The random stochastic cost frontier and policy implications:

Evidence from the Mexican banking sector, 1998-2006

Carlos Pestana Barros a; Nicolas Peypoch b and Jonathan Williams c

a Instituto Superior de Economia e Gestão, Technical University of Lisbon, Rua Miguel Lupi, 20,1249-068

Lisbon, Portugal, cbarros@iseg.utl.pt

b GEREM, Département des Sciences Economiques et de Gestion, Université de Perpignan, 52 avenue Paul

Alduy, F-66860 Perpignan, France, peypoch@univ-perp.fr

c Centre for Banking and Finance, Business School, Bangor University, Bangor, Gwynedd, UK, LL57 2DG.

jon.williams@bangor.ac.uk.

Abstract

A random stochastic cost frontier model is specified for a sample of Mexican banks operating

between 1998 and 2006. Our results show that the random frontier accounts for heterogeneity

between banks, which can be explained by variation in bank outputs. The non-random frontier

performs poorly and confounds heterogeneity with inefficiency. We demonstrate that the

choice of frontier model influences the design of public policy. Following Berger et al (2005),

we create a set of indicators to identify changes in bank governance. The relationships

between changes in bank governance and bank cost confirm that the consolidation process

significantly lowers costs at Mexican banks with foreign bank acquisition of domestic banks

lowering costs more effectively than domestic M&A. Our results support the decision made

by the Mexican authorities to change policy in 1995 and to facilitate foreign bank penetration.

Keywords: Mexico, banks, random frontier, foreign banks.

JEL Classification: G21, D24, C23

Corresponding author: J. Williams, Business School, Bangor University, Bangor,

Gwynedd, UK, LL57 2DG. jon.williams@bangor.ac.uk

2

1. Introduction

Typically, firm-level inefficiency can be measured as the deviation of each unit from a best

practice frontier that represents the underlying technology of an industry. Frontiers are

constructed using either parametric methods like stochastic frontier analysis (see Aigner et al,

1977; Battese and Corra, 1977; Meeusen and van den Broeck, 1977), or non-parametric

methods like data envelopment analysis (see Farrell, 1957; Banker et al, 1984). Some studies

suggest that the specification of best practice frontiers should accommodate heterogeneity

between firms because failure to do so may “seriously distort” inefficiencies (Greene, 2005a,

p. 270; Mester, 1997; Orea and Kumbhakar, 2004). There is the additional concern that policy

design may be faulty if policy recommendations are drawn from a mis-specified frontier. To

account for these anomalies, a recommended solution is to estimate the random stochastic

frontier (see Greene, 2005a, b).

Our objectives in this paper are two-fold. First, we estimate both random and non-random

stochastic cost frontiers to quantify the confounding effect on heterogeneity on inefficiency

and to determine the preferred model. Second, we wish to identify how effective each model

is in evaluating public policy. Our application is to the Mexican banking sector over the

period from 1998 to 2006. Following the 1994 Tequila crisis, the Mexican authorities carried

out a second round of bank privatisation and allowed foreign banks to participate. The

resulting increase in the level of market concentration has been driven by foreign bank

penetration. Foreign banks captured the Mexican market at a faster pace than in any other

country and now control more than 80% of banking sector assets. In our frontier model we

specify a set of governance indicators (suggested by Berger et al, 2005) that are expected to

show the effect of changes in bank governance resulting from consolidation on bank cost. The

estimated parameters on the governance indicators can determine the effectiveness of policy.

From a policy standpoint, foreign bank penetration can not only recapitalise troubled

domestic banks, but there are expected efficiency gains to consider (see Clarke et al, 2003).

Foreign bank entry, via competitive effects, should condition domestic bank behaviour with

abnormal profits competed away and lower overhead costs (Claessens et al, 2001). In short,

policymakers expect foreign bank penetration to improve domestic banking sector efficiency,

Claessens and Jensen (2000). However, foreign banks face diseconomies when operating

subsidiaries at distance that may prevent the efficient operation of foreign-owned banks

3

(Berger et al, 2000).1 Also, it is suggested that the stake of foreign owners needs to very high

(over 70%) if cost efficiency gains are to be achieved at acquired domestic banks that require

restructuring (Claessens and Jansen, 2000). Evidence on foreign acquisitions of domestic

banks in Latin America suggests bank efficiencies are affected, because of the assimilation of

the subsidiary into parent bank processes and adoption of strategies designed to raise asset

quality (Crystal et al, 2002).

Our approach is to apply the random stochastic cost frontier model to determine the

underlying cost structure of a panel of Mexican banks between 1998 and 2006. We use

quarterly financial statements sourced from Comisión Nacional Bancaria y de Valores

(CNBV), the Mexican banking and securities commission. The data commence in March

1998 and end in December 2006. So far as we are aware, the random frontier model is applied

in one other study of the banking industry, an application to US banks (Greene, 2005a). Our

results are expected to indicate the merit of policy-induced changes in bank ownership

structure and governance that have occurred since 1997.

The remainder of the paper is organised as follows: in Section 2, we describe developments in

the Mexican banking sector. In Section 3, we present the theoretical framework whilst the

preferred model and data are set out in Section 4. In Section 5 we present and discuss the

results and finally, section 6 offers some conclusions.

