Corporate Capital Structure Actions Murray Z. Frank and Tao Shen December 21, 2015 Abstract Existing empirical models of corporate leverage do a good job of predicting the cross section pattern of debt and equity repurchases. However, they do a poor job predicting debt and equity issuing. To improve the performance we use a large number of macroeconomic variables in reduced rank regression to estimate leverage targets based on firm-specific sensitivities to four common factors. This model gets the correct cross section patterns of issuing and repurchasing. The four factors load heavily on asset tangibility, taxation, corporate overhead, and volatility. The model performs particularly well for larger, profitable, and dividend paying firms. Smaller, high growth, and technology firms are not as well predicted by the model. JEL classification: G32, C38 Keywords: corporate leverage target, equity and debt issuing, reduced rank regression. Murray Z. Frank, Department of Finance, University of Minnesota, Minneapolis, MN 55455. Tao Shen, Department of Finance, Tsinghua University, Beijing, China. E-mail addresses: murra280@umn.edu (M. Frank), shentao@sem.tsinghua.edu.cn (T. Shen). We thank Viral Acharya, Tarun Chordia, Harry DeAngelo, Bob Goldstein, Jeremy Graveline, Arthur Korteweg, Hong Liu, Evygeny Lyandres, Guofu Zhou and seminar participants at China International Finance Conference, Tsinghua Finance Workshop, and University of Minnesota for helpful comments. We alone are responsible for any errors.
1 Introduction In an average year between 1982 and 2011, 43% of publicly traded American firms issue significant amounts of debt, 13% repurchase a significant amount of debt, 14% issue significant amounts of equity, and 8% repurchase a significant amount of equity. 1 More than half of the firms (58.3%) undertake one or more significant actions to alter their capital structure in a typical year. A key objective for the literature on corporate capital structure is, of course, to account for these four types of decisions. Since there are many empirical papers on corporate leverage, it is natural to ask: how well do the available models predict which firms undertake each of these types of actions (issuing debt, repurchasing debt, issuing equity, and repurchasing equity)? The purpose of this paper is to provide an answer. We find that the existing models have real difficulty with both debt and equity issuing decisions. So the second purpose of this paper is to provide an alternative empirical model of leverage targets to help to address this problem. Our empirical model uses a large number of macroeconomic variables that are reduced to four common factors. Four factors turn out to be sufficient to address the issuing decisions problem. Because the four-factor model proves helpful on average we then consider some of the strengths, weaknesses, and potential interpretation of the model. To answer the initial question we use the empirical methods from Fama and French (2002), Welch (2004), Kayhan and Titman (2007), Frank and Goyal (2009), and Faulkender, Flannery, Hankins, and Smith (2012), to estimate leverage targets. 2 For each paper, both book leverage and market leverage targets are estimated for each firm in each year. This provides 10 candidate leverage targets to study for each firm in each year. To evaluate a particular empirical method, each firm/year is sorted into one of six groups according to the distance between actual leverage and the estimated leverage target. The issuing and repurchasing decisions across the groups are compared. The prediction is simple. Suppose that a firm is not at the estimated leverage target. If the estimated target is a good reflection 1 We use the conventional definition that 5% or more of total assets is a significant amount. As shown in the online appendix, similar patterns are obtained when nearby thresholds are used. 2 It is worth keeping in mind that these papers have a variety of motivations, and their empirical models are not designed to pass the test that we consider. Nonetheless, it does seem informative to consider how these empirical models relate to active corporate decisions in the debt and equity markets. 1
of a true leverage target then on average that firm will actively adjust towards the estimated target. For each method of estimating the target, we examine whether firms typically do so. We find that all of the models do a good job predicting the cross section pattern of debt repurchases and equity repurchases. However, all of the models struggle with debt and equity issuing. When market leverage targets are studied, none of the models get the correct pattern for equity issuance. When book leverage targets are studied, none of the models get the correct pattern for debt issuance. Since all of these models get important patterns backwards, something is missing from all of these models. It is known that corporate issuing decisions are sensitive to whether times are good or bad within an industry (e.g., Frank and Goyal, 2014). This opens the possibility that perhaps market conditions matter in a way that is not adequately reflected by time dummy variables. To explore this possibility we need an alternative method to measure conditions. There are more than a hundred macroeconomic variables commonly available, and little theoretical guidance as to which might be critical. In order to reduce them to a more parsimonious model of leverage we use reduced rank regressions. 3 We estimate a model with four common factors and firm-specific loadings on the factors. The data suggest that at least four factors are needed, and more than four factors does not provide much extra benefit. The four factors load most heavily on asset tangibility, taxation, corporate overhead, and volatility. To test the efficacy of this approach, the method is used to determine the corporate leverage target for each firm in each year. As before, firms are sorted into groups based on the difference between their actual leverage and their estimated leverage targets. For this method, we find that firms above target tend to take more leverage reducing actions than the firms that are below target. Firms that are below target leverage tend to take more leverage increasing actions than firms that are above target. So this method produces leverage targets that get the cross section patterns correct for all four types of actions debt issues and repurchases as well as equity issues and repurchases. The results have a number of implications for the literature. First, the existing models 3 We also try principal components analysis, but it does not perform as well as reduced rank regressions. Those results are in Table 6, column 1. 2
