Xefficiency in banking Looking beyond the balance sheet

1、x-efficiency in banking:looking beyond the balance sheetbyjeffrey a. clark professor of financeflorida state universityandthomas f. siemssenior economist and policy advisorfederal reserve bank of dallasabstractthe distribution free and stochastic econometric frontier estimation methods are used to d

2、erive bank specific measures of cost and profit x-efficiency. this is done to investigate the importance of including aggregate measures of off-balance sheet (obs) activities. the results indicate that economic cost and production cost x-efficiency estimates increase with the inclusion of the obs me

3、asure, while profit x-efficiency estimates are largely unaffected. in addition, the composition of banks obs activities appears to help explain inter-bank differences in cost and profit x-efficiency estimates, whereas bank size and the mix between on and off-balance sheet banking activities are larg

4、ely uncorrelated with the x-efficiency estimates.february 2001please do not quote without permission of the authors: jeffrey a. clark, (904) 644-8211, and thomas f. siems, (214) 922-5129, .the authors would like to thank the editor, allen n. berger, two

5、anonymous referees and david b. humphrey for their extremely helpful comments and suggestions for improving the quality of this paper. any remaining errors are, or course our own. the views expressed in this paper do not necessary represent those of the federal reserve bank of dallas or the federal

6、reserve system.x-efficiency in banking:looking beyond the balance sheetdetermining the cost and revenue efficiency of financial intermediaries is important in a world economy characterized by sudden change and rapid innovation. changing laws and regulations (such as interstate banking and branching,

7、 the expansion of banking powers, and intensified competition from nonbank financial institutions) coupled with improved telecommunications and computer technologies have raised questions concerning the competitive viability of banks of different sizes and types. further, a frequently cited rational

8、e for the ongoing consolidation of the u.s. banking industry through mergers and acquisitions is the need to improve cost and revenue efficiencies. berger, hunter, and timme (1993) argue that increased efficiencies might result in improved profitability, more intermediated funds, better prices and s

9、ervice quality for consumers. increased efficiencies may also improve safety and soundness if some of the savings are applied toward capital buffers to absorb risk. but, the opposite effects might be expected if the evolution of the industry results in less efficient institutions.over the past fifte

10、en years, commercial banks share of total u.s. financial intermediation assets has fallen from 35 percent to 20 percent. the number of banks has also dropped from approximately 14,500 to around 8,500 today. taken together, these observations are used as anecdotal evidence to support the hypothesis t

11、hat banking is a declining industry. the view of banking as a declining industry has not gone unchallenged. boyd and gertler (1994) and kaufman and mote (1994) argue that significant portions of the banking business have moved beyond the traditional balance sheet. they argue that industry output is

12、thus significantly mismeasured by focusing only on the on-balance activities of banks. both studies note that off-balance sheet activities (hereafter obs) such as loan origination, sales, servicing, securitization, standby letters of credit, and derivative securities, are expanding rapidly. after au

13、gmenting aggregate measures of on-balance sheet assets with estimates of aggregate obs activities, these studies conclude that banking is not declining but, more accurately, changing. for example, between 1990 and 1999, commercial banks increased the notional value of their financial derivative acti

14、vities by more than 600 percent. non-interest income, which is heavily influenced by obs activities, has increased as a percentage of total income from 19 percent in the late 1970s to nearly 46 percent by 1999. thus, it is increasingly important to include these activities in any evaluation of the e

15、fficiency and competitive positioning of commercial banks. given the changing nature of banking and the growth of obs activities, estimating cost and profit efficiency without incorporating these activities may not be accurate or meaningful. omitting obs activities could seriously understate actual

16、bank output and seriously bias empirical estimates of the relationships between bank size and both cost and profit efficiency.the purpose of this study is to investigate the impact of obs activities on the measurement of x-efficiency in the banking industry. both the distribution free and the stocha

17、stic econometric frontier estimation methods are utilized to derive bank specific measures of cost and profit x-efficiency, with and without the inclusion of aggregate measures of obs activities. further, the potential relationship between x-efficiency scores, bank size and the composition of obs ac

18、tivities is examined. the results of the paper indicate that it is both statistically and economically important to include obs activities in bank cost functions. economic cost and production cost x-efficiency estimates increase with the inclusion of the obs measure. however, while there is some sta

19、tistical support for including an obs measure in the profit function, derived profit x-efficiency estimates are largely unaffected. the results also indicate that the composition of obs activities may help to explain inter-bank differences in cost and profit x-efficiency estimates. in particular, ba

