Capital structure: The case of firms issuing debt

Abstract

This study reinvestigates the relationship between financial leverage and firm characteristics in a cross-sectional setting and a panel setting. Monte-Carlo simulation-based inference results confirm the finding of Barraclough (2007) that a cross-sectional multiple regression model sharing common divisors suffers from a latent spurious ratio problem. To avoid the spurious ratio problem, variables in changes instead of ratios are adopted in two panel models: a first-differenced fixed-effects panel model and a dynamic Generalized Method of Moments panel model. The two models respectively integrate fixed effects (e.g. the persistence nature of financial leverage) and endogeneity features of financial leverage decisions. Model results suggest past realization of debt explains most of the current debt level after controlling for endogeneity. We find no significant association between debt and firm characteristics.

JEL Classification: G32, H20

Keywords

capital structure endogeneity panel model spurious ratio

1. Introduction

Leverage ratios and firm characteristics can vary across firms and across time within a firm. At the micro level, do firm characteristics drive the leverage variation? If so, which firm-specific factors affect financial leverage? According to the irrelevance theorem of Modigliani and Miller (1958), no certain association should be found between firm characteristics and financial leverage. Under the assumption of a frictionless world, a firm can arbitrarily choose its capital structure without incurring any costs. Other researchers try to relax the assumption and examine whether this theory still holds in the real world with frictions (such as financial distress costs, information asymmetry between debt–equity holder, agency conflicts between shareholder and manager, etc.). To date, however, there is no uniform answer to this question as the empirical findings are mixed and conflicting even when some common approaches accompanied by commonalities in the variables are used. For example, some researchers find a positive relationship between debt and profitability (Frank and Goyal, 2009; MacKay and Phillips, 2005) while others find a negative relationship (Baker and Wurgler, 2002; Fama and French, 2002; Faulkender and Petersen, 2006; Rajan and Zingales, 1995; Titman and Wessels, 1988). So, what causes the conflicting results?

This paper argues that one cause can be a spurious ratio problem arising from the misuse of ratios in multiple regression models commonly adopted in the literature. The spurious ratio problem refers to the fact that misleading inferences that may be drawn when standard statistical tests (such as t-statistics) are applied to multiple ordinary least squares (OLS) regression models using ratio variables. The problem can exist in both cross-sectional and panel settings. First, following Barraclough (2007) we confirm that ratio variables used in a cross-sectional multiple regression analysis can lead to spurious inferences, and that this may account for some of the conflicting results observed in the literature. With a sample of US long-term debt issuances, we investigate the determinants of financial leverage by building a multiple regression model with proxies for tangibility, size, uniqueness, profitability and growth. These variables are commonly adopted in the literature, and most of them are scaled by total assets as a size adjustment. We argue that such scaling plagues traditional capital structure tests by inducing a spurious ratio problem.

Second, to avoid the spurious ratio problem and also better capture the persistence feature and endogeneity issues in financial leverage decisions, we introduce a first-differenced fixed-effects panel model and a dynamic system Generalized Method of Moments (GMM) model, respectively (both using variables in changes instead of ratios). Our dynamic system GMM panel model results suggest that past realization of debt explains most of the current debt level after controlling for endogeneity; in addition, no association is found between debt changes and firm-specific characteristics after considering fixed effects and endogeneity in this study.

The spurious ratio problem associated with multivariate regression analyses was first noted by Pearson (1897). Pearson shows that in the case where three uncorrelated identically distributed random variables X, Y, Z have the same coefficient of variation (standard deviation divided by expected value), the expected correlation coefficient estimator between Y/Z and X/Z¹ is 0.5 when, in fact, the correlation between Y and X is 0. The contradictory results indicate that the coefficient estimators are biased in the model using ratios, and hence misleading inferences may be drawn. Kronmal (1993) further examines the spurious ratio problem and shows that the coefficient estimators are biased when ratios are used in dependent and independent variables.

