predicted and actual costs from individual bank mergers

Journal of Economics and Business 56 (2004) 137–157

Predicted and actual costs from individualbank mergers

Santiago Carbó Valverdea, David B. Humphreyb,∗a University of Granada, Granada, Spain

b Department of Finance, School of Business, Florida State University, Tallahassee, FL 32306-1042, USA

Received 8 August 2002; received in revised form 25 April 2003; accepted 30 May 2003

Abstract

Using translog, Fourier, and cubic spline cost functions, we predict scale-related cost effects from22 individual mergers among Spanish savings banks over 1986–2000. Our individual predictions areas good as those made by merger participants themselves since they, and we, only correctly predictthe sign change one-third of the time. Our cost models do a better job in accurately predicting theaverage or expected value of the cost effect for all mergers as a group. Overall, unit cost was reducedby about 0.50%, raising asset returns by 4%, and improving resource utilization.© 2004 Elsevier Inc. All rights reserved.

JEL classification: G21; G34

Keywords: Mergers; Cost prediction; Savings banks

1. Introduction

Banks grow in two ways. They expand as the market they are currently in generates moredeposits and opportunities for expanding loans. But mostly they grow through mergers andacquisitions. Announcements of mergers by merging banks are invariably positive. Theyfocus on how their merger will save operating costs, deliver a broader mix of services, andpermit them to be more competitive with larger domestic or international banks. Simplyput, the main publicly-stated rationale for a merger is to achieve greater scale economies,although it is also the case that management compensation is typically higher at largerinstitutions (Dermine, 1999).

∗ Tel.: +1-850-688-0638; fax:+1-850-644-4225.E-mail address: [email protected] (D.B. Humphrey).

0148-6195/$ – see front matter © 2004 Elsevier Inc. All rights reserved.doi:10.1016/j.jeconbus.2003.05.001

138 S. Carbo Valverde, D.B. Humphrey / Journal of Economics and Business 56 (2004) 137–157

The potential for scale benefits have been verified in both academic cost function es-timates and consultant analyses of banking lines of business. Even so, academic studiesof bank mergers typically find that on average mergers seem neither to lower nor raiseunit cost overall. Indeed, pre- and post-merger cost comparisons using (a) simple costratios (Rhoades, 1993), (b) sophisticated cost frontier analyses (Berger, 1998; Berger &Humphrey, 1992), or (c) case studies of individual merging banks (Rhoades, 1998)havehad a difficult time supporting the a priori notion that unit cost falls with a merger. Andwhile banking consultants have developed experienced-based checklists of where cost sav-ings may be realized if a merger is properly implemented, they too find that most mergersdo not generate significant cost reductions.

Most merger cost analyses have been performed using U.S. banks. The few studies ofbanking mergers in Europe suggest that the results may be somewhat different. First, equitymarket event studies for Europe (Cybo-Ottone & Murgia, 2000) have found significantlypositive abnormal equity returns associated with merger announcements, a result which isnot often found for the U.S. (Hannan & Wolken, 1989; Hawawini & Swary, 1989). Second,a study of over 492 mergers and acquisitions within the European Union over 1988–1993indicated that average operating cost tended to fall after a merger (Vander Vennet, 1997).Also, using procedures similar to those used here, the average effect of banking mergers inNorway is estimated to have reduced unit cost by 2–3% overall (Humphrey & Vale, 2002).Additional analyses for Italy (Resti, 1998) and the U.K. (Haynes & Thompson, 1999) alsoindicated some post-merger gains in bank cost efficiency and productivity.

With respect to Spain, an early study of merger cost effects found small to insignificantcost benefits (Raymond, 1994) as did a later cost analysis of 18 mergers (Fuentes & Sastre,1999). Although various productivity measures showed improvement, this apparently didnot strongly carry over to costs. A later comparison of pre-with post-merger costs for thesame set of merging institutions found that the observed reduction in costs at merginginstitutions seemed to be no different on average from the cost reductions experienced bythe industry as a whole (Carbó, Humphrey, & Rodriguez, 2003).

The analysis of merger cost effects has so far been primarily focused on the average effectof mergers. In this paper we extend the analysis to individual bank mergers. Our primarypurpose is to address a common problem faced by regulatory and antitrust authorities:namely, to predict the likely cost effect of a merger in order to gauge the reasonablenessof cost benefits announced by the merger participants themselves. This, and an assessmentof how the merger may affect market competition, are the two essential components indetermining whether or not to approve a merger application.

Following earlier work byMcAllister and McManus (1993), we specify inSection 2twocost functions with an enhanced ability, compared to the translog form, to accurately identifylocal scale effects for banking firms. McAllister and McManus compared the translog withthe Fourier form, a kernel regression, and a linear spline and found large differences inscale effects across size-classes of U.S. banks. A few other cost studies have used a Fourierform (e.g.,Berger & Mester, 1997). More recently,Wheelock and Wilson (2001)contrastedthe translog with the Fourier form, a kernel regression, and a linear polynomial smoothingprocedure in estimating scale and product mix effects for U.S. banks. Generally, they foundthat while significant scale economies existed for banks up to about $200 million in assets,the point estimates of scale economies for larger institutions were not significantly different

S. Carbo Valverde, D.B. Humphrey / Journal of Economics and Business 56 (2004) 137–157 139

from constant cost. We plan a similar analysis for Spanish savings banks using the translog,the Fourier form, and a cubic spline (which is similar to a kernel regression). Fortunately, dueto an important but overlooked paper bySuits, Mason, and Chan (1978), our cubic splinefunction—a series of connected polynomials—can be fitted using standard econometrictechniques as opposed to non-parametric estimation.1

The scale economy estimates obtained with the translog, Fourier, and cubic spline costfunctions are used inSection 3to predict the expected cost effect of each of 22 individualsavings bank mergers in Spain over 1986–2000. That is, we predict the change in unitcost from scale effects alone for each merger as well as for all mergers together. We alsodetermine, for each merger separately, the actual change in unit cost pre- to post-mergerand contrast it with the cost change experienced for the industry as a whole for the sametime period. The predicted and actual cost effects for each merger are then compared. Ourpredictions are only about as good as those made by the merger participants themselves.Participants predict a cost reduction in all mergers but only about one-third of the timeis a reduction actually realized. Similarly, we are only able to correctly predict the signof the merger-related cost change (up or down) about one-third of the time, although ourprediction of theaverage merger-cost effect is close to that actually experienced. We alsoexplore some of the (measurable) reasons why individual merger cost predictions may notbe realized either by us or merger participants. Our results here are disappointing as theexplanatory power is low.Section 4contains summary and conclusions.

