On the Capital Structure of Foreign Subsidiaries: Evidence from Panel Data Quantile Regression Models

1 Introduction

There is an extensive debate about the effects of corporate taxation on financial decisions. The Pecking Order Theory (POT) and the Trade-Off Theory (TOT) compete to be better predictors of a company’s financial choices. According to the Pecking Order Theory (POT), companies prefer internal financing to debt and equity. Moreover, debt is preferred to new equity issuances since it has lower associated information costs, as noted by Myers (1984, 1993) and Myers and Majluf (1984). This implies that the higher the profit, the less a firm borrows. Moreover, the POT predicts that corporate taxation has a negligible effect on firms’ capital structure. According to the Trade-Off Theory (TOT), proposed by Kraus and Litzenberger (1973), a company optimizes its debt financing (and, hence, its capital structure) by balancing the marginal costs and tax benefits of debt. In this case, business taxation matters.

In their original articles, both theories disregard the fact that many firms operate in an international context and belong to multinational groups. For this reason, over the last few decades, tax economists have focused on the capital structure of multinational companies. Starting from some pioneering articles (such as Grubert and Slemrod 1998; Hines 1999), which focused on U.S. multinational companies (MNCs), scholars have studied the allocation of debt among subsidiaries. Results show that taxation matters in this context.

Another aspect often overlooked by both the POT and TOT as well as by the studies on multinational companies’ decision-making is the heterogeneity of firms, which is frequently driven by unknown factors.

For these reasons, we aim to estimate the effects of taxation and profitability on leverage in an international environment, taking into account firm heterogeneity. In doing so, we use a new estimation approach, providing a more effective analysis of tax and profit effects on firms’ financial decisions. As will be shown, the empirical implications are considerably more complex than previously found.

In this paper, we use a sample of European foreign subsidiaries. The use of such a dataset (provided by Orbis) has at least two main advantages. Firstly, it allows us to compare our findings with those reported in the growing literature on the capital structure of multinational companies (see, e.g. Feld et al. 2013; Frank and Goyal 2024, as well as the articles cited therein). Of course, this allows us to account for both the parents’ and subsidiaries’ tax rates (provided by the Oxford University Centre for Business Taxation, https://oxfordtax.sbs.ox.ac.uk/cbt-tax-database), thereby studying an important aspect of capital structure.

Secondly, the heterogeneity of tax rates across countries is a major source of variability in the tax advantage of debt and allows us to obtain a clearer identification of its effects on capital structure. The choice to focus on European companies is dictated by the balance of two potentially contrasting needs: on the one hand, to have the necessary heterogeneity in corporate tax rates; on the other, to maintain an adequate homogeneity of the institutional and market structures within which companies operate. Our preferred dataset includes 29 countries that share many characteristics and, at the same time, have already been studied by several scholars (see, e.g. Miniaci et al. 2014).

As pointed out, most scholars have estimated the effects of taxation and profitability on companies’ capital structure by using a panel approach. As pointed out by Frank and Goyal (2024), the omission of potential heterogeneous behaviours among companies is one of the main drawbacks of the existing empirical corporate finance literature. In particular, standard linear panel data models allow scholars to estimate the average impact of profitability and taxation on capital structure, thereby ignoring the potential heterogeneity of the effects at different levels of firm indebtedness.^[1] To overcome this limitation, we therefore use a quantile regression (QR) method.

