Problem Loans and Cost Efficiency in Commercial Banks

Allen N. Berger

Board of Governors of the Federal Reserve System

Robert DeYoung

Office of the Comptroller of the Currency

Office of the Comptroller of the Currency

Economic and Policy Analysis Working Paper 95-5

December 1995

* The views expressed are those of the authors, and do not necessarily reflect those of the Office of

the Comptroller of the Currency, the Department of the Treasury, the Board of Governors, or their

staffs. Any whole or partial reproduction of material in this paper should include the following

citation: Berger, Allen N., and Robert DeYoung, “Problem Loans and Cost Efficiency in

Commercial Banks,” Office of the Comptroller of the Currency, E&PA Working Paper 95-5,

December 1995.

_____________________________________________________________________________________________

The authors thank Bob Avery, Paul Bauer, Gary Ferrier, Kevin Jacques, Julapa Jagtiani, Bill Lang, Tom Lutton, Joe

Mason, Andrea Resti, Bernie Shull, and Gary Whalen for very helpful comments; Maria Montano and Joe Scalise for

exceptional research support; and Claire Emory for editorial assistance. 

Please address questions to Robert DeYoung, Bank Research Division, Office of the Comptroller of the Currency,

Washington, DC 20219, phone (202) 874-5427, fax (202) 874-5394, e-mail robert.deyoung@occ.treas.gov.
1

* Any whole or partial reproduction of material in this paper should include the following citation:

Berger, Allen N., and Robert DeYoung, “Problem Loans and Cost Efficiency in Commercial

Banks,” Office of the Comptroller of the Currency, E&PA Working Paper 95-5, December 1995.

I. Introduction

Over the last several years, two strands of research in the field of financial institutions have

received a great amount of attention. One is the issue of problem loans. Virtually all research on

the causes of bank and thrift failures find that failing institutions have large proportions of

nonperforming loans (past due and nonaccrual) prior to failure. Demirguc-Kunt (1989) reported that

the majority of pre-1990s bank failure studies found asset quality to be a statistically significant

predictor of insolvency. More recent studies (e.g., Whalen 1991, Barr and Siems 1994) have

reinforced this finding. 

A second strand of literature deals with the productive efficiency of financial institutions.

A number of studies have found that most institutions have high costs and low profits relative to

institutions on the “best-practice” efficient frontier. Various studies of mergers, agency problems,

corporate governance, branching strategies, foreign ownership, etc. provide evidence that estimates

of frontier efficiency are significantly related to the structure, conduct, and performance of financial

institutions. Berger, Hunter, and Timme (1993) reviewed much of this literature.

What is largely missing from the literature is an analysis of the intersection of these two

strands of research -- that is, the relationships between problem loans and cost efficiency at financial

institutions. On the surface, these two topics might appear to be unrelated, because operations

personnel typically do not participate in screening and monitoring loan customers, and because loan

officers and review personnel typically do not participate in overseeing operations costs. Despite

this apparent dichotomy, issues of problem loans and cost efficiency are in fact related in several
2

important ways. The recent empirical literature suggests at least three significant links between these

two topics.

First, a number of researchers have found that failing banks tend to be very cost inefficient,

that is, located far from the best-practice frontier (see, for example, Berger and Humphrey 1992;

Coyne, McManus, and Stagliano 1993; Barr and Siems 1994; Wheelock and Wilson 1994; Becher,

DeYoung, and Lutton 1995). Thus, in addition to having high ratios of problem loans, banks

approaching failure also tend to have low levels of measured cost efficiency. DeYoung and Whalen

(1994) showed that declines in average cost efficiency tend to precede increases in average problem

loans for banks approaching failure, while a number of other studies have found negative

contemporaneous relationships between efficiency and problem loans even among banks that do not

fail (Eisenbeis and Kwan 1994, Hughes and Moon 1995, Resti 1995). Cost-inefficient banks may

tend to have loan performance problems for a number of reasons. For example, banks with poor

senior management may have problems in monitoring both their costs and theirloan customers, with

the losses of capital generated by both these phenomena potentially leading to failure. We will refer

to this as the “bad management” hypothesis. Alternatively, loan quality problems may be caused by

an event exogenous to the bank, such as an unanticipated regional economic downturn. The

expenses associated with the nonperforming loans that result (e.g., extra monitoring, negotiating

workout arrangements, seizing and disposing of collateral, diverted managerial focus) can create the

appearance, if not the reality, of low cost efficiency. We will refer to this as the ‘bad luck’

hypothesis. These and other hypotheses linking problem loans to cost efficiency are investigated in

the next section.

The second empirical link between problem loans and productive efficiency appears in
 DeYoung (forthcoming) regressed management quality ratings on examination ratings for capital adequacy, asset 1

quality, earnings quality, and liquidity. Although all of the exam components were significantly and positively related

to management quality, asset quality had the largest coefficient value. 

3

studies that use supervisory examination data. Peristiani (1993) and DeYoung (forthcoming) both

found measured cost efficiency to be positively related to examiners' ratings of bank management

quality. Moreover, the latter study found that banks’ management quality ratings were more strongly

related to their asset quality ratings than to any of their other examination ratings. A relationship 1

between asset quality and cost efficiency (via management quality) is consistent with the failed bank

data cited above, and suggests that the negative relationship between problem loans and cost

efficiency holds for the population of banks as a whole as well as for failing banks.

Third, some recent studies of bank efficiency have directly included measures of

nonperforming loans in cost or production relationships. The stated purposes of this adjustment are

to control for the extra costs associated with nonperforming loans and/or to control for underwriting

and monitoring expenditures that influence loan quality. Berg, Førsund, and Jansen (1992) made

the original observation and included nonperforming loans in a nonparametric study of bank

production. Hughes and Mester (1993), Mester (1994a, 1994b), and Hughes, Lang, Mester, and

Moon (1995) applied the concept to parametric estimations of bank cost functions and efficiency.

As discussed at length in the next section, whether this procedure improves or hinders the estimation

of cost efficiency depends upon the underlying reason for the relationship between costs and

nonperforming loans.

Thus, a number of important policy and research issues rest on identifying the underlying

relationship between problem loans and measured cost efficiency. These include discovering the

primary cause of problem loans and bank failures (e.g., external shocks, poor management practices,
4

or a purposeful lack of managerial oversight); determining the most important supervisory focus for

promoting safety and soundness at banks (e.g., loan quality, portfolio diversification, management

quality, or cost efficiency); and deciding how to estimate the cost efficiency of financial institutions

(with or without controls for problem loans). While we obviously cannot provide definitive answers

for all of these important questions, we attempt to shed some light on these issues by analyzing an

empirical model that tests a number of competing and complementary hypotheses involving the

inter-temporal relationships among problem loans, cost efficiency, and financial capital. 

We conduct tests of four hypotheses using Granger-causality analysis. To our knowledge,

this paper contains the first tests of any type of the “bad luck,” “bad management,” and “skimping”

hypotheses (described in full below), as well as the first Granger-causality test of the well-known

“moral hazard” hypothesis. Granger-causality analysis can distinguish between these alternative

cases in a way that standard cross-section econometric analysis cannot. This is because several of

these hypotheses yield identical predictions for the contemporaneous relationships between problem

loans and cost efficiency, but strikingly different predictions for the inter-temporal patterns.

Although application of the Granger-causality methodology to microeconomic banking data is

unusual, it is not unprecedented (see Berger 1995). We acknowledge that the inter-temporal

relationships that we measure are gross statistical associations that do not necessarily prove

economic causation. Nevertheless, they can indicate which among the alternative hypotheses is

consistent with the data. In the process of our analysis we also find some interesting results

concerning the estimation of cost efficiency. Specifically, we find that measured cost efficiency

varies substantially with the degree of flexibility in the specification of the cost equation and the

error structure.
5

The empirical results suggest that the inter-temporal statistical relationships between problem

loans and cost efficiency run in both directions for U.S. commercial banks between 1985 and 1994.

The data suggest that high levels of nonperforming loans Granger-cause or predict reductions in

measured cost efficiency, possibly reflecting the extra costs of administering problem loans. This

result supports the bad luck hypothesis. Low levels of cost efficiency are also found to Grangercause or predict increases in nonperforming loans, suggesting that cost-inefficient managers are also

poor loan managers. This result supports the bad management hypothesis. The moral hazard and

skimping hypotheses are only consistent with subsets of the data.

The remainder of the paper is organized as follows. Section II presents our four hypotheses,

identifies their key empirical implications, and discusses their consequences for policy and research.

Section III describes the econometric model, and Section IV explains how the efficiency estimates

were constructed. Section V describes the data, followed by the empirical results in Section VI.

Economic and policy conclusions are addressed in Section VII.

II. Alternative Hypotheses for the Relationship between Problem Loans and Measured

Cost Efficiency

Here we outline our four hypotheses -- bad luck, bad management, skimping, and moral

hazard -- each of which implies a different inter-temporal relationship in the data. These hypotheses

are not mutually exclusive, and any one of the four could dominate the behavior of a given subset

of banks. The empirical analysis that follows is designed to determine which among these

hypotheses are relatively important for the banking industry as a whole.

Figure 1 displays the expected time patterns of the variables predicted by the hypotheses.

For convenience, we will couch all of the descriptions in terms of increases in problem loans, which
 An example of this are the expenses that a bank incurs to manage and eventually dispose of other real estate owned 2

(OREO) that was seized as collateral for failed loans.

