**Descriptive statistics of variables**

To give an overall description of data employed in the model, descriptive statistics are used to determine the minimum, maximum, mean, and standard deviation as follows.

Table 4.1

Summary of Descriptive Statistics Descriptive Statistics

VARIABLE | OBS | MEAN | STD. DEV. | MIN | MAX |

ZSCORE | 80 | 2.951 | .362 | 2.382 | 4.294 |

ROA | 80 | 17.541 | 2.663 | 5.879 | 23.233 |

SIZE | 80 | 2.26e + 10 | 1.78e + 10 | 1.29e + 09 | 8.93e + 10 |

FR | 80 | 2.874 | .453 | 2.345 | 4.425 |

CR | 80 | 53.114 | 5.629 | 38.503 | 65.473 |

LIQ | 80 | 19.389 | 5.21 | 10.717 | 33.111 |

BC | 80 | 42.945 | 4.628 | 14.157 | 48.067 |

GDP | 80 | 8.047 | 1.409 | 6.057 | 9.564 |

RITR | 80 | − .216 | 4.519 | -7.3 | 5.25 |

The Table 4.1 reveals the financial stability of private commercial banks in Ethiopia between 2016 and 2020 based on the Z-score metric. The mean Z-score of 2.951 indicates that these banks generally maintained adequate equity to cover potential losses, supported by positive returns on assets and equity, as well as stable return patterns. Despite slight variation with a standard deviation of 0.362, the range from a minimum Z-score of 2.382 to a maximum of 4.294 suggests consistent but not significant differences in financial stability among the sampled banks. This period did not see any substantial losses that would threaten the banks' equity, attributed to their increasing profitability, sufficient capital adequacy, and stable returns. Overall, the findings underscore the resilience and sound financial health of private commercial banks in Ethiopia during the study period.

The Z-score is a crucial measure indicating a bank's ability to absorb returns variability with its capital, as described by (Köhler, 2015). A higher Z-score signifies greater financial stability and lower risk of insolvency. (Köhler, 2015) categorizes Z-scores: Z > 2.99 indicates no financial problems, 1.88 < Z < 2.99 suggests slight issues, and Z < 1.88 indicates serious financial problems or defaults. In the study of private banks in Ethiopia from 2016 to 2020, Z-scores ranged from 2.382 to 4.294. The mean Z-score of 2.951 suggests moderate financial stability overall, with a low likelihood of imminent financial instability among the sampled banks.

Commercial banks in Ethiopia, on average, maintained a moderate liquidity position with a LIQ ratio of 19.389%, ranging from 10.717–33.111%. The standard deviation of 5.21% indicates substantial variability in liquidity levels among these banks during the study period. This variability was the highest among the variables examined, reflecting significant differences in liquidity management among private commercial banks in Ethiopia.

The bank size (SIZE) variable exhibited significant dispersion, with a mean value of 22,600,000,000 and a large standard deviation of 17,800,000,000. The range extended from a minimum of 1,290,000,000 to a maximum of 89,300,000,000, indicating considerable variation in bank sizes among the sampled institutions. Larger banks have the advantage of offering a broader range of financial services and attracting more funds, which can lead to more efficient customer service through economies of scale derived from their size.

During the study period, Ethiopian private commercial banks, on average, allocated 53.114% of their total assets to loans and advances, reflecting their exposure to credit risk (CR). This proportion ranged from 38.503–65.473%, indicating varying strategies in credit allocation among banks. The standard deviation of 5.629% underscores the diversity in how banks manage their credit portfolios. Comparing these credit proportions directly across banks may be complex due to differing levels of stability and risk management practices.

The study's industry-specific factor, bank concentration (BC), measured by the Herfindahl–Hirschman Index (HHI), averaged 42.945% during the sample period. The HHI ranged from a minimum of 14.157% to a maximum of 48.067%, indicating moderate market concentration among selected banks. The standard deviation of 4.628% suggests some variability in market concentration levels within the industry. This index serves as a measure of firm size distribution and competition intensity among banks in the studied context. On the other side, the return on assets (ROA) indicates that the minimum return was 5.879% while the maximum is 23.233%. The mean value of return on asset(ROA) of private commercial banks was 17.541, which indicates that the private commercial banks were earning an average return of 17.541% on their asset during the sample period under study with a standard deviation of 2.663% Furthermore, the result of the descriptive statistics for funding risk(FR) measured by equity to total asset plus deposit to total asset divided to standard deviation of deposit over total assets shows the deposit mobilization of the banks was 2.874 on average, with a minimum of 2.345 and a maximum of 4.425 with a standard deviation of 0.453.