The use of conditional quantile regression (CQR) models to investigate the heterogeneity of the conditional quantile partial effects (CQPE) has become commonplace. In particular, it has led to interesting results for companies in the United States, as well as in European and developing countries (e.g. Fattouh et al. 2005, 2008; Arshanapalli and Nelson 2014; Aviral and Raveesh 2015; Chay et al. 2015; Gu et al. 2015). For instance, CQR models can show the heterogeneity of responses to tax benefits. However, such effects are conditional on the specific values of other control variables (e.g. company size) and therefore they often lack a policy interpretation. In most cases, policymakers are indeed concerned with the effects of a corporate tax rate change on the unconditional distribution of the target variable. For example, a government should be interested in analyzing the effects of a variation in tax rate on the distribution of corporate indebtedness of the entire population. In standard regression analyses (based on the conditional mean of the outcome variable), the conditional partial effect averages up to its unconditional counterpart. When quantile regression is used, this relationship does not hold in general and to recover the effects on the unconditional distribution from the CQR estimates is often impractical. For this reason, Firpo et al. (2009) suggest an alternative and manageable way to recover the unconditional quantile partial effects (UQPE) for cross-sectional data. In the case of panel data, their method must be adapted to take into account that observations from the same firm are not independent over time and that unobserved company-specific, time-persistent factors may affect the capital structure of the companies. Hence, our empirical strategy adapts Firpo et al. (2009) QR techniques for estimating the effects on the unconditional distribution of corporate leverage to the case of panel data. The use of panel data allows us to control for heterogeneity due to observable and unobservable company-specific factors. Referring to QR enables us to assess systematically whether the impact of profitability and taxation is homogeneous across different levels of indebtedness. The existence of unobserved heterogeneity, possibly correlated with some observable characteristics, makes the estimation of the parameters a non-trivial problem. We face this challenge by estimating UQPEs with fixed effects and correlated random effects models.

We show that the evidence of how the company leverage reacts to changes in taxes and profitability varies with the estimation approach (fixed vs. correlated random effects) and the quantiles of the unconditional distribution considered. In particular, the impact of profitability on leverage is always negative, with unconditional partial effects that are increasing. As regards the tax benefits arising from interest deductibility, the quantile regressions show that tax changes have quite heterogeneous effects on leverage. Indeed, subsidiary tax rates have positive partial effects on the lower quantiles of the leverage distribution, and these effects tend to vanish moving towards the right tail of the distribution. A symmetrical trend is seen when looking at the parent companies’ tax rate changes.

The structure of the article is as follows. Section 2 discusses the relevant literature on the effects of taxation and profitability on corporate capital structure. Section 3 discusses some preliminary evidence on the capital structure of our sample of European foreign-owned subsidiaries. Section 4 briefly introduces possible strategies to estimate the UQPE with panel data and shows the estimated effects of tax rates and profitability on subsidiary leverage. Section 5 provides a summary of our results and discusses some policy implications.

2 Capital Structure, Profitability and Corporate Taxation: Relevant Literature

The POT and the TOT are two major financial theories that explain how firms choose their capital structure. According to the POT (see, e.g. Myers and Majluf 1984), firms prefer internal financing (i.e. retained earnings) over external financing (debt or equity) because of information asymmetry. Indeed, managers know more about the company than investors. Moreover, POT states that new equity issues may signal that the firm might be overvalued, which can reduce stock prices. For this reason, debt is the preferred external financial source. According to the TOT, proposed by Kraus and Litzenberger (1973), firms balance the benefits and costs of debt to determine the optimal capital structure. Since interest payments are at least partially tax-deductible, debt financing reduces a firm’s tax burden. On the other hand, the higher the leverage the higher the risk of financial distress and bankruptcy. Hence, at the margin, the marginal tax benefit of interest deductibility is equal to the marginal cost of default. As a consequence, we can say that the POT does not consider taxation, whereas the TOT considers it crucial (see, e.g. Graham et al. 2013; Leland 1994). In other words, if the tax benefit of borrowing rises, the TOT predicts that, coeteris paribus, it is optimal to increase borrowing.

As pointed out, many authors (see, e.g. Myers 1993) think that the effect of profitability on company leverage is a key element in responding to the debate between the two theories. Indeed, Myers (1993) says that the inverse relationship between leverage and profitability, found in many empirical articles, is the most convincing evidence that the TOT fails to describe firms’ financial choices. In other words, the higher the profitability, the lower the default cost and the higher the leverage should be. The reaction of TOT supporters is quite heterogeneous. On the one hand, scholars like Abel (2018) respond to Myers’ criticisms by proposing dynamic models where leverage can change over time: in this case, profitability can have a negative effect on indebtedness even under the standard trade-off mechanism.^[2] On the other hand, some TOT supporters show that the sign of the leverage-profitability relationship is ambiguous as it crucially depends on the stochastic process followed by profitability. In particular, Sarkar and Zapatero (2003) show that, as long as the corporate earnings process is mean reverting, the TOT implies a negative profitability-leverage relationship. Similar findings are obtained by Agliardi et al. (2024, 2025).

