Introduction

Concentration in the banking sector is an ongoing concern, as it affects the performance and efficiency of commercial banks, which could impact investment and economic growth. Likewise, the concentration of funds in key financial institutions can lead to fragility in the financial sector (^{Fohlin and Jaremski, 2020}).

On the other hand, competition is considered one of the market structures with the most desirable characteristics. This is because competition brings benefits such as stimulating innovation, lowering prices, increasing product and service quality, increasing welfare, and accelerating economic growth (^{Banya and Biekpe, 2017}).

Currently, research related to banking competition focuses on two aspects: economic growth and financial stability. The idea that competition in the banking sector is a key factor in obtaining higher growth rates has increased interest in this topic.

Evidence from various studies suggests that countries exhibiting higher levels of competition can obtain higher growth rates and achieve higher per capita income levels than countries exhibiting lower rates of competition. These studies include those of ^{Jayakumar et al. (2018)}, ^{Diallo and Koch (2018)}, ^{Coccorese (2017)}, ^{Banya and Biekpe (2017)}, ^{Caggiano and Calice (2016)}, and ^{de Guevara and Maudos (2017)}. The findings of these studies have prompted the consideration that competition could affect economic growth in the long run.

Specifically, this paper proposes to empirically test the assumption that bank competition promotes economic growth in the long run. In other words, it tests the market power hypothesis in the long run.

To this end, two measures of competition are examined: the Boone index and the Lerner index. The former evaluates market power and the latter measures competition through efficiency. In addition, the banking sector centralization is analyzed through the concentration index of the five most important banks. Gross Domestic Product per capita by purchasing power parity was used as the dependent variable. Three different samples are proposed, three for each variable considered in the study. Each sample contains three subsamples: high, medium and low income. The Fully Modified Ordinary Least Squares (FMOLS) method developed by ^{Pedroni (2000)}, and the Dynamic Ordinary Least Squares (DOLS) method were used.

This study is organized as follows: the data section describes the variables, the composition of the different samples used and their basic statistics. The methodology section specifies the methodological procedures used. The results section shows the main findings of the econometric estimations, and finally, the conclusions section records the study's contributions.

Literature review

The debate about the effects of bank competition on economic growth is far from being defined. The literature studying the effect of bank competition on economic growth can be classified into two main approaches: the first is the traditional market power approach which argues that the lack of competition in the banking market increases the cost of financing and decreases the availability of financial services (Owen and Pereira, 2018). Moreover, given the absence of competition in the market, it is observed that the number of investment projects that receive financing is lower and therefore, economic growth decreases. Therefore, the fact that the banking sector enjoys market power will reduce incentives to invest in sectors that are more dependent on external financing, thus reducing their potential growth. Some papers supporting this approach include ^{Mitchener and Wheelock (2013)}, ^{Adu-Asare Idun and Aboagye (2014)}, ^{Caggiano and Calice (2016)}, ^{Banya and Biekpe (2017)}, and ^{Rakshit and Bardhan (2019)}.

The alternative approach argues that competition can have a negative impact on credit. One of the reasons why this situation may occur is that competition may interact with the level of asymmetric information in the market. That is, this approach argues that competitive banking systems can reduce the creation of relations between credit applicants and banks by reducing the incentive for banks to invest in soft information. Therefore, less competitive markets may be associated with greater credit availability, in line with the work of ^{Petersen and Rajan (1995)} and ^{Dell'Ariccia and Marquez (2004)}. Some papers whose results support the alternative approach are ^{Cetorelli and Gambera (2001)}, Bonaccorsi di Patti and Dell'Ariccia (2001) and de Guevara and Maudos (2011).

On the other hand, the work of ^{Dayé, Housa, and Reding (2016)} argues that lenders need to make the best decisions when choosing projects to be financed. For this purpose, the quality of the information (the company's financial statements, the actual risk of the project, and other characteristics) disclosed by loan applicants is important. Therefore, if the information is of poor quality, opaque or unavailable, as is the case for small and medium-sized companies, lenders will be more reluctant to finance them. This can lead to some information asymmetries, such as the adverse selection problem, which would mean that some less risky and good quality projects are displaced by poorer quality and riskier projects. To avoid this situation, borrowers and loan applicants have developed several coping strategies. One such strategy is to minimize the cost of obtaining information through centralizing information in public credit registries and private credit bureaus. Specifically, the existence of private credit bureaus has been found to significantly reduce information asymmetries, according to ^{Triki and Gajigo (2014)}. However, this institution is absent in many countries, especially developing ones (^{Dayé, Housa, and Reding, 2016}).

