Capital structure decisions under classical and imputation tax systems: a natural test for tax effects in Australia.

Abstract:

The paper investigates determinants of capital structure, focusing on tax incentives for debt. The paper makes use of a panel of Australian firms in two tax regimes: a classical regime, and a dividend imputation regime. An important feature is the identification of the economic model using Bayesian selection methods. This methodology offers a new way of examining and assessing interactions between variables where there are competing explanations, noisy data and no unifying theory. As hypothesized, the results demonstrate a significant tax coefficient during the classical era and an insignificant tax coefficient in the imputation era. Risk and signalling variables, represented by firm size, Z-score, operating risk and asset base are also found to help explain capital structure choice.

Keywords:

TAXATION; IMPUTATION; CAPITAL STRUCTURE; BAYESIAN VARIABLE SELECTION.

1. Introduction

Understanding and explaining corporate capital structure is one of the most challenging issues in modern financial economics. Modigliani and Miller (1958) show that capital structure is irrelevant if capital markets are perfect. Since that time, dozens of theories and hundreds of articles have been written that seek to explain which market imperfections make capital structure relevant (see Harris & Raviv 1990; Graham 2003 for reviews). For example, Modigliani and Miller (1963) show that if interest is tax deductible but equity payout is not, and corporate profits are taxed, there is a tax incentive for firms to finance with debt.

This paper attempts to identify the factors that are most important in describing corporate capital structure. It uses an experimental design and statistical technique to address key problems that arise in empirical capital structure research. The first of these is that there is no unifying theory that nests all of the candidate theories and variables hypothesized to explain capital structure. This poses a statistical problem for empirical researchers because there is no clear set of structural equations or moment conditions that one could write down to simultaneously test all of the capital structure theories, and hence determine which set of variables are optimal. In practice, the standard approach is to perform a linear regression that contains the key variables a particular paper is investigating, as well as a host of 'control variables' empirically included to 'hold constant' non-modelled influences. These other factors include asset type, financial risk, firm size and non-debt tax shields. (1) However, there is often no statistical justification for adopting this common approach. The current paper deals with this issue by using a Bayesian technique (described below) that performs a statistically justified variable selection to choose the factors that are deemed most likely to explain observed capital structure.

The second problem with many empirical capital structure investigations is that the explanatory variables are often correlated, which can make it difficult to identify unambiguously the root cause of observed capital structure. Consider the hypothesis that high tax rate firms should use more debt than low tax rate firms. This is an important hypothesis because the tax benefits of debt are often modelled as the primary benefit of using debt; therefore, it would be helpful to unambiguously document that tax rates and debt usage are positively correlated. (2)

There has been progress in terms of unambiguously identifying tax effects in terms of measuring tax rates with sophisticated simulation techniques (Graham 1996a, b) and in addressing the endogeneity of the effective corporate marginal tax rate (Graham, Lemmon & Schallheim 1998). However, tax rates are correlated with size, profitability and other factors hypothesized to explain capital structure, so it is possible that a significant tax coefficient might be spurious in the sense that it actually captures a nontax influence (typically, these other factors are controlled for in a multivariate regression sense--but these controls might be imperfect). In this paper an experimental design that allows isolation of tax effects separately from other capital structure influences is used. (3) This is done by examining a panel of Australian firms in two different tax regimes, one where there is a tax incentive to use debt and one where there is not. This allows for each firm to be its own control for nontax influences, thereby isolating the effect of tax incentives on corporate debt usage.

Prior to 1986, Australia had a classical tax system like that in the United States, in which there is a tax incentive to finance with debt. After a 1986 tax reform, Australia adopted an integrated (i.e. dividend imputation) tax system in which, attached to dividend payments, shareholders receive a tax credit for taxes paid at the corporate level. This imputation effectively puts dividends on the same footing as interest deductions from the corporate perspective, thereby eliminating the tax benefit of debt. The main result is that there is a positive and significant tax coefficient in the classical system, as hypothesized, but the coefficient is not significantly different from zero in the imputation regime (as expected). If the significant tax rate in the classical tax system were proxying for some nontax effect, it would be expected to also be significant in the imputation era. The fact that it is not solidifies the case that there are tax incentives to use debt under the classical tax system.

In the language of the Bayesian model, the posterior probability is 84% that corporate tax rates are a positive, causal influence on the corporate use of debt in the classical system. The paper describes below how an OLS regression is just one of many possible empirical specifications. The significance of the tax coefficient is also confirmed in an OLS regression. The Bayesian statistical approach allows inference of the importance of other, nontax variables. Asset tangibility (with a 100% posterior probability of causally influencing debt decisions) is the most important capital structure influence. The probability of bankruptcy, equity beta, and to a lesser extent firm size, dividend yield and growth opportunities also help explain debt policy.

Similar Bayesian techniques have been used recently to investigate asset pricing issues such as investor portfolio choice and the equity market risk premium, for example Pastor and Stambaugh (1999, 1997). There are two basic types of analyses: variable selection and model selection. Variable selection involves identifying from a group of variables that subset which best describes the data under analysis and has been recently used by Kandel, McCulloch and Stambaugh (1995), and as cited above. Model selection involves selecting a model/s from a prescribed group those which best describe the data. In this paper the variable selection technique is used to select the best empirical model in terms of explaining corporate capital structure. To the best of the author's knowledge, this is the first paper that uses Bayesian techniques in a corporate finance context.

The Bayesian process offers information about the linear association between the dependent and explanatory variables on the basis of the estimated joint posterior distribution of all variables of interest. Typically this is what multivariate regression analysis seeks to address by the use of control variables. However these controls might be imperfect, that is, a coefficient may be spurious in the sense that it actually captures nontax influences. (4) The outcome is that the results from the variable selection process are robust against a number of factors such as over-fitting and data mining. The method we use also addresses multicollinearity, innovation outliers, and heteroskedasticity. More details are provided in Section II and in the appendix.

The remainder of this paper is structured as follows. Section 2 discusses capital structure theories and the variables that we use to proxy for theoretical inputs. Section 3 provides an overview of the Bayesian variable selection methodology. Section 4 details the data and variable construction. Section 5 reports results and section 6 concludes. The appendix details the Bayesian econometric methodology.

2. Theoretical Explanations of Debt Policy

2.1 Tax Explanations of Debt Policy

The tax rules under which a firm operates are an important factor influencing corporate debt policy. The standard assumption, dating back to Modigliani and Miller (1963) is that there is a positive tax incentive to use debt financing. This incentive occurs because corporations make interest payments out of pretax income but make equity payments after corporate income taxes have been paid. What is usually not emphasized is that this incentive only applies under a classical tax system, like that in the United States. In fully integrated, or dividend imputation, tax system shareholders receive a tax credit for taxes paid at the corporate level with their dividends, which is equivalent to the corporation paying dividends out of pretax income. Therefore, under a full imputation tax system, there is no tax incentive to finance with debt.

This paper exploits a change in the tax system in Australia to isolate tax incentives to use debt in the classical tax system. Prior to a 1987 tax reform, Australia operated under a classical tax system. In 1987 an integrated tax system was implemented specifically to reduce the after all taxes differential between debt and equity financing. The study utilizes a panel of firms that operated under both tax regimes. If taxes exert a positive influence on debt use in the classical system, the hypothesis is that there should be a positive coefficient on a tax variable included as an explanatory factor. It is hypothesized that a significant coefficient on the tax variable during the imputation regime should not be identified. If it is found this would be consistent with the tax variable proxying for some non represented effect and cloud the interpretation of the significant coefficient during the classical era.

The marginal tax rate (MTR) proxy by construction incorporates the substitution effect of non-debt tax shields as hypothesized in DeAngelo and Masulis (1980) and demonstrated by MacKie-Mason (1990). Marginal tax rate captures the substitution effect since low MTRs will occur only in those firms who are unable to utilize all their tax shields.

