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Research DivisionFederal Reserve Bank of St. Louis

Working Paper Series

The Evolution of Scale Economies in U.S. Banking

David C. Wheelock

and

Paul W. Wilson

Working Paper 2015-021A

http://research.stlouisfed.org/wp/2015/2015-021.pdf

August 2015

FEDERAL RESERVE BANK OF ST. LOUIS

Research Division

P.O. Box 442St. Louis, MO 63166

______________________________________________________________________________________

The views expressed are those of the individual authors and do not necessarily reflect official positions of

the Federal Reserve Bank of St. Louis, the Federal Reserve System, or the Board of Governors.

Federal Reserve Bank of St. Louis Working Papers are preliminary materials circulated to stimulate

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cleared with the author or authors.



The Evolution of Scale Economies in

U.S. Banking

David C. Wheelock Paul W. Wilson∗

August 2015

Abstract

Continued consolidation of the U.S. banking industry and general increase in thesize of banks has prompted some policymakers to consider policies to discourage banksfrom getting larger, including explicit caps on bank size. However, limits on the size of banks could entail economic costs if they prevent banks from achieving economies of scale. The extent of scale economies in banking remains unclear. This paper presentsnew estimates of returns to scale for U.S. commercial banks based on nonparametric,local-linear estimation of bank cost, revenue and profit functions. We present estimatesfor both 2006 and 2012 to compare the extent of scale economies in banking some fouryears after the financial crisis and two years after enactment of the Dodd-Frank Act

with scale economies prior to the crisis. We find that most banks faced increasingreturns to scale in cost in both years, though results for the very largest banks in 2012are somewhat sensitive to specification. Further, most banks faced decreasing returnsin revenue in both years, though nearly all banks could still increase revenue and profitby becoming larger.

∗Wheelock: Research Department, Federal Reserve Bank of St. Louis, P.O. Box 442, St. Louis, MO 63166–

0442; [email protected]. Wilson: Department of Economics and School of Computing, Division of Com-puter Science, Clemson University, Clemson, South Carolina 29634–1309, USA; email [email protected] research was conducted while Wilson was a visiting scholar in the Research Department of the FederalReserve Bank of St. Louis. We thank the Cyber Infrastructure Technology Integration group at ClemsonUniversity for operating the Palmetto cluster used for our computations. We thank Peter McCrory for re-search assistance. The views expressed in this paper do not necessarily reflect official positions of the FederalReserve Bank of St. Louis or the Federal Reserve System. JEL classification nos.: G21, L11, C12, C13, C14.Keywords: banks, returns to scale, scale economies, non-parametric, regression.



1 Introduction

The financial crisis of 2008–09 raised new concerns about the size and complexity of the

world’s largest banking organizations. Many of the largest banks are now considerably

bigger than they were before the crisis. For example, on December 31, 2006, the largestU.S. commercial bank (Bank of America) had total assets of $1.2 trillion, with two other

banks (JP Morgan Chase and Citibank) also having more than $1 trillion of assets. By

contrast, on June 30, 2014, the largest U.S. bank (JP Morgan Chase) had $2.0 trillion of

assets and three others had more than $1 trillion of assets. The largest banks also have

amassed a greater share of total U.S. bank assets. For example, between December 2006 and

June 2014, the share of U.S. commercial bank assets held by the largest four commercial

banks rose from 39 percent to 44 percent.

Are banks destined to become ever larger and, if so, is that cause for concern? The

answer to this question depends, in part, on why banks have been getting larger. The

policy implications are likely different if banks are growing larger to exploit technologically-

driven economies of scale than if government policies that encourage large size or excessive

risk taking are driving bank growth. Of particular concern is the perception that regulators

consider very large banks “too-big-to-fail” (TBTF), which would provide an implicit funding

subsidy to banks that exceed a certain size threshold. The Dodd-Frank Wall Street Reform

and Consumer Protection Act of 2010 was intended to eliminate TBTF by establishing a

formal process for resolving failures of large financial institutions, as well as by imposing a

tighter financial regulatory regime. However, some economists and policymakers argue that

Dodd-Frank does not go far enough to contain TBTF, and that banks should be subject to

firm caps on their size (e.g., Fisher and Rosenblum, 2012). The imposition of size limits on

banks could have a downside, however, if they prevent banks from achieving economies of

scale (as noted, e.g., by Stern and Feldman, 2009). Hence, the extent to which there are scale

economies in banking is an important question that has attracted renewed interest among

researchers and policy makers.Conventional wisdom, based largely on studies that use data from the 1980s and 1990s,

holds that banks exhaust scale economies at low levels of output, e.g., $100–$300 million

of total assets. However, several recent studies find evidence of increasing returns to scale

1



among much larger banks, including banks with more than $1 trillion of assets. Improved

estimation methods and data could explain the difference in findings between older studies

and more recent ones.1 However, recent advances in technology and changes in regulation are

often thought to have favored larger banks, and perhaps increased the size range over which

banks could experience increasing returns to scale (Berger, 2003; Mester, 2005). Wheelock

and Wilson (2009) find that larger banks experienced larger gains in productivity over 1985–

2004 than did smaller banks. Feng and Serletis (2009) find similar evidence for 1998–2005.

These studies suggest that technological advances may have also generated increasing returns

to scale for banks.

Using a variety of methodologies and datasets, recent studies have tended to find more

evidence of substantial economies of scale in banking, with some finding that even the very

largest banks operate under increasing returns to scale. Wheelock and Wilson (2012) usenonparametric methods to estimate scale economies in a cost minimization framework and

find that as recently as 2006, even the largest U.S. banking organizations operated un-

der increasing returns to scale. Hughes and Mester (2013) estimate returns to scale in

a value-maximization model that explicitly incorporates the risk-expected return tradeoffs

confronted by bank managers. Using data for 2003, 2007, and 2010, the study also finds

evidence of significant increasing returns to scale, especially for banks with more than $100

billion of assets. Similarly, Becalli et al. (2015) find that the largest European banks operate

under increasing returns to scale, with greater returns for the largest banks. Further evidenceof scale economies is reported in Kovner et al. (2014), who find that large banks have lower

operating costs than small banks. Using data for 2001-12, the study finds that as bank size

increases, noninterest expense relative to assets or income declines. By contrast, Feng and

Zhang (2014) use a random-coefficients translog output distance function model to estimate

scale economies for a sample of banks with at least $1 billion of assets during 1997-2010

and find that most banks in the sample faced constant returns to scale. Likewise, Restrepo-

Tobon and Kumbhakar (2015) find that only 35-45 percent of the largest U.S. bank holding

1 Studies of scale economies in banking from the 1980s and before typically relied on estimation of translogor other parametric specifications of bank cost functions. However, subsequent studies, including the presentpaper, find that the translog function is a misspecification of bank cost relationships and therefore can leadto erroneous estimates of returns to scale. See McAllister and McManus (1993) and Wheelock and Wilson(2001) for discussion and evidence on the bias introduced by estimating bank scale economies from a translogcost function.

2



companies exhibit increasing returns when estimated from an input-distance function, and

65–80 percent when estimated from a cost function.

Although recent studies have tended to find that most banks face increasing returns to

scale, at least as measured from a cost relationship, questions remain. Most studies use data

on banks from before the financial crisis of 2008–09 or just shortly thereafter. However, many

of the largest U.S. banks have continued to grow even bigger since the crisis, perhaps to the

point of exhausting potential scale economies. Moreover, changes in bank regulation, notably

the Dodd-Frank Act of 2010, may have affected the extent of scale economies available for

U.S. banks by altering the environment in which banks operate. Hence, the findings of studies

that use recent data might differ from those using older data, especially for the largest banks.

Further, most studies estimate returns to scale from the perspective of bank cost, whereas

few have considered whether there are returns to scale in terms of bank revenues or profits.Although estimates of returns to scale from a cost perspective provide an indication of

whether society’s resources are employed efficiently in providing banking services, economies

of scale in revenue or profit are of concern to bank shareholders, as well as to policymakers

interested in the forces driving industry consolidation.

In this paper, we report estimates of returns to scale for all U.S. commercial banks in

2006.Q4 and 2012.Q4, which enables us to compare the extent of scale economies in banking

some four years after the financial crisis and two years after enactment of Dodd-Frank with

estimates of scale economies prior to the crisis.2 Moreover, we provide estimates of scaleeconomies for revenue and profit, as well as in terms of cost. Prior to the financial crisis of

2008–09, bank profit rates (measured by return of average assets (ROA) or equity (ROE))

were positively correlated with bank size (total assets). However, larger banks tended to have

lower (more negative) rates of return during 2008–09. Since then, profit rates have again

generally be higher for larger banks, though not as consistently as before the crisis.3 Analysis

2 We acknowledge, however, that many of the rules called for in the Dodd-Frank Act have yet to befully implemented, as are changes in capital and liquidity requirements stemming from international agree-ments. For comparison, we also report estimates of scale economies for 1984.Q4 and 1998.Q4 in the separateAppendix E, which is available from the authors on request.

3 Simple regressions of ROA (and ROE) on the log of total assets for the fourth quarters of 2001–2012 yieldpositive and statistically significant slope coefficients for 2001 through 2007, negative coefficients (statisticallysignificant for ROA, but insignificant for ROE) for 2008–09, and positive coefficients for 2010–12 (statisticallysignificant for 2011–12, but insignificant for 2010). In addition, over most years except 2008–09, the largestfive percent of banks had higher ROA and ROE than the next largest five percent.

3



of returns to scale for alternative measures of profit in the context of a model that allows for

the production of multiple outputs, including off-balance sheet outputs, can provide a more

complete picture of the relationship between bank profits and scale.

Compared with studies of scale economies from a cost perspective, there has been little

research on revenue or profit economies in banking. However, several studies have estimated

revenue and profit relationships for banks to study such topics as revenue economies of scope

(Berger et al., 1996), profit efficiency (e.g., Berger and Mester, 1997), and profit productivity

(Berger and Mester, 2003). In addition to economies of scope, Berger et al. (1996) estimate

revenue ray-scale economies for a sample of banks using data for 1978, 1984 and 1990. That

study finds evidence of significant revenue scale economies in 1978 and 1984, especially for

banks with less than $500 million of assets, but not in 1990. We are unaware of any more

recent studies that examine revenue or profit scale economies for banks. Berger and Mester(2003) argue, however, that studies that ignore revenues when evaluating bank performance

may be misleading. For example, Berger and Mester (2003) find that during the 1990s, banks

became less productive in terms of cost (essentially that cost per unit of output rose after

controlling for output quantities, input prices, and various environmental conditions), but

more productive at generating profits. The study attributes this finding to efforts by banks

to increase profits by providing more or better quality services that raise their revenues by

more than they increase costs. Similarly, an examination of the evolution of returns to scale

from a revenue or profit perspective could provide a more complete picture of scale economiesin banking than a focus solely on cost economies of scale.

We use a nonparametric, local-linear estimator to estimate cost, revenue and profit re-

lationships from which we estimate returns to scale for U.S. commercial banks. The non-

parametric approach avoids the potential for functional-form specification error associated

with parametric estimation. Although nonparametric estimators are plagued by the “curse

of dimensionality,” i.e., slow convergence rates (compared to parametric estimators) that

become exponentially slower with more model dimensions, we take steps to mitigate this

problem. First, we estimate our models using a large dataset consisting of over one mil-

lion observations on all U.S. commercial banks for 1984–2013. Second, we employ principal

components techniques to reduce the dimensions of our empirical models. Our methods are

similar to those of Wheelock and Wilson (2012), but whereas Wheelock and Wilson (2012)

4



studied only cost economies and used a dataset that ended in 2006, here we estimate rev-

enue and profit relationships, as well as a cost relationship, from which we derive estimates

of expansion-path scale economies for cost, revenue and profit. Further, we estimate scale

economies for banks in 2012 (as well as earlier years), and thus we are able to examine how

scale economies may have changed since the financial crisis and after the enactment of the

Dodd-Frank legislation. In addition, we report estimates of scale economies for each of the

very largest banks, as well as for several different models to gauge how robust the results

are to alternative specifications of cost, revenue and profits. Whereas Wheelock and Wilson

(2012) find that as recently as 2006, even the very largest banks operated under increas-

ing returns to scale, we find that for 2012, the results are less clear cut. Estimates of cost

economies for the very largest banks are sensitive to how cost is measured. Further, we find

that the largest banks face decreasing returns in revenue and profit in the sense that anincrease in output levels leads to a less-than-proportionate increase in revenues and profits.

Nonetheless, we find evidence that among the largest banks, which have grown ever larger

in recent years, revenues and profits still increase as output levels increase.

In the next section, we discuss the microeconomic specification of our cost, revenue,

and profit functions and introduce statistics to measure returns to scale. In Section 3,

we introduce the econometric specification, and in Section 4 we discuss the nonparametric

methods we use for estimation and inference. Section 5 presents our empirical findings, and

conclusions are given in Section 6.

2 Microeconomic Specification

To establish notation, let x ∈ R p+ and y ∈ R

q+ denote column-vectors of p input quantities

and q output quantities, respectively. Let w ∈ R p denote the column-vector of input prices

corresponding to x, and let r ∈ Rq denote the column-vector of output prices corresponding

to y. Then variable costs are given by C := wx, which firms (banks) seek to minimize

with respect to x, subject to h(x,y) = 0 where h(·, ·) represents the product-transformationfunction that determines the possibilities for transforming input quantities x into output

quantities y. Solution to the constrained minimization problem yields a mapping Rq+ ×R

p →

5



R p+ such that x = x(y,w); substitution into C = w x yields

C = w x = w x(y,w)

= C (y,w) (2.1)

where C (y,w) is the variable cost function.

The story so far is part of the standard microeconomic theory of the firm (e.g., see

Varian, 1978). Under perfect competition in output markets, the same body of theory implies

that banks maximize revenue R := ry with respect to output quantities, again subject to

h(x,y) = 0, yielding the solution y = y(r,x). Substitution then yields R = ry(r,x) =

Rs(x,r), i.e., a standard revenue function that maps input quantities and output prices to

revenue. Conditions on h(x,y) required for existence of the revenue (and profit) function(s)

are discussed by Fuss and McFadden (1978) and Laitinen (1980).

Banking studies, however, often estimate alternative revenue or profit functions where

revenue (or profit) are functions of output levels and input prices. As discussed, for example,

by Berger and Mester (1997), the alternative revenue and profit functions provide a means of

controlling for unmeasured differences in output quality across banks, imperfect competition

in bank output markets (which gives banks some pricing power), any inability of banks to

vary output quantities in the short-run, and inaccuracy in the measurement of output prices. 4

In addition, available data on U.S. banks make it difficult to observe prices of outputs unless

the outputs are heavily aggregated.

Following Berger et al. (1996) and others, we assume that banks maximize revenue with

respect to output prices r, subject to g(y,w,r) = 0, where g() is an implicit function

representing the bank’s opportunities for transforming given output levels y and input prices

w into output prices r. Solution of this constrained optimization problem yields a mapping

Rq+ × R

p → Rq such that r = r(y,w); then R = r y = r(y,w)y = R(y,w), where R(y,w)

is the alternative revenue function introduced by Berger et al. (1996).

Turning to profits, let P = r

w

and Q = y

−x

. Standard theory suggeststhat firms operating in perfectly competitive input and output markets maximize profit

π := P Q with respect to Q, subject to h(x,y) = 0. Solution of the constrained optimization

problem yields Q = Q(P ); substituting this back into the profit function π = P Q gives

4 See also Berger et al. (1996) or Berger and Mester (2003) for more discussion.

6



π = P Q(P ) = πs(w, r), i.e., the standard profit function that maps input and output

prices into profit. Under imperfect competition in output markets, however, banks maximize

profit with respect to input quantities x and output prices r, subject to h(x,y) = 0 and

g(y,w,r) = 0. The solution results in a mapping Rq+ × R

p → R p+ such that x = x(y,w),

and a mapping R1+ × R

p → Rq such that r = r(y,w). Substituting these into the profit

function gives

π = P Q =

r(y,w) w y −x(y,w)

= π(y,w) (2.2)

where π(y,w) is the alternative profit function that maps output quantities and input prices

to profit.

Note that the cost function C (y,w) must be homogeneous of degree one with respect toinput prices w since the cost minimization problem implies that factor demand equations

must be homogeneous of degree zero in input prices. However, as noted by Berger et al.

(1996), there is no such requirement for the alternative revenue function. Without addi-

tional assumptions, the alternative revenue function is neither homogeneous with respect

to input prices w nor homogeneous with respect to output quantities y. Consequently,

the alternative profit function is also neither homogeneous with respect to input prices w

nor output quantities y. Nonetheless, banking studies routinely impose linear homogeneity

with respect to input prices on the alternative revenue profit function. Restrepo-Tob on and

Kumbhakar (2014) show that the alternative revenue function is not linearly homogeneous in

input prices unless output prices move in unison with input prices, and present an example

showing how incorrectly imposing linear homogeneity on the alternative profit function can

produce erroneous results. Accordingly, we do not impose homogeneity on the alternative

revenue function, neither with respect to output quantities nor with respect to input prices. 5

To measure returns to scale using the cost function, we define

E C,i := δC (yi,wi) − C (δ yi,wi)δC (yi,wi)

>=< 0 ⇐⇒ IRS

CRSDRS

(2.3)

5 Restrepo-Tobon and Kumbhakar (2014) do not include y in the pricing possibilities function g(), andsuggest (in their footnote 5, page 336) that the alternative revenue function is homogeneous of degree onein output levels. They suggest this result “will likely be unaffected” if y is included in g(), but this is trueif and only if additional assumptions are made on g().

7



where δ > 1 is a constant and yi is the observed vector of output quantities produced by

the ith bank facing observed input prices wi. Clearly, E C,i < 1. The statistic E C,i measures

expansion-path scale economies as the difference between δ times the cost of producing out-

put quantities yi and the cost of producing output quantities scaled by the factor δ . If this

difference is positive (zero, negative), then returns to scale are increasing (constant, decreas-

ing). The difference is normalized by dividing by δC (yi,wi). To interpret the magnitude of

E C,i, note that (2.3) can be rearranged by writing (1 − E C,i)δC (yi,wi) = C (δ yi,wi); hence

if firm i increases its output by a factor δ > 1, its cost increases by a factor (1 − E C,i)δ . For

example, if δ = 1.1 and E C,i = 0.05, then firm i incurs a 4.5-percent increase in cost when it

increases its output level by 10 percent since 1.1 × (1 − 0.05) ≈ 1.045.

The measure defined in (2.3) has an additional interpretation. First, re-arrange terms in

(2.3) to obtain

δ (1 − E C,i) = C (δ yi,wi)

C (yi,wi)

>=<

1. (2.4)

Some algebra reveals that (2.4) holds if and only if

E C,i

<

=>

1 − δ −1; (2.5)

for δ = 1.1, (1 − δ −1) ≈ 0.09091. Hence values of E C,i less than 0.09091 indicate that a

10 percent increase in output levels results in an increase in total (variable) cost, whereasvalues of E C,i greater than 0.09091 indicate that a 10 percent increase in output reduces cost.

Of course, it is probably unlikely, but perhaps not impossible, for an increase in output to

reduce total cost.

As in many empirical studies, we use measures of net revenues that can take negative

values. Of course, net profits can also be negative. Therefore, to measure returns to scale

from the alternative revenue function, we define

E R,i :=

R(δ yi,wi) − δR(yi,wi)

δ |R(yi,wi)|

>

=<

0 ⇐⇒

IRS

CRSDRS

. (2.6)

In addition, we define

E π,i := π(δ yi,wi) − δπ(yi,wi)

δ |π(yi,wi)|

>

=<

0 ⇐⇒

IRS

CRSDRS

(2.7)

8



to measure returns to scale from the alternative profit function. In the definitions of E R,i

and E π,i, the constant factor δ multiplies output levels y in the first term in the numerator,

in contrast to the definition of E C,i in (2.3), where δ multiplies output levels y in the second

numerator term. Similarly, δ multiplies the second term in the numerators of E R,i and E π,i,

rather than the first term as in (2.3). These differences reflect the fact that banks attempt

to maximize revenue and profit but minimize cost.

The denominators in (2.6) and (2.7) involve absolute values to account for the possibility

that measured revenue or profit can be negative. Consider the scale measure E π,i defined

in (2.7); similar reasoning applies to the scale measure E R,i defined in (2.6). In the most

common scenario (by far), π(yi,wi) > 0 and π(δ yi,wi) > 0.6 Then (2.7) can be rearranged

to write (1 + E π,i)δπ(yi,wi) = π(δ yi,wi). Clearly, in this case E π,i ≥ −1. Increasing output

levels by a factor δ > 1 causes profit to increase (decrease) by a factor (1 + E π,i)δ > (<) 1.If, for example, an increase in output levels by a factor δ = 1.1 leads to an increase in profit

by a factor (1 + 0.05) × 1.1 = 1.155, i.e., an increase in output levels by 10 percent leads to

a 15.5 percent increase in profits, then E π,i = 0.05.

Alternatively, re-write (2.7) to obtain

δ (1 − E π,i) = π(δ yi,wi)

π(yi,wi)

<

=>

1 (2.8)

as profit (increases, remains the same, decreases) when output levels are expanded by a

factor δ . It is easy to show that (2.8) holds if and only if

E π,i

>

=<

1 − δ −1

. (2.9)

For δ = 1.1, (1 − δ −1) ≈ −0.09091. Hence for E π,i > −0.09091, increasing output levels by

10 percent increases profit, even if at a decreasing rate when E π,i ∈ (−0.09091, 0). Again,

an analogous story holds for revenue and the measure E R,i defined in (2.6).

The next section provides details on variable specifications and the specific models we

estimate in order to obtain predicted values with which to estimate the returns-to-scale

measures defined in (2.3)–(2.7). Later, Section 4 describes how we estimate the models

presented in the next section and how we make inferences.

6 Negative values of revenue or profit affects how the values of the returns-to-scale measures E R,i and E π,ishould be interpreted; see Appendix A for details.

9



3 Econometric Specification

Specifying versions of the cost function C (y,w) and the alternative revenue and profit func-

tions R(y,w) and π(y,w) for estimation in order to obtain estimates of the returns-to-scale

measures E C,i, E R,i, and E π,i involves choices on two dimensions: (i) definitions of responseand explanatory variables, and (ii) functional forms. Regarding the latter choice, we use

fully nonparametric estimation methods, discussed further below in Section 4, which avoids

the need to impose specific functional forms. With regard to the first choice, studies have

used a variety of measures of cost, revenue and profit based on accounting information from

the Reports of Income and Condition (i.e., “call reports”) submitted by banks to regulators.

In the absence of single, widely agreed upon measures of variable cost, revenue and profit,

we estimate our models using several alternative measures, as well as different specifications

of right-hand-side (RHS) explanatory variables, to provide robustness checks.

Our specification of RHS explanatory variables closely follows Wheelock and Wilson

(2012) and most of the banking literature. We define five inputs and five outputs that,

with one exception (the measure of off-balance sheet output), are those used by Berger and

Mester (2003). Specifically, we define the following output quantities: consumer loans (Y 1),

real estate loans (Y 2), business and other loans (Y 3), securities (Y 4), and off-balance sheet

items (Y 5) consisting of net noninterest income.7

We define three variable input quantities: purchased funds, consisting of the sum of total

time deposits of $100,000 or more, foreign deposits, federal funds purchased, demand notes,

trading liabilities, other borrowed money, mortgage indebtedness and obligations under capi-

talized leases, and subordinated notes and debentures (X 1); core deposits, consisting of total

deposits less time deposits of $100,000 or more (X 2); and labor services, measured by the

number of full-time equivalent employees on payroll at the end of each quarter (X 3). The

first input quantity, X 1, is intended to capture non-core deposit (and non-equity) sources of

7 Wheelock and Wilson (2012) measure off-balance sheet items as noninterest income less service chargeson deposits. However, since 2007, service charge revenue has exceeded other noninterest income for manybanks. Hence, to avoid negative values, we do not subtract service charges on deposits in the computationof net noninterest income in the present study. Of the commonly used measures of off-balance sheet output,net noninterest income is the most consistently measurable across banks and over time. However, as a net,rather than gross measure of income, it is potentially a biased measure of off-balance sheet output becauselosses would appear to reduce off-balance sheet output. Data are not reported that would permit calculationof a gross measure of noninterest income. See Clark and Siems (2002) for discussion of alternative measuresof off-balance sheet activity.

10



investment funds for the bank (see Berger and Mester (2003) for more detail). We measure

the prices of purchased funds (W 1), core deposits (W 2), and labor services (W 3) by dividing

total expenditure on the given input by its quantity.8

We define an additional input quantity, physical capital (X 4), consisting of premises and

other fixed assets. Physical capital is typically treated as quasi-fixed because its measured

price, W 4, is perhaps at best a dubious representation of market prices. However, as a

robustness check, we treat X 4 as a variable input in some specifications, with its price,

W 4, measured by dividing expenditures on premises and other fixed assets by X 4. Finally,

we treat financial equity capital (X 5) as a quasi-fixed input.9 With the exception of labor

input (which is measured as full-time equivalent employees) and off-balance sheet output

(which is measured in terms of net flow of income), our inputs and outputs are stocks

measured by dollar amounts reported on bank balance sheets, consistent with the widelyused “intermediation” model of Sealey and Lindley (1977).

In addition to the variables defined above, we index quarters 1984.Q1 through 2013.Q2

by setting T = 1 for 1984.Q1, T = 2 for 1984.Q2, . . ., T = 118 for 2013.Q2. Although

T is an ordered, categorical variable, we treat it as continuous since it can assume a wide

range of possible values. The regulatory environment and the production technology of

banking changed a great deal over the nearly 30 years covered by our data; including T

as an explanatory covariate allows functional forms to change over time. Two features

of our estimation strategy allow a great deal of flexibility. First, because we use a fullynonparametric estimation method, we impose no constraints on how T might interact with

other explanatory variables. Second, the local nature of our estimator means that when we

estimate cost at a particular point in time, observations from distant time periods will have

little or no effect on the estimate. Typical approaches that involve estimation of a fully

parametric translog cost functions by OLS or some other estimation procedure are not local

in the sense that when cost is estimated at some point in the data space, all observations

contribute to the estimate with equal weight. Moreover, the typical approach requires the

imposition of a specific functional form a priori for any interactions among explanatory

8 Unlike Wheelock and Wilson (2012), we do not subtract deposit fee income from interest on depositsof less than $100,000 when calculating W 2 because doing so would imply negative prices for a large numberof banks in the low interest rate environment that prevailed after 2007.

9 Including equity capital as a (quasi-fixed) input controls somewhat for differences in risk across banks(as discussed in Berger and Mester (2003)).

11



variables.10

To control for differences in costs associated with holding company affiliation, we define

M = 1 for commercial banks that are owned by a multi-bank holding company (M = 0

otherwise).11 In a fully parametric setting, one might include a binary dummy variable such

as M and perhaps allow for interactions with a few continuous variables. In our nonpara-

metric paradigm, however, we impose no constraints on how M might interact with other

explanatory variables. As discussed in the separate Appendix D, we use a bandwidth specific

to the binary dummy variable to optimize the amount of smoothing across the two categories

of data identified by M ∈ 0, 1.

Turning to the response variables, we consider six different specifications of bank costs.

The first three treat physical capital as a quasi-fixed input:

C l :=W 1X 1 + W 2X 2 + W 3X 3

C 2 :=total interest expense

− service charges on deposit accounts in domestic offices

+ salaries and employee benefits

C 3 :=total interest expense + total non-interest expense − W 4X 4

The next three cost variables, C 4, C 5, and C 6 correspond to C 1, C 2, and C 3, respectively,

with the addition of expenditures W 4X 4 on physical capital (hence treating physical capitalas a variable input). Among the various specifications, C 1 and C 4 provide the tightest link

with the explanatory variables, since C 1 simply sums expenses on the variable inputs X 1,

X 2, and X 3 while C 4 adds expenses on X 4. In this sense, C 1 and C 4 are similar to the

specification of cost in Wheelock and Wilson (2001, 2012). Following Berger and Mester

(2003), the measures C 2 and C 5 subtract services charge revenue from interest expense to

capture the net cost of attracting deposits. Finally, C 3 and C 6 are broad definitions that

include components of noninterest expense other than labor costs. As such, these measures

may include some “fixed” as well as variable costs, but as seen below in Section 5, this makes

10 The local nature of our estimator is discussed in more detail below in Section 4 and in a separateAppendix D, which is available from the authors upon request.

11 In addition to controlling for holding company membership, Wheelock and Wilson (2012) includeddummy variables to reflect historical branching restrictions on banks. We do not include controls for branch-ing regulations here, however, since full interstate branching has been in effect since 1999.

12



little qualitative difference in our empirical results. Table B.1 in the separate Appendix B

(available from the authors on request) reports correlations between the six cost variables

normalized by W 3 over all periods in our study; the correlation coefficients range from 0.9659

to 0.9996.

We also estimate returns to scale for three measures of revenue:

R1 :=total interest income + total non-interest income

+ realized gains (losses) on held-to-maturity securities

+ realized gains (losses) on available-for-sale securities

− provision for loan and lease losses

− provision for allocated transfer risk reserves

− service charges on domestic accounts in domestic offices;

R2 :=R1 + service charges on domestic accounts in domestic offices;

R3 :=total interest income + total non-interest income.

(R1) is the definition of bank revenue used by Berger and Mester (2003). (R2) adds service

charges on deposits to R1, whereas (R3) is simply the sum of total interest and total nonin-

terest income. The three revenue variables are highly correlated in our data (Table B.1 in

the separate Appendix B shows correlation coefficients ranging from 0.9519 to 0.9988).

Finally, we consider several measures of bank profits. Berger and Mester (2003) measure

profits by π1 := R1 − C 2. π2 := R1 − C 5 differs from π1 only in the treatment of physical

capital as a variable input, rather than as quasi-fixed.

Our remaining profit measures are defined in terms of R2 and R3: π3 := R2 − C 1,

π4 := R2 − C 3, π5 := R2 − C 4, π6 := R2 − C 6, π7 := R3 − C 1, π8 := R3 − C 3, π9 := R3 − C 4,

and π10 := R3 − C 6. Note that to avoid double counting of service charge revenue, we do

not define profit measures that subtract C 2 or C 5 from either R2 or R3. Correlations among

the ten profit variables, over all periods in our study, are shown in Table B.3 in the separate

Appendix B, and range from 0.7826 to greater than 0.99995.

All of the specifications estimated below include as RHS variables the vector

y :=

Y 1 Y 2 Y 3 Y 4 Y 5

(3.1)

13



of output quantities defined above. In addition, our cost function specifications include either

w1 :=W 1W 3

W 2W 3

X 4 X 5 T M

(3.2)

or

w2 := W 1W 3

W 2W 3

W 4W 3 X 5 T M , (3.3)

with the price of labor (W 3) serving as the numeraire. With w1, physical capital is treated

as a quasi-fixed input, whereas with w2, physical capital is treated as a variable input.

As discussed in Section 2, we do not impose linear homogeneity on our alternative revenue

and profit functions. Consequently, depending on whether physical capital is treated as a

quasi-fixed or variable input, our alternative revenue and alternative profit functions include

on the RHS (in addition to y) either

w3 := W 1 W 2 W 3 X 4 X 5 T M (3.4)

or

w4 :=

W 1 W 2 W 3 W 4 X 5 T M

. (3.5)

We estimate various cost, revenue, and profit functions for banks. We estimate cost

functions of the form

C j/W 3 = m j(y,wk) + ε j, (3.6)

j ∈ 1, 2, . . . , 6 with k = 1 for j ∈ 1, 2, 3 or k = 2 for j ∈ 4, 5, 6, reflecting whether

physical capital is treated as quasi-fixed or variable. Below, we refer to the six different cost

functions as models 1–6. Models j ∈ 7, 8, 9 consist of revenue functions of the form

R j− = m j(y,w3) + ε j (3.7)

where = 6, using the three revenue measures R1, R2, and R3 and treating physical capital

as a quasi-fixed input. Similarly, models j ∈ 10, 11, 12 replace w3 with w4 in (3.7) with

= 9, thereby treating physical capital as a variable input. Models 13–22 consist of profit

functions of the formπ j−12 = m j(y,wk) + ε j, (3.8)

j ∈ 13, 14, . . . , 22 and k ∈ 3, 4 with the choice of k depending on whether the

particular cost measure used to define π j−12 treats physical capital as quasi-fixed (k = 3) or

variable (k = 4).

14



In each model 1–22 we assume E (ε j) = 0 so that the functions m j() are conditional mean

functions. In addition, we assume the densities of the continuous RHS variables are twice

continuously differentiable at each point where the conditional mean functions are estimated,

but otherwise make no functional form assumptions regarding the m j(). For each model j

with left-hand side, dependent variable represented by Y j , we assume the moment condition

E (| Y j|2+η | y,w1) exists for some η > 0 and is continuous at (y,wk) when the conditional

mean function is estimated at (y,wk). One may view the conditional mean functions as

either parametric but of unknown form, or nonparametric (i.e., infinitely parameterized).

We provide details on estimation and inference below in Section 4, and in the separate

Appendix D, which is available from the authors upon request.

To construct the variables described above, we use data on U.S. commercial banks for

1984.Q1–2013.Q2 from the quarterly call reports filed by all commercial banks. We usethe seasonally adjusted, quarterly gross domestic product implicit price deflator to convert

all dollar amounts to constant 2009 dollars. After pooling data across 118 quarters and

deleting observations with missing or implausible values, 1,072,453 observations remain for

estimation. Summary statistics are provided in Tables B.4–B.8 of the separate Appendix B,

which is available from the authors upon request.

4 Details on Estimation and Inference

Various approaches exist for estimating conditional mean functions such as those in the

models described above in Section 3. A common approach is to specify a fully parametric

translog functional form for the conditional mean function and then estimate the parameters

via least-squares methods. However, our data easily reject the translog specification using

specification tests similar to those used by Wheelock and Wilson (2001, 2012); see the

separate Appendix C (available from the authors on request) for details.

Rejection of the translog functional form is hardly surprising. The translog function is

merely a quadratic in log-space, and this limits the variety of shapes the conditional meanfunction is permitted to take. Further, the translog is derived from a Taylor expansion of the

cost (or revenue, or profit) function around the means of the data; one should not expect it to

fit well data that are highly variable and highly skewed as are U.S. banking data.12 Several

12 The summary statistics for banks’ total assets given in Tables A.2–A.5 in the separate Appendix B

15



studies have noted that the parameters of a translog function are unlikely to be stable when

the function is fit globally across units of widely varying size; see, for example, Guilkey et al.

(1983) and Chalfant and Gallant (1985) for Monte Carlo evidence, and Cooper and McLaren

(1996) and Banks et al. (1997) for empirical evidence involving consumer demand, Wilson

and Carey (2004) for empirical evidence involving hospitals, and McAllister and McManus

(1993), Mitchell and Onvural (1996), and Wheelock and Wilson (2001, 2012) for empirical

evidence involving banks.

We use fully nonparametric methods to avoid likely specification errors. Although non-

parametric methods are less efficient than parametric methods in a statistical sense when

the true functional form is known, nonparametric estimation avoids the risk of specification

error when the true functional form is unknown, as in the present application. We use fully

nonparametric local-linear estimators modified along the lines of Li and Racine (2004), Wil-son and Carey (2004) and Wheelock and Wilson (2011, 2012) to handle discrete covariates.

Both the local-linear estimator as well as the Nadaraya-Watson kernel regression estimator

(Nadaraya, 1964; Watson, 1964) are examples of local order- p polynomial estimators with

p = 1 and 0, respectively. For a locally-fit polynomial of order p used to estimate a condi-

tional mean function, going from an even value to an odd value of p results in a reduction

of bias with no increase in variance (e.g., see Fan and Gijbels (1996) for discussion). Hence,

we use a local-linear estimator to estimate conditional mean functions, resulting in lower

asymptotic mean square error than one would obtain with the Nadaraya-Watson estimator.Nonparametric regression models can be viewed as infinitely parameterized; as such, any

parametric regression model (such as an assumed translog functional form) is nested within

a nonparametric regression model. Clearly, adding more parameters to a parametric model

affords greater flexibility. Nonparametric regression models represent the limiting outcome

of adding parameters, and may be viewed as the most general encompassing model that a

particular parametric specification might be tested against.13

reveal that the distribution of banks’ sizes is heavily skewed to the right. In fact, estimates of Pearson’s

moment coefficient of skewness for total assets in each of 118 quarters range from 31.42 to 49.96. Moreover,skewness is increasing over time, despite the consolidation in the industry over the years covered by ourdata. Regressing the skewness coefficients for each quarter on the time variable T yields a positive estimateof the slope coefficient, 0.01557, that is significantly different from zero at .1 significance.

13 Several methods for nonparametric regression exist. Cogent descriptions of nonparametric regressionand the surrounding issues are given by Fan and Gijbels (1996, chapter 1), Hardle and Linton (1999), andHenderson and Parmeter (2015). Hardle and Mammen (1993) propose a test of a parametric regression

16



Most nonparametric estimators suffer from the “curse of dimensionality,” i.e., convergence

rates fall as the number of model dimensions increases. The convergence rate of our local-

linear estimator is n1/(4+d) where d is the number of distinct, continuous RHS variables.

Although the convergence rate is unaffected by the inclusion of the binary dummy variable

M , there are d = 10 RHS variables in (cost function) models 1–6, and d = 11 RHS variables in

(revenue or profit function) models 7–22. The slow convergence rate of our estimator means

that for a given sample size, the order (in probability) of the estimation error we incur with

our nonparametric estimator will be larger than the order of the estimation error one would

achieve using a parametric estimator in a correctly specified model with the usual parametric

rate n1/2. However, our nonparametric estimation strategy avoids specification error that

would likely render meaningless any results that might be obtained using a misspecified

model. We adopt the view of Robinson (1988), who argues that parametric models are likelymisspecified and should be viewed as root-n in consistent instead of root-n consistent.14

To mitigate the curse of dimensionality in our applications, we (i) use a large sample with

more than one million observations and (ii) employ a simple dimension-reduction method.

Multicollinearity among regressors is often viewed as an annoyance, but here we use the

multicollinearity in our data to reduce dimensionality, thereby increasing the convergence

rate of our estimators and reducing estimation error. We do this by transforming the contin-

uous RHS variables in each model to principal components space. Principal components are

orthogonal and eigensystem analysis can be used to determine the information content of each principal component. In our cost models (models 1–6), we sacrifice a small amount of

information by using only the six principle components of the data represented by (y, w1)

or (y, w1) that correspond to the six largest eigenvalues, hence reducing the number of

RHS variables in our regressions from ten to six. These six principal components account for

approximately 94.82 percent of the independent linear information in the sample in models

against a nonparametric alternative where the test statistic is an estimate of the integrated square differencebetween the two regressions. Although we do not implement the Hardle and Mammen in order to avoidcomputational expense, it seems almost certain the test would reject the translog parametric model in viewof the results from our simple specification tests discussed above and in the separate Appendix C.

14 Convergence results for nonparametric estimators are often expressed in terms of order of convergencein probability. Briefly, for a sequence (in n) of estimators θn of some scalar quantity θ, we can write θ = θ + O p(n−a) when θ converges to θ at rate na, and we say that the estimation error is of order in

probability n−a. This means that the sequence of values na| θn − θ| is bounded in the limit (as n → ∞) inprobability. See Serfling (1980) or Simar and Wilson (2008) for additional discussion.

17



1–3 where the RHS variables are given by (y, w1), and roughly 94.34 percent in models

4–6 where the RHS variables (y, w2) are used. We also use the first six principal com-

ponents of the continuous RHS variables in the revenue and profit models (models 7–22),

accounting for 92.67 and 92.14 percent of the independent linear information in (y, w2) or

(y, w4), respectively, and reducing the problem from eleven to six continuous dimensions.

The transformation to principal-components space can be inverted, and the interpretation of

the estimators of the conditional mean functions in models 1–22 based on six principal com-

ponents of the RHS variables is straightforward because our estimator is fully nonparametric.

Additional details about our principal components transformation and nonparametric esti-

mation strategy are provided in a separate Appendix D, available from the authors upon

request.

To use the local-linear estimator we must select two bandwidth parameters to controlthe smoothing over continuous and discrete dimensions in the data. We use least-squares

cross-validation to choose the bandwidths. This amounts to choosing bandwidth values that

minimize an estimate of mean integrated square error. In the continuous dimensions, we use

a κ-nearest-neighbor bandwidth and a spherically symmetric Epanechnikov kernel function.

This means that when we estimate cost, revenue, or profit at any fixed point of interest in

the space of the RHS variables, only the κ observations closest to the fixed point of interest

can influence estimated cost at that point. In addition, among these κ observations, the

influence that a particular observation has on estimated cost diminishes with distance fromthe point at which cost is being estimated. Our estimator is thus a local estimator, and

is very different than typical, parametric, global estimation strategies (e.g., OLS, maximum

likelihood, etc.) where all observations in the sample influence (with equal weight) estimation

at any given point in the data space. Moreover, because we use nearest-neighbor bandwidths,

our bandwidths automatically adapt to variation in the sparseness of data throughout the

support of our RHS variables.

For statistical inference about our estimates of returns to scale, we use the wild bootstrap

introduced by Hardle (1990) and Hardle and Mammen (1993), which allows us to avoid

making specific distributional assumptions. We estimate confidence intervals along the lines

used in Wheelock and Wilson (2011, 2012). Although our estimators are asymptotically

normal, the asymptotic distributions depend on unknown parameters; the bootstrap allows

18



us to avoid the need to estimate these parameters, which would introduce additional noise. 15

5 Empirical Results

We estimate models 1–22 described above in Section 3 using the methods described earlier inSection 4, and substitute resulting estimates of cost, revenue, and profit into the returns-to-

scale measures defined Section 2 to obtain estimates E C,i, E R,i and E π,i. We use the bootstrap

methods mentioned in Section 4 and described in the separate Appendix D to make inference

about the corresponding true values E C,i, E R,i and E π,i.

Table 1 reports the number of banks operating under increasing returns (IRS), constant

returns (CRS), and decreasing returns to scale (DRS) in 2006.Q4 and 2012.Q4, as estimated

from the various models.16 Similar to other recent studies, our estimates of scale economies

from cost models 1–6 indicate that a majority of U.S. banks operate under increasing returns

to scale. Regardless of the definition of cost, or whether physical capital is treated as a

variable or quasi-fixed input, we reject constant returns in favor of increasing returns for

some 84–92 percent of banks in 2006.Q4 (based on a 0.1 level of significance). We reject

constant returns in favor of decreasing returns for well less than 1 percent of banks. The

percentages for 2012.Q4 are very similar to those for 2006.Q4, indicating little change in

returns to scale for the vast majority of banks between 2006 and 2012.

Turning to estimates of returns to scale based on the revenue measures in models 7–

12, we reject constant returns in favor of increasing returns for much smaller percentages

of banks than we do for returns to scale based on cost. For 2006.Q4, we reject constant

returns in favor of increasing returns in revenue for 5 percent or fewer banks (at the 0.1

level of significance). By contrast, we reject constant returns in favor of decreasing returns

for anywhere from 28 to 76 percent of banks in 2006.Q4, depending on specification and

definition of revenue. Results for 2012.Q4 are again similar.

Results for profit models 13–22 are mixed, although for a given model, the results are

similar for both 2006.Q4 and 2012.Q4. Models 16, 19, and 20 suggest the number of banksfacing decreasing returns to scale is twice or more than the number of banks facing increasing

15 Additional details about our inference methods are given in a separate Appendix D, which is availablefrom the authors upon request.

16 Results for 1984.Q4 and 1998.Q4 are presented in the separate Appendix E (available from the authorson request).

19



returns at 0.1 significance. Models 13–15, 17, 18, and 22 indicate the reverse, while model 21

indicates the numbers of banks facing increasing or decreasing returns to scale are roughly

similar.

Table 2 provides information about the distribution of estimates of returns to scale across

the various models. Specifically, the table reports means, quartiles, 1 and 99 percentiles for

E C,i, E R,i and E π,i. The distributions of E C,i are quite similar across models 1–6. The estimates

provide an indication of the increase in cost associated with a given increase in the level

of output. For example, the median value of E C,i for model 1 in 2006.Q4 implies that a 10

percent increase output would generate a 6.8 percent increase in cost, i.e., (1.1×(1−0.0289))

per Equation (2.4).

The distributions of estimates of E R,i are seen to vary somewhat across models 7–12, and

the distributions of E π,i vary still more across models 13–22, reflecting the mixed results inTable 1 discussed above. As in Table 1, the results in Table 2 for a particular model are

similar for both 2006.Q4 and 2012.Q4.

The median values of E R,i for 2006.Q4 and 2012.Q4 in models 7–12 range from −0.0308

to −0.0184. These values imply that a 10-percent increase in output leads to an increase in

revenue between 1.1 × (1 − 0.0308) ≈ 6.6 and 1.1 × (1 − 0.0184) ≈ 7.8 percent. Although

the increase in revenue is less than proportionate with the increase in outputs, revenue

nonetheless increases. The median values of

E π,i for 2006.Q4 and 2012.Q4 in models 13–22

range from −0.0259 to 0.0270, with an average value of −0.0121. This value indicates that a10-percent increase in output is accompanied by a 1.1 × (1 − 0.0121) ≈ 8.7-percent increase

in profit. As with revenue, profit increases less than proportionately, but still increases with

the increase in output levels.

Estimates of returns to scale for the largest banks are likely of particular interest. As of

2012.Q4, 26 banks had assets of at least $50 billion (in 2009 dollars). Accordingly, Tables

3–8 report results for 2006.Q4 and 2012.Q4 for the 26 largest banks by total assets. Tables 3

and 4, which present estimates of E C,i for each bank, show that we reject constant returns to

scale in favor of increasing returns for most of the largest banks in both years, regardless of

model specification or definition of cost. There are some differences across models, however,

and somewhat fewer rejections of constant returns for the very largest banks in 2012. For

example, we are unable to reject constant returns to scale for the largest bank in 2012

20



(JP Morgan Chase) in three of the six models. Of the remaining estimates for that bank,

we reject constant returns in favor of decreasing returns to scale for two models (models

1-2) and in favor of increasing returns for one model (model 6). Models 1-2 employ the

narrowest definitions of cost, whereas model 6 uses the most expansive definition. The point

estimates of E C,i from models 1–2 indicate that JP Morgan Chase would incur a 12 percent

increase in cost as a result of a 10 percent increase in output. The estimate from model

6, however, indicates that the bank would experience just a 7 percent increase in cost from

a 10 percent increase in output. Of course, because the different models involve somewhat

different definitions of cost, the results across the models are not necessarily inconsistent

with one another, and some of the differences reflect statistical uncertainty. However, the

differences do caution against drawing strong conclusions about returns to scale for JP

Morgan Chase in 2012.Q4. Similarly, the estimates of E C,i for the other three banks withmore than $1 trillion of total assets in 2012.Q4 also provide ambiguous information about

the extent of scale economies for those banks.

Estimates of E R,i, reported in Tables 5–6, provide considerable evidence that most of the

largest banks faced decreasing returns in terms of revenue in both 2006.Q4 and 2012.Q4.

Estimates of E R,i significantly less than 0 (indicated by asterisks in the tables) indicate

rejection of constant returns in favor of decreasing returns to scale. Only a few of the

estimates in Tables 5–6 are found to be significantly greater than 0 (e.g., JP Morgan Chase

and Bank of America in model 9, 2012.Q4), while most of the estimates are significantly less

than zero. Note, however, that nearly all of the estimates of E R,i are larger than −0.0909,

indicating that revenue increases with an increase in output, though by a smaller percentage

than the increase in output.17

Results for the very largest banks are again somewhat mixed, especially for 2012.Q4. For

JP Morgan Chase, we fail to reject constant returns in revenue for models 8 and 11, reject

in favor of decreasing returns for models 7, 10, and 12, and reject in favor of increasing

returns for model 9. Similarly, we fail to reject constant returns for three of six revenue

models for the second largest bank (Bank of America) and for five of six models for the third

17 Three estimates in Table 6—all for Bank of NY Mellon—are flagged with a footnote ((2)) to indicate R(δ y,w) < 0, which affects how the magnitude of the estimated returns-to-scale measure should be inter-preted as discussed in Appendix A. However, in all three cases, the estimates are insignificantly differentfrom 0.

21



largest bank (Citibank). Estimates of the impact of a 10 percent increase in output on the

revenue of JP Morgan Chase range from a 7 percent increase (model 10) to an 11 percent

increase (model 9). Among the “big four” banks in 2006.Q4 and 2012.Q4, however, all of the

estimates for these banks in Tables 5–6 are greater than −0.0909, indicating that revenues

increase with output, though perhaps at less-than-proportionate rates.

Tables 7–8 show estimates of E π,i for the 26 largest banks in 2004.Q4 and 2012.Q4. As

with the results for revenue, the results for profit are mixed, with most estimates suggesting

either constant or decreasing returns to scale. Only a few estimates are significantly larger

than 0, indicating increasing returns to scale in profit. Of course, profit is the difference

between revenue and cost, and as noted above, we find evidence of increasing returns to

scale on the cost side, but decreasing returns on the revenue side. In view of the results in

Tables 7–8, the net effect of the cost and revenue results is that most of the largest banksface either constant or decreasing returns to scale with respect to profit. Nonetheless, most

of the estimates in Tables 7–8—and all of the estimates for the big four banks—across the 10

different profit models are larger than −0.0909, suggesting that profits increase with output

levels, though in most cases at less-than-proportionate rates.18

6 Conclusions

Many of the largest banks in the United States became even larger during the financial crisis

of 2007-08 and in subsequent years. The Dodd-Frank Act of 2010 is intended to ensure that

even the largest banks can be liquidated if they are insolvent. However, the Act has not

been put to the test and some critics argue that more aggressive measures are needed to

limit the size of banks. The potential cost of such limits in terms of foregone returns to scale

are thus an important topic of ongoing research. However, the question of returns to scale

is relevant not only for the very largest banks, but also for regulators and others interested

in the forces driving ongoing industry consolidation. Moreover, whereas most studies have

focused solely on returns to scale in cost, information about returns to scale in revenue andprofit are also relevant to bank shareholders and policymakers.

18 In Table 8, for 2012.Q4, seven estimates are flagged with footnote ( (2)) to indicate π(δ y,w) < 0, andtwo estimates are flagged with footnote ((3)) to indicate that π(y,w) < 0 and π(δ y,w) < 0. Only two of these estimates are significantly different 0. See Appendix A for discussion of how the magnitudes of theseestimates should be interpreted.

22



Our estimates indicate that the turmoil of 2007-08 appears to have had little impact on

returns to scale for most U.S. banks. Using a variety of definitions of cost and alternative

models, we find that most U.S. banks faced increasing returns to scale in cost in both 2006

and 2012. In addition, we find that a large percentage faced decreasing returns in revenue

in both years. Our results for profit are more mixed, and vary across definitions of profit

and models. However, where we find evidence of decreasing returns in revenue or profit, we

also find that nearly all banks would see increased revenue and profit from producing more

output—just less than proportionate increases.

