X-efficiency and convergence of productivity among the national commercial banks in
China
By
Michael K. Fung
Assistant Professor, School of Accounting and Finance
Faculty of Business
Hong Kong Polytechnic University, Hong Kong, PRC
And
M. K. Leung
Associate Professor, School of Accounting and Finance
Faculty of Business
Hong Kong Polytechnic University, Hong Kong, PRC
X-efficiency and convergence of productivity among the national commercial banks
in China
Michael K. Fung*,
M. K. Leung*
Abstract
This paper seeks to estimate and compare the productivity of the national commercial
banks in China during the period of 1996 to 2005. Change in the level of X-efficiency or
total factor productivity is measured by change in overall technical efficiency (TE),
which is decomposed into pure technical efficiency (TEV) change and scale efficiency
(SE) change. The focus of this study is placed on whether the productivity of these
commercial banks converges in the expanding Chinese economy. First, the results
suggest the big four banks have been operating with decreasing returns to scale and they
have a statistically significant lower SE and TE than the other national commercial banks.
Second, the findings provide long-run evidence for absolute convergence in TVE, but not
for absolute convergence in SE, among the Chinese banks. A plausible explanation is that
the operations and production plans of a Chinese bank are technically simple and
unsophisticated due to the various restrictions imposed. Furthermore, all banks have
equal access to the government-directed technologies that can speedily transmit across
banks. Third, the findings provide long-run evidence for the conditional convergence in
SE, but not for the conditional convergence in TVE, among the Chinese banks. This
means that the steady-state SE and TE to which a Chinese bank is converging are
conditional on the bank’s own level of X-efficiency, which is significantly influenced by
the education level of its workforce. A recruitment policy with emphasis on educated
staff members will increase the competitiveness of a Chinese bank in the long run.
Furthermore, the implementation of specific government policies such as capital injection
into the big four banks can influence bank productivity. All these may infer that the
productivity convergence path of the Chinese banks is not an easily predictable one. If
the government can carry on the bank reforms with an increased focus on de-regulation,
allowing commercial banks to engage in a wider scope of operations, it appears that
significant gains in efficiency of the overall Chinese banking industry could be
forthcoming. Further research in this direction is warranted.
* School of Accounting and Finance, Faculty of Business, Hong Kong Polytechnic
University, PRC. We would like to acknowledge the financial support provided by the
Hong Kong Polytechnic University (Project code: A-PH04)
JEL No. D24, G21
Keywords: commercial banks, convergence, productivity, China

Correspondence: Dr. M.K. Leung, School of Accounting and Finance, Faculty of Business, Hong Kong
Polytechnic University, Hunghom, Kowloon, Hong Kong. Tel: (+852)--2766-7125. Fax: (+652)-2356 9550.
Email: [email protected]
2
1. Introduction
In China, as a result of the 1978 reform, the banking sector has been growing
rapidly in tandem with the fast growth of the economy. 1 At present, the Chinese
commercial banking sector is dominated by the big four central government-owned
nationwide commercial banks (the Agricultural Bank of China, the Bank of China, the
China Construction Bank2, and the Industrial and Commercial Bank) and the thirteen
joint-stock nationwide commercial banks. All these banks have been permitted to
compete among themselves across the whole country since 1996. The size of the big four
banks is much larger than that of the joint-stock banks.3 It will be of practical interest to
estimate and compare the efficiency of these two groups of banks, which is instrumental
to the future growth and structure of the whole Chinese banking sector. The first
objective of this paper is to test the hypothesis that the big four banks have a lower Xefficiency score than the joint-stock banks.
It is observed that the joint-stock banks have been growing more quickly and
gaining market share at the expense of the big four banks.4 The second objective of the
paper is to test the hypothesis of “absolute convergence”. If technologies are public goods
that can speedily transit the boundaries of firms, and productivity gains from scale
1
In China, during the period 1996 to 2005, the assets of all banking institutions have grown at an annual
rate of 16.6% as against a nominal yearly growth rate of gross domestic income of 11%. [Sources: China
Statistical Yearbook and Almanac of China’s Finance and Banking (ACFB), various issues].
2
Before 1996, the China Construction Bank was called the People’s Construction Bank of China.
3
In 2005, the average asset value for the big four banks was Rmb yuan (Rmb) 4914.5 billion, which was
more than 10 times that of the joint-stock commercial banks at Rmb 484.4 billion. The asset size of the
Bank of China (the smallest among the big four) was 2.7 times that of the Bank of Communications (the
largest among all other joint-stock banks). [Source: ACFB, 2006].
4
Between 1996 and 2005, the nationwide joint-stock banks and the big four banks have registered a yearly
increase of 25.3% and 17.1% of their assets respectively. See Table 1 for the market shares of the big four
and the joint-stock banks.
3
economies decrease with bank size, the initially smaller banks will grow more quickly
than the larger banks. In the steady state, all the banks will end up being of the same size
and converge to the same level of productivity. However, since X-efficiency can be
determined by some bank-specific factors influencing cost and revenue generation, banks
might converge to different levels of steady-state productivity. The third objective of this
study therefore is to test for the hypothesis of “conditional convergence.” This implies
that initial differences in X-efficiency among banks can create permanent differences in
productivity among them. To the best of our knowledge, there have been so far no similar
studies on the convergence of productivity among Chinese banks.
The paper is organised as follows. The institutional development of the banking
sector in China is first reviewed. The theoretical foundation and research methodology are
then presented. Based on these, the data set and the empirical results are analyzed and
discussed. The paper concludes with some policy implications for the government.
2. Institutional development of the banking sector in China
Before the 1978 economic reform, China virtually had only one bank, the
People’s Bank of China (PBOC), within which other banks were subsumed as internal
specialist departments.5 Within the planned economy, the PBOC’s primary mission was
to allocate funds administratively to state-owned enterprises to enable them to fulfil their
production plans. The bank therefore did not operate with economic efficiency as a
primary consideration.
5
Prior to the 1978 reform, the Bank of China and the Agricultural Bank of China largely functioned as the
foreign exchange and agriculture administrative divisions of the PBOC.
4
In 1979, as part of the reform, the mono-bank system was broken up, resulting in
the reinstatement and formation of the three large wholly state-owned national
specialized banks: the Bank of China (BOC) for foreign trade and exchange; the China
Construction Bank (CCB) for physical infrastructure construction; and the Agricultural
Bank of China (ABC) for the development of rural areas. In 1984, when the PBOC was
officially made the country’s central bank, its commercial operations in cities were taken
over by the newly established Industrial and Commercial Bank of China (ICBC). Since
then, the big four state-owned banks, have become an oligopoly in the Chinese banking
market in regard to loans and deposits, and the number of employees and branches.
