What Do We Really Know About Corporate Hedging? A Meta-Analytical Study

This paper employs meta-analysis to aggregate and systematically analyze the mixed empirical evidence on the determinants of corporate hedging reported in 132 previously published studies covering data from more than 73,000 firms. Among the fourteen proxy variables analyzed by multivariate meta-analysis, three variables emerge as reliable explanatory factors for corporate hedging decisions supporting the bankruptcy and financial distress hypothesis: dividend yield (positive sign), liquidity (negative sign), and size (positive sign). Moreover, for tax-loss carry forwards (positive sign) and research and development (positive sign), our findings indicate a weak impact on corporate hedging behavior reflecting tax reasons, the coordination between financing and investment, and agency conflicts between shareholders and debtholders. Regarding the asymmetric information and agency conflicts of equity hypothesis, we find no explanatory power. The further analysis of heterogeneity via meta-regression reveals several factors that determine the mixed empirical evidence reported in previous studies. First, the results indicate that studies analyzing firms from North America report, on average, a lower impact of leverage on the corporate hedging decision. Moreover, studies examining more recent data samples tend to find a weaker relation between tangible assets and hedging, R&D and hedging respectively. Overall, our results encourage scientific research to put more emphasis on finer-grained examinations of hedging variations and to discover rationales of corporate hedging extending classical financial theories.


Introduction
The motivation for non-financial firms to engage in corporate hedging is one of the most intensively discussed topics in corporate finance research. Neoclassical finance theory claims that under the conditions of a perfect capital market, hedging on the firm level does not create additional value, since shareholders can perfectly hedge their position (Modigliani and Miller 1958). However, more recent financial theory suggests that when financial markets are not frictionless, there are several ways through which corporate hedging can increase firm value in the sense of the maximization of shareholder value (Bessembinder 1991;DeMarzo and Duffie 1991;Froot et al. 1993;Smith and Stulz 1985). In this manner, This assessment arises from the fact that vote counts collapse the observed estimates into a few categories based on their statistical significance, do not present an economic magnitude for the aggregated effects, and ignore differences of sample sizes and precision of the findings reported in the primary studies (see, among others, Borenstein et al. 2009;Hedges and Olkin 1985;Stanley and Doucouliagos 2012). 3 To overcome the shortcomings of vote counting, Arnold et al. (2014) calculate weighted averages for a set of 15 different hedging determinants across a sample of 37 primary studies. Contradicting Aretz and Bartram (2010), their main result is that financial distress costs induce firms to hedge. In addition, they find weak evidence that the underinvestment problem and the dependence on costly external financing influence corporate hedging behavior. However, their univariate meta-analysis approach bears an essential caveat, since the computation of mean values across primary studies does not account for interactions between the examined proxy variables. Riley (2009) shows that ignoring these dependencies in a metaanalysis can lead to a heavily biased estimation of the aggregated results. Furthermore, independent testing of correlated effects increases the chance of finding spuriously significant results (Bender et al. 2008). Beyond the threat of biased estimates caused by the assumption of uncorrelated proxy variables, none of the mentioned reviews explores the sources of heterogeneity among the primary studies' results.
Hence, explanations for the mixed empirical evidence are still missing. We contribute to the existing literature and especially the two previous reviews on the determinants of corporate hedging in several ways as illustrated in Table 1.   (INSERT TABLE 1) First, the field of corporate hedging is characterized by its multivariate interrelations (Jackson et al. 2011;Mavridis and Salanti 2013;Nam et al. 2003). For example, in the case of existing corporate taxes, a combination of several influencing factors determines firm value creation through corporate hedging, such as volatility of pre-tax income, convexity of the tax function, and the amount of tax payments. For this reason, we employ the first multivariate meta-analysis in corporate finance research. This approach simultaneously integrates reported results for the fourteen most frequently analyzed hedging determinants based on manually collected data from a sample of 132 primary studies. The data availability from a sufficiently large number of studies allows to apply this multivariate approach, which requires reported estimates for the bivariate relations among all proxy variables. The number of articles included in this study is about three times larger than the samples analyzed by Aretz and Bartram (2010) or Arnold et al. 4 (2014). In this way, we aim to comply with the requirement of any meta-analysis to examine the population of studies available in order to avoid systematic biases due to misspecification and publication selection while incorporating the multidimensional nature of empirical research findings (Stanley and Doucouliagos 2012). Moreover, this comprehensive data set increases the number of observations from different data sources and time periods, which reduces the impact of sampling errors within individual primary studies. In a second type of analysis, we employ meta-regression to explain the heterogeneity among the reported effect estimates by exploring the impact of regional differences, study quality, and observation period on the reported results. Finally, we consider the presence of a potential data mining bias, publication selection bias, and misspecification bias. These aspects have not been investigated in the other reviews on corporate hedging so far.
In summary, our multivariate estimates of the aggregated primary studies' results provide evidence for the bankruptcy and financial distress hypothesis. In this respect, we obtain statistically significant results (at least at a significance level of 5%) for the following proxy variables: dividend yield (positive sign), liquidity (negative sign), and firm size (positive sign). In addition, we find weak explanatory power for the tax-loss carry forwards variable and the research and development (R&D) proxy (each at a significance level of 10%). This indicates weak support for the corporate tax hypothesis and agency costs of debt argument. Furthermore, we cannot find consistent evidence for the hypothesis that hedging alleviates asymmetric information and agency conflicts between managers and shareholders. Overall, these results differ from Aretz and Bartram (2010) and Arnold et al. (2014), since the former also find evidence for the asymmetric information hypothesis and both reviews identify some support for hedging to be driven by the motivation of firms to avoid agency conflicts of debt. The further analyses reveal that our main findings are robust against data mining bias and publication selection bias. Solely the results for interest coverage ratio, capital expenditure, and R&D seem to be slightly distorted towards reporting stronger and statistically significant results. Moreover, the impact of financial distress costs measured by the corporate 5 leverage ratio are found to be less pronounced for US firms. Finally, the relation between tangible assets and corporate hedging, as well as R&D expenses and hedging decreases over time.
The remainder of the paper is structured as follows. Section 2 provides an overview of the four basic hypotheses of firm value creation by corporate hedging. Section 3 serves as a short introduction to the methodology of multivariate meta-analysis. Section 4 presents the search for literature, the data preparation, and descriptive statistics. Section 5 reports our empirical findings, which are discussed in the subsequent Section 6. Section 7 concludes.

