Monte Carlo Simulations and Capital Structure Research

ABSTRACT

The evolution of the debt ratio under alternative types of managerial behavior can generate non-standard leverage processes. This creates problems for statistical inference in empirical capital structure research. We argue in this paper that when the data generating process is not standard, a useful way to evaluate the appropriateness of inferences and the empirical methodology is via Monte Carlo simulations that mimic the data generating process under alternative assumptions about managerial behavior. We illustrate with several examples.

I. INTRODUCTION

Capital structure research is one area in Finance where, even with more than 40 years of ‘evidence’ before us, we are not much wiser today than before. There is a lack of consensus on even the most fundamental questions. At some level, most of this research tries to get to the issue of what motivates managerial financing decisions. Theory suggests various motives, including managerial self-interest, indifference, or shareholder value maximization. Empirical researchers have come up with various ways to test these theories, but invariably, research has resulted in different, and often conflicting, answers. This paper is not about an evaluation of the collective evidence.¹ Instead, our objective here is to argue that an important reason why empirical research has been inconclusive is a failure to recognize that in the realm of capital structure research, one is dealing with data generating processes that are quite non-standard. To date, research in this area has paid inadequate attention to two important issues: (a) the extent to which existing estimation methodologies for standard processes are appropriate and (b) the types of relationships between the debt ratio and other firm characteristics (including the determinants suggested by theory) that can be expected under different types of financing behavior. We argue in this paper that when the data generating process is not a standard one, a useful way to evaluate the appropriateness of inferences and the empirical methodology is via Monte Carlo simulations that mimic the data generating process under alternative assumptions about managerial behavior.

There are several reasons why capital structure data are unique and present special challenges. First, of course, is the fact that the primary variable of interest is the debt ratio, which is bounded in the unit interval.² Monte Carlo simulations by Shyam-Sunder and Myers (1999), Leary and Roberts (2005), Chang and Dasgupta (2009), and Iliev and Welch (2010) show that because the dependent variable is a bounded ratio, mean reversion can occur even when data are generated under the assumption of non-target behavior or infrequent adjustment. Moreover, Monte Carlo simulations by Huang and Ritter (2009), Iliev and Welch (2010), and Elsas and Florysiak (2010) show that when the dependent variable of interest is a ratio, properties of common estimators designed for standard processes are no longer valid.³ Second, capital structure data often involve severel unbalanced panels, comprising of many young firms with only a few years of data, and large firms that have survived for long periods. This creates additional challenges for estimation methodology (Huang and Ritter 2009). Third, and especially relevant to our agenda in this paper, the process that maps a debt ratio at the beginning of the period to one at the end of the period is also quite complicated, and involves interactions of financing choice with investment and payout decisions. In other words, the change in the debt ratio depends not only on the type of financing raised, but also the amount, which depends on the financing deficit.⁴ The latter, in turn, is determined by firms' investment needs and availability of internal funds. Further, the change in the debt ratio is also affected by how much is retained by the firm, because this affects book equity. Therefore, it becomes difficult to determine from the evolution of the debt ratio whether a given firm-specific variable affects the debt ratio because it affects the amounts of financing deficit and retentions, or whether it is a determinant of a desired capital structure, i.e., the ‘target’ debt ratio.

Of course, this makes the problem of estimating the target debt ratio, challenging exercise in itself, even more difficult. Many of the tests are joint tests of the existence of an optimal (or target) debt ratio and convergence to that target. However, the target has to be estimated, and can be time varying. This creates a problem of identification:⁵ unless the target is estimated very precisely, it is impossible to determine whether large and sustained movements of the debt ratio in a particular direction reflect movements away from the target, or represent movements in the direction of the target in response to underlying shocks that shift the target.⁶ Estimates based on past data are more subject to this problem, so several researchers attempt to utilize all the available data; however, this creates a ‘look-ahead bias’ that has been insufficiently recognized in the literature.

Monte Carlo simulations can address many of these problems. For example, as discussed above, one use of such simulations consists of generating data under alternative assumed processes and examining the properties of various estimators in recovering the true parameters underlying the processes. Such exercises are especially useful in the context of estimating the so-called ‘speed of adjustment’ in the actual data to a target debt ratio. Huang and Ritter (2009), Elsas and Florysiak (2010, 2011), and Iliev and Welch (2010) are examples of papers that take this approach.

The scope for Monte Carlo simulations, however, is not limited to estimating specific parameters for an assumed leverage process. In Chang and Dasgupta (2006, 2007), we present several examples on how such simulations can improve inferences in empirical work.⁷ In this paper, we revisit some of these examples, and present some new ones.⁸ Our applications of the simulation methodology developed in Chang and Dasgupta (2006, 2007) focus on the importance of the financing deficit and retentions in generating the leverage series that we observe.⁹ We also draw on Hovakimian and Li (2011), who perform simulations similar to Chang and Dasgupta (henceforth, CD simulations), to show how the incorporation of firm-fixed effects in debt ratio regressions as well as debt/equity choice models greatly exaggerate the evidence for target behavior due to the look-ahead bias. In addition, we examine the analysis of variance (ANOVA) as in Lemmon et al. (2008) to understand what we can learn about the contribution of observed and unobserved firm-specific variables to the explained variation in leverage ratios in time series and cross section. We also explore the fragility of inferences based on probit and multinomial logit models of debt/equity choices in issuance and repurchase activity. Finally, we illustrate how simulations can be useful in detecting whether constructs that are meant to capture certain types of financing activity are successful in doing so. In particular, we focus on Kayhan and Titman's (2007) modification of Baker and Wurgler's (2002)‘external finance weighted market-to-book’ measure to see whether it has any incremental contribution even after controlling for the market-to-book ratio, an issue on which there has been much controversy.

The rest of the paper is organized as follows. In Section II, we describe the data and our simulation samples. Section III presents the results of five different exercises. Finally, Section IV concludes.

II. DATA AND SAMPLES

A. Actual data and variables

Our actual data sample, S(actual data), consists of firms listed in the Compustat Industrial Annual Files at any point between 1971 and 2008. We obtain data on stock prices and returns from the Center for Research on Security Prices (CRSP) files. Following common practice, we exclude financial, insurance, and real estate firms (SIC code 6000–6900), regulated utilities (SIC code 4900–4999), and firms with missing book values of assets. Following previous studies of target adjustment models, we restrict the sample to firms with at least 20 years of continuous balance sheet items.¹⁰ This also ensures that in simulated samples, the debt ratio evolves via random financing for a sufficiently long period of time so that the resulting simulated leverage ratios do not closely resemble the actual leverage. The final data set is an unbalanced panel consisting of 46,956 firm-year observations. Firm characteristics, such as the market-to-book assets ratio and the EBITDA-to-assets ratio, are winsorized at the 0.5% level at both tails of the distribution to mitigate the impact of outliers or misrecorded data. All dollar values are converted into 2000 constant dollars.

Book leverage (D/A) is defined as the ratio of book debt to total assets. Book debt is the sum of total liabilities and preferred stock minus deferred taxes and convertible debt.¹¹ When preferred stock is missing, we replace it with the redemption value of preferred stock. Book equity is then defined as total assets minus book debt. We drop firm-year observations where book leverage is negative or exceeds one.

We define net equity and net debt issues using balance sheet data.¹² Following the accounting identity that book equity equals balance sheet retained earnings plus paid-in share capital, we define net equity issues (Nei) as the change in book equity (ΔE) minus the change in retained earnings (ΔRE). Net debt issues (Ndi) are then defined as the change in total assets less the change in retained earnings and net equity issues. One key variable of our interest, the financing deficit (DEF), is the difference between the change in total assets and the change in retained earnings. This variable is positive (DEF>0) when the firm invests more than it internally generates, and by definition, this deficit must be filled by the net issues of debt and/or equity. In contrast, the financing deficit takes a negative value (DEF<0) when the firm internally generates more funds than it invests, in which case the resulting financing surplus (or the negative financing deficit) has to be used to repurchased debt and/or equity. In other words, the financing deficit is equal to the sum of the net debt and the net equity issued. This accounting identity can be written as follows:

• (1)

We include in regressions a set of explanatory variables that have been shown by prior literature to influence capital structure (see, among others, Flannery and Rangan 2006; Chang and Dasgupta 2009; Frank and Goyal 2009), including the market-to-book asset ratio (M/B), profitability (EBITDA/A), firm size (Size) measured as the log value of total assets, tangibility of assets (PPE/A), research and development expense to sales ratio (R&D/S), a dummy variable (RDD) that takes the value of one when R&D is missing in Compustat and zero otherwise, and annual stock return (StkRtn) obtained by compounding monthly stock returns over the entire fiscal year.

Table 1 provides detailed definitions of these variables and reports the summary statistics for the actual data sample. In roughly two-thirds (67.6%) of the firm-years, firms have positive financing deficits. Roughly 70% (69.6%) of the positive financing deficits are financed with debt issues. In contrast, roughly 75% (74.7%) of the financing surpluses (negative deficits) are associated with debt reductions.

Table 1.   Summary statistics (actual data)

	Mean	Median	Standard deviation
Actual data are collected from Industrial Compustat and CRSP for the years 1971–2008. Total assets (A) is the book value of total assets. Book leverage (D/A) is defined as total debt divided by total assets. Total debt is equal to total liabilities plus preferred stock minus deferred taxes and convertible debt. Market-to-book ratio (M/B) is defined as (market value of equity+total debt)/total assets. Market value of equity is defined as the number of shares outstanding multiplied by closing stock price at the end of the fiscal year. Profitability (EBITDA/A) is income before depreciation and amortization divided by book value of assets. Tangibility (PPE/A) is the net PPE to assets ratio. R&D/S is research and development expenses divided by net sales. Annual cumulative stock return (StkRtn) is obtained by compounding monthly stock returns over the fiscal year. Net equity issues (Nei) are equal to the change in total equity minus the change in retained earnings. Net debt issues (Ndi) are defined as the change in total assets minus the change in total equity. Financing deficit (DEF) equals the sum of net equity issued and net debt issued. Newly retained earnings (ΔRE) is the change in retained earnings. Dollar figures are in millions.
Total assets (A)	3227	224.2	16,813
Book leverage (D/A)	0.443	0.445	0.189
Market-to-book ratio (M/B)	1.613	1.261	1.302
Profitability (EBITDA/A)	0.092	0.098	0.125
Tangibility (PPE/A)	0.329	0.288	0.207
R&D to sales ratio (R&D/S)	0.045	0.002	0.361
Annual stock return (StkRtn)	0.187	0.101	0.556
Deficit to assets ratio (DEF/A)	0.087	0.038	0.220
Newly retained earnings to assets ratio (ΔRE/A)	0.030	0.037	0.094
Percentage of firms having positive financing deficit (DEF/A>0%)	67.6
Percentage of firms having large positive financing deficit (DEF/A>5%)	44.9
Percentage of firms having large negative financing deficit (DEF/A<−5%)	15.2
Average percentage of financing deficit financed with debt in positive financing deficit years	69.6
Average percentage of financing deficit used for debt reduction in negative financing deficit years	74.7
Firm-years	46,956

B. Simulation samples

We generate simulation samples under a number of alternative assumptions about financing behavior. Our simulated samples are based on the actual sample of firms in Compustat described in Section II.A. We assume that all firms in the simulation sample have the same initial debt ratio as in the actual data, and, importantly, we assume – in all cases except one to be discussed below – that the financing deficit (DEF) and newly retained earnings (ΔRE) are the same as in the actual data for every firm-year. All other variables are also as in the actual data with the exception of the mix of debt and equity. The mix of debt and equity is determined by the initial debt ratio and the outcome of successive ‘coin toss’ experiments described below.