Since the late 1980s, the government, in a bid to instil more competition into the
banking sector, has permitted the establishment of joint-stock commercial banks in major
cities. The organisational form of the wholly-owned big four banks and the joint-stock
banks was governed by the Company Law of 1993.6 In 1994, three wholly state-owned
policy banks (the China Development Bank, the Export and Import Bank of China and the
China Agricultural Development Bank) were established to support state development
policies in the areas of infrastructure construction, trade and the agricultural sector.7 The
policy banks are to take over the policy lending made by the big four banks which could
6
A joint-stock bank is governed by a board of directors of which members are appointed by the major
shareholders. Among the 13 joint-stock banks, with the exception of the China Minseng Bank and China
Zheshang Bank whose stocks were held mainly by non-state-owned enterprises, the major shareholders of
the other 11 commercial banks comprise local government or its subsidiaries and other state-owned firms.
7
The mandates of the three policy banks are as follows: The China Development Bank is to provide
development financing for infrastructure constructions across the country. The Export-Import Bank of China is
to promote export of mechanical and electronic products, hi-tech products, offshore construction projects and
investment projects. The Agricultural Development Bank of China is to provide working capital to firms
purchasing grain, cotton to ensure national food security, farmers’ interests and rural development. In 2006,
total assets of the three policy banks were 15.6% of the total assets of the big four banks.[Sources: the websites
of the policy banks].
5
focus on commercial lending driven by profits or efficiency considerations. In the same
year, the PBOC established and managed the national inter-bank market infrastructure for
trading and settlement of foreign exchange based in Shanghai. In 1995, the enactment of
the nationwide Central Bank Law and the Commercial Bank Law provided a legal
foundation for the then regulator, the PBOC and an operational framework for the
development of profit-oriented commercial banking in China. 8 Under the Commercial
Bank Law, commercial banks in China were required to manage their portfolios by asset
and liability ratios. In 1996, the PBOC institutionalised the money market transactions
and trading in bonds within the existing inter-bank infrastructure for commercial banks
and other financial institutions. To integrate into the international central bank
community, the PBOC also joined the Bank for International Settlements in November
1996.
From 1996, with the implementation of the formal regulatory and supervisory
framework, the big four banks were no longer confined in their specialized operations
and they have gradually established themselves as profit-driven state commercial banks
competing with one another and the joint-stock commercial banks all over the country.9
In 2005, there were altogether 13 joint-stock banks. They are (in sequence of the year of
establishment): the China Merchant Bank (1987); the Shenzhen Development Bank
(1987) the China CITIC Bank (1987), the Bank of Communications (1988), the Industrial
Bank (1988), the Hua Xia Bank (1992); the China Everbright Bank (1992), the
8
In April 2003, the China Banking Regulatory Commission was established to take over the supervisory
role of banks from the PBOC, which would henceforth focus on the formulation and implementation of
monetary policy.
9
Depending on the terms of their operating license from the CBRC, banking institutions can provide
services all over the country (nationwide commercial banks), in a city (city commercial banks), in a district
within a city (urban credit co-operatives), in a rural town or village (rural commercial banks or rural credit
co-operatives).
6
Guangdong Development Bank (1993), the Shanghai Pudong Development Bank (1993),
the China Minsheng Banking Corporation (1996), the Evergrowing Bank (2003), the
China Zheshang Bank (2004), and the Bohai Bank (2005). In the absence of developed
financial markets the banking institutions have provided most funds to enterprises.10
Due to their long history and the specialised roles entrusted to them, the big four banks
are much larger in asset size than the 13 joint-stock banks. However, the big four banks
have also inherited the legacy of substantial non-performing loans, accumulated from the
lending to relatively inefficient state-owned enterprises, and a rigid administrative
structure given their state ownership. The joint-stock banks in turn have a more flexible
structure in their personnel and business strategy. They have a greater flexibility in
recruiting qualified staff and reward them with market remuneration. They are also
generally given more freedom to choose their customers and to meet their needs with new
products. Following China’s entry to the World Trade Organization (WTO) in December
2001 and a more liberal policy environment for bank operations and structure of
ownership, Chinese banks have increasingly engaged in more intense competition
amongst themselves and with foreign banks.11 Table 1 shows that the market shares (in
terms of assets) of the big four banks and the joint-stock banks have been around 70%
during the period 2003 to 2005. It can also be seen that the joint stock banks and other
banking institutions have captured a higher market share at the expense of the big four
banks.
10
In 2005, 85% of funds to enterprises were provided by banking institution, with the remaining offered by
the financial markets. (See PBOC Monetary Policy Implementation Report 2005).
11
Foreign banks were only able to compete with Chinese banks on a nationwide basis from December 2006,
five years after China’s accession to the WTO when all the restrictions on the scope and location of
operations were lifted.
7
We now turn to the estimation and analysis of the productivities of the big four
banks and the joint-stock nationwide commercial banks. More specifically, we examine
whether the productivity of these banks is converging and if so, how quickly and by what
means.
[Insert Table 1 here]
3. Empirical Formulation and Major Hypotheses
3.1 X –efficiency
In his path-breaking paper, Farrell (1957) proposed an index of a firm’s overall
efficiency which could be multiplicatively partitioned into an allocative component and a
technical component. Whereas allocative efficiency measures the extent of deviation
from the least cost combination of inputs, for given input prices, technical efficiency is a
measure of how effectively a firm transforms inputs into a given level of output, for a
given state of technology. Leibenstein (1966) argued that variations in technical
efficiency could be related to X-efficiency - “the initially undefined type of efficiency” of
a firm. According to him, the level of X-efficiency is significantly influenced by the
motivation of managers and workers to reduce costs, which, in turn, is positively related
to the degree of external competition and of marketization for some important inputs such
as labor services.
X-efficiency is also, it is argued, a more significant means of
increasing the overall economic efficiency of a firm than allocative efficiency.
8
Notwithstanding the criticisms of Leibenstein’s theory of X-efficiency [see Stigler (1976)
for the main arguments], the institutional arrangements of the Chinese banking sector
appear to have fitted analytically well with the underlying notions of X-efficiency as
further defended by Leisbenstein (1978). Furthermore, as detailed pricing information is
not available and commercial banks in China are not completely free to price their inputs
and outputs due to interest rate controls, this study will focus on X-efficiency and its
determinants.
Two major approaches are commonly used in analyses of efficiency, namely, the
non-parametric approach [e.g., data envelopment analysis (DEA)] and the parametric
approach [e.g., stochastic frontier analysis (SFA)]. It is generally impossible to determine
which of these two major approaches dominates the other because the true level of
efficiency is unknown. In this study, DEA, a non-parametric mathematical programming
approach, is adopted because it allows efficiency measurement without the need for a
specific production functional form. In addition, DEA is particularly suited to working
with samples of limited size (Evanoff and Israilevich, 1991),12 a significant advantage
given the relatively small number of national commercial banks in China. Under the DEA
approach, the technical efficiency index is explicitly derived as a ratio of weighted
outputs to weighted inputs. Hence, the technical efficiency index can also be perceived
as an index of the total factor productivity.