As pointed out, this POT versus TOT debate mainly focuses on representative firms and therefore skips two important aspects, such as firms’ heterogeneity and their behaviour in an international setting. For this reason, tax economists have mainly looked at the capital structure from a slightly different perspective, i.e. by focusing on the financial decisions of multinational companies (MNCs). In particular, tax scholars have been studying the ability of MNCs to shift debt from high to low-tax jurisdictions, an aspect that is not considered by the POT.^[3] Feld et al. (2013) noted that Desai et al. (2004) were among the pioneers in examining the balance sheet data of foreign subsidiaries of U.S. multinational corporations (MNCs). The study of non-U.S. MNCs later started due to advancements in firm-level datasets. One of the main aims of this literature was to study debt shifting, i.e. the use of debt to reduce MNCs’ tax burden. This approach typically looks at the differential between the subsidiary’s and the parent company’s tax rate (τ _S and τ _p , respectively) as the main determinant of debt shifting within a multinational group: scholars expect that τ _s stimulates the subsidiary’s leverage and that the opposite is true when τ _p rises.^[4]

Subsequently, studies were mainly on Europe. For instance, Overesch and Wamser (2010) studied the effects of parent companies’ tax rates on their own capital structure. Moreover, using the effective cross-border tax rates, Huizinga et al. (2008) estimated a negative impact of parent company taxation on subsidiaries’ leverage. As shown by Miniaci et al. (2014), however, the effects of a change in the parent company tax rate are much more complex because taxes affect both the MNC’s borrowing decisions and the distribution of debt among its entities. It is worth noting that, as shown by Harju and Matikka (2016) in the case of Finland, not only large companies but also small and medium-sized enterprises (SMEs) are sensitive to tax incentives when it comes to deciding where to shift profits and debts. The meta-analysis of the empirical literature on corporate capital structure by Feld et al. (2013) highlighted the complexity of tax effects at a multinational level and supported the idea that the international tax system does affect the financing decisions of multinational firms.^[5]

As pointed out, most empirical works use panel datasets with a large number of companies and a short time period. Typically, they use linear models and they rarely pay attention to the fact that the effects of changes in tax rates and/or profitability on the debt ratios may differ at different levels of indebtedness. There are some relevant exceptions, such as Lemmon et al. (2008) and Baker and Wurgler (2002), that stress the persistence of leverage: this highlights the relevance of time-invariant components, and therefore the need to fully account for the panel structure of data, which is typically omitted by most of the existing articles using a quantile approach. Regarding the tax literature, Fattouh et al. (2008) also apply CQR methods to study the choice of leverage ratio made by UK-listed companies. They find that the estimated effect of explanatory variables differs at different quantiles of the distribution with the sign of some of the estimated effects that vary across quantiles. Gu et al. (2015) adopt a QR approach as a robustness check in their study of taxation in international banking, without fully addressing the longitudinal nature of the data.

Like standard linear regression models, the consistency of the estimated parameters, and hence the reliability of the policy prescriptions, crucially depends on the likelihood of the assumption made about the existing relationship between the observable and non-observable heterogeneity of the companies. In principle, the existence of such unobserved components can invalidate results, and therefore, should be accounted for. Nevertheless, scholars often ignore this issue (e.g. Chay et al. 2015). To our knowledge, the only exception is Ferrarini et al. (2017), who studies Chinese listed companies’ leverage, using the fixed effect conditional quantile regression (as suggested by Powell 2022).

Note that all these papers use conditional QR models. This may undermine the policy implications of the estimated results. Holland et al. (2024) use unconditional QR models to study the cross-border investments of a panel of firms. However, they do not consider the role played by the unobserved time-invariant heterogeneity of the companies. In our paper, instead, we contribute to the literature by applying the unconditional quantile regression models to the case of panel data with fixed or correlated random effects. We will show that the policy implications depart from those consolidated in the literature. In particular, only a portion of companies is affected by taxation and the effect of profitability crucially depends on firms’ starting leverage ratio. This result can help policymakers to implement more effective policies.

