BSc Economics and Business
( BSc ECB. Specialization in Finance )
The Regulatory Capital :
Crucial Determinant of the Bank Profitability
Yanghoo Woo ( 11429747 ) June, 2020
Supervisor : Oscar Soons Professor : Philippe Versijp
Abstract
This research investigates the impact of regulatory capital on the bank profitability. Additionally, the effect of the G SIBs and country label into the impact is analyzed. In order to conduct the research, the STATA data set is selected and the fixed effect model of panel
data is employed. The data set contains 28480 observations of 7120 banks and some
observations have default values. Thus, the default observations, 760 observations, are dropped off and the remaining 27720 observations are analyzed. Through the STATA, three regressions are run and each of them contains the dependent variable and several independent variables. The dependent variable of the regressions is bank profitability which is measured by the Return on Assets (ROA). Among the independent variables, the regulatory capital which is measured by tier 1 ratio is primarily concentrated on regression analyses. Additionally, particular variables which indicate whether the banks are GSIBs and US banks are included into the 2nd and 3rd regressions and their effects on the profitability are investigated. As a result, it is found that the profitability of banks would increase as the tier 1 ratio increases. This implies that the regulatory capital has the positive impact on bank profitability. However, the profitability of G SIBs decreases when the tier 1 ratio increases. Thus, the regulatory capital has a negative effect into the profitability of G SIBs. Moreover, it is estimated that the impact of regulatory capital differs between US banks and EU banks. This paper gives statistical and economic interpretations of the results.
Table of Contents
1. Introduction
32. Literature Reviews
62-1. Determinants of the bank profitability
62-2. The regulatory capital and bank profitability
92-3. Effect of G SIBs label and countries in the relationship
113. Data Description and Methodology
134. Results and Analyses
195. Discussions
266. Limitations and further research
297. Conclusion
308. Appendix
311. Introduction
Banks increasingly provide a wide range of services to their customers in financial markets. For instance, customers can deposit their money into banks, borrow money from banks to fund their businesses and trade foreign currencies through banks. As those services of banks tend to facilitate customers’ needs, the number of the customers steadily has increased around the world (Demirguc et al., 2018).
However, customers may need to be cautious when they deposit their money into banks
since some banks may become unable to satisfy their obligations for the deposits of
customers and they, therefore, go bankrupt. Thus, it would be essential for customers to realize whether their banks will fail so as to prevent the deposit loss. According to De Guindos(2019), banks with high profitability are far less likely to fail. As banks generate positive profits and the profits can be used to meet their obligations, the banks can establish a powerful protection against the insolvency which leads to the bank failure. Thus, it would be clear that the bank profitability is the yardstick of banks’ success and the profitability becomes a prime concern to customers when they analyze whether banks would fail.
As the profitability of banks comes into spotlight, several researches regarding determinants of the profitability were conducted. According to Ahmad and Wang (2018), there are two types of determinants of bank profitability, internal and external determinants. Specifically, the internal variables include the operating efficiency and a capital ratio whereas the inflation rate, GDP growth and GDP per capita are the external variables. Especially, the capital ratio is considered as a prime determinant of the bank profitability in several existing researches. For instance, Lee and Hsieh (2013) put an emphasis on the capital ratio among several determinants and the authors primarily attempt to discover the relationship between the bank capital and profitability in their research.
Moreover, banking regulators also consider the bank capital a crucial device to enhance the profitability of banks. For instance, the Basel III committee on banking supervision selects a capital ratio as a major tool in increasing the bank profitability (Marc and Peter, 2010). According to Fidrmuc and Lind (2020), the Basel III was established in response to the financial crisis in 2008 which led the bank failures and the rising needs for bailout programs.
In order to prevent the financial crisis from reoccurring in the future, the regulators of the Basel III consented to increase the regulatory capital ratio at which banks should hold. This movement to the Basel III implies that higher capital requirement for banks can increase their profitability and prevent bank failures. This underlying logic of the Basel III can be supported by Kohlscheen, Murcia, and Contreras (2018). Their findings are that banks with a higher capital ratio tend to be more profitable since the higher ratio makes banks to have lower prospective bankruptcy costs and to face lower costs of funding.
However, the effect of regulatory capital on the profitability would be controversial. Compared to the several findings which show a positive relationship between a capital ratio and bank profitability, Poledna, Bochmann, and Thurner (2016) suggest that a negative relationship can exist under certain circumstances. In their research, profitability of G SIBs is investigated rather than that of general banks. The G SIBs stands for the Global Systemically Important Banks and it is measured by means of a size, substitutability, complexity, interconnectedness and global activity of a bank (Yuksel, 2014). In other words, G SIBs would be far bigger than general banks and they are so systemically important that their failure can trigger financial crises worldwide.
In order to demonstrate whether the profitability of G SIBs grows as regulatory capital increases, they create computer simulations in which different amounts of regulatory capital are added to G SIBs. At the first, it is found that profitability decreases when an amount of regulatory capital required by the Basel III is added since a loss of efficiency of operations from the capital expansion would be greater than a benefit of that. Secondly, profitability increases when the regulatory capital surcharge exceeds the amount which is required by the Basel III. Thus, the researcher claim that the effect of regulatory capital on profitability of G SIBs could be negligible, even negative, unless G SIBs hold regulatory capital more than a certain level. This finding implies that general banks and G SIBs tend to experience different impacts of regulatory capital on their profitability.
Additionally, the effect of regulatory capital can differ in terms of a country in which a bank is located. According to Kanter (2013), the adequate capital requirements for US banks to increase their profitability would not be appropriate for the EU banks. He claims that the EU banks could have competitive disadvantage against US banks if the european banks follow
the US capital requirements. This implies that a capital requirement can have positive impacts on the profitability of banks in a country and negative impacts on that of those in another country simultaneously. Thus, the relationship between regulatory capital and profitability can differ among banks in different countries.
As mentioned above, several existing papers suggest that there are various determinants of the bank profitability. Especially, the regulatory capital seems to have a considerable attention among the determinants. Many researchers are keen to discover its impact on the profitability and banking regulators primarily aim to set an adequate level of capital ratio for enhancing profitability of banks. However, there are a lot of factors which can determine profitability, aside from the regulatory bank capital. Moreover, the effect of regulatory capital on the profitability tends to differ among countries and it can be influenced by the G SIBs label as the previous research illustrates.