We take the initial book leverage ratio of each firm from Compustat.¹³ From the second year onwards, we update leverage according to the financing rule that firms follow. For each simulated sample, the simulated end-of-period total equity is the sum of the simulated beginning-of-period total equity plus net equity issued and the change in retained earnings. The simulated end-of-period debt is the beginning-of-period debt plus the new net debt issued.

The first two simulation samples, denoted as S(p, actual deficit), are generated using actual financing deficit and newly retained earnings; p represents the probability of debt issue/repurchase.

• •
  S(p=0.5, actual deficit): If the financing deficit is positive, we assume that firms decide whether to issue debt or equity by tossing a coin, that is, there is a 50% chance for equity issuance and a 50% chance for debt issuance. Similarly, firms are assumed to retire debt or equity with equal probability when the financing deficit is negative. This sample is generated because it is the most intuitive form of ‘random financing’: a firm flips a fair coin to decide whether it should issue (repurchase) debt or equity, without any regard to the current debt ratio or a target.
• •
  S(p=empirical frequency, actual deficit): Here, we assume that conditional on the actual deficit being positive (negative), the probability of debt and equity issuance (repurchase) corresponds to the empirical frequencies in the overall actual data when dual issues are excluded. The probability of debt issuance is approximately 0.70 (equity issuance 0.30), and the probability of debt retirement is approximately 0.75 (equity repurchase 0.25) as discussed in Section II.A. This sample is generated because if, in fact, target behavior is not followed widely, then a sample in which debt and equity are issued and repurchased with fixed probabilities in accordance with the actual empirical frequencies is likely to reproduce results similar to those obtained using the actual data. Moreover, note that the actual empirical probabilities conform reasonably closely to what pecking order behavior would suggest: both for issuance and repurchase activities, debt appears to be the preferred security. Thus, if much of the observed empirical regularities can be reproduced for this sample, it follows that pecking order behavior is a reasonable description of actual behavior.

The decision to preserve the actual financing deficit for the purpose of generating the simulation samples may appear not to be innocuous. One immediate advantage is that the size of the firm remains the same in each firm-year in the simulated and the actual samples, because the book value of assets increases by the amount of the financing deficit plus newly retained earnings. This makes it easier to interpret variables such as the market-to-book ratio in the context of the simulation samples. For example, if the market value of the firm is not affected by the choice of financing, the market-to-book ratio in the actual data is still the right one for the simulated data. As our simulations do not stipulate an optimal debt ratio, we might as well pretend that Modigliani and Miller's (1958) result holds. One could also argue that target behavior is less related to the magnitude of the deficit (especially, whether it is positive or negative) than the form of financing chosen. For example, a firm that is underlevered (i.e., has a negative deviation from the target) could either issue debt or buy back equity to move closer to the target. Shyam-Sunder and Myers (1999) also seem to take the view that the primary determinants of the financing deficit, namely, investment opportunities and internal funds, are exogenous. However, the magnitude of the deficit does determine the extent to which a firm is able to adjust its debt ratio – so for a firm following target behavior, the financing deficit must be at least to some extent endogenous.

To eliminate the possibility that any replications of evidence consistent with target behavior in the simulated samples could be related to endogeneity of the actual financing deficit, we also construct a sample S(p=empirical frequency, random deficit) described as follows.

• •
  S(p=empirical frequency, random deficit): Here we assume both the financing deficit scaled by total assets (DEF/A) and the change in retained earnings scaled by total assets (ΔRE/A) are randomly drawn from normal distributions with the same means and standard deviations as those in the actual data (the means are 0.087 and 0.030, and the standard deviations are 0.220 and 0.094 for DEF/A and ΔRE/A, respectively, as reported in Table 1). Firms are assumed to issue (retire) debt or equity following the empirical frequencies in the actual data.

It is also worth pointing out that even if the deficit size were correlated with the deviation from the target in the actual data, such a relationship is unlikely to persist in our simulations as the leverage ratio evolves in response to random financing. Further, even if such a correlation persists, as financing is random, it is unlikely that this should generate a move necessarily toward the target in the same way as in the actual data. Therefore, taken together, it does not appear as though the endogeneity of the financing deficit could explain replication of evidence consistent with target behavior in our simulation samples.

C. Why use random financing as a benchmark?

It is important to point out that our objective in using samples generated under the assumption of random financing as a benchmark is not to propose that, in reality, financing is random. Rather, this choice is motivated by the fact that we do not know a great deal about the reasons underlying firms' financing choices. Actual financing behavior is presumably affected by the resolution of state variables that are observed by firm insiders but unobserved or imperfectly observed by researchers; therefore, modeling financing as random reflects the probabilities with which these state variables are jointly realized. Random financing with fixed probabilities of issuance or repurchase of a particular type of security thus incorporates a wide class of theories of financing, but excludes trade-off behavior. The latter requires that the probability of equity (debt) issuance (repurchase) is high when the debt ratio is above the target, and that the probability of debt (equity) issuance (repurchase) is high when the debt ratio is below the target. Our simulations are constructed so that we know whatever the patterns occurring in the simulated data are not caused by debt ratio targeting.

III. EMPIRICAL RESULTS

A. The coefficients of firm-specific variables in leverage regressions

In Chang and Dasgupta (2009), we point out a major difficulty in interpreting coefficients of firm-specific variables in leverage regressions. Many of these variables also affect the financing deficit and retained earnings, which, in turn, affect leverage ratios even when the firm does not follow target behavior. It has been suggested to us that controlling for the deficit and retentions in leverage regressions should ‘solve’ the problem. Here, we show that while this is sensible and most likely improves the inference, it does not solve the problem.

Table 2 shows the results. The model being estimated is the conventional target adjustment mode. The adjustment model is specified as

• (2)

where the target adjustment coefficient (λ) is >0 if firms adjust toward the target, and it is strictly <1 if there exist some positive adjustment costs. The terms and T_t denote, respectively, the debt ratio and the leverage target at t. The expression is called the ‘deviation from the target.’ This model can be rewritten as

• (3)

Table 2.   Target adjustment model with firm-fixed effects

Dependent variable (D/A)t	(1)	(2)	(3)	(4)	(5)	(6)
	S(actual data)	S(p=empirical frequency, actual deficit)	S(p=empirical frequency, random deficit)	S(actual data)	S(p=empirical frequency, actual deficit)	S(p=empirical frequency, random deficit)
Actual data are collected from Industrial Compustat and CRSP for the years 1971–2008. Section II discusses how the simulated data are generated. The dependent variable is book leverage (D/A). Independent variables include the lagged leverage ratio, the market-to-book asset ratio (M/B), profitability (EBITDA/A), firm size (Size) measured as the log value of total assets, tangibility of assets (PPE/A), research and development expense to sales ratio (R&D/S), a dummy variable (RDD) that takes the value of 1 when R&D is missing in Compustat and 0 otherwise, and annual stock return (StkRtn) obtained by compounding monthly stock returns over the entire fiscal year. The regression models are estimated with firm-fixed effects and year-fixed effects. For S(actual data), t-statistics in parentheses are calculated from the Huber–White sandwich heteroskedasticity consistent errors, which are corrected for correlation across observations for a given firm. Coefficients significant at the 10%, 5%, and 1% levels are, respectively, marked with ^*, ^**, and ^***. For simulated samples, the reported parameter estimates are the average coefficients obtained from 500 replications of the simulation. 95% confidence intervals are included in square brackets and coefficients are marked with ‘a’ if 95% conference intervals do not span zero. In all columns, intercepts and year dummies are included but not reported.
(D/A)t−1	0.779^***	0.828^a	0.800^a	0.804^***	0.842^a	0.823^a
	(174.5)	[0.821, 0.834]	[0.794, 0.806]	(192.0)	[0.836, 0.847]	[0.817, 0.829]
M/B	−0.003^***	0.001	0.000	−0.007^***	−0.002^a	0.000
	(−3.9)	[−0.001, 0.002]	[−0.002, 0.001]	(−7.4)	[−0.004, −0.000]	[−0.001, 0.001]
EBITDA/A	−0.075^***	−0.075^a	−0.003	0.033^***	0.049^a	−0.002
	(−6.1)	[−0.096, −0.055]	[−0.016, 0.010]	(3.5)	[0.026, 0.072]	[−0.014, 0.009]
Size	−0.002^**	−0.001	0.000	0.001^**	0.000	0.000
	(−2.3)	[−0.004, 0.000]	[−0.001, 0.002]	(2.0)	[−0.001, 0.003]	[−0.001, 0.002]
PPE/A	−0.001	0.016^a	0.005	−0.008^*	0.008	0.003
	(−0.1)	[0.006, 0.025]	[−0.008, 0.020]	(−1.9)	[−0.001, 0.0017]	[−0.007, 0.014]
R&D/S	−0.001	0.005	0.000	−0.008^**	−0.001	0.000
	(−0.4)	[−0.002, 0.012]	[−0.005, 0.004]	(−2.0)	[−0.009, 0.006]	[−0.004, 0.004]
RDD	0.001	−0.002	0.000	0.001	−0.002	0.000
	(0.4)	[−0.006, 0.002]	[−0.004, 0.005]	(0.5)	[−0.006, 0.002]	[−0.002, 0.004]
StkRtn	−0.010^***	−0.003^a	0.000	−0.009^***	−0.000	0.000
	(−9.5)	[−0.004, −0.001]	[−0.001, 0.002]	(−9.1)	[−0.002, 0.000]	[−0.001, 0.002]
(DEF/A)t				0.134^***	0.137^a	0.226
				(35.8)	[0.126, 0.147]	[0.216, 0.236]
(ΔRE/A)t				−0.341^***	−0.406^a	−0.362
				(−39.9)	[−0.424, −0.388]	[−0.374, −0.351]
R^2/N	0.83/46,956	0.85/46,956	0.79/46,956	0.87/46,956	0.88/46,956	0.85/46,956

The leverage target is supposed to be the result of an optimization exercise in which firms trade off the costs and benefits of debt. These costs and benefits are related to firm characteristics. Therefore, the target T_i,t for firm i at t is stipulated to be of the form

• (4)

where X_i,t−1 is a vector of time-varying firm characteristics that are pre-determined at time t, f_i represents a time-invariant firm characteristic, and v_t captures the time effect. Tests involve estimating the model obtained from substituting (4) into (3), that is,

• (5)

The interest of empirical research centers around (a) the magnitude of the coefficient of the lagged dependent variable (1−λ), which is supposed to be <1 if firms adjust to a target, and is smaller the larger ‘speed of adjustment’ parameter λ, and (b) whether the signs of the coefficients on the firm-specific variables conform to the theoretical predictions regarding how the target debt ratio should be related to these variables.

We estimate the following model in a panel setting using firm-fixed effects as in Flannery and Rangan (2006):¹⁴

• (6)

The dependent variable is the leverage ratio (D/A). The independent variables are the lagged leverage ratio and firm-specific control variables lagged one period, which are defined in Table 1. We estimate equation (6) for the actual data as well as a number of simulation samples. For simulated samples, we report average parameter estimates from 500 replications of the simulation, as well as the corresponding 95% confidence intervals.

In column (1) of Table 2, we report the coefficient estimates for equation (6) for the actual data sample S(actual data). The estimated coefficient on lagged leverage is 0.779, which is larger than those reported in Flannery and Rangan (2006) and Chang and Dasgupta (2009).¹⁵ More importantly, for the S(p=empirical frequency, actual deficit), and S(p=empirical frequency, random deficit) samples in columns (2) and (3), the estimated coefficient on lagged leverage appears comparable (0.828 and 0.800, respectively) to that in column (1). This shows that mechanical mean reversion can give rise to comparable estimated speeds of adjustment as in the actual data. Moreover, since this is true even when the financing deficit is random [column (3)], these adjustment speeds do not reflect some properties of the actual deficit that could be driving mean reversion.

