fragility, and financial crisis”

This paper examines how competition affects bank fragility and how this relation var- ies in normal times and during a financial crisis using the data from Indonesian commercial banking industry. The author finds significant evidence, both statistically and economically, that more competition reduces bank fragility. In particular, the author finds that a decrease in Herfindahl – Hirschman Index (HHI) of deposits by 100 points leads to an increase in bank Z-score by 14.22 percent from its mean. Similarly, a decrease in HHI of loans by 100 points leads to an increase in Z36 by 20.44 percent. This finding is consistent across different kinds of robustness tests, including endogeneity, as well as alternative bank fragility and competition measures. However, this competi- tion-stability nexus holds only in normal times and is reversed during a financial crisis. This suggests that the impact of competition on bank fragility is conditional on the economic condition. paper contributes to the strand of literature about the impact of competition on bank fragility. In particular, this paper sheds light that the relation between competition and bank fragility can be different in normal time and financial crisis. Using the data from the Indonesian banking industry, I document significant evidence that more competition leads to lower bank fragility in the overall sample period, supporting the competition-stability hypothesis. This finding is robust to endogeneity as well as to different bank fragility and competition measures. Interestingly, during a financial crisis, I find that less competition helps to lower bank fragility. The policy implication of these findings is essential, especially for the government. In particular, the government should design different policies in normal times and during a financial crisis. Bank regulation that supports bank competition should be nurtured in normal times. However, such bank regulation that intensifies competition should be relaxed during a financial crisis.

As in other industries, most policy makers and academicians believe that more competition in the banking industry will benefit the economy. For example, President Obama (2010) in one of his speeches asserts, "The American people will not be served by a financial system that comprises just a few massive firms. That's not good for consumers; it's not good for the economy". Meanwhile, previous research has shown that more competition in the banking industry increases per capita income growth (Jayaratne & Strahan, 1996), reduces loan rate (Rice & Strahan, 2010), improves income distribution (Beck et al., 2010), and promotes innovation (Chava et al., 2013). However, the nexus between competition and bank fragility has still been a controversial debate. On the one hand, more competition shrinks a bank's ability to reap profit and results in lower charter value, which induces the bank to compensate it by taking higher risk (e.g., Keeley, 1990;Hellmann et al., 2000;Repullo, 2004). On the other hand, more competition makes bank loans cheaper, which lessens moral hazard incentives of borrowers to shift into riskier projects and draws a safer set of borrowers (e.g., Boyd & De Nicolo, 2005;Boyd et al., 2006;Akins et al., 2016). Moreover, more competition might promote a less concentrated banking system with fewer too-big-to-fail (TBTF) banks that benefit most from the government's implicit or explicit bailout program (Berger et al., 2009).
The recent global financial crisis has shown once more how disruptive a financial crisis to the economy. Laeven and Valencia (2013) show that during 1970-2011, the world's median output loss and fiscal cost caused by banking crises are 23.2 and 6.8 percent of GDP, respectively 1 . Financial economists have studied financial crises extensively. However, the literature on how competition affects bank fragility in normal times and during a financial crisis is still relatively sparse. This gap in the literature is surprising considering that competition is one of the main determinants of bank fragility.
This paper aims to fill the gap by providing novel evidence from the Indonesian commercial banks industry. Mulyaningsih and Daly (2011) show that Indonesia has experienced material changes in its banking structure after the 1997 Asian financial crisis, which results in more consolidated banking industry. This makes Indonesia a good laboratory to test the relation between competition and bank fragility. Moreover, focusing on a single country dataset ensures greater homogeneity that mitigates the omitted variables bias.  (Berger & Bouwman, 2013). Therefore, the sample covers longer period than the previous studies (e.g., Akins et al., 2016) and includes both crisis and normal times. Finally, I also perform instrumental variable (IV) techniques to ensure that the reverse causality problem does not bias my findings, as well as other robustness checks.
In summary, for the overall sample and during normal times, I find that banks in a more competitive market are less fragile to insolvency, consistent with the competition-stability hypothesis. Meanwhile, during a financial crisis, my findings suggest that less competition promotes higher bank stability, consistent with the competition-fragility hypothesis.
The remainder of this paper is structured as follows. Section 1 provides literature review and hypotheses development. Section 2 describes the methodology, variables, and data. Section 3 presents the empirical results and robustness checks. Final section concludes the paper.

