A meta-analysis: capital structure and firm performance

Modigliani and Miller first proposition (1958)

This research is among the pioneers attempting to unravel the relationship between capital structure and firm value. Their proposition, usually referred to as MM theorem, was first introduced in 1958, and it brought up the most intriguing question about the relevance of funding decisions toward corporate performance. In particular, they argue that any changes in the current proportions of debt and equity cannot affect the value of the firm, which means no capital structure is better or worse, and firm values remain irrelevant to different levels of leverage (Modigliani and Miller, 1958).

Modigliani and Miller alternative propositions (1963)

Using tax-deductible expenditure, the appearance of interest promotes lower tax payments and thus improves the firm's general cash flows (Miller and Modigliani, 1963). Indeed, the two economists also discovered that the firm value is now positively related to financial leverage, which implies that corporations are fully capable of maximizing their values by raising their debt levels.

Trade-off Theory

states that the capital decision of one firm involves a trade-off between the tax benefit of debts and the costs of financial distress (Kraus and Litzenberger, 1973).

When adopting the trade-off theory, each firm tends to set its own targeted debt-to-equity ratio and strives to achieve the expected optimum which varies with the characteristics of different firms (Myers, 1984)

Agency Theory

proposed by Jensen and Meckling (1976) and Myers (1977) investigates the influence of capital structure under a new perspective of corporate governance. Since the theory is developed on the basis of previous models, it shows consistent results with the trade-off theory. In general, agency problems involve the participation of three parties including managers, shareholders and creditors.

Agency problems between shareholders and managers

The first type of conflict is rooted when the managers own less than 100% of the share of the firm's assets, which induces less motivation behind their acts to maximize the firm value for shareholder's best interest (Jensen and Meckling, 1976) With a low level of debt, managers will own more freedom to spend the firm's free cash flows, and hence they easily take on low-return projects and acquire unnecessary physical assets to enlarge the firm size, which is believed to reflect their own reputation. For such reasons, managers increase the agency costs of equity, which is detrimental to the firm performance. On the contrary, if the firm is funded by higher amount of leverage, the commitment to fulfill interest payments leaves managers with less freedom to distribute the cash flows; therefore, they are required to be more efficient in choosing investments and generally improve the firm performance.

Agency problems between shareholders and creditors

The second conflict arises when two groups of investors prefer different levels of risk-taking behaviors. In particular, shareholders may have the incentive to either take considerably risky projects or move toward underinvestment (Ross et al., 2013; Westerfield and Jaffe, 2013). Regarding the former motive in which shareholders take part in high-risk investments, they shall receive extra return if the projects succeed and share losses with their counterpart in any case of failure (Jensen and Meckling, 1976). Concerning the second incentive, if a firm owns excessive amount of leverage, the significant probability of bankruptcy would discourage shareholders to take on new investments despite positive NPVs; hence, the firm becomes underinvested (Myers, 1977).

Pecking Order Theory

is an alternative to the trade-off model that declares a negative relationship between firm's performance and its decision of financing. There are two rules as proposed by the pecking order (Myers, 1984): (1) use internal financing and (2) issue safer securities first. In other words, the preference of financial instruments shall be prioritized as follows: internally generated funds, debt and equity. The driving force behind this arrangement generally stems from the problems of information asymmetry. According to Ross et al. (2013), in some cases where the managers wish to embark on a risky project but the lenders, due to discrepancy of information, stay rather optimistic about the venture, the issuance of debt would be much likely to be overpriced just as the equity issuance. It leads to a major problem in which investors eventually recognize the pattern of issuing decisions for both equity and debt whenever they are overvalued under the managers' perspective. As a result, any public offering can then become less than a success since this phenomenon creates a never-ending cycle of skepticism between investors and managers of the firm.

Signaling Theory

is proposed by Ross (1977) in which the choice of debt-to-equity ratio is independent of the optimum concept and rather represented by the willingness of a firm in sending certain messages to the investors. Profitable firms sometimes attempt to push up the stock price by excessively increasing debt over its optimal level and mislead the market to believe in its inflated growth opportunity in the future. Indeed, they believe that the extra cost of issuing debts shall prevent less profitable firms from taking advantages of higher leverage as compared to those with better performance, despite the managers' attempt to fool the public (Ross et al., 2013). Additionally, Myers and Majluf (1984) propose the tendency in which managers are rather reluctant to issue equity when it is believed to be undervalued; consequently, investors tend to perceive issuance of stocks as a bad signal, assuming that managers offer equity to the public only if it is fairly priced or overpriced. In short, the relationship between leverage and firm performance is found positive under the signaling theory.

Among the five theories, only MM and Signaling support the positive relationship between leverage and firm performance, while the other three theories – Agency, Trade-off and Pecking order – support the negative relationship.

3.1.1 Meta-analysis

Meta-analysis, as explained by Borenstein et al. (2011), refers to the statistically synthesized results from a series of studies collected through a methodological procedure. According to Glass (1976), meta-analysis can be considered as “the analysis of analyses” where individual researches are gathered with the aim to integrate their knowledge and findings. In particular, meta-analysis allows separate empirical outcomes of different papers to be aggregated and compared after being transformed into one common metric called the effect size.