A traditional way of thinking about target behavior has been to examine the determinants of target leverage. The leverage target is supposed to be the result of an optimization exercise in which firms trade off the costs and benefits of debt. These costs and benefits are related to firm characteristics. Therefore, considerable attention has been paid to the issue of finding proxies for the costs and benefits of leverage, and examining whether these proxies have consistent signs in leverage regressions such as equation (5).

We note that several firm-specific variables are significant in the actual data [column (1)] and the simulated data sample S(p=empirical frequency, actual deficit) [column (2)]. The significance of firm-specific variables is usually taken as evidence that the firm's optimal or target debt ratio is related to firm characteristics. Yet, in column (2), where the data are generated under random financing, many of the firm-specific variables are still significant. Therefore, our results show that even when a firm does not follow target behavior, firm characteristics can affect the mean debt ratio.

To understand why, it is useful to consider the sample S(p=empirical frequency, random deficit) and the estimation results reported in column (3). Except for lagged leverage, all firm-specific variables are insignificant. Recall that while in this sample the deficit and retained earnings are randomly drawn in each firm-year, the simulated sample in column (2) is based on the actual deficit and retained earnings. Hence, it appears that the firm-specific variables affect the debt ratio partly because they are related to the actual deficit and the actual changes in retained earnings. The change in retained earnings enters the denominator of book leverage and thus has a mechanical negative effect on the latter. Further, if in any particular sample debt is issued and repurchased more frequently than equity (e.g., due to pecking order behavior), then any variable that increases the likelihood of a positive deficit (as opposed to a negative one) will be positively related to the debt ratio. This is true, for example, for the sample S(p=empirical frequency, actual deficit) in column (2) of Table 2, in which debt is issued or repurchased more than 70% of the time.¹⁶

Note also that for our simulation samples, as we deviate from the actual debt ratios in the data, the actual stock returns (StkRtn) are not meaningful measures of returns to shareholders. However, the financing deficit and newly retained earnings are related to stock returns, and stock returns thus possibly affect leverage ratios in the simulation samples through these channels.

If the effects of financing deficit and retentions contaminate the interpretation of the firm-specific variables in the estimation of equation (6), could inclusion of these two variables as ‘controls’ resolve the problem? In columns (4)–(6), we control for the deficit-to-assets ratio (DEF/A) and the newly retained earnings deflated by total assets (ΔRE/A). Both variables are highly significantly in regressions. Note that, in the actual data, the coefficient of profitability (EBITDA/A) turns positive after the deficit and the change in retained earnings are controlled for, which is encouraging for trade-off theory.¹⁷ Fewer variables are significant in column (5) than in column (2), suggesting the controlling for the deficit and retentions may help remove some of the confounding effects of firm-specific variables on the leverage ratio. However, in column (5), both the market-to-book ratio and profitability are still significant.¹⁸ In particular, the coefficient of profitability is about the same in column (5) as it is in column (4). This makes it difficult to interpret the positive coefficient of profitability in column (4) as evidence in favor of target behavior. Overall, these results suggest that controlling for the deficit and retained earnings cannot purge the confounding affects of firm-specific variables.

B. Sources of variation and firm-fixed effects

In a thought-provoking paper, Lemmon, Roberts, and Zender (2008) (LRZ hereafter) show that firm-specific variables account for a very small fraction of the explained variation in the leverage ratio, in time series and cross section. ANOVA analysis indicates that firm-fixed effects contribute as much as 95% of the explained variation! It has been suggested that this implies that we know very little about the determinants of capital structure.

In Table 3, we report the results of ANOVA analysis similar to LRZ for six different samples, presented in panels A–F. For each sample, we report six sets of results corresponding to six different model specifications. The actual sample results are in panel A, and the remaining panels represent results from various simulation samples.

Table 3.   Variance decompositions

Panel A: S(actual data)
	(1)	(2)	(3)	(4)	(5)	(6)
Firm-fixed effects	1.00	.	0.97			0.94
Year-fixed effects	.	1.00	0.03		0.05	0.03
Industry-fixed effects	.	.			0.27
M/B	.	.		0.15	0.09	0.00
EBITDA/A	.	.		0.15	0.15	0.03
Size	.	.		0.63	0.40	0.00
PPE/A	.	.		0.01	0.00	0.00
R&D/S	.	.		0.03	0.03	0.00
RDD	.	.		0.03	0.01	0.00
StkRtn	.	.		0.00	0.01	0.00
Adjusted-R^2	0.54	0.01	0.56	0.17	0.23	0.57

Panel B: S(p=empirical frequency, actual deficit, actual initial leverage)
	(1)	(2)	(3)	(4)	(5)	(6)
Firm-fixed effects	1.00	.	0.99			0.97
Year-fixed effects	.	1.00	0.01		0.03	0.00
Industry-fixed effects	.	.			0.29
M/B	.	.		0.00	0.01	0.00
EBITDA/A	.	.		0.87	0.62	0.03
Size	.	.		0.10	0.03	0.00
PPE/A	.	.		0.00	0.00	0.00
R&D/S	.	.		0.00	0.00	0.00
RDD	.	.		0.01	0.01	0.00
StkRtn	.	.		0.02	0.02	0.00
Adjusted-R^2	0.51	0.00	0.52	0.09	0.11	0.53

Panel C: S(p=empirical frequency, random deficit, actual initial leverage)
	(1)	(2)	(3)	(4)	(5)	(6)
Firm-fixed effects	1.00	.	0.99			0.99
Year-fixed effects	.	1.00	0.01		0.13	0.01
Industry-fixed effects	.	.			0.41
M/B	.	.		0.19	0.17	0.00
EBITDA/A	.	.		0.04	0.03	0.00
Size	.	.		0.49	0.14	0.00
PPE/A	.	.		0.09	0.02	0.00
R&D/S	.	.		0.08	0.07	0.00
RDD	.	.		0.09	0.02	0.00
StkRtn	.	.		0.02	0.03	0.00
Adjusted-R^2	0.38	0.00	0.38	0.01	0.02	0.38

Panel D: S(p=empirical frequency, actual deficit, random initial leverage)
	(1)	(2)	(3)	(4)	(5)	(6)
Firm-fixed effects	1.00	.	0.99			0.97
Year-fixed effects	.	1.00	0.01		0.05	0.01
Industry-fixed effects	.	.			0.29
M/B	.	.		0.00	0.00	0.00
EBITDA/A	.	.		0.98	0.65	0.02
Size	.	.		0.00	0.00	0.00
PPE/A	.	.		0.01	0.00	0.00
R&D/S	.	.		0.00	0.00	0.00
RDD	.	.		0.01	0.00	0.00
StkRtn	.	.		0.01	0.01	0.00
Adjusted-R^2	0.41	0.00	0.52	0.07	0.09	0.53

Panel E: S(p=Target(1), actual deficit, actual initial leverage)
	(1)	(2)	(3)	(4)	(5)	(6)
Firm-fixed effects	1.00	.	0.93			0.74
Year-fixed effects	.	1.00	0.07		0.03	0.04
Industry-fixed effects	.	.			0.24
M/B	.	.		0.07	0.05	0.03
EBITDA/A	.	.		0.43	0.38	0.18
Size	.	.		0.47	0.30	0.00
PPE/A	.	.		0.01	0.00	0.00
R&D/S	.	.		0.00	0.00	0.00
RDD	.	.		0.02	0.00	0.00
StkRtn	.	.		0.00	0.00	0.00
Adjusted-R^2	0.33	0.01	0.36	0.24	0.32	0.43

Panel F: S(p=Target(0.7), actual deficit, actual initial leverage)
	(1)	(2)	(3)	(4)	(5)	(6)
The table reports variance decompositions of book leverage (D/A) for several different model specifications for the actual and simulated data. Actual data are collected from Industrial Compustat and CRSP for the years 1971–2008. Sections II and III discusses how the simulated data are generated. Each column corresponds to a different model specification for leverage. The figures in the body of the table are the fractions of the total Type III partial sum of squares for each effect in the model. We divided the partial sum of squares for each effect by the total partial sum of squares across all effects in the model, so that the sum across the effects in each column adds up to one. Explanatory variables include firm-fixed effects, fiscal-year-fixed effects, two-digit SIC industry-fixed effects, the market-to-book asset ratio (M/B), profitability (EBITDA/A), firm size (Size) measured as the log value of total assets, tangibility of assets (PPE/A), research and development expense to sales ratio (R&D/S), a dummy variable (RDD) that takes the value of 1 when R&D is missing in Compustat and 0 otherwise, and annual stock return (StkRtn) obtained by compounding monthly stock returns over the entire fiscal year.
Firm-fixed effects	1.00	.	0.98			0.90
Year-fixed effects	.	1.00	0.02		0.03	0.02
Industry-fixed effects	.	.			0.22
M/B	.	.		0.03	0.02	0.01
EBITDA/A	.	.		0.75	0.61	0.07
Size	.	.		0.18	0.11	0.00
PPE/A	.	.		0.00	0.00	0.00
R&D/S	.	.		0.00	0.00	0.00
RDD	.	.		0.03	0.00	0.00
StkRtn	.	.		0.00	0.01	0.00
Adjusted-R^2	0.39	0.00	0.39	0.12	0.16	0.43

We note from column (6) in panel A that, consistent with LRZ, when firm-fixed effects are included along with other firm-specific explanatory variables, the fixed effects account for 94% of the explained variation. Also consistent with LRZ, comparing column (4) and column (6), the inclusion of fixed effects improves the R² from 17% to 57%. Clearly, there is a great deal of the variation (especially cross-sectional variation that persists through time) that standard firm-specific variables cannot explain.

However, does this point to missing or omitted factors affecting leverage that researchers need to focus on? Not necessarily. Consider panel B, which reports variance decomposition results for the simulation sample S(p=empirical frequency, actual deficit). As discussed before, this data generating process comes close to representing pecking order behavior: firms issue or repurchase debt roughly 70% of the time. We pretty much know everything about this process.¹⁹ Yet, as column (6) of panel B shows, firm-fixed effects account for 97% of the variation, and the R² in panel B improves from a mere 9% in column (4) to 53% in column (6). However, there is no obvious missing time-persistent firm characteristic that affects the data generating process here.

We say ‘obvious’ in the last sentence because the sample is still generated on the basis of the actual financing deficits and retentions, and the initial leverage ratio is the actual one in the data. The samples in panels C and D relax each of these features. In panel C, the simulation is based on randomly drawn financing deficit and retained earnings, while that in panel D replaces the actual initial leverage with one that is randomly drawn from the unit interval. We get qualitatively very similar results.²⁰

One of the main purposes of this exercise is to show that, for the part of the variation in the actual data that firm characteristics can explain, one can learn a lot from a comparison of the results in the different panels. First, note from column (4) of panel A that firm size (book value of assets) accounts for a very high proportion of the explained variation. LRZ do not find such a high contribution of firm size, possibly because of a different definition of size and a different sample.²¹ The market-to-book ratio and profitability are the other two major contributors to the explained variation in the actual data. In column (4) of panel B, the effect of profitability swamps everything else. That profitability matters in the simulation samples is not surprising: except when the retentions are randomly drawn, the empirical correlation between profitability and retentions is high, and retained earnings affect the denominator of the book debt ratio. What is surprising is that the influence of profitability is so much reduced in the actual data. This suggests that managers do not passively follow a 70/30 rule as is assumed in for the data process of panel B – they respond actively to the variations in the other factors aside from profitability. This is reminiscent of Welch (2004): managers are active, but are they rebalancing?