used in the empirical literature provide a better account of the cross section pattern of repurchasing decisions than of issuing decisions. Issuing and repurchasing are not just different points on the same linear function where the sign changes. As far as we know the fact that the existing models have such a hard time with debt and equity issuing decisions is new to the literature. Recognition of this fact may be important to help guide future improvements to the empirical models. Second, the existing empirical models generally impose an assumption of common coefficients, apart from the intercepts. Empirically it seems that allowing for coefficient heterogeneity is important. This fact is closely connected to DeAngelo and Roll (2015). Third, our estimates show that common factors are important particularly for the issuing decisions. This may be helpful as the literature attempts to understand the connections between corporate finance and macroeconomics. Finally, the fact that reduced rank regression produced empirical models that outperform principal components suggests that this approach might have other applications in finance where reducing a large number of variables to a more parsimonious model is of interest. Section 2 describes the data and how we construct the sample. Section 3 estimates leverage targets for firms using the methods in a number of papers from the literature. In each case the ability of the estimated target to correctly sign the cross sectional differences in active adjustments to leverage is studied. Section 4 provides estimates of leverage targets using many factors and reduced rank regression to derive a four-factor model. This model is then tested in the same manner as the previous approaches. Section 5 studies the robustness of the results on several dimensions. In order to highlight the strengths and the weaknesses of the approach Section 6 compares the characteristics of firms that are well explained by the model to the firms that are poorly explained. Section 7 uses simulation to examine the impact of measurement error on the method. Section 8 concludes. 2 Data The firm data are from the annual Compustat/CRSP merged file. We drop foreign companies, and the companies with a SIC code that is between 4900 and 4999, between 3
6000 and 6999, or greater than 9000. All firm-level variables are winsorized at 1% level on each tail every year. The details of individual items are listed in the online appendix. The impact of the data cleaning steps is provided in Table A1. 2.1 Variables and Summary Statistics There are a number of closely related leverage definitions in the literature. Following Frank and Goyal (2009), market leverage is defined as, T DM it = (DLT T it + DLC it )/(P RCC it CSHP RI it +DLT T it +DLC it +P ST KL it T XDIT C it ). Book leverage is defined as T DA it = (DLT T it + DLC it )/AT it. 4 The item names are defined by Compustat. DLTT is long term debt with maturity exceeding one year, DLC is debt in current liabilities, PRCC is year-end common share price, CSHPRI is common shares outstanding (as used to calculate earnings per share), PSTKL is preferred stock liquidating value, and TXDITC is deferred taxes and investment tax credit. In each case i denotes the firm and t denotes the year. For the later analysis, we focus on a sample of firms that have at least 10-year non-missing leverage values over the period 1982-2011. In total we have 3994 firms. Descriptive statistics are provided in Table 1. As is common, the necessary data cleaning and matching procedures results in a sample that is slightly larger and more stable than the entire population of firms in the USA economy. Our sample of firms have an average life of 20.49 years which is longer than the unrestricted population average. The average market leverage is 0.273 which is not far from what is usually obtained. As is common the market to book ratio is greater than one at a mean of 1.421. Overall, this table shows that our data looks very much like the data generally studied. 2.2 How Common are Leverage Adjustments? Table 2 provides summary statistics on the four main categories of firm actions. In the top panel each of four actions is divided by total assets and then the basic descriptive statistics 4 It might be interesting to decomposing different types of debt as in Rauh and Sufi (2010). We focus on the traditional leverage ratios because we are concerned with comparability with other studies of leverage adjustment. 4
for all firms are reported. The second panel provides information about the fraction of firms that undertake a non-trivial amount of each action in each year. Since many firms choose values of zero, this gives a distinct perspective from the simple averaging in the top panel. The third panel provides correlations of the actions. The top panel shows that on average the dominant type of action is debt issuance. The average firm issues 10.6% of the total assets in the form of debt in a year. Debt repurchases are only 2.1% of total assets. The average firm issues 4.4% of total assets in the form of equity and has equity repurchases that are 1.1% of assets. There is considerable cross section variation as shown by the standard deviations and the percentile values. It might appear from these numbers that corporate capital structure actions are small. That would be a misinterpretation. Many firms make almost no adjustment in a typical year. However, when a firm takes action it is often a fairly large fraction of total assets. The distributions for each type of action are plotted in Figure 1. Because firm actions are continuous variables, each bin represents an interval which has a size of 0.005. In the first bin, the percentage of real zeros is 46% for equity issues, 86% for debt issues, 84% for equity repurchases, and 89% for debt repurchases. For all four types of actions there is a spike at zero action and another spike reflecting action that is above 14.5%. The spike above 0.145 is a cumulation of a variety of larger numbers. From the 4 panels it is obvious that debt issuing is the most common action that is strictly greater than zero and debt issues are greater than zero for more than half of the firms. In sharp contrast equity issues, equity repurchases, and debt repurchases are each roughly zero more than half the time. The distributions provide motivation for the second panel of Table 2. It tabulates the fraction of firms which undertake a non-trivial amount of each action in each year. The standard 5% of total assets is used as the threshold for defining non-trivial. The basic patterns are the same if we use 4% and 6% thresholds. These are tabulated in an online appendix. The most common occurrence for a firm in a year is to issue debt (43%) followed in order by, no major action (41.7%), issue equity (14%), repurchase debt (12.5%), and repurchase equity (7.8%). So far the four kinds of decisions have been discussed as if they were independent. Of 5
