Role of Bank Regulation on Bank Performance: Evidence from Asia-Pacific Commercial Banks

The banking industry is an essential financial intermediary, thus the efficient operation of banks is vital for economic development and social welfare. However, the 2008 global financial crisis triggered a reconsideration of the banking systems, as well as the role of government intervention. The literature has paid little attention to the banking industry in the Asia-Pacific region in the context of bank efficiency. This study employs double bootstrap data envelopment analysis to measure bank efficiency and examine the relationship between regulation, supervision, and state ownership in commercial banks in the Asia-Pacific region for the period 2005 to 2014. Our results indicate that excluding off-balance sheet activities in efficiency estimations lead to underestimating of the pure technical efficiency, while overestimating the scale efficiency of banks in the Asia-Pacific region. Cross-country comparisons reveal that Australian banks exhibit the highest levels of technical efficiency, while Indonesian banks exhibit the lowest average. Our bootstrap regression results suggest that bank regulation and supervision are positively related to bank technical efficiency, while state ownership is not significantly related to bank efficiency. Furthermore, our findings show that tighter regulation and supervision are significantly related to higher efficiency for small and large-sized banks.


Introduction
Banking industries, as primary financial intermediaries, provides liquidity and payment services, transforms deposits into loans, and manages and monitors investment projects (Freixas and Rochet 2008). The efficient operation of banks not only enhances economic development, but also influences the income distribution of the economy (Barth et al. 2004). However, the 2008 Global Financial Crisis (GFC) provides evidence that banking industries are not always stable. Before the 2008 GFC, banking industries, especially those in the United States (US), were heavily involved in the real estate bubble and credit boom, through off-balance sheet (OBS) activities. The collapse of the banking industries in 2008 quickly spread to the global financial system (Kim et al. 2013).
In addition to the prevalent OBS activities (DeYoung and Torna 2013; Engle et al. 2014), inefficient regulation and supervision (Brunnermeier 2009) in the banking industries are among other possible reasons for the recently fragile financial system and massive economic turmoil. That GFC also triggered the reconsideration of the official interventions in the financial system (Cihak and Demirgüç-Kunt 2013). In practice, regulation and supervision define capital standards, set requirements for entry into the banking market, frame acceptable ownership structures, and provide business guidelines for the banking industries (Barth et al. 2013).
Compared to countries in other regions, most countries in the Asia-Pacific region have a bank-dominated financial system. Financial systems in the Asia-Pacific region have undergone profound deregulation and privatisation since the 1970s. Following the deregulation, banking industries in the Asia-Pacific region have experienced rapid growth in loans and investments. After the 1997 Asian Financial Crisis (AFC), governments in the region implemented a series of structural changes (and reforms), both in the banking systems, and regulatory and supervisory mechanisms. Following the 2008 GFC, most countries in the Asia-Pacific region had fully implemented the Basel II Accord, and were in a better position to introduce Basel III Accord regulations (International Monetary Fund 2013).
There are two main rationales for the existence of bank regulation and supervision. Firstly, regulation and supervision can mitigate potential conflicts of interest and externalities in the banking system, and thereby benefit the banking industry and social welfare (Kilinc and Neyapti 2012). Secondly, regulation and supervision can maintain the stability of fragile banking systems and function as a safety net for the financial system (Kroszner 1998). However, regulation and supervision are associated with extra costs for the banking systems. It is also difficult to reach equilibrium between different regulatory rules (Freixas and Rochet 2008).
As another major tool of government intervention in the banking industry, state ownership has been widely observed in the banking industry globally. The degree of state ownership in banks depends on factors such as economic and financial development, property rights, and financial openness (La Porta et al. 2002). Theoretically, there are two views supporting government ownership in the financial markets: Development and political views. The development view contends that some financial markets are not sufficiently developed for banks to be functional. Therefore, governments need to participate in the financial institutions to enhance the country's financial and economic development (Gerschenkron 1962). In the political view, state ownership in the banking industry is a way for politicians to affect banks' decisions and achieve their political objectives. When the government owns the bank, it will allocate capital resource to its supporters and gain votes (Shleifer and Vishny 1994;Shleifer 1998).
This paper investigates the impacts of the inclusion of OBS activities in bank efficiency measurement. Furthermore, we examine the relationship between bank regulation, supervision and state ownership with bank efficiency in the Asia-Pacific region. The remainder of the study is organised as the follows: Section 2 provides an overview of the Asia-Pacific banking industries; Section 3 reviews the related literature; Section 4 describes the data and methodology; Section 5 discusses the empirical results; and Section 6 concludes the paper.