In contrast to Pearson and Kronmal who focus on bias corrections in estimators, Barraclough (2007) introduces an alternative solution to this problem by improving statistical inference procedures. She uses a Monte-Carlo simulation technique to generate critical values for the coefficient slopes, the t-values and the adjusted R-squared estimates. The simulation-based confidence intervals for t-values are then compared with conventional levels. The simulation results of Barraclough (2007) show that the critical values are higher than conventional levels for all the scenarios, allowing for different levels of correlation between the set of X variables, the set of Z variables and cross-correlation between the X and Z variables.² Therefore, significant associations may be concluded according to standard statistical inference, whilst in fact the correlations are spurious. In this study, we consider the spurious ratio problems and modify Barraclough’s simulation technique for testing different models. Consistent with Barraclough (2007), we find the simulated confidence intervals for estimates have much wider ranges than those under conventional levels in the multivariate regression models using ratios. In contrast, our results suggest no spurious ratio problem in the two panel models when using variables in changes instead of ratios, as the simulation-based statistical inference is similar to conventional levels.

The remainder of the paper is organized as follows: Section 2 summarizes the conflicting empirical results using ratio regression models in capital structure literature; Section 3 discusses data collection procedures and presents descriptive statistics on long-term debt issuers; Section 4 builds on the work of Barraclough (2007) to generate the cut-off values for estimates using the Monte-Carlo simulation method and identifies the spurious ratio problem in regression models of firm leverage on firm characteristics; Section 5 uses the same simulation technique and shows the first-differencing fixed-effects panel models and system GMM panel models are free from the spurious ratio problem; finally, the results of the estimation of the models are presented and discussed. Section 6 concludes.

2. Literature review

2.1. Ratio regression models in capital structure studies

Some capital structure studies suggest that the decision of debt issuance which leads to a higher leverage ratio breaks the equilibrium of taxation benefit, bankruptcy cost, agency cost and managerial entrenchment, etc. Consequently, the debt issuance decision may affect firm value. The earliest framework in this field is the irrelevance theory developed by Modigliani and Miller (1958). They show that in a world with no tax, the value of a firm and the average cost of funds from all sources are independent of leverage. Since then, numerous empirical studies have attempted to test if the conclusion still holds in a world with taxes and other frictions. There are three dominant theoretical explanations: trade-off (Kraus and Litzenberger, 1973), pecking order (Myers and Majluf, 1984) and market timing theory (Baker and Wurgler, 2002). Empirically the most common methodology used is to perform a regression between the leverage ratio (book, market leverage or leverage differences) and firm characteristics such as assets tangibility, firm size, profitability, uniqueness, and growth to assess how these characteristics affect a firm’s financial leverage. In practice, these proxies along with debt are adjusted for size by scaling by the book value of total assets (or alternatively, sales and the market value of total assets). However, we argue that this adjustment for firm size causes a spurious ratio problem, as first documented more than a hundred years ago by Pearson (1897). Capital structure has continued to puzzle researchers and there is as yet no consensus regarding how a firm’s characteristics affect debt leverage.³ In this paper, we select five (four of them are ratios) of the 39 factors examined by Frank and Goyal (2003), in which the variables are classified as Tier 1 and Tier 2 robust factors.

2.2. Panel data models in capital structure studies

Rather than cross-sectional leverage variations, more recent studies examine how financial leverage changes over time. They suggest that even if a firm has a target capital structure, the target may not be static, but evolves with the firm’s history (Fischer et al., 1989; Goldstein et al., 2001; Harris and Raviv, 1991; Kayhan and Titman, 2007; Shyam-Sunder and Myers, 1999). Panel data models can improve the efficiency of econometric estimates as they integrate the time-varying features, in terms of a firm’s history, whilst cross-sectional models fail on this point.

Previous studies find a firm tends to keep a stable capital structure despite evidence of moving toward more moderate levels of debt leverage. Lemmon et al. (2008) find that firms tend to maintain their financial leverage levels of over 20 years. In addition, they report an R-squared of 60% using a fixed-effects panel regression model. The R-squared value suggests the unobservable fixed effects are able to explain more than half of a firm’s debt leverage. We consider the fixed effects using a first-differencing approach.

In addition to fixed effects, Ozkan (2001) suggests that the shocks which affect a firm’s capital structure decision also influence its firm characteristics. To address the simultaneity problem, which is one form of endogeneity, Ozkan uses a first-differencing GMM method developed by Arellano and Bond (1991), with an unbalanced panel sample of UK firms. However, Ozkan’s model suffers from the latent spurious ratio problem due to using ratios. Likewise, La Rocca et al. (2009) propose a dynamic GMM model of current debt level and lagged debt level along with a group of firm characteristics ratio variables to estimate the target leverage of a firm in Italy. Their model again contains some explanatory variables in ratios, hence still suffers from the spurious ratio problem. We show that our dynamic system GMM model can be used to address endogeneity issues in capital structure whilst avoiding the latent spurious ratio problem.

