Ebook Assessing Bankruptcy Prediction Models: A Stochastic Frontier Approach
Bankruptcy prediction has been routinely studied by academics, practitioners, and regulators. The well-known prediction models include discriminant analysis model (Altman, 1968), Merton model (Merton, 1974; Vassalou and Xing, 2004), logit model (Ohlson, 1980), and probit model (Zmijewski, 1984), to name only a few. The common principal of these approaches is that the models are developed using single-period data of firms. Shumway (2001) pointed out that such prediction processes are static in nature, since they ignore the changing characteristics of firms through time. In order to avoid possible loss of prediction power due to using static models, Shumway (2001) and Chava and Jarrow (2004) proposed a discrete-time hazard model (DHM) using multiple-period data for bankruptcy prediction. Their novel model applies the idea of survival analysis (Cox and Oakes, 1984), and has the advantage of using all available information of firms to build up a prediction system so that each firm’s bankruptcy risk at each time point can be determined. Thus DHM is a dynamic forecasting model.
The performance of bankruptcy prediction models was mainly assessed in the literature by performing prediction-oriented tests; see for example the above references. Recently, Hillegeist et al. (2004) proposed a different approach for doing it. They compared the information content about credit risk provided by out-of-sample values of probability of bankruptcy (PB) based on Merton model, Z-Score based on discriminant analysis model, and O-Score based on logit model. Their results show that PB based on Merton model provides significantly more information than Z-Score and O-Score. In contrast, Agarwal and Taffler (2008) pointed out that there is little difference between PB based on Merton model and Z-Score, in terms of predictive ability and information content. The results in Hillegeist et al. (2004) and Agarwal and Taffler (2008) were developed by comparing “static” bankruptcy prediction models.
In this paper, PB derived from the “static” Merton model (PB-Merton) is compared with that obtained from the “dynamic” DHM (PB-DHM) on their information content about firm’s technical inefficiency. To do it, a stochastic frontier model with firm-specific technical inefficiency effects in a panel framework (Battese and Coelli, 1995) is considered. A firm is characterized as technically inefficient if it is not able to reach maximum output given its available resources and technology. Analyzing the relationship between PB and economic efficiency is particularly important because economic-based efficiency measures are reasonable indicators of the long-term health and prospects of firms. We believe that this study is the first one to connect PB with technical inefficiency.
Stochastic frontier analysis is a method of economic modeling. It has been widely used to estimate technical inefficiencies of production of firms; see for example, the manuscripts by Kumbhakar and Lovell (2003) and Coelli et al. (2005). It also has been used in studies of corporate financial decision and bank efficiency; see for example, Hunt-McCool et al. (1996), Baek (2004), Fries and Taci (2005), Lensink et al. (2008), and Kauko (2009). There are many software packages having capabilities to estimate the stochastic frontier model, for example, FRONTIER, LIMDEP, and STATA, etc.
In this paper, the linkages between PB and technical inefficiency are analyzed using a stochastic frontier model. The explanatory variables for technical inefficiency effects in the stochastic frontier model are taken as the out-of sample PB and control variable Age. The parameters of the production function are estimated simultaneously with those of technical inefficiency effects in the stochastic frontier model. To compare PB-Merton and PB-DHM, their out-of sample values were computed for the 1996-2005 period. After deriving out-of sample PB-Merton and PB-DHM, the stochastic frontier model with firm-specific technical inefficiency effects was estimated for the 1996-2005 period. The studied data were collected from both COMPUSTAT and CRSP databases. Our final sample for building the stochastic frontier model consists of 6,228 firms with 35,080 firm-year observations.
Our empirical results suggest that, after controlling for the firm’s age, PB-Merton is positively related to technical inefficiency. The same remark also applies to PB-DHM. The result agrees with our expectation and indicates that if a firm has larger PB, then it is less technically efficient. Our empirical results also show that the technical efficiency of production of a bankrupt firm tends to decrease as the time point progresses toward its bankrupt time. This result coincides with the fact that economic-based efficiency measures are reasonable indicators of the long-term health and prospects of firms. Finally, to test the null hypothesis that the information content about firm’s technical inefficiency provided by PB-DHM is not more than that generated by PB-Merton, a procedure in Vuong (1989) based on the log-likelihood statistic was performed. The null hypothesis of interest was rejected at 1% level of significance. The test result indicates a potential increase of information content by using PB-DHM instead of PB-Merton as the credit risk proxy of firms.
The paper is organized as follows. Section 2 introduces DHM, Merton model, and stochastic frontier model with firm-specific technical inefficiency effects. Section 3 describes the data collecting process. Section 4 presents empirical results. Finally, concluding remarks are given in Section 5.
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