Determinants of corporate hedging
By incorporating capital market imperfections, scholars have developed several hypotheses explaining why hedging at the firm level can add value to shareholders (e.g., Bessembinder 1991;DeMarzo and Duffie 1991;Froot et al. 1993;Smith and Stulz 1985). These theories especially gain in importance due to the increasing volatility in financial markets, in particular foreign exchange rates, interest rates, and commodity prices, which drive a firm's market value to the extent to which it depends on the development of these risk factors (Rawls and Smithson 1990). Following previous literature (e.g., Aretz and Bartram 2010;Arnold et al. 2014;Guay and Kothari 2003;Kürsten 2006), the theoretical hypotheses can be subsumed under the maximization of shareholder value. Within the shareholder value maximization theory, we review four hypotheses that explain how corporate hedging increases firm value by (1) reducing the corporate tax burden, (2) lowering bankruptcy and financial distress costs, (3) mitigating asymmetric information and agency conflicts of equity, as well as (4) improving the coordination of financing & investment policy and alleviating agency conflicts of debt.
As most of these theoretical arguments are not directly observable, academics make use of proxy variables to test whether firms with properties according to the hedging hypotheses are more likely to hedge. Table   2 sums up our analyzed proxy variables for each of the hypotheses together with the hypothetical signs and variable definitions. As these variables are the standard proxies examined in the majority of the 6 hedging literature, we do not further discuss them. Excellent discussions of the proxy variables are provided, among others, by Bartram et al. (2009), Géczy et al. (1997), or Haushalter (2000. (INSERT TABLE 2) 2.1 Corporate taxes Mayers and Smith (1982) as well as Smith and Stulz (1985) show that if a firm faces a convex tax function (i.e., taxes increase overproportionally with taxable income), corporate hedging can increase post-tax firm value by reducing the volatility of pre-tax income. This is due to Jensen's inequality as less volatile cash flows lead to a lower expected tax liability. Thus, we receive the following hypothesis H1, which we test by tax-loss carry forwards as proxy variable: H1: Firms use corporate hedging as an instrument to profit from tax advantages.

Bankruptcy and financial distress costs
Volatile future cash flows and a high leverage may induce situations in which a firm's liquidity is insufficient to fully meet its contractually fixed payment obligations (Rawls and Smithson 1990). This increases the risk of bankruptcy and the firm might encounter direct and indirect costs of financial distress (Jensen and Meckling 1976). Since corporate hedging lowers cash flow volatility and therefore also the default probability, it reduces expected costs of financial distress and adds value to the firm (Brown and Toft 2002;Hahnenstein and Röder 2003;Smith and Stulz 1985;Stulz 1996). Thus, we receive the following hypothesis H2, which we test by dividend yield, interest coverage ratio, leverage ratio, liquidity, profitability, size, and tangible assets as proxy variables: H2: Firms use corporate hedging as an instrument to reduce the risk of bankruptcy and financial distress costs. 7 2.3 Asymmetric information and agency conflicts of equity 1 DeMarzo andDuffie (1991, 1995) show that information asymmetries can arise from a manager's proprietary information on the firm's dividend stream. Due to preferred managerial access to corporate information, shareholders cannot fully replicate the firm's hedging decision. Accordingly, under information asymmetry firms can hedge more effectively than its shareholders. Such informational asymmetries may result from high expenses for disseminating necessary information to the shareholders, whereby the costs increase with firm complexity (Dolde and Mishra 2007), or from protecting information transmission to competitors (Marshall and Weetman 2007). By reducing the variability of the corporate cash flow and thus lowering the noise in the firm's dividend stream, hedging can be used as an instrument to overcome informational asymmetries between shareholders and managers. Hence, we receive the following hypothesis H3, which we test by institutional investors, option ownership, and share ownership as proxy variables: H3: Firms use corporate hedging to reduce information asymmetry and to mitigate agency conflicts of equity.