Dividend policy is interrelated with the tax incentive to finance with debt. Under tax imputation, shareholders of firms that pay dividends receive a tax credit equal to the Australian corporate tax paid on the gross profits that generated the income used to pay dividends. For example, a firm who pays Australian tax at 33% and pays a $1 dividend is deemed to have made the tax payment of 33cents on behalf of the investor. Therefore, the recipient of the dividend receives a tax credit of $0.33 and a cash dividend of $0.67 equal to a total imputed dividend of $1. This tax credit sometimes referred to as a 'franking credit,' can be used to offset tax owed on the dividend or any other income. Dividends that carry a tax credit equal to the full Australian corporate tax rate are 'fully franked.' Tax legislation defines which groups of investors are eligible to benefit from this tax credit. Therefore only certain subgroups of investors in the Australian equity market have a value for the tax credit, typically these investors are domestic individuals and pension funds. Where investors cannot utilize the tax credit, for example tax exempt and foreign investors they will not wish to receive franked dividends but prefer equity income as a capital payment or unfranked dividend. Depending on the presence of equity clienteles based on tax preferences for franked dividends there is either a negative or no association between change in debt and dividend yield.

2.2 Nontax Explanations of Debt Policy

The trade-off theory of capital structure suggests that firms will ex ante balance the tax benefits of debt against the expected costs of financial distress. Therefore it is hypothesized that, ceteris paribus, firms with higher ex ante expected costs of financial distress use less debt. In addition to financial risk, risk can also arise from the nature of the business in which a firm operates, that is, firms with large operating risk, as measured by asset beta, will use less debt.

Many debt contracts are collateralized by a specific fixed asset. Therefore, all else equal, firms that use more fixed assets in the production process should use more debt financing. Moreover, relative to intangible assets, fixed assets are more valuable in liquidation and hence support a higher debt capacity.

Myers (1977) argues that shareholders of a firm with risky fixed claims in its capital structure will potentially forgo positive NPV investments if project benefits accrue to the firm's existing bondholders. Myers suggests that the incentive to underinvest (resulting from the conflict between bondholders and stockholders) can be mitigated by reducing the amount of debt in the firm's capital structure, by including restrictive covenants in the debt contracts, or by shortening the maturity of the firm's debt obligations. This argument suggests that firms with more growth options in their investment opportunity sets should use less long-term fixed-rate debt.

Agency costs can occur when a firm has excess free cash flow. Jensen (1986) argues that a firm can issue debt to disgorge cash from the firm. Having contractually fixed interest obligations due each quarter provides the discipline to force companies to operate efficiently, thereby reducing agency costs. If firms follow Jensen's suggested course of action, one expects to find a positive association between debt use and changes in free cash flows. In contrast to this argument, the pecking order hypothesis (Myers & Majluf 1984; Shyam-Sunder & Myers 1992) proposes that firms only finance with debt when internally generated free cash flow is low. This implies a negative relation between debt and free cash flow.

Size-based theories suggest that large firms are more likely to be debt financed than their smaller counterparts. This might occur because large companies are more diversified and have more stable cash flows. Additionally, large firms might be able to exploit economies of scale in issuing securities. Because of information asymmetries, smaller firms also are likely to face higher costs for obtaining external funds. Therefore, debt usage is expected to be positively related to the size of the firm.

Firms with plentiful growth (investment) opportunities will use little debt. If a firm were to encounter distress or be forced to liquidate, growth options would be worth relatively little (Myers 1977). The paper measures growth opportunities (lagGO) as the one-year lagged market value of equity over book value of equity capital, and expect lagGO to be negatively correlated with changes in debt. Firms with large value of lagGO are expected to issue little or no debt.

Australian firms can be dichotomized into two main groups: industrial firms and resource firms. Resource firms are characterized by greater volatility in earnings and are more cyclical. We conjecture that resource firms use less debt.

3. Bayesian Variable Selection Methodology

The standard approach used in empirical capital structure research is to perform a multivariate analysis regressing the debt ratio on a collection of explanatory variables. The significant factors are those with p-values smaller than a pre-chosen cutoff like 0.05. One issue that arises with this approach is that the variables are tested as part of one big multivariate system, although the variables come from a collection of different (often univariate) economic models. There is no unifying theoretical model of corporate capital structure that helps the researcher know which is the 'best' specification, and which variables should be included in the presence of others. The standard approach interprets the explanatory variables that have significant p-values as providing the best specification. However, this approach does not inform the researcher how much better or worse the specification would be if various subsets of the collection of possible variables were used to model corporate capital structure.

Lacking a theoretical approach that tells us which model is ideal, the current paper turns to Bayesian econometrics to select statistically the ideal, or best, model from among the dozens of possible permutations. In particular, a Bayesian variable selection method that explicitly incorporates the uncertainty of the capital structure interactions is applied to data analysis. The uncertainty results because there is little agreement in the literature concerning the form of the ideal model explaining capital structure. Moreover, the factors that are hypothesized to explain capital structure do not combine into obvious nested models.

The remainder of this section provides an intuitive explanation of why variable selection is an appropriate tool to investigate capital structure, and the difficulties that face the researcher who makes use of classical statistics selection procedures. The Bayesian methodology used (that of Smith & Kohn 1996) is also outlined. The details are provided in the appendix.

3.1 General Discussion

Classical statistical techniques are commonly used to estimate underlying 'true' parameters, implicitly assuming that there is a single 'true' model. Testing procedures assess whether or not the observed measure is likely to come from the underlying true population. Variable selection in the classical setting often implicitly assumes that the identified 'winner' will be in fact this 'true' underlying model. This is not necessarily the case (Chatfield 1995). When the underlying model is not known the researcher can only hope that the selected model is the best estimate of the true model.

As mentioned above, there is no single definitive model describing the economic variables that drive the debt decision, nor how these variables might influence one another. In fact, several different models can fit a given data set relatively well. These candidate empirical models can consist of different collections of variables and therefore imply different answers to the questions of interest. This plethora of candidate models can be thought of as model uncertainty. Raftery (1994) states that the researcher has three choices when facing model uncertainty: (1) pick one model and assume it is the true or best model (the usual solution adopted); (2) choose numerous the models and discuss all of them (a cumbersome procedure); or, (3) take explicit account of model uncertainty in the construction of the test procedures. The Bayesian variable selection technique follows the third approach.

3.2 Non-Nested Models and Model Averaging

Classical model selection procedures usually assume that the competing models of capital structure are nested. This in fact may not be the case, where the researcher compares competing hypotheses that represent different views of the phenomenon, for example tax-based explanations of capital structure versus signalling explanations. Classical tests for non-nested models can be difficult to implement and interpret. For example, in the comparison of two models, two tests are made, one with each model as the null hypothesis. These tests are not always easy to interpret, and in some circumstances the test fails to reject both models as null, or (particularly in large samples) both are rejected. In these cases it is not possible to choose between the competing models.

A common feature of corporate finance data is that a number of models may provide a similar fit of the data. A classical procedure that identifies a single best model might ignore information in the near-to-best models. The Bayesian variable selection technique permits construction of parameter estimates for a probability weighted average model.

The parameter estimates of the average model contain information that is missed when choosing a single 'best' model. It also allows for the incorporation of information from non-nested models without forcing the researcher to choose between them.

In summary, the Bayesian variable selection process calculates the posterior probabilities for all the alternatives. This permits the researcher to select among a collection of candidate variables. Because the Bayesian process describes posterior distributions, it offers information concerning the relative suitability of variables and can identify more than one model that describes the data well. In this case the parameter estimates of the simplest of the models are often chosen (Kass & Raftery 1995). The parameter estimates of an average model can also be identified. This average model can be interpreted as the most 'sensible' model to explain the associations of interest based on the joint posterior distribution of the variables (Box & Tiao 1992) and is the method used here.