1.
The traditional "competition-fragility hypothesis" suggests that tougher bank competition decreases franchise value and results in higher risk taking (Marcus, 1984;Keeley, 1990;Demsetz et al., 1996;Carletti & Hartmann, 2003;Craig & Dinger, 2013). On the other hand, the "competition-stability hypothesis" contends that lower competition in the loan market may induce banks to charge higher interest rates to their borrowers and results in higher banks' risk-taking either via moral hazard or adverse selection channel ( explain why they find competition affecting bank risk in the same way before and during the crisis. Moreover, the paper does not address the potential reverse causality problem between competition and bank fragility. I address all of these concerns in this paper.
Why does competition may affect bank fragility differently in normal times and financial crises? A financial crisis usually involves significant losses in banking industry due to high nonperforming loans or fire sales of assets in response to bank runs (e.g., Laeven & Valencia, 2013). In this harsh time, a bank might benefit from a substantial market power, since it may attract deposits with lower rate due to flight-to-safety. This will mitigate the decline on the bank's profit, preserve its charter value, and lessen the incentives to take high risks. Accordingly, I hypothesize that during a financial crisis, less competition is associated with less bank fragility (competition-fragility hypothesis). Since loan prices are typically high during a financial crisis due to a contraction in credit supply (e.g., Accordingly, the third hypothesis to test in this paper is: H3: The relationship between competition and bank fragility is different in normal times and during a financial crisis.

2.
Following Berger et al. (2017), I use Z-score as the main proxy of overall (inverse) bank fragility. The Z-score measures the number of standard deviations below the mean by which a bank's profits would have to fall to exhaust its capital. Higher Z-score shows less bank fragility and vice versa. As the baseline, I compute the Z-score over three years or 36 months (Z36), from time t3 5 to 2 The purpose of the allowance is to cover credit losses that are probable and estimable on the date of financial reporting (Office of the Comptroller of the Currency, 1996). 3 The deposit insurance cap rate data are from the Indonesian Deposit Insurance Corporation (IDIC)'s website (www.lps.go.id) and the Indonesian Financial Statistics published by the Bank of Indonesia. The monthly inflation rates are from the Indonesian Statistical Bureau (www.bps.go.id).
time t. I also use the Z-score over two years (Z24) and five years period (Z60) as robustness checks.
Other measures of bank fragility that I use as additional robustness checks are nonperforming loans ratio (NPL/TL) and allowance for loans losses to total loans ratio (ALL/TL). While the NPL ratio is a historical risk measure, the ALL ratio is more forward-looking measure of a bank's loans portfolio 2 . A bank with higher NPL/TL or ALL/TL is more fragile to insolvency.
Following the U.S. Department of Justice and Federal Trade Commission (2010), I use the Herfindahl -Hirschman Index (HHI) as the main proxy of bank competition. In order to capture (inverse) bank competition in both deposit and loan markets, I calculate HHI of deposits (HHID) and loans (HHIL) to use in the baseline regressions. In robustness checks, I use the 4-firms concentration ratio in deposits (CR4D) and loans markets (CR4L) as alternative measures of bank competition (e.g., Mirzaei et al., 2013).
In order to ensure that other factors do not confound the impact of competition to bank fragility, I control for a number of bank-level characteristics and macroeconomic environments 3 . Moreover, I control for bank fixed effects to mitigate the potential omitted variable bias caused by any time invariant bank-specific factor. Table 1 provides detailed definitions of all variables used in this paper.
The baseline model specification to test the impact of competition on bank fragility in a multivariate setting is as follows: where Z denotes the main measure of (inverse) bank fragility, HHI is the main measure of (inverse) bank competition, Controls is the vector of bank characteristics and macroeconomic controls, is the bank fixed effect, and is the error term. I estimate the OLS regression in Equation 1 with robust standard errors clustered at the bank level to correct possible heteroscedasticity and Table 1.

