4.3 Descriptive statistics A preliminary study of our data sample provided the main descriptive statistics of dependent and explanatory var...
4.3 Descriptive statistics A preliminary study of our data sample provided the main descriptive statistics of dependent and explanatory variables. Table 2 shows the main descriptive statistics for the variables used in the analysis for the entire sample and for firms during their life cycle, according to the groups sorted by the cluster analysis approach. A brief review of the entire sample shows that the means and medians of several of the variables were asymmetrically distributed. However, since small and medium-sized firms typically comprise a heterogeneous group, this result was not unexpected. Only the variable SIZE was not asymmetrically distributed. Furthermore, in the entire sample, financial debt relative to the capital of the mean firm was about 45%. A comparison of the mean value with the median value, and considering the standard deviation (about 31%), showed that financial debt, as source of finance, varied considerably across firms.
6. Capital Structure Determinants at Different Stage of Their Life Cycle: Cluster Analysis Results To verify the existence of different capital-structure determinants for firms at different stages of their life cycle, in this section the sample was sorted according to a cluster analysis approach. Instead of using a deterministic approach, for example, by identifying, alternatively, young firms as those less than 5, 10, or 15 years old, we applied an inductive criteria. The cluster analysis approach revealed whether there were structural differences arising within the sample, and allowing to sort it, independently of the arbitrary sorting criteria. The number of clusters leading to the greatest separation (distance) was not known a priori but was computed from the data. The goal was to minimize variability within the clusters and maximize variability between clusters. The two-step cluster analysis employed here is an exploratory tool designed to reveal natural groupings (or clusters) within a dataset that would otherwise not be apparent (He at al. 2005, Chiu et al. 2001).
The algorithm had several desirable features that differentiated it from traditional clustering techniques. First of all, it allowed for the handling of continuous variables (by assuming variables to be independent, a joint multinomial-normal distribution was applied to continuous variables) and automatically selecting the number of clusters (by comparing the values of a model-choice criterion across different clustering solutions, the procedure automatically determined the optimal number of clusters). Four clusters representing different features were automatically identified. Cluster 1 was not representative and was deleted, as it consisted of less then 1% of the firms in the entire sample. Cluster 2 represented about 14,5% of the entire sample and consisted of old firms with an average age of 58 years and a standard deviation of 13.2 (8.9% sales growth on average).
Cluster 3 (about 39,7% of the whole sample) comprised mainly middle-aged firms (28 years old) with a standard deviation of 6.3 (10.2% sales growth on average). Cluster 4 (about 45,0% of the entire sample) represented young firms with an average age of 11 years and a standard deviation of 5 (17.7% sales growth on average). According to the characteristics of the clusters obtained, showed in table 4, clusters 4, 3 and 2, i.e., young, middle (growing), and old firms, were analyzed. Table 5 shows the main descriptive statistics for the three clusters.
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