Further insights can be gained by comparing results in panel C with other panels. In panel C, the only deterministic influence on the evolution of leverage comes from the distribution of the initial leverage. Thus, column (4) shows the contribution of the firm-specific variables to the cross-sectional variation of the actual initial leverage only. Most of the firm-specific variables now explain a non-negligible proportion of the variation. Size remains the most important contributor. Profitability is less important than it is in panel A and much less so than it is in panel B. The latter is expected since in this sample, the link between profitability and retentions is broken, so profitability does not track the subsequent evolution of leverage. However, comparing column (4) in panel C with column (4) in panel A, it appears that this link is an important source of the time series variation in the leverage ratio in the actual data.

It is also instructive to compare panels C and D. In the latter panel, the initial leverage is randomly chosen from the unit interval, but the deficit and retained earnings are as in the actual data. When financing is mechanical, the empirical link between profitability and retained earnings is the strongest source of variation in the leverage ratio. The other firm characteristics, such as size and M/B, also affect the financing deficit and retentions, but these links are a far less important source of variation in the leverage ratio.

Finally, in panels E and F, we introduce two new simulation samples [studied in Chang and Dasgupta 2009, Table 2, column (5)]. These samples are generated under the assumption of target behavior. Specifically, the sample S(p=target(π), actual deficit, actual initial leverage) assumes that the financing deficit, retained earnings, and the initial leverage are all as in the actual data. The firm moves in the direction of an assumed target (i.e., if (D/A)_i,t−1−T_i,t>0 and the deficit is positive (negative), it issues (repurchases) equity (debt); if (D/A)_i,t−1−T_i,t<0 and the deficit is positive (negative), it issues (repurchases) debt (equity)) with probability π>0.5. Clearly, the higher is π, the more vigorous the target behavior. The assumed target is a function of firm-specific variables: we simply use the predicted value from the OLS estimate from equation (6) for the actual data without the firm-fixed effect parameter as the target for firm i in period t.²²

In column (6) of panel E, we observe that if the target behavior is vigorous (π=1, that is, firms move in the direction of the target with probability 1 through their issuance/repurchase activities), firm-fixed effects contributes about 74% to the explained variation, which is substantially lower than what we have observed for all the other samples so far. Most of the contribution from the firm-specific variables comes from profitability. In contrast, from panel F, we see that if the target behavior is less vigorous (π=0.7), firm-fixed effects contribute about 90% to the explained variation, which is closer to the figure in the actual data. As the target is a function of firm-specific variables in the simulations in these two panels, leverage changes are more sensitive to changes in firm-specific variables when target behavior is more vigorous, which is why firm-specific variables account for a higher fraction of the explained variation in panel E. Clearly, the sensitivity of leverage changes in the actual data to firm-specific variables is closer to what is in evidence in panel F than in panel E. In other words, if there is target behavior in the actual data, it is at best modest.

Next, we consider models of debt–equity choices in issuance and repurchase decisions, and demonstrate the fragile nature of inferences based on these models.

C. Firm-fixed effects and look-ahead bias

This section draws heavily on Hovakimian and Li (2011) who perform CD simulations to illustrate the look-ahead bias. The use of firm-fixed effect regressions is common in capital structure research. The incorporation of firm-fixed effects dramatically increases estimates of the speed of adjustment in debt ratio regressions similar to equation (6) (e.g., Flannery and Rangan 2006), as well as in probit models of issuance and repurchase where the coefficient of interest is that of the deviation from the target, defined as (D/A)_i,t−1−T_i,t. Flannery and Rangan (2006) argue that the firm-fixed effect allows a more precise estimate of the target, and thus a more precise (and faster) estimate of the speed of adjustment or movement toward the target.

There is a well-known bias associated with the fixed-effect estimator (Nickell 1981; Bond 2002) in samples for which N– the number of periods for which data are available – is not large. Here, we illustrate how the speed of adjustment can be greatly exaggerated even for our sample (for which we require N to be at least 20) due to the ‘look-ahead bias.’ Essentially, this bias occurs because ‘including each firm's fixed effect as part of its target leverage induces a mechanical relation between leverage adjustments and the estimated fixed effect’ (Parsons and Titman 2009). The importance of this bias for capital structure research is compelling if it also shows up in a simulated leverage sample in which there is no active target behavior, and thus there is no issue of ‘mis-measurement’ of the target. We consider this now. In Section III.D, we show that a similar problem arises in models of the debt–equity choice.

Panel A of Table 4 reports the estimation of the target adjustment model for the actual data, S(actual data). Independent variables include the lagged leverage ratio and the firm-specific control variables in equation (6). However, to save space, we only report the coefficients on the lagged leverage ratio in the table. We estimate the model using OLS in column (1) and with firm-fixed effects in column (2). The coefficient on the lagged leverage ratio increase from 0.889 in column (1) to 0.779 in column (2), implying a much faster speed of adjustment if the model is estimated with firm-fixed effects. This finding is consistent with Flannery and Rangan (2006). However, as the first two columns in panel B show, we obtain a similar order-of-magnitude increase in the ‘speed of adjustment’ for the simulation sample S(p=empirical frequency, actual deficit) when we introduce firm-fixed effects. Of course, the latter effect is mechanical – it is not the case that in the simulation data, there is an active adjustment going on at the firm level to some target and we are simply mis-measuring the target.²³

Table 4.   Target adjustment model, firm-fixed effects, and look-ahead bias

Dependent variable (D/A)t	(1)	(2)	(3)	(4)	(5)	(6)
	OLS	Firm-fixed effects	OLS	OLS	OLS	Firm+Period fixed effects
Actual data are collected from Industrial Compustat and CRSP for the years 1971–2008. Section II discusses how the simulated data S(p=empirical frequency, actual deficit) is generated. The dependent variable is book leverage (D/A). Independent variables include the lagged leverage ratio and the market-to-book asset ratio (M/B), profitability (EBITDA/A), firm size (Size), tangibility of assets (PPE/A), research and development expense to sales ratio (R&D/S), a dummy variable (RDD) that takes the value of 1 when R&D is missing in Compustat and 0 otherwise, and annual stock return (StkRtn). is the average (actual or simulated) leverage ratio throughout the sample period. is the past average (actual or simulated) leverage ratio computed between the first year the firm entering the sample and t−1. is the future average (actual or simulated) leverage ratio computed from the current year t to the firm's last year (N) in our sample. For S(actual data), t-statistics in parentheses are calculated from the Huber–White sandwich heteroskedasticity consistent errors, which are corrected for correlation across observations for a given firm. Coefficients significant at the 10%, 5%, and 1% levels are, respectively, marked with ^*, ^**, and ^***. For the simulated sample, the reported parameter estimates are the average coefficients obtained from 500 replications of the simulation. 95% confidence intervals are included in square brackets and coefficients are marked with ‘a’ if 95% conference intervals do not span zero. In all columns, intercepts, year dummies, and firm-specific control variables are included but not reported.
Panel A: S(actual data)
(D/A)t−1	0.889^***	0.779^***	0.779^***	0.870^***	0.715^***	0.682^***
	(329.0)	(174.5)	(180.9)	(229.9)	(171.3)	(118.7)
			0.218^***
			(41.0)
				0.035^***
				(8.4)
					0.302^***
					(66.4)
R^2/N	0.82/46,956	0.83/46,956	0.83/46,956	0.82/46,956	0.85/46,956	0.85/46,956
Panel B: S(p=empirical frequency, actual deficit)
(D/A)t−1	0.921^a	0.828^a	0.826^a	0.925^a	0.750^a	0.742^a
	[0.916, 0.925]	[0.821, 0.834]	[0.819, 0.833]	[0.918, 0.933]	[0.743, 0.757]	[0.732, 0.752]
			0.185^a
			[0.178,0.193]
				−0.009^a
				[−0.016,−0.001]
					0.258^a
					[0.252,0.264]
R^2/N	0.84/46,956	0.85/46,956	0.86/46,956	0.84/46,956	0.87/46,956	0.87/46,956

In the next three columns, we include three firm-specific means (rather than fixed effects) to ‘improve’ the target estimate. is the average leverage ratio throughout the sample period for each firm. is the past average leverage ratio computed between the first year the firm entering our sample and t−1. is the future average leverage ratio computed from the current year t to the firm's last year (N) in our sample. Of course, the estimates in columns (3) and (5) suffer from the look-ahead bias. The inclusion of in column (3) is similar to a firm-fixed effect because it utilizes all N periods of observations on the dependent variable at every point of time, and not surprisingly, it gives almost the same estimate as in column (2) for both samples. However, inclusion of in column (5) aggravates the look-ahead bias and the estimated speeds of adjustment are much higher, possibly because it is effectively measured over a smaller N. As expected, in column (4) has no effect on the estimated speed of adjustment and is itself economically insignificant for the simulation sample. Interestingly, for the actual sample, while this past average leverage ratio is statistically significant, it is economically small compared with the coefficient on lagged leverage, and like the simulation sample, its inclusion has a small effect on the estimated adjustment speed. It is surprising that the past average debt ratio has such low information content regarding the future target to which leverage is supposed to adjust.

Finally, in column (6), we show how the bias in estimated speeds of adjustment can be exacerbated when samples are split around specific events, such as CEO turnover. Suppose that the researcher is interested in examining whether CEO ‘style’ affects capital structure policy. Following Bertrand and Schoar (2003), one approach might be to introduce CEO fixed effects and test whether this leads to a significant increase in the estimated speed of leverage adjustment and R² even after controlling for firm-fixed effects. However, a CEO turnover effectively breaks the sample period of a firm into two sub-periods; thus, adding CEO fixed effects essentially shortens the average estimation period for each firm-CEO pair (i.e., aggravates the ‘small N’ problem). This could result in a higher estimated adjustment speed and R².

In column (6) of Table 4, for the actual data and the simulated sample, we divide the time line for each firm into two sub-periods. Specifically, for a firm with the number of firm-years equal to N in our sample, we randomly select a breaking point between [0.3N, 0.7N] and break all observations of a firm into before-break and after-break sub-periods.²⁴ The breaking points are designed to mimic the CEO changes. We then define a firm-period dummy variable for each firm each sub-period, and estimate equation (6) using the firm-period fixed effects. Compared with column (2), column (6) of Table 4 suggests that higher R² and higher estimated speed of adjustment are achieved if we include the firm-period fixed effects.

We revisit the look-ahead bias in Section III.D in the context of probit models of the debt/equity choice.

D. Probit and multinomial logit models of debt/equity choices

i. Probit models

Target behavior implies that the probability of debt and equity issuance or repurchase should be related in a particular way to the firm's debt ratio and the debt ratio target. In particular, if the firm's debt ratio is above an estimated target, then the firm should be more likely to issue equity as opposed to debt, and more likely to repurchase debt as opposed to equity. The opposite should be the case if the debt ratio is below target. As our simulation samples are generated under the assumption that conditional on the deficit being positive (negative), the firms have a fixed probability of issuing debt (repurchasing debt), the issuance/repurchase decisions in the simulated samples should have no such characteristic. Nor should the issuance/repurchase decisions in the simulated samples be related to any firm characteristics, whereas in the actual data, variables such as the market-to-book ratio (reflecting equity market conditions) or profitability (reflecting the need for tax shields) could affect issuance or repurchase decisions. Hence, probit models of the debt versus equity choice would seem to be an ideal way to distinguish target behavior from random financing.