The Bayesian methodology addresses outliers and multicollinearity. Outliers are considered by constructing different population density functions for the data. The procedure weights the data points on the basis of an assessment of which population they are most likely to have come from. Multicollinearity is addressed because the sampler covers the entire model space. In instances where the posterior probabilities of models with one or other of the correlated variables are close to models with both, Bayesian model selection reflects this by choosing models with one of the two variables more frequently than models that include both. This process means that the selection avoids both when one is sufficient, but also shows that either variable could be used. The final outcome of the Bayesian variable selection method is that the researcher is provided with a large amount of statistically robust information concerning the data under examination.

4. Data Sources and Variable Design Issues

The sample is based on the Global Vantage database. Global Vantage includes Australian firms that are part of the Australian Stock Exchange All Ordinaries Share Price Index. This index is comprised of approximately 270 firms. The market value of the shares of all firms comprising the index is approximately 90% of the market value of all shares traded on the Australian Stock Exchange. Bank and finance firms and companies whose sole value comes from gold because gold firms were tax exempt until 1991 are excluded. In some instances, the Global Vantage data is supplemented with data from the CRIF (5) database and hand collected data from annual reports.

The sample contains 67 firms that exist every year 1982-1993. The focus on this set of firms, even though this sample is subject to survivorship bias, is because each firm is used as its own control for non-tax incentives to use debt. The 67 firms account for approximately 75% of the total market capitalization of the Australian Stock Exchange at the time.

The data analysis is performed on three subsets of the data: 1982-1986 (the classical tax system, where there is a tax advantage to debt); 1989-1993 (the dividend imputation tax system, in which there is no tax advantage to debt); and, 1994-1998 (an unbalanced panel data set). The starting date for the early period is set to avoid significant regulatory changes that occurred in the Australian debt market in the early 1980s. The latter periods are selected to observe debt policy after tax reform but avoid the transitional years 1986 and 1987. The first imputation subset runs across a period of recession in the Australian economy, whereas the later subset is during a period of healthy economic performance.

The remainder of this section describes the variable definitions and related issues

4.1 Dependent Variable

The dependent variable ([DELTA]DEBT) is the first difference in book value of total debt standardized by the market value of the firm (market equity plus book debt). Total rather than just long term debt is used because the primary hypothesis investigates tax incentives to use debt. Short-term debt accounted for an average of 28.5% of total debt during the sample period. Total debt as a percentage of the market value of the firm ranges from zero to 430% with a mean of 68% and a median of 36% over the sample period.

Changes in debt, rather than levels, are examined for two reasons. First, as pointed out in MacKie-Mason (1990) and Graham (1996a), debt levels represent the accumulation of many years of debt decisions, potentially affected by many different tax and nontax influences over the years, which might make it difficult to identify tax effects affecting debt levels in any given year. Moreover, transactions costs can limit the size or frequency of recapitalizations to the optimal capital structure. By focusing on changes in debt, all that is required is that firms move towards their optimal debt ratios in response to tax and other economic incentives.

The second reason for examining changes in debt is that there can be a spurious negative association between debt levels (i.e. debt ratios) and marginal tax rates. As debt ratios and interest deductions increase, effective marginal tax rates decrease because it becomes more likely that a firm will be tax exhausted and not pay taxes in some states of nature. As the probability that a firm does not pay taxes increases, its expected tax rate decreases (see Graham, Lemmon & Schallheim 1998). The test examines whether the lagged marginal tax rate affects current-period changes in debt, thereby avoiding this spurious negative influence on the tax variable coefficient.

4.2 Explanatory Variables

4.2.1 Tax Variables The economic marginal tax rate is defined as the present value of all present and future taxes owed from earning an extra dollar of income today. Recent research highlights several advantages to calculating marginal tax rates using simulation methods that account for historic and forecasted future income (Shelving 1990; Graham 1996a, 1996b). Simulated tax rates can capture the effects of the current tax status of a firm (is an extra dollar earned today taxable or not), the tax-reducing benefit of existing tax-loss carryforwards (do loss carryforwards shield current and future income from taxes, thereby delaying when taxes will be owed on an extra dollar earned today, thereby reducing the economic marginal tax rate), and the probability of encountering future losses (which in some tax regimes can be carried back to offset taxes owed on an extra dollar earned today, effectively reducing the current period tax rate). The simulated tax rate captures the effect of future carrybacks because it forecasts the probability of future tax losses that can be carried back to obtain a refund on taxes paid today.

Manzon (1994) proposes a tax rate that captures some of the advantages of the simulated marginal tax rate but is easier to calculate. The Manzon tax rate equals the top statutory tax rate for profitable firms. If the firm is unprofitable, the tax rate equals the top statutory tax rate discounted N periods, where N equals the firm's year-end accumulated tax-loss carryforward divided by the firm's expected annual taxable income. For example, assume that the statutory corporate tax rate is 35%. If a firm earns $1 million every year but year t, and has a loss in year t that leads to a tax-loss carryforward of $4 million at the end of year t, its Manzon year t tax rate is 0.35/(1+r) (4). The intuition is that a hypothetical extra dollar earned today (i.e. making the total loss $1 less than $4 million) would lead to increased tax liability in year t+4.

Graham (1996b) demonstrates that the simulated marginal tax rate is the best available tax rate in a tax system (like that in the US) that allows firms to carry forward and carry back tax-losses. In contrast, Graham finds that the Manzon (1994) tax rate is a poor variable in such an environment. The shortcoming of the Manzon tax rate is that it does not anticipate the probability of future losses that can be carried back to offset current period taxes. However, this weakness is not important in Australia because Australian firms are not permitted to carry back losses. Pattenden (2002) reports that the Manzon tax rate is nearly as good as the simulated tax rate in a tax environment without carrybacks, such as Australia.

Further the data set does not contain sufficient history to permit calculation of the simulated tax rate for analysis. Instead, a variation of the Manzon tax rate in is used (MTR). A variation is constructed because firms are not required to report NOL carryforwards in Australia, which makes it impossible to calculate N as an input into the Manzon tax rate. The tax variable is constructed assuming that profitable firms are taxed at the top statutory tax rate. For loss firms, it is assumed that N equals four for all firms (approximately half of the seven year carryforward period current during the study). This assumption works against finding significant tax coefficients in the classical era. Firms with small (large) losses should have a smaller (possibly larger) N than assumed; therefore, the study assigns tax rates that are too small (possibly too large) for firms with small (large) losses. Given that it is expected that firms with small losses (i.e. relatively high tax rates) probably use more debt than firms with large losses (i.e. relatively small tax rates), the assumption that N = 4 for all firms induces a negative bias in the tax coefficient.

The value used as the taxable income to compute the marginal tax rate above is the firms reported net taxable income less depreciation. This adjustment allows for a measure of the effects of non debt tax shields rather than using a depreciation variable. The difficulty with using a depreciation variable is that many highly profitable firms have large depreciation schedules which are not debt substitutes.

Following Graham (1996a), the lagged tax rate is set as explanatory variable. The idea is that the tax rate at the end of one year affects the debt decisions in the coming 12 months. Also, using a lagged tax rate ensures that the tax variable is not endogenously affected by current-period debt policy. A positive relation between MTR and debt usage in the classical period and no relation in the dividend imputation period are hypothesized.

The remaining tax variable is dividend yield, which is measured as aggregate dividends in a given year divided by year-end shares outstanding. A negative relation between debt usage and dividend yield in the classical era and an uncertain or positive relation in the imputation era is predicted.

