Trade-Off theory

The capital structure theory presented by ^{Bradley, Gregg, and Kim (1984)} is known as the capital structure equilibrium theory or trade-off theory, which explains that the company's financing decisions are conducted to evaluate whether the tax benefit is greater than the costs incurred by the company as a result of debt. The main benefit of debt is the tax deductibility of interest, which is greater as the tax rate increases, this benefit is reflected as savings and promotes increased levels of indebtedness; on the other hand the most important costs are moneywise, operating costs and the potential cost of bankruptcy as a consequence of not paying a debt.

^{Miller (1988)} showed how taxes can affect the debt-equity ratio. He demonstrated that under some conditions the optimal capital structure can be financed by debt due to a preferential tax treatment. The substitution of debt for equity allows the company to get surplus by reducing the firm tax payment, the surplus can be transferred to investors, and the firm value does not need to increase.

The Hierarchical Order theory

An additional point of view is from ^{Myers and Majluf (1984)} who provided a new theory where firms select capital structure not only on cost of resources, but they also take into account relevant information of the dividend policy. The hierarchical order theory states that if there are information asymmetries, then it cannot be set a fair value for the stock in the market, then the value criteria, in the choice of the capital structure, is not adequate and must be corrected, one solution corresponds to modify the capital structure in order to be financed from its own resources and better credit conditions.

In their research they showed that under conditions of undervalued share price, if the company makes a new placement to finance the effect of undervaluation produces a utility for new investors, and a loss to the original shareholders, since this is unacceptable to shareholders, the company must initially be financed with the resources issued by the profits and it will be forced to modify the reinvestment factor and dividend policy.

If the business requires more resources it must go in debt and will always search for the cheapest financing, an alternative is to issue debt and reduce placement requirements. The hierarchical order theory explains why companies, when are undervalued, require financing, the first alternative is to use their own funds and modify the rate of reinvestment; secondly the companies make low to high cost loans and, as a last resource, they place shares in the market.

^{Sarmiento (2005)} found that the capital structure of the private sector in Colombia in 1994 mainly depended on debt and the structure has changed from the profit reinvestment. ^{Tenjo et al. (2006)} point out that as a consequence of a stock market with low level of development, the shares is one of the resources less used in the financial process, and emphasise that problems such as imperfect information and credit concentration are associated to problems related to the Hierarchical Order theory.

The variables

For the construction of the econometric model as a dependent variable was selected the level of debt (ID), this variable reflects the relationship that exists among its own resources and the funded resources used by the company to support its assets.

The independent variables that explain the debt are: capital intensity (tangibility), size, growth rate and profitability of the company.

Capital intensity is the tangible capital required for production, is a point of comparison between similar companies and represents the relationship between productive assets and total assets. Both the research of ^{Myers and Majluf (1984)} and ^{Rajan and Zingales's (1995)} state that there is a causal relationship between tangibility (TG) and leverage (LG) of firms in a positive way. Companies that have a greater amount of productive assets have a higher level of leverage.

The size of firms is assumed to be the natural logarithm of the volume of sales in each period, according to ^{Rajan and Zingales (1995)} the size of the firm is an indicator of leverage.

The company's growth refers to the increase or decrease of its income; it is an indicator that helps to know if the company has more market participation or product diversification, establishing a positive signal. Rajan and Zingales, as an approach for the level of growth opportunities to the firms, use the variable growth, developed as market-to-book. These authors suggest that one might expect a negative relationship between growth opportunities and debt levels. ^{Myers (1977)} also holds that firms with high growth opportunities tend to have low debt ratios.

Profitability is a discussion point among the Hierarchical Order theory and the Trade-off theory. On the Trade-off theory the greater the profitability of the company is, it will have more reasons to issue debt. On the other hand, the hierarchical order theory assumes that the higher the income of the companies is, they will have a lower level of debt, in an initial stage. Therefore, the trade-off theory relates profitability and leverage in a positive way, while the theory of Hierarchical Order expects otherwise. The measurement of profitability is through the relationship of net income before taxes divided by total assets.