3. Data

Some studies include both public straight and convertible long-term debt, resulting in larger sample sizes than the sample of public straight debt issuances only. However, earlier survey studies suggest that issuers generally regard convertible debt as a delayed equity offering (Brigham, 1966; Hoffmeister, 1977; Pilcher, 1955). Therefore, it is inappropriate to include convertible debt in the sample. In addition, several studies include both public and private long-term debts; however, the offering dates are not publicly ascertained for private debts, which weakens data reliability. Further, a number of studies focus on debt maturity by considering short and long-term debt as substitutes, contrary to previous studies which examine the substitution effects between equity and debt.

This study focuses on leverage increases that are caused by public straight long-term debt issuances. In doing this, our research purpose is better defined, even though the sample size is smaller. The sample inclusion is in line with our initiative to compare our results with those of equity–debt substitute studies, while at the same time to avoid problems in sample selection.

A number of data selection criteria are imposed. First, we only include issuers of publicly issued straight debts with maturity of more than 1 year from the SDC platform over the period of 1986–2006 which results in excluding issuances without announcement information. Second, firms without financial information on the Compustat or price information on the CRSP are dropped. Third, firms in a regulated utility or a financial sector with the SIC codes of 4900–4999 and 6000–6999 are excluded, since these firms are very different from their industry counterparts in terms of both assets structure and funding sources. Fourth, firms with missing information on total assets, sales, share outstanding and share price for the fiscal year-end prior to the debt offerings are deleted. Fifth, to eliminate the possible impacts of other events within the firms, issuers with any of the following events occurring 30 calendar days before and after the announcement dates of debt offerings are excluded: ordinary share issue, convertible bond issue, stock split, share repurchase, and merger & acquisition. Sixth, companies issuing straight long-term debt more than once during the sample fiscal years are excluded, because with two consecutive debt announcements occurring in the same financial year it is difficult to isolate the joint effect of these events. After imposing all the selection criteria, the final cross-sectional time series sample which is used in Section 4 consists of 719 debt issue observations from 454 firms; while in Section 5, an unbalanced panel data sample of 6864 observations from the same 719 issue firms during the sample period is used.

Panel B of Table 1 presents summary statistics on the variables. These statistics are then compared with the estimations on all firms which are obtained from the Compustat without imposing our selection criteria (thereafter ‘All Compustat sample’). Results indicate that these two samples are very different in firm characteristics. The median of net sales in our LT debt issuances sample is US$2093 million, which is more than 20 times larger than that of ‘All Compustat sample’. This size difference suggests larger firms have relatively easier access to public debt markets, consistent with previous studies (Frank and Goyal, 2009). Similar patterns are also observed in other variables. For instance, the book-leverage (market-leverage) ratio is 56% (36%) in our sample and is 38% (24%) in the ‘All Compustat sample’, confirming the finding of Lemmon and Zender (2009) that financially unconstrained firms have higher debt capacities, thus they primarily use debt to meet their deficits, while constrained firms (which tend to be small or with high growth) issue more equity (Table 2).

Table 1.

Variable definition and sample descriptive statistics

Symbol	Name	Compustat data item
Panel A: Variable definition
s	Net sales	SALE
ppe	Net property, plant & equipment	PPENT, if missing then use PPEGT
mva	Market value of assets	AT-(AT-LT-PSTKL+TXDITC+ DCVT)+CSHO*PRCC_F
r&d	Research & Development expenditures	RDIP
ebitda	Operating income before depreciation	OIBDP
d	Total debts	AT-(AT-LT-PSTKL+TXDITC+DCVT)
ta	Total assets	AT

Panel B: Comparison of summary statistics of two samples over the period of 1985–2005

Our sample (All Compustat sample)

Variable	Mean	Median	Std Dev	Num. of obs
s	5287 (1111)	2093(93)	8614 (6117)	719 (94060)
ppe	1859 (407)	722 (17)	3385 (2484)	719 (94060)
mva	9330 (2102)	3183 (142)	19835 (14611)	719 (94060)
r&d	110 (26)	0 (0)	404 (220)	719 (94060)
ebitda	764 (160)	297 (8)	1277 (1026)	719 (94060)
d	2930 (751)	1138 (34)	4907 (7396)	719 (94060)
ta	4947 (1234)	2039 (90)	8577 (9373)	719 (94060)

Notes: Panel A of this table presents definition and Compustat data items of the variables used throughout the paper. Panel B presents means, medians and standard deviations of the firm-level variables used in our sample of US firms with long-term public debt issuances and All Compustat-firm sample (in parentheses) respectively from 1996–2006. The values of our sample variables are sourced from the financial year prior to the offering announcement dates. All values are in millions US dollars.