4.2.2 Nontax Variables The probability of bankruptcy is measured using a variant of Altman's Z score (Z-score) (see Mackie-Mason 1990; Graham 1996a). Izan (1984) developed a version of Z-score specifically for Australia. The variation used here is described in Bishop, Crapp, Faff and Twite (1988) and has been shown to predict bankruptcy well in Australia.

(1.2 current assets + 1.4 retained earning + 3.3 taxable income + sales)/total assets + 0.6 market cap/ total debt (1)

Z-scores are trimmed at +5 to prevent extreme values influencing the results. The range to plus five is sufficient to estimate the likelihood of financial distress, since it is well outside the default range (below 1.81).

Operating risk is proxied with asset beta, calculated as

[[beta].sub.e]/(1+D/E).

The equity beta ([beta]e) is estimated using a 48 month estimation period for each firm prior to the firm year. Debt (D) is total debt and equity (E) is the market value of equity. Firms with high operating risk are considered less likely to issue debt, particularly in economic recessions (Ross 1985). Debt usage is expected to be negatively related to asset beta ([beta]ASS).

Growth options (lagGO) are measured as the one-year lagged market value of equity over book value of equity capital. Growth options are lagged so that actions taken in the current period can not affect the variable. Free cash flow ([DELTA]FCF) is measured as change in net income plus depreciation, standardized by total assets. It is assumed that reinvestment in working capital is equal to depreciation. A positive relation between debt usage and both lagGO and [DELTA]FCF is hypothesized.

Asset tangibility ([DELTA]TAN)is measured as the change in fixed assets standardized by total assets. The change in firm size ([DELTA]SIZE) is captured as In real [sales.sub.t]--ln real [sales.sub.t-1]. A positive relation between ([DELTA]DEBT) and changes in both asset tangibility and firm size is expected.

Finally, a dummy variable is used to indicate whether a firm is part of the industrial (1) or resource sector (0). The coefficient on this dummy is hypothesized to be positive.

5. Results

Descriptive statistics for all three periods are set out below in tables 1 and 2. The results of the Bayesian analysis for each period are detailed separately.

The correlations in table 1 identify a strong correlation between change in debt ([DELTA]DEBT) and change in tangible assets ([DELTA]TAN). This flows through to the results of the analysis. Table 2 shows that change in debt declines from the early classical tax period to the last imputation tax period. This suggests that overall companies reduced the level of debt funding across the period of the study and moved to equity funding as an alternative. This change is supported by other studies of the dividend and equity practices of Australian firms during this time (e.g. Pattenden & Twite 2004). Other notable changes include a decline in growth options and a decline in free cash flow.

The Bayesian results document the estimated parameters for the average model. As well as the average beta estimates, the five most popular models of the total possible models ([2.sup.10]) in each subset are detailed. These are the sets of variables that were selected most frequently. The average model is essentially a weighted combination of the most popular models. The posterior distribution of each indicator variable is documented. This gives an indication of the relative importance of the variables in explaining the change in debt.

The control for outliers allows the association between each variable and change in debt to be characterized with less noise. The use of the Bayesian methodology in this situation supports the arguments of such papers as Graham (1996a) and Scholes and Wolfson (1992), that the absence of expected effects in much empirical work may be a result of noise in the measurement methodology.

5.1 Years 1982-1986

The results of the Bayesian analysis are set out in tables 3, 4 and 5.

Table 3 documents the five most popular models identified and shows that there is very little distinction between the five and that one model dominates. This is indicated by the percentage of times each model is chosen. If one model were really better than all the others it would be chosen with a much higher frequency. Such a result is a common outcome in corporate finance where a number of models may be similar in their ability to describe the data associations. The results of table 3 support the choice of an averaging process for the parameter estimates rather than the estimates arising from a single model. Marginal tax rate was consistently preferred as an explanatory variable for change in debt during this period. Other important variables identified include tangible assets and risk variables.

The evidence from the most popular models is confirmed by the results in tables 4 and 5. Table 4 documents the average beta estimates and their standard errors. The results here support the economic contentions in the hypotheses that high marginal tax rate firms will issue more debt under a classical tax system. Firms with significant asset backing tend to issue debt and firms with a high probability of bankruptcy or with operating risk tend to issue less debt. Firm size is also associated with changes in debt indicating that as firms grow their capacity to issue and use debt increases.

Table 5 provides the posterior distribution of the indicator variable and evidences the percentage of times a parameter was selected in the sampling period. This allows a ranking of the influence of the economic variables on changes in debt. It reinforces the results of the average beta estimates in table 4. The posterior probability distribution of the MTR is 94% whiles that of tangible assets and Z-score are 100%. This result demonstrates that these three variables dominate the models relative to the other variables. Beta of assets, growth options and size are all marginally important being chosen approximately 50% of the time across all the model possibilities.

It can be seen that the model selection process identifies probability of bankruptcy, tangible fixed assets, marginal tax rate, and risk as important factors influencing change in debt. Growth options and size are also found to be significant.

A comparison of tables 3 and 5 illustrates the improvement in information flow from the Bayesian methodology; the posterior distribution of the indicator variable is across all the inputs and is more informative than a single set of variables. Table 3 indicates that in the most popular model set size is not identified as a variable of interest. However, from the posterior probability density of the indicator variables it can be seen that size is of considerable interest in explaining change in debt (probability of 0.436).

Overall, the results of the Bayesian analysis of the firms between 1982 1986 give strong support for the theoretical expectations of the interactions between debt and firm characteristics in a classical tax system.

5.2 Years 1989-1993

This period was a time of economic recession in Australia with a focus on firm stability and quality. This concern is captured in the strength of some of the control variables such as size and risk in the results for this period. The five most popular models from the Bayesian analysis (table 6) offer some interesting insights into the interactions between change in debt and the variables of interest in this period. Notably the marginal tax rate is not always selected as a determinant of change in debt. Tangible assets and firm size are the most important variables, also Z-score a measure of financial risk.

The parameter estimates of the average model and the percentage of times variables are selected support the findings of table 6.

In table 7 the average beta estimates demonstrate that there is little association between tax and debt in this period. There is also support for a strong positive association between free cash flow and debt as well as tangible assets and size. These measures support the theories that strong liquid firms with good assets bases tend to issue more debt.

Table 8, percentage of times a variable is selected, illustrates the unimportance of the tax variable. Table 8 shows considerable support for associations between Z-score and free cash flow with change in debt where Z-score is identified 65% of the time and free cash flow 60%. Size as measured by change in real sales is more strongly identified in this sub period, 99% of the time across all the model alternatives. As noted above in a recession economy the presence of strong revenues is more likely to be associated with a tendency to increase debt obligations.

5.3 Years 1994-1998

The final period comprises of a sample of firms which is somewhat different to the sample used in the previous periods. This sample of firms comprised a number of the firms in the other two periods but includes some new firms and has lost some of the previous firms. This allows a control for survivorship bias effects in the sample. Table 9 sets out the most popular models and MTR is not chosen in any of these five models. Again however, size and tangible assets are strong model choice variables.

The estimated beta measures (table 10) demonstrate that in the period tangible assets and size as a measure of firm profitability and asset base are positively associated with change in debt. Also free cash flow, growth options and operating risk are all negatively associated with debt. These results support the information and risk arguments for capital structure choice.

The absence of a significant measure for the marginal tax rate as found in the earlier imputation sub-period supports the hypothesis that under an imputation tax regime the preference for debt funding driven by corporate taxes is removed.

Table 11 sets out the posterior probabilities for the period and endorses the conclusions drawn from the beta estimates. In particular it is observed that the probability of the marginal tax rate being chosen across all the models is only 18% whilst free cash flow, growth options, beta of assets are all important being identified approximately 50% of the time. Size is present 100% of the time.