Therefore, this paper will investigate whether the regulatory capital is a determinant of bank profitability and whether the effect of regulatory capital differs in terms of G SIBs label and countries. Firstly, relevant literatures to the research question above will be illustrated and revised. The literature review will be based on three previous papers which illustrate a set of determinants of bank profitability, a methodological framework for measuring an impact of a capital ratio on the profitability and a process in which G SIBs label and countries influence on the relationship between regulatory capital and bank profitability. On the basis of the literature review, several variables which affect to the bank profitability and proxies for the variables will be selected. Secondly, a description of proper data used in this research and an explanation of research methodology taken in it will be provided. Thirdly, numerical and statistical results will be given and analyzed whether the results are reliable to answer the research question. Finally, discussions of the results found, limitations of this paper, descriptions of possible needs for further research and brief summary will be followed.
2. Literature Reviews
2-1. Determinants of the bank profitability
As a profit of banks gives a buffer against an insolvency problem which would lead the bank failure, the higher profitability of banks is increasingly considered as a significant objective for banks to achieve. Hence, several studies are conducted regarding the determinants and their impacts on the profitability. According to Ahmad and Wang (2018), the determinants of bank profitability can be categorized into two groups, the bank-specific and the macroeconomic.
Firstly, the bank-specific factors consist of a bank size, cost to income ratio and capital ratio. Specifically, the size of banks is expected to have a positive impact on the profitability since larger banks would benefit from the economies of scale and economies of scope. In other words, it is highly likely for larger banks to have greater operational efficiency and a higher level of diversification into their products than smaller banks due to the larger size. In case of the cost to income ratio, a relationship between this ratio and the profitability would be negative. As the ratio briefly implies how much operational costs are needed to generate total revenue, the lower ratio means that banks are able to raise funds at lower costs. Thus, the profitability would increase as the ratio becomes lower.
The last component of the bank-specific factors is the capital ratio. Ahmad and Wang (2018) claim that there are both positive and negative implications of a capital ratio for banks. As a bank holds more capital relative its total assets, its creditworthiness would increase so significantly that the bank would face lower funding costs. Moreover, additional needs for external fundings tend to be reduced when banks contain sufficient capital relative to their assets. Thus, a bank with a higher capital ratio would be more profitable. On the other hand, banks would become less available to provide loans to customers as they are required to hold more capital. Fundamentally, banks lend money to customers at a certain interest rate and make profits when they receive interest from the customers. Therefore, a bank would be less profitable as it is required to hold more capital and to provide less loans. However, this decrease in bank profitability is far less than the increase in the profitability from the higher
capital ratio. Thus, the overall effect of the higher capital ratio on bank profitability would be positive.
Secondly, the macroeconomic factors include the economic growth and inflation. Ahmad and Wang (2018) briefly claim that the economic growth leads banks to be more profitable. They mainly concentrate on the relationship between the inflation and bank profitability. The effect of inflation into bank profitability tends to be complicated since it relies on various conditions. For instance, the higher inflation leads banks to set a higher interest rate (Navoda, Selliah, and John, 2015). Thus, banks would have more opportunity to establish profit margins. This makes banks to be more profitable. However, the higher inflation can also make banks to pay more to depositors so considerably that it can lower the profitability of the
banks unless revenues of the banks from the profit margins exceed the costs paid to
depositors.
In order to investigate the effects of the variables above into bank profitability empirically, Ahmad and Wang (2018) use a panel data set with a sample of 4995 banks in 11 countries for 5 years from 2001 to 2015. The data for the bank-specific factors is extracted from the Fitch-IBCA Bank database and the data sources of the macroeconomic factors are the World Bank and International Monetary Fund (IMF) database. They use ROA (Return on Assets), ROE (Return on Equity) and NIM (Net Interest Margin) as measurement tools for the bank profitability.
The investigation approach of Ahmad and Wang (2018) which is described above can be supported by other studies. For example, Capraru and Ihnatov (2015) select proxies for the bank profitability which are identical to which Ahmad and Wang (2018) use in their research. Additionally, Capraru and Ihnatov (2015) also categorize the independent variables into the bank specific and macroeconomic factors. Further, they describe how the variables affect to the bank profitability and their descriptions are parallel to the idea of Ahmad and Wang (2018).
Likewise other papers employ fundamental concepts of Ahmad and Wang (2018), this
literature provides several starting points for this research paper. Firstly, various determinants of bank profitability are suggested and their effects on the profitability are analyzed. The determinants suggested are a size of a bank, cost to income ratio, inflation and economic
growth. Moreover, a proxy for bank profitability and an adequate methodology of an investigation are illustrated.
2-2. The regulatory capital and bank profitability
There is no doubt that several determinants of bank profitability exist. Among the
determinants, some are the most commonly introduced in various existing researches, such as the capital ratio, size of banks, and inflation. However, there would be an distinction among the researches in terms of which factor is concentrated mainly on. As this paper aims to discover the relationship between the regulatory capital and bank profitability, a literature which focuses on an impact of the regulatory capital on the profitability will be followed below.
Lee and Hsieh (2013) claim that regulatory capital would be a prime determinant of bank profitability. In order to provide relevant evidences for this view, they describe how banking regulators reacted to financial crises in their research. In response to the Global Financial Crisis (GFC) from 2007 to 2008 which led many bank failures, banking regulators suggested that banks might need to hold more capital so as to prevent failures of the banks. As the Basel III refers that an additional capital injection to banks can increase profitability of the banks, banking regulators considered regulatory capital as the most significant driver which increases bank profitability (Hessou and Lai, 2018).
Additionally, Lee and Hsieh (2013) claim that previous studies are focused on banks in EU or US so primarily that they select banks in Asian countries. Thus, 2276 banks in 42 Asian countries are selected as a sample and a period from 1994 to 2008 is chosen for the sample. In case of the research technique, the Generalized Method of Moments (GMM) for dynamic panel data is employed since this technique can tackle the endogeneity bias far better than the basic OLS estimation. An usefulness of the GMM is explained by Ullah, Akhtar, and Zaefarian (2018) specifically. With using this technique, Lee and Hsieh (2013) make an equation in order to investigate the relationship between the bank capital and profitability.
πit = α0 + α π1 it−1 + α CP 2 it + α F ′ it + λ i + η , ∀i, . it t (1)
Where πit, α1,CPit, Fit, λi, ηit denotes the i th bank’s profitability in year t, estimated persistence coefficient for profitability, level of bank capital, set of explanatory variables, unobserved bank-specific effect, idiosyncratic error term respectively. Here, the t and i refer time period and banks individually. The explanatory variables are a liquidity risk, credit risk, market concentration, supervisory power and market discipline.