Coordination of financing & investment policy and agency conflicts of debt
High leverage and a low present value of the firm may give rise to the following agency conflicts of debt, because under these conditions managers may have incentives to transfer wealth from bondholders to shareholders. First, managers may forego positive net present value projects if the expected project gains are required to satisfy fixed payment obligations to the bondholders (Myers, 1977). Corporate hedging can relieve this problem, as a reduction of cash flow variability increases the probability that shareholders are residual owners after reimbursing the bondholders. Moreover, when external financing is more costly than internal financing (Myers and Majluf, 1984), firms may forgo profitable investments due to a lack of internal funds. Froot et al. (1993) show that under this condition, corporate hedging may be used as 8 instrument to coordinate the availability of internal funds. Secondly, managers acting in the best interest of shareholders may give rise to asset substitution by replacing low-risk assets with high-risk investments (Smith and Warner, 1979). This is because shareholders' equity positions are a call option on the company's assets, and high variance projects enlarge option value (Mason and Merton, 1985). However, for fixed payment receivers this exchange of assets raises additional risk. Hence, bondholders anticipating the opportunistic behavior of management claim higher returns or protective bond covenants, due to increasing risk and higher agency costs (Jensen and Meckling, 1976). Corporate hedging adds value to the firm by lowering the project's risk and accordingly diminishing agency costs which arise from the managerial incentive of asset substitution. Campbell and Kracaw (1990) additionally contribute that also credible commitments to hedge (for example, obligated hedging of interest rate risks via debt covenants) reduce agency costs of debt by lowering the incentive to asset substitution. Thus, we receive the following hypothesis H4, which we test by capital expenditures, R&D expenses, and Tobin's Q as proxy variables: H4: Firms use corporate hedging as an instrument to coordinate investment and financing policies and to mitigate agency conflicts of debt.

Methodology of multivariate meta-analysis
The objective of this multivariate meta-analysis is to comprehensively test the hedging determinants on an aggregated empirical level across a broad set of primary studies. In detail, we investigate the relationship between fourteen proxy variables and the corporate hedging behavior, which is modeled as a dummy variable that is equal to one for hedgers and zero otherwise. 2 As effect size measure for this relationship we use the Pearson correlation coefficient between each proxy variable ( = 1, … , ) and the hedging variable reported in study ( = 1, … , ). 9 Due to the multidimensional behavior of the firm characteristics used as proxy variables for the hedging hypotheses, primary studies on corporate hedging usually test their hypotheses through multivariate analyses. These interrelations must be considered on a meta-level as well. Thus, in addition to correlations between the hedging variable and each proxy variable, correlations among the proxy variables must also be incorporated in the aggregation. In the case that all proxy variables are investigated in each primary study, we could extract * = ( + 1)/2 correlations from each study of interest.
As the variance of the raw correlations strongly depends on the correlation coefficient itself, all computations are performed in the variance-stabilizing Fisher's z-scale and are later transferred back into the correlation metric for interpretation.
Using this correlational data as input, meta-analysis aims to derive the best effect estimate for the unknown population correlation by calculating a weighted mean effect across all observations from the sample studies. For the estimation of the mean effect, we use a generalized least squares (GLS) estimator to derive the z-transformed mean correlation vector (Raudenbush 1988) Here, ̂ is a * × 1 column vector containing the effect size parameters to be estimated. X is an indicator matrix with k stacked * × * identity matrices that show which correlations are given in each study. is a block-diagonal variance-covariance matrix containing the k study specific variance-covariance matrices + on its diagonal. is a * column vector storing the observed effect sizes * from all k studies.
In the matrix , the diagonal elements capture the study-specific effect size variation and the off-diagonal elements are the estimated covariances 3 among the effect sizes. ² define the * × * -matrix . The weights are calculated by adding to each study-specific covariance-matrix . This weighting scheme assigns higher weights to more precise studies. Furthermore, ² explicitly models the fact that the true population effect is not unique, but varies across primary studies (between-study variation). Hence, this parameter captures unobserved heterogeneity among the reported effect sizes. A model that includes an 3 To estimate the covariances, we apply the large sample approximation according to Olkin and Siotani (1976 with as a × 1 vector of standardized regression coefficients, and as the GLS estimator ̂ from Equation (1), which is transformed back into the correlation scale and organized as a matrix.
is a × 1 matrix with the correlations between the hedging variable Y and each proxy variable X, where p is the number of proxies used as predictors. is a × matrix capturing the correlations among the proxy variables. Accordingly, estimates the average impacts of the proxy variables on the corporate hedging decision, while accounting for dependencies among the proxies.

