Financial fragility and the distribution of firm growth rates
In the case of a simple univariate analysis, as in equation (3), the amount of information which can be obtained running a QR regression is roughly equivalent to the information available through visual inspection of the conditional density functions. In Figure 8.3, histograms of the empirical densities of growth rates are reported for the two populations of risky and riskless firms. To help the reader’s eye, we superimpose the estimate of an asymmetric power exponential distribution, which better captures the asymptotic behaviour in the tails (Bottazzi and Secchi, 2011). The plots confirm the scale-shift effect of the RR dummy and its role in the tails of the distribution.8 In conclusion, the distribution of growth rates of risky and non-risky firms is significantly different. This is true both in the aggregate and if one considers young and old firms separately. This result suggests that the limited access to external finance which is plausibly implied by a bad score of the CeBi-CERVED credit risk rating plays a relevant role in shaping the operating performances of firms. As we will see in the next section, this result remains unchanged when multivariate models are considered.