Overview of Banking Industries in the Asia-Pacific Region
The banking system has dominated the financial system and has played a vital role in the economic development of the Asia-Pacific region over the previous two decades. Before the 1997 AFC, the Asia-Pacific region experienced financial deregulation and reforms, followed by rapid economic growth relative to the US and European countries. Throughout 1990 to 1996, the region experienced significant foreign capital inflow, high levels of domestic consumption, booming investments, and excessive credit expansion.
However, impotent regulation and supervision during the period of financial deregulation and reform exposed the system's weaknesses (Fu et al. 2014) in the region. Except for Australia, most economies in the region were severely affected by the 1997 AFC. More specifically, South Korea, Indonesia, Malaysia, the Philippines, and Thailand were directly affected, while Hong Kong, Singapore, and Japan were indirectly affected and experienced negative economic growth during this period. Following the 1997 AFC, governments in the region began a series of structural reforms and prudential regulatory policies to revive the economy and financial industry. Specifically, the supervisory authorities in the Asian region have contributed to the banks' better asset quality after the 1997 AFC (Rosenkranz and Lee 2019). In compliance with the more conservative regulatory policies, banks in the Asia-Pacific region have mostly increased their capital ratios (Capannelli and Filippini 2010). More surprisingly, the Asia-Pacific banking industry maintained a high return on assets (ROA) ratio during the 2008 GFC. Furthermore, the average ROA in the Asia-Pacific region was almost twice that of the rest of the world, as of the end of 2014; this was largely contributed by the rapid growth of the Chinese and Indonesian banking sectors (McKinsey Company 2016).

Efficiency Measurement
Efficiency is a commonly used concept to describe a firm's performance. The basic idea of efficiency measurement is to compare the observed production to the optimal production which operates on the production frontier. Parametric and nonparametric approaches are often used to conduct the approximation of the frontier and efficiency estimation. Both approaches are benchmarking methods, which exploit the distance function between observed production and the production frontier. Among the various techniques stemming from these two approaches, the two most popular approaches employed in the banking literature are the stochastic frontier analysis (SFA) (a parametric approach) and data envelopment analysis (DEA) (a nonparametric approach) (Fethi and Pasiouras 2010).

Inclusion of Off-Balance Sheet Activities in Efficiency Estimation
Considering the expansion in banks' business scopes during development of the industry, researchers currently recognise the importance of incorporating the off-balance sheet (OBS) activities in bank efficiency estimations. While most studies directly include OBS activities into efficiency estimations (see for example , Drake 2001;Drake and Hall 2003;Radić et al. 2012;Sufian et al. 2012), only limited numbers of studies provide any justification for the inclusion of OBS activities in efficiency estimations (Rogers 1998;Mester 1996;Clark and Siems 2002;Lieu et al. 2005;Pasiouras 2008a;Pasiouras 2010, 2014). These studies provide ambiguous evidence on the impacts of OBS activities inclusion in bank efficiency measurement. Rogers (1998) measured the efficiency of more than 10,000 commercial banks (including branches) in the US over the period 1991 to 1995. The author's results indicate that cost and profit efficiencies of commercial banks would both be underestimated when OBS activities are omitted. Similarly, Clark and Siems (2002) examined the impact of including OBS activities on US bank efficiency over the period 1992 to 1997. They concluded that OBS activities are useful for explaining variations in banks' costs and profits. The cost efficiency is higher with the inclusion of OBS activities, but their results demonstrate little changes in the profit efficiency measurement for the banks. Using the SFA approach, Lieu et al. (2005) measurde the cost efficiency of the Taiwanese banking industry from 1998 to 2001. They found that omitting OBS activities would lead to underestimating a bank's cost efficiency by 55%. In a study of the Greek banking industry from 2000 to 2004, Pasiouras (2008b) found that bank cost efficiencies are not significantly affected by omitting OBS activities as an output.
Using large samples from multiple banking industries around the world, Lozano-Vivas and Pasiouras ( , 2014 examined the impact of including OBS activities on cost efficiency, profit efficiencies, and Malmquist productivities measurements. They found mixed results. Lozano-Vivas and Pasiouras (2010) explored the cost and profit efficiency for 87 countries banks from 1999 to 2006 and found that cost efficiency would have been higher when considering OBS activities, while the results for profit efficiency were mixed. Using data from 84 countries over the period 1999 to 2006, Lozano-Vivas and Pasiouras (2014) estimated the Malmquist cost and profit productivity for banks. They found that bank profit productivity was higher with OBS activities, while cost productivity was not significantly affected. Moreover, their results suggested that the exclusion of OBS activities should jeopardise the regression results when examining the relationship between environmental factors and bank performance.

