Data
To analyze whether bank competition and efficiency influence bank stability, bank-level data of competition, efficiency, financial stability and bank-level control variables—bank size and liquidity—are sourced from financial statements of concerned banks which are available at their websites and Dhaka Stock Exchange library. In addition, data of country-level control variables—governance—are collected from The Worldwide Governance Indicators dataset [53], regulation is collected from Economic Freedom Index [26], and others are collected from World Development Indicator [54] for the period 2009–2017, which constitute a balance panel of 270 observations. Data sources and variable definitions are presented in “Appendix” Table 6. Prior to the analysis, all data are winsorized at 1st and 99th percentile to reduce the influence of outliers.
Financial stability
To measure financial stability, a wide range of indicators were devised following the global financial crises of 1980s and 1990s, like Z-score, probability of bankruptcy, standard deviation of ROA, nonperforming loan ratio and so on, among which Z-score is very common and used by many researchers [6, 10, 27, 32, 37]. Z-score measures the insolvency risk of a bank; a larger value indicates a lesser risk of bankruptcy and a higher bank stability. We use natural logarithm of the Z-score to measure bank financial stability that accounts for skewness in the data. Z-score is computed as follows:
$$Z{\text{-score}}_{\text{it}} = \frac{{{\text{ROA}}_{\text{it}} + \left( {\frac{E}{\text{TA}}} \right)_{\text{it}} }}{{\sigma {\text{ROA}}_{\text{it}} }}$$
(1)
where ROA is the return on assets, E/TA represents the equity to total assets ratio, and \(\sigma {\text{ROA}}\) denotes the standard deviation of return on assets. We use three-year rolling time windows to compute the standard deviation of ROA to allow for time variation in the denominator of the Z-score. In addition, standard deviation of return on asset (hereafter,\(\sigma {\text{ROA}}\)) and nonperforming loan ratio (NPL) are also used as a measure of financial stability [1, 32] to check the robustness of the estimations.
Competition
To determine competition H-statistic, concentration ratios, Lerner index, Boone indicator and other measures could be used. Structural measures like HHI (Herfindahl–Hirschman index) represent competition through level of concentration, which is found as a delicate proxy of competition [20] and therefore could generate misleading outcomes. Moreover, a high degree of industry concentration does not necessarily imply a less competitive market [39]. On the other hand, Lerner index is also criticized for not being able to confine the degree of product substitutability [51], whereas Boone indicator, introduced by Boone [16, 17], is found to overcome these shortcomings and employed by some researchers like Schaeck and Cihák [46], Saif-Alyousfi et al. [45], Kasman and Kasman [32], Saha and Dutta [44]. Following the relevance, this study also uses Boone indicator to measure the competition. Boone [17] calculates the level of competition by estimating the elasticity of a firm performance, in terms of its market shares, with respect to its marginal costs, as follows:
$$\ln \;({\text{Market}}\;{\text{share}})_{\text{it}} = \alpha + \beta \ln \;({\text{Marginal}}\;{\text{cost}})_{\text{it}}$$
(2)
where the coefficient β denotes the Boone indicator. Following Schaeck and Cihák [46], we approximate the marginal costs by calculating the average variable costs as marginal costs cannot be observed directly. For the baseline GMM estimation and robustness check, we use market share of total loan (hereafter, Boone loan) and market share of total deposits (hereafter, Boone deposit), respectively, to estimate Boone indicator. In principle, Boone indicator argues that competition creates a negative relation between performance and marginal cost that becomes stronger at a higher level of competition. Higher negative value of the Boone indicator signifies higher competition; therefore, we transform Boone indicator to its respective positive value to facilitate interpretation.
Efficiency
Many researchers used data envelopment analysis (DEA) to measure efficiency; however, efficiency ratios—working capital ratio, asset turnover ratio and operating efficiency—are simple and easy to understand and can be used to measure prevailing operational efficiency in an organization [52]. In this paper, we use different efficiency ratios, namely net interest margin, working capital ratio, asset turnover ratio and operating efficiency ratio, to measure bank efficiency. Since different efficiency ratios are highly correlated, substitutable or complementary in nature, the simultaneous use of those indicators in a model may produce unreliable results. Therefore, to overcome this problem of over-parameterizations and multicollinearity, we use different efficiency ratios to construct efficiency index applying the PCA [28]. Before applying the PCA, all indicators are normalized using the following equation:
$${\text{nmx}} = \frac{{X_{i} - X_{\hbox{min} } }}{{X_{\hbox{max} } - X_{\hbox{min} } }}$$
(3)
where \(X_{\hbox{min} }\) is the minimum data point and \(X_{\hbox{max} }\) is the maximum data point.
