rdtv ffn n bnn - Federal Reserve Bank of Chicago/media/publications/economic... · rdtv ffn n bnn l...

Productive efficiencyin banking

Douglas D. Evanoff and

Philip R. Israilevich

Then a new CEO came in whoasked, ... "What do we have toproduce by way of results?"Every one of his store manag-ers knew the answer, "We

have to increase the amount each shopperspends per visit." Then he asked, "Do any ofour stores actually do this?" Three or four—out of 30 or so did it. "Will you then tell us,"the new CEO asked, "what your people do thatgives you the desired results?"'

Introduction

In the above epigraph the managers areattempting to identify, in a particular context,the firms which are doing the best job of ac-complishing the company objectives. Suchfirms are known as the best practice firms.Economists typically make similar inquiriesconcerning the production process. Theyaddress the issue by theoretically defining thebest practice firm, empirically identifying it,determining its resource utilization, and thenevaluating how others compare to it. Moregenerally, economists, like the new CEO, areconcerned with productive efficiency.

Because of changes taking place in thebanking industry, the importance of efficiencyhas increased substantially. As geographic andproduct deregulation occurs, the resultingincrease in competition should place banks in asituation where their success will depend ontheir ability to adapt and operate efficiently inthe new environment. Banks unable to do sowill have difficulty surviving.

Most studies of bank efficiency haveconcentrated on cost advantages resulting fromthe scale of production. In fact, this is probablyone of the most researched topics in banking.'There are, however, other aspects of efficiencywhich students of the industry have just begunto evaluate. For example, do the producers ofbanking services effectively combine theirproductive inputs? Once employed, do theyuse the inputs effectively? If not, how ineffi-cient are they? What allows them to continueto do this and stay in business? Given its im-portance in the deregulated environment, it isimperative that the various aspects of bankefficiency be understood and empiricallyanalyzed.

In this article we discuss the concept ofefficiency in production, define its variousaspects and the means to measure it, and reviewthe relevant literature concerning inefficiencyin the banking industry. Our major conclusionis that there appears to be significant inefficien-cy in banking. Inefficiency resulting fromoperating at an inappropriate scale of operationis probably in the range of 10-20 percent ofcosts. However, by emphasizing the role ofscale, researchers have essentially overlooked amajor portion of bank inefficiency. The evi-dence suggests that inefficiencies resulting

The authors are economists at the Federal ReserveBank of Chicago. Helpful comments on earlierdrafts by Herb Baer, Paul Bauer, Allen Berger, DaveHumphrey, Curt Hunter, Carl Pasurka, and SherrillShaffer are gratefully acknowledged. The viewsexpressed, however, are those of the authors andare not necessarily shared by others.

FEDERAL RESERVE BANK OF CHICAGO 11

from the suboptimal utilization of inputs islarger than that resulting from other factors.According to a majority of studies, banksoperate relatively efficiently with respect to theoptimal combination of inputs, yet many arevery inefficient in converting these inputs intooutputs. This inefficient utilization of inputsaccounts for an additional 20-30 percent ofcosts. This is particularly interesting because itimplies that, to a great extent, the future viabili-ty of an individual bank is under its own con-trol. To the extent that bank inefficiency can beaccurately measured, it appears that the largestinefficiencies are not the result of regulation ortechnology, but result directly from an under-utilization of factor inputs by bank manage-ment. This inefficiency will most likely declinein the future as bankers respond to increasedcompetitive pressures and strive to becomemore efficient. Failing this, the inefficient firmswill become prime merger candidates to beacquired and restructured.

The article proceeds as follows. In thenext section we define, discuss, and illustratethe components of production efficiency. Wethen evaluate the alternative means to generatemeasures of efficiency. A review of the litera-ture on bank efficiency is then presented. Thefinal section summarizes and evaluates policyconcerns. We have also included an extensivereference list for readers interested in moredetailed analysis of productive efficiency.

Production efficiency

The economic theory of the firm assumesthat production takes place in an environmentin which managers attempt to maximize profitsby operating in the most efficient mannerpossible. The competitive model suggests thatfirms which fail to do so will be driven fromthe market by more efficient ones. However,when natural entry barriers or regulation weak-en competitive forces, inefficient firms maycontinue to prosper. That is, true firm behav-ior may vary from that implied by the competi-tive model as managers attempt to maximizetheir own well-being instead of profits, or findthat they are not required to operate veryefficiently to remain in business.

Variations from productive efficiency canbe broken down into input and output inducedinefficiencies. By input inefficiency we meanthat, for a given level of output, the firm is notoptimally using the factors of production .

Overall input inefficiency resulting from thesuboptimal use of inputs can be decomposedinto allocative and pure technical inefficiency.Allocative inefficiency occurs when inputs arecombined in sub-optimal proportions. Regula-tion is typically given as a major reason for thisoccurrence. Pure technical inefficiency occurswhen more of each input is used than shouldbe required to produce a given level of output.This occurrence is more difficult to explain, butis typically attributed to weak competitiveforces which allow management to "get away"with slackened productivity. Combining thesetwo notions of inefficiency we get the overallinefficiency resulting from the improper use ofinputs.' The distinction between the two typesof inefficiency is important because they maybe caused by totally different forces.

Productive efficiency requires optimizingbehavior with respect to outputs as well asinputs. With respect to outputs, optimal behav-ior necessitates production of the level andcombination of outputs corresponding to thelowest per unit cost production process. Anoptimal output level is possible if economiesand diseconomies of scale exist at differentoutput levels. Economies of scale exist if, overa given range of output, per unit costs declineas output increases. Increases in per unit costcorrespond to decreasing returns to scale. Ascale efficient firm will produce where there areconstant returns to scale; that is, changes inoutput result in proportional changes in costs.Because it involves the choice of an inefficientlevel, scale inefficiency is considered a form oftechnical inefficiency. Thus total technicalinefficiency includes both pure technical andscale inefficiency; that is, inefficient levels ofboth inputs and outputs.

Additional cost advantages may result fromproducing more than one product. For example,a firm may be able to jointly produce two ormore outputs more cheaply than producingthem separately. If the cost of joint productionis less than the cost resulting from independentproduction processes, economies of scope aresaid to exist. Diseconomies of scope exist ifthe joint production costs are actually higherthan specialized or stand-alone production ofthe individual products.

A final point should be mentioned concern-ing the various categories of inefficiency. Puretechnical inefficiency is entirely under thecontrol of, and results directly because of, the

12 ECONOMIC PERSPECTIVES

behavior of the producer. Output inefficiencyand allocative inefficiency may, from theperspective of the firm, be unavoidable. Forexample, a firm optimally using factor inputsmay find that per unit cost declines over theentire range of market demand. While increas-ing production would generate cost savings orefficiencies, the characteristics of marketdemand may not justify it. Failure to exploitscope advantages may also result from factorsoutside of the control of the firm. In banking,the array of allowable activities is obviouslyconstrained by regulation. This may precludepotential gains from the joint production ofvarious financial services. Finally, as men-tioned earlier, allocative inefficiency may occuras a direct result of regulation. For example,during the 1970s, banks were restricted withrespect to the explicit rates they could paydepositors. As market rates rose above allow-able levels, banks frequently substituted implic-it interest payments in the form of improvedservice levels; for example, more offices percapita or per area, see Evanoff (1988). Thisresulted in an over-utilization of physicalcapital relative to other factor inputs. In thiscase, regulation was the driving force behindthe resulting allocative inefficiency. The pointis that much inefficiency may be beyond thecontrol of the individual firm.

In the following sections we illustrate theinefficiencies described above and discussalternative methods used to empirically capturethem. The reader who is most interested in ananalysis of efficiency in banking may skipdirectly to the section entitled "The role ofproduction inefficiency in banking: A surveyof the literature."

Illustrating input efficiencyThe notions of input inefficiencies can be

illustrated as shown in Figure 1. Assume that x,and x2 are two factor inputs required to producea single output, y. Isoquant /-/' depicts variousefficient combinations of the two inputs whichcan be used to produce a specific level ofoutput, y,. Isoquants further to the right corre-spond to higher levels of output, those to theleft to lower levels of output. For example, theoutput level associated with isoquant 11-11' isless than y i . For a given set of input prices, theisocost line, P-P' , represents the various combi-nations of inputs which generate the same levelof expenditures. Isocost lines further to the right

correspond to higher level of expenditures oninputs. The slope of the isocost line is, obvi-ously, determined by input prices.