Bank Regulation and Supervision, and Bank Efficiency
Previous studies provide inconclusive evidence with regards to the relationship between regulation, supervision and bank performance using data from various countries or regions. As one of the first studies at the international level, Barth et al. (2004) find that activity restrictions are negatively related to bank efficiency. While market discipline can significantly boost bank efficiency, capital regulation and supervision power are not significantly related to bank performance. In addition, that state ownership is negatively related to bank efficiency. In a study by Barth et al. (2004), bank efficiency was measured with net interest margin and overhead costs (that is, lower net interest margins and overhead costs indicating higher bank efficiency).
Using 715 banks from 95 countries in 2003, Pasiouras (2008a) found empirical evidence to support the implementation of three pillars in the Basel II Accord. The authors' result indicates a positive correlation between capital adequacy regulation, official supervisory power, and market discipline with bank technical efficiency. Furthermore, deposit insurance has no significant relationship with bank efficiency. They also found that government and foreign ownership were associated with lower bank efficiency. In Chortareas et al.'s (2012) study, however, market discipline was found to be negatively related to the European banks' technical efficiency.
After measuring both cost and profit efficiency for banks from 74 countries from 2000 to 2004, Pasiouras et al. (2009) concluded that both official supervision and market discipline were positively related to both efficiency measurement. Additionally, they found that capital regulation would increase cost efficiency while reducing profit efficiency during the period. In contrast, activity restrictions improved profit efficiency but reduced cost efficiency. However, Lozano-Vivas and  study revealed that supervisory power was negatively related to cost efficiency and positively related to profit efficiency based on a larger dataset from 1999 to 2006.
More recently, Luo et al. (2016) examined the profit efficiency of banks from 140 countries over the period 1999 to 2011, and found that capital regulation, market discipline, and activity restrictions had positive relationships with bank efficiency. However, official supervision power was negatively related to bank efficiency. Focusing on banks from African countries, Triki et al. (2017) suggested that the impacts of regulation and supervision on bank performance depend on the bank size and risks. While other regulatory policies show no significant impact, capital stringency is found to be positively related to large banks with low risks.
Rather than using individual regulatory policies, Gardener et al. (2011) created a comprehensive regulatory index to capture information of the three pillars in the Basel Accord in their study of East Asian banking industries. Their results suggest that bank regulation is negatively related to technical efficiency while positively related to allocative efficiency. Moreover, that those relationships are not significant for state-owned banks, suggesting that regulation and supervision do not impact the performance of state-owned banks.

State Ownership in the Banking Industry
Most previous studies provide empirical evidence which supports the "political view" of state ownership and argue that state ownership is related to less development in the banking industry (Barth et al. 2001;La Porta et al. 2002); less profitability (Micco et al. 2007;Cornett et al. 2010;Lin and Zhang 2009); and lower profits and cost efficiency (Berger et al. 2005;Bonin et al. 2005;Perera et al. 2007;Margono et al. 2010). However, a few studies find that state-owned banks are more efficient (Gardener et al. 2011;Wang et al. 2014;Dong et al. 2014;Berger et al. 2009) than other types of banks and are related to higher stockholder value (Hossain et al. 2013). Other studies (Barry et al. 2008), however, find no significant difference between state-owned banks and privately-owned banks. Micco et al. (2007) argues that state-owned banks in developing countries have higher costs and lower profits, while those in developed countries have no significant difference in costs and profits. Some studies in the Indonesian banking industry suggest that state-owned banks are found to be less efficient (Perera et al. 2007;Margono et al. 2010;Shaban and James 2018).
In contrast with the previous argument that state ownership impedes bank performance, Gardener et al. (2011) suggest that state-owned banks in developing Asian countries are more efficient than other types of banks. Hossain et al. (2013) also notes that state ownership is a desirable government intervention mechanism used to reduce the negative impact on shareholder value in the Asia-Pacific banking industry. Empirical evidence revealed the better performance of China's four largest state-owned banks (Wang et al. 2014;Dong et al. 2014;Tan and Anchor 2017) over other banks in China. After estimating bank efficiency in Hong Kong, Indonesia, Korea, Malaysia, the Philippines, and Thailand, Barry et al. (2008) found that state-owned banks were not significantly different from privately-owned banks.

Data Sources
The bank-level financial data used in this study are comprised of data from unconsolidated statements of individual banks taken from the BvD Bankscope database. When unconsolidated statements are not available, consolidated statements are used instead. Only active commercial banks in Australia, China, Hong Kong, Indonesia, Japan, New Zealand, Singapore, and Thailand were used as sample banks in this study. To capture the overall banking industry characteristics, observations with less than three consecutive years of available data were omitted. Therefore, the sample data decreased from 5610 to 3749 observations for 544 banks. Due to the data validation requirements for DEA approaches, observations with missing, zero, or negative values in the inputs or outputs variables were dropped. As a result, a total sample of 2186 bank-year observations was obtained.
Data on bank regulation and supervision was obtained from the World Bank (2007,2011). Considering that there were changes in bank regulatory and supervisory policies in most countries following the 2008 GFC, regulation and supervision data from the 2007 survey were used for the period 2005 to 2008. Those regulatory and supervisory data obtained from the 2011 survey were used for the period 2009 to 2014. Bank ownership data were constructed using ownership data provided in the BvD Bankscope database. Other country-level data was obtained using the Global Financial Development Database and World Governance Indicators Database. Appendix A Table A1 provides details of the definition and source of each variable used in this study.