Variable Definition
Main dependent variable (bank fragility measure) An inverse measure of bank fragility or overall financial risk, calculated as mean ROA mean Equity / GTA / ROA . Higher value indicates lower bank fragility. The mean and standard deviation () are calculated over 3 years (36 months) from time to time t. ROA is the bank's return on assets, calculated as the ratio of net income to Gross Total Assets (GTA). Equity / GTA is the bank's capitalization ratio.

Alternative bank fragility measures
An alternative measure of Z-score with the mean and standard deviation calculated over 2 years (24 months). Higher value indicates lower financial risk.
Z-score60 (Z60) An alternative measure of Z-score with the mean and standard deviation calculated over 5 years (60 months). Higher value indicates lower financial risk.
NPL ratio (NPL/TL) A measure of credit risk calculated as the ratio of nonperforming loans (past due at least 90 days or in nonaccrual status) to total loans. Higher value indicates riskier loan portfolio.
All ratio (ALL/TL) An alternative measure of risk on a bank's loans portfolio calculated as the ratio of allowance for loans losses to total loans.

HHI of deposits (HHID)
A proxy of bank competition calculated as the sum of squared deposit shares of all banks in the market. This measure takes values between zero and 10,000 with higher values indicating less competition. HHI close to zero means that a market is perfect competition, while HHI equal to 10,000 belongs to a monopoly market.

HHI of loans (HHIL)
An alternative proxy of bank competition calculated as the sum of squared loan shares of all banks in the market. This measure takes values between zero and 10,000 with higher values indicating less competition. HHI close to zero means that a market is perfect competition, while HHI equal to 10,000 belongs to a monopoly market.

CR4 of deposits (CR4D)
An alternative proxy of bank competition calculated as the sum of deposit shares of four largest banks in the market. This measure takes values between zero and 100% with higher values indicating less competition.

CR4 of loans (CR4L)
An alternative proxy of bank competition calculated as the sum of loan shares of four largest banks in the market. This measure takes values between zero and 100% with higher values indicating less competition.

Control variables
Log of gross total assets (LGTA) The natural logarithm of Gross Total Assets (GTA). GTA is defined as total assets + allowance for loan losses, following Berger and Bouwman (2013).

Asset diversification ratio (ADR)
A measure of earning assets composition in a bank's balance sheet calculated as Net loans Other earning assets 1 Total earning assets following Laeven and Levine (2007). This measure takes values between zero and one with higher values indicating greater diversification.
Overhead costs ratio (OHR) A proxy for the bank's overhead cost structure calculated as the ratio of overhead expenses to GTA.

Listed dummy (LB)
A dummy variable equals 1 if the bank is listed on a stock exchange or is part of a bank holding company that is listed on a stock exchange, and 0 otherwise.

BHC dummy (BHC)
A dummy variable equals 1 if the bank is part of a bank holding company, and 0 otherwise.

Deposit insurance cap rate (DICR)
The ceiling rate for interest on bank deposits that is set by Indonesia Deposit Insurance Corporation (IDIC) on a monthly basis.
Crisis dummy (CRISIS) A dummy variable equals 1 for the financial crisis period, and 0 otherwise.
Bank FE Bank fixed effects represented by a dummy variable for each bank.