Static methods

The process starts with an ordinary least squared (OLS ) regression, pooling or combining the 602 observations. The leverage function can be represented as follows:

(1)

where i stands for the i _th cross-sectional unit and t for the t _th time period. LG represents the level of indebtedness (leverage), TG stands for tangibility, SZ and GT are the size and growth of the firm respectively and PF is the level of profitability. The error term u _it is assumed to satisfy white-noise assumptions that is, independently and identically distributed with zero mean, constant variance σ² and serially uncorrelated, which is denoted as u ∼ I.I.D. (0, σ²⁾. The symbols β₀ to β₄ are the coefficients to be estimated. The results from Eq. (1) are reported in Column 1 of Table 2.

Table 2 Results from the regressions. 

Notes: The dependent variable is leverage.

* Significant at 1%.

♦ Significant at 10%. p value in parenthesis.

Source: Own computation with information from Economática (2015).

It is worth noting that the traditional OLS approach has to major drawbacks. It assumes that the intercept value of the countries is the same and it does not control for country-specific factors. In order to test whether these are implausible assumptions, two panel estimation methods, which take into account the specific nature of the countries, are performed. The first estimation is the fixed effect model (FE ), which lets the intercept vary for every firm by adding dummy variables that control firm-specific effects, the vector of group dummy variables can be represented by β _{0 i}. So as to explore whether the dummies belong to the model an F test is conducted. The null hypothesis is that the additional coefficients equal zero, that is β _{0 i} is a constant intercept β₀ for all the firms (H₀ : β _{0 i} = β₀ ). In the present analysis the additional regressors are statistically different from cero and therefore they belong to the model. The results from the fixed effect regression are reported in Column 2 of Table 2.

We also conduct a FE specification in which the intercept varies for every time period by adding dummy variables that control time-specific effects, the vector of time dummy variables can be represented by β _{0 t}, and the null hypothesis is (H₀ : β _{0 t} = β₀ . In this case, it was found that all the additional regressors are also statistically significant and the F test rejects the null hypothesis. What it is interesting to note is that the intercept coefficients of the leverage variable decrease linearly over time, about 0.2 points per quarter, as presented in Fig. 1.

Fig. 1 Time intercept across periods for the leverage variable. 

The time intercept equation of the leverage variable is:

(2)

where Period is the time variable for the 43 time observations, INTLG represents the time intercepts of the leverage variable, t is the t _th time observation and u _t is the error term. The R₂ of Eq. (2) is 0.8082, the Dikey-Fuller test on the residuals u _t, also known as the Engle-Granger cointegration test rejects the null H₀ : the error term has a unit root. Thus the equation is cointegrated, which indicates that the time intercepts of the leverage variable have a long-run decreasing trend over time.

The second panel estimation is the random effect model (RE ). In this specification, differences across countries are captured through a disturbance term ω _it, which follows ωit=εi+uit, where ¿ _i is an unobservable term that represents the individual specific error component, and u _it is the combined time series and cross-section error component. The model assumes that ¿ _i is not correlated to any explanatory variable X _kit in the equation. The Breusch and Pagan Lagrange Multiplier (BPLM ) test ⁽¹⁹⁷⁹⁾ is designed to test random effects. The null hypothesis is that the individual-specific variance is zero, that is H₀ : σu2=0. In the present analysis the BPLM test rejects the null hypothesis that is, there are random effects in the model.¹ The results are presented in Table 2, Column 3.

The results obtained from the two previous models show that there are firm-specific effects. Now it is important to define which of the two models - FE or RE - is more convenient. In order to do so we apply the ^{Hausman test for specification (1978)}. The null hypothesis is that the regressors X _kit and the unobservable individual specific random error ¿ _i are uncorrelated, that is H₀ : Corr (Xkit,εi)=0. If the test statistic, based on an asymptotic χ² distribution rejects the null, then the random effect estimators are biased and the fixed effect model is preferred. The p value obtained from the Hausman test tends to cero and hence, the null is rejected, which indicates that the RE estimates are inconsistent and the FE would be more appropriate. The result from the test is reported in Column 3 of Table 2.