Our estimates for the very largest banks—those with assets in excess of $1 trillion—are

the most sensitive to alternative definitions and models. Whereas we find robust evidence

that the very largest banks faced increasing returns to scale in cost in 2006, the results for

2012 are decidedly mixed. These results suggest that by 2012, the very largest banks mayhave reached a size at which opportunities for scale economies are exhausted, though the

limited number of observations on such large banks, and hence statistical uncertainty, make

drawing firm conclusions about these banks impossible. Our results also show that the very

largest banks face decreasing returns in revenue, but again, results for returns to scale in

profit for these banks are somewhat sensitive to definitions and model choice.

The fact that somewhat mixed results on returns to scale are obtained for the largest

banks is perhaps not surprising. It is well-known that the distribution of bank size is heavily

skewed, with a long right tail, causing data for the largest banks to be sparse relative to datafor smaller banks. As discussed in Section 4, our nearest-neighbor bandwidths automatically

adapt to the sparseness of the data in different regions of the data, but nonetheless the

data-sparseness makes it difficult to estimate returns to scale for the largest banks. Some

variability in the estimates should be expected.

Although estimates of our returns-to-scale statistics for the largest banks are mixed,

particularly for returns to scale in terms of revenue or profit, the estimates in Tables 5–8

are in almost every case larger than −0.0909, providing strong evidence that the revenues

and profits of the largest banks are still increasing with output levels, although at less-

than-proportionate rates. This is consistent with the continued growth in size among the

largest banks, and is also consistent with the relation between ROA and ROE and bank-size

discussed in Section 1.

23



Appendix A Interpretation of Scale Measures when

Revenue or Profit is Negative

As noted in Section 2, either π(yi,wi) or π(δ yi,wi)—or R(yi,wi) or R(δ yi,wi)—might be

negative, affecting how the magnitude of estimates of E π,i and E R,i are interpreted. Thus

there are four cases to consider. In the discussion that follows, consider the scale measure

E π,i based on the alternative profit function; similar reasoning applies to the scale measure

E R,i based on the alternative revenue function.

In the most common scenario, π(yi,wi) > 0 and π(δ yi,wi) > 0, and this case is dis-

cussed in Section 2. The other three cases are infrequent, and arise when π(yi,wi) < 0 or

π(δ yi,wi) < 0. We consider each of the three possible cases here.

1. π(yi,wi) < 0, π(δ yi,wi) > 0.In this case, increasing output levels by a factor δ > 1 increases profit. Also in this

case, (2.7) can be written as (1 −E π,i)δπ(yi,wi) = π(δ yi,wi), implying E π,i > 1. Hence

returns to scale are increasing in this case. If E π,i = 1.05 and δ = 1.1, then increasing

output levels by 10 percent leads to profits increasing by 100 + (1 − 1.05) × 100 = 105

percent from an initial negative value to a positive value. Alternatively, (2.7) can be

rearranged to show the difference π(δ yi,wi) − δπ(yi,wi) > 0 equals E π,iδ |π(yi,wi|; if

E π,i = 1.05 and δ = 1.1, then increasing output levels by 10 percent increases profit

to a positive level equal to (1 − 1.05) × 1.1 = 0.55 times the magnitude of the profits

that were negative before the increase. Whether the increase is big or small in absolute

terms depends on the starting point, i.e., the magnitude of π(yi,wi).

2. π(yi,wi) > 0, π(δ yi,wi) < 0.

In this case, increasing output levels by a factor δ > 1 decreases profit. Since

π(yi,wi) > 0, (2.7) can again be rewritten as (1+E π,i)δπ(yi,wi) = π(δ yi,wi). Clearly,

E π,i < −1 since π(δ yi,wi) < 0. Hence returns to scale are decreasing in this case. If

E π,i = −1.05 and δ = 1.1, then increasing output levels by 10 percent reduces profit by

100+( 1+ E π,i)δ × 100 = 105.5 percent. As in the previous case, whether the absolute

change in profit is big or small depends on the starting point.

3. π(yi,wi) < 0, π(δ yi,wi) < 0.

Using reasoning along the lines leading to (2.9), profit (increases, remains unchanged,

24



decreases) as E π,i (>, =, <)1−δ −1 ≈ 0.09091 for δ = 1.1. In this case we also have again

(1 − E π,i)δπ(yi,wi) = π(δ yi,wi). Since both profit terms are negative, E π,i < 1 and

Returns to scale are either increasing, constant, or decreasing depending on whether

E π,i is greater than, equal to, or less than 0. Increasing output levels by a factor δ

causes profits to fall by a factor (1 − E π,i)δ ; for If E π,i = 0.05 and δ = 1.1, a 10 percent

increase in output levels results in profits that are still negative, but 4.5 percent greater

than before the increase in output.

25



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28



Table 1: Counts of Banks Facing IRS, CRS, and DRS

.1 signif. .05 signif. .01 signif.

Model LHS Period IRS CRS DRS IRS CRS DRS IRS CRS DRS1 C 1/W 3 2006.Q4 6016 797 6 5649 1165 5 4793 2023 3

2012.Q4 4689 640 3 4417 912 3 3750 1580 2

2 C 2/W 3 2006.Q4 5830 983 6 5430 1384 5 4499 2315 52012.Q4 4545 783 4 4237 1092 3 3545 1785 2

3 C 3/W 3 2006.Q4 5734 1075 10 5350 1460 9 4397 2416 62012.Q4 4514 812 6 4176 1151 5 3442 1885 5

4 C 4/W 3 2006.Q4 6103 659 5 5734 1028 5 4885 1879 32012.Q4 4761 534 1 4483 812 1 3846 1450 0

5 C 5/W 3 2006.Q4 6129 633 5 5741 1022 4 4913 1851 32012.Q4 4786 509 1 4517 779 0 3863 1433 0

6 C 6/W 3 2006.Q4 6292 473 2 6028 737 2 5295 1470 22012.Q4 4944 351 1 4736 559 1 4161 1134 1

7 R1 2006.Q4 142 3831 2846 81 4135 2603 40 4492 2287

2012.Q4 102 3064 2166 67 3287 1978 29 3554 1749

8 R2 2006.Q4 215 4186 2418 145 4491 2183 60 4856 19032012.Q4 150 3374 1808 85 3610 1637 33 3863 1436

9 R3 2006.Q4 23 1636 5160 14 1822 4983 5 2022 47922012.Q4 26 1316 3990 22 1456 3854 12 1637 3683

10 R1 2006.Q4 363 4519 1885 230 4868 1669 114 5192 14612012.Q4 279 3550 1467 173 3787 1336 87 4037 1172

11 R2 2006.Q4 215 4186 2418 145 4491 2183 60 4856 19032012.Q4 150 3374 1808 85 3610 1637 33 3863 1436

12 R3 2006.Q4 54 1543 5170 37 1739 4991 30 1949 47882012.Q4 28 1165 4103 25 1298 3973 17 1470 3809

13 π1 2006.Q4 808 5604 407 473 6024 322 166 6413 2402012.Q4 609 4437 286 352 4749 231 105 5058 169

14 π2 2006.Q4 1425 5119 223 887 5695 185 348 6278 141

2012.Q4 1127 4005 164 711 4456 129 288 4915 93

15 π3 2006.Q4 807 5604 408 474 6024 321 166 6414 2392012.Q4 609 4436 287 349 4752 231 106 5057 169

16 π4 2006.Q4 1325 1505 3989 1231 1738 3850 1085 2099 36352012.Q4 980 1195 3157 880 1391 3061 771 1648 2913

17 π5 2006.Q4 1421 5121 225 883 5700 184 349 6276 1422012.Q4 1128 4004 164 711 4455 130 287 4916 93

18 π6 2006.Q4 2628 3239 900 2251 3666 850 1694 4276 7972012.Q4 2024 2537 735 1744 2855 697 1292 3340 664

19 π7 2006.Q4 338 4748 1733 225 5123 1471 124 5543 11522012.Q4 255 3785 1292 159 4079 1094 79 4444 809

20 π8 2006.Q4 946 1169 4704 862 1342 4615 728 1633 44582012.Q4 668 963 3701 607 1105 3620 510 1321 3501

21 π9 2006.Q4 853 4955 959 584 5380 803 300 5860 607

2012.Q4 711 3821 764 489 4152 655 250 4529 517

22 π10 2006.Q4 1906 4150 711 1476 4657 634 894 5334 5392012.Q4 1531 3203 562 1201 3594 501 732 4127 437

29



Table 2: Quantiles and Means for Estimates of Returns to Scale Indices

Model LHS Period 0.01 0.25 0.50 Mean 0.75 0.99

1 C 1/W 3 2006.Q4 −0.0251 0.0155 0.0289 0.0287 0.0420 0.08122012.Q4 −0.0289 0.0159 0.0288 0.0287 0.0423 0.0811

2 C 2/W 3 2006.Q4 −0.0311 0.0141 0.0287 0.0283 0.0427 0.08652012.Q4 −0.0369 0.0145 0.0286 0.0282 0.0429 0.0857

3 C 3/W 3 2006.Q4 −0.0337 0.0144 0.0296 0.0294 0.0447 0.09262012.Q4 −0.0375 0.0145 0.0293 0.0292 0.0446 0.0910

4 C 4/W 3 2006.Q4 −0.0184 0.0139 0.0240 0.0238 0.0339 0.06232012.Q4 −0.0177 0.0141 0.0240 0.0239 0.0342 0.0627

5 C 5/W 3 2006.Q4 −0.0192 0.0145 0.0248 0.0245 0.0349 0.06382012.Q4 −0.0203 0.0148 0.0246 0.0245 0.0349 0.0634

6 C 6/W 3 2006.Q4 −0.0131 0.0149 0.0237 0.0235 0.0325 0.05752012.Q4 −0.0133 0.0150 0.0237 0.0237 0.0324 0.0570

7 R1 2006.Q4 −0.1149 −0.0464 −0.0308 −0.0281 −0.0136 0.0739

2012.Q4 −0.1111 −0.0452 −0.0298 −0.0284 −0.0139 0.08538 R2 2006.Q4 −0.1297 −0.0473 −0.0300 −0.0252 −0.0113 0.1098

2012.Q4 −0.1250 −0.0468 −0.0292 −0.0229 −0.0103 0.1042

9 R3 2006.Q4 −0.0652 −0.0379 −0.0289 −0.0289 −0.0201 0.01022012.Q4 −0.0659 −0.0378 −0.0288 −0.0287 −0.0198 0.0123

10 R1 2006.Q4 −0.0884 −0.0321 −0.0189 −0.0133 −0.0040 0.09052012.Q4 −0.0888 −0.0316 −0.0184 −0.0153 −0.0034 0.0932

11 R2 2006.Q4 −0.1297 −0.0473 −0.0300 −0.0252 −0.0113 0.10982012.Q4 −0.1250 −0.0468 −0.0292 −0.0229 −0.0103 0.1042

12 R3 2006.Q4 −0.0424 −0.0262 −0.0208 −0.0201 −0.0148 0.01052012.Q4 −0.0425 −0.0267 −0.0210 −0.0203 −0.0150 0.0101

13 π1 2006.Q4 −0.8940 −0.0739 −0.0243 0.0089 0.0308 1.61692012.Q4 −0.7020 −0.0695 −0.0218 0.0222 0.0321 1.3229

14 π2 2006.Q4 −0.7689 −0.0545 −0.0072 0.0665 0.0546 1.7902

2012.Q4 −0.7425 −0.0509 −0.0034 0.1658 0.0605 2.364215 π3 2006.Q4 −0.8943 −0.0739 −0.0243 0.0087 0.0308 1.6169

2012.Q4 −0.7020 −0.0694 −0.0218 0.0221 0.0321 1.3236

16 π4 2006.Q4 −0.0615 −0.0377 −0.0259 0.0529 −0.0089 0.99932012.Q4 −0.0590 −0.0373 −0.0258 0.1104 −0.0106 0.8635

17 π5 2006.Q4 −0.7689 −0.0545 −0.0073 0.0660 0.0546 1.78132012.Q4 −0.7424 −0.0508 −0.0034 0.1666 0.0605 2.3716

18 π6 2006.Q4 −5.2434 −0.1532 0.0270 0.6313 0.2941 8.43532012.Q4 −4.4839 −0.1492 0.0269 0.5259 0.2981 7.9252

19 π7 2006.Q4 −0.0845 −0.0395 −0.0240 −0.0183 −0.0067 0.09272012.Q4 −0.0836 −0.0393 −0.0230 −0.0200 −0.0057 0.0869

20 π8 2006.Q4 −0.0493 −0.0285 −0.0202 0.0285 −0.0091 0.39982012.Q4 −0.0483 −0.0282 −0.0203 0.0118 −0.0096 0.3023

21 π9 2006.Q4 −0.1054 −0.0367 −0.0165 0.0041 0.0067 0.2507

2012.Q4 −0.1011 −0.0359 −0.0157 0.0136 0.0083 0.359122 π10 2006.Q4 −0.5842 −0.0659 −0.0065 0.1854 0.0767 2.6833

2012.Q4 −0.5201 −0.0665 −0.0045 0.1722 0.0809 2.4381

30



T a b l e 3 : R e t u r n s t o S c a

l e ( C o s t ) f o r L a r g e s t B a n k s b y T o t a l A s s e t s ,

2 0 0 6 . Q

4

A s s e t s

N a m e

( b i l l i o n s o f 2

0 0 9 $ )

M o d e l 1

M o d e l 2

M o d e l 3

M o d e l 4

M o d e l 5

M o d e l 6

B A N K O F A M

E R N A

1 2 3 9

0 . 0 0 2 4 ∗ ∗ ∗

− 0 . 0 0 5 8

0 . 0 0 6 7 ∗ ∗ ∗

0 . 0 1 6 8 ∗ ∗ ∗

0 . 0 2 1 1 ∗ ∗ ∗

0 . 0 2 4 5 ∗ ∗ ∗

J P M O R G A N C H A S E B K N A

1 2 2 4

0 . 0 2 3 5 ∗ ∗ ∗

0 . 0 0 7 8 ∗ ∗

0 . 0 3 0 7 ∗ ∗ ∗

0 . 0 2 5 8 ∗ ∗ ∗

0 . 0 2 8 1 ∗ ∗ ∗

0 . 0 2 1 7 ∗ ∗ ∗

C I T I B A N K N A

9 5 4

0 . 0 0 4 4

− 0 . 0 0 0 3

0 . 0 0 5 0 ∗ ∗ ∗

0 . 0 1 7 0 ∗ ∗ ∗

0 . 0 1 4 4 ∗ ∗ ∗

0 . 0 2 4 1 ∗ ∗ ∗

W A C H O V I A B K N A

5 3 9

0 . 0 1 9 4 ∗ ∗ ∗

0 . 0 2 4 2 ∗ ∗ ∗

0 . 0 2 0 9 ∗ ∗ ∗

0 . 0 1 1 1 ∗ ∗ ∗

0 . 0 1 4 4 ∗ ∗ ∗

0 . 0 1 7 6 ∗ ∗ ∗

W E L L S F A R G

O B K N A

4 1 6

0 . 0 2 1 4 ∗ ∗ ∗

0 . 0 3 0 4 ∗ ∗ ∗

0 . 0 2 5 0 ∗ ∗ ∗

− 0 . 0 0 1 2

0 . 0 0 1 0 ∗ ∗ ∗

0 . 0 1 0 2 ∗ ∗ ∗

U S B K N A

2 2 6

0 . 0 3 0 1 ∗ ∗ ∗

0 . 0 3 8 2 ∗ ∗ ∗

0 . 0 2 0 2 ∗ ∗ ∗

0 . 0 6 0 1 ∗ ∗ ∗

0 . 0 6 8 6 ∗ ∗ ∗

0 . 0 4 0 9 ∗ ∗ ∗

S U N T R U S T B

K

1 9 0

0 . 0 2 0 6 ∗ ∗ ∗

0 . 0 2 2 3 ∗ ∗ ∗

0 . 0 0 8 9 ∗ ∗ ∗

0 . 0 2 1 3 ∗ ∗ ∗

0 . 0 1 5 4 ∗ ∗ ∗

0 . 0 1 7 2 ∗ ∗ ∗

H S B C B K U S A N A

1 7 3

0 . 0 3 2 9 ∗ ∗ ∗

0 . 0 3 0 5 ∗ ∗ ∗

0 . 0 0 3 3

0 . 0 4 4 9 ∗ ∗ ∗

0 . 0 4 1 1 ∗ ∗ ∗

0 . 0 4 5 7 ∗ ∗ ∗

N A T I O N A L C

I T Y B K

1 4 0

− 0 . 0 2 5 7 ∗ ∗

− 0 . 0 3 6 8 ∗ ∗ ∗

0 . 0 0 6 0

0 . 0 2 4 1 ∗ ∗ ∗

0 . 0 2 4 2 ∗ ∗ ∗

0 . 0 2 5 6 ∗ ∗ ∗

R E G I O N S B K

1 1 5

0 . 0 2 9 1 ∗ ∗ ∗

0 . 0 2 0 8 ∗ ∗ ∗

0 . 0 1 2 3 ∗ ∗

0 . 0 2 8 5 ∗ ∗ ∗

0 . 0 2 2 7 ∗ ∗ ∗

0 . 0 2 7 2 ∗ ∗ ∗

B R A N C H B K G & T C

1 0 7

0 . 0 3 9 6 ∗ ∗ ∗

0 . 0 4 0 7 ∗ ∗ ∗

0 . 0 3 0 2 ∗ ∗ ∗

0 . 0 2 2 5 ∗ ∗ ∗

0 . 0 2 1 5 ∗ ∗ ∗

0 . 0 2 7 3 ∗ ∗ ∗

C O U N T R Y W I D E B K N A

9 7

0 . 0 4 8 8 ∗ ∗ ∗

0 . 0 4 8 5 ∗ ∗ ∗

0 . 0 3 4 9 ∗ ∗ ∗

0 . 0 3 5 1 ∗ ∗ ∗

0 . 0 3 5 5 ∗ ∗ ∗

0 . 0 3 0 2 ∗ ∗ ∗

K E Y B A N K N

A

9 4

0 . 0 3 6 2 ∗ ∗ ∗

0 . 0 4 8 2 ∗ ∗ ∗

0 . 0 1 6 3 ∗ ∗ ∗

0 . 0 1 8 9 ∗ ∗ ∗

0 . 0 2 1 5 ∗ ∗ ∗

0 . 0 2 4 2 ∗ ∗ ∗

P N C B K N A

9 2

0 . 0 2 8 5 ∗ ∗ ∗

0 . 0 2 2 4 ∗ ∗ ∗

0 . 0 2 5 7 ∗ ∗ ∗

0 . 0 2 6 0 ∗ ∗ ∗

0 . 0 2 7 9 ∗ ∗ ∗

0 . 0 3 3 1 ∗ ∗ ∗

B A N K O F N Y

9 2

0 . 0 2 9 0 ∗ ∗ ∗

0 . 0 1 5 1 ∗ ∗ ∗

0 . 0 2 6 4 ∗ ∗ ∗

0 . 0 0 8 8 ∗ ∗ ∗

− 0 . 0 0 1 2

0 . 0 2 3 8 ∗ ∗ ∗

C H A S E B K U

S A N A

8 4

0 . 0 0 5 3 ∗ ∗ ∗

0 . 0 0 7 3 ∗ ∗ ∗

−

0 . 0 0 4 0

0 . 0 1 4 5 ∗ ∗ ∗

0 . 0 0 8 3 ∗ ∗ ∗

− 0 . 0 2 2 2 ∗ ∗ ∗

C O M E R I C A B K

6 1

− 0 . 0 1 4 3

− 0 . 0 2 8 7 ∗ ∗ ∗

−

0 . 0 1 2 9

0 . 0 1 4 9 ∗ ∗ ∗

0 . 0 1 6 1 ∗ ∗ ∗

0 . 0 1 1 6 ∗ ∗

B A N K O F T H

E W E S T

5 8

0 . 0 1 6 7 ∗ ∗ ∗

0 . 0 1 7 6 ∗ ∗ ∗

0 . 0 1 0 8 ∗ ∗ ∗

0 . 0 6 8 0 ∗ ∗ ∗

0 . 0 5 6 2 ∗ ∗ ∗

0 . 0 2 5 6 ∗ ∗ ∗

M A N U F A C T U

R E R S & T R A D E R S T C

5 8

0 . 0 1 0 8 ∗ ∗ ∗

0 . 0 1 1 4 ∗ ∗ ∗

0 . 0 1 9 0 ∗ ∗ ∗

0 . 0 0 8 7 ∗ ∗ ∗

0 . 0 0 7 3 ∗ ∗ ∗

0 . 0 1 1 2 ∗ ∗ ∗

F I F T H T H I R D B K

5 8

− 0 . 0 1 9 1

− 0 . 0 3 1 6

−

0 . 0 1 5 6

0 . 0 4 0 3 ∗ ∗ ∗

0 . 0 3 6 7 ∗ ∗ ∗

0 . 0 4 6 2 ∗ ∗ ∗

U N I O N B K O

F C A N A

5 4

0 . 0 2 9 6 ∗ ∗ ∗

0 . 0 2 7 3 ∗ ∗ ∗

0 . 0 3 4 3 ∗ ∗ ∗

0 . 0 3 7 0 ∗ ∗ ∗

0 . 0 3 6 7 ∗ ∗ ∗

0 . 0 3 4 7 ∗ ∗ ∗

N O R T H E R N T C

5 2

0 . 0 4 8 7 ∗ ∗ ∗

0 . 0 5 0 7 ∗ ∗ ∗

0 . 0 5 2 0 ∗ ∗ ∗

0 . 0 7 6 5 ∗ ∗ ∗

0 . 0 8 1 1 ∗ ∗ ∗

0 . 0 4 7 1 ∗ ∗ ∗


5 1

0 . 0 1 2 6 ∗ ∗ ∗

0 . 0 0 2 9

0 . 0 0 7 8 ∗ ∗

0 . 0 4 2 5 ∗ ∗ ∗

0 . 0 3 7 4 ∗ ∗ ∗

0 . 0 3 7 0 ∗ ∗ ∗

M & I M A R S H A L L & I L S L E Y B K

5 0

0 . 0 2 2 8 ∗ ∗ ∗

0 . 0 2 2 9 ∗ ∗ ∗

0 . 0 2 8 8 ∗ ∗ ∗

0 . 0 1 2 8 ∗ ∗ ∗

0 . 0 0 9 0 ∗ ∗ ∗

0 . 0 1 2 7 ∗ ∗ ∗

C H A R T E R O N E B K N A

4 8

0 . 0 2 1 6 ∗ ∗ ∗

0 . 0 1 1 1 ∗ ∗ ∗

0 . 0 3 5 3 ∗ ∗ ∗

0 . 0 0 6 6 ∗ ∗ ∗

0 . 0 1 3 4 ∗ ∗ ∗

0 . 0 2 7 3 ∗ ∗ ∗

H A R R I S N A

4 3

0 . 0 4 2 3 ∗ ∗ ∗

0 . 0 5 0 4 ∗ ∗ ∗

0 . 0 4 2 5 ∗ ∗ ∗

0 . 0 4 3 5 ∗ ∗ ∗

0 . 0 3 4 6 ∗ ∗ ∗

0 . 0 3 4 1 ∗ ∗ ∗

D e p . V a r .

C 1 / W 3

C 2 / W 3

C 3 / W 3

C 4 / W 3

C 5 / W 3

C 6 / W 3

R H S V a r s .

( y , w 1 )

( y , w 1 )

( y , w 1 )

( y , w 2 )

( y , w 2 )

( y , w 2 )

N O T E : S t a t i s t i c a l s i g n i fi c a n c e a t t h e t e n fi v e , o r o n e p e r c e n t l e

v e l s i s d e n o t e d b y o n e , t w o , o r t h r e e a s t e

r i s k s , r e s p e c t i v e l y .

31



T a b l e 4 : R e t u r n s t o S c a

l e ( C o s t ) f o r L a r g e s t B a n k s b y T o t a l A s s e t s ,

2 0 1 2 . Q

4

A s s e t s

N a m e


0 0 9 $ )

M o d e l 1

M o d e l 2

M o d e l 3

M o d e l 4

M o d e l 5

M o d e l 6


1 7 6 9

− 0 . 0 1 7 7 ∗ ∗ ∗

− 0 . 0 1 8 2 ∗

0 . 0 0 0 2

− 0 . 0 1 3 2

− 0 . 0 1 9 6

0 . 0 2 5 1 ∗ ∗ ∗

B A N K O F A M

E R N A

1 3 8 0

− 0 . 0 0 5 6

− 0 . 0 0 6 6

−

0 . 0 0 1 6

0 . 0 2 0 3 ∗ ∗ ∗

0 . 0 0 6 7 ∗ ∗

0 . 0 2 9 3 ∗ ∗ ∗

C I T I B A N K N

A

1 2 6 5

0 . 0 0 4 0 ∗ ∗ ∗

− 0 . 0 0 4 8

0 . 0 0 3 4 ∗

0 . 0 2 5 4 ∗ ∗ ∗

0 . 0 0 5 3 ∗ ∗

0 . 0 2 3 5 ∗ ∗ ∗

W E L L S F A R G

O B K N A

1 1 7 3

− 0 . 0 0 9 2 ∗ ∗ ∗

− 0 . 0 1 8 7 ∗ ∗ ∗

0 . 0 0 5 7 ∗ ∗

0 . 0 1 6 5 ∗ ∗ ∗

0 . 0 0 3 7 ∗

0 . 0 2 7 8 ∗ ∗ ∗

U S B K N A

3 2 5

0 . 0 0 0 7

0 . 0 0 7 0 ∗

0 . 0 0 8 2 ∗ ∗

0 . 0 2 0 6 ∗ ∗ ∗

0 . 0 2 0 3 ∗ ∗ ∗

0 . 0 1 1 9 ∗ ∗ ∗

P N C B K N A

2 7 7

− 0 . 0 0 2 5

− 0 . 0 1 0 4

0 . 0 4 6 0 ∗ ∗ ∗

0 . 0 1 8 1 ∗ ∗ ∗

0 . 0 1 6 6 ∗ ∗ ∗

0 . 0 1 9 3 ∗ ∗ ∗

B A N K O F N Y

M E L L O N

2 5 8

0 . 0 0 4 4

− 0 . 0 0 1 4

0 . 0 2 1 2 ∗ ∗ ∗

0 . 0 5 4 7 ∗ ∗ ∗

0 . 0 5 1 7 ∗ ∗ ∗

0 . 0 4 5 9 ∗ ∗ ∗

S T A T E S T R E

E T B & T C

1 9 8

0 . 0 1 7 0 ∗ ∗ ∗

0 . 0 0 8 4

0 . 0 3 1 5 ∗ ∗ ∗

0 . 0 5 1 2 ∗ ∗ ∗

0 . 0 4 4 6 ∗ ∗ ∗

0 . 0 2 6 8 ∗ ∗ ∗

T D B K N A

1 9 1

0 . 0 4 2 5 ∗ ∗ ∗

0 . 0 5 5 1 ∗ ∗ ∗

0 . 0 2 5 8 ∗ ∗ ∗

0 . 0 0 7 4 ∗ ∗ ∗

0 . 0 1 0 8 ∗ ∗ ∗

0 . 0 1 3 1 ∗ ∗ ∗


1 8 1

0 . 0 6 6 8 ∗ ∗ ∗

0 . 0 7 2 3 ∗ ∗ ∗

0 . 0 4 3 8 ∗ ∗ ∗

0 . 0 5 1 0 ∗ ∗ ∗

0 . 0 3 6 5 ∗ ∗ ∗

0 . 0 2 3 9 ∗ ∗ ∗


1 6 7

0 . 0 7 8 8 ∗ ∗ ∗

0 . 1 0 8 4 ∗ ∗ ∗

0 . 0 2 3 3 ∗ ∗ ∗

− 0 . 0 0 2 2 ∗

0 . 0 1 2 4 ∗ ∗ ∗

0 . 0 1 7 8 ∗ ∗ ∗

S U N T R U S T B

K

1 6 0

0 . 0 5 2 5 ∗ ∗ ∗

0 . 0 5 4 9 ∗ ∗ ∗

0 . 0 3 1 0 ∗ ∗ ∗

0 . 0 4 7 6 ∗ ∗ ∗

0 . 0 5 2 7 ∗ ∗ ∗

0 . 0 3 5 5 ∗ ∗ ∗

F I A C A R D S V C N A

1 5 6

0 . 0 1 8 9 ∗ ∗ ∗

0 . 0 1 8 4 ∗ ∗ ∗

0 . 0 3 6 8 ∗ ∗ ∗

0 . 0 1 3 5 ∗ ∗ ∗

0 . 0 1 2 3 ∗ ∗ ∗

0 . 0 2 6 6 ∗ ∗ ∗

R E G I O N S B K

1 1 4

0 . 0 3 3 8 ∗ ∗ ∗

0 . 0 1 8 6 ∗ ∗ ∗

0 . 0 3 1 0 ∗ ∗ ∗

0 . 0 3 2 0 ∗ ∗ ∗

0 . 0 3 4 7 ∗ ∗ ∗

0 . 0 2 7 3 ∗ ∗ ∗


1 1 1

0 . 0 7 1 9 ∗ ∗ ∗

0 . 0 7 3 9 ∗ ∗ ∗

0 . 0 5 1 7 ∗ ∗ ∗

0 . 0 4 5 5 ∗ ∗ ∗

0 . 0 4 8 1 ∗ ∗ ∗

0 . 0 3 4 9 ∗ ∗ ∗

R B S C I T I Z E N

S N A

1 0 0

0 . 0 0 3 8 ∗ ∗

− 0 . 0 0 0 0 ∗

−

0 . 1 2 8 3 ∗ ∗ ∗

0 . 0 1 8 1 ∗ ∗ ∗

0 . 0 2 1 5 ∗ ∗ ∗

0 . 0 0 7 7 ∗ ∗ ∗

N O R T H E R N T C

9 0

0 . 0 2 8 9 ∗ ∗ ∗

0 . 0 2 0 8 ∗ ∗ ∗

0 . 0 5 2 6 ∗ ∗ ∗

0 . 0 5 4 3 ∗ ∗ ∗

0 . 0 5 3 5 ∗ ∗ ∗

0 . 0 4 8 1 ∗ ∗ ∗

B M O H A R R I S B K N A

8 8

0 . 0 3 2 1 ∗ ∗ ∗

0 . 0 5 8 3 ∗ ∗ ∗

0 . 0 3 1 0 ∗ ∗ ∗

− 0 . 0 2 3 6

0 . 0 0 0 7 ∗

0 . 0 0 8 6 ∗ ∗ ∗

K E Y B A N K N

A

8 1

0 . 0 1 6 1 ∗ ∗ ∗

0 . 0 1 9 2 ∗ ∗ ∗

0 . 0 2 5 9 ∗ ∗ ∗

0 . 0 0 6 0 ∗ ∗ ∗

0 . 0 1 1 6 ∗ ∗ ∗

0 . 0 1 1 4 ∗ ∗ ∗

S O V E R E I G N

B K N A

7 8

0 . 0 0 9 2 ∗ ∗ ∗

0 . 0 1 3 7 ∗ ∗ ∗

0 . 0 2 4 2 ∗ ∗ ∗

0 . 0 2 3 9 ∗ ∗ ∗

0 . 0 2 4 2 ∗ ∗ ∗

0 . 0 4 6 1 ∗ ∗ ∗

M A N U F A C T U


7 7

0 . 0 5 9 3 ∗ ∗ ∗

0 . 0 5 4 8 ∗ ∗ ∗

0 . 0 7 5 2 ∗ ∗ ∗

0 . 0 2 8 2 ∗ ∗ ∗

0 . 0 2 4 7 ∗ ∗ ∗

0 . 0 1 4 2 ∗ ∗ ∗

D I S C O V E R B

K

6 9

− 0 . 0 0 1 4

− 0 . 0 0 0 9

0 . 0 2 3 3 ∗ ∗ ∗

− 0 . 0 0 5 5

− 0 . 0 1 6 8

0 . 0 2 5 8 ∗ ∗ ∗

C O M P A S S B K

6 5

0 . 0 3 4 6 ∗ ∗ ∗

0 . 0 2 8 9 ∗ ∗ ∗

0 . 0 8 5 1 ∗ ∗ ∗

0 . 0 4 0 7 ∗ ∗ ∗

0 . 0 4 0 8 ∗ ∗ ∗

0 . 0 4 1 3 ∗ ∗ ∗

C O M E R I C A B K

6 1

0 . 0 1 6 5 ∗ ∗ ∗

0 . 0 1 9 9 ∗ ∗ ∗

0 . 0 3 2 2 ∗ ∗ ∗

0 . 0 1 7 3 ∗ ∗ ∗

0 . 0 1 5 9 ∗ ∗

0 . 0 2 9 3 ∗ ∗ ∗

B A N K O F T H

E W E S T

6 0

0 . 0 1 0 9 ∗ ∗ ∗

− 0 . 0 1 2 7

0 . 0 2 7 6 ∗ ∗ ∗

0 . 0 1 1 6 ∗ ∗ ∗

0 . 0 1 3 6 ∗ ∗ ∗

0 . 0 1 5 5 ∗ ∗ ∗

H U N T I N G T O

N N B

5 3

0 . 0 4 3 4 ∗ ∗ ∗

0 . 0 4 7 3 ∗ ∗ ∗

0 . 0 2 4 2 ∗ ∗ ∗

0 . 0 3 9 7 ∗ ∗ ∗

0 . 0 4 5 0 ∗ ∗ ∗

0 . 0 2 1 4 ∗ ∗ ∗

D e p . V a r .

C 1 / W 3

C 2 / W 3

C 3 / W 3

C 4 / W 3

C 5 / W 3

C 6 / W 3

R H S V a r s .

( y , w 1 )

( y , w 1 )

( y , w 1 )

( y , w 2 )

( y , w 2 )

( y , w 2 )




32



T a b l e 5 : R e t u r n s t o S c a l e

( R e v e n u e ) f o r L a r g e s t B a n k s

b y T o t a l A s s e t s ,

2 0 0 6 . Q

4

A s s e t s

N a m e


0 0 9 $ )

M o d e l 7

M o d e l 8

M o d e l 9

M o d e l 1 0

M o d e l 1 1

M o d e l 1 2

B A N K O F A M

E R N A

1 2 3 9

− 0 . 0 1 5 7 ∗ ∗ ∗

− 0 . 0 1 1 6

−

0 . 0 0 9 3 ∗ ∗ ∗

− 0 . 0 3 8 8 ∗ ∗ ∗

− 0 . 0 1 1 6

− 0 . 0 2 3 6 ∗ ∗ ∗


1 2 2 4

− 0 . 0 3 1 8 ∗ ∗ ∗

− 0 . 0 4 2 6 ∗ ∗ ∗

−

0 . 0 3 0 3 ∗ ∗ ∗

− 0 . 0 4 6 0 ∗ ∗ ∗

− 0 . 0 4 2 6 ∗ ∗ ∗

− 0 . 0 3 2 7 ∗ ∗ ∗

C I T I B A N K N A

9 5 4

− 0 . 0 2 2 6 ∗ ∗ ∗

− 0 . 0 2 9 9 ∗ ∗ ∗

−

0 . 0 1 9 7 ∗ ∗ ∗

− 0 . 0 4 6 3 ∗ ∗ ∗

− 0 . 0 2 9 9 ∗ ∗ ∗

− 0 . 0 2 9 8 ∗ ∗ ∗


5 3 9

− 0 . 0 4 4 5 ∗ ∗ ∗

− 0 . 0 3 9 8 ∗ ∗ ∗

−

0 . 0 2 6 4 ∗ ∗ ∗

− 0 . 0 6 1 9 ∗ ∗ ∗

− 0 . 0 3 9 8 ∗ ∗ ∗

− 0 . 0 3 4 2 ∗ ∗ ∗

W E L L S F A R G

O B K N A

4 1 6

− 0 . 0 5 8 2 ∗ ∗ ∗

− 0 . 0 7 2 8 ∗ ∗ ∗

−

0 . 0 1 9 3 ∗ ∗ ∗

− 0 . 0 2 6 6 ∗ ∗ ∗

− 0 . 0 7 2 8 ∗ ∗ ∗

− 0 . 0 1 0 6 ∗ ∗ ∗

U S B K N A

2 2 6

− 0 . 0 4 6 4 ∗ ∗ ∗

− 0 . 0 4 8 7 ∗ ∗ ∗

−

0 . 0 2 2 9 ∗ ∗ ∗

− 0 . 0 2 3 0 ∗ ∗ ∗

− 0 . 0 4 8 7 ∗ ∗ ∗

− 0 . 0 1 1 9 ∗ ∗ ∗

S U N T R U S T B

K

1 9 0

− 0 . 0 1 5 1 ∗ ∗ ∗

− 0 . 0 1 4 0 ∗ ∗ ∗

−

0 . 0 1 5 4 ∗ ∗ ∗

− 0 . 0 3 5 2 ∗ ∗ ∗

− 0 . 0 1 4 0 ∗ ∗ ∗

− 0 . 0 3 6 0 ∗ ∗ ∗


1 7 3

− 0 . 0 1 2 4

− 0 . 0 1 7 7

−

0 . 0 1 2 2 ∗ ∗ ∗

− 0 . 0 5 0 6 ∗ ∗ ∗

− 0 . 0 1 7 7

− 0 . 0 3 1 4 ∗ ∗ ∗

N A T I O N A L C

I T Y B K

1 4 0

− 0 . 0 4 2 2 ∗ ∗ ∗

− 0 . 0 5 4 3 ∗ ∗ ∗

−

0 . 0 3 6 5 ∗ ∗ ∗

− 0 . 0 4 6 8 ∗ ∗ ∗

− 0 . 0 5 4 3 ∗ ∗ ∗

− 0 . 0 2 9 9 ∗ ∗ ∗

R E G I O N S B K

1 1 5

− 0 . 0 3 6 4 ∗ ∗ ∗

− 0 . 0 4 2 6 ∗ ∗ ∗

−

0 . 0 2 0 9 ∗ ∗ ∗

− 0 . 0 4 0 2 ∗ ∗ ∗

− 0 . 0 4 2 6 ∗ ∗ ∗

− 0 . 0 2 9 0 ∗ ∗ ∗


1 0 7

− 0 . 0 5 7 2 ∗ ∗ ∗

− 0 . 0 5 0 4 ∗ ∗ ∗

−

0 . 0 3 5 4 ∗ ∗ ∗

− 0 . 0 4 1 0 ∗ ∗ ∗

− 0 . 0 5 0 4 ∗ ∗ ∗

− 0 . 0 2 6 5 ∗ ∗ ∗


9 7

− 0 . 0 9 4 0 ∗ ∗ ∗

− 0 . 0 9 4 7 ∗ ∗ ∗

−

0 . 0 6 2 2 ∗ ∗ ∗

− 0 . 0 8 5 8 ∗ ∗ ∗

− 0 . 0 9 4 7 ∗ ∗ ∗

− 0 . 0 3 3 8 ∗ ∗ ∗

K E Y B A N K N A

9 4

− 0 . 0 3 6 1

− 0 . 0 9 6 0 ∗ ∗ ∗

− 0 . 0 2 6 6

− 0 . 0 2 3 5

− 0 . 0 9 6 0 ∗ ∗ ∗

− 0 . 0 3 2 1 ∗ ∗ ∗

P N C B K N A

9 2

− 0 . 0 3 1 9

− 0 . 0 2 6 4 ∗ ∗ ∗

− 0 . 0 0 5 3

− 0 . 0 3 1 9 ∗ ∗ ∗

− 0 . 0 2 6 4 ∗ ∗ ∗

− 0 . 0 2 3 1 ∗ ∗ ∗

B A N K O F N Y

9 2

− 0 . 0 5 9 8 ∗ ∗ ∗

− 0 . 0 4 8 4 ∗ ∗ ∗

−

0 . 0 4 3 5 ∗ ∗ ∗

− 0 . 0 2 9 7 ∗ ∗ ∗

− 0 . 0 4 8 4 ∗ ∗ ∗

− 0 . 0 1 8 7 ∗ ∗ ∗

C H A S E B K U

S A N A

8 4

− 0 . 0 4 9 5 ∗ ∗ ∗

− 0 . 0 4 6 8 ∗ ∗ ∗

0 . 0 1 1 6 ∗ ∗ ∗

− 0 . 0 4 6 3 ∗ ∗ ∗

− 0 . 0 4 6 8 ∗ ∗ ∗

− 0 . 0 0 9 3

C O M E R I C A B

K

6 1

− 0 . 0 5 5 5 ∗ ∗ ∗

− 0 . 0 5 3 2 ∗ ∗ ∗

−

0 . 0 4 0 6 ∗ ∗ ∗

− 0 . 0 5 1 0 ∗ ∗ ∗

− 0 . 0 5 3 2 ∗ ∗ ∗

− 0 . 0 3 4 0 ∗ ∗ ∗

B A N K O F T H

E W E S T

5 8

− 0 . 0 2 0 1

− 0 . 0 6 3 1 ∗ ∗ ∗

−

0 . 0 3 5 5 ∗ ∗ ∗

− 0 . 0 1 1 6 ∗ ∗ ∗

− 0 . 0 6 3 1 ∗ ∗ ∗

− 0 . 0 1 9 2 ∗ ∗ ∗

M A N U F A C T U


5 8

− 0 . 0 2 8 2 ∗ ∗ ∗

− 0 . 0 1 8 1 ∗ ∗ ∗

−

0 . 0 1 2 7 ∗ ∗ ∗

− 0 . 0 1 7 1 ∗ ∗ ∗

− 0 . 0 1 8 1 ∗ ∗ ∗

− 0 . 0 3 3 8 ∗ ∗ ∗


5 8

− 0 . 0 0 2 3

− 0 . 0 3 1 3

−

0 . 0 2 2 7 ∗ ∗ ∗

− 0 . 0 3 2 2 ∗ ∗ ∗

− 0 . 0 3 1 3

− 0 . 0 2 1 4 ∗ ∗ ∗

U N I O N B K O

F C A N A

5 4

− 0 . 0 5 0 0 ∗ ∗ ∗

− 0 . 0 4 9 4 ∗ ∗ ∗

−

0 . 0 3 1 0 ∗ ∗ ∗

− 0 . 0 4 3 1 ∗ ∗ ∗

− 0 . 0 4 9 4 ∗ ∗ ∗

− 0 . 0 3 3 1 ∗ ∗ ∗

N O R T H E R N T C

5 2

− 0 . 0 6 4 5 ∗ ∗ ∗

− 0 . 0 6 9 7 ∗ ∗ ∗

−

0 . 0 5 7 2 ∗ ∗ ∗

− 0 . 0 2 6 8 ∗ ∗ ∗

− 0 . 0 6 9 7 ∗ ∗ ∗

− 0 . 0 3 4 8 ∗ ∗ ∗


5 1

− 0 . 0 4 7 8 ∗ ∗ ∗

− 0 . 0 7 3 9 ∗ ∗ ∗

−

0 . 0 1 9 6 ∗ ∗ ∗

− 0 . 0 4 6 5 ∗ ∗ ∗

− 0 . 0 7 3 9 ∗ ∗ ∗

− 0 . 0 2 4 1 ∗ ∗ ∗


5 0

− 0 . 0 6 0 4 ∗ ∗ ∗

− 0 . 0 6 2 4 ∗ ∗ ∗

−

0 . 0 2 3 4 ∗ ∗ ∗

− 0 . 0 5 9 5 ∗ ∗ ∗

− 0 . 0 6 2 4 ∗ ∗ ∗

− 0 . 0 1 7 9 ∗ ∗ ∗


4 8

0 . 0 4 5 0 ∗ ∗ ∗

0 . 0 4 6 6 ∗ ∗ ∗

− 0 . 0 0 1 4

− 0 . 0 2 9 8 ∗ ∗ ∗

0 . 0 4 6 6 ∗ ∗ ∗

− 0 . 0 3 4 8 ∗ ∗ ∗

H A R R I S N A

4 3

− 0 . 0 3 0 5 ∗ ∗ ∗

− 0 . 0 3 9 2 ∗ ∗ ∗

−

0 . 0 3 4 8 ∗ ∗ ∗

0 . 0 0 0 0

− 0 . 0 3 9 2 ∗ ∗ ∗

− 0 . 0 1 8 4 ∗ ∗ ∗

D e p . V a r .

R 1

R 2

R 3

R 1

R 2

R 3

R H S V a r s .

( y , w 3 )

( y , w 3 )

( y , w 3 )

( y , w 4 )

( y , w 4 )

( y , w 4 )

N O T E : S t a t i s t i c a l s i g n i fi c a n c e ( d i ff e r e n c e f r o m 0 ) a t t h e t e n , fi v e , o r o n e p e r c e n t l e v e l s i s d e n o t e d b y o n

e , t w o , o r t h r e e a s t e r i s k s , r e s p e c t i v e l y .

33



T a b l e 6 : R e t u r n s t o S c a l e

( R e v e n u e ) f o r L a r g e s t B a n k s


2 0 1 2 . Q

4

A s s e t s

N a m e

( b i l l i o n s o f 2 0 0 9 $ )

M o d e l 7

M o d e l 8

M o d e l 9

M o d e l 1 0

M o d e l 1 1

M o d e l 1 2


1 7 6 9

− 0 . 0 0 9 5 ∗

− 0 . 0 0 6 1

0

. 0 0 6 3 ∗ ∗

− 0 . 0 3 0 7 ∗ ∗ ∗

− 0 . 0 0 6 1

− 0 . 0 0 9 8 ∗ ∗ ∗

B A N K O F A M E R N

A

1 3 8 0

− 0 . 0 0 6 5

− 0 . 0 0 8 4

0

. 0 0 7 0 ∗ ∗ ∗

− 0 . 0 6 0 5 ∗ ∗ ∗

− 0 . 0 0 8 4

− 0 . 0 2 2 5 ∗ ∗ ∗

C I T I B A N K N A

1 2 6 5

− 0 . 0 0 5 6

− 0 . 0 2 1 9

− 0

. 0 0 1 1

− 0 . 0 1 0 7

− 0 . 0 2 1 9

− 0 . 0 2 5 4 ∗ ∗ ∗

W E L L S F A R G O B K

N A

1 1 7 3

− 0 . 0 1 0 3 ∗ ∗ ∗

− 0 . 0 1 4 1 ∗ ∗ ∗

0

. 0 0 4 7 ∗ ∗ ∗

− 0 . 0 3 0 8 ∗ ∗ ∗

− 0 . 0 1 4 1 ∗ ∗ ∗

− 0 . 0 1 6 7 ∗ ∗ ∗

U S B K N A

3 2 5

0 . 0 0 7 7

− 0 . 0 1 3 1

0

. 0 0 1 0

− 0 . 0 2 2 3 ∗ ∗ ∗

− 0 . 0 1 3 1

− 0 . 0 1 2 2 ∗ ∗ ∗

P N C B K N A

2 7 7

− 0 . 0 1 6 7 ∗ ∗ ∗

− 0 . 0 0 7 7

− 0

. 0 0 1 7

− 0 . 0 2 3 5 ∗ ∗ ∗

− 0 . 0 0 7 7

− 0 . 0 1 3 0 ∗ ∗ ∗

B A N K O F N Y M E L L O N

2 5 8

− 0 . 9 3 1 3

− 1 . 6 5 4 9 ( 2 )

0

. 0 0 8 2

− 1 . 0 9 8 8 ( 2 )

− 1 . 6 5 4 9 ( 2 )

− 0 . 0 3 1 7 ∗ ∗ ∗

S T A T E S T R E E T B &

T C

1 9 8

− 0 . 2 2 9 2

− 0 . 1 9 3 2

0

. 0 8 8 3 ∗ ∗ ∗

− 0 . 2 1 6 3 ∗

− 0 . 1 9 3 2

− 0 . 0 2 5 7 ∗ ∗ ∗

T D B K N A

1 9 1

0 . 0 2 1 4 ∗ ∗ ∗

0 . 0 0 6 3 ∗

− 0

. 0 0 4 6

0 . 0 1 6 1 ∗ ∗

0 . 0 0 6 3 ∗

− 0 . 0 0 9 1 ∗ ∗ ∗


1 8 1

− 0 . 0 7 6 7 ∗ ∗ ∗

− 0 . 0 7 0 5 ∗ ∗ ∗

− 0

. 0 4 5 8 ∗ ∗ ∗

− 0 . 1 0 9 7 ∗ ∗ ∗

− 0 . 0 7 0 5 ∗ ∗ ∗

− 0 . 0 8 5 3 ∗ ∗ ∗


1 6 7

− 0 . 0 6 2 6 ∗ ∗ ∗

− 0 . 0 7 6 2 ∗ ∗ ∗

− 0

. 0 1 5 8 ∗

− 0 . 0 2 4 7 ∗ ∗ ∗

− 0 . 0 7 6 2 ∗ ∗ ∗

− 0 . 0 2 0 3 ∗ ∗ ∗

S U N T R U S T B K

1 6 0

− 0 . 0 0 4 4

− 0 . 0 2 5 8 ∗ ∗ ∗

− 0

. 0 2 2 5 ∗ ∗ ∗

− 0 . 0 1 8 5 ∗ ∗ ∗

− 0 . 0 2 5 8 ∗ ∗ ∗

− 0 . 0 2 2 9 ∗ ∗ ∗


1 5 6

− 0 . 0 7 5 3 ∗ ∗ ∗

− 0 . 0 7 2 7 ∗ ∗ ∗

− 0

. 0 2 0 9 ∗ ∗ ∗

− 0 . 0 2 1 4 ∗ ∗ ∗

− 0 . 0 7 2 7 ∗ ∗ ∗

0 . 0 4 1 5 ∗ ∗ ∗

R E G I O N S B K

1 1 4

− 0 . 0 5 2 3 ∗ ∗ ∗

− 0 . 0 7 0 5 ∗ ∗ ∗

− 0

. 0 4 2 2 ∗ ∗ ∗

− 0 . 0 5 2 5 ∗ ∗ ∗

− 0 . 0 7 0 5 ∗ ∗ ∗

− 0 . 0 3 5 5 ∗ ∗ ∗


1 1 1

− 0 . 0 2 9 9 ∗ ∗ ∗

− 0 . 0 1 8 4 ∗ ∗ ∗

− 0

. 0 2 1 8 ∗ ∗ ∗

− 0 . 0 3 8 6 ∗ ∗ ∗

− 0 . 0 1 8 4 ∗ ∗ ∗

− 0 . 0 2 7 8 ∗ ∗ ∗

R B S C I T I Z E N S N A

1 0 0

0 . 0 5 3 9 ∗ ∗ ∗

− 0 . 0 5 4 6 ∗ ∗

− 0

. 0 1 5 3 ∗ ∗ ∗

− 0 . 0 3 9 5 ∗ ∗ ∗

− 0 . 0 5 4 6 ∗ ∗

− 0 . 0 1 9 4 ∗ ∗ ∗

N O R T H E R N T C

9 0

0 . 0 0 5 9

− 0 . 0 0 5 2

0

. 0 4 2 3 ∗ ∗

− 0 . 0 5 9 6 ∗ ∗ ∗

− 0 . 0 0 5 2

− 0 . 0 2 8 2 ∗ ∗ ∗

B M O H A R R I S B K N

A

8 8

− 0 . 0 0 6 6

− 0 . 0 0 0 7

− 0

. 0 2 2 2 ∗ ∗ ∗

0 . 0 1 4 0 ∗ ∗ ∗

− 0 . 0 0 0 7

− 0 . 0 2 1 7 ∗ ∗ ∗

K E Y B A N K N A

8 1

− 0 . 0 1 7 5 ∗ ∗ ∗

− 0 . 0 2 5 2 ∗ ∗ ∗

− 0

. 0 1 2 0 ∗ ∗ ∗

− 0 . 0 1 5 3 ∗ ∗ ∗

− 0 . 0 2 5 2 ∗ ∗ ∗

− 0 . 0 2 8 0 ∗ ∗ ∗

S O V E R E I G N B K N A

7 8

0 . 0 3 4 4 ∗ ∗ ∗

0 . 0 1 0 5 ∗ ∗

− 0

. 0 2 5 4 ∗ ∗ ∗

− 0 . 0 7 4 8 ∗ ∗ ∗

0 . 0 1 0 5 ∗ ∗

− 0 . 0 6 4 1 ∗ ∗ ∗

M A N U F A C T U R E R S

& T R A D E R S T C

7 7

0 . 0 0 1 6

− 0 . 0 0 2 6

− 0

. 0 2 2 8 ∗ ∗ ∗

− 0 . 0 2 3 6 ∗ ∗ ∗

− 0 . 0 0 2 6

− 0 . 0 2 6 8 ∗ ∗ ∗

D I S C O V E R B K

6 9

− 0 . 0 4 7 6 ∗ ∗ ∗

− 0 . 0 5 0 1 ∗ ∗ ∗

− 0

. 0 2 1 2

− 0 . 0 4 7 0 ∗ ∗ ∗

− 0 . 0 5 0 1 ∗ ∗ ∗

− 0 . 0 0 8 3

C O M P A S S B K

6 5

− 0 . 0 1 5 9

0 . 0 1 8 6 ∗ ∗

− 0

. 0 3 8 4 ∗ ∗ ∗

− 0 . 0 3 4 2 ∗ ∗ ∗

0 . 0 1 8 6 ∗ ∗

− 0 . 0 2 5 4 ∗ ∗ ∗

C O M E R I C A B K

6 1

− 0 . 0 3 8 1

− 0 . 0 4 3 3

− 0

. 0 3 4 7

− 0 . 0 8 0 9 ∗ ∗ ∗

− 0 . 0 4 3 3

− 0 . 0 3 6 8 ∗ ∗ ∗

B A N K O F T H E W E

S T

6 0

0 . 0 0 9 6 ∗ ∗ ∗

0 . 0 1 1 4 ∗ ∗ ∗

− 0

. 0 1 7 8 ∗ ∗ ∗

0 . 0 0 5 5 ∗ ∗ ∗

0 . 0 1 1 4 ∗ ∗ ∗

− 0 . 0 2 1 1 ∗ ∗ ∗

H U N T I N G T O N N B

5 3

− 0 . 0 1 6 8

− 0 . 0 2 9 8

− 0

. 0 3 7 6 ∗ ∗ ∗

− 0 . 0 1 1 2

− 0 . 0 2 9 8

− 0 . 0 2 7 8 ∗ ∗ ∗

D e p . V a r .