Table 2.

Pearson cross-correlation of variables in our cross-sectional sample

Variable	ppe	ln(s)	r&d	ebitda	ln(ta)	ln(mva)
ppe	1
ln(s)	0.53	1
r&d	0.29	0.34	1
ebitda	0.8	0.63	0.62	1
ln(ta)	0.63	0.9	0.37	0.69	1
ln(mva)	0.58	0.88	0.41	0.71	0.96	1
d	0.74	0.61	0.59	0.85	0.69	0.66

4. Models and results

4.1. Multiple regression models using ratios

To examine the spurious ratio problem in the regression models, two static regression models (Model 1 and Model 2) are used. Given the empirical evidence in the literature, the models posit that leverage (book leverage or market leverage) of a public company is determined by its firm characteristics of assets structure, size, uniqueness, profitability and growth.

Model 1: Book-leverage regression model

\frac{d_{i}}{t a_{i}} = b_{0} + b_{1} \frac{p p e_{i}}{t a_{i}} + b_{2} \ln (s_{i}) + b_{3} \frac{r & d_{i}}{s_{i}} + b_{4} \frac{e b i t d a_{i}}{t a_{i}} + b_{5} \frac{m v a_{i}}{t a_{i}} + δ_{i}

(1)

Model 2: Market-leverage regression model

\frac{d_{i}}{m v a_{i}} = b_{0} + b_{1} \frac{p p e_{i}}{t a_{i}} + b_{2} \ln (s_{i}) + b_{3} \frac{r & d_{i}}{s_{i}} + b_{4} \frac{e b i t d a_{i}}{t a_{i}} + b_{5} \frac{m v a_{i}}{t a_{i}} + ε_{i}

(2)

where:

- d_i denotes the book value of total debts;

- ta_i is the book value of total assets;

- ppe_i is the value of net property, plant and equipment;

- s_i represents net sales;

- r & d_i is research and development expenditure;

- ebitda_i is operating income before interests, income tax and depreciation & amortization;

- mva_i is market value of assets, calculated as the book value of total assets less book value of equity plus market value of equity; and

- δ_i,ε_i are the error terms, with mean 0 and identically independently distributed.

4.2. Simulation-based statistical inference and results

We follow the Monte-Carlo simulation technique developed by Barraclough (2007) to establish the simulation-based statistical inference.

Panel A-1 and B-1 of Table 3 report the critical values for the book and market-leverage regression models at the 95% confidence intervals, respectively. For instance, in Panel A-1, the cut-off t-values for coefficients range from the narrowest of [−1.31, +1.29] (ppe/ta) to the widest of [−11.38, 12.2] (Intercept), and the corresponding t-statistics for (mva/ta) ranges from [−2.34, +2.34], in contrast to [−3.51, +3.46] observed in (ebitda/ta). The results are similar to Barraclough (2007), in which the coefficient slopes are far from zero; the critical t-statistics are higher than the standard level of [−1.96, +1.96] in well-specified regression models. Noticeably, the adjusted R-squared is required to exceed 63% to be significant at the equation level. Similar findings are observed in the market-leverage model of Panel B-1.

Table 3.

Monte-Carlo simulation-based statistical inference for the financial leverage models and model results using actual sample

Panel A-1: Book-leverage regression model: $\frac{d_{i}}{t a_{i}} = b_{0} + b_{1} \frac{p p e_{i}}{t a_{i}} + b_{2} \ln (s_{i}) + b_{3} \frac{r & d_{i}}{s_{i}} + b_{4} \frac{e b i t d a_{i}}{t a_{i}} + b_{5} \frac{m v a_{i}}{t a_{i}} + δ_{i}$
Prob.level		Intercept		ppe/ta		ln(s)		r&d/s		ebitda/ta		mva/ta
Y=d/ta	b ₀	t(b₀)	b ₁	t(b₁)	b ₂	t(b₂)	b ₃	t(b₃)	b ₄	t(b₄)	b ₅	t(b₅)	R-squared
2.50%	11.38	−2.42	−1.31	−3.23	−1.38	−2.45	−4.66	−3.3	−3.94	−3.51	−1.64	−2.34	0.63
97.50%	12.2	2.49	1.29	3.22	1.34	2.4	4.66	3.32	3.92	3.46	1.61	2.34

