Which firms survive in a crisis? Investigating Gibrat’s Law in Greece 2001–2014

Abstract

The paper employs a panel dataset of more than 40,000 Greek firms over the period 2001–2014 to examine the size-related patterns of survival and turnover growth before and after the financial and debt crisis that hit Greece in 2010. Our findings suggest that larger-size firms were, in general, more likely to survive in the market than smaller size ones and this relative advantage only grew further during the crisis. However, the rate of growth in turnover for the surviving firms is negatively associated with their size, thus refuting Gibrat’s Law in Greece.

Appendix: alternative estimations of survival probability models

Ιn this section we investigate how deviations from our panel data Probit estimation setup may affect robustness of our results. As we have used a ‘population averaged’ Maximum Likelihood estimator, our results are robust to unobserved heterogeneity across firms (Wooldridge 2002, Ch.15, pp. 486). We have also allowed for an unstructured within group correlation; this makes our results robust to possible presence of serial correlation. Compared to the simple Pooled Probit estimates with robust standard errors, shown in Table

Table 11 Pooled probit estimation of survival effects

11 in this Appendix, our coefficient estimates are quite similar, with few differences found to be larger than 5% in absolute value (the standard errors differ significantly, nevertheless). More specifically, for Manufacturing and Recreation firms the coefficient estimates of all effects (except those of year dummy variables) show negligible differences. The same holds for the (point) estimates of the effects of size, leverage, profitability and market share across all sectors. This implies that, at least for these cases, unobserved heterogeneity and/or serial correlation do not bias our results.

We also allowed for a specific form of heteroscedasticity that depends on firm size. This is equivalent to a Probit model with transformed data so that each explanatory variable is divided by the square root of firm size. Results are shown in Table

Table 12 Heteroscedastic Pooled Probit estimation of survival effects

12 in this Appendix and show substantial differences, regarding the magnitude of the estimated effects and their standard errors. The estimates for the Trade sector are affected the most, indicating that this sector is most sensitive to this particular data transformation, perhaps because it consists of relatively larger firms than the other sectors (see Fig. 9). Nevertheless, the estimated effects remain roughly similar in direction to our previous results.

As another robustness check we experimented on a different link function and estimated a complementary log–log model as in Gorg and Spaliara (2014) and Guarilia et al. (2016). According to this setup, the link function Φ(.) is specified as 1 − exp[− exp(.)], which is a non-symmetric function in the interval [0, 1] and may better therefore characterize more extreme events. The Population Averaged Maximum Likelihood estimates under unspecified within group correlation is shown in Table

Table 13 Complementary log–log model estimation of survival effects

13 in this Appendix. Similar to our previous results, these are robust to unobserved heterogeneity and serial correlation. As shown in Table 13, the results are quite similar to our initial Probit estimates. Positive size effects after 2008 are found to be statistically significant in more sectors, leaving only Recreation and TLC sectors with statistical insignificant size effects after the beginning of the crisis.

The duration of firms’ survival up to their exit (or end of the sample) is incorporated in the model via inclusion of firms’ age in the set of explanatory variables. Nevertheless, the exact period each firm enters the sample may convey important information for firm survival and is not taken explicitly into account in the current setup. To account for this we employ two typical survival models, which are closely related in our current discrete time setup. The first is the Cox (1972) proportional hazard model applied in discrete time as in Box (2008). This is a frequently used semi-parametric approach that estimates the hazard function $h\left(t\right)={h}_{0}(t)\mathrm{exp}(.)$, where t is survival time and the arguments (.) in the exponential function coincide with those in the Probit function Φ(.) in (1). ${h}_{0}(t)$ is a baseline hazard function, which remains unspecified. Estimation results are shown in Table

Table 14 Cox proportional hazard model estimation of survival effects

14 in this Appendix; the direction of the effects remains roughly similar to our Probit estimation. Notice that the model estimates firm hazard (not survival) rates and therefore the effects have the opposite signs from those in the Probit model.

The second survival model is a fully parametric one and assumes that the previous baseline hazard function ${h}_{0}(t)$ is exponential. We also allow for random effects in order to capture unobserved firm specific heterogeneity. Results are shown in Table

Table 15 Exponential proportional hazard model estimation

15 in this Appendix and are similar to the Cox proportional hazard model, remaining therefore consistent with our initial Probit model estimates.