Data
We Interventions as a general framework for the literature search and the subsequent meta-analysis (Higgins and Green 2011).

Inclusion criteria
We consider only studies investigating non-financial firms because companies from the financial sector do not necessarily use derivatives exclusively for hedging purposes but also for trading or speculative activities (e.g., Allayannis and Weston 2001; Gay and Nam 1998;Heaney and Winata 2005). However, we do not exclude studies containing both financial and non-financial firms, if the sample was taken from a broad stock market index. Moreover, the hedging proxy must be modeled as a dummy variable in the primary studies. Additionally, we focus on studies meeting the following criteria, which are constitutive elements for the conduction of a multivariate meta-analysis: (1) The correlation coefficient between the proxies and the hedging dummy should either be directly reported in the study, or otherwise should be computable from the reported descriptive statistics 6 (e.g., t-statistic from a test of independent groups or standardized mean difference between hedgers and non-hedgers). If there is no sufficient data available, the authors must provide us the required effect size data to be included in the analysis. 7 (2) The study's sample size must be extractable to calculate the effect size variation and hence the study weights.
(3) The correlations among the proxy variables have to be stated in the primary study. However, this is not a necessary requirement to be included, because the direct effects between the hedging dummy and the proxies also carry useful information for multivariate meta-analysis. summary, we reached a total number of 2,790 studies identified by the search command. After sorting the results by the inclusion criteria, we cut the sample to 67 relevant studies.
In the next step, we explicitly searched for gray literature. By screening the electronic working paper database SSRN (via ProQuest) and using the same search strategy as for published articles, we received another 18 relevant studies (from an initial sample of 808 studies). Additionally, we found 6 relevant studies in the Dissertations and Theses database (ProQuest).
In the following step, we performed a backward search by screening the reference lists of the 91 studies identified as relevant after the search in the electronic databases. Furthermore, we screened the publication lists of the authors appearing more than twice in our interim list from the database search. Finally, we conducted a forward search via the 'cited by'-option in Google Scholar. Another 76 relevant studies were identified in this step.
At the end of the search process, we reached a sample of 167 relevant primary studies meeting the inclusion criteria -with 54 of them providing full correlation matrices for the hedging dummy and the other proxy variables, 69 studies reporting at least the direct effects between the proxy variables and the hedging dummy, and 44 studies with none of the required data published. 10 Thus, we finally sent a studyspecific request mail to the authors of all studies with missing data. 11 In response, 12 authors provided us with additional data. As common in meta-analysis, we treat studies as independent, if the same authors use different data sets or different authors use the same data set (Hunter and Schmidt 2004;Stanley and Doucouliagos 2012). In this regard, we had to exclude 3 studies due to insufficient data or dependencies in the sample. 12 Consequently, our final sample consists of 132 primary studies. 13 From this pool of studies, 10 The list of excluded studies from the initial sample of 167 relevant studies is available on request from the authors. 11 We sent a request mail to the authors of 113 studies with missing data and two weeks later a reminder mail to the authors and co-authors. From 10.62% of the contacted authors we received additional data. 22.12% rejected to provide us with the correlational data from their study, and from the remaining 67.26% we did not receive a response to our request. 12 If studies use an identical sample of firms, we use each proxy variable from this sample only once. Beside the studies from Bartram (Bartram et al. 2009;Bartram et al. 2011;Bartram 2015) and Lin et al. , the studies from Nguyen and Faff , 2007 are also based on the same data sample. As the studies by Nguyen and Faff additionally investigate similar variables, we had to exclude Nguyen and Faff (2006) and Nguyen and Faff (2010) from our sample. Furthermore, dependencies also arise when a study reports results for different groups, which dependent on each other (e.g., for disjoint observation periods, different hedging intensities, etc.). As some firms could be in several groups, as in the case of dependent results within one study, we include the subsample with the largest sample size. 13 The studies are listed in Online Appendix B together with the study characteristics. The corresponding references are listed in Online Appendix C.

13
we have manually collected 1,627 Pearson correlation coefficients covering the relation between the fourteen hedging determinants and the hedging dummy variable as well as the interactions among the hedging determinants.