R 1

R 2

R 3

R 1

R 2

R 3

R H S V a r s .

( y , w 3 )

( y , w 3 )

( y , w 3 )

( y , w 4 )

( y , w 4 )

( y , w 4 )

N O T E : S t a t i s t i c a l s i g n i fi c a n c e ( d i ff e r e n c e f r o m 0 ) a t t h e t e n , fi

v e , o r o n e p e r c e n t l e v e l s i s d e n o t e d b y o n

e , t w o , o r t h r e e a s t e r i s k s , r e s p e c t i v e l y . S u p e r s c r i p t ( 1 ) , ( 2 ) , o r

( 3 ) i n d i c a t e ( r e s p e c t i v e l y ) δ R ( y , w ) < 0 a n d R ( δ y , w ) > 0 ; δ R ( y , w ) > 0 a n d R ( δ y , w ) < 0 ; o r δ R ( y , w ) < 0 a n d R ( δ y , w ) < 0 . S e e A p p e n d i x A f o r i n t e r p r e t a t i o n

34



T a b l e 7 : R e t u r n s t o S c a l e ( P r o fi t ) f o r L a r g e s t B a n k s b

y T o t a l A s s e t s ,

2 0 0 6 . Q

4

A s s e t s

N a m e

( b i l l i o n s o f 2 0 0 9 $ )

M o d e l 1 3

M o d e l 1 4

M o d e l 1 5

M o d e l 1 6

M o d e l 1 7

B A N K

O F A M E R N A

1 2 3 9

− 0 . 0 0 6 2

− 0 . 0 3 4 9

− 0 . 0 0 6 2

− 0 . 0 6 6 9 ∗ ∗ ∗

− 0 . 0 3 4 9


1 2 2 4

− 0 . 0 6 6 1 ∗ ∗ ∗

− 0 . 0 7 2 2 ∗

∗ ∗

− 0 . 0 6 6 1 ∗ ∗ ∗

− 0 . 0 6 8 5 ∗ ∗ ∗

− 0 . 0 7 2 2 ∗ ∗ ∗

C I T I B A N K N A

9 5 4

− 0 . 0 5 3 9 ∗ ∗ ∗

− 0 . 0 4 5 6

− 0 . 0 5 3 9 ∗ ∗ ∗

− 0 . 0 6 3 2 ∗ ∗ ∗

− 0 . 0 4 5 6

W A C H

O V I A B K N A

5 3 9

− 0 . 0 5 5 6 ∗ ∗

− 0 . 0 8 1 8 ∗

∗ ∗

− 0 . 0 5 5 6 ∗ ∗

− 0 . 0 6 5 0 ∗ ∗ ∗

− 0 . 0 8 1 8 ∗ ∗ ∗

W E L L S F A R G O B K N A

4 1 6

− 0 . 1 3 3 2 ∗

− 0 . 0 3 8 0 ∗

∗ ∗

− 0 . 1 3 3 2 ∗

− 0 . 0 6 3 5 ∗ ∗ ∗

− 0 . 0 3 8 0 ∗ ∗ ∗

U S B K

N A

2 2 6

− 0 . 0 7 2 4 ∗ ∗ ∗

− 0 . 0 3 8 9 ∗

∗ ∗

− 0 . 0 7 2 4 ∗ ∗ ∗

− 0 . 0 5 2 0 ∗ ∗ ∗

− 0 . 0 3 8 9 ∗ ∗ ∗

S U N T R U S T B K

1 9 0

− 0 . 0 1 2 3

− 0 . 0 2 8 0 ∗

∗ ∗

− 0 . 0 1 2 3

− 0 . 0 5 5 3 ∗ ∗ ∗

− 0 . 0 2 8 0 ∗ ∗ ∗

H S B C

B K U S A N A

1 7 3

− 0 . 0 0 1 8

− 0 . 0 6 0 5 ∗

∗ ∗

− 0 . 0 0 1 8

− 0 . 0 5 7 7 ∗ ∗ ∗

− 0 . 0 6 0 5 ∗ ∗ ∗

N A T I O

N A L C I T Y B K

1 4 0

− 0 . 0 6 2 0

− 0 . 0 3 5 8 ∗

∗ ∗

− 0 . 0 6 2 0

− 0 . 0 5 4 8 ∗ ∗ ∗

− 0 . 0 3 5 8 ∗ ∗ ∗

R E G I O

N S B K

1 1 5

− 0 . 0 4 5 5 ∗ ∗ ∗

− 0 . 0 4 8 3 ∗

∗ ∗

− 0 . 0 4 5 5 ∗ ∗ ∗

− 0 . 0 3 8 5 ∗ ∗ ∗

− 0 . 0 4 8 3 ∗ ∗ ∗


1 0 7

− 0 . 0 4 9 6 ∗ ∗ ∗

− 0 . 0 4 3 4 ∗

∗ ∗

− 0 . 0 4 9 6 ∗ ∗ ∗

− 0 . 0 5 2 8 ∗ ∗ ∗

− 0 . 0 4 3 4 ∗ ∗ ∗


9 7

− 0 . 0 9 5 7 ∗ ∗ ∗

− 0 . 0 8 6 0 ∗

∗ ∗

− 0 . 0 9 5 7 ∗ ∗ ∗

− 0 . 0 9 9 6

− 0 . 0 8 6 0 ∗ ∗ ∗

K E Y B A N K N A

9 4

− 0 . 0 7 4 0

0 . 0 0 3 3

− 0 . 0 7 4 0

− 0 . 0 3 7 2 ∗ ∗ ∗

0 . 0 0 3 3

P N C B

K N A

9 2

− 0 . 0 3 3 7

− 0 . 0 6 1 2 ∗

∗ ∗

− 0 . 0 3 3 7

− 0 . 0 4 5 7 ∗ ∗ ∗

− 0 . 0 6 1 2 ∗ ∗ ∗

B A N K

O F N Y

9 2

− 0 . 0 6 3 9 ∗ ∗ ∗

− 0 . 0 4 2 4 ∗

∗ ∗

− 0 . 0 6 3 9 ∗ ∗ ∗

− 0 . 0 5 1 7 ∗ ∗ ∗

− 0 . 0 4 2 4 ∗ ∗ ∗

C H A S E B K U S A N A

8 4

− 0 . 0 5 4 7 ∗ ∗ ∗

− 0 . 0 5 9 2 ∗

∗ ∗

− 0 . 0 5 4 7 ∗ ∗ ∗

− 0 . 0 2 8 5 ∗ ∗ ∗

− 0 . 0 5 9 2 ∗ ∗ ∗

C O M E

R I C A B K

6 1

− 0 . 0 9 4 9 ∗ ∗ ∗

− 0 . 0 6 2 8 ∗

∗ ∗

− 0 . 0 9 4 9 ∗ ∗ ∗

− 0 . 0 4 6 2 ∗ ∗ ∗

− 0 . 0 6 2 8 ∗ ∗ ∗

B A N K

O F T H E W E S T

5 8

− 0 . 0 5 8 5

− 0 . 0 1 2 1

− 0 . 0 5 8 5

− 0 . 0 3 0 8 ∗ ∗ ∗

− 0 . 0 1 2 1

M A N U

F A C T U R E R S & T R A D E R S T C

5 8

− 0 . 0 2 1 1 ∗ ∗ ∗

− 0 . 0 2 7 2 ∗

∗ ∗

− 0 . 0 2 1 1 ∗ ∗ ∗

− 0 . 0 3 4 6 ∗ ∗ ∗

− 0 . 0 2 7 2 ∗ ∗ ∗

F I F T H

T H I R D B K

5 8

− 0 . 0 3 9 8

− 0 . 0 2 5 2 ∗

∗ ∗

− 0 . 0 3 9 8

− 0 . 0 3 7 3 ∗ ∗ ∗

− 0 . 0 2 5 2 ∗ ∗ ∗

U N I O N

B K O F C A N A

5 4

− 0 . 0 5 3 7 ∗ ∗ ∗

− 0 . 0 2 3 0 ∗

∗ ∗

− 0 . 0 5 3 7 ∗ ∗ ∗

− 0 . 0 0 5 8 ∗ ∗ ∗

− 0 . 0 2 3 0 ∗ ∗ ∗

N O R T H E R N T C

5 2

− 0 . 0 7 0 9 ∗ ∗ ∗

− 0 . 0 0 6 3

− 0 . 0 7 0 9 ∗ ∗ ∗

− 0 . 0 4 6 3 ∗ ∗ ∗

− 0 . 0 0 6 3

F I F T H

T H I R D B K

5 1

− 0 . 0 7 0 3 ∗ ∗ ∗

− 0 . 0 4 8 6 ∗

∗ ∗

− 0 . 0 7 0 3 ∗ ∗ ∗

− 0 . 0 2 0 6 ∗ ∗ ∗

− 0 . 0 4 8 6 ∗ ∗ ∗

M & I M

A R S H A L L & I L S L E Y B K

5 0

− 0 . 0 6 3 3 ∗ ∗ ∗

− 0 . 0 8 6 0 ∗

∗ ∗

− 0 . 0 6 3 3 ∗ ∗ ∗

0 . 0 0 1 0 ∗ ∗ ∗

− 0 . 0 8 6 0 ∗ ∗ ∗


4 8

0 . 1 0 5 3 ∗ ∗ ∗

− 0 . 0 5 4 1 ∗

∗ ∗

0 . 1 0 5 3 ∗ ∗ ∗

− 0 . 0 2 2 8 ∗ ∗ ∗

− 0 . 0 5 4 1 ∗ ∗ ∗

H A R R I S N A

4 3

− 0 . 0 2 5 4

0 . 0 5 8 8 ∗

∗ ∗

− 0 . 0 2 5 4

− 0 . 0 3 8 0 ∗ ∗ ∗

0 . 0 5 8 8 ∗ ∗ ∗

D e p . V

a r .

π 1

π 2

π 3

π 4

π 5

R H S V

a r s .

( y , w 3 )

( y , w 4 )

( y , w 3 )

( y , w 3 )

( y , w 4 )



35



T

a b l e 7 : R e t u r n s t o S c a l e ( P r o fi t ) f o r L a r g e s t B a n k s b y T o t a l A s s e t s ,

2 0 0 6 . Q

4 ( c o n t i n u e d )

A s s e t s

N a m e

( b i l l i o n s o f 2 0 0 9 $ )

M o d e l 1 8

M o d e l 1

9

M o d e l 2 0

M o d e l 2 1

M o d e l 2 2

B A N K

O F A M E R N A

1 2 3 9

0 . 0 1 9 5

− 0 . 0 1 2 5 ∗

∗ ∗

− 0 . 0 6 4 2 ∗ ∗ ∗

− 0 . 0 1 5 9 ∗ ∗ ∗

− 0 . 0 1 7 5


1 2 2 4

− 0 . 1 5 9 6 ∗ ∗ ∗

− 0 . 0 2 9 2 ∗

∗ ∗

− 0 . 0 6 3 5 ∗ ∗ ∗

− 0 . 0 4 3 7 ∗ ∗ ∗

− 0 . 1 2 5 0 ∗ ∗ ∗

C I T I B A N K N A

9 5 4

− 0 . 0 9 0 6 ∗ ∗ ∗

− 0 . 0 2 2 7 ∗

∗ ∗

− 0 . 0 5 9 7 ∗ ∗ ∗

− 0 . 0 3 5 1 ∗ ∗ ∗

− 0 . 0 5 8 9 ∗ ∗ ∗

W A C H

O V I A B K N A

5 3 9

− 0 . 2 3 0 5 ∗ ∗ ∗

− 0 . 0 4 3 3 ∗

∗ ∗

− 0 . 0 6 0 7 ∗ ∗ ∗

− 0 . 0 4 6 0 ∗ ∗ ∗

− 0 . 0 2 6 9


4 1 6

− 0 . 0 3 5 0

− 0 . 0 1 4 6

− 0 . 0 5 9 3 ∗ ∗ ∗

− 0 . 0 0 8 6

− 0 . 0 1 9 7 ∗ ∗ ∗

U S B K

N A

2 2 6

− 0 . 0 6 5 4

− 0 . 0 1 3 2

− 0 . 0 4 6 7 ∗ ∗ ∗

− 0 . 0 0 8 4 ∗ ∗ ∗

− 0 . 0 5 3 2 ∗ ∗ ∗

S U N T R U S T B K

1 9 0

− 0 . 0 6 5 6 ∗ ∗ ∗

0 . 0 0 0 2

− 0 . 0 4 6 0 ∗ ∗ ∗

− 0 . 0 4 4 4 ∗ ∗ ∗

− 0 . 0 4 8 7 ∗ ∗ ∗

H S B C

B K U S A N A

1 7 3

− 0 . 2 6 4 1

− 0 . 0 0 6 7

− 0 . 0 5 5 6 ∗ ∗ ∗

− 0 . 0 2 3 6 ∗ ∗ ∗

− 0 . 0 4 8 8 ∗ ∗ ∗

N A T I O

N A L C I T Y B K

1 4 0

0 . 1 0 9 5 ∗ ∗ ∗

− 0 . 0 3 7 9 ∗

∗ ∗

− 0 . 0 4 5 1 ∗ ∗ ∗

− 0 . 0 1 0 1

0 . 0 4 6 2

R E G I O

N S B K

1 1 5

− 0 . 1 0 6 9 ∗ ∗ ∗

− 0 . 0 1 3 0 ∗

∗ ∗

− 0 . 0 4 9 6 ∗ ∗ ∗

− 0 . 0 3 8 9 ∗ ∗ ∗

− 0 . 0 6 7 8 ∗ ∗ ∗


1 0 7

0 . 0 2 0 7

− 0 . 0 4 5 4 ∗

∗ ∗

− 0 . 0 4 0 3 ∗ ∗ ∗

− 0 . 0 1 3 5 ∗ ∗ ∗

− 0 . 0 3 7 2

C O U N

T R Y W I D E B K N A

9 7

− 0 . 0 9 2 9 ∗ ∗ ∗

− 0 . 0 8 9 9 ∗

∗ ∗

− 0 . 0 9 2 4 ∗ ∗ ∗

− 0 . 0 7 0 6 ∗ ∗ ∗

− 0 . 0 8 6 6 ∗ ∗ ∗

K E Y B A N K N A

9 4

− 0 . 4 9 8 7 ∗ ∗ ∗

− 0 . 0 2 5 8 ∗

− 0 . 0 1 8 2 ∗ ∗ ∗

− 0 . 0 2 0 5

− 0 . 0 3 6 4

P N C B

K N A

9 2

− 0 . 1 7 7 1 ∗ ∗ ∗

0 . 0 1 4 5

− 0 . 0 2 6 9 ∗ ∗ ∗

− 0 . 0 3 4 9 ∗ ∗ ∗

− 0 . 0 2 7 6

B A N K

O F N Y

9 2

− 0 . 0 2 1 3 ∗ ∗ ∗

− 0 . 0 2 3 7 ∗

∗ ∗

− 0 . 0 3 5 9 ∗ ∗ ∗

− 0 . 0 1 3 9 ∗ ∗ ∗

− 0 . 0 1 7 4 ∗ ∗ ∗


8 4

− 0 . 3 4 4 1 ∗ ∗ ∗

0 . 0 2 3 8 ∗

∗ ∗

− 0 . 0 3 2 6 ∗ ∗ ∗

0 . 0 0 5 5

− 0 . 0 5 7 6 ∗ ∗ ∗

C O M E

R I C A B K

6 1

− 0 . 0 7 5 5

− 0 . 0 3 7 3 ∗

∗ ∗

− 0 . 0 3 3 5 ∗ ∗ ∗

− 0 . 0 2 9 3 ∗ ∗ ∗

− 0 . 0 4 1 6 ∗ ∗ ∗

B A N K

O F T H E W E S T

5 8

0 . 0 3 3 2 ∗ ∗

− 0 . 0 6 0 4 ∗

∗ ∗

− 0 . 0 1 7 6 ∗ ∗ ∗

− 0 . 0 1 3 4

0 . 0 2 2 6 ∗ ∗ ∗

M A N U


5 8

− 0 . 4 0 6 9

0 . 0 1 1 0 ∗

− 0 . 0 1 1 1 ∗ ∗ ∗

− 0 . 0 3 1 1 ∗ ∗ ∗

− 0 . 0 5 2 6

F I F T H

T H I R D B K

5 8

− 0 . 0 1 2 0

− 0 . 0 3 5 2 ∗

∗ ∗

− 0 . 0 2 4 6 ∗ ∗ ∗

− 0 . 0 0 3 8

− 0 . 0 0 0 2

U N I O N

B K O F C A N A

5 4

− 0 . 0 8 9 8

− 0 . 0 3 5 2 ∗

∗ ∗

− 0 . 0 1 7 8 ∗ ∗ ∗

− 0 . 0 2 4 5 ∗ ∗ ∗

− 0 . 0 4 0 5 ∗

N O R T H E R N T C

5 2

0 . 0 3 4 6 ∗ ∗

− 0 . 0 6 0 0 ∗

∗ ∗

− 0 . 0 2 9 7 ∗ ∗ ∗

− 0 . 0 2 1 4 ∗ ∗ ∗

− 0 . 0 0 8 9

F I F T H

T H I R D B K

5 1

0 . 2 7 1 0 ∗ ∗ ∗

− 0 . 0 4 0 0 ∗

∗ ∗

− 0 . 0 1 3 7 ∗ ∗ ∗

− 0 . 0 1 3 9 ∗ ∗ ∗

− 0 . 0 1 1 8

M & I M


5 0

− 0 . 1 2 2 0 ∗ ∗ ∗

− 0 . 0 0 9 7 ∗

∗ ∗

0 . 0 0 3 2 ∗ ∗ ∗

− 0 . 0 3 3 7 ∗ ∗ ∗

− 0 . 0 3 5 4 ∗ ∗ ∗


4 8

0 . 0 3 0 1

0 . 0 1 1 2

− 0 . 0 2 4 0 ∗ ∗ ∗

− 0 . 0 4 0 7 ∗ ∗ ∗

0 . 1 6 5 1 ∗ ∗ ∗

H A R R I S N A

4 3

0 . 0 0 4 7

− 0 . 0 2 5 5

− 0 . 0 2 3 2 ∗ ∗ ∗

0 . 0 3 5 1 ∗ ∗ ∗

0 . 4 1 2 2 ∗ ∗ ∗

D e p . V

a r .

π 6

π 7

π 8

π 9

π 1

0

R H S V

a r s .

( y , w 4 )

( y , w 3 )

( y , w 3 )

( y , w 4 )

( y , w

4 )



36



T a b l e 8 : R e t u r n s t o S c a l e ( P r o fi t ) f o r L a r g e s t B a n k s b

y T o t a l A s s e t s ,

2 0 1 2 . Q

4

A s s e t s

N a m e


0 0 9 $ )

M o d e l 1 3

M o d e l 1 4

M o d e l 1 5

M o d e l 1 6

M o d e l 1 7

J P M O R G A N

C H A S E B K N A

1 7 6 9

− 0 . 0 3 0 4 ∗ ∗ ∗

− 0 . 0 4 9 9 ∗ ∗ ∗

− 0 . 0 3 0 4 ∗ ∗ ∗

− 0 . 1 1 9 7 ∗ ∗ ∗

−

0 . 0 4 9 9 ∗ ∗ ∗

B A N K O F A M

E R N A

1 3 8 0

− 0 . 0 2 5 8 ∗ ∗ ∗

− 0 . 0 5 5 0 ∗ ∗ ∗

− 0 . 0 2 5 8 ∗ ∗ ∗

− 0 . 0 7 1 8 ∗ ∗ ∗

−

0 . 0 5 5 0 ∗ ∗ ∗

C I T I B A N K N

A

1 2 6 5

0 . 0 1 7 7 ∗

− 0 . 0 1 8 0

0 . 0 1 7 7 ∗

− 0 . 1 5 5 1 ∗ ∗ ∗

−

0 . 0 1 8 0

W E L L S F A R G

O B K N A

1 1 7 3

− 0 . 0 1 7 1 ∗ ∗ ∗

− 0 . 0 3 3 6 ∗ ∗ ∗

− 0 . 0 1 7 1 ∗ ∗ ∗

− 0 . 1 1 7 9 ∗ ∗ ∗

−

0 . 0 3 3 6 ∗ ∗ ∗

U S B K N A

3 2 5

− 0 . 0 1 2 1

− 0 . 0 2 7 1 ∗ ∗ ∗

− 0 . 0 1 2 1

− 0 . 0 6 5 7 ∗ ∗ ∗

−

0 . 0 2 7 1 ∗ ∗ ∗

P N C B K N A

2 7 7

− 0 . 0 2 3 8 ∗ ∗ ∗

− 0 . 0 2 1 1 ∗ ∗ ∗

− 0 . 0 2 3 8 ∗ ∗ ∗

− 0 . 0 6 3 6 ∗ ∗ ∗

−

0 . 0 2 1 1 ∗ ∗ ∗

B A N K O F N Y

M E L L O N

2 5 8

− 4 . 6 3 7 1 ( 2 )

− 1 . 3 9 6 7 ( 2 )

− 4 . 6 3 7 1 ( 2 )

− 0 . 0 4 3 1 ∗ ∗ ∗

−

1 . 3 9 6 7 ( 2 )

S T A T E S T R E

E T B & T C

1 9 8

− 0 . 3 4 1 2

− 0 . 2 6 5 7

− 0 . 3 4 1 2

− 0 . 0 5 2 0 ∗ ∗ ∗

−

0 . 2 6 5 7

T D B K N A

1 9 1

0 . 0 1 1 5 ∗

0 . 0 2 2 3 ∗ ∗ ∗

0 . 0 1 1 5 ∗

− 0 . 0 5 4 0 ∗ ∗ ∗

0 . 0 2 2 3 ∗ ∗ ∗

H S B C B K U S

A N A

1 8 1

− 0 . 0 5 1 5 ∗ ∗ ∗

− 0 . 0 8 3 5 ∗ ∗ ∗

− 0 . 0 5 1 5 ∗ ∗ ∗

− 0 . 0 5 1 2 ∗ ∗ ∗

−

0 . 0 8 3 5 ∗ ∗ ∗

B R A N C H B K

G & T C

1 6 7

− 0 . 0 7 8 2 ∗ ∗ ∗

− 0 . 0 1 5 4 ∗ ∗ ∗

− 0 . 0 7 8 2 ∗ ∗ ∗

− 0 . 0 5 4 8 ∗ ∗ ∗

−

0 . 0 1 5 4 ∗ ∗ ∗

S U N T R U S T B

K

1 6 0

− 0 . 0 4 4 3 ∗ ∗ ∗

− 0 . 0 1 6 4 ∗ ∗ ∗

− 0 . 0 4 4 3 ∗ ∗ ∗

− 0 . 0 6 3 9 ∗ ∗ ∗

−

0 . 0 1 6 4 ∗ ∗ ∗


1 5 6

− 0 . 0 8 2 3 ∗ ∗ ∗

− 0 . 0 2 5 8

− 0 . 0 8 2 3 ∗ ∗ ∗

0 . 0 8 2 2 ( 3 )

−

0 . 0 2 5 8

R E G I O N S B K

1 1 4

− 0 . 0 6 8 4 ∗ ∗ ∗

− 0 . 0 5 3 3 ∗ ∗ ∗

− 0 . 0 6 8 4 ∗ ∗ ∗

− 0 . 0 3 4 6 ∗ ∗ ∗

−

0 . 0 5 3 3 ∗ ∗ ∗


1 1 1

− 0 . 0 0 8 1

− 0 . 0 3 8 7 ∗ ∗ ∗

− 0 . 0 0 8 1

− 0 . 0 6 5 0 ∗ ∗ ∗

−

0 . 0 3 8 7 ∗ ∗ ∗

R B S C I T I Z E N

S N A

1 0 0

0 . 1 6 0 7 ∗ ∗ ∗

− 0 . 0 3 8 7

0 . 1 6 0 7 ∗ ∗ ∗

− 0 . 0 5 3 7 ∗ ∗ ∗

−

0 . 0 3 8 7

N O R T H E R N T C

9 0

− 0 . 0 0 2 9

− 0 . 0 6 3 2

− 0 . 0 0 2 9

− 0 . 0 4 3 5 ∗ ∗ ∗

−

0 . 0 6 3 2


8 8

0 . 0 0 5 9 ∗

0 . 0 1 9 6 ∗ ∗ ∗

0 . 0 0 5 9 ∗

− 0 . 0 5 5 2 ∗ ∗ ∗

0 . 0 1 9 6 ∗ ∗ ∗

K E Y B A N K N

A

8 1

− 0 . 0 1 4 5

0 . 0 0 4 1

− 0 . 0 1 4 5

− 0 . 0 5 9 2 ∗ ∗ ∗

0 . 0 0 4 1

S O V E R E I G N

B K N A

7 8

0 . 0 4 1 1 ∗ ∗ ∗

− 0 . 1 0 0 1 ∗ ∗ ∗

0 . 0 4 1 1 ∗ ∗ ∗

− 0 . 0 2 1 1 ∗ ∗ ∗

−

0 . 1 0 0 1 ∗ ∗ ∗

M A N U F A C T U


7 7

0 . 0 3 7 2 ∗ ∗ ∗

− 0 . 0 2 2 6 ∗ ∗ ∗

0 . 0 3 7 2 ∗ ∗ ∗

− 0 . 0 4 4 0 ∗ ∗ ∗

−

0 . 0 2 2 6 ∗ ∗ ∗

D I S C O V E R B

K

6 9

− 0 . 0 6 0 3 ∗ ∗ ∗

− 0 . 0 5 2 9 ∗ ∗ ∗

− 0 . 0 6 0 3 ∗ ∗ ∗

− 0 . 0 2 0 5 ∗ ∗ ∗

−

0 . 0 5 2 9 ∗ ∗ ∗

C O M P A S S B K

6 5

0 . 0 1 2 5

− 0 . 0 2 6 7 ∗ ∗ ∗

0 . 0 1 2 5

− 0 . 0 1 8 0 ∗ ∗ ∗

−

0 . 0 2 6 7 ∗ ∗ ∗

C O M E R I C A B K

6 1

− 0 . 0 3 9 7

− 0 . 0 8 3 5 ∗ ∗ ∗

− 0 . 0 3 9 7

− 0 . 0 4 3 3 ∗ ∗ ∗

−

0 . 0 8 3 5 ∗ ∗ ∗

B A N K O F T H

E W E S T

6 0

0 . 0 1 9 5 ∗ ∗ ∗

0 . 0 4 5 4 ∗ ∗ ∗

0 . 0 1 9 5 ∗ ∗ ∗

− 0 . 0 5 5 2 ∗ ∗ ∗

0 . 0 4 5 4 ∗ ∗ ∗

H U N T I N G T O

N N B

5 3

− 0 . 0 1 8 8

− 0 . 0 0 1 5

− 0 . 0 1 8 8

− 0 . 0 4 3 3 ∗ ∗ ∗

−

0 . 0 0 1 5

D e p . V a r .

π 1

π 2

π 3

π 4

π 5

R H S V a r s .

( y , w 3 )

( y , w 4 )

( y , w 3 )

( y , w 3 )

( y , w 4 )




( 3 ) i n d i c a t e ( r e s p e c t i v e l y ) δ π ( y , w ) < 0 a n d π ( δ y , w ) > 0 ; δ π ( y , w ) > 0 a n d π ( δ y , w ) < 0 ; o r δ π ( y , w ) <

0 a n d π ( δ y , w ) < 0 . S e e A p p e n d i x A f o r

i n t e r p r e t a t i o n

37



T

a b l e 8 : R e t u r n s t o S c a l e ( P r o fi t ) f o r L a r g e s t B a n k s b y T o t a l A s s e t s ,

2 0 1 2 . Q

4 ( c o n t i n u e d )

A s s e t s

N a m e


0 0 9 $ )

M o d e l 1 8

M o d e l 1 9

M o d e l 2 0

M o d e l 2 1

M o d e l 2 2

J P M O R G A N

C H A S E B K N A

1 7 6 9

0 . 1 3 9 0

− 0 . 0 0 1 1

− 0 . 0 7 0 1 ∗ ∗ ∗

− 0 . 0 3 5 5 ∗ ∗

−

0 . 0 2 0 1

B A N K O F A M

E R N A

1 3 8 0

− 0 . 1 7 3 2

0 . 0 0 8 0 ∗ ∗ ∗

− 0 . 0 6 8 8 ∗ ∗ ∗

− 0 . 0 1 7 4

0 . 0 2 5 4

C I T I B A N K N

A

1 2 6 5

− 0 . 0 9 6 2

− 0 . 0 0 5 5

− 0 . 0 7 6 6 ∗ ∗ ∗

− 0 . 0 1 2 9

−

0 . 0 0 1 7

W E L L S F A R G

O B K N A

1 1 7 3

− 0 . 2 7 3 6 ∗

0 . 0 0 0 1

− 0 . 0 6 8 2 ∗ ∗ ∗

− 0 . 0 1 3 4 ∗

−

0 . 0 6 8 2

U S B K N A

3 2 5

− 0 . 0 2 4 0 ∗ ∗ ∗

− 0 . 0 0 2 2

− 0 . 0 6 0 6 ∗ ∗ ∗

0 . 0 0 2 3 ∗

−

0 . 0 1 6 5

P N C B K N A

2 7 7

0 . 0 1 6 8 ∗ ∗

− 0 . 0 0 5 8 ∗ ∗ ∗

− 0 . 0 6 1 2 ∗ ∗ ∗

− 0 . 0 0 1 1

0 . 0 2 1 0 ∗ ∗ ∗

B A N K O F N Y

M E L L O N

2 5 8

1 . 3 9 4 7

− 0 . 0 1 0 7

− 0 . 0 3 5 7 ∗ ∗ ∗

− 0 . 0 4 3 7 ∗ ∗ ∗

−

0 . 1 0 0 8

S T A T E S T R E

E T B & T C

1 9 8

− 1 . 3 7 1 6 ( 2 )

0 . 0 2 9 1 ∗

− 0 . 0 4 0 5 ∗ ∗ ∗

− 0 . 0 3 9 0 ∗ ∗ ∗

−

0 . 1 0 4 0 ∗ ∗ ∗

T D B K N A

1 9 1

0 . 1 8 8 8 ∗ ∗ ∗

− 0 . 0 0 0 7

− 0 . 0 5 2 6 ∗ ∗ ∗

0 . 0 0 2 8

0 . 1 3 4 3 ∗ ∗ ∗

H S B C B K U S

A N A

1 8 1

− 0 . 8 3 4 1 ∗ ∗ ∗ ( 3 )

− 0 . 0 5 4 8 ∗ ∗ ∗

− 0 . 0 3 7 1 ∗ ∗ ∗

− 0 . 0 8 6 4 ∗ ∗ ∗

−

3 . 7 6 9 4 ∗ ∗ ∗ ( 2 )

B R A N C H B K

G & T C

1 6 7

− 0 . 0 0 5 1

0 . 0 0 2 0

− 0 . 0 5 2 1 ∗ ∗ ∗

− 0 . 0 1 7 1 ∗ ∗ ∗

−

0 . 0 0 6 2

S U N T R U S T B

K

1 6 0

− 0 . 0 7 0 1 ∗ ∗ ∗

− 0 . 0 2 3 4 ∗ ∗ ∗

− 0 . 0 5 9 3 ∗ ∗ ∗

− 0 . 0 0 5 8

−

0 . 0 4 2 0 ∗ ∗ ∗


1 5 6

− 0 . 0 3 0 3

− 0 . 0 2 2 8 ∗ ∗ ∗

0 . 0 8 3 6 ( 3 )

0 . 0 4 7 1 ∗ ∗ ∗

−

0 . 0 2 9 4 ∗

R E G I O N S B K

1 1 4

− 0 . 0 9 6 1

− 0 . 0 4 0 6 ∗ ∗ ∗

− 0 . 0 4 6 7 ∗ ∗ ∗

− 0 . 0 3 5 0 ∗ ∗ ∗

−

0 . 1 2 0 7


1 1 1

0 . 0 3 4 0

− 0 . 0 2 7 1 ∗ ∗ ∗

− 0 . 0 6 1 7 ∗ ∗ ∗

− 0 . 0 1 5 0 ∗ ∗ ∗

0 . 0 0 2 8

R B S C I T I Z E N

S N A

1 0 0

0 . 3 6 8 9 ∗ ∗ ∗

− 0 . 0 0 8 7

− 0 . 0 4 4 8 ∗ ∗ ∗

− 0 . 0 5 5 7 ∗ ∗ ∗

0 . 3 5 8 6 ∗ ∗ ∗

N O R T H E R N T C

9 0

− 0 . 0 4 1 2 ∗ ∗ ∗

0 . 0 1 0 1

− 0 . 0 3 3 5 ∗ ∗ ∗

− 0 . 0 4 3 4 ∗ ∗ ∗

−

0 . 0 6 0 0 ∗ ∗ ∗


8 8

0 . 4 2 7 6 ∗ ∗ ∗

− 0 . 0 5 0 8 ∗ ∗ ∗

− 0 . 0 5 0 3 ∗ ∗ ∗

− 0 . 0 2 2 0 ∗

0 . 1 2 9 3 ∗ ∗ ∗

K E Y B A N K N

A

8 1

− 0 . 0 7 4 4 ∗ ∗ ∗

− 0 . 0 1 6 6 ∗ ∗ ∗

− 0 . 0 5 3 5 ∗ ∗ ∗

− 0 . 0 1 9 1

−

0 . 0 1 9 0

S O V E R E I G N

B K N A

7 8

− 0 . 2 5 3 6 ∗ ∗ ∗

0 . 0 0 5 7

0 . 0 0 5 5 ∗ ∗ ∗

− 0 . 0 6 6 6 ∗ ∗ ∗

−

0 . 0 1 9 4

M A N U F A C T U


7 7

− 0 . 0 8 1 7 ∗ ∗ ∗

− 0 . 0 2 7 2 ∗ ∗ ∗

− 0 . 0 3 7 5 ∗ ∗ ∗

− 0 . 0 3 3 9 ∗ ∗ ∗

−

0 . 0 6 9 4 ∗ ∗ ∗

D I S C O V E R B

K

6 9

− 0 . 0 4 4 1 ∗ ∗ ∗

0 . 0 0 0 3

− 0 . 0 3 8 8 ∗ ∗ ∗

− 0 . 0 1 5 1 ∗ ∗ ∗

−

0 . 0 6 3 8 ∗ ∗ ∗

C O M P A S S B K

6 5

− 0 . 0 0 4 4

− 0 . 0 2 8 1 ∗ ∗ ∗

− 0 . 0 4 1 0 ∗ ∗ ∗

− 0 . 0 2 3 1 ∗ ∗ ∗

0 . 1 9 5 9 ∗ ∗

C O M E R I C A B K

6 1

− 0 . 0 1 7 3

− 0 . 0 2 3 4 ∗ ∗

− 0 . 0 3 1 2 ∗ ∗ ∗

− 0 . 0 5 2 3 ∗ ∗ ∗

−

0 . 2 0 0 2 ∗ ∗ ∗

B A N K O F T H

E W E S T

6 0

0 . 0 8 9 1 ∗ ∗ ∗

− 0 . 0 5 4 6 ∗ ∗ ∗

− 0 . 0 4 8 0 ∗ ∗ ∗

− 0 . 0 2 4 1

0 . 0 6 3 6 ∗ ∗ ∗

H U N T I N G T O

N N B

5 3

− 0 . 0 1 8 8

− 0 . 0 3 6 4 ∗ ∗ ∗

− 0 . 0 4 7 7 ∗ ∗ ∗

− 0 . 0 2 1 1 ∗ ∗ ∗

0 . 0 4 3 4

D e p . V a r .

π 6

π 7

π 8

π 9

π 1 0

R H S V a r s .

( y , w 4 )

( y , w 3 )

( y , w 3 )

( y , w 4 )

( y , w 4 )







38



The Evolution of Scale Economies in

U.S. Banking: Appendices B–F

David C. Wheelock Paul W. Wilson∗

August 2015

∗Wheelock: Research Department, Federal Reserve Bank of St. Louis, P.O. Box 442, St. Louis, MO 63166–

0442; [email protected]. Wilson: Department of Economics and School of Computing, Division of Com-puter Science, Clemson University, Clemson, South Carolina 29634–1309, USA; email [email protected]. Thisresearch was conducted while Wilson was a visiting scholar in the Research Department of the Federal ReserveBank of St. Louis. We thank the Cyber Infrastructure Technology Integration group at Clemson University foroperating the Palmetto cluster used for our computations. We thank Peter McCrory for research assistance.The views expressed in this paper do not necessarily reflect official positions of the Federal Reserve Bank of St. Louis or the Federal Reserve System. JEL classification nos.: G21, L11, C12, C13, C14. Keywords: banks,returns to scale, scale economies, non-parametric, regression.



Contents

B Summary Statistics for Data Used for Estimation 1

C Test of Translog Specifications 10

D Details of Non-parametric Estimation and Inference 11

D.1 Dimension reduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11D.2 Non-parametric estimation of conditional mean functions . . . . . . . . . . . . 13D.3 Practical issues for implementation . . . . . . . . . . . . . . . . . . . . . . . . 16

E Additional Results for 1984.Q4 and 1998.Q4 19

F Results Obtained while Imposing Homogeneity with Respect to Input

Prices 30

i



List of Tables

B.1 Correlation Matrices for Dependent Variables, All Periods (Part A) . . . . . . 2B.2 Correlation Matrices for Dependent Variables, All Periods (Part B) . . . . . . 3B.3 Correlation Matrices for Dependent Variables, All Periods (Part C) . . . . . . 4

B.4 Quantiles and Means for Variables used in Estimation, 1984.Q4 . . . . . . . . 5B.5 Quantiles and Means for Variables used in Estimation, 1998.Q4 . . . . . . . . 6B.6 Quantiles and Means for Variables used in Estimation, 2006.Q4 . . . . . . . . 7B.7 Quantiles and Means for Variables used in Estimation, 2012.Q4 . . . . . . . . 8B.8 Quantiles and Means for Variables used in Estimation, All Quarters . . . . . . 9E.9 Counts of Banks Facing IRS, CRS, and DRS . . . . . . . . . . . . . . . . . . . 20E.10 Quantiles and Means for Estimates of Returns to Scale Indices . . . . . . . . . 21E.11 Returns to Scale (Cost) for Largest Banks by Total Assets, 1984.Q4 . . . . . . 22E.12 Returns to Scale (Cost) for Largest Banks by Total Assets, 1998.Q4 . . . . . . 23E.13 Returns to Scale (Revenue) for Largest Banks by Total Assets, 1984.Q4 . . . . 24E.14 Returns to Scale (Revenue) for Largest Banks by Total Assets, 1998.Q4 . . . . 25

E.15 Returns to Scale (Profit) for Largest Banks by Total Assets, 1984.Q4 . . . . . 26E.15 Returns to Scale (Profit) for Largest Banks by Total Assets, 1984.Q4 (continued) 27E.16 Returns to Scale (Profit) for Largest Banks by Total Assets, 1998.Q4 . . . . . 28E.16 Returns to Scale (Profit) for Largest Banks by Total Assets, 1998.Q4 (continued) 29F.17 Counts of Banks Facing IRS, CRS, and DRS (imposing homogeneity with re-

spect to input prices) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31F.18 Counts of Banks Facing IRS, CRS, and DRS (imposing homogeneity with re-

spect to input prices) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32F.19 Quantiles and Means for Estimates of Returns to Scale Indices (imposing ho-

mogeneity with respect to input prices) . . . . . . . . . . . . . . . . . . . . . . 33

F.20 Quantiles and Means for Estimates of Returns to Scale Indices (imposing ho-mogeneity with respect to input prices) . . . . . . . . . . . . . . . . . . . . . . 34F.21 Returns to Scale (Revenue) for Largest Banks by Total Assets, 1984.Q4 (im-

posing homogeneity with respect to input prices) . . . . . . . . . . . . . . . . 35F.22 Returns to Scale (Revenue) for Largest Banks by Total Assets, 1998.Q4 (im-



posing homogeneity with respect to input prices) . . . . . . . . . . . . . . . . 38F.25 Returns to Scale (Profit) for Largest Banks by Total Assets, 1984.Q4 (imposing

homogeneity with respect to input prices) . . . . . . . . . . . . . . . . . . . . 39F.25 Returns to Scale (Profit) for Largest Banks by Total Assets, 1984.Q4 (imposing

homogeneity with respect to input prices, continued) . . . . . . . . . . . . . . 40F.26 Returns to Scale (Profit) for Largest Banks by Total Assets, 1998.Q4 (imposing

homogeneity with respect to input prices) . . . . . . . . . . . . . . . . . . . . 41

ii



F.26 Returns to Scale (Profit) for Largest Banks by Total Assets, 1998.Q4 (imposinghomogeneity with respect to input prices, continued) . . . . . . . . . . . . . . 42

F.27 Returns to Scale (Profit) for Largest Banks by Total Assets, 2006.Q4 (imposinghomogeneity with respect to input prices) . . . . . . . . . . . . . . . . . . . . 43

F.27 Returns to Scale (Profit) for Largest Banks by Total Assets, 2006.Q4 (imposing

homogeneity with respect to input prices, continued) . . . . . . . . . . . . . . 44F.28 Returns to Scale (Profit) for Largest Banks by Total Assets, 2012.Q4 (imposing

homogeneity with respect to input prices) . . . . . . . . . . . . . . . . . . . . 45F.28 Returns to Scale (Profit) for Largest Banks by Total Assets, 2012.Q4 (imposing

homogeneity with respect to input prices, continued) . . . . . . . . . . . . . . 48

iii



B Summary Statistics for Data Used for Estimation

Tables B.1–B.3 give correlations for the various dependent variables. Each table contains two

panels. The first panel in each table gives pieces of the lower-triangular part of the correlation

matrix for dependent variables used in Models 1–22. Since the revenue variables R1, R2,and R3 are used in Models 7–9 and then again in Models 10–12, the correlation matrix of

dependent variables has dimensions (19 × 19). We partition this matrix by writingA

B C

so that A is (9 × 9), B is (10 × 9), and C is (10 × 10). Then we display A in the top panel

of Table B.1, B in the top panel of Table B.2, and C in the top panel of Table B.3. The

bottom panels of Tables B.1–B.3 contain pieces of a similar correlation matrix where we have

divided the revenue and profit variables by the price of labor in order to impose homogeneity

with respect to input prices in Models 23–32 as discussed in the text.1

Tables B.4–B.7 give summary statistics for left-hand and right-hand side variables used

in Models 1-22 over the 4 quarters in which returns-to-scale are estimated (i.e., 1984.Q4,

1998.Q4, 2006.Q4, and 2012.Q4). Table B.8 gives similar summary statistics over all quarters

used for estimation (i.e., 1984.Q1–2013.Q2).

All dollar amounts have been converted to constant 2009 dollars using the quarterly, sea-

sonally adjusted, gross domestic product implicit price deflator.

1 In Table B.3, the correlations for π3, π1 and π5, π2 are shown as 1.0000 due to rounding. The correlationfor π3, π1 is 0.99999987, while the correlation for π5, π2 is 0.99999983.