If the objective of the producer is to pro-duce a particular level of output at minimumcost then the optimal input combination inFigure 1 is at point E. That is, given factorprices, output y, can be optimally produced byemploying x units of input x, and x2° units ofinput x2. Any other combination of the inputsalong the P-P' isocost line would generate lessoutput for the same cost. For example, theinput combinations corresponding to points Wor Z would result in similar expenditures oninputs, but generate the lower level of outputassociated with isoquant 11-11' . Alternatively,the production of y, using any combination ofinputs other than that corresponding to point Ewould cost more. Therefore, at point E, inputefficiency exists.°

To illustrate input inefficiency, supposethat the observed combination of inputs used bya particular firm to produce y, is at point A inFigure 1. We know that inefficiency existsbecause E was shown above to correspond tothe most efficient combination of inputs toproduce y1 . Comparing the input utilization atpoint A to that at E we can derive the level ofinefficiency resulting from the suboptimal useof inputs. In order to illustrate allocative andpure technical inefficiency, we have drawn aline from the origin to point A. Along this linedifferent levels of factor inputs are employedbut the ratio between the two inputs is fixed at

FEDERAL RESERVE BANK OF CHICAGO

13

FIGURE 2

Pure technical efficiency measuredin terms of outputs

ou put

Totalproduct

xA)

the actual ratio (that is, the ratio at point A).Reference points along this line and on isoquantI-1' and isocost line P-P' are highlighted.Consider allocative inefficiency first. Point Crepresents a level of costs equal to that of theefficient production process at point E becauseit is on line P-P' . Point B corresponds to anoutput level equal to y1 because it is on isoquantI-1'. Therefore, the distance CB corresponds toadditional production expenses resulting fromthe suboptimal allocation of inputs. That is,allocative inefficiency exists because we arenot on the isocost line, P-P' . Formally, OC/OBis a measure of allocative efficiency. Valuesless than 1.0 reflect inefficiency. 5

For this same example, we can also depictpure technical inefficiency resulting fromproducing at point A. We have seen thatproducing y 1 using .,rai and x2" involves allocativeinefficiency because point A is to the right ofline P-P' and ray OA does not go through pointE. However, there is additional inefficiencybecause point A is above isoquant /-/'. That is,the combination of inputs associated with pointA should enable the firm to produce a level ofoutput greater than y1 . (It should be able toproduce output y3 corresponding to isoquant

.) Given that the isocost line depicts totalexpenditures used in production, distance CAconstitutes a less than optimal usage of allinputs and corresponds to additional productionexpenses. Therefore, overall input inefficiencyis measured as OCIOA. Because OC/OB isattributed to allocative inefficiency, the remain-ing portion, OB/OA, can be attributed to puretechnical inefficiency. Since these are radialmeasures, overall input inefficiency is theproduct of the two subcomponents, that is,OCIOA = (OC/OB) • (OB/OA).

The pure technical inefficiency shown inFigure 1 can also be illustrated in terms ofoutput, instead of input, using a total output ortotal product relationship as depicted in Figure2. The ratio of input usage, x1/x2, is held fixedby assumption in Figure 2 to represent inputcombinations along the ray OA in Figure 1.Since the fixed input ratio precludes the analy-sis of allocative efficiency, we are analyzingonly pure technical efficiency. Because changesin inputs result in proportional changes inoutput (the total product curve is linear) wehave constant returns to scale as was assumedin Figure 1. Employing AT units of input x i we

could produce an output level y if the inputswere fully utilized. This corresponds to point Bin Figure 1. Similarly, using xal units of input xiwe should be able to produce y3. Again, thiscorresponds to point A in Figure 1. However, ifinputs are not used effectively, that is if techni-cal inefficiency exists, the resulting productionpoint will be below the total product curve.That is, pure technical inefficiency occurs whenwe operate beneath the total product relation-ship. For example, the pure technical ineffi-ciency depicted in Figure 1 corresponds to thatfound at point G in Figure 2, where inputs areunder-utilized and x", only generates an outputlevel of y1 . If we are producing y at point A inFigure 1 or, equivalently, at point G in Figure2, pure technical inefficiency is measured withrespect to inputs as OB/OA and with respect tooutputs as AG/AM. The inefficiency measuresare equivalent. This illustration is importantbecause it indicates that technical inefficiencycan be measured in terms of either inputs oroutputs. Below we drop the constant returns toscale assumption and expand on this outputinefficiency measure.

Illustrating output efficiency

Point E in Figure 1 corresponds to the leastcost, most efficient means to produce y1 . How-ever, because of particular characteristics of theproduction technology, this level of output maynot be the optimal one to produce. For exam-ple, it may be that over a certain range ofoutputs, economies of scale exist. Production


FIGURE 3

Technical efficiency withvarying returns to scale

ou put

Totalproduct

- -+G

xa

2

Pure technical efficiency interms of costs

efficiency, therefore, requires optimal decisionsconcerning both input and output levels. InFigure 3 we have dropped the assumption ofconstant returns to scale. The productionprocess is now characterized by increasingreturns up to point R, constant returns at R, anddecreasing returns at output levels above R.Now the firm corresponding to point G inFigure 3 is technically inefficient for tworeasons. First, there is pure technical ineffi-ciency resulting from the under-utilization ofinputs; that is, we are beneath the total productcurve. If inputs are fully utilized, inputshould produce the higher output level corre-sponding to point M, that is, y3 . Second, wehave decreasing returns to scale at the currentlevel of output since the production process isnot represented as the linear relationship OH.The output not produced because of scaleinefficiency can be measured as HM. Thisoutput is what could have been produced ifinputs were used efficiently and constantreturns to scale existed at this output level.Therefore, for the input usage depicted at pointA, the input efficient firm could produce atpoint M, and the input and scale efficient firmcould produce at point H. As explained above,scale inefficiency is generally considered aform of technical inefficiency because it in-volves the choice of an inefficient level. Thus,total technical inefficiency includes puretechnical and scale inefficiency; that is, ineffi-ciency in the use of both inputs and outputs.

Figure 4 depicts the reference points justdiscussed in Figure 3 in terms of productioncost. The total product relationship in Figure 3corresponds to the average cost relationshipdepicted in Figure 4. Points H and R eachcorrespond to constant returns to scale and,therefore, correspond to minimum points onaverage cost relationships. Total technical

inefficiency can be depicted here as the ratio ofthe average costs. For the example just dis-cussed, total technical inefficiency is equal toAC HIACG. The alternative measures of ineffi-ciency illustrated in Figures 1 through 4 areequivalent and correspond to the alternativemeans of calculating inefficiency estimatescommonly cited in the literature.

In the above discussion we assumed theproduction of a single output for illustrativepurposes. Additional cost advantages mayresult from multiproduct production. Forexample, economies may exist for the jointproduction of two or more outputs, relative tothe stand-alone production of the individualproducts. That is, scope advantages may exist.More formally, economies of scope exist in thejoint production of Q1 and Q 2 if

(1) + C2] > C12

where C 1 and C, are the cost of producing Q 1

and Q, independently (that is, as stand-aloneprocesses), and C12, is the cost of joint produc-tion. With multiproduct production, some


15

A multiproduct cost relationship

fixed cost of production can be spread acrossthe outputs and there may be synergies whenthe two products are produced jointly. Amultiproduct cost relationship which exhibitsproduction synergies between the two outputs,y 1 and y2 , is illustrated in Figure 5. Joint pro-duction moves the cost off the "lip" of therelationship onto the inner surface. Potentialcost gains obviously exist.

Measuring production inefficiencies

The relationships depicted in the abovefigures, as well as all standard textbook presen-tations of the production process, presentextreme values; that is, the maximum outputthat can be produced from a given set of inputs,or the minimum cost required to produce agiven level of output. However, when attemptsare made to generate estimates of the produc-tion process we typically abstract from theextreme values. The traditional approach toevaluating the production process is to assumethe standard competitive model is appropriateand to estimate an average production, cost, orprofit function. 6 Realizing that this restrictivemodel may not adequately describe the produc-tion process (and definitely avoids efficiency

issues), methods have been developed whichallow for variations in this approach. Wediscuss these variations in this section. Themethodologies differ from each other in anumber of ways, not the least of which is aresult of differences in assumptions imposed inthe analysis. The restrictiveness of theseassumptions is determined by the individualdata sets. Each of the methods discussed hereis superior to the basic competitive model aslong as the assumptions employed are correct.More will be said about this later.

While the concept of firm efficiency israther straightforward, various difficulties areencountered when attempting to measure it.Essentially, one needs to derive the best prac-tice firm, or the production frontier whichdepicts the maximum performance possible byfirms, and contrast existing firms to this stan-dard. Ideally, we would compare firm perfor-mance to the true frontier, however, the bestthat can be achieved is an empirical frontier orbest practice firm generated from the observeddata. Once the best practice firm is established,input related pure technical and allocativeefficiency, and output related scale and scopeefficiency, can be analyzed. For example,assuming constant returns to scale in Figure 1,all firms can be compared to one producing atpoint E.

Differences in estimates of firm efficiencytypically result from different means of gener-ating the best practice firm. There are twogeneral approaches used to model this relation-ship. First, the parametric or econometricapproach employs statistical methods to esti-mate an efficient cost frontier. Second, thenonparametric or deterministic approach isbased on the linear programming approach foroptimal allocation of resources called dataenvelopment analysis (DEA). This technique isused to directly generate individual frontiers foreach firm. Below we discuss alternative meth-odologies within these two broad categories.

It should be emphasized that empiricalmeasures of inefficiency are no different fromestimated parameters in any economic model.The model may mistakenly reflect measure-ment errors or specification errors for produc-tive inefficiency. As the literature on bankingdevelops, more comprehensive models shouldbe analyzed.


Parametric approach: Shadowprice models

To generate estimates of allocative effi-ciency, one can use the parametric approachdeveloped by Lau and Yotopoulos (1971) andrefined by Atkinson and Halvorsen (1980,1984). 7 This method assumes that firms arecombining the factor inputs correctly, but thatthe combination is not necessarily based onobserved prices. Rather, there are factors inaddition to explicit market prices which enterthe firm's employment decision process. Theseadditional factors are combined with the explic-it prices to generate shadow prices which aremore comprehensive and which determinefactor utilization. These additional factorstypically include distortions induced by union-ism, regulation, or managerial goals other thanprofit maximization. These alternative goalsmay include profit satisficing or expensepreference behavior.8

More formally, a basic contention ofeconomic theory is that, in competitive mar-kets, the optimal level of employment for eachfactor of production can be determined byemploying additional units until the last dollarspent on each factor yields the same amount ofproductivity. That is,

f. f.(2) L. , for i j = 1, , m,

P. P.

wheref.af ax, is the marginal product ofinput i, and P i is the price of input i, or

f P.