5.4 Period Comparison

The differences between the periods can be seen in figure 1, which represents the posterior densities of the indicator variables. The most important difference between the sample tax periods is that in the later periods marginal tax rate is not identified as an important variable. By 1988 dividend imputation and other tax reforms were in place and by 1994 were well established in the economy. The results offer strong support for the contention that under an integrated tax system there is no tax advantage to debt.

[FIGURE 1 OMITTED]

Tangible assets, firm size and financial risk (measured as Z-score) are identified across the data as significant in explaining changes in debt within a firm. This makes economic sense in that a strong asset backing together with a strong revenue base would be expected to be associated with optimal debt usage. Similarly, beta of assets as a measure of operating risk is identified as important. This effect is more observable in the earlier period, which was a booming economy with high debt equity ratios. These factors all provide support for the signalling and risk theories of capital structure determinants.

Growth options were less significant in the middle period or economic downturn. However, the increase in significance of free cashflow in the second period is noteworthy. This supports the conclusions drawn from the increased importance of revenues under this economic state. In recession conditions firms issuing debt will be more likely to have excess cash flows with which they can meet debt obligations and which can act as a means of managing agency incentives within the firm.

6. Conclusion

This paper examined the factors, specifically tax, identified in economic theory as significant in the capital structure decision. The reason for this examination is that, given the potential size of the interest tax shield available, it seems unreasonable that marginal tax rates would not play a deciding factor in the debt equity decision under a tax regime that favours debt over equity. Similarly, in a tax regime that discounts the value of the tax saving the association should be less prominent.

An important result of the present paper is that the analysis finds strong evidence both for the association of marginal tax rates and debt changes posited by theory in classical tax world, and little or no association in an integrated tax system. The clarity of this result is in distinction to a number of previous studies. It is postulated that the use of careful measurement and testing methodology have removed noise frequently generated around the tax effect.

The analysis used dynamic measures to represent the variables of interest rather than levels. This is intended to remove both measurement problems and specification difficulties. The variables suggested by the theoretical work in capital structure were scrutinized using Bayesian variable selection procedures.

The Bayesian estimation procedure identifies the best model or models to describe the data's interactions. The Bayesian selection process works from a full set of information concerning the joint posterior distribution of the variables under examination whilst controlling for outliers in a parsimonious manner. As a result the associations between the dependent and explanatory variables could be described with less noise.

The sample periods offer important empirical support for the theoretical associations of capital structure debates. In the case of the integrated tax regime the uncertainty of some variables suggests that more attention could be paid to assessing theoretical models of the capital structure associations in a dividend imputation tax system. It may be that variables such as inflation or investor clienteles play a role in the determination of debt equity choices that are more critical than under a classical model.

Appendix

Bayesian Model Selection Procedure

The Bayesian model selection procedure follows Smith and Kohn (1996). It is assumed that the model is y = XB + [epsilon], where y is an n x 1 vector, X is an n x m matrix of variables, B an m x 1 vector of coefficients and [epsilon] ~ N (0, [[sigma].sup.2]-In). The intention is to estimate the vector of betas on the basis that the model used best describes the variable associations under examination.

Bayesian variable selection is based on posterior estimates of the density function of an indicator variable associated with the betas. The indicator variable, [gamma], is m x 1 and [[gamma].sub.i] = 0 or 1. If [[gamma].sub.i] = 0 [[beta].sub.i] = [[gamma].sub.i] = 1 [[beta].sub.i] [not equal to] 0. When [[gamma].sub.i] is zero the corresponding column of xs is dropped from the linear model. Therefore, given [gamma], [[beta].sub.[gamma]] consists of all the [[beta].sub.i] for which [[gamma].sub.i] = 1 and [X.sub.[gamma]] is all those columns of [X.sub.i] for which [[gamma].sub.i] = 1.

To reward parsimony, the Bayesian procedure identifies models with minimum MSE, giving a penalty for the number of variables. Hence, the selection process is a trade off between MSE and parameter quantity. The adjustment for the trade-off is made in the conditional probability of the dependent variable by incorporating a term that decreases exponentially with increasing parameters, [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] . Here c is a large number equal to the number of observations and [q.sub.[gamma]] is the number of parameters included in the evaluation. This trade-off rewards parsimony because the simplest model will be selected from among those that have similar MSEs.

A common concern regarding Bayesian methods is that prior assumptions can unduly influence the posterior density. However, the prior distribution used is not significant in shaping the posterior probabilities since it is strongly dominated by the likelihood (Box and Tiao 1992).

The model can also be structured to account for outliers in the model selection process, outliers are captured in the error term using an indicator variable [kappa], so that [epsilon]~N (0, [[kappa].sup.2][[sigma].sup.2]) where [kappa] is 1 normally and larger (10, for example) if it is an outlier. For most observations the outlier is not present. Let K be a diagonal matrix with diag([[kappa].sub.1], [[kappa].sub.2], ..., [kappa].sub.n).

On this basis the prior for [[beta].sub.[gamma]] conditional on [gamma], X, K and [[sigma].sup.2] is constructed [[beta].sub.[gamma]] ~ N (0, [c[sigma].sup.2][([X.sub.[gamma]'['K[X.sub.[gamma]).sup.-1]). A large value of c implies a more diffuse (uncertain) prior. Typically, c is often set equal to n (the sample size). The prior on ln[[sigma].sup.2] is taken as proportional to a constant; where P([[sigma].sup.2]) [infinity] 1/[[sigma].sup.2]. It is assumed that the gammas are independent with p([[gamma].sub.i]=1) = 0.5. This flat prior on the gammas exhibits no preferences for a particular model, all models are equally likely.

The process used is based on a Markov chain Monte Carlo procedure. (6) The probability densities are constructed using Gibbs sampling generating from P([[gamma].sub.i]|y, K, [[gamma].sub.j][not equal to]i) because it is possible to integrate out [beta] and [[sigma].sup.2]. The removal of [beta] and [[sigma].sup.2] reduces the dependence between successive iterates which leads to faster convergence and more information per iterate. Gibbs sampling is a Markov chain Monte Carlo method for sampling from posterior distributions. The method is based on constructing a Markov chain whose equilibrium distribution is that of the posterior distribution of [gamma]. The Gibbs sampler starts with an arbitrary starting value for the gammas,[[gamma].sup.[0]], and makes successive random drawings from the conditional distribution of K and [gamma]. This process generates [K.sup.[1]] that together with [[gamma].sup.[0]] generates [[gamma].sup.[1]] which in turn is used to generate [K.sup.[2]], [[gamma].sup.[2]] and so. After an initial warm up period the Gibbs sampler is drawing from the posterior distribution of [gamma] and K. In this paper a warm up of 170 iterations and a run of 300 iterations are used.

However, to implement this process the probability of p([[gamma].sup.i]|[gamma], K, [[gamma].sub.j][not equal to]i) first needs to be derived.

The sampler is:

for j = 0, ...,p generate [[gamma].sub.j] | [y.sub.j], K, [[gamma].sub.i[not equal to]j]

for t = 1, ..., n generate [[kappa].sub.t] | [[gamma].sub.j], [gamma], [[kappa].sub.s[not equal to]t]

The generation process for gamma is briefly described. The conditional probability of gamma is given as

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

The conditional posterior for [[gamma].sub.j] is Bernoulli and the probability of a 1 being obtained is as follows:

p([[gamma].sub.j] = 1|y, K,[[gamma].sub.j[not equal to]i])[infinity] p(y|K,[[gamma].sub.j= 1],[[gamma].sub.i[not equal to]j])p([[gamma].sub.j] = 1)

p([[gamma].sub.j]=0|y, K, [[gamma].sub.j[not equal to]i])[infinity] p(y| K,[[gamma].sub.j=0],[[gamma].sub.i[not equal to]j])p([[gamma].sub.j] = 0)

We identify p(y| K,[[gamma].sub.j=1],[[gamma].sub.i[not equal to]j]) thus

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

this gives the required probability from which to generate [[gamma].sub.j].