We follow the approach outlined in Hovakimian et al. (2001), but deviate from this paper to show that how one estimates the target can have a substantial effect on the inferences regarding target behavior.²⁵ As in Hovakimian et al. (2001), our estimation procedure involves two stages. In the first stage, we estimate four proxies for the target leverage ratio by running the following four regressions

• (7)

• (8)

• (9)

• (10)

In the above four models, the dependent variable is the leverage ratio, I_i,t represents the two-digit SIC industry for firm i (there is a time subscript because a firm's industry can change over time in our sample), and f_i and v_t represent firm-fixed effects and year-fixed effects, respectively. X is the same set of firm-specific control variables as in equation (6); however, we exclude lagged leverage. The proxies for the target leverage ratio are the fitted values of the above four regression, denoted as T_OLS, T_{Firm−Fixed Effects}, T_Past, and T_Future, respectively.

The purpose of this first-stage regression is to provide an estimate of each firm's optimal or target leverage ratio.²⁶ In the second-stage model, we examine how firms that raise external funds choose the form of financing. The firm's choices of the form of financing are modeled using two probit models as follows:

• (11)

and

• (12)

where Pr stands for the probability of debt being issued in equation (11) and the probability of debt being retired in equation (12), and F denotes the normal cumulative distribution function. In equation (11), Disu_i,t takes a value of 1 if the net debt issued by company i in fiscal year t constitutes more than 5% of its total assets, and 0 if the net equity issued exceeds 5% of its total assets.²⁷ Only issue years in which the company issues net debt or equity exceeding 5% of its book value of assets are considered; years in which both are issued or the issue falls below the 5% cutoff are not included in the model. In equation (12), Dbuy_i,t takes a value of one if the net debt retired by company i in fiscal year t constitutes more than 5% of its total assets, and 0 if the net equity repurchased exceeds 5% of its total assets. Years in which both debt and equity are repurchased or the size of a repurchase is below the 5% cutoff are not included in the model.

The key variable of interest is the deviation from the target leverage ratio (Devi), which is measured as the difference between the leverage ratio (lagged 1 year) and the target debt ratio (T_i,t) which is the predicted value from one of the specifications for the target leverage in equations (7)–(10):

• (13)

Trade-off theories of capital structure imply that firms have target debt ratios. If maintaining a target debt ratio is important, then firms should choose the form of financing that offsets the deviation from their target. Thus, the coefficient on the deviation from the target should be negative in probit models of issuance and positive in probit models of repurchase.

The control variables Z are typically included to capture non-target-related reasons for leverage adjustment, but could include some of the variables in X.²⁸ In our specifications, we do not take a stand on which variables represent target behavior and which represent non-target-related behavior, and the sets X and Z are the same, except for the inclusion of industry or firm dummies in equations (7) and (8), respectively, and the firm-specific mean leverage ratios in equations (9) and (10).²⁹ Thus, our deviation variables could equivalently be interpreted as deviations from these industry or firm-specific averages.

Table 5 presents the results for the actual data. We report the marginal effect, which measures the effect of a one unit change in the continuous explanatory variables (a change from 0 to 1 for dummy explanatory variables) on the dependent variable. The coefficient of the deviation from the target variable has a sign consistent with target behavior in all specifications. However, in the issuance model in panel A, the estimated marginal effect is four times (five times) as large in magnitude when the firm-fixed effect (the firm's future average debt ratio) is included in the target estimation as when it is estimated using OLS with industry dummies in column (1). We also obtain a higher estimate of the marginal effect of deviation in the repurchase model in panel B when fixed effects or the future average debt ratio is incorporated in the target. However, here, the difference is not as large.

Table 5.   Deviation from target and debt–equity choice (actual data and probit models)

Panel A: Issuance decisions (dependent variable: Disu)
	T=TOLS	T=TFirm−Fixed Effects	T=TPast	T=TFuture
	(1)	(2)	(3)	(4)
(D/A)t−1−T	−0.152^***	−0.603^***	−0.255^***	−0.760^***
	(−5.6)	(−18.7)	(−7.6)	(−24.5)
M/B	−0.041^***	−0.039^***	−0.040^***	−0.040^***
	(−11.3)	(−10.9)	(−11.1)	(−10.6)
EBITDA/A	0.372^***	0.380^***	0.370^***	0.395^***
	(7.3)	(8.4)	(7.6)	(8.6)
Size	0.016^***	0.015^***	0.016^***	0.014^***
	(7.9)	(7.7)	(8.0)	(7.0)
PPE/A	−0.100^***	−0.098^***	−0.102^***	−0.095^***
	(−4.9)	(−4.9)	(−4.9)	(−4.6)
R&D/S	−0.099^*	−0.089^*	−0.096^*	−0.103^*
	(−1.8)	(−1.8)	(−1.8)	(−1.8)
RDD	−0.007	−0.007	−0.007	−0.009
	(−0.8)	(−0.8)	(−0.8)	(−1.0)
StkRtn	−0.052^***	−0.045^***	−0.051^***	−0.041^***
	(−10.2)	(−8.8)	(−9.9)	(−8.2)
Pesudo-R^2/N	0.06/18,147	0.10/18,147	0.07/18,147	0.13/18,147

Panel B: Repurchase decisions (dependent variable: Dbuy)
	T=TOLS	T=TFirm−Fixed Effects	T=TPast	T=TFuture
	(5)	(6)	(7)	(8)
Actual data are collected from Industrial Compustat and CRSP for the years 1971–2008. The dependent variable, Disu (Dbuy), takes a value of 1 if conditional on issuance (repurchase), debt is issued (repurchased), and 0 if equity is issued (repurchased). Independent variables include the deviation from target, the market-to-book asset ratio (M/B), profitability (EBITDA/A), firm size (Size) measured as the log value of total assets, tangibility of assets (PPE/A), research and development expense to sales ratio (R&D/S), a dummy variable (RDD) that takes the value of 1 when R&D is missing in Compustat and 0 otherwise, and annual stock return (StkRtn) obtained by compounding monthly stock returns over the entire fiscal year. The proxies for the target leverage ratio, TOLS, TFirm−Fixed Effects, TPast, and TFuture, are the fitted values of four regression reported in Appendix B. z-statistics in parentheses are calculated from the Huber–White sandwich heteroskedasticity consistent errors, which are corrected for correlation across observations for a given firm. Coefficients significant at the 10%, 5%, and 1% levels are, respectively, marked with ^*, ^**, and ^***. The reported coefficients represent the marginal effects that describe the change in the probability of debt issuance or repurchase for an infinitesimal change in each continuous independent variable and the discrete change in the probability for dummy variables.
(D/A)t−1−T	0.941^***	1.309^***	1.050^***	1.498^***
	(24.1)	(26.8)	(21.7)	(30.5)
M/B	−0.042^***	−0.044^***	−0.043^***	−0.041^***
	(−8.4)	(−9.2)	(−7.4)	(−10.0)
EBITDA/A	−0.589^***	−0.596^***	−0.600^***	−0.566^***
	(−6.8)	(−7.2)	(−7.0)	(−7.5)
Size	−0.032^***	−0.032^***	−0.034^***	−0.026^***
	(−12.0)	(−11.8)	(−12.4)	(−10.2)
PPE/A	−0.032	−0.021	−0.020	−0.010
	(−1.1)	(−0.7)	(−0.7)	(−0.4)
R&D/S	−0.025	−0.038	−0.034	−0.027
	(−0.9)	(−1.6)	(−1.5)	(−1.2)
RDD	0.023^**	0.020^*	0.022^*	0.015
	(2.0)	(1.8)	(1.8)	(1.4)
StkRtn	0.023^***	0.022^**	0.023^***	0.014^*
	(2.6)	(2.5)	(2.6)	(1.8)
Pesudo-R^2/N	0.20/9138	0.22/9138	0.18/9138	0.29/9138

We now turn to the simulated data. We focus on the sample S(p=0.5, actual deficit) in Table 6. As our simulations assume that the probabilities of debt or equity issuance (repurchase) conditional on the deficit being positive (negative) are exogenous, neither the deviation of leverage from an estimated target nor firm characteristics should have any explanatory power in probit models of debt versus equity choice. Surprisingly, however, in column (1) (panel A – issuance model) and column (4) (panel B – repurchase model), the deviation from target variable is significant, as are some firm-specific variables. What accounts for this result?

Table 6.   Deviation from target and debt–equity choice (S(p=0.5, actual deficit) and probit models)

Panel A: Issuance decisions (dependent variable: Disu)
	Corners cases are not corrected	Corners cases are corrected	Corners cases are corrected
	(1)	(2)	(3)
	T=TOLS	T=TOLS	T=TFirm−Fixed Effects
(D/A)t−1−T	−0.126^a	−0.008	−0.398^a
	[−0.162, −0.090]	[−0.042, 0.026]	[−0.451, −0.346]
M/B	−0.006^a	0.000	0.000
	[−0.012, −0.001]	[−0.004, 0.005]	[−0.004, 0.006]
EBITDA/A	0.252^a	0.005	0.001
	[0.205, 0.299]	[−0.044, 0.055]	[−0.049, 0.052]
Size	0.002	0.000	0.000
	[−0.000, 0.005]	[−0.003, 0.003]	[−0.003, 0.003]
PPE/A	0.012	0.005	0.003
	[−0.022, 0.047]	[−0.030, 0.040]	[−0.032, 0.038]
R&D/S	−0.025^a	0.000	0.002
	[−0.043, −0.007]	[−0.016, 0.017]	[−0.015, 0.020]
RDD	0.000	0.000	0.000
	[−0.012, 0.013]	[−0.013, 0.012]	[−0.012, 0.013]
StkRtn	0.005	0.000	0.001
	[−0.007, 0.019]	[−0.015, 0.013]	[−0.011, 0.015]
Pesudo-R^2/N	0.01/20,282	0.00/20,309	0.01/20,399

Panel B: Repurchase decisions (dependent variable Dbuy)
	Corners cases are not corrected	Corners cases are corrected	Corners cases are corrected
	(4)	(5)	(6)
	T=TOLS	T=TOLS	T=TFirm−Fixed Effects
Section II discusses how the simulated data, S(p=0.5, actual deficit), is generated. The dependent variable, Disu (Dbuy), takes a value of 1 if conditional on issuance (repurchase), debt is issued (repurchased), and 0 if equity is issued (repurchased). Independent variables include the deviation from target, the market-to-book asset ratio (M/B), profitability (EBITDA/A), firm size (Size) measured as the log value of total assets, tangibility of assets (PPE/A), research and development expense to sales ratio (R&D/S), a dummy variable (RDD) that takes the value of 1 when R&D is missing in Compustat and 0 otherwise, and annual stock return (StkRtn) obtained by compounding monthly stock returns over the entire fiscal year. The proxy for the target leverage ratio TOLS is the fitted values of the regression of the simulated leverage ratio on firm-specific control variables, industry dummies, and year dummies. TFirm−Fixed Effects is estimated with firm-fixed effects. The reported parameter estimates are the average coefficients obtained from 500 replications of the simulation, which represent the marginal effects which describe the change in the probability of debt issuance or repurchase for an infinitesimal change in each continuous independent variable and the discrete change in the probability for dummy variables. 95% confidence intervals are included in square brackets and coefficients are marked with ‘a’ if 95% conference intervals do not span zero.
(D/A)t−1−T	0.547^a	0.024	0.268^a
	[0.499, 0.594]	[−0.018, 0.067]	[0.203, 0.334]
M/B	0.008	0.000	−0.001
	[−0.003, 0.020]	[−0.011, 0.011]	[−0.013, 0.009]
EBITDA/A	−0.379^a	0.004	0.028
	[−0.491, −0.267]	[−0.092, 0.100]	[−0.069, 0.126]
Size	0.000	0.000	0.000
	[−0.004, 0.006]	[−0.006, 0.005]	[−0.004, 0.006]
PPE/A	0.015	0.001	0.000
	[−0.025, 0.056]	[−0.067, 0.069]	[−0.070, 0.069]
R&D/S	0.022	0.001	−0.001
	[−0.021, 0.065]	[−0.025, 0.028]	[−0.028, 0.025]
RDD	0.002	0.000	0.001
	[−0.028, 0.033]	[−0.025, 0.026]	[−0.025, 0.028]
StkRtn	0.001	0.000	−0.002
	[−0.012, 0.014]	[−0.020, 0.019]	[−0.022, 0.017]
Pesudo-R^2/N	0.07/6957	0.00/7165	0.01/7165

To ensure that the simulated leverage ratios are bounded between 0 and 1, in a small number of cases (<3% of all issue and repurchase years) we deviate from random financing when the debt ratio is near the corner (i.e., close to 0 or 1). In particular, when the debt ratio is close to 1 and the firm has low book equity and negative retained earnings, we force an equity issuance even though the random outcome calls for debt issuance. Similarly, when the debt ratio is close to 0, the firm has a financing surplus, and a debt repurchase is called for by the coin toss, there may not be enough debt to repurchase. In that case, we assume an equity issuance. Thus, we deviate from the 50:50 random rule near the boundaries and the debt ratio is more likely to move toward the target in these regions. Only roughly 3% of the observations are affected.³⁰ Nonetheless, columns (1) and (4) in Table 6 show even such an apparently innocuous deviation from the random outcome can have a major impact on probit models.