Lee and Hsieh (2013) use four variables to measure bank profitability, πit. The variables are the return on asset (ROA), return on equity (ROE), net interest margin (NIM) and net interest revenue against average assets (NR). For a level of capital, CPit, equity-to-assets ratio is employed. The four variables for the profitability are expressed as a form of a percent.
Their findings, which are derived from the GMM dynamic panel data technique, indicate that a bank profit increases significantly as the bank capital expands. Thus, it is relevant that the regulatory capital can be a determinant of the bank profitability. Additionally, it is found that NIM and NR show a persistence of profit while ROA and ROE do not. To put it another way, a profit measured by NIM or NR tends to have higher α1in the equation (1) so that the profit is more likely to resemble a previous year’s profit if NIM or NR is used. This persistence of profit would generate a bias which makes a regression analysis distorted.
The emphasis of Lee and Hsieh (2013) on the regulatory capital can also be found in the paper of the Basel Committee (2011). According to the paper, an increase in the regulatory capital tends to increase bank profitability significantly. Thus, the Basel III committee primarily regulates a capital ratio as it aims to increase the bank profitability.
Therefore, this literature provides useful concepts for this research paper. Firstly, it clearly suggests that the regulatory capital is the major determinant of the bank profitability. Moreover, it introduces effective technique which can be used to test the relationship in the research question. Further, it is shown that ROA and ROE could be better proxies for bank profitability than NIM and NR. As profitability is measured by ROA or ROE, the sole effect of regulatory capital on profitability would be precisely measured and a potential bias from previous profits can be eliminated.
2-3. Effect of G SIBs label and countries in the relationship
The previous literatures illustrate that the regulatory capital of banks tends to increase the profitability of banks. However, there would be particular conditions under which the relationship can vary. Thus, two literatures will be analyzed on the basis of their findings in order to realize the conditions.
The first condition is suggested by Poledna, Bochmann, and Thurner (2016). They conduct a research in order to analyze whether the profitability of G SIBs increases as the G SIBs are required more regulatory capital in accordance with the Basel III. Fundamentally, the Basel III aims to enhance the profitability of banks through expanding the regulatory capital which the banks should hold. Therefore, it is relevant to say that the research is conducted to recognize whether the GSIBs label affects to the impact of regulatory capital on the bank profitability. In short, the first condition would be the G SIBs label.
Initially, the researchers describe distinctive features of G SIBs. Fundamentally, G SIBs are systematically more important than other banks. Specifically, the systematic importance of bank is measured by its size, interconnectedness to other financial institutions, complexity of its operations, substitutability and its global activity. Based on the importance which is measured by the several features of a bank, certain banks are identified as the G SIBs.
Therefore, G SIBs would have various characteristics which distinguish them from other banks. Firstly, G SIBs tend to have far bigger size than other banks in terms of the tier 1 capital. Secondly, activities of G SIBs are highly likely to affect to those of other banks. Thus, the failure of G SIBs is not only a problem for G SIBs themselves, but it is also a threat for the other banks. Moreover, the business, structure, and operations of G SIBs would be considerably complex. Due to the great complexity of G SIBs, huge costs and time are necessary when G SIBs need financial aids. Further, it would be much more difficult to replace G SIBs than other banks when G SIBs fail. For example, as an amount of tier 1 capital of G SIBs is tremendous, a replacement of the G SIBs requires a huge amount of tier 1 capital. This makes the replacement hard to be achieved. Furthermore, G SIBs contribute
substantially to the global financial market since they trade a large share of total money traded worldwide.
Those characteristics of G SIBs imply that a failure of G SIBs poses tremendous threats to the global economy. Hence, the Basel III suggests particular capital requirements to G SIBs since they are too significant to fail and they have distinctive features from other banks. This suggestion aims at increasing profitability of G SIBs and preventing failures of them more effectively. Additionally, the researchers illustrate specific capital ratios for G SIBs on the basis of the Basel III. The particular capital requirements are shown in Table 1 below.
[ Table 1 ] Capital Requirements for G SIBs under the Basel III
Bucket Bucket
Threshold
Capital Requirement by the Basel III for G SIBs
( Tier 1 capital as a percentage of risk-weighted assets)
5 530-629 3.5 %
4 430-529 2.5 %
3 330-429 2.0 %
2 230-329 1.5 %
1 130-229 1.0 %
G SIBs are categorized into five buckets (from bucket 1 to bucket 5) on the basis of their significance measured. Each of buckets has a threshold which indicates a range of significance. A bank is assigned to a bucket if its significance lies on the bucket’s threshold. Thus, a bucket would imply a group of banks which have similar significance. The highest bucket, bucket 5, involves banks with the highest significance, whereas the lowest bucket, bucket 1, involves banks with the lowest significance. The capital requirements, which indicate the tier 1 capital as a percentage of risk-weighted assets, are 1.0%, 1.5%, 2.0%, 2.5% and 3.5% for bucket 1, 2, 3, 4 and 5 respectively. Thus, each of G SIBs has one required capital ratio under the Basel III in the basis of which bucket the bank is included in.
In order to investigate whether the required capital ratios for G SIBs affect to their profitability, the researchers create a computer simulation which enables them to predict bank profitability under a certain capital ratio. Fundamentally, G SIBs before the Basel III regulation would follow a lower capital ratio than the Basel III capital requirements. Through
the simulation with the Basel III capital ratio, it is found that profitability of G SIBs increases as the G SIBs are required to follow the higher capital ratio suggested by the Basel III. However, the increase is negligible. Thus, they conclude that G SIBs’ profitability barely increase with the higher capital ratio.
Aside from the GSIB label, Herring (2018) claims that the effect of regulatory capital can differ in terms of an operating country. Specifically, the author mentions that a country has a unique policy and it tends to influence on the effectiveness of regulatory capital into bank profitability. For instance, the US policy and regulation system would mainly aim to control distributions of banks’ profits, rather than to sustain a financial stability by increasing the profitability of banks. Thus, under US policy, a higher capital ratio of US banks would reduce their earning powers far more than a reduction on costs of funding. This implies that profitability of US banks decreases as they are required to hold more regulatory capital.
As the two literatures in this section suggest, the impact of regulatory capital on the bank profitability can be influenced by other factors, such as the GSIBs label and a country in which a bank operates. Therefore, this paper will investigate whether G SIBs label affects to the relationship between regulatory capital and bank profitability. Additionally, it will compare the effect of regulatory capital on the US bank profitability and EU bank profitability, likewise Kanter (2013) investigates that the same capital ratio can have a positive effect on the profitability of US banks and a negative impact on that of EU banks simultaneously.