2. Accurate estimation of scale effects

We wish to identify the “expected value” of the cost effect of a banking merger. As such,we rely on average relationships rather than those associated with a cost frontier. If mostbanks are on or close to the cost frontier, then this result will be captured as an average inour analysis. If this is not the case, our merger cost predictions will not be influenced bybasing them on the subset of most efficient banks which is unlikely to be representative ofan expected merger outcome.2

2.1. Translog, Fourier, and cubic spline cost functions

A translog cost function, typically specified as quadratic in outputs, yields scale economyestimates that permit only one local minimum for average cost across banks of varying

1 Non-parametric estimation was required in McAllister and McManus (1993), Wheelock and Wilson (2001), aswell asAdams, Berger, and Sickles (1999). While clearly feasible, non-parametric estimation has three drawbacks:(1) it is not familiar to most economists; (2) it does not produce standard errors for easy hypothesis testing, sobootstrapping procedures are needed instead; and (3) it requires the assumption that the relationship being estimatedwith non-parametric techniques is orthogonal to the rest of the econometric model when a combined approach isused.

2 There are a number of cost frontier models but the composed error stochastic frontier model typically assumesthat cost inefficiency follows a half-normal distribution such that the majority of banks are on or very close to thecost frontier. This assumption has been weakly tested and appears to be unsupported (Berger, 1993; Bauer, Berger,& Humphrey, 1993).


size. As well, since all countries have many more small banks than large institutions, costeconomies predicted for large banks will likely be underestimated when important scaleeconomies exist for smaller institutions. In minimizing the sum of squared errors, greaterweight is given to the more numerous observations on small banks. This can affect the fit ofthe entire average cost curve and reduce the accuracy of the fit and scale estimates for largebanks. This is one explanation for why the translog typically estimates a lower optimal banksize (where average cost is at its minimum) when all banks are in the sample but a higheroptimal size when only larger banks are in the sample set. Another explanation is that largerbanks enjoy greater leverage. With a lower ratio of capital to assets, these institutions enjoya lower total cost of equity for their size. Since equity costs are often excluded from theanalysis, this can understate scale effects at larger banks.

Some recent studies have addressed these issues by: (a) incorporating the cost of equityinto the analysis (Clark, 1996); (b) using a Fourier cost function which can improve thelocal identification of the average cost curve and allow for more than one local average costminimum (Mitchell & Onvural, 1996); or (c), both (Berger & Mester, 1997). We do the sameand additionally contrast scale economies obtained using the translog and Fourier formswith those derived from a cubic spline. Our cubic spline is a piece-wise, regression-based,third order polynomial approximation that has great flexibility in locally identifying scaleeffects across banks of differing size. Using a specification developed bySuits et al. (1978),it is possible to estimate the spline using standard econometric techniques (which facilitatesmodeling and hypothesis testing) rather than the usual non-parametric derivation.

The translog cost function (1) is estimated jointly withn − 1 cost share equations:

ln TC = α0 +2∑

i=1

αi ln Qi + 1

2

2∑i=1

αi,i(ln Qi)2 + 1

2

2∑i�=j

αi,j(ln Qi ln Qj)

+2∑

i=1

3∑k=1

δi,k(ln Qi ln Pk) +3∑

k=1

βk ln Pk + 1

2

3∑k=1

3∑m=1

βk,m(ln Pk ln Pm)

+ θ1 ln T + 1

2θ2 ln(T)2 (1)

Sk = βk +3∑

m=1

βk,m ln Pm +2∑

i=1

δi,k ln Qi

where TC is the total operating and interest expenses plus the imputed cost of equity capital;3

Qi,j, i, j: value of loan and security (and other asset) banking outputs; andPk,m, k, m: threeinput prices: the average interest rate paid for borrowings and retail deposits, the averageexpense per man-hour, and an approximation to the cost of physical capital (which includesthe opportunity cost of equity capital or reserves);4 T: a time indicator variable used to

3 The true cost of equity capital cannot be computed for the savings banks in our sample because their equityis not traded and they are mutually held institutions.

4 More specifically the three input prices are: price of funding (a weighted average of the price of borrowedmoney—3-month money market interest rate—and the average interest rate on deposits); average labor cost per


reflect time-related technical change; and;Sk: the cost shares for the funding and laborinputs (the share for the physical and equity capital input is deleted to avoid singularity).

The Fourier form we use adds sin and cos terms to the translog cost function. As ourmain concern is to allow for greater flexibility in the local identification of scale effects,the sin and cos terms are applied to the output (Q) measure. The Fourier form is a globallyflexible approximation since the respective sin and cos terms are mutually orthogonal overthe [0, 2�] interval. The Fourier function (2) is estimated jointly with the cost shares:

ln TC = translog cost function+2∑

i=1

(τ1i sin(ln Q∗i ) + τ2i sin(2 lnQ∗

i )

+ τ3i sin(3 lnQ∗i )) +

2∑i=1

(τ4i cos(ln Q∗i ) + τ5i cos(2 lnQ∗

i )

+ τ6i cos(3 lnQ∗i )) + τ7 sin(ln Q∗

i + ln Q∗j ) + τ8 cos(ln Q∗

i + ln Q∗j )

+ τ9 sin(2 lnQ∗i + ln Q∗

j ) + τ10 cos(2 lnQ∗i + ln Q∗

j )

+ τ13 sin(ln Q∗i + 2 lnQ∗

j ) + τ14 cos(ln Q∗i + 2 lnQ∗

j ) (2)

Sk = βk +3∑

m=1

βk,m ln Pm +2∑

i=1

δi,k ln Qi

The new terms are lnQ∗ = ln Q ·YQ+ZQ, YQ = (0.8·2π)/(max lnQ−min lnQ), ZQ =0.2π − min lnQ · YQ, andπ = 3.141593. . . , so that lnQ∗ is essentially expressed inradians.5

Like the Fourier form, the cubic spline is very flexible. In effect, a cubic polynomialbetween cost and output is fitted for each of the bank size-classes that are of interest. Thiscan comprise one size-class (all banks together) or, for even greater flexibility, separatesize-classes covering small, medium, and large banks. In our application we identify sevensize-class cutoffs, giving eight size-class intervals and eight fitted cubic polynomials. Theprocedure is somewhat similar to dividing up all banks into eight size categories and sepa-rately estimating the cost–output relationship within each category and connecting the fittedresults. Building onSuits et al. (1978), the cubic spline is expressed as:

ln TC = α0 +2∑

i=1

[αi(ln Qi − ln Qmini )

+ πi(ln Qi − ln Qmini )2 + φ1,i(ln Qi − ln Qmin

i )3]

+7∑

J=1

2∑i=1

(φJ+1,i − φJ,i)(ln Qi − ln QJi )3DJ

i

manhour; and price of physical capital and equity (both represented by capital depreciation expenditures dividedby the value of physical capital, as market values of equity are not available).