(3)f, for i j = 1, , m,

Pi

where f /4 is the marginal rate of technicalsubstitution between the inputs. This relation-ship corresponds to the tangency of the isoquantand the isocost curve (point E) in Figure 1.

Given input prices and the predeterminedlevel of output as the only constraint, theoptimal combination of inputs, as in Equation(3), can be derived to minimize cost. However,if additional constraints exist (for example,regulatory constraints), they need to be ac-counted for and incorporated into the optimiza-tion process. Concerning the employmentdecision, Equation (3) becomes

f P*(4) L = ± , for i j 1, , m,f.1

where P; is the effective or shadow price ofinput i, and the marginal rate of technicalsubstitution between the inputs is set equal tothe ratio of the shadow prices of the inputs.Given competitive markets and the absence ofadditional binding constraints, shadow andactual prices are equal and the employmentdecision is not affected.

Because the shadow prices of the inputs arenot directly observable, Lau and Yotopolousdeveloped a means to estimate them along withother parameters of the cost relationship.Assuming shadow prices are proportional tomarket prices, shadow prices can be approxi-mated by

(5) P: =103,, for i = 1, , m,

where k, input-specific.' Again, if the addi-tional constraints are not binding, all shadowprices equal the respective market prices, thatis, k, = 1 for all i.

Standard econometric techniques can thenbe used to generate cost estimates employingthe additional information. That is, the stan-dard cost structure

(6) C = C(P, Q, Z),

where C depicts costs, Q outputs, P explicitfactor prices, and Z additional pertinent exoge-nous variables, is replaced with

(7) Cs = Cs(kP, Q, Z),

where kP denotes shadow factor prices, and k isestimated along with the other parameters inthe cost function.°

The shadow price model also allows one tocalculate the optimal (unobserved) input combi-nation given observed prices, P. This combina-tion is relevant for measuring the cost differ-ences resulting from production under competi-tive conditions and those when additionalbinding constraints exist. In the bankingindustry, these additional constraints are typi-cally thought to be regulatory induced. Thecost differences can be determined by contrast-ing costs when market prices equal shadow


prices (k = 1) to that found using the estimatedshadow prices (k = k where k denotes theestimated value for k). The difference betweenthe two cost values will be the result of combin-ing inputs in a suboptimal manner.

Estimation of the cost function will yield k,values which can be considered to reflect theeffect of binding constraints on average. Ideal-ly, the k measure would be firm specific.However, statistical problems typically makethis prohibitive in terms of the degrees offreedom required for the estimation procedure.All the parametric approaches cited below havethis same shortcoming. Some progress towardresolving this shortcoming has recently beenmade; see Evanoff and Israilevich (1991,1990a).

One of the advantages of the shadow pricemodel approach is that it allows for the estima-tion of returns to scale and scope along withallocative efficiency. However, pure technicalefficiencies can not be measured by this ap-proach although, as discussed later, this short-coming can also be partially resolved.

Parametric approach: Stochasticcost frontiers

Another more comprehensive parametricapproach for measuring efficiency is to usestochastic frontier models. With this approach,the cost frontier is empirically estimated andfirm specific deviations from the frontier areattributed to productive inefficiencies. Anumber of alternative parametric techniquescan be used to generate the frontier. The majordifference between these techniques is in themaintained assumptions which, obviously, canproduce significantly different results. Therestrictiveness of these assumptions is deter-mined by the individual data sets. Here wesummarize alternative parametric methods usedto develop the frontier.

Using a parametric approach, the standardcost structure is typically generated by impos-ing a specific functional form on the data andobtaining the "best fit" by minimizing devia-tions from the estimated structure. For exam-ple, the estimated total cost relationship may befitted to the data to produce a relationship suchas TC in Figure 6. However, when evaluatingefficiency, we are interested in the best practicefirm or the cost frontier. We are not interestedin the average relationship, rather we arelooking for a minima in the data. Therefore,

adjustments to the standard estimation proce-dures are required. Typically the standardparametric procedure is adjusted by employinga more complex error structure. A "composed"error can be used which consists of two compo-nents: one is the standard statistical noisewhich is randomly distributed about the rela-tionship, and the other consists entirely ofpositive deviations from the cost structure (thatis, a one-sided disturbance term) and representsinefficiency." Stated crudely, the resultingfrontier is simply a transformation of TC inFigure 6 (shifted downward) to generate thebest cost relationship instead of the averagerelationship.

For example, and more formally, assume astochastic frontier model which consists of thefollowing cost and share equations:

(8) lnCh=lnCh+lnT h +lnA+uh ;

(9) = + + u th , for i = 1, , m;

13 th

where In denotes the natural log, and CA, and MAh

are observed cost and factor shares for firm h.Ch is the lowest production cost relationship orthe cost frontier, 1n7,, reflects additions to costresulting from pure technical inefficiency, MAreflects additions to cost resulting from alloca-tive inefficiency, and u, is a random error. A MFis the efficient share equation, b, depicts sharedistortions resulting from allocative inefficien-cy, u th captures random distortions from effi-


cient shares, and B h is the composed error term.Measures of technical inefficiency are

calculated as firm specific deviations from thefrontier and are derived from the additionalerror term discussed above. Since technicalinefficiency can result only in increases to totalcost, this error structure must consist entirely ofnon-negative values. That is, this component ofthe error structure is one-sided relative to thefrontier. Choice of a specific one-sided distri-bution could obviously influence the empiricalresults."

As with the shadow price model, allocativeinefficiency is computed as an average for thesample and is not firm specific. InA is non-negative as deviations from use of the optimalcombination of inputs can lead only to addi-tions to cost. However, b, can be positive ornegative suggesting over- or under-utilizationof a particular input.

Obviously, InA and h are related becausesuboptimal combinations of factor inputs (b, #0) result in additions to cost. However, empiri-cally modeling this relationship is problematic.One standard means to do it is to imposerestrictions on the relationship reflecting priorknowledge. For example, assuming increasedcosts occur only when mistakes are made (A =0 only when b,=-. 0), and that large mistakescost more than small ones, one can impose arelationship between allocative mistakes andcost increases:13

(10) In A = b' F

where F is a diagonal matrix with nonnegativeelements. Positive elements of F representweights for each b,. For example,fii representsthe relative effect of allocative distortions fromfactor i on the increased production costs. Tosummarize, the additional cost of allocativeinefficiency is a weighted sum of squaredmistakes from the misallocation of each input.The (nonnegative) weights are additionalparameters to be estimated.

An alternative approach to generate a costfrontier is to utilize a cost structure consistingof cost and share equations, but to sever thelink between the error terms of the cost andshare equations. That is, the share equationsare used only for efficiency gains in parameterestimation; not to link suboptimal combinationsof inputs to increases in cost. Under this

approach, both allocative and technical ineffi-ciencies are depicted as one-sided errors fromthe cost frontier. Therefore, the estimatedsystem of Equations 8 and 9 becomes

(11) ln = ln CF, + + u„

(12) Mn = + u ih , for i = 1, , m,

where the error term depicting inefficiency, v h ,can be decomposed into its two components(that is, MT + InA) using techniques developedby Kopp and Diewert (1982) and refined byZieschang (1983). This approach essentiallyignores information concerning the relationshipbetween disturbances in the cost and shareequations, but is easier to work with than theabove approach and does not necessarilygenerate results inferior to more complicatedlinkage approaches. This is particularly true ifthe more complicated approach, which istypically based on a set of untested assump-tions, incorrectly models the linkage.

This attempt to simplify the methodologybrings us to the most recent approach intro-duced by Berger and Humphrey (1990). Theseauthors take the view that the preceding meth-odologies impose rather restrictive ad hocassumptions concerning the data, the validity ofwhich are questionable. For example, theassumed linkage between the error structure inthe share cost equations, discussed above, couldbe inaccurate as could the assumptions con-cerning the one-sided error distribution. Topartially remedy these problems the authorsdeveloped a "thick frontier" approach. Insteadof imposing restrictive characteristics on thecost relationship to generate a true frontier orfrontier edge, a thick frontier is estimated froma subsample of the data which, based on apriori information, is considered to be anefficient subgroup. This group is then com-pared to another group which, based on a prioriinformation, is considered an inefficient sub-group. Therefore the authors are able to relaxthe restrictive assumptions employed in themethodologies discussed above, but at the costof using a somewhat ad hoc means to catego-rize the data into efficient and inefficientgroups.

This approach was implemented usingbanking sector data by assuming subgroupscould be delineated based on their average cost


per dollar of output. The data were then strati-fied by size and divided into quartiles and thelowest and highest cost quartiles were contrast-ed. After accounting for differences resultingfrom market characteristics, the remainingdifferences between the two groups wereassumed to constitute inefficiency. This can bedistributed into its allocative and technicalcomponents using procedures similar to thoseof Kopp and Diewert discussed above. Obvi-ously, this approach lacks precision and alsoimposes some rather ad hoc assumptions todevelop the subgroups and produce the frontier.However, the assumptions may be less restric-tive than those made in the more elaboratemodels discussed above. In fact, some of themaintained assumptions in these models werestatistically tested and rejected by Berger andHumphrey. As a result, the relatively easy-to-implement approach may perform quite well ingenerating a rough measure of the extent ofproduction inefficiency in an industry. 14

Nonparametric approach

While intuitively appealing, and somewhatsimilar to the procedures commonly used toestimate standard cost relationships, the para-metric approaches have been criticized forrequiring more information than is typicallyavailable for estimation of the cost frontier. Inan attempt to decrease the required information,some have chosen to use a nonparametric,linear programming approach known as dataenvelopment analysis (DEA).