Instrumental variables
Age (AGE) Bank age calculated as year -year of establishment.
Age squared (AGESQ) The squared term of bank age.
within-bank serial correlation problems (Rogers, 1993). I make sure that all right-hand side variables are predetermined to the dependent variable, because some researchers argue that this can mitigate the reverse causality problem to some extent (e.g., Duchin et al., 2010). The coefficient of interest in Equation 1 is , which will be positive if the competition-fragility hypothesis is true, and negative if the competition-stability hypothesis is true.
To test the impact of competition on bank fragility during a financial crisis, I estimate the following regression specification: where CRISIS is a dummy variable equal to one for the financial crisis period, and zero otherwise.  5 . Further, I exclude Sharia (Islamic) commercial banks from the sample due to material differences in banking practices with the conventionally operated commercial banks 6 . I end the sample period in December 2011, because the bank regulator imposes a new IFRSbased-accounting rule for allowance for loans losses (ALLs) starting in January 2012 7 . This rule makes ALLs prior and after January 2012 not comparable.
My initial sample comprises of 7,772 bank-month observations. After removing Sharia banks and observations with zero gross total assets (GTA) 8 , total deposits, total loans, or total assets, the sample available for multivariate analyses has 7,597 bank-month observations. Finally, I winsorize all unbounded financial variables at 3 percent level on the top and bottom of their distributions in order to mitigate the impact of outliers, following Berger and Bouwman (2013) 9 . Table 2 presents summary statistics for all variables used in this paper. Moreover, there seems to be no serious pairwise correlations between the main independent variables and other control variables that can potentially lead to a multicollinearity problem 10 . Table 3 presents the main OLS regression estimates of the inverse measure of bank fragility (Z36) on competition, as specified in Equation 1. Models 1-3 use HHID as the proxy of bank competition, while Models 4-6 use HHIL. Models 1 and 4 include no control variables, Models 2 and 5 control for bankspecific variables, and Models 3 and 6 control for bank-specific, as well as macroeconomic variables. All estimates include bank fixed effects and standard errors are clustered at bank level. I find that the coefficient of bank competition is negative and statistically significant in each of the model specifications. This result is also economically material.

Main regression results
In particular, holding all bank-specific and macroeconomic variables at their means, a decrease in HHID by 100 points leads to an increase in Z36 by 14.22 percent from its mean. Similarly, a decrease in HHIL by 100 points leads to an increase in Z36 by 20.44 percent 11 . This suggests that more competition is associated with less bank fragility, supporting the competition-stability hypothesis (hypothesis 2). 9 Unbounded financial variables can take any value between , and, therefore, might suffer from outlier problem. 10 I follow a rule-of-thumb in Gujarati (2004, p. 359) who suggests that there might be a serious multicollinearity problem between two regressors if the pairwise correlation between them exceeds 0.80. The pairwise correlation table is not shown in this paper for brevity, but it is available by request as an Appendix. 11 The coefficient of HHID in Model 3 is -0.016. This means that holding all regressors at their means, a decrease in HHID by 100 points will translate to an increase in Z36 by 1.60 from its mean (11.251). In other words, Z36 will increase by 14.22% from its mean when the HHID decreases by 100 points. By the same logic, the coefficient of HHIL in Model 6 (-0.023) implies that Z36 will increase by 20.44% from its mean when the HHIL decreases by 100 points. I use an incremental of HHID and HHIL of 100 points to examine the economic significance of the main findings following the approach in the Horizontal Merger Guidelines (U.S. Department of Justice and Federal Trade Commission, 2010) to assess whether a bank merger will increase the local market concentration materially.
In terms of control variables, the coefficients of bank size (LGTA) and its squared term (LGTA SQ) are statistically significant in all regression specifications that control them. The inflection point of the bank size varies between 6.35 and 7.03 (real GTA between IDR 572.49 billion and IDR 1.13 trillion). These values are between the 25 th percentile and the median, which means that there is a "U-shaped" relation between bank size and fragility. Next, overhead cost ratio (OHR) has negative and statistically significant coefficients in most of the regression specifications, consistent with the notion that cost inefficient banks tend to be riskier (Demirguc-Kunt & Huizinga, 2010). Meanwhile, none of the asset diversification ratio (ADR), listed dummy (LB), and Bank Holding Company dummy (BHC) is statistically significant. In terms of macroeconomic controls, I find some evidence that higher deposit insurance cap rate (DICR) leads to higher bank fragility. However, I find no evidence the monthly inflation rate (INF) is related to bank fragility.

