Abstract:In the presence of frictions firms adjust their capital structure only infrequently. As a consequence, in a dynamic economy the leverage of most firms, most of the time, is likely to differ from the ``optimum'' leverage at the time of readjustment. This paper explores the empirical implications of this observation. A calibrated dynamic trade-off model with adjustment costs is used to simulate firms' capital structure paths. The results of standard cross-sectional tests on this data are found to be qualitatively - and, in some cases, even quantitatively - consistent with those reported in the empirical literature. In particular, the standard interpretation of some test results would lead to the rejection of the model used to generate the data. The framework can explain a number of observed puzzles related to leverage. In particular, in the simulated cross-sectional samples leverage: (a) is inversely related to profitability; (b) can be largely explained by stock returns; (c) is mean-reverting. The results suggest that, in the presence of infrequent adjustment, cross-sectional properties of economic variables in dynamics may be fundamentally different from those derived assuming that they are always at their target levels. Taken together, the results suggest a rethinking of the way capital structure tests are conducted.

Keywords: Capital structure, dynamic economy, trade-off model, simulations, asset liquidity, refinancing point, profitability, stock returns, credit spreads.
JEL classification codes: G12, G32.
Download the paper: PDF version
Note: New version will appear very soon

Model Solution: Mathematica codes
Main Mathematica code
Additional Mathematica code

Model Solution: MATLAB codes
Main MATLAB code
Additional MATLAB code 1
Additional MATLAB code 2

Data Generation: Stage 1: Rebalancing: MATLAB codes and data
Main MATLAB code
Data on volatility
Data on costs

Data Generation: Stage 2: Dynamics: MATLAB code
Main MATLAB code

Estimation of debt issuance costs
The paper states that "This author's unreported calculation using the Fixed Income Securities Database (see Davydenko and Strebulaev (2003) for a description) over the period 1980--2000 suggests that the average underwriting and management spread is about 0.05% in yield which is consistent with a proportional cost of 1%, e.g. for a risk-free perpetuity when the risk-free rate is 5%."
Download the appendix

Autocorrelation of regression coefficients
The paper states that "Unreported results demonstrate that average coefficient on profitability is autocorrelated and behaves like an AR(1) process with observed maximum of about 0.75 and thus (see Fama and French (2002, p. 12)) the corresponding multiplication factor is 2.5. In other words, $t$-statistics are required to be around 5.0, rather 2.0, to reject the null hypothesis. The autocorrelation of the other coefficients is of the same order."
Download the appendix

Modelling of restructuring
Restructuring is assumed to occur instantaneously; thus, the costs that result from the time spent in default are modelled implicitly as restructuring costs. In other words, firms emerge from the reorganization process very quickly (albeit having lost a fraction $\alpha$ of their existing assets). It is easy to change the dynamics of the model, requiring firms to spend a randomly specified time in bankruptcy (using distributions established by empirical research, e.g. Franks and Torous (1989)). This modification is likely to have a negligible impact on cross-sectional dynamics (the only change is a small temporary reduction in the number of firms in the cross-section). Note also that in default the new owners continue to operate an unlevered firm yielding cash flows whose evolution is unchanged: one possible interpretation is that only rights are transferred to new owners, and $\alpha$ is the cost incurred in the course of this transfer.

More on empirical studies of distress
In Asquith, Gertner, and Scharfstein (1994) paper that is cited in the paper, the sample of distressed companies was restricted to firms which issued junk debt (i.e. originally non-investment grade debt). The motivation was to locate firms in financial, not economic, distress. I am not aware of any papers that study the so-called ``fallen angels'' (firms that lost their investment-grade rating) in financial distress. In another stream of research, Gilson (1990) and Gilson, John, and Lang (1990) study companies with the worst performance on NYSE and AMEX. Half of their sample that restructured debt, restructured through private workouts, and another half filed for Ch. 11.

Another way of modelling asset liquidity
Another variation of the model that I have considered is the one in which the firm starts selling assets proportionately to its value if the firms reaches the liquidity boundary. This model produces substantially lower leverage. It is unsatisfactory for at least two reasons: first, proportional asset sales mean that at least initially equityholders not only cover coupons with asset sales but also increase dividends. Second, asset sales continue if economic conditions of the firm improve until the next refinancing cycle. Introducing more realistic selling-to-cover condition (where assets are sold only in the amount needed to cover current coupon) makes the problem intractable.

Asset liqudiity: relation to the literature
Morellec (2001) also incorporates the model of asset liquidity. I compare his and mine models in the introduction. In addition to that discussion, in Morellec (2001) residual proceeds of asset sales accrue to equityholders. This decreases the attractiveness of bonds to debtholders and decreases optimal leverage substantially. In my paper proceeds from asset sales are used %exclusively to paid down outstanding debt.

Asset sales: anecdotal evidence
Anecdotal evidence from the financial press reports suggests that asset sales occur often and that asset sales costs may be even higher than those reported in Pulvino (1998). I have looked at all cases involving asset sales reported by the Financial Times between January and September 2003: results suggest that according to these reports, the discount may be up to 40-50%.

Comments on taxes
I ignore state taxes. While Graham (1999; 2000) estimates that state taxes may be about 0.025 to the total tax rate, he does not use state tax information in most of the analysis in order to minimize the effect of measurement error in the state tax rate. In addition, Gordon and Lee (1999) showed that marginal corporate tax rates appear to differ significantly between large and small firms. As such, the marginal tax rate used here is more typical of that faced by large firms. An estimate of the cross-section of marginal tax rates across firms can be obtained from the distribution described in Graham (1999; 2000). The difficulty arises in identifying the marginal personal tax rates (Mayer (1990), (Rajan and Zingales (1995)).

Additional comments on cross-sectional method
Bradley, Jarrell, and Kim (1984), in fact, used average characteristics of firms over many years. What is important, however, is that values of leverage and explanatory variables they used were defined contemporaneously. Also, in Rajan and Zingales (1995) as well as other tests, endogeneity in its wide definition can arise also because of omitted variables and measurement error. None of these reasons influence my analysis. Finally, Rajan and Zingales also employ a censored Tobit model since, in some cases, they face negative values of leverage which they truncate. They also report (their footnote 28) that the corresponding OLS results are very similar.

Welch regressions without a constant
Welch (2004) also reports the result of the estimation of the same equation without a constant. Both his and mine results are robust to such change in specification.
Details will be soon added here

Term structure of the IDR coefficient
I also extended the Welch study by producing a term structure of the coefficient on the implied debt ratio for each year up to $k=20$. The results show that the empirical and simulated term structure have similar patterns.
Details will be soon added here

Notes: Section IV of the paper reports a number of robustness tests. To save the space, it reports only a small fraction of them deemed to be more important and also presents only a summary of the results. An appendix to the paper (not included in the main version) discusses these robustness tests in detail). In this pdf file this appendix is provided.
Appendix will be soon added here

Notes: As a background analysis for this project, I replicated a number of empirical results reported in the literature. For the purposes of the porject, I checked robustness of these results for some particular configurations of data, e.g. only for value firms (with relatively high book-to-market), with hypothesized relatively small transaction costs, etc. Surprisingly, I have not found some distributional result on capital structure in the literature and have produced them as well. The pdf files below reports and discuss some of these results.
Description of dataset a nd sample selection: soon to be added
Distribution of leverage: soon to be added
Cross-sectional regressions of leverage determinants: soon to be added
Regressions on changes in leverage: soon to be added
Leverage and stock returns: soon to be added