Separately, the work of ^{Ajisafe and Ajide (2014)} analyzes the long-term relation between competition in the banking sector and economic growth in Nigeria, using the period 1986-2012. They use the vector error correction method to perform the short-term analysis. They employ the banking concentration ratio as a variable to measure banking competition and performed Johansen's cointegration test to examine the existence of a long-term relation in the model. The results of the study show that bank competition has a positive effect on growth both in the short run, according to the results of the vector error correction model, and in the long run, as suggested by the cointegration test and the likelihood ratio test.

In this context, this research extends the existing literature in the following points: 1) By analyzing the relation between competition in the banking sector and long-run economic growth using panel data techniques. 2) The sample is divided into low, middle and high-income countries to empirically analyze whether asymmetric information problems derived from the absence of private credit bureaus- following the work of ^{Dayé, Housa and Reding (2016)}-can affect the relation between competition and economic growth. And 3) Three different samples are proposed, three for each variable considered in the study; these samples are composed of 112, 86, and 110 countries.

Data

The database consists of three different samples. The countries in each sample are classified according to their income into three classes: high, middle, and low. The classification was made according to a World Bank standard, except that the upper middle-income and lower middle-income classes were merged into a single class, called middle income. The first sample is constituted by two variables, the Gross Domestic Product per capita expressed in purchasing power parity at constant 2011 prices (GDPppp) as the dependent variable and the Boone index (Boone) as the independent variable. The period considered covers 1999 to 2014. The number of countries that make up this sample is 112 countries. The second sample comprises the variable (GDPppp) as the dependent variable and the Lerner index (Lerner) as the independent variable; the period to be examined is from 1996 to 2014. This sample is composed of 86 countries. Finally, the third sample comprises the variables (GDPppp) and the bank concentration index of the three most important banks (Concentration); the period under study is from 1996 to 2017. For this sample, data were obtained from 110 countries.

Different study periods are used in each sample since data for countries are not available for the calculation of competition indices in each sample; therefore, the selection of the period to be studied was made considering this situation. Consequently, nine panels of unbalanced data are considered, three for each sample, as shown in Table (1). The list of countries that make up each panel is also indicated. It is worth mentioning that these tables and lists can be found in the Appendix section.

One of the first market concentration indicators to consider is the concentration index, defined as the sum of the market shares of the largest firms in the market (^{Lijesen, Nijkamp and Rietveld, 2002}). Therefore, the concentration index is calculated as follows:

Where S_i is the market share for each bank. If the concentration index for the five largest banks is less than 50%, the banking sector is considered to be competitive.

The Lerner index represents the margin of price over marginal costs and is an indicator of the degree of market power. It is also an indicator of the proportion "level" by which price exceeds the marginal cost and is calculated as follows:

Where PTA_it is financial revenues between total assets for bank i and time t and MCTA_it is the marginal cost of total assets for bank i and time t. If the value of the Lerner index is 0, it is assumed that the market is in perfect competition; if the Lerner index is 1, the market is in a monopoly; and between 0 and 1, the market shows monopolistic competition.

The Boone index, presented by ^{Schaeck and Cihák (2013)}, is manifested as the elasticity of profits with respect to marginal costs. It is expressed as follows:

Where π_it measures the profits in bank i at time t. β is the Boone indicator, a is the market size, and c_it denotes marginal costs.

The rationale behind the indicator is that more efficient companies earn higher profits. Therefore, when the Boone index is negative, it points to greater competition because the repositioning effect is greater. The information for the Lerner, Boone, and Concentration variables comes from the Global Financial Development Database, whereas the data for the GDPppp variable comes from the World Development Indicators database.

Tables (3), (4) and (5) show the descriptive statistics for the samples: Boone, Lerner, and Concentration, respectively.

Methodology

Three different measures of competition are used to analyze the long-run relation between competition in the banking sector and economic growth: the Lerner index, the Boone indicator, and the bank concentration index for the three most important banks. Based on the above, the following models are proposed to analyze the long-term relation between competition in the banking sector and economic growth:

These three models will be estimated three times, once for each income level. The cross-sectional dependence test is performed for all variables as a first step to test for the existence of this relation. The first- and second-generation unit root tests are performed in the second step. The third step consists of estimating the Pedroni panel cointegration test. Finally, the FMOLS and DOLS methods to estimate three different models are used, one for each measure of competition.

Results

In order to determine the appropriate estimation method, it is necessary to test whether the variables are stationary or non-stationary and their order of integration. Likewise, the cross-sectional dependence or cross-sectional correlation must also be considered for the variables used in the study to decide which unit root test for panel data to apply.

Table (6) contains the results of the test for cross-sectional dependence in the variables used. The results suggest that it is possible to reject the null hypothesis for all variables at 1% significance level in most cases. Therefore, the residuals from the standard panel regression will be correlated simultaneously, which should be addressed while performing the unit root tests forX panel.