6

is the most interesting case for policy purposes. All of the arguments could similarly be made for

the less interesting case in which problem loans decrease. 

Bad Luck

Under the bad luck hypothesis shown in Appendix A, external events (e.g., a regional

recession) precipitate an increase in problem loans for the bank. The important distinguishing

implication of the bad luck hypothesis is the relationship between problem loans and measured cost

efficiency. After the loans become past due or nonaccruing, the bank begins to expend additional

managerial effort and expense dealing with these problem loans. These extra operating costs

include, but are not limited to (1) the additional monitoring of the delinquent borrowers and the

value of their collateral, (2) the expense of analyzing and negotiating possible workout arrangements,

(3) the costs of seizing, maintaining, and eventually disposing of collateral if default later occurs ,

2

(4) the additional costs of defending the bank's safety and soundness record to bank supervisors

during future examinations, and (5) the diversion of managerial attention away from solving other

operations problems. Most of these costs, especially the costs associated with loan workout and

default, are incurred well after the loan becomes past due. Under the bad luck hypothesis, therefore,

significant cost increases are expected to occursometime after the increase in problem loans. Thus,

we expect increases in nonperforming loans to Granger-cause, i.e., temporally precede, decreases

in measured cost efficiency under this hypothesis. 

It is important to note that under the bad luck hypothesis the extra expenses of dealing with

problem loans will create the appearance, although not the reality, of lower cost efficiency. Faced
7

with an increase in nonperforming loans not of their own doing, even the most cost efficient banks

will have to purchase the additional inputs necessary to produce the loan monitoring outputs required

to administer these problem credits. 

Bad Management

Under the bad management hypothesis shown in Appendix A, poor bank management is the

catalyst for a negative relationship between problem loans and measured cost efficiency. Under this

hypothesis, low measured cost efficiencyis a signal of bad management practices. Subpar managers

do not sufficiently monitor their expenses, which results in low cost efficiency, and also do not

practice adequate loan underwriting and monitoring. As “bad” managers, they may (1) have poor

skills in credit scoring and therefore choose a relativelyhigh proportion of loans with low or negative

net present values, (2) be less than fully competent in appraising the value of collateral pledged

against the loans, and (3) have difficulty monitoring the borrowers after the loans are issued to assure

that covenants are obeyed and the funds are prudentially invested. These underwriting and

monitoring problems eventually lead to high numbers of nonperforming loans as borrowers fall

behind in their loan repayments.

The key identifying prediction of the bad management hypothesis is the temporal relationship

between problem loans and measured cost efficiency, which has the opposite ordering from that

predicted by the bad luck hypothesis. Low cost efficiency is expected to precede or Granger-cause

higher nonperforming loans, because insufficient cost controls should reduce measured cost

efficiency almost immediately, whereas poor loan management will become apparent only after time

passes, the loan portfolio becomes seasoned and delinquencies begin to mount. This delay will be
 The General Accounting Office (1990) found evidence that troubled banks systematically underreport nonperforming

3

loans. Anecdotal evidence to this effect has also been reported in the financial press (e.g., Wall Street Journal, April

25, 1994).

 It is common practice to use nonperforming loan ratios as a proxy for loan quality, chiefly because other dimensions

4

of service and product quality are difficult to measure. One exception is Faulhaber (1995), who uses survey data to

show that increases in customer satisfaction are with slightly increased costs. 

8

exacerbated if managers do not immediately record nonperforming loans on the balance sheet. For 3

example, a bank may lend the borrower additional funds to repay principal and interest on existing

loans, thus avoiding having to report problem credits as nonperforming loans. 

Skimping

The ‘skimping’ hypothesis is shown in panel C of Appendix A. This hypothesis is based on

an insight by Berg, Førsund, and Jansen (1992) -- which has been developed further by Hughes and

Mester (1993), Mester (1994a, 1994b), and Hughes, Lang, Mester, and Moon (1995) -- that the

amount of resources allocated to loan underwriting and monitoring may affect both loan quality and

measured cost efficiency. Here, the critical decision of the bank lies in the tradeoff between short4

term operating costs and future loan performance problems. A bank maximizing long-run profits

may rationally choose to have lower costs in the short run by skimping on the resources devoted to

underwriting and monitoring loans, but bear the consequences of greater loan performance problems

and the possible costs of dealing with these problems in the future. The lower amount of effort

devoted to screening loan customers, appraising collateral, and monitoring borrowers after loans are

issued makes the bank appear to be cost efficient in the short run because fewer operating expenses

can support the same quantity of loans and other outputs. The stock of nonperforming loans likely

remains unaffected in the short run, because it takes time before borrowers fall behind in their

repayments. However, the inattention to the loan portfolio becomes apparent later on after a
 Moral hazard incentives might occur for a number of reasons, particularly when a bank experiences financial 5

distress. For example, shareholders might exploit creditors by substituting riskier assets for safer ones if creditors

do not have sufficient information or time to react. Also, if deposit insurance is imperfectly risk-priced, there may

be incentives for banks to undertake risks that will be borne largely by the insurer.

 Any number of events may occur after the increase in nonperforming loans (e.g., an increase in operations costs to 6

deal with these loans), but we exclude these possibilities from Figure 1 because they are not needed to identify the

moral hazard hypothesis. Furthermore, we do not necessarily predict further erosion of capital after nonperforming

loans increase -- the expected return from increasing portfolio risk could be either positive or negative, depending

upon whether the additional revenues from higher loan rates are offset by the costs of dealing with the higher expected

nonperforming loans.

9

relatively high proportion of borrowers have become delinquent on their loans. 

Underthe skimping hypothesis, the Granger-causality between measured cost efficiency and

nonperforming loans has the same temporal ordering as the bad management hypothesis. However,

it has the opposite sign -- skimping implies a positive Granger-causation from measured efficiency

to problem loans. 

Moral Hazard

The moral hazard hypothesis shown in Appendix A is the classical problem of excessive risktaking when another party is bearing part of the risk and cannot easily charge for that risk. Under 5

this hypothesis, a loss of earnings from any source -- including the effects of the other three

hypotheses shown in Appendix A -- reduces the bank’s financial capital. Once capital has eroded,

the bank responds to moral hazard incentives by increasing the riskiness of its loan portfolio, which

results in higher nonperforming loans on average in the future. Thus, we identify the moral hazard

hypothesis by the prediction that capital negatively Granger-causes nonperforming loans. Because

6

banks with ample capital likely do not face moral hazard incentives, we test the moral hazard

hypothesis for a subsample of the data that only includes banks with equity-to-asset ratios below the

population median.
10

Note that, unlike the other three theories in Appendix A, the moral hazard hypothesis is not

a theory of the relationship between problem loans and measured cost efficiency, but rather of the

relationship between problem loans and bank capital ratios. We include it for several reasons. First,

moral hazard gives an alternative explanation for nonperforming loans, so the effects of measured

cost efficiency on nonperforming loans could be biased if the potential effects of capital were

neglected. Second, moral hazard effects can accentuate or magnify the effects of the other three

hypotheses, each of which may cause a reduction in the bank's capital ratio. Finally, it is important

to include moral hazard because it is a leading theory of problem loans and bank failures with

different policy implications from the other hypotheses.

It is important to distinguish between the moral hazard and the skimping hypotheses because

they are similar in several respects. Under both hypotheses, banks intentionally take on additional

credit risk in their loan portfolios that tends to result in extra nonperforming loans, and in both

scenarios this risk-taking may or may not pay off in terms of higher long-run earnings and capital

for individual banks. However, the economics of these two hypotheses are quite different. The main

purpose of skimping is to save real resources on operating costs, whereas the main purpose of moral

hazard is to shift costs to other parties. Skimping creates a social loss only if the total losses

associated with the poorly performing loan portfolio exceed the value of the real resources saved by

skimping on loan underwriting and monitoring. In contrast, moral hazard behavior is a complete

waste from a social viewpoint, since it simply exploits externalities without creating any value. 

In an extreme case, all four hypotheses could affect the same bank at the same time. For

example, bad luck could befall a poorly managed bank that also happens to be skimping on loan

monitoring expenses, and that bank might then respond to moral hazard incentives in an attempt to
11

recapitalize itself. The Granger-causality tests defined in the next section are designed to reveal the

industry-wide, or average, inter-temporal relationships among the variables.

Public Policy and Research Implications of the Hypotheses

Each of the four hypotheses has different implications for public policy and future research.

The main implications are summarized in Appendix B. The bad luck hypothesis suggests that bank

failures are caused primarily by uncontrollable external events, such as a regional downturn or the

failure of a large employer in a small bank's lending area. The hypothesis implies that prudential

regulation and supervision could reduce the risk of failure by limiting banks' exposures to external

shocks (e.g., limits on loan concentrations, allowing interregional diversification through interstate

mergers and loan sales, or encouraging low loan-to-asset ratios) or by better insulating banks from

external shocks (e.g., requiring high levels of capital). For the purposes of research, the bad luck

hypothesis suggests that local or regional economic conditions are important determinants of bank

performance. Furthermore, if the bad luck hypothesis dominates the other explanations of the

relationship between problem loans and measured cost efficiency, future efficiency measurement

should control for nonperforming loans in the cost function. This would help remove by statistical

means the extra costs of dealing with nonperforming loans -- which were caused by bad luck, not

by managerial inefficiency -- rather than erroneously counting these extra costs as inefficiency as

is the case in conventional cost analyses that ignore the effects of problem loans.

