n = 4.3.1 Tamaño de Muestra
RESULTADOS, DISCUSIÓN, CONCLUSIONES, RECOMENDACIONES 6.1 Resultados
In this section we apply a formal survival analysis to the two metrics of debt-type structure to measure the duration of stability in debt-type structures. We graphically depict the stability of these metrics based on the Kaplan-Meier Estimator and study the determinants of higher stability using parametric survival regressions. We use a logit model to determine the selection of each of the main debt types in the debt structures.
3.4.1.1
Survival analysis of the debt heterogeneity index (HHI)
Figure 3.1 reports the Kaplan-Meier survival estimates for the debt heterogeneity index, HHI. The vertical axis shows the survival probabilities and the horizontal axis shows the number of
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years from base year 0 to the year of an event. Panels A and B report the results for debt heterogeneity fluctuations beyond the 10% and 20% thresholds, respectively. We observe that only about 10% (25%) of the firms retain their original HHI values after 11 years using the 10% (20%) change threshold. The important take-away from these graphs is that the relative composite weighting of different debt types in the debt structure is short-lived for individual firms.
[Please insert Figure 3.1 here]
3.4.1.2
Survival analysis of the predominant (main) debt type
We now address an unexplored aspect of the findings of Colla, Ippolito, and Li (2013); namely, that primary debt-type specialization may involve a different debt type at different points in time. To illustrate, a firm whose primary debt type is lines of credit in year 1 and notes in year 2 would be classified as specializing in its debt structure using the methodology of Colla, Ippolito, and Li (2013). However, this could be interpreted as not indicating main debt-type stability over longer periods of time. Thus, in this section, we address the following question: Do firms rely on the same single debt type as their major debt type on an ongoing basis?
The Kaplan-Meier survival curve using the main source of debt financing (main debt type in the 1D-T rank-ordered index) based on the sample firms for each year is plotted in Figure 3.2. The solid dark line shows the estimated survival function and the two light lines are 95% confidence intervals. Based on this figure, we observe that 63% (50%) of the firms maintain the same debt type over a 5 (full 11) year period. The stability of the main debt type is in stark contrast with the instability indicated by the HHI. This infers that firms tend to have an ongoing preference for the same single main debt type, and that this preference does not extend to less dominant debt types.
[Please insert Figure 3.2 here]
3.4.1.3
Survival analysis of debt-type ranks
In this section, we study the survival of the two debt-type ranks indexes. As discussed earlier,
changes in the sequence of different debt types in the rank structure indicate the end of a stable debt-type rank policy. Based on the 7D-T ranks ordered index plotted in Panel A of Figure 3.3, we observe that almost all firms change the structure of their debt preferences after 11 years, and only
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this test, however, is that the sensitivity of this index to any change in the debt structure may bias it towards finding more instability. Specifically, changes in less important debt types (e.g., rank
orders of 6th and 7th) are not as important as changes in the main debt types (1st and 2nd in the rank
structure) and therefore the instability result in this figure may be inflated. To account for any possible effects from ranking instabilities of less frequently or intensely used debt types, we plot the 2D-T rank ordered index in Panel B of Figure 3.3. The resulting survival graph is almost identical to that in Panel A. While the main debt type is largely stable, the second debt type is highly unstable. Firms change or discontinue the second important source of their debt financing often, and almost as often as they change or discontinue debt types of much lower importance in
the debt-type structure. This result shows that the main debt type (1st in the debt-type structure) is
unique in debt structure decisions, and its stability cannot be extended to any other debt type. Therefore, we suggest that studies of capital and debt structures should account for the determinants of stability of the main debt type and the determinants of the main debt type.
[Please insert Figure 3.3 about here]
One final problem with the rank-ordered index is that it may still be too limiting in terms of capturing changes in the rank-ordered debt-type structure. To examine this possibility, we measure the similarity between debt ranks in the firm’s debt structure using Kendall’s tau-b and Spearman’s
Rho15 measures. These indexes are less sensitive compared to the simple rank-ordered index in
that minor changes in the debt preference structure translate into only small changes in the similarity index. To implement this test, we compare the debt-type rank index for every firm across every two years; e.g. the debt rank index in 2001 is compared to that in 2002, the debt rank index in 2002 is compared to that in 2003, and so on. We then investigate how long it takes for the Kendall’s tau-b (Spearman’s Rho) to change by more than 10% or 20% compared to its previous values. A stable rank-ordered debt-type policy ends the first time a change in the Kendall’s tau (Spearman’s Rho) exceeds 10% (20%). Results are shown in Figures 3.4 and 3.5 using the Kendal’s tau index and Spearman’s Rho, respectively. The graphs in each Panel A (B) depict the results with the 10% (20%) threshold. We observe almost no stability in the debt ranks for both of
15 This rank correlation coefficient is defined as the Pearson correlation between the ranked variables.
This measure suggests an alternative similarity index between the ranks of different debt types across different years.
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these measures. After 11 years (10 comparisons) and using Kendal’s tau index, almost all firms have changed their debt preferences beyond 10%, and almost 88% of the firms have done so using the 20% threshold. Similar results are obtained based on Spearman’s Rho index. These results confirm our previous findings that debt structure and debt preferences are highly volatile.
[Please insert Figures 3.4 and 3.5 here]