مدل سازی غیر خطی از اهرم هدف با متغیرهای تعیین کننده پنهان - شواهد جدید در نظریه تجارت کردن

This paper applies a nonlinear structural equation framework to analyze dynamic capital structure choice. I test the hypothesis that firms adjust leverage towards a time-varying target, and that this target is determined by solving an optimization problem: optimal leverage is achieved when the difference between the expected net present value of the tax shield and the expected net present value of the costs of insolvency is maximized. Results indicate that firm size is an important determinant of the validity of this simple trade-off model.

This paper applies a new methodology to analyze firms' behaviour when adjusting their capital structure over time. By means of nonlinear structural equation modelling, a joint hypothesis is tested: first, that firms adjust their capital structure towards a moving target, and second, that this target is chosen so as to maximize the difference between the debt tax shield and costs of insolvency. Uncertainty about the value of future tax savings and the probability of insolvency is accomodated by applying a structural model of corporate default along the lines of Merton (1974), which has been specified using a jump-diffusion process so that it is capable of reproducing empirical patterns of credit spreads. This is achieved by explicitly stating the optimization problem that reflects the trade-off, and testing whether the actual target towards which observed capital structures converge can be proxied by the optimal solution. It is found that the explanatory power of the trade-off model depends on firm size: it can explain up to 24% of the variation of leverage adjustments of medium-sized firms, but only 16% (11%) for firms in the smallest (largest) size subsample. In addition, the explanatory power of the trade-off model is compared to a model that captures any linear relationship between company variables and target leverage and that does not distinguish between different theories of capital structure choice. The trade-off model explains most of the variation that is explained by linear relationships for medium-sized firms, but only around half of it for the smallest and largest firms. The approach taken here combines the theoretical concept of nonlinear dynamic models of optimal leverage, as in Goldstein et al., 2001 and Dangl and Zechner, 2004, with the idea of empirical adjustment models, such as recently applied by Byoun (2008), which, however, usually specify the target as a linear function of company variables. 1 This linear approach suffers from a number of drawbacks. First, establishing a significant linear relationship between a company variable and the leverage target can provide support for the claim that a certain company characteristic plays a role in determining the capital structure target. However, in a number of cases, different theories on capital structure choice lead to the same hypothesis regarding the relationship between an observable determinant variable and target leverage.2 In such a case, the statistical analysis cannot provide criteria for or against a particular theory. The hypothesis of this paper is rather that a specific model of the underlying economic decision and coordination problem can explain observable patterns of leverage. The approach taken here is based on the trade-off theory and could act as a benchmark for future attempts to model that problem. If observable patterns will be explained better (or worse) by a different model, this would be a challenge to (or support for) the trade-off theory. Second, specifying the target as a linear function ignores nonlinear relationships between firm characteristics and target leverage. Instead, this paper specifies target leverage as a non-parametric function of company characteristics. This approach is consistent with the hypothesis that coordination on the capital market leads to a capital structure that maximizes the value of the total cash stream flowing to shareholders and debtholders. Third, theories predict relationships between corporate characteristics and target leverage, while empirical studies usually assess relationships between observable variables and target leverage. This ignores measurement error, and neglects additional information on the same characteristic that could be provided by different observable variables. In contrast, in this study, relevant corporate characteristics – asset volatility and loss given default – are defined as latent variables in a structural equation framework, where a number of observable instrumental variables are used to estimate the latent characteristics ( Table 1).Leverage has various effects on firm value beyond the tax shield and costs of insolvency, such as agency effects (see Jensen, 1986, Jensen and Meckling, 1976 and Myers, 1977) and signalling effects, see Myers and Majluf, 1984 and Ross, 1977. However, CFO survey results indicate that taxes on company level and the risk of insolvency are more important factors for real-world capital structure decisions than agency costs or signalling issues, see Graham and Harvey (2001), pp. 11 ff. for the U.S. market, Bancel and Mittoo (2004), pp. 113 ff. and Brounen, De Jong, and Koedijk (2006), pp. 1414 ff. for the European market. However, managers might be hesitant to admit that their decisions are governed by agency issues, so that survey results could understate the true relevance of agency costs. Furthermore, survey results show that the majority of managers aim at attaining or maintaining a capital structure target. Theoretical relationships between the tax shield, the costs of insolvency and the value of the firm are straightforward, whereas some agency or signalling effects imply costs associated with debt as well as benefits. Because of that, there is no robust model that quantifies these costs and benefits, and it suggests that this ambiguity prevents decision-makers from assigning too much weight to them. This provides support for concentrating on the trade-off model in empirical studies. Apart from that, there are leverage effects that pertain to redistributing wealth between different investors. These play a significant role in managers' decision-making. Market timing seems to be especially important (see e.g. Baker & Wurgler, 2002). By timing the capital markets, directors can exploit private information and transfer wealth from new shareholders or debtholders to old shareholders. Survey results support the case for the importance of market timing (see e.g. Graham and Harvey, 2001 and Bancel and Mittoo, 2004). These effects cannot be incorporated into the value optimization problem suggested in this study, and variation in leverage adjustments beyond those that can be ascribed to the trade-off theory are likely to be strongly influenced by distributional effects. The results of this paper suggest that the relative importance of different effects with an influence on capital structure decisions varies with firm characteristics, most noticeably with firm size. The rest of the paper is structured as follows. Section 2 briefly presents relevant results from the empirical literature on capital structure, while Section 3 describes the model and its calibration and estimation. Section 4 provides details on data sources and adjustments, Section 5 presents and discusses the results and Section 6 concludes.