course they are not. Issuing debt and repurchasing equity both serve to increase leverage. Issuing equity and repurchasing debt both serve to reduce leverage. Issuing debt and issuing equity both serve to increase the firm s assets, while repurchasing debt and equity do the reverse. So a natural question is whether the issuances and repurchases are complementary, or substitutes. Either could happen depending on whether the firm is attempting to alter a leverage ratio or to alter firm size, or has some other motivation altogether. The third panel of Table 2 provides correlations among the four types of actions under consideration. The first point to note is that empirically most of the correlations are small. The strongest correlation is a positive correlation between debt issues and debt repurchases. Presumably this reflects, at least in part, refinancing actions when interest rates change. Historically many debt contracts include a call provision. Thus if interest rates drop, the firm can save money by calling the old bonds and issuing new bonds. Equity issuing is significantly negatively correlated with equity repurchasing. However, the magnitude of the coefficient is surprisingly small at just 0.027. Equity issuing is positively correlated with debt repurchasing. Debt issuing is positively correlated with equity repurchasing. These issuing correlations make sense if they reflect intentional leverage rebalancing by the firms. It should be kept in mind that all of these correlations, while statistically highly significant, are modest in magnitude. Table 3 provides information about the autocorrelation structure of the four types of decisions. Both panels report the correlations at date t with date t 1. In the upper panel the actual values of the issuing and repurchasing decisions are used. In the lower panel those values are replaced with dummies. In each case the dummy takes on a value of 1 if the magnitude of the decision is equal to or greater than 5% of the total asset of the firm. Thus the correlation is between major rebalancing at one date and the next. The two panels show the same basic patterns. Empirically Table 3 shows that positive autocorrelation is the usual case. If a firm issues equity this year it is more likely (correlation 0.340) to do so again next year. If a firm issues more debt it is more likely (0.513) to do so again next year. The same is true for repurchases of each type of security. A firm that repurchases equity this year is more likely (0.439) to repurchase equity next year. A firm that repurchases debt this year is more likely 6
(0.280) to repurchase debt next year. There are also strong lagged cross effects. A firm that issues equity this year is less likely ( 0.046) to repurchase equity next year. A firm that repurchases equity this year is less likely ( 0.045) to issue equity next year. The debt pattern is different. A firm that issues debt this year is more likely (0.116) to repurchase debt next year. A firm that repurchases debt this year is more likely (0.095) to issue debt next year. Many of these descriptive statistics seem suggestive of leverage rebalancing. The difference between debt and equity is striking. The lower panel shows that the same patterns apply to major actions as apply in general. These descriptive statistics do not indicate how these actions relate to leverage targets. For that we need to have a method to identify the target, which is the issue we turn to next. 3 How Effective are Existing Models? Leverage targets are not directly observable. They must be estimated on some basis. The methods that we examine are from Fama and French (2002), Welch (2004), Kayhan and Titman (2007), Frank and Goyal (2009), and Faulkender, Flannery, Hankins, and Smith (2012). We follow definitions and econometric approach used in each study when estimate the target leverage. For each paper we estimate the leverage model for book leverage and for market leverage separately. The dependent variable is leverage, which is denoted by L i,t. The independent variables are a number of firm and industry variables which are one year lagged. The independent variables typically include: firm size, change of assets, tangibility, market-tobook ratio, profitability, depreciation, dividend payout, R&D expense, and industry median leverage. Different studies include slightly different variables. For example, Fama and French (2002) include target dividend payout ratio which is estimated from another set of regressions. Kayhan and Titman (2007) use industry fixed effects instead of industry median leverage. Faulkender, Flannery, Hankins, and Smith (2012) include firm fixed effects. The definitions of the same concept can vary somewhat across papers. Fama and French (2002) define total debt as the difference between total asset and book equity, while other 7