Efficiency Estimation: Bootstrap DEA Approach
Similar to the conventional benefit/cost theory, the fundamental idea of efficiency measurement is to estimate a ratio of weighted outputs to weighted inputs for each decision-making unit (DMU) (Cook and Seiford 2009). In the efficiency estimation, banks operating on the production frontier are the best-practice banks with efficiency scores of one. Those operating away from the frontier are considered to be inefficient, with efficiency scores less than one. Depending on the distance from the sample banks to the frontier, the DEA approach is employed to estimate relative efficiencies ranging from 0 to 1 (Cook and Seiford 2009) for all individual banks.
Assume there are I banks in the sample data; each bank uses N inputs to produce M outputs. The input X i for the i-th bank is an N × 1 vector and the output Y i is an M × 1 vector for the i-th bank. Thus, the production set for bank i can be denoted as (X i , Y i ). To measure the input-orientated technical efficiencies for bank i, the constant return to ccale (CRS) model solves the following linear programming problem as in Equation (1): where θ is a scalar, and λ is a vector of constant. The efficiency estimated using Equation (1) is the overall technical efficiency. After taking various external restrictions and influences into consideration, and assuming that there exists scale inefficiency as well as technical inefficiency in the banks during the production process, the variable return to scale (VRS) model can be used to separate the technical inefficiency into pure technical inefficiency and scale inefficiency. To estimate pure technical efficiency for bank i, Equation (2) solves the linear programming problems: where θ is a scalar, λ is a vector of constant, and e is an I × 1 vector of ones. The VRS model measures bank efficiency using a benchmark of similar-sized bank groups (Coelli et al. 2005). After excluding the impact of scale inefficiency, the technical efficiencies estimated using the VRS model are greater or equal to those estimated through the CRS model (Pasiouras 2008a) scale efficiency (SE) can be calculated as: To deal with the issue of asymptotic distribution of estimated efficiency, Wilson (2000, 2007) proposed a smoothed bootstrapping DEA model to provide a more reliable interpretation of efficiency scores.
To consider the distinctive production opportunities for banks operating in different countries, O'Donnell et al. (2008) introduced the idea of meta-frontier for firms operating in different groups and facing various circumstances. The meta-frontier production possibility set T contains all the feasible input-output combinations for banks from all different groups, which can be expressed in a simple function, as: The input-orientated efficiency score, which gives the maximum amount of input reduction for bank i is defined as meta-frontier technical efficiency (MTE). Assuming there are K (K > 1) countries in the sample, the technical efficiency for bank i in country k can be defined as group technical efficiency (GTE). Specifically, the technology gap ratio (TGR) for bank i in country k is defined as: when TGR i k equals 1, the group-frontier is tangent to the meta-frontier. In other words, the larger the TGR k , the more advanced the technology adopted by banks in country k.
Based on recent literature, our study employed the intermediation approach for input and output selection. Additionally, to analyse the impact of the inclusion of OBS activities, we estimated bank efficiency using four models with different input and output selections and examined whether the incorporation of OBS activities significantly affect bank efficiency measurements in the Asia-Pacific region (see Table 1). To capture the impact of OBS activities on efficiency estimations, "off-balance sheet items" were considered as an additional output to describe the aggregation of guarantees, acceptances and documentary credits, committed credit facilities, managed securitised assets, other exposure to securitisations, and other bank contingent liabilities. Additionally, "loan loss provisions" were also considered to be one of the inputs which indicate problem loans in the banking industry, following Charnes et al. (1990); Altunbas et al. (2000); Drake and Hall (2003); Pasiouras (2008b); and Hall et al. (2012)'s studies.
After obtaining four sets of efficiencies using 4 different models, we employed the Kruskal-Wallis test to examine if the differences between Models 1 and 2, and Models 3 and 4 were significantly different from zero. Furthermore, we used the Skillings-Mack test to test the rankings of the efficiencies from 4 Models. All of the efficiency estimates are bias-corrected using the Bootstrap DEA approach following Simar and Wilson (2007

Bootstrap Truncated Regression Model
To measure the impact of regulation, supervision, and state ownership on bank efficiency, the bootstrap truncated regression model was employed using bias-corrected bank efficiencyθ as the dependent variable. Three bias-corrected efficiency measurements were used in the regression model. Specifically, pure technical efficiency (PTE) was used to measure bank efficiency by using minimum inputs to produce a given level of outputs; scale efficiency (SE) was used to measure the efficiency of exploiting the optimal operating scale, and the technology gap ratio (TGR) was used to measure the gap between technology in one country to the best production technology in the Asia-Pacific region. The regression models are specified as follows: where PTE k,i denotes the bias-corrected pure technical efficiency for bank i in country k, SE k,i denotes the bias-corrected scale efficiency for bank i in country k; TGR k,i denotes the bias-corrected technology gap ratio for bank i in country k. The independent variables are REG k is a vector of bank regulation and supervision indicators in country k; Ownership k,i is a dummy variable, which equals 1 when the bank is classified as state-owned; Bank i,k is a vector of bank-specific characteristics for bank i in country k, and Country k is a vector of country-specific characteristics for country k; YEAR Dummy is the year dummy variable from 2005 to 2014; Country Dummy is the country dummy variable for the sample countries; ε k,i is the error term.