5 SeeMitchell and Onvural (1996)andBerger and Mester (1997).


+1

2

2∑i�=j

αi,j(ln Qi ln Qj) +2∑

i=1

3∑k=1

δi,k(ln Qi ln Pk) +3∑

k=1

βk ln Pk

+ 1

2

3∑k=1

3∑m=1

βk,m(ln Pk ln Pm) + θ1 ln T + 1

2θ2 ln(T)2 (3)

Sk = βk +3∑

m=1

βk,m ln Pm +2∑

i=1

δi,k ln Qi

where lnQmini is the log of the minimum value of the loan or security output variable,J

indexes the seven loan or security size-class divisions, lnQJi is the log of each of these seven

size-class divisions,6 DJi is a special dummy variable.7 Since all of the cost–output curva-

ture properties are obtained from the eight separately fitted cubic polynomial intervals inthe cubic spline, there is no need to specify the quadratic own terms 1/2

∑αi,i(ln Qi)

2

that are contained in (1) and (2). Even so, output is allowed to interact with itself in1/2

∑ ∑i�=jαi,j(ln Qi ln Qj)

2 and with input prices in (3). While many studies find lit-tle significance in the

∑ ∑δi,k(ln Qi ln Pk) quantity/price interactions, over the business

cycle variations in funding costs relative to labor expenses can affect the input mix ofliabilities between retail deposits and money market or interbank funding.8

Accurate local identification of scale economies is important when attempting to predictthe cost effect from banking mergers. Aside from changes in the average price of physicalinputs (if any), or the possibility of facing lower debt funding rates due to larger size, all theother cost effects of a merger will be reflected in a scale economy measure. This includescost reductions achieved by consolidating back and front office operations (which reduceslabor requirements and eliminates overlapping branch offices) as well as the cost effect fromrestructuring management policies and procedures (which would otherwise be captured bymeasured changes in average frontier cost efficiency). As well, our scale estimates willreflect those costs that are directly associated with size-specific changes in loan portfoliorisk and asset diversification.9

6 In addition to minimum and maximum values, the size-class cutoffs (lnQJi ) for loans are the log of: 0.204,

0.319, 0.926, 2.01, 4.09, 7.81, and 11.42 (in billions of Euros). For securities, lnQJi are the log of: 0.084, 0.307,

0.541, 0.920, 1.75, 3.61, and 7.21 (in billions of Euros).7 Let DJ = D1, D2, . . . , D7 represent seven vectors of dummy variables.D1 is zero for all loan (security)

values< 0.204 (0.084) billion and 1 for all other values.D2 is zero for all loan (security) values< 0.313 (0.307)billion and 1 for all other values. And so on following the size-class cutoffs of the previous footnote until we getto D7 which is zero for all loan (security) values< 11.42 (7.21) billion and 1 otherwise.

8 This interaction does not need a spline function. The resulting parameters (δi,k) are equivalent to the averagerelationship betweenJ output splines andJ price splines for each of the lnQi ln Pk combinations. The same holdsfor the parameterαi,j for the lnQi ln Qj interactions.

9 To the degree that larger size is correlated with cost changes from size-related changes in loan risk, assetdiversification, product mix, or even changes in frontier cost efficiency, they will properly be reflected in ourscale estimates. In this regard, we are using a more all-encompassing scale measure than that typically shown intextbooks. Identifying the exact source of these size-associated cost changes is not the purpose of this paper. Thepolicy issue we are interested in deals with cost changes associated with size changes as this will affect the pricingof banking services to the public almost regardless of their source.


1 2 3 4 5 6 7 8 9 10 11

6

6.5

7

7.5

8

8.5

9

9.5

10

Bank b (acquired bank)

Bank a (acquiring bank)

Merged bank a+b (post-merger)

Merged bank a+b (pre-merger)o

AVERAGE COST

OUTPUT

1

2

3

4

Fig. 1. Two ways to account for post mergers in panel data.

2.2. Accounting for mergers with panel data

When scale economies are present, it makes a difference how mergers are accountedfor with panel data. Assume bank a, the larger of two banks at point 2 inFig. 1, acquiresbank b at point 1. Bank a expands in size to a+ b (point 4) while bank b disappears fromthe post-merger data set. This is how mergers actually affect the reported data in what isnecessarily an unbalanced panel of all banks over time. In past studies of scale economiesusing panel data, it has been common to create a balanced panel by backward aggregatingall banks that have merged. That is, data on bank a is artificially merged with data on bankb backwards in time, giving point 3, for pre-merger periods. An alternative way to create abalanced panel would be to include only the final acquiring bank (bank a) in the sample setgoing backwards in time, artificially excluding all acquired banks (bank b).

If scale economies exist, using backward aggregation results in comparing a higherpre-merger average cost at point 3 with a lower post-merger average cost at point 4. How-ever, this merger-generated reduction in unit cost will be associated with little change inoutput level.10 Indeed, the effect will appear to be a movement toward a cost frontier ratherthan a scale effect. In contrast, by including only the acquiring bank in the sample, we willbe comparing point 2 with point 4 and any merger-generated reduction in unit cost will beassociated with the rise in output from combining banks a and b. By including only theacquiring bank in the sample the merger process will be seen as a series of output and cost“jumps” which is how it is viewed by the acquiring bank.

10 If there are no scale economies then point 3 will be the same as point 4 and there is no bias with backwardaggregation.