Although there are various permutations tothe DEA approach, the basic objective is to"envelop" the data by producing a piecewiselinear fit via linear programming techniques.That is, instead of using regression techniquesto fit a smooth relationship, a piecewise linearsurface is produced which borders the observa-tions, for example, the broken line q.-q. inFigure 7. The technique identifies observationsfor which the firm is producing a given level ofoutput with the fewest inputs. These will beobservations on the frontier. All other observa-tions will be given an efficiency measure basedon the distance from the frontier and indicatingthe extent to which inputs are being effectivelyutilized. This is comparable to the measure ofpure technical inefficiency, OB/OA, for obser-vation A in Figure 1.

The technique allows for the derivation ofa frontier for each firm in the sample based on

the output and input utilization of all firms in thesample. As a simple example for the two input,one output case, the linear programming problemfor technical inefficiency could be written as

(13) Min OA ,

subject to qA q1 + 112 q2 + + qn

cyx, 111)( +112 x l2 [V x7

OAX A2s )( + p,2 + + x3

11, 1 0,

where OA is the fraction of the actual inputswhich could be used to optimally produce thegiven level of output, qA, for observation A; x,and x2 are quantities of the two inputs; are theweights generated for each observation via thelinear programming optimization process toobtain the optimal value for 0; A is the observa-tion we are evaluating, and superscripts denoteindividual firms. Again, OA OB/OA for firmA in Figure 1 or Figure 7. Therefore, we arefinding the lowest fraction of the inputs usedwhich would produce an output level at least asgreat as that actually produced by firm A.Additional linear programs can be solved toderive allocative inefficiency. A more completedescription and an example of DEA analysiswhich has been applied to the banking industryis presented in the Box.


Example of a data envelopment analysis (DEA) program applied to banking

Technical inefficiency is measured as thedifference between the observed behavior of bank Ato that which would occur if bank A were on theproduction frontier. Therefore, the unobservedfrontier must be projected. This is done via DEAanalysis by developing a program which determinesthe minimum required amount of inputs necessaryfor bank A to produce as much, or more, of each ofthe outputs currently being produced. The inputvector is chosen based on the observed behavior ofthe sample firms. Again, this reduces to a linearprogramming problem. For example, for bank A, thetechnically efficient combination of inputs is deter-mined as

(1) Min OA ,

H

s.t. 5E 1,th • c:,h=1

OA. xA�E 1.th xih ,

•

h=1

H

zAS Eµh •zh,h=1

zA �,E µh •• es ,h=1

i = 1, , m,

j = 1, , n,

s 1, , s r ,

s = 'S'

H

1.th � 0, h = 1, , H, E 1,th = 1,h=1

where OA is our radial measure of technical efficien-cy for firm A, q, is the output vector, p!' is a vector ofweights assigned to each observation (an intensityvector) which determines the combination of tech-nologies of each firm to form the production frontier,xh is the observed amount of input j used by firm h,and z is a vector of additional exogenous variables.'There are two types of these exogenous variables;those that need to be maximized, 4 for s = 1, , sr ,and those that should be minimized, z" for s = s + 1,

, S. An example of these exogenous variables inbanking would be the number of branch offices.Banks would, ceteris paribus, want to minimize thenumber of branch offices required to provide a givenlevel of output. The output of each firm in thesample is weighted in such a way that the combina-tion of observed outputs, i, is not less than the outputactually produced by firm A. Thus the frontier forfirm A is constructed as a weighted technology fromthe sample. If OA = 1, then firm A is as efficient asany firm in the sample, that is, firm A is on thefrontier. If OA < 1 then firm A is inefficient.

Allocative inefficiency for firm A can bederived by determining overall inefficiency and

technical inefficiency, and then taking the differencebetween the two. To determine overall inefficiency,take the observed input prices wA faced by the bankA and assume cost minimizing behavior:

(2) Min„A E WA • xA,j= ,

i = 1, ,m,

j = 1, , n,

s = 1, , Sr ,

s = s r.„ , S,

H

� 0, h = 1, , H, E )th = 1.h=1

The optimization process determines the mini-mum input vector, xA* for the observed price vectorrvA. Scalar wA• xA* is the minimum production costfor the vector of outputs qA. Overall inefficiency forany firm, h, is therefore the ratio of cost of theobserved and the best practice bank: 2

(3) Oh = (wh • xh) / (wh • xh*) —1.

The difference between the costs of technicallyefficient production and overall efficient productiondetermines the cost resulting from allocative ineffi-ciency. That is, A' = [(wh • Oh* • xh)/ (wh • x")] —1 isan index of allocative inefficiency for firm h, andOh* is the optimal value of Oh determined inEquation (1). 3

FOOTNOTES

'The sum of the weights 1.th used in the optimizationprocess is restricted to unity to allow for varyingreturns to scale. See Afriat (1972). The appropriatenumber of constraints for exogenous variables isdifficult to determine and the estimated inefficiencyfor a given model typically varies inversely with thenumber chosen.2The inequality in the linear program implies freedisposability of both inputs and outputs.'Technical inefficiency, determined in Equation 1,obviously is the difference between overall andallocative inefficiency: Th = Oh —Ah.

H

s .t. I-th • c: ,h=1

X Ai E 1.1h x jhh=1

H

ZAh=1

H

� ith • zhoh=1


Comparison of the parametric andnonparametric approaches

Using either the parametric or DEA ap-proach, the goal is to generate an accuratefrontier. However the two methods use signifi-cantly different approaches to achieve thisobjective. Because the parametric approachgenerates a stochastic cost frontier and the DEAapproach generates a production frontier, andbecause the methodologies are fundamentallydifferent, one should expect differences in theefficiency projections. Which methodology ispreferable?

There are advantages and disadvantageswith each of the procedures. The parametricapproach for generating cost relationshipsrequires (accurate) information on factor pricesand other exogenous variables, knowledge ofthe proper functional form of the frontier andthe one-sided error structure (if used), and anadequate sample size to generate reliablestatistical inferences. The DEA approach usesnone of this information, therefore, less data isrequired, fewer assumptions have to be made,and a smaller sample can be utilized.'s Howev-er, statistical inferences cannot be made usingthe nonparametric approach.

Another major difference is that the para-metric approach includes a random error termaround the frontier, while the DEA approachdoes not. Consequently, the DEA approachwill account for the influence of factors such asregional factor price differences, regulatorydifferences, luck, bad data, extreme observa-tions, etc., as inefficiency. 16 Therefore, onewould expect the nonparametric approach toproduce greater measured inefficiency." Theimportance of this difference should not beunderstated because single outliers can signifi-cantly influence the calculated efficiencymeasure for each firm using the DEA approach.

Obviously, one would like to be able totake comfort in the fact that either approachgenerates similar results. This is more likely tooccur if the sample analyzed has homogeneousunits which utilize similar production process-es. However, similar results have not beenfound in the literature. In fact, it is common forstudies contrasting results produced from thetwo methodologies to find no correlationbetween the efficiency estimates. This has alsooccurred in studies of efficiency for the bankingsector. We next review some of that literature.

The role of production inefficiency inbanking: A survey of the literature

In this section we review the literature onproductive efficiency for financial institutions.Most of the studies reviewed, particularly thoseanalyzing input efficiency, were conductedrecently and involve flexible functional formsand state of the art research techniques. For amore comprehensive review of much of theearlier literature on output efficiency, whichtypically utilized somewhat restrictive function-al forms and single output measures, the readeris referred to Gilbert (1984).

Output efficiency

The production process has been one of themost extensively investigated topics in banking.A major purpose of most of these studies hasbeen to obtain estimates of scale elasticities,that is, to evaluate how bank costs change withchanges in the level of output'8 More recently,efforts have also been made to estimate econo-mies of scope; that is, advantages from the jointproduction of multiple outputs.

Concerning scale economies, if changes inbank costs are proportional to changes in outputthen the scale elasticity measure equals 1.0 andall cost advantages resulting from the scale ofproduction are being fully exploited. If thechanges are not proportional, that is, varyingreturns to scale exist, then efficiency gainscould be obtained by leaving the productionprocess unchanged, but altering the quantity ofoutput produced. Scale elasticities less thanone imply that increases in output wouldproduce less than proportional increases incosts. Efficiency gains, therefore, could beobtained by increasing the scale of production.This is typically a justification given for bankmerger activity. Efficiency gains could beobtained by reducing production levels ifdecreasing returns to scale exist; that is, thescale elasticity is greater than 1.0.