studies use the sum of short-term and long-term debt as the proxy. Various studies use different econometric methods. These include Fama-MacBeth regression (Fama and French, 2002), Tobit regression (Kayhan and Titman, 2007), OLS regression (Frank and Goyal, 2009), and two-step GMM (Faulkender, Flannery, Hankins, and Smith, 2012). Table A2 provides more detailed descriptions of the various models. For each paper we get a fitted leverage value, T i,t, which we call target leverage. It is based on the information in year t 1. The study by Welch (2004) is slightly different from the others. It tests whether debt ratios readjust to their previous level, and the implicit target is therefore the previous leverage. In particular, the leverage in year t 1, t 3, t 5, and t 10 are used as the target in year t. If the leverage in year t 1 is used as the target for the next year, then it implies that firms already reach the target and no actions are required during year t. To avoid this problem we use the leverage in year t 5 as the target. In the spirit of Welch (2004), we also use the average historical leverage from year 1 to t 1 as the target for year t in unreported test, and the results are similar. We compare actual leverage to the predicted or target value for each firm in each year for each paper s model and for both book and market notions of leverage. Define the leverage gap as G i,t = L i,t 1 T i,t. Next, we sort G i,t at the end of year t 1, into six categories from far above target to far below target. After sorting the firm/years into categories we calculate the magnitudes of the leverage adjusting actions associated with each type of action in each category. Suppose that the empirical model under consideration provides a good estimate of the firm s actual leverage target. Then over-levered firms (far above target) should take steps to reduce leverage. Under-levered firms (far below target) should take steps to increase leverage. If the these patterns are not observed, then the corporate issuing decisions must be reflecting forces that are missing from the estimated model. We test the statistical hypothesis of no difference across the categories, against the alternative hypothesis that the magnitudes are greater in the direction suggested by the target. In Table 4, the upper panel carries out the analysis for market leverage, and the lower panel does the same analysis for book leverage. Column 1 provides the expected signs of the differences. Column 2 follows one version of Welch (2004) in using the year t 5 leverage as 8
the target. He finds that subsequent actions do not appear to adjust leverage ratios to their previous values. We also find a mixture of signs. For market leverage debt repurchases and equity repurchases are correctly signed, but debt issues and equity issues are not. Column 3 uses the empirical leverage factor model from Frank and Goyal (2009). The results are fairly similar to column 2. Column 4 considers the model from Faulkender, Flannery, Hankins, and Smith (2012), column 5 is for Kayhan and Titman (2007), and column 6 is for Fama and French (2002). None of the models is fully satisfactory. In the upper panel for market leverage targets, all of the models have the correct signs for debt repurchases and equity repurchases. Only the Faulkender, Flannery, Hankins, and Smith (2012) model has the correct sign for debt issues. None of the models have the right sign for equity issuance. They all have the wrong sign and, what is worse, the differences are statistically significant at 1% level. In the lower panel for book leverage targets, these models perform a bit better overall than for market leverage. Once again all the models get debt repurchases and equity repurchases correct. The targets from Welch (2004), Faulkender, Flannery, Hankins, and Smith (2012) and Fama and French (2002) have the right sign for equity issues as well. However, all of the models have the sign wrong on debt issues. Overall, among this set of methods the approach in Faulkender, Flannery, Hankins, and Smith (2012) performs the best. This may in part reflect the fact that it was originally motivated with target adjusting behavior in mind. However, all of these methods have serious problems with corporate issuing decisions. Something more is needed. 4 The Reduced Rank Regression Model Because all of the past models struggle with issuing decisions, an alternative method is proposed in this section. We observe that many previous methods sharply restrict the information set to just a handful of independent variables. This is often done as a routine matter without much explicit justification. It is well understood that the restricted set of variable is likely to exclude some things that firms care about. The fixed-effects specifications will only solve the problem if the omitted factors take the form of an intercept term. If they 9
take another form, the standard approach can generate coefficient estimates that are often biased toward zero. To include a more comprehensive set of information and capture time varying effect, we focus on reduced rank regressions which are shown to be an effective approach. 5 4.1 Method To explain how this works, note that the data has N firms and T years. We observe the leverage, Y t = (Y 1,t,..., Y N,t ), and t = 1,.., T. It is hypothesized that these outputs reflect the impact of a set of M input variables X t = (X 1,t,..., X M,t ). So Y t is of dimension N 1, and X t is of dimension M 1. A traditional multivariate linear regression model is, Y t = µ + ΘX t + ε t. (1) The unknowns to be estimated are µ, Θ, and ε t, where µ is an N 1 matrix, Θ is an N M matrix of regression coefficients, and ε t is an N 1 matrix of well behaved errors with mean zero. The true specification of X t is not known. There are at least two concerns. First, if M > T, standard OLS runs into a problem with degrees of freedom. The number of coefficients to be estimated in Θ is N M, which is larger than the number of observations N T. This is not feasible and so the number of variables, M, must be restricted. Second, the model assumes that the set of regression coefficients, Θ, is common across firms. In reality it is quite possible for firms to have differing coefficients from one another. It is even possible for a given coefficient to have the opposite signs at different firms. Suppose that half the firms have a true coefficient of +1 on a given variable and the other half of the firms have a true coefficient of 1 on the same variable. regression it is not unlikely that we will not be able to reject the hypothesis that the true coefficient in the population is zero even though it is not zero for any individual firm. Reduced rank regression helps with both issues. The idea is introduced by Anderson 5 The reduced rank regression is almost a polar opposite to the structural models (e.g., Strebulaev and Whited, 2011). Instead of imposing structural assumptions on an a prior basis it keeps the structural assumptions to a minimum. The resulting model does not offer a test of any particular structural model of leverage. It does offer a parsimonious hurdle for further empirical work. In a 10