Data preparation
A requirement for the feasibility of multivariate meta-analysis is the estimation of the complete correlation matrix between the proxy variables and the hedging dummy. Thus, we consider all proxies for which the correlation with other variables is reported in at least one study. As several of these correlations are not given in any of the primary studies, we focus on the fourteen most frequently examined hedging determinants (see Table 2).
As sample size for the hedgers and non-hedgers group we use the number of firms investigated in the primary study instead of the firm year observations. 14 In some studies, we had to do apply the following adjustments to incorporate their findings. First, some authors use the opposite assignment for the hedging dummy, i.e., '0' for the hedgers group and '1' for the non-hedgers group. In this case, we changed the sign of the correlations. Second, seven studies do not contain any measures for the estimation of correlations.
In this case, we use statements from the article's text to extract the direction and magnitude of the proxy variable. 15 Third, some studies report the reciprocal value of the proxy variables (e.g., book-to-market value instead of market-to-book value). In this case, we use the reciprocal means and estimate the variance approximation of the reciprocal elements. Afterwards, we calculate the mean differences and convert the values to the Pearson correlation coefficient. In total, about a third of the estimates is based on firm data from a single year, while the remaining part of studies examines more than one year. The regional distribution of the collected estimates reveals a dominance of North American studies (45%) in the corporate hedging literature. Nevertheless, more than half of the observations is based on data from other geographical regions, especially from Europe (25%) and the Pacific (11%). Consequently, there is a certain proportion of studies investigating firms from the same country and identical or overlapping time periods (e.g., US studies commonly examine S&P 500 firms). 16 Therefore, effect sizes might be related across studies if different authors use similar data sets.

Descriptive statistics
This issue cannot be fully account by the multivariate meta-analysis approach. However, the wide distribution across time weakens the threat of non-independent study results. Moreover, we address the issue in our analysis of heterogeneity, where we explicitly account for these two levels of data dependencies (across countries and time) in our estimation method. Additionally, we measure the impact of time and regional effects on the reported primary studies' results within a meta-regression analysis. journals having a SJR ranking above (below) 1.00. Therefore, it appears discussable why considering lowquality studies in meta-analysis. We explicitly include these studies in the sample due to the following reasons. First, the inclusion of unpublished and low-quality studies leads to a broader and more comprehensive sample covering multiple countries and time periods. This approach significantly enhances the power of our meta-analytical findings (Whiston and Li 2011). As the exclusion of these studies would dramatically reduce our sample, it would not be possible to conduct multivariate meta-analysis for all fourteen proxy variables. Second, we explicitly account for study quality in our analysis. Within the multivariate meta-analysis, the weighting approach (see matrix in Equation 1) is based on the withinstudy variation, i.e. observations from low-quality studies with small sample sizes and thus larger variation in their estimates receive a lower weight in the analysis. Third, excluding unpublished studies would reduce the observed time period, as new studies that might not have gone through the referee process would be excluded. Moreover, 'low-quality' studies often focus on firms from other countries than the US. Excluding these articles would lead to a strong country-level clustering in our observations because a larger fraction of findings would refer to US firms. Fourth, we conduct a robustness tests via meta-regression analysis, which explicitly models the impact of publication quality on the reported results.

Empirical results
We aggregate the reported effects for the hedging determinants across our sample of 132 primary studies using multivariate meta-analysis. 17 For each proxy variable we examine the null hypothesis of no relationship with the hedging dummy variable. In the following section, we first address the issue of between-study variation in more detail, because this is important for the question of using a fixed or random effects model in our analysis. Afterwards, we present our main results for each of the four hedging hypotheses. Further, we describe the findings from the analysis of heterogeneity. Therein, we test for the impact of study quality, time effects, and regional differences. Moreover, we explicitly analyze data mining bias and publication selection bias.

Multivariate meta-analysis
For the correct specification of the multivariate model, one main aspect of meta-analysis is the detection and consideration of between-study variation. As the effect sizes are collected from studies examining data from different countries and time periods, it would be problematic to assume that there is one single underlying population effect across all studies in our sample (Borenstein et al. 2009;Card 2012;Lipsey and Wilson 2001). In the case of heterogeneity, the effect size variation is not only driven by sampling error but also by variation between studies. For example, country-specific regulation or firm characteristics influence the true effect size, although the initial decision to hedge is the same. The Cochran's Q-test is a commonly applied test for heterogeneity in meta-analysis that measures the excess variation beyond sampling error. The Q-test results in a test statistic of 41,056.49 18 , which obviously leads to a rejection of the null hypothesis of homogenous effect sizes at all common significance levels. We consider this aspect of heterogeneous effect sizes by applying random effects estimation, which explicitly accounts for the between-study variation.
The estimates of the linear model estimated by multivariate meta-analysis are displayed in Table 4. 19 (INSERT TABLE 4) Regarding the corporate tax hypothesis (H1), the results reveal weak empirical evidence. The aggregated effect for tax-loss carry forwards is 0.0711 and slightly significant at the 10% level (p-value of 0.0956).
The positive sign of the estimate indicates that hedging companies can better time the use of tax-loss carry forwards, which results from the reduction in cash flow volatility hedging. This leads to an increase in the present value of tax preference items (Géczy et al. 1997).
The proxy variables used to test the bankruptcy and financial distress costs hypothesis (H2) show high significance levels (at least at 5%) for the influences of dividend yield ( = 0.0741, = 0.0202 ), liquidity ( = −0.0893, = 0.0108), and firm size ( = 0.2148, = 0.0002). The estimate for firm size is clearly the dominating effect across these variables in terms of statistical and economic significance.
The positive sign of the size effect provides evidence that economies of scale are highly relevant for hedging firms. The finding that more liquid firms tend to hedge more is in line with theoretical predictions that financial liquidity enables greater flexibility in meeting financial requirements, which helps to mitigate financial distress costs. Consequentially, cash management can help to build a financial buffer acting as a substitute for hedging (Géczy et al. 1997). Moreover, the results show that corporate dividend policy influences corporate hedging behavior. The positive aggregated effect for dividend yield can be explained by the fact that higher dividend payments lower the availability of internal funds required for payments to fixed claimholders, which leads to raising expected costs of financial distress ). In addition, Kalay (1982) argues that higher dividend payouts introduce underinvestment problems and associated costs occurring from agency conflicts between shareholders and bondholders. Therefore, firms offering higher dividend payments to their shareholders have more incentives to engage in hedging to avoid distress costs and underinvestment problems. The findings for liquidity and dividend yield also pronounce the important interactions between hedging and other corporate financial decision, namely cash management and dividend policy.
Regarding the coordination of financing & investment policy and agency conflicts of debt hypothesis (H4), the results show ambiguous empirical evidence. The estimated mean effects reveal a positive relation between R&D expenses and corporate hedging, which confirms the hypothesized direction ( = 0.092, = 0.0541). As R&D expenses measure the availability of growth options in a firm's investment opportunity set, firms with greater R&D expenses can benefit more from the risk reduction of corporate hedging through lower risk of underinvestment problems and associated agency costs (Choi et al. 2013).
In addition, neither capital expenditures for property, plant and investment, nor Tobin's Q show significant results at any conventional levels. The latter is especially astonishing, because the number of observations for Tobin's Q is relatively high in comparison to the other variables. However, besides the ability to capture underinvestment, Tobin's Q can also be interpreted as a risk factor in multifactor models 18 or a measure for additional value in case of superior corporate governance. This might explain the nonsignificant results.