Our preferred approach is to only include acquiring banks in the balanced panel data set.However, if we had estimated our cost models using backward aggregated data, the scaleestimates would have shown a smaller cost reduction as a bank becomes larger. For example,if the scale estimate is 0.94 when using only acquiring banks, this estimate often becomes0.95—showing a smaller scale benefit—when backward aggregated data are used. As wereport next, we have made 24 scale estimates (three cost models times eight size-classes).Nine show reduced scale economies using backward aggregated data while five show greatereconomies. Almost all of these differences are by one percentage point (0.01). Thus, onbalance, backward aggregation of the data seems to lead to reduced scale benefits.

Except for size, merging savings banks were quite similar to the (simple or asset-weighted)average for the industry.11 Merging savings banks had, on average,7.3 billion in assetswhile the industry average was4.1 billion. Even so, they had identical ratios of totalcosts to assets (3.42%) and almost identical ratios of deposits to assets (74.7 and 75.1%,respectively), and loans to assets (65.3 and 65.8%) as did the average savings bank in theindustry. Only the ratio of losses to assets was significantly different in a means test, withmerging banks having a slightly higher ratio (i.e., 0.23 versus 0.22% for the industry). Theseresults hold for the entire 1986–2000 period as well as two sub-periods (1986–1992 and1993–2000) which capture some of the pre-merger and post-merger years for our sampleof 47 savings banks observed at 6-month intervals.12

2.3. Scale economies by bank size

Scale economies for Spanish savings banks over 1986–2000 across eight size-classes areshown inTable 1. For the translog, Fourier, and cubic spline cost functions, all point estimatesindicate economies of scale for each size-class. This differs from earlier results for the U.S.(McAllister & McManus, 1993; Wheelock & Wilson, 2001) which showed a U-shaped aver-age cost relationship (indicating scale diseconomies) for the largest banks using the translogform.13 However, although all translog scale estimates are significantly different from 1 orconstant average costs, many estimates from the Fourier and the cubic spline are not.14

11 Spanish savings banks are mutual organizations. Although they do not have private shareholders, they competewith each other and commercial banks in a liberalized and open financial market (since the late 1980s). Asdemonstrated inAltunbas, Carbo, and Molyneux (2003), mutual and co-operative organizations in Europe aregenerally just as or slightly more cost efficient than commercial banks.

12 Savings banks collected fee income and provided off-balance-sheet services (but on a smaller scale thanoccurred at commercial banks). Expenses associated with these activities are captured in our cost measures.

13 Another difference is that including the cost of equity in total cost lowers the estimated scale effect. If thescale elasticity is 0.95 when equity is included (equivalent to reserves for savings banks), the elasticity more oftenthan not falls to 0.94 or 0.93 when equity cost is not included in total cost. This is the opposite of results obtainedfor the U.S. (cf.Hughes, Mester, & Moon, 2001) where equity holdings tend to decline as a percent of total costas a bank becomes larger (lowering cost). Starting from the very smallest institutions in Spain, equity holdings asa percent of total cost first fall, then experience a long rise (raising costs), and only fall again for the very largestsize-class.

14 These tests relied upon a bootstrapping procedure (Johnston & DiNardo, 1997). The percentile method wasused to construct the 95% confidence interval in a single tail test of difference from 1. Bootstrapping was usedsince we wish to show the average scale effect across all banks rather than an output weighted average which overrepresents large banks.


Table 1Elasticities of total costs to total loans and securities

Size class Asset size (billions) Translog Fourier Spline N

1 Minimum–0.3 0.94∗ 0.94 0.92∗ 1332 0.3–0.6 0.95∗ 0.93∗ 0.93∗ 833 0.6–1.5 0.96∗ 0.93∗ 0.94∗ 3654 1.5–3.0 0.95∗ 0.96 0.96 3695 3.0–6.0 0.95∗ 0.95∗ 0.95∗ 2336 6.0–12.0 0.95∗ 0.92∗ 0.94∗ 1477 12.0–18.0 0.95∗ 0.95 0.90 288 18.0–maximum 0.96∗ 0.96 0.90 52

Total sample 0.95∗ 0.94 0.94∗ 1410All loans 0.68∗ 0.68∗ 0.68∗ 1410All securities 0.27∗ 0.27∗ 0.26∗ 1410

The asterisk (∗) indicates a scale elasticity significantly different from 1 at the 95% level of confidence in a singletail test. Parameter estimates are given inAppendix A.

At the mean of the data, scale economy point estimates for loan and security outputs arevirtually identical (at 0.94–0.95) across the different cost functions, as are the output-specificcost elasticities for loans (0.68) and securities (0.27) separately.15 The mean marginal cost ofmaking and monitoring a loan is0.094 for each Euro of loan extended while the marginalcost of purchasing and holding securities is0.066 for each Euro of securities held. If oneis only interested in the scale effect at the mean of the data, then any one of the three costfunctions can be used as each gives almost the same result.

It is also tempting to conclude that the apparent similarity of the scale estimates in manysize-classes also means that there is little difference between the cost functions. However,it turns out that small percentage point differences in scale estimates across different costfunctions can lead to sometimes large differences in bank return on assets or ROA (a measureof profitability). For example, take the one percentage point difference in the mean scaleeconomy estimate between the translog (0.95) and the spline (0.94). A merger that increasesthe size of the mean bank by 50% will, with a scale estimate of 0.95, generate a 13% rise inROA.16 In contrast, if the scale estimate was only one percentage point lower at 0.94, the rise

15 Our scale results are robust to using a weighted average of the realized return on loans and securities as theopportunity cost of a bank’s physical and financial capital. Use of this alternative price (in place of our capitaldepreciation measure—see footnote 4) reduces the scale economy benefit for some size-classes by one percentagepoint for the Fourier and cubic spline functions (but not the translog). A referee suggested that a shadow price forphysical and financial capital be used instead. This could be obtained from a variable cost function where capitalis treated as “fixed” in the short-run. Unfortunately, the mean value of the resulting shadow price was negativeand the variable cost function was not concave. As the mean value of either of our approximate prices of physicaland financial capital were positive (10.6% for our capital depreciation measure and 9.4% for the average returnon loans and securities) and our total cost specification was always concave, we did not use the variable costformulation nor its associated shadow price.