In contrast to the bad luck hypothesis, the bad management hypothesis implies that bank

failures primarily result from poor managers who allow both costs and loan losses get out of control

and deplete the financial capital of the bank. This suggests that bank supervision and bank research

should consider cost efficiency along with other traditional predictors of troubled banks such as loan
 See Udell (1989) for a discussion of internal loan reviews at banks. 7

12

losses and credit risk. Also in contrast to the bad luck hypothesis, the bad management hypothesis

implies that cost efficiency measurement should not control for nonperforming loans in the cost

function. This is because nonperforming loans spring from the same source as the efficiency being

measured -- the poor job of management in conducting the affairs of the bank. If the bad

management hypothesis is dominant, controlling for nonperforming loans in the cost function

artificially increases measured cost efficiency by removing statistically the part of the cost

inefficiencies that is correlated with inefficient portfolio management.

The policy and research implications of the skimping hypothesis are different from those of

the other hypotheses on several grounds. First, because bankmanagers who skimp purposely devote

fewer inputs to loan underwriting and monitoring, which on average causes nonperforming loans to

increase, bank supervisors and researchersstudying bank failure might be advised to examine banks'

internal credit control procedures (e.g., loan review, collateral appraisal). Second, the skimping 7

hypothesis implies that it may be inappropriate to measure cost efficiency in the short-run, because

skimping banks are engaging in long-run strategies. Estimates of short-run cost efficiency will differ

depending upon where in Appendix A, panel C the cost efficiency measurement takes place --

skimping banks have relatively low short-run costs when loan quality is good, but may have

relatively high short-run costs once nonperforming loans increase. A better strategy may be to

estimate long-run cost efficiency using several years of cost data -- years in which skimping saves

on costs would be averaged with years in which the nonperforming loans may force up costs. Third,

the skimping hypothesis implies that the cost function should not control for nonperforming loans,

because these performance problems are endogenous to the skimping bank's optimization strategy,
 See Berger, Hancock, and Humphrey (1993); DeYoung and Nolle (1995); Akhavein, Swamy, and Taubman (1995);

8

and Humphrey and Pulley (1995) for estimates of profit efficiency for banks.

13

which may or may not be more efficient than other strategies. Under the skimping hypothesis,

including nonperforming loans in the cost function effectively holds constant an endogenous

outcome, and makes skimping banks appear more efficient over the long run by not counting the

extra costs that may be created by the skimping strategy. Finally, the skimping hypothesis would

also tend to favor estimation of long-run profit efficiency in place of either short-run or long-run

cost efficiency. Output quality is a choice variable for banks under the skimping hypothesis, and

output quality affects on both costs (lower underwriting and monitoring costs) and revenues

(higher expected nonperforming loans). Thus, cost minimization and revenue maximization

cannot be well separated under this hypothesis. Similar to the arguments for cost efficiency, 8

measurement of profit efficiency should not control for nonperforming loans under the skimping

hypothesis because nonperforming loans are an outcome of the bank’s optimization strategy.

Under the moral hazard hypothesis, failure can result when banks take additional risks in

response to declining financial capital. This hypothesis implies that bank supervisors should monitor

capital ratios carefully and require actions to raise the ratios quickly when they become low, similar

to the intent of the prompt corrective action feature of the FDIC Improvement Act of 1991.

Additional implications of this hypothesis suggest that bank regulators and researchers continue their

traditional focus on the effects of capital, how to measure it, and how to better set and enforce capital

requirements. Because the moral hazard hypothesis is not a theory of the relationship between

problem loans and measured cost efficiency, it contains no implications for whether cost efficiency

measurement should control for nonperforming loans.
14

III. The Econometric Model

We applyGranger-causality techniques to the data on nonperforming loans, measured shortrun cost efficiency, equity capital, and some control variables to test which of the four hypotheses --

bad luck, bad management, skimping, and/or moral hazard -- are consistent with the data. The

model is sufficiently general that almost any combination of these hypotheses could be supported

by the data. Of the four hypotheses, only two are mutually exclusive -- the bad management and

skimping hypotheses predict opposite signs for the Granger-causality from measured cost efficiency

to nonperforming loans -- and hence cannot be simultaneously supported by the same set of data.

Again, we note that Granger-causality tests are gross statistical associations. As with any

econometric procedure, application of Granger-causality to the data can only indicate consistency

or inconsistency with an hypothesis, not proof of economic causation. However, because our

hypotheses each imply unique time-ordered and signed relationships among pairs of the three

important variables (nonperforming loans, cost efficiency, and capital), Granger-causality tests may

indicate which of our hypotheses are consistent or inconsistent with the data on U.S. commercial

banks.

The Granger-causality model is specified as follows:

i,t 1 i,lag i,lag i,lag i,lag t i t i 1i,t (1) NPL = f (NPL , X-EFF , CAP , RWA , YEAR, REGION , YEAR!REGION ) + ,

i,t (2) X-EFF = 2 i,lag i,lag i,lag i,lag t i t i 2i,t f (NPL , X-EFF , CAP , RWA , YEAR, REGION , YEAR!REGION ) + ,

i,t 3 i,lag i,lag i,lag i,lag t i t i 3i,t (3) CAP = f (NPL , X-EFF , CAP , RWA , YEAR, REGION , YEAR!REGION ) + ,

Definitions and descriptive statistics for all of these variables are shown in Table 1.
15

Table 1

Definitions and Descriptive Statistics for Variables

in the Granger-Causation Model.

(Statistics are for the four-lag model, N = 57,655.)

 mean std. dev.

NPL Nonperforming Loan Ratio = dollar 0.0168 0.0209

value of loans that are either 90 days 

past-due or are no longer accruing interest, 

divided by the value of total loans. 

X-EFF X-Efficiency = short-term cost 0.9224 0.0381

efficiency, i.e., percent of maximum cost 

efficiency achieved by bank based on the 

estimated best-practice cost frontier for the 

year in question.

CAP equity capital ratio = total equity capital 0.0892 0.0292

divided by gross total assets.

RWA risk-weighted asset ratio = estimated 0.5661 0.1275

ratio of total risk-weighted assets to gross 

total assets.

 % of observations 

NE = 1 if bank is located in Connecticut, 1.49 %

Maine, Massachusetts, New Hampshire, 

Rhode Island, or Vermont; = 0 otherwise.

SW = 1 if bank is located in Louisiana, Texas, 14.53 %

or Oklahoma; = 0 otherwise.

CA = 1 if bank is located in California; = 0 2.49 %

otherwise.

YEAR(89) = 1 in 1989; = 0 otherwise. 17.60 %

YEAR(90) = 1 in 1990; = 0 otherwise. 17.33 %

YEAR(91) = 1 in 1991; = 0 otherwise. 17.07 %

YEAR(92) = 1 in 1992; = 0 otherwise. 16.69 %

YEAR(93) = 1 in 1993; = 0 otherwise. 16.28 %

YEAR(94) = 1 in 1994; = 0 otherwise. 15.03 % 
16

The i,t dependent variable in equation (1) is the nonperforming loan ratio NPL . This ratio

equals loans that are either past-due at least 90 days or in nonaccrual status divided by total loans at

bank i in year t. NPL is the most commonly agreed-upon definition of problem loans in both the

research literature and the trade press. NPL also has the benefit of being almost exclusively

objectively defined -- it is less subject to regulatory discretion than are other measures of loan

quality, such as loan loss provisions and charge-offs.

The dependent va i,t riable in equation (2) is estimated cost efficiency X-EFF , which measures

the short-term cost X-efficiency of bank i relative to its peers in year t, or how close the bank is to

the estimated best-practice cost frontier for all banks in that year. As shown in the next section, we

estimate efficiency on a short-term basis and do not control for nonperforming loans in the

estimation. We need to observe short-term fluctuations in efficiency in order to test for intertemporal patterns between efficiency and other variables. We also need to estimate cost efficiency

without controlling for nonperforming loans in order to test for relationships between measured

efficiency and nonperforming loans. Depending upon which of the four hypotheses are most

consistent with the data, this procedure may or may not be the best way to measure cost efficiency.

The thi i,t rd dependent variable is the ratio of equity capital to assets, CAP . CAP measures

the bank's financial cushion for absorbing portfolio losses. For testing the moral hazard hypothesis

in equation (1), CAP is a good measure of how much shareholders have at risk in the portfolio,

which largely determines their ability and incentive to shift risk and losses to uninsured creditors and

the deposit insurer by investing in risky loans. The capital equation also serves as a check of the bad

luck and bad management hypotheses. Both of these hypotheses culminates in reduced capital, so

we would expect increases in NPL and/or decreases in X-EFF to Granger-cause reductions in CAP
 New England includes Connecticut, Maine, Massachusetts, New Hampshire, Rhode Island, and Vermont. The 9

Southwest includes Louisiana, Oklahoma, and Texas.

17

under these hypotheses, although this equation by itself cannot distinguish among the other

hypotheses. 

The right-hand-side variables in equations (1) - (3) include lagged values of all the dependent

variables, as is standard procedure for Granger-causality models. That is, we attempt to determine

whether var i j iiable Y Granger-causes variable Y by testing whether the past history of Y adds

j i,lag

information in predicting Y , after taking into account the past history of all the Y’s. We use NPL

i,t i,t-s to denote a vector containing s lags of NPL (i.e., NPL , where s=1,...,S). The other lag variables

are denoted similarly. In our empirical application below, we estimate the model using three, four,

and five annual lags of the variables (i.e., s = 3,4,5). Although we report the results of the four-lag

model only, the three- and five-lag models produce the same qualitative results.