2. Developments in the Mexican banking sector

The Mexican banking sector has had to contend with major changes mainly resulting from

episodes of financial crisis. In response to the onset of the debt crisis in 1982 commercial

banks were nationalised. A process of bank restructuring followed that sought to realise

economies of scale by reducing the number of banks from 60 to 18 between 1982 and 1991.

This policy of consolidation created an oligopoly with the largest three banks holding 60% of

banking sector assets (Montes-Negret and Landa, 2001).

The first of two bank privatisation programmes began in 1991. The 1991 privatisation

programme failed abruptly with the onset of the Tequila Crisis in 1994-95. The crisis revealed

1 Operational diseconomies associated with distance are heightened by barriers relating to the following: culture, language, currency, the host regulatory and supervisory structure, and explicit and/or implicit rules against foreign banks (Berger et al, 2000).

4

serious problems in the banking sector which a combination of weak property rights and

ineffective bank regulation failed to prevent imprudent behaviour by newly privatised banks

(Haber, 2005). Compounding problems was the fact that banks had been sold at inflated

prices which caused the new (and often inexperienced) owners to assume higher risks (see

Hoshino, 1996; Montes-Negret and Landa, 2001; Haber, 2005). The 1991 privatisation

process failed to the tune of a bail-out costing an estimated $65 billion (Haber, 2005). Unlike

bank privatisation in Argentina and Brazil, the 1991 Mexican programme restricted foreign

banks from entering the auctions. After the 1994-95 financial difficulties, the authorities

liberalised the treatment of foreign ownership of domestic banks in the second round of bank

privatisations. The result was a large-scale transfer of bank ownership from domestic to

foreign hands with foreign banks acquiring nearly all of the large domestic-owned banks.

There are three phases of foreign entry into the Mexican market (Haber and Musacchio,

2005). The first phase is 1991 to 1995 and it is characterised by foreign banks establishing

representative offices or subsidiaries in Mexico, which were mainly small institutions

specialising in investment banking. The second phase took place in 1996 during which time

the 1991-95 foreign entrants acquired small domestic banks and entered the retail market. At

this time, the proportion of banking sector assets held by foreign banks stood at 4%. The third

phase, and the phase covered in this paper, is 1997 to 2004. The 1995 repeal of restrictions on

foreign bank entry became effective in 1997 allowing foreign banks to acquire the large

domestic banks. By 2004, foreign banks controlled 82% of banking sector assets up from 16%

in 1997; the increase in foreign bank penetration raised the level of market concentration with

the largest five banks owning 83% of assets in 2004 compared to 75% in 1997 (Schulz, 2006).

However, the rise in concentration has not weakened competition in the Mexican banking

sector (Yeyati and Micco, 2007; Yildirim and Philippatos, 2007; Gelos and Roldós, 2004).

There is evidence of “supercompetition” in the market, which implies that banks produce at

output levels where marginal cost exceeds marginal revenue as banks take current losses in

exchange for expected market share (Gruben and McComb, 2003).

Several benefits accrued from foreign bank penetration in Mexico. A major benefit was the

recapitalisation of the banking sector after the collapse in 1994-95: between 1997 and 2004,

foreign banks increased sector capitalisation by over US$8.8 billion or 42% of total banking

sector capital in 2004 (Schulz, 2006). Improvements in accounting standards and better

screening of borrowers realised cost savings via reduced default rates, that were returned to

5

customers through narrower interest margins, and which positively affected asset quality and

accelerated the reduction of bad debt. Lower administrative costs at foreign banks released

downward pressure on such costs across all banks. In other words, foreign bank entry altered

domestic bank behavior which fostered improved bank efficiency (Haber and Musacchio,

2005). The view that foreign bank entry raised efficiency has been challenged with claims that

the effect was limited because the low level of competitive intensity in the banking sector

lowered pressures for banks to improve operational efficiency (Schulz, 2006). The problems

associated with enforcing property rights remains an impediment to which foreign banks have

responded by being more risk averse (to improve asset quality). However, risk aversion has

not produced a difference in the rates of return and profitability over domestic-owned banks

(Haber and Musacchio, 2005; Haber, 2005) which is consistent with findings in the literature

on foreign bank entry.

3. Theoretical Framework

The stochastic frontier model is characterised by the utilisation of a two component error

term. A symmetric component captures the random variation of the frontier across firms,

statistical noise, measurement error, and random shocks external to firm control. The other

component is a one-sided variable capturing inefficiency relative to the frontier. The

stochastic cost frontier is written as:

[1] 1,2, t N,1,2, i ; ).( TituitveitXitC …=…=

+= β

Where Cit represents a scalar cost of bank i in the t-th period; Xit is a vector of known inputs

and outputs; β is a vector of unknown parameters to be estimated; the vit are independently and

identically distributed N(0,σ2v) random errors that are independently distributed of the Uit’s,

which are non-negative random variables accounting for the cost of inefficiency in

production; the uit are assumed to be positive and distributed normally with zero mean and

variance 2uσ . In this application, the uit have a half-normal distribution truncated at zero,

signifying that each bank’s cost lies on or above the cost frontier. This implies that deviations

from the frontier are evidence of bank management quality.

6

The total variance is defined as 222uv σσσ += . The contribution of the error term to the total

variation is as follows: )21/(22 λσσ +=v . The contribution of the inefficient term is:

)21/(222 λλσσ +=u . Where 2vσ is the variance of the error term v, 2

uσ is the variance of

the inefficient term u and λ is defined asvu

σσ

λ = , providing an indication of the relative

contribution of u and v to ε = u + v.

