Firm Bankruptcy Prediction : A Bayesian Model Averaging Approach ∗

I use Bayesian model averaging of hazard models to examine which determinants of rm bankruptcy proposed in the literature are robust to model uncertainty, a researcher's lack of precise knowledge about the true model behind an observed empirical relationship. I investigate di erences in bankruptcy determinants by industry and assess the performance of model averaging in out of sample predictions. After allowing for model uncertainty, the number of variables robustly correlated with rm bankruptcy is smaller than the number of variables found to be signi cant predictors elsewhere. I nd accuracy gains in out of sample predictions in most industries. ∗I would like to thank Karl Scholz, Jane Cooley Fruehworth, Chris Taber, Steven Durlauf, Bruce Hansen, and participants in the UW-Madison Public Finance research seminar for their useful comments and suggestions. Special thanks to Bill Taylor at the Center for High Throughput Computing at the University of Wisconsin for invaluable assistance with computational tasks. All remaining errors are my own. †Department of Economics, University of Hawaii-Manoa; jtraczyn@hawaii.edu. Bankruptcy prediction is of interest to the creditors, customers, or suppliers of any rm, as well as policymakers and current and potential investors. Financial institutions require assessments of a rm's future prospects, including the risk of bankruptcy, to accurately price rm assets. A good predictive model of bankruptcy should be both accurate and make the best use of data available to the researcher. The interest in nding a model for rm bankruptcy prediction is re ected in the number of papers that have proposed and tested di erent variables and models. Even early papers in the literature have commented on the wide variety of explanatory variables available and attempt to nd those that are most strongly correlated with rm bankruptcy. Altman (1968) introduces multiple discriminant analysis to incorporate correlations between explanatory variables, a perceived weakness in the contemporary literature. Altman (1968, p. 590) considers 22 potential covariates before settling on the 5 that comprise the Z-Score, noting that every [previous] study cited a di erent ratio as being the most e ective. Ohlson (1980) advocates a probabilistic model of bankruptcy, relaxing restrictions on the variancecovariance structure of explanatory variables imposed by multiple discriminant analysis. Ohlson (1980, p. 118) also faces a large number of choices for explanatory variables, with those chosen selected simply because they appear to be the ones most frequently mentioned in the literature before using a subset of these variables to create the O-Score. Both of these papers popularized a new technique to address a weakness of contemporary methods in rm bankruptcy prediction, using the preferred approach to evaluate which potential explanatory variables from the literature were still correlated with bankruptcy after accounting for the problems that the methodology was designed to address. Since Shumway (2001), hazard models have represented the forefront of rm bankruptcy forecasting. The standard procedure in this literature is for researchers to select a set of covariates to use as predictors of rm bankruptcy and declare a variable to be an important predictor if its parameter estimate is statistically signi cantly di erent from 0. This procedure ignores model uncertainty, the uncertainty as to which explanatory variables should be included in the hazard model. If there are J potential explanatory variables available, a researcher must pick from 2 possible models to estimate. Estimating only one speci cation of the hazard model is e ectively assuming that the chosen speci cation is the correct model of rm bankruptcy with certainty, ignoring the uncertainty as to which speci cation is correct. Even when estimating several speci cations of the hazard model, researchers must make ad hoc decisions as to which alternative speci cations to explore and how to interpret the degree of sensitivity of the results. Tables I and II de ne a number of variables popular in the See Shumway (2001) and Chava and Jarrow (2004) for discrete time hazard models, and Du e et al. (2007) for a continuous time hazard model.