20、nks with greater volumes of loan commitments, lines of credit and credit guarantees exhibit higher cost and profit x-efficiency. further, though less robust, banks with greater derivatives activities exhibit reduced cost and profit x-efficiency. neither bank size nor the off-to-on balance sheet mix

21、of banking activities are found to be systematically and robustly related to cost or profit x-efficiency estimates.section 1 of the paper provides an abbreviated literature review. the estimation methodologies and efficiency benchmarks are discussed in section 2. sections 3 and 4 present the perform

22、ance metrics and functional forms. sections 5 and 6 discuss the derivation of the three alternative measures of aggregate obs activities, describe the data used, and provide variable definitions. sections 7 and 8 present and discuss the empirical results. the final section provides a summary and con

23、clusions.1.a brief review of the relevant literature1.1x-efficiency and bank sizein recent years, much of the focus of bank efficiency research has shifted away from attempts to measure scale and scope economies and towards measuring and explaining x-efficiency. leibenstein (1966) coined the term “x

24、-efficiency” to describe the difference between actual and minimum cost. x-inefficiencies refer to deviations from the efficient (or best-practice) frontier, where the inefficiencies could result from allocative, technical, scale, or scope inefficiencies, or result from a deficiency of market pressu

25、res from the firms environment. gardner and grace (1993). the motivation for this shift in focus has been the finding (berger and humphrey 1991) that inefficiency appears to far exceed the presence of any scale or scope economies in banking. in an early review of the x-efficiency literature in banki

26、ng, berger, hunter, and timme (1993) report a preponderance of evidence that larger banks are more x-efficient (i.e., closer to the efficient frontier) than smaller banks. however, the choice of measurement method also appears to affect the level of measured x-efficiency. a more recent review of thi

27、s literature by berger and humphrey (1997) finds that, on average, cost and productive efficiency average approximately 84 percent when parametric estimation techniques are used, and approximately 72 percent when non-parametric techniques are used. thus, there appear to be significant performance de

28、viations from the best practice banks. several recent studies have examined the inter-bank sources of these inefficiencies. berger and humphrey (1997) report that very little of the inter-bank differences in efficiency scores are correlated with potential correlates such as size, market concentratio

29、n and organizational form. and, in many instances, variables that did appear to have some explanatory power were not under the direct control of managers. finally, they caution that for ex post regressions to be informative, authors should demonstrate that their results are robust across more than o

30、ne frontier technique, since the various efficiency techniques can sometimes produce different efficiency rankings. 1.2off-balance sheet activity and bank efficiencyrecent studies of bank efficiency have begun to explicitly incorporate measures of aggregate obs activities into their analyses. intere

31、sted readers should see hunter and timme (1995), hughes and mester (1998), rogers (1998), jagtiani, nathan, and sick (1995), and jagtiani and khanthavit (1996). also, deyoung (1994) includes fee-based income in a translog cost function. berger and mester (1997) include a risk-weighted measure of obs

32、 loan guarantees in both production cost and profit efficiency estimates. however, they do not directly test for the economic and statistical significance of excluding it from the cost and profit functions. they did report that a regression of the cost and profit efficiency measures on a dummy varia

33、ble representing significant usage of swaps, futures and forwards contracts indicates that obs activities do not appear to be consistently related to efficiency. however, in most cases these studies do not examine either the statistical or economic significance of including an obs measure. among the

34、 studies which do examine this significance, jagtiani, nathan, and sick (1995) and jagtiani and khanthavit (1996) fail to use the available frontier estimation methods. consequently, parameter estimates of the respective cost functions may be confounded by the presence of significant inefficiency. i

35、f so, and if bank inefficiency is related to size and product mix, derived estimates of efficiency measures must be viewed with some degree of restraint. in addition, these authors use a credit equivalent approximation. while this is intended to approximate the amount of on-balance-sheet assets that

36、 would result in a comparable relative risk exposure, it does not capture the volume of obs activities or, more importantly, their ability to generate income or costs. more recently, rogers (1998) tested the statistical and economic significance of including a measure of obs activities in production

37、 cost, revenue and profit functions. rogers uses net non-interest income as the measure of obs activities and employs the distribution free frontier estimation method. rogers reports evidence indicating that including net non-interest income increases both mean cost and mean profit efficiency scores

38、, but does not increase mean revenue efficiency. however, there is no attempt to investigate whether the results are robust to alternative estimation methods or alternative measures of aggregate obs activities such as the credit equivalent measure used by jagtiani, nathan, and sick and jagtiani and

39、khanthavit. further, rogers does not investigate the sensitivity of the derived efficiency measures to the relative composition of the obs activities that generate the net non-interest income measure he employs.2.empirical methodsthe bank efficiency literature provides empirical evidence of small bu