Further analyses
To verify the robustness of our multivariate results, we perform two types of robustness tests: (1) investigation of data mining bias, (2) analysis of publication bias and exploration of heterogeneity.

Data Mining Bias
First, we account for the fact that primary studies use different definitions for the examined proxy variables. Due to the large amount of emerging primary studies, this effect is even amplified. By using the testing methodology developed by Harvey et al. (2016), we consider the so-called data mining bias. In this manner, we account for the fact that various alternative variable definitions are used for the proxy variables. This large variety of definitions might by reasoned by an opportunistic behavior of researchers to favor certain findings. The corresponding results are displayed in Table 5.
( INSERT TABLE 5) As an assumption for this test, we suppose that authors select the variable definitions of the proxies to reach significant results. This means, the larger the variety of different variable definitions for the same proxy variable, the higher the risk of biased primary studies' results driven by data-mining activities. To control for an overestimation of the multivariate effects arising from data-mining, we have to accommodate the test statistics of our results. Therefore, we calculate an adjusted 5% significance level for each proxy variable to get a more conservative limit. In the case of a high number of different variable definitions in relation to the number of effect size observations, the probability level is diminished in order to provide a more conservative significance level. For example, the significance level for dividend yield decreases from 5% to 2.17%. In some cases, the variable definitions are quite consistent across the sample of effect sizes, which leads to an increasing probability level (larger than 5%). For a conservative estimation, we leave these probability levels at 5% instead of increasing them as, for example, in the case of tax-loss carry forwards. As a result from this robustness test, it appears that our strongly significant 19 findings are not affected by data mining bias as these estimates are still significant even when applying the more conservative, adjusted significance levels. For example, in the case of dividend yield, the 5% significance level is adjusted to 2.17% due to solely 7 different variable definitions used in 41 studies.
However, the estimated p-value for dividend yield ( = 0.0202) is still significant at the adjusted significance level. The same conclusions hold for liquidity and size.

Publication bias and analysis of heterogeneity
In this section, we test the heterogeneity of our dataset using a similar approach as presented by This test procedure follows the idea of the Egger's test (Egger et al. 1997). Overall, the general metaregression model can be formularized as with the error term following a normal distribution with an expected value of zero and a variance set to the variance of the effect sizes according to The estimated regression coefficients ,…, measure the explanatory power of the independent variables for the variation of the z-transformed correlation coefficients. Thus, they indicate whether a certain variable systematically influences the reported results. For example, a significant positive effect for could be interpreted as finding that studies with US data, on average, report larger effects for a certain hedging determinant than non-US studies. where the effect tends to be more in line with the hypothesized positive sign. Additionally, we reveal significant temporal differences at the 5% level for tangible assets with a coefficient of −0.0679 and R&D with a coefficient of −0.0112. According to the empirical signs derived from multivariate analysis, the impact of tangible assets on the decision to hedge becomes less apparent over time. Furthermore, studies covering more recent data tend to report lower effect sizes for R&D expenses.