3. Data Description and Methodology
As the literatures above commonly refer that the regulatory capital would have a significant impact on the bank profitability, this research paper will empirically demonstrate the existence of the impact and it will analyze whether the impact is significant in a statistical viewpoint. Further, a variation in the impact due to the other factors, such as the GSIBs label and the countries, will be investigated.
The data source of this paper is a STATA data set which is a combination of the Orbis Bank Focus and IMF data for US banks and European banks. Fundamentally, the data set tends to
be valid and reliable in this research. Firstly, this research aims to investigate whether the regulatory capital is a determinant of the bank profitability. As the data set contains numerical values of the profitability and the determinants, it would be a relevant source for this research. Secondly, the periods of data is between 2015 and 2018. This implies that the data is up-to-date. Additionally, the size of sample is sufficiently large to obtain meaningful results. Moreover, the source is derived from established institutions. Thus, the dataset would have high creditworthiness.
The sample of the data set is selected from 7120 banks in 28 countries for a period of 2015-2018 and it consists of 28480 observations. The observations contain values of several variables which are related to the banks, such as the ROA, tier 1 ratio, total assets and tier 1 capital. According to Shiu and Sun (2014), a number of observations of a balanced panel dataset should be equal to a number of periods multiplied by panel members. In this case, observations should be 28480 which is 7120 * 4 if the sample is a balanced panel dataset. Thus, the sample is the strongly balanced panel dataset. Among the 28480 observations, the value of variables is omitted in certain observations. Thus, the observations with default values are dropped from the STATA. Through the STATA, 760 observations are dropped and remaining 27720 observations will be investigated in this paper.
In order to investigate the impact of regulatory capital on the bank profitability, this research set the profitability as a dependent variable, and determinants of the profitability as independent variables. As the literature in section 2.2 suggests, ROA (return on assets) or ROE (return on equity) can be a better proxy for the profitability than NIM and NR since the profitability measured by ROA or ROE does not include the effect of persistence of profits.
Between the superior proxies, ROA and ROE, ROA would be the best proxy for the bank
profitability as the ROE measurement has some drawbacks. According to Kohlscheen,
Murcia, and Contreras (2018), the ROE measurement can provide a skewed explanation of the bank profitability since it tends to be highly variable. For example, the depreciation lowers the net income of banks and, in turn, it lowers the ROE. In case of a start-up bank, the ROE would decrease as it requires more equity to grow its business. Additionally, as the ROE solely reflects the net income and equity and it does not take into consideration the obligations, a bank which has huge debts still can have the high ROE and it can be seen highly profitable if the ROE is selected as a proxy for the bank profitability. Therefore, the
proxy for bank profitability in this research will be the ROA. As the literature in section 2.2, the ROA will be expressed by a percent. Thus it can be calculated by the equation (2).
001 × P rofit (loss) after taxT otal assets (2)
The independent variables consist of the bank-specific, banking system specific and macroeconomic factors. The literature in section 2.2 and Capraru and Ihnatov (2015) show that these independent variables are significant determinants of the bank profitability. The following table 2 shows the variables specifically.
[ Table 2 ] Independent Variables
Independent Variables Proxy for Factors
1. Bank-Specific Factors
Size of Bank Natural Logarithm of Total Assets
Capital Ratio Tier 1 Capital Ratio (percent)
Credit Risk Loan Loss Reserves / Gross Loans (percent)
Liquidity Risk Liquid Assets / Total Assets (percent)
Management Efficiency Cost to Income Ratio (percent)
2. Banking System Specific Factor
Market Concentration HH Index (annual percent change)
3. Macroeconomics Factors
Inflation CPI (annual percent change)
Economic Growth Real GDP Growth (annual percent change)
In case of the bank-specific factors, the first component is a size of a bank. This is measured by a natural logarithm of total assets of a bank. As a size of a bank becomes bigger, the bank would have the economies of scale and economies of scope which can make banks more profitable. The second factor is the capital ratio. This is the prime determinant which this
research concentrates on. The capital ratio can be measured by various proxies, such as the tier 1 capital ratio, total capital ratio and leverage ratio (Hessou and Lai, 2018). Among the proxies for the capital ratio, this research will use the tier 1 capital ratio since it is correlated with the core capital of banks at most. Additionally, the Basel III committee claims that a regulation of tier 1 capital is the most simple and efficient way to increase bank profitability (Basel Committee, 2011). The other components are the credit risk, liquidity risk and management efficiency which are measured by the loan loss reserves to gross loans, liquid assets to total assets, and cost to income ratio respectively.
Apart from the bank-specific factors, banking system specific factors and macroeconomic factors are also parts of independent variables. The market concentration which is measured by HH index is the sole component of banking system specific factor. This sole factor would indirectly affect to the profitability through changing a level of market competition. According to Basel Committee (2011), the higher market concentration will lower the market competition so moderately that overall banks’ profitability in the market would decrease. In case of the macroeconomic factors, the inflation and economic growth, which are measured by the CPI index and real GDP growth individually, are involved. The section 2.1 gives an explanation why those two would influence on the bank profitability.
Fundamentally, this research will use the STATA to run research regressions and the significance level will be set at 5% for all tests following in this paper. Additionally, the robust standard error will be employed for all test. This is because that the robust standard error would ensure an unbiased standard error under the heteroscedasticity. Further, the robust standard error is adequate even under homoskedasticity since it can give a conventional OLS standard error when there is no heteroscedasticity (Kezdi, 2003).
The first regression which shows the variables used in this research is followed in the equation (3) below :
rofitabilityP (π )it = C + β1SIZEit+ β2CPit+ β3CRit+ β4LRit+ β5ME it
MC IF EG
Where πit is the bank profitability of bank i at time t which is measured by ROA and i = 1, … , N, t = 2015, 2016, 2017, 2018. The β indicates a coefficient of each parameter. The C,
, , , , , , , , denotes a constant of the regression,
SIZEit CPit CRit LRit MEit MCit IFit EGit eIT
size of bank, capital ratio measured by the tier 1 capital ratio, credit risk, liquidity risk, management efficiency, market concentration, inflation, economic growth and an error term respectively.