The model described thus far is equivalent to a vector-autoregressive (VAR) specification

in three variables. However, we also include a number of control variables in all three equations.

Because NPL, X-EFF, and CAP are often strongly affected by regional or transitory conditions, we

need to control in at least a crude fashion for the economic environment of the bank. We therefore

t

specify YEAR , a set of dummy variables for each year of the data (excluding a base year), which

accounts for changes in the macroeconomy and changes in the regulatory treatment of banks over

i time. We also specify REGION , a set of three dummies that indicate whether the bank was located

in New England, in the Southwest, or in California, because these three geographic regions suffered

particularly bad economic downturns relative to the rest of the country during parts of the sample

period. The YEAR and REGION variables appear interactively to account for the fact that regional 9
RWA is designed to capture credit risk taking into account a number of factors such as the type of borrower and the 10

existence of collateral and guarantees. The risk weights have been shown to be positively related to the probability of

failure and to some accounting and market measures of risk, although the correspondence has been shown to be relatively

weak (see Avery and Berger 1991; Cordell and King 1995; Jones and King 1995).

 Including lagged values of RWA on the right-hand-side of equation (1) does not control for moral hazard behavior.

11

When a bank responds to moral hazard incentives by taking increased risks, these risks are likely taken in secret by

substituting higher risk loans for lower risk loans within a risk-weighted asset loan category, which is not reflected in

RWA. 

18

difference i,t s in economic conditions change over time. Finally, we specify RWA as the ratio of riskweighted assets (according to the Basle Accord) to gross total assets for bank i in year t, and include

lagged values of RWA in all three equations. RWA provides a crude control for credit risk, and at

the very least includes more information than do simple loan-to-asset ratios. We include RWA

10

because certain portfolio mixes will naturally yield more nonperforming loans, because low

measured cost efficiency may reflect the costs associated with a more loan-intensive balance sheet,

and because capital markets and bank regulators may require banks with certain lending strategies

to have higher capital ratios.11

Equations (1) - (3) are estimated separately using OLS techniques and a panel of data over

T years (t = 1,...,T) and N banks (i = 1,...,N), with specifications of 3, 4, and 5 annual lags (S = 3, 4,

or 1,i,t 2,i,t 3,i,t 5). The terms å , å , and å are independent random error terms. There is no serious concern

about the correlations among the random error terms either within an equation or across the three

equations, because of the specification of the right-hand-side variables. Including three to five years

of lags of the dependent variables in each equation should absorb the bulk of any serial correlation

in the three error terms. Similarly, including the YEAR, REGION, and YEAR*REGION variables

absorbs any cross-section correlation that is constant across banks within a year, across banks within

a region, or across banks in a region in a particular year. Also, because the same right-hand-side
19

variables are specified for each of the three equations, there is no need to take account of the

correlations across the error terms in the different equations. In such a specification, OLS and GLS

yield identical estimators.

The key empirical implications of the four hypotheses are easily summarized in terms of the

coefficients of equations (1) - (3). For example, the main identifying prediction of the bad luck

hypothesis is a negative sum of the coefficients on the NPL lags in the X-EFF equation (2). That is,

the bad luck hypothesis predicts that measured cost efficiencywill be lower in the several years after

high nonperforming loans are reported as the bank has to expend resources dealing with negotiations,

defaults, disposing of collateral, etc. We focus on the sum of the lag coefficients, rather than the

individual lag coefficients, because the sum measuresthe total effect of past NPL on current X-EFF,

and because the sum is more accurately measured than its individual parts due to collinearity among

the individual lagged values. Unlike most Granger-causality exercises, we are most interested in

whether the sum of the coefficients is positive or negative, not whether the individual coefficients

are all equal to zero. Note that including the other right-hand-side variables in the equation makes

our tests more stringent, because (in the case of equation (2)) we are controlling for any predictive

effects of lagged cost efficiency, lagged capital, lagged risk-weighted assets, year, and region on

current measured efficiency. 

Similarly, the bad management hypothesis predicts that the sum of the coefficients on the XEFF lags in the NPL equation (1) will be negative. The effects of subpar management on operations

should be observed in higher costs rather quickly, whereas the nonperforming loan data will reflect

the impact of poor management on the loan portfolio only after borrowers have fallen behind in their

loan repayments and after the bank has recognized and actually reported this phenomenon. Under
20

the skimping hypothesis, the sum of the coefficients on the X-EFF lags in the NPL equation (1) will

be positive, as the banks that improved their measured short-run cost efficiency in the past by

intentionally reducing expenditures on loan underwriting and monitoring develop more problem

loans in the present. Since the bad management and skimping hypotheses predict opposite signs for

the sum of the lagged X-EFF coefficients in the NPL equation, we view this coefficient sum as the

net effect of these two opposing theories. The final hypothesis, moral hazard, predicts that the sum

of the coefficients on the CAP lags in the NPL equation (1) will be negative, as banks with low

capital in the past took increased risks in response to incentives created by low capital, which may

result in high levels of problem loans in the present. We test the moral hazard hypothesis only for

a subsample of thinly capitalized banks, because banks with high levels of capital do not face moral

hazard incentives.

Finally, although all of the empirical implications that uniquely distinguish among the four

hypotheses are contained in equations(1) and (2), we have included the capital equation (3) because

it is important to complete the overall model and verify the basic relationships that are being

investigated. The bad luck and bad management hypotheses all predict that either nonperforming

loans, cost efficiency, or both Granger-cause equity capital. In equation (3) we expect to find a

negative sum of coefficients on the NPL lags and a positive sum of coefficients on the X-EFF lags,

although we cannot distinguish among these hypotheses using this equation. Such findings would

extend the stylized facts from the literature that problem loans and inefficiencies are strongly

associated with losses of bank capital.

IV. The Cost Efficiency Model

We used the econometric frontier approach (EFA) to generate an annual estimate of cost
 See Bauer (1990) for a review of EFA methods. We cannot use the distribution-free approach because it only 12

generates long-run estimates of cost efficiency. We cannot use the thick cost frontier approach because it estimates

cost efficiency only for groups of banks. We do not use data envelopment analysis because it is often difficult to

compare the efficiency of individual institutions using this approach. Berger, Hunter, and Timme (1993) discussed

the relative strengths and weaknesses of these approaches. 

 As estimated here, cost inefficiency includes both technical and allocative inefficiencies. These inefficiencies may

13

be the result of numerous managerial (and other) phenomena, including expense preference behavior, agency

problems, managerial incompetence, and the degree of managerial effort.

 The half normal distribution, which is a special case of the truncated normal distribution, restricts the probability 14

density of the cost inefficiency term to decrease monotonically across banks, whereas the truncated normal does not.

21

efficiency for each bank i in each year t. In the EFA method, a frontier cost function is estimated 12

using a statistical procedure that decomposes the error term into two parts. One part captures

random disturbances and is assumed to follow a symmetric normal distribution and the other part

is assumed to capture cost inefficiency. A one-sided distribution (usually the half normal) is 13

imposed on the cost inefficiency portion of the error term, since inefficiency cannot be negative. We

impose a truncated normal distribution on the inefficiency term, which is shown by Stevenson (1980)

to be more general and flexible than the typical assumption of a half normal distribution.14

We specify the Fourier-flexible functional form for the cost function. This functional form

combines a standard translog functional form with the non-parametric Fourier functional form.

Because the translog form is only a local approximation, it may perform poorly for observations

far from the sample means. In contrast, the Fourier-flexible form adds trigonometric

transformations of the variables to globally approximate the underlying cost function over the

entire range of data. Mitchell and Onvural (1992), McAllister and McManus (1993), Berger,

Leusner, and Mingo (1994), and Berger, Cummins, and Weiss (1995) all found that the Fourierflexible form dominates the translog.
 We estimated equation (4) using maximum likelihood techniques, and imposed the standard symmetry and 15

homogeneity restrictions on the translog portion of the model. Factor share equations were omitted because

application of the usual cross-equation restrictions would impose the assumption that the given input proportions were

the allocatively efficient ones (see Berger 1993, p. 266).

 Transactions deposits include demand deposits, NOW accounts, automatic transfer service accounts, and telephone 16

and pre-authorized transfer accounts. Fee-based income equals gross noninterest income less both service charges

on deposit accounts and gains(losses) from securities and foreign exchange trading. Fee-based income is included to

control for activities other than deposits and loans such as off-balance sheet activities and trust services.

 The price of labor equals salaries and benefits divided by the number of full time equivalent workers. The price

17

of physical capital equals expenditures on equipment and premises divided by the book value of physical assets. 

22

We estimated the following operating cost function for each year t in our analysis:

15

where the subscript that identifies individual banks has been dropped for simplicity. OC is

operating (noninterest) expense; Y is a vector of outputs including commercial loans, consumer

loans, real estate loans, transactions deposits, and fee-based income; W is a vector of input prices

16

including the prices of labor and physical capital; LIMIT and UNIT are, respectively, dummy

17

variables equal to 1 for banks in states that restricted or banned branch banking during the sample
 See Berger, Leusner, and Mingo (1994) for a derivation of, and a justification for, this truncation. Because of 18

computational limitations, we restricted j= k= l in the triple summation terms.