**Two-Step System GMM Model Regression Result**

The final model used in this study for testing the formulated hypothesis was a two-step system GMM due to the fact it is an efficient estimator in the presence of Autocorrelation and Heteroscedasticity.

Table 4.2

Two-Step System GMM Model Result

Dynamic panel-data estimation, | two-step | system | GMM | |

Group variable: id | | Number of obs | = | 64 |

Time variable : year | | Number of groups | = | 16 |

Number of instruments = 16 | | Obs per group: min | = | 4 |

Wald chi2(9) = 2.47e + 06 | | avg | = | 4.00 |

Prob > chi2 = 0.000 | | max | = | 4 |

Zscore | Coef. | St.Err. | t-value | p-value | [95% Conf | Interval] | Sig |

L.score | .371 | .131 | 2.83 | .005 | .114 | .628 | *** |

Roa | 3.455 | 1.306 | 2.64 | .008 | .895 | 6.016 | *** |

Size | − .121 | .048 | -2.51 | .012 | − .215 | − .026 | ** |

Fr | .319 | .236 | 1.36 | .175 | − .142 | .781 | |

Cr | -1.544 | .497 | -3.11 | .002 | -2.518 | − .57 | *** |

Liq | 1.843 | .864 | 2.13 | .033 | .151 | 3.536 | ** |

Bc | − .004 | .002 | -1.88 | .06 | − .008 | 0 | * |

Gdp | .07 | .022 | 3.24 | .001 | .028 | .113 | *** |

Ritr | − .042 | .012 | -3.66 | 0 | − .065 | − .02 | *** |

Constant | 1.266 | .593 | 2.14 | .033 | .104 | 2.427 | ** |

Mean dependent var | 2.998 | SD dependent var | 0.361 | |

Number of obs | 64 | Chi-square | 2466638.752 | |

**** p < .01, ** p < .05, * p < .1* |

Arellano-Bond test for AR (1) in first differences: z = -1.56 Pr > z = 0.119 |

Arellano-Bond test for AR (2) in first differences: z = -1.17 Pr > z = 0.241 |

Sargan test of overid. restrictions: chi2(6) = 7.26 Prob > chi2 = 0.298 |

(Not robust, but not weakened by many instruments.) |

Hansen test of overid. restrictions: chi2(6) = 4.21 Prob > chi2 = 0.649 |

(Robust, but weakened by many instruments.) |

Number of Instruments = 16 |

Number of Groups = 16 |

Source: Own Computation via Stata 14, 2024 |

The two-step system GMM estimation results demonstrate a significant positive relationship (β = 0.3712244, z = 2.8, p = 0.005 < 0.01) between the previous year's Z-score (PYFS), a measure of financial stability, and the current year's financial health of banks. This indicates that banks maintaining stability in one year tend to exhibit stronger financial health in the following year compared to less stable banks. The persistence of financial stability over time within banks underscores the influence of past stability levels on current financial health. This finding aligns with previous studies by (Pham et al., 2021), Pascual et al, (2015) and, Edimealem, (2014).

The coefficient of return on assets (ROA) as a profitability proxy is significant (β = 3.455147, z = 2.64, p = 0.008 < 0.01), indicating a positive relationship between ROA and the Z-score proxy for financial stability of private commercial banks during the study period. This suggests that as banks' return on assets increases, their financial stability, as indicated by the Z-score, also improves, making them less likely to face financial instability. This finding is consistent with studies such as Tan & Anchor, (2016), (Ali, 2015) ,Ghenimi et al., (2017),and Koskei, (2020) which similarly found a positive and significant link between profitability (ROA) and financial stability in various banking contexts. These studies argue that profitable banks are better equipped to maintain stability by accumulating reserves from profits, enhancing their resilience compared to less profitable counterparts.