3 Data and Descriptive Evidence

As argued, we focus on the effects of both profitability and taxation on the capital structure of foreign-owned companies. With respect to other companies, the tax incentives for foreign-owned subsidiaries vary both over time and cross-nationally, depending on the fiscal residence of their owners. Data on financial statements are collected from Orbis (by Bureau van Dijk), which provides standardized annual balance sheets and profit & loss items for millions of companies around the world as well as information on their legal form and ownership structure. We selected companies satisfying at least one of the following criteria: (i) more than 15 employees; (ii) operating revenue of at least 1 million euros; (iii) total assets of at least 2 million euros. This approach excludes subsidiaries that are considered microenterprises according to EU regulation, focusing on small, medium and large enterprises. We focused on European limited companies and limited liability companies whose ultimate owner in August 2018 was a company resident abroad in a known country and was neither an individual nor a family. We excluded all the companies operating in the financial and insurance services (NACE code K), in public administration and defence (NACE code O), and the activities of households as employers (NACE code T) and of extraterritorial organisations (code U).

We define the ultimate owner as the company, which (directly or indirectly) holds at least 50 % of a subsidiary’s shares. We set a high share of ownership because a parent company with a lower level of (direct or indirect) ownership may be unable to fully determine a subsidiary’s capital structure. After excluding observations with unrealistic account data and few outliers (top and bottom 0.05 % of the relevant ratios), we obtained a sample of 70,160 subsidiaries controlled by foreign companies, with all the necessary unconsolidated accounts data covering the years from 2009 to 2017 (average number of years = 5.8, see Table 1).

Company data were matched with information on statutory tax rates and Effective Marginal Tax Rates (EMTRs) provided by the Oxford University Centre for Business Taxation.

Table 1 shows the average subsidiary statutory tax rate τ _s and the average parent statutory tax rate τ _p by subsidiary country. For instance, we see the 1,158 Austrian subsidiaries in our sample face an average statutory tax rate of 25 %, while the average statutory tax rate of their foreign ultimate owners is 21.96 %. On average, the differential between subsidiary and parent company tax rates is −1.3 % (i.e. 23.86 %–25.16 %, see the last row). When we use the EMTRs, the number of subsidiaries in the sample reduces, because of missing data about Bosnia and Herzegovina and Serbia (see Table 1). With the EMTR, the tax rate differential is about −2.8 %. Moreover, for 41.2 % (37.2 %) of subsidiaries, the statutory (effective marginal) tax rate is higher than their ultimate owner’s tax rate: this could suggest that parent companies strategically locate their subsidiaries in low-tax countries (see, e.g. Devereux and Maffini 2007, and the references in Herger and Kotsogiannis 2016). Furthermore, comparing statutory tax rates and EMTRs reveals that the former ones are higher, mainly because the latter may be reduced by the tax advantage of interest deductibility.

Table 2 shows the distribution of subsidiaries in each host country according to the home country of their parent companies, based on the full sample of companies. This gives a clear picture of the weight of each home (parent) – host (subsidiary) country tax differential. For example, more than 1/3 of Austrian foreign-owned subsidiaries are held by German companies. Moreover, we can see that: (i) about 1/5 of the subsidiaries are owned by a global US ultimate owner; (ii) about 28 % are owned by either a German, British or French company. Hence, the within-Europe and the US-European tax differentials are by far the most relevant. Hence, they will play a major role in our regression analysis.

Table 3 shows the median values of the main balance sheet items and ratios, conditional on the residence country. The empirical literature uses book data rather than mark-to-market values. We also follow this approach due to the characteristics of the dataset. Book and mark-to-market values are likely to be close only for listed companies, due to the application of international accounting principles (IAS/IFRS). As regards non-listed companies (the large majority of the companies in the sample) however, accounting principles allow us to calculate historical rather than fair values. In this case, the book value of one item may differ from its fair value.