The Levin, Lin, and Chu( LLC) test developed by ^{Levin et al. (2002)}, Breitung, Im, Pesharan and Shin (IPS), the ADF − Fisher and PP − Fisher tests, developed by ^{Choi (2001)}, and the CADF test are used to test the stationarity of the variables. The CADF test is a second-generation test that allows cross-sectional dependence to be considered.

The IPS, ADF − Fisher and PP − Fisher tests are related to the null hypothesis "panels contain an individual unit root," while the LLC and Breitung tests examine the null hypothesis "panel contains a common unit root." The variables must exhibit non-stationarity in levels and be stationary in first differences to be first-order integrated I(1). If the variables are first-order integrated I(1), one can proceed to test for the long-run relation of cointegration. Unit root tests were carried out using the specification for regression that incorporates intercept and trend. Tables (7), (8), and (9) present the unit root test results for the countries that exhibit evidence of first-order integration I(1).

Table (7) presents the results of the unit root tests, which show that GDP PPP and Boone are non-stationary in levels, but become stationary in first differences; therefore, they are integrated of first order I(1). As for the tests in levels, only the PP − Fisher test shows evidence against the Boone variable being non-stationary. Meanwhile, for the GDPppp variable, all tests point to the variable being stationary. The PP − Fisher and CADF tests in first differences for the Boone variable provide evidence in favor of the variable being stationary. Although only two tests out of six provide evidence that the variable is stationary, it was considered that the CADF test, which takes into account the cross-sectional dependence, should have more weight. The results of this test show evidence that the variable is stationary. For the GDPppp variable, only the Breitung test exhibits evidence against GDPppp being stationary. Therefore, the Pedroni cointegration test is performed for this sample.

Table (8) shows the results of the unit root tests for the sample of low-income countries. The LLC,Breitung, ADF − Fisher, and PP − Fisher tests provide evidence in favor of the Concentration variable being stationary, while the IPS and CADF tests indicate that the variable is non-stationary. As in the previous case, more importance is given to the CADF test; therefore, the Concentration variable is considered non-stationary in level. On the other hand, all the level tests indicate that GDPppp is nonstationary. Likewise, the first differences tests indicate that the Concentration and GDPppp variables are stationary. Therefore, the condition that the variables are non-stationary in levels and stationary in first differences is fulfilled.

Table (9) shows the results of the unit root tests for the sample of high-income countries for the Concentration variable. The level tests that find evidence against the Concentration variable being nonstationary are LLC and ADF − Fisher; the rest of the tests point to the Concentration variable being nonstationary. As for the GDPppp variable, the IPS, ADF − Fisher, PP − Fisher and CADF tests show that it is non-stationary in level. The first difference tests for both variables show that both are stationary. In this case, it is found that the cointegration test can be performed between the selected variables because they are integrated of first order.

In order to test for cointegration between GDPppp and the variables measuring the level of competition, the Pedroni cointegration test for panel data is used. This test is performed for the following samples: Boone low income, Concentration low income, and Concentration high income. The test was performed with three deterministic specifications: intercept, intercept and trend, and no intercept and no trend. Tables (10), (11) and (12) present the results of the test using the intercept and trend specification.

The results of the cointegration test for the sample of low-income countries for the Boone variable with the intercept and trend specification are shown in Table (10). In this specification, the hypothesis of no correlation is rejected for eight out of eleven statistics. In the deterministic specification with intercept, the hypothesis of no correlation is rejected in one out of eleven statistics. In the third deterministic specification without intercept and trend, four out of eleven statistics reject the hypothesis of no correlation. Therefore, the results indicate that out of three specifications, the hypothesis of correlation is accepted in two.

Table (11) shows the results of the Pedroni cointegration test for the low-income sample with the Concentration variable. The results show that five out of eleven statistics reject the hypothesis of no correlation. As for the specification with intercept, three out of eleven statistics reject the hypothesis of no correlation. The results of the specification without intercept and trend show that all statistics reject the hypothesis of correlation. Consequently, two out of three specifications indicate that correlation exists.

Table (12) contains the results of the Pedroni cointegration test for the high-income sample with the Concentration variable. The results of the deterministic specification, including intercept and trend, show that six out of eleven statistics lead to a rejection of the hypothesis of no correlation. In the deterministic specification, including intercept, nine out of eleven statistics provide evidence against the hypothesis of no correlation. The specification that considers a deterministic model without trend or intercept rejects the hypothesis of no correlation in three out of eleven statistics. Therefore, two out of three specifications provide evidence against the hypothesis of no correlation.

The results of the Pedroni test allow arguments in favor of a cointegration relation for the three samples analyzed: Boone low income, Concentration low income, and Concentration high income.