Since estimation procedures of equation (1) yield merely the residual ε, rather than the

inefficiency term u, this term must be calculated indirectly. In the case of panel data, such as

that used in this paper, Battese and Coelli (1988) use the conditional expectation of uit,

conditioned on the realised value of the error term )( ituitvit +=ε , as an estimator of uit. In

other words, [ ]itituE ε/ is the mean inefficiency for the ith bank at time t.

However, an approach is needed for handling unmeasured heterogeneity in the panel data if

we are not to bias the estimates of inefficiency. This issue is dealt with using the random

stochastic frontier model shown in equation [2]:

itititiit uvwc ++++= xβ ')( 0β [2]

where the variables are in logs and iw is a time invariant, firm-specific random term that

captures firm heterogeneity.

For estimation, the identification condition is assumed which states that the random

components of the coefficients be uncorrelated with the explanatory variables. A second issue

concerns the stochastic specification of the inefficiency term u. For the latter, we assume the

half normal distribution.

In order to estimate the parameters of the model, we construct the likelihood function using

the approach proposed by Greene (2005b). With the previous assumptions, the conditional

density of cit given iw is:

7

itiitititit

iit wcwcf xβ')( , 2)|( 0 −+−=⎟⎠⎞

⎜⎝⎛Φ⎟

⎠⎞

⎜⎝⎛= βε

σλε

σε

φσ

[3]

Where φ is the standard normal distribution and Φ the cumulative distribution function. The

parameters λ and σ2 are defined above.

Conditioned on iw , the T observations for bank i are independent and, therefore, the joint

density for the T observations is:

∏=

⎟⎠⎞

⎜⎝⎛Φ⎟

⎠⎞

⎜⎝⎛=

T

t

ititiiTi wccf

11

2)|,...,(σλε

σε

φσ

[4]

The unconditional joint density is obtained by integrating the heterogeneity out of the density:

iiw

T

t

ititiTii dwwgccfL

i

)(2),...,(1

1 ∫∏=

⎟⎠⎞

⎜⎝⎛Φ⎟

⎠⎞

⎜⎝⎛==

σλε

σε

φσ

[5]

The log likelihood, ∑i

iLlog , is then maximized with respect to the parameters β0, β, σ, λ

and any parameters appearing in the distribution of wi . The integral in equation [5] will be

intractable. Since equation [5] can be rewritten in the equivalent form,

⎥⎦

⎤⎢⎣

⎡⎟⎠⎞

⎜⎝⎛Φ⎟

⎠⎞

⎜⎝⎛== ∏

=

T

t

ititwiTii ii

EccfL1

12),...,(

σλε

σε

φσ

[6]

we propose to compute the log likelihood by simulation. Averaging the function in equation

[6] over sufficient draws from the distribution of wi will produce a sufficiently accurate

estimate of the integral in equation [5] to allow parameter estimation (see Gourieroux and

Monfort, 1996; Train, 2003). The simulated log likelihood is:

∑ ∏∑= ==

⎥⎦

⎤⎢⎣

⎡⎟⎠⎞

⎜⎝⎛Φ⎟

⎠⎞

⎜⎝⎛=

R

r

T

t

iritiritN

is

wwR

L1 11

0||21log),,,,(logσ

λεσ

εφ

σθσλβ β [7]

where θ includes the parameters of the distribution of wi and wir is the rth draw for observation

i. Based on the panel data, Table 3 presents the maximum likelihood estimators of model [1].

4. Model specification and data

We employ the intermediation approach to model bank production in which banks are

considered to be intermediators of financial services that purchase input in order to generate

earning assets (Sealey and Lindley, 1977).2 The translog functional form is used to model the

2 There are several approaches to modelling the bank production process: the production approach, user-cost approach, value added approach and dual approach (see Berger and Humphrey, 1992).

8

underlying cost structure of the Mexican banking industry. Following Berger and Mester

(1997), the cost function specifies three outputs, three inputs and two netputs.3 In addition, the

ratio of non-performing loans-to-gross loans (NPL) is used to account for differences in risk

across banks (see Mester, 1996). The specification of the model is completed by the inclusion

of a set of governance indicators, which account for the effect of static, selection and dynamic

changes in bank governance on bank cost. Following Berger et al (2005) the governance

indicators are specified by dummy variables. The static dummy is applied to banks whose

ownership or governance structure did not change between 1998 and 2006. The static

governance indicators show foreign-owned banks and private-owned banks. The selection

dummy is given to banks that were selected for either foreign acquisition or domestic M&A.

There are two dynamic variables allowing us to separate the short-term effects of governance

change from the longer term. The short-term dynamic dummy variable of 1 is given to banks

when a governance change takes place and for each quarter afterwards. The long-term dummy

variable equals two, and is given to banks whose governance has changed from the second

quarter of change onwards. Two exit variables are specified (failure and absorbed): for failed

(liquidated) banks, a value of 1 is given to those banks with zero to all others; banks exiting

due to their absorption by acquiring banks have a value of 1 with zero to all others. The static

dummy variable that identifies domestic private-owned banks is excluded from the model,

which allows the coefficients to be interpreted with respect to domestic private ownership. A

priori foreign bank acquisition is expected to lower bank costs in relation to domestic private

ownership. Governance indicators have been applied in studies of bank efficiency in

Argentina (Berger et al, 2005); bank productivity in Brazil (Nakane and Weintraub, 2005);

and bank performance in SE Asia (Williams and Nguyen, 2005). The stochastic cost frontier

is written in equation [8] as:

3 Our choice of bank output is consistent with the established literature. This is important because the definition and measurement of output could significantly affect the level of bank efficiency (Berger and Humphrey, 1997).