3.1.2 Meta-regression

Besides the purpose of obtaining a generalized empirical evidence on the relation of two variables, meta-analysis can also be advanced into meta-regression, or meta-regression analysis, which performs closer scrutiny on the third elements that potentially influence the strength of relationship.

According to Higgins and Green (2011), meta-regression is quite similar in essence to simple regressions where a dependent variable is forecasted by one or more explanatory variables. However, meta-regression should be distinguished from simple regressions by two means. Firstly, the weight of each study is assigned based entirely on the precision of its effect estimates, in which larger studies tend to have stronger influence as compared to the smaller ones. Secondly, the existence of residual heterogeneity that cannot be explained by independent variables should be recognized and allowed in the analysis, giving rise to the term “random-effects meta-regression” (Thompson and Sharp, 1999).

3.1.3 Generalized models and assumptions

According to Field and Gillet (2010), meta-analysis can be conceptualized using two models of fixed and random effects. The fixed-effect model assumes that selected studies are sampled from only one population of which the average effect is fixed and implies homogeneity among individual effect sizes. Alternatively, random-effect model proposes the existence of heterogeneity by which the true effect size varies from study to study. Let us assume that a study of a total n studies produces an estimate, y_i, for the effect of interest and a standard error, σi. The basis of meta-analysis as well as meta-regression is presented below, with a simplified mathematical demonstration (Harbord and Higgins, 2008).

1. Fixed-effects meta-regression is the extension of fixed-effect meta-analysis where the mean effect, θ, is developed into a linear predictor, βxi, such that.

yi= βxi+ ϵi, where ϵi ∼ N(0, σi2), β is a (k × 1) vector of coefficients and xi is a (1 × k) vector of k covariates in study i.

• (2) Random-effects meta-regression, similarly, is extended from the random-effects meta-analysis with consideration of the covariates.

yi= βxi+ui+ ϵi, where ui ∼ N(0,  τ2) and ϵi ∼ N(0, σi2).

3.2.1 Data collection

The process of collecting and evaluating data for a meta-analysis is of critical importance since it is one of the most significant factors that can contribute to the analytical success. Overall, a total number of 32 journals, reviews and school presses were selected [1] besides online libraries and publishing platforms, namely, Elsevier, JSTOR, ResearchGate, Wiley, SSRN and Springer. There were 50 papers with 340 studies chosen from 2004 to 2019, of which data ranged from 1998 to 2017.

3.2.2 Data evaluation and final sample size

After the first stage of massive data collection, four additional standards were established as predetermined requirements for the following screening procedure.

First of all, the general search for papers on relationship between capital structure and firm performance leads to two ways of defining main dependent variables where a minority of 7.4% choose leverage ratios and the other 92.6% choose firm value indicators. While there is no threshold on the number of studies needed for a meta-analysis (Pigott and Terri, 2012), it remains more preferable to keep the data collected at its potential maximum.

Secondly, proxy for firm value can be divided into two main groups: accounting-based measures including return on asset (ROA), return on equity (ROE) and market-based ratio such as Tobin's Q.

Thirdly, further steps of data processing require the provision of at least two following figures: (1) beta coefficients of regression, and (2) t-statistics or p-value, which means studies without these numbers are also excluded.

Lastly, statistically significant outcomes tend to be utilized repeatedly in multiple works of the same authors under different forms such as dissertations, working papers and journal articles. At the end of the screening process, the final data officially consist of 34 papers which propose 245 studies served as observations for this meta-analysis. The time period also changed, as it now covers researches during 2012–2019, with a data set dated from 2000 to 2017.

5.1.1 Standardized effect sizes

It is noted that the values of “r” obtained from separate papers remain dependent on different research designs and not yet synthesized; thus, they are not directly interpretable. It explains why Pearson “r” should be transformed into a standardized measure of Fisher score “Zr” before combining the average true effect. According to Hedges and Olkin (1985), Rosenthal (1991) and Hedges and Vevea (1998), the transformation of “r” into “Zr” is proved to be capable of correcting skewness problems in the distribution of Pearson correlation coefficient. This statement is also supported by prior research of Silver and Dunlap (1987) who also observed a less distorted distribution in “r” with the complement of Fisher standardization.

One noticeable problem detected during data collection is that not all studies in management and finance provide Pearson “r” correlation in their analysis (Rocca, 2010). Fortunately, Cooper and Hedges (1994) suggested a way of retrieving “r” using the t-Students as illustrated by Eqn 1.

Next step is to convert r_i into Fisher Z-score by Eqn 2 (Field and Gillett, 2010).

5.1.2 Weights under fixed-effects model

The first approach is based on a model which states that if the sample size is large enough, residual errors will converge toward 0 (Hedges and Olkin, 1985), thus indicating an increase in the level of accuracy as more subjects are added to the sample of interest:

In the second approach, it is recalled that fixed-effects model assumes one true effect size θ for every study, and its only source of error is reflected in the within-study variances, σi2. In particular, with a smaller standard error, the estimation of effect size is appraised as more rigorous. Consequently, it leads to Eqn 4, which simply shows the reverse relation between within-study variances and weights allocated to selected studies (Hedges and Vevea, 1998).