Bank Regulation and Supervision Variables
Together with activity restrictions, the three pillars of the Basel Accord II were used as regulation and supervision variables in the regression models. As discussed in the introduction, the three pillars are capital requirements, official supervision power and market discipline. Activity restrictions in the banking industry were also included to capture restrictions imposed on non-bank activities in 1 More methodology descriptions can be found in the study of Simar and Wilson (2007).
the Asia-Pacific banking sectors. The four indicators of bank regulation and supervision are denoted as capital regulation CAP k , official supervisory power SPPOWER k , market discipline MKDSPL k , and activity restrictions ACRS k . Bank regulation and supervision data are obtained primarily from the Bank Regulation and Supervision Survey (Barth et al. 2007(Barth et al. , 2012.
Based on Barth et al.'s (2001Barth et al.'s ( , 2007Barth et al.'s ( , 2008Barth et al.'s ( , 2012 descriptions, regulation and supervision variables are constructed through assigning "1" or "0" to several survey questions, where regulation and supervision authorities from various countries give answers of "yes" or "no". 2 CAP k was the index of capital regulation to measure the initial and overall capital requirements for banks in country k. This index was constructed using answers from five survey questions. The range of the capital requirement was from 0 to 7. A higher value indicates more stringency in the country's capital regulation.
SPPOWER k assessed the extent of official supervisory power to oversee, monitor, and discipline managers, directors, and auditors of banks in country k. Fourteen questions were surveyed to obtain the value of supervisory power. Variables ranged from 0 to 14 for each country. Similar to capital requirements, higher values show stronger supervisory power from regulatory authorities.
MKDSPL k measures information disclosure to shareholders, auditors, and the public, and whether any credit ratings are required by regulatory authorities for banks in country k. There were seven questions for this variable. Therefore, the value of market discipline ranged from 0 to 7. A higher value indicates a more informative and transparent banking industry.
ACRS k was the proxy of non-bank activity restrictions in real estate investment, insurance underwriting and selling, brokering and dealing securities, and all businesses of mutual fund industries in country k. For each category of activities, there were four answers: 1 (unrestricted), 2 (permitted); 3 (restricted); and 4 (prohibited). Thus, the value of ACRS k ranged from 0 to 12. A higher value of activity restriction indicates more restrictions on nonbank activities in the banking industry.

State Ownership
The variable Ownership k,i was used to examines the relationship between bank ownership and efficiency. Historical ownership data for each sample bank was obtained from the BvD Bankscope database. The global ultimate ownership (GUO) of banks and historical information of direct owners were considered when constructing the variable. Since 20% of the ownership is typically sufficient to have control rights in the banks' operation decisions (La Porta et al. 1999), the benchmark of 20% was used in this study to identify whether the government had control rights. For each bank, shareholders with shares of more than 3% in the bank were considered each year. If the shareholder was a central government, local government, or sole state-owned enterprise in country k, the shareholder was regarded as the government. The dummy variable Ownership k,i equaled one when the aggregate ownership of government in bank i of country k was greater than 20%. Similarly, we also identified foreign-owned banks for comparison. A bank was identified as foreign-owned when a single foreign shareholder owned more than 20% of the bank share. If the bank was neither state-owned nor foreign-owned, it was classified as a privately-owned bank.

Control Variables
To control the impact of other bank-specific characteristics on bank efficiency, this study included a set of bank-specific variables Bank i,k in the regression models. The bank-specific variables were Banksize i,k is calculated as the logarithm of total assets to capture bank scale characteristics. EQTA i,k is proxied as the ratio of total equity divided by total assets, to control the level of capitalisation in banks. The other three variables are used to capture three types of risks in banks. The first variable 2 The World Bank Regulatory and Supervisory survey questions are available upon request.
is OBSTA i,k is calculated as off-balance sheet items divided by total assets. A higher OBSTA i,k value suggests higher risks accompanied by a higher ratio of off-balance sheet activities. The second variable, risk proxy LLPTL i,k is used to capture credit risk, calculated as loan loss provisions over total loans. A higher LLPTL i,k value indicates a higher bank credit risk. The last risk measurement is LIQTA i,k , which controls bank liquidity risk levels. LIQTA i,k is calculated as liquid assets over total assets. A higher LIQTA i,k value indicates lower liquidity risk in bank i in country k.
Except for bank-specific variables, country-specific variables were also included in our regression models to account for variations in bank operating environments. We considered five country-level variables: Real GDP growth (GDP_growth k ), inflation rate (INF k ), concentration (HHI k ), banking industry development (PrCrGDP k ), and institutional governance environment INS_ENV k . GDP_growth k is measured as the annual growth rate of GDP to control for macroeconomic conditions of the country. Additionally, inflation INF k is measured by the annual rate of the implicit GDP deflator.
Finally, three remaining variables were used to capture the characteristics of the countries' banking industries. The first variable is concentration (Herfindahl Hirschman Index-HHI). HHI k is calculated as the sum of the square of deposit shares for each bank in all banks of that country. The PrCrGDP k describes the level of bank claims to the private sector to GDP, which is used to capture the intermediation activities of the banking industry in one country (Pasiouras 2008a). The last variable, institutional governance indicator INS_ENV k is used to control the institutional environment for countries. Initially, there are six dimensions of governance environment: Voice and accountability (Voice), political stability and absence of violence/terrorism (Stability), government effectiveness (Gov_E f f ), regulatory quality (Reg_Qua), the rule of law (Rule_Law), and control of corruption (Corruption). Each of these variables ranges between −2.5 and 2.5. Since these six variables are highly correlated, we employed principal component analysis to create a new variable INS_ENV k to measure the overall governance environment of each country. Table 2 shows the mean and standard deviation values of each input and output variable for efficiency estimations, from 2005 to 2014. All of the bank data were obtained from the BvD Bankscope database, and data have been adjusted using the GDP deflator in 2005. Table 3 provides the descriptive statistics of the regression models' variables for the full sample data over the period 2005 to 2014. The pairwise correlation coefficients between the independent variables are shown in Appendix A Table A2. Based on the correlation matrix, the absolute values of most of the correlation coefficients are smaller than 0.3 and the maximum absolute value of the correlation coefficients is less than 0.7. Thus, multicollinearity was not a major concern in our regression models.