As the STATA data set contains time series observations of a number of banks, the panel data regression seems relevant to be used. In order to select an adequate model of the panel regression among several models, the Hausman test is conducted through the STATA. This gives a suggestion on which model is more relevant between the fixed effect model and random effect model. The result of the Hausman test is shown in table 3 of the Appendix.
The hausman test results in p-value of 0.0000 under 5% significance level. Thus, the null hypothesis is rejected since the p-value is less than 0.05. This result implies that the fixed effect model is preferred since it would give more consistent results than the random effect model. Hence, the fixed effect model will be used to analyze the regression expressed in
equation (3). This aims to provide an empirical evidence which shows an impact of
regulatory capital on bank profitability as the tier 1 capital ratio is a part of the independent variables of the regression.
Apart from the regression analysis based on the equation (3), this paper will discover whether G SIBs and other banks show different tendencies for their profitability to increase as a larger amount of capital is required for them to hold. In order to investigate this effect of G SIBs label into the relationship between regulatory capital and bank profitability, another regression will be used as shown in equation (4).
rofitabilityP (π )it = C + β1SIZEit+ β2CPit+ β3CRit+ β4LRit+ β5ME it
MC IF EG
+ β6 it+ β7 it+ β8 it+ β GSIB9 it+ β10IGSIBit+ eIT (4)
This equation shows that GSIBit and IGSIBit are added into the equation (3). The GSIBit is the dummy variable which indicates 1 if a bank is labeled as G SIB and 0 otherwise. The
is the interaction variable of the tier 1 capital ratio and G SIB dummy variable. As the
IGSIBit
G SIB variable is added, the effect of G SIBs label into the relationship between the tier 1 capital ratio (CPit) and profitability ( ) can be analyzed. Thus, if the G SIBs labelπit
influences on the impact of regulatory capital, two regressions of equation (3) and equation (4) would give different coefficients of the tier 1 capital ratio ( CPit). Further, a sole effect of regulatory capital on the profitability can be measured more precisely when the interaction variable is added since the tier 1 capital ratio and G SIB variable can be significantly correlated.
Additionally, this paper will investigate whether the impact of regulatory capital on bank profitability differ between US banks and EU banks. In order to conduct the investigation, a modified regression equation (5) will be created.
rofitabilityP (π )it = C + β1SIZEit+ β2CPit+ β3CRit+ β4LRit+ β5ME it
MC IF EG CT Y ICT Y
+ β6 it+ β7 it+ β8 it+ β9 it+ β10 it+ eIT (5)
As the equation (5) illustrates, additional variables, CT Yit and ICT Y itare included into the equation (3). The CT Yit and ICT Y it indicate a country dummy variable and an interaction variable of the tier 1 capital ratio and country variable. The country dummy variable will be 1 if the country of banks in the data set is US and will be 0 otherwise. Specifically, the 0 value implies EU banks since the STATA data set contains US banks and EU banks solely. This regression would provide a different coefficient of CPit from the coefficient of CPit in equation (3) if the country affects to the impact of regulatory capital on profitability. Thus, it is possible to discover the effect of a country into the relationship between the capital and profitability through this regression.
Furthermore, it is possible for the regression analysis to suffer from the endogeneity bias. According to Ullah, Akhtar, and Zaefarian (2018), the endogeneity in a regression model implies that an explanatory variable is correlated with the error term. The endogeneity would pose several problems of the regression analysis. For example, researchers might get incorrect coefficients of explanatory variables, inconsistent estimates and insignificant
coefficients due to the endogeneity bias. The authors illustrate main causes of the endogeneity and suggest research methods to tackle the endogeneity bias. As they describe, the endogeneity is derived from several sources, such as the omitted variable, measurement error and simultaneity. Moreover, the dynamic generalized method of moments model (GMM) and two-stage least squares (2SLS) are suggested by the authors as alternative research methods to deal with the endogeneity bias. Therefore, this research will investigate whether the endogeneity bias exists in regression analyses. Further, alternative regressions will be suggested if the regressions of equation (3), (4) and (5) face the endogeneity problems.
4. Results and Analyses
As the previous section describes, three regression analyses of equation (3), (4), and (5) were conducted through the STATA. This section will describe results from the regression analyses and detailed explanations of the results will be provided. As the regressions were run by the STATA, coefficients of independent variables, p-values of the coefficients and the constant of regression will be provided. The impact of an independent variable on the dependent variable is estimated by the coefficients and their p-values show whether the impact is statistically significant. Among the coefficients, a coefficient of the tier 1 ratio will be primarily concerned since the coefficient tells how much the profitability is expected to change as the tier 1 ratio increases by one percent. Thus, empirical evidences regarding the impact of regulatory capital on the bank profitability will be suggested.
Firstly, the result of the regression of equation (3) is shown in the table 4 below. The coefficient of tier 1 ratio ( ) is 0.0139 expressed in the bold font. The sign of the coefficient β2
is + which tends to be omitted in general. Therefore, the value of the coefficient implies that the tier 1 ratio has a positive impact on the dependent variable, bank profitability. Specifically, the profitability is expected to increase by 0.0139 percentage points (1.39%) as the tier 1 ratio increases by 1 % when all other variables are held constant. The condition under which all other variables are held constant will be referred as the ceteris paribus in this research paper. However, this impact of the tier 1 ratio seems insignificant since the
coefficient has the p-value of 0.157. Fundamentally, the p-value for each coefficient tests the following hypothesis :
: The independent variable has no effect into the dependent variable
H0
: The independent variable has effect into the dependent variable
H1
Under the significance level (5%), the null hypothesis ( H0) is rejected if the p-value is less than 0.05. In case of the p-value for the β2, 0.157, the null hypothesis is not rejected. This implies that the tier 1 ratio has no statistically significant effect into the bank profitability.
[ Table 4 ] STATA Regression Result : Equation ( 3 )
Number of Observations : 27,720
roaa Coefficients Robust
Std. Error. t P>t [ 95% Confidence Interval ] size -0.0003 0.0090 -0.0400 0.970 -0.0179 0.0173 tier1ratio 0.0139 0.0098 1.4200 0.157 -0.0053 0.0331 loan loss reserves ratio -0.0110 0.0081 -1.3600 0.175 -0.0270 0.0049 lrisk 0.0073 0.0055 1.3300 0.184 -0.0035 0.0181 cost to income ratio -0.0196 0.0040 -4.9200 0.000 -0.0274 -0.0118 HH index -0.0125 0.0029 -4.3500 0.000 -0.0181 -0.0068 inflation 0.1231 0.0477 2.5800 0.010 0.0296 0.2167 gdp growth 0.0830 0.0217 3.8200 0.000 0.0404 0.1256 constant 2.1732 0.3187 6.8200 0.000 1.5485 2.7978
Apart from the first regression which shows a general impact of the tier 1 ratio, two regressions based on the equation (4) and (5) were run through the STATA. Compared to the equation (3), the equation (4) and (5) have additional variables.