5.1.3 Weights under random-effects model

While fixed-effects model allows no heterogeneity, random-effects model does the exact opposite, which results in the appearance of second variance component, τ2, during the computation of weights. Accordingly, the value of between-study variance must be incorporated as illustrated in Eqn 5 (Hedges and Olkin, 1985, Hedges and Vevea, 1998).

The estimation of between-study variance, τ2, proposed by Hedges and Olkin (1985), is provided below.

where k is the total number of studies; yi is the effect size in study i; y¯ is the average effect size of k studies; σi2 is the within-study variance in study i.

However, this method only works when τ2 is non-negative. In practice, several researches have shown the possibility of negative value of τ2. It is then set back to 0 according to the rule stated above and seemingly denies the existence of heterogeneity. To promote a more effective measure, Chung et al. (2013) suggested the use of DerSimonian and Laird's (1986) estimate that employs method of moment estimator as follows:

yi is the effect size in study i;

n is the total number of studies;

μˆ is defined by the formula μˆ= ∑iyi/si2∑i1/si2

5.1.4 Overall effect size

Eqn 8 provides the calculation of “Zr” as suggested by Hedges and Olkin (1985) and Hedges and Vevea (1998), which takes into account the distribution of the weights:

Zri is the standardized effect size of study i;

wi is the corresponding weight of study i among a total of k studies.

The standard error for weighted average “Zr” is calculated as below.

wi is the corresponding weight of study i among a total of k studies.

After achieving the mean value of “Zr,” it must be converted into its correlation form for final conclusions on the strength of relationship between capital structure and firm performance. Borenstein et al. (2011) introduced the conversion formula for “r” in the following equation.

Zr¯ is the weighted mean of effect sizes from k studies.

For the interpretation of results, Cohen (1977) proposed the “rules of thumb” as Table 8.

6.1.1 Moderating variables

In moderator analysis, the standardized effect size of leverage on firm performance, “Zr”, becomes the dependent variable since it represents the magnitude of impacts and is sensitive to different strength across studies (Rocca, 2010). Meanwhile, other paper-specific features that potentially induce controversial results should be chosen as the explanatory variables (Wolf, 1986; Rosenthal, 1991). In particular, the examination of heterogeneity utilizes dichotomous covariates and subgroups of observations according to various categorical characteristics. Since dummy variables are employed in the regression, the coefficients would emphasize on the differences of effect sizes between subgroups in comparison with another nominated subgroup of which all dummy variables are assigned to 0 (Higgins and Green, 2011). We use the moderator variables as dummy variable. For example, D-publication = 1 if the study is published, and = 0 otherwise. Theses moderating variables are based on hypotheses H2-H8.

6.1.2 Econometric method

Many researchers suggest the use of random-effects model as the proper method for meta-regression, such as Hedges and Olkin (1985), Cooper and Hedges (1994) and Hedges and Vevea (1998). This method considers both within-study variance, σi2, and between-study variance, τ2, which means two sources of errors due to two levels of sampling are addressed simultaneously . Furthermore, in contrast to fixed-effect model that assumes homogeneity across studies, random-effects model accepts “residual heterogeneity,” which is the between-study variance component that cannot be explained by the covariates. In conclusion, for the reasons above, random-effects meta-regression is selected as the appropriate method for moderator investigation.

In fact, the default estimation method for τ2 by “metareg” is the restricted maximum likelihood (REML) since this model takes into account the problem of autocorrelation and works well with unbalanced or correlated data (Rocca, 2010). Hence, it is suggested by both Thompson and Sharp (1999) and Viechtbauer (2005), who also perform comparison among methods and conclude that REML is generally the preferable approach in meta-regression. Therefore, based on the aforementioned opinions, REML is decided to be the benchmark model for this moderator analysis. However, two other options of moment-estimator and empirical Bayes will also be included to increase the robustness of investigation.

6.2.1 Initial regression models

After performing “metareg” command in Stata 14, the initial regression model uses eight independent variables such as D_publication, D_development, D_listed, D_industry, D_strategy, D_proxy, D_ols, D_fem and D_rem. In general, the moderating effect on the relationship between capital structure and firm performance is the joint contribution of publication status, factor of industry and proxy of firm performance. Hence, three hypotheses with respect to these moderators, including H2, H5 and H7, are statistically supported, while the remaining statements are rejected.

6.2.2 Final regression models

The final models are conducted with the participation of three significant variables discovered in previous section, including D_publication, D_industry and D_proxy.

In comparison with Table 11, all values of the adjusted R² generally increase, especially in the case of moments method where it turns from an abnormal negative figure to a positive number despite remaining extremely low (0.32%), confirmed together with the F-statistics, which implies a considerable rise in overall significance of each model.

On the other hand, VIF test shows remarkable reduction in value for all regressors, and hence produces smaller mean VIF at only 2.02, much below 10, confirming the absence of multicollinearity in the regression.

Meanwhile, no change is observed in the index of variability, I². It is understandable since the proportion of variation due to between-study variance is independent of the moderators taken into account.