(1951) and a good modern textbook treatment is provided by Izenman (2008). In an ordinary regression each explanatory variable gets its own coefficient. However, when the rank is reduced, there are fewer available channels through which the explanatory variables can affect leverage. The model is forced to do as well as it can through that reduced number of channels. Given the sum of squares criterion function, the estimated parameters provide an optimal method. The method reduces the dimension of X that affects Y. The key step is to have the rank of the coefficient matrix be less than full, rank(θ) = r min{m, N}. There are two full-rank matrices, A (N r), and B (r M), such that Θ = AB. Equation (7) is replaced by, Y t = µ + ABX t + ε t = µ + AF t + ε t (2) The reduced rank factors are F t = BX t which is an r 1 vector. In a linear regression the goal is to optimally estimate µ and Θ. In the reduced rank regression the goal is to optimally estimate µ, A and B. For a given rank r, the optimal estimates of µ, A and B are found by minimizing, W (r) = E [ (Y t µ ABX t ) (Y t µ ABX t ) ] where the expectation E is taken over time period t. 6 To carry out the reduced rank regression, we have to take a stand on the rank. Our main results are based on a rank of four. This rank is first chosen based on statistical tests. We perform rank trace test as suggested by Izenman (2008). We also analyze the number of principal components in firm leverage. The results from both methods suggest that four factors are reasonable. More detail is provided in the online appendix. The four-factor model performs well in the later empirical analysis of actual firm decisions. Allowing for an increase to rank of five does not change the inferences to be drawn about firm firm actions. Reducing the rank to three causes a significant worsening of the model. 6 See Izenman (2008) for a generalization that introduces a weighting matrix that is not an identity matrix. 11
4.2 Information Set What kind of market level information ought to be included in the reduced rank regressions? It is not clear. We know anecdotally that real corporate decision makers know many things, and they actively monitor developments in the economy and in the markets that affect their corporation. Their information set is therefore quite large when they consider corporate leverage. As outside observers we cannot directly measure their actual information set. We can, nonetheless observe many things that the decision makers might plausible consider. Our information set includes both macroeconomic information as well as firm-specific information. This is a set of 146 variables that might potentially matter. The set of macroeconomic variables under consideration follows Ludvigson and Ng (2009), and Stock and Watson (2012). The macroeconomic data come from the FRED database of the St. Louis Federal Reserve. The transformation of the original macro series follows Ludvigson and Ng (2009). The details of individual items are listed in the online appendix. To extract common factors, we require a balanced panel of leverage and a reasonable number of observations in the time dimension. It is well-known that firms enter and exit so that the panel of data is not balanced. There is no fully satisfactory way to deal with this problem. We start with firms that exist from 1982 to 2011. Following Strebulaev and Yang (2013), we drop firms that average less than 5% market leverage during this period. There are 43 such firms, and it leaves us a balanced panel of 475 firms. The potential explanatory variables are a balanced panel of 146 variables from 1982 to 2011. We have both macroeconomic variable time series and firm-level data. In order to make the firm-level variables comparable in structure to the macroeconomic time series we aggregate across firms at each date. So the firm-level explanatory variables from Frank and Goyal (2009) are aggregated in each year with a market value weighted average. 7 variable names and details are in the online appendix. The balanced panel is used to extract the underlying common factors. The The common factors are then used to estimate factor loadings for a broader population of firms that 7 We also examine what happens if the firm-level variables are maintained in an unaggregated form. These results are presented in Table 6, column 6. The results in that case are quite similar to the main reduced rank regression results. 12
have at least 10-year non-missing leverage values over the period 1982-2011. The broader population has 3519 firms. In total we have 3994 firms. The later analysis illustrates that the factors extracted from the firms with balance observations are helpful for the broader population of firms that do not have a full set of data. 4.3 Evidence To understand the impact of the four common factors, we estimate a series of time-series regressions, one regression for each firm i. It should be stressed that α i is an intercept for a time series regression for firm i, it is not a firm dummy variable in a panel regression. The time series regressions are, Y i,t = α i + β i,1 F 1,t + β i,2 F 2,t + β i,3 F 3,t + β i,4 F 4,t + ε i,t. (3) The F j, refers to the jth factor, and the Y i, is a leverage time series. This regression (3) is run for each firm in the sample. Histograms of the typical R 2 (adjusted R 2 ) values are depicted in Figure 2. The upper panel shows results for the 475 firms that were used to extract the common factors. This can be viewed as an in-sample test. The lower panel shows results for 3519 firms that were not used to estimate the common factors. This is a type of an out-of sample test in the sense that the factors were not extracted from these firms. Both samples have median R 2 values that are quite close to 60%. Clearly there is a great deal of heterogeneity among firms, but the model does appear to be capturing a significant fraction of variation. We also consider the model performance for aggregated data which are time series for the 25th, 50th, and 75th percentiles of firm leverage over the period 1982-2011. The period 1982-2008 is used to fit the model. The period 2009-2011 is used as an out-of-sample test. Figure 3 shows the results. From the top to bottom, the lines without markers are the 25th, 50th and 75th percentile firm leverage. The line with markers shows the fitted values. A vertical dashed line is used to show the dividing line between the in-sample and out-of-sample time periods. The four factors do a good job both within-sample and also out-of-sample. The fact the model is able to pick up the turning point in 2010 is notable. 13