 We also do not include either financial capital or the price of borrowed funds in the cost function, because our cost 19

measure excludes interest expense.

23

period. The error term ç is a composite expression: ç = lnU + lnV, where lnU captures cost

 

inefficiency and is distributed as a truncated normal variable, and lnV captures random error and

j j m

is distributed as a normal variable. The Z values are functions that rescale the lnY and the lnW

so that they fall on the interval [.1*2B , .9*2B]. 18

We estimate an operating cost function (i.e., noninterest expense only) because operating

costs have been shown elsewhere to comprise the bulk of excess costs at banks (see Berger and

Humphrey (1991)); because the costs associated with credit evaluation, loan monitoring, and

administering to problem loans are mainly noninterest expenses; and because interest cost

inefficiencies are substantially affected by interest rate levels, which vary considerably during our

sample period. As discussed above, we do not control for loan quality in the cost function,

because we do not want to remove from our estimates of cost efficiency the expenses that are

correlated with inefficient portfolio management. We estimate 10 separate annual cost frontiers,

19

rather than estimating a common frontier across time, because conditions change from year-to-year --

that is, the technology or bank that is most efficient in one year may not be the most efficient in

another year.

We construct the cost efficiency variable X-EFF as follows. Using equation (4), we

estimate the expected value of the inefficiency term lnU conditional on 0, due to Jondrow, Lovell,

Materov, and Schmidt (1977). We then transform the estimates of lnU so that they vary positively

wi i,t th cost efficiency, rather than with cost inefficiency. For bank i in year t, X-EFF equals
24

Umin i /U , the estimated value of U for the most efficient bank divided by the estimated value of U

for bank i, where U = e . Thus, X-EFF is positive, increases with cost efficiency, and has an upper lnU

bound of one. 

V. Data

The data set consists of an unbalanced panel of annual observations of U.S. commercial

banks from 1985 through 1994. Some years have a greater number of observations than others

because of failure, acquisition, or entry during the sample period. We exclude observations for

which at least five years worth of lagged variables could not be observed. The size of the panel that

we actually used in the estimations depended on the number of lags included in the model -- there

were 69,742 observations, 57,780 observations, and 46,504 observations, respectively, when s = 3,

4, and 5 lags. Table 1 shows definitions and sample means and standard deviations for the variables

used in the four-lag Granger-causality model.

All variables were constructed using end-of-year data from the annual Reports of Condition

and Income (call reports) for 1985 through 1994, with the exception of UNIT and LIMIT, which

were constructed from information in Amel (1993). We use annual data because end-of-year call

report data are more accurate than quarterly call report data and to reduce the amount of random

error in the cost efficiency estimation. By using annual data, however, we may understate the

magnitude of any Granger causation among NPL, X-EFF, and CAP if a substantial amount of the

inter-temporal effects associated with our four hypotheses occur within a year.

Operating costs (OC) and the numerators used to construct the input prices (W) are flow

variables that reflect accumulated activity over the course of each year. The nonperforming loan

ratio (NPL), the capital ratio (CAP), the risk-weighted asset ratio (RWA), the cost function output
 This also caused even more observations to be deleted from the Granger-causality tests because five lags of 20

efficiency were needed for these tests.

 Tests using data from other years during the sample period yielded similar results. 

21

25

vector (Y), and the denominators used to construct input prices are stock variables, and are included

here as averages of beginning-of-year and end-of-year values. Because the natural log of zero equals

-4, a small positive amount ($1,000) was added to all output variables for all banks. A small number

of observations in each year were excluded from the efficiency estimations because either assets or

total costs were reported as zero, because input prices could not be constructed, or because

constructed input prices were unrealistically large or small.20

VI. Results

Efficiency Estimation Results

Means and standard deviations for the annual estimates of cost efficiency are displayed in

Table 2. The average bank is between 90 percent and 95 percent efficient over the sample period,

a higher level of cost efficiency than is found in most other econometric frontier (EFA) studies of

commercial banks. The likely reason for this difference is our more general and flexible

specification. Earlier EFA studies may have understated cost efficiency by imposing too much

structure on both the cost function (by using the translog form) and on the inefficiency term (by using

the half normal distribution). 

To examine this issue, we estimated X-EFF for three additional variants of the cost model.

A comparison of the results using data from 1994 is shown in Table 3. Variant A shows the 1994 21

values using the Fourier-flexible form and specifies the truncated normal distribution for lnU; variant

B uses the Fourier-flexible form but imposes a half normal distribution on lnU; variant C uses a
26

Table 2

Estimated X-Efficiency, 1985-1994

 N mean std. dev. 

1985 12,606 0.9180 0.0460

1986 12,343 0.9402 0.0217

1987 11,933 0.9499 0.0195

1988 11,546 0.9086 0.0476

1989 11,278 0.9266 0.0345

1990 11,027 0.9071 0.0456

1991 10,753 0.9123 0.0522

1992 10,452 0.9122 0.0425

1993 10,130 0.9290 0.0318

1994 9,622 0.9466 0.0178
27

Table 3

Estimates of X-Efficiency, 1994

Various functional forms and distributional assumptions.

 and indicate significantly different from the mean of (A) at the 1 percent and 5 percent levels. ** *

rank order

 correlation 

 mean std. dev. with (A) 

A. Fourier-flexible,

truncated normal 0.9466 0.0178

B. Fourier-flexible,

half normal 0.9191 0.0312 0.9999 **

C. Translog,

truncated normal 0.8989 0.0411 0.9688 **

D. Translog,

half normal 0.8780 0.0517 0.9690 **
These results stand in contrast to Hunter and Timme (1993), who found that the rank efficiency ordering of banks 22

is sensitive to how the cost function is specified, and also to Bauer, Berger, and Humphrey (1993), who found that

the rank efficiency ordering of banks varies with efficiency approach.

 We also directly tested the restrictions implied by a translog specification. That is, we tested whether the 23

coefficients on all of the trigonometric terms in the Fourier-flexible form were jointly equal to zero. The F-statistic

implied a rejection of the translog null hypothesis at the 1 percent level for both the half normal and the truncated

normal specifications.

28

standard translog form (i.e., drops the sine and cosine terms) and specifies a truncated normal

distribution for lnU; and variant D uses the translog form and imposes a half normal distribution on

lnU. Thus, Variant A is the model used throughout this paper and is the least restrictive, variant D

is the model generally used elsewhere and is the most restrictive, and variants B and C lie between

these extremes. Estimated X-efficiency is significantly lower when the translog is substituted for

the Fourier-flexible, and is also significantly lower when the half normal distribution is substituted

for the truncated normal distribution. Hence, the structure most often employed in the literature

(variant D) maymisdiagnose some of the variability in the cost data as inefficiency, and shows about

twice as much inefficiency as the most general form used her (variant A). Nevertheless, the rank

efficiency ordering of the banks is very similar across the four variants. Finally, neither the

functional form of the cost function nor the distribution imposed on the inefficiency terms

substantially affect the rank efficiency ordering of the banks in our sample. 

22 , 23

Granger-Causality Test Results

Table 4 displays the coefficient estimates from equations (1)-(3) using four lags on the righthand-side variables. All of the major results were robust to the number of lags included in the model

-- results using three and five lags are not shown here in order to conserve space. 

In the X-EFF equation, we find evidence in support of the bad luck hypothesis. The sum of
29

Table 4

Granger-Causality Tests

Four lags.

(1) NPL (2) X-EFF (3) CAP

INTERCEPT .0011 .2266** -.0032*

(0.61) (83.92) (2.43)

NPL(-1) .5626** -.1316** -.0146**

(140.45) (22.99) (5.19)

NPL(-2) .0593** .0099 .0142**

(13.56) (1.58) (4.61)

NPL(-3) .0084* .0351** .0092**

(2.09) (6.13) (3.27)

NPL(-4) .0134** .0267** .0075**

(4.18) (5.84) (3.33)

 NPL(total) .6437** -.0599** .0163**

 (183.31) (11.94) (6.70)

X-EFF(-1) -.0164** .5940** .0070**

(6.34) (160.98) (3.89)

X-EFF(-2) .0056 .1809** -.0022

(1.83) (41.50) (1.06)

X-EFF(-3) .0062 -.0162** .0045*

(1.94) (3.54) (2.02)

X-EFF(-4) -.0022 .0032 .0055**

(0.84) (0.86) (3.00)

X-EFF(total) -.0068** .7619** .0148**

 (3.35) (263.04) (10.44)

CAP(-1) -.0540** -.0538** .9358**

(9.21) (6.41) (227.47)

CAP(-2) .0418** .0521** -.0225**

(5.11) (4.46) (3.92)

CAP(-3) .0305** .0119 .0131*

(3.67) (1.01) (2.24)

CAP(-4) .0011 -.0056 .0074

(0.19) (0.65) (1.74)

 CAP(total) .0194** .0046 .9338**

 (7.63) (1.27) (521.84)

RWA(-1) .0102** .0178** -.0184**

 (8.21) (10.05) (21.15)

RWA(-2) .0057** -.0171** .0063**

(3.51) (7.38) (5.51)

RWA(-3) .0016 -.0032 .0017

(1.02) (1.40) (1.53)

RWA(-4) -.0035** .0014 .0028**

(2.96) (0.85) (3.43)

 RWA(total) .0140** -.0011 -.0076**

 (23.95) (1.29) (18.14)