The results from the FE model show that tangibility, size and profit of the firms are negatively related to the indebtedness level, while growth has a positive relationship with the debt. It is interesting to note that all the firm dummy variables are highly significant. In average the intercepts of the Mexican and Brazilian firms are higher than the other Latin American firms in the sample, and they tend to oscillate above 0.951 for both countries. The Colombian intercepts are the lowest; in average they are located around 0.68. In other words, the initial level of indebtedness of Colombian firms is lower than the firms from other countries in the sample.

In order to explore if the variables involved in the model have a long-term relationship we apply a cointegration test to the FE specification. Initially we explore whether the dependent variable and the regressors show a unit-root process. The analysis is conducted applying the ^{Levin-Lin-Chu unit root test (2002)}, with one and two lags of the dependent variable, and in the cases it is required we incorporate a trend variable on the equation. The results indicate that the leverage, size, growth and profit variables are stationary as the test rejects the null hypothesis H₀ : there is unit root, in all the specifications, at conventional significance levels. The tangibility variable has to be differenced once to become stationary. The results are reported in Table 3.

Table 3 Levin–Lin–Chu unit-root test with no trend. 

* Significant at 1%.

** Significant at 5%.

Source: Own computation with information from ^{Economatica (2015)}.

So as to test for cointegration we apply both the ^{Levin-Lin-Chu} and the ^{Im, Pesaran, and Shin (2003)} on the residuals of the FE regression. In both cases the tests suggest that there is a long-run relationship in the equation as reject the null hypothesis of unit root on the residuals. Although tangibility does not have the same order of integration than the other variables, the linear combination of the series is I (0) and cancels out stochastic trends in them. The results are shown in Table 4.

Table 4 Cointegration test for the FE equation unit root test on the residuals. 

* Significant at 1%.

Source: Own computation with information from ^{Economatica (2015)}.

We also explore whether the coefficients vary across firms and for every variable. In this case interactive or differential slope dummies are constructed by multiplying each of the firm dummies by each of the explanatory variables. Table 5 presents four equations, in each one the interactive dummies are disaggregated by firm for a specific explanatory variable, and the remaining three variables are incorporated aggregating all the firms. Column 1 shows the disaggregation of the slop coefficient for the tangibility variable. We observe that the slopes of the Colombian firms are all negative and statistically significant, and two of the three Peruvian firms have negative and statistically significant slopes, all or most of the slope coefficients from the Mexican, Chilean and Brazilian firms are positive and statistically significant. Hence, we can say that the result from the Colombian and Peruvian firms is more robust and in general the level of indebtedness declines as the tangibility increases. When the slope of the size variable is disaggregated, in Column 2, it is possible to see that the results are more homogeneous because in all the firms, with the exception of Peñoles Industria in México, the coefficients are negative and statistically significant, which means that the level of indebtedness falls as the size rises. In the case of the growth variable desegregation, in Columns 3, the Colombian and Peruvian firms also present more robust results, because all of the firms and most of the firms respectively have negative and significant sign, which suggests that the firms have a reduction of debt as they increase growth; whereas the Mexican, Chilean and Brazilian firms tend to have positive sings. In Column 4 we present the slope coefficients from the profit of the mining companies and find that they are all negative and statistically significant, and hence this variable seems to have the most robust effect on the dependent variable.

Table 5 Desagregation of slope coefficients by firm and variables. 

Notes: The dependent variable is leverage. Own computation with information of ^{Economatica (2015)}.

* Significant at 1%.

** Significant at 5%.

♦ Significant at 10%.

p Value in parenthesis.

Dynamic methods

Before adopting the FE specification as the final estimation, it is important to keep in mind that the error term u _it is assumed to satisfy white-noise assumptions and therefore, an AR(1) test should be conducted. In this respect, the modified ^{Bhargava, Franzini, and Narendranathan (1982)} Durbin-Watson test (modified DW) and ^{Baltagi and Wu LBI (1999)} test are performed. The results are reported in Column 2 of Table 1. In this case, both tests reject the null hypothesis H₀ : no first order serial correlation.