The KS are generated in a similar fashion to the innovation outliers in Barnett, Kohn and Sheather (1996).

[??] is found such that p ([gamma]|y, K) is maximized over all [gamma] which will be the most popular model. Once is found [??] which is the estimator of [gamma] it can be used to estimate [beta] [??] by least squares

[beta][??] = [([X.sub.[??]]'K[X.sub.[??]]).sup.-1] [X.sub.[??]]' [K.sub.y]

The Bayesian variable selection technique uses information concerning the frequency that a particular variable is identified as significant in all the possible combinations of variables. This permits construction of parameter estimates for an average model. This average model is a probability-weighted specification (7) based on the subsets of parameters that are identified as being close to equally able to describe the associations in the data. One can obtain E[[beta]|y,[gamma]] from the Markov chain Monte Carlo using the Rao- Blackwell procedure;

E([beta]|y) = [summation over ([gamma])]E([beta] | y, [gamma], K)p([gamma] | y, K).

The author would like to acknowledge comments and suggestions from John Graham in particular, Greg Clinch, Doug Foster, Tom Smith, Garry Twite, Justin Wood, and seminars participant's at AGSM, Monash University, University of Queensland and RMIT as well as an anonymous referee. Also thanks to Glen Barnett for programming the Bayesian routines used in this research. All errors and omissions are the authors'.

(Date of receipt of final transcript: October 13, 2005. Accepted by Doug Foster & Garry Twite, Area Editors.)

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(1.) Papers detailing these associations include: Gordon (1971), Myers (1977), Jensen (1986), Fischer and Heinkel (1989), Harris and Raviv (1990), and MacKie-Mason (1990).

(2.) The empirical evidence on the influence of corporate taxes on capital structure choice is conflicting and inconclusive, for example, Bradley, Jarrell and Kim (1984) and Titman and Wessels (1988)--US and Gatward and Sharpe (1996)--Australia.

(3.) Several recent papers investigate whether the trade-off theory or the pecking-order theory better explains debt ratios: such as Shyum-Sunder and Myers (1992), Frank and Goyal (2000).

(4.) This problem is embedded in the approaches adopted by both Gatward and Sharpe (1996) and Twite (2001), who find conflicting evidence on the relationship between taxes and capital structure. Gatward and Sharpe (1996) find no support for taxes in explaining financing choices; however, Twite (2001) finds support for a tax basis in capital choice. His paper finds strong support for an equity for debt swap in financing post imputation.

(5.) Centre for Research in Finance a database maintained by the Australian Graduate School of Management that contains price, market capitalization, equity issuance data.

(6.) For more detailed discussion and proofs of this method see George and McCulloch (1993) or Smith and Roberts (1993).

(7.) The Rao-Blackwell procedure is used to select the average model. Defining K to be an indicator variable used to identify the existence of outliers, E ([beta]|y, K) = [summation over ([gamma])] E ([beta]| y, [gamma], K)p([gamma]|y, K) Chatfield (1995) provides more details discussion of model averaging.

Kerry Pattenden, School of Business and Economics, H69, University of Sydney, NSW 2006. Email: [e-mail]

Table 1
Correlations Between Variables for the Three Periods in the Study

The top right-hand triangle is the correlations for the period
1982-1988, the classical tax period. The lower left-hand triangle
(italic) is the period 1992-1993, immediately after the change to an
integrated tax system, this period was also marked by an economic
recession. The third set of correlations are those for the period
1994-1998 this is a period when the new tax regime is well
established and the economic recession is passing and past.

The variables are change in total debt ([DELTA]DEBT), marginal tax
rate measure (MTR), change in free cash flows ([DELTA]FCF), lagged
growth opportunities (LagGO), change in tangible assets
([DELTA]TAN), a measure of bankruptcy, Z-score, beta of assets
([beta]asset), change in log of sales ([DELTA]SIZE), an interaction
term between free cash flow and growth options ([DELTA]FGO), dividend
yield (DIV) and an industry dummy (Inddum).

              [DELTA]DEBT     MTR     [DELTA]FCF   Lag GO

[DELTA]DEBT                 -0.058       0.151     -0.069
MTR              0.281                  -0.034     -0.115
[DELTA]FCF      -0.099      -0.168                 -0.087
Lag GO          -0.064      -0.367       0.195
[DELTA]TAN       0.57        0.276      -0.213     -0.215
Z-score          0.152       0.282       0.048     -0.349
[beta]asset     -0.046       0.009      -0.002     -0.035
[DELTA]SIZE      0.455       0.207       0.031      0.067
[DELTA]FGO       0.023      -0.174       0.764      0.421
DIV              0.053      -0.035       0.017      0.034
Ind dum          0.019       0.193      -0.059     -0.154

MTR              0.125
[DELTA]FCF      -0.123      -0.059
Lag GO           0.04       -0.025      -0.11
[DELTA]TAN       0.458       0.101      -0.102      0.015
Z-score          0.202       0.237      -0.152     -0.216
[beta]asset     -0.076      -0.147      -0.009      0.025
[DELTA]SIZE      0.145       0.126       0.154      0.05
[DELTA]FGO      -0.091      -0.023       0.941     -0.042
DIV              0.076       0.041      -0.421      0.175
Ind dum          0.05        0.004       0.07      -0.081

              [DELTA]TAN   Z-score   [beta]asset   [DELTA]SIZE

[DELTA]DEBT      0.469     -0.357      -0.096         0.327
MTR              0.006      0.302      -0.262        -0.072
[DELTA]FCF       0.179      0.068       0.065         0.265
Lag GO          -0.124     -0.291      -0.144        -0.061
[DELTA]TAN                 -0.07        0.138         0.319
Z-score          0.119                  0.225        -0.048
[beta]asset      0.059      0.239                     0.129
[DELTA]SIZE      0.345      0.024      -0.088
[DELTA]FGO      -0.137      0.025      -0.157         0.059
DIV              0.062     -0.096      -0.061         0.017
Ind dum          0.023      0.276      -0.156        -0.097

MTR
[DELTA]FCF
Lag GO
[DELTA]TAN
Z-score          0.139
[beta]asset      0.035     -0.043
[DELTA]SIZE      0.35       0.212       0.033
[DELTA]FGO      -0.125     -0.136      -0.007         0.096
DIV              0.072      0.079       0.009         0.003
Ind dum         -0.028      0.24       -0.254         0.031

              [DELTA]FGO     DIV     Ind dum

[DELTA]DEBT      0.068     -0.112     0.057
MTR             -0.087      0.018     0.077
[DELTA]FCF       0.531     -0.001     0.067
Lag GO           0.474      0.46     -0.168
[DELTA]TAN       0.085     -0.095     0.019
Z-score         -0.026     -0.181    -0.06
[beta]asset      0.038     -0.247    -0.064
[DELTA]SIZE      0.112     -0.087    -0.018
[DELTA]FGO                  0.334    -0.094
DIV              0.005               -0.047
Ind dum         -0.089     -0.041

MTR
[DELTA]FCF
Lag GO
[DELTA]TAN
Z-score
[beta]asset
[DELTA]SIZE
[DELTA]FGO
DIV             -0.431
Ind dum          0.064     -0.039

Table 2
Descriptive Statistics of the Independent and Dependent Variables

The table sets out descriptive statistics for the three periods
analysed; panel A is the classical period 1982-1988; panel B the first
imputation period 1989-1993 and panel C the second imputation period
with a subset of firms that is not exactly the same as previously,
1994-1998.