According to most research (e.g. Desai et al. 2008), we define leverage as the ratio between debt (long- and short-term liabilities) and total assets. Among the financial ratios, we consider those suggested by Frank and Goyal (2009) and Fan et al. (2012) as the main determinants of leverage, together with the factors of financial distress identified by Altman (2000).^[6] This implies that we use the following control variables: the turnover (as a proxy for the firm size); the Return On Assets (ROA); the fixed/total assets ratio; the working capital/total assets ratio; the variation of shareholder funds over total assets; a dummy variable to identify those firms with negative Earnings Before Interests and Taxes (EBIT) in the previous year and the per capita GDP growth rate. Like most empirical works, we define ROA as the EBIT/Total assets ratio.^[7]

Since our sample typically consists of many small to medium size companies and a few large ones, we use median values to summarize the characteristics of our sample. The median value of operating revenues is quite homogeneous across countries: it ranges from 8 to 11 million euros. Table 3 also shows the heterogeneity of the average national PPP per capita GDP growth rates of the European countries during the sample period:^[8] it ranges from −0.7 % for Greek firms to +5.5 % for Estonian enterprises. Furthermore, the ROA shows high variability: it ranges from a median of 3 % for Greece to 8.3 % for Norway. Moreover, the overall median ROA is positive (5.7 %), although, on average, about 23 % of subsidiaries made losses in the previous year.

4 Regression Analysis

Conditional Quantile Regression (CQR) was first proposed by Koenker and Bassett Jr. (1978) as an alternative to the mean regression methods. This approach is particularly useful when the independent variables have potentially varying effects at different points of the conditional distribution of the response variable. Hence, QR models are applied whenever the object of interest is the entire conditional distribution of the outcome variable: in medicine (i.e. to study extremely low infant birthweight, e.g. Abrevaya and Dahl 2008); in finance (to estimate the Value-at-Risk, e.g. Engle and Manganelli 2004); in labour economics (e.g. Firpo et al. 2009); and in corporate finance (e.g. Fattouh et al. 2008).

As in the standard conditional mean regression framework, when panel data is available, QR models must face the problem of unobserved time-invariant heterogeneity (see Galvão and Kato 2018 for a review of QR methods for panel data). Given the outcome variable Y _it for unit i at time t, and the conditioning exogenous variables X i = X i 1 , X i 2 , … , X i T , the CQR approach specifies and estimates the relationship between the observed values of the conditional variables, x _i , and the quantile τ of the outcome Y _it , that is Q τ Y i t | x i .^[9] This allows the investigators to identify and estimate what Firpo et al. (2009) call Conditional Quantile Partial Effects, which under the assumption of linearity of Q τ Y i t | x i is:

While the marginal expected value is linked to the conditional expected value by the law of iterated expected values, in the case of quantiles, this link is missing: the quantile τ of the unconditional distribution of the outcome variable, Q τ Y i t , is not the average of the conditional quantiles τ, Q τ Y i t | x i . Consequently, the effect of a marginal change of a control variable on Q τ Y i t , which Firpo et al. (2009) call Unconditional Quantile Partial Effect, UQPE _τ , cannot be easily recovered from the C Q P E τ x i . From a policy perspective, UQPE _τ is often the main object of interest (for a discussion see, e.g. Borah and Basu 2013, and, for the case of a binary policy variable, Borgen et al. 2023). Some authors suggested how to recover the UQPE _τ from the CQR models, but these procedures require quite cumbersome computations (e.g. Machado and Mata 2005).

For cross-sectional data, Firpo et al. (2009) suggest how to approximate the UQPE _τ . This article bases estimation procedures on the concept of the re-centred influence function (RIF). The influence function I F Y ; v F Y of a distributional statistic ν(F _Y ) accounts for the influence of individual observations on that distributional statistic. If the statistic of interest is the τ-th quantile, q _τ , the influence function is:

Its re-centred version is defined as R I F Y i , q τ = q τ + I F Y i , q τ . The expectation of R I F Y i , q τ conditional on X _i defines the RIF regression model:

As E m τ X i = q τ , the RIF regression model can be interpreted as a form of unconditional QR model, and the UQPE _τ can be estimated as changes of m τ x i . If m τ x i = x i ′ β τ , model (3) is linear and UQPE _τ  =  β _τ . Firpo et al. (2009) also propose a two-stage estimation procedure for β _τ . In the first stage, q _τ is estimated using the sample analog of the unconditional τ-th quantile and f Y q τ using kernel methods. In the second stage, OLS are used in the regression of the estimated

on the observed covariates x i .^[10]