Let TEi ,t and TEVi ,t be the input-oriented technical efficiency indices for the i-th
decision-making unit (DMU) at time t under constant returns to scale (CRS) and variable
returns to scale (VRS), respectively. It can be shown that
12
Non-parametric frontiers for the data set were estimated by linear programming using DEAP 2.1, written
by Coelli (1996).
9
TEi ,t  TEVi ,t  SEi ,t ,
(1)
where SEi ,t is the scale efficiency index for the i-th DMU at time t [see Banker et al.
(1984)]. As such, technical efficiency is decomposed into “pure” technical efficiency (i.e.,
TEVi ,t ) and scale efficiency ( SEi ,t ). Technical efficiency ( TEi ,t ) then measures the
effectiveness of management in implementing a technically efficient production plan and
in operating at the minimum efficient scale [see Berger et al. (1993)], which indicates the
level of X-efficiency as defined by Leibenstein (1966). Managerial effectiveness is
related to the degree of complexity of the production plan, and the ease with which the
bank has access to the best possible inputs and the prevailing technology. X-efficiency
will increase if managers can increase bank size to achieve economies of scale [Hughes
and Mester (1998), Berger and Mester (1997)], or if they can reduce the size of a very
large bank to reduce scale diseconomies [Hunter and Timme (1995)].
X-efficiency therefore is determined by firm-specific factors facilitating
managerial effectiveness, and by opportunities for more effective input utilization which,
in turn, can be influenced by government policies. An increase in X-efficiency or total
factor productivity can be captured by the improvement of “pure” technical efficiency
and scale efficiency.13
13
In this paper, we do not take into account of technical progress as a determinant of productivity increase
since proxy measure for bank technology in China is not available. Also, as it is argued later, bank
technology is a public good that transmit readily among banks in China over time due to prevalent public
ownership.
10
The previous section shows that the big four banks are much larger and appear to
be less efficient than the other national commercial banks. Equation (1) thus can be used
to test the following alternative hypotheses:
Hypothesis 1a: the big four banks have a lower TEV than the other banks
Hypothesis 1b: the big four banks have a lower SE than the other banks
Hypothesis 1c: the big four banks have a lower TE than the other banks
The results will provide a basis for the subsequent analysis of the convergence of
productivity among the national commercial banks in China.
3.2 Convergence
Following the studies of Baumol (1986) and Barro (1991) on the tests for the
convergence of real income per capita among countries, we extend the two major
concepts of convergence, namely, -convergence and -convergence to the commercial
banks in China. Convergence of the -type considers whether the growth in a firm’s
productivity exhibits a negative correlation with its current level of productivity. In other
words, absolute -convergence implies that firms with a lower level of productivity have
faster growth rates than firms with a higher level of productivity. Convergence of the type considers whether the dispersion of productivity levels among firms diminishes over
time.
Existing tests for -convergence are based on a regression of an output measure a)
on its lagged values (to test for absolute convergence), and b) on its lagged values and
other “conditioning variables”, i.e., behavioral parameters, (to test for conditional
convergence). Absolute convergence means that each firm moves toward the same
11
steady-state productivity, whereas conditional convergence suggests that each firm has its
own steady-state productivity to which it is converging. Absolute convergence in
productivity relies on the assumption that the only differences across firms lie in their
initial level of productivity. Under this assumption, firms will converge over time if a
common level of steady-state productivity exists for all firms, and if technologies are
public goods that can speedily transit the boundaries of firms. On the other hand,
conditional convergence implies that firms have different steady states if they have
different behavioral parameters governing productivity, and that the growth rate of a firm
declines as the firm approaches its own steady state. Hence, the conditional convergence
and absolute convergence hypotheses coincide only if all firms have the same steady state.
In this study, both absolute and conditional convergence in productivity are tested
in two ways – a long-run (cross-section) test and a short-run (pooled cross-section timeseries) test for convergence in TEV and SE. Let Ai,t be a measure of firm i’s productivity
at time t. The regression equations of the long-run (L) and short-run (S) tests for absolute
convergence have the following forms:
g iA( L )  ln A2 i  ln A1i   A( L )   A( L ) ln A1i   iA( L ) ,
A1i  t 1 Ai ,t / s ,
s
(2.1)
A2i  t su 1 Ai ,t /(T  s  u)
T
g iA,t( S )  ln Ai ,t  ln Ai ,t 1   A( S )  A( S ) ln Ai ,t 1   iA,t( S ) ,
(2.2)
where g iA( L ) is the growth rate of firm i’s productivity from the initial period to the final
period; t = 1, …,s is the initial period; t = s+u+1, …, T is the final period; and u = T – 2s
 0 is the time lag between the initial and final periods. Absolute -convergence implies
that  A(.) < 0.
12
The regression equations of the long-run (L) and short run (S) tests for conditional
convergence have the following forms:
g iA( L )  ln A2 i  ln A1i   A( L )   A( L ) ln A1i   A( L ) X 1i   iA( L ) ,
(3.1)
A1i  t 1 Ai ,t / s , X 1i  t 1 X i ,t / s , A2i  t su 1 Ai ,t /(T  s  u) ,
s
s
T
and
giA,t( S )  ln Ai ,t  ln Ai ,t 1   A( S )   A( S ) ln Ai ,t 1   A( S ) X i ,t 1  iA,t( S ) .
(3.2)
Conditional -convergence implies that  A(.) < 0. X i ,t is a vector of firm-specific
characteristics which holds constant the steady-state productivity level of firm i.
Although Sala-i-Martin (1996) showed that a necessary condition for the existence of convergence is the existence of -convergence, a negative coefficient for -convergence
could merely be the result of measurement errors and random shocks instead of real
convergence. This is the so-called “regression towards the mean” [see Friedman (1992)
and Quah (1993)]. Therefore, if -convergence is to measure real convergence, it has to
coincide with -convergence. Tests for -convergence consider the movements of a
measure of dispersion, such as standard deviation. Lichtenberg (1994) found that the
degree of convergence depends not only on the degree of mean-reversion (i.e.,  A(.) and
 A(.) ), but also on the variance of the disturbance relative to the variance of the initial
productivity. He therefore suggested a test statistic, c A(.)  R 2 /  2 , for the hypothesis of
-convergence, where  = 1   A(.) and 1   A(.) for equations (2) and (3), respectively.
This test statistic has an F( NT  k , NT  k ) distribution, where k is the number of
explanatory variables.