The regression of the equation (4) includes additional variables, the GSIB and IGSIB. The former is a dummy variable which shows whether banks are G SIBs and the latter is an interaction variable of the tier 1 ratio and GSIB. The dummy variable and interaction variable have coefficients, β9 and β10 respectively. The coefficients measure impacts of the variables on the profitability. As the variables are present in the equation (4), this regression is able to provide additional information. The regression provides a statistical evidence in which G SIBs and non-G SIBs have different impacts of tier 1 ratio on their profitability. Specifically, the coefficient of tier 1 ratio ( β2) indicates an impact of tier 1 ratio on the profitability when banks are not G SIBs. However, the coefficient ( β2) is not sufficient to explain the impact when banks are G SIBs. As the interaction variable (IGSIB) is present in the equation (4), the tier 1 ratio does not only directly affect to the profitability, but it also indirectly influence on the profitability through the interaction variable. Thus, the impact of tier 1 ratio on the profitability of G SIBs should be measured by the sum of β2 and β10.
The regression result is shown in the table 5 below. The coefficients of tier 1 ratio ( ) and β2 IGSIB (β10) are 0.0142 and -0.0236 respectively and their p-values are 0.154 and 0.173 individually. Through the coefficients, the impact of tier 1 ratio on the profitability can be investigated. When banks are not G SIBs, the coefficient of tier 1 ratio ( ) sufficiently β2
shows the impact of tier 1 ratio. Thus, the profitability of non-G SIBs would increase by 1.42% as the tier 1 ratio increases by 1%. In case of G SIBs, the profitability is estimated to decrease by 0.94% as the tier 1 ratio increases by 1%. This estimation of G SIBs is calculated by β2 + β10. However, the p-values of the tier 1 ratio and IGSIB are greater than 0.05. Thus, this result seems to be statistically insignificant.
[ Table 5 ] STATA Regression Result : Equation ( 4 )
Number of Observations : 27,720
roaa Coefficients Robust
Std. Error. t P>t [ 95% Confidence Interval ] size 0.0173 0.0115 1.5100 0.132 -0.0052 0.0398 tier1ratio 0.0142 0.0099 1.4300 0.154 -0.0053 0.0337 loan loss reserves ratio -0.0107 0.0085 -1.2500 0.211 -0.0274 0.0060 lrisk 0.0073 0.0065 1.1100 0.267 -0.0056 0.0201 cost to income ratio -0.0191 0.0041 -4.7100 0.000 -0.0271 -0.0112 HH index 0.0075 0.0038 1.9600 0.050 0.0000 0.0150 inflation -0.0358 0.0405 -0.8800 0.377 -0.1152 0.0436 gdp growth 0.0647 0.0205 3.1600 0.002 0.0246 0.1048 GSIB -0.0066 0.2102 -0.0300 0.975 -0.4187 0.4055 GSIB#c.tier1ratio 1 -0.0236 0.0173 -1.3600 0.173 -0.0575 0.0103 constant 0.7539 0.5539 1.3600 0.174 -0.3318 1.8397
The year & country fixed effects are included robust standard errors & significance level (5%)
Compared to the previous regression of equation (4), a country dummy variable (CTY) and an interaction variable (ICTY) are involved in the equation (5) instead of the GSIB and IGSIB. The country variable (CTY) indicates whether banks are US banks or EU banks and the interaction variable (ICTY) measures an interaction of tier 1 ratio and the CTY. Thus, the regression of the equation (5) can measure the impact of tier 1 ratio on the profitability under the effect of the country variable. The coefficients of the tier 1 ratio and ICTY are β2and β10
respectively.
This regression enables to identify an increase in profitability due to the tier 1 ratio between US banks and EU banks. In specific, β2+β10measures the change in profitability of US banks
due to an increase in tier 1 ratio by 1%, whereas the coefficient of tier 1 ratio ( β2)measures
the change in profitability of EU banks by an increase in tier 1 ratio by 1%.
The result of the regression of equation (5) is illustrated in the table 6 below. The estimated coefficients of the tier 1 ratio and ICTY are 0.0040 and 0.0125 respectively and their p-values are 0.135 and 0.337 individually. This result provides how the impact of tier 1 ratio differs between US banks and EU banks. As β2 is 0.0040, it is estimated that the profitability of EU
banks increases by 0.4% as the tier 1 ratio increases by 1%. For the US banks, the
profitability would increase by 1.65% ( + β2 β10) as the tier 1 ratio increases by 1%. In case of the significance of this regression, the variables tend to provide insignificant impacts on the profitability since p-values of β2and β10are greater than 0.05.
[ Table 6 ] STATA Regression Result : Equation ( 5 )
Number of Observations : 27,720 roaa Coefficient s Robust Std. Error. t P>t [ 95% Confidence Interval ] size 0.0141 0.0103 1.3700 0.170 -0.0061 0.0342 tier1ratio 0.0040 0.0026 1.5000 0.135 -0.0012 0.0092 loan loss reserves ratio -0.0084 0.0071 -1.1800 0.238 -0.0225 0.0056 lrisk 0.0077 0.0056 1.3700 0.170 -0.0033 0.0186 cost to income ratio -0.0192 0.0039 -4.9100 0.000 -0.0268 -0.0115 HH index 0.0042 0.0029 1.4300 0.154 -0.0016 0.0099 inflation 0.0058 0.0430 0.1300 0.893 -0.0785 0.0900 gdp growth 0.0643 0.0192 3.3600 0.001 0.0268 0.1019 CTY 0.5319 0.2136 2.4900 0.013 0.1132 0.9506 CTY#c.tier1ratio 1 0.0125 0.0130 0.9600 0.337 -0.0130 0.0380 constant 0.9525 0.4236 2.2500 0.025 0.1220 1.7830
The results of regression (3), (4), and (5) are summarized in the table 7 below. In short, without additional variables, an increase in tier 1 ratio by 1% would increase the bank profitability by 1.39%. This implies that the regulatory capital has a positive effect into the bank profitability. However, the impact of regulatory capital tends to change as additional variables are included. The GSIB dummy variable and interaction variable are included in the regression (4). This shows that the profitability of non-G SIBs would increase by 1.42% as the tier 1 ratio increases by 1%, whereas the profitability of G SIBs is estimated to decrease by 0.94% as the tier 1 ratio increases by 1%. From this result, it is relevant that the G SIBs label clearly affects to the impact of regulatory capital on the bank profitability.