Panel A-2: Actual result of the book-leverage regression model
Y=d/ta	b ₀	t(b₀)	b ₁	t(b₁)	b ₂	t(b₂)	b ₃	t(b₃)	b ₄	t(b₄)	b ₅	t(b₅)	R-squared
	61.96***	−14.89	−5.76*	−1.78	0.43	0.77	−101.93***	−3.24	−24.19	−1.64	1.51	0.96	0.02

Panel B-1: Market-leverage regression model: $\frac{d_{i}}{m v a_{i}} = b_{0} + b_{1} \frac{p p e_{i}}{t a_{i}} + b_{2} \ln (s_{i}) + b_{3} \frac{r & d_{i}}{s_{i}} + b_{4} \frac{e b i t d a_{i}}{t a_{i}} + b_{5} \frac{m v a_{i}}{t a_{i}} + ε_{i}$
Prob.level		Intercept		ppe/ta		ln(s)		r&d/s		ebitda/ta		mva/ta

Y=d/ta	b ₀	t(b₀)	b ₁	t(b₁)	b ₂	t(b₂)	b ₃	t(b₃)	b ₄	t(b₄)	b ₅	t(b₅)	R-squared
2.50%	−10.78	−2.48	−1.08	−3.11	−1.20	−2.48	−4.37	−3.41	−3.66	−3.61	−1.31	−2.29	0.66
97.50%	10.36	2.46	1.11	3.11	1.20	2.47	4.25	3.34	3.73	3.63	1.32	2.38

Panel B-2: Actual result of the market-leverage regression model
Y=d/ta	b ₀	t(b₀)	b ₁	t(b₁)	b ₂	t(b₂)	b ₃	t(b₃)	b ₄	t(b₄)	b ₅	t(b₅)	R-squared
	70.21***	20.74	−1.27	−0.51	−0.07	−0.18	−22.10	−1.12	−58.08***	−5	−10.36***	−10.14	0.44

Notes: Panel A-1 and B-1 of the table presents the Monte-Carlo simulation-based statistical inference results using the variance-covariance relationship in the variables of a sample of US long-term public debt issuances from 1986–2006. 10,000 simulation replication runs are performed to each model using the information of actual sample size (719) and the sample variance covariance relationship between variables in the models. The critical values for the t-statistics are within the range of the 2.5 and 97.5 percentiles which correspond to tests of significance at the two-tailed 5% probability level; the 95^th percentile adjusted R-squared is reported as the 5% cut-off R-squared value. Panel A-2 and B-2 presents the actual sample regression results. Definition of variables is provided in Table 1. ***, **, and * indicate statistical significance at the 1%, 5%, and 10% levels respectively using the simulation statistical inference.

Panels A-2 and B-2 of Table 3 show the results of Model 1 and Model 2 using the actual pooled cross-sectional sample. In Model 1 (the book-leverage regression model), neither tangibility (ppe/ta) nor uniqueness (r&d/s) variables are significant when compared with the simulation-based boundaries in Table 3, even though they are significant under conventional levels. In addition, all the adjusted R-squared values obtained from the regressions are lower than their corresponding critical values. Compared with Lemmon et al. (2008) who report the adjusted R-squared ranges from 18–29% in traditional leverage regression models, our market-leverage regression model appears to outperform the traditional models, even where it is statistically insignificant Tangibility and uniqueness are both negatively significant in the book-leverage model, which is consistent with Leary and Roberts (2005) and Faulkender and Petersen (2006), whilst these two characteristics appear to be insignificant in Model 2 (the market-leverage model). However, profitability and growth exhibit opposite results, as they are found to be significantly negative in the market-leverage model, with no significance observed in the book-leverage model. In summary, the results in Table 3 exhibit strong evidence of the spurious ratio problem in regression models using ratios, as pointed out by Pearson (1897), Kronmal (1993) and Barraclough (2007). Therefore, alternative models should be considered to address the spurious ratio problem.