13
From equation (1), the technical efficiency (TE) of a bank at a particular point in
time is composed of pure technical efficiency (TEV) and scale efficiency (SE). Therefore,
the long-run (L) and short run (S) tests for the absolute convergence of TEV, SE and TE
are specified as follows:
g iTEV ( L )  ln TEV 2 i  ln TEV 1i   TEV ( L )  TEV ( L ) ln TEV 1i   iTEV ( L ) ,
(4.1)
(S )
(S )
,
g iTEV
 ln TEVi ,t 1   TEV ( S )  TEV ( S ) ln TEVi ,t   iTEV
,t 1
,t 1
(4.2)
g iSE ( L )  ln SE 2 i  ln SE1i   SE ( L )  SE ( L ) ln SE1i   iSE ( L ) ,
(5.1)
(S )
SE ( S )
(S )
g iSE
 SE( S ) ln SEi ,t   iSE
,t 1  ln SEi ,t 1  
,t 1 .
(5.2)
Note that TEi ,t  TEVi ,t  SEi ,t . TEV1i (or SE1i ) and TEV 2 i (or SE2 i ) are
analogous to A1i and A2 i in equation (2). If all banks have a common efficient scale,
they will continue to expand to fully exploit the gains from the scale economy until the
minimum efficient scale is reached. In other words, the only difference between banks
lies in their initial sizes, and they tend to converge to the same size and end up with the
same level of scale efficiency in the steady state (i.e., SE (.)  0 ). Similarly, if all banks
have the same behavioral characteristics that determine the level of X-efficiency, they
tend to converge to the same level of pure technical efficiency (i.e., TEV (.)  0 ).
Equations (4) - (6) can be used to test for the following alternative hypotheses:
Hypothesis 2a: Absolute convergence in TEV exists among banks.
Hypothesis 2b: Absolute convergence in SE exists among banks.
14
For each of the above hypotheses to be supported, the conditions for both  convergence and  -convergence have to be satisfied. According to equation (1),
convergence in TE among banks is warranted if both Hypotheses 2a and 2b are accepted.
The long-run (L) and short-run (S) tests for the conditional convergence of TEV, SE, and
TE can be conducted by estimating the following equations:
g iTEV ( L )  ln TEV 2 i  ln TEV 1i   TEV ( L )   TEV ( L ) ln TEV 1i   TEV ( L ) X 1i   iTEV ( L ) , (6.1)
(S )
(S )
,
giTEV
 ln TEVi ,t 1   TEV ( S )   TEV ( S ) ln TEVi ,t   TEV ( S ) X i ,t  iTEV
,t 1
,t 1
(6.2)
g iSE ( L )  ln SE 2 i  ln SE1i   SE ( L )   SE ( L ) ln SE1i   SE ( L ) X 1i   iSE ( L ) ,
(7.1)
(S )
SE ( S )
(S )
giSE
  SE( S ) ln SEi ,t   SE( S ) X i ,t  iSE
,t 1  ln SEi ,t 1  
,t 1 ,
(7.2)
X i ,t in equations (6) – (7) is a vector of the firm-specific determinants of X-efficiency,
which holds constant the steady-state technical efficiency of firm i. In contrast to
Hypothesis 2a, equation (7) implies that banks with different behavioral characteristics
will converge to different sizes and end up with different levels of scale efficiency in the
steady state if  SE (.)  0 . Similarly, if  TEV (.) < 0, equations (7) implies that banks with
different behavioral characteristics will converge to different levels of pure technical
efficiency. Equations (7) - (9) can be used to test for the following alternative hypotheses:
Hypothesis 3a: conditional convergence in TEV exists among banks.
Hypothesis 3b: conditional convergence in SE exists among banks.
For each of the above hypotheses to be supported, the conditions for both  convergence and  -convergence have to be satisfied. According to equation (1),
conditional convergence in TE among banks is warranted if: Hypotheses 3a and 3b are
accepted; Hypotheses 3a and 2b are accepted; or, Hypotheses 3b and 2a are accepted
15
4. Data
This paper has employed the intermediation approach in defining the input and
output components of banking services (Sealey and Lindley, 1997). Commercial banks in
China collect deposits and employ labor and fixed capital to transform these funds into
interest and non-interest incomes. The three components in the input vector are deposits
(Di,t), labour input (Li,t), and fixed capital (Ki,t). Di,t is defined as the sum of interestbearing and non-interest-bearing deposits from customers, other banks and the central
bank. Li,t is measured by the number of employees. Ki,t is the book value of net fixed
assets (land, buildings and equipment).
In China, commercial banks are subject to many controls in the strategic interests
of financial stability. They have been prohibited from providing insurance, securities and
trust services directly. Benchmark interest rates on loans and deposits are determined by
the central bank. With these restrictions as well as foreign exchange control in place, the
number of products offered by commercial banks in China is very limited. In this study,
the interest incomes (INTIN i,t) and non-interest incomes (NONINTIN i,t) are considered as
outputs. While INTIN are mainly derived from loans and national bond holdings,
NONINTIN i,t include fee incomes from providing guarantees, foreign exchange services,
and commission incomes from insurance companies and fund management companies
selling their insurance policy and investment funds at bank branches.14 As such, INTINi,t
and NONINTINi,t are the two components in the output vector.
16
Four bank-specific factors (Xi,t) are included as determinants of X-efficiency,
namely, ownership type, the scope of domestic coverage, the extent of international
operations, and the education level of staff. They are defined as a dummy variable
(OWNi,t) =1 for joint-stock ownership, or =0 otherwise; the number of offices run by the
bank on the Mainland (DOF i,t); the number of countries in which the bank has branches
(FBR i,t); and the percentage of staff holding a post-secondary qualification or above
(EDU i,t). Table 2 shows the summary statistics of the input, output and bank-specific
variables.
[Insert Table 2 here]
A priori, joint-stock ownership may help to mitigate the agency problem between
owners and managers, and to enhance managerial incentives (See Berger et al., 1993). A
large number of domestic offices may generate more business opportunities and bring in
scale economies. Moreover, international operations do not only bring in more business
opportunities but also the benefits of risk diversification (Ursacki and Vertinsky, 1992).
Finally, a high proportion of more educated staff will promote product innovation and
reduce credit and operation risks (Leung and Young, 2005). Ceteris paribus, each factor
is expected to increase the X-efficiency of a bank.
14
Trading in bonds, PBOC bills, foreign exchange and derivative products is limited due to the financial
controls and the absence of an active money market rate in pricing these products.
17
The analysis focused on an initial sample containing 17 nationwide commercial
banks. Data have been collected for the period 1996 to 2005. 1996 was chosen as the
start year since, as previously discussed, the government had by then built a formal legal
and regulatory infrastructure upon which all nationwide commercial banks grew, with
their operations being essentially motivated by profit (efficiency) considerations.
As only 12 banks have complete records for the data period, the working sample has
1080 observations before the creation of lagged variables. 15 The data on all input and
output variables were taken from financial statements of the banks in Almanac of China’s
Finance and Banking. The data were then cross checked for their consistency from the
Bankscope and annual reports of banks. Bank-specific data are collected from the
Bankers’ Almanac, Bankscope, and fieldwork interviews with Chinese banks in Shanghai
in 2006 and 2007.