In order to estimate the long-run coefficient for the samples above, the Fully Modified Ordinary Least Squares (FMOLS) method, developed by ^{Pedroni (2000)}, and the Dynamic Panel Least Squares (DOLS) method are used. Each of these methods has three different estimators: pooled, weighted pooled, and pooled mean. In this research, the weighted pooled estimator proposed in the works of ^{Pedroni (2001)} and Kao and Chiang (2000) was used, which allows for different long-run variations among the crosssection for heterogeneous panels. Moreover, the DOLS method is an extension of the model with lags and leads of the differences between the dependent and independent variables and makes it possible to overcome the problem of asymptotic endogeneity and serial correlation. As with the FMOLS method, the weighted estimator developed by ^{Mark and Sul (2003)} is used, which allows for heterogeneous variation in the long run.

Table (13) shows the results of the estimations with the FMOLS and DOLS methods for the Boone low income sample. The results show a positive long-run relation between the level of competition measured by the Boone index and economic growth when the FMOLS method is considered. A 1% increase in the Boone variable would mean a 34-dollar decrease in the GDPppp variable. The Boone variable is statistically significant. It is worth mentioning that negative values of the Boone variable mean more competition, so an increase in this variable would mean less competition. The results of the DOLS method indicate that the Boone variable is not statistically significant.

The results of the estimations with the FMOLS and DOLS methods for the Concentration lowincome sample are shown in Table (14). In both estimations, a negative relation between GDPppp and Concentration is found. The estimation using the FMOLS method indicates that a 1% increase in the Concentration variable implies a 14.6 dollar decrease in the GDPppp variable. Conversely, the estimation using the DOLS method indicates that a 1% increase in the variable means a decrease of 14.3 dollars in the GDPppp variable. In both estimation models, the Concentration variable is statistically significant at 1%.

The estimation results for the Concentration high income sample are shown in Table (15). In both FMOLS and DOLS estimations, a negative relation between Concentration and GDPppp is found. A 1% increase in the Concentration variable suggests a 49.8 dollar reduction in the GDPppp variable according to the FMOLS estimation results. Meanwhile, the DOLS estimation results indicate that a 1% increase in the Concentration variable would mean a decrease of 108 dollars in the GDPppp variable. Both variables are statistically significant at 1% in the two estimations used.

Consequently, the results for the Concentration low income and Concentration high income samples exhibit a negative relation between Concentration and GDPppp. The growth-reducing effect is greater in the Concentration high income sample, while the results for the Boone low income sample indicate a positive relation between competition and GDPppp. It is important to highlight that of the estimation methods, in only one is the coefficient statistically significant for this sample.

Conclusions

Nine samples were studied, three for each market structure measure. First, Pesaran's CD test was performed to look for evidence of cross-sectional codependence. The results show evidence in favor of the presence of cross-sectional dependence for all variables. For this reason, in addition to using the first generation LLC,Breitung, IPS, ADF − Fisher, and PP − Fisher tests, the second generation CADF test was used, which considers cross-sectional dependence. The results of the unit root tests show evidence of first-order integration I(1) for the samples: Boone low income, Concentration low income, and Concentration high income.

Consequently, Pedroni cointegration tests were performed for these three samples. Evidence was found to favor a long-term cointegration relation for all three samples. Finally, estimations were performed using the FMOLS and DOLS methods. Evidence of a negative long-term relation of cointegration between the level of bank concentration and economic growth was found for the Concentration low income and Concentration high income samples. These results are consistent with the theoretical prediction that more bank competition translates into higher economic growth. Therefore, the evidence found supports the market power approach. Similarly, a positive long-run cointegration relation was found between efficiency, as measured by the Boone index, and economic growth. The evidence comes from the Boone low income sample. This result also supports the market power approach.

On the other hand, the results of the three samples, Concentration low income, Concentration high income and Boone low income are consistent with the findings of the works of ^{Mitchener and Wheelock (2013)}, ^{Adu-Asare Idun and Aboagye (2014)}, ^{Caggiano and Calice (2016)}, ^{Banya and Biekpe (2017)}, and ^{Rakshit and Bardhan (2019)}. Meanwhile, in the work of ^{Ajisafe and Ajide (2014)}, which studies the relation between competition in the banking sector and economic growth in the case of Nigeria, both short-term and long-term estimation techniques are employed. Their results show that in both the short and long run, the relation between banking competition and economic growth is positive and consistent with the results obtained. Additionally, no evidence is found that the estimation results are affected by the level of income. The correlation coefficients found are high for both estimates for the Concentration high income and Boone low income samples with an average of .9.

The empirical results obtained in this study suggest that bank competition could be beneficial for economic growth. That is, as banking competition increases through the channel of efficiency and decreased concentration, this ultimately means increased economic growth. Therefore, it is suggested to implement measures that restrict the concentration of funds in a small number of banking institutions, as well as measures that encourage competition in the banking sector through policies that strengthen efficiency in the sector. On the other hand, a limitation of this analysis is that no control variables are incorporated. The findings suggest an important question: what would be the effect of competition in the banking sector on the stability of the sector in the long run?