16 As mean total cost (TC) is 324.6 million and mean total assets (TA) are4087 million, the weightedaverage value of average cost is0.07942 per Euro of assets. A merger that increases the size of the mean bank by50% reduces post-merger average cost to 0.07810 (from (TC+ 0.95(0.5)TC)/(TA+ (0.5)TA), where 0.95 is thescale elasticity). The merger will have reduced unit cost by 1.662% which reduces the TC/TA ratio by 0.00132.


Table 2Rise in return on assets from a 50% increase in size

Size class Asset size (billions) Translog Fourier Spline

1 Minimum–0.3 19% 20% 25%2 0.3–0.6 15 20 213 0.6–1.5 13 20 194 1.5–3.0 14 10 125 3.0–6.0 13 13 136 6.0–12.0 12 20 157 12.0–18.0 10 11 238 18.0–maximum 9 11 27

Total sample 13% 15% 16%

4 5 6 7 8 9 10 11

0.065

0.070

0.075

0.080

0.085

0.090

0.095

0.100

0.105

0.110

ln(Total Assets)

Fitted Cubic Spline (solid line)

Fig. 2. Predicted average cost of loans and securities from a cubic spline (input prices and technical change heldconstant at mean values).

in ROA would be 16%. While these two scale estimates may not be significantly different ina strict statistical sense, merger decisions are made using point estimates without statisticaltesting.17 Applying the same calculation procedure to the scale estimates ofTable 1, weshow the implied increases in ROA if the (weighted) mean bank in each size-class entereda merger that expanded its size by 50%. The implied changes in ROA shown inTable 2are at times quite different depending on the cost function used to determine the scale

If the ROA is 0.01, this cost reduction will increase ROA by 13% (if passed on entirely to profits). Lower ROAs,which are more typical, would raise this percentage.

17 Indeed, given the diverse outcomes experienced for mergers to date, it is unlikely that pre-merger cost savingestimates would ever be statistically significant.


elasticities. Thus, small differences in scale economies nevertheless lead to changes in unitcost sufficient to have an important impact on bank profitability.

A detailed picture of how unit cost varies with savings bank size (the log of total as-sets) is presented inFig. 2. The scatter diagram shows the predicted values of average costfrom the cubic spline estimation (3) for 47 banks over 1986–2000. The predicted values donot form a single line since the output mix between loans and securities varies across thesample.18 The solid line in the figure shows how a cubic spline would fit these predictedvalues. It is clear that predicted average cost falls rapidly until the log of assets reaches 7( 1.1 billion), is relatively flat up to 8 (3.0 billion), falls rapidly again after 9 (8.1 bil-lion), rises somewhat after 10 (22.0 billion) and then falls again. It is this variation that weare interested in and use next to provide predictions of changes in average cost associatedwith individual mergers. This prediction will depend on the size of the merging acquir-ing bank pre- and post-merger (which is more precise than using the mean size-classes ofTable 1).

3. Merger cost effects from scale economies

3.1. Predicting merger cost effects

When bank a acquires bank b in yeart, the reported data for yeart will contain thebalance sheet items, cost, and income statements of the new larger bank—bank a+ b.For yeart − 1 and all previous years the reported data contains separate information forbanks a and b as they were prior to their merger. In order to predict ex ante the costeffects of this merger we artificially merge banks a and b in yeart − 1 in a separateunbalanced panel data set. This gives us the level of loan and security outputs. Thesevalues are then used to determine the predicted average cost of a representative bank ofsize a+ b in t − 1 based on our balanced panel estimation from the translog, Fourier, andcubic spline cost functions. The same procedure is followed to determine the predictedaverage cost of a representative bank with an output level of the size of bank a in yeart − 1.19

More formally, letf(·) represent the mapping of outputs, input prices, and technology tothe total cost of a bank the size of bank a alone in yeart − 1 and then to the size of a bankthe size of a+b in the same year. Using this estimated mapping the predicted average costsare:

ACa,t−1 = f(Q1,a,t−1, Q2,a,t−1, Pa,t−1, Tt−1)

Q1,a,t−1 + Q2,a,t−1

ACa+b,t−1 = f(Q1,a,t−1 + Q1,b,t−1, Q2,a,t−1 + Q2,b,t−1, Pa,t−1, Tt−1)

(Q1,a,t−1 + Q1,b,t−1) + (Q2,a,t−1 + Q2,b,t−1)

18 This variation can not be attributed to changes in input prices or technical change over time as these variablesare held constant at their mean value inFig. 2.

19 Note that yeart in each case is the actual year of the merger. Thus, the average level of input prices andtechnical change will also refer to yeart − 1 (rather than to the mean of the entire sample as inFig. 2).


Table 3Predicted effect on average cost from mergers (PctAC)

Translog Fourier Cubic spline

Percent change in AC (PctAC) −0.69% −0.66% −1.00%Number of AC increase (+) 8 8 9Number of AC decrease (−) 14 14 13Percent change total cost 49.6 48.0 46.3Percent change total output 48.5 48.5 48.5Marginal scale economy 1.02 0.99 0.96Implied rise in ROA 6.0 5.7 8.7

The predicted percent change in weighted average cost (AC) due to scale effects from all 22 mergers togetheris shown in the first row (calculated from(ACa+b,t−1 − ACa,t−1)/ACa,t−1. The number of negative (positive)changes indicate the number of bank mergers that are predicted to reduce (increase) average cost. Percent changesin total cost and total loan plus security outputs refer to the sum of all 22 mergers. Dividing the former by thelatter gives a marginal scale economy value that refers to the predicted overall merger effect.

The percent change in average cost predicted to be associated with the scale effect of amerger is:

PctAC= (ACa+b,t−1 − ACa,t−1)

ACa,t−1× 100

where inQi,h,t−1, i = 1, 2; h= a, b, is the quantity of outputi of bank h in yeart − 1, andPa,t−1 is the vector of input prices of bank a in yeart − 1. Hence ACa,t−1 is the predictedaverage cost of bank a before the merger, and ACa+b,t−1 is the predicted average cost ofbank a assuming it—1 year ahead of the actual merger—had reached thejoint size of thetwo merging banks a+ b. In calculating both ACa,t−1 and ACa+b,t−1 we use the inputprice vectorPa,t−1 and so disregard any effect on input prices from the merger due toincreased market power or change in funding composition. Thus, what we consider here isa broad economies of scale effect. PctAC is calculated using each of the three cost functionspecifications, translog, Fourier, and cubic spline. Negative values predict a reduction inaverage cost while positive values predict a rise.