5. Results
In Table 3, the summary statistics of TE, TEV and SE , as well as their
differences for the big four and the other joint-stock banks, are presented. Whereas the
big four banks have a slightly higher TEV than the other banks, the difference is not
statistically significant. On the other hand, the big four have lower SE and TE scores and
these differences are statistically significant. Within the sampling period, the big four
15
The Evergrowing Bank , the China Zheshang Bank and the Bohai Bank did not have complete records
for the data period as they started their business after 1996. Meanwhile, due to incomplete data on the
China Everbright Bank and the Guangdong Development Bank, these banks were also excluded from the
analysis.
18
banks mainly operated with decreasing returns to scale.16 The results about the relative
inefficiency of the big four banks have reinforced the findings of previous studies on the
efficiency of Chinese banks. [See Berger et al. (2007), Chen et al. (2005) and Fu and
Heffernan (2007)]. To summarise, Hypothesis 1a is rejected but the difference is not
significant. Hypotheses 1b and 1c are supported by empirical evidence.
[Insert Table 3 here]
On an anecdotal note, government specific policies might explain the changes in
technical efficiency of the big four banks between 1996 and 2005. In a bid to increase
their efficiency, the government has injected capital into the big four banks and arranged
to purchase non-performing loans from them in 1998 and 2000.
In August 1998, the big four banks purchased bonds worth a total of Rmb 270
billion issued by Ministry of Finance (MOF) with reserve deposits. The MOF injected
the entire proceeds as capital into the big four banks which saw an equal reduction of
their liabilities to the PBOC through a re-call of the loans to the bank. The balance sheets
of the four banks remained unchanged [see Mo (1999)]. This capital injection increased
their interest incomes (output) arising from holding interest-bearing national bonds, and
decreased the banks’ funds from the PBOC (input). This may explain the increase in the
16
Between 1996 and 2005, the big four banks operated with either decreasing returns to scale (DRS) or
constant returns to scale (CRS) only, with DRS and CRS accounting for 85% and 15% of the total number
of firm-year observations respectively.
19
overall technical efficiency of the big four banks from 1997 to 1998 (See Table 4).
In 2000, the four state-owned bank asset management companies (AMCs)
purchased non-performing loans totaling Rmb 1.39 trillion at book value made to stateowned enterprises before 1995.17 Each AMC issued 10-year bonds, guaranteed by the
MOF to its partner bank to finance the purchase of the bank’s assets transferred to them.
If all loan disposals were from loans overdue for more than 1 year and their interest
incomes had not been recorded, the overall technical efficiency of the banks would have
increased through a rise in interest incomes from bonds issued by the AMCs.18
A peculiar finding in Table 4 is that the technical efficiency of the big four banks
actually dropped after the loan-disposal exercise in 2000. The drop may be attributed to
the fact that some loans overdue for less than 1 year (with interest incomes) were
disposed, or some interest incomes on loans overdue for more than 1 year had not been
written off before they were transferred to the AMCs.
[Insert Table 4 here]
We now turn to an investigation of whether convergence of productivity among
the Chinese banks has occured. In table 5, the sampling period is divided into two blocks:
1996-2000; and 2001-2005. This table shows that the sampled banks experienced positive
17
In 1999, four state-owned asset management companies (AMCs) were established, with each partnering
and purchasing non-performing loans (classified as overdue, idle and bad loans) from one big four bank:
Huarong with (ABC); Great Wall with (BOC), Cinda (CCB); and Orient (ICBC).
18
According to the Accounting Regulations for Financial Institutions issued by the Ministry of Finance in
1993, interests on loans overdue for more than 1 year should not be recorded as incomes.
20
growth in all components of TE. Some preliminary evidence for convergence can also be
discerned. First, the declining dispersion of growth across banks could be an indication of
 -convergence. Second, the narrowing gap between the maximum and minimum values
for each TE component implies that the initially most unproductive banks grew faster
than the initially most productive ones.
[Insert Table 5 here]
Long-run tests for the hypotheses of absolute convergence (i.e., Hypotheses 2a –
2c) were conducted by estimating equations (4.1), (5.1) and (6.1) by the method of
ordinary least squares. To allow for different time lags between the initial and final
periods, the two equations were estimated for values of u (the time lag between the initial
and final periods) of 0, 2, and 4. The results of the long-run tests for absolute
convergence in pure technical efficiency (TEV), scale efficiency (SE) and overall
technical efficiency (TE) appear in Table 6.
[Insert Table 6 here]
21
In Table 6, the estimates for TEV ( L ) and  SE ( L ) are all significantly negative for all
values of u, which is evidence for mean reversion (i.e.,  -convergence). cTEV ( L ) and
c SE ( L ) are the test statistics based on Lichtenberg (1994) for  -convergence in TEV and
SE, respectively. If  -convergence is to measure real convergence, it has to coincide
with  -convergence [Friedman (1992) and Quah (1993)]. The results with regard to  convergence are mixed: cTEV ( L ) is significant for all values of u, while c SE ( L ) are
significant only when u = 4.
[Insert Table 7 here]
Table 7 presents the results of the short-run tests for absolute convergence in pure
technical efficiency (TEV) and scale efficiency (SE). For both TEV and SE, the negatively
significant  -coefficients are consistent with the results of the long-run tests. However,
the results show that cTEV (S ) and c SE ( S ) are far from significant. Hence, despite the
significance of TEV (S ) and  SE ( S ) , the short-run test provides no evidence for absolute
convergence in pure technical efficiency and scale efficiency.
In sum, the LR tests provide full support for Hypothesis 2a, but not for Hypothesis 2b.
Moreover, the insignificant convergence coefficient in the SR test implies that the
convergence in pure technical efficiency among banks may only be a long-run
phenomenon.
22
The evidence suggests that a common steady-state level of scale efficiency does
not exist among the Chinese banks. Indeed, these banks will converge unconditionally to
the same level of pure technical efficiency in the steady state, as if they had the same
behavioural characteristics. A plausible explanation is that the operations and production
plans of a Chinese bank are technically simple and unsophisticated due to the various
restrictions imposed. Furthermore, all banks, be they wholly or majority-owned by the
government, have equal access to the government-directed technologies that can speedily
transmit across banks. 19 The findings are inconsistent with the results that absolute
convergence in any measures of efficiency does not exist among bank holding companies
in the U.S [See Fung (2006)].
[Insert Table 8 here]
Table 8, shows the results of the LR tests for the convergence of efficiency on the
determinants of X-efficiency by including four additional explanatory variables:
education level of staff (EDU), number of countries in which the bank has branches
(FBR), ownership type (OWN), and number of offices run by the bank in the Mainland
China (DOF). The estimates of  and c are significant for both TEV and SE, which
indicate a certain form of convergence. First, conditional convergence in TEV is rejected
19
The PBOC has owned and provided the technical infrastructure for national payment systems and the
inter-bank markets for foreign exchange, funds transfer and clearing, trading and settlement in bonds,
money market products such as PBOC bills, and corporate bills.