9

( ) ( ) ( )

( ) ( ) ( )

( ) ( ) ( ) ( ) ( ) ( )

( ) ( ) ( ) ( ) ( ) ( )

( ) ( )[ ] ]8[lnlnln21ln

/ln/ln/ln/ln/ln/ln

/ln/ln/ln/ln/ln/ln21

/ln/ln/ln

/ln)/ln(/ln21/ln

9

1

2111

2

1

3

1

2

1

3

12

2

122232

3

1

2

122

2

1

3

1

2

122

3

122

3

1

2

12

3

1

3

132

3 2

232

32

11123

ccii

ii

r i r kr

rkkrriirkiik

k

ssrrs

rj mmkkm

kjiij

i

krr

i kkkii

lk lrrlkli

lii

DNPLNPL

ZZPPZZZQPPZQ

zZzZzPzPzQzQ

TZZTPPTzQ

zzPPZQTTzpVC

μεκρρ

ϖκ

φϕθ

λλλ

φϕβττα

+++++

++Ω+

⎥⎦

⎤⎢⎣

⎡+++

+++

+++++=

∑

∑ ∑∑ ∑∑∑

∑∑∑ ∑∑∑

∑∑ ∑

∑ ∑∑

=

= = = = ==

=== ===

== =

= ==

where

lnVC/p3z2 is the natural logarithm of variable cost (the sum of interest paid, personnel

expense and non-interest expense). T is a time trend

lnQi is the natural logarithm of bank output (gross customer loans, securities, and other

earning assets);

lnPk is the natural logarithm of ith variable input prices (the prices of customer deposits

(interest paid on customer deposits/customer deposits), other funds (interest paid on

subordinated debt, bonds, interbank deposits/non-deposit funds) and non-interest expense

(personnel, administrative and depreciation expense/fixed assets));

lnZr is the natural logarithm of fixed netput quantities (physical capital and equity);

lnNPLi is the natural logarithm of non-performing loans /gross loans. It is a proxy for the

asset quality of each bank.

Di are the set of governance indicators:

D1 = dummy indicating a foreign-owned bank in which there was no change in governance

between 1998 and 2006. Equals 1 or 0 for all periods for a bank.

D2 = dummy indicating a bank that underwent at least one foreign acquisition between 1998

and 2006. Equals 1 or 0 for all periods for a bank.

D3 = dummy indicating a bank that underwent at least one domestic M&A between 1998 and

2006. Equals 1 or 0 for all periods for a bank.

D4 = dummy indicating a bank exited the sample after being absorbed by another bank.

Equals 1 for exiting banks or 0 for all periods for a bank.

10

D5 = dummy indicating a bank was liquidated and exited the market. Equals 1 for failing

banks or 0 for all periods for a bank.

D6 = dummy indicating the quarters following foreign acquisition. Equals 0 before acquisition

& 1 after. Equals 0 for all banks that did not undergo foreign acquisition.

D7 = dummy indicating the years following domestic M&A. Equals 0 prior to domestic M&A

and 1 after. Equals 0 for all banks that did not undergo a domestic M&A.

D8 = dummy indicating the quarters following foreign acquisition. Equals 0 prior to

acquisition and 2, 3, 4 … afterwards. Starts in the second quarter following the governance

change. Equals 0 for all banks that did not undergo foreign acquisition.

D9 = dummy indicating the quarters following domestic M&A. Equals 0 prior to M&A and 2,

3, 4 … afterwards. Starts in the second quarter following the governance change. Equals 0 for

all banks that did not undergo M&A.

εi are identical and independently distributed random variables, which are independent of the

μi, which are non-negative random variables that are assumed to account for inefficiency.

α, τ, β, ψ, λ, θ, φ, κ, Ω, ϖ, ρ, and κ are the parameters to be estimated using maximum

likelihood methods.

Standard restrictions of linear homogeneity in input prices and symmetry of the second order

parameters are imposed on the cost function. Whilst the cost function must be non-increasing

and convex with regard to the level of fixed input and non-decreasing and concave with

regard to prices of the variable inputs, these conditions are not imposed, but may be inspected

to determine whether the cost function is well-behaved at each point within a given data set.

Table 1 here

The quarterly bank financial statements data are sourced from the Comisión Nacional

Bancaria y de Valores (CNBV), the Mexican banking and securities commission that collates

this information for commercial banks. To create the governance indicators, we identified the

dates on which changes in bank ownership took place or banks exited the market from various

sources including: Graf (1999), Schulz (2006), BankScope and Thomson Analytics as well as

company websites. The data range from March 1998 to December 2006. There are 43 banks

in the sample with the maximum number of quarters equal to 36. Due to governance changes

11

and exit, the panel is unbalanced and has 1,199 observations. Table 1 shows the descriptive

statistics of the sample prior to taking logs. We deflate the original peso-denominated data by

the Mexican GDP deflator and convert into US dollars using the exchange rate at end

December 2000 (sourced from the Federal Reserve Bank of New York).