Our data set contains usable data on 22 Spanish savings bank mergers that occurred atvarious times during 1986-2000. For these 22 mergers we calculate the predicted percentchange in average cost for all merging banks as a group due to scale effects (PctAC) asdescribed above.20 Our average results are reported inTable 3.

20 To reflect the different predicted total cost (TC) and output levels (Q) among merging banks, weighted averagecost in Table 3 is computed from a ratio of averages:

(∑22r=1TCa+b,t−1,r/

∑22r=1Qa+b,t−1,r

)−

(∑22r=1TCa,t−1,r/

∑22r=1Qa,t−1,r

)

∑22r=1TCa,t−1,r/

∑22r=1Qa,t−1,r

wherer refers to the merger number. A simple average of 22 average cost values (an average of ratios as in∑22r=1[(ACa+b,t−1,r − ACa,t−1,r)/ACa,t−1,r ] would weight all merging banks equally even though their effect on

industry cost is different.


For all three cost functions, the predictedaverage effect of 22 mergers is that unit costmay fall by from 0.66 to 1%. Although from 8 to 9 mergers are predicted to raise unit cost,this is offset by the 13–14 mergers that may lower cost.21 As noted in the last row ofTable 3,if this average cost reduction were realized, and if each merging bank had a return on assetsof 0.01, the reduction in unit cost would translate into an average rise in ROA of from 5.7 to8.7%. The predicted change in unit cost and ROA from the 22 mergers is much lower thanthat illustrated inTable 2for three reasons. First, although the average change in bank sizedue to mergers is 48.5% (Table 3) and thus is similar to the 50% size change assumed forTable 2, there was considerable dispersion about this mean. Indeed, 10 mergers expandedthe acquiring banks’ size by less than 50% while 5 others expanded their size by more than100%. Second, the figure shown is the average predicted reduction in unit cost from scaleeconomies and combines predicted increases with predicted decreases in unit cost. Third,17 out of the 22 merging banks were in the area of the cost curve inFig. 2 that is closestto constant cost and thus relatively small scale economies. Specifically, for 17 banks theirpre- and post-merger size was within the range where the log of total assets was higher than7 ( 1.1 billion) but below 9 ( 8.1 billion) in Fig. 2.

3.2. Actual merger cost effects

We estimate the cost effect of a merger by first determining how average cost at a mergingbank has changed between two 6-month periods prior to and two 6-month periods duringand after the merger. This comparison should minimize the inclusion of cost changes un-related to the merger. However, since some have suggested that including the period of themerger may also include some “temporary” merger-related transition expenses, we skipthe two 6-month periods during and after the merger and instead compute the post-mergeraverage cost from the following two 6-month periods. In the first case, there is no transitionperiod while in the second there is as much as a one-year transition between the pre- andpost-merger unit cost calculations.22

The percent change in average cost for each merging bank is then compared to thepercent change in average cost for the banking industry as a whole between the same twosets of 6-month periods.23 If average cost for all banks falls by 1% (say during a periodwhen interest rates are falling) while average cost for a merging bank falls by 3% then itis presumed that actual average cost at the merging bank experienced a net reduction of2% (actually, two percentage points). The maintained hypothesis is that changes in costsexperienced by the industry will also be experienced to an equal degree by the mergingbank.

21 Using a bank-specific weighted average of the return on loans and the return on securities in place of ourcapital depreciation measure would change the first row in Table 3 to−0.71,−0.93, and−1.35%, respectively.This gives a slightly greater expected cost reduction from a merger. Only for the cubic spline are the number ofAC increases/decreases altered (from 9 and 13 in Table 3 to 7 and 15, respectively) with this alternative measureof the (opportunity) cost of physical and financial capital.

22 Due to a lack of data, the inclusion of a transition period meant that two mergers that occurred in the firsthalf of 2000 had to be deleted, leaving 20 mergers rather than 22.

23 Average cost for the banking industry is the ratio of all banks’ cost for a period divided by all banks’ valueof loan plus security output (a ratio of averages—not an average of ratios).


Table 4Frequency of actual and predicted change in average cost for 22 individual mergers

Percent change in bank size 0–25% 25–50% 50–75% 75–100% 100–150%

Number of mergers 5 5 4 4 5

Frequency

Percent change in average cost Actual 1 Actual 2 Translog Fourier Spline

10 to 15 2 45 to 10 6 4 1 11 to 5 4 4 3 5 30 to 1 2 1 5 2 5

0 to−1 2 1 2 3 2−1 to−5 4 2 12 8 11−5 to−10 1 2 3−10 to−15 1 2

The column labeled Actual 1 has no transition period for the pre- and post-merger average cost change calculationfor 22 mergers. The column Actual 2 has a one-year transition and covers 20 mergers.

This procedure was applied separately for each of the 10 different 6-month periods thatour mergers occurred. The frequency distributions of the estimated change in actual averagecost using no transition period (Actual 1) and a one-year transition period (Actual 2) areshown inTable 4, along with the frequency distributions of the predicted changes from thetranslog, Fourier, and spline functions. The top ofTable 4shows the percent changes in loanplus security output associated with mergers. The average change in size from a merger is64% in Spain and has been around 50% in the U.S. (cf.Berger & Humphrey, 1992).

Merging banks have (to our knowledge) never announced that their proposed merger wasexpected to increase costs. Indeed, merger announcements and materials presented to com-petition authorities in their defense emphasize the positive aspects expected to be associatedwith a merger. These concern expected cost savings, planned expansions in service mix, andthe need to become larger to better serve domestic markets and/or address international com-petition. In our case, the estimated changes in actual average cost increased more often thanthey decreased (rising in 14 or 13 cases, falling in 8 or 7 cases). Our predictions essentiallyare the reverse. That is, we predict more decreases (13–14 cases) than increases (8–9).

Although merger participants predict that all mergers will lower expenses, only 8 out of22 (or 7 out of 20) seem to actually succeed in reducing their unit costs. Thus, in only aboutone-third of the mergers are the participants themselves able to accurately predict the signof the cost change. As we only predict that the majority (13–14) of mergers will realizecost reductions, our predictions are less optimistic than those of the participants. Even so,we too are only successful in predicting the sign of the merger cost effect (up or down) inabout one-third of the cases.24

24 This holds especially for the largest mergers. The seven largest mergers in absolute terms accounted for 64%of the total change from all mergers. Predictions from the cubic spline suggested that all seven would reduce costswhile the translog predicted six cost reductions and the Fourier predicted five. In contrast, only in two or threecases out of seven did average cost apparently actually fall.