23
for u = 2 and 4 because none of the conditioning variables are statistically significant.
This result is consistent with that from the LR test for absolute convergence in TEV (see
Table 6). Second, conditional convergence of SE for all values of u is evidenced by the
significant coefficient of EDU.
[Insert Table 9 here]
Moreover, Table 9, shows the results of the SR tests for the convergence of
efficiency on the determinants of X-efficiency by including 11 firm dummies and four
additional explanatory variables (the same as in Table 8).
Again, conditional
convergence in TEV is rejected because none of the conditioning variables are
statistically significant. Conditional convergence of SE is evidenced by the significant
coefficient of DOF and the 8 significant firm dummies.
To conclude, Hypothesis 3a is rejected in both the LR and SR tests, while
Hypothesis 3b is accepted in both the LR and SR tests. According to equation (1), as
Hypotheses 3b and 2a are accepted, conditional convergence in TE among Chinese banks
is confirmed. This means that the steady-state SE and TE to which a Chinese bank is
converging are conditional on the bank’s own level of X-efficiency, which is
significantly influenced by the education level of its workforce.
OWN and FBR are relatively unimportant in determining the X-efficiency of the
Chinese banks. The adoption of a joint-stock structure appears to have no impact on the
24
conditional convergence of the productivity, even though BOC and CCB went through a
corporate restructuring to become a joint-stock bank in 2004, and ICBC followed suit in
2005. This is because, even though a joint-stock national commercial bank has a wider
shareholder base, its majority shareholders involve local government or its subsidiary and
other state-owned firms. In addition, the senior management personnel of a joint-stock
bank needs to be approved by the government and many of them have either worked in
the PBOC or the big four banks before. As such, its operations are subject to the same
central and local government policy influences as the big four banks.20 Meanwhile, apart
from the BOC which has the most extensive international network among PRC
commercial banks, the scale of international operations of all other banks is not large and
the benefits from diversification are limited. FBR therefore is not a significant
determinant of the X-efficiency.
Moreover, DOF is only found to have a significant impact on the conditional
convergence in SE in the short run. Apparently, an increase in the number of offices will
eventually set in scale diseconomies, especially as most bank offices in China are labourintensive in providing retail banking services. EDU is found to be a significant
determinant of scale efficiency and overall technical efficiency in the long run. So, a
higher proportion of educated staff will increase the minimum efficient scale and the
overall technical efficiency in the steady state to which it will converge. With a more
flexible structure than the state banks in employing staff on market terms, the joint-stock
banks are expected to have a higher SE and TE in the steady state.
20
It has been stated explicitly in the Commercial Bank Law that all commercial banks in China need to
follow the guidance of the state industrial policy to make loans to meet economic and social development
needs (See Commercial Bank Law (1995) and (2003), Chap 4, article no.34).
25
6. Conclusions
For historical and political reasons, the big four banks have remained the largest
national commercial banks with extensive branch networks all over the country. In this
study, there is evidence that they have been operating with decreasing returns to scale and
have a statistically significant lower scale and overall technical efficiencies than the other
national commercial banks.
This study provides evidence of convergence among Chinese banks. The path of
convergence is different from that in the U.S. whereby the initially smaller and less
productive banks grow faster than the larger and more productive banks so as to catch up
with them in size and productivity. In China, whereas the smaller joint-stock banks grow
faster than the big four banks in assets, the big four banks need to catch up with the jointstock banks in terms of productivity. The study shows that the national commercial banks
in China converge unconditionally to a common pure technical efficiency and this is
probably attributed to the relatively unsophisticated bank operations due to controls and
the prevalent state ownership. It is further shown that a Chinese bank will converge to its
own scale efficiency and overall technical efficiency in the long run, conditional on the
bank’s level of X-efficiency which in turn is significantly influenced by the education
level of its staff. In this regard, a human resources development policy focusing on staff
education would appear to be important means of enhancing future bank competitiveness.
Political considerations such as concerns over employment of state-owned
enterprises and social stability have continued to prompt the big four banks to lend to
inefficient state-owned enterprises. The big four banks may not be able to shut down
26
unprofitable branches on a large scale and this is especially the case for the operations of
the Agricultural Bank of China in the rural areas. Furthermore, the implementation of
specific government policies such as capital injection into the big four banks can
influence bank productivity. All these may infer that the path of productivity convergence
of the Chinese banks is not an easily predictable one. If the government can carry on
bank reforms with an increased focus on de-regulation, allowing commercial banks to
engage in a wider scope of operations, and with less government administrative influence
over bank operations, it appears that significant gains in efficiency of the overall Chinese
banking industry could be forthcoming. Further research in this direction is warranted.
27
References
Banker, R.D., Charnes, A., and Cooper, W.W. (1984), ‘Some models for estimating
technical and scale inefficiencies in data envelopment analysis’, Management
Science, 30, 1078-1092.
Barro, R.J. (1991), ‘Economic growth in a cross section of countries’, Quarterly Journal
of Economics, 106, 407-443.
Berger, A.N., Hasan, I., and Zhou, M. (2007), ‘Bank ownership and efficiency in China:
what lies ahead in the world’s largest nation?’, Bank of Finland Research,
Discussion papers 16. 2007, Bank of Finland, Finland.
Berger, A.N., Hunter, W.C., and Timme, S.G. (1993), ‘The efficiency of financial
institutions: A review and preview of research past, present, and future’, Journal
of Banking and Finance, 17, 221-249.
Berger, A.N. and Mester, L.J. (1997), ‘Inside the black box: What explains differences in
the efficiencies of financial institutions’, Journal of Banking and Finance, 21,
895-974.
Baumol, W.J. (1986), ‘Productivity growth, convergence, and welfare: what the long-run
data show’, American Economic Review, 76, 1072-1085
Chen, X., Skully, M., and Brown, K. (2005), ‘Banking efficiency in China: Application
of DEA to pre- and post-deregulation eras: 1993–2000’, China Economic Review,
16(3), 229-245.
Coelli, T.J. (1996), ‘A guide to DEAP Version 4.1: A data envelopment analysis
(computer) program’, CEPA Working Paper 96/08, Centre for Efficiency and
Productivity Analysis, University of New England.
Evanoff, D.D. and Israilevich, P.R. (1991), ‘Productive efficiency in banking’,
Econometric Perspectives, 15, 11-32.
Farrell, M.J. (1957), ‘The measurement of productive efficiency’, Journal of the Royal
Statistical Society, Series A 120, 253-281.
Friedman, M. (1992), ‘Do old fallacies ever die?’, Journal of Economic Literature, 30(4),
2129-2132.
Fu, X., and Heffernan, S. (2007), ‘‘Cost X-efficiency in China’s banking sector’, China
Economic Review, 18(1), 35-53.