In the case of panel data, and similarly to the case of the standard conditional mean regression models, the QR models need to take into consideration the presence of unobserved firm-specific time-invariant factors which, if omitted, can cause the inconsistency of the estimates of the parameters of interest, β _τ . In the Firpo et al. (2009) context, one possibility is to assume that α _i enters m τ x i additively, that is m τ α i τ , x i = α i τ + x i t ′ β τ . As α _iτ is unobservable, at the second stage regression α _iτ can be considered as part of the error term. For OLS to provide consistent estimates of β _τ , α _iτ must be uncorrelated with X _i . This assumption is often difficult to make. For example, in our case, it would mean assuming that the unobservable characteristics that determine the firm’s capital structure (α _iτ ) are uncorrelated with the size of the firm (one of the variables in X _i ).

A possible approach to tackle the problem is to admit that α _iτ and X _i can be correlated and that E α i τ | x i = x ̄ i ′ φ τ . In this correlated random effect framework, similar to Abrevaya and Dahl (2008), the UQPE _τ can be estimated via an enriched RIF regression model:

It is possible to abandon the parametric assumption E α i τ | x i = x ̄ i ′ φ τ (or similar ones) considering α _iτ as a unit-specific fixed effect to be included in the RIF regression model:

Under strict exogeneity conditions of X _i with respect to any random component, β _τ can estimated using a standard linear within-group estimator (e.g. Borgen 2016).

The two modelling approaches differ for the conditional expected values considered, with E R I F Y i t , q τ | x i = E α R I F Y i t , q τ | x i , α i τ . Therefore, the vectors β _τ in the two equations coincide only if the assumption E α i τ | x i = x ̄ i ′ φ τ holds. For the policy maker, E R I F Y i t , q τ | x i should be the main object of interest, because α _iτ is unobservable. We therefore estimate the UQPE at different quantiles using the correlated random effects approach (equation (5)) and use the fixed effects estimates (equation (6)) as a robustness check.

Our dependent variable Y _it is equal to the logarithm of the leverage ratio of company i at time t. The set of covariates includes those considered in Table 3. We have used lagged financial statements, because we assume that the leverage at time t is chosen at least one year in advance, given the information available at time t − 1. Among our control variables, we include current tax rates. The reason is straightforward: while tax rates are usually known at the beginning of year t, the value of leverage is calculated at the end of year t. This implicitly implies a lag. In our regressions, we use both statutory tax rates and Effective Marginal Tax Rates (EMTRs). The former are a straightforward measure of taxation and are widely used in studies of corporate capital structure. Similarly, EMTRs – which incorporate not only tax rates but also some characteristics of the tax base (such as partial deductibility, if applicable) – are also widely used in capital structure analyses. Like many other studies, we do not consider Effective Average Tax Rates (EATRs), since they typically affect investment or location decisions.

Furthermore, we include a set of time dummy variables, to control for common business cycle; dummies for the subsidiary and the parent countries; the subsidiary industry; the incorporation period;^[11] the fact that the subsidiary is a public limited company (rather than a private limited one) and the size of the industrial group the subsidiary belongs to (based on the number of subsidiaries controlled by the same parent company).^[12] Note that, in the fixed effects models, all the possible time-invariant characteristics are implicitly taken into consideration.

Figure 1 shows the distribution of leverage for our sample companies. As can be seen, most of them show a leverage ratio below 100 %. However, a non-negligible number of operating businesses show a leverage ratio that is higher than 100 %: this means that the value of equity is negative. In this case, the companies likely show a negative value of net worth, due to their Generally Accepted Accounting Principles, which does not cause default. The median company leverage is 62.5 %.

Figure 1:

The distribution of firms’ leverage.

To present the results, we plot the estimated UQPE _τ for the main regressors, together with their 95 % confidence intervals, for the 10th, …, 90th quantiles. For the sake of brevity, the numerical results for all the covariates are shown in Tables A3–A6 in the Appendix. We estimate the equations first using the EMTRs and then using the statutory tax rates. We compute the confidence intervals by cluster bootstrapping, with clusters defined by the subsidiary-parent country pairs.