The variables are change in total debt ([DELTA]DEBT), marginal tax
rate measure (MTR), change in free cash flows ([DELTA]FCF), lagged
growth opportunities (LagGO), change in tangible assets ([DELTA]TAN), a
measure of bankruptcy, Z-score, beta of assets (([beta]asset), change
in log of sales ([DELTA]SIZE), an interaction term between free cash
flow and growth options ([DELTA]FGO) and dividend yield (DIV).

               Mean       Median    StDev    Minimum    Maximum

Panel A: Data from 1982-1988 period classical tax regime. 268
observations

[DELTA]DEBT    0.04091   0.01783   0.10735   -0.434      0.56691
MTR            0.42963   0.46      0.0706     0.26195    0.46
[DELTA]FCF     0.03638   0.02286   0.05569   -0.1169     0.51678
Lag GO         1.3266    1.0759    1.2837     0.1256    12.9732
[DELTA]TAN     0.08555   0.05365   0.12166   -0.265      0.80198
Z-score        2.4922    2.5736    1.368      0.0931     5
[beta]asset    0.6535    0.5878    0.3813     0.06       2.17
[DELTA]SIZE    0.2222    0.1402    0.5615    -2.8506     2.3726
[DELTA]FGO     0.04207   0.0208    0.09182   -0.0919     0.88593
DIV            0.07213   0.06373   0.08518    0          0.77728

Panel B.: Data from 1989-1993 period the early integrated tax regime
period. Observations 268. The companies in panels A and B are the same.

[DELTA]DEBT   -0.01857   0         0.1613    -1.42525    0.27881
MTR            0.41018   0.39      0.07198    0.29974    0.49
[DELTA]FCF     0.0251    0.0084    0.1791    -0.4496     1.6908
Lag GO         0.9703    0.739     0.8176     0.2441     7.3315
[DELTA]TAN     0.0202    0.0438    0.1919    -1.8363     0.3649
Z-score        2.3672    2.362     1.5663     0          5
[beta]asset    0.5713    0.5472    0.2619     0.01       1.4457
[DELTA]SIZE    0.0131    0.054     0.4126    -4.6384     1.4374
[DELTA]FGO     0.0528    0.0062    0.4737    -0.9591     6.4628
DIV            0.04876   0.03765   0.08429    0          1.03881

Panel C: Data from 1994-1998 period after the new tax system is well
established. Number of observations is 245, some companies in this
panel are different to the previous two panels. Some companies have
dropped out and others have been added.

[DELTA]DEBT    0.00297   0.0003    0.10549   -0.6041   0.69018
[DELTA]DEBT    0.33136   0.33      0.03569    0.18      0.39
MTR           -0.00206   0.0077    0.13465   -0.946    0.69214
[DELTA]FCF     0.6435    0.5968    0.3547    -1.7206   2.8544
Lag GO         0.0329    0.0382    0.1617    -1.382    1.0703
[DELTA]TAN     2.5985    2.9153    1.5369    -2.0247      5
Z-score        0.7329    0.7308    0.3143     0.0087     1.79
[beta]asset    0.0377    0.0577    0.4914    -5.3001   2.4636
[DELTA]SIZE   -0.00656   0.00442   0.11809   -0.8891   0.53914
[DELTA]FGO     0.05321   0.03902   0.0977     0      0.96826
DIV

Table 3
The Most Popular Models Selected; A One Indicates That the
Parameter is Included in the Model

Times chosen details that the particular set of variables indicated
with a one was selected as a suitable representation of the equation
y = XB[gamma] + [epsilon] the given percentage of the 300 iterations.
For example, [DELTA]debt = f[MTR, [DELTA]TAN, Z-score, [beta]assets,
[DELTA]SIZE, DIVY] is identified 7% of the time.

The variables are intercept (Inter), marginal tax rate measure (MTR),
change in free cash flows ([DELTA]FCF), lagged growth opportunities
(LagGO), change in tangible assets ([DELTA]TAN), a measure of
bankruptcy, Z-score, beta of assets (([beta]asset), change in log of
sales ([DELTA]SIZE), an interaction term between free cash flow and
growth options ([DELTA]FGO), dividend yield (DIV) and an industry
dummy (Inddum).

Times        Inter   MTR   [DELTA]   LagGO   [DELTA]   Z-score
Chosen (%)                   FCF               TAN

8.2            0      1       0        1        1         1
5.2            0      1       0        0        1         1
4              0      1       0        0        1         1
4              0      1       0        0        1         1
2.7            0      1       0        0        1         1

Times        [beta]   [DELTA]   [DELTA]   DIV   Ind
Chosen (%)   asset     SIZE       FGO           dum

8.2            0         0         0       0     0
5.2            0         0         0       0     0
4              1         0         0       0     0
4              1         1         0       1     0
2.7            0         1         0       0     0

Table 4
Beta Estimates with Standard Errors for the Average Model

The average beta estimates are constructed using a Rao-Blackwell
weighting (see appendix). The model used is y = X[B.sub.[gamma]] +
[epsilon], where y is change in debt ([DELTA]DEBT). Standard errors
have been calculated using the estimated covariance matrix of the
parameters to give an indication of the significance of the estimates
in the average model in line with classical statistical measures.

The explanatory variables are intercept (Inter), marginal tax rate
measure (MTR), change in free cash flows ([DELTA]FCF), lagged growth
opportunities (LagGO), change in tangible assets ([DELTA]TAN), a
measure of bankruptcy, Z-score, beta of assets ([beta]asset), change
in log of sales ([DELTA]SIZE), an interaction term between free cash
flow and growth options ([DELTA]FGO), dividend yield (DIV) and an
industry dummy (Inddum).

Variable       Beta Estimate   Std Error

Intercept         0.0114        0.0118
MTR               0.2021        0.0365
[DELTA]FCF        0.0149        0.0296
LagGO             -0.0037       0.0023
[DELTA]TAN        0.4197        0.0382
Z-score           -0.0235       0.0031
[beta]assets      -0.0146       0.0075
[DELTA]SIZE       0.0086        0.0055
[DELTA]FGO        0.0060        0.0167
DIVY              -0.0257       0.0257
Inddum            -0.0003       0.0034

Table 5
Posterior Probabilities of the Indicator Variables: Percentage of
Times a Variable was Selected by the Process (as a decimal)

This table sets out the posterior probability that an X variable is
chosen in a model subset to explain the dependent variable. For
example [DELTA]TAN is in every one of all the possible models.

The variables are intercept (Inter), marginal tax rate measure (MTR),
change in free cash flows ([DELTA]FCF), lagged growth opportunities
(LagGO), change in tangible assets ([DELTA]TAN), a measure of
bankruptcy, Z-score, beta of assets ([beta]asset), change in log of
sales ([DELTA]SIZE), an interaction term between free cash flow and
growth options ([DELTA]FGO), dividend yield (DIV) and an industry
dummy (Inddum).

Intercept    MTR     [DELTA]   LagGO    [DELTA]   Z-score
                       FCF                TAN

0.2200      0.9400   0.1640    0.4960   1.0000    1.0000

Intercept   [beta]   [DELTA]   [DELTA]    DIV     Inddum
            assets    SIZE      FGO

0.2200      0.5040   0.4360    0.1200   0.2720    0.1680

Table 6
The Most Popular Models Selected; A One Indicates That the
Parameter is Significant

Times chosen details that the particular set of variables indicated
with a one was selected as a suitable representation of the equation
y = X[B.sub.[gamma]] + [epsilon] t the given percentage of the 300
iterations. For example, [DELTA]debt = f[[DELTA]FCF, [DELTA]TAN,
Z-score, [DELTA]SIZE] is identified 5.7% of the time.