This paper investigates firms' behaviour when they adjust their capital structures, which is particularly relevant for valuing debt instruments, because the risk of insolvency is sensitive to the firm's capital structure policy. The hypothesis that leverage converges to a time-varying target implied by the trade-off theory of capital structure choice is tested. For that, an optimization problem for capital structure choice based on the trade-off between the expected debt tax shield and expected costs of insolvency is set up. The problem is solved for optimal leverage as a function of two latent company characteristics: asset volatility and losses in case of corporate default. Due to the unobservability of these, a nonlinear structural equation model is developed to measure these latent variables and estimate an adjustment-type model for corporate capital structure simultaneously. This allows an assessment of the explanatory power of the trade-off model relative to a linear specification which accomodates any linear relationship between firm characteristics and leverage. From a methodological viewpoint, the contribution of this study lies in a simulation-based estimation procedure for a structural equation model of dynamic leverage with a nonlinear target leverage specification. Modelling the capital structure target as a linear combination of company characteristics has the result that any theory which implies a relation between this kind of company characteristic and the capital structure target can receive support by observing a significant coefficient. However, this means that linear regression models will not allow the rejection of a theory on capital structure choice, unless any other theory would imply an insignificant relation or a relation with a different sign. The model presented here indicates how much of observed capital structure changes can be explained by the trade-off theory. Results suggest that leverage converges to a target — and that the choice of this target is dominated by the trade-off theory for medium-sized firms, but only partially influenced by the trade-off theory for very small and very large firms. However, the trade-off model cannot fully explain capital structure decisions; nor can it provide as much explanatory power as a linear specification of target leverage. Factors other than tax and insolvency costs influence capital structure choice. Among these are value effects, which imply that changes to leverage result in changes of the value of the total cash flow stream flowing to equityholders and debtholders. Agency costs or signalling effects are a good example. Distributional effects relating to a redistribution of wealth between old and new equityholders and bondholders, such as market timing effects, are also relevant. Although the results suggest that the trade-off theory is relevant to some considerable extent, questions remain regarding how much of the variation in capital structure adjustments that can generally be explained by capital structure theories is truly determined by the trade-off concept. The reason is that we do not have a reasonable model that incorporates the trade-off theory and also other effects such as agency costs, signalling or market timing effects. If, for example, agency cost effects could be incorporated into a nonlinear model explicitly by estimating the marginal effect of debt on agency costs, a better proxy for target leverage could be found compared to the proxies used to date. Furthermore, the decision whether to actively adjust or not, which is a result of trading off deviation costs against adjustment costs, could be specified as part of the optimization problem of capital structure policy. Industry- and size-related variation in the speed of adjustment, as found in this paper, indicate that the determinants of decisions regarding the frequency and the intensity of measures to alter the capital structure could be a relevant issue for further investigation. Byoun (2008) formulates the idea of a “unified theory on capital structure”. A unified theory would argue that bankruptcy costs, the tax shield, signalling effects, agency costs, financial flexibility, transaction costs in general and also costs to alleviate informational asymmetries all influence the current leverage ratio. It would require an hypothesis on the relationship between heterogeneous firm characteristics, market conditions and target leverage, and an hypothesis on the relationship between target leverage, adjustment costs, the previous path of leverage and the predicted next step. It would be based on discrete adjustments to leverage, because an adjustment will take place as soon as the benefit of adjustment exceeds the cost of deviation. This study is a first and basic step in that direction, as it defines a model of target leverage as a function of firm characteristics and one macroeconomic variable (the interest rate) based on economic theory and not on empirical relationships. However, it can serve as a framework for elaborations.