1



T a b l e B . 1 : C o r r e l a t i o n M

a t r i c e s f o r D e p e n d e n t V a r i a b

l e s , A l l P e r i o d s ( P a r t A )

C 1 / W 3

C 2 / W 3

C 3 / W 3

C 4 / W 3

C 5 / W 3

C 6 / W 3

R 1

R 2

R 3

H o m o g e n e i t y w

r t p r i c e s n o t i m p o s e d o n r e v e n u e , p

r o fi t v a r i a b l e s :

C 1 / W 3

1 . 0 0 0 0

C 2 / W 3

0 . 9 9 5 2

1 . 0 0 0 0

C 3 / W 3

0 . 9 7 6 9

0 . 9 6 7 6

1 . 0 0 0 0

C 4 / W 3

0 . 9 9 9 1

0 . 9 9 1 8

0 . 9 8 0 0

1 . 0 0 0 0

C 5 / W 3

0 . 9 9 7 5

0 . 9 9 8 7

0 . 9 7 4 6

0 . 9 9 6 3

1 . 0 0 0 0

C 6 / W 3

0 . 9 7 6 8

0 . 9 6 5 9

0 . 9 9 9 6

0 . 9 8 0 9

0 . 9 7 4 2

1 . 0 0 0 0

R 1

0 . 9 6 3 5

0 . 9 5 0 0

0 . 9 7 3 4

0 . 9 6 9 2

0 . 9 6 0 2

0 . 9 7 6 0

1 . 0 0 0 0

R 2

0 . 9 6 1 5

0 . 9 4 3 5

0 . 9 7 2 2

0 . 9 6 8 2

0 . 9 5 5 1

0 . 9 7 5 4

0 . 9 9 8 8

1 . 0 0 0 0

R 3

0 . 9 2 3 2

0 . 8 9 9 4

0 . 9 4 6 4

0 . 9 3 4 0

0 . 9 1 5 9

0 . 9 5 1 9

0 . 9 6 3 5

0 . 9 6 7 7

1 . 0 0 0 0

C 1 / W 3

C 2 / W 3

C 3 / W 3

C 4 / W 3

C 5 / W 3

C 6 / W 3

R 1 / W 3

R 2 / W 3

R 3 / W 3

H o m o g e n e i t y

w r t p r i c e s i m p o s e d o n r e v e n u e , p r o

fi t v a r i a b l e s :

C 1 / W 3

1 . 0 0 0 0

C 2 / W 3

0 . 9 9 5 2

1 . 0 0 0 0

C 3 / W 3

0 . 9 7 6 9

0 . 9 6 7 6

1 . 0 0 0 0

C 4 / W 3

0 . 9 9 9 1

0 . 9 9 1 8

0 . 9 8 0 0

1 . 0 0 0 0

C 5 / W 3

0 . 9 9 7 5

0 . 9 9 8 7

0 . 9 7 4 6

0 . 9 9 6 3

1 . 0 0 0 0

C 6 / W 3

0 . 9 7 6 8

0 . 9 6 5 9

0 . 9 9 9 6

0 . 9 8 0 9

0 . 9 7 4 2

1 . 0 0 0 0

R 1 / W 3

0 . 9 6 3 5

0 . 9 5 0 0

0 . 9 7 3 4

0 . 9 6 9 2

0 . 9 6 0 2

0 . 9 7 6 0

1 . 0 0 0 0

R 2 / W 3

0 . 9 6 1 5

0 . 9 4 3 5

0 . 9 7 2 2

0 . 9 6 8 2

0 . 9 5 5 1

0 . 9 7 5 4

0 . 9 9 8 8

1 . 0 0 0 0

R 3 / W 3

0 . 9 5 9 4

0 . 9 4 1 8

0 . 9 7 7 6

0 . 9 6 6 4

0 . 9 5 3 8

0 . 9 8 0 6

0 . 9 9 0 6

0 . 9 9 1 9

1 . 0 0 0 0

2





l e s , A l l P e r i o d s ( P a r t B )

C 1 / W 3

C 2 / W 3

C 3 / W 3

C 4 / W 3

C 5 / W 3

C 6 / W 3

R 1

R 2

R 3




π 1

0 . 7 9 0 3

0 . 7 5 4 5

0 . 8 4 0 4

0 . 8 0 8 3

0 . 7 7 9 7

0 . 8 4 9 7

0 . 9 1 0 6

0 . 9 1 7 6

0 . 9 4 0 3

π 2

0 . 7 7 0 4

0 . 7 3 4 7

0 . 8 2 3 4

0 . 7 8 7 8

0 . 7 5 9 2

0 . 8 3 2 1

0 . 9 0 0 5

0 . 9 0 7 1

0 . 9 2 5 1

π 3

0 . 7 9 0 3

0 . 7 5 4 5

0 . 8 4 0 4

0 . 8 0 8 3

0 . 7 7 9 7

0 . 8 4 9 7

0 . 9 1 0 6

0 . 9 1 7 6

0 . 9 4 0 3

π 4

0 . 6 9 1 8

0 . 6 5 4 0

0 . 6 7 8 1

0 . 7 0 8 0

0 . 6 7 7 2

0 . 6 9 0 8

0 . 8 1 6 7

0 . 8 2 5 2

0 . 8 2 4 6

π 5

0 . 7 7 0 4

0 . 7 3 4 7

0 . 8 2 3 4

0 . 7 8 7 8

0 . 7 5 9 2

0 . 8 3 2 1

0 . 9 0 0 5

0 . 9 0 7 1

0 . 9 2 5 1

π 6

0 . 6 1 5 7

0 . 5 7 8 9

0 . 5 9 3 2

0 . 6 3 0 2

0 . 5 9 9 9

0 . 6 0 5 3

0 . 7 5 2 9

0 . 7 6 0 8

0 . 7 4 7 7

π 7

0 . 8 1 1 3

0 . 7 7 7 5

0 . 8 6 8 3

0 . 8 2 8 8

0 . 8 0 2 0

0 . 8 7 6 7

0 . 9 0 7 6

0 . 9 1 4 8

0 . 9 6 7 3

π 8

0 . 7 7 6 0

0 . 7 3 9 8

0 . 7 8 6 7

0 . 7 9 2 6

0 . 7 6 3 5

0 . 7 9 7 8

0 . 8 7 0 3

0 . 8 7 9 0

0 . 9 2 7 4

π 9

0 . 7 9 9 1

0 . 7 6 5 5

0 . 8 5 9 4

0 . 8 1 6 2

0 . 7 8 9 5

0 . 8 6 7 3

0 . 9 0 1 0

0 . 9 0 7 9

0 . 9 6 0 0

π 1 0

0 . 7 4 3 1

0 . 7 0 7 2

0 . 7 5 0 6

0 . 7 5 8 8

0 . 7 2 9 8

0 . 7 6 1 3

0 . 8 4 4 7

0 . 8 5 3 1

0 . 8 9 9 6

C 1 / W 3

C 2 / W 3

C 3 / W 3

C 4 / W 3

C 5 / W 3

C 6 / W 3

R 1 / W 3

R 2 / W 3

R 3 / W 3




π 1 / W 3

0 . 8 2 1 9

0 . 7 9 0 3

0 . 8 7 1 1

0 . 8 3 6 8

0 . 8 1 1 7

0 . 8 7 8 0

0 . 9 4 2 1

0 . 9 4 6 8

0 . 9 3 2 5

π 2 / W 3

0 . 7 9 5 6

0 . 7 6 4 0

0 . 8 4 8 5

0 . 8 0 9 9

0 . 7 8 4 9

0 . 8 5 4 8

0 . 9 2 6 7

0 . 9 3 1 0

0 . 9 1 4 5

π 3 / W 3

0 . 8 2 1 9

0 . 7 9 0 3

0 . 8 7 1 1

0 . 8 3 6 7

0 . 8 1 1 7

0 . 8 7 8 0

0 . 9 4 2 1

0 . 9 4 6 8

0 . 9 3 2 5

π 4 / W 3

0 . 7 0 8 7

0 . 6 7 4 6

0 . 6 8 8 2

0 . 7 2 2 2

0 . 6 9 4 5

0 . 6 9 9 3

0 . 8 3 2 5

0 . 8 3 9 0

0 . 8 0 1 4

π 5 / W 3

0 . 7 9 5 6

0 . 7 6 4 0

0 . 8 4 8 5

0 . 8 0 9 9

0 . 7 8 4 9

0 . 8 5 4 8

0 . 9 2 6 7

0 . 9 3 1 0

0 . 9 1 4 5

π 6 / W 3

0 . 6 2 1 6

0 . 5 8 8 2

0 . 5 9 3 5

0 . 6 3 3 6

0 . 6 0 6 2

0 . 6 0 4 1

0 . 7 5 8 9

0 . 7 6 4 8

0 . 7 2 0 5

π 7 / W 3

0 . 8 4 4 0

0 . 8 1 5 1

0 . 9 0 1 2

0 . 8 5 8 2

0 . 8 3 5 7

0 . 9 0 7 0

0 . 9 3 9 1

0 . 9 4 3 6

0 . 9 6 1 0

π 8 / W 3

0 . 8 0 5 5

0 . 7 7 4 2

0 . 8 1 2 1

0 . 8 1 9 1

0 . 7 9 4 2

0 . 8 2 1 2

0 . 8 9 8 5

0 . 9 0 4 6

0 . 9 1 6 7

π 9 / W 3

0 . 8 2 6 5

0 . 7 9 8 0

0 . 8 8 7 8

0 . 8 4 0 3

0 . 8 1 8 0

0 . 8 9 3 0

0 . 9 2 8 2

0 . 9 3 2 2

0 . 9 5 1 3

π 1 0 / W 3

0 . 7 6 4 7

0 . 7 3 3 8

0 . 7 6 9 0

0 . 7 7 7 5

0 . 7 5 2 7

0 . 7 7 7 7

0 . 8 6 6 4

0 . 8 7 2 1

0 . 8 8 5 8

3





l e s , A l l P e r i o d s ( P a r t C )

π 1

π 2

π 3

π 4

π 5

π 6

π 7

π 8

π 9

π 1 0




π 1

1 . 0 0 0 0

π 2

0 . 9 9 8 3

1 . 0 0 0 0

π 3

1 . 0 0 0 0

0 . 9 9 8 3

1 . 0 0 0 0

π 4

0 . 9 2 1 4

0 . 9 2 5 6

0 . 9 2 1 4

1 . 0 0 0 0

π 5

0 . 9 9 8 3

1 . 0 0 0 0

0 . 9 9 8 3

0 . 9 2 5 6

1 . 0 0 0 0

π 6

0 . 8 7 0 5

0 . 8 8 1 4

0 . 8 7 0 5

0 . 9 9 0 1

0 . 8 8 1 4

1 . 0 0 0 0

π 7

0 . 9 6 9 6

0 . 9 6 1 4

0 . 9 6 9 6

0 . 8 5 0 0

0 . 9 6 1 4

0 . 7 8 2 6

1 . 0 0 0 0

π 8

0 . 9 3 6 0

0 . 9 2 9 7

0 . 9 3 6 0

0 . 9 2 1 4

0 . 9 2 9 7

0 . 8 7 7 4

0 . 9 5 9 8

1 . 0 0 0 0

π 9

0 . 9 6 6 8

0 . 9 6 0 8

0 . 9 6 6 8

0 . 8 4 7 3

0 . 9 6 0 8

0 . 7 8 3 3

0 . 9 9 9 0

0 . 9 5 9 5

1 . 0 0 0 0

π 1 0

0 . 9 1 6 2

0 . 9 1 3 5

0 . 9 1 6 2

0 . 9 2 0 3

0 . 9 1 3 5

0 . 8 8 6 1

0 . 9 4 1 2

0 . 9 9 6 3

0 . 9 4 4 0

1 . 0 0 0 0

π 1 / W 3

π 2 / W 3

π 3 / W 3

π 4 / W 3

π 5 / W 3

π 6 / W 3

π 7 / W

3

π 8 / W 3

π 9 / W 3

π 1 0 / W 3




π 1 / W 3

1 . 0 0 0 0

π 2 / W 3

0 . 9 9 8 0

1 . 0 0 0 0

π 3 / W 3

1 . 0 0 0 0

0 . 9 9 8 0

1 . 0 0 0 0

π 4 / W 3

0 . 9 0 9 1

0 . 9 1 2 5

0 . 9 0 9 1

1 . 0 0 0 0

π 5 / W 3

0 . 9 9 8 0

1 . 0 0 0 0

0 . 9 9 8 0

0 . 9 1 2 5

1 . 0 0 0 0

π 6 / W 3

0 . 8 5 7 4

0 . 8 6 7 9

0 . 8 5 7 4

0 . 9 9 0 1

0 . 8 6 7 9

1 . 0 0 0 0

π 7 / W 3

0 . 9 6 7 4

0 . 9 5 9 1

0 . 9 6 7 4

0 . 8 2 9 1

0 . 9 5 9 1

0 . 7 6 0 7

1 . 0 0 0 0

π 8 / W 3

0 . 9 3 1 8

0 . 9 2 4 8

0 . 9 3 1 8

0 . 9 1 5 4

0 . 9 2 4 8

0 . 8 7 0 8

0 . 9 5 3 5

1 . 0 0 0 0

π 9 / W 3

0 . 9 6 4 4

0 . 9 5 8 7

0 . 9 6 4 4

0 . 8 2 5 1

0 . 9 5 8 7

0 . 7 6 0 6

0 . 9 9 8 8

0 . 9 5 2 3

1 . 0 0 0 0

π 1 0 / W 3

0 . 9 1 2 2

0 . 9 0 9 5

0 . 9 1 2 2

0 . 9 1 4 8

0 . 9 0 9 5

0 . 8 8 0 6

0 . 9 3 4 8

0 . 9 9 6 1

0 . 9 3 7 0

1 . 0 0 0 0

4



Table B.4: Quantiles and Means for Variables used in Estimation, 1984.Q4

0.01 0.25 0.50 Mean 0.75 0.99

C 1/W 3 1.4753E−01 2.7201E−01 3.8789E−01 1.7344E+00 5.9948E−01 3.1625E+00

C 2/W 3 1.3891E−01 2.5750E−01 3.6611E−01 1.6760E+00 5.6568E−01 2.9980E+00C 3/W 3 1.6414E−01 3.1352E−01 4.4680E−01 2.1578E+00 6.8755E−01 3.5346E+00C 4/W 3 1.5436E−01 2.9099E−01 4.1436E−01 1.8084E+00 6.3908E−01 3.3802E+00C 5/W 3 1.4737E−01 2.7578E−01 3.9308E−01 1.7499E+00 6.0717E−01 3.2277E+00C 6/W 3 1.7276E−01 3.3075E−01 4.7303E−01 2.2318E+00 7.2513E−01 3.7926E+00R1 −5.5969E+02 3.2642E+03 6.3516E+03 3.3952E+04 1.3055E+04 4.1765E+05R2 −3.6107E+02 3.4170E+03 6.6418E+03 3.4850E+04 1.3625E+04 4.2829E+05R3 9.7051E+02 3.9519E+03 7.3516E+03 3.7298E+04 1.4769E+04 4.5368E+05π1 −5.5997E+02 3.2637E+03 6.3513E+03 3.3950E+04 1.3054E+04 4.1765E+05π2 −5.6000E+02 3.2637E+03 6.3513E+03 3.3950E+04 1.3054E+04 4.1765E+05π3 −3.6128E+02 3.4167E+03 6.6412E+03 3.4848E+04 1.3624E+04 4.2829E+05π4 −3.6133E+02 3.4167E+03 6.6411E+03 3.4848E+04 1.3624E+04 4.2829E+05π5 −3.6131E+02 3.4167E+03 6.6411E+03 3.4848E+04 1.3624E+04 4.2829E+05π6 −3.6137E+02 3.4166E+03 6.6410E+03 3.4848E+04 1.3624E+04 4.2829E+05π7 9.7024E+02 3.9508E+03 7.3504E+03 3.7296E+04 1.4769E+04 4.5368E+05π8 9.7023E+02 3.9507E+03 7.3502E+03 3.7296E+04 1.4769E+04 4.5368E+05

π9 9.7022E+02 3.9507E+03 7.3503E+03 3.7296E+04 1.4769E+04 4.5368E+05π10 9.7021E+02 3.9506E+03 7.3501E+03 3.7296E+04 1.4769E+04 4.5368E+05

Y 1 3.7455E+02 3.2130E+03 7.4187E+03 3.3125E+04 1.6577E+04 4.6597E+05Y 2 8.4228E+02 6.3399E+03 1.3140E+04 1.1779E+05 2.8546E+04 1.1288E+06Y 3 3.1057E+02 4.7370E+03 1.1842E+04 4.8931E+04 2.7355E+04 6.4206E+05Y 4 3.1899E+03 1.4557E+04 2.8682E+04 1.2671E+05 5.8794E+04 1.6072E+06Y 5 2.2643E+01 1.8986E+02 4.1782E+02 3.9177E+03 9.8901E+02 5.3714E+04W 1 9.3977E−03 5.6699E−02 7.7288E−02 7.5205E−02 9.2481E−02 1.5823E−01W 2 3.2446E−02 6.3431E−02 7.1657E−02 7.0519E−02 7.8449E−02 1.0196E−01W 3 2.1255E+01 3.2428E+01 3.7571E+01 4.0922E+01 4.5335E+01 9.4868E+01W 4 −3.4305E−01 1.7908E−01 2.8221E−01 4.1727E−01 4.6126E−01 2.5707E+00W 1/W 3 2.0948E−04 1.3690E−03 1.9625E−03 2.0104E−03 2.5196E−03 4.8715E−03W 2/W 3 5.8753E−04 1.4694E−03 1.8526E−03 1.8967E−03 2.2342E−03 3.7292E−03W 4/W 3 −8.9881E−03 4.6347E−03 7.4355E−03 1.0581E−02 1.1830E−02 6.1803E−02X 4 4.1658E+01 4.9242E+02 1.1300E+03 5.0866E+03 2.5416E+03 6.4656E+04X 5 7.9299E+02 3.0307E+03 5.5037E+03 2.0037E+04 1.0579E+04 2.2684E+05M 0.0000E+00 0.0000E+00 0.0000E+00 2.7102E−01 1.0000E+00 1.0000E+00

ASSETS 8.6571E+03 3.4093E+04 6.4916E+04 3.2673E+05 1.3078E+05 3.9710E+06

NOTE: Dollar figures are given in thousands of constant 2009 dollars.

5




0.01 0.25 0.50 Mean 0.75 0.99

C 1/W 3 1.0031E−01 2.2067E−01 3.4480E−01 1.6601E+00 5.6565E−01 3.9495E+00

C 2/W 3 9.2536E−02 2.0195E−01 3.1428E−01 1.5992E+00 5.1679E−01 3.5619E+00C 3/W 3 1.1833E−01 2.6702E−01 4.2184E−01 2.7102E+00 6.9310E−01 4.8809E+00C 4/W 3 1.0832E−01 2.4103E−01 3.7638E−01 1.8133E+00 6.2025E−01 4.1927E+00C 5/W 3 1.0139E−01 2.2247E−01 3.4671E−01 1.7525E+00 5.7159E−01 3.9426E+00C 6/W 3 1.2588E−01 2.8615E−01 4.5314E−01 2.8635E+00 7.4706E−01 5.3423E+00R1 6.4637E+02 3.4627E+03 6.8138E+03 6.0382E+04 1.4421E+04 7.3278E+05R2 7.0567E+02 3.6606E+03 7.1761E+03 6.3553E+04 1.5238E+04 7.6927E+05R3 8.7882E+02 3.8095E+03 7.4561E+03 6.5699E+04 1.5757E+04 8.0572E+05π1 6.4512E+02 3.4615E+03 6.8091E+03 6.0381E+04 1.4420E+04 7.3278E+05π2 6.4505E+02 3.4614E+03 6.8090E+03 6.0380E+04 1.4420E+04 7.3278E+05π3 7.0489E+02 3.6598E+03 7.1724E+03 6.3552E+04 1.5238E+04 7.6927E+05π4 7.0448E+02 3.6592E+03 7.1721E+03 6.3551E+04 1.5238E+04 7.6927E+05π5 7.0470E+02 3.6597E+03 7.1721E+03 6.3552E+04 1.5238E+04 7.6927E+05π6 7.0429E+02 3.6592E+03 7.1721E+03 6.3550E+04 1.5238E+04 7.6927E+05π7 8.7786E+02 3.8093E+03 7.4515E+03 6.5697E+04 1.5756E+04 8.0572E+05π8 8.7761E+02 3.8093E+03 7.4514E+03 6.5696E+04 1.5756E+04 8.0572E+05

π9 8.7777E+02 3.8093E+03 7.4515E+03 6.5697E+04 1.5756E+04 8.0572E+05π10 8.7752E+02 3.8092E+03 7.4513E+03 6.5696E+04 1.5756E+04 8.0572E+05

Y 1 2.9711E+02 2.7127E+03 5.9972E+03 6.3257E+04 1.3760E+04 7.9181E+05Y 2 5.5746E+02 6.3489E+03 1.3170E+04 1.8373E+05 2.8121E+04 1.5275E+06Y 3 1.0997E+03 1.2541E+04 3.0227E+04 1.8047E+05 7.1920E+04 2.3691E+06Y 4 3.9651E+03 1.7733E+04 3.3973E+04 2.4679E+05 7.0737E+04 2.9501E+06Y 5 3.0080E+01 2.5328E+02 5.9120E+02 1.5717E+04 1.5575E+03 1.8338E+05W 1 1.4337E−02 4.0262E−02 4.6045E−02 4.5278E−02 5.0553E−02 8.2275E−02W 2 1.6350E−02 3.0472E−02 3.5222E−02 3.4920E−02 3.9635E−02 5.2114E−02W 3 2.8471E+01 4.1992E+01 4.8989E+01 5.2195E+01 5.8719E+01 1.0344E+02W 4 3.6919E−02 1.8492E−01 2.7207E−01 4.1691E−01 4.2666E−01 2.5663E+00W 1/W 3 2.4339E−04 7.1117E−04 9.1020E−04 9.3418E−04 1.1198E−03 1.9257E−03W 2/W 3 2.3046E−04 5.5566E−04 7.0766E−04 7.2058E−04 8.6371E−04 1.3595E−03W 4/W 3 7.1858E−04 3.7308E−03 5.6046E−03 8.1643E−03 8.5846E−03 4.9230E−02X 4 3.7750E+01 6.1491E+02 1.5553E+03 9.3334E+03 3.6444E+03 9.4311E+04X 5 1.1552E+03 4.8638E+03 9.2463E+03 5.8077E+04 1.8629E+04 6.8517E+05M 0.0000E+00 0.0000E+00 0.0000E+00 2.9076E−01 1.0000E+00 1.0000E+00

ASSETS 1.1172E+04 4.7055E+04 9.1663E+04 6.7576E+05 1.8851E+05 7.9856E+06


6




0.01 0.25 0.50 Mean 0.75 0.99

C 1/W 3 8.6396E−02 2.0656E−01 3.1948E−01 6.4617E−01 5.3673E−01 3.7101E+00

C 2/W 3 7.9125E−02 1.8777E−01 2.9070E−01 5.9345E−01 4.8822E−01 3.4231E+00C 3/W 3 1.0206E−01 2.5078E−01 3.9511E−01 8.1370E−01 6.5977E−01 4.9515E+00C 4/W 3 9.1889E−02 2.2559E−01 3.5349E−01 7.1303E−01 5.8902E−01 4.1471E+00C 5/W 3 8.5341E−02 2.0749E−01 3.2260E−01 6.6031E−01 5.3938E−01 3.8818E+00C 6/W 3 1.0911E−01 2.6958E−01 4.2740E−01 8.8056E−01 7.1181E−01 5.3798E+00R1 6.6153E+02 3.7505E+03 7.9880E+03 9.4411E+04 1.8500E+04 6.1629E+05R2 7.2479E+02 3.9516E+03 8.4242E+03 9.9782E+04 1.9620E+04 6.4828E+05R3 8.3433E+02 4.1414E+03 8.7882E+03 1.0282E+05 2.0255E+04 6.7012E+05π1 6.6127E+02 3.7504E+03 7.9846E+03 9.4410E+04 1.8500E+04 6.1629E+05π2 6.6123E+02 3.7504E+03 7.9843E+03 9.4410E+04 1.8500E+04 6.1629E+05π3 7.2439E+02 3.9513E+03 8.4241E+03 9.9781E+04 1.9620E+04 6.4828E+05π4 7.2089E+02 3.9513E+03 8.4241E+03 9.9781E+04 1.9620E+04 6.4828E+05π5 7.2433E+02 3.9513E+03 8.4241E+03 9.9781E+04 1.9620E+04 6.4828E+05π6 7.2086E+02 3.9512E+03 8.4241E+03 9.9781E+04 1.9620E+04 6.4828E+05π7 8.3216E+02 4.1412E+03 8.7876E+03 1.0282E+05 2.0254E+04 6.7012E+05π8 8.3209E+02 4.1412E+03 8.7875E+03 1.0282E+05 2.0254E+04 6.7012E+05

π9 8.3215E+02 4.1412E+03 8.7876E+03 1.0282E+05 2.0254E+04 6.7012E+05π10 8.3208E+02 4.1412E+03 8.7875E+03 1.0282E+05 2.0254E+04 6.7012E+05


ASSETS 1.2639E+04 6.0354E+04 1.2265E+05 1.3310E+06 2.7918E+05 8.7403E+06


7




0.01 0.25 0.50 Mean 0.75 0.99

C 1/W 3 4.1898E−02 1.1384E−01 1.8860E−01 7.2896E−01 3.3471E−01 2.5698E+00

C 2/W 3 3.5632E−02 9.9556E−02 1.6378E−01 6.8002E−01 2.8908E−01 2.3722E+00C 3/W 3 6.0120E−02 1.6509E−01 2.8068E−01 1.0493E+00 5.0169E−01 4.0764E+00C 4/W 3 4.7104E−02 1.3279E−01 2.2073E−01 8.4408E−01 3.9346E−01 3.0572E+00C 5/W 3 4.2093E−02 1.1947E−01 1.9642E−01 7.9514E−01 3.4926E−01 2.8172E+00C 6/W 3 6.3392E−02 1.8457E−01 3.1168E−01 1.1644E+00 5.6228E−01 4.5109E+00R1 4.4756E+02 3.0779E+03 6.2687E+03 8.6116E+04 1.3628E+04 4.6780E+05R2 5.0801E+02 3.2613E+03 6.6464E+03 9.1502E+04 1.4557E+04 5.1174E+05R3 6.5108E+02 3.4551E+03 7.0805E+03 9.8027E+04 1.5382E+04 5.0272E+05π1 4.4732E+02 3.0778E+03 6.2684E+03 8.6116E+04 1.3626E+04 4.6780E+05π2 4.4729E+02 3.0778E+03 6.2683E+03 8.6116E+04 1.3626E+04 4.6780E+05π3 5.0782E+02 3.2609E+03 6.6459E+03 9.1502E+04 1.4557E+04 5.1174E+05π4 5.0775E+02 3.2604E+03 6.6457E+03 9.1501E+04 1.4557E+04 5.1174E+05π5 5.0779E+02 3.2606E+03 6.6458E+03 9.1502E+04 1.4557E+04 5.1174E+05π6 5.0772E+02 3.2604E+03 6.6455E+03 9.1501E+04 1.4557E+04 5.1174E+05π7 6.5086E+02 3.4551E+03 7.0798E+03 9.8026E+04 1.5382E+04 5.0272E+05π8 6.5069E+02 3.4545E+03 7.0794E+03 9.8026E+04 1.5382E+04 5.0272E+05

π9 6.5081E+02 3.4550E+03 7.0796E+03 9.8026E+04 1.5382E+04 5.0272E+05π10 6.5064E+02 3.4530E+03 7.0793E+03 9.8026E+04 1.5382E+04 5.0272E+05


ASSETS 1.6598E+04 7.5074E+04 1.4920E+05 2.0362E+06 3.1477E+05 1.1115E+07


8



Table B.8: Quantiles and Means for Variables used in Estimation, All Quarters

0.01 0.25 0.50 Mean 0.75 0.99

C 1/W 3 7.3908E−02 2.1257E−01 3.3032E−01 1.6301E+00 5.3952E−01 3.5753E+00

C 2/W 3 6.4349E−02 1.9255E−01 3.0063E−01 1.5666E+00 4.9291E−01 3.2855E+00C 3/W 3 9.6489E−02 2.6325E−01 4.0689E−01 2.8348E+00 6.6474E−01 4.5194E+00C 4/W 3 8.2477E−02 2.3318E−01 3.6146E−01 1.7336E+00 5.8978E−01 3.8987E+00C 5/W 3 7.3771E−02 2.1396E−01 3.3227E−01 1.6701E+00 5.4284E−01 3.6068E+00C 6/W 3 1.0422E−01 2.8304E−01 4.3779E−01 2.9382E+00 7.1479E−01 4.8481E+00R1 5.0095E+02 3.1656E+03 6.2806E+03 4.8265E+04 1.3401E+04 5.3857E+05R2 5.6900E+02 3.3544E+03 6.6316E+03 5.0978E+04 1.4136E+04 5.6894E+05R3 8.2763E+02 3.5574E+03 6.9649E+03 5.5178E+04 1.4822E+04 6.1035E+05π1 4.9992E+02 3.1647E+03 6.2799E+03 4.8263E+04 1.3400E+04 5.3857E+05π2 4.9978E+02 3.1646E+03 6.2797E+03 4.8263E+04 1.3399E+04 5.3857E+05π3 5.6800E+02 3.3536E+03 6.6310E+03 5.0977E+04 1.4135E+04 5.6894E+05π4 5.6737E+02 3.3534E+03 6.6308E+03 5.0975E+04 1.4135E+04 5.6894E+05π5 5.6772E+02 3.3535E+03 6.6310E+03 5.0976E+04 1.4135E+04 5.6894E+05π6 5.6725E+02 3.3533E+03 6.6308E+03 5.0975E+04 1.4135E+04 5.6894E+05π7 8.2662E+02 3.5564E+03 6.9642E+03 5.5176E+04 1.4821E+04 6.1035E+05π8 8.2621E+02 3.5562E+03 6.9638E+03 5.5175E+04 1.4821E+04 6.1030E+05

π9 8.2652E+02 3.5563E+03 6.9641E+03 5.5176E+04 1.4821E+04 6.1035E+05π10 8.2619E+02 3.5561E+03 6.9638E+03 5.5175E+04 1.4821E+04 6.1030E+05


ASSETS 1.0241E+04 4.3029E+04 8.5713E+04 6.9861E+05 1.8462E+05 7.0732E+06


9



C Test of Translog Specifications

In order to provide a simple test of the translog specification for our cost, revenue, and profit

equations, we divide our data into 118 × 2 = 236 groups, where each group contains observa-

tions from the same quarter and with the same value of the holding-company dummy variableM . For observations in each of the 236 groups, we create two mutually exclusive, collectively

exhaustive subsamples containing (i) observations on banks with total assets up to the median

of total assets, and (ii) observations on banks with total assets greater than the median of

total assets (medians are over all banks within a given group). For each model m ∈ 1, 22,

we specify a translog form for the conditional mean function after omitting the time (T ) and

holding-company (M ) variables from the RHSs of the models. For each subsample in each

of 236 groups, we estimate via ordinary least squares (OLS) each of 22 models with translog

specifications. For a given model m, this yields parameter estimates βmj and corresponding

covariance matrix estimates Σmj = ( nmj

nmj−K m)(X mjX mj)−1X mjdiag( ε2

mji)X mj(X mjX mj)−1,

where j ∈ 1, 2, X mj is the (nmj × K m) matrix of RHS variables (including interaction

terms) used in the translog specification and the εmji are the OLS residuals for model m,

group j . The factor ( nmj

nmj−K m) scales up the usual White (1980) heteroskedasticity-consistent

covariance estimator as suggested by Davidson and MacKinnon (1993) to account for the fact

that squared OLS-estimated residuals tend to underestimate squares of true residuals.

Finally, for a given group, we compute the Wald statistic W = ( βm1 − βm2

)( Σm1 + Σm2)−1( βm1 − βm2) to test the null hypothesis H 0 : βm1 = βm2 versus the alternative hypoth-

esis H 1 : βm1 = βm2. Rejection of the null provides evidence against the translog specification

within a given group. The resulting p-values for the 236 × 22 = 5, 192 Wald tests range

from 10−151917.215 to 0.99999979. Only 6 out of 5,192 p-values are greater than 0.1, and the

median p-value is 10−319.918 (i.e., essentially zero). Our splitting of data into 236 cells where

observations in a given cell are from the same quarter and have the same value of the holding

company variable M allows the translog parameters to vary across quarters as well as across

holding-company membership. Even so, we find overwhelming evidence against the translogspecification.

10



D Details of Non-parametric Estimation and Inference

D.1 Dimension reduction

Non-parametric regression methods typically suffer from the well-known curse of dimension-

ality, a phenomenon that causes rates of convergence to become slower, and estimation error

to increase dramatically, as the number of continuous right-hand side variables increases (the

presence of discrete dummy variables does not affect the convergence rate of our estimator).

We use eigensystem analysis and principal components to help mitigate this problem. The

idea is to sacrifice a relatively small amount of information in the data to permit a reduction

in dimensionality that will have a large (and favorable) impact on estimation error.

We begin by applying marginal transformations to the continuous right-hand side RHS

variables in Models 1–22 listed in Section 3. The marginal transformations are chosen to yield

distributions that are approximately normal. For Y j , j ∈ 1, 2, 3, we use log(Y j). For Y 4 and

Y 5, we use log(log(Y 4)) and log(log(Y 5 + 1)). For W j/W 3, j ∈ 1, 2, 4, we use log(W j/W 3).

For X 4 we use log(X 4), and for X 5 we use log(log(X 5 + 4)). For W 1 and W 2 we use log(W 1)

and log(W 2). For W 3 we use 2(W 1/2

3 − 1), and for W 4 we use log(log(W 4 + 1)). For T we use

Φ−1(T /120), where Φ−1(·) denotes the standard normal quantile function.

For an (n × 1) vector V define the function ψ1(·) : Rn → Rn such that

ψ1(V ) ≡ (V − n−1iV ) n−1V V − n−2V iiV −1/2

(D.1)

where i denotes an (n × 1) vector of ones. The function ψ1(·) standardizes a variable by

subtracting its sample mean and then dividing by its sample standard deviation. We apply

this function to marginal transformations of the continuous RHS variables in each model.

For model j ∈ 1, . . . , 22, let K j be the number of continuous RHS variables, and let A j

be the (n × K j) matrix with columns containing the standardized, marginal transformations

of the continuous RHS variables in the given model. Let Λ j be the (K j × K j) matrix whose

columns are the eigenvectors of the correlation matrix of Pearson correlation coefficients for

pairs of columns of A j, and let λ jk be the eigenvalue corresponding to the kth eigenvector in

the kth column of Λ j, where the columns of Λ j, and their corresponding eigenvalues, have

been sorted so that λ j1 ≥ . . . ≥ λ jK j . Then let P j = A jΛ j. The matrix P j has dimensions

(n × K j), and its columns are the principal components of A j. It is well-known that principal

11



components are orthogonal. Moreover, for each k ∈ 1, 2, . . . , K j, the quantity

φ jk =

k=1 λ j

K i=1 λ ji

(D.2)

represents the proportion of the independent linear information in A j that is contained in thefirst k principal components, i.e., the first k columns of P j.

Using our data, we find φ jk = 0.5689, 0.8251, 0.8651, 0.8968, 0.9230, 0.9482, 0.9679,

0.9832, 0.9943, and 1.0000. for k = 1, . . . , 10 (respectively) for models j ∈ 1, 2. For

models j ∈ 3, 4 we find φ jk = 0.4992, 0.7594, 0.8490, 0.8858, 0.9173, 0.9434, 0.9648, 0.9829,

0.9943, and 1.0000. For models j ∈ 5, 8, 22, we find φ jk = 0.5193 0.7653, 0.8365, 0.8761,

0.9022, 0.9267, 0.9498, 0.9699, 0.9847, 0.9949, and 1.0000. For models j ∈ 6, 7, 9, 10 we

find φ jk = 0.4522 0.6966, 0.7927, 0.8592, 0.8955, 0.9214, 0.9455, 0.9652, 0.9841, 0.9950, and

1.0000. As discussed in Section 3, we use the first 6 principal components in each case, omitting

the last 4 in models 1–4, and the last 5 in models 5–22. In doing so, we sacrifice a relatively

small amount of information, while retaining 92.14 to 94.82 percent of the independent linear

information in the sample, in order to reduce the dimensionality of our estimation problem by

4 or 5 dimensions in the space of the continuous covariates. We regard this as a worthwhile

trade-off given the curse of dimensionality.

Now write model j , j ∈ 1, . . . , 22 from the list of models given in Section 3 as

Y ji = m j(X ji , M i) + εi (D.3)

where Y ji is the ith observation, i = 1, . . . , n on left-hand side (LHS) variable in model j,

X ji is the vector of ith observations on K j continuous RHS variables in model j, and M i is

the ith observation on the holding company dummy variable. Let Y j = Y ji . . . Y jn

and

define the function ψ(·) : Rn → Rn such that

ψ2(V ) := ψ1 (log(V − min(V ) + 1)) . (D.4)

Instead of estimating (D.3) directly, we estimate the model

Y+ ji = m+

j (X+ ji , M i) + ξ i (D.5)

where E (ξ i) = 0, and VAR(ξ i) = σ2(X+ ji, M i). Y+

ji is the ith element of the (n×1) vector Y+ j =

ψ2( Y ji), X+ij is the row vector containing the ith observations on ψ3(P j,·1), . . . , ψ3(P j,·6), with

12



P j,·k denoting the kth column of the principal component matrix P j and ψ3(·) : Rn → Rn

such that

ψ3(P j,·k) := P j,·k

n−1P j,·kP j,·k − n−2P j,·kiiP j,·k−1/2

. (D.6)

The transformation ψ3(P j,·k) of

P j,·k has (constant) unit variance. Moreover, all of the

transformations that have been introduced can be inverted. Hence, given estimated val-

ues M +

= m+

j (X+ j1, M 1) . . . m+

j (X+ jn, M n)

, straightforward algebra yields estimated or

predicted values Y ji = Y j1 . . . Y jn = ψ−1

2

M +

. (D.7)

As discussed below, we use a local linear estimator to estimate m+ j (X

+ ji , M i). Although

this estimator is weakly consistent, it is asymptotically biased. Moreover, even if

m+ j (X

+ ji, M i)

were unbiased , use of the nonlinear transformation in (D.7) means that Y ji obtained from

(D.7) would not, in general, be unbiased because of the linearity of the expectations operator.

Furthermore, even if an unbiased estimator of Y ji were available, plugging such an estimator

into the returns-to-scale measures E C,i, E R,i, and E π,i defined in Section 2 to obtain estimators E C,i, E R,i, and E π,i involves additional nonlinear transformations. Fortunately, any bias in the

resulting estimates E C,i, E R,i, and E π,i can be corrected while making inference about returns

to scale; as discussed below in Section D.3, we employ a bias-corrected bootstrap method

when estimating confidence intervals for our returns-to-scale measures.

D.2 Non-parametric estimation of conditional mean functions

Local polynomial estimators are discussed by Fan and Gijbels (1996), and are a generalization

of the Nadaraya-Watson (Nadaraya, 1964; Watson, 1964) kernel estimator which amounts to

fitting locally a polynomial of order p = 0. The local-linear estimator that we employ has

less bias, but no more variance than the Nadaraya-Watson estimator; see Fan and Gijbels for

explanation.

In order to motivate the local-linear estimator, suppose that the sample is split into two

sub-samples of observations according to whether M = 0 or M = 1. Conditioning on M = 0,

we can write the conditional mean function in (D.5) as m+(X+ | M = 0) while suppressing

subscripts j and i. Recall that X+ is a vector of length 6. Now consider a Taylor expansion

13



of m+(X+ | M = 0) in a neighborhood of an arbitrary point (X+0 , M = 0) so that

m+(X+ | M = 0) =m+(X+0 | M = 0) +

∂ m+(X+0 | M = 0)

∂ X+ (X+ − X+0 )

+ (X+ − X+

0 )

∂ 2m+(X+0 | M = 0)

∂ X+X+ (X+ − X+

0 ) + . . . . (D.8)

Truncating the expansion after the linear term suggests estimating the conditional mean

function at (X+0 | M = 0) by solving the locally-weighted regression problem

α0 α = argminα0,α

ni=1

Y ji − α0 − (X+

ji − X+0 )α

2K

(X+

ji − X+0 )

|H |

1(M i = 0) (D.9)

where 1(·) is the indicator function, K(·) : R6 → R1 is a piecewise continuous multivariate

kernel function satisfying . . . R6K(t) dt = 1 and K(t) = K(−t), t ∈ R6; H is an 6 × 6

symmetric matrix of bandwidths; α0 is a scalar, and α is an vector of length 6.

The solution to the least squares problem in (D.9) is α0 α =X+

ΨX+−1

X+Ψ Y, (D.10)

where Y+ = Y+ j1 . . . Y+

jn

, Ψ = diag

K

|H |−1(X+ ji − X+

0 )1(M i = 0)

, and X+ is an

(n × 7) matrix with ith row given by

1 (X+ ji − X+

0 )

. The fitted value α0 provides an

estimate

m+(X+

0 | M = 0) of the conditional mean function m+(X+0 | M = 0) at an arbitrary

point (X+

0 | M = 0).2

The weighted least-squares solution in (D.10) amounts to a kernel-weighted least-squares

regression of Y+ on X+ using the sub-sample of observations where M = 0. Of course,

one can repeat the exercise outlined here to condition on M = 1 by simply changing the

argument to the indicator function in (D.9) from M i = 0 to M i = 1. In other words, the

analysis so far amounts to splitting the sample into two sub-samples according to whether

2 The fitted values in α provide estimates of elements of the vector ∂ m+(X0)/∂ X. However, if the objectis to estimate first derivatives, mean-square error of the estimates can be reduced by locally fitting a quadraticrather than a linear expression (see Fan and Gijbels, 1996 for discussion); this increases computational costs,

which are already substantial for the local linear fit. Moreover, determining the optimal bandwidths becomesmore difficult and computationally more burdensome for estimation of derivatives. See Hardle (1990, pp. 160–162) for discussion of some of the issues that are involved with bandwidth selection for derivative estimation.Note an arbitrary point of interest X0 in the space of the untransformed, continuous RHS variables in (D.3)corresponds to X+

0 in the transformed data space obtained by applying the same marginal transformations usedto obtain Aj to the elements of X0, post-multiplying the result by Λj , and then applying the transformationψ3(·) in (D.6) to the first 6 elements of the product while dropping the remaining elements.

14



M = 0 or M = 1, and then analyzing each group separately and independently. However,

this approach does not make efficient use of the data because each sub-sample may contain

some information that would be useful for estimation on the other sub-sample. In addition,

splitting into sub-samples reduces sample sizes, thereby increasing mean-square error of our

estimates. The local linear estimator can be adapted to allow smoothing across the two sub-

samples (thereby using all of the available data for estimation) by modifying the weights in

the weighting matrix Ψ introduced in (D.10) and then letting the data determine how much

smoothing is appropriate. Aitchison and Aitken (1976) discuss the use of a discrete kernel

for discrimination analysis. Bierens (1987) and Delgado and Mora (1995) suggest augmenting

the Nadaraya-Watson estimator with a discrete kernel, and prove that the estimator remains

consistent and asymptotically normal. Racine and Li (2004) establish convergence rates for the

Nadaraya-Watson estimator with mixed continuous-discrete data, and Li and Racine (2004)extend these results to the local-linear estimator. The good news is that the convergence rate

with both continuous and discrete covariates is the same as the rate with the same number

of continuous variables, but no discrete variables; i.e., adding discrete covariates to the RHS

does not reduce the convergence rate.

In order to remove conditioning on the discrete dummy variable, define the discrete kernel

function

G (M i | M 0, h1) = h1−|M i−M 0|1 (1 − h1)|M i−M 0| (D.11)

where h1 ∈ [ 12 , 1] is a bandwidth parameter.

Note that limh1→1

G (M i | M 0, h1) equals either 1 or 0, depending on whether M i = M 0 or

M i = M 0, respectively. In this case, estimation yields the same results as would be obtained if

estimation was performed separately on each of the two sub-samples delineated by the dummy

variable. Alternatively, limh1→1/2

G (M i | M 0, h1) = 1 regardless of whether M i = M 0 or M i = M 0;

in this case, there is complete smoothing over the two categories, and including the dummy

variable has no effect relative to the case where it is ignored.

We specify the kernel function K(·) : R

→ R

1

+ as an -variate, spherically symmetricEpanechnikov kernel with a single, scalar bandwidth h0; i.e.,

K(t) = ( + 2)

2S (1 − tt)1(tt ≤ 1) (D.12)

where 1(·) again represents the indicator function, S = 2π/2/Γ(/2), and Γ(·) denotes the

15



gamma function (recall that for each of the transformed models represented by (D.5), = 6).

The spherically symmetric Epanechnikov kernel is optimal in terms of asymptotic minimax

risk; see Fan et al. (1997) for details and a proof.

Let D = 0, 1. Then an estimate m+

X+0 , M 0 of the conditional mean function in (D.5)

at an arbitrary point X+0 , M 0 ∈ R

6 × D is given by α0 obtained from

α0 α = argminα0,α

ni=1

Y ji − α0 − (X+

ji − X+0 )α

2K

(X+

ji − X+0 )

|H |

G (M i | M 0, h1)

(D.13)

where M 0 ∈ D. The solution to the least-squares problem in (D.13) is given by

α0

α

=X+

ΩX+−1

X+Ω Y, (D.14)

where X

+

is defined as in (D.10) and the (n × n) matrix Ω of weights is given by

Ω = diag

K

(X+

ji − X+0 )

|H |

G (M i | M 0, h1)

. (D.15)

Finally, recall that the principal components transformation pre-whitens the data; in ad-

dition, the principal components are orthogonal. Orthogonality suggests setting off-diagonal

elements to zero. The transformation in (D.6) ensures that the columns of X+ have con-

stant, unit variance, suggesting use of the same bandwidth in each direction. Hence we set

H = diag h(X+0 ) so that |H | = h(X+

0 ), = 6 and h(X+0 ) is an adaptive, scalar-valued

bandwidth depending on the point (X+0 ) in the space of the continuous, transformed RHS

variables where the conditional mean function is to be evaluated.

D.3 Practical issues for implementation

To implement our estimator, we must choose values for the bandwidths h(X+0 ) and h1. For

the discrete variables, we employ a (globally) constant bandwidth, while for the continuous

variables we use an adaptive, nearest-neighbor bandwidth. We define h(X+0 ) for any particular

point X+0 ∈ R

as the maximum Euclidean distance between X+0 and the κ nearest points

in the observed sample X+ ji

ni=1, κ ∈ 2, 3, 4, . . .. Thus, given the data and the point

X+0 , the bandwidth h(X+

0 ) is determined by κ, and varies depending on the density of the

continuous explanatory variables locally around the point X+0 ∈ R

at which the conditional

mean function is estimated. This results in a bandwidth that is increasing with decreasing

16



density of the data around the point of interest, X+0 . More smoothing is required where data

are sparse than where data are dense; our nearest-neighbor bandwidth adapts automatically

to the density of the data. The discrete kernels in (D.15) in turn give more (or less) weight

to observations among the κ nearest neighbors that are close (or far) away along the time

dimension, or that are in the same (or different) category determined by the combination of

binary dummy variables.

Note that we use a nearest-neighbor bandwidth rather than a nearest-neighbor estimator .

The bandwidth is used inside a kernel function, and the kernel function integrates to unity.

Loftsgaarden and Quesenberry (1965) use this approach in the density estimation context to

avoid nearest-neighbor density estimates (as opposed to bandwidths) that do not integrate to

unity (see Pagan and Ullah, 1999, pp. 11-12 for additional discussion). Fan and Gijbels (1994;

1996, pp. 151–152) discuss nearest-neighbor bandwidths in the regression context.As a practical matter, we set for models j ∈ 1, . . . , 22 κ = [ωn], where ω ∈ (0, 1), n

represents the sample size, and [a] denotes the integer part of a (here, we suppress subscripts

j on κ and ω). We optimize the choice of values for the bandwidth parameters for each model

j by minimizing a least-squares cross-validation function; i.e., we select values ω h1

= argmin

ω,h1

ni=1

Y+ ji − m+

j,−i(X+ ji, M i)

2, (D.16)

where m+ j,−i(X

+ ji , M i) is computed the same way as m

+ j j (X+

ji , M i), except that the ith diagonal

element of the weighting matrix Ω is replaced with zero. The least-squares cross validation

function approximates the part of mean integrated square error that depends on the band-

widths.3

Once appropriate values of the bandwidth parameters have been selected, the conditional

mean function can be estimated at any point (X+0 , M 0) ∈ R

× D. We then estimate the

returns-to-scale measures defined in the text by replacing the cost terms with estimates ob-

tained from the relation (D.7). To make inferences about returns to scale, we use the wild

3

Choice of κ by cross validation has been proposed by Fan and Gijbels (1996) and has been used byWheelock and Wilson (2001, 2001, 2011, and 2012), Wilson and Carey (2004), and others. Time requiredto compute the cross validation function once is of order O(n2), and it must be computed many times inorder to find optimal values of the bandwidths. With more than one million observations, this presents aformidable computational burden. However, the problem is trivially parallel; using n p CPUs, the computationtime required for each evaluation of the cross-validation function is only slightly more than 1/n p times thetime that would be required on a single processor. We performed all computations on the Palmetto clusteroperated by Clemson University’s Cyber Infrastructure Technology Integration (CITI) group.

17



bootstrap proposed by Hardle (1990) and Hardle and Mammen (1993).4 After B replications,

we obtain a set bootstrap estimates m∗

j,b(·)Bb=1

, which we substitute into the definitions of

the returns-to-scale measures given in the text. Letting S denote the relevant returns-to-scale

measure, we have the original estimate S and the bootstrap estimates S bB

b=1

. to obtain

bootstrap values S ∗b and E ∗b for particular values of X+ and M , with b = 1, . . . , B.

To make inference about S , we use the bias-correction method described by Efron and

Tibshirani (1993). In particular, we estimate (1 − α) × 100-percent confidence intervals by S ∗(α1), S ∗(α2)

, where S ∗(α) denotes the α-quantile of the bootstrap values S ∗b , b = 1, . . . , B,

and

α1 = Φ

ϕ0 + ϕ0 + ϕ(α/2)

1 −

ϕ0 + ϕ(α/2)

, (D.17)

α2 = Φ ϕ0 + ϕ0 + ϕ(1−α/2)

1 − ϕ0 + ϕ(1−α/2) , (D.18)

Φ(·) denotes the standard normal distribution function, ϕ(α) is the (α × 100)-th percentile of

the standard normal distribution, and

ϕ0 = Φ−1

# S ∗b < S

B

, (D.19)

with Φ−1(·) denoting the standard normal quantile function (e.g., Φ−1(0.95) ≈ 1.6449).

4 Ordinary bootstrap methods are inconsistent in our context due to the asymptotic bias of the estimator;see Mammen (1992) for additional discussion.

18



E Additional Results for 1984.Q4 and 1998.Q4

Tables E.9–E.16 show estimates for 1984.Q4 and 1998.Q4, similar to Tables 1–8 in the paper,

with revenue and profit functions estimated without imposing homogeneity with respect to

input prices.

19



Table E.9: Counts of Banks Facing IRS, CRS, and DRS

.1 signif. .05 signif. .01 signif.