The variables are intercept (Inter), marginal tax rate measure (NITR),
change in free cash flows ([DELTA]FCF), lagged growth opportunities
(LagGO), change in tangible assets ([DELTA]TAN), a measure of
bankruptcy, Z-score, beta of assets ([beta]asset), change in log of
sales ([DELTA]SIZE), an interaction term between free cash flow and
growth options ([DELTA]FGO), dividend yield (DIV) and an industry
dummy (Inddum).

Times        Inter   MTR   [DELTA]FCF   LagGO   [DELTA]TAN
Chosen (%)

5.7            0      0        1          0         1
5              0      0        0          0         1
2              1      1        1          0         1
2.7            0      1        1          1         1
2.7            1      1        1          0         1

Times        Z-score   [beta]asset [DELTA]SIZE  [DELTA]FGO
Chosen (%)

5.7             1          0           1            0
5               1          0           1            0
2               1          0           1            0
2.7             1          0           1            0
2.7             1          0           1            0

Times        DIV   Ind dum
Chosen (%)

5.7           0       0
5             0       0
2             0       0
2.7           0       0
2.7           1       0

Table 7
The Estimated Parameters for the Average Model with Standard
Errors

The average beta estimates are constructed using a Rao-Blackwell
weighting (see appendix). The model used is y = X[B.sub.[gamma]] +
[epsilon], where y is change in debt ([DELTA]DEBT). Standard errors
have been calculated using the estimated covariance matrix of the
parameters to give an indication of the significance of the estimates
in the average model in line with classical statistical measures.

The explanatory variables are intercept (Inter), marginal tax rate
measure (NITR), change in free cash flows ([DELTA]FCF), lagged growth
opportunities (LagGO), change in tangible assets ([DELTA]TAN), a
measure of bankruptcy, Z-score, beta of assets ([beta]asset), change in
log of sales ([DELTA]SIZE), an interaction term between free cash flow
and growth options ([DELTA]FGO), dividend yield (DIV) and an industry
dummy (Inddum).

Variable       Beta Estimate   Std Error

Intercept         -0.0089       0.0100
MTR                0.0311       0.0255
[DELTA]FCF         0.0358       0.0185
LagGO             -0.0020       0.0023
[DELTA]TAN         0.3189       0.0297
Z-score           -0.0040       0.0017
[beta]assets      -0.0056       0.0053
[DELTA]SIZE        0.0674       0.0097
[DELTA]FGO         0.0022       0.0046
DIV               -0.0380       0.0285
Inddum             0.0008       0.0035

Table 8
Posterior Probabilities of the Indicator Variables: Percentage of
Times the Parameter was Chosen (as a decimal)

This table sets out the posterior probability that an X variable is
chosen in a model subset to explain the dependent variable. For example
[DELTA]TAN is in every one of all the possible models.

The variables are intercept (Inter), marginal tax rate measure (MTR),
change in free cash flows ([DELTA]FCF), lagged growth opportunities
(LagGO), change in tangible assets ([DELTA]TAN), a measure of
bankruptcy, Z-score, beta of assets ([beta]asset), change in log of
sales ([DELTA]SIZE), an interaction term between free cash flow and
growth options ([DELTA]FGO), dividend yield (DIV) and an industry dummy
(Inddum).

Intercept    MTR     [DELTA]FCF   LagGO    [DELTA]TAN   Z-score

0.2960      0.3400     0.6040     0.2160     1.0000     0.6560

Intercept  [beta]assets  [DELTA]SIZE  [DELTA]FGO    DIV    Inddum

0.2960        0.2480        0.9960      0.1440    0.3680   0.2000

Table 9
The Most Popular Models Selected; A One Indicates That the
Parameter is Significant

Times chosen details that the particular set of variables indicated
with a one was selected as a suitable representation of the equation
y = X[B.sub.[gamma]] + [epsilon] t the given percentage of the 300
iterations. For example, [DELTA]debt = f[[DELTA]FCF, LagGO
[DELTA]TAN, [DELTA]SIZE, [DELTA]FGO] is identified 5% of the time.

The variables are intercept (Inter), marginal tax rate measure (NITR),
change in free cash flows ([DELTA]FCF), lagged growth opportunities
(LagGO), change in tangible assets ([DELTA]TAN), a measure of
bankruptcy, Z-score, beta of assets ([beta]asset), change in log of
sales ([DELTA]SIZE), and interaction term between free cash flow and
growth options ([DELTA]FGO), dividend yield (DIV) and an industry
dummy (Inddum).

Times         Inter   MTR   [DELTA]FCF   LagGO   [DELTA]TAN
Chosen (%)

5               0      0        1          1         1
2               0      0        1          1         1
2               0      0        0          0         1
2               0      0        1          1         1
2.2             0      0        0          0         1

Times         Z-score   [beta]asset   [DELTA]SIZE   [DELTA]FGO
Chosen (%)

5                0           0             1            1
2                0           0             1            0
2                0           1             1            0
2                0           0             1            1
2.2              0           1             1            0

Times         DIV   Ind
Chosen (%)          dum

5              0     0
2              0     0
2              0     1
2              0     1
2.2            0     0

Table 10
The Estimated Parameters for the Average Model with Standard
Errors

The average beta estimates are constructed using a Rao-Blackwell
weighting (see appendix). The model used is y = X[B.sub.[gamma] +
[epsilon], where y is change in debt ([DELTA]DEBT). Standard errors
have been calculated using the estimated covariance matrix of the
parameters to give an indication of the significance of the estimates
in the average model in line with classical statistical measures.

The explanatory variables are intercept (Inter), marginal tax rate
measure (MTR), change in free cash flows ([DELTA]FCF), lagged growth
opportunities (LagGO), change in tangible assets ([DELTA]TAN), a
measure of bankruptcy, Z-score, beta of assets ([beta]asset),change in
log of sales ([DELTA]SIZE), an interaction term between free cash flow
and growth options ([DELTA]FGO), dividend yield (DIV) and an industry
dummy (Inddum).

Variable      Beta Estimate   Std Error

Intercept        -0.0076       0.0084
MTR               0.0053       0.0243
[DELTA]FCF       -0.0825       0.0442
LagGO            -0.0104       0.0056
[DELTA]TAN        0.3670       0.0294
Z-score           0.0008       0.0010
(3assets         -0.0088       0.0056
[DELTA]SIZE       0.0222       0.0079
[DELTA]FGO        0.0468       0.0480
DIV               0.0064       0.0151
Inddum            0.0066       0.0046

Table 11
Posterior Probabilities of the Indicator Variables: Percentage of
Times the Parameter was Chosen (as a decimal).

This table sets out the posterior probability that an X variable is
chosen in a model subset to explain the dependent variable. For
example, [DELTA]TAN is in every one of all the possible models.

The variables are intercept (Inter), marginal tax rate measure
(MTR), change in free cash flows ([DELTA]FCF), lagged growth
opportunities (LagGO), change in tangible assets ([DELTA]TAN), a
measure of bankruptcy, Z-score, beta of assets ([beta]asset), change
in log of sales ([DELTA]SIZE), an interaction term between free cash
flow and growth options ([DELTA]FGO), dividend yield (DIV) and an
industry dummy (Inddum).

Intercept    MTR     [DELTA]FCF   LagGO    [DELTA]TAN   Z-score

0.2400      0.1840     0.5080     0.4800     1.0000     0.2040

Intercept   ([beta]assets)   [DELTA]SIZE   [DELTA]FGO

0.2400          0.4240         0.7600        0.3520

Intercept    DIV     Inddum

0.2400      0.1560   0.4320