These simulations illustrate that inferences based on probit models can be extremely fragile, and can be sensitive to the behavior of a very small fraction of ‘unusual’ firms. For example, in the actual data, a small percentage of financially distressed firms may deviate from non-target behavior when they are close to the boundary and issue equity or repurchase debt. It is difficult to rule out the possibility that such cases account for the significant coefficients for the deviation variable in columns (1) and (4) of Table 5, which are comparable with those in Table 6, and suggest target behavior. Yet, this would be the wrong inference because a majority of the firms may be following non-target behavior most of the time away from the boundaries.

We now return to the look-ahead bias. To confirm that the corner cases are responsible for the significant coefficients in our simulations, we mechanically remove the corner cases by assuming that the issuance decision at the corner does conform to the coin toss, and we allow the debt ratio to hit the boundary. Columns (2) and (5) indicate that the deviation from target and firm-specific variables are no longer significant, which is exactly what one would expect for random financing. However, in columns (3) and (6) we use the regression targets estimated with firm-fixed effects. Once again, the deviation from target is highly significantly even after the corner cases are corrected. This is nothing but a manifestation of the look-ahead bias discussed in Section III.C.

ii. Multinomial logit models

The above results show that probit models of the debt–equity choice can be highly fragile and sensitive to the behavior of a small number of unusual firms. However, a bigger problem arises if one uses multinomial models that simultaneously model issuance and repurchase decisions (e.g., Hovakimian 2004; Chen and Zhao 2006). To illustrate the nature of the problem, we work with a simulation sample in which the corner cases are all removed, so that there is no deviation from the random outcome. As we saw in columns (2) and (4) of Table 6, for this sample, when the target is estimated in a way that avoids the look-ahead bias, probit models do not result in any significant coefficients for the explanatory variables, which is consistent with the fact that conditional on the deficit being positive (negative), the probability of debt issuance (repurchase) is fixed. However, multinomial logit models, which try to simultaneously model debt and equity issuance and repurchase decisions, are not conditioned on the deficit being positive or negative. Therefore, variables that are correlated with the size of the deficit will affect the probability of issuance or repurchase of a particular security. The problem is exacerbated by the fact that not only the sign, but also the size of the deficit matters – since only issues or repurchases that exceed a certain percentage of total assets in absolute value are typically considered as issuance or repurchase activities.

Table 7 shows the results for a multinomial regression for both actual and the simulated data (specifically, the S(p=0.5, actual deficit) sample). Five categories of transactions are considered: (1) no transaction (i.e., transaction size below 5% of book value of assets in absolute value), (2) equity issue, (3) debt issue, (4) equity repurchase, and (5) debt retirement.³¹ We use the first category as the base category, i.e., probabilities are estimated for the other choices relative to this category, and assume financing decisions can be described as

• (14)

where P_i,t,k denotes the probability of firm i in year t falling into the kth financing category (k=2, 3, 4, 5). Devi, defined in equation (13), is the deviation from the OLS target (T_OLS). Z is the same set of control variables as in equations (11) and (12).

Table 7.   Multinomial logistic regression (with corner cases corrected in S(p=0.5, actual deficit))

Dependent variable: Pi,t,k	Equity issue	Debt issue	Equity repurchase	Debt reduction
Actual data are collected from Industrial Compustat and CRSP for the years 1971–2008. Section II describes how the simulated samples S(p=0.5, actual deficit) is generated. In simulation, we correct the corner cases where a ‘coin toss’ could potentially cause the issuance or repurchase decision to deviation from that dictated by the outcome of the random draw. The table presents the results of a multinomial regression for both the actual data and the S(p=0.5, actual deficit) sample. Five categories of transactions are considered: (1) no transaction (i.e., transaction size below 5% of book value of assets), (2) equity issue, (3) debt issue, (4) equity repurchase, and (5) debt reduction. Debt (equity) issues/repurchases are identified if firms' net debt (equity) issued/repurchased divided by total assets is >5%. The first category is used as the base category, i.e., probabilities are estimated for the other choices relative to this category. Financing decisions can be described as , where Pi,t,k denotes the probability of firm i in year t falling into the kth financing category (k=2, 3, 4, 5). Devi is the deviation from target. The target leverage ratio is the predicted value from the regression reported in column (1) of Appendix B. For S(actual data), z-statistics are in parentheses and coefficients significant at the 10%, 5%, and 1% levels are, respectively, marked with ^*, ^**, and ^***. For simulated samples, the reported parameter estimates are the average coefficients obtained from 500 replications of the simulation. 95% confidence intervals are included in square brackets.
Panel A: S(actual data)
(D/A)t−1−TOLS	0.011	1.466^***	−0.875^***	4.471^***
	(0.1)	(14.7)	(−3.7)	(38.1)
M/B	0.295^***	0.195^***	0.274^***	0.000
	(11.7)	(10.2)	(10.5)	(0.0)
EBITDA/A	−1.195^***	−0.344^**	0.681^**	−2.760^***
	(−3.9)	(−2.2)	(2.0)	(−15.8)
Size	−0.097^***	−0.030^***	0.094^***	−0.100^***
	(−6.7)	(−4.0)	(6.1)	(−10.8)
PPE/A	0.410^***	−0.165^**	−0.909^***	−0.767^***
	(2.6)	(−2.0)	(−5.1)	(−7.4)
R&D/S	0.060	−0.101^*	−0.089	−0.152^***
	(1.3)	(−1.9)	(−1.0)	(−2.6)
RDD	0.068	0.094^***	0.087	0.138^***
	(1.1)	(3.0)	(1.3)	(3.5)
StkRtn	0.507^***	0.350^***	−0.077	0.064^**
	(13.7)	(15.7)	(−1.5)	(2.0)
Pseudo R^2	0.05
Observations	46,956
Panel B: S(p=0.5, actual deficit)
(D/A)t−1−TOLS	0.675^a	0.644^a	1.32^a	1.44^a
	[0.584, 0.766]	[0.519, 0.768]	[1.17, 1.48]	[1.27, 1.60]
M/B	0.198^a	0.199^a	−0.031^a	−0.032^a
	[0.188, 0.208]	[0.187, 0.211]	[−0.063, 0.001]	[−0.063, −0.001]
EBITDA/A	−0.49^a	−0.459^a	−2.46^a	−2.46^a
	[−0.632, −0.349]	[−0.614, −0.305]	[−2.65, −2.28]	[−2.62, −2.30]
Size	−0.034^a	−0.034^a	−0.068^a	−0.069^a
	[−0.041, −0.028]	[−0.041, 0−.027]	[−0.081, −0.054]	[−0.080, −0.057]
PPE/A	0.082^a	0.103^a	−1.03^a	−1.02^a
	[0.008, 0.156]	[0.028, 0.178]	[−1.18, −0.887]	[−1.16, −0.890]
R&D/S	−0.015	−0.013	−0.029	−0.022
	[−0.060, 0.030]	[−0.072, 0.045]	[−0.121, 0.062]	[−0.118, 0.073]
RDD	0.048^a	0.046^a	0.141^a	0.143^a
	[0.021, 0.074]	[0.020, 0.072]	[0.090, 0.193]	[0.089, 0.196]
StkRtn	0.435^a	0.432^a	−0.124^a	−0.127^a
	[0.409, 0.460]	[0.404, 0.461]	[−0.180, −0.067]	[−0.182, −0.071]
Pseudo R^2	0.02
Observations	45,035

Panel A of Table 7 reveals that in the actual data, firms with high debt ratio deviation are less likely to repurchase equity and more likely to repurchase debt (relatively to no transaction). This is consistent with target behavior. However, they are more likely to issue debt, which is inconsistent with target behavior, and there is no significant effect on the likelihood of equity issuance. These results are very similar to those in Hovakimian (2004). In the simulated data (panel B of Table 7), remarkably, many variables are significant, even though the corner cases have been removed for this sample. In fact, the firms with higher leverage deviation are now significantly more likely to issue equity, consistent with target behavior.

It is not difficult to see what is going on in panel B. Note that the coefficients in the first two columns of panel B (corresponding to the issuance decisions) are almost identical for every explanatory variable, and the same is true of the coefficients in the last two columns (corresponding to the repurchase decisions). Since ‘no transactions’ is the base category, variables that increase the likelihood of a positive deficit relative to no transaction will have positive significant effects in the issuance columns. Similarly, variables that increase the likelihood of a negative deficit relative to no transaction will have positive significant effects in the repurchase columns. This explains why we obtain almost identical coefficients for both types of issuance, and similarly for both types of repurchase. Interestingly, a number of variables increase the likelihood of both a positive and a negative deficit relative to no transactions. In particular, the deviation from target variable is associated with both more issuance and repurchase activities of both types of securities, indicating that it is positive correlated with the absolute size of the deficit. Note that for the panel B sample, there is no real target – the estimated ‘target’ is the predicted value of the simulated debt ratio from a leverage regression. One possible explanation for the positive sign of the deviation variable in both issuance and repurchase regressions is that the deficit is persistent:³² firms are further away from the predicted leverage when the magnitude of the deficit in the previous period is high; however, since the magnitude of deficit this period is then also likely to be high, we obtain a positive correlation between the deviation and the magnitude of the deficit.

For the actual sample, we also observe a similar feature in the debt and equity issue regressions. Most variables have similar signs in these two regressions. This suggests that issuance activity is largely affected by the size of the deficit, and less by the sign of the deviation from target. In the repurchase regressions, we see some departures from this pattern. For example, the market-to-book ratio has a positive effect on equity repurchase, but is insignificant in debt retirement regression; profitability has a positive effect on equity repurchases but affects the probability of debt repurchases negatively. Hovakimian (2004) also notes similar results for repurchases. Overall, our findings suggest that we need to interpret the results of multinomial logit regressions with caution because of the confounding effect of control variables on the deficit.

E. Market timing

Whether or not market-timing behavior has a persistent effect on observed capital structure is a controversial issue in the literature. Baker and Wurgler (2002) (BW hereafter) show that a ‘past external finance-weighted’ market-to-book ratio (a weighted average of a firm's past market-to-book ratios which takes a higher value if it raised external finance (debt or equity) when its market-to-book ratio was high) has a negative effect on current debt ratios. The idea behind this measure is that if firms had issued equity in the past to finance the deficit when the market-to-book was high, then this measure should be negatively related to today's debt ratio if the firms do not rebalance quickly.

