Financial constraints and firm dynamics

The generally accepted finding is that FCs hamper the growth prospects of firms and that this effect is stronger for younger and smaller firms (see Angelini and Generale 2008). These findings are in line with the recent theoretical literature on financing and growth models (see Cooley and Quadrini 2001; Albuquerque and Hopenhayn 2004; Clementi and Hopenhayn 2006), largely based on the models of industrial dynamics in Jovanovic (1982) and Hopenhayn (1992).

Cabral and Mata (2003) find that the evolution of the FSD is determined by firms ceasing to be financially constrained, while Fagiolo and Luzzi (2006) and Angelini and Generale (2008) conclude that FCs are not the main determinant of FSD evolution. At least part of the explanation for such seemingly contrasting evidence may come from the different proxies of FCs employed in these studies. Cabral and Mata (2003) measure FCs with age, assuming that younger firms are more constrained, while Fagiolo and Luzzi (2006) and Angelini and Generale (2008) adopt reported cash flow and survey-based measure of FCs, respectively.

These shares are computed with respect to National Accounts data by sector of activity, as reported by Eurostat. Pistaferri et al. (2010) report similar figures; they also report that the CeBi database contains approximately 7 % of all Italian manufacturing firms.

For 2003, the annual report of the Italian Statistical Office (ISTAT 2005) provides the following distribution: 82 % of firms have <10 employees; 15 % have 10–49 employees; 2 % have 50–249 employees, and 1 % have >250 employees. In our data there is a very mild overrepresentation of medium-sized to larger firms: 78 % of firms have <10 employees; 13 % fall in the 10–249 employee size class; 8 % have 50–249 employees and 1 % have >250 employees.

Explored alternatives encompass relative ranking in the cross-sectional distribution of variables supposed to strongly correlate with the availability of external finance, such as age (Cabral and Mata 2003), cash flow (Fazzari et al. 1988; Kaplan and Zingales 1997, 2000) cash flow sensitivity of cash (Almeida et al. 2004) or multivariate index based on sets of financial ratios (Cleary 1999; Lamont et al. 2001; Whited and Wu 2006; Musso and Schiavo 2008), or measures based on surveys, where managers or entrepreneurs are asked to make a self-assessment of the difficulties they face in accessing financing from banks or other institutions (Winker 1999; Angelini and Generale 2008; Campello et al. 2010).

Nominal sales are deflated via 3-digit sectoral production price indexes made available by the Italian Statistical office, base year 2000. A basic cleaning procedure to remove a few outlying observations is applied (see Appendix 1.1 for details). Reported results refer to pooled data over 2001–2003, as 1 year is lost due to the use of 1-year lagged FC status.

The very high mean value of 35,067 firms found within HFC old firms is explained by the presence of a quite large firm (actually the largest in the dataset) which is old and HFC over the sample period. The mean size falls to 20,665 employees if we exclude this single firm from the sample.

Since we cannot follow cohorts of firms in our data, a comparison across firms of different age is the only way to approach studying the relationship between size, age and FCs.

Here as well as throughout the work, estimates of densities are obtained using the Epanenchnikov kernel with the bandwidth set using the optimal rule described in Silverman (1986, p. 48).

The test is introduced in Fligner and Policello (1981) and can be interpreted as a test of stochastic dominance in the case of asymmetric samples. Pair-wise tests on the distributions reported in Fig. 1 confirm significant differences, with very small p scores (<10⁻⁶ in all cases).

Notice that the extended generalized gamma distribution applied in Cabral and Mata (2003), which possesses only one shape parameter, would not have allowed to independently account for the different behaviors observed in the two tails.

Due to the short time window of our database we cannot directly test the persistence in firm financial conditions over a long span of time. The analysis of transition matrix between FC classes reveals a significant persistence. The average 1-year probability to remain in the same class is 81.03 % for NFC firms, 75.51 % for MFC firms and 57.88 % for HFC firms.

At the same time, separate estimation by FC class allows us to drop the condition of orthogonality with the residuals that is needed if we pool the data on the entire sample and include the FC proxy among the regressors. Since our analysis below reveals significant differences in the distribution of residuals across the FC classes, pooled estimates of Eq. (3) with FC dummies would likely produce biased results.

See Appendix 1.2 for a formal derivation of these results.

An explanation of the emergence of this stylized fact, based on the idea of dynamic increasing returns, is presented in Bottazzi and Secchi (2006).

Plots obtained with 35 bins. The procedure is robust to variation in the number of bins.

Results available upon request.

This corresponds to assume that the error term follows an AEP distribution with b _l = b _r = 1, and with a _l and a _r estimated from data.

Assuming some degree of persistence in financial conditions, this result is sufficient to explain the lack of Gaussianization in the right tail of the FSD observed in the group of old HFC firms (cf. Fig. 2 above).

The estimates for MFC firms are not presented here to keep the figures more readable. The results (available upon request) substantially replicate the findings obtained for NFC firms and thus do not affect the main conclusions.

We nonetheless explored maximum likelihood estimates of Eq. (5) with firm fixed effects and Gaussian residuals, pooling across FC classes and adding two dummy indicators for firms belonging to MFC and HFC class. The HFC dummy coefficient turned out negative and significant, suggesting that the explanatory power of ratings is not washed away by the inclusion of time invariant heterogeneity.

The use of GOM implies, by definition, that we do not consider the cash flow generated by no- operating earnings and losses. These should not be very relevant, however, since we are working with manufacturing firms. Moreover, due to the limited data availability, we cannot consider the cash flows absorbed by taxes. Assuming, as a first approximation, a constant tax rate, this would amount to a constant and consequently irrelevant shift in the value of our regressor.

As done for sales, both GOM and ASSETS are deflated with appropriate sectoral price indexes, at the 3-digit level of industry disaggregation.

We also estimated two alternative specifications, both aiming at the inclusion of negative GOM in the regression. First, using the ratio GOM/ASSETS yields a non-significant coefficient for this further variable and only results in a moderate and homogenous reduction of the heteroskedastic parameter across classes. Second, we introduced a dummy with a value of 1 when GOM is positive, and 0 otherwise: this turned significant in all classes, but without affecting the other coefficients. Further, we also experimented with a GMM-SYS estimator, but standard Sargan/Hansen tests confirm that the time span of the database is too short to identify a valid set of instruments among past levels and past differences of the covariates. All results are available upon request.

We also explored a further specification considering two-period lags of size, ASSETS and GOM. This allows for a check of varying effects over time and provides a further control for possible endogeneity of covariates at t − 1. The estimates of λ retain their signs and magnitudes, again displaying negligible values for NFC firms, and then become increasingly negative as FCs become stronger. Second lag coefficients of GOM and ASSETS absorb part of the first lag effects of these variables. The most noticeable difference compared to the estimates presented in Table 2 is a significant reduction in the age coefficient, whose magnitude becomes comparable with that of the other regressors and across FC classes. Also notice that estimates of the extended model in Eq. (6) by employment classes confirm the minor role of censoring in driving the findings: patterns in λ reproduce the estimates reported in Table 3 above. All the results are available upon request.