 1, 1993
Assessing Real Interest Rates
by John B. Carlson
August 15, 1993
Airline Deregulation: Is It Tim e
to Finish the Job?
by Paul W . Bauer and
Ian Gale
September 1, 1993
T h e Decline in U.S. Saving Rates:
A Cause for Concern?
by Jagadeesh Gokhale
September 15, 1993
Credibility Begins with a Clear
C o m m i t m e n t to Price Stability
by Jerry L. Jordan
October 1, 1993
Th e Budget Reconciliation Act
of 1993: A S u m m a r y Report
by David Altig and
Jagadeesh Gokhale
October 15, 1993
Long-Term Health Care: Is Social
Insurance Desirable?
by Jagadeesh Gokhale and
Lydia K. Leovic
D e c e m b e r 15, 1993
Monetary' Policy and Inflation:
1993 in Perspective
by Gregory A. Bauer and
John B. Carlson
January 1, 1994
Report of the Fourth District
Economists’Roundtable
by Michael F. Bryan and
John B. Martin
January 15, 1994
Are Service-Sector Jobs Inferior?
by M a x D u p u y and
Mark E. Schweitzer
February 1, 1994
Th e National Depositor
Preference L a w
by James B. T h o m s o n
February 15, 1994
Issues in C R A Reform
by Mar k S. Sniderman
March 1, 1994
Back to the Future: A V i e w
of Prospective Deficits through
the Prism of the Past
by David Altig and
Jagadeesh Gokhale
March 15, 1994
Central Bank Independence
by O w e n F. H u m p a g e
April 1, 1994
Health Care Reform from a
Generational Perspective
by David Altig and
Jagadeesh Gokhale
April 15, 1994
Lessons from the Collapse of
Three State-Chartered Private
Deposit Insurance Funds
by Walker F. T o d d
M a y 1, 1994
Assessing Progress toward Price
Stability: Looking Forward and
Looking Backward
by John B. Carlson
M a y 15, 1994
T he Go ve rnment’
s Role in the
Health Care Industry: Past,
Present, and Future
by Charles T. Carlstrom
June 1, 1994
Are the Japanese to Blame
for O u r Trade Deficit?
by O w e n F. H u m p a g e
June 15, 1994
A Beginner’
s Guide to the U.S.
Payments System
by Paul W . Bauer
July 1, 1994
@FedFRASER