Absolute values of t-statistics are in parentheses ( ). 
30

** and * indicate significance at the 1 percent and 5 percent levels, respectively.
31

Table 4 (continued)

(1) NPL (2) X-EFF (3) CAP

YEAR(90) .0018** -.0207** -.0019**

(6.39) (51.41) (9.48)

YEAR(91) .0012** -.0077** .0007**

(4.15) (19.49) (3.77)

YEAR(92) -.0018** -.0065** .0020**

(6.76) (17.18) (10.94)

YEAR(93) -.0020** .0080** .0033**

(7.28) (20.21) (17.05)

YEAR(94) -.0024** .0147** -.0002

(8.38) (36.59) (1.23)

NE .0155** .0019 -.0015*

(13.98) (1.20) (1.96)

NE*YEAR(90) .0049** .0036 -.0022

(3.06) (1.58) (1.90)

NE*YEAR(91) -.0023 -.0098** -.0046**

(1.36) (4.12) (3.94)

NE*YEAR(92) -.0136** -.0064** .0014

(7.91) (2.63) (1.14)

NE*YEAR(93) -.0115** -.0016 .0024*

(6.56) (0.63) (1.99)

NE*YEAR(94) -.0126** .0003 .0027*

(7.02) (0.12) (2.12)

SW .0084** .0056** -.0036**

(19.16) (8.99) (11.77)

SW*YEAR(90) -.0056** -.0088** .0009*

(9.14) (10.05) (2.05)

SW*YEAR(91) -.0063** -.0090** .0028**

(10.36) (10.30) (6.50)

SW*YEAR(92) -.0063** -.0088** .0043**

(10.27) (10.07) (10.03)

SW*YEAR(93) -.0070** -.0044** .0046**

(11.33) (5.04) (10.54)

SW*YEAR(94) -.0070** -.0022* .0029**

(11.15) (2.48) (6.50)

CA -.0023* .0065** .0024**

(2.07) (4.18) (3.11)

CA*YEAR(90) .0013 .0001 .0033**

(0.83) (0.05) (3.07)

CA*YEAR(91) .0139** -.0098** -.0034**

(9.44) (4.66) (3.34)

CA*YEAR(92) .0146** -.0126** -.0026*

(10.14) (6.10) (2.56)

CA*YEAR(93) .0157** -.0128** -.0053**

(11.03) (6.26) (5.34)

CA*YEAR(94) .0071** -.0033 .0001

(4.96) (1.63) (0.11)

Adjusted R .4944 .6892 .8722 2

N 57,655 57,655 57,655

Absolute values of t-statistics are in parentheses ( ). 

** and * indicate significance at the 1 percent and 5 percent levels, respectively.
i j These calculations reflect only the direct effect of changes in lagged Y on current Y because these direct effects 24

are the most appropriate measures for the hypotheses we are testing. We exclude indirect effects -- such as the effect

i j of lagged Y on current Y through other lagged values of the Y’s -- from our calculations in order to avoid mixing

the inter-temporal effects associated with our four different hypotheses.

32

the lagged NPL coefficients is -.0599 and is significant at the 1 percent level. Thus, the Grangercausality results are consistent with the notion that after loans become past due or nonaccruing,

operating costs rise because of the difficulty in dealing with these loans, as predicted by the bad luck

hypothesis. However, the economic impact of this result was small -- for the average bank, a one

standard deviation increase in NPL (from .0168 to .0377) predicts a cumulative reduction in

measured cost efficiency over four years from .9224 to .9211, or a 1.7 percent increase in average

inefficiency. Note that the lagged coefficient sums on CAP and RWA were not significantly

24

different from zero in this equation.

The results of the NPL equation suggest that the bad management hypothesis dominates the

skimping hypothesis. The sum of the coefficients on the lagged X-EFF variables equals -.0068 and

is significant at the 1 percent level. Thus, Granger-causality suggests that after measured cost

efficiency declines, nonperforming loans increase because of poor loan portfolio management, as

predicted by the bad management hypothesis. The economic impact of this result is also small -- for

the average bank, a one standard deviation reduction in X-EFF (from .9224 to .8843) predicts a

cumulative increase in the nonperforming loan ratio over four years from .0168 to only .0171, or a

1.8 percent increase in nonperforming loans. As expected, the lagged RWA coefficient sums are

positive and significant in the NPL equation. This result suggests that a relatively risky loan

portfolio mix will eventually yield relatively high numbers of nonperforming loans.

The moral hazard hypothesis prdicts that reductions in capital lead to increases in
 We selected the subsample based on the median values of CAP(-1). 25

33

nonperforming loans, at least for thinly capitalized banks, because these banks are most likely to face

moral hazard incentives. Perhaps surprisingly, when the NPL equation is estimated for the entire

population of banks the sums of the lagged CAP coefficients are positive and significant. However,

this is not an appropriate test of the moral hazard hypothesis, because banks with high or adequate

levels of capital likely do not face moral hazard incentives, we test the moral hazard hypothesis by

estimating the NPL equation separately using only the annual observations for which CAP was

below the population median. Partial results of these regressions are shown in the first panel in 25

Table 5. The sum of the coefficients on the lagged CAP variables equals -.0510 and is significant

at the 1 percent level. These data support the moral hazard hypothesis, and suggest that, on average,

thinly capitalized banks take increased portfolio risk, which results in higher levels of problem loans

in the future. For the average low-capital bank, a one standard deviation reduction in CAP (from

.0712 to .0578) predicts a cumulative increase in the nonperforming loan ratio over four years from

.0186 to .0193, or a 3.8 percent increase in nonperforming loans. Although the overall impact of this

result is small, it may be quite large for some individual banks, given that our results are effectively

an average of the behavior of banks that do, and banks that do not, respond to moral hazard

incentives.

As stated above, the CAP equation does not allow us to distinguish between any of our four

major hypotheses, but is included for completeness because three of the four hypotheses culminate

in a loss of capital. The sum of the coefficients on the lagged X-EFF variables was positive,

evidence that cost-inefficient banks are likely to have low and perhaps even negative earnings, which
34

Table 5

Granger-Causality Tests

Partial Results for Subsample Estimations. Four lags.

coefficient t-statistics 

 estimates (absolute values)

Dependent variable is NPL 

Banks with CAP(-1) less than population median in individual years (N = 28,826, adjusted R .5103). 2 =

CAP(-1) -.1575** (11.99)

CAP(-2) .0855** (6.20)

CAP(-3) .0084 (0.65)

CAP(-4) .0126 (1.35)

CAP(total) -.0510** (4.86)

Dependent variable is CAP 

Banks with CAP(-1) less than population median in individual years (N = 28,826, adjusted R .5039). 2 =

NPL(-1) -.0302** (8.96)

NPL(-2) .0160** (4.32)

NPL(-3) .0110** (3.20)

NPL(-4) .0112** (4.07)

 NPL(total) .0080* (2.58)

Dependent variable is CAP 

Banks with CAP(-1) greater than population median in individual years (N = 28,826, adjusted R .8557). 2 =

NPL(-1) -.0068 (1.45)

NPL(-2) .0067 (1.34)

NPL(-3) .0024 (0.53)

NPL(-4) -.0002 (0.05)

NPL(total) .0021 (0.52)

 

Dependent variable is NPL 

Banks with X-EFF(-1) greater than population median in every year (N = 12,756, adjusted R .4943). 2 =

X-EFF(-1) .0002 (0.02)

X-EFF(-2) .0117 (1.00)

X-EFF(-3) .0133 (1.17)

X-EFF(-4) -.0019 (0.25)

X-EFF(total) .0233** (3.13)

** and * indicate significance at the 1 percent and 5 percent levels, respectively.
 A survivor bias in our data set may contribute to this result. Because we use end-of-year data we only observe the 26

low-capital banks that survived the year, not the low-capital banks that failed during that year. The expected negative

relationship between increasing problem loans and reductions in capital is likely to be strongest in failing banks, since

these banks essentially lost all of their capital. 

 We selected these subsamples based on the median values of CAP(-1). 27

35

Granger-cause reductions in capital. The sum of the lagged RWA coefficients is negative and

significant, evidence that higher risk lending strategies also Granger-cause reductions in capital on

average. However, the sum of the lagged NPL coefficients is positive and significant, a counterintuitive result suggesting that high levels of nonperforming loans Granger-cause high capital ratios.

It is possible that banks with high and low levels of capital behave differently in response to

increases in problem loans. In particular, thinly capitalized banks may be under pressure from bank

regulators, uninsured creditors, and the capital markets to improve their marginal capital positions,

while banks with large capital cushions can afford to book loan losses without altering their lending

or capital strategies. To investigate this possibility, we estimated the CAP equation using only the 26

annual observations for which CAP was above the population median, and then once again using

only the annual observations for which CAP was below the population median. Partial results of 27

these regressions are shown in the second and third panels in Table 5. We continue to find that

nonperforming loans positively Granger-cause capital ratios at the low-capital banks, which suggests

that these banks take action to replenish capital after nonperforming loans increase, perhaps under

pressure from regulators and markets. This result disappears at the high-capital banks for which we

find no Granger-causality between nonperfoming loans and capital. 