Model LHS Period IRS CRS DRS IRS CRS DRS IRS CRS DRS1 C 1/W 3 1984.Q4 11277 1510 9 10597 2191 8 8990 3801 5

1998.Q4 7388 754 16 7107 1039 12 6362 1787 9

2 C 2/W 3 1984.Q4 10932 1854 10 10175 2613 8 8461 4328 71998.Q4 7059 1075 24 6674 1461 23 5814 2327 17

3 C 3/W 3 1984.Q4 10780 2000 16 10020 2762 14 8259 4526 111998.Q4 7061 1073 24 6638 1500 20 5834 2307 17

4 C 4/W 3 1984.Q4 11075 1217 6 10414 1878 6 8911 3384 31998.Q4 6899 1193 5 6433 1660 4 5459 2635 3

5 C 5/W 3 1984.Q4 11130 1162 6 10458 1836 4 8954 3341 31998.Q4 6909 1182 6 6471 1621 5 5433 2661 3

6 C 6/W 3 1984.Q4 11453 842 3 10974 1321 3 9646 2649 31998.Q4 7005 1086 6 6567 1525 5 5602 2491 4

7 R1 1984.Q4 257 7256 5283 154 7805 4837 69 8467 4260

1998.Q4 204 4395 3559 125 4844 3189 59 5341 27588 R2 1984.Q4 386 7948 4462 242 8518 4036 96 9176 3524

1998.Q4 262 4939 2957 156 5391 2611 59 5842 2257

9 R3 1984.Q4 50 3098 9648 36 3443 9317 17 3842 89371998.Q4 78 3167 4913 50 3492 4616 31 3908 4219

10 R1 1984.Q4 649 8224 3425 406 8817 3075 202 9403 26931998.Q4 465 5654 1978 282 6114 1701 112 6587 1398

11 R2 1984.Q4 386 7948 4462 242 8518 4036 96 9176 35241998.Q4 262 4939 2957 156 5391 2611 59 5842 2257

12 R3 1984.Q4 82 2775 9441 62 3108 9128 47 3497 87541998.Q4 95 4311 3691 56 4724 3317 24 5249 2824

13 π1 1984.Q4 1484 10573 739 868 11340 588 284 12077 4351998.Q4 955 6307 896 607 6810 741 239 7350 569

14 π2 1984.Q4 2605 9297 396 1632 10345 321 647 11412 239

1998.Q4 1458 5988 651 947 6605 545 407 7259 431

15 π3 1984.Q4 1483 10571 742 866 11343 587 285 12077 4341998.Q4 953 6308 897 607 6811 740 238 7350 570

16 π4 1984.Q4 2443 2858 7495 2234 3312 7250 1964 3969 68631998.Q4 1336 632 6190 1290 719 6149 1200 907 6051

17 π5 1984.Q4 2602 9298 398 1628 10349 321 647 11411 2401998.Q4 1459 5989 649 946 6605 546 405 7260 432

18 π6 1984.Q4 4749 5881 1668 4080 6640 1578 3050 7759 14891998.Q4 2998 3672 1427 2594 4147 1356 2005 4812 1280

19 π7 1984.Q4 627 8989 3180 405 9694 2697 214 10528 20541998.Q4 641 5500 2017 438 5994 1726 210 6569 1379

20 π8 1984.Q4 1721 2247 8828 1565 2585 8646 1321 3117 83581998.Q4 1090 823 6245 1031 919 6208 938 1105 6115

21 π9 1984.Q4 1605 8938 1755 1098 9715 1485 560 10593 1145

1998.Q4 1472 5580 1045 1024 6166 907 505 6852 740

22 π10 1984.Q4 3507 7488 1303 2734 8406 1158 1661 9642 9951998.Q4 2567 4571 959 2049 5195 853 1290 6070 737

20



Table E.10: Quantiles and Means for Estimates of Returns to Scale Indices


1 C 1/W 3 1984.Q4 −0.0271 0.0156 0.0289 0.0287 0.0421 0.08091998.Q4 −0.0310 0.0182 0.0327 0.0327 0.0475 0.0925

2 C 2/W 3 1984.Q4 −0.0334 0.0143 0.0286 0.0283 0.0427 0.08571998.Q4 −0.0452 0.0162 0.0332 0.0328 0.0500 0.1031

3 C 3/W 3 1984.Q4 −0.0349 0.0145 0.0294 0.0293 0.0446 0.09071998.Q4 −0.0382 0.0162 0.0330 0.0329 0.0495 0.0999

4 C 4/W 3 1984.Q4 −0.0183 0.0140 0.0240 0.0239 0.0341 0.06251998.Q4 −0.0247 0.0117 0.0237 0.0236 0.0359 0.0709

5 C 5/W 3 1984.Q4 −0.0196 0.0146 0.0248 0.0245 0.0350 0.06361998.Q4 −0.0272 0.0119 0.0251 0.0247 0.0375 0.0743

6 C 6/W 3 1984.Q4 −0.0134 0.0149 0.0237 0.0236 0.0324 0.05751998.Q4 −0.0255 0.0114 0.0232 0.0228 0.0342 0.0669

7 R1 1984.Q4 −0.1126 −0.0457 −0.0304 −0.0283 −0.0138 0.0775

1998.Q4 −0.0965 −0.0458 −0.0306 −0.0288 −0.0137 0.05448 R2 1984.Q4 −0.1278 −0.0469 −0.0297 −0.0244 −0.0109 0.1053

1998.Q4 −0.1069 −0.0478 −0.0296 −0.0284 −0.0110 0.0653

9 R3 1984.Q4 −0.0653 −0.0379 −0.0289 −0.0289 −0.0200 0.01131998.Q4 −0.0773 −0.0421 −0.0296 −0.0293 −0.0173 0.0237

10 R1 1984.Q4 −0.0888 −0.0320 −0.0187 −0.0143 −0.0038 0.09121998.Q4 −0.0797 −0.0338 −0.0184 −0.0167 −0.0023 0.0673

11 R2 1984.Q4 −0.1278 −0.0469 −0.0297 −0.0244 −0.0109 0.10531998.Q4 −0.1069 −0.0478 −0.0296 −0.0284 −0.0110 0.0653

12 R3 1984.Q4 −0.0425 −0.0264 −0.0209 −0.0202 −0.0148 0.01021998.Q4 −0.0554 −0.0276 −0.0187 −0.0185 −0.0098 0.0214

13 π1 1984.Q4 −0.7907 −0.0719 −0.0231 0.0116 0.0314 1.47321998.Q4 −0.1830 −0.0543 −0.0223 −0.0068 0.0122 0.3213

14 π2 1984.Q4 −0.7628 −0.0531 −0.0057 0.1075 0.0575 1.9141

1998.Q4 −0.1521 −0.0383 −0.0112 0.0141 0.0213 0.399815 π3 1984.Q4 −0.7907 −0.0719 −0.0231 0.0114 0.0314 1.4758

1998.Q4 −0.1830 −0.0543 −0.0223 0.0113 0.0122 0.3213

16 π4 1984.Q4 −0.0605 −0.0374 −0.0258 0.0760 −0.0094 0.97281998.Q4 −0.0487 −0.0286 −0.0214 0.0134 −0.0105 0.5455

17 π5 1984.Q4 −0.7632 −0.0532 −0.0057 0.1075 0.0575 1.91411998.Q4 −0.1521 −0.0383 −0.0112 0.0140 0.0213 0.3998

18 π6 1984.Q4 −4.8781 −0.1514 0.0272 0.5782 0.2961 8.30371998.Q4 −1.3999 −0.0992 0.0025 0.0009 0.1524 4.1224

19 π7 1984.Q4 −0.0845 −0.0394 −0.0236 −0.0191 −0.0063 0.08961998.Q4 −0.0900 −0.0406 −0.0222 −0.0173 −0.0016 0.0999

20 π8 1984.Q4 −0.0489 −0.0283 −0.0202 0.0205 −0.0092 0.36171998.Q4 −0.0500 −0.0280 −0.0200 0.0080 −0.0093 0.2837

21 π9 1984.Q4 −0.1036 −0.0363 −0.0161 0.0080 0.0074 0.3237

1998.Q4 −0.1015 −0.0334 −0.0111 −0.0001 0.0145 0.193722 π10 1984.Q4 −0.5501 −0.0661 −0.0055 0.1772 0.0782 2.5363

1998.Q4 −0.3338 −0.0614 −0.0012 0.2082 0.0777 1.4071

21



T a b l e E . 1 1 : R e t u r n s t o S

c a l e ( C o s t ) f o r L a r g e s t B a n k s


1 9 8 4 . Q

4

A s s e t

s

N a m e

( b i l l i o n s o f

2 0 0 9 $ )

M o d e l 1

M o d e l 2

M o d e l 3

M o d e l 4

M o d e l 5

M o d e l 6

C I T I B A N K N A

2 0 7

0 . 0 2 5 9 ∗ ∗ ∗

0 . 0 2 5 4 ∗ ∗ ∗

0 . 0 2 1 6 ∗ ∗ ∗

0 . 0 2 3 6 ∗ ∗ ∗

0 . 0 2 7 5 ∗ ∗ ∗

0 . 0 2 8 4 ∗ ∗ ∗

B A N K O F A M

E R N T & S A

1 8 8

0 . 0 1 4 3 ∗ ∗ ∗

0 . 0 1 2 9 ∗ ∗ ∗

0 . 0 2 1 5 ∗ ∗ ∗

0 . 0 0 8 4 ∗ ∗ ∗

0 . 0 0 5 8 ∗ ∗ ∗

0 . 0 1 3 9 ∗ ∗ ∗

C H A S E M A N H A T T A N B K N A

1 4 3

0 . 0 2 3 9 ∗ ∗ ∗

0 . 0 2 3 9 ∗ ∗ ∗

0 . 0 2 2 7 ∗ ∗ ∗

0 . 0 1 8 2 ∗ ∗ ∗

0 . 0 1 8 0 ∗ ∗ ∗

0 . 0 1 9 8 ∗ ∗ ∗

M O R G A N G U

A R A N T Y T C

1 1 1

− 0 . 0 2 3 4

− 0 . 0 2 9 2

−

0 . 0 3 2 1

0 . 0 1 2 2 ∗ ∗ ∗

0 . 0 0 8 7 ∗ ∗ ∗

0 . 0 0 9 5 ∗ ∗ ∗

M A N U F A C T U

R E R S H A N T C

1 0 8

0 . 0 1 8 5 ∗ ∗ ∗

0 . 0 1 7 9 ∗ ∗ ∗

0 . 0 2 0 4 ∗ ∗ ∗

0 . 0 1 8 2 ∗ ∗ ∗

0 . 0 1 8 2 ∗ ∗ ∗

0 . 0 2 0 4 ∗ ∗ ∗

C H E M I C A L B

K

9 3

0 . 0 2 6 6 ∗ ∗ ∗

0 . 0 2 6 4 ∗ ∗ ∗

0 . 0 2 5 4 ∗ ∗ ∗

0 . 0 1 9 0 ∗ ∗ ∗

0 . 0 1 8 0 ∗ ∗ ∗

0 . 0 1 8 3 ∗ ∗ ∗

B A N K E R S T C

7 8

0 . 0 0 9 3 ∗ ∗ ∗

0 . 0 0 7 0 ∗ ∗ ∗

0 . 0 0 4 5 ∗ ∗ ∗

0 . 0 2 7 8 ∗ ∗ ∗

0 . 0 3 1 1 ∗ ∗ ∗

0 . 0 2 6 6 ∗ ∗ ∗

S E C U R I T Y P A C I F I C N B

6 9

0 . 0 1 7 7 ∗ ∗ ∗

0 . 0 1 4 3 ∗ ∗ ∗

0 . 0 2 0 8 ∗ ∗ ∗

0 . 0 1 3 0 ∗ ∗ ∗

0 . 0 1 0 8 ∗ ∗ ∗

0 . 0 1 5 2 ∗ ∗ ∗

F I R S T N B O F

C H I C A G O

6 3

0 . 0 1 0 6 ∗ ∗ ∗

0 . 0 0 8 4 ∗ ∗ ∗

0 . 0 1 0 8 ∗ ∗ ∗

0 . 0 1 0 9 ∗ ∗ ∗

0 . 0 1 0 3 ∗ ∗ ∗

0 . 0 1 3 3 ∗ ∗ ∗

C O N T I N E N T A L I L N B & T C C H I C A G O

5 4

0 . 0 3 2 6 ∗ ∗ ∗

0 . 0 3 1 3 ∗ ∗ ∗

0 . 0 3 1 8 ∗ ∗ ∗

0 . 0 1 3 2 ∗ ∗ ∗

0 . 0 1 5 6 ∗ ∗ ∗

0 . 0 1 7 9 ∗ ∗ ∗

M E L L O N B K

N A

4 2

0 . 0 2 2 3 ∗ ∗ ∗

0 . 0 2 1 2 ∗ ∗ ∗

0 . 0 2 1 9 ∗ ∗ ∗

0 . 0 1 3 6 ∗ ∗ ∗

0 . 0 1 0 4 ∗ ∗ ∗

0 . 0 1 2 6 ∗ ∗ ∗

W E L L S F A R G

O B K N A

4 2

0 . 0 1 9 8 ∗ ∗ ∗

0 . 0 2 0 7 ∗ ∗ ∗

0 . 0 2 3 8 ∗ ∗ ∗

0 . 0 2 4 1 ∗ ∗ ∗

0 . 0 2 1 8 ∗ ∗ ∗

0 . 0 3 0 2 ∗ ∗ ∗

M A R I N E M I D

L A N D B K N A

3 9

0 . 0 0 7 8 ∗ ∗ ∗

0 . 0 0 2 5 ∗ ∗

0 . 0 1 9 5 ∗ ∗ ∗

0 . 0 1 2 3 ∗ ∗ ∗

0 . 0 0 9 8 ∗ ∗ ∗

0 . 0 1 6 9 ∗ ∗ ∗

C R O C K E R N B

3 9

0 . 0 2 5 2 ∗ ∗ ∗

0 . 0 2 5 9 ∗ ∗ ∗

0 . 0 2 9 8 ∗ ∗ ∗

0 . 0 4 9 0 ∗ ∗ ∗

0 . 0 4 9 8 ∗ ∗ ∗

0 . 0 4 5 1 ∗ ∗ ∗

F I R S T I N T R S

T B K O F C A

3 6

0 . 0 1 1 3 ∗ ∗ ∗

0 . 0 0 9 2 ∗ ∗ ∗

0 . 0 1 5 4 ∗ ∗ ∗

0 . 0 3 1 8 ∗ ∗ ∗

0 . 0 3 3 1 ∗ ∗ ∗

0 . 0 2 9 9 ∗ ∗ ∗

F I R S T N B O F

B O S T O N

3 2

0 . 0 1 8 6 ∗ ∗ ∗

0 . 0 1 6 9 ∗ ∗ ∗

0 . 0 2 1 8 ∗ ∗ ∗

0 . 0 2 0 9 ∗ ∗ ∗

0 . 0 1 9 1 ∗ ∗ ∗

0 . 0 2 1 2 ∗ ∗ ∗

I R V I N G T C

3 1

0 . 0 3 7 6 ∗ ∗ ∗

0 . 0 3 8 7 ∗ ∗ ∗

0 . 0 4 6 4 ∗ ∗ ∗

0 . 0 1 2 7 ∗ ∗ ∗

0 . 0 1 0 3 ∗ ∗ ∗

0 . 0 1 4 3 ∗ ∗ ∗

R E P U B L I C B A

N K D A L L A S N A

2 5

0 . 0 1 3 4 ∗ ∗ ∗

0 . 0 1 4 1 ∗ ∗ ∗

0 . 0 1 2 1 ∗ ∗ ∗

0 . 0 0 8 9 ∗ ∗ ∗

0 . 0 0 7 9 ∗ ∗ ∗

0 . 0 1 0 0 ∗ ∗ ∗

B A N K O F N Y

2 5

0 . 0 2 0 0 ∗ ∗ ∗

0 . 0 2 0 6 ∗ ∗ ∗

0 . 0 2 1 9 ∗ ∗ ∗

0 . 0 2 1 4 ∗ ∗ ∗

0 . 0 1 9 9 ∗ ∗ ∗

0 . 0 2 5 3 ∗ ∗ ∗

N A T I O N A L B

K O F D E T R O I T

2 1

0 . 0 3 9 7 ∗ ∗ ∗

0 . 0 4 2 1 ∗ ∗ ∗

0 . 0 3 7 1 ∗ ∗ ∗

0 . 0 1 2 8 ∗ ∗ ∗

0 . 0 1 2 1 ∗ ∗ ∗

0 . 0 1 6 6 ∗ ∗ ∗

T E X A S C O M M E R C E B K N A

2 1

0 . 0 2 5 4 ∗ ∗ ∗

0 . 0 2 4 8 ∗ ∗ ∗

0 . 0 4 0 7 ∗ ∗ ∗

0 . 0 3 8 3 ∗ ∗ ∗

0 . 0 3 7 9 ∗ ∗ ∗

0 . 0 4 0 3 ∗ ∗ ∗

R E P U B L I C N B O F N Y

2 0

0 . 0 2 8 7 ∗ ∗ ∗

0 . 0 2 9 8 ∗ ∗ ∗

0 . 0 2 6 6 ∗ ∗ ∗

0 . 0 3 0 8 ∗ ∗ ∗

0 . 0 2 4 7 ∗ ∗ ∗

0 . 0 2 7 3 ∗ ∗ ∗

I N T E R F I R S T

B K D A L L A S N A

1 8

0 . 0 2 8 9 ∗ ∗ ∗

0 . 0 2 7 6 ∗ ∗ ∗

0 . 0 1 7 6 ∗ ∗ ∗

0 . 0 1 6 0 ∗ ∗ ∗

0 . 0 1 2 9 ∗ ∗ ∗

0 . 0 2 2 5 ∗ ∗ ∗

N C N B N B O F

N C

1 7

0 . 0 2 1 3 ∗ ∗ ∗

0 . 0 1 9 7 ∗ ∗ ∗

0 . 0 2 4 6 ∗ ∗ ∗

0 . 0 1 1 3 ∗ ∗ ∗

0 . 0 0 8 1 ∗ ∗ ∗

0 . 0 1 6 7 ∗ ∗ ∗

F I R S T C I T Y N B O F H O U S T O N

1 7

0 . 0 1 8 4 ∗ ∗ ∗

0 . 0 1 9 9 ∗ ∗ ∗

0 . 0 1 0 0 ∗ ∗ ∗

0 . 0 2 2 6 ∗ ∗ ∗

0 . 0 3 1 1 ∗ ∗ ∗

0 . 0 1 5 7 ∗ ∗ ∗

S O U T H E A S T

B K N A

1 6

0 . 0 1 5 5 ∗ ∗ ∗

0 . 0 1 4 9 ∗ ∗ ∗

0 . 0 1 7 2 ∗ ∗ ∗

0 . 0 1 4 1 ∗ ∗ ∗

0 . 0 1 0 7 ∗ ∗ ∗

0 . 0 2 0 3 ∗ ∗ ∗

D e p . V a r .

C 1 / W 3

C 2 / W 3

C 3 / W 3

C 4 / W 3

C 5 / W 3

C 6 / W 3

R H S V a r s .

( y , w 1 )

( y , w 1 )

( y , w 1 )

( y , w 2 )

( y , w 2 )

( y , w 2 )




22



T a b l e E . 1 2 : R e t u r n s t o S

c a l e ( C o s t ) f o r L a r g e s t B a n k s


1 9 9 8 . Q

4

A s s e t s

N a m

e

( b i l l i o n s o f 2 0

0 9 $ )

M o d e l 1

M o d e l 2

M

o d e l 3

M o d e l 4

M o d e l 5

M o d e l 6

C I T I B A N K N

A

3 7 6

0 . 0 1 3 4 ∗ ∗ ∗

0 . 0 1 0 2 ∗ ∗ ∗

0 . 0 1 0 2 ∗ ∗

0 . 0 1 5 3 ∗ ∗ ∗

0 . 0 0 8 2 ∗ ∗ ∗

0 . 0 0 6 0 ∗ ∗

N A T I O N S B A

N K N A

3 6 2

0 . 0 3 0 2 ∗ ∗ ∗

0 . 0 2 8 7 ∗ ∗ ∗

0 . 0 3 7 6 ∗ ∗ ∗

0 . 0 1 6 5 ∗ ∗ ∗

0 . 0 2 1 5 ∗ ∗ ∗

0 . 0 2 7 2 ∗ ∗ ∗

B A N K O F A

M E R N T & S A

3 1 6

− 0 . 0 0 0 8

− 0 . 0 0 7 8

− 0 . 0 0 1 3

0 . 0 1 6 3 ∗ ∗ ∗

0 . 0 1 2 6 ∗ ∗ ∗

0 . 0 2 1 7 ∗ ∗ ∗

F I R S T U N I O

N N B

2 7 7

0 . 0 1 5 2 ∗ ∗ ∗

0 . 0 1 4 9 ∗ ∗ ∗

0 . 0 4 0 6 ∗ ∗ ∗

0 . 0 2 9 1 ∗ ∗ ∗

0 . 0 3 1 3 ∗ ∗ ∗

0 . 0 3 3 6 ∗ ∗ ∗

W E L L S F A R

G O B K N A

1 0 9

0 . 0 2 0 2 ∗ ∗ ∗

0 . 0 0 8 4 ∗ ∗

0 . 0 3 0 7 ∗ ∗ ∗

0 . 0 3 3 1 ∗ ∗ ∗

0 . 0 3 2 4 ∗ ∗ ∗

0 . 0 2 7 7 ∗ ∗ ∗

K E Y B A N K N A T A S S N

9 3

0 . 0 4 8 7 ∗ ∗ ∗

0 . 0 6 0 9 ∗ ∗ ∗

0 . 0 4 7 0 ∗ ∗ ∗

0 . 0 4 0 3 ∗ ∗ ∗

0 . 0 4 6 5 ∗ ∗ ∗

0 . 0 3 1 3 ∗ ∗ ∗

F L E E T N B

9 2

0 . 0 3 2 3 ∗ ∗ ∗

0 . 0 4 5 7 ∗ ∗ ∗

0 . 0 0 8 9 ∗ ∗ ∗

0 . 0 0 7 9 ∗ ∗ ∗

0 . 0 0 6 8 ∗ ∗

0 . 0 0 8 3 ∗ ∗ ∗

P N C B K N A

8 9

0 . 0 1 2 8 ∗ ∗ ∗

0 . 0 1 6 1 ∗ ∗ ∗

0 . 0 1 7 3 ∗ ∗

0 . 0 2 2 9 ∗ ∗ ∗

0 . 0 2 9 6 ∗ ∗ ∗

0 . 0 2 2 4 ∗ ∗ ∗

B A N K B O S T O N N A

8 8

0 . 0 1 5 6 ∗ ∗ ∗

0 . 0 1 3 6 ∗ ∗ ∗

0 . 0 2 9 3 ∗ ∗ ∗

− 0 . 0 0 5 8

− 0 . 0 1 2 2 ∗ ∗

− 0 . 0 0 2 0

U S B K N A

8 6

0 . 0 7 1 7 ∗ ∗ ∗

0 . 0 8 8 9 ∗ ∗ ∗

0 . 0 4 2 2 ∗ ∗ ∗

0 . 0 4 9 3 ∗ ∗ ∗

0 . 0 5 6 6 ∗ ∗ ∗

0 . 0 3 3 4 ∗ ∗ ∗

F I R S T N B O

F C H I C A G O

8 6

0 . 0 3 8 5 ∗ ∗ ∗

0 . 0 3 4 5 ∗ ∗ ∗

0 . 0 3 8 6 ∗ ∗ ∗

0 . 0 2 7 7 ∗ ∗ ∗

0 . 0 2 9 1 ∗ ∗ ∗

0 . 0 3 6 0 ∗ ∗ ∗

W A C H O V I A

B K N A

7 8

0 . 0 6 3 2 ∗ ∗ ∗

0 . 0 8 0 3 ∗ ∗ ∗

0 . 0 4 4 5 ∗ ∗ ∗

0 . 0 3 8 1 ∗ ∗ ∗

0 . 0 4 3 6 ∗ ∗ ∗

0 . 0 3 0 5 ∗ ∗ ∗

B A N K O F N

Y

7 6

0 . 0 2 1 8 ∗ ∗ ∗

0 . 0 2 1 2 ∗ ∗ ∗

0 . 0 3 2 7 ∗ ∗ ∗

0 . 0 1 4 8 ∗ ∗ ∗

0 . 0 1 1 0 ∗ ∗ ∗

0 . 0 1 9 6 ∗ ∗ ∗


5 8

0 . 0 1 2 8 ∗ ∗

0 . 0 1 7 0 ∗ ∗

0 . 0 1 2 2 ∗ ∗

0 . 0 2 9 5 ∗ ∗ ∗

0 . 0 3 5 0 ∗ ∗ ∗

0 . 0 2 8 6 ∗ ∗ ∗

S T A T E S T R E E T B & T C

5 6

0 . 0 5 9 9 ∗ ∗ ∗

0 . 0 5 6 9 ∗ ∗ ∗

0 . 0 5 4 7 ∗ ∗ ∗

0 . 0 1 8 7 ∗ ∗ ∗

0 . 0 1 5 6 ∗ ∗ ∗

0 . 0 3 0 6 ∗ ∗ ∗

M E L L O N B K

N A

5 2

0 . 0 4 0 5 ∗ ∗ ∗

0 . 0 3 1 1 ∗ ∗ ∗

0 . 0 4 1 9 ∗ ∗ ∗

0 . 0 1 9 1 ∗ ∗ ∗

0 . 0 2 5 6 ∗ ∗ ∗

0 . 0 1 9 9 ∗ ∗ ∗

S O U T H T R U S T B K N A

4 6

0 . 0 2 3 7 ∗ ∗ ∗

0 . 0 2 9 8 ∗ ∗ ∗

0 . 0 0 6 3 ∗ ∗ ∗

0 . 0 2 2 1 ∗ ∗ ∗

0 . 0 1 7 6 ∗ ∗ ∗

0 . 0 1 7 3 ∗ ∗ ∗

R E G I O N S B K

4 2

0 . 0 1 6 5 ∗ ∗ ∗

0 . 0 1 5 3 ∗ ∗

− 0 . 0 3 1 5

0 . 0 1 5 8 ∗ ∗ ∗

0 . 0 1 5 5 ∗

0 . 0 3 5 3 ∗ ∗ ∗

M A R I N E M I

D L A N D B K

4 2

0 . 0 2 1 9 ∗ ∗ ∗

0 . 0 1 8 9 ∗ ∗ ∗

0 . 0 1 2 3 ∗ ∗

− 0 . 0 0 1 7 ∗ ∗

0 . 0 0 4 4 ∗ ∗ ∗

− 0 . 0 1 5 4

C H A S E M A N

H A T T A N B K U S A N A

4 0

0 . 0 1 0 6 ∗ ∗ ∗

0 . 0 0 4 0 ∗ ∗

0 . 0 2 8 8 ∗ ∗ ∗

0 . 0 0 9 0 ∗ ∗ ∗

0 . 0 0 6 9 ∗ ∗ ∗

0 . 0 1 8 6 ∗ ∗ ∗

U N I O N B K O F C A N A

4 0

− 0 . 0 0 0 1 ∗

− 0 . 0 1 7 0

0 . 0 1 5 6 ∗ ∗ ∗

0 . 0 1 4 6 ∗ ∗ ∗

0 . 0 0 0 4

0 . 0 0 2 1 ∗

N A T I O N A L C I T Y B K

3 7

0 . 0 2 6 7 ∗ ∗ ∗

0 . 0 2 9 3 ∗ ∗ ∗

0 . 0 2 4 1 ∗ ∗ ∗

0 . 0 2 9 4 ∗ ∗ ∗

0 . 0 3 0 2 ∗ ∗ ∗

0 . 0 5 2 8 ∗ ∗ ∗

S U M M I T B K

3 7

0 . 0 3 5 6 ∗ ∗ ∗

0 . 0 3 2 7 ∗ ∗ ∗

0 . 0 0 1 6 ∗

0 . 0 1 2 0 ∗ ∗ ∗

0 . 0 0 9 7 ∗ ∗ ∗

0 . 0 0 4 0 ∗ ∗

C O M E R I C A

B K

3 6

0 . 0 2 4 8 ∗ ∗ ∗

0 . 0 1 3 7 ∗ ∗ ∗

0 . 0 3 7 5 ∗ ∗ ∗

0 . 0 2 2 3 ∗ ∗ ∗

0 . 0 2 5 0 ∗ ∗ ∗

0 . 0 2 6 4 ∗ ∗ ∗

N O R W E S T B

K M N N A

3 6

0 . 0 1 4 9 ∗ ∗ ∗

0 . 0 1 2 8 ∗ ∗ ∗

0 . 0 3 4 0 ∗ ∗ ∗

0 . 0 2 2 6 ∗ ∗ ∗

0 . 0 3 3 7 ∗ ∗ ∗

0 . 0 3 2 7 ∗ ∗ ∗

F L E E T B K N

A

3 5

0 . 0 1 3 9 ∗ ∗ ∗

0 . 0 0 1 9 ∗

0 . 0 2 4 7 ∗ ∗ ∗

0 . 0 1 0 3 ∗ ∗ ∗

0 . 0 0 0 2 ∗

0 . 0 1 7 3 ∗ ∗ ∗

D e p . V a r .

C 1 / W 3

C 2 / W 3

C

3 / W 3

C 4 / W 3

C 5 / W 3

C 6 / W 3

R H S V a r s .

( y , w 1 )

( y , w 1 )

( y , w 1 )

( y , w 2 )

( y , w 2 )

( y , w 2 )




23



T a b l e E . 1 3 : R e t u r n s t o S c a

l e ( R e v e n u e ) f o r L a r g e s t B a n k s b y T o t a l A s s e t s ,

1 9 8 4 . Q

4

A s s e t s

N a m e

( b i l l i o n s o f 2 0 0 9 $ )

M o d e l 7

M o d e l 8

M o d e l 9

M o d e l 1 0

M o d e l 1 1

M o d e l 1 2

C I T I B A N K N A

2 0 7

− 0 . 0 4 7 9 ∗ ∗ ∗

− 0 . 0 3 8 6 ∗ ∗ ∗

−

0 . 0 2 2 9 ∗ ∗ ∗

− 0 . 0 4 3 7 ∗ ∗ ∗

− 0 . 0 3 8 6 ∗ ∗ ∗

− 0 . 0 2 8 1 ∗ ∗ ∗

B A N K O F A M

E R N T & S A

1 8 8

− 0 . 0 4 8 8 ∗ ∗ ∗

− 0 . 0 3 7 5

−

0 . 0 3 1 8 ∗ ∗ ∗

− 0 . 0 5 2 1 ∗ ∗ ∗

− 0 . 0 3 7 5

− 0 . 0 2 5 1 ∗ ∗ ∗

C H A S E M A N H

A T T A N B K N A

1 4 3

− 0 . 0 2 9 3 ∗ ∗ ∗

− 0 . 0 1 3 6

−

0 . 0 2 1 8 ∗ ∗ ∗

− 0 . 0 3 0 5 ∗ ∗ ∗

− 0 . 0 1 3 6

− 0 . 0 2 6 6 ∗ ∗ ∗

M O R G A N G U

A R A N T Y T C

1 1 1

− 0 . 0 4 6 8 ∗ ∗ ∗

− 0 . 0 4 2 4 ∗ ∗ ∗

−

0 . 0 0 2 8 ∗ ∗ ∗

− 0 . 0 5 8 1 ∗ ∗ ∗

− 0 . 0 4 2 4 ∗ ∗ ∗

− 0 . 0 3 4 8 ∗ ∗ ∗

M A N U F A C T U

R E R S H A N T C

1 0 8

− 0 . 0 3 8 9 ∗ ∗ ∗

− 0 . 0 2 7 7 ∗ ∗ ∗

−

0 . 0 2 2 5 ∗ ∗ ∗

− 0 . 0 3 4 2 ∗ ∗ ∗

− 0 . 0 2 7 7 ∗ ∗ ∗

− 0 . 0 2 5 1 ∗ ∗ ∗

C H E M I C A L B

K

9 3

− 0 . 0 1 5 6

− 0 . 0 1 3 7

−

0 . 0 2 3 7 ∗ ∗ ∗

− 0 . 0 4 0 9 ∗ ∗ ∗

− 0 . 0 1 3 7

− 0 . 0 2 0 0 ∗ ∗ ∗

B A N K E R S T C

7 8

− 0 . 0 2 0 8 ∗ ∗ ∗

− 0 . 0 2 3 4 ∗ ∗ ∗

−

0 . 0 0 3 7

− 0 . 0 1 3 1

− 0 . 0 2 3 4 ∗ ∗ ∗

− 0 . 0 1 7 0 ∗ ∗ ∗

S E C U R I T Y P A

C I F I C N B

6 9

− 0 . 0 2 2 9 ∗ ∗ ∗

− 0 . 0 2 5 6

−

0 . 0 1 7 2 ∗ ∗ ∗

− 0 . 0 1 5 0

− 0 . 0 2 5 6

− 0 . 0 1 8 8 ∗ ∗ ∗

F I R S T N B O F

C H I C A G O

6 3

− 0 . 0 0 8 5

− 0 . 0 1 2 0 ∗ ∗ ∗

−

0 . 0 2 1 9 ∗ ∗ ∗

− 0 . 0 2 7 4

− 0 . 0 1 2 0 ∗ ∗ ∗

− 0 . 0 1 3 4 ∗ ∗ ∗

C O N T I N E N T A

L I L N B & T C C H I C A G O

5 4

0 . 0 5 5 0 ∗ ∗ ∗

0 . 0 6 0 5 ∗ ∗ ∗

−

0 . 0 0 7 2 ∗ ∗ ∗

0 . 0 2 2 8 ∗

0 . 0 6 0 5 ∗ ∗ ∗

− 0 . 0 2 6 7 ∗ ∗ ∗

M E L L O N B K

N A

4 2

− 0 . 0 1 4 8

− 0 . 0 1 0 4

−

0 . 0 2 1 7 ∗ ∗ ∗

− 0 . 0 2 3 7 ∗ ∗ ∗

− 0 . 0 1 0 4

− 0 . 0 2 0 2 ∗ ∗ ∗

W E L L S F A R G

O B K N A

4 2

− 0 . 0 4 0 0 ∗ ∗ ∗

− 0 . 0 3 9 5 ∗ ∗ ∗

−

0 . 0 3 2 0 ∗ ∗ ∗

− 0 . 0 1 8 8

− 0 . 0 3 9 5 ∗ ∗ ∗

− 0 . 0 2 5 0 ∗ ∗ ∗

M A R I N E M I D

L A N D B K N A

3 9

− 0 . 0 3 3 6 ∗ ∗ ∗

− 0 . 0 2 9 6

−

0 . 0 1 6 3 ∗ ∗ ∗

− 0 . 0 2 0 1 ∗ ∗ ∗

− 0 . 0 2 9 6

− 0 . 0 1 5 0 ∗ ∗ ∗

C R O C K E R N B

3 9

− 0 . 0 4 3 5 ∗ ∗ ∗

− 0 . 0 0 2 8

−

0 . 0 2 0 0 ∗ ∗ ∗

− 0 . 0 1 0 5

− 0 . 0 0 2 8

− 0 . 0 1 7 9 ∗ ∗ ∗

F I R S T I N T R S T B K O F C A

3 6

− 0 . 0 1 5 6

0 . 0 0 8 3

−

0 . 0 1 4 1 ∗ ∗ ∗

− 0 . 0 3 3 9 ∗ ∗ ∗

0 . 0 0 8 3

− 0 . 0 2 4 0 ∗ ∗ ∗

F I R S T N B O F

B O S T O N

3 2

− 0 . 0 5 8 0 ∗ ∗ ∗

− 0 . 0 5 8 3 ∗ ∗ ∗

−

0 . 0 1 4 9 ∗ ∗ ∗

− 0 . 0 4 2 9 ∗ ∗ ∗

− 0 . 0 5 8 3 ∗ ∗ ∗

− 0 . 0 2 5 2 ∗ ∗ ∗

I R V I N G T C

3 1

− 0 . 0 0 0 6

− 0 . 0 0 7 1

−

0 . 0 0 6 1

− 0 . 0 4 1 1 ∗ ∗ ∗

− 0 . 0 0 7 1

− 0 . 0 2 8 0 ∗ ∗ ∗

R E P U B L I C B A

N K D A L L A S N A

2 5

0 . 0 0 3 5

0 . 0 2 2 4 ∗

−

0 . 0 2 7 7 ∗ ∗ ∗

0 . 0 3 2 2

0 . 0 2 2 4 ∗

− 0 . 0 1 3 5 ∗ ∗ ∗

B A N K O F N Y

2 5

− 0 . 0 3 5 7 ∗ ∗ ∗

− 0 . 0 4 3 9 ∗ ∗ ∗

−

0 . 0 2 6 0 ∗ ∗ ∗

− 0 . 0 4 8 4 ∗ ∗ ∗

− 0 . 0 4 3 9 ∗ ∗ ∗

− 0 . 0 1 8 4 ∗ ∗ ∗

N A T I O N A L B K O F D E T R O I T

2 1

− 0 . 0 2 6 4 ∗ ∗ ∗

− 0 . 0 2 9 9 ∗ ∗ ∗

−

0 . 0 1 4 0 ∗ ∗ ∗

− 0 . 0 2 2 4 ∗ ∗ ∗

− 0 . 0 2 9 9 ∗ ∗ ∗

− 0 . 0 2 3 2 ∗ ∗ ∗

T E X A S C O M M

E R C E B K N A

2 1

− 0 . 0 0 5 8

0 . 0 4 7 0 ∗ ∗

−

0 . 0 2 1 4 ∗ ∗ ∗

− 0 . 0 5 2 9 ∗ ∗ ∗

0 . 0 4 7 0 ∗ ∗

− 0 . 0 2 4 2 ∗ ∗ ∗


2 0

− 0 . 0 4 2 2 ∗ ∗ ∗

− 0 . 0 4 3 1 ∗ ∗ ∗

−

0 . 0 2 6 5 ∗ ∗ ∗

− 0 . 0 5 1 2 ∗ ∗ ∗

− 0 . 0 4 3 1 ∗ ∗ ∗

− 0 . 0 1 3 5 ∗ ∗ ∗

I N T E R F I R S T

B K D A L L A S N A

1 8

0 . 0 0 2 3

0 . 0 2 3 0 ∗ ∗

−

0 . 0 0 4 4

− 0 . 0 0 6 2

0 . 0 2 3 0 ∗ ∗

− 0 . 0 2 0 9 ∗ ∗ ∗

N C N B N B O F

N C

1 7

− 0 . 0 3 3 9 ∗ ∗ ∗

− 0 . 0 2 9 0 ∗ ∗ ∗

−

0 . 0 2 3 8 ∗ ∗ ∗

− 0 . 0 3 2 1 ∗ ∗ ∗

− 0 . 0 2 9 0 ∗ ∗ ∗

− 0 . 0 2 0 1 ∗ ∗ ∗


1 7

− 0 . 0 1 3 8

− 0 . 0 1 7 2

−

0 . 0 1 9 2 ∗ ∗ ∗

− 0 . 0 1 4 8 ∗ ∗ ∗

− 0 . 0 1 7 2

− 0 . 0 1 8 6 ∗ ∗ ∗

S O U T H E A S T

B K N A

1 6

− 0 . 0 3 5 7 ∗ ∗ ∗

− 0 . 0 3 1 4 ∗ ∗ ∗

−

0 . 0 1 8 2 ∗ ∗ ∗

− 0 . 0 3 3 9 ∗ ∗ ∗

− 0 . 0 3 1 4 ∗ ∗ ∗

− 0 . 0 2 5 5 ∗ ∗ ∗

D e p . V a r .

R 1

R 2

R 3

R 1

R 2

R 3

R H S V a r s .

( y , w 3 )

( y , w 3 )

( y , w 3 )

( y , w 4 )

( y , w 4 )

( y , w 4 )

N O T E : S t a t i s t i c a l s i g n i fi c a n c e a t t h e t e n , fi v e , o r o n e p e r c e n t l e v e l s i s d e n o t e d b y o n e , t w o , o r t h r e e a s t e r i s k s , r e s p e c t i v e l y .

24



T a b l e E . 1 4 : R e t u r n s t o S c a

l e ( R e v e n u e ) f o r L a r g e s t B a n k s b y T o t a l A s s e t s ,

1 9 9 8 . Q

4

A s s e t s

N a m

e


0 9 $ )

M o d e l 7

M o d e l 8

M

o d e l 9

M o d e l 1 0

M o d e l 1 1

M o d e l 1 2

C I T I B A N K N

A

3 7 6

− 0 . 0 1 5 4 ∗

− 0 . 0 2 1 8 ∗ ∗ ∗

− 0 . 0 0 9 8 ∗ ∗

− 0 . 0 2 8 7 ∗ ∗ ∗

− 0 . 0 2 1 8 ∗ ∗ ∗

− 0 . 0 2 6 6 ∗ ∗ ∗

N A T I O N S B A

N K N A

3 6 2

− 0 . 0 3 5 2 ∗ ∗ ∗

− 0 . 0 3 2 7 ∗ ∗ ∗

− 0 . 0 2 3 3 ∗ ∗ ∗

− 0 . 0 1 4 1 ∗ ∗ ∗

− 0 . 0 3 2 7 ∗ ∗ ∗

− 0 . 0 2 1 4 ∗ ∗ ∗

B A N K O F A

M E R N T & S A

3 1 6

0 . 0 2 3 4 ∗ ∗

0 . 0 1 0 7

− 0 . 0 1 3 4 ∗

− 0 . 0 2 2 8 ∗ ∗ ∗

0 . 0 1 0 7

− 0 . 0 3 3 9 ∗ ∗ ∗

F I R S T U N I O

N N B

2 7 7

− 0 . 0 1 4 4

− 0 . 0 3 0 4 ∗ ∗ ∗

− 0 . 0 2 8 8 ∗ ∗ ∗

− 0 . 0 2 6 5 ∗ ∗ ∗

− 0 . 0 3 0 4 ∗ ∗ ∗

− 0 . 0 3 0 1 ∗ ∗ ∗

W E L L S F A R

G O B K N A

1 0 9

− 0 . 0 2 5 6 ∗ ∗ ∗

− 0 . 0 3 0 5 ∗ ∗ ∗

− 0 . 0 4 0 3 ∗ ∗ ∗

− 0 . 0 0 7 9

− 0 . 0 3 0 5 ∗ ∗ ∗

− 0 . 0 2 4 1 ∗ ∗ ∗


9 3

− 0 . 0 3 3 2 ∗ ∗ ∗

− 0 . 0 2 4 1 ∗ ∗ ∗

− 0 . 0 1 2 8 ∗ ∗ ∗

− 0 . 0 0 0 0

− 0 . 0 2 4 1 ∗ ∗ ∗

− 0 . 0 2 5 8 ∗ ∗ ∗

F L E E T N B

9 2

− 0 . 0 0 7 6

− 0 . 0 1 0 1

− 0 . 0 1 2 6 ∗

− 0 . 0 3 0 8 ∗ ∗ ∗

− 0 . 0 1 0 1

− 0 . 0 3 3 4 ∗ ∗ ∗

P N C B K N A

8 9

− 0 . 0 2 9 1 ∗ ∗ ∗

− 0 . 0 1 0 6

− 0 . 0 1 2 3 ∗ ∗ ∗

− 0 . 0 2 3 9 ∗ ∗ ∗

− 0 . 0 1 0 6

− 0 . 0 2 8 8 ∗ ∗ ∗


8 8

− 0 . 0 1 5 1 ∗ ∗ ∗

− 0 . 0 1 6 8 ∗ ∗ ∗

− 0 . 0 1 9 9 ∗ ∗ ∗

− 0 . 0 1 5 5 ∗ ∗ ∗

− 0 . 0 1 6 8 ∗ ∗ ∗

− 0 . 0 2 2 4 ∗ ∗ ∗

U S B K N A

8 6

− 0 . 0 4 4 5 ∗ ∗ ∗

− 0 . 0 3 8 2 ∗ ∗ ∗

− 0 . 0 2 2 8 ∗ ∗ ∗

− 0 . 0 0 9 2 ∗ ∗ ∗

− 0 . 0 3 8 2 ∗ ∗ ∗

− 0 . 0 2 4 1 ∗ ∗ ∗

F I R S T N B O

F C H I C A G O

8 6

− 0 . 0 8 0 4 ∗ ∗ ∗

− 0 . 1 1 8 0 ∗ ∗ ∗

− 0 . 0 4 8 1 ∗ ∗ ∗

− 0 . 0 3 2 7 ∗ ∗ ∗

− 0 . 1 1 8 0 ∗ ∗ ∗

− 0 . 0 3 2 2 ∗ ∗ ∗

W A C H O V I A

B K N A

7 8

− 0 . 0 4 0 8 ∗ ∗ ∗

− 0 . 0 2 4 5 ∗ ∗ ∗

− 0 . 0 2 5 7 ∗ ∗ ∗

− 0 . 0 4 1 3 ∗ ∗ ∗

− 0 . 0 2 4 5 ∗ ∗ ∗

− 0 . 0 3 6 1 ∗ ∗ ∗

B A N K O F N

Y

7 6

− 0 . 0 5 8 3 ∗ ∗ ∗

− 0 . 0 6 1 8 ∗ ∗ ∗

− 0 . 0 2 8 2 ∗ ∗ ∗

0 . 0 0 2 3

− 0 . 0 6 1 8 ∗ ∗ ∗

− 0 . 0 2 3 1 ∗ ∗ ∗


5 8

− 0 . 0 2 3 4 ∗ ∗ ∗

− 0 . 0 2 1 2 ∗ ∗ ∗

− 0 . 0 2 2 0 ∗ ∗ ∗

− 0 . 0 3 7 6 ∗ ∗ ∗

− 0 . 0 2 1 2 ∗ ∗ ∗

− 0 . 0 2 7 7 ∗ ∗ ∗


5 6

− 0 . 0 5 3 9 ∗ ∗ ∗

− 0 . 0 7 4 5 ∗ ∗ ∗

− 0 . 0 4 7 1 ∗ ∗ ∗

− 0 . 0 4 6 0 ∗ ∗ ∗

− 0 . 0 7 4 5 ∗ ∗ ∗

− 0 . 0 0 8 5

M E L L O N B K

N A

5 2

− 0 . 0 6 5 1 ∗ ∗ ∗

− 0 . 0 7 3 5 ∗ ∗ ∗

− 0 . 0 4 6 8 ∗ ∗ ∗

− 0 . 0 0 6 8

− 0 . 0 7 3 5 ∗ ∗ ∗

− 0 . 0 2 5 2 ∗ ∗ ∗


4 6

− 0 . 0 2 5 0 ∗ ∗ ∗

− 0 . 0 3 6 2 ∗ ∗ ∗

− 0 . 0 2 6 7 ∗ ∗ ∗

− 0 . 0 4 4 8 ∗ ∗ ∗

− 0 . 0 3 6 2 ∗ ∗ ∗

− 0 . 0 2 3 8 ∗ ∗ ∗

R E G I O N S B K

4 2

− 0 . 0 7 1 9 ∗ ∗ ∗

− 0 . 0 5 8 8 ∗ ∗ ∗

− 0 . 0 4 7 6 ∗ ∗ ∗

− 0 . 0 6 7 1

− 0 . 0 5 8 8 ∗ ∗ ∗

− 0 . 0 2 2 3 ∗ ∗ ∗

M A R I N E M I

D L A N D B K

4 2

− 0 . 0 1 4 6 ∗

− 0 . 0 0 4 9

− 0 . 0 1 8 8 ∗ ∗ ∗

− 0 . 0 6 7 0 ∗ ∗ ∗

− 0 . 0 0 4 9

− 0 . 0 2 7 2 ∗ ∗ ∗

C H A S E M A N


4 0

− 0 . 0 5 6 5 ∗ ∗ ∗

− 0 . 0 6 3 9 ∗ ∗ ∗

− 0 . 0 3 7 5 ∗ ∗ ∗

− 0 . 0 4 7 4 ∗ ∗ ∗

− 0 . 0 6 3 9 ∗ ∗ ∗

− 0 . 0 0 7 6 ∗ ∗ ∗


4 0

− 0 . 0 2 7 9 ∗ ∗

− 0 . 0 6 2 1 ∗ ∗ ∗

− 0 . 0 2 8 3 ∗ ∗ ∗

− 0 . 0 0 7 3

− 0 . 0 6 2 1 ∗ ∗ ∗

− 0 . 0 1 8 8 ∗ ∗ ∗


3 7

− 0 . 0 2 9 0 ∗

− 0 . 0 3 0 0 ∗

− 0 . 0 2 8 9 ∗ ∗ ∗

− 0 . 0 2 0 9 ∗ ∗ ∗

− 0 . 0 3 0 0 ∗

− 0 . 0 2 6 5 ∗ ∗ ∗

S U M M I T B K

3 7

− 0 . 0 4 2 8 ∗ ∗ ∗

− 0 . 0 3 7 0 ∗ ∗ ∗

− 0 . 0 3 9 9 ∗ ∗ ∗

− 0 . 0 3 2 3 ∗ ∗ ∗

− 0 . 0 3 7 0 ∗ ∗ ∗

− 0 . 0 1 7 1 ∗ ∗ ∗

C O M E R I C A

B K

3 6

− 0 . 0 4 3 0 ∗ ∗ ∗

− 0 . 0 4 5 1 ∗ ∗ ∗

− 0 . 0 3 1 0 ∗ ∗ ∗

− 0 . 0 0 2 4

− 0 . 0 4 5 1 ∗ ∗ ∗

− 0 . 0 2 0 2 ∗ ∗ ∗

N O R W E S T B

K M N N A

3 6

− 0 . 0 5 3 4 ∗ ∗ ∗

− 0 . 0 4 9 1 ∗ ∗ ∗

− 0 . 0 2 1 1 ∗ ∗ ∗

− 0 . 0 3 1 2 ∗ ∗ ∗

− 0 . 0 4 9 1 ∗ ∗ ∗

− 0 . 0 2 6 9 ∗ ∗ ∗

F L E E T B K N

A

3 5

0 . 0 2 8 5 ∗ ∗

0 . 0 4 4 2 ∗ ∗

− 0 . 0 0 4 9 ∗ ∗ ∗

0 . 0 0 3 0

0 . 0 4 4 2 ∗ ∗

− 0 . 0 2 1 4 ∗ ∗ ∗

D e p . V a r .

R 1

R 2

R 3

R 1

R 2

R 3

R H S V a r s .

( y , w 3 )

( y , w 3 )

( y , w 3 )

( y , w 4 )

( y , w 4 )

( y , w 4 )


25



T a b l e E . 1 5 : R e t u r n s t o S c a l e ( P r o fi t ) f o r L a r g e s t B a n k s


1 9 8 4 . Q

4

A s s e t s

N a m e

( b i l l i o n s o f 2 0 0 9 $ )

M o d e l 1 3

M o d e l 1 4

M o d e l 1 5

M o d e l 1 6

M o d e l 1 7

C I T I B A N K N A

2 0 7

− 0 . 0 8 7 6 ∗ ∗ ∗

− 0 . 0 5 9 4 ∗ ∗ ∗

− 0 . 0 8 7 6 ∗ ∗ ∗

− 0 . 0 5 1 0 ∗ ∗ ∗

−

0 . 0 5 9 4 ∗ ∗ ∗

B A N K O F A M

E R N T & S A

1 8 8

− 0 . 0 7 6 7

− 0 . 1 6 7 3 ∗ ∗

− 0 . 0 7 6 7

− 0 . 0 4 2 5 ∗ ∗ ∗

−

0 . 1 6 7 3 ∗ ∗ ∗

C H A S E M A N H

A T T A N B K N A

1 4 3

0 . 0 0 3 4

− 0 . 0 4 1 3

0 . 0 0 3 4

− 0 . 0 3 8 7 ∗ ∗ ∗

−

0 . 0 4 1 3

M O R G A N G U

A R A N T Y T C

1 1 1

− 0 . 0 6 3 3 ∗ ∗ ∗

0 . 0 0 6 1

− 0 . 0 6 3 3 ∗ ∗ ∗

− 0 . 0 4 4 7 ∗ ∗ ∗

0 . 0 0 6 1

M A N U F A C T U

R E R S H A N T C

1 0 8

− 0 . 0 2 9 9

− 0 . 0 3 2 9

− 0 . 0 2 9 9

− 0 . 0 3 1 7 ∗ ∗ ∗

−

0 . 0 3 2 9

C H E M I C A L B

K

9 3

− 0 . 0 0 6 3

− 0 . 0 5 6 2

− 0 . 0 0 6 3

− 0 . 0 2 3 5 ∗ ∗ ∗

−

0 . 0 5 6 2

B A N K E R S T C

7 8

− 0 . 0 2 9 5

0 . 0 1 5 3

− 0 . 0 2 9 5

− 0 . 0 4 4 6 ∗ ∗ ∗

0 . 0 1 5 3

S E C U R I T Y P A

C I F I C N B

6 9

− 0 . 1 1 7 1

− 0 . 1 3 1 7

− 0 . 1 1 7 1

− 0 . 0 2 8 3 ∗ ∗ ∗

−

0 . 1 3 1 7

F I R S T N B O F

C H I C A G O

6 3

0 . 1 5 5 4 ∗

− 0 . 0 6 1 2

0 . 1 5 5 4 ∗

− 0 . 0 2 2 9 ∗ ∗ ∗

−

0 . 0 6 1 2

C O N T I N E N T A


5 4

0 . 2 9 0 7 ∗ ∗ ∗

0 . 1 6 7 0 ∗ ∗ ∗

0 . 2 9 0 7 ∗ ∗ ∗

− 0 . 0 3 8 7 ∗ ∗ ∗

0 . 1 6 7 0 ∗ ∗ ∗

M E L L O N B K

N A

4 2

− 0 . 0 2 7 9

− 0 . 1 2 3 5

− 0 . 0 2 7 9

− 0 . 0 2 3 4 ∗ ∗ ∗

−

0 . 1 2 3 5

W E L L S F A R G

O B K N A

4 2

− 0 . 0 3 5 0

0 . 0 4 4 5

− 0 . 0 3 5 0

− 0 . 0 3 5 4 ∗ ∗ ∗

0 . 0 4 4 5

M A R I N E M I D

L A N D B K N A

3 9

− 0 . 2 9 6 7

0 . 0 0 8 9

− 0 . 2 9 6 7

0 . 0 1 3 4 ∗ ∗ ∗

0 . 0 0 8 9

C R O C K E R N B

3 9

8 . 5 2 5 5 ∗ ∗ ∗ ( 1 )

0 . 4 6 6 8 ∗ ∗ ∗ ( 3

)

8 . 5 2 4 4 ∗ ∗ ∗ ( 1 )

− 0 . 0 2 6 4 ∗ ∗ ∗

0 . 4 6 6 8 ∗ ∗ ∗ ( 3 )


3 6

− 0 . 0 0 1 7

− 0 . 0 0 5 5

− 0 . 0 0 1 7

− 0 . 0 1 1 3 ∗ ∗ ∗

−

0 . 0 0 5 5

F I R S T N B O F

B O S T O N

3 2

− 0 . 0 7 1 8

− 0 . 0 5 4 7

− 0 . 0 7 1 8

− 0 . 0 0 7 7 ∗ ∗ ∗

−

0 . 0 5 4 7

I R V I N G T C

3 1

0 . 0 9 6 2

− 0 . 0 5 7 4 ∗ ∗ ∗

0 . 0 9 6 2

− 0 . 0 1 6 1 ∗ ∗ ∗

−

0 . 0 5 7 4 ∗ ∗ ∗

R E P U B L I C B A

N K D A L L A S N A

2 5

0 . 3 7 6 6 ∗ ∗ ∗

0 . 4 9 9 2 ∗ ∗ ( 3 )

0 . 3 7 6 6 ∗ ∗ ∗

0 . 0 2 0 8 ∗ ∗ ∗

0 . 4 9 9 2 ∗ ∗ ( 3 )

B A N K O F N Y

2 5

− 0 . 0 0 9 1

− 0 . 0 3 8 9 ∗

− 0 . 0 0 9 1

− 0 . 0 3 0 4 ∗ ∗ ∗

−

0 . 0 3 8 9 ∗


2 1

− 0 . 0 2 7 7

− 0 . 0 2 2 6

− 0 . 0 2 7 7

− 0 . 0 2 2 6 ∗ ∗ ∗

−

0 . 0 2 2 6

T E X A S C O M M

E R C E B K N A

2 1

0 . 1 7 7 7

0 . 0 3 2 4 ∗ ∗ ∗

0 . 1 7 7 7

− 0 . 0 2 1 7 ∗ ∗ ∗

0 . 0 3 2 4 ∗ ∗ ∗


2 0

− 0 . 0 1 0 7

− 0 . 0 4 6 7 ∗ ∗ ∗

− 0 . 0 1 0 7

− 0 . 0 2 5 1 ∗ ∗ ∗

−

0 . 0 4 6 7 ∗ ∗ ∗

I N T E R F I R S T

B K D A L L A S N A

1 8

0 . 2 3 8 8 ∗ ∗ ∗

0 . 0 7 9 0

0 . 2 3 8 8 ∗ ∗ ∗

0 . 0 0 0 5 ∗ ∗ ∗

0 . 0 7 9 0

N C N B N B O F

N C

1 7

− 0 . 0 4 1 0 ∗ ∗ ∗

− 0 . 0 3 0 9 ∗ ∗ ∗

− 0 . 0 4 1 0 ∗ ∗ ∗

− 0 . 0 0 6 3

−

0 . 0 3 0 9 ∗ ∗ ∗


1 7

− 0 . 0 2 7 4

0 . 0 0 8 3

− 0 . 0 2 7 4

0 . 0 0 0 3 ∗ ∗ ∗

0 . 0 0 8 3

S O U T H E A S T

B K N A

1 6

− 0 . 0 3 8 5 ∗ ∗ ∗

− 0 . 0 6 4 9 ∗ ∗ ∗

− 0 . 0 3 8 5 ∗ ∗ ∗

− 0 . 0 2 0 9

−

0 . 0 6 4 9 ∗ ∗ ∗

D e p . V a r .