The study's analysis, as noted in Tables 4.9, reveals that the coefficient of bank size (SIZE) is negative and statistically significant (β = -0.21206529, z = -2.51, p = 0.012 < 0.05), contrary to expectations. This suggests that, holding other variables constant, an increase in bank size by one percent in log of total assets leads to an average decrease of -0.21206529 in the Z-score, indicating reduced financial stability. This finding aligns with agency theory and Size Fragility theory, which predict a negative relationship between size and financial stability, but contradicts stewardship and size stability theories that anticipate a positive relationship. Similar results have been found in prior studies such as Adusei, (2015) ,Pham et al., (2021), Kiemo et al., (2019) ,Ozili, (2018) and, Edimealem, (2014), which also reported a negative and significant impact of size on banking stability, suggesting diseconomies of scale as banks grow beyond a certain size. Belete, (2013) additionally highlighted the significant costs Ethiopian banks incur to acquire fixed assets, potentially exacerbating instability in larger and more monopolized banks compared to smaller counterparts.

The study measured funding risk (FR) in Ethiopian private commercial banks using a ratio involving deposits, total assets, equity, and their standard deviation, aiming to understand its impact on financial stability. Contrary to expectations, the analysis found a statistically insignificant positive impact of funding risk on financial stability (β = 0.3194531, z = -1.36, p = 0.175 > 0.1). This result suggests that funding risk does not significantly influence bank stability, diverging from the initial hypothesis that predicted a negative relationship. Therefore, there is insufficient evidence to conclude that funding risk is a primary determinant of financial stability in Ethiopian private commercial banks based on this study's findings.

Table 4.13 in the study confirms a negative relationship between credit risk (CR) and the financial stability of Ethiopian commercial banks (β = -1.544111, z = -3.11, p = 0.002 < 0.01), aligning with the research hypothesis. The findings indicate that a one unit increase in credit risk results in an average decrease of -1.544111 in banks' financial stability. Higher credit risk, evidenced by increased loans to total assets, adversely impacts banks by escalating non-performing loans, reducing income, and indirectly undermining financial stability. This outcome resonates with previous research, including studies by Ghenimi et al., (2017), by Adusei, (2015), and Ali & Puah, (2018), all of which underscore the negative association between credit risk and bank stability.

The study reveals a positive and statistically significant association between liquidity ratio (LIQ), measured by liquid assets to total assets, and the Z-score of private commercial banks in Ethiopia (β = 1.843472, z = 2.13, p = 0.033 < 0.05). This indicates that higher liquidity ratios are correlated with greater financial stability among these banks, allowing them to effectively manage unexpected withdrawals or credit demands. This finding is consistent with prior research by Ghenimi et al., (2017) and Kiemo et al., (2019),which also observed that increased liquidity levels contribute positively to bank stability. They argue that banks with robust liquidity positions are less susceptible to financial shocks and better equipped to maintain their financial health by meeting maturing obligations promptly.

The study identifies a negative and statistically significant relationship (β = -0.0036984, z = -1.88, p = 0.060 < 0.1) between bank concentration (BC), measured by the Herfindahl–Hirschman Index (HHI), and bank financial stability in Ethiopia. This unexpected finding suggests that as market power among banks increases, financial stability tends to decrease, despite one commercial bank dominating a significant portion of the sector. This aligns with previous research by Boyd & De Nicoló, (2005), and Čihák & Hesse, (2010), which also highlight the negative implications of banking market concentration on stability due to higher loan interest rates, moral hazard issues, and potential "too-big-to-fail" risks.

The study explores the relationship between GDP growth rate and bank financial stability, finding a statistically significant positive impact (β = 0.0701874, z = 3.24, p = 0.001 < 0.01). This indicates that as GDP growth increases, bank stability also increases, likely due to heightened demand for credit and financial services in a growing economy. The findings support the Demand Following Hypothesis, which posits that economic growth drives demand for bank services, thereby enhancing their financial performance and stability. These results are consistent with earlier studies by Adusei, (2015) who reported that the economic growth has a positive impact on the bank financial stability.

The study indicates a significant negative impact of real interest rates (RITR) on the financial stability of private commercial banks in Ethiopia (β = -0.042395, z = -3.66, p = 0.000 < 0.01). A one percent increase in interest rates is associated with a decrease of approximately − 0.042395 units in bank stability, highlighting the sensitivity of bank stability to interest rate changes. This result is in line with the findings of Karim et al.,(2019), Koskei,(2020), and Edimealem, (2014). Pascual et al., (2015), concluded that weakening economic conditions with an indicator of increasing interest rates could increase non-performing loans and hence reduce bank stability.