The effect of neglecting the slope parameters’ heterogeneity on dynamic models of corporate capital structure

Abstract

We present a parsimonious representation of debt-ratio dynamics that is able to nest the Trade-Off, Pecking-Order and Market-Timing theoretical models, at the same time avoiding the poolability of the slope parameters. The inference on the heterogeneous speed of adjustment of the firm towards the target debt ratio is based on a comparison of the unit root results from both individual company and (this is a relative novelty in the case of micro-data) panel data. Results show that company behavior is largely heterogeneous with regard to the theory underlying the historical data. Our proposed methodology may be usefully employed in order to identify sub-samples of companies behaving in an homogeneous manner, and can be extended to study the empirical capital structure models with more appropriate quantitative instruments. This would avoid the arbitrary a priori selection of sub-samples and the imposition of untested poolability assumptions as commonly occurs in the empirical literature.

Keywords:

• Corporate finance
• Heterogeneity of agents
• Time series analysis
• Econometrics

JEL Classification::

• C1
• C2
• C12
• C22
• C23
• G3
• G32

Acknowledgements

We would like to thank the following for their useful comments and advice: three anonymous referees, Gianni Amisano, Badi Baltagi, Bob Chirinko, Matteo Ciccarelli, Stéphane Gregoir, Bronwyn Hall, Cheng Hsiao, Jacques Mairesse, Massimiliano Marcellino, Adrian Pagan, Lucio Picci, and Joe Zhang; those who attended the 58th Annual Meeting of the Midwest Finance Association (Chicago, IL, March 4–7 2009), the 1st Workshop on Dynamic Econometrics held in memory of Carlo Giannini (University of Pavia, June 2005), and seminars held at the School of Finance and Economics (UTS, Sydney), Bank of Italy, Prometeia, and at the Universities of Bologna, Brescia, Ferrara, and Rome.

Notes

^†Raymar (1991) and Sarkar and Zapatero (2003) are both examples of theoretical models that suggest that earning processes are heterogeneous and exhibit mean-reverting tendencies; hence, they support the hypothesis of stationary a_i (L) dynamics. Alti (2006) demonstrates that the impact of market timing on leverage vanishes at the end of the second year; such limited persistence of MT shocks justifies the stationary b_i (L) dynamics.

^†It could be argued that there is a non-zero probability that the PO/MT-like debt ratio will explode (the firm's solvency condition cannot be met). Nevertheless, from the theoretical point of view, Fama and French (2002) point out that there are certain forces preventing this happening. Firms that pay dividends can maintain lower debt ratios by lowering payouts, while non-payers may need to borrow more to finance investments but, given both current and future borrowing costs, they tend to preserve low-risk debt capacity until positive net cash flows arrive, or through financial slacks. From the empirical point of view, the conclusion that debt ratios are integrated processes cannot be true in a very strict sense because integrated series are unbounded, while debt ratios are bounded between zero and one. Nevertheless, when sample data suggest that the statistical characteristics of debt ratios are closer to those of integrated than of stationary series, to analyse the empirics of corporate capital structure it is appropriate to treat these series as if they were stochastic trends (e.g. Hall et al. (1992, note 5)). See also the discussion of the results in section 3.1.

^‡We assume that the speed of adjustment π_i is albeit heterogeneous constant over time. Such an assumption is commonly made by the relevant empirical literature on dynamic corporate capital structure and, in this respect, our model results are comparable with those in table 1. Estimation results of time-varying (pooled) adjustment models have recently been reported by Cook and Tang (2008).

^§The statistical appropriateness of this assumption will be assessed by means of residual autocorrelation tests.

^†Furthermore, POLS also leads to residuals that are strongly first- and second-order autocorrelated.

^‡Given that all instrumental-variables estimators are applied to models in differences, the detection of first-order autocorrelated residuals is in keeping with the assumption of white noise errors ε_it in equation (4). Of course, all other higher-order autocorrelation tests must not reject the null hypothesis.

^§As further evidence, we estimate in appendix B a leverage regression (i.e. a general model of the same kind as those proposed by the literature summarized in table 1). Once again, the results are in line with those of tables 1 and 2.

^†Papers 2 and 5 are the only exceptions to the rule. However, Bontempi (2002) lacks the necessary time dimension (only 5.4 years, on average), and Alti (2006) focuses on a particular sub-sample (firms in years subsequent to their IPO).

^‡In this context, Hansen (1995) and Elliott and Jansson (2003) tests could also be used with the aim of improving the power of inferences on π_i by including additional (stationary) variables. However, in doing so, we would depart from the parsimonious univariate approach suggested here. As further discussed in the conclusions, these—as well as other—possible extensions to the multivariate approach will be developed by future research.

^†The framework we have depicted assumes that the error cross-section dependence can be approximated by a single factor model, while other procedures allow for (and consistently estimate) more factors in the panel series of interest (see, e.g., Bai and Ng (2004). It is therefore important that the factor structure of our data set is investigated in the light of IC_{p 1}(k), IC_{p 2}(k), and IC_{p 3}(k) criteria (Bai and Ng 2002). The results—not reported but available upon request—are clearcut: all three criteria suggest one as the most appropriate number of factors in our panel, supporting the assumption on which our results are based.

^‡On the basis of a detailed Monte Carlo study using alternative time-series unit-root/stationarity tests, Burke (1994) shows that the 10% significance level gives better results, in terms of test size and power, than the 5% level.

^§For the sake of homogeneity with the other columns, KPSS reports the number of non-rejections of the stationarity null.

^†Even though the integration property is invariant to temporal aggregation, the finite sample power of the testing procedures may fall when low-frequency data (such as annual accounting data) are used, because of the small number of available observations (Marcellino 1999).

^‡See also the theoretical considerations in the footnote above about solvency condition.

^†However, we must be careful in doing such a comparison because of the possible finite T bias of the mean group estimator, as it is only consistent, while, for example, the GMM-dif estimator with fixed T is consistent.

^†The CH variant is less affected than the MW variant by size distortions when N is large, as in our case.

^‡Pictures of the legislative and institutional context within which Italian companies operate are given by Bontempi (2002) for corporate capital structure models, and by Rondi et al. (1994) and Bianco et al. (2009) for real investment models. Detragiache et al. (2000) describe the practice of multiple borrowing.

^§Because of the few publicly traded firms, in what follows we restrict the economic interpretation of our results to the PO behaviour. Considerations on MT are reported in appendix B.

^†Because of the few publicly traded firms, we cannot compute for the whole sample the debt ratios at market values. Among alternative deflators, we checked the use of sales: the results are qualitatively unchanged, although the model's performance is a little worse due to the noise that affects sales data. Concerning the insensitivity of the estimation results to scaling, see, for example, Shyam-Sunder and Myers (1999, p. 228) and Frank and Goyal (2003, p. 222).

^‡Debt variation represents new borrowing net of the current portion of outstanding long-term debt due for repayment during each period. This last component, however, is almost irrelevant in Italy given that short-term debt amounts to more than 80% of total debt.

^†Investment in intangibles (II) can also have a positive effect on bank debt because technology expenses and soft capital inputs are more discretionary and more vulnerable to managerial spending, borrowing reduces a firm's resources that are freely available to managers, and a bank represents the favourite source of debt financing if companies do not want to reveal information (such as existing R&D projects), the secrecy of which is of crucial importance to their competitive advantage.

^†Panetta and Violi (1999), using a century of Italian data, estimate an unconditional equity premium at 4%: despite its numerical relevance, this long-run average excess return is constant over time. As such, the fixed effects capture the premium's influence on the relative cost parameter, thus avoiding biased estimates.