Abstract
This paper illustrates the importance of referring to a dynamic approach when forecasting firms bankruptcies, paying a particular attention to French SMEs. Based on Shummay’s (J Bus 74:101–124, 2001), we build a duration model and extend it by incorporating unobservable heterogeneity. Moreover, we resort to a dynamic dichotomous specification in which “right side” censored data are taken into account. We emphasize the complexity of the calculations of integrals that must be implemented and show how to overcome this challenge by applying the Geweke, Hajivassiliou and Keane algorithm which involves the technique of the simulated maximum likelihood. The findings prove that our dynamic approach, which integrates macroeconomic variables and takes account of both random effects and exogenous shocks, provides credible results. Besides, our method provides the predictive content of macroeconomic variables and the unobservable heterogeneity, which is helpful in forecasting firms bankruptcies.
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Notes
More anecdotically, we can also mention unexpected risks (fire, equipment failure, etc.), or the aftermath of the bankruptcy of the company’s main customer, or of its biggest supplier. For all these reasons, SMEs generally prefer raising a short-term cash reserve to better absorb possible temporary shocks rather than resorting to debt, at sometimes tough terms.
If one refers to the expertise of the Observatory of Companies at the Banque de France, one must delay the explanatory variables by at least one year. It also calls for delays of two or three years for the ratios used in the discriminant analysis.
This equates obtaining some values of
with \(\varepsilon _{i}\sim N\left( 0,\Omega \right) ,\) where \(P=\left[ a_{i1},b_{i1}\right] \times \left[ a_{i2},b_{i2}\right] \times \cdots \times \left[ a_{iK},b_{iK}\right] \).If \(Z\sim N(0,1)\), then the distribution function of the standard truncated distribution on [a, b] is given by the following formula:
$$\begin{aligned} F(z)=P(Z<z/Z\in [a,b])=\frac{\Phi (z)-\Phi (a)}{\Phi (b)-\Phi (a)}, \end{aligned}$$where \(\Phi (z)\) is the cumulative distribution function of the standard normal distribution.
Besides, if random variable U is uniformly distributed on [0, 1], then variable \(F^{-1}(U)\) has F as a cumulative distribution function. To generate iid draws from a normal distribution truncated on [a, b], just take the realization of the following random variable:
$$\begin{aligned} F^{-1}(u)=\Phi ^{-1}\left[ u\left[ \Phi (b)-\Phi (a)\right] +\Phi (a)\right] , \end{aligned}$$where u is uniformly distributed on [0, 1].
These variables were also used by Bruneau et al. (2011).
We specify here the ceteris paribus condition. Indeed, for a given level of investment in tangible assets, if the added value increases, then the investment rate decreases. Over the period in question, the company’s default probability will therefore decline, only if the tangible investment level increases more than the value added.
The fact that the estimated results here have the same sign as with Shumway’s estimate exempts us from explaining again the economic relations of the variables considered with the risk of default.
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Abid, I., Mkaouar, F. & Kaabia, O. Dynamic analysis of the forecasting bankruptcy under presence of unobserved heterogeneity. Ann Oper Res 262, 241–256 (2018). https://doi.org/10.1007/s10479-016-2143-2
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DOI: https://doi.org/10.1007/s10479-016-2143-2