5. Results

We estimate the random stochastic cost frontier model in equation [8] and report the

estimated parameters in Table 2. For comparison, we report also the parameters derived from

a non-random specification of the cost function. How do we interpret these results? First, we

can conclude that the random frontier model better describes the underlying cost structure of

Mexican banks than the non-random or homogenous frontier model. This is the main result of

the paper. It supports claims that non-random frontier models fail to disentangle firm-level

heterogeneity from inefficiency with the implication that inefficiency will be biased. In our

models, the estimated lambda from the random frontier implies that 25.9% of bank costs are

attributable to inefficiency whereas the comparative figure is 66.3% for the non-random

frontier. This means that 40.4% of bank costs can be explained by heterogeneity within the

sample banks. Thus, failing to account for heterogeneity in the specification of the cost

function will seriously bias estimated efficiencies, which has implications for the design of

public policy since it is clear that one hat will not fit all. Similar conclusions are reached by

Greene (2004, 2005b). Further support for the specification of the random frontier is drawn

from a likelihood test of the goodness of fit between the two models. Since the likelihood test

has a chi-square distribution higher for the random frontier, we conclude that the random

model better fits the data than the non-random model (see Table 2).

Table 2 here

Generally speaking, the estimated parameters from the non-random and random cost frontiers

tend to have the same signs although the magnitude of coefficients and their T-statistics can

vary. The models appear to be consistent with expectations: cost increases with output, one

input price, and netput. The estimated parameters on the time trend and its quadratic term

indicate that the cost of Mexican banks is decreasing over time at a diminishing rate. We

identify two random parameters, which are bank loans and securities. This implies that the

source of heterogeneity between banks operating in Mexico between 1998 and 2006 rests in

their balance sheet structures, which may be an indication of specialisation in production

12

possibly relating to bank size. This result also signifies that Mexican banks are relatively

homogenous on the other variables.

In the following paragraphs, we shall discuss the effects that risk and bank governance have

on bank cost since this is one of our objectives, and also because the variation in estimated

parameters derived from the two models is greatest for these variables. In other words, there

is the possibility that the design of public policy could be adversely affected should biased

estimated parameters be used as a reference for policy formulation.

As noted by Mester (1996), the proportion of non-performing loans in a bank’s loan portfolio

indicates the level of credit risk assumed by a bank. If the amount of non-performing loans is

high, this may be an indication that a bank has expended too few resources towards credit

evaluation and subsequent monitoring of borrowers. This is evidence of skimping behaviour

which states that banks deliberately choose not to expend resources but produce excessively

risky loans as a direct consequence of their decision. The parameter estimates for the non-

random frontier show a very large and significant coefficient for NPL (-6.315). This suggests

that more risky banks with larger proportions of non-performing loans have lower costs,

which is evidence of skimping. That the quadratic term (NPL2) is significantly positive

implies that whereas costs fall as NPLs rise, there is a point at which increases in NPLs will

result in higher costs. Based on these findings, it would be reasonable for bank regulators to

take corrective action against skimpers. However, is such action warranted by the estimated

parameters of the random frontier model? The answer is clearly not. Whilst the estimated

parameter on NPL (and NPL2) has the same sign in both models, in the random model it is not

significant suggesting that there is no strong statistical evidence of Mexican banks engaging

in skimping behaviour.

Having demonstrated there is potential for poorly designed policies emanating from estimated

relationships between variables, we turn to discuss the effects of governance changes on bank

costs referring only to the estimated relationships drawn from the random frontier model.

However, we draw the readers’ attention to the fact that for five of the nine variables, the

random frontier produces significant relationships between bank governance and bank cost

that are insignificant in the non-random model. The static governance indicator (D1) shows

that banks which were foreign-owned across all quarters between 1998 and 2006 have

significantly lower costs than domestic private-owned banks. This finding is consistent with

13

evidence from Argentina (Berger et al, 2005) and the literature on foreign bank entry in

general. Similarly, static foreign-owned banks are more profit efficient in SE Asia (Williams

and Nguyen, 2005) and productive in Brazil (Nakane and Weintraub, 2005). The selection

variables reveal a contrasting picture regarding the consolidation process in Mexico. Whereas

banks selected for foreign acquisition (D2) had significantly higher costs than domestic

private-owned banks, those banks selected by domestic banks (D3) had significantly lower

costs than the control group. It is improbable that this difference reflects anything other than

foreign banks acquired the larger, domestic-owned banks because of a shortage of sufficiently

capitalised domestic suitors. The evidence on foreign acquisitions from Mexico differs to that

observed elsewhere. In Argentina, there is no statistically significant difference in the ratio of

costs-to-assets between domestic private-owned banks and banks selected for foreign

acquisition (Berger et al, 2005). On the contrary, the available evidence from SE Asia shows

that foreign banks cherry-pick their acquisitions and select banks with significantly higher

profit (but not cost) efficiencies than domestic, private-owned banks (Williams and Nguyen,

2005). However, the Mexican results for banks selected for domestic M&A is consistent with

evidence from SE Asia, but not with Argentina where the selected banks had significantly

higher costs in comparison with the control group.

