The interest in the prediction of frms’ bankruptcy is increasing in the recent recession period 2008–۲۰۱۲, when, in Italy, the number of distressed manufacturing frms increased sharply. The most popular model applied by bankruptcy researchers is the logit model (logistic regression model). In the present paper we extend this classical model in two diferent ways, to take into account the spatial efects that can highly afect bankruptcy probability. We propose to apply the spatial Autologistic model and the Logit Regression Tree, with the aim to fnd evidence of spatial dependence and spatial heterogeneity in bankruptcy probability, of the manufacturing frms of Prato and Florence (Italy). Our application shows that spatial contagion efects are an important issue when modelling bankruptcy probability. Moreover, the application of the regression tree analysis shows the presence of three diferent clusters, with heterogeneous behaviours.

Introduction

The interest of empirical literature on the frm’s performance in terms of survival or exit from the market has recently increased, due to the worldwide negative efect of the recent recession on frms’ crises. In Italy, where the enterprise system is characterized by family running small-sized frms, the economic crisis of 2008 signifcantly worsened the fnancial situation of the frms (Ferretti et al. 2016), and the number of distressed manufacturing frms increased sharply during this period. Financial structure, like leverage, plays a key role in the solvency of frms and during the crises it is deteriorated, together with the accumulation of the trade debt of the Italian frms. Bonaccorsi di Patti et al. (2015) and Fort et al. (2013) are few references on this topic. Early attempts to predict corporate failure in a univariate context used the ratio analysis (Beaver 1966), which was later extended by Altman (1968) to the multivariate case. More recently, the most popular model applied by bankruptcy researchers is the logit model (logistic regression model). Since in this case the outcomes are between two discrete alternatives, fail and non-fail, bankruptcy classifcation is an appropriate application for a binary choice model and logit model is commonly used in such qualitative response studies. For a review on the models applied in the bankruptcy analysis, see Gissel et al. (2007). In the time domain, an alternative way to model bankruptcy is the use of duration models, that allow to estimate the length of the time until failure (Manjon-Antolin and Arauzo-Carod 2008). The survival of frms depends on several factors, that can be distinguished between internal factors (i.e. frm-specifc) and external factors. The latter are related to the environment in which the frm operates and can be summarised in industry, spatial and business-cycle factors. Empirical analysis in diferent nations [see, e.g., Giovannetti et al. (2011) and Mariani et al. (2013) for Italy, Bernard and Jensen (2007) for the US, Box (2008) for Sweden, Bellone et al. (2006) for France, Disney et al. (2003) for the UK] has produced interesting fndings, not always with according results that may bring to stylized facts. The role of frmsspecifc factors in determining frm failure, like age and size, is central in theoretical frm-survival models, however empirical evidence is not unanimous. Although Esteve-Pérez et al. (2004), Fackler et al. (2013) and Strotmann (2007) show that small frms exhibit a shorter life expectation, Varum and Rocha (2012) assert conversely that smaller enterprises may be more fexible in adjusting to downturns, being more able to exploit market niches and activities characterized by agglomeration economies, and being less reliant on formal credits compared with larger frms (Tan and See 2004). Moreover, Agarwal and Gort (2002) found that the age efect has an inverted-U shape (Esteve-Pérez and Mañez-Castillejo 2008) and size-age infuences may also difer across industries (Giovannetti et al. 2011; Lopez-Garcia et al. 2007): large frms that operate in high-tech sectors have higher probability of survival than small frms in traditional sectors.