In case of regression (5), a country dummy variable (CTY) and an interaction variable (ICTY) are included. As a result, the profitability of EU banks would increase by 0.4% if the tier 1 ratio increases 1%. For the US banks, the profitability is estimated to increase by 1.64% if the tier 1 ratio increases 1%.
In sum, the regression analyses indicate that the tier 1 ratio has a positive effect into the bank profitability as β2shows. However, G SIBs would experience a decrease in their profitability when the tier 1 ratio increases. This is because that the tier 1 ratio has not only a positive effect into the profitability (β2), but it also has a negative effect into the profitability indirectly (β10) through the interaction variable. In this case, the negative effect exceeds the positive effect. Thus, an overall effect of the tier 1 ratio into the profitability of G SIBs would become negative. Moreover, it is found that the profitability of US banks would increase more than that of EU banks as the tier 1 ratio increases as 1%. Therefore, it can be concluded that the impact of tier 1 ratio is affected by the G SIBs label. Furthermore, the impact differs between US banks and EU banks. When there are no effect of the G SIBs label and country label, the regulatory capital would be positively related to the bank profitability.
[ Table 7 ] Coefficient of tier 1 ratio and Interaction Variable
Regression (3) Regression (4) Regression (5)
Coefficients tier 1 ratio (β2) 0.0139 (0.157) 0.0142 (0.154) 0.0040 (0.135) Interaction Variable (β10) . -0.0236 (0.173) 0.0125 (0.337) β2+β10 0.0139 = 1.39% -0.0094 = -0.94% 0.0164 = 1.64%
( ) : the p-value of coefficient is in the parenthesis significance level ( 5 % )
Even though the coefficients are statistically insignificant, the results are clearly parallel to the idea of Ahmad and Wang (2018) in the economic sense. As section 2-1 describes, banks would face lower costs of funding when they hold a large amount of capital since their creditworthiness tends to increase as they have sufficient capital. Thus, in the economic sense, the tier 1 ratio would be positively related to the profitability of banks. This relationship is shown through the coefficient of tier 1 ratio ( β2). Additionally, the results show that the positive impact of tier 1 ratio on the bank profitability can be influenced by the G SIBs likewise Poledna, Bochmann, and Thurner (2016) found in their paper. Even though the impact of tier 1 ratio on the profitability differs between their study and this research, both studies would clearly suggest that different regulations should be set for G SIBs and non-G SIBs.
Further, the regression (5) provides a statistical evidence of the explanation which is given by Kanter (2013). The researcher claims that the profitability of US banks would be more sensitive to the capital ratio. Thus, an increase in the profitability of US banks tends to be higher than EU banks when the US and EU banks both are required to hold more capital identically. Therefore, US and EU banks may need to follow different regulations in order to enhance their profitability.
5. Discussions
There are underlying mechanisms which possibly lead the estimated results shown in the table 7 above. Additionally, the results may provide explanations of banking regulations in reality.
Firstly, the regression (3) shows that the bank profitability increases as the tier 1 ratio increases. According to Ahmad and Wang (2018), an increase in regulatory capital does not only reduce the funding costs of banks, but it also eliminates the opportunity of banks to provide loans. They claim that the overall effect of regulatory capital would rely on the magnitude of the benefits and drawbacks from an increase in the capital. Moreover, their findings show that the overall effect would typically be positive. This is also illustrated by Kohlscheen, Murcia and Contreras (2018). Thus, the positive coefficient of tier 1 ratio in the regression (3) implies that the reduction in funding costs exceeds the loss of lending when banks are required to hold more capital.
However, the positive overall effect mentioned above would not be applicable to the G SIBs. As the regression (4) indicates, the profitability of G SIBs tends to decrease as the tier 1
ratio increases. According to Poledna, Bochmann and Thurner (2016), an increase in
regulatory capital for G SIBs tends to lead that the loss of opportunity to provide loans is far greater than the reduction in the funding costs. Thus, the overall effect of the higher capital ratio becomes negative. This is shown in the sum of coefficients ( β2+β10) the regression (4). This negative overall effect tends to be concerned significantly by banking regulators in reality. For example, Basel Committee (2011) shows that there is a distinctive capital requirement for G SIBs since a capital ratio for non-G SIBs is an inadequate requirement for G SIBs.
Additionally, the regression (5) describes that the profitability of US banks would increase further than EU banks as the tier 1 ratio increases. The underlying mechanism in the result is illustrated by Kanter (2013). Compared to the EU banks, US banks would face far lower costs of funding from a higher capital ratio. This idea can be supported by Zanakis and Gary (1992). They claim that the creditworthiness of US banks would be more sensitive to the regulatory capital which the banks hold. In other words, the creditworthiness of US banks
would increase further than that of EU banks when identical amounts of regulatory capital are additionally held by US and EU banks. As the cost of funding decreases by higher creditworthiness, US banks tend to face lower costs of funding than EU banks as the tier 1 ratio increases. This idea implies that the profitability of US bank increases further than that of EU bank when the tier 1 ratio increases for both banks.
Apart from the underlying mechanisms, this section will investigate the significance of the results. The regression results in the previous section seem statistically insignificant since the p-values of the coefficients in the table 7 are all greater than 0.05. This insignificance could be derived from several reasons. According to Ullah, Akhtar, and Zaefarian (2018), research results can be insignificant due to the inadequate sample, multicollinearity and endogeneity bias.
Firstly, the sample would be adequately selected as section 3 describes. Secondly, the VIF test through the STATA can be run in order to evaluate the multicollinearity of regressions. As the table 8 illustrates below, the regressions do not face the multicollinearity problem since their mean value of VIF are less than 10.
[ Table 8 ] VIF Tests for Multicollinearity
Regression (1) Regression (2) Regression (3)
Mean VIF 3.04 9.91 4.96
Multicollinearity No No No
The multicollinearity is defined as ‘Yes’ if the mean VIF is greater than 10, ‘No’ otherwise
Finally, the endogeneity bias can be investigated by the Durbin-Wu-Hausman test via the STATA. This tests the hypothesis below:
: The variables are exogenous
H0
: The variables are endogenous
H1
As the table 9 below shows, the tests for the regressions result in the p-values which are all less than 0.05. Thus, the regressions would contain the endogeneity bias. The bias tends to be
a main cause which lead the regressions to provide statistically insignificant results. Ullah, Akhtar, and Zaefarian (2018) claim that several factors can cause the endogeneity, such as the omitted variable bias, measurement error and simultaneity.