That not all mergers reduce costs is well-known to banking consultants. This conclusionwas reinforced in a recent detailed case study of bank mergers in the U.S. Nine mergersamong large banks were selected because of a strong prior expectation for being successful,although only four of the nine succeeded in reducing unit cost (Rhoades, 1998). Drawingon the experience of banking mergers in other countries, unexpected outcomes—due topoor planning, back office data processing and integration difficulties, and a poor fit ofmanagement cultures—are not uncommon and, as seen here, make predictions regardingindividual mergers difficult.

3.3. Predicting the average effect of mergers

If we can not do better than a coin flip in predicting the apparent direction of the costchange for individual bank mergers, perhaps we can do better in predicting theexpectedvalue of the actual change in cost from mergers in general. The average predicted percentchange in merger-related average cost for the three cost functions was shown at the top ofTable 3. For the translog, Fourier, and cubic spline, these were, respectively,−.69,−.66,and−1.00% suggesting that, on average, the expected change in merger-related unit costlies between a 0.6 and a 1% reduction.25

The distribution of estimated changes in actual average cost associated with mergers wasshown inTable 4(Actual 1 and 2). These estimated actual cost changes are now weightedby the share that each merger’s change in output is of the total change in output for allmergers. This shows how important each merger’s cost change is relative to all mergersand generates the distribution shown inFig. 3.26 Each bar shows the number of mergersassociated with the output share weighted cost change on theX-axis. The estimated density(solid line) is skewed to the left. Using Actual 1, which has no transition period, the outputweighted average cost effect of all 22 mergers has been to raise unit cost by 0.07%. UsingActual 2, which can have a one-year transition period and is shown inFig. 3, the weightedaverage effect of 20 mergers has been to lower unit costs by−0.95%.27

The bulk of the actual merger-related cost changes inFig. 3are centered about zero. Thisfact, and the small absolute changes actually experienced, yield the result that none of the20 merger cost changes shown inFig. 3are significantly different from zero, although thelargest negative and largest positive values were significantly different from each other.28

25 Or a 0.71 to 1.35% reduction using a bank-specific weighted average of the return on loans and securities asthe opportunity cost of physical capital and equity.

26 A single observation inFig. 3 can be expressed as((ACpost − ACpre)/ACpre)m − ((MACpost −MACpre)/MACpre) where ACpre refers to pre-merger average cost, similarly for ACpost, form = 1, . . . ,20 merging banks. The mean pre-merger average cost for all 47 banks is MACpre= ∑

TCi/∑

Qi and similarlyfor MACpost.

27 A simple average of the unit cost changes is 2% but this does not give us an accurate picture of the overalleffect of mergers on industry cost. Only 20 mergers are included inFig. 3as two mergers occurring in the first 6months of 2000 did not have sufficient data for the post-transition, one-year post-merger period.

28 An approximate standard error for each of the 20 statistics inFig. 3was obtained by bootstrapping((ACpost−ACpre)/ACpre)m −((MACpost−MACpre)/MACpre)i for one value ofm but all 47 values ofi, giving 20 samplesof 47 observations each. The bootstrapped standard errors were used to form a 95% confidence interval about eachof the 20 merger cost change statistics.


-4.0 -3.5 -3.0 -2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5

0.2

0.4

0.6

0.8

1.0

1.2

11

11

4

3

Estimated

Density(solid line)

RelativeFrequency

Fig. 3. Relative importance of changes in merger-related unit cost.

This is not surprising since almost all studies of the cost effects of mergers have found thatthese effects can be positive or negative and are usually absolutely small. When submittinginformation to support approval of a proposed banking merger, the participants give onlypoint estimates. They do not test for statistical significance. In what follows, we do thesame. If costs are found to fall or rise after a merger, it is little consolation ex post to knowex ante that the expected outcome may be statistically insignificant—losses or gains willstill be realized.

The average reduction in unit cost is driven by the fact that the largest merger experienceda pre- to post-merger net reduction in unit cost, relative to the industry, of 11%. This onemerger accounted for 28% of the total change in output associated with all mergers andwas three times the size of the next largest merger. If we exclude this merger and another“outlier” that experienced the greatest rise in unit cost, then the cost effect of mergers isseen to be approximately centered on zero. While strong cost effects from a single largemerger can have a marked impact on the average, it is also the case that choice of the lengthof the transition period matters. For example, recalculating the data underlyingFig. 3usinga two-year (rather than a one-year) transition period suggested that the net reduction inunit cost was only−0.05% (not−0.95%). Since certain temporary costs are known to beassociated with a merger, it is important to have a transition period. Taking the average ofour one- and two-year-transition period results, the net effect of savings bank mergers inSpain has been to reduce unit cost by 0.50%. Although small, if this cost reduction waspassed on entirely to profits, ROA could rise by 4%.29

29 As reported in an earlier footnote, the weighted average value of average cost was0.07942 per Euro ofassets. If this unit cost fell by 0.50% and the existing return on assets was 0.01, ROA could rise by 4%.


Overall, it seems safe to conclude that savings bank mergers in Spain succeeded in re-ducing unit cost. As well, the predicted expected value of this reduction from any one ofthe three cost function models inTable 3are not far from our estimate of what was likelyexperienced. While the cost models do a poor job in predicting the cost effect from anindividual merger, they do a better job in an expected value context. We now explore rea-sons why some mergers may have succeeded in reducing expenses while others apparentlyhave not.

3.4. Explaining cost changes at merging banks

Based on case studies (e.g.,Rhoades, 1998), unit cost after a merger can be reducedby eliminating overlapping branch offices, reducing the number of workers per office,expanding deposits per office, substituting ATMs for offices, realizing scale economies inprocessing operations, and learning how to make a later merger work based on experiencefrom an earlier one. These are influences we can measure.

Using two regression-based approaches (not shown), we attempted to identify whichinfluence among the five listed above may best explain the change in relative average costfor our 22 merging banks pre- to post-merger. The cost change and all variables noted wereexpressed relative to changes experienced for the industry as a whole for the same pre- andpost-merger time periods for each merger. As reported in a working paper (same title), ourresults were disappointing.