Although much effort has been spentevaluating scale economies, it is one of themost disagreed upon topics in banking. Forexample, a number of studies find cost advan-tages from size to be fully exhausted at relative-ly low levels of output. Even when potentialeconomies exist they appear to be relativelysmall. Some of these studies are summarized inTable 1 which presents the estimated scaleelasticity for the average bank in the sample,the range of the estimates for all banks, and the


TABLE 1

Economies of scale estimates for small banks

AuthorScale elasticity

at sample mean'

Range ofscale elasticity

measure

Relevant range forsignificant scale(dis)economiesb

Benston, Hanweck U 1.09 0.89 - 1.24 Diseconomies above $25 millionand Humphrey (1982) B 1.10 0.97 - 1.16 Diseconomies above $25 million

Berger, Hanweck U 1.04 0.87 - 1.21 Diseconomies above $100 millionand Humphrey (1987) B 1.03 1.00 - 1.03 No significant (dis)economies

Cebenoyan (1988) U 1.08* 0.88 - 1.39 Diseconomies above $50 millionB 0.97 0.92 - 1.03 Economies above $100 million

Gilligan andSmirlock (1984)c U 0.99 0.98 - 1.10 Economies above $10 million

and diseconomies above$50 million

Gilligan, Smirlockand Marshall (1984)

U 1.03* 0.93 - 1.27 Economies below $25 millionand diseconomies above$100 million

B 1.02* 0.94 - 1.17 Economies below $25 millionand diseconomies above$100 million

Kolari and Zardkoohi B (n.a.) 0.99 - 1.02 No significant (dis)economies(1987) U In.a.) 0.88 - 0 .93 Economies below $100 million

Lawrence and Shay 0.99 0.91 - 0.99 Economies below $100 million(1986)

'Calculated as (d InC/d MO) for single output measures or E Id InCld InY) for all i=outputs. Benston, Hanweck andHumphrey (1982) calculated a scale elasticity augmented for output expansion via office expansion.'In these studies the banks are grouped by deposit size for calculation of the scale elasticity measure. The figurespresented are for the minimum bound on the group where statistically significant (dis)economies were realized.'Gilligan and Smirlock did not use the FCA data, as did the other studies, but did evaluate institutions similar in sizeto those in the FCA sample.*Denotes statistically significant difference from 1.0.Note: U and B represent unit and branch bank subsamples, respectively. Many of the studies provided results fora number of years and/or are based on alternative output measures. When multiple sets of findings were provided,the results reported here are for the most recent year, based on earning assets as the output measure, and use theintermediation approach (i.e., dollar value of funds transformed to assets).

level of output at which significant advantagesor disadvantages from the scale of productionoccurs. Basically, the results imply that scaleadvantages are fully exhausted once an institu-tion achieves a size of approximately $100-200million, a relatively small bank in the UnitedStates.° Higher output levels result in eitherconstant or decreasing returns to scale.

The implications from these results are thatvery small banks are inefficient because theyoperate under increasing returns to scale, andinefficiencies may exist for banks above ap-proximately $100-200 million in deposits. Theextent of the inefficiency, however, would notappear to be very large: scale elasticitiestypically range from .95 to 1.05. These find-

ings would appear to run counter to the argu-ments typically found in the popular bankingpress which imply that merger activity, desiresto expand geographically, and product expan-sion are all driven by the desire to reap costadvantages; for example, see Moynihan (1991).

However, this may partially result from thefact that, until very recently, most of the bankcost studies excluded large institutions; the veryones which are most interested in expanding.Most of the studies presented in Table 1 uti-lized the Federal Reserve's Functional CostAnalysis (FCA) survey data which typicallyincludes only institutions with less than onebillion dollars in assets. Although banks in thissize group constitute over 95 percent of all


23

TABLE 2

Results from large bank cost studies

Range of

Size at whichcalculated

economies ofAuthor

scale elasticities'

scale are exhausted'

Berger andHumphrey (1990)

0.98 - 1.03'

0.3 billion'0.92 - 1.06'

0.08 billion'

Clark (1984)

0.95 - 0.96

Non-exhaustedthrough $500millionh

Evanoff andIsrailevich (1990►

0.98

5.5 billion

Hunter andTimme (1986)'

1.05

$4.2 billion'0.97

$12.5 billion'

Hunter, Timmeand Yang (1990)

0.86 - 1.14

$25.0 billion

Noulas, et al. (1990)

0.97 - 1.09

$6.0 billion

Shaffer (1988)

0.949 Non-exhaustedthrough $140 billion''

Shaffer (1984)

0.95

Non-exhaustedthrough $50 billionh

Shaffer and David(1991)' 0.92

$37.0 billion

*The reported values are based on elasticity calculations for alternativeasset size groups (when available). Statistical significance is not takeninto account for figures reported in this column—that is, the calculatedvalues may not be significantly different from 1.0 in a statistical sense.'The values should be considered approximations. The authorsfrequently reported scale elasticity measures for a group of bankscovering a relatively broad size range, for example, 10-25 billion. If thecalculated value was insignificantly different from 1.0, then banks upto $25 billion were said to have constant returns to scale. Unlike thefigures reported in the previous column, whether or not a calculatedscale elasticity is significantly different from 1.0 in a statistical senseis all important for figures in this column.'For one bank holding companies. The value is probably biaseddownward. This is the sample mean value at which the calculatedscale elasticity was insignificantly different from 1.0.'For multibank holding companies. See note c.

°Branch bank results for the low cost banks.'Unit bank results for low cost banks.'For a $10 billion bank.'Non-exhausted for the entire sample.

The values are calculated at the sample mean.Note: Many of the studies provided results for a number of yearsand/or are based on alternative output measures. When multiple setsof findings were provided, the results reported here are for the mostrecent year, are based on earning assets as the output measure, anduse the intermediation approach.

banks in the United States, theyconstitute only about 30 percent ofthe nation's banking assets. Itexcludes the larger banks which aremost active in merger activity(Rhoades 1985) and most vocalabout expanded product and geo-graphic expansion powers.

Table 2 provides a summary ofresults from recent studies whichhave analyzed larger financialinstitutions; typically in excess ofone billion dollars. The evidencesuggests that scale advantages existwell beyond the $100-200 millionrange. While typically significantin a statistical sense, the scaleelasticity measure is close to 1.0.Again, the measures tend to rangefrom .95 to 1.05. Therefore, thestudies employing data for largerbanks tend to argue against thefinding that inefficiencies resultingfrom diseconomies of scale set in atrelatively low levels of output.However, the most typical conclu-sion the authors draw from thesebank cost studies is that potentialgains from altering scale via inter-nal growth or merger activity arerelatively minor. 20

It should be emphasized,however, that the scale elasticitymeasure is not a measure of ineffi-ciency. This may partially explainsome of the disagreement betweenpast research studies claimingpotential savings from growth arenot very great because scale elastic-ity measures are not very differentfrom 1.0, and the popular bankingpress which typically claims thatsignificant cost savings could begained by expanding the bank scaleof operation. Relatively minorscale elasticity deviations from 1.0can actually result in nontrivialinefficiency." To determine poten-tial gains from scale advantages,the relative comparison is the production costsof existing banks to that of the most efficientsized bank. For example, assuming scaleadvantages are exhausted at a $5 billion bank,how does the production cost for ten existing

$500 million banks compare to that resultingfrom the one large bank? The scale elasticitymeasure is required to estimate the cost differ-ence, however it by itself is not a measure ofinefficiency.22


TABLE 3

Estimated scale inefficiencies in banking

AuthorCalculated

scale inefficiency

(percent)

Aly, et al. (1990) 3.3"

Berger and Humphrey (1990) 4.2b12.7°

Clark (1984) 18.3°

Elyasiani and Mehdian (1990a) 38.9"

Evanoff and [srailevich (1990) 16.6

Gilligan, Smirlock and Marshall (1984) 5.0"4.3b

Hunter, Timme, and Yang (1990) 26.6

Lawrence and Shay (1986) 5.5

Noulas, et al. (1990) 2.7

Shaffer (1984) 12.0d

k Shaffer (1988) 10.0d

The scale elasticity for the "efficient" firm was .9637 since scaleadvantages were not exhausted in the data sample. The calculatedinefficiency would be larger if we extrapolated outside the studydata sample.

'Denotes branch banks.

'Taken directly from the cited study.

"The inefficiency measure is biased downward because datalimitations necessitated using an "inefficient" size bank which wasnot the most inefficient in the sample.

uDenotes unit banks.

Note: The reported inefficiencies were derived assuming prices,exogenous variables, and product mix were constant across banks(for example, at the sample mean), and that the cost representationcould be approximated by MC= a+ b (InQ) + .5c(In0) 2 (where 0represents output). Evaluating only inefficiency resulting fromproduction in the range of increasing returns to scale, the data werecentered about the values of the inefficient bank. Hence, for thisbank, the scale elasticity measure is simply the coefficient b. The costof production for the scale efficient bank is InC= a + b IMF • 01+ .5c[ln(F• 0)]2 where F is the size of the efficient firm relative to the inefficient one.The scale elasticity for the efficient bank is d InC/d In(F • Q)= b + c In(F •0) = 1.0. Scale inefficiency is the difference between cost values of thetwo banks relative to F, that is, F+ CE/Cs ] -1, where c, and CE denotecosts of the inefficient and efficient bank, respectively. The samemethodology could be used to calculate inefficiency resulting fromproduction in the range of decreasing returns to scale. In the studiesconsidered, scale measures are typically reported for various size ranges.Unless noted, the calculated inefficiency is based on the smallest bank inthe size group in which statistically significant economies of scaleexisted, relative to the largest bank in the size category in whichminimum efficient scale existed (that is, the scale measure was notsignificantly different from 1.0 in a statistical sense). Details areavailable from the authors. By holding product mix constant we restrictthe cost savings to scale effects only; precluding any savings resultingfrom altering the mix. This implicitly assumes either that the mix isactually invariant over the banks considered or that the scale efficientbank analyzed is equal in size to the scale efficient bank observed in thedata. Given the assumptions employed and the relatively broad sizecategories reported in the studies considered, the reported inefficienciesshould be considered rough approximations.

Using the actual scale esti-mates and sample data from anumber of bank cost studies,measures of scale inefficiencywere calculated and are presentedin Table 3. The reported ineffi-ciencies are for banks producingin the range of increasing returnsto scale. They suggest that poten-tial gains resulting from scaleinefficiency are not trivial. Whilesome of the studies suggest ineffi-ciencies in the range of fivepercent, estimates in the 10-20percent range are not uncommon,and they range up to nearly 40percent. The major point is thatalthough their importance istypically played down in the bankcost literature, scale inefficienciesappear to be significant enough towarrant efforts by banks toachieve an efficient scale?'