Discussion
In the following, we first compare our main results with the ten highest quality primary studies included in  , , which can be seen as representatives of empirical 21 In addition to a mixed effects multilevel model as displayed in Table 6, we also applied a simple ordinary least squares model as shown in Online Appendix F. Overall, both models show quite similar results. 22 For the selection of studies we used the VHB-JOURQUAL3 and incorporate studies, which are classified as A+.

22
literature in this field of research covering firm data for the time period from 1993 to 2015. Furthermore, we compare the results with the existing (univariate) reviews by Aretz and Bartram (2010) and Arnold et al. (2014). The univariate results reported in these studies are contrasted with the findings of our multivariate meta-analysis as outlined in Table 7.
( INSERT TABLE 7) For the corporate tax hypothesis (H1), we are generally in line with existing literature. All studies in our comparison testing this variable do not find a strongly significant effect.
The bankruptcy and financial distress costs hypothesis (H2) represents the most frequently confirmed hypothesis. For dividend yield our finding of a positive effect is also confirmed by two of five primary studies as well as by Arnold et al. (2014). For leverage, five of ten primary studies and the two reviews state a significantly positive effect. In this case, our estimates contradict with the majority of studies.
These deviations might be driven by a notable endogeneity between capital structure and the decision to hedge, as corporate hedging might also be seen as the starting point of the capital structure decision For the asymmetric information and agency conflicts of equity hypothesis (H3) the picture is the same as for the coordination of financing & investment policy and agency conflicts of debt hypothesis (H4). For both theories, existing studies partially proclaim strong evidences due to overestimation, which is not confirmed by our multivariate results. Deviations of our results exists in terms of institutional investors and R&D expenses. In both cases, four studies confirm a significantly positive association with the hedging dummy variable, which might be specifically driven by spurious effects in univariate analyses.
Following this, a further aspect that becomes apparent from Despite its power to model interrelations between multiple effect sizes, there are several issues to be critically considered when conducting a (multivariate) meta-analysis and interpreting its results. Limiting 24 factors, which are incorporated only in few primary studies, comprise the 'endogeneity and identification problems' as well as 'empirical modeling of structural relations' as emphasized by Aretz and Bartram (2010). This means that the causality of the variables is not unique. For example, many determinants of leverage also influence hedging strategies and vice versa. A promising methodology to address the problem of endogeneity in a meta-analysis using secondary data is the meta-analytic structural equation modeling (MASEM) approach presented by Cheung and Chan (2005). If a combined correlation matrix (similar to the GLS estimator presented in this paper) can be generated, this pooled correlation matrix could then be analyzed using structural equation models. Furthermore, it should be considered that possible nonlinearities in the dependency structure are not captured by our multidimensional model.     This table shows the results for the proxy variables used to test the corporate hedging hypotheses in a multivariate meta-analysis. Names of the proxy variables are listed in the first column, and the second column shows the specific hypothesized sign; the third column shows the number of firm observations summed up from the primary studies testing the respective proxy variable. Next, the results from multivariate meta-analysis are presented. Using the standardized regression slopes b from the multivariate linear model and their standard deviations SE(b) for each proxy variable, we calculate the z-statistic and the corresponding p-value to test the null hypotheses of = 0. *, ** and *** indicate the rejection of the null hypotheses at the 10%, 5%, and 1% probability levels. Significant effects are highlighted in bold type. This table sums up the proxy variables reviewed in the multivariate analysis. The second column contains the number of different variable operationalizations that we aggregated in our proxy variable definitions. The following column includes their hypothetical sign for the impact on the corporate hedging decision. Beside, the results (empirical signs and p-values) revealed from multivariate meta-analysis are presented, followed by the results using adjusted p-values to test the presence of data mining bias. *, ** and *** indicate the rejection of the null hypotheses at the 10%, 5%, and 1% probability levels. Significant effects are highlighted in bold type. a If one study uses several variations for a specific proxy variable, we only considered the definition with the least deviation related to the other studies testing the same proxy variable. A spot check revealed that the underlying sample covers most variations in the proxy-specific definitions. b To account for the usage of different variable definitions and the possible data mining bias, we adjusted the p-values similar to Harvey et al. (2016). Therefore, we used the Bonferroni correction respectively its exact version (the Sidak correction), both adjusting for the fact that the probability of a type I error in a multiple test differs from the error probability in a single test. However, in this connection we had to account for two issues (for details, see for example Abdi 2007). First, there are ns number of studies applying the same variable definition. This effect leads to a change in the probability of the type I error in ns trials. Second, there are the number of variable definitions nv leading to an increase in the probability of a type I error. Altogether, this results in a probability a(PF) of making as least one type I error, which depends on the probability of making a type I error a(PT), when only dealing with a specific test. Consequently, the adjusted probabilities can be expressed as follows: In case ns=nv there is no probability adjustment, because both effects equalize. In the other case (ns<nv), following Harvey et al. (2016), different studies applying the different definition lead to similar results. Hence, the probability of making a type 1 error in the first study depends on the probability in the second study. We model this dependence structure by applying a binary variable (0 = reject the null hypothesis; 1 = accept the null hypothesis). Due to the fact that we use a binary variable, the correlation coefficient can be easily calculated and comprises the complete dependence structure of the variables (in our case, a refers to a(PF)): Inverting the equation, the correlation structure can be fixed and the joint probability of making a type I error can be calculated as follows: After applying the calculation of the probability for a quasi-independent event = 1 − 1 − , the formula changes to ( ) = 1 − 1 − A look at the different studies shows a high dependency between the p-values of different studies having the same variable definition. Hence, we decided to use a high correlation Korr=0.8 in order to adjust for the correlation effect. Only those values were depicted, for which a(PT)<0.05. This table presents the results for meta-regression analysis. This approach allows the inspection of systematic variations in the effect sizes. As dependent variable, we use the z-transformed effect sizes measuring the direct influences of each proxy variable on the hedging dummy variable. As independent variables, we use explanatory variables representing study quality, observation period, regional effects, and publication bias. In this regard, the number of citations is calculated as the logarithm of [(Google Scholar citations)/(age of the study) + 1]. The number of citations was collected on January 13, 2017. The number of citations is preferred, as it considers study-specific quality characteristics and it is available for each study, including unpublished works. As a remarkable part of literature examines hedging data from US firms, we include a dummy variable that indicates whether a study uses US data (= 1 for US studies, 0 otherwise). To consider potential temporal variation due to regulatory changes or the development of financial markets, the mean observation year of a sample is integrated in the analysis. Finally, we investigate the existence of a potential publication selection bias in the reported results. As commonly included in meta-regression analysis research, our model contains the standard deviation of the effect size as explanatory variable. The estimated regression model in general terms corresponds to We estimate this model by a multilevel mixed-effects regression with country and time level effects. This estimation procedure controls for data dependencies between firm observations from the same country and the same decade. The table shows the regression coefficients, with the corresponding t-statistics are reported in brackets below. *, ** and *** indicate the rejection of the null hypotheses at the 10%, 5%, and 1% probability levels. Significant effects are highlighted in bold type.
This table compares the results of this study with the most influential studies published in journals, which are classified as A+ in the VHB-JOURQUAL3. For these studies, we integrated the reported information as considered in the multivariate meta-analysis. Hence, we refer to reported information on mean difference tests or correlation matrices. Additionally, we also contrast our findings with the results from the two existing literature reviews by Aretz and Bartram (2010) and Arnold et al. (2014). Beside the hypothesized signs, significant results at the 5% level are displayed by '+' or '-' for positive and negative relations, zero otherwise.