The eigenvalues of the four components are 1.56, 0.98, 0.85 and 0.59, respectively, suggesting that the first component has eigenvalue higher than one and explains 39% variations of the four ratios. We consider only the first component to construct the efficiency index for all our bank-year observations and again normalize the resulted index using minmax normalization. The Kaiser–Meyer–Olkin (KMO) measures of sampling adequacy are 0.56, and the p values for the Bartlett’s test of sphericity are lower than the 0.01 significance level, which confirms the suitability of the variables used in the PCA. Additionally, we use operating efficiency ratio for the robustness check of the estimation.
Control variables
To control the bank-specific heterogeneity and economic condition, we use different control variables. Similar to Jeon and Lim [30], loan to deposit is used to control the liquidity and log of total asset is used to control bank size, which is also used by Kasman and Kasman [32] and Jeon and Lim [30]. Furthermore, similar to Ahamed and Mallick [1] to control the fluctuations of economic activity, log of GDP per capita and GDP growth rate (gGDP) are used. To account for the variation of governance and regulation over time, a composite index of governance, constructed similar to Dutta and Saha [24], and regulation is used. Additionally, financial depth measured by broad money to GDP and log of real GDP are used as alternative control variables for robustness check.
Model
To estimate the direct causal effect of competition and efficiency, we use the following model, where an interaction term of competition and efficiency is also included to capture the degree of change in competition–stability nexus at different levels of efficiency.
$$\begin{aligned} {\text{Financial Stability}}_{\text{it}} & = \beta_{0} + \beta_{1} {\text{Financial Stability}}_{{{\text{it}} - 1}} + \beta_{2} {\text{Competition}}_{{{\text{it}} - 1}} + \beta_{3} {\text{Competition}}_{{{\text{it}} - 1}}^{2} \\ & \quad + \beta_{4} {\text{Efficiency}}_{{{\text{it}} - 1}} + \beta_{5} {\text{Competition}}_{{{\text{it}} - 1}} \times {\text{Efficiency}}_{{{\text{it}} - 1}} + \mathop \sum \limits_{j = 1}^{k} \gamma_{j} X_{{{\text{it}} - 1,j}} + \nu_{t} + \varepsilon_{\text{it}} \\ \end{aligned}$$
(4)
where subscripts i and t indicate bank and time, respectively, the dependent variable \({\text{Financial Stability}}_{\text{it}}\) is measured by either log (Z-Score) or σROA or NPL, the lagged value of this variable is included as regressors to capture the persistence of financial stability. \({\text{Competition}}_{{{\text{it}} - 1}}\) is the 1-year lagged term of competition for bank i measured by either Boone loan or Boone deposit. Additionally, following Berger et al. [13], we use a quadratic term of competition to capture the nonlinear properties of competition–stability relationship. Other independent variables like \({\text{Efficiency }}_{{{\text{it}} - 1}}\) are measured by either efficiency index constructed by PCA or operating efficiency ratio. \(X_{it - 1,j}\) is a set of {k} variables controlling for bank-specific and macroeconomic factors. β’s are the parameter vectors, \(\nu_{t}\) are the year dummies and \(\varepsilon_{\text{it}}\) is the unobserved disturbance. We take lag of all explanatory variables to reduce the endogeneity issues. The inclusion of time dummies captures the effect of any event that affects the variables of interest for all banks and ensures that the estimates are not biased because of the occurrence of any such events. To address the possible endogeneity, we apply the two-step system GMM [14]. The system GMM estimator provides consistent and efficient estimates, overcomes the unobserved effects and endogeneity problem and is a better fit for panel studies with fewer time observations like this study. We also check the robustness of the validity of the instruments and any possible autocorrelation using the Sargan test and Hansen J statistic of over-identifying restrictions and Arellano–Bond (AR) test, respectively.