The evidence concerningefficiency gains from economiesof scope is not conclusive. Studiesto date typically focus on theoutputs currently produced andfind very slight or no potential forefficiency gains; for example, seeBenston, et al. (1982), Cebenoyan(1990), Clark (1988), Hunter,Timme, and Yang (1990), Law-rence and Shay (1986), and Mester(1987). 24 However, the methodol-ogies used to evaluate advantagesfrom joint production have typi-cally been criticized on thegrounds that most functionalforms utilized for bank costanalysis are ill suited for analyzingeconomies of scope. Additionally,the evaluation of potential effi-ciency gains is commonly preclud-ed as a result of regulation. Sincenumerous products cannot beprovided by banks, there is noavailable quantitative means toevaluate the joint cost relationshipor potential efficiency gains.

Input efficiencyWhile much research has

been conducted evaluating output


25

efficiency, only recently has input efficiencybeen considered. The evidence suggests that theassumption of input efficiency, common in moststudies of bank production, is typically violated.Table 4 presents summary findings for recentstudies evaluating input efficiency in banking.

While substantially different techniques wereused in the studies reviewed, the results aresurprisingly similar. Total input inefficiency iscommonly in the range of 20-30 percent, and isas high as 50 percent in one of the studies. Thisimplies that significant cost savings could berealized if bank management more efficientlyutilized productive inputs.

Breaking down the study findings into moredetail, allocative inefficiency is typically found tobe relatively minor and, with one exception,dominated by technical inefficiency. 25 Evanoffand Israilevich (1990a, 1990b, 1991) found thatthe allocative inefficiency that does exist results

from the overuse of physical capital relative toother inputs. As mentioned earlier, this isconsistent with expectations since past bankregulation did not allow price competition inthe market for deposits. As a result, it appearsthat banks simply responded by competingusing alternative means such as service levels.The introduction of numerous branch officesresulted in brick-and-mortar competitioninstead of price competition. While the typical-ly small allocative inefficiency estimate cannotbe ignored as a potential source of future costsavings in banking, it does suggest that thefrequent criticism of bank regulation based onthe burden it imposes on the bank productionprocess may be somewhat exaggerated. Appar-ently the optimal mix of factor inputs is onlymarginally affected by regulation.

The results presented in Table 4 suggestthat the major source of input inefficiency is

TABLE 4

Input inefficiency in banking

Author ApproachOverall inputinefficiency

Allocativeinefficiency

Pure technicalinefficiency

percent

Berger and Humphrey (1990)b Parametric 24.8 MinimalBerger and Humphrey (1990)° Parametric 20.2 Minimal

Elyasiani and Mehdian (1990b) d Parametric 13.6

Evanoff and Israilevich (1990)a Parametric 22.0 1.0 21.0

Evanoff, Israilevich, and Merris(1990) Parametric 1.8

Ferrier and Lovell (1990) Parametric 26.0 17.1 8.9

Aly, et al. (19901a Nonparametric 50.7 14.9 35.8

Elyasiani and Mehdian (1990a) Nonparametric 11.7

Ferrier and Lovell (1990) Nonparametric 21.0 5.0 16.0

Gold and Sherman (1985)° Nonparametric 27.9

For the 1972-87 period. Subperiods produced different results.bFor branch banks.

'For the most inefficient decision making unit.dFor 1980. Scale inefficiency was also calculated to be 38.9%.°Scale inefficiency was also calculated to be 3.1%.

For unit banks.Note: The figures presented are the level of inefficiency relative to the firm using its inputs efficiently. Thestudies frequently reported inefficiency relative to the observed firm or efficiency as a percentage of inpututilization (see Figure 1 for an illustration of input inefficiency measures). These measures were converted to themeasure presented here. Gaps in the results are due to the fact that not all studies considered all componentsof inefficiency.

26

ECONOMIC PERSPECTIVES

pure technical inefficiency. Simply put, firmsuse too much input per unit of output. Com-bined with the finding of relatively smallallocative inefficiency, this implies that bankmanagers do a relatively good job of choosingthe proper input mix, but then simply under-utilize all factor inputs. 26 This inefficiencyobviously cannot be sustained over time if thebanks are subject to competitive forces. Com-paring the findings summarized in Tables 3 and4, it is apparent that the inefficiencies resultingfrom the suboptimal use of inputs are somewhatlarger than those resulting from producingsuboptimal levels of output. 27

Causes of inefficiency and implicationsfor the future

There are a number of possible explana-tions for the inefficiency in banking. Basically,the expected causes should be the same as thosefound in any industry. As discussed earlier,economic theory suggests that allocative ineffi-ciency is driven by market distortions fromfactors such as regulation. Pure technicalinefficiency may be the result of weak marketforces (induced by market structure or regula-tion) which allow bank management to becomeremiss and to continue their inefficient behav-ior. Scale and scope induced inefficiency maybe the result of either market or regulatoryforces which make the optimal level and mix ofoutputs unachievable. Some analysts wouldalso argue that bank size should be a determi-nant of efficiency. According to this argument,larger banks may have more astute manage-ment and/or be more cost conscious because ofgreater pressure from owners concerningbottom-line profits. Additionally, these banksare typically located in the larger, more com-petitive markets which may induce a moreefficient production process.

The evidence suggests that these forces areindeed operative in determining efficiencylevels in banking. Analyzing data for largebanks over the 1972-87 period, Evanoff andIsrailevich (1990a, 1990b, 1991) found alloca-tive inefficiency to be related to alternativemeasures of regulatory stringency. It was alsofound to be greater in regions characterized bymore restrictive state level regulation, andsignificantly less after industry deregulationoccurred in the early 1980s. Allocative effi-ciency has not been found to be related to banksize (for example, Aly, et al. 1990). This,

however, should not be surprising since ineffi-ciency may occur although the bank is operat-ing efficiently in response to shadow marketprices (that is, those including market distor-tions).

The evidence also suggests that puretechnical inefficiency is induced by regulation,and some evidence exists suggesting that itresults from elements of market structure.Berger and Humphrey (1990) found that theinefficiency was greater, on average, for bankslocated in the more restrictive unit bankingstates than those in states allowing branching.Additional analysis of data used in Evanoff andIsrailevich (1990b) produced similar findings.28

Pure technical inefficiency has also been foundto be negatively associated with bank size[Berger and Humphrey (1990), Aly, et al.(1990), Elyasiani and Mehdian (1990a), Ran-gan, et al. (1988)]. To the extent that smallinstitutions are located in the smaller, leastcompetitive markets, the absence of marketpressures could be producing the higher levelsof inefficiency. Aly, et al. (1990) tested thiscontention more directly by relating puretechnical inefficiency to bank location. Bankslocated in large metropolitan areas were foundto be significantly more efficient than those insmaller markets, suggesting market structuremay influence efficiency levels. The evidencehere, however, is also not conclusive. It may bethat cost savings realized by urban banks mayexist because the increased population densitymakes possible less costly delivery systems.This cost savings may be interpreted as beingdriven by greater market competition in theurban markets while actually it is simply afunction of demographics.

Scale and scope diseconomies are alsoexpected to be partially determined by regula-tory forces. Unit banking restrictions forcebanks to expand at one physical location in-stead of allowing them to expand by openingadditional offices to serve customers. Disecon-omies of scale may set in at the individualoffice causing higher cost for larger singleoffice institutions. Expansion via new officeshas been shown to be more cost effective.Review of the findings presented in Tables 1and 2 indicates that diseconomies of scale aretypically larger in unit banking markets. Anal-ysis which combines data for both unit andbranch banks usually find that the larger unitbanks typically operate under conditions of


27

diseconomies of scale; see for example,Evanoff, Israilevich, and Merris (1990). Le-Compte and Smith (1990) also found thatinefficiency resulting from not producing theproper mix of outputs, and therefore failing totake advantage of economies from joint produc-tion, was greater under conditions of morestringent regulation.

What are the implications of these find-ings? Given the important role regulationapparently serves in determining efficiencylevels, the recent trend toward industry deregu-lation should result in improved efficiency.Reductions in entry barriers resulting in lessregulatory-created market protection, and fewerregulatory-induced market distortions shouldsignificantly increase competitive pressures.The beneficial aspects of increased competitionwill be accomplished by weeding out the lessefficient firms. Obviously, in an environmentof deregulation and increased competition,reducing pure technical inefficiency could be amajor determinant of firm survival.

Merger activity in the financial servicesindustry will probably increase in the future asbanks strive to compete in the deregulatedmarket. The deregulation will provide bankswith both the desire and the ability to expandacquisition activity. Scale inefficient firms willbe absorbed to exploit cost advantages. Firmswhose management does an inadequate job ofutilizing factor inputs may soon find it difficultto survive in the more competitive market.They will be required to eliminate the ineffi-ciency or become prime targets for acquiringfirms looking to "trim the fat" from new acqui-sitions." Given that pure technical inefficiencyis so significant in banking, and given that it isthe one aspect of efficiency over which the firmhas direct control, one would expect significantincreases in bank productive efficiency in thecoming years.