The model is not simply extrapolating a linear trend line. DeAngelo and Roll (2015) provide a stark challenge to the idea that leverage is quite stable over long periods of time as in Lemmon, Roberts, and Zender (2008). They stress that a wide variety of dynamic patterns are observed across firms. A particularly telling aspect of their paper is that they plot the time series of leverage for firms in the Dow Jones Industrial Average over many decades. It is hard to avoid the impression that a wide variety of patterns are observed. Firms do not return rapidly to previous levels and various firms move in different directions at the same time. In order to address this issue Figure 4 plots the leverage time paths for 22 large firms over our sample time period. While our time frame is not as lengthy, the leverage patterns exhibit much the same challenging behavior as documented by DeAngelo and Roll (2015). A wide range of leverage patterns are observed across firms, with only weak evidence of rapid reversion to long term average values. For each firm we also plot the leverage target as implied by the common factor model. These series are indicated with small plus marks. To quantify how well the target and the actual leverage match, for each firm we also report the R 2 of a regression using the common factor model to explain the observed leverage. Most of the R 2 values are above 0.5. The lowest R 2 is for Navistar at 0.305. Even for this firm, the model does appear to reflect the longer term trends, even as it misses some of the shorter term volatility. A visual inspection of these plots show that the actual leverage and the target leverage follow firm-specific trends. For most firms, actual leverage is a bit more variable than our estimate of the target leverage. All firms remain fairly close to the implied target most of the time. It is rare for a firm to deviate from the target for more than a few years. From the values of the R 2 we know that the fits are not perfect. However, visual inspection suggests strongly that the four common factors do capture important elements. These firms do revert to the time-varying targets fairly rapidly, but the target is not a time invariant debt/equity ratio. In Table 5, we use the four common factors to estimate the target. For each firm, we estimate a time series regression. The dependent variable is the book or market leverage in year t, and the independent variables are the four common factors in year t 1. The 14
fitted value is the target. We calculate the leverage gap and then examine whether the cross section patterns are correct. The upper panel in Table 5 reports results for market leverage and the lower panel is for book leverage. The row labelled gap gives the magnitude of the average firm-specific leverage gap relative to the target for firms that are in each of the six categories. The market leverage gap ranges from 0.174 for the firms that are far above target leverage to 0.166 for the firms that are far below target. So there is a fair bit of spread across the categories. The book leverage spread is only slightly narrower. For each of the categories of active leverage changes we report the average magnitude within the category. Each magnitude is scaled by total assets. In each case the magnitude of the action is bounded below by zero. These are actions, not net actions. Before we start we believe that the empirical model provides target estimates. An estimate will be measured with error. Accordingly we expect to observe some actions that go opposite to the model predictions. Indeed the magnitude of such actions can be used to approximate the error rate for our target estimates. For a firm above target leverage, that firm ought to repurchase debt and it ought to issue equity, all else equal. For a firm below target leverage, that firm ought to issue debt and repurchase equity. If the target estimates are actually unrelated to what the firm is paying attention to, then we ought to find such actions equally distributed across the six leverage categories. To test this idea we focus on the column labelled Difference. This reports the result of the statistical hypothesis test comparing column 1 to column 6 for each type of action. If the model is working, then for debt repurchases and equity issuances we ought to get a positive and significant difference. For debt issuances and equity repurchases we ought to get negative and significant differences. These predicted patterns are observed, and they are statistically significant both for market leverage and for debt leverage. In fact debt and market leverage give fairly similar coefficients. So the reduced rank regression approach is picking up forces that the traditional empirical models do not reflect. Like the traditional models, the repurchasing patterns are properly predicted. Unlike the traditional models the issuing patterns are also properly predicted. 15
The results in Table 5 show that the reduced rank target estimates are potentially useful. However, they also suggest that there is still significant room for further improvement. To see this suppose that the method had perfectly generated the firm s target. Then we ought not to see any issuance or repurchases in the wrong direction. This is evidently not the case. For instance, if all the relevant forces were reflected in the estimated target, then the far below leverage target firms would never issue equity. They would repurchase equity and issue debt. Yet we see that instead of being zero in column 6 the coefficient is 0.032. As predicted this is smaller than the value in column 1 i.e. 0.038. So the difference is of the right sign, but a substantial amount of the activity is not captured. Similar issues are observed for the other categories as well. Thus our inference is that the reduced rank regression approach is offering a step in the right direction, but there is still a great deal of unexplained variation relative to the estimated model. 5 How Robust is the Approach? There are a variety of closely related alternatives to the model just presented. A number of these are collected in Table 6. Rather than reporting a large mass of numbers for each model, we report the test statistics that corresponds to what is reported in the Difference column in Table 5. This conveys the message from the large mass of numbers. Column 2 uses the exact same data, but instead of reduced rank regression it uses four principle components factors to compute the target. This is motivated by the fact that principle components analysis is a well known method to reduce a large data set to a more manageable set of factors. In column 2 we see that it gets the wrong sign for equity issuance. This wrong sign is reported to be statistically significant. So we conclude from column 2 that principle components does not offer an improvement. Sticking to reduced rank regressions, the next question is whether the use of four factors is a good choice. In the online appendix we discuss the fact that the rank trace test motivates the use of four factors. However, a statistical test is not equivalent to examining the actual corporate financial actions. So columns 3 and 4 of Table 6 examine what happens if either a three-factor or a five-factor reduced rank regression model is used. The three-factor model, 16