Fung, M. (2006), ‘Scale economies, X-efficiency, and convergence of productivity
among bank holding companies’, Journal of Banking and Finance, 30, 2857-2874
Hughes, J.P. and Mester, L.J. (1998), ‘Bank capitalization and cost: Evidence of scale
economies in risk management and signaling’, Review of Economics and
Statistics, 314-325.
28
Hunter, W.C. and Timme, S.G. (1995), ‘Core deposits and physical capital: A reexamination of bank scale economies and efficiency with quasi-fixed assets’,
Journal of Money, Credit and Banking, 27, 165-185.
Leibenstein, H. (1966), “Allocative efficiency vs. X-efficiency”, American Economic
Review, 56:392-415
Leibenstein, H. (1978), “X-inefficiency Xists – Reply to an Xorcist”, American
Economic Review, 68: 203-211
Leung, M. K. and Young, T. (2005). “Entry of Foreign Banks in Shanghai: Implications
for Business Strategies in an Increasingly Competitive Market.” Managerial and
Decision Economics 26, 387-395.
Mo, Y.K. (1999). ‘A review of recent banking reforms in China’, BIS Policy Papers No.
7 - Strengthening the Banking System in China: Issues and Experience
Lichtenberg, F.R. (1994), ‘Testing the convergence hypothesis’, Review of Economics
and Statistics, 76(3), 576-579.
Quah, D. (1993), ‘Galton’s fallacy and tests of the convergence hypothesis’,
Scandinavian Journal of Economics, 95(4), 427-443.
Sala-i-Martin, X.X. (1996), ‘The classical approach to convergence analysis’, Economic
Journal, 106, 1019-1036.
Sealey, C. and Lindley, J. (1997), ‘Inputs, outputs, and a theory of production and cost at
depository financial institutions’, Journal of Finance, 32, 1251-1266.
Stigler, G. (1976), “The Xistence of X-efficiency”, American Economic Review, 66:213216.
Ursacki, T. and Vertinsky, I. (1992). “Choice of Entry Timing and Scale by Foreign
Banks in Japan and Korea.” Journal of Banking and Finance 16, 405-421.
29
List of Tables
Table 1: The market share by assets of different types of banking institutions in China
2003
2004
2005
Big four
58.2%
53.6%
52.5%
Joint-stock nationwide
commercial banks
14.6%
14.9%
15.5%
City commercial banks
5.6%
5.4%
5.4%
Others a
21.6%
26.1%
26.6%
Sources: PBOC for 2003, China Banking Regulatory Commission for 2004 and 2005
Note a:‘Others’ include the three policy banks, rural commercial banks, foreign banks, urban and
rural credit co-operatives, finance companies, trust and investment companies, financial
leasing companies and postal savings.
30
Table 2: Summary statistics of inputs, outputs and bank-specific variables
Mean
Stdev
Max
Min
Deposits (D i,t)
(customers + inter-bank
government)
1118065.1
1417163
5805015
6760.38
Fixed Assets (K i,t)
(Rmb million)
21657.074
27281.945
112272
111.38
Employees (L i,t)
136582.442
192679.58
567230
364
Interest incomes
51636.439
61675.654
224457
284.66
2663.254
3616.51
14523
4.13
0.651
0.478
1
0
10040.538
16028.847
65870
15
2.042
2.888
9
0
69.488
16.518
97.4
24.3
(INTIN i,t)
(Rmb million)
Non-interest incomes
(NONINTIN i,t)
(Rmb million)
Ownership (OWN i,t)
Domestic offices (DOF i,t)
No. of foreign countries
with a branch (FBR i,t)
Education level (%)
(EDUi,t)
31
Table 3: Summary statistics of overall technical efficiency, pure technical efficiency and
scale efficiency for the big four and other banks
Big four banks
Other banks
Difference
Overall technical efficiency
1996 – 2005
0.777
(0.141)
0.921
(0.127)
-0.144*
(t-statistic = -1.722)
0.977
(0.048)
0.971
(0.066)
0.006
(t-statistic = 0.179)
0.795
(0.138)
0.948
(0.109)
-0.153*
(t-statistic = -1.936)
Pure technical efficiency
1996 – 2005
Scale efficiency
1996 - 2005
Notes: Standard deviations are shown in parentheses. * - significant at 5% level (d.o.f. =
118).
32
Table 4: Technical efficiency index of the big four banks during 1997 to 2000
ABC
BOC
CCB
ICBC
0.686
0.691
0.696
0.524
1997
1998
0.893
1
0.814
1
1999
0.898
1
0.878
1
2000
0.712
0.85
0.685
0.78
33
Table 5: Summary statistics of overall technical efficiency, pure technical efficiency and
scale efficiency for all banks during the period of 1996 to 2005
Mean
1996-2000
2001-2005
0.857
0.910
Mean
1996-2000
2001-2005
0.973
0.982
Mean
1996-2000
2001-2005
0.881
0.926
Overall technical efficiency (TE)
Max
Min
1
1
0.424
0.612
Pure technical efficiency (TEV)
Max
Min
1
1
0.738
0.844
Scale efficiency (SE)
Max
Min
1
1
The sample includes 12 banks from 1996 to 2005.
34
0.424
0.663
Stdev
0.168
0.113
Stdev
0.068
0.038
Stdev
0.161
0.104
Table 6: Long-run (cross-section) tests for absolute convergence in pure technical efficiency (TEV) and scale efficiency (SE)
TEV ( L )
SE ( L )
Lag
Dependent variable = g i
Dependent variable = g i
u=0
 -convergence: TEV ( L ) = -0.845**
 -convergence: SE ( L ) = -0.465**
(-4.435)
 -convergence: c
TEV ( L )
= 18.296**
R2 = 0.663
u=2
 -convergence: c
= 0.655
R2 = 0.433
Absolute convergence: accepted
Absolute convergence: rejected
 -convergence: 
 -convergence: SE ( L ) = -0.612**
TEV ( L )
 -convergence: c
TEV ( L )
= -0.735**
(-3.192)
= 3.632*
R2 = 0.505
u=4
(-2.764)
SE ( L )
(-3.513)
 -convergence: c
SE ( L )
= 2.024
R2 = 0.552
Absolute convergence: accepted
Absolute convergence: rejected
 -convergence: 
 -convergence: SE ( L ) = -0.843**
TEV ( L )
 -convergence: c
TEV ( L )
= -0.982**
(-4.838)
= 1516.67**
(-4.691)
 -convergence: c
SE ( L )
= 19.203**
R2 = 0.701
R2 = 0.688
Absolute convergence: accepted
Absolute convergence: accepted
Notes: The equations,
g iTEV ( L )  ln TEV 2 i  ln TEV 1i   TEV ( L )  TEV ( L ) ln TEV 1i   iTEV ( L ) , and
g iSE ( L )  ln SE 2 i  ln SE1i   SE ( L )  SE ( L ) ln SE1i   iSE ( L ) ,
35
were estimated by ordinary least squares. TEV1i 

s
t 1
TEVi ,t / s and TEV 2i  t su 1TEVi ,t /(T  s  u) . SE1i TE1i , SE2 i and TE2 i are
T
defined similarly. The sample includes 12 banks from 1996 to 2005. Values in parentheses are t-statistics for the estimated coefficients.
c  R 2 /(1   ) 2 ~F(N-2, N-2) is the test statistic for  -convergence suggested by Lichtenberg (1994). ** stands for significance at 1% level.