Endogeneity
An endogeneity problem might arise from a reverse causality between bank fragility and competition. For example, a financially stable bank might have sufficient resources to increase its market power (reduce bank competition) by acquiring other banks. Alternatively, a bank might increase its risk in order to increase returns and grow larger, which results in more market power (e.g., Berger et al., 2009). In order to address this potential problem, I run Instrumental Variable (IV) regressions with a Generalized Method of Moments (GMM) estimator. This estimation technique, which was introduced by Hansen (1982), does not require distributional assumptions on the error terms and is more efficient than 2SLS to address heteroscedasticity (Hall, 2005). Moreover, since bank fragility measures might be serially correlated, I cluster the standard errors at the bank level using a formula-tion proposed by Arellano (1987). I employ bank age (AGE) and its squared term (AGESQ) as instruments for bank competition in the IV-GMM regressions. The economic theory predicts that as a bank becomes more mature and earns positive economic profits, new entrants will be attracted to enter the industry (e.g., Baumol et al., 1988;Baumol & Lee, 1991). Consequently, competition tends to get tougher as the bank matured.  13 . These indicate that both of the instruments satisfy the relevance criterion for good instruments. Next, the first-stage results show that Hansen-J-statistics in all specified models are not statistically significant. This suggests that both instruments have also met the exogeneity criterion (overidentifying restriction) for good instruments 14 .
The second-stage results are qualitatively similar with the main findings using OLS in Table 3. In terms of magnitude, HHID coefficients are very close between the OLS and IV-GMM, while the HHIL IV-GMM coefficients are larger than the OLS' counterpart. The latter might suggest that OLS underestimate the causal effect between HHIL and bank risk.

Other robustness checks: alternative measures of risk and competition
As additional robustness checks, firstly, I use different alternative measures of bank fragility other than Z36: 24 months -Z-score (Z24), 60 months -Z-score (Z60), NPL/TL, and ALL/TL. Next, I use four-bank concentration ratios of deposits (CR4D) and loans (CR4L) as alternative measures of bank competition. Following Carlson and Mitchener (2006), I calculate the CR4 as the sum of deposit or loan shares of four largest banks in the market for each time period. The results from all of these ro- 15 These results are available upon request as an Appendix.
bustness checks are consistent with the main findings, in which more competition decreases bank fragility 15 . Table 5 presents the OLS regression estimates of the inverse measure of bank fragility (Z36) on competition and its interaction with financial crisis, as specified in Equation 2. Models 1-4 use different measures of bank competition -HHIL, HHID, CR4D, and CR4L, respectively -and all of them control for bank-specific, as well as macroeconomic variables and bank fixed effects. The re-  sults show that competition is statistically significant and negatively associated with Z36 in all of the specified models. On the contrary, the interaction term between bank competition and crisis has positive and statistically significant coefficients in all of the specified models. These findings imply that market power helps to reduce bank fragility during a financial crisis. Therefore, whether competition affects bank fragility positively or negatively is conditional on the economic condition. In normal times, as shown by the main findings, more competition increases bank stability, but in a financial crisis, the impact is reversed. This finding provides strong evidence on hypothesis 3.

Competition and financial crisis
This paper contributes to the strand of literature about the impact of competition on bank fragility. In particular, this paper sheds light that the relation between competition and bank fragility can be different in normal time and financial crisis. Using the data from the Indonesian banking industry, I document significant evidence that more competition leads to lower bank fragility in the overall sample period, supporting the competition-stability hypothesis. This finding is robust to endogeneity as well as to different bank fragility and competition measures. Interestingly, during a financial crisis, I find that less competition helps to lower bank fragility. The policy implication of these findings is essential, especially for the government. In particular, the government should design different policies in normal times and during a financial crisis. Bank regulation that supports bank competition should be nurtured in normal times. However, such bank regulation that intensifies competition should be relaxed during a financial crisis.     Notes: ***, **, * indicate significance at the 1%, 5%, and 10% levels, respectively. This table shows the relation between competition and bank fragility using several different alternative measures. The regressions are OLS with robust standard errors clustered at bank level to correct for heteroscedasticity and within-bank serial correlation. Panel A reports the regression estimates using several alternative measures of bank fragility: Z-score24, Z-score60, NPL ratio, and ALL ratio. The key explanatory variable is bank competition that is proxied by Herfindahl-Hirschman Index (HHI): columns (1) to (4) use HHI of deposits, while columns (5) to (6) use HHI of loans. All columns control for bank-specific and macroeconomic variables, as well as bank fixed effects. Panel B reports the regression estimates using several alternative measures of bank competition: columns (1) to (3) use CR4 of deposits, while columns (4) to (6) use CR4 of loans. The dependent variable is (inverse) bank fragility that is proxied by Z-score36. In terms of control variables used, columns (1) and (4) control for bank fixed effects only. Columns