Although we find no evidence in support ofthe skimping hypothesisin Table 4, these results

do not preclude the possibility of skimping in individual banks. Our Granger-causality results are

average relationships, so it is possible that the bad management relationship that exists in the
 We selected the subsample based on the median values of X-EFF(-1). We required banks to be relatively cost 28

efficient in every year, rather than just in individual years, to avoid including banks that only appeared to be efficient

in individual years because they were skimping. This sampling procedure ensures that we observed only long-run cost

efficient banks -- long-run cost-efficient skimpers as well as long-run cost-efficient non-skimpers.

36

majority of banks simply dominates the skimping relationship that exists in a few banks. We might

expect to find concentrations of “skimpers” among the most cost-efficient banks, i.e., banks that

consistently skimp on loan underwriting and monitoring in order to cut costs, but manage the

resulting loan quality problems in a cost effective fashion. To investigate this possibility, we

estimated the NPL equation for the subsample of banks that were consistently cost efficient, having

efficiency greater than the median in every year of our analysis. Partial results of these regressions 28

are shown in the fourth panel in Table 5. In the NPL equation, the sum of the lagged X-EFF

coefficients equals .0233 and is significant at the 1 percent level, suggesting that measured cost

efficiency positively Granger-causes nonperforming loans among highly efficient banks, supporting

the skimping hypothesis for this subset of banks. For the average bank in this subsample, a one

standard deviation increase in X-EFF (from .9522 to .9675) predicts a cumulative increase in the

nonperforming loan ratio over four years from .0128 to .0132, or a 3.1 percent increase in

nonperforming loans. To the extent that skimping behavior did occur, it is not at all clear that these

banks were materially harmed -- all of the banks in this subsample managed to remain among the

most cost-efficient banks in the industry for the entire sample period. These results may reflect

optimizing behavior among the most cost-efficient banks in the industry -- banks that, at the margin,

willingly accepted the marginal increases in loan problems in exchange for marginal cuts in

underwriting and monitoring expenses.

VII. Conclusions
37

Loan quality at financial institutions has received close scrutinysince the failure waves in the

commercial banking and thrift industries. Simultaneous with these developments, the empirical

literature on productive efficiency in financial institutions has burgeoned. In this paper, we weave

together these two strands ofresearch. We employGranger-causality techniques to test whether cost

efficiency in banks pre-dates loan quality, whether loan quality pre-dates cost efficiency, or both,

using pooled cross section-time series data on nonperforming loans, operating cost efficiency, equity

capital ratios, and other variables for U.S. commercial banks between 1985 and 1994. 

We test three hypotheses regarding the intertemporal relationships between loan quality and

efficiency. The “bad luck” hypothesis posits that exogenous events can cause nonperforming loans

to increase, and that after time passes the extra expenses associated with these loans (e.g., more

intensive monitoring, negotiating workout arrangements, handling collateral if default occurs) will

be reflected in lower measured cost efficiency. Hence, nonperforming loans should negatively

Granger-cause cost efficiency. The “bad management” hypothesis posits that poorly run banks do

bad jobs at both cost control and at loan underwriting and monitoring, and that after time passes this

slack leads to increases in problem loans as borrowers fall behind on their loan repayments. Hence,

low cost efficiency should precede increases in nonperforming loans, i.e., cost efficiency should

negatively Granger-cause nonperforming loans. The “skimping” hypothesis posits that banks might

achieve low costs by under-spending on loan underwriting and monitoring in the short run, and after

time passes this slack results in increases in problem loans. Hence, measured cost efficiency should

positively Granger-cause nonperforming loans. We also examine the familiar “moral hazard”

hypothesis by testing whether equity capital negatively Granger-causes nonperforming loans.

Our results suggest that the inter-temporal relationships between loan quality and cost
38

efficiency run in both directions. The data provide support for the bad luck hypothesis. Increases

in nonperforming loans tend to be followed bydecreases in measured cost efficiency, suggesting that

problem loans cause banks to increase spending on monitoring, working out, and/or selling off

problem loans. For the industry as a whole, the data favor the bad management hypothesis over the

skimping hypothesis -- decreases in measured cost efficiency are generally followed by increases in

nonperforming loans, evidence that bad management practices are manifested not only in excess

expenditures, but also in subpar underwriting and monitoring practices that eventually lead to

nonperforming loans. For a subset of banks that are consistently efficient, however, increases in

measured cost efficiency precede increases in nonperforming loans, consistent with the skimping

hypothesis that banks trade short-run expense reductions for long-run reductions in loan quality.

Finally, decreases in bank capital ratios precede increases in nonperforming loans for banks with low

capital ratios, evidence that thinly capitalized banks may respond to moral hazard incentives by

taking increased portfolio risks. 

Depending on whether or not these results are confirmed by future research, our findings may

have research and policy implications. The bad luck hypothesis implies that the major risks facing

financial institutions are exogenous events, and as such supports policies that limit the exposure of

institutions to external shocks and/or insulate institutions from the effects of shocks. In contrast, the

bad management hypothesis implies that the major risks facing financial institutions are caused

internally, and implies that cost efficiency be included as an indicator of potentially troubled banks.

The empirical results also have implications for estimating the efficiency of financial

institutions. The empirical support for the bad luck hypothesissuggeststhat controlsfor loan quality

may be needed to avoid understating cost efficiency at unlucky banks, while the evidence supporting
39

the bad management hypothesis implies that controlling for loan quality may overstate cost

efficiency at poorly run banks. Neither hypothesis clearly dominates the other. The skimping

hypothesis, which received much less empirical support, also suggests that controls for loan quality

be excluded when estimating efficiency. Ultimately, whether or not one controls for loan quality

should rest on the particular efficiency application at hand. We also find that measured cost

efficiency varies substantially with the degree of flexibility in the specification of the cost equation

and the error structure. Measured cost efficiency is lower when the specification is less flexible,

perhaps because some of the misspecification is measured as cost inefficiency. 

The skimping hypothesis also implies that efficiency estimation should use several years of

cost or profit data, so that years in which skimping saves on costs would be averaged with years in

which the resulting nonperforming loans force costs up and revenues down. Similarly, profit

efficiency is preferred over cost efficiencyunder the skimping hypothesis. This is because both costs

and revenues are affected by the decision to skimp.

We stress the limitations of our analysis. The inter-temporal relationships revealed by

Granger-causality techniques are gross statistical associations only, and do not necessarily prove

economic causation. However, these relationships are indicative of which among the alternative

hypotheses are consistent with the data. Future research might use other statistical techniques to

reveal the inter-temporal relationships between loan quality and productive efficiency in financial

institutions; attempt to decompose the determinants of loan quality into internal versus exogenous

factors; or focus on the empirical consequences of controlling for loan quality when estimating

efficiency. 
40

References

Akhavein, Jalal D., P.A.V.B. Swamy, and Stephen B. Taubman, "A General Method for

Deriving the Efficiencies of Banks from a Profit Function," Board of Governors of the 

Federal Reserve System, working paper, 1995.

Amel, Dean, "State Laws Affecting Commercial Bank Branching, Multibank Holding Company

Expansion, and Interstate Banking," Board of Governors of the Federal Reserve System,

working paper, 1993.

Avery, Robert B., and Allen N. Berger, "Risk-Based Capital and Deposit Insurance Reform,"

Journal of Banking and Finance 15: 847-874, 1991.

Barr, Richard, and Thomas Siems, "Predicting Bank Failure Using DEA to Quantify

Management Quality," Federal Reserve Bank of Dallas, Financial Industry Studies

Working Paper No. 1-94, January 1994.

Bauer, Paul W., "Recent Developments in the Econometric Estimation of Frontiers," Journal of

Econometrics, 46: 39-56, 1990.

Bauer, Paul W., Allen N. Berger, and David B. Humphrey, "Efficiency and Productivity Growth

in U.S. Banking," in H.O. Fried, C.A.K. Lovell, and S.S. Schmidt, eds., The

Measurement of Productive Efficiency: Techniques and Applications, Oxford: Oxford

University Press: 386-413, 1993.

Becher, David, Robert DeYoung, and Thomas Lutton, "Projecting Resolved Assets in Banks: 

A Comparison of Different Methods," Office of the Comptroller of the Currency,

working paper, 1995.

Berg, Sigbjørn, Finn Førsund, and Eilev Jansen, "Malmquist Indices of Productivity

Growth during the Deregulation of Norwegian Banking, 1980-89," Scandinavian Journal 

of Economics 94, 1992. 

Berger, Allen N., "Distribution-Free Estimates of Efficiency in the U.S. Banking Industry and

Tests of the Standard Distributional Assumptions," Journal of Productivity Analysis 4:

261-292, 1993.

Berger, Allen N., "The Relationship between Capital and Earnings in Banking," Journal of

Money, Credit, and Banking 27: 432-56, 1995.

Berger, Allen N., Cummins, J. David, and Mary A. Weiss, “The Coexistence of Multiple 

Distribution Systems for Financial Services: The Case of Property-Liability Insurance,” 

working paper, 1995. 
41

Berger, Allen N., Diana Hancock, and David B. Humphrey, "Bank Efficiency Derived from the

Profit Function," Journal of Banking and Finance, 17: 317-347, 1993.

Berger, Allen N., and David B. Humphrey, "Measurement and Efficiency Issues in Commercial

Banking," in Z. Griliches, ed., Output Measurement in the Service Sectors, National

Bureau of Economic Research, Studies in Income and Wealth, Vol. 56, University of

Chicago Press (Chicago, IL): 245-79, 1992.

Berger, Allen N., William Hunter, and Stephen Timme, "The Efficiency of Financial

Institutions: A Review and Preview of Research Past, Present, and Future,"Journal of 

Banking and Finance, 17: 221-249, 1993.