Bank Efficiency and Non-Traditional Activities
To examine the impact of including OBS activities on bank efficiency estimations, Table 4 presents the average TE (technical efficiency), PTE (pure technical efficiency), and SE (scale efficiency) scores of 4 different models relative to the meta-frontier. After bias-correction, the TE, PTE and SE estimates had smaller means and standard deviations, which supports Fallah-Fini et al.'s (2012) statement that banks appear to be efficient under traditional DEA approach, but might not be efficient using the bootstrap DEA approach. According to Simar and Wilson (2007) and Fallah-Fini et al. (2012), one possible reason for the existence of such a large bias is that there are not enough observations to construct the correct frontier.
Without considering the asset quality of the banking industry, the comparison between bank efficiency of Models 1 and 2 show that the average TE and PTE scores are higher after with the inclusion of OBS activities. However, the average SE score is lower after incorporating non-traditional activities.
Similarly, compared to Model 3, the average TE and PTE estimates are higher, and the average SE estimates are lower in Model 4. To test whether differences in bank efficiencies were significantly different from zero, we followed Lozano-Vivas and , and conducted the Kruskal-Wallis tests to compare between Models 1 and 2, as well as Models 3 and 4. The results are presented in Table 5. 3 Model 1 excludes both off-balance sheet (OBS) and LLP in the efficiency estimation; Model 2 includes OBS and excludes LLP in the efficiency estimation; Model 3 consists of the LLP but excludes the OBS in the estimation; Model 4 includes both OBS and LLP in the estimation.   Table 6 indicates that efficiency estimates from the four models were significantly different, based on the small p-values for PTE (Panel A), TE (Panel B), and SE (Panel C). Furthermore, based on the information from the ranking statistics (WSumCRank and WSum/SE), we can confirm our observations in Table 4. Model 2 had higher average PTEs and TEs than those in Model 1, and Model 4 had higher PTEs and TEs than those in Model 3. In addition, after the inclusion of OBS activities, the SEs in Model 2 (Model 4) were lower than those in Model 1 (Model 3).  Table 7 shows the average meta-frontier PTE score of 0.9039 for Australian banks was the highest, relative to the average level of other countries, followed by Hong Kong (0.8958) and Japan (0.8847). In contrast, Indonesian banks had the lowest average meta-frontier PTE estimate of 0.7312, which suggests that an average bank in Indonesia can reduce inputs by 26.88% compared to the most efficient banks in the Asia-Pacific region, to produce the same level of outputs.
Combining the information of group-frontier PTE and meta-frontier PTE, the range of the TGR scores for the sample countries ranged from 0.8610 (Indonesia) to 0.9227 (Japan). Compared to the meta-frontier PTE, the relatively small range of TGRs suggests that the distances between the country-frontiers and meta-frontier were similar among the sample countries. For example, the average TGR for Australian banks of 0.9091 indicates that Australian banks operating on the frontier can improve and move towards the meta-frontier by reducing inputs by 9.09%.