Summary and conclusions

The purpose of this study has been todiscuss productive efficiency at a conceptuallevel and to review the relevant literature forthe banking industry. We categorize efficiencyinto input and output related measures. Outputinefficiency results from producing suboptimal

output levels or a suboptimal combination ofoutputs. Input inefficiency results from produc-tion using a sub-optimal input mix (allocativeinefficiency) and not effectively utilizing theinputs employed (pure technical inefficiency).A review of existing bank cost studies suggeststhat banks have substantial room to increaseproductive efficiency and, as a result, to signifi-cantly lower costs. Although the range offindings in the studies surveyed is relativelybroad, it is not uncommon to find 10-20 percentbank scale inefficiency generated by producingat suboptimal output levels. Allocative ineffi-ciency is typically found to be relatively minor;usually less than five percent. Pure technicalinefficiency, however, is apparently quitesignificant; in the range of 20-30 percent.Combining these three effects results in sub-stantial potential cost savings for banks.

What are the major causes of bank ineffi-ciency? The evidence suggests that industryregulation is a dominant source. Allocativeinefficiency, although relatively minor, isdirectly induced by regulation. Inefficienciesresulting from not producing the optimalcombination of outputs have also been shownto be related to regulation. However, the majorsource of inefficiency, pure technical ineffi-ciency, is managerially induced. That is, theabsence of competitive forces, which is alsoinfluenced by industry regulation, has allowedbanks to continue to operate in spite of the factthat management has not effectively utilizedthe resources available to them.

Given that the industry is undergoing aprocess of significant deregulation, the findingsfrom these studies have both positive andnegative implications for banking. As deregu-lation continues, the increased competitivepressures will force banks to operate moreefficiently. Those unable to do so by adjustingto the new competitive environment will havedifficulty surviving. However, one of the majorsources of inefficiency, pure technical ineffi-ciency, is directly under the control of thebanks themselves. Therefore, they will havecontrol of their own destiny. In light of therecent significant number of branch closingsand cost saving campaigns aimed at reducingpayrolls, it would appear that efforts to improvebank efficiency are already underway.

28

ECONOMIC PERSPECTIVES

FOOTNOTES

1Drucker (1991).

2However, the research process continues because ofdifferences in results from previous studies, methodologies,assumptions, output definitions, etc. For a review of someof these studies see Gilbert (1984), Clark (1988), orHumphrey (1990).

3These definitions of productive inefficiency wereintroduced by Farrell (1957). They are radial measures andcoincide with much of the discussion that follows. Foralternative measures of (in)efficiency see Fare and Lovell[1978].

°At this stage we are ignoring the potential for economiesof scale. Farrell assumed a linearly homogeneousproduction process; that is, constant returns to scale. Weassume, as discussed below, that any gains from scaleadvantages would result in a higher level isoquant for agiven efficient combination of inputs.

'For example, if production was allocatively efficient themeasure would, obviously, be OE/OE = 1.0; that is, pointsB, C, and E would coincide.

6Typically we assume profit maximization as the objectiveunder competitive conditions, that is, frictionless marketsand the absence of monopoly power and regulatorydistortions. In this model the production, cost, and profitfunctions are essentially alternative means of evaluating thesame optimization process, that is, the production process.The cost relationship is frequently evaluated instead of theproduction function because less information is required.When discussing frontier analysis, it is irrelevant whetherthe cost or production side is considered. However,empirically, the choice of a cost, production, or profitrepresentation may generate different results because theresearcher is required to use approximations for the truefunctional forms of these representations.

7 As a byproduct, the methodology also allows for theestimation of scale and scope induced inefficiency. It doesnot, however, allow for estimates of pure technicalinefficiency.

8 However, this is an empirical approach, therefore the truecause of the distortion in factor prices could be generatedby a number of things, including data measurement errors,etc.

'Using this methodology, the shadow price approximationscan be interpreted as first-order Taylor's series expansionsof arbitrary shadow-price functions. It should beemphasized that there is nothing special about the linearrelationship. Alternative specifications can and should beconsidered; for example, see Evanoff and Israilevich (1991,1990a).

10 Typically, factor share equations are derived from the costrelationship via Shephard's Lemma and the system of costand share equations are jointly estimated. The additional

share equations provide increased efficiency of theestimates. The share equations are derived from theshadow cost relationship.

"For a lucid description of these models, see Bauer (1990).The foundation for this approach was developed by Aigner,Lovell and Schmidt (1977). See also Fare, Grosskopf, andLovell (1985).

"One sided distributions which have been used inestimation include the half-normal, exponential, truncatednormal and the Gamma distribution. Again, see Bauer(1990) and the sources cited.

"This is the linkage employed in Ferrier and Lovell (1990)in their study of bank efficiency.

"The approach can also be combined with others toincorporate additional information. For example, Evanoffand Israilevich (1990b) augmented the thick frontierapproach by estimating shadow cost functions for high andlow cost banks. In this way, estimates of allocativeinefficiency could be obtained directly from the modelinstead of using an auxiliary, somewhat arbitrary,procedure to decompose the total inefficiency into itscomponent parts.

"Technical inefficiency can be calculated ignoring thisinformation. Measures of allocative efficiency requireinformation on factor prices.

16 Evanoff and Israilevich (1991) found significant regionaldifferences in bank production techniques and levels ofefficiency.

'Surprisingly, Ferrier and Lovell (1990) find exactly theopposite in their analysis of banks.

"More formally, the scale elasticity measure is thepercentage change in cost relative to the percentage changein output, or alnClalnQ. One major issue in bank coststudies is determining what constitutes output. Althoughdefining output is difficult in any service oriented industry,there seems to be more controversy with respect tobanking. However, of the measures used to date, thefindings tend to be similar regardless of the measureemployed; see Humphrey (1990).

"In 1989, over three-quarters of U.S. banks had less than$100 million in assets; see FDIC (1989). However, banksover 1000 times this size also existed.

20 It is possible that scale estimates could be biased as aresult of misspecifying the cost relationship. For example,the standard assumption of efficient utilization of factorinputs, if incorrect, could produce misleading findingsconcerning scale (dis)advantages. However, Berger andHumphrey (1990), Evanoff and Israilevich (1990b) andEvanoff, Israilevich, and Merris (1990) found scaleestimates were not substantially different when inputinefficiency was accounted for.


"The distinction between the scale elasticity andinefficiency measures has been emphasized in Shaffer(1988) and Shaffer and David (1991). Using data from aprevious study, Shaffer and David show that a scaleelasticity of .99 could result in a 25% cost savings ifproduction was shifted from small to large banks.

22Actually the scale inefficiency will be determined by thedifference in average cost between the efficient andinefficient firm. The elasticity at the output levelcorresponding to the inefficient firm gives us informationabout cost changes at slightly larger or slightly smalleroutput levels. Neither of these levels is relevant fordetermining inefficiency since we never produce at theselevels. For efficiency analysis, production takes placeeither at the efficient or the inefficient firm; therefore onlythe corresponding two average cost values are relevant.Whereas the elasticity measure gives percentage changes incost induced by incremental changes in output, in thebanking studies analyzed in Table 3 the difference in outputbetween the efficient and inefficient firm is not incremental.

'Caution should be taken in deriving policy implicationsfrom findings concerning scale efficiency alone. Theremay be alternative factors which partially offset thesepotential gains. In fact, in viewing bank data, Humphrey(1990) finds the average cost across all bank size groups tobe amazingly similar. That, combined with the potentialefficiency gains from scale economies discussed here,suggest that there may be some factors counteracting thesepotential efficiencies. However, with respect to scaleefficiency alone, there would appear to be significantpotential gains for banking.

"Some studies have, however, found significant advantag-es resulting from joint production; for example, Gilligan,Smirlock, and Marshall (1984), and Evanoff and Israilevich(1990b). However, the finding of relatively small or noscope economies is most typical. The methodologiesutilized to generate estimates of scope economies havebeen critiqued in Pulley and Humphrey (1990). This isobviously a rich area for future research.

25 Although Aly et al.(1990) find evidence of greaterallocative inefficiency than most of the studies reviewed,the major exception to the norm is the study by Ferrier andLovell (1990). Using a parametric approach the authors

found significant allocative inefficiency (over 17 percent).However, as mentioned earlier, the reliability of thesetechniques decreases significantly when non-homogeneousdecision making units are considered. The data for thisstudy included mutual savings banks, credit unions, savingsand loan associations, and "noncommercial" institutions.Nearly a third of the sample was made up of noncommer-cial banks. Given that the technology for these institutionsmay differ from that of commercial banks, one wouldexpect these observations to have a substantial influence onthe error structure of the estimates. The authors themselveseven state that some of these observations do significantlyinfluence their results (Ferrier and Lovell, p. 243). Sincethe distribution of the errors is the major determinant of theefficiency measure, this may bias the results concerningcommercial bank efficiency. The study also found that theallocative efficiency resulted from an over-utilization oflabor relative to the other factors. This is precisely theopposite of what one, intuitively, would expect in banking(see Evanoff and Israilevich 1990b). Finally, the measuresused for factor prices may bias the results toward findingallocative inefficiency resulting from over-utilization oflabor (Berger and Humphrey 1990, p. 21).

26This finding has implications for the bank expensepreference literature, for example, Mester (1989).Typically it is assumed that managers of the expensingbank prefer one input to others—usually labor. The resultspresented here suggest that a more restricted form ofexpense preference, a preference for all the inputs to thesame degree, may best describe the situation in banking.

27However, this excludes any inefficiencies resulting fromscope disadvantages which cannot be empirically captured.

28The evidence on this, however, is not conclusive. Aly, etal. (1990) found no significant efficiency difference acrossunit and branch banks.