much like principal components, does not do a good job with the equity issuance decision. In this case the coefficient is not statistically significant. In column 4 we report results for a five-factor model. By construction the five factors include the original four factors and then adds the next best additional factor. The added factor might introduce noise, or it might improve the fit. Empirically the five-factor model performs much like the four-factor model. The signs on all actions are the same as in the four-factor model. The model does get equity issuance correct. The test statistics are a bit stronger, but not all that much. We infer from columns 3 and 5 that the four factors are the minimal number needed for current purposes. The five factors do not make things worse, but they do not offer a dramatic improvement either. So for parsimony we prefer to stick with the four-factor reduced rank model. With either principal components or reduced rank regressions there is an issue of factor interpretation. To deal with this issue we follow Ludvigson and Ng (2009) and use univariate regressions to study how the individual data items relate to each factor. In column 5 we regress each of the four factors on each of the original variables, one at a time. In each case we examine the R 2 to see how closely related the factor is to each variable. This permits us to investigate the connection between the factors and underlying data. The first factor is most highly connected to asset tangibility. The second factor is related to taxation. The third factor is most closely connected to corporate overhead. The fourth factor is connected to stock market volatility. Tangibility affects firms borrowing capacity, and their ability to tap and time the capital market. The tax effects are relatively hard to clearly identify in the data, and their proxies often appear insignificant in empirical studies using panel data approach, as in Frank and Goyal (2009). It is noteworthy that tax related variables prove to be related to the first two factors. The importance of volatility may reflect the fact that the variation of market leverage is partially driven by the equity price fluctuations. Further discussion and details are provided in the online appendix. A natural idea is that perhaps we can replace the four factors with the four individual series that are most highly correlated with each of the factors. To see how it affects results, for each factor we select the single original data series that has the highest R 2. We then drop 17
the reduced rank factors and instead estimate a model that consists of these top 4 variables. This provides a test of whether univariate interpretations are sufficient. If it works that would be nice for interpretive purposes. Unfortunately the answer is, no. In column 5 we again find the by now familiar problem with equity issuance. The traditional models use firm factors to provide leverage estimates, while the reduced rank method uses firm loadings on common factors. These are not necessarily an either/or choice. Perhaps a combined model might be better. In column 6 of Table 6 a hybrid target model is estimated. It uses seven firm factors that are frequently used in the literature, and the four reduced rank factors. This hybrid model performs quite similarly to the simpler four-factor model from Table 5. Reintroducing the seven extra factors is not helpful. In column 7 we consider the possibility that the four-factor model might be working because it accidentally picks up the impact of the positive autocorrelation in the issuing decisions. To address this concern we construct a second kind of hybrid model. This time the issuing and repurchasing of debt and equity from the previous year are treated as four explanatory variables in addition to the usual four factors from reduced rank regressions. The same cross sectional tests as usual are carried out and column 7 shows the results. Empirically this makes only a small difference, and that difference is in the wrong direction. For book leverage the results are similar to the difference column in Table 5. For market leverage the model has trouble with equity issuance, which is now statistically insignificant. So adding the extra controls for potential autocorrelation does not prove helpful. 6 What Kinds of Firms are Not Well Explained? In Table 5 it is quite apparent that the cross section patterns are correct. However, it is also apparent that there is much activity that is not in the predicted directions. This is the variation that the model is not capturing. To understand the strengths and weaknesses of the model, we next ask, which kinds of firms are well characterized, and which are not? In order to answer this question we proceed as follows. For each firm we run time series regressions of market leverage on the four factors. For each firm we record the R 2 of that time series regression. Next we sort firms into quintiles according to the R 2. Then for each 18