40、t statistically significant production cost inefficiencies. further, there is some evidence that the degree of inefficiency may be systematically related to bank size. thus, the potential exists for traditional measures of efficiency to be biased by the presence of inefficiency in the data. therefor

41、e it is important to utilize an estimation method capable of controlling for the effects of inefficiency. because there is no consensus concerning the appropriate methodology to use, and because previous research indicates some tendency for the estimates to be sensitive to the estimation method, bot

42、h the distribution-free and stochastic econometric frontier methods are utilized here. this methodology follows berger and mester (1997).2.1 the efficiency concept 2.1.1 cost efficiencycost efficiency measures the extent to which a firms costs approach the costs for a best practice or least cost fir

43、m under the ceteris paribus assumption. it is typically measured by estimating a cost function in which variable costs are the dependent variables and the independent variables include variable output(s), input prices, fixed inputs, variables capturing differences in the economic environment, random

44、 error, and inefficiency. a general version of this cost function can be written as:c = c(q, w, d, uc, ec) (1)where c denotes total variable costs, q denotes variable output(s), w denotes a vector of variable input prices, d denotes a vector of economic and environmental variables that may impact co

45、st performance, uc denotes an inefficiency factor that pushes the firms costs above those of the most efficient firm, and ec denotes random error. the random error term ec incorporates both measurement error and the impact of luck on performance. the inefficiency factor is generally assumed to inclu

46、de both allocational and productive inefficiencies. for simplicity, it is generally assumed that the inefficiency and random error terms can be separated from the remainder of the cost function. after taking logs of both sides of equation (1), the cost function can be depicted as:ln c = c(q, w, d) +

47、 (ln uc + ln vc)(2)where c denotes a particular functional form for the cost function and (ln uc + ln vc) is a composite error term comprised of random error (vc) and an inefficiency factor (uc) that pushes the firms costs above those of a best practice or most cost efficient firm. using the paramet

48、er estimates from the cost function of equation (2), a firm specific measure of relative cost efficiency can be calculated as follows: (3)where is the minimum of the across all sample firms. this relative cost efficiency measure should be interpreted as firm f is x percent as efficient as the best p

49、ractice or most efficient firm, and can theoretically fall in the interval (0,1. 2.1.2 profit efficiencyanalogous to cost efficiency, profit efficiency measures the extent to which a firms profits fall below the profit of the best practice firm, ceteris paribus. conceptually, profits are also assume

50、d to be a function of variable output(s), input prices, and economic environmental variables that may impact profit performance. under the traditional assumptions that a firm purchases all of its inputs and sells all of its outputs in perfectly competitive input-output markets, a firms profits will

51、depend on the input and output prices encountered in those markets. thus, the firm regards output and input prices as given and selects the levels of outputs and inputs to utilize. however, these assumptions do not fit the economic environment faced by many firms. berger and mester (1997) note that

52、when there are significant inter-firm differences in product quality, outputs that are not completely variable, output markets that are not perfectly competitive, or imperfectly constructed proxies for output prices, an alternative specification for the profit function may produce better results. th

53、e profit function takes the following form:ln p = p(q, w, d) + (ln up + ln vp) (4)where q, w, and d are as defined above, p denotes profit, up denotes an inefficiency factor that pushes the firms profits below those of the most efficient firm, and vp denotes random error. thus, a firms relative prof

54、it efficiency can be computed using the following expression: if firms in the sample exhibit negative profits, then a constant of a size sufficient to eliminate the negative value is added to the profits of all firms in the sample. this procedure is necessary to compute ln p and does not alter the r

55、esulting parameter estimates of the profit function. however, the profit efficiency formula must be slightly altered by subtracting the constant from both the numerator and denominator of equation (5). (5)several parametric methods have been used to disentangle random error, vf, from inefficiency, u

56、f, so that the cost and profit efficiency measures of equations (3) and (5) can be effectively computed. because these computed measures of relative efficiency may depend upon the empirical methods used to disentangle the components of the composite error term, both the distribution free and stochas

57、tic econometric estimation methods are utilized. since both methods have been described in previous papers, only a brief description is provided here.2.2stochastic econometric frontier method the stochastic econometric frontier estimation method (hereafter sefm) is one of two standard parametric est

58、imation methods used to estimate the parameters of cost and profit functions with composite error terms of the type described in equations (2) and (4). the first component is a two-sided error term, ln, representing random fluctuations unrelated to inefficiencies. the second component is a one-sided error term, ln, which represents inefficiency. the sefm procedure requires that assumptions be made about the distributions of these two types of error. the random error component, ln, is conventionally assumed to be normally dist