5. Panel models using changes

The above section demonstrates that a conventional statistical inference is invalid when ratios are used in OLS regression models. Therefore, solutions to the spurious ratio problem will be found either be in performing a simulation-based inference like the above in which ratios are in use, or in adopting OLS regression models without ratio variables. We next demonstrate the latter solution by proposing two panel models, in which variables in changes instead of ratios are used. The use of changes in variables is motivated by Graham (1996), who tests how the incremental (rather than static level) use of debt affects a firm’s marginal tax rates. In addition, fixed effects are considered in the two panel regression models and, specifically, a dynamic system GMM model (Blundell and Bond, 1998) is used to address endogeneity issues.

To show that variables in changes will not result in the spurious ratio problem, we generate critical values using simulated dynamic panel data (DPD) for both panel models (Model 3 and Model 4) with modifications to the Monte-Carlo simulation procedures developed by Barraclough (2007). The modification is made by generating an unbalanced panel data of 6864 observations (719 firms for 21 years), in which these observations are grouped by firm identification and time to reflect the sample’s panel setting.

5.1. The first-differencing fixed-effects panel model and results

Y_{i t} = α_{i} + X_{i t} β + ϕ_{i t}, t = 1, 2, \dots \dots, T

(3)

where

- Y_it denotes the book value of debt;

- α_i presents a vector of time-constant unobserved effects for each firm and it is arbitrarily correlated with the X_it term;

- X_it denotes the vector of explanatory variables: ppe, s, r&d, ebitda, mva; and the intercept term;

- ϕ_it is the error term, with mean 0 and uncorrelated to all Xs.

We initially implement the first-differencing transformation within firm to eliminate the time-invariant unobserved effects (α_i), and then apply the OLS estimation method.

Panel A-1 of Table 4 reports the simulated critical values for Model 3. All the slope coefficients for X variables are close to the true value of 0, with the t-values ranging from [−1.97, +1.98] (changes in ppe, D.ppe) to [−2.23, +2.23] (changes in sales, D.s), which are close to the conventional 95% confidence level of [−1.96, +1.96].

Table 4.

Monte-Carlo simulation-based inference for the two fixed-effects panel models and actual sample results

Panel A-1: The first-differenced fixed-effects panel regression model
Prob.level		D.ppe		D.s		D.r&d		D.ebitda		D.mva
Y=d/ta	b ₁	t(b₁)	b ₂	t(b₂)	b ₃	t(b₃)	b ₄	t(b₄)	b ₅	t(b₅)
2.50%	−0.05	−1.97	−0.01	−2.23	−0.34	−1.97	−0.11	−1.97	−0.01	−2.20
97.50%	0.05	1.98	0.01	2.23	0.34	2.01	0.11	2.01	0.01	2.25

Panel A-2: The first-differenced fixed-effects model result using actual sample
	b ₁	t(b₁)	b ₂	t(b₂)	b ₃	t(b₃)	b ₄	t(b₄)	b ₅	t(b₅)
	0.79***	8.20	0.14***	3.08	0.84***	2.63	−0.21	−1.15	0.01	1.19

Panel B-1: The dynamic system GMM panel model
Prob.level		Intercept		L.d		ppe		s		r&d		ebitda		mva

Y=debt	b ₀	t(b₀)	b ₁	t(b₁)	b ₂	t(b₂)	b ₃	t(b₃)	b ₄	t(b₄)	b ₅	t(b₅)	b ₆	t(b₆)
2.50%	−696.85	−2.05	−0.02	−1.97	−0.08	−2.05	−0.01	−2.07	−0.46	−2.08	−0.23	−1.99	−0.01	−2.01
97.50%	679.52	2.00	0.03	2.07	0.07	1.98	0.01	0.02	0.45	2.03	0.24	2.06	0.01	2.08

Panel B-2: Actual result of the market-leverage regression model
Y=debt	b ₀	t(b₀)	b ₁	t(b₁)	b ₂	t(b₂)	b ₃	t(b₃)	b ₄	t(b₄)	b ₅	t(b₅)	b ₆	t(b₆)
	1.73	0.02	0.93***	24.57	0.04	0.78	0.02**	2.1	−0.15	−0.40	0.38	0.29	0.01	0.02

Notes: Arellano-Bond test for AR(1): Z-value=-5.02 Sargan test of overid. Chi2(6)=182.53 Num of instruments=32