Figure 1: Distribution of sample observations over time and over world regions
The plot in the left column shows the distribution of the sample start year for each study included in the sample. The pie graph in the right column depicts the distribution of the countries covered by the primary studies. 'Multi' refers to studies examining more than one country.

Online Appendix. Supplementary data
Supplementary data associated with the article can be found in the Online Appendix. Search command for ScienceDirect tak(hedg* or derivative*) and (abs(use) or abs(using) or abs(usage) or abs(polic*) or abs(activit*)) and tak(compan* or corporat* or firm*) and tak(sample* or evidence or result* or data or investigat* or test* or empiric* or survey* or examine*)

SORTING OF RESULTS
Steps for sorting of results (1) Elimination by study title, (2) elimination by study's abstract, (3) elimination by screening content and (4) eliminating studies with no or negative response from the authors to our data request email.

Online Appendix B.
Overview of the studies included in the meta-analysis This table presents the results for meta-regression analysis. This approach allows the inspection of systematic variations in the effect sizes. As dependent variable, we use the z-transformed effect sizes measuring the direct influences of each proxy variable on the hedging dummy variable. As independent variables, we use explanatory variables representing study quality, observation period, regional effects, and publication bias. In this regard, the number of citations is calculated as the logarithm of [(Google Scholar citations)/(age of the study) + 1]. The number of citations was collected on January 13, 2017. The number of citations is preferred, as it considers study-specific quality characteristics and it is available for each study, including unpublished works. As a remarkable part of literature examines hedging data from US firms, we include a dummy variable that indicates whether a study uses US data (= 1 for US studies, zero otherwise). To consider potential temporal changes due to regulatory changes or the development of financial markets, the mean observation year of a sample is integrated in the analysis. Finally, we investigate the existence of a potential publication selection bias in the reported results. As commonly included in meta-regression analysis research, our model contains the standard deviation of the effect size as explanatory variable. The estimated regression model in general terms corresponds to ' )* = + , + + . ( )* + + . /01210345 ) + + . 63&1ℎ 9:;&0<2 =042&> ) + + . ?;24 >;2& )* + @ )* , @ )* ∼ 6(0; ( )* E ).
The upper part of the table shows the regression coefficients, with the corresponding t-statistics are reported in brackets below. *, ** and *** indicate the rejection of the null hypotheses at the 10%, 5%, and 1% probability levels. Significant effects are highlighted in bold type.