With the UQPE _τ , we focus on the marginal (unconditional) distribution of the log-leverage and describe, for example, how the quantile Q τ Y i t changes if every subsidiary company has a 1 percentage point increase in the tax rate, thus providing a clear indication to the policy makers on how the entire distribution of the leverage responds to changes in fiscal policy. Before showing the estimation of the UQPE _τ , we consider the evidence from standard linear regression models based on panel data. The first row of Table A1 in the Appendix shows that the within-group fixed effects estimate of the parameter of the subsidiary EMTR is 0.0819 (std. err. 0.0403), whereas that of its parent company EMTR is −0.0453 (std. err. 0.0565). That is, on average, a 1 percentage point increase of the subsidiary EMTR is associated with a 0.08 % increase in its leverage. However, a change in the parent-company EMTR does not seem to affect the subsidiary leverage. For the ROA, the estimated value −0.1545 (std. err. 0.0134) is consistent with the prediction of the static POT. The second row of Table A1 shows the results of a linear correlated random effects model. As can be seen, the estimated parameters of the subsidiary EMTR and the ROA are larger (0.1204 with std. err. 0.0408 and −0.3302 with std. err. 0.0219, respectively), whereas that of the parent EMTR is still not significantly different from zero (−0.0867, std. err. 0.0688). When the statutory tax rates are used (Table A2), nothing relevant changes for the ROA. However, the estimated tax rate parameters change their magnitude: that of the subsidiary tax rate is about 0.4 both with the fixed effects and the correlated random effects models; that of the parent tax rate ranges between −0.3675 (std. err. 0.1388) for the fixed effects and −0.2842 (std. err. 0.138) for the correlated random effects.

The remaining rows of Tables A1 and A2 show the estimates of the same parameters of interest using standard cross-sectional CQR, without fully addressing the longitudinal nature of the data, as most of the existing empirical literature does. The estimates convey two main messages: tax changes affect mostly the lower quantiles of the conditional distribution, and a greater value of the ROA reduces all the conditional quantiles, but with different intensities. These results show that relying on linear models can lead to omitting relevant heterogeneities of the associations between, on one side, the tax and profitability variables and, on the other side, the leverage ratio. Moreover, the sign of the estimated partial effects on the conditional quantiles can differ from that on the mean. For instance, a change in the fixed assets/total assets ratio is associated with an increase in the mean of the leverage according to the estimated linear models, whereas it is associated with a reduction for all the considered deciles. We will show that the contradiction between these two pieces of evidence will vanish by using appropriate estimation methods for panel data QR models.

Figure 2 shows the UQPE _τ for the main covariates when the panel structure of the data is accounted using a correlated random effects approach (see equation (5), see Table A3 for the numerical values). The impact of the subsidiary’s tax rate is always estimated to be positive. An increase of 1 percentage point in the subsidiary’s EMTR is associated with an increase of about 0.2 % (std. err. 0.0596) of the 10th percentile of the unconditional distribution of the leverage. However, the estimated partial effects decrease moving towards higher quantiles reducing to a mere 0.03 % (std. err. 0.0185) for the 90th percentile. The parent company’s EMTR has either a negative or null impact on the leverage: the partial effect is about −0.3 for the lowest decile and it increases to zero by the 3rd decile, with confidence intervals that are wide and always include the zero.

Figure 2:

Unconditional quantile partial effects, correlated random effects model, tax rates: effective marginal tax rates. The specification includes also dummies for time; subsidiary and parent countries; industry; incorporation period; public limited companies and size of the industrial group the subsidiary belongs to, together with the firm-specific means of the time-varying variables. The dotted lines delimit the 95 % confidence bands. Standard errors are clustered, with clusters defined by the subsidiary-parent country pairs and computed by cluster bootstrapping.

This heterogeneous impact of the parent company’s EMTR may be due to a twofold effect: first, at lower quantiles of leverage, tax devices, such as thin-cap and earning-stripping rules, are less relevant as firms can deduct more interest expenses. Hence, the tax incentive to borrow is stronger. At higher quantiles of leverage, however, the same devices limit the deductibility of interest expenses and hence a tax rate change has a lower or negligible impact; second, the choice among alternative forms of financing, and therefore the capital structure, is less flexible at higher quantiles of leverage. In this case, credit constraints may arise and prevent companies from modifying the leverage ratio following a change in the tax incentives. Finally, while subsidiaries’ EMTRs have a positive impact on the distribution of leverage – except at the 90th decile – this effect is negative and statistically significant for parent companies EMTR only on the left-hand side of the distribution. This suggests that there is room for debt shifting only among the least-leveraged subsidiaries: in such cases, the tax-rate differential affects debt strategies within the group.

