Different causes of closure of Small Business Enterprises: alternative models for competing risks survival analysis


Abstract


We examine the time until closure of Small Business Enterprises in Umbria, Italy between 2008 and 2013, and the factors that influence it. Earlier analysis, using Cox regression, considered failure (closure) from any cause. However, there are different reasons for inactivity: voluntary winding-up (1808 of
15184 firms in our data, 59.3% of the 3049 failures); bankruptcy (236, 7.7%); and closure without action by creditors or courts (1005, 33.0%). While the earlier analysis provides a valuable overall picture, it is also interesting to ex-
amine the separate causes, their rates of occurrence and which factors influence them separately. We do this using competing risks analyses, employing both of the regression methods that are prominent in the literature, based
on cause-specific and sub-distribution hazard functions (Fine-Gray model). Furthermore, a proportional odds model was used to estimate cumulative incidences of failure by cause. Data included the firm's year of foundation, location, legal form and sector of activity. Financial indexes were constructed
from annual balance sheets. The date and reason for closure were recorded if the firrm ceased activity. Findings included major differences between types of firm; for example, cooperatives had greatly increased hazards for winding-up
(HR of 2.44 and 2.61 in the two approaches) but greatly reduced hazards for closure (0.48 and 0.45) compared to publicly traded companies. All-causes analysis averaged these strong effects into an insignicant one (1.05). Coefficients from the proportional odds model were similar to those from the
Fine-Gray model, but have the advantage of interpretability.

Keywords: bankruptcy; survival analysis; competing risks; cause-specific hazards; sub-distribution hazards; proportional odds

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