π 1

π 2

π 3

π 4

π 5

R H S V a r s .

( y , w 3 )

( y , w 4 )

( y , w 3 )

( y , w 3 )

( y , w 4 )

N O T E : S t a t i s t i c a l s i g

n i fi c a n c e a t t h e t e n , fi v e , o r o n e p e r c e n

t l e v e l s i s d e n o t e d b y o n e , t w o , o r t h r e e a s t e r i s k s , r e s p e c t i v e l y . S u p e r s c r i p t ( 1 ) , ( 2 ) , o r ( 3 ) i n d i c a t e

( r e s p e c t i v e l y ) δ π ( y , w ) < 0 a n d π ( δ y , w ) > 0 ; δ π ( y , w ) > 0 a n d

π ( δ y , w ) < 0 ; o r δ π ( y , w ) < 0 a n d π ( δ y , w ) < 0 .

26



T a

b l e E . 1 5 : R e t u r n s t o S c a l e ( P r o fi t ) f o r L a r g e s t B a n k s b y T o

t a l A s s e t s ,

1 9 8 4 . Q

4 ( c o n t i n u e d

)

A s s e t s

N a m e

( b i l l i o n s o f 2 0 0 9 $ )

M o d e l 1 3

M o d e l 1 4

M o d e l 1 5

M o d e l 1 6

M o d e l 1 7

C I T I B A N K N A

2 0 7

− 0 . 0 4 6 6

− 0 . 0 3 1 7 ∗ ∗ ∗

− 0 . 0 5 4 3 ∗ ∗ ∗

− 0 . 0 2 1 8 ∗ ∗ ∗

−

0 . 0 7 1 0 ∗ ∗ ∗

B A N K O F A M

E R N T & S A

1 8 8

− 1 . 9 2 9 5 ( 2 )

− 0 . 0 4 1 1 ∗ ∗ ∗

− 0 . 0 4 6 4 ∗ ∗ ∗

− 0 . 0 3 7 3 ∗ ∗ ∗

−

0 . 0 1 6 7

C H A S E M A N H

A T T A N B K N A

1 4 3

− 0 . 0 0 9 5

− 0 . 0 3 2 0 ∗ ∗ ∗

− 0 . 0 3 4 5 ∗ ∗ ∗

− 0 . 0 3 0 9 ∗ ∗ ∗

−

0 . 0 0 3 1

M O R G A N G U

A R A N T Y T C

1 1 1

0 . 0 0 0 6

− 0 . 0 1 7 8 ∗ ∗ ∗

− 0 . 0 3 3 2 ∗ ∗ ∗

− 0 . 0 4 0 0 ∗ ∗ ∗

−

0 . 0 0 4 6

M A N U F A C T U

R E R S H A N T C

1 0 8

0 . 0 0 1 0

− 0 . 0 2 8 1 ∗ ∗ ∗

− 0 . 0 3 5 9 ∗ ∗ ∗

− 0 . 0 2 1 6 ∗ ∗ ∗

−

0 . 0 4 2 8 ∗ ∗ ∗

C H E M I C A L B

K

9 3

− 0 . 0 9 8 1

− 0 . 0 1 6 2 ∗ ∗

− 0 . 0 2 6 8 ∗ ∗ ∗

− 0 . 0 0 8 8

−

0 . 0 6 0 7 ∗

B A N K E R S T C

7 8

0 . 1 4 4 0 ∗ ∗ ∗

− 0 . 0 0 5 5 ∗ ∗ ∗

− 0 . 0 3 9 8 ∗ ∗ ∗

0 . 0 0 2 5

0 . 0 1 8 7

S E C U R I T Y P A

C I F I C N B

6 9

− 0 . 7 0 0 9

− 0 . 0 2 9 9 ∗ ∗ ∗

− 0 . 0 4 1 5 ∗ ∗ ∗

− 0 . 0 1 8 4 ∗ ∗ ∗

−

0 . 0 2 4 7

F I R S T N B O F

C H I C A G O

6 3

− 0 . 1 7 2 0

− 0 . 0 2 2 1 ∗ ∗

− 0 . 0 4 3 4 ∗ ∗ ∗

0 . 0 1 5 5 ∗

0 . 0 2 6 2 ∗ ∗ ∗

C O N T I N E N T A


5 4

0 . 1 7 5 3 ∗ ∗ ∗

− 0 . 0 0 2 9

− 0 . 0 2 9 1 ∗ ∗ ∗

− 0 . 0 1 9 5 ∗ ∗

0 . 0 1 0 3 ∗

M E L L O N B K

N A

4 2

− 0 . 0 5 3 3

− 0 . 0 2 7 1 ∗ ∗ ∗

− 0 . 0 3 3 8 ∗ ∗ ∗

− 0 . 0 1 0 9 ∗ ∗

0 . 0 3 3 5 ∗ ∗

W E L L S F A R G

O B K N A

4 2

0 . 2 6 8 0 ∗ ∗ ∗

− 0 . 0 2 0 1 ∗ ∗ ∗

− 0 . 0 4 0 3 ∗ ∗ ∗

− 0 . 0 1 4 4

0 . 0 7 2 2 ∗ ∗ ∗

M A R I N E M I D

L A N D B K N A

3 9

0 . 2 8 7 2 ∗ ∗ ∗

− 0 . 0 2 0 6 ∗ ∗ ∗

− 0 . 0 2 7 2 ∗ ∗ ∗

− 0 . 0 0 4 9

0 . 1 3 1 8 ∗ ∗ ∗

C R O C K E R N B

3 9

0 . 1 6 9 3 ∗ ∗ ∗ ( 3 )

− 0 . 0 0 5 0

− 0 . 0 3 3 1 ∗ ∗ ∗

0 . 0 3 6 7 ∗ ∗

0 . 1 9 8 1 ∗ ∗ ∗


3 6

0 . 1 4 3 4 ∗ ∗ ∗

− 0 . 0 2 4 4 ∗ ∗ ∗

− 0 . 0 3 1 3 ∗ ∗ ∗

0 . 0 1 7 0

0 . 0 2 4 2 ∗ ∗

F I R S T N B O F

B O S T O N

3 2

0 . 1 8 5 6 ∗ ∗ ∗

− 0 . 0 0 4 9

− 0 . 0 1 9 0 ∗ ∗ ∗

− 0 . 0 2 8 4 ∗ ∗ ∗

−

0 . 0 0 4 8

I R V I N G T C

3 1

− 0 . 0 4 2 2

− 0 . 0 4 0 5 ∗ ∗ ∗

− 0 . 0 2 0 1 ∗ ∗ ∗

− 0 . 0 5 0 9 ∗ ∗ ∗

−

0 . 0 2 3 7

R E P U B L I C B A

N K D A L L A S N A

2 5

− 0 . 3 5 6 7 ( 3 )

− 0 . 0 0 7 5

0 . 0 0 7 5 ∗ ∗ ∗

− 0 . 0 1 4 0 ∗ ∗ ∗

0 . 0 3 3 8

B A N K O F N Y

2 5

− 0 . 0 1 1 3

− 0 . 0 0 3 2

− 0 . 0 2 2 0 ∗ ∗ ∗

0 . 0 1 6 6

−

0 . 0 0 4 5


2 1

0 . 0 0 1 2

− 0 . 0 2 0 8 ∗ ∗ ∗

− 0 . 0 2 2 2 ∗ ∗ ∗

− 0 . 0 2 6 1 ∗ ∗ ∗

0 . 0 6 8 0 ∗ ∗ ∗

T E X A S C O M M

E R C E B K N A

2 1

− 0 . 0 4 2 1

− 0 . 0 2 5 0 ∗ ∗ ∗

− 0 . 0 1 0 7 ∗ ∗ ∗

− 0 . 0 2 2 6 ∗ ∗ ∗

−

0 . 0 7 1 8 ∗ ∗ ∗


2 0

0 . 0 3 6 7 ∗ ∗

− 0 . 0 2 8 9 ∗ ∗ ∗

− 0 . 0 0 8 7 ∗ ∗ ∗

− 0 . 0 2 7 2 ∗ ∗ ∗

−

0 . 0 2 8 1 ∗ ∗ ∗

I N T E R F I R S T

B K D A L L A S N A

1 8

6 . 8 2 8 3 ∗ ∗ ∗ ( 1 )

0 . 0 0 3 3

0 . 0 0 4 2

− 0 . 0 2 2 0

0 . 0 6 5 1

N C N B N B O F

N C

1 7

0 . 0 4 0 7

− 0 . 0 3 7 1 ∗ ∗ ∗

0 . 0 0 6 2 ∗ ∗ ∗

− 0 . 0 3 7 0 ∗ ∗ ∗

−

0 . 0 0 9 5 ∗ ∗ ∗


1 7

0 . 0 7 0 9 ∗ ∗ ∗ ( 3 )

− 0 . 0 4 7 4 ∗ ∗ ∗

0 . 0 1 9 3 ∗ ∗ ∗

− 0 . 0 3 7 9 ∗ ∗ ∗

−

0 . 0 4 7 5

S O U T H E A S T

B K N A

1 6

− 0 . 0 2 4 4

− 0 . 0 3 0 1 ∗ ∗ ∗

− 0 . 0 1 8 0 ∗ ∗ ∗

− 0 . 0 5 7 7 ∗ ∗ ∗

−

0 . 0 4 7 6 ∗ ∗ ∗

D e p . V a r .

π 6

π 7

π 8

π 9

π 1 0

R H S V a r s .

( y , w 4 )

( y , w 3 )

( y , w 3 )

( y , w 4 )

( y , w 4 )






27



T a b l e E . 1 6 : R e t u r n s t o S c a l e ( P r o fi t ) f o r L a r g e s t B a n k s


1 9 9 8 . Q

4

A s s e t s

N a m e

( b i l l i o n s o f 2 0 0 9 $ )

M o d e l 1 3

M o d e l 1 4

M o d e l 1 5

M o d e l 1 6

M o d e l 1 7

C I T I B

A N K N A

3 7 6

− 0 . 0 5 9 2 ∗ ∗ ∗

− 0 . 0 4 2 1 ∗ ∗

∗

− 0 . 0 5 9 2 ∗ ∗ ∗

− 0 . 0 5 9 4 ∗ ∗ ∗

− 0 . 0 4 2 1 ∗ ∗ ∗

N A T I

O N S B A N K N A

3 6 2

− 0 . 0 5 3 5 ∗ ∗ ∗

− 0 . 0 3 1 6

− 0 . 0 5 3 5 ∗ ∗ ∗

− 0 . 0 6 7 0 ∗ ∗ ∗

− 0 . 0 3 1 6

B A N K

O F A M E R N T & S A

3 1 6

0 . 0 3 5 5 ∗

0 . 0 0 4 7

0 . 0 3 5 5 ∗

− 0 . 0 5 9 0 ∗ ∗ ∗

0 . 0 0 4 7

F I R S T U N I O N N B

2 7 7

− 0 . 0 1 4 4

0 . 0 0 2 0

− 0 . 0 1 4 4

− 0 . 0 6 0 0 ∗ ∗ ∗

0 . 0 0 2 0


1 0 9

− 0 . 0 2 8 5

0 . 0 0 2 7

− 0 . 0 2 8 5

− 0 . 0 5 5 2 ∗ ∗ ∗

0 . 0 0 2 7

K E Y B

A N K N A T A S S N

9 3

− 0 . 0 2 6 6

0 . 0 2 9 5

− 0 . 0 2 6 6

− 0 . 0 3 8 1 ∗ ∗ ∗

0 . 0 2 9 5

F L E E

T N B

9 2

0 . 0 3 0 3 ∗

− 0 . 0 4 4 6 ∗ ∗

∗

0 . 0 3 0 3 ∗

− 0 . 0 4 4 0 ∗ ∗ ∗

− 0 . 0 4 4 6 ∗ ∗ ∗

P N C

B K N A

8 9

0 . 0 0 6 1

− 0 . 0 4 7 1 ∗ ∗

∗

0 . 0 0 6 1

− 0 . 0 4 8 1 ∗ ∗ ∗

− 0 . 0 4 7 1 ∗ ∗ ∗

B A N K

B O S T O N N A

8 8

0 . 0 0 9 9

− 0 . 0 4 2 4 ∗ ∗

∗

0 . 0 0 9 9

− 0 . 0 4 8 8 ∗ ∗ ∗

− 0 . 0 4 2 4 ∗ ∗ ∗

U S B

K N A

8 6

− 0 . 0 3 6 4 ∗ ∗ ∗

− 0 . 0 0 6 0 ∗ ∗

∗

− 0 . 0 3 6 4 ∗ ∗ ∗

− 0 . 0 3 6 2 ∗ ∗ ∗

− 0 . 0 0 6 0 ∗ ∗ ∗

F I R S T N B O F C H I C A G O

8 6

− 0 . 2 2 5 1 ∗ ∗ ∗

− 0 . 0 2 8 7 ∗ ∗

∗

− 0 . 2 2 5 1 ∗ ∗ ∗

− 0 . 0 4 1 8 ∗ ∗ ∗

− 0 . 0 2 8 7 ∗ ∗ ∗


7 8

− 0 . 0 4 3 0 ∗ ∗ ∗

− 0 . 0 4 3 1 ∗ ∗

∗

− 0 . 0 4 3 0 ∗ ∗ ∗

− 0 . 0 3 8 6 ∗ ∗ ∗

− 0 . 0 4 3 1 ∗ ∗ ∗

B A N K

O F N Y

7 6

− 0 . 0 9 3 6 ∗ ∗ ∗

0 . 0 2 4 2 ∗ ∗

∗

− 0 . 0 9 3 6 ∗ ∗ ∗

− 0 . 0 3 8 5 ∗ ∗ ∗

0 . 0 2 4 2 ∗ ∗ ∗

R E P U

B L I C N B O F N Y

5 8

− 0 . 0 0 1 7

− 0 . 0 3 2 7

− 0 . 0 0 1 7

− 0 . 0 3 9 4 ∗ ∗ ∗

− 0 . 0 3 2 7

S T A T

E S T R E E T B & T C

5 6

− 0 . 0 5 3 5 ∗ ∗ ∗

− 0 . 0 6 8 0 ∗ ∗

∗

− 0 . 0 5 3 5 ∗ ∗ ∗

− 0 . 0 3 7 4 ∗ ∗ ∗

− 0 . 0 6 8 0 ∗ ∗ ∗

M E L L O N B K N A

5 2

− 0 . 0 7 5 3 ∗ ∗ ∗

− 0 . 0 0 7 5

− 0 . 0 7 5 3 ∗ ∗ ∗

− 0 . 0 1 5 4 ∗ ∗ ∗

− 0 . 0 0 7 5

S O U T

H T R U S T B K N A

4 6

− 0 . 0 2 9 4

− 0 . 0 8 1 1 ∗ ∗

∗

− 0 . 0 2 9 4

− 0 . 0 2 9 7 ∗ ∗ ∗

− 0 . 0 8 1 1 ∗ ∗ ∗

R E G I

O N S B K

4 2

− 0 . 0 7 9 5 ∗ ∗ ∗

− 0 . 0 4 1 5 ∗ ∗

− 0 . 0 7 9 5 ∗ ∗ ∗

− 0 . 0 3 1 3 ∗ ∗ ∗

− 0 . 0 4 1 5 ∗ ∗

M A R I N E M I D L A N D B K

4 2

0 . 0 2 6 1 ∗ ∗ ∗

− 0 . 0 8 9 0 ∗ ∗

∗

0 . 0 2 6 1 ∗ ∗ ∗

− 0 . 0 1 2 5 ∗ ∗ ∗

− 0 . 0 8 9 0 ∗ ∗ ∗

C H A S E M A N H A T T A N B K U S A N A

4 0

− 0 . 0 5 5 7 ∗ ∗ ∗

− 0 . 0 4 4 5 ∗ ∗

∗

− 0 . 0 5 5 7 ∗ ∗ ∗

− 0 . 0 7 1 3 ∗ ∗ ∗

− 0 . 0 4 4 5 ∗ ∗ ∗

U N I O

N B K O F C A N A

4 0

− 0 . 0 3 6 5 ∗ ∗

0 . 0 0 1 3

− 0 . 0 3 6 5 ∗ ∗

− 0 . 0 2 8 3 ∗ ∗ ∗

0 . 0 0 1 3

N A T I

O N A L C I T Y B K

3 7

0 . 0 0 8 8

− 0 . 0 1 0 7

0 . 0 0 8 8

− 0 . 0 3 0 9 ∗ ∗ ∗

− 0 . 0 1 0 7

S U M M I T B K

3 7

− 0 . 0 1 9 0

− 0 . 0 4 4 9 ∗ ∗

∗

− 0 . 0 1 9 0

− 0 . 0 0 7 6 ∗ ∗ ∗

− 0 . 0 4 4 9 ∗ ∗ ∗

C O M E R I C A B K

3 6

− 0 . 0 5 7 0 ∗ ∗ ∗

− 0 . 0 3 6 1 ∗ ∗

∗

− 0 . 0 5 7 0 ∗ ∗ ∗

− 0 . 0 2 6 1 ∗ ∗ ∗

− 0 . 0 3 6 1 ∗ ∗ ∗

N O R W

E S T B K M N N A

3 6

− 0 . 0 5 5 8 ∗ ∗ ∗

− 0 . 0 4 0 2 ∗ ∗

∗

− 0 . 0 5 5 8 ∗ ∗ ∗

− 0 . 0 2 0 8 ∗ ∗ ∗

− 0 . 0 4 0 2 ∗ ∗ ∗

F L E E

T B K N A

3 5

0 . 0 4 3 9

0 . 0 1 2 3

0 . 0 4 3 9

0 . 0 0 9 9 ∗ ∗ ∗

0 . 0 1 2 3

D e p . V a r .

π 1

π 2

π 3

π 4

π 5

R H S V a r s .

( y , w 3 )

( y , w 4 )

( y , w 3 )

( y , w 3 )

( y , w 4 )


28



T a

b l e E . 1 6 : R e t u r n s t o S c a l e ( P r o fi t ) f o r L a r g e s t B a n k s b y T o

t a l A s s e t s ,

1 9 9 8 . Q

4 ( c o n t i n u e d

)

A s s e t s

N a m

e


0 9 $ )

M o d e l 1 3

M o d e l 1 4

M o d e l 1 5

M o d e l 1 6

M o d e l 1 7

C I T I B A N K N A

3 7 6

0 . 2 6 6 3 ( 3 )

− 0 . 0 0 9 1

− 0 . 0 5 0 7 ∗ ∗ ∗

− 0 . 0 1 9 9 ∗

− 0 . 1 8 9 2

N A T I O N S B A

N K N A

3 6 2

− 0 . 0 2 4 8 ∗ ∗ ∗

− 0 . 0 4 5 3 ∗ ∗ ∗

− 0 . 0 6 2 4 ∗ ∗ ∗

− 0 . 0 1 6 3

− 0

. 0 6 0 7 ∗ ∗ ∗

B A N K O F A

M E R N T & S A

3 1 6

− 0 . 2 0 3 2

− 0 . 0 1 8 0 ∗ ∗ ∗

− 0 . 0 5 0 8 ∗ ∗ ∗

− 0 . 0 2 9 4 ∗ ∗ ∗

− 0 . 0 0 9 2

F I R S T U N I O

N N B

2 7 7

− 0 . 1 3 4 1 ∗ ∗

− 0 . 0 4 6 3 ∗ ∗ ∗

− 0 . 0 5 2 7 ∗ ∗ ∗

− 0 . 0 3 1 7 ∗ ∗ ∗

− 0 . 0 5 2 3

W E L L S F A R

G O B K N A

1 0 9

− 0 . 1 1 0 4 ∗ ∗ ∗

− 0 . 0 4 3 1 ∗ ∗ ∗

− 0 . 0 4 3 0 ∗ ∗ ∗

− 0 . 0 3 5 8

− 0 . 0 6 2 5


9 3

0 . 1 1 6 4 ∗ ∗ ∗

0 . 0 1 4 3

− 0 . 0 2 0 6 ∗ ∗ ∗

− 0 . 0 1 9 0

0

. 0 7 6 1 ∗ ∗

F L E E T N B

9 2

− 0 . 0 2 7 8 ∗ ∗ ∗

0 . 0 0 1 5

− 0 . 0 2 8 5 ∗ ∗ ∗

− 0 . 0 4 5 6 ∗ ∗ ∗

− 0

. 0 5 7 6 ∗ ∗ ∗

P N C B K N A

8 9

− 0 . 2 2 4 6 ∗ ∗

0 . 0 1 3 6

− 0 . 0 3 8 5 ∗ ∗ ∗

− 0 . 0 3 5 8 ∗ ∗

− 0 . 0 0 5 3

B A N K B O S T

O N N A

8 8

− 0 . 0 9 0 3

− 0 . 0 0 5 5

− 0 . 0 3 8 9 ∗ ∗ ∗

− 0 . 0 1 7 8

− 0 . 0 1 7 4

U S B K N A

8 6

− 0 . 0 1 1 7

− 0 . 0 1 5 2

− 0 . 0 1 5 8 ∗ ∗ ∗

0 . 0 0 8 9

− 0

. 0 4 1 2 ∗ ∗ ∗

F I R S T N B O

F C H I C A G O

8 6

− 0 . 4 5 7 5

− 0 . 0 3 3 2

− 0 . 0 2 5 4 ∗ ∗ ∗

− 0 . 0 4 8 7 ∗ ∗ ∗

− 0 . 3 5 3 0

W A C H O V I A

B K N A

7 8

− 0 . 0 5 4 0 ∗ ∗ ∗

− 0 . 0 2 8 5 ∗ ∗ ∗

− 0 . 0 2 5 7 ∗ ∗ ∗

− 0 . 0 3 0 7 ∗ ∗ ∗

− 0

. 0 3 4 0 ∗ ∗ ∗

B A N K O F N

Y

7 6

− 0 . 1 8 2 2 ∗ ∗ ∗

0 . 0 3 1 1 ∗ ∗ ∗

− 0 . 0 3 0 4 ∗ ∗ ∗

− 0 . 0 1 9 0 ∗ ∗ ∗

− 0 . 0 1 9 0


5 8

− 0 . 0 3 6 7

− 0 . 0 0 7 5

− 0 . 0 4 9 1 ∗ ∗ ∗

− 0 . 0 3 0 5 ∗ ∗ ∗

− 0

. 0 4 3 4 ∗ ∗ ∗


5 6

− 0 . 0 3 1 6

− 0 . 0 1 9 9 ∗ ∗ ∗

− 0 . 0 5 1 5 ∗ ∗ ∗

− 0 . 0 0 7 4

− 0 . 0 2 4 3

M E L L O N B K N A

5 2

− 0 . 0 5 1 5

− 0 . 0 2 9 7 ∗ ∗ ∗

− 0 . 0 0 2 1 ∗ ∗ ∗

− 0 . 0 2 6 2

− 0 . 0 0 5 6

S O U T H T R U

S T B K N A

4 6

− 0 . 1 4 2 9 ∗ ∗ ∗

− 0 . 0 3 2 9 ∗ ∗ ∗

− 0 . 0 5 7 4 ∗ ∗ ∗

− 0 . 0 4 9 9 ∗ ∗ ∗

− 0

. 1 0 0 7 ∗ ∗ ∗

R E G I O N S B

K

4 2

− 0 . 0 9 0 3 ∗ ∗ ∗

− 0 . 0 1 6 2

− 0 . 0 2 5 4 ∗ ∗ ∗

− 0 . 0 2 2 8

− 0 . 0 9 6 7


4 2

− 0 . 0 3 0 7

− 0 . 0 0 9 0

− 0 . 0 1 0 6 ∗ ∗ ∗

− 0 . 0 4 7 3 ∗ ∗ ∗

− 0 . 0 5 0 7


4 0

− 0 . 0 2 7 3

− 0 . 0 3 5 7 ∗ ∗ ∗

− 0 . 0 7 2 7 ∗ ∗ ∗

− 0 . 0 0 5 1

− 0

. 0 3 4 1 ∗ ∗ ∗


4 0

0 . 0 8 0 9

− 0 . 0 2 6 6 ∗ ∗ ∗

− 0 . 0 0 8 9 ∗ ∗ ∗

− 0 . 0 1 1 5

0 . 0 0 6 9 ∗

N A T I O N A L

C I T Y B K

3 7

0 . 0 0 2 8

− 0 . 0 2 0 0 ∗ ∗ ∗

− 0 . 0 1 7 6 ∗ ∗ ∗

− 0 . 0 1 2 7 ∗ ∗ ∗

− 0

. 0 2 2 6 ∗ ∗ ∗

S U M M I T B K

3 7

− 0 . 1 9 3 9 ∗

− 0 . 0 3 2 0 ∗

− 0 . 0 1 4 5 ∗ ∗ ∗

− 0 . 0 2 9 1 ∗ ∗ ∗

− 0 . 1 3 4 9

C O M E R I C A

B K

3 6

− 0 . 0 1 2 3

− 0 . 0 1 9 4 ∗ ∗ ∗

− 0 . 0 0 7 7 ∗ ∗ ∗

− 0 . 0 3 8 8 ∗ ∗ ∗

0 . 0 0 7 2

N O R W E S T B K M N N A

3 6

− 0 . 0 6 1 6 ∗ ∗ ∗

− 0 . 0 0 8 5

− 0 . 0 2 1 4 ∗ ∗ ∗

− 0 . 0 1 9 5

− 0 . 0 2 6 0

F L E E T B K N A

3 5

0 . 1 7 5 9 ∗ ∗ ∗

− 0 . 0 0 8 4

0 . 0 0 0 9 ∗ ∗ ∗

0 . 0 0 7 4

0 . 0 0 6 6 ∗

D e p . V a r .

π 6

π 7

π 8

π 9

π 1 0

R H S V a r s .

( y , w 4 )

( y , w 3 )

( y , w 3 )

( y , w 4 )

( y , w 4 )






29



F Results Obtained while Imposing Homogeneity with

Respect to Input Prices

Tables F.17–?? show estimates similar to Tables 1–8 in the paper, but with revenue and profit

functions estimated while imposing homogeneity with respect to input prices.

30



Table F.17: Counts of Banks Facing IRS, CRS, and DRS (imposing homogeneity with re-spect to input prices)

.1 signif. .05 signif. .01 signif.Model LHS Period IRS CRS DRS IRS CRS DRS IRS CRS DRS

1 C 1/W 3 1984.Q4 11277 1510 9 10597 2191 8 8990 3801 51998.Q4 7388 754 16 7107 1039 12 6362 1787 9

2 C 2/W 3 1984.Q4 10932 1854 10 10175 2613 8 8461 4328 71998.Q4 7059 1075 24 6674 1461 23 5814 2327 17

3 C 3/W 3 1984.Q4 10780 2000 16 10020 2762 14 8259 4526 111998.Q4 7061 1073 24 6638 1500 20 5834 2307 17

4 C 4/W 3 1984.Q4 11075 1217 6 10414 1878 6 8911 3384 31998.Q4 6899 1193 5 6433 1660 4 5459 2635 3

5 C 5/W 3 1984.Q4 11130 1162 6 10458 1836 4 8954 3341 31998.Q4 6909 1182 6 6471 1621 5 5433 2661 3

6 C 6/W 3 1984.Q4 11453 842 3 10974 1321 3 9646 2649 31998.Q4 7005 1086 6 6567 1525 5 5602 2491 4

7 R1/W 3 1984.Q4 87 4189 8520 51 4680 8065 22 5272 75021998.Q4 64 1703 6391 47 1910 6201 29 2188 5941

8 R2/W 3 1984.Q4 247 8007 4542 145 8657 3994 69 9397 33301998.Q4 275 4329 3554 184 4718 3256 82 5242 2834

9 R3/W 3 1984.Q4 360 7519 4917 214 8134 4448 85 8938 37731998.Q4 712 5449 1997 428 5992 1738 177 6562 1419

10 R1/W 3 1984.Q4 324 8202 3772 185 8856 3257 74 9548 26761998.Q4 360 5355 2382 220 5802 2075 89 6306 1702

11 R2/W 3 1984.Q4 247 8007 4542 145 8657 3994 69 9397 33301998.Q4 275 4329 3554 184 4718 3256 82 5242 2834

12 R3/W 3 1984.Q4 601 9386 2311 317 10057 1924 80 10734 14841998.Q4 1032 5973 1092 619 6576 902 213 7196 688

13 π1/W 3 1984.Q4 552 9553 2691 287 10244 2265 76 10936 17841998.Q4 336 4775 3047 220 5251 2687 108 5810 2240

14 π2/W 3 1984.Q4 1260 10428 610 706 11156 436 205 11805 2881998.Q4 768 5819 1510 469 6404 1224 179 7019 899

15 π3/W 3 1984.Q4 551 9557 2688 285 10244 2267 76 10937 17831998.Q4 336 4775 3047 220 5251 2687 108 5810 2240

16 π4/W 3 1984.Q4 0 12796 0 0 12796 0 0 12796 01998.Q4 0 8158 0 0 8158 0 0 8158 0

17 π5/W 3 1984.Q4 1258 10428 612 710 11153 435 206 11804 2881998.Q4 768 5819 1510 469 6403 1225 179 7019 899

18 π6/W 3 1984.Q4 1363 8018 2917 885 8765 2648 325 9627 23461998.Q4 1121 4662 2314 902 5115 2080 620 5691 1786

19 π7/W 3 1984.Q4 1400 9955 1441 865 10769 1162 330 11648 8181998.Q4 1381 5813 964 905 6469 784 389 7211 558

20 π8/W 3 1984.Q4 407 1306 11083 348 1505 10943 242 1846 107081998.Q4 385 664 7109 331 784 7043 274 959 6925

21 π9/W 3 1984.Q4 2952 8366 980 2088 9367 843 1069 10545 6841998.Q4 2404 5026 667 1789 5734 574 999 6647 451

22 π10/W 3 1984.Q4 1751 3000 7547 1565 3375 7358 1249 3983 70661998.Q4 1472 2434 4191 1307 2759 4031 1027 3272 3798

31



Table F.18: Counts of Banks Facing IRS, CRS, and DRS (imposing homogeneity with re-spect to input prices)

.1 signif. .05 signif. .01 signif.Model LHS Period IRS CRS DRS IRS CRS DRS IRS CRS DRS

1 C 1/W 3 2006.Q4 6016 797 6 5649 1165 5 4793 2023 32012.Q4 4689 640 3 4417 912 3 3750 1580 2

2 C 2/W 3 2006.Q4 5830 983 6 5430 1384 5 4499 2315 52012.Q4 4545 783 4 4237 1092 3 3545 1785 2

3 C 3/W 3 2006.Q4 5734 1075 10 5350 1460 9 4397 2416 62012.Q4 4514 812 6 4176 1151 5 3442 1885 5

4 C 4/W 3 2006.Q4 6103 659 5 5734 1028 5 4885 1879 32012.Q4 4761 534 1 4483 812 1 3846 1450 0

5 C 5/W 3 2006.Q4 6129 633 5 5741 1022 4 4913 1851 32012.Q4 4786 509 1 4517 779 0 3863 1433 0

6 C 6/W 3 2006.Q4 6292 473 2 6028 737 2 5295 1470 22012.Q4 4944 351 1 4736 559 1 4161 1134 1

7 R1/W 3 2006.Q4 49 2258 4512 27 2521 4271 13 2823 39832012.Q4 38 1715 3579 24 1909 3399 9 2165 3158

8 R2/W 3 2006.Q4 140 4230 2449 84 4568 2167 46 4960 18132012.Q4 99 3347 1886 58 3629 1645 22 3940 1370

9 R3/W 3 2006.Q4 171 4056 2592 93 4376 2350 31 4799 19892012.Q4 169 3107 2056 111 3369 1852 52 3704 1576

10 R1/W 3 2006.Q4 183 4520 2064 103 4883 1781 46 5252 14692012.Q4 137 3525 1634 79 3801 1416 28 4106 1162

11 R2/W 3 2006.Q4 140 4230 2449 84 4568 2167 46 4960 18132012.Q4 99 3347 1886 58 3629 1645 22 3940 1370

12 R3/W 3 2006.Q4 334 5181 1252 184 5528 1055 48 5911 8082012.Q4 255 4017 1024 129 4326 841 32 4608 656

13 π1/W 3 2006.Q4 301 5102 1416 151 5466 1202 43 5808 9682012.Q4 223 3961 1148 119 4261 952 30 4568 734

14 π2/W 3 2006.Q4 721 5689 357 393 6128 246 111 6494 1622012.Q4 522 4533 241 304 4811 181 92 5085 119

15 π3/W 3 2006.Q4 300 5105 1414 151 5466 1202 43 5809 9672012.Q4 223 3962 1147 117 4261 954 30 4568 734

16 π4/W 3 2006.Q4 0 6819 0 0 6819 0 0 6819 02012.Q4 0 5332 0 0 5332 0 0 5332 0

17 π5/W 3 2006.Q4 720 5689 358 396 6126 245 112 6493 1622012.Q4 521 4533 242 305 4810 181 92 5085 119

18 π6/W 3 2006.Q4 748 4424 1595 478 4833 1456 178 5287 13022012.Q4 586 3438 1272 388 3763 1145 141 4150 1005

19 π7/W 3 2006.Q4 729 5339 751 446 5752 621 153 6228 4382012.Q4 601 4114 617 382 4472 478 164 4830 338

20 π8/W 3 2006.Q4 227 678 5914 201 780 5838 137 966 57162012.Q4 156 551 4625 127 636 4569 92 779 4461

21 π9/W 3 2006.Q4 1642 4570 555 1170 5129 468 592 5795 3802012.Q4 1262 3622 412 886 4046 364 462 4540 294

22 π10/W 3 2006.Q4 966 1708 4093 858 1920 3989 683 2268 38162012.Q4 757 1229 3310 684 1385 3227 546 1635 3115

32



Table F.19: Quantiles and Means for Estimates of Returns to Scale Indices (imposing ho-mogeneity with respect to input prices)


1 C 1/W 3 1984.Q4 −0.0271 0.0156 0.0289 0.0287 0.0421 0.08091998.Q4 −0.0310 0.0182 0.0327 0.0327 0.0475 0.0925

2 C 2/W 3 1984.Q4 −0.0334 0.0143 0.0286 0.0283 0.0427 0.08571998.Q4 −0.0452 0.0162 0.0332 0.0328 0.0500 0.1031

3 C 3/W 3 1984.Q4 −0.0349 0.0145 0.0294 0.0293 0.0446 0.09071998.Q4 −0.0382 0.0162 0.0330 0.0329 0.0495 0.0999

4 C 4/W 3 1984.Q4 −0.0183 0.0140 0.0240 0.0239 0.0341 0.06251998.Q4 −0.0247 0.0117 0.0237 0.0236 0.0359 0.0709

5 C 5/W 3 1984.Q4 −0.0196 0.0146 0.0248 0.0245 0.0350 0.06361998.Q4 −0.0272 0.0119 0.0251 0.0247 0.0375 0.0743

6 C 6/W 3 1984.Q4 −0.0134 0.0149 0.0237 0.0236 0.0324 0.05751998.Q4 −0.0255 0.0114 0.0232 0.0228 0.0342 0.0669

7 R1/W 3 1984.Q4 −0.0704 −0.0388 −0.0297 −0.0292 −0.0202 0.01841998.Q4 −0.0665 −0.0399 −0.0304 −0.0291 −0.0202 0.0179

8 R2/W 3 1984.Q4 −0.1078 −0.0446 −0.0289 −0.0272 −0.0125 0.07051998.Q4 −0.0933 −0.0454 −0.0292 −0.0272 −0.0117 0.0585

9 R3/W 3 1984.Q4 −0.0901 −0.0432 −0.0273 −0.0264 −0.0107 0.04501998.Q4 −0.1091 −0.0486 −0.0250 −0.0226 0.0007 0.0855

10 R1/W 3 1984.Q4 −0.0938 −0.0374 −0.0238 −0.0232 −0.0087 0.06941998.Q4 −0.0771 −0.0343 −0.0204 −0.0186 −0.0058 0.0558

11 R2/W 3 1984.Q4 −0.1078 −0.0446 −0.0289 −0.0272 −0.0125 0.07051998.Q4 −0.0933 −0.0454 −0.0292 −0.0272 −0.0117 0.0585

12 R3/W 3 1984.Q4 −0.0778 −0.0325 −0.0179 −0.0172 −0.0025 0.04891998.Q4 −0.1017 −0.0379 −0.0153 −0.0133 0.0085 0.0953

13 π1/W 3 1984.Q4 −0.3574 −0.0527 −0.0310 −0.0207 −0.0066 0.33101998.Q4 −0.0971 −0.0440 −0.0271 −0.0220 −0.0089 0.0894

14 π2/W 3 1984.Q4 −0.1807 −0.0366 −0.0155 −0.0053 0.0079 0.29101998.Q4 −0.0757 −0.0284 −0.0140 −0.0097 0.0017 0.0937

15 π3/W 3 1984.Q4 −0.3573 −0.0527 −0.0310 −0.0207 −0.0067 0.33061998.Q4 −0.0971 −0.0440 −0.0271 −0.0220 −0.0088 0.0894

16 π4/W 3 1984.Q4 0.0000 0.0000 0.0000 0.0000 0.0000 0.00001998.Q4 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

17 π5/W 3 1984.Q4 −0.1806 −0.0366 −0.0155 −0.0065 0.0079 0.29421998.Q4 −0.0757 −0.0284 −0.0140 −0.0096 0.0018 0.0937

18 π6/W 3 1984.Q4 −0.9463 −0.0527 −0.0283 0.6960 0.0025 1.03881998.Q4 −0.0951 −0.0298 −0.0152 0.0700 0.0023 0.3113

19 π7/W 3 1984.Q4 −0.1346 −0.0522 −0.0219 −0.0178 0.0102 0.14791998.Q4 −0.1497 −0.0559 −0.0184 −0.0130 0.0225 0.1808

20 π8/W 3 1984.Q4 −0.0481 −0.0312 −0.0246 −0.0228 −0.0169 0.02191998.Q4 −0.0449 −0.0264 −0.0203 −0.0149 −0.0136 0.0504

21 π9/W 3 1984.Q4 −0.1831 −0.0513 −0.0086 0.0223 0.0429 0.49161998.Q4 −0.1984 −0.0539 −0.0011 0.0441 0.0603 0.3981

22 π10/W 3 1984.Q4 −0.0406 −0.0233 −0.0152 0.0054 −0.0039 0.23851998.Q4 −0.0365 −0.0176 −0.0094 0.0053 0.0009 0.1984

33



Table F.20: Quantiles and Means for Estimates of Returns to Scale Indices (imposing ho-mogeneity with respect to input prices)


1 C 1/W 3 2006.Q4 −0.0251 0.0155 0.0289 0.0287 0.0420 0.08122012.Q4 −0.0289 0.0159 0.0288 0.0287 0.0423 0.0811

2 C 2/W 3 2006.Q4 −0.0311 0.0141 0.0287 0.0283 0.0427 0.08652012.Q4 −0.0369 0.0145 0.0286 0.0282 0.0429 0.0857

3 C 3/W 3 2006.Q4 −0.0337 0.0144 0.0296 0.0294 0.0447 0.09262012.Q4 −0.0375 0.0145 0.0293 0.0292 0.0446 0.0910

4 C 4/W 3 2006.Q4 −0.0184 0.0139 0.0240 0.0238 0.0339 0.06232012.Q4 −0.0177 0.0141 0.0240 0.0239 0.0342 0.0627

5 C 5/W 3 2006.Q4 −0.0192 0.0145 0.0248 0.0245 0.0349 0.06382012.Q4 −0.0203 0.0148 0.0246 0.0245 0.0349 0.0634

6 C 6/W 3 2006.Q4 −0.0131 0.0149 0.0237 0.0235 0.0325 0.05752012.Q4 −0.0133 0.0150 0.0237 0.0237 0.0324 0.0570

7 R1/W 3 2006.Q4 −0.0699 −0.0387 −0.0297 −0.0291 −0.0202 0.01812012.Q4 −0.0706 −0.0391 −0.0298 −0.0292 −0.0202 0.0208

8 R2/W 3 2006.Q4 −0.1062 −0.0447 −0.0292 −0.0259 −0.0126 0.07212012.Q4 −0.1098 −0.0448 −0.0290 −0.0289 −0.0124 0.0646

9 R3/W 3 2006.Q4 −0.0904 −0.0431 −0.0271 −0.0266 −0.0108 0.04182012.Q4 −0.0911 −0.0434 −0.0274 −0.0261 −0.0105 0.0503

10 R1/W 3 2006.Q4 −0.0945 −0.0374 −0.0239 −0.0245 −0.0084 0.06902012.Q4 −0.0922 −0.0375 −0.0239 −0.0217 −0.0093 0.0694

11 R2/W 3 2006.Q4 −0.1062 −0.0447 −0.0292 −0.0259 −0.0126 0.07212012.Q4 −0.1098 −0.0448 −0.0290 −0.0289 −0.0124 0.0646

12 R3/W 3 2006.Q4 −0.0788 −0.0322 −0.0178 −0.0169 −0.0020 0.04862012.Q4 −0.0764 −0.0329 −0.0183 −0.0175 −0.0031 0.0498

13 π1/W 3 2006.Q4 −0.3636 −0.0526 −0.0308 −0.0233 −0.0067 0.37602012.Q4 −0.3623 −0.0526 −0.0311 −0.0024 −0.0066 0.2990

14 π2/W 3 2006.Q4 −0.1801 −0.0371 −0.0156 −0.0053 0.0079 0.30442012.Q4 −0.1807 −0.0365 −0.0155 −0.0052 0.0080 0.2911

15 π3/W 3 2006.Q4 −0.3636 −0.0526 −0.0308 −0.0232 −0.0068 0.37602012.Q4 −0.3623 −0.0526 −0.0311 −0.0024 −0.0066 0.2988

16 π4/W 3 2006.Q4 0.0000 0.0000 0.0000 0.0000 0.0000 0.00002012.Q4 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

17 π5/W 3 2006.Q4 −0.1799 −0.0371 −0.0156 −0.0051 0.0079 0.30442012.Q4 −0.1806 −0.0365 −0.0155 −0.0082 0.0080 0.2942

18 π6/W 3 2006.Q4 −0.7794 −0.0517 −0.0279 1.1827 0.0026 0.89262012.Q4 −1.2043 −0.0543 −0.0285 0.1086 0.0021 1.3522

19 π7/W 3 2006.Q4 −0.1331 −0.0519 −0.0225 −0.0183 0.0097 0.14662012.Q4 −0.1367 −0.0521 −0.0211 −0.0169 0.0108 0.1545

20 π8/W 3 2006.Q4 −0.0490 −0.0312 −0.0245 −0.0226 −0.0167 0.02352012.Q4 −0.0473 −0.0312 −0.0247 −0.0230 −0.0171 0.0208

21 π9/W 3 2006.Q4 −0.1897 −0.0513 −0.0084 0.0162 0.0429 0.45272012.Q4 −0.1756 −0.0515 −0.0091 0.0307 0.0430 0.5451

22 π10/W 3 2006.Q4 −0.0406 −0.0230 −0.0149 0.0089 −0.0034 0.22552012.Q4 −0.0406 −0.0238 −0.0158 0.0016 −0.0045 0.2538

34



T a

b l e F . 2 1 : R e t u r n s t o S c a l e ( R e v e n u e ) f o r L a r g e s t B a n k s


1 9 8 4 . Q

4 ( i m

-

p o s i n g h o m o g e n e i t y w i t h r e s p e c t t o i n p u t p r i c e s

)

A s s e t s

N a m e

( b i l l i o n s o f 2 0 0 9 $ )

M o d e l 7

M o d e l 8

M o d e l 9

M o d e l 1 0

M o d e l 1 1

M o d e l 1 2

C I T I B A N K N A

2 0 7

− 0 . 0 4 3 0 ∗ ∗ ∗

− 0 . 0 3 7 5 ∗ ∗ ∗

−

0 . 0 1 5 8 ∗ ∗ ∗

− 0 . 0 2 7 3

− 0 . 0 3 7 5 ∗ ∗ ∗

− 0 . 0 3 1 0 ∗ ∗ ∗

B A N K O F A M

E R N T & S A

1 8 8

− 0 . 0 3 8 6 ∗ ∗ ∗

− 0 . 0 3 6 9

−

0 . 0 0 4 0

− 0 . 0 4 5 3 ∗ ∗ ∗

− 0 . 0 3 6 9

− 0 . 0 2 2 4 ∗ ∗ ∗

C H A S E M A N H

A T T A N B K N A

1 4 3

− 0 . 0 3 9 0 ∗ ∗ ∗

− 0 . 0 1 7 9

−

0 . 0 2 3 3 ∗ ∗ ∗

− 0 . 0 1 0 7

− 0 . 0 1 7 9

− 0 . 0 3 1 5 ∗ ∗ ∗

M O R G A N G U

A R A N T Y T C

1 1 1

− 0 . 0 2 3 5 ∗ ∗ ∗

− 0 . 0 2 3 9

−

0 . 0 0 1 8

− 0 . 0 1 9 7 ∗ ∗ ∗

− 0 . 0 2 3 9

− 0 . 0 1 6 7 ∗ ∗ ∗

M A N U F A C T U

R E R S H A N T C

1 0 8

− 0 . 0 3 2 9 ∗ ∗ ∗

− 0 . 0 3 1 4 ∗ ∗ ∗

−

0 . 0 2 0 6 ∗ ∗ ∗

0 . 0 0 1 4

− 0 . 0 3 1 4 ∗ ∗ ∗

− 0 . 0 3 2 4 ∗ ∗ ∗

C H E M I C A L B

K

9 3

− 0 . 0 3 4 9 ∗ ∗ ∗

− 0 . 0 3 9 8 ∗ ∗ ∗

−

0 . 0 1 9 2 ∗ ∗ ∗

− 0 . 0 5 8 6

− 0 . 0 3 9 8 ∗ ∗ ∗

− 0 . 0 2 4 9 ∗ ∗ ∗

B A N K E R S T C

7 8

− 0 . 0 4 6 0 ∗ ∗ ∗

− 0 . 0 5 0 6 ∗ ∗ ∗

−

0 . 0 0 4 2 ∗

− 0 . 0 2 1 8 ∗ ∗ ∗

− 0 . 0 5 0 6 ∗ ∗ ∗

− 0 . 0 1 4 8 ∗ ∗ ∗

S E C U R I T Y P A

C I F I C N B

6 9

− 0 . 0 2 2 3 ∗ ∗ ∗

− 0 . 0 2 1 8 ∗ ∗ ∗

−

0 . 0 2 7 3 ∗ ∗ ∗

− 0 . 0 1 3 6 ∗ ∗ ∗

− 0 . 0 2 1 8 ∗ ∗ ∗

− 0 . 0 2 4 4 ∗ ∗ ∗

F I R S T N B O F

C H I C A G O

6 3

− 0 . 0 2 9 3 ∗ ∗ ∗

− 0 . 0 3 0 8 ∗ ∗ ∗

−

0 . 0 2 2 7 ∗ ∗ ∗

− 0 . 0 0 3 9

− 0 . 0 3 0 8 ∗ ∗ ∗

− 0 . 0 3 3 3 ∗ ∗ ∗

C O N T I N E N T A


5 4

− 0 . 0 2 1 1 ∗ ∗ ∗

0 . 0 3 7 5

−

0 . 0 0 4 2

− 0 . 0 1 1 6

0 . 0 3 7 5

− 0 . 0 0 5 6 ∗ ∗ ∗

M E L L O N B K N A

4 2

− 0 . 0 1 1 8 ∗ ∗ ∗

− 0 . 0 1 0 7 ∗

−

0 . 0 0 9 4 ∗ ∗ ∗

− 0 . 0 0 9 2

− 0 . 0 1 0 7 ∗

− 0 . 0 1 6 5 ∗ ∗ ∗

W E L L S F A R G

O B K N A

4 2

− 0 . 0 2 6 8 ∗ ∗ ∗

− 0 . 0 0 9 4

−

0 . 0 1 6 7 ∗ ∗ ∗

− 0 . 0 2 7 0 ∗ ∗ ∗

− 0 . 0 0 9 4

− 0 . 0 0 9 6 ∗ ∗ ∗

M A R I N E M I D

L A N D B K N A

3 9

− 0 . 0 3 5 0 ∗ ∗ ∗

− 0 . 0 2 5 0

−

0 . 0 1 8 5 ∗ ∗ ∗

− 0 . 0 2 8 6 ∗ ∗ ∗

− 0 . 0 2 5 0

− 0 . 0 1 8 9 ∗ ∗ ∗

C R O C K E R N B

3 9

− 0 . 0 1 1 6

0 . 0 1 4 1 ∗ ∗

−

0 . 0 1 3 9 ∗ ∗ ∗

− 0 . 0 6 9 0 ∗ ∗ ∗

0 . 0 1 4 1 ∗ ∗

− 0 . 0 2 5 3 ∗ ∗ ∗


3 6

− 0 . 0 3 8 5 ∗ ∗ ∗

− 0 . 0 3 2 2 ∗ ∗ ∗

−

0 . 0 0 6 1

− 0 . 0 4 5 3 ∗ ∗ ∗

− 0 . 0 3 2 2 ∗ ∗ ∗

− 0 . 0 0 5 5

F I R S T N B O F

B O S T O N

3 2

− 0 . 0 6 2 5 ∗ ∗ ∗

0 . 0 2 2 9

−

0 . 0 0 4 2

− 0 . 0 4 1 7 ∗ ∗ ∗

0 . 0 2 2 9

− 0 . 0 2 9 0 ∗ ∗ ∗

I R V I N G T C

3 1

− 0 . 0 2 0 1

− 0 . 0 1 5 9 ∗ ∗ ∗

0 . 0 0 0 8

− 0 . 0 3 3 6 ∗ ∗ ∗

− 0 . 0 1 5 9 ∗ ∗ ∗

− 0 . 0 1 7 8 ∗ ∗ ∗

R E P U B L I C B A

N K D A L L A S N A

2 5

− 0 . 0 2 4 8 ∗ ∗ ∗

0 . 0 0 2 3

−

0 . 0 1 2 0

− 0 . 0 2 0 0 ∗ ∗ ∗

0 . 0 0 2 3

− 0 . 0 4 1 3 ∗ ∗ ∗

B A N K O F N Y

2 5

− 0 . 0 2 3 2 ∗

− 0 . 0 3 1 8

−

0 . 0 2 2 5 ∗ ∗ ∗

− 0 . 0 3 7 6 ∗ ∗ ∗

− 0 . 0 3 1 8

− 0 . 0 1 2 3 ∗ ∗ ∗


2 1

− 0 . 0 3 4 7 ∗ ∗ ∗

− 0 . 0 4 4 2 ∗ ∗ ∗

−

0 . 0 2 3 0 ∗ ∗ ∗

− 0 . 0 1 9 1 ∗ ∗ ∗

− 0 . 0 4 4 2 ∗ ∗ ∗

− 0 . 0 1 4 1 ∗ ∗ ∗

T E X A S C O M M

E R C E B K N A

2 1

− 0 . 0 2 9 1 ∗ ∗ ∗

− 0 . 0 0 1 4 ∗ ∗ ∗

−

0 . 0 0 7 9

− 0 . 0 7 1 5 ∗ ∗ ∗

− 0 . 0 0 1 4 ∗ ∗ ∗

− 0 . 0 3 5 4 ∗ ∗ ∗


2 0

− 0 . 0 5 9 0 ∗ ∗ ∗

− 0 . 0 5 7 2 ∗ ∗ ∗

0 . 0 0 6 1

− 0 . 0 6 3 7 ∗ ∗ ∗

− 0 . 0 5 7 2 ∗ ∗ ∗

− 0 . 0 2 2 3 ∗ ∗ ∗

I N T E R F I R S T

B K D A L L A S N A

1 8

− 0 . 0 3 6 4 ∗ ∗ ∗

− 0 . 0 4 6 4 ∗ ∗

−

0 . 0 1 8 9 ∗ ∗ ∗

− 0 . 0 3 2 1 ∗ ∗ ∗

− 0 . 0 4 6 4 ∗ ∗

− 0 . 0 2 6 1 ∗ ∗ ∗

N C N B N B O F

N C

1 7

− 0 . 0 2 7 2 ∗ ∗ ∗

− 0 . 0 2 8 8 ∗ ∗ ∗

−

0 . 0 2 9 6 ∗ ∗ ∗

− 0 . 0 2 5 5 ∗ ∗ ∗

− 0 . 0 2 8 8 ∗ ∗ ∗

− 0 . 0 1 9 9 ∗ ∗ ∗

F I R S T C I T Y N

B O F H O U S T O N

1 7

− 0 . 0 1 3 3 ∗ ∗ ∗

0 . 0 2 5 0

−

0 . 0 2 2 6

− 0 . 0 0 6 3

0 . 0 2 5 0

− 0 . 0 3 0 7 ∗ ∗ ∗

S O U T H E A S T

B K N A

1 6

− 0 . 0 3 1 3 ∗ ∗ ∗

− 0 . 0 3 3 7 ∗ ∗ ∗

−

0 . 0 2 4 2 ∗ ∗ ∗

− 0 . 0 3 9 1 ∗ ∗ ∗

− 0 . 0 3 3 7 ∗ ∗ ∗

− 0 . 0 1 5 0

D e p . V a r .