29This does not imply that there will no longer be smallbanks. While most of the bank cost literature has assumedhomogeneous outputs, recent research suggests that banksfrequently find a market niche in an attempt to differentiatethemselves from others. Efficient banks which are able tofill a needed market niche should continue to prosper in aderegulated environment. See Amel and Rhoades (1988).

REFERENCES

Afriat, Sydney, "Efficiency estimation ofproduction functions," International EconomicReview, 13, 1972, pp. 568-598.

Aigner, Dennis, C.A. Knox Lovell, and PeterSchmidt, "Formulation and estimation ofstochastic frontier production function models,"Journal of Econometrics, 6, 1977, pp. 21-37.

Aly, Hassan Y., Richard Grabowski, CarlPasurka, and Nanda Rangan, "Technical, scale,and allocative efficiencies in U.S. banking: an

empirical investigation," The Review of Econom-ics and Statistics, 72, 1990, pp. 211-218.

Amel, Dean F., and Stephen A. Rhoades,"Strategic groups in banking," The Review ofEconomics and Statistics, 70, 1988, pp. 685-689.

Atkinson, Scott E., and Robert Halvorsen,"Parametric efficiency tests, economies of scale,and input demand in U.S. electric power genera-tion," International Economic Review, 25, 1984,pp. 647-662.


Atkinson, Scott E., and Robert Halvorsen, "Atest of relative and absolute price efficiency inregulated utilities," The Review of Economics andStatistics, 62, 1980, pp. 185-196.

Bauer, Paul W., "Recent developments in theeconometric estimation of frontiers," Journal ofEconometrics, 46, 1990, pp. 39-56.

Benston, George, Gerald A. Hanweck, andDavid B. Humphrey, "Scale economies inbanking," Journal of Money, Credit, and Banking,14, 1982, pp. 435-456.

Berger, Allen N., Gerald A. Hanweck, andDavid B. Humphrey, "Competitive viability inbanking: Scale, scope, and product mix econo-mies," Journal of Monetary Economics, 16, 1987,pp. 501-520.

Berger, Allen N., and David B. Humphrey,"The dominance of inefficiencies over scale andproduct mix economies in banking," forthcomingin Journal of Monetary Economics, 28, 1991.Also in Finance and Economics DiscussionSeries, 107, Board of Governors of the FederalReserve System, 1990.

Cebenoyan, A. Sinan, "Multiproduct costfunctions and scale economies in banking," TheFinancial Review, 23, 1988, pp. 499-512.

Cebenoyan, A. Sinan, "Scope economies inbanking: the hybrid box-cox function," TheFinancial Review, 25, 1990, pp. 115-125.

Clark, Jeffrey A., "Estimation of economies ofscale in banking using a generalized functionalform," Journal of Money, Credit, and Banking,16, 1984, pp. 53-67.

Clark, Jeffrey A., "Economies of scale and scopeat depository financial institutions: A review of theliterature," Economic Review, Federal ReserveBank of Kansas City, 1988, p. 16-33.

Drucker, Peter F., "Don't change corporateculture—use it," The Wall Street Journal, March28, 1991, p. A 14.

Elyasiani, Elyas, and Seyed M. Mehdian, "Anonparametric approach to measurement ofefficiency and technological change: The case oflarge U.S. commercial banks," Journal ofFinancial Services Research, 4, 1990a, pp. 157-168.

Elyasiani, Elyas, and Seyed M. Mehdian,"Efficiency in the commercial banking industry, aproduction frontier approach," Applied Econom-ics, 22, 1990b, pp. 539-551.

Evanoff, Douglas D., "Branch banking andservice assessibility," Journal of Money, Credit,and Banking, 1988, pp. 191-202.

Evanoff, Douglas D., and Philip R. Israilevich,"Cost economies and allocative efficiency in largeU.S. commercial banks," Proceedings of aConference on Bank Structure and Competition,26, 1990a, pp. 152-169.

Evanoff, Douglas D., and Philip R. Israilevich,"Deregulation, cost economies and allocativeefficiency of large commercial banks," Issues inFinancial Regulation, Federal Reserve Bank ofChicago Working Paper 90-19, 1990b.

Evanoff, Douglas D., and Philip R. Israilevich,"Regional differences in bank efficiency andtechnology," The Annals of Regional Science, 25,1991, pp. 41-54.

Evanoff, Douglas D., Philip R. Israilevich, andRandall C. Merris, "Relative efficiency,technical change, and economies of scale for largecommercial banks," Journal of RegulatoryEconomics, 2, 1990, pp. 281-298.

Fare, R.J., Shawna Grosskopf, C.A. KnoxLovell, The measurement of efficiency of produc-tion, Boston, Kluwer Academic Publishers, 1985.

Fare, R.J., and C.A. Knox Lovell, "Measuringthe technical efficiency of production," Journal ofEconomic Theory, 19, 1978, pp. 150-162.

Farrell, M.J., "The measurement of productiveefficiency," Journal of Royal Statistical Analysis,A, 120, 1957, pp. 253-281.

FDIC, "Statistics on banking," Federal DepositInsurance Corporation, Washington, GPO, 1989.

Ferrier, Gary D., and C.A. Knox Lovell,"Measuring cost efficiency in banking: Economet-ric and linear programming evidence," Journal ofEconometrics, 46, 1990, pp. 229-245

Gilbert, R. Alton, "Bank market structure andcompetition," Journal of Money, Credit, andBanking, 16, 1984, pp. 617-644.

Gilligan, Thomas W., and Michael L. Smirlock,"An empirical study of joint production and scale

FEDERAL RESERVE RANK OF CHICAGO 31

economies in commercial banking," Journal ofBanking and Finance, 8, 1984, pp. 67-77.

Gilligan, Thomas W., Michael L. Smirlock, andWilliam Marshall, "Scale and scope economiesin the multi-product banking firm," Journal ofMonetary Economics, 13, 1984, pp. 393-405.

Humphrey, David B., "Why do estimates of bankscale economies differ?," Economic Review,Federal Reserve Bank of Richmond, 1990, pp. 38-50.

Hunter, William C., and Stephen G. Timme,"Technical change, organization form, and thestructure of bank production," Journal of Money,Credit, and Banking, 18, 1986, pp. 152-166.

Hunter, William C., Stephen G. Timme, andWon Keun Yang, "An examination of costsubadditivity and multiproduct production in largeU.S. banks," Journal of Money, Credit, andBanking, 22, 1990, pp. 504-525.

Kolari, James, and Asghar Zardkoohi, "Bankcost, structure, and performance," Lexington,D.C., Heath Publishers.

Kopp, Raymond, and W. Erwin Diewert, "Thedecomposition of frontier cost function deviationsinto measures of technical and allocative efficien-cy," Journal of Econometrics, 18, 1982, pp. 319-331.

Lau, L. J., and P. A. Yotopoulos, "A test forrelative efficiency and application to Indianagriculture," American Economic Review, 61,1971, pp. 94-109.

Lawrence, Colin, and Robert Shay, "Technolo-gy and financial intermediation in a multiproductbanking firm: an econometric study of U S banks,1979-82," in Colin Lawrence and Robert Shay(ed.), Technological Innovation, Regulation, andthe Monetary Economy, Cambridge, Ballinger,1986, pp. 53-92.

Lecompte, Richard, L. B., and Stephen D.Smith, "Changes in the cost of intermediation:The case of savings and loans," Journal ofFinance, 45, 1990, pp. 1337-1345.

Mester, Loretta J., "A multiproduct cost study ofsavings and loans," Journal of Finance, 42, 1987,pp. 423-445.

Mester, Loretta J., "Testing for expensepreference behavior: Mutual and stock savingsand loans," Rand Journal of Economics, 20, 1989,483-498.

Moynihan, Jonathan P., "Banking in the 90s—where will the profits come from?," Proceedingsof a Conference on Bank Structure and Competi-tion, Federal Reserve Bank of Chicago, 27, 1991.

Noulas, Athanasios G., Subhash C. Ray, andStephen M. Miller, "Returns to scale and inputsubstitution for large U.S. banks," Journal ofMoney, Credit, and Banking, 22, 1990, pp. 94-108.

Pulley, Lawrence B., and David B. Humphrey,"Correcting the instability of bank scope econo-mies from the translog model: A compositefunction approach," paper presented at theFinancial Management Association meetings,Orlando Florida, October, 1990.

Rangan, Nanda, Richard Grabowski, HassanAly, and Carl Pasurka, "The technical efficiencyof U.S. banks," Economic Letters, 28, 1988, pp.169-75.

Rhoades, Stephen A., "Mergers and acquisitionsby commercial banks," Staff Studies, 142, Boardof Governors of the Federal Reserve System,1985.

Shaffer, Sherrill, "Scale economies in multiprod-uct firms," Bulletin of Economic Research, 1,1984, pp. 51-58.

Shaffer, Sherrill, "A revenue-restricted cost studyof 100 large banks," Federal Reserve Bank ofNew York, unpublished research paper, 1988.

Shaffer, Sherrill, and Edmond David, "Econo-mies of superscale in commercial banking,"Applied Economics, 23, 1991, pp. 283-293.

Sherman, H. David, and Franklin Gold, "Bankbranch operating efficiency," Journal of Bankingand Finance, 9, 1985, pp. 297-315.

Zieschang, Kimberly D., "A note on the decom-position of cost efficiency into technical andallocative components," Journal of Econometrics,23, 1983, pp. 401-405.


Date post:	06-Feb-2018
Category:	Documents
Upload:	vuminh
View:	216 times
Download:	0 times

rdtv ffn n bnn - Federal Reserve Bank of Chicago/media/publications/economic... · rdtv ffn n bnn l...

Documents