To cope with the autocorrelation, we should analyse the possibility that the problem emerge owed to model misspecification, that is, because of a lagged dependent variable is not incorporated in the model. Therefore, the static specification in Equation 1 is extended and transformed into a dynamic panel data model (DPDM) by adding a lagged dependent variable as follows.

(3)

where X is the vector of the four explanatory variables introduced previously. The inclusion of a lagged dependent variable incorporates a source of persistence over time: correlation between the right hand regressor y _it−1 and the error term u _it. In addition, DPDMs are characterised by individual effects η _i caused by heterogeneity among the individuals.² As a result, it is necessary to apply different estimations and testing procedures for model 3.

To estimate Eq. (3), we use the GMM, for DPDMs, initially proposed by ^{Arellano and Bond (1991)} and ^{Arellano and Bover (1995)}. Firstly, the estimation method eliminates country-effects η _i by expressing the dynamic equation in first differences as follows:

(4)

On the basis of the following standard moment conditions:

that is, lagged levels of LG _it are uncorrelated with the error term in first difference, the method uses lagged endogenous variables as instruments to control for likely endogeneity of the lagged dependent variable, reflected in the correlation between this variable and the error term in the transformed equation. The GMM estimation obtained is known as the difference estimator.

^{Blundell and Bond (1998)} argued that the GMM estimator obtained after first differencing has been found to have large finite sample bias and poor precision. The limitations of the estimator are owed to weak instruments, since they contend that lagged levels of the series provide weak instruments for the first difference.

To improve the properties of the standard first-differenced GMM estimator, they justified the use of an extended GMM estimator, on the basis of the following moment condition:

that is, there is no correlation between lagged differences of LG _it and the country-specific effects. The method therefore uses lagged differences of Y _it as instruments for equations in levels, in addition to lagged levels of Y _it as instruments for the equation in first differences. The extended method is known as the system GMM estimation (sys-GMM). It encompasses a regression equation in both differences and levels, each one with its specific set of instrumental variables. The sys-GMM estimation not only improves precision but also reduce finite sample bias. Results are reported in Column 4 of Table 2.

The GMM estimations, both difference and system, assume that the disturbances u _it are not serially correlated. If this were the case, there should be evidence of first order serial correlation in differenced residuals u _it − u _it−1 and no evidence of second-order serial correlation in the differenced residuals (^{Doornik, Arellano, & Bond, 2002}). It is an important assumption because the consistency of the GMM estimator hinges upon the fact that E[Δu_itΔu_it−2]=0. Consequently, tests of autocorrelation up to order 2 in the first-differenced residuals should be available.

The tests of serial correlation in the first differenced residuals are in keeping with the maintained assumption of no serial correlation in u _it. The AR(2) tests fail to reject the null hypothesis that the first-differenced residual error term is not second order serially correlated, whereas by construction, the AR(1) test rejects the null (at 1% level of significance) that the process does not exhibit first-order serial correlation. The results for the system model are reported in Columns 4 of Table 2.

So as to assess the validity of the instruments, a Sargan test of over identifying restrictions, proposed by ^{Arellano and Bond (1991)} is also performed. Under the null hypothesis that the instruments are not correlated with the error process, the Sargan Tests is asymptotically distributed as a chi-square with as many degrees of freedom as over identifying restrictions. The test is unable to reject the validity of the instruments, if the acceptance area is extended up to 95% of the distribution; the result of the test for the system specification is reported in Column 4 of Table 2.

We can observe that the lagged dependent variable enters positively and statistically significant in the GMM system equation, and the magnitude of the coefficient is high (0.781). This result indicates that debt is associated to more debt and the lagged value of indebtedness is an important determinant of present values. On the other hand, two explanatory variables, size and growth become not statistically significant. The tangibility variable becomes positive and statistically significant at the 10% level. Only the profitability coefficient keeps the same sign and the level of significance (1%) compared to the OLS, FE and RE equations.