R 1 / W 3

R 2 / W 3

R 3 / W 3

R 1 / W 3

R 2 / W 3

R 3 / W 3

R H S V a r s .

( y , w 3 )

( y , w 3 )

( y , w 3 )

( y , w 4 )

( y , w 4 )

( y , w 4 )



35



T a



1 9 9 8 . Q

4 ( i m

-


)

A s s e t s

N a m

e


0 9 $ )

M o d e l 7

M o d e l 8

M

o d e l 9

M o d e l 1 0

M o d e l 1 1

M o d e l 1 2

C I T I B A N K N

A

3 7 6

− 0 . 0 1 9 7 ∗ ∗ ∗

− 0 . 0 1 0 6

− 0 . 0 1 0 5 ∗ ∗ ∗

− 0 . 0 2 7 8 ∗ ∗ ∗

− 0 . 0 1 0 6

− 0 . 0 2 6 3 ∗ ∗ ∗

N A T I O N S B A

N K N A

3 6 2

− 0 . 0 2 8 0 ∗ ∗ ∗

− 0 . 0 4 2 7 ∗ ∗ ∗

− 0 . 0 2 9 2 ∗ ∗ ∗

− 0 . 0 1 7 8 ∗ ∗ ∗

− 0 . 0 4 2 7 ∗ ∗ ∗

− 0 . 0 1 5 2 ∗ ∗ ∗

B A N K O F A

M E R N T & S A

3 1 6

− 0 . 0 1 0 1 ∗ ∗ ∗

0 . 0 1 1 1

0 . 0 1 8 5 ∗ ∗ ∗

− 0 . 0 1 7 8 ∗ ∗

0 . 0 1 1 1

− 0 . 0 2 9 1 ∗ ∗ ∗

F I R S T U N I O

N N B

2 7 7

− 0 . 0 3 1 0 ∗ ∗ ∗

− 0 . 0 2 7 0 ∗ ∗ ∗

− 0 . 0 3 5 2 ∗ ∗ ∗

− 0 . 0 3 0 5 ∗ ∗ ∗

− 0 . 0 2 7 0 ∗ ∗ ∗

− 0 . 0 2 9 0 ∗ ∗ ∗

W E L L S F A R

G O B K N A

1 0 9

− 0 . 0 3 4 6 ∗ ∗ ∗

− 0 . 0 4 5 4 ∗ ∗ ∗

− 0 . 0 0 6 6

− 0 . 0 1 9 5 ∗ ∗ ∗

− 0 . 0 4 5 4 ∗ ∗ ∗

− 0 . 0 3 9 1 ∗ ∗ ∗


9 3

− 0 . 0 4 2 7 ∗ ∗ ∗

− 0 . 0 2 6 7 ∗ ∗ ∗

− 0 . 0 1 1 8 ∗ ∗ ∗

− 0 . 0 0 4 1

− 0 . 0 2 6 7 ∗ ∗ ∗

− 0 . 0 3 9 8 ∗ ∗ ∗

F L E E T N B

9 2

− 0 . 0 1 3 3

0 . 0 0 6 2 ∗

− 0 . 0 1 3 2

− 0 . 0 1 8 1 ∗ ∗ ∗

0 . 0 0 6 2 ∗

− 0 . 0 0 7 6

P N C B K N A

8 9

− 0 . 0 3 3 9 ∗ ∗ ∗

− 0 . 0 1 5 5

− 0 . 0 0 3 3

− 0 . 0 0 9 1

− 0 . 0 1 5 5

− 0 . 0 2 8 2 ∗ ∗ ∗


8 8

− 0 . 0 1 3 9 ∗ ∗ ∗

− 0 . 0 0 3 1

− 0 . 0 2 1 3 ∗ ∗ ∗

− 0 . 0 2 8 5 ∗ ∗ ∗

− 0 . 0 0 3 1

− 0 . 0 1 2 9 ∗ ∗ ∗

U S B K N A

8 6

− 0 . 0 1 8 0 ∗ ∗ ∗

− 0 . 0 2 2 3 ∗ ∗ ∗

− 0 . 0 1 4 6 ∗ ∗ ∗

− 0 . 0 2 2 1 ∗ ∗ ∗

− 0 . 0 2 2 3 ∗ ∗ ∗

− 0 . 0 2 4 9 ∗ ∗ ∗

F I R S T N B O

F C H I C A G O

8 6

− 0 . 0 4 3 2 ∗ ∗ ∗

− 0 . 0 5 4 8 ∗ ∗ ∗

− 0 . 0 3 2 8 ∗ ∗ ∗

− 0 . 0 5 8 0 ∗ ∗ ∗

− 0 . 0 5 4 8 ∗ ∗ ∗

− 0 . 0 3 3 4 ∗ ∗ ∗

W A C H O V I A

B K N A

7 8

− 0 . 0 2 9 8 ∗ ∗ ∗

− 0 . 0 3 8 6 ∗ ∗ ∗

− 0 . 0 3 1 8 ∗ ∗ ∗

− 0 . 0 2 5 2 ∗ ∗ ∗

− 0 . 0 3 8 6 ∗ ∗ ∗

− 0 . 0 2 0 0 ∗ ∗ ∗

B A N K O F N

Y

7 6

− 0 . 0 1 7 0 ∗ ∗ ∗

− 0 . 0 2 7 1

− 0 . 0 3 0 4 ∗ ∗ ∗

− 0 . 0 0 9 8

− 0 . 0 2 7 1

− 0 . 0 2 3 5 ∗ ∗ ∗


5 8

− 0 . 0 3 6 3 ∗ ∗ ∗

− 0 . 0 5 3 4 ∗ ∗ ∗

− 0 . 0 3 3 8 ∗ ∗ ∗

− 0 . 0 0 3 5

− 0 . 0 5 3 4 ∗ ∗ ∗

− 0 . 0 2 3 2 ∗ ∗ ∗


5 6

− 0 . 0 7 6 3 ∗ ∗ ∗

− 0 . 0 7 5 2 ∗ ∗ ∗

− 0 . 0 4 5 8 ∗ ∗ ∗

− 0 . 0 6 1 0 ∗ ∗ ∗

− 0 . 0 7 5 2 ∗ ∗ ∗

− 0 . 0 4 5 1 ∗ ∗ ∗

M E L L O N B K

N A

5 2

− 0 . 0 4 3 7 ∗ ∗ ∗

− 0 . 0 5 8 0 ∗ ∗ ∗

− 0 . 0 2 9 1 ∗ ∗ ∗

− 0 . 0 3 0 7 ∗ ∗ ∗

− 0 . 0 5 8 0 ∗ ∗ ∗

− 0 . 0 4 5 8 ∗ ∗ ∗


4 6

− 0 . 0 1 7 3 ∗ ∗ ∗

0 . 0 0 3 3

− 0 . 0 1 7 5

− 0 . 0 6 5 9 ∗ ∗ ∗

0 . 0 0 3 3

− 0 . 0 5 8 8 ∗ ∗ ∗

R E G I O N S B K

4 2

− 0 . 0 4 6 5 ∗ ∗ ∗

− 0 . 0 2 3 4 ∗ ∗ ∗

− 0 . 0 8 3 3 ∗ ∗ ∗

− 0 . 0 4 7 6 ∗ ∗ ∗

− 0 . 0 2 3 4 ∗ ∗ ∗

0 . 0 2 5 4

M A R I N E M I

D L A N D B K

4 2

− 0 . 0 3 7 0 ∗ ∗ ∗

− 0 . 0 3 0 9 ∗ ∗ ∗

− 0 . 0 4 5 4 ∗ ∗ ∗

− 0 . 0 1 4 0 ∗ ∗ ∗

− 0 . 0 3 0 9 ∗ ∗ ∗

− 0 . 0 0 9 2

C H A S E M A N


4 0

− 0 . 0 5 3 8 ∗ ∗ ∗

− 0 . 0 6 2 8 ∗ ∗ ∗

− 0 . 0 4 7 8 ∗ ∗ ∗

− 0 . 0 4 6 3 ∗ ∗ ∗

− 0 . 0 6 2 8 ∗ ∗ ∗

− 0 . 0 3 4 6 ∗ ∗ ∗


4 0

− 0 . 0 0 9 3

− 0 . 0 0 2 8

− 0 . 0 2 9 9

0 . 0 0 0 9

− 0 . 0 0 2 8

− 0 . 0 3 6 5 ∗ ∗ ∗


3 7

− 0 . 0 4 4 3 ∗ ∗ ∗

− 0 . 0 2 7 3 ∗ ∗ ∗

− 0 . 0 4 0 3 ∗ ∗ ∗

− 0 . 0 5 2 9 ∗ ∗ ∗

− 0 . 0 2 7 3 ∗ ∗ ∗

− 0 . 0 3 2 0 ∗ ∗ ∗

S U M M I T B K

3 7

− 0 . 0 3 0 4 ∗ ∗ ∗

− 0 . 0 2 7 5 ∗ ∗ ∗

− 0 . 0 3 0 5 ∗ ∗ ∗

− 0 . 0 3 2 3 ∗ ∗ ∗

− 0 . 0 2 7 5 ∗ ∗ ∗

− 0 . 0 0 8 3

C O M E R I C A

B K

3 6

− 0 . 0 5 3 1 ∗ ∗ ∗

− 0 . 0 5 5 1 ∗ ∗ ∗

− 0 . 0 0 9 7

− 0 . 0 2 2 0 ∗ ∗ ∗

− 0 . 0 5 5 1 ∗ ∗ ∗

− 0 . 0 1 9 3 ∗ ∗ ∗

N O R W E S T B

K M N N A

3 6

− 0 . 0 2 8 3 ∗ ∗ ∗

− 0 . 0 2 8 3 ∗ ∗ ∗

− 0 . 0 4 5 5 ∗ ∗ ∗

− 0 . 0 2 1 8 ∗ ∗

− 0 . 0 2 8 3 ∗ ∗ ∗

− 0 . 0 0 0 6

F L E E T B K N

A

3 5

− 0 . 0 4 2 5 ∗ ∗ ∗

− 0 . 0 4 2 3 ∗ ∗ ∗

− 0 . 0 4 1 6 ∗ ∗ ∗

− 0 . 0 2 3 4 ∗ ∗ ∗

− 0 . 0 4 2 3 ∗ ∗ ∗

− 0 . 0 1 3 5 ∗ ∗ ∗

D e p . V a r .

R 1 / W 3

R 2 / W 3

R

3 / W 3

R 1 / W 3

R 2 / W 3

R 3 / W 3

R H S V a r s .

( y , w 3 )

( y , w 3 )

( y , w 3 )

( y , w 4 )

( y , w 4 )

( y , w 4 )



36



T a



2 0 0 6 . Q

4 ( i m

-


)

A s s e t s

N a m e


0 0 9 $ )

M o d e l 7

M o d e l 8

M o d e l 9

M o d e l 1 0

M o d e l 1 1

M o d e l 1 2

B A N K O F A M

E R N A

1 2 3 9

− 0 . 0 2 4 5 ∗ ∗ ∗

− 0 . 0 3 8 6 ∗ ∗ ∗

−

0 . 0 2 2 2 ∗ ∗ ∗

− 0 . 0 3 9 9 ∗ ∗ ∗

− 0 . 0 3 8 6 ∗ ∗ ∗

− 0 . 0 3 5 4 ∗ ∗ ∗


1 2 2 4

− 0 . 0 3 2 5 ∗ ∗ ∗

− 0 . 0 3 1 4

−

0 . 0 3 9 2 ∗ ∗ ∗

− 0 . 0 4 8 5 ∗ ∗ ∗

− 0 . 0 3 1 4

− 0 . 0 6 2 4 ∗ ∗ ∗

C I T I B A N K N A

9 5 4

− 0 . 0 2 1 6 ∗ ∗ ∗

− 0 . 0 1 0 7 ∗ ∗ ∗

−

0 . 0 0 6 0 ∗ ∗ ∗

− 0 . 0 2 7 2 ∗ ∗ ∗

− 0 . 0 1 0 7 ∗ ∗ ∗

− 0 . 0 2 6 6 ∗ ∗ ∗


5 3 9

− 0 . 0 2 9 1 ∗ ∗ ∗

− 0 . 0 4 4 2 ∗ ∗ ∗

−

0 . 0 1 9 9 ∗ ∗ ∗

− 0 . 0 2 6 0 ∗ ∗ ∗

− 0 . 0 4 4 2 ∗ ∗ ∗

− 0 . 0 2 5 1 ∗ ∗ ∗

W E L L S F A R G

O B K N A

4 1 6

− 0 . 0 2 8 6 ∗ ∗ ∗

− 0 . 0 1 9 8 ∗ ∗ ∗

−

0 . 0 3 2 3 ∗ ∗ ∗

− 0 . 0 4 1 6 ∗ ∗ ∗

− 0 . 0 1 9 8 ∗ ∗ ∗

− 0 . 0 3 9 9 ∗ ∗ ∗

U S B K N A

2 2 6

− 0 . 0 2 6 9 ∗ ∗ ∗

− 0 . 0 1 6 3 ∗ ∗ ∗

− 0 . 0 0 3 9

− 0 . 0 2 3 9

− 0 . 0 1 6 3 ∗ ∗ ∗

− 0 . 0 2 8 4 ∗ ∗ ∗

S U N T R U S T B

K

1 9 0

− 0 . 0 2 5 8 ∗ ∗ ∗

− 0 . 0 1 5 5 ∗ ∗ ∗

0 . 0 3 1 4 ∗ ∗ ∗

− 0 . 0 2 0 1

− 0 . 0 1 5 5 ∗ ∗ ∗

− 0 . 0 3 6 8 ∗ ∗ ∗


1 7 3

− 0 . 0 2 4 8 ∗ ∗ ∗

− 0 . 1 1 6 1 ∗ ∗ ∗

− 0 . 0 0 6 7

− 0 . 0 6 0 7 ∗ ∗ ∗

− 0 . 1 1 6 1 ∗ ∗ ∗

− 0 . 0 0 4 1

N A T I O N A L C

I T Y B K

1 4 0

− 0 . 0 0 2 0

− 0 . 0 4 3 7 ∗

0 . 0 0 2 8

− 0 . 0 0 5 2 ∗ ∗ ∗

− 0 . 0 4 3 7 ∗

− 0 . 0 0 1 0

R E G I O N S B K

1 1 5

− 0 . 0 4 4 1 ∗ ∗ ∗

− 0 . 0 4 2 3 ∗ ∗ ∗

−

0 . 0 3 4 7 ∗ ∗ ∗

− 0 . 0 3 5 8 ∗ ∗ ∗

− 0 . 0 4 2 3 ∗ ∗ ∗

− 0 . 0 3 6 7 ∗ ∗ ∗


1 0 7

− 0 . 0 3 8 2 ∗ ∗ ∗

− 0 . 0 4 6 0 ∗ ∗ ∗

−

0 . 0 3 0 2 ∗ ∗ ∗

− 0 . 0 3 5 7 ∗ ∗ ∗

− 0 . 0 4 6 0 ∗ ∗ ∗

− 0 . 0 5 8 6 ∗ ∗ ∗


9 7

− 0 . 0 9 3 1 ∗ ∗ ∗

− 0 . 0 9 5 8 ∗ ∗ ∗

−

0 . 0 5 7 2 ∗ ∗ ∗

− 0 . 0 8 7 8 ∗ ∗ ∗

− 0 . 0 9 5 8 ∗ ∗ ∗

− 0 . 0 2 2 7 ∗ ∗ ∗

K E Y B A N K N A

9 4

− 0 . 0 0 3 0

− 0 . 0 1 6 9

0 . 0 3 5 4 ∗ ∗ ∗

− 0 . 0 3 8 4 ∗ ∗ ∗

− 0 . 0 1 6 9

0 . 0 1 7 0 ∗ ∗

P N C B K N A

9 2

− 0 . 0 5 3 4 ∗ ∗ ∗

− 0 . 0 6 3 2 ∗ ∗ ∗

− 0 . 0 0 6 2

− 0 . 0 5 6 7 ∗ ∗ ∗

− 0 . 0 6 3 2 ∗ ∗ ∗

− 0 . 0 3 8 3 ∗ ∗ ∗

B A N K O F N Y

9 2

− 0 . 0 2 6 2 ∗ ∗ ∗

− 0 . 0 5 1 9 ∗ ∗ ∗

−

0 . 0 4 4 0 ∗ ∗ ∗

0 . 0 0 1 3

− 0 . 0 5 1 9 ∗ ∗ ∗

− 0 . 0 4 7 6 ∗ ∗ ∗

C H A S E B K U

S A N A

8 4

− 0 . 0 4 0 9 ∗ ∗ ∗

− 0 . 0 3 2 9 ∗ ∗ ∗

−

0 . 0 2 0 4 ∗ ∗ ∗

− 0 . 0 3 0 5 ∗ ∗ ∗

− 0 . 0 3 2 9 ∗ ∗ ∗

− 0 . 0 3 5 7 ∗ ∗ ∗

C O M E R I C A B

K

6 1

− 0 . 0 5 4 3 ∗ ∗ ∗

− 0 . 0 7 5 6 ∗ ∗ ∗

−

0 . 0 4 6 0 ∗ ∗ ∗

− 0 . 0 1 6 8

− 0 . 0 7 5 6 ∗ ∗ ∗

− 0 . 0 0 8 7 ∗ ∗ ∗

B A N K O F T H

E W E S T

5 8

− 0 . 0 4 7 9 ∗ ∗ ∗

− 0 . 0 2 5 4 ∗ ∗ ∗

−

0 . 0 4 0 8 ∗ ∗ ∗

− 0 . 0 7 2 0 ∗ ∗ ∗

− 0 . 0 2 5 4 ∗ ∗ ∗

− 0 . 0 1 6 1 ∗ ∗

M A N U F A C T U


5 8

0 . 0 0 1 0

− 0 . 0 0 5 9

−

0 . 0 4 2 0 ∗ ∗ ∗

0 . 0 3 4 7 ∗

− 0 . 0 0 5 9

− 0 . 0 3 9 7 ∗ ∗ ∗


5 8

− 0 . 0 2 9 9 ∗ ∗ ∗

− 0 . 0 1 7 8

− 0 . 0 0 7 5

− 0 . 0 3 9 3 ∗ ∗ ∗

− 0 . 0 1 7 8

− 0 . 0 3 5 7 ∗ ∗ ∗

U N I O N B K O

F C A N A

5 4

− 0 . 0 4 9 8 ∗ ∗ ∗

− 0 . 0 5 3 9 ∗ ∗ ∗

−

0 . 0 4 4 4 ∗ ∗ ∗

− 0 . 0 0 5 7

− 0 . 0 5 3 9 ∗ ∗ ∗

− 0 . 0 4 3 3 ∗ ∗ ∗

N O R T H E R N T C

5 2

− 0 . 0 2 8 0 ∗ ∗ ∗

− 0 . 0 4 0 2 ∗ ∗ ∗

− 0 . 0 0 9 5

− 0 . 0 7 4 0 ∗ ∗ ∗

− 0 . 0 4 0 2 ∗ ∗ ∗

− 0 . 0 1 3 8 ∗ ∗ ∗


5 1

− 0 . 0 1 7 3

− 0 . 0 4 4 6 ∗ ∗ ∗

−

0 . 0 6 2 1 ∗ ∗ ∗

− 0 . 0 4 7 6 ∗ ∗ ∗

− 0 . 0 4 4 6 ∗ ∗ ∗

− 0 . 0 3 2 4 ∗ ∗ ∗


5 0

− 0 . 0 4 9 2 ∗ ∗ ∗

− 0 . 0 8 8 9 ∗ ∗ ∗

−

0 . 0 2 7 5 ∗ ∗ ∗

− 0 . 0 4 2 2 ∗ ∗ ∗

− 0 . 0 8 8 9 ∗ ∗ ∗

− 0 . 0 4 3 8 ∗ ∗ ∗


4 8

− 0 . 0 2 4 0 ∗ ∗

− 0 . 0 4 1 9 ∗ ∗ ∗

− 0 . 0 2 4 4

0 . 0 0 4 2

− 0 . 0 4 1 9 ∗ ∗ ∗

− 0 . 0 4 5 9 ∗ ∗ ∗

H A R R I S N A

4 3

− 0 . 0 1 5 2

0 . 0 4 3 3 ∗ ∗

− 0 . 0 2 2 5

− 0 . 0 1 6 7

0 . 0 4 3 3 ∗ ∗

− 0 . 0 0 5 8

D e p . V a r .

R 1 / W 3

R 2 / W 3

R 3 / W 3

R 1 / W 3

R 2 / W 3

R 3 / W 3

R H S V a r s .

( y , w 3 )

( y , w 3 )

( y , w 3 )

( y , w 4 )

( y , w 4 )

( y , w 4 )



37



T a



2 0 1 2 . Q

4 ( i m

-


)

A s s e t s

N a m e

( b i l l i o n s o f 2 0 0 9 $ )

M o d e l 7

M o d e l 8

M o d e l 9

M o d e l 1 0

M o d e l 1 1

M o d e l 1 2


1 7 6 9

− 0 . 0 2 1 8 ∗ ∗ ∗

− 0 . 0 0 6 8

0

. 0 7 1 4 ∗ ∗ ∗

− 0 . 0 1 9 8 ∗ ∗ ∗

− 0 . 0 0 6 8

− 0 . 0 0 4 1

B A N K O F A M E R N

A

1 3 8 0

− 0 . 0 1 9 1 ∗ ∗ ∗

− 0 . 0 0 6 0

0

. 0 0 7 8

− 0 . 0 2 0 2

− 0 . 0 0 6 0

− 0 . 0 2 9 0 ∗ ∗ ∗

C I T I B A N K N A

1 2 6 5

− 0 . 0 1 1 2 ∗ ∗ ∗

− 0 . 0 1 2 3 ∗

− 0

. 0 2 5 5

− 0 . 0 0 6 5

− 0 . 0 1 2 3 ∗

− 0 . 0 3 4 0 ∗ ∗ ∗

W E L L S F A R G O B K

N A

1 1 7 3

− 0 . 0 1 9 9 ∗ ∗ ∗

− 0 . 0 0 8 0

− 0

. 0 0 3 6

− 0 . 0 1 3 8

− 0 . 0 0 8 0

− 0 . 0 2 8 9 ∗ ∗ ∗

U S B K N A

3 2 5

− 0 . 0 1 3 5 ∗ ∗ ∗

− 0 . 0 2 2 6 ∗ ∗ ∗

− 0

. 0 2 0 6 ∗ ∗ ∗

− 0 . 0 2 5 4 ∗ ∗ ∗

− 0 . 0 2 2 6 ∗ ∗ ∗

− 0 . 0 2 2 1 ∗ ∗ ∗

P N C B K N A

2 7 7

− 0 . 0 2 9 0 ∗ ∗ ∗

0 . 0 0 1 5

− 0

. 0 0 3 1 ∗ ∗ ∗

− 0 . 0 3 1 0 ∗ ∗ ∗

0 . 0 0 1 5

− 0 . 0 1 7 4 ∗ ∗ ∗

B A N K O F N Y M E L L O N

2 5 8

0 . 1 6 8 9

− 2 . 5 6 4 6 ( 3 )

− 0

. 0 3 1 6 ∗ ∗ ∗

− 4 9 . 5 8 1 8 ( 3 )

− 2 . 5 6 4 6 ( 3 )

− 0 . 0 4 2 3 ∗ ∗ ∗

S T A T E S T R E E T B &

T C

1 9 8

− 0 . 0 8 5 7 ∗ ∗ ∗

− 0 . 2 9 7 9

− 0

. 0 4 3 9 ∗ ∗ ∗

− 0 . 4 9 1 7

− 0 . 2 9 7 9

− 0 . 0 4 5 9 ∗ ∗ ∗

T D B K N A

1 9 1

− 0 . 0 2 4 7 ∗ ∗ ∗

− 0 . 0 2 8 4 ∗ ∗ ∗

− 0

. 0 1 7 2 ∗ ∗ ∗

− 0 . 0 1 8 2 ∗ ∗ ∗

− 0 . 0 2 8 4 ∗ ∗ ∗

− 0 . 0 0 7 4 ∗ ∗ ∗


1 8 1

0 . 1 2 0 4 ∗ ∗ ∗

− 0 . 0 6 4 2 ∗ ∗ ∗

− 0

. 0 2 7 4 ∗ ∗ ∗

− 0 . 0 6 6 0 ∗ ∗ ∗

− 0 . 0 6 4 2 ∗ ∗ ∗

− 0 . 0 4 3 4 ∗ ∗ ∗


1 6 7

− 0 . 0 3 1 3 ∗ ∗ ∗

− 0 . 0 1 8 5 ∗ ∗ ∗

− 0

. 0 1 4 8 ∗ ∗ ∗

0 . 0 5 3 1 ∗ ∗ ∗

− 0 . 0 1 8 5 ∗ ∗ ∗

− 0 . 0 1 8 2 ∗ ∗ ∗

S U N T R U S T B K

1 6 0

− 0 . 0 0 7 4 ∗ ∗ ∗

− 0 . 0 5 8 9 ∗ ∗ ∗

− 0

. 0 2 5 1 ∗ ∗ ∗

− 0 . 0 2 4 8 ∗ ∗ ∗

− 0 . 0 5 8 9 ∗ ∗ ∗

− 0 . 0 1 4 2 ∗ ∗ ∗


1 5 6

− 0 . 0 5 2 3 ∗ ∗ ∗

− 0 . 0 5 0 8 ∗ ∗ ∗

− 0

. 0 1 6 6 ∗ ∗ ∗

− 0 . 0 2 7 5 ∗ ∗ ∗

− 0 . 0 5 0 8 ∗ ∗ ∗

− 0 . 0 0 9 4

R E G I O N S B K

1 1 4

− 0 . 0 4 0 9 ∗ ∗ ∗

− 0 . 0 3 1 0 ∗ ∗ ∗

− 0

. 0 0 3 3

− 0 . 0 2 0 9

− 0 . 0 3 1 0 ∗ ∗ ∗

− 0 . 0 1 5 4 ∗ ∗ ∗


1 1 1

0 . 0 1 1 3

− 0 . 1 1 9 4 ∗ ∗ ∗

− 0

. 0 3 8 1 ∗ ∗ ∗

− 0 . 0 2 6 0

− 0 . 1 1 9 4 ∗ ∗ ∗

− 0 . 0 0 5 0 ∗ ∗ ∗

R B S C I T I Z E N S N A

1 0 0

− 0 . 0 3 3 7 ∗ ∗ ∗

0 . 0 5 1 6 ∗ ∗ ∗

− 0

. 0 1 8 9 ∗

0 . 0 5 1 8 ∗ ∗ ∗

0 . 0 5 1 6 ∗ ∗ ∗

− 0 . 0 3 0 3 ∗ ∗ ∗

N O R T H E R N T C

9 0

− 0 . 0 7 6 5 ∗ ∗ ∗

− 0 . 0 6 8 5 ∗ ∗ ∗

− 0

. 0 1 3 2 ∗ ∗ ∗

− 0 . 0 6 9 5

− 0 . 0 6 8 5 ∗ ∗ ∗

− 0 . 0 5 3 3 ∗ ∗ ∗

B M O H A R R I S B K N

A

8 8

− 0 . 0 6 0 6 ∗ ∗ ∗

− 0 . 0 1 4 8

− 0

. 0 1 3 1 ∗ ∗ ∗

0 . 0 5 4 2 ∗ ∗ ∗

− 0 . 0 1 4 8

− 0 . 0 0 7 9 ∗ ∗ ∗

K E Y B A N K N A

8 1

0 . 0 4 5 8 ∗ ∗ ∗

− 0 . 0 2 2 6

− 0

. 0 1 3 5 ∗ ∗ ∗

− 0 . 0 0 6 7

− 0 . 0 2 2 6

− 0 . 0 0 6 5

S O V E R E I G N B K N A

7 8

− 0 . 0 5 0 4 ∗ ∗ ∗

− 0 . 0 2 2 6 ∗ ∗ ∗

− 0

. 0 2 7 9 ∗ ∗ ∗

− 0 . 0 8 9 2 ∗ ∗ ∗

− 0 . 0 2 2 6 ∗ ∗ ∗

− 0 . 0 3 9 2 ∗ ∗ ∗

M A N U F A C T U R E R S

& T R A D E R S T C

7 7

− 0 . 0 5 8 3 ∗ ∗ ∗

− 0 . 0 7 0 1 ∗ ∗ ∗

− 0

. 0 8 5 5 ∗ ∗ ∗

− 0 . 0 5 2 3

− 0 . 0 7 0 1 ∗ ∗ ∗

− 0 . 0 3 0 4 ∗ ∗ ∗

D I S C O V E R B K

6 9

− 0 . 0 4 2 8 ∗ ∗ ∗

− 0 . 0 4 1 4 ∗ ∗ ∗

0

. 0 1 4 8 ∗

− 0 . 0 6 2 2 ∗ ∗ ∗

− 0 . 0 4 1 4 ∗ ∗ ∗

− 0 . 0 2 7 1 ∗ ∗ ∗

C O M P A S S B K

6 5

− 0 . 0 3 6 9 ∗ ∗ ∗

− 0 . 0 9 3 5 ∗ ∗ ∗

− 0

. 0 0 9 3 ∗ ∗ ∗

− 0 . 0 5 9 1 ∗ ∗ ∗

− 0 . 0 9 3 5 ∗ ∗ ∗

− 0 . 0 0 6 0 ∗ ∗ ∗

C O M E R I C A B K

6 1

− 0 . 0 5 4 7 ∗ ∗ ∗

− 0 . 0 3 3 6 ∗ ∗ ∗

− 0

. 0 2 0 8 ∗ ∗ ∗

− 0 . 0 7 0 7 ∗ ∗ ∗

− 0 . 0 3 3 6 ∗ ∗ ∗

− 0 . 0 4 4 3 ∗ ∗ ∗

B A N K O F T H E W E

S T

6 0

0 . 0 0 8 7 ∗ ∗

0 . 0 5 4 6 ∗ ∗ ∗

− 0

. 0 2 8 2 ∗ ∗ ∗

0 . 0 0 1 1 ∗

0 . 0 5 4 6 ∗ ∗ ∗

− 0 . 0 3 8 4 ∗ ∗ ∗

H U N T I N G T O N N B

5 3

− 0 . 0 8 2 2 ∗ ∗ ∗

− 0 . 0 3 1 1 ∗ ∗ ∗

− 0

. 0 3 2 0 ∗ ∗ ∗

− 0 . 0 1 6 0

− 0 . 0 3 1 1 ∗ ∗ ∗

− 0 . 0 2 7 6 ∗ ∗ ∗

D e p . V a r .

R 1 / W 3

R 2 / W 3

R 3 / W 3

R 1 / W 3

R 2 /

W 3

R 3 / W 3

R H S V a r s .

( y , w 3 )

( y , w 3 )

( y , w 3 )

( y , w 4 )

( y , w 4 )

( y , w 4 )




( 3 ) i n d i c a t e ( r e s p e c t i v e l y ) δ R ( y , w ) < 0 a n d R ( δ y , w ) > 0 ; δ R ( y , w ) > 0 a n d R ( δ y , w ) < 0 ; o r δ R ( y , w ) < 0 a n d R ( δ y , w ) < 0 . S e e A p p e n d i x A f o r i n t e r p r e t a t i o n

38



T a

b l e F . 2 5 : R e t u r n s t o S c a l e ( P r o fi t ) f o r L a r g e s t B a n k s b y T

o t a l A s s e t s ,

1 9 8 4 . Q

4 ( i m p o s i n g

h o m o g e n e i t y w i t h

r e s p e c t t o i n p u t p r i c e s )

A s s e t s

N a m e

( b i l l i o n s o f 2 0 0 9 $ )

M o d e l 1 3

M o d e l 1 4

M o d e l 1 5

M o d e l 1 6

M o d

e l 1 7

C I T I B A

N K N A

2 0 7

− 0 . 0 6 1 1

0 . 0 3 0 3

− 0 . 0 6 1 1

0 . 0 0 0 0

0 . 0 3

0 3

B A N K


1 8 8

− 0 . 0 4 1 6

− 0 . 0 3 2 3

− 0 . 0 4 1 6

0 . 0 0 0 0

− 0 . 0 3

2 3

C H A S E

M A N H A T T A N B K N A

1 4 3

− 0 . 0 7 6 0 ∗

− 0 . 0 5 6 9

− 0 . 0 7 6 0 ∗

0 . 0 0 0 0

− 0 . 0 5

6 9

M O R G A N G U A R A N T Y T C

1 1 1

− 0 . 0 0 4 0

− 0 . 0 3 1 9 ∗ ∗ ∗

− 0 . 0 0 4 0

0 . 0 0 0 0

− 0 . 0 3

1 9 ∗ ∗ ∗

M A N U F A C T U R E R S H A N T C

1 0 8

− 0 . 0 5 2 5

− 0 . 1 3 3 7

− 0 . 0 5 2 5

0 . 0 0 0 0

− 0 . 1 3

3 7

C H E M I C A L B K

9 3

− 0 . 0 5 3 9 ∗ ∗ ∗

− 0 . 0 1 7 2

− 0 . 0 5 3 9 ∗ ∗ ∗

0 . 0 0 0 0

− 0 . 0 1

7 2

B A N K E

R S T C

7 8

− 0 . 0 1 0 0

− 0 . 0 1 7 0 ∗ ∗ ∗

− 0 . 0 1 0 0

0 . 0 0 0 0

− 0 . 0 1

7 0 ∗ ∗ ∗

S E C U R

I T Y P A C I F I C N B

6 9

− 0 . 0 5 6 4 ∗ ∗ ∗

− 0 . 0 2 4 4 ∗ ∗ ∗

− 0 . 0 5 6 4 ∗ ∗ ∗

0 . 0 0 0 0

− 0 . 0 2

4 4 ∗ ∗ ∗

F I R S T

N B O F C H I C A G O

6 3

− 0 . 0 4 4 9 ∗ ∗ ∗

− 0 . 1 8 2 7

− 0 . 0 4 4 9 ∗ ∗ ∗

0 . 0 0 0 0

− 0 . 1 8

2 7

C O N T I

N E N T A L I L N B & T C C H I C A G O

5 4

0 . 2 6 5 3 ∗

− 0 . 0 8 2 5

0 . 2 6 5 3 ∗

0 . 0 0 0 0

− 0 . 0 8

2 5

M E L L O

N B K N A

4 2

− 0 . 0 1 9 2 ∗ ∗ ∗

− 0 . 0 5 9 2 ∗ ∗ ∗

− 0 . 0 1 9 2 ∗ ∗ ∗

0 . 0 0 0 0

− 0 . 0 5

9 2 ∗ ∗ ∗

W E L L S

F A R G O B K N A

4 2

− 0 . 0 7 3 5

− 0 . 0 3 5 8

− 0 . 0 7 3 5

0 . 0 0 0 0

− 0 . 0 3

5 8

M A R I N

E M I D L A N D B K N A

3 9

− 0 . 0 4 8 4 ∗ ∗ ∗

− 0 . 0 6 0 7 ∗ ∗ ∗

− 0 . 0 4 8 4 ∗ ∗ ∗

0 . 0 0 0 0

− 0 . 0 6

0 7 ∗ ∗ ∗

C R O C K

E R N B

3 9

− 0 . 0 0 6 4

− 0 . 0 1 8 7

− 0 . 0 0 6 4

0 . 0 0 0 0

− 0 . 0 1

8 7

F I R S T

I N T R S T B K O F C A

3 6

− 0 . 0 7 3 9 ∗ ∗ ∗

− 0 . 0 0 4 6

− 0 . 0 7 3 9 ∗ ∗ ∗

0 . 0 0 0 0

− 0 . 0 0

4 6

F I R S T

N B O F B O S T O N

3 2

0 . 0 1 6 0

− 0 . 0 1 5 8 ∗ ∗ ∗

0 . 0 1 6 0

0 . 0 0 0 0

− 0 . 0 1

5 8 ∗ ∗ ∗

I R V I N G

T C

3 1

0 . 0 5 2 0 ∗

− 0 . 0 5 4 3

0 . 0 5 2 0 ∗

0 . 0 0 0 0

− 0 . 0 5

4 3

R E P U B

L I C B A N K D A L L A S N A

2 5

− 0 . 0 0 5 2

0 . 0 5 8 3

− 0 . 0 0 5 2

0 . 0 0 0 0

0 . 0 5

8 3

B A N K

O F N Y

2 5

− 0 . 0 5 7 2

− 0 . 0 3 8 3 ∗ ∗ ∗

− 0 . 0 5 7 2

0 . 0 0 0 0

− 0 . 0 3

8 3 ∗ ∗ ∗


2 1

− 0 . 0 1 4 8 ∗ ∗ ∗

− 0 . 0 3 2 1

− 0 . 0 1 4 8 ∗ ∗ ∗

0 . 0 0 0 0

− 0 . 0 3

2 1

T E X A S

C O M M E R C E B K N A

2 1

− 0 . 1 3 8 3

− 0 . 0 1 1 6

− 0 . 1 3 8 3

0 . 0 0 0 0

− 0 . 0 1

1 6

R E P U B

L I C N B O F N Y

2 0

− 0 . 0 8 0 1 ∗ ∗ ∗

0 . 0 0 3 1

− 0 . 0 8 0 1 ∗ ∗ ∗

0 . 0 0 0 0

0 . 0 0

3 1

I N T E R F I R S T B K D A L L A S N A

1 8

0 . 0 3 7 3

0 . 0 3 4 4

0 . 0 3 7 3

0 . 0 0 0 0

0 . 0 3

4 4

N C N B N B O F N C

1 7

− 0 . 0 2 9 0 ∗ ∗ ∗

− 0 . 0 4 4 6 ∗ ∗ ∗

− 0 . 0 2 9 0 ∗ ∗ ∗

0 . 0 0 0 0

− 0 . 0 4

4 6 ∗ ∗ ∗

F I R S T

C I T Y N B O F H O U S T O N

1 7

− 0 . 0 2 6 0

0 . 0 0 6 7

− 0 . 0 2 6 0

0 . 0 0 0 0

0 . 0 0

6 7

S O U T H

E A S T B K N A

1 6

− 0 . 0 4 7 7 ∗ ∗ ∗

− 0 . 0 1 7 4

− 0 . 0 4 7 7 ∗ ∗ ∗

0 . 0 0 0 0

− 0 . 0 1

7 4

D e p . V a r .

π 1 / W 3

π 2 / W 3

π 3 / W 3

π 4 / W 3

π 5

/

W 3

R H S V a r s .

( y , w 3 )

( y , w 4

)

( y , w 3 )

( y , w 3 )

( y , w 4 )



39



T a



1 9 8 4 . Q

4 ( i m p o s i n g


r e s p e c t t o i n p u t p r i c e s , c o n t i n

u e d )

A s s e t

s

N a m e

( b i l l i o n s o f 2 0 0 9 $ )

M o d e l 1 3

M o d e l 1 4

M o d e l 1 5

M o d e l 1 6

M o d e l 1 7

C I T I B A N K N A

2 0 7

− 0 . 0 8 5 1 ∗ ∗ ∗

− 0 . 0 2 0 7

− 0 . 0 6 1 0 ∗ ∗ ∗

0 . 0 0 7 7 ∗ ∗

−

0 . 0 5 4 5 ∗ ∗ ∗

B A N K O F A M

E R N T & S A

1 8 8

− 0 . 0 5 3 1 ∗ ∗ ∗

0 . 0 3 6 9 ∗ ∗ ∗

− 0 . 0 5 7 2 ∗ ∗ ∗

− 0 . 0 0 6 2

−

0 . 0 5 1 2 ∗ ∗ ∗

C H A S E M A N H A T T A N B K N A

1 4 3

− 0 . 0 6 7 3 ∗ ∗ ∗

− 0 . 0 2 2 9

− 0 . 0 4 9 9 ∗ ∗ ∗

− 0 . 0 2 0 3 ∗ ∗ ∗

−

0 . 0 3 7 9 ∗ ∗ ∗

M O R G A N G U

A R A N T Y T C

1 1 1

− 0 . 0 3 7 2 ∗ ∗ ∗

− 0 . 0 0 8 1 ∗ ∗ ∗

− 0 . 0 4 9 1 ∗ ∗ ∗

− 0 . 0 2 7 2 ∗ ∗ ∗

−

0 . 0 5 0 1 ∗ ∗ ∗

M A N U F A C T U

R E R S H A N T C

1 0 8

− 0 . 0 9 6 8 ∗ ∗

− 0 . 0 1 9 6

− 0 . 0 5 0 6 ∗ ∗ ∗

− 0 . 0 0 3 8

−

0 . 0 4 1 6 ∗ ∗ ∗

C H E M I C A L B

K

9 3

− 0 . 0 6 0 6 ∗

0 . 0 1 1 8 ∗ ∗

− 0 . 0 2 2 4 ∗ ∗ ∗

− 0 . 0 1 6 1 ∗ ∗ ∗

−

0 . 0 1 2 1 ∗ ∗ ∗

B A N K E R S T C

7 8

− 0 . 0 4 5 7 ∗ ∗ ∗

− 0 . 0 1 9 0 ∗ ∗ ∗

− 0 . 0 5 0 0 ∗ ∗ ∗

− 0 . 0 3 1 6 ∗ ∗ ∗

−

0 . 0 5 0 5 ∗ ∗ ∗

S E C U R I T Y P A C I F I C N B

6 9

− 0 . 0 8 4 6 ∗ ∗ ∗

− 0 . 0 1 7 3

− 0 . 0 4 1 7 ∗ ∗ ∗

0 . 0 2 0 0

−

0 . 0 2 8 3 ∗ ∗ ∗

F I R S T N B O F

C H I C A G O

6 3

− 0 . 1 1 6 7 ∗ ∗ ∗

− 0 . 0 2 0 3 ∗ ∗ ∗

− 0 . 0 3 5 9 ∗ ∗ ∗

− 0 . 0 7 7 4 ∗ ∗ ∗

−

0 . 0 2 5 4 ∗ ∗ ∗

C O N T I N E N T A L I L N B & T C C H I C A G O

5 4

− 0 . 0 3 8 0

− 0 . 0 1 4 9

− 0 . 0 4 7 0 ∗ ∗ ∗

− 0 . 0 0 7 8

−

0 . 0 4 4 2 ∗ ∗ ∗

M E L L O N B K

N A

4 2

− 0 . 0 7 4 6 ∗ ∗ ∗

− 0 . 0 1 3 2

− 0 . 0 2 7 2 ∗ ∗ ∗

− 0 . 0 0 2 9

−

0 . 0 1 6 5 ∗ ∗ ∗

W E L L S F A R G

O B K N A

4 2

− 0 . 0 6 4 4

− 0 . 0 0 0 1

− 0 . 0 2 8 6 ∗ ∗ ∗

− 0 . 0 3 2 7 ∗ ∗ ∗

−

0 . 0 1 6 5 ∗ ∗ ∗

M A R I N E M I D

L A N D B K N A

3 9

− 0 . 6 6 1 3 ∗ ∗

− 0 . 0 2 9 3 ∗ ∗ ∗

− 0 . 0 3 2 3 ∗ ∗ ∗

− 0 . 0 0 5 6

−

0 . 0 2 8 0 ∗ ∗ ∗

C R O C K E R N B

3 9

− 0 . 1 2 3 3

0 . 0 0 2 4

− 0 . 0 4 0 8 ∗ ∗ ∗

− 0 . 0 3 0 7 ∗ ∗ ∗

−

0 . 0 2 5 8 ∗ ∗ ∗

F I R S T I N T R S

T B K O F C A

3 6

− 0 . 1 3 6 2

− 0 . 0 0 4 1

− 0 . 0 2 9 3 ∗ ∗ ∗

− 0 . 0 1 3 4

−

0 . 0 2 1 2 ∗ ∗ ∗

F I R S T N B O F

B O S T O N

3 2

− 0 . 0 6 2 0

− 0 . 0 1 0 2

− 0 . 0 5 3 3 ∗ ∗ ∗

− 0 . 0 4 4 2

−

0 . 0 4 8 3 ∗ ∗ ∗

I R V I N G T C

3 1

− 0 . 0 5 1 0

− 0 . 0 3 3 9 ∗

− 0 . 0 2 1 9 ∗ ∗ ∗

− 0 . 0 6 5 1 ∗ ∗ ∗

−

0 . 0 0 7 8 ∗ ∗ ∗

R E P U B L I C B A

N K D A L L A S N A

2 5

− 0 . 1 3 4 9

− 0 . 0 4 6 7

− 0 . 0 0 6 5 ∗ ∗ ∗

− 0 . 0 1 4 5

−

0 . 0 2 4 2 ∗ ∗ ∗

B A N K O F N Y

2 5

− 0 . 0 9 0 9

− 0 . 0 1 9 8

− 0 . 0 3 3 1 ∗ ∗ ∗

− 0 . 0 1 7 2

−

0 . 0 2 8 1 ∗ ∗ ∗

N A T I O N A L B

K O F D E T R O I T

2 1

0 . 0 4 1 7

− 0 . 0 2 9 0

− 0 . 0 2 3 5 ∗ ∗ ∗

− 0 . 0 0 1 9

−

0 . 0 0 8 9 ∗ ∗ ∗

T E X A S C O M M E R C E B K N A

2 1

− 0 . 1 0 4 2 ∗ ∗ ∗

− 0 . 0 0 2 2

0 . 0 0 7 1 ∗ ∗ ∗

− 0 . 0 4 5 7 ∗ ∗ ∗

−

0 . 0 1 1 9 ∗ ∗ ∗


2 0

− 0 . 1 1 0 4 ∗ ∗ ∗

0 . 0 0 1 8

− 0 . 0 1 3 0 ∗ ∗ ∗

− 0 . 0 4 6 8 ∗ ∗ ∗

−

0 . 0 2 7 7 ∗ ∗ ∗

I N T E R F I R S T

B K D A L L A S N A

1 8

− 0 . 1 1 4 5 ( 3 )

− 0 . 0 2 2 0

0 . 0 3 1 2 ∗ ∗ ∗

− 0 . 0 2 5 1 ∗ ∗ ∗

−

0 . 0 2 5 2 ∗ ∗ ∗

N C N B N B O F

N C

1 7

− 0 . 0 2 6 0 ∗ ∗ ∗

− 0 . 0 3 8 0 ∗ ∗ ∗

0 . 0 0 0 1 ∗ ∗ ∗

− 0 . 0 1 3 4

−

0 . 0 2 8 5 ∗ ∗ ∗


1 7

− 0 . 1 9 2 8

− 0 . 0 3 4 8

0 . 0 2 6 2 ∗ ∗

0 . 0 0 1 9

−

0 . 0 1 0 1 ∗ ∗ ∗

S O U T H E A S T

B K N A

1 6

− 0 . 0 4 8 7 ∗ ∗ ∗

− 0 . 0 1 3 2

− 0 . 0 1 7 0 ∗ ∗ ∗

− 0 . 0 0 1 3

−

0 . 0 2 0 3 ∗ ∗ ∗

D e p . V a r .

π 6 / W 3

π 7 / W 3

π 8 / W 3

π 9 / W 3

π 1 0 / W 3

R H S V a r s .