There is controversy, however, regarding what the BW variable really captures. Leary and Roberts (2005) present non-parametric analysis that suggests that the BW variable reflects the historical average market-to-book ratio (a proxy for growth opportunities) rather than market timing. Kayhan and Titman (2007) propose a decomposition of BW's measure into a term that reflects the covariance between the past market-to-book and the past financing deficit, and a term that reflects the past (unweighted) average market-to-book ratio. They show that the latter term drives BW's results.³³

Here, we focus on the Kayhan and Titman (2007) decomposition of BW's market-timing variable. The BW ‘external finance weighted-average’ market-to-book ratio is defined as follows:

• (15)

where DEF_s denote external financing (or equivalently, financing deficit) at time s and the summations are taken starting at the first year firms enter our sample. Kayhan and Titman (2007) propose a decomposition of the BW timing measure that incorporates the average past market-to-book ratio (a measure of growth opportunities) and the covariance between issuance activity and the market-to-book ratio (a measure of timing activity). They show that

• 

where and denote, respectively, the past average deficit and average market-to-book ratio.³⁴ Only the first term (KTCov) captures BW's timing intuition. The second term (KTMB) is simply the historical average market-to-book which proxies for investment opportunities.³⁵

We generate simulation samples to address two questions: (a) can the KTCov variable reflect market-timing behavior? (b) does a significant negative coefficient for this variable in debt ratio regressions reject the null hypothesis that there is no market-timing behavior? Our simulation results suggest that the answer to the first question is in the affirmative: the KTCov variable has a negative significant coefficient in leverage ratio regressions in the presence of market-timing behavior, and this coefficient becomes larger in magnitude as the likelihood of market-timing behavior increases. However, we find that even when there is no market timing, if firms are following vigorous target behavior, the coefficient of KTCov remains significantly negative. Thus, the answer to the second question is in the negative. It is important to note, however, that these conclusions are subject to two important qualifications – first, the way in which market-timing behavior is introduced in our simulations, and second, the sample. In other words, these are not general propositions, but illustrative of the difficulty of drawing inferences based on measures that otherwise appear intuitive and well motivated.

In Table 8, we estimate the following model:

• (16)

Table 8.   Market timing and capital structure

Dependent variable (D/A)t	(1)	(2)	(3)
	S(actual data)	S(p=0.5, actual deficit)	S(market timing, p=0.5, actual deficit)
Actual data are collected from Industrial Compustat and CRSP for the years 1971–2008. Sections II and III describe how the simulated samples are generated. The dependent variable is the book leverage (D/A). The control variables are firm characteristics that are lagged 1 year and defined in Table 2. KTCov is the covariance between issuance activity and the market-to-book ratio. KTMB is the historical average market-to-book ratio. denotes the past average deficit. The constant term is included in the regression but not reported. The reported coefficients are estimated using Fama and MacBeth (1973) approach with t-statistics reported in parentheses. Coefficients significant at the 10%, 5%, and 1% levels are, respectively, marked with ^*, ^**, and ^***. For simulated samples, the reported parameter estimates are the average coefficients obtained from 500 replications of the simulation. 95% confidence intervals are included in square brackets and coefficients are marked with ‘a’ if 95% conference intervals do not span zero.
KTMB	−0.039^***	−0.024^a	−0.014^a
	(−19.3)	[−0.036, −0.012]	[−0.023, −0.006]
KTCov	−0.013^***	0.000	−0.049^a
	(−7.5)	[−0.005, 0.006]	[−0.061, −0.037]
1/	−0.002	−0.001	−0.039^a
	(−0.7)	[−0.003, 0.000]	[−0.049, −0.030]
M/B	0.004	0.007^a	−0.004
	(1.1)	[0.000, 0.014]	[−0.009, 0.000]
EBITDA/A	−0.360^***	−0.648^a	−0.62^a
	(−8.1)	[−0.708, −0.588]	[−0.653, −0.586]
Size	0.028^***	0.006^a	0.000
	(9.5)	[0.002, 0.011]	[−0.001, 0.002]
PPE/A	−0.066^***	−0.008	−0.02
	(−6.8)	[−0.041, 0.024]	[−0.042, 0.001]
R&D/S	−0.243^***	0.028	0.034
	(−4.1)	[−0.038, 0.094]	[−0.015, 0.085]
RDD	0.008^*	0.012	0.007
	(2.0)	[−0.001, 0.027]	[−0.001, 0.015]
StkRtn	−0.010^*	0.011^a	−0.021^a
	(−1.9)	[0.004, 0.017]	[−0.025, −0.016]
R^2/N	0.24/46,675	0.11/32,532	0.14/44,712

Note that we control for the inverse of the average financing deficit, because the negative effect of KTCov could be driven by the denominator. The first column presents results on the actual sample, the second on the sample S(p=0.5, actual deficit), and the third on a new ‘market timing’ simulation sample S(market timing, p=0.5, actual deficit). This latter sample is generated as follows. If the firm's stock return in a year is above the 75th percentile of its own stock return distribution, we assume this signifies ‘good times’ for the firm: the firm then issues equity with probability 1 if the actual deficit is positive, and repurchases debt with probability 1 if the actual deficit is negative. If the firm-specific stock return is below the 25th percentile, we assume the firm issues debt with probability 1 if the actual deficit is positive, and repurchases equity if the actual deficit is negative. When stock returns are not extreme, we assume firms follow random financing (p=0.5).

For the actual sample, we note that both KTMB and KTCov have significant negative coefficients, whereas the market-to-book itself has an insignificant positive coefficient. The coefficient of KTMB remains negative and significant in column (2) where the sample is generated under the assumption of random financing. KTCov, however, is insignificant. KTCov becomes negative and significant in column (3), when market-timing behavior is introduced. Note that the only difference between the samples in columns (2) and (3) is that in the latter sample, the firm has an equity (debt) bias when stock returns are in the upper (lower) 25th percentile. The KTCov variable is sensitive to this change, consistent with BW's and KT's intuition.

Unfortunately, this does not mean that we can necessarily associate market-timing behavior with a negative significant coefficient of KTCov. In Table 9, we change our simulation slightly. The simulation samples are denoted S(market timing(π), target behavior, actual deficit). Here, the default financing is target behavior.³⁶ If stock returns are in the upper or lower 25th percentile, the firm engages in the market-timing behavior described in the previous paragraph with probability π. With probability 1−π, it engages in target behavior (i.e., moves in the direction of the target with probability 1). If the stock returns are not in the upper or lower 25th percentile, the firm again follows target behavior. By allowing π to change, we change the intensity of timing behavior. The results presented in Table 9 show that as market-timing behavior becomes more intense, the coefficient of KTCov becomes more negative. However, even for pure target behavior (π=0), the coefficient of KTCov is significantly negative. Thus, it appears that at least for our sample and the particular type of timing behavior we assume, it is possible for both components of BWMB (KTMB and KTCov) to be negative when firms follow target behavior aggressively.

Table 9.   The likelihood of market timing and coefficients of timing measures

	Coefficients and 95% confidence intervals of
	(1)	(2)
	KTMB	KTCov
The simulation samples, S(market timing(π), target behavior, actual deficit), have the default financing as target behavior. If stock returns are in the upper or lower 25th percentile, the firm engages in the market timing behavior described in Section III with probability π. With probability 1−π, it engages in target behavior (i.e., moves in the direction of the target with probability 1). If the stock returns are not in the upper or lower 25th percentile, the firm again follows target behavior. The dependent variable is the book leverage (D/A). KTCov is the covariance between issuance activity and the market-to-book ratio. KTMB is the historical average market-to-book ratio. We include intercepts, year dummies, and the same control variables as in Table 8, but their coefficients are not reported. We only report coefficients of KTCov and KTMB for different values of π. The reported parameter estimates are the average coefficients obtained from 500 replications of the simulation. 95% confidence intervals are included in square brackets and coefficients are marked with ‘a’ if 95% conference intervals do not span zero.
π=0	−0.014^a	−0.012^a
	[−0.014, −0.014]	[−0.012, −0.012]
π=0.1	−0.014^a	−0.014^a
	[−0.017, −0.012]	[−0.019, −0.009]
π=0.25	−0.014^a	−0.016^a
	[−0.017, −0.011]	[−0.025, −0.008]
π=0.5	−0.014^a	−0.024^a
	[−0.018, −0.010]	[−0.032, −0.016]
π=0.75	−0.013^a	−0.035^a
	[−0.017, −0.009]	[−0.043, −0.027]
π=0.9	−0.013^a	−0.041^a
	[−0.016, −0.009]	[−0.047, −0.035]
π=1	−0.012^a	−0.047^a
	[−0.012, −0.012]	[−0.047, −0.047]

IV. CONCLUSION

Empirical capital structure research is challenging because the data generating processes are non-standard and standard approaches can lead to incorrect inferences. A number of recent papers are relying on Monte Carlo simulations to learn where standard approaches fall short, and how the approaches can be modified. In this paper, we try to extend this agenda of research. We consider five specific examples where our simulation methodology sheds new light on how inferences can be improved, or flawed inferences can be avoided. While we do not pursue this agenda here, we believe that much of empirical corporate finance research could benefit from simulation approaches.

Footnotes

1. 1 Excellent recent survey papers are Parsons and Titman (2009) and Graham and Leary (2011).

2. 2 In fact, there is even a controversy about what the appropriate debt ratio is. See Welch (2011) in this issue of the journal for a comprehensive discussion of this subject.

3. 3 See also Elsas and Florysiak (2011), forthcoming in part II of the special issue on ‘Financing and Capital Structure’ in this journal.

4. 4 The financing deficit is the difference between a firm's requirement for funds (due to investment and dividend payments) and internally generated funds, and is equal to the sum of net issue of debt plus net issue of equity. A negative deficit corresponds to a net repurchase of securities.

5. 5 Iliev and Welch (2010) argue that except for the OLS estimator, some other common estimators of the speed to adjustment to a target leverage ratio are not sensitive to target measurement.

6. 6 For example, high stock returns may reflect new growth options that call for a lower target debt ratio. However, high stock returns may also temporarily overvalue the equity, and firms may issue equity to benefit from mispricing without any attempt to subsequently rebalance. If the target is not precisely estimated, it is impossible to distinguish the two motives.

7. 7 In the published version of our paper (Chang and Dasgupta 2009), we consider a subset of these issues.

8. 8 See Welch (2010)‘Why I do not understand capital structure research’ for more discussions and insights, especially the section ‘How would random leverage evolve?’.

9. 9 An important difference between the CD simulations and Iliev and Welch's (2010)‘placebo process’ is that CD preserve the actual financing deficit and retained earnings series. Scrambling this series then allows CD to examine the contribution of the financing deficit and retentions to the evolution of leverage under the assumed financing behavior. Of course, this reflects the view that the financing deficit and retentions are not entirely dictated by capital structure considerations.

10. 10 Among others, Jalilvand and Harris (1984), Titman and Wessels (1988), Leary and Roberts (2005), Fama and French (2002), and Flannery and Rangan (2006) exclude companies for which continuous data are not available. As robustness checks, we include firms that have no gaps in data on the relevant balance sheet items for 5 years and/or drop firms involved in large asset sales and significant mergers (identified by Compustat footnote code AB), and obtain similar results.

11. 11 The definition of the leverage ratio follows Fama and French (2002), Baker and Wurgler (2002), and Kayhan and Titman (2007). Our results are robust to alternative definitions of debt, such as the sum of short-term debt and long-term debt. The results of this robustness check and other robustness checks that are not tabulated are available from authors on request.