Arellano-Bond test for AR(2): Z-value=0.70 Sargan test of overid. Chi2(6)=9.39

This table presents the Monte-Carlo simulation statistical inference results using the information of a sample of US long-term public debt issuances from 1986–2006. The information about the actual firm-year sample size (6864) and sample variance–covariance relationship is used to simulate panel data. 10,000 simulation replication runs are performed to a first-differenced fixed-effects model (Panel A-1) and a dynamic system GMM panel model (Panel B-1); all variables in changes are used in both models. Definition of variables is provided in Table 1. The critical values for the t-statistics are within the range of the 2.5 and 97.5 percentiles which correspond to tests of significance at the two-tailed 5% probability level; the 95^th percentile adjusted R-squared is reported as the 5% cut-off R-squared value. Panel A-2 and B-2 presents the actual sample regression results. ***, **, and * indicate statistical significance at the 1%, 5% and 10% levels respectively using the simulation-based statistical inference.

Panel A-2 of Table 4 shows the result of Model 3 (the first-differencing fixed-effects panel model) using the actual panel sample. Results suggest that the changes in collateral asset, sales, and R&D expenditures are positively correlated to the changes in debt for every two adjacent years within a firm. These findings can be linked to practice: we expect to see that expanding size (total assets value), increasing collateral assets value (more asset purchases) and more funds being made available to spend on R&D are associated with more debt initiatives in a firm.

5.2. The dynamic system GMM panel model and results

We now move to a dynamic system GMM panel model. Again, to identify the spurious ratio problem, we employ the same Monte-Carlo simulation technique as in Section 4. To address the concern that explanatory variables are not strictly exogenous, we use the dynamic system GMM model developed by Blundell and Bond (1998) which also includes fixed effects. Efficient estimation combines the set of moment conditions for the first-differenced equations with the additional moment conditions implied for the level equations as follows:

E [Δ Y_{1 t} - α_{1} Δ Y_{1 t} - α_{2} Δ X_{1 t}]

E [(Δ Y_{1 t} - α_{1} Δ Y_{1 t - 1} - α_{2} Δ X_{1 t}) Y_{2 t - 2}]

E [(Δ Y_{1 t} - α_{1} Δ Y_{1 t - 1} - α_{2} Δ X_{1 t}) X_{1 t - 2}]

E [Δ Y_{1 t} - α_{0} - α_{1} Y_{1 t - 1} - α_{2} X_{1 t}]

E [(Y_{1 t} - α_{0} - α_{1} Y_{1 t - 1} - α_{2} X_{1 t}) Δ Y_{2 t - 1}]

E [(Y_{1 t} - α_{0} - α_{1} Y_{1 t - 1} - α_{2} X_{1 t}) Δ Y_{1 t - 1}]

where

- ΔY_1t−1 denotes the first difference of book value of debt;

- X_{i, t} denotes the vector of explanatory variables: ppe, s, r&d, ebitda, mva.

Panel B-1 of Table 4 reports the simulated t-values ranging from the narrowest of [−1.97, +2.07] (one-year lagged debt, L.d) to the widest of [−2.08, +2.03] (Research and development expenditure, r&d) for the dynamic system GMM coefficient estimates. The simulation-based critical values are close to the conventional interval of [−1.96, +1.96] which suggests no spurious ratio problem evidenced in the dynamic system GMM model using variable changes.

Panel B-2 of Table 4 shows the result of the dynamic system GMM model. The lagged debt variable (L.d) is significant, with a correlation coefficient of 0.93 and corresponding t-value of 24.57; size (s) with a slope coefficient of 0.02, t-value of 2.10 is significant at the 95% confidence level. It suggests that the past realization of debt explains most of current debt, and once the lagged debt term is added as an explanatory variable other firm characteristics are either insignificant (ppe, r&d, ebitda, mva, according to their t-values) or have minor effects (s, according to its slope coefficient). Our result suggests that once endogeneity is controlled for, there is no significant relationship between debt and firm characteristics.

6. Conclusion

This study explores the spurious ratio problem caused by sharing common divisors in multiple regression models evidenced in the capital structure literature. Without correction, the over-estimated t-values and R-squared under traditional statistical inferences can provide misleading evidence of a significant association between independent and dependent variables. In order to shed light on this problem, we show how the Monte-Carlo simulation technique developed by Barraclough (2007) provides reliable statistical inferences when the parametric conventional inference is invalid.