For ROA, the UQPE _τ is always negative and increases from −0.3379 (std. err. 0.099) for the first decile to −0.1632 (std. err. 0.0109) for the 90th percentile. That is, a generalised 1 percentage point increase in ROA is associated with about 0.34 % decrease in the first decile of the leverage distribution and a reduction of 0.16 % of the ninth decile: coeteris paribus, a generalised increase in profitability shifts the entire marginal distribution of leverage to the left. The estimated UQPE _τ supports the POT.

Past negative EBIT has the effect of widening the gap between the left and right tails of the leverage distribution, keeping the former firm and shifting the latter upwards. Similarly, an increase in the variation of shareholder funds reduces lower levels of leverage relatively more than higher levels. The opposite happens for an increase in the fixed assets/total assets ratio and the company size (proxied by the turnover). In these cases, the highest level of leverage does not significantly change, whereas the lower levels increase, with the consequence that the overall distribution of leverage is compressed towards higher values. Vice versa, an increase in the working capital/total assets ratio and the GDP growth rate compress the marginal distribution of the leverage towards lower values. All these results are consistent with the partial effects estimated on the mean (see Table A1) and inform on what originates such average effects, providing useful insights to the policymaker.

Figure 3 (see Table A4) shows the estimated UQPE _τ for the same specification but using the fixed effects estimation approach. Although the levels may differ for some of the variables, the patterns of the UQPE _τ are qualitatively similar to those obtained with the correlated random effects estimation, with the latter tending to be more precise. In this case, the working capital-to-assets ratio has a positive impact on the lower deciles and a negative one on the upper ones, with the combined outcome to compress the leverage distribution. Overall, we can say that the fixed effects estimates confirm the main indications of the correlated random effects estimates.

Figure 3:

Unconditional quantile partial effects, fixed effects model, tax rates: effective marginal tax rates. The specification includes also dummies for time; subsidiary and parent countries; industry; incorporation period; public limited companies and size of the industrial group the subsidiary belongs to. The dotted lines delimit the 95 % confidence bands. Standard errors are clustered, with clusters defined by the subsidiary-parent country pairs and computed by cluster bootstrapping.

Finally, we estimate the UQPE _τ using the statutory tax rates rather than the EMTRs (Figures 4 and 5, Tables A5 and A6). The magnitude of the statutory tax rates’ semi-elasticity is much higher than that estimated with the EMTRs. Moreover, the shapes and levels of the curves are similar to those obtained with the EMTRs, except for the tax rates. The estimated UQPE _τ for the statutory tax rates is more precise, and the size of the effects is larger than that of the EMTRs: for instance, according to the correlated random effects estimates, an increase of 1 percentage point in the statutory tax rate of the subsidiary increases the 10th unconditional percentile by about 0.94 % (std. err. 0.2475), whereas a 1 percentage point reduction in the statutory tax rate of the parent company is associated with an increase of 1.31 % (std. err. 0.2885). Looking at the statutory tax rates, it is more likely to find cases in which there is room for debt shifting. This is due to the fact that, in most cases, parent companies’ statutory tax rates show a negative and statistically significant effect. The converse is true for parent companies’ EMTRs: only in some cases is their estimated semi-elasticity statistically significant. To sum up, simpler tax measures appear to have a stronger effect.

Figure 4:

Unconditional quantile partial effects, correlated random effects model, tax rates: statutory tax rates. The specification includes also dummies for time; subsidiary and parent countries; industry; incorporation period; public limited companies and size of the industrial group the subsidiary belongs to, together with the firm-specific means of the time-varying variables. The dotted lines delimit the 95 % confidence bands. Standard errors are clustered, with clusters defined by the subsidiary-parent country pairs and computed by cluster bootstrapping.

Figure 5:

Unconditional quantile partial effects, fixed effects model, tax rates: effective marginal tax rates. The specification includes also dummies for time; subsidiary and parent