Impact of Bank Regulation, Supervision, and Ownership on Bank Efficiency
To examine whether bank regulation, supervision, and state ownership in banks have significant influences on bank performance, the second-stage bootstrap regression model (Simar and Wilson 2007) was employed in this study. The pairwise correlated coefficients of the independent variables indicated no major issues of multicollinearity in the regression (see Appendix A Table A2). Additionally, robust standard errors were used in all the regression models to address potential heteroskedasticity problems.
Year dummy and country dummy variables were included in the regression model to capture the impact of time and other unspecified country-specific characteristics. Table 8 shows the regression results of the relationship between regulation, supervision and bank efficiencies (that is, PTE-pure technical efficiency, SE-scale efficiency, and TGR-technology gap ratio) using the full sample data of 2186 bank-year observations. Overall, the regression results show that regulation and supervision policies are positively related to pure technical efficiency and technology gap ratio of banks in the Asia-Pacific region. Following the first pillar of the Basel Accord, the capital requirement had a positive relationship with PTE and TGR at a 1% significance level. Consistent with previous empirical studies (Lozano-Vivas and Pasiouras 2010; Barth et al. 2013;Luo et al. 2016), stricter capital requirements can reduce the incentive to engage in risky behavior, and therefore improve the bank performance. The positive relationship between capital regulation and scale efficiency was insignificant.   Table A1 for definitions and information about the independent variables. *, **, *** indicates 10%, 5% and 1% levels of significance, respectively. Source: Author's calculations.
Similar to the capital requirement, the second pillar of the Basel Accord (that is, the official supervision power), is positively related to both PTE and TGR at 5% significance level. Under the "official supervision approach," greater official supervision power is believed to increase credit flow to firms which are well-connected with banks (Levine 2004) and enhances bank performance. Furthermore, a powerful official supervision regime can improve bank efficiency through increased competition in the banking industry (Barth et al. 2008). Empirically, our result is consistent with Pasiouras (2008a) and Luo et al.'s (2016) findings on global banking industries. Hirtle et al. (2016) found similar results in the US bank-holding companies. Official supervisory power is not significantly related to banks' scale efficiency.
The significantly positive coefficients of market discipline on PTE, SE, and TGR estimates support the "private monitoring approach" hypothesis, in which regulation and supervision policies promoting private monitoring in banks can induce better performance. By requiring banks to disclose adequate information to the public, market discipline can encourage private sectors to monitor banks with lower information and transaction costs (Barth et al. 2008). Table 8 shows that market discipline is the only regulation and supervision variable which is significantly (at a 5% significance level) related to the scale efficiency of banks in the Asia-Pacific region.
Banks with more activity restrictions tend to have higher performance, in both pure technical efficiency and technology gap ratios. These findings are similar to Barth et al.'s (2004) discussion that restricting banks engagement in security underwriting, insurance underwriting, and real estate investments would limit the conflicts of interest between stakeholders. Furthermore, narrowing the range of activities can reduce risky behaviours caused by moral hazards (Boyd et al. 1998) and positively affect bank performance. There is no evidence to suggest a significant relationship between activity restrictions and scale efficiency.
The existence of a deposit insurance scheme in each country has no significant relationship with bank performance according to our results. Additionally, state ownership is not significantly related to bank performance in the Asia-Pacific region. Bank-specific characteristics exhibit significant relationships with bank efficiencies. For example, bank size is positively related to technical efficiency and technical gap ratio, indicating that larger banks have better management and technology in their production processes. However, bank scale efficiency tends to be lower for larger banks, possibly due to the fact that most banks in the Asia-Pacific region expanded too quickly and operated at decreasing returns to scale during the 10-year sample period.
In addition, banks with higher capital ratios performed better in all three efficiency estimates. When banks hold more capital, managers tend to be more risk-averse in terms of operation, and therefore these banks would exhibit better performance. Our results are consistent with most of the previous studies in bank performance (see Demirgüç-Kunt and Huizinga 1999;Goddard et al. 2004;Sufian and Habibullah 2010;Fiordelisi et al. 2011;and Pessarossi and Weill 2015).
The level of liquid assets (LIQTA) in banks has a negative relationship with technical efficiency and technical gap ratio, but no significant correlation with scale efficiency. One possible reason for a higher level of liquid assets could be that banks would raise more liquid assets to reduce risks during times of uncertainty and unfavourable industry conditions (Radić et al. 2012). Thus, banks tend to have a lower performance during those times. Moreover, liquid assets are believed to be less profitable than illiquid assets and reduce investment opportunities for banks managers. The negative relationship between liquid ratio and technical gap ratio implies that holding more liquid assets would widen the distance from the group frontiers to the meta-frontier in banking industry.
The coefficients of GDP growth are not significantly related to bank performance, while a higher inflation rate has a positive relationship with scale efficiency and a negative impact on technology gap ratio. The concentration (HHI) of the banking industry appears unrelated to bank performance in the Asia-Pacific region. Furthermore, the negative coefficients of PrCrGDP indicate a negative relationship between private credit from banks to GDP and bank performance, suggesting that financial markets with more lending to private credit have relatively lower bank performance. The overall institutional environment of banks exhibits no significant relationship with bank performance in the Asia-Pacific region.

Regulation, Supervision, and Bank Size
After categorising banks into three size groups-small, medium and large, based on banks' total assets, we conducted further analysis to examine if the impacts of regulation, supervision, and state ownership on bank efficiency would be different in different sized groups. Table 9 shows the regression results for each bank groups, using meta-frontier efficiency from Model 4 as the dependent variable. Our findings in Table 9 suggest that stricter regulation and supervision policies are mostly positively related to small-sized banks, but not to medium or large-sized banks.
The first three columns in Table 9 compare the impact of regulation, supervision, and state ownership on pure technical efficiency for three sized bank groups. Tighter capital regulation and market discipline are significantly related to higher pure technical efficiency of small banks at a 1% significant level. At the 10% significance level, activity restriction is positively associated with the pure technical efficiency of small banks. While official supervisory power has no significant relationship with the technical efficiency of small and medium banks, it is positively related to large bank efficiency at a 5% significance level. None of the regulatory and supervisory policies are significantly related to the pure technical efficiency of medium-sized banks.
Columns 4 to 6 in Table 9 summarise the regression results on scale efficiency for different-sized banks. The official supervision power and market discipline are significantly related to the scale efficiency of small banks. Additionally, market discipline is also positively related to large-sized banks' scale efficiency. There is no significant impact of bank regulation and supervision on medium-sized banks. Compared to the pure technical efficiency, scale efficiencies of banks are less affected by regulation and supervision. The deposit insurance scheme is positively related to the small-sized banks' scale efficiency at the 10% significance level.
The relationships of regulation and supervision and bank technology gap ratio are shown in columns 7 to 9 in Table 9. All four regulatory and supervisory indicators are positively related to the technology gap ratio of small banks. For large banks, official supervisory power is positively associated with the technology gap ratio. The medium-sized banks' technology gap ratios are not affected by any of the regulation and supervision indicators.  Table A1 for definitions and information on the independent variables. *, **, *** indicate 10%, 5% and 1% levels of significance, respectively. Source: Author's calculations.