36
Table 7: Short-run (pooled cross-section time-series) tests for absolute convergence in
pure technical efficiency (TEV) and scale efficiency (SE)
Dependent variable =
Dependent variable =
TEV ( S )
(S )
g i ,t 1
g iSE
,t 1
Coefficient
convergence
for
 -convergence
R2
Absolute convergence

-
TEV ( S )  -0.562**
(-7.279)
SE (S )  -0.472**
(-8.000)
cTEV ( S )  0.578
cSE (S )  0.505
0.333
0.376
Rejected
rejected
Notes: The equations
(S )
(S )
,
g iTEV
 ln TEVi ,t 1   TEV ( S )  TEV ( S ) ln TEVi ,t   iTEV
,t 1
,t 1
and
(S )
SE ( S )
(S )
g iSE
 SE( S ) ln SEi ,t   iSE
,t 1  ln SEi ,t 1  
,t 1 ,
were estimated by ordinary least square. The sample includes 12 banks from 1996 to 2005.
Values in parentheses are t-statistics. c  R 2 /(1   ) 2 ~F( NT  k , NT  k ) is the test statistic
for  -convergence suggested by Lichtenberg (1994), where k is the number of explanatory
variables. ** stands for significance at 1% level.
37
Table 8: Long-run tests for conditional convergence in pure technical efficiency (TEV),
and scale efficiency (SE) – with determinants of X-efficiency.
Panel (8a): u = 0
Dependent variable = g iTEV ( L )
Dependent variable = g iSE ( L )
 TEV ( L )  -0.868**
 SE (L )  -0.827**
(-5.373)
(-6.509)
cTEV (L)  33.587**
cSE(L)  26.645**
EDU i
FBRi
OWN i
DOFi
0.002* (2.478)
0.004* (2.911)
0.008 (1.905)
0.008 (1.608)
0.000 (-0.012)
0.040 (0.668)
0.000 (1.132)
0.000 (-0.475)
Adj. R 2
0.765
0.893
Accepted
accepted
Dependent variable = g iTEV ( L )
Dependent variable = g iSE ( L )
 TEV ( L )  -0.790**
 SE (L )  -0.871**
(-3.695)
(-10.592)
cTEV (L)  7.264**
cSE(L)  54.462**
0.002 (2.192)
0.004** (3.175)
0.007 (1.484)
-0.001 (-0.259)
-0.013 (-0.318)
-0.007 (-0.164)
0.000 (0.948)
0.000 (-1.986)
0.566
0.952
Rejected
accepted
Coefficient for  -convergence
 -convergence
Conditional convergence
Panel (8b): u = 2
Coefficient for  -convergence
 -convergence
EDU i
FBRi
OWN i
DOFi
Adj. R 2
Conditional convergence
38
Panel (8c): u = 4
Coefficient for  -convergence
 -convergence
EDU i
FBRi
OWN i
DOFi
Adj. R 2
Conditional convergence
Notes: The equations
Dependent variable = g iTEV ( L )
Dependent variable = g iSE ( L )
 TEV ( L )  -1.005**
 SE (L )  -0.875**
(-5.106)
(-9.458)
cTEV (L)  19937.44**
cSE(L)  57.154**
0.002 (1.989)
0.004* (3.028)
0.007 (1.373)
-0.003 (-0.538)
-0.019 (-0.379)
-0.072 (-1.196)
0.000 (0.967)
0.000 (-2.016)
0.706
0.945
Rejected
accepted
g iTEV ( L )  ln TEV 2i  ln TEV 1i   TEV ( L )   TEV ( L ) ln TEV 1i   TEV ( L ) X 1i  iTEV ( L ) , and
g iSE ( L )  ln SE 2i  ln SE1i   SE ( L )   SE ( L ) ln SE1i   SE ( L ) X 1i  iSE ( L ) ,
were estimated by ordinary least square. The sample includes 12 banks from 1996 to 2005.
Variables included in X1i are: education level of staff (EDU), number of countries that the bank
has branches (FBR), ownership type (OWN = 1 if majority privately-owned), and number of
offices on the mainland (DOF). Values in parentheses are t-statistics for the estimated coefficients.
c  R 2 /(1   ) 2 ~F( N  k , N  k ) is the test statistic for  -convergence suggested by
Lichtenberg (1994), where k is the number of explanatory variables. ** stands for significance at
1% level. * stands for significance at 5% level.
39
Table 9: Short-run (pooled cross-section time-series) tests for conditional convergence in pure
technical efficiency (TEV) and scale efficiency (SE) – with determinants of X-efficiency
(S )
(S )
Dependent variable = g iTEV
Dependent variable = g iSE
,t 1
,t 1
Coefficient for  convergence
 TEV (S )  -0.739**
 SE (S )  -0.531**
(-7.823)
(-8.111)
cTEV (S )  1.466*
cSE(S )  1.396*
EDU it
0.000 (0.467)
-0.001 (-0.486)
FBRit
0.004 (1.677)
0.022 (1.340)
OWN it
0.015 (0.767)
-0.056 (-0.845)
DOFit
0.000 (0.180)
0.000** (4.281)
0
8
0.316
0.481
Rejected
accepted
 -convergence
Number of
dummies*
Adj. R 2
significant
Conditional convergence
Notes: The equations,
firm-
(S )
(S )
, and
g iTEV
 ln TVEi ,t 1   TEV ( S )   TEV ( S ) ln TEVi ,t   TEV ( S ) X i ,t  iTEV
,t 1
,t 1
(S )
SE ( S )
(S )
g iSE
  SE( S ) ln SEi ,t   SE( S ) X i ,t  iSE
,t 1  ln SEi ,t 1  
,t 1 ,
were estimated by ordinary least square. The sample includes 12 banks from 1996 to 2005. Variables
included in X it are: education level of staff (EDU), number of countries that the bank has branches
(FBR), ownership type (OWN = 1 if majority privately-owned), and number of offices on the mainland
(DOF).
Values
in
parentheses
are
t-statistics
for
the
estimated
coefficients.
c  R 2 /(1   ) 2 ~F( NT  k , NT  k ) is the test statistic for  -convergence suggested by Lichtenberg
(1994), where k is the number of explanatory variables. ** stands for significance at 1% level. * stands
for significance at 5% level.
40