12. 12 As a robustness check, we also define debt and equity issues using the cash flow statements. Following Shyam-Sunder and Myers (1999) and Frank and Goyal (2003), we define equity issues as the sale of common and preferred stock less the purchase of common and preferred stock. Debt issues are defined as long-term debt issuance minus long-term debt reduction plus changes in current debt. Financing deficit is then defined as the sum of the change in net working capital, investments, and cash dividends, net of internally generated cash flow. These alternative definitions have little impact on our results. We prefer the measures constructed from balance sheets as they offer more non-missing observations than those defined using cash flow statement data.

13. 13 Even though we assume no apparent target for simulated samples, because we start off the simulations at the initial debt ratio of the firms in the actual data, it is conceivable that this initial debt ratio is a target debt ratio that is related to firm characteristics (Lemmon et al. 2008). To ensure that the use of actual initial leverage ratios is not driving our results, we replicate all empirical tests using simulation samples where all firms start their leverage ratios at 0.2 or 0.8 and document essentially the same findings.

14. 14 Recent literature points out many problems with the fixed-effects estimator – see Huang and Ritter (2009), Iliev and Welch (2010), and Elsas and Florysiak (2010). See also Section III.B.

15. 15 Chang and Dasgupta (2009) demonstrate that firms appear to exhibit a slower speed of adjustment (higher coefficients on lagged leverage) if the target adjustment model is estimated over a longer period of time. We require firms to have at least 20 years of continuous balance sheet items, thus firms in our sample have longer estimation periods than those in Flannery and Rangan (2006) and Chang and Dasgupta (2009).

16. 16 To verify the validity of this interpretation, we artificially create a new hypothetical deficit series: hypothetical deficit=actual deficit+0.1 ×Z, where Z is a pseudo firm characteristic randomly drawn for each firm from the uniform distribution. We then create the simulation sample S(empirical frequency, hypothetical deficit) and estimate equation (6) on this sample with Z as an additional regressor. Z has an average coefficient of 0.013 with a 95% confidence interval of [0.010, 0.015], confirming our conjecture. In the actual data, the financing deficit and the change in retained earnings are related to the set of firm-specific variables in Table 2. Consistent with the mechanical effects of the deficit and retained earnings on the debt ratio, in general, we find that variables that affect the change in retained earnings positively (negatively) and the financing deficit negatively (positively) have a negative (positive) sign in the first two columns. Appendix A presents regression results of the deficit and retained earnings on the control variables in equation (6).

17. 17 The negative coefficient of profitability on leverage has been hard to reconcile with target behavior, and is one piece of evidence that is robust and consistently cited as evidence against target behavior. If we believe that firms' retention of a part of their profits are not motivated by target leverage considerations, then the fact that the leverage ratio is positively related to profitability after purging the direct effect of retentions on leverage can be considered as evidence in support of target behavior.

18. 18 To understand why, note that the change in the book debt ratio can be decomposed following Baker and Wurgler (2002) as follows: . Here, Nei denotes net equity issues and Ndi represents net debt issues. Controlling for the deficit and retentions cannot eliminate the effects of firm-specific variables because the coefficient varies across firms and over time, and is likely to be correlated with firm-specific variables when the financing deficit is the actual deficit. Given that profitability is a fairly persistent firm characteristic, one expects that higher profitability will contribute to lower deficits and therefore a lower leverage ratio when financing is according to the empirical frequency. Therefore, the average coefficient of change in retained earnings will overstate the negative impact of retentions on the change in the debt ratio for high profitability firms, and profitability will retain a positive coefficient even when the financing deficit and retained earnings are controlled for in the regressions. High market-to-book, on the other hand, contributes to a higher financing deficit and debt ratio, but affects retentions positively (see column (2) in Appendix A). Consequently, the negative coefficient of the market-to-book adjusts for the fact that the negative effect of retained earnings is understated by the coefficient of retained earnings in the regression.

19. 19 Our conclusions do not change even if we assume extreme pecking order behavior, i.e., firms issue or repurchase debt with probability 1. Thus, ‘randomness’ of financing is not really crucial here.

20. 20 In results not reported here, we also generated data under the assumption that the financing deficit, retained earnings, and initial leverage are all random. Not surprisingly, firm fixed effects account for all the explained variation.

21. 21 LRZ define size as the natural logarithm of net sales, while we use the natural logarithm of total assets in the analysis.

22. 22 The results of the OLS regression are tabulated in column (1) of Appendix B.

23. 23 Note that the increase in R² is only 0.01 from column (1) to column (2) in both panels. This is normally the case if one controls for the lagged leverage ratio.

24. 24 In particular, the breaking point is set equal to the integer part of 0.3+0.4 ×y×N, where y is a random draw of the standard uniform distribution on the interval [0, 1], and N is the number of firm-years of the firm in the sample.

25. 25 This exposition is similar to that in Hovakimian and Li (2011).

26. 26 We use linear regressions to estimate the first-stage equation. Leverage ratio, the dependent variable in the first-stage regression is, by definition, censored from both below (by the value of 0) and above (by the value of 1). As a robustness check, we estimate the equation using tobit regression with double censoring. Untabulated results show that this alternative way of estimating target does not change our main results.

27. 27 A fixed cutoff for defining large debt/equity issues is used in many previous studies, including Hovakimian et al. (2001), Leary and Roberts (2005), and Chang et al. (2006). Alternative cutoffs of 1%, 3%, or 10% make little difference to the results that follow.

28. 28 This is because proxies are imperfect, and the same variable could capture a target motive and a non-target motive for issuance or repurchase. For example, the market-to-book ratio can be a proxy for growth opportunities which can affect the target negatively, but can also lead to movements away from the target if a firm below target wants to take advantage of favorable equity valuation and issue equity.

29. 29 As a robustness check, we closely follow Hovakimian et al.'s (2001) choices of firm-specific variables for X and Z. Specifically, in the first-stage model, we have X include Size, tangibility (PPE/A), the selling expenses to sales ratio, R&D/S, and RDD as determinants of the target leverage ratio. In the second-stage model, we have Z include EBITDA/A, the net operating loss carry forwards divided by total assets, StkRtn, M/B, an indicator variable that is equal to one when issuing equity dilutes the firm's earnings per share more than issuing debt does. This alternative specification does not change our main results that follow.

30. 30 Reassuringly, unreported robustness checks suggest that removing these corner cases or forcing the issuance/repurchase decisions at corners to conform to the coin toss has no effect on any of the results reported in earlier tables (Tables 2–4).

31. 31 We do not consider dual issues, dual repurchases, case of equity issuance combined with debt reduction, and debt issuance combined with equity repurchase as independent categories as these cases do not occur very often in the actual data, and of course, not at all in the simulated data.

32. 32 The first-order autocorrelation coefficient of financing deficit (DEF/A) for the actual data is 0.2, which is significant at the 1% level.

33. 33 Liu (2009) argues that the past market-to-book matters because leverage adjusts slowly to changes in the market-to-book ratio on account of adjustment costs. Hovakimian (2006) also makes the point that BW variable captures future growth potential rather than market timing.

34. 34 More specifically, if one multiplies both sides of equation (15) by and divides both sides by t, equation (15) can be transformed to , the right-hand side of which can be further written as

35. 35 Note that the two terms (KTCov and KTMB) are somewhat different from Kayhan and Titman's (2007) yearly timing and long-term timing measures. Kayhan and Titman's measures are not deflated by average past external financing.

36. 36 Target behavior is modeled as in the sample S(p=target(1), actual deficit, actual initial leverage) in panel E of Table 3.

Appendices

APPENDIX A

Table A1.   Determinants of financing deficit and newly retained earnings

Dependent variables	(1)	(2)
	DEF/A	ΔRE/A
Actual data are collected from Industrial Compustat and CRSP for the years 1971–2008. The dependent variables are Def/A in column (1) and ΔRE/A in column (2). Financing deficit (DEF) equals the difference between the change in total assets and the change in retained earnings. Newly retained earnings (ΔRE) is the change in retained earnings. The control variables are firm characteristics that are lagged 1 year. Market-to-book ratio (M/B) is defined as (market value of equity+total debt)/total assets. Market value of equity is defined as the number of shares outstanding multiplied by closing stock price at the end of the fiscal year. Profitability (EBITDA/A) is income before depreciation and amortization divided by book value of assets. Tangibility (PPE/A) is the net PPE to assets ratio. R&D/S is research and development expenses divided by net sales. Annual cumulative stock return (StkRtn) is obtained by compounding monthly stock returns over the fiscal year. The constant terms are included in regressions but not reported. t-statistics in parentheses are calculated from the Huber−White sandwich heteroskedasticity consistent errors, which are corrected for correlation across observations for a given firm. Coefficients significant at the 10%, 5%, and 1% levels are, respectively, marked with ^*, ^**, and ^***. Year dummies and two-digit SIC industry-fixed effects are included in both regressions.
M/B	0.036^***	0.003^***
	(23.1)	(4.5)
EBITDA/A	−0.138^***	0.350^***
	(−9.3)	(15.3)
Size	−0.007^***	−0.001^***
	(−12.1)	(−5.3)
PPE/A	0.026^***	−0.001
	(3.6)	(−0.5)
R&D/S	0.022^***	−0.018^***
	(3.3)	(−5.1)
RDD	0.004^*	0.000
	(1.8)	(0.1)
StkRtn	0.053^***	0.021^***
	(19.6)	(18.1)
N	46,956	46,956
R^2	0.11	0.30

APPENDIX B

Table B1.   Estimation of target leverage ratios for the actual data

Dependent variable (D/A)t	(1)	(2)	(3)	(4)
	OLS	Firm-fixed effects	OLS	OLS
Actual data are collected from Industrial Compustat and CRSP for the years 1971–2008. The dependent variable is book leverage (D/A). Independent variables include the market-to-book asset ratio (M/B), profitability (EBITDA/A), firm size (Size) measured as the log value of total assets, tangibility of assets (PPE/A), research and development expense to sales ratio (R&D/S), a dummy variable (RDD) that takes the value of 1 when R&D is missing in Compustat and 0 otherwise, and annual stock return (StkRtn) obtained by compounding monthly stock returns over the entire fiscal year. is the past average leverage ratio computed between the first year the firm entering the sample and t−1. is the future average leverage ratio computed from the current year t to the firm's last year (N) in our sample. t-statistics in parentheses are calculated from the Huber−White sandwich heteroskedasticity consistent errors, which are corrected for correlation across observations for a given firm. Coefficients significant at the 10%, 5%, and 1% levels are, respectively, marked with ^*, ^**, and ^***.
M/B	−0.021^***	−0.006^***	−0.010^***	−0.007^***
	(−19.8)	(−7.2)	(−11.6)	(−12.6)
EBITDA/A	−0.302^***	−0.225^***	−0.228^***	−0.132^***
	(−11.6)	(−8.9)	(−10.8)	(−10.4)
Size	0.029^***	−0.002	0.018^***	0.000
	(62.3)	(−1.5)	(45.1)	(0.2)
PPE/A	0.005	0.022^***	0.016^***	0.002
	(1.0)	(2.6)	(3.6)	(0.6)
R&D/S	−0.043^***	−0.016^***	−0.023^***	−0.015^***
	(−10.0)	(−4.2)	(−6.2)	(−5.3)
RDD	0.021^***	0.001	−0.003^*	0.009^***
	(10.8)	(0.6)	(−1.9)	(6.9)
StkRtn	0.012^***	−0.000	−0.004^**	0.007^***
	(6.9)	(−0.0)	(−2.4)	(6.0)
			0.742^***
			(150.6)
				0.843^***
				(211.7)
Industry dummies	Yes	No	Yes	Yes
Year dummies	Yes	Yes	Yes	Yes
N	46,956	46,956	46,956	46,956
R^2	0.23	0.59	0.50	0.63