quintile we examine the mean value for a number of firm characteristics. Finally we test the hypothesis that the mean value of the characteristic in the highest quintile is the same as it is in the lowest quintile. The results are reported in Table 7. The bottom row reports the adjusted R 2. For the lowest quintile the value is 0.130 while for the highest quintile the value is 0.860. So there really is considerable variation across firms. For the middle quintile the value is 0.593 which is not too bad for such a parsimonious model. On an a priori basis it is not clear what kinds of firms might be better accounted for and which would be worse. In the data we observe that the high R 2 firms (those that are relatively well explained) have higher leverage, greater profits, more assets, greater tangibility of assets, pay more dividends, and have more variable stock returns. The low R 2 firms (those that are more poorly explained) have more capital expenditure, do more research and development, have more corporate overhead (SGA), have more net operating loss carry forwards, and have a higher average stock return. There are a variety of other variables for which no significant difference is obtained. After observing these patterns there is a sense in which the performance is understandable. To improve the fit for such firms it will presumably be necessary to introduce data beyond the usual Compustat/CRSP or macroeconomic variables. In broad brush terms it appears that the reduced rank approach performs better for larger and more traditional firms and it performs worse for smaller and more innovative firms that are investing heavily. 7 Measurement Error In previous literature, a frequent motive for leverage target estimation is to examine the speed of adjustment. Commonly it is reported that firms adjust fairly slowly towards their leverage targets. In this paper we use the leverage targets to examine the directions of firm actions. Given that the previous models have difficulty with issuing decisions, it may not be surprising that the resulting adjustment speeds are slow. In this section, we show that measurement error in the target can be the culprit behind the slow speed estimates, and that the reduced rank regression, by providing more effective estimates of the target can address 19
this issue. In particular, we examine two potential sources for measurement error. The first type is related to the target model specification. The traditional approach assumes a common coefficient on firm factors. It is possible that firm specific coefficients are important in generating targets. The second type is related to the information set. The traditional approach uses a limited set of information which only considers the usual control variables while the omitted variables may not be fully captured by firm fix effects. We examine how these two types of measurement error interacts with the true speed of adjustment in simulated data. We first simulate a panel of firm leverage and one firm factor with N firms and T periods. Then we use both traditional approach with firm fixed effects and reduced rank regression to estimate the target. With the targets, we estimate a standard partial adjustment model. The details are presented in the appendix. Table 8 reports the estimated adjustment speed in the simulated data. In the upper panel we consider only the first type of measurement error. The target leverage is just driven by the firm factor but its coefficient is firm specific. In the second second panel, we consider both types of measurement error. The target leverage is driven by the firm factor and other variables, and their coefficients are firm specific. In columns 1 to 3 we consider cases in which the true adjustment speed is fast, and in columns 4 to 6 we consider cases in which the true adjustment speed is slow. In columns 1 and 4 the true target is known and is used. In columns 2 and 5, a traditional model is estimated. In columns 3 and 6, reduced rank regression is used to infer the target. When we use that actual target in estimation the R 2 is around 0.5 depending on the exact specification. In each case the coefficient on the leverage gap is numerically very close to λ, as it should be. This is an upper bound on how well such a model could perform. The traditional empirical model provides estimated targets. When we do that, the λ coefficients that are biased towards zero. In most cases the R 2 is a bit below half as large as when the true target is used. The performance of the reduced rank regression is, of course, not as good as when the true target is used. However, it is quite a bit better than when the traditional estimates of target are used. For example, in the upper panel when λ = 0.9, the true target has an 20
R 2 = 0.532, while the traditional model has an R 2 = 0.342, and the reduced rank model has an R 2 = 0.394. More importantly the coefficient on the leverage gap are respectively 0.688 and 0.795. So we find that measurement error does tend to bias the coefficient towards zero. However, the magnitude of that bias is mitigated in the case of reduced rank regressions and as result the speed of adjustment is estimated to be faster. This reflects the intuitively reasonable fact that the adjustment is towards a time-varying target, not to a time-invariant target. 8 The fact that measurement error biases the coefficient towards zero should not be surprising. That is a common impact of univariate measurement error in econometrics. However, in the case of target adjustment models this bias may actually be misinterpreted as a substantive effect. It would be interpreted as slow adjustment. This may suggest that part of the reason that many studies find slow leverage target adjustment could be due, at least in part to poorly measured targets. 8 Conclusion This paper uses the models from several of well known capital structure papers to estimate leverage targets. We examine whether the estimated targets help explain the cross section of firm capital structure actions. The key findings follow. 1) The models do a good job of predicting the cross section pattern of debt and equity repurchases. They have serious trouble predicting the cross section of debt and equity issuance. 2) We use reduced rank regression to estimate a four-factor model. This model does a reasonable job with the cross section of both issuing and repurchasing decisions. 3) The model seems able to provide a reasonable account of the leverage patterns among the Dow Jones firms that is stressed by DeAngelo and Roll (2015). 4) Of course, some firm s actions are better predicted than other s. Large traditional firms are relatively well explained. Small high growth firms are relatively poorly explained by the model. 5) Measurement error in the leverage targets may 8 It has been observed that when firm fixed effects are included the estimated speed of adjustment is faster, see Huang and Ritter (2009) and Flannery and Rangan (2006). This makes sense if the firm fixed effects are providing a better proxy for the true targets even if that improvement still does not fully allow for time variation in the targets. 21