Comparison of the Predictive Power Results by EWS

alarm, where Type 1 error is 8% and Type 2 error is 13%. This indicates that the model reveals 72 fragility episodes whereas 6 episodes are missed. On the other hand, while the model finds 60 tranquil periods, 8 of them are false alarms.

The second-best model is the Model 16. The BSFI of the model is constructed with credit risk and market risk proxying these risk factors by the variables of BC and FL respectively. The BSFI of the Model 16 is:

𝐵𝑆𝐹𝐼_𝑖,𝑡=

([(𝐵𝐶𝑡−𝐵𝐶𝑡−1) 𝑁𝑃𝐹𝑡−1⁄ ]−𝜇𝐵𝐶

𝜎𝐵𝐶 )+([(𝐹𝐿𝑡−𝐹𝐿𝑡−1) 𝐹𝐿𝑡−1⁄ ]−𝜇𝐹𝐿

𝜎𝐹𝐿 )

2 (18)

Model 16 captures the fragility episodes of Islamic banks by 85% and tranquil episodes by 84%. The overall predictive performance of the model is 85% where Type 1 and Type 2 errors of the model are reported as 15% and 16%, respectively.

Looking at the third best model in terms of the predictive performance, Model 10, the BSFI of the model is constructed by using credit risk, market risk and profitability risk factors by using BC, Tier and ROE respectively. That is:

𝐵𝑆𝐹𝐼_𝑖,𝑡=

([(𝐵𝐶𝑡−𝐵𝐶𝑡−1) 𝑁𝑃𝐹𝑡−1⁄ ]−𝜇𝐵𝐶

𝜎𝐵𝐶 )+([(𝑡𝑖𝑒𝑟𝑡−𝑡𝑖𝑒𝑟𝑡−1) 𝑡𝑖𝑒𝑟𝑡−1⁄ ]−𝜇𝑡𝑖𝑒𝑟

𝜎𝑡𝑖𝑒𝑟 )+([(𝑅𝑂𝐸𝑡− 𝑅𝑂𝐸𝑡−1⁄ ]−𝜇𝑅𝑂𝐸

𝜎𝑅𝑂𝐸 )

3 (19)

While the predictive performance of the model for the fragility episodes is 79%, it is 89%

for the tranquil episodes. As one can see, the model captures the tranquil episodes better than the fragility episodes. Further, the Type 1 error of the model is 21% while the Type 2 error is 11%.

Note that the first three EWS models in Figure 24 which give the highest predictive power results among our EWS models are constructed by employing the credit risk factor. In addition, in all of these three models, credit risk is proxied by BC rather than the NPF.

Although including the FL as a proxy to measure the market risk reveals higher predictive power results, there is a slight difference in the predictive power of the Model 16 and

Model 10. This is due to the impact of the profitability risk factor. Using ROE as a profitability risk factor enhances the predictive power of the EWS models for Islamic banking system. Moreover, all of these models are built by omitting the liquidity risk from the BSFIs.

It should be noted that the first 14 models are constructed incorporating the credit risk factor. Accordingly, the results reveal that omitting credit risk from any crisis definition for Islamic banks reduces the predictive power of the constructed EWS. In addition, Model 5 appears to be the model with the lowest predictive power. The BSFI of the model is constructed by using credit risk (BC), liquidity risk (DEP) and market risk (tier) factors as follows:

𝐵𝑆𝐹𝐼_𝑖,𝑡=

([(𝐵𝐶𝑡−𝐵𝐶𝑡−1) 𝑁𝑃𝐹𝑡−1⁄ ]−𝜇𝐵𝐶

𝜎𝐵𝐶 )+([(𝐷𝐸𝑃𝑡−𝐷𝐸𝑃𝑡−1) 𝐷𝐸𝑃𝑡−1⁄ ]−𝜇𝐷𝐸𝑃

𝜎𝐷𝐸𝑃 )+([(𝑡𝑖𝑒𝑟𝑡−𝑡𝑖𝑒𝑟𝑡−1) 𝑡𝑖𝑒𝑟𝑡−1⁄ ]−𝜇𝑡𝑖𝑒𝑟

𝜎𝑡𝑖𝑒𝑟 )

3 (20)

Although the model is comprised of credit risk factor (BC), we believe that such outcome of low performance stems from the impact of the liquidity risk factor (DEP). In other words, as explained above, the bank runs do not significantly associate with the fragility of Islamic banks to banking crisis between 2008 and 2018. Thus, the DEP proxy does not enhance the predictive power performances of the models. The same result is also valid for the second and the third worst models (Model 1 and Model 23). Therefore, one can conclude that bank runs do not play a significant role in defining the BSFI for Islamic banks. In other words, the liquidity risk factor does not increase the rate of correctly predicted crisis episodes of the EWS.

In this chapter, we thoroughly examine the impact of BSFI definition on the predictive performance of the EWS models for Islamic banks. The changing impacts are elaborated in two sub sections as the in terms of the choice of the risk factors and the choice of the proxies to measure those risk factors while defining BSFIs. Our results indicate that, despite the fact that the banking fragility indices are defined considering the same risk factors, the predictive power of EWS is highly sensitive to the proxies that are used to measure those risks and their combinations.

To identify which proxies, reveal more successful results in terms of the prediction power of the EWS models, we make pairwise comparisons between models. For example, to measure credit risk, we employ two different proxies i.e. NPF and BC. In addition, we use either FL or Tier to measure the market risk factor. According to our findings, using CB or NPF in a BSFI for Islamic banks do not reveal very different predictive power results. Therefore, the credit risk can be proxied by both proxies. However, if the BSFI is constructed by considering only the credit risk and market risk factors, BC proxy increases the predictive performance of the EWS rather than that of NPF. In terms of the market risk, on the other hand measuring the market risk using FL rather than using Tier gives better prediction results.

To examine the impact of the risk factors variations themselves on the predictive power rates, we alternately omit some of them from BSFI definitions. For instance, to test whether bank runs are important in explaining the fragility of Islamic banks to banking crises, we omit liquidity risk factors in some of the BSFIs. We find that omitting the liquidity risk factor does not reduce the predictive power of the EWS models. This finding is in line related literature on the conventional banking system suggesting that liquidity risk do not play a major role in explaining banking crises. Regarding the credit risk factor, the results indicate that regardless of the choice of the proxy to measure the market risk, liquidity risk or profit risk; including the credit risk factor increases the predictive performance. In terms of the market risk factor, we observe that including FL into the BSFIs increases the predictive power of the EWS models. On the other hand, we observe weak evidence for the models that the BSFIs that are constructed by tier proxy as a market risk factor. Apart from the existing literature, we further incorporate profitability risk in our performance analyses. We find that profitability risk plays significant roles in constructing a successful BSFI for Islamic banks. When we include ROE into the BSFIs, the predictive performances of all models increase. This is indeed consistent with the related literature emphasizing Islamic banks are more vulnerable to profitability risk than conventional banks, where there is uncertainty in the context of forthcoming returns on their assets (Elgari 2003; Kozarevic e al., 2014).