預測公司破產事件之研究

Abstract

本文使用半母數羅吉特模型（semiparametric logit model）建立一個公司破產事件的預測方法，並將之應用在追蹤性（prospective）或稱簡單隨機（simple random）資料，以及個案控制（case-control）或稱選擇性（choice-based）資料。我們使用區域概似方法（local likelihood approach）估計半母數羅吉特模型中未知參數，且研究這些估計式的漸近偏差量與變異數（asymptotic bias and variance）。我們證明當應用這個半母數羅吉特模型至前述兩種不同類型資料上，其所對應的破產預測方法是相同的。因此我們的預測方法可以直接應用到這兩種重要類型的資料。實證研究結果顯示，我們的預測方法較Altman (1968)的區別分析模型（discriminant analysis model）、Ohlson（1980）的線性羅吉特模型（linear logit model）、以及Merton (1974)與Bharath and Shumway (2004) 的KMV-Merton模型等所建立的預測方法，能夠產生較小的樣本外誤差率（out-of-sample error rate）。 另外，本文使用離散型倖存模型（discrete-time survival model； Allison, 1982），預測公司發生財務危機的機率。我們以最大概似法（maximum likelihood method）估計該模型的參數值，導出參數估計式的漸近常態分配（asymptotic normal distribution），進而估計公司發生財務危機的機率。藉由此機率估計值，我們可建立財務危機預警模型，並用以分析及預測台灣股票上市公司發生財務危機的機率。實證研究結果顯示，本文所介紹的離散型倖存模型對公司財務危機的預測，比線性羅吉特模型，有更好的樣本外預測能力。

Bankruptcy prediction methods based on a semiparametric logit model are proposed for prospective (simple random) and case-control (choice-based) data. The unknown quantities in the model are estimated by the local likelihood approach, and the resulting estimators are analyzed through their asymptotic biases and variances. Our semiparametric bankruptcy prediction methods using these two types of data are shown to be essentially equivalent. Thus our proposed prediction model can be directly applied to data sampled from the two important designs. Empirical studies demonstrate that our prediction method is more powerful than alternatives based on the discriminant analysis model (Altman 1968), the linear logit model (Ohlson 1980), and the KMV-Merton model (Merton 1974; Bharath and Shumway 2004), in the sense of yielding smaller out-of-sample error rates. The discrete-time survival model (Allison 1982) is applied to predict the probability of financial distress. The maximum likelihood method is employed to estimate the values of parameters in the model. The resulting estimates are analyzed by their asymptotic normal distributions, and are used to estimate the probability of financial distress for each firm under study. Using such estimated probability, a strategy is developed to identify failing firms, and is applied to study the probability of financial distress for firms listed in Taiwan Stock Exchange. Empirical studies demonstrate that our strategy developed from the discrete-time survival model can yield more accurate out-of-sample forecasts than the alternative method based on the linear logit model in Ohlson (1980).