Robustness Check: Tobit Regression and Fractional Logit Regression
This study employs the Simar and Wilson (2007) bootstrap truncated regression model to examine the relationship between bank regulation, supervision, ownership and bank efficiency. In previous studies, different types of regression models were used in the second stage after obtaining the DEA efficiency estimates. For example, most of the previous studies (Pasiouras 2008a;Sufian 2009;Gardener et al. 2011;Ab-Rahim et al. 2012;Huang and Fu 2013) used the Tobit regression to identify determinants of bank efficiency. Alternatively, Ramalho et al. (2010) suggested that fractional logit regression is the most natural way for second-stage regression.
To check the robustness of our regression results, we applied both fractional logit regression and Tobit regression in the second stage, to examine the relationship between regulation, supervision, ownership and bank performance (see Table 10). In both regressions, we used technical efficiency, scale efficiency, and technology gap ratio in Model 4 as the dependent variables, with the same independent variables as in the previous analysis.
Columns 1 to 3 in Table 10 show the results of fractional logit regression, which are similar to the results in Table 8. Regulation and supervision are positively related to bank pure technical efficiency and technology gap ratios. Additionally, market discipline is positively associated with bank scale efficiency in the Asia-Pacific region. However, we observe that the coefficient estimates in the fractional logit regression are larger than those in the truncated regression, and there are some variations in the Z-value compared to bootstrap truncated regression results.
Columns 4 to 6 in Table 10 display the Tobit regression results of bank efficiency. Even though the coefficients of variables have the same signs, we observe that supervision power and market discipline are not significantly related to pure technical efficiency. All four regulation and supervision indices exhibited positive relationships with the technology gap ratio of banks. Similar to the discussion in Section 5.3, deposit insurance schemes and state ownership were not significantly related to bank performance in both fractional logit and Tobit regression models.

Conclusions
This study examined the impacts of off-balance sheet activities on bank efficiency measurement, and investigated the relationship between regulation, supervision, state ownership and bank efficiency. Our results showed that omitting off-balance sheet activities while estimating bank efficiency using bootstrap DEA approach would significantly underestimate the pure technical efficiency and overall technical efficiency, while overestimating the scale efficiency of banks. Furthermore, we identified the positive relationship between regulation, supervision, and bank efficiency, especially in small-sized banks. However, no significant relationship between state ownership with bank performance was found in this study.
Our findings have imperative policy implications. Firstly, our results have highlighted the impact of including non-traditional bank activities when measuring bank efficiency. Precise information relating to bank performance is essential for policy-making decisions, such as capital requirements and information disclosure. Correctly estimated efficiency could reveal the banks' intrinsic value and potential investment return in the future. Such information could further assist investors' and bank managers' decision making. Secondly, regulatory and supervisory authorities could impose customized regulatory and supervisory policies on different sized banks. While smaller banks benefit more from stricter policies, regulatory authorities could relax the requirements for medium and large-sized banks to exploit operational efficiency. Finally, since state ownership is found to be insignificantly related to bank performance, it could be an appropriate tool for governments to intervene in the banking industry during financial turmoil to maintain the intermediary function of banks.
There exist several limitations of the current study. First, we used the nonparametric DEA approach to estimate bank efficiency. Compared to the parametric approaches, the DEA method assumes the random error to be zero, which could affect the precision of efficiency estimation. Second, due to the data availability of bank regulation and supervision, we used the 2007 and 2011 World Bank Regulatory and Supervisory Survey to cover the 10-year sample period. Therefore, the timeliness and frequency of data could have potentially limited the validity of our results. Last, our sample covered eight countries in the Asia-Pacific region based on data availability. There were five developed countries and three developing countries. Even though these countries can capture the diversity and common characteristics of the Asia-Pacific banking industries, questions remain whether our results can be applied to all banking industries in the region.
In future studies, we recommend different approaches, such as the stochastic frontier analysis approach, to estimate bank efficiency to avoid potential biases arising from the zero-error assumption of the DEA approach. Future researchers can collect more detailed bank-specific and country-specific data from more sample countries. Using these detailed data, future researchers can explore the timely changes in regulatory policies and their impacts on bank performance, and provide evidence which can be used to benefit the stakeholders in all the banks in the Asia-Pacific region.
Author Contributions: Z.Y. contributed to the research design and data analysis, writing, and formal analysis of the research. C.G. and Z.L. supervised the research. Z.Y. and C.G. helped with the modifying of the manuscript and final editorial clarifications and corrections. All authors contributed to the writing, reviewing, and correction of this manuscript.
Funding: This research received no external funding.
Acknowledgments: Baiding Hu has provided valuable insights into the methodology and statistical analysis of the the study.

Conflicts of Interest:
The authors declare no conflict of interest. Institutional governance index, consists of voice and accountability, political stability and absence of violence or terrorism, government effectiveness, regulatory quality, the rule of law, control of corruption.

Appendix A
Calculated using data from World Governance Indicators database  Table A1 for definitions for variables. * indicates 5% level of significance. Source: Author's calculation.