The two exit variables capture the acquisition and absorption of viable banks into another

bank (D4) and the closure of unviable banks (D5). In the first case, the significant estimated

parameter might reflect the probability that banks exiting the sample in this manner are

relatively attractive to potential acquirers because of their impressive level of cost control. In

the second case, it would appear that the onset of financial distress may suddenly afflict a

bank in the sense that no discernible trend in bank costs indicates the eventuality of

liquidation. Or, lower costs could indicate skimping behaviour that has potential and adverse

longer term implications for banks. The second finding is consistent with the evidence from

SE Asia (Williams and Nguyen, 2005) but not Brazil (Nakane and Weintraub, 2005).

The short-term dynamic governance indicators show the once-and-for-all effect of the

acquisition by foreign banks (D6) and acquisition by domestic banks (D7). In both cases, the

effect of foreign acquisition or domestic M&A is to lower bank costs with respect to the

period prior to the change in governance. Judging by the size of the estimated parameters, we

suggest that foreign acquisition lowers bank costs to a greater extent than domestic M&A,

which is consistent with expectations in the literature. Both types of governance change have

14

been found not to significantly alter bank costs in Argentina (Berger et al, 2005) whilst

significant improvements in cost efficiency are observed in SE Asia (Williams and Nguyen,

2005). Finally, the long-term dynamic variables are specified in order to capture some of the

differences between the short-term and long-term effects of changes in bank governance.

They allow us “to test whether the banks continue to evolve in predicted ways after a

governance change versus tend to return to prior behaviour” (Berger et al, 2005, p. 2194).

Clearly, the estimated parameters have far-reaching implications for the evaluation of public

policy especially the decision to allow freedom of entry for foreign banks. The estimated

parameter on long term acquisition by foreign banks (D8) implies that the longer term effect

of foreign bank acquisition of domestic banks is to significantly lower bank costs, in

accordance with predictions in the established literature. Furthermore, the effect of foreign

bank acquisitions is more powerful than that of domestic M&A (D9), which also significantly

lowers bank costs over time. In brief, the bank consolidation process in Mexico has resulted

in significantly lower bank costs, with foreign bank acquisitions having the greatest impact.

Similar evidence is observed in SE Asia (Williams and Nguyen, 2005). Our findings not only

confirm the appropriateness of the policy change on foreign bank entry made in 1995, but

they constitute further evidence of the benefits associated with using changes in bank

governance (and especially the sale of domestic banks to foreign banks) to effect a stronger

bank performance in terms of cost control. As noted above, the strength of our results and

implications for policy formulation are conditional on the selection of a correctly specified

frontier, which in the present case is the random stochastic cost frontier.

6. Conclusion

Failure to account for heterogeneity between firms can seriously distort bank efficiencies. In

this paper, we apply the random stochastic cost frontier model to avoid this problem.

Comparing the random and non-random cost frontiers for the sample of Mexican banks, we

find that whereas 25.9% of bank costs can be attributed to inefficiency in the random model,

the corresponding figure for the non-random model is 66.3%. This suggests that more than

40% of bank cost relates to heterogeneity between banks, and which is incorrectly attributed

to inefficiency in the non-random model. Our results show that the observed heterogeneity

relates to variations between banks in terms of their output, namely, loans and securities –

which may be a function of differences in specialisation possibly relating to bank size.

15

Although there is consistency in the signing of parameters derived from the random and non-

random frontiers, there are inconsistencies in terms of the magnitude of estimated parameters

and in the level of statistical significance. As an example, we explain how the estimated

parameters on the NPL variable and its quadratic term from the non-random frontier can be

construed as evidence of skimping behaviour at Mexican banks, which has direct implications

for bank regulatory policy. However, this evidence is not supported by the random frontier

with the implication that regulatory design may be faulty unless the correctly specified model

is used in policy formulation.

This is one of the earliest studies of the effect that the repeal of restrictive legislation on

foreign ownership of domestic banks has had on the costs of the Mexican banking sector.

Although restrictions were repealed in 1995 they became effective in 1997. Our dataset of

quarterly data begin in March 1998 and end in December 2006. Using a set of indicators

suggested by Berger et al (2005) to identify the effects that governance changes have had on

bank cost, we suggest that the policy of facilitating an increase in foreign bank penetration has

been successful in terms of producing lower costs. Not only does foreign acquisition of

domestic banks create a once-and-for-all reduction in bank costs relative to pre-take over,

there is a significant longer term effect, which implies that foreign bank ownership is

associated with more effective cost control and management. Whilst, consolidation between

domestic-owned banks also produces results in the same direction, the impact of governance

changes involving foreign acquisition is considerably larger.

16

References

Aigner, D.J.; Lovell, C.A.K., Schmidt, P., 1977. Formulation and estimation of stochastic

frontier production function models. Journal of Econometrics 6, 21-37.

Banker, R. D., Charnes, A., Cooper, W.W., 1984. Some Models for Estimating Technical

and Scale Inefficiencies in Data Envelopment Analysis. Management Science 30, 1078-

1092.

Battese, G.E., Corra, G.S., 1977. Estimation of a Production Frontier Model: With application

to the pastoral zone of Eastern Australia. Australian Journal of Agricultural Economics 21,

169-179.

Battese, G.E., Coelli, T.J., 1988. Prediction of firm-level technical efficiencies with a

generalised frontier production function and panel data. Journal of Econometrics 38, 387-399.

Berger, A.N., Humphrey, D.B., 1992. Measurement and efficiency issues in commercial

banking. In Z. Griliches (ed) Output Measurement in the Service Sectors, National Bureau of

Economic Research (Chicago: University of Chicago Press), 245-279.