Only the scale variable and the number of prior mergers (a “learning curve” effect) werestatistically significant, but only at the 90% level of confidence. The overall explanatorypower was weak (adjustedR2 = 0.09). While these results are consistent with viewsexpressed by banking consultants in the popular press, we had hoped to explain more of thevariation. Apparently, influences that strongly determine merger cost outcomes are related tothings we can not easily measure such as poor integration of data processing and back officeoperations, the exit of competent managers, power struggles when management culturesare not well matched as well as perhaps an overly optimistic view of what can actually beachieved in a merger.

4. Summary and conclusions

Mergers and acquisitions have been the primary way in which currently large bankshave become large. Public announcements of mergers invariably note that unit costs areexpected to fall with the merger, primarily by achieving a larger scale of operation. Whilescale economies do in fact exist in many services offered by banks, not all bank merg-ers have experienced cost reductions. Indeed, on average, most studies find that unit costsare little changed. However, the vast majority of these studies have been for U.S. banks.We investigate the cost effects of banking mergers over 1986–2000 for savings banksin Spain, a country with a different regulatory, branch, and payment structure thanthe U.S.

Our goal is to accurately predict the merger-related cost effects of over 20 individualbank mergers. While the translog cost function is most often used in these exercises, it is


possible that greater accuracy in determining scale effects may be achieved with an evenmore flexible form. Thus, we also estimate Fourier and cubic spline cost functions andcompare these results with those from the translog.

These cost predictions are then compared to an estimate of how costs have actuallychanged at each merging bank, after controlling for cost changes affecting all banks. Thegood news is that our cost predictions for individual mergers are about as good as thosemade by merger participants themselves. The bad news is that they and we only correctlypredict the sign of the merger-associated cost change one-third of the time. While somemergers apparently reduced unit cost by 11%, others experienced cost increases of a similarsize. On balance, most of the mergers experienced small negative or positive changes inunit cost centered about zero.

In attempting to “explain” why some mergers were successful while others were not, weconfirmed that merger-associated changes in unit cost are negatively related to the expansionof output from a merger. As well, banks engaging in more than one merger seem to learnfrom their experience. Thus, the major determinants, among those we can measure, arescale economies and learning by doing.

We do a better job in accurately predicting the average or expected value of the cost effectfor all mergers as a group. As an output weighted average, the set of mergers we examinesucceeded in reducing unit cost by about 0.50%. If this cost benefit were entirely passedon to profits, the return on assets would rise by 4%. Overall, these mergers have apparentlyimproved resource allocation, although not by much. Our results suggest that there is a pre-sumption for small cost benefits from mergers on average but efforts to accurately predict thecost effect for an individual merger—by participants or academics—are likely to be incor-rect in sign. Even so, a merger is more likely to be successful if it is large (greater potentialfor scale benefits) and is being initiated by a bank that has merged before (learning effect).

Acknowledgments

We thank the financial support received from the “Ayudas a la Investigación en las areasde Economia, la Demografia y Estudios de Poblacion y los Estudios Europeos” of theFundacion BBVA in the project “Integracion, competencia y eficiencia en los mercadosfinancieros europeos.” Santiago Carbo also acknowledges the research grant received fromSEC2002-0034 of MCYT and FEDER.

Appendix A. Parameters for the translog, Fourier and cubic spline cost functions

All estimated cost functions met the output regularity condition for each size class(non-negative predicted marginal costs) as well as the overall price regularity condition(cost function concavity). The number of observations was 1410 in the pooled set of 50 sav-ings banks observed over 1986–2000 at 6-month intervals. The log likelihood was 6767.57(translog), 6807.87 (Fourier), 6802.16 (cubic spline). Standard errors were computed froma heteroskedastic-consistent matrix (Robust–White) and the Durbin–Watson statistics are:1.70695 (translog), 1.74803 (Fourier), 1.74308 (cubic spline).


Translog Fourier Cubic Spline

Parameter Estimate Parameter Estimate Parameter Estimate

α0 0.3858∗ α0 −24.8731∗ α0 15.1627∗α1 0.6294∗ α1 2.8683∗ α1 1.5819∗α2 0.3713∗ α2 2.8194∗ α2 1.3028∗α11 0.1392∗ α11 −0.0517 π1 0.1224∗α22 0.1343∗ α22 −0.0839 π2 0.0716α12 −0.2664∗ α12 −0.2646∗ α12 −0.1343∗β1 0.8337∗ β1 0.8363∗ β1 0.8365∗β2 0.1040∗ β2 0.1040∗ β2 0.1009∗β11 0.2071∗ β11 0.2075∗ β11 0.2072∗β22 0.1003∗ β22 0.1021∗ β22 0.1026∗β12 −0.1056∗ β12 −0.1070∗ β12 −0.1069∗θ1 0.0185 θ1 0.0215 θ1 0.0213θ2 −0.0385∗ θ2 −0.0390∗ θ2 −0.0381∗δ11 0.0233∗ δ11 0.0238∗ φ11 −0.968E−02δ12 −0.0210∗ δ12 −0.0219∗ φ21 0.0632δ21 −0.151E−02 δ21 0.129E−02 φ31 −0.0135δ22 −0.570E−02 δ22 −0.547E−02 φ41 −0.0181mdum −0.0162 τ11 0.0474 φ51 0.0412

τ21 0.0783 φ61 −0.1151∗τ31 −0.0310 φ71 0.3594∗τ12 0.0793 φ81 −0.1497∗τ22 0.0950∗ φ12 0.398E−02τ32 0.0267 φ22 −0.0296∗τ41 1.0215∗ φ32 0.0955∗τ51 0.1937∗ φ42 −0.0537τ61 0.0290 φ52 0.341E−02τ42 0.9609∗ φ62 −0.0311τ52 0.2233∗ φ72 0.1334∗τ62 0.0736 φ82 −0.2575∗τ7 −0.1142 δ11 0.0236∗τ8 −0.0414 δ12 −0.0223∗τ9 0.0461 δ21 0.142E−02τ10 0.0492 δ22 −0.497E−02τ13 −0.0192 mdum −0.0185τ14 −0.0637mdum −0.0231

∗ Significantly different from zero at the 95% level of confidence.


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predicted and actual costs from individual bank mergers

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