( y , w 4 )

( y , w 3 )

( y , w 3 )

( y , w 4 )

( y , w 4 )







40



T a



1 9 9 8 . Q

4 ( i m p o s i n g



A s s e t s

N a m e

( b i l l i o n s o f 2 0 0 9 $ )

M o d e l 1 3

M o d e l 1 4

M o d e l 1 5

M o d e l 1 6

M o d e l 1 7

C I T I B

A N K N A

3 7 6

− 0 . 0 2 8 2 ∗ ∗ ∗

− 0 . 0 4 5 7 ∗ ∗

∗

− 0 . 0 2 8 2 ∗ ∗ ∗

0 . 0 0 0 0

− 0 . 0 4 5 7 ∗ ∗ ∗

N A T I O N S B A N K N A

3 6 2

− 0 . 0 2 5 4 ∗ ∗ ∗

− 0 . 0 4 1 9 ∗ ∗

∗

− 0 . 0 2 5 4 ∗ ∗ ∗

0 . 0 0 0 0

− 0 . 0 4 1 9 ∗ ∗ ∗

B A N K


3 1 6

− 0 . 0 1 4 5 ∗ ∗ ∗

− 0 . 0 4 0 4 ∗ ∗

∗

− 0 . 0 1 4 5 ∗ ∗ ∗

0 . 0 0 0 0

− 0 . 0 4 0 4 ∗ ∗ ∗


2 7 7

− 0 . 0 4 0 4 ∗ ∗ ∗

− 0 . 0 3 7 8 ∗ ∗

∗

− 0 . 0 4 0 4 ∗ ∗ ∗

0 . 0 0 0 0

− 0 . 0 3 7 8 ∗ ∗ ∗


1 0 9

− 0 . 0 4 5 7 ∗ ∗ ∗

− 0 . 0 1 2 6 ∗ ∗

∗

− 0 . 0 4 5 7 ∗ ∗ ∗

0 . 0 0 0 0

− 0 . 0 1 2 6 ∗ ∗ ∗

K E Y B

A N K N A T A S S N

9 3

− 0 . 0 2 3 0 ∗ ∗ ∗

− 0 . 0 2 7 9 ∗ ∗

∗

− 0 . 0 2 3 0 ∗ ∗ ∗

0 . 0 0 0 0

− 0 . 0 2 7 9 ∗ ∗ ∗

F L E E

T N B

9 2

− 0 . 0 1 0 7

− 0 . 0 2 2 7 ∗ ∗

∗

− 0 . 0 1 0 7

0 . 0 0 0 0

− 0 . 0 2 2 7 ∗ ∗ ∗

P N C B K N A

8 9

− 0 . 0 4 0 5 ∗ ∗ ∗

− 0 . 0 2 2 6 ∗ ∗

∗

− 0 . 0 4 0 5 ∗ ∗ ∗

0 . 0 0 0 0

− 0 . 0 2 2 6 ∗ ∗ ∗

B A N K

B O S T O N N A

8 8

− 0 . 0 1 3 8

− 0 . 0 1 8 0 ∗ ∗

∗

− 0 . 0 1 3 8

0 . 0 0 0 0

− 0 . 0 1 8 0 ∗ ∗ ∗

U S B

K N A

8 6

− 0 . 0 2 8 6 ∗ ∗ ∗

− 0 . 0 2 8 6 ∗ ∗

∗

− 0 . 0 2 8 6 ∗ ∗ ∗

0 . 0 0 0 0

− 0 . 0 2 8 6 ∗ ∗ ∗


8 6

− 0 . 0 3 5 3 ∗ ∗ ∗

− 0 . 0 0 0 1

− 0 . 0 3 5 3 ∗ ∗ ∗

0 . 0 0 0 0

− 0 . 0 0 0 1


7 8

0 . 0 1 0 5

− 0 . 0 3 4 7 ∗ ∗

∗

0 . 0 1 0 5

0 . 0 0 0 0

− 0 . 0 3 4 7 ∗ ∗ ∗

B A N K

O F N Y

7 6

− 0 . 0 1 3 4 ∗ ∗ ∗

− 0 . 0 0 9 2 ∗ ∗

∗

− 0 . 0 1 3 4 ∗ ∗ ∗

0 . 0 0 0 0

− 0 . 0 0 9 2 ∗ ∗ ∗

R E P U

B L I C N B O F N Y

5 8

− 0 . 0 6 0 1 ∗ ∗ ∗

− 0 . 0 2 1 4 ∗ ∗

∗

− 0 . 0 6 0 1 ∗ ∗ ∗

0 . 0 0 0 0

− 0 . 0 2 1 4 ∗ ∗ ∗

S T A T


5 6

− 0 . 0 9 7 0 ∗ ∗ ∗

− 0 . 0 5 5 7 ∗ ∗

∗

− 0 . 0 9 7 0 ∗ ∗ ∗

0 . 0 0 0 0

− 0 . 0 5 5 7 ∗ ∗ ∗

M E L L

O N B K N A

5 2

− 0 . 0 5 3 5 ∗ ∗ ∗

− 0 . 0 3 9 8 ∗ ∗

∗

− 0 . 0 5 3 5 ∗ ∗ ∗

0 . 0 0 0 0

− 0 . 0 3 9 8 ∗ ∗ ∗

S O U T

H T R U S T B K N A

4 6

− 0 . 0 0 1 6

− 0 . 0 3 4 2 ∗ ∗

− 0 . 0 0 1 6

0 . 0 0 0 0

− 0 . 0 3 4 2 ∗ ∗

R E G I

O N S B K

4 2

− 0 . 0 5 1 0 ∗ ∗ ∗

− 0 . 0 2 8 9 ∗ ∗

∗

− 0 . 0 5 1 0 ∗ ∗ ∗

0 . 0 0 0 0

− 0 . 0 2 8 9 ∗ ∗ ∗


4 2

− 0 . 0 3 6 6 ∗ ∗ ∗

− 0 . 0 4 0 5 ∗ ∗

∗

− 0 . 0 3 6 6 ∗ ∗ ∗

0 . 0 0 0 0

− 0 . 0 4 0 5 ∗ ∗ ∗

C H A S

E M A N H A T T A N B K U S A N A

4 0

− 0 . 0 6 2 4 ∗ ∗ ∗

− 0 . 0 5 2 1 ∗ ∗

∗

− 0 . 0 6 2 4 ∗ ∗ ∗

0 . 0 0 0 0

− 0 . 0 5 2 1 ∗ ∗ ∗

U N I O

N B K O F C A N A

4 0

− 0 . 0 1 2 9

− 0 . 0 0 9 9

− 0 . 0 1 2 9

0 . 0 0 0 0

− 0 . 0 0 9 9


3 7

− 0 . 0 3 9 6 ∗ ∗

− 0 . 0 3 2 2 ∗ ∗

∗

− 0 . 0 3 9 6 ∗ ∗

0 . 0 0 0 0

− 0 . 0 3 2 2 ∗ ∗ ∗

S U M M

I T B K

3 7

− 0 . 0 5 2 3 ∗ ∗ ∗

− 0 . 0 1 2 2

− 0 . 0 5 2 3 ∗ ∗ ∗

0 . 0 0 0 0

− 0 . 0 1 2 2

C O M E R I C A B K

3 6

− 0 . 0 9 9 1 ∗ ∗ ∗

− 0 . 0 2 8 9 ∗ ∗

∗

− 0 . 0 9 9 1 ∗ ∗ ∗

0 . 0 0 0 0

− 0 . 0 2 8 9 ∗ ∗ ∗

N O R W

E S T B K M N N A

3 6

− 0 . 0 4 5 9 ∗ ∗ ∗

− 0 . 0 3 3 6 ∗ ∗

∗

− 0 . 0 4 5 9 ∗ ∗ ∗

0 . 0 0 0 0

− 0 . 0 3 3 6 ∗ ∗ ∗

F L E E

T B K N A

3 5

− 0 . 0 4 3 1 ∗ ∗ ∗

− 0 . 0 2 7 2 ∗ ∗

− 0 . 0 4 3 1 ∗ ∗ ∗

0 . 0 0 0 0

− 0 . 0 2 7 2 ∗ ∗

D e p . V a r .

π 1 / W 3

π 2 / W 3

π 3 / W 3

π 4 / W 3

π 5 / W

3

R H S V a r s .

( y , w 3 )

( y , w 4 )

( y , w 3 )

( y , w 3 )

( y , w 4 )



41



T a



1 9 9 8 . Q

4 ( i m p o s i n g



u e d )

A s s e t s

N a m e

( b i l l i o

n s o f 2 0 0 9 $ )

M o d e l 1 3

M o d e l 1 4

M o d e l 1 5

M o d e l 1 6

M o d e l 1 7

C I T I B A N K N A

3 7 6

− 0 . 0 4 1 8 ∗ ∗ ∗

− 0 . 0 1 2 1 ∗ ∗

∗

− 0 . 0 5 3 2 ∗ ∗ ∗

− 0 . 0 4 5 3 ∗ ∗

− 0 . 0 5 7 9 ∗ ∗ ∗

N A T I

O N S B A N K N A

3 6 2

− 0 . 0 5 8 0 ∗ ∗ ∗

− 0 . 0 5 9 3 ∗ ∗

∗

− 0 . 0 6 0 0 ∗ ∗ ∗

− 0 . 0 0 2 6

− 0 . 0 6 3 6 ∗ ∗ ∗

B A N K O F A M E R N T & S A

3 1 6

− 0 . 0 3 9 4 ∗ ∗ ∗

0 . 0 1 2 0 ∗ ∗

∗

− 0 . 0 5 2 4 ∗ ∗ ∗

− 0 . 0 1 5 2 ∗ ∗ ∗

− 0 . 0 5 6 7 ∗ ∗ ∗


2 7 7

− 0 . 0 4 9 2 ∗ ∗ ∗

− 0 . 0 3 5 1 ∗ ∗

∗

− 0 . 0 5 5 4 ∗ ∗ ∗

− 0 . 0 0 6 5 ∗ ∗ ∗

− 0 . 0 5 5 5 ∗ ∗ ∗


1 0 9

− 0 . 0 2 9 2 ∗ ∗ ∗

− 0 . 0 1 0 5

− 0 . 0 3 9 6 ∗ ∗ ∗

0 . 0 2 5 1 ∗ ∗ ∗

− 0 . 0 3 8 2 ∗ ∗ ∗


9 3

− 0 . 0 4 0 4 ∗ ∗ ∗

− 0 . 0 2 5 7

− 0 . 0 2 7 8 ∗ ∗ ∗

0 . 1 4 0 6 ∗ ∗ ∗

− 0 . 0 2 1 4 ∗ ∗ ∗

F L E E

T N B

9 2

− 0 . 0 4 2 7 ∗ ∗ ∗

− 0 . 0 1 0 0

− 0 . 0 3 1 6 ∗ ∗ ∗

0 . 0 0 1 5

− 0 . 0 3 2 9 ∗ ∗ ∗

P N C

B K N A

8 9

− 0 . 0 4 2 3 ∗ ∗ ∗

0 . 0 0 0 1

− 0 . 0 3 0 5 ∗ ∗ ∗

− 0 . 0 8 1 4

− 0 . 0 2 8 4 ∗ ∗ ∗


8 8

− 0 . 0 2 9 6 ∗ ∗ ∗

− 0 . 0 4 9 8 ∗ ∗

∗

− 0 . 0 3 2 7 ∗ ∗ ∗

− 0 . 0 3 6 5 ∗ ∗ ∗

− 0 . 0 3 0 7 ∗ ∗ ∗

U S B

K N A

8 6

− 0 . 0 4 0 6 ∗ ∗ ∗

0 . 0 3 5 9 ∗ ∗

∗

− 0 . 0 2 5 4 ∗ ∗ ∗

0 . 0 5 9 1 ∗ ∗ ∗

− 0 . 0 2 5 4 ∗ ∗ ∗


8 6

− 0 . 0 1 3 7

− 0 . 0 2 5 7 ∗ ∗

∗

− 0 . 0 1 4 8 ∗ ∗ ∗

− 0 . 0 3 8 5 ∗ ∗

− 0 . 0 1 2 9 ∗ ∗ ∗


7 8

− 0 . 0 2 6 5 ∗ ∗ ∗

− 0 . 0 2 8 7

− 0 . 0 2 1 2 ∗ ∗ ∗

− 0 . 0 3 0 3

− 0 . 0 2 0 7 ∗ ∗ ∗

B A N K O F N Y

7 6

− 0 . 0 2 9 9 ∗ ∗ ∗

− 0 . 0 2 9 6 ∗ ∗

− 0 . 0 3 0 8 ∗ ∗ ∗

0 . 0 4 1 9 ∗ ∗ ∗

− 0 . 0 3 1 3 ∗ ∗ ∗

R E P U

B L I C N B O F N Y

5 8

− 0 . 0 3 9 4 ∗ ∗ ∗

− 0 . 0 5 0 8 ∗ ∗

∗

− 0 . 0 1 6 0 ∗ ∗ ∗

− 0 . 0 3 3 8 ∗ ∗ ∗

− 0 . 0 2 6 9 ∗ ∗ ∗

S T A T


5 6

− 0 . 0 7 2 4 ∗ ∗ ∗

− 0 . 0 5 6 9 ∗ ∗

∗

− 0 . 0 4 4 1 ∗ ∗ ∗

− 0 . 0 1 9 3

− 0 . 0 3 6 5 ∗ ∗ ∗

M E L L O N B K N A

5 2

− 0 . 0 2 4 4 ∗ ∗ ∗

− 0 . 0 4 2 1 ∗ ∗

∗

− 0 . 0 2 8 5 ∗ ∗ ∗

− 0 . 0 3 4 6

− 0 . 0 1 6 1 ∗ ∗ ∗

S O U T

H T R U S T B K N A

4 6

− 0 . 0 3 5 4 ∗ ∗ ∗

− 0 . 0 1 0 3

− 0 . 0 2 9 9 ∗ ∗ ∗

− 0 . 0 9 5 9 ∗ ∗ ∗

− 0 . 0 2 6 5 ∗ ∗ ∗

R E G I O N S B K

4 2

− 0 . 0 4 5 0 ∗ ∗ ∗

− 0 . 0 9 1 4 ∗ ∗

∗

− 0 . 0 1 7 9 ∗ ∗ ∗

0 . 0 4 1 3

− 0 . 0 2 9 5 ∗ ∗ ∗


4 2

− 0 . 0 3 4 7 ∗ ∗ ∗

− 0 . 0 3 3 3 ∗ ∗

− 0 . 0 2 4 3 ∗ ∗ ∗

0 . 0 0 2 6

− 0 . 0 2 5 8 ∗ ∗ ∗


4 0

− 0 . 0 6 1 4 ∗ ∗ ∗

− 0 . 0 5 3 8 ∗ ∗

∗

− 0 . 0 7 0 3 ∗ ∗ ∗

− 0 . 0 5 2 5 ∗ ∗ ∗

− 0 . 0 6 2 6 ∗ ∗ ∗

U N I O

N B K O F C A N A

4 0

− 0 . 0 4 6 6 ∗ ∗

− 0 . 0 0 5 3

0 . 0 0 1 5 ∗ ∗ ∗

− 0 . 0 5 5 5 ∗ ∗ ∗

− 0 . 0 1 3 7 ∗ ∗ ∗

N A T I

O N A L C I T Y B K

3 7

− 0 . 0 5 8 0 ∗ ∗ ∗

− 0 . 0 3 6 1

− 0 . 0 0 5 7 ∗ ∗ ∗

0 . 0 0 8 0

− 0 . 0 1 7 9 ∗ ∗ ∗

S U M M I T B K

3 7

− 0 . 0 0 5 2

− 0 . 0 3 6 8

− 0 . 0 1 2 3 ∗ ∗ ∗

0 . 0 1 7 1

− 0 . 0 2 7 9 ∗ ∗ ∗

C O M E R I C A B K

3 6

− 0 . 0 3 4 1 ∗

− 0 . 0 1 5 1

− 0 . 0 1 1 9 ∗ ∗ ∗

− 0 . 0 4 5 0

− 0 . 0 1 3 9 ∗ ∗ ∗

N O R W

E S T B K M N N A

3 6

− 0 . 0 4 7 9 ∗ ∗ ∗

− 0 . 0 6 7 8 ∗ ∗

∗

− 0 . 0 1 1 5 ∗ ∗ ∗

− 0 . 0 0 5 2

− 0 . 0 3 1 3 ∗ ∗ ∗

F L E E

T B K N A

3 5

− 0 . 0 1 4 3

− 0 . 0 6 4 4 ∗ ∗

∗

− 0 . 0 0 8 6 ∗ ∗ ∗

− 0 . 0 2 8 6

− 0 . 0 1 0 4 ∗ ∗ ∗

D e p . V a r .

π 6 / W 3

π 7 / W 3

π 8 / W 3

π 9 / W 3

π 1 0 / W

3

R H S V a r s .

( y , w 4 )

( y , w 3 )

( y , w 3 )

( y , w 4 )

( y , w 4 )



42



T a



2 0 0 6 . Q

4 ( i m p o s i n g



A s s e t s

N a m e

( b i l l i o n s o f 2 0 0 9 $ )

M o d e l 1 3

M o d e l 1 4

M o d e l 1 5

M o d e l 1 6

M o d e l 1 7

B A N K

O F A M E R N A

1 2 3 9

− 0 . 0 4 5 9 ∗ ∗ ∗

− 0 . 0 5 4 5 ∗

∗ ∗

− 0 . 0 4 5 9 ∗ ∗ ∗

0 . 0 0 0 0

− 0 . 0 5 4 5 ∗ ∗ ∗


1 2 2 4

− 0 . 0 3 6 5 ∗ ∗ ∗

− 0 . 0 5 4 2 ∗

∗ ∗

− 0 . 0 3 6 5 ∗ ∗ ∗

0 . 0 0 0 0

− 0 . 0 5 4 2 ∗ ∗ ∗

C I T I B A N K N A

9 5 4

− 0 . 0 3 6 3 ∗ ∗ ∗

− 0 . 0 4 2 3

− 0 . 0 3 6 3 ∗ ∗ ∗

0 . 0 0 0 0

− 0 . 0 4 2 3

W A C H

O V I A B K N A

5 3 9

− 0 . 0 4 0 1 ∗ ∗ ∗

− 0 . 0 4 7 7 ∗

∗ ∗

− 0 . 0 4 0 1 ∗ ∗ ∗

0 . 0 0 0 0

− 0 . 0 4 7 7 ∗ ∗ ∗


4 1 6

− 0 . 0 4 8 0 ∗ ∗ ∗

− 0 . 0 4 3 6 ∗

∗ ∗

− 0 . 0 4 8 0 ∗ ∗ ∗

0 . 0 0 0 0

− 0 . 0 4 3 6 ∗ ∗ ∗

U S B K

N A

2 2 6

− 0 . 0 4 2 9 ∗ ∗ ∗

− 0 . 0 3 5 9 ∗

∗ ∗

− 0 . 0 4 2 9 ∗ ∗ ∗

0 . 0 0 0 0

− 0 . 0 3 5 9 ∗ ∗ ∗

S U N T R U S T B K

1 9 0

− 0 . 0 2 4 1 ∗ ∗ ∗

− 0 . 0 4 5 0 ∗

∗ ∗

− 0 . 0 2 4 1 ∗ ∗ ∗

0 . 0 0 0 0

− 0 . 0 4 5 0 ∗ ∗ ∗

H S B C

B K U S A N A

1 7 3

0 . 0 1 6 5 ∗ ∗ ∗

− 0 . 0 0 2 8

0 . 0 1 6 5 ∗ ∗ ∗

0 . 0 0 0 0

− 0 . 0 0 2 8

N A T I O

N A L C I T Y B K

1 4 0

0 . 0 4 5 7 ∗ ∗ ∗

− 0 . 0 3 0 5 ∗

∗ ∗

0 . 0 4 5 7 ∗ ∗ ∗

0 . 0 0 0 0

− 0 . 0 3 0 5 ∗ ∗ ∗

R E G I O

N S B K

1 1 5

− 0 . 0 4 8 8 ∗ ∗ ∗

− 0 . 0 4 8 1 ∗

∗ ∗

− 0 . 0 4 8 8 ∗ ∗ ∗

0 . 0 0 0 0

− 0 . 0 4 8 1 ∗ ∗ ∗


1 0 7

− 0 . 0 5 5 5 ∗ ∗ ∗

− 0 . 0 1 5 3 ∗

∗ ∗

− 0 . 0 5 5 5 ∗ ∗ ∗

0 . 0 0 0 0

− 0 . 0 1 5 3 ∗ ∗ ∗


9 7

− 0 . 0 9 3 6 ∗ ∗ ∗

− 0 . 0 8 2 5 ∗

∗ ∗

− 0 . 0 9 3 6 ∗ ∗ ∗

0 . 0 0 0 0

− 0 . 0 8 2 5 ∗ ∗ ∗

K E Y B A N K N A

9 4

0 . 0 1 9 8 ∗ ∗

− 0 . 0 1 1 2 ∗

∗ ∗

0 . 0 1 9 8 ∗ ∗

0 . 0 0 0 0

− 0 . 0 1 1 2 ∗ ∗ ∗

P N C B

K N A

9 2

− 0 . 1 1 0 5 ∗ ∗ ∗

− 0 . 0 0 6 0 ∗

∗ ∗

− 0 . 1 1 0 5 ∗ ∗ ∗

0 . 0 0 0 0

− 0 . 0 0 6 0 ∗ ∗ ∗

B A N K

O F N Y

9 2

− 0 . 0 4 2 2 ∗ ∗ ∗

− 0 . 0 0 6 2 ∗

∗ ∗

− 0 . 0 4 2 2 ∗ ∗ ∗

0 . 0 0 0 0

− 0 . 0 0 6 2 ∗ ∗ ∗


8 4

− 0 . 0 5 0 9 ∗ ∗ ∗

− 0 . 0 5 4 5 ∗

∗ ∗

− 0 . 0 5 0 9 ∗ ∗ ∗

0 . 0 0 0 0

− 0 . 0 5 4 5 ∗ ∗ ∗

C O M E

R I C A B K

6 1

− 0 . 0 7 0 4 ∗ ∗ ∗

− 0 . 0 0 7 9

− 0 . 0 7 0 4 ∗ ∗ ∗

0 . 0 0 0 0

− 0 . 0 0 7 9

B A N K

O F T H E W E S T

5 8

0 . 0 5 0 4 ∗ ∗ ∗

− 0 . 0 1 7 3 ∗

0 . 0 5 0 4 ∗ ∗ ∗

0 . 0 0 0 0

− 0 . 0 1 7 3 ∗

M A N U


5 8

0 . 0 2 5 2 ∗ ∗ ∗

− 0 . 0 2 1 2 ∗

∗ ∗

0 . 0 2 5 2 ∗ ∗ ∗

0 . 0 0 0 0

− 0 . 0 2 1 2 ∗ ∗ ∗

F I F T H

T H I R D B K

5 8

− 0 . 0 3 5 1 ∗ ∗ ∗

0 . 0 0 0 4 ∗

∗ ∗

− 0 . 0 3 5 1 ∗ ∗ ∗

0 . 0 0 0 0

0 . 0 0 0 4 ∗ ∗ ∗

U N I O N

B K O F C A N A

5 4

− 0 . 0 6 7 4 ∗ ∗ ∗

− 0 . 0 2 8 8 ∗

∗ ∗

− 0 . 0 6 7 4 ∗ ∗ ∗

0 . 0 0 0 0

− 0 . 0 2 8 8 ∗ ∗ ∗

N O R T H E R N T C

5 2

− 0 . 0 2 5 1 ∗ ∗ ∗

− 0 . 0 1 4 9 ∗

∗ ∗

− 0 . 0 2 5 1 ∗ ∗ ∗

0 . 0 0 0 0

− 0 . 0 1 4 9 ∗ ∗ ∗

F I F T H

T H I R D B K

5 1

− 0 . 0 3 8 3 ∗ ∗ ∗

− 0 . 0 3 0 7 ∗

∗ ∗

− 0 . 0 3 8 3 ∗ ∗ ∗

0 . 0 0 0 0

− 0 . 0 3 0 7 ∗ ∗ ∗

M & I M


5 0

− 0 . 0 7 3 1 ∗ ∗ ∗

− 0 . 0 3 4 7

− 0 . 0 7 3 1 ∗ ∗ ∗

0 . 0 0 0 0

− 0 . 0 3 4 7


4 8

− 0 . 0 4 7 9

− 0 . 0 4 0 1 ∗

∗ ∗

− 0 . 0 4 7 9

0 . 0 0 0 0

− 0 . 0 4 0 1 ∗ ∗ ∗

H A R R I S N A

4 3

− 0 . 0 5 1 8 ∗ ∗

− 0 . 0 2 6 1 ∗

− 0 . 0 5 1 8 ∗ ∗

0 . 0 0 0 0

− 0 . 0 2 6 1 ∗

D e p . V

a r .

π 1 / W 3

π 2 / W 3

π 3 / W 3

π 4 / W 3

π 5 / W 3

R H S V

a r s .

( y , w 3 )

( y , w 4 )

( y , w 3 )

( y , w 3 )

( y , w 4 )



43



T a



2 0 0 6 . Q

4 ( i m p o s i n g



u e d )

A s s e t s

N a m e

( b i l l i

o n s o f 2 0 0 9 $ )

M o d e l 1 3

M o d e l 1

4

M o d e l 1 5

M o d e l 1 6

M o d e l 1 7

B A N K

O F A M E R N A

1 2 3 9

− 0 . 0 6 0 8 ∗ ∗ ∗

− 0 . 0 3 3 5 ∗

∗ ∗

− 0 . 0 6 3 3 ∗ ∗ ∗

− 0 . 0 3 9 6 ∗ ∗ ∗

− 0 . 0 6 8 5 ∗ ∗ ∗


1 2 2 4

− 0 . 0 6 3 7 ∗ ∗ ∗

− 0 . 0 4 1 1 ∗

∗ ∗

− 0 . 0 6 4 5 ∗ ∗ ∗

− 0 . 0 9 2 2 ∗ ∗ ∗

− 0 . 0 7 4 2 ∗ ∗ ∗

C I T I B A N K N A

9 5 4

− 0 . 0 6 2 9 ∗ ∗ ∗

− 0 . 0 0 8 7

− 0 . 0 6 4 9 ∗ ∗ ∗

− 0 . 0 1 7 9 ∗ ∗ ∗

− 0 . 0 6 9 4 ∗ ∗ ∗

W A C H

O V I A B K N A

5 3 9

− 0 . 0 6 0 3 ∗ ∗ ∗

− 0 . 0 1 2 8

− 0 . 0 5 9 6 ∗ ∗ ∗

− 0 . 0 3 1 3 ∗ ∗ ∗

− 0 . 0 6 3 4 ∗ ∗ ∗

W E L L

S F A R G O B K N A

4 1 6

− 0 . 0 5 4 3 ∗ ∗ ∗

− 0 . 0 3 2 1 ∗

∗ ∗

− 0 . 0 5 5 6 ∗ ∗ ∗

− 0 . 0 6 4 4 ∗ ∗ ∗

− 0 . 0 6 0 4 ∗ ∗ ∗

U S B K N A

2 2 6

− 0 . 0 4 0 0 ∗ ∗ ∗

− 0 . 0 0 1 1

− 0 . 0 4 9 7 ∗ ∗ ∗

− 0 . 0 5 1 3 ∗ ∗ ∗

− 0 . 0 5 5 1 ∗ ∗ ∗

S U N T R U S T B K

1 9 0

0 . 0 0 5 3

0 . 0 7 6 1 ∗

∗ ∗

− 0 . 0 4 7 0 ∗ ∗ ∗

− 0 . 0 3 9 7 ∗ ∗ ∗

− 0 . 0 4 8 9 ∗ ∗ ∗

H S B C

B K U S A N A

1 7 3

0 . 0 2 1 5

− 0 . 0 0 7 9

− 0 . 0 3 8 2 ∗ ∗ ∗

− 0 . 0 7 0 7 ∗ ∗ ∗

− 0 . 0 3 2 1 ∗ ∗ ∗

N A T I O

N A L C I T Y B K

1 4 0

0 . 0 0 8 8

0 . 0 3 2 0

− 0 . 0 4 5 2 ∗ ∗ ∗

0 . 0 3 4 5 ∗ ∗ ∗

− 0 . 0 4 5 5 ∗ ∗ ∗

R E G I O

N S B K

1 1 5

− 0 . 0 0 6 5

− 0 . 0 4 7 7 ∗

∗ ∗

− 0 . 0 3 0 1 ∗ ∗ ∗

− 0 . 0 4 6 6 ∗ ∗ ∗

− 0 . 0 3 4 1 ∗ ∗ ∗

B R A N

C H B K G & T C

1 0 7

0 . 0 4 3 5 ∗ ∗ ∗

− 0 . 0 3 2 2 ∗

∗ ∗

− 0 . 0 2 9 0 ∗ ∗ ∗

− 0 . 0 3 2 7

− 0 . 0 2 3 0 ∗ ∗ ∗

C O U N

T R Y W I D E B K N A

9 7

− 0 . 0 9 2 3 ∗ ∗ ∗

− 0 . 0 7 5 3 ∗

∗ ∗

− 0 . 0 8 7 2 ∗ ∗ ∗

− 0 . 0 5 1 8 ∗ ∗ ∗

− 0 . 0 5 2 1 ∗ ∗ ∗

K E Y B

A N K N A

9 4

− 0 . 0 1 3 3 ∗ ∗ ∗

0 . 0 2 1 7 ∗

∗

− 0 . 0 3 0 1 ∗ ∗ ∗

− 0 . 0 1 6 9

− 0 . 0 2 5 3 ∗ ∗ ∗

P N C B

K N A

9 2

0 . 0 1 9 8

− 0 . 0 2 7 4

− 0 . 0 3 0 8 ∗ ∗ ∗

− 0 . 0 1 7 3 ∗ ∗ ∗

− 0 . 0 3 0 2 ∗ ∗ ∗

B A N K

O F N Y

9 2

0 . 0 0 0 5

− 0 . 0 3 9 3 ∗

∗ ∗

− 0 . 0 2 7 8 ∗ ∗ ∗

− 0 . 0 7 2 4 ∗ ∗ ∗

− 0 . 0 2 5 9 ∗ ∗ ∗


8 4

− 0 . 0 5 1 1 ∗ ∗ ∗

− 0 . 0 1 9 4 ∗

∗ ∗

− 0 . 0 3 9 3 ∗ ∗ ∗

− 0 . 0 4 2 1 ∗ ∗ ∗

− 0 . 0 5 4 6 ∗ ∗ ∗

C O M E

R I C A B K

6 1

− 0 . 0 0 6 2

− 0 . 0 0 9 8

− 0 . 0 0 7 5 ∗ ∗ ∗

− 0 . 0 4 3 3 ∗ ∗ ∗

− 0 . 0 1 2 4 ∗ ∗ ∗

B A N K

O F T H E W E S T

5 8

0 . 0 2 3 6 ∗ ∗

− 0 . 0 5 7 2 ∗

∗ ∗

− 0 . 0 0 7 9 ∗ ∗ ∗

0 . 0 3 2 2 ∗ ∗ ∗

− 0 . 0 2 5 1 ∗ ∗ ∗

M A N U


5 8

0 . 0 0 3 2 ∗ ∗ ∗

− 0 . 0 5 4 7 ∗

∗ ∗

− 0 . 0 1 3 9 ∗ ∗ ∗

− 0 . 0 6 0 5 ∗ ∗ ∗

− 0 . 0 2 4 0 ∗ ∗ ∗

F I F T H

T H I R D B K

5 8

0 . 0 2 2 0 ∗

− 0 . 0 1 1 6

− 0 . 0 2 0 3 ∗ ∗ ∗

− 0 . 0 2 8 9 ∗ ∗ ∗

− 0 . 0 3 1 2 ∗ ∗ ∗

U N I O N

B K O F C A N A

5 4

− 0 . 0 6 6 2

− 0 . 0 4 5 7 ∗

∗ ∗

− 0 . 0 1 4 4 ∗ ∗ ∗

− 0 . 0 3 6 3 ∗ ∗ ∗

− 0 . 0 2 4 9 ∗ ∗ ∗

N O R T H E R N T C

5 2

− 0 . 0 1 4 8 ∗ ∗ ∗

0 . 0 0 0 1

− 0 . 0 0 6 3 ∗ ∗ ∗

0 . 0 2 3 3 ∗ ∗

− 0 . 0 1 7 3 ∗ ∗ ∗

F I F T H

T H I R D B K

5 1

− 0 . 0 5 1 2 ∗ ∗ ∗

− 0 . 0 3 9 7

− 0 . 0 1 7 1 ∗ ∗ ∗

− 0 . 0 2 4 9 ∗ ∗ ∗

− 0 . 0 2 2 4 ∗ ∗ ∗

M & I M


5 0

− 0 . 0 7 8 2

− 0 . 0 4 2 2

− 0 . 0 1 9 1 ∗ ∗ ∗

− 0 . 0 5 8 6 ∗ ∗ ∗

− 0 . 0 2 2 1 ∗ ∗ ∗


4 8

− 0 . 0 8 8 4 ∗ ∗ ∗

0 . 0 4 9 3 ∗

∗

− 0 . 0 1 0 8 ∗ ∗ ∗

− 0 . 0 7 6 1 ∗ ∗ ∗

− 0 . 0 1 7 9 ∗ ∗ ∗

H A R R

I S N A

4 3

− 0 . 0 5 4 4 ∗ ∗ ∗

0 . 0 6 9 7 ∗

∗

− 0 . 0 0 2 1 ∗ ∗ ∗

0 . 0 6 8 8 ∗ ∗

− 0 . 0 3 2 7 ∗ ∗ ∗

D e p . V

a r .

π 6 / W 3

π 7 / W 3

π 8 / W 3

π 9 / W 3

π 1 0 /

W 3

R H S V

a r s .

( y , w 4 )

( y , w 3 )

( y , w 3 )

( y , w 4 )

( y , w

4 )



44



T a



2 0 1 2 . Q

4 ( i m p o s i n g



A s s e t s

N a m e


0 0 9 $ )

M o d e l 1 3

M o d e l 1 4

M o d e l 1 5

M o d e l 1 6

M o d e l 1 7


1 7 6 9

− 0 . 0 3 8 3 ∗ ∗ ∗

− 0 . 0 5 9 4 ∗ ∗ ∗

− 0 . 0 3 8 3 ∗ ∗ ∗

0 . 0 0 0 0

−

0 . 0 5 9 4 ∗ ∗ ∗

B A N K O F A M

E R N A

1 3 8 0

− 0 . 0 3 5 0 ∗ ∗ ∗

− 0 . 0 6 0 6 ∗ ∗ ∗

− 0 . 0 3 5 0 ∗ ∗ ∗

0 . 0 0 0 0

−

0 . 0 6 0 6 ∗ ∗ ∗

C I T I B A N K N

A

1 2 6 5

− 0 . 0 2 6 0 ∗ ∗ ∗

− 0 . 0 5 6 6 ∗ ∗ ∗

− 0 . 0 2 6 0 ∗ ∗ ∗

0 . 0 0 0 0

−

0 . 0 5 6 6 ∗ ∗ ∗

W E L L S F A R G

O B K N A

1 1 7 3

− 0 . 0 3 3 4 ∗ ∗ ∗

− 0 . 0 5 8 9 ∗ ∗ ∗

− 0 . 0 3 3 4 ∗ ∗ ∗

0 . 0 0 0 0

−

0 . 0 5 8 9 ∗ ∗ ∗

U S B K N A

3 2 5

− 0 . 0 2 0 2 ∗ ∗ ∗

− 0 . 0 4 0 3 ∗ ∗ ∗

− 0 . 0 2 0 2 ∗ ∗ ∗

0 . 0 0 0 0

−

0 . 0 4 0 3 ∗ ∗ ∗

P N C B K N A

2 7 7

− 0 . 0 3 1 7 ∗ ∗ ∗

− 0 . 0 4 3 5 ∗ ∗ ∗

− 0 . 0 3 1 7 ∗ ∗ ∗

0 . 0 0 0 0

−

0 . 0 4 3 5 ∗ ∗ ∗

B A N K O F N Y

M E L L O N

2 5 8

− 0 . 0 6 9 7

− 0 . 0 3 8 7

− 0 . 0 6 9 7

0 . 0 0 0 0

−

0 . 0 3 8 7

S T A T E S T R E

E T B & T C

1 9 8

− 0 . 0 7 7 7 ∗ ∗ ∗

− 0 . 0 3 5 5 ∗ ∗ ∗

− 0 . 0 7 7 7 ∗ ∗ ∗

0 . 0 0 0 0

−

0 . 0 3 5 5 ∗ ∗ ∗

T D B K N A

1 9 1

− 0 . 0 3 3 9 ∗ ∗ ∗

− 0 . 0 1 2 2 ∗ ∗ ∗

− 0 . 0 3 3 9 ∗ ∗ ∗

0 . 0 0 0 0

−

0 . 0 1 2 2 ∗ ∗ ∗


1 8 1

0 . 0 1 6 2

− 0 . 0 3 8 5 ∗ ∗ ∗

0 . 0 1 6 2

0 . 0 0 0 0

−

0 . 0 3 8 5 ∗ ∗ ∗


1 6 7

− 0 . 0 2 7 5

− 0 . 0 1 2 9 ∗ ∗ ∗

− 0 . 0 2 7 5

0 . 0 0 0 0

−

0 . 0 1 2 9 ∗ ∗ ∗

S U N T R U S T B

K

1 6 0

− 0 . 0 0 5 6 ∗ ∗ ∗

− 0 . 0 5 3 1 ∗ ∗ ∗

− 0 . 0 0 5 6 ∗ ∗ ∗

0 . 0 0 0 0

−

0 . 0 5 3 1 ∗ ∗ ∗


1 5 6

− 0 . 0 5 5 1 ∗ ∗ ∗

− 0 . 0 5 9 4 ∗ ∗ ∗

− 0 . 0 5 5 1 ∗ ∗ ∗

0 . 0 0 0 0 ( 3 )

−

0 . 0 5 9 4 ∗ ∗ ∗

R E G I O N S B K

1 1 4

− 0 . 0 6 0 5 ∗ ∗ ∗

− 0 . 0 5 2 2 ∗ ∗ ∗

− 0 . 0 6 0 5 ∗ ∗ ∗

0 . 0 0 0 0

−

0 . 0 5 2 2 ∗ ∗ ∗


1 1 1

− 0 . 0 3 7 5 ∗ ∗ ∗

− 0 . 0 6 0 4 ∗ ∗ ∗

− 0 . 0 3 7 5 ∗ ∗ ∗

0 . 0 0 0 0

−

0 . 0 6 0 4 ∗ ∗ ∗

R B S C I T I Z E N

S N A

1 0 0

− 0 . 0 0 8 3

− 0 . 0 0 5 5 ∗ ∗ ∗

− 0 . 0 0 8 3

0 . 0 0 0 0

−

0 . 0 0 5 5 ∗ ∗ ∗

N O R T H E R N T C

9 0

− 0 . 0 8 3 8 ∗ ∗ ∗

0 . 0 2 7 4

− 0 . 0 8 3 8 ∗ ∗ ∗

0 . 0 0 0 0

0 . 0 2 7 4


8 8

− 0 . 0 2 3 7 ∗ ∗ ∗

0 . 0 2 6 4

− 0 . 0 2 3 7 ∗ ∗ ∗

0 . 0 0 0 0

0 . 0 2 6 4

K E Y B A N K N

A

8 1

0 . 0 7 3 0 ∗ ∗ ∗

0 . 0 1 0 3 ∗ ∗ ∗

0 . 0 7 3 0 ∗ ∗ ∗

0 . 0 0 0 0

0 . 0 1 0 3 ∗ ∗ ∗

S O V E R E I G N

B K N A

7 8

− 0 . 0 4 8 0 ∗ ∗

0 . 0 0 5 6 ∗ ∗ ∗

− 0 . 0 4 8 0 ∗ ∗

0 . 0 0 0 0

0 . 0 0 5 6 ∗ ∗ ∗

M A N U F A C T U


7 7

− 0 . 0 5 2 6 ∗ ∗ ∗

− 0 . 0 3 2 5 ∗ ∗ ∗

− 0 . 0 5 2 6 ∗ ∗ ∗

0 . 0 0 0 0

−

0 . 0 3 2 5 ∗ ∗ ∗

D I S C O V E R B

K

6 9

− 0 . 0 5 0 9 ∗ ∗ ∗

− 0 . 0 5 2 2 ∗ ∗ ∗

− 0 . 0 5 0 9 ∗ ∗ ∗

0 . 0 0 0 0

−

0 . 0 5 2 2 ∗ ∗ ∗

C O M P A S S B K

6 5

− 0 . 0 5 3 7 ∗ ∗ ∗

− 0 . 0 5 8 1 ∗ ∗ ∗

− 0 . 0 5 3 7 ∗ ∗ ∗

0 . 0 0 0 0

−

0 . 0 5 8 1 ∗ ∗ ∗

C O M E R I C A B K

6 1

− 0 . 0 4 5 8 ∗ ∗ ∗

− 0 . 0 3 1 4 ∗ ∗ ∗

− 0 . 0 4 5 8 ∗ ∗ ∗

0 . 0 0 0 0

−

0 . 0 3 1 4 ∗ ∗ ∗

B A N K O F T H

E W E S T

6 0

0 . 0 7 2 8 ∗ ∗ ∗

− 0 . 0 1 8 7 ∗ ∗ ∗

0 . 0 7 2 8 ∗ ∗ ∗

0 . 0 0 0 0

−

0 . 0 1 8 7 ∗ ∗ ∗

H U N T I N G T O

N N B

5 3

− 0 . 0 6 4 1 ∗ ∗ ∗

− 0 . 0 4 0 6 ∗ ∗ ∗

− 0 . 0 6 4 1 ∗ ∗ ∗

0 . 0 0 0 0

−

0 . 0 4 0 6 ∗ ∗ ∗

D e p . V a r .

π 1 / W 3

π 2 / W 3

π 3 / W 3

π 4 / W 3

π 5 / W 3

R H S V a r s .

( y , w 3 )

( y , w 4 )

( y , w 3 )

( y , w 3 )

( y , w 4 )







45



References

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Delgado, M. A. and J. Mora (1995), On asymptotic inferences in nonparametric and semi-parametric models with discrete and mixed regressors, Investigaciones Economicas 19,435–467.

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Mammen, E. (1992), When Does Bootstrap Work? Asymptotic Results and Simulations ,Berlin: Springer-Verlag.

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Pagan, A. and A. Ullah (1999), Nonparametric Econometrics , Cambridge: Cambridge Uni-versity Press.

Racine, J. and Q. Li (2004), Nonparametric estimation of regression functions with bothcategorical and continuous data, Journal of Econometrics 119, 99–130.

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Wheelock, D. C. and P. W. Wilson (2001), New evidence on returns to scale and product mixamong U.S. commercial banks, Journal of Monetary Economics 47, 653–674.

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47



2 8 : R e t u r n s t o S c a l e ( P r o fi t ) f o r L a r g e s t B a n k s b y T


2 0 1 2 . Q

4 ( i m p o s i n g



u e d )

A s s e t s


0 0 9 $ )

M o d e l 1 3

M o d e l 1 4

M o d e l 1 5

M o d e l 1 6

M o d e l 1 7

K N A

1 7 6 9

− 0 . 0 6 5 6 ∗ ∗ ∗

0 . 0 0 3 1

− 0 . 0 9 0 4 ∗ ∗ ∗

− 0 . 0 1 4 9

−

0 . 0 7 6 9 ∗ ∗ ∗

1 3 8 0

− 0 . 0 6 2 3 ∗ ∗ ∗

− 0 . 0 1 1 7 ∗ ∗ ∗

− 0 . 0 7 3 5 ∗ ∗ ∗

− 0 . 0 1 6 3

−

0 . 0 7 6 8 ∗ ∗ ∗

1 2 6 5

− 0 . 0 5 7 6 ∗ ∗ ∗

− 0 . 0 0 2 6

− 0 . 1 0 5 9 ∗ ∗ ∗

− 0 . 0 4 8 4 ∗ ∗ ∗

−

0 . 0 7 7 4 ∗ ∗ ∗

1 1 7 3

− 0 . 0 6 1 0 ∗ ∗ ∗

− 0 . 0 0 7 7 ∗

− 0 . 0 8 7 9 ∗ ∗ ∗

− 0 . 0 3 1 4 ∗ ∗ ∗

−

0 . 0 7 5 6 ∗ ∗ ∗

3 2 5

− 0 . 0 3 3 4 ∗ ∗ ∗

− 0 . 0 3 4 0 ∗ ∗ ∗

− 0 . 0 6 2 0 ∗ ∗ ∗

− 0 . 0 0 9 8 ∗ ∗ ∗

−

0 . 0 6 7 7 ∗ ∗ ∗

2 7 7

− 0 . 0 3 9 2 ∗ ∗ ∗

− 0 . 0 1 0 7 ∗ ∗ ∗

− 0 . 0 6 2 2 ∗ ∗ ∗

− 0 . 0 0 2 6

−

0 . 0 6 8 5 ∗ ∗ ∗

N

2 5 8

− 0 . 0 3 5 8

− 0 . 0 5 0 6 ∗ ∗ ∗

− 0 . 0 5 1 7 ∗ ∗ ∗

− 0 . 0 2 1 9 ∗ ∗ ∗

−

0 . 0 6 7 2 ∗ ∗ ∗

1 9 8

− 0 . 0 2 4 9 ∗ ∗ ∗

− 0 . 0 4 9 2 ∗ ∗ ∗

− 0 . 0 5 1 3 ∗ ∗ ∗

− 0 . 0 1 4 3

−

0 . 0 6 2 9 ∗ ∗ ∗

1 9 1

− 0 . 0 2 2 0 ∗ ∗ ∗

− 0 . 0 1 3 0 ∗ ∗ ∗

− 0 . 0 5 5 3 ∗ ∗ ∗

0 . 0 1 9 6 ∗ ∗ ∗

−

0 . 0 6 0 5 ∗ ∗ ∗

1 8 1

− 0 . 0 1 0 9 ∗ ∗ ∗

− 0 . 0 2 3 0 ∗ ∗ ∗

− 0 . 0 5 3 2 ∗ ∗ ∗

− 0 . 0 2 1 4 ∗ ∗ ∗

−

0 . 0 6 3 4 ∗ ∗ ∗

1 6 7

0 . 0 0 1 1 ∗ ∗ ∗

− 0 . 0 1 1 0 ∗ ∗ ∗

− 0 . 0 5 3 0 ∗ ∗ ∗

0 . 0 1 7 5 ∗ ∗ ∗

−

0 . 0 5 4 7 ∗ ∗ ∗

1 6 0

− 0 . 0 4 6 0 ∗ ∗ ∗

− 0 . 0 2 4 4 ∗ ∗ ∗

− 0 . 0 6 0 0 ∗ ∗ ∗

0 . 0 0 3 2

−

0 . 0 6 4 2 ∗ ∗ ∗

1 5 6

0 . 0 8 4 7 ∗ ∗ ( 3 )

− 0 . 0 1 4 1

0 . 0 8 4 2 ( 3 )

− 0 . 0 0 3 1

0 . 1 0 7 5 ( 3 )

1 1 4

− 0 . 0 4 3 0

0 . 0 1 1 7 ∗ ∗ ∗

− 0 . 0 3 9 9 ∗ ∗ ∗

− 0 . 0 2 4 9 ∗ ∗ ∗

−

0 . 0 3 9 2 ∗ ∗ ∗

1 1 1

− 0 . 0 5 4 8 ∗ ∗ ∗

− 0 . 0 3 2 1 ∗ ∗ ∗

− 0 . 0 6 0 1 ∗ ∗ ∗

0 . 0 1 1 9 ∗ ∗ ∗

−

0 . 0 6 2 5 ∗ ∗ ∗

1 0 0

0 . 0 3 4 8

− 0 . 0 2 2 8

− 0 . 0 4 5 1 ∗ ∗ ∗

− 0 . 0 5 7 1 ∗ ∗ ∗

−

0 . 0 3 0 0 ∗ ∗ ∗

9 0

0 . 0 1 6 0

− 0 . 0 2 3 0 ∗ ∗ ∗

− 0 . 0 4 3 9 ∗ ∗ ∗

− 0 . 0 4 4 9 ∗ ∗ ∗

−

0 . 0 5 4 3 ∗ ∗ ∗

8 8

− 0 . 0 1 9 5 ∗ ∗ ∗

− 0 . 0 1 0 4 ∗ ∗ ∗

− 0 . 0 4 9 6 ∗ ∗ ∗

− 0 . 0 0 8 7

−

0 . 0 5 2 8 ∗ ∗ ∗

8 1

− 0 . 0 2 7 7 ∗ ∗ ∗

− 0 . 0 0 3 2

− 0 . 0 5 4 8 ∗ ∗ ∗

0 . 0 0 7 2

−

0 . 0 5 3 3 ∗ ∗ ∗

7 8

0 . 0 2 9 2 ∗ ∗

− 0 . 0 3 9 5 ∗ ∗ ∗

− 0 . 0 1 6 6 ∗ ∗ ∗

− 0 . 0 6 2 5 ∗ ∗ ∗

−

0 . 0 0 6 5 ∗ ∗ ∗

T R A D E R S T C

7 7

0 . 0 0 2 0 ∗ ∗ ∗

− 0 . 1 0 5 1 ∗ ∗ ∗

− 0 . 0 3 8 5 ∗ ∗ ∗

− 0 . 0 4 3 7 ∗ ∗ ∗

−

0 . 0 2 4 8 ∗ ∗ ∗

6 9

− 0 . 0 7 4 8 ∗ ∗ ∗

0 . 0 2 3 6 ∗ ∗

− 0 . 0 5 0 5 ∗ ∗ ∗

− 0 . 0 2 5 7 ∗ ∗ ∗

−

0 . 1 4 3 7

6 5

− 0 . 0 3 1 0 ∗ ∗ ∗

− 0 . 0 0 1 8

− 0 . 0 3 3 3 ∗ ∗ ∗

0 . 0 0 5 1 ∗ ∗ ∗

−

0 . 0 2 4 5 ∗ ∗ ∗

6 1

0 . 0 7 6 7

− 0 . 0 2 0 3 ∗ ∗ ∗

− 0 . 0 3 9 2 ∗ ∗ ∗

− 0 . 0 3 7 7 ∗ ∗ ∗

−

0 . 0 2 3 5 ∗ ∗ ∗

6 0

0 . 0 0 9 5 ∗ ∗ ∗

− 0 . 0 2 0 7 ∗ ∗ ∗

− 0 . 0 4 8 1 ∗ ∗ ∗

− 0 . 0 5 7 5 ∗ ∗ ∗

−

0 . 0 4 1 2 ∗ ∗ ∗

5 3

− 0 . 0 3 0 5 ∗ ∗ ∗

− 0 . 0 1 6 7 ∗ ∗ ∗

− 0 . 0 4 1 4 ∗ ∗ ∗

− 0 . 0 5 5 3 ∗ ∗ ∗

−

0 . 0 2 4 2 ∗ ∗ ∗

π 6 / W 3

π 7 / W 3

π 8 / W 3

π 9 / W 3

π 1 0 / W 3

( y , w 4 )

( y , w 3 )

( y , w 3 )

( y , w 4 )

( y , w 4 )

d i ff e r e n c e f r o m 0 ) a t t h e t e n , fi



w ) < 0 a n d π ( δ y , w ) > 0 ; δ π ( y , w ) > 0 a n d π ( δ y , w ) < 0 ; o r δ π ( y , w ) <



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