Berger, A.N., Humphrey, D.B., 1997. Efficiency of financial institutions: international survey

and directions for future research. European Journal of Operational Research 98, 2, April,

175-212.

Berger, A.N., Mester, L.J., 1997. Inside the black box: What explains differences in the

efficiencies of financial institutions? Journal of Banking and Finance 21, 895-947.

Berger, A.N., DeYoung, R., Genay, H., Udell, G.F., 2000. Globalisation of Financial

Institutions: Evidence from Cross-Border Banking Performance, Brookings-Wharton Papers

on Financial Services 3, 23-158.

Berger, A.N., Clarke, G.R.G., Cull, R., Klapper, L., Udell, G.F., 2005. Corporate governance

and bank performance: A joint analysis of the static, selection, and dynamic effects of

domestic, foreign, and state ownership. Journal of Banking and Finance 29, 2179-2221.

17

Clarke, G., Cull, R., Martinez Peria, M.S., Sánchez, S.M., 2003. Foreign bank entry:

Experience, implications for developing economies, and agenda for further research. The

World Bank Research Observer 18, 1, 25-59.

Claessens, S., Jansen, M., 2000. Internationalisation of Financial Services, WTO – World

Bank (2000), Kluwer Law International, Chapter 1.

Claessens, S., Demirgüç-Kunt, A., Huizinga, H., 2001. How does foreign entry affect

domestic banking markets, Journal of Banking and Finance 25, 891-911.

Crystal, J.S., Dages, B.G., Goldberg, L., 2002. Has foreign bank entry led to sounder banks in

Latin America? Current Issues in Economics and Finance 8, 1, 1-6.

Farrell, M.J., 1957. The Measurement of Productive Efficiency. Journal of the Royal

Statistical Society, Series A, 120, 3, 253-290.

Gelos, R.G., Roldós, J., 2004. Consolidation and market structure in emerging market

banking systems. Emerging Markets Review 5, 39-59.

Gourieroux, C., Monfort, A., 1996. Simulation Based Methods: Econometric Methods.

(Oxford University Press, Oxford, UK).

Graf, P., 1999. Policy responses to the banking crisis in Mexico. In Bank Restructuring in

Practice, BIS Policy Papers, No. 6, 164-182.

Greene, W., 2004. Distinguishing between heterogeneity and efficiency: stochastic frontier

analysis of the World Health Organisation’s panel on national health care systems. Health

Economics 13, 959-980.

Greene, W., 2005a. Reconsidering heterogeneity in panel data estimators of the stochastic

frontier model. Journal of Econometrics 126, 269-303.

18

Greene, W., 2005b. Fixed and random effects in stochastic frontier models. Journal of

Productivity Analysis 23, 7-32.

Gruben, W.C., McComb, R.P., 2003. Privatization, competition, and supercompetition in the

Mexican commercial banking system. Journal of Banking and Finance 27, 229-249.

Haber, S., Musacchio, A., 2005. Foreign banks and the Mexican economy, 1997–2004.

Stanford Center for International Development Working Paper.

Haber, S., 2005. Mexico’s experiments with bank privatization and liberalization, 1991-2003.

Journal of Banking and Finance 29, 2325-2353.

Hoshino, T., 1996. Privatization of Mexico’s public enterprises and the restructuring of the

private sector. The Developing Economies XXXIV-1, 34-60.

Meeusen, W., van den Broeck, J., 1977. Efficiency estimation from a Cobb-Douglas

production function with composed error. International Economic Review 18, 435-444.

Mester, L.J., 1996. A study of bank efficiency taking into account risk-preferences, Journal of

Banking and Finance 20, 1025-1045.

Mester, L., 1997. Measuring Efficiency at US banks: Accounting for heterogeneity is

important. European Journal of Operational Research 98, 230-424.

Montes-Negret, F., Landa, L., 2001. Interest rate spreads in Mexico during liberalization. In

Caprio, G., P. Honohan and J.E. Stiglitz (eds) Financial liberalization: How far? How fast?

(Cambridge University Press).

Nakane, M.I., Weintraub, D.B., 2005. Bank privatization and productivity: Evidence for

Brazil. Journal of Banking and Finance 29, 2259-2289.

Orea, L., Kumbhakar, S., 2004. Efficiency measurement using a latent class stochastic

frontier model. Empirical Economics 29, 169-183.

19

Schulz, H., 2006. Foreign banks in Mexico: New conquistadors or agents of change?

University of Pennsylvania.

Sealey, C., Lindley, J.T., 1977. Inputs, outputs and a theory of production and cost at

depository financial institution, Journal of Finance 32, 1251-1266.

Train, K., 2003. Discrete Choice Methods with Simulation (Cambridge University Press,

Cambridge, UK).

Williams, J., Nguyen, N., 2005. Financial liberalisation, crisis and restructuring: A

comparative study of bank performance and bank governance in South East Asia. Journal of

Banking and Finance 29, 8-9, 2119-2154.

Yeyati, E.L., Micco, A., 2007. Concentration and foreign penetration in Latin American

banking sectors: Impact on competition and risk. Journal of Banking and Finance 31, 1633-

1647.

Yildirim, H.S., Philippatos, G.C., 2007. Restructuring, consolidation and competition in Latin

American banking markets. Journal of Banking and Finance 31, 629-639.