Berger, Allen N., John H. Leusner, and John J. Mingo, "The Efficiency of Bank Branches,"

Board of Governors of the Federal Reserve, Finance and Economics Discussion Series

Paper 94-26, 1994.

Board of Governors of the Federal Reserve System, Federal Reserve Bulletin, Washington, D.C.,

volumes 73 (1987) through 79 (1993).

Cordell, Lawrence R., and Kathleen K. King, "A Market Evaluation of the Risk-Based Capital

Standards for the U.S. Financial System," Journal of Banking and Finance, 19: 531-562,

1995.

Coyne, Christopher, Ginette McManus, and A. J. Stagliano, "Data Envelopment Analysis and

Management Performance: An Empirical Investigation of Small U.S. Banks," Small

Firm Financial Research Symposium, California State University, Long Beach, 1993. 

Demirguc-Kunt, Asli, "Deposit-Institution Failures: A Review of the Empirical Literature,"

Federal Reserve Bank of Cleveland, Economic Review, Quarter 4, 1989.

DeYoung, Robert, "Fee-Based Services and Cost Efficiency in Commercial Banks," Federal

Reserve Bank of Chicago, Proceedings: The Declining Role of Banks, May: 501-519,

1994.

DeYoung, Robert, "X-Efficiency and Management Quality in National Banks," forthcoming,

Journal of Financial Services Research.

DeYoung, Robert, and Daniel E. Nolle, "Foreign-Owned Banks in the U.S.: Earning Market

Share or Buying It?,” Office of the Comptroller of the Currency, Working Paper 95-2,

March 1995.
42

DeYoung, Robert, and Gary Whalen, "Is a Consolidated Banking Industry a More Efficient

Banking Industry?," Office of the Comptroller of the Currency, Quarterly Journal,

volume 13, number 3, September 1994.

Eisenbeis, Robert, and Simon Kwan, “An Analysis of Inefficiencies in Banking: A Stochastic 

Cost Frontier Approach,” working paper, 1994.

Elbadawi, I., A.R. Gallant, and G. Souza, "An Elasticity Can Be Estimated Consistently Without

A Priori Knowledge of the Functional Form," Econometrica, 51: 1731-1753, 1983.

Federal Financial Institutions Examination Council, Reports of Condition and Income, 1984-

1993.

Faulhaber, Gerald R., “Banking Markets: Productivity, Risk, and Customer Satisfaction,” The

Wharton School, University of Pennsylvania, working paper, 1995.

General Accounting Office, Report to the Congress on the Bank Insurance Fund, GAO/AFMD90-100 (September 1990).

Hughes, Joseph P., William Lang, Loretta J. Mester, and Choon-Geol Moon, “Recovering 

Technologies that Account for Generalized Managerial Preferences: An Application to 

Non-Risk-Neutral Banks,” forthcoming in Proceedings: The New Tool Set, Assessing 

Innovations in Banking, Federal Reserve Bank of Chicago, May 1995.

Hughes, Joseph P., and Loretta J. Mester, "A Quality and Risk-Adjusted Cost Function for

Banks: Evidence on the 'Too-Big-To-Fail' Doctrine," The Journal of Productivity

Analysis, 4: 293-315, 1993.

Hughes, Joseph P., and Choon-Geol Moon, “Measuring Bank Efficiency when Managers Trade 

Return for Reduced Risk,” working paper, 1995.

Humphrey, David, and Lawrence Pulley, "Banks' Responses to Deregulation: Profits, 

Technology, and Efficiency," working paper, March 1995.

Hunter, William C., and Stephen Timme. "Core Deposits and Physical Capital: A

Reexamination of Bank Scale Economies and Efficiency with Quasi-Fixed Inputs," 

Journal of Money, Credit, and Banking, 27: 165-185, 1995. 

Jondrow, James, C.A. Knox Lovell, Ivan Materov, and Peter Schmidt, “On the Estimation of

Technical Inefficiency in the Stochastic Frontier Production Function Model," Journal of 

Econometrics, 19: 233-238, 1982.
43

Jones, David S., and Kathleen K. King, "The Implementation of Prompt Corrective Action,"

Journal of Banking and Finance, 19: 491-510, 1995.

McAllister, Patrick H., and Douglas McManus, “Resolving the Scale Efficiency Puzzle in 

Banking,” Journal of Banking and Finance, 17: 389-405, 1993.

Mitchell, Karlyn, and Nur M. Onvural, "Economies of Scale and Scope at Large Commercial

Banks: Evidence from the Fourier Flexible Functional Form," North Carolina State

University, working paper, November 1992.

Mester, Loretta, "Efficiency of Banks in the Third Federal Reserve District," Federal Reserve

Bank of Philadelphia, Working Paper No. 94-1, 1994a.

Mester, Loretta, "How Efficient Are Third District Banks?," Federal Reserve Bank of

Philadelphia, Business Review, January 1994b.

Peristiani, Stavros, "Evaluating the Postmerger X-Efficiency and Scale Efficiency of U.S.

Banks," Federal Reserve Bank of New York, working paper, 1993.

Resti, Andrea, “Linear Programming and Econometric Methods for Bank Efficiency Evaluation: 

An Empirical Comparison Based on a Panel of Italian Banks,” working paper, 1995.

Stevenson, Rodney E., "Likelihood Functions for Generalized Stochastic Frontier Estimation,"

Journal of Econometrics, 13: 58-66, 1980.

Wall Street Journal, “Bank of Boston Top Managers Knew of Weak Loans Ahead of ‘89 

Disclosure,” April 25, 1994.

Whalen, Gary, "A Proportional Hazards Model of Bank Failure: An Examination of

Its Usefulness as an Early Warning Tool," Federal Reserve Bank of Cleveland, Economic

Review, Quarter 1, 1991.

Wheelock, David C. and Paul W. Wilson, "Explaining Bank Failures: Deposit Insurance,

Regulation, and Efficiency," Review of Economics and Statistics, 77, 1995. 
44

Appendix A

Intertemporal Patterns Underlying the Four Hypotheses

A. Bad Luck

1. A bank experiences bad luck (e.g., regional recession). Nonperforming loans increase

as borrowers fall behind in their loan repayments.

2. After the increase in nonperforming loans, measured cost efficiency decreases

because of extra costs of monitoring, workouts, default, etc.

3. Financial capital erodes in response to lost revenues, higher loan loss provisions, and

greater costs associated with nonperforming loans. 

Key Identifying Empirical Implication: Nonperforming loans negatively Granger-cause

measured cost efficiency. 

B. Bad Management

1. Managers: (a) fail to control costs, yielding low cost efficiency in the short term, and

(b) are perform poorly at loan underwriting and monitoring.

2. Because of bad underwriting and monitoring, nonperforming loans eventually

increase as unqualified and/or poorly monitored borrowers begin to fall behind in loan

payments.

3. Equity capital erodes because cost inefficiency, lost revenues, and high loan loss

provisions that depress earnings.

Key Identifying Empirical Implication: Measured cost efficiency negatively Grangercauses nonperforming loans.
45

Appendix A

C. Skimping

1. Managers choose to skimp on loan underwriting and monitoring, which reduces

operating costs and increases measured cost efficiency in the short run. 

2. Nonperforming loans increase in the long-run as poorly monitored borrowers fall

behind in loan repayments.

3. Costs may increase and measured short-run cost efficiency may decrease due to extra

costs of managing nonperforming loans.

4. Capital ratio may erode in response to the revenue loss, higher provisions, and

possibly higher costs from nonperforming loans. 

Key Identifying Empirical Implication: Measured short-run cost efficiency positively

Granger-causes nonperforming loans. 

D. Moral Hazard

1. Decline in earnings from any source -- including the first three hypotheses -- erodes

financial capital.

2. In response to the low level of capital, the bank responds to moral hazard incentives

by increasing loan risk.

3. As a result of the increase in risk-taking, banks eventually have higher nonperforming

loans on average.

Key Identifying Empirical Implication: Capital ratio negatively Granger-causes

nonperforming loans ratio.
46

Appendix B

Public Policy and Research Implications of the Four Hypotheses

A. Bad Luck

1. Regulation and supervision should continue to emphasize low portfolio credit risk (e.g.,

loan-to-asset ratios, risk-weighted asset ratios, loan concentration ratios, geographic

diversification). 

 

2. Bank failure research should focus on regional economic conditions as well as other

traditional factors.

3. When estimating efficiency, the cost function, profit function, or production relationship

should control for loan quality.

B. Bad Management

1. Bank supervision and bank failure research should include cost efficiency along with loan

losses, credit risk, and other predictors of troubled banks.

2. When estimating efficiency, the cost function, profit function, or production relationship

should not control for loan quality.

C. Skimping

1. Bank supervision and bank failure research should continue to concentrate on banks’

credit control practices (e.g., loan review, collateral appraisal) as well as emphasizing

other traditional factors.

2. Cost efficiency should be estimated only using long-run models and several years of data,

to let the fluctuations caused by long-run cost strategies average out over time. Profit

efficiency models may be superior to cost efficiency models.

3. When estimating efficiency, the cost function, profit function, or production relationship

should not control for loan quality.

D. Moral Hazard

1. Bank supervision, bank regulation, and bank failure research should continue their

traditional focus on the effects of capital, measuring capital, and setting and enforcing

capital requirements.