A two-part fractional regression model for the financial leverage decisions of micro, small, medium and large firms

Abstract

In this paper we examine the following two hypotheses, which traditional theories of capital structure are relatively silent about: (i) the determinants of financial leverage decisions are different for micro, small, medium and large firms; and (ii) the factors that determine whether or not a firm issues debt are different from those that determine how much debt it issues. Using a binary choice model to explain the probability of a firm raising debt and a fractional regression model to explain the relative amount of debt issued, we find strong support for both hypotheses. Confirming recent empirical evidence, we find also that, although larger firms are more likely to use debt, conditional on their having some debt, firm size is negatively related to the proportion of debt used by firms.

Keywords:

• Capital structure
• Financial leverage
• Zero leverage
• Micro firms
• SMEs
• Fractional data
• Two-part model

Acknowledgements

The authors thank the referees for their valuable suggestions and remarks, which have improved substantially the paper. Helpful comments were also given by Esmeralda A. Ramalho and seminar participants at the University of Porto, ISEG/UTL, the 2006 ASSET Annual Meeting, the First Meeting of the Portuguese Economic Journal and the 2nd International Workshop on Computational and Financial Econometrics. Financial support from Fundação para a Ciência e a Tecnologia is gratefully acknowledged (grant PTDC/ECO/64693/2006). The authors are also grateful to Banco de Portugal for providing the data set.

Notes

†The European Charter for Small Enterprises is available online at http://europa.eu.int/comm/enterprise/enterprise_policy/charter/docs/charter_en.pdf

†The only exception to this practice seems to be Lopez-Gracia and Aybar-Arias (2000), who considered a partition of the SME group similar to ours but restricted their investigation to an analysis of variance of the influence of size and business sector on the financial behaviour of firms. There are also some recent papers which treat SMEs as a uniform group throughout most of the analysis but include robustness tests on firm size, reestimating their main models for size-based sub-samples (e.g. Cassar and Holmes 2003).

‡Papers somewhat related to the study of the capital structure of micro firms are those examining the financing decisions of family business owners (e.g. Romano et al. 2001), since many micro firms are indeed family businesses. However, many family businesses cannot be classified as micro enterprises.

§Actually, there are two exceptions to this case: (i) some firms may have negative book values of equity, implying leverage ratios higher than 1; however, such firms are typically excluded from empirical studies on capital structures; and (ii) a small number of earlier applications focussed on debt-to-equity ratios, which are not bounded from above; however, using linear regression models to explain such ratios is still not appropriate, since the (high) number of firms with null leverage ratios remains the same.

†Note that some authors consider the ACT as a part of the TOT since it focusses also on the benefits and costs of debt. However, in contrast to tax-based and bankruptcy theories, which are inter-dependent, the ACT originates a complete theory of capital structure, so we opted for considering it separately.

†Most authors argue that the capital structure of financial corporations must be analysed separately because their financial responsibilities are not strictly comparable with those of other firms; see for example Rajan and Zingales (1995, p. 1424).

‡In the latter case, another reason led us to exclude such firms. As described in table 2, our regression model uses the ratio between depreciation and negative earnings before interest, taxes and depreciation (EBITDA) as a proxy for non-debt tax shields (NDTS). Since the inclusion of firms with negative earnings would create a discontinuity in the NDTS measure at zero euros of EBITDA, we opted for discarding such firms (see Jensen et al. (1992, p. 253, footnote 9), for a similar procedure in a different context).

†In particular, alternatively to the explanatory variables described in table 2, we considered the following proxies: the ratio between tangible assets and total assets for the attribute ‘Tangibility’, the natural logarithm of assets for ‘Size’, the ratios between net income and assets and earnings before interest, taxes and depreciation and assets for ‘Profitability’, and the percentage change in sales for ‘Growth’.

‡Due to data limitations, we considered only five categories of industries: Manufacturing (2905 firms), Construction (879), Wholesale and Retail Trade (124), Transport and Communication (455), and Other Industries (329).

†Note that size is included in two different ways in our analysis, both as a quantitative variable (sales) and as a nominal variable (size-based group of firms), since we are assuming that the effects of size, as measured by sales, on the capital structure of firms may vary depending on whether the firm is in fact micro, small, medium or large sized.

†The fractional regression model that assumes a logistic specification for G(·) can be easily computed in Stata using the following command line:

where LR denotes the leverage ratio and EVj, j = 1, …, k are the explanatory variables. Stata includes also alternative specifications for G(·).

‡Two-part (or hurdle) models are relatively common in the econometric literature of count data; see Mulhahy (1986) for a seminal paper.

†Recently, Cook et al. (2008) used also a two-part model to explain capital structure choices. Their approach is similar to ours but differs in two important aspects. First, in the second part of the model, they assume a beta distribution for the conditional distribution of (the positive values of) Y given X and then estimate the parameters γ by ML. As the beta distribution is not a member of the linear exponential family, in addition to the correct specification of E(Y|X, Y ∈ (0, 1) and Pr(Y* = 1|X) required by our model, in their case it is also essential that the true distribution of Y conditional on X is indeed the beta distribution. Second, while we opted for using a two-part model in order to be able to test a specific hypothesis about capital structure choices, they were forced to do so: the beta distribution can only be applied to observations on the open interval (0, 1).

‡In the former case we do not need to test for heteroskedasticity since regression models for continuously measured proportions with a finite number of boundary observations are always heteroskedastic and the estimation method adopted, QML, takes that into account.

†In particular, we found that the LTD decisions of micro and small firms in the Construction sector are significantly different from those of their counterparts in other industries.