20

Table 1: Descriptive Statistics (in natural logarithms)

Variable Description Minimum Maximum Mean Standard deviation

VC/p3*z2 -3.987 1.100 -1.417 0.916 T Time 1 36 17.45

10.37

T2 Time square 1 1296

412

387.07

Q1 Gross loans 0.108 2.721 1.202 0.605 Q2 Securities -0.029 1.524 0.741 0.288 Q3 Other earning assets 0.150 1.613 0.813 0.297 P1 Price of customer deposits 0.0006 0.698 0.367 0.151 P2 Price of other funds 0.0006 0.826 0.385 0.166 Z1 Price of non-interest expense -0.013

0.876

0.430

0.167

Z2 Fixed assets 0 1.837

0.774

1.026

NPL Equity 0.609

0.812

0.707

0.025

D1 Non-performing loans-loans 0 1 0.289

0.453

D2 Foreign all 0 1 0.211

0.408

D3 Selected for foreign acquisition 0 1 0.199

0.399

D4 Selected for M&A 0 1 0.032

0.177

D5 Exit via absorption 0 1 0.012

0.111

D6 Exit via liquidation 0 1 0.124

0.330

D7 ST foreign 0 1 0.109

0.312

D8 ST M&A 0 1 1.209

4.015

D9 LT foreign 0 1 0.967

3.581

21

Table 2: Parameter estimates: Non-random and random stochastic cost frontiers

Non-random frontier

Random frontier Non-random frontier

Random frontier

Coefficients Coefficients Coefficients Coefficients Variables

(t-ratio) (t-ratio)

Variables

(t-ratio) (t-ratio) 0.864 -0.213* 0.187 0.012 Constant

(-0.106) (-2.286) Q1P2

(0.436) (1.568) -0.066** -0.04* 1.721** 0.673** T (-11.912) (-2.157)

Q2P2 (2.800) (4.219)

0.0006** 0.052** -0.466 -0.319* T2 (7.372) (3.218)

Q3P2 (-0.632) (-2.217)

0.133 -0.208 -0.424** Q1 (1.314)

― Q1Z12 (-1.774) (-3.983)

0.587** -1.152** -0.031* Q2 (2.761)

― Q2Z12 (-4.819) (-2.568)

1.546** 0.832** -2.095** -0.984** Q3 (8.878) (4.392)

Q3Z12 (-10.394) (-3.218)

1.028 0.935** 6.829** 0.523 P1 (1.098) (2.782)

P1Z (5.763) (1.784)

-0.028 -0.4000** 0.213 0.213* P2 (-0.030) (-4.388)

P2Z (0.188) (2.452)

0.545 0.257** -6.315** -0.945 Z1 (1.808) (3.782)

NPL (-2.963) (-1.218)

-0.007** -0.019** 2.26 0.735** TQ1 (-4.505) (-2.694)

NPL2 (1.629) (4.215)

-0.004 -0.0053 -0.175** -0.068** TQ2 (-1.200) (-1.564)

D1 – foreign all (-4.775) (-3.892)

-0.012** -0.012** 0.039 0. 217** TQ3 (-3.567) (-3.021)

D2 – selected for foreign acquisition (0.817) (3.219)

0.034 0.018** -0.005 -0.136* TP1 (1.818) (3.293)

D3 – selected for domestic M&A (-0.142) (-2.421)

0.061** 0.014** -0.195** -0.158 TP2 (3.348) (3.125)

D4 – exit via absorption (-3.486) (-1.673)

0.049** 0.015** -0.061 -0.021* TZ1 (8.315) (3.352)

D5 - exit by liquidation (-0.599) (-2.217)

0.373** 0.127** -0.197** -0.247** Q12 (11.674) (3.728)

D6 – ST foreign (-3.810) (-3.138)

-0.063 -0.289** 0.113** -0.015** Q1Q2 (-1.269) (-2.935)

D7 – ST M&A (2.778) (-4.563)

-0.255** -0.012** -0.006 -3.918** Q1Q3 (-4.681) (-2.745)

D8 – LT foreign (-1.794) (-5.088)

-0.053 -0.052** -0.007 -0.012* Q22

(-0.506) (-3.518)

D9 – LT M&A

(-1.957) (-2.325) -0.109 -0.021 Mean for Random Parameter Q2Q3

(-0.966) (-1.782) 0.253** -0.23* -0.126**

Q1 ― (3.091) Q32

(-2.191) (-3.278) 0.088

-2.459* -0.128*

Q2 ―

(0.562) P12 (-2.512) (-2.521) Scale Parameters for Dists. Of Random Parameter -1.531 -0.326 0.1490** P1P2

(-1.681) (-0.289) Q1 ―

(5.212) P22 -0.553 -0.562 Q2 ― 0.2394**

22

(-0.698) (-0.217) (4.793) 1.578** 0.921** 0.663** 0.259** Z2 (8.611) (2.893)

λ = σu / σv

(3.919) (5.118)

-0.768 -0.178 0.263** 0.124** Q1P2 (-1.734) (-1.328)

σ = [σ2v + σ2

u]1/2

(13.975) (4.586)

-0.563 -0.562 Log likelihood 29.915 32.108 Q2P1 (-0.828) (-1.034) Likelihood ratio test 6.179 9.218 1.555* 0.132 p-value 15.35 14.321 Q3P1 (1.978) (1.532) 0.187 0.012 Q1P2

(0.436) (1.568) Observations 1,199 1,199 *, ** = significant at the 5% & 1% levels.