We further apply the same simulation procedures to two panel models using variables in changes instead of ratios, and no spurious ratio problem is evidenced. These two models are more appropriate to investigate capital structure theories after considering the persistence character of capital structure (fixed effects) and endogeneity problems, respectively. Results indicate changes in collateral assets, size and R&D expenditures are positively associated with changes in debt values in the first-differencing fixed-effects model. While past debt level and size explain most of current debt level in the dynamic system GMM model. This suggests no significant relationship between debt and firm characteristics.

Footnotes

Funding

This research received no specific grant from any funding agency in the public, commercial, or not-for-profit sectors.

Notes

References

Arellano

Bond

(1991) Some tests of specification for panel data: Monte-Carlo evidence and an application to employment. Review of Economic Studies 58: 277–297.

Baker

Wurgler

(2002) Market timing and capital structure. Journal of Finance 57: 1–32.

Barraclough

(2007) Scaling regression equations: Solution or problems? Working Paper, Vanderbilt University.

Blundell

Bond

(1998) Initial conditions and moment restrictions in dynamic panel data models. Journal of Econometrics 87: 115–143.

Brigham

(1966) An analysis of convertible debentures: Theory and some empirical evidence. Journal of Finance 21: 35–54.

Fama

French

(2002) Testing tradeoff and pecking order predictions about dividends and debt. Review of Financial Studies 15: 1–37.

Faulkender

Petersen

(2006) Does the source of capital affect capital structure? Review of Financial Studies 15: 45–79.

Fischer

Heinkei

Zechner

(1989) Dynamic capital structure choice: Theory and tests. Journal of Finance 44: 19–40.

Frank

Goyal

(2003) Testing the pecking order theory of capital structure. Journal of Financial Economics 67: 217–248.

10.

Frank

Goyal

(2009) Capital structure decisions: Which factors are reliably important? Financial Management 38: 1–37.

11.

Goldstein

Leland

(2001) An EBIT-based model of dynamic capital structure. Journal of Business 74: 483–512.

12.

Graham

(1996) Debt and the marginal tax rate. Journal of Financial Economics 41: 41–73.

13.

Harris

Raviv

(1991) The theory of capital structure. Journal of Finance 46: 297–356.

14.

Hoffmeister JR (1977) Use of convertible debt in the early 1970s: A reevaluation of corporate motives. Quarterly Review of Economics and Business 17: 23–31.

15.

Kayhan

Titman

(2007) Firms’ history and their capital structures. Journal of Financial Economics 83: 1–32.

16.

Kraus

Litzenberger

(1973) A state-preference model of optimal financial leverage. Journal of Finance 28: 911–922.

17.

Kronmal

(1993) Spurious correlation and the fallacy of the ratio standard revisited. Journal of Royal Statistical Society 156: 379–392.

18.

La Rocca

Gerace

. (2009) Effect of diversification on capital structure. Accounting & Finance 49: 799–826.

19.

Leary

Roberts

(2005) Do firms rebalance their capital structure? Journal of Finance 60: 2575–2619.

20.

Lemmon

Roberts

Zender

(2008) Back to the beginning: Persistence and the cross-section of corporate capital structure. Journal of Finance 63: 1575–1608.

21.

Lemmon

Zender

(2009) Debt capacity and tests of capital structure theories. Journal of Financial and Quantitative Analysis 45: 1161–1187.

22.

MacKay

Phillips

(2005) How does industry affect firm financial structure? Review of Financial Studies 18: 1433–1466.

23.

Modigliani

Miller

(1958) The cost of capital, corporation finance and the theory of investment. The American Economic Review 48: 261–297.

24.

Myers

Majluf

(1984) Corporate financing and investment decisions when firms have information that investors do not have. Journal of Financial Economics 13: 187–224.

25.

Ozkan

(2001) Determinants of capital structure. Journal of Business Finance & Accounting 28: 175–198.

26.

Pearson

(1897) Mathematical contributions to the theory of evolution—On a form of spurious correlation which may arise when indices are used in the measurement of organs. Proceedings of the Royal Statistical Society 60: 489–498.

27.

Pilcher

(1955) Raising Capital with Convertible Securities. Ann Arbor, MI: University of Michigan Press.

28.

Rajan

Zingales

(1995) What do we know about capital structure? Some evidence from international data. Journal of Finance 50: 1421–1460.

29.

Shyam-Sunder

Myers

(1999) Testing the static tradeoff against pecking order models of capital structure. Journal of Financial Economics 51: 219–244.

30.

Titman

Wessels

(1988) The determinants of capital structure choice. Journal of Finance 43: 1–19.