The measurement error is less likely to be a main reason for the endogeneity in this paper. This is because that the variables in this paper are selected in the basis of established papers as the section 2 describes. Moreover, the variables are frequently used in previous papers and they are considered as adequate variables to investigate the bank profitability and its determinants. Further, the omitted variable bias would not be a main cause since this research uses the fixed effect model to deal with the omitted variable bias to some extent.
Thus, the simultaneity tends to be the prime cause of the endogeneity in this paper. This idea is supported by The World Bank (2013). They claim that the retained earnings derived from profits can be an important source of capital. This claim implies that capital of banks can increase as the banks have more retained earnings. Therefore, the tier 1 ratio and the profitability in regressions are dependent on each other simultaneously. This would lead that the regressions face the simultaneous causality, simultaneity of the the profitability and tier 1 ratio.
[ Table 9 ] Durbin-Wu-Hausman Tests for Endogeneity
Regression (1) Regression (2) Regression (3)
P-values
Durbin (score) 0.0207 0.0492 0.0178
Wu-Hausman 0.0207 0.0494 0.0178
Endogeneity Yes Yes Yes
The endogeneity is defined as ‘Yes’ if the p-values are less than 0.05, ‘No’ otherwise In order to tackle the simultaneity in regressions, Ullah, Akhtar and Zaefarian (2018) suggest that the the dynamic generalized method of moments model (GMM) is an adequate technique to be used when data is the panel data. They claim that the GMM can provide consistent and significant results even if the panel data has the endogeneity bias. Therefore, the GMM technique may need to be employed in further research so as to minimize the endogeneity bias.
6. Limitations and further research
The previous sections provide the empirical evidence in which the impact of regulatory capital on the bank profitability is investigated. Additionally, possible challenges, such as the endogeneity bias, insignificance of coefficients and multicollinearity are illustrated and statistical techniques are suggested in order to deal with the problems.
However, the other factors which are not included in the regressions of previous sections can considerably affect to the bank profitability and they can cause the omitted variable bias of the regressions. In this case, the findings of this research would not be perfectly relevant to explain the impact of regulatory capital on the profitability. For instance, McMillan (2015) claims that current financial regulations do not adequately reflect the current situations in which the profitability of banks highly depends on their ability to provide digital services internationally. In order to investigate the bank profitability more precisely, the author suggests that technical innovations and digital revolutions are necessary to be concerned. For instance, banks with the poor mobile banking services will face low profitability even though they hold a huge amount of regulatory capital. In this case, the effect of regulatory capital into the profitability is mitigated and the regulatory capital has no measurable impact on the profitability.
Further, an economic circumstance can cause the impact of regulatory capital on the profitability to be variable. For instance, the Coronavirus (COVID-19) outbreak poses an economic downturn worldwide and it disturbs the banking regulations to function properly. Under the economic condition, an increase in regulatory capital held in banks barely increases their profitability (Fernandes, 2020). Statistically, the impact of greater regulatory capital on the profitability seems highly insignificant.
Therefore, further researches may be necessary to explain the relationship between regulatory capital and bank profitability more precisely. Moreover, the technical innovations and digital revolutions need to be considered as significant factors when the determinants of bank profitability are investigated. Further, an adequate capital ratio for increasing bank profitability needs to reflect the economic conditions which can affect to the effect of regulatory capital into the bank profitability.
7. Conclusion
As the past experience of the financial crisis 2008 verifies that the bank failure can pose severe problems for the global economy, the bank profitability becomes a prime concern since it would ensure the sustainability of banks. Thus, countless studies are conducted in order to identify the determinants of bank profitability. Among several determinants, many researchers and banking regulators agree that the regulatory capital has a huge impact on the profitability. Therefore, it is investigated in this paper that the regulatory capital is the prime determinant of bank profitability. Moreover, additional factors which can influence on the effect of regulatory capital are analyzed in order to provide more precise relationship between the regulatory capital and bank profitability. The additional variables are the G SIBs label and country label.
Consequently, it is found that the profitability of banks tends to increase as more regulatory capital is required for banks to hold. However, this effect found is affected by the extra variables. In specific, the profitability of G SIBs would decrease as the tier 1 ratio increases whereas the profitability of non-G SIBs increases at a higher tier 1 ratio. Additionally, US banks shows a larger impact of regulatory capital on the profitability than EU banks.
Therefore, this research provides empirical evidences in which the regulatory capital is the determinant of bank profitability and the impact of regulatory capital is affected by other variables, such as the G SIBs and country label. The evidences would be helpful when banking regulators create adequate regulations so as to increase bank profitability. In accordance with the results, it would be suggested that banking regulations should be aimed at increasing the regulatory capital and bank profitability subsequently. This idea is shown in reality through the Basel III. Moreover, the G SIBs and country label of banks should be concerned when regulations are made since their effectiveness can differ due to the labels.
Apart from the variables which are investigated in this paper, the technical innovations of banks and economic circumstances tend to have considerable impacts on the bank profitability increasingly. Hence, it would be essential that further research is conducted when existing papers are unable to provide precise evidences of the relationship between the bank profitability and its determinants.
Appendix
[ Table 3 ] STATA Result of the Hausman Test
--- Coefficients --- Significance level ( 5% )
(b) fixed (B) random (b-B) Difference sqrt(diag(V_b-V_B)) S.E. tier1ratio 0.0025 0.0057 -0.0032 0.0008 loanlossre~o -0.0283 -0.0268 -0.0014 0.0009 costtoinco~o -0.0076 -0.0082 0.0007 0.0001 HHindex 0.0069 -0.0043 0.0113 0.0028 inflation 0.0251 0.0312 -0.0061 0.0043 gdpgrowth 0.0554 0.0616 -0.0062 0.0028 size 0.0048 -0.0059 0.0108 0.0461 lrisk -0.0093 -0.0068 -0.0025 0.0006
b = consistent under Ho and Ha; obtained from xtreg B = inconsistent under Ha, efficient under Ho; obtained from xtreg
Test: Ho: difference in coefficients not systematic chi2(8) = (b-B)'[(V_b-V_B)^(-1)](b-B) = 190.26
Prob>chi2 = 0.0000
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