利用混合機率分配探討農會信用部發生擠兌的危險率

Applying the Mixture Probability Distribution to Investigate the Risk of Bank Runs in the Credit Department of Farmer's Institutions

學界應用Schmidt and Witte (1989)的區分母體持續時間模型時，通常在「持續時間」的部分，假設它為單一分配函數。當我們將這個模型應用到農會信用部發生擠兌的問題上，發現它的危險率函數呈現雙峰的形狀，而由於單一分配函數並無法具有雙峰型危險率函數，此時如繼續假設單一分配函數，並不恰當。因比本文在「持續時間j的部分，選擇混合機率分配函數，例如二個log-normal 、log-logistic 、或一個log-normal及log-logistic 、或一個log-normal或log-logistic及Weibull，這些都可產生雙峰型危險率函數。我們以混合機率分配重新估計區分母體持續時間模型，並且以AIC值、概似比檢定丶,－檢定比較各種不同的區分母體持續時間模型的優劣，結果顯示混合機率的區分母體持續時間模型優於單一分配的模型。實證結果發現，在「持續時間」的部分，擔保放款占放款比、是否參加存保的參數估計值為正而且顯著，擔保放款占放款比愈高者或巳參加存保者，發生擠兌的時間愈晚，即擠兌危險率愈低。

In the academic circle, it is usually hypothesized as a single distribution function for the duration model while applying to Schmidt and Witte's (1989) split population duration model. When we applied this model to the bank runs in the Credit Department of Farmer's Institutions, it has discovered that there is a bimodal distribution in the hazard rate function, and that is not apropos to continuously hypothesizing it as a single distribution function for the reason that a single distribution function does not include a bimodal distribution hazard function. In this study, we chose a mixed distribution function for the duration model, for example, two log-normal and log-logistic; one log-normal and log-logistic; one log-normal, and one log-normal with Weibull, which could all produce a bimodal distribution hazard rate function. After that, we used these mixed distributions to re-estimate the split population duration model; also used the AIC Value, Likelihood Ratio Test, and t-test to compare the quality of different models, and it showed that the mixed split population duration model is better than the single distribution model. From this empirical result, we have found that the parameter estimating value of both the ratio of insured borrowing to total borrowing and whether to join deposit insurance are positive and significant. For the customers who have high ratio of insured borrowing to total borrowing or have joined deposit insurance would likely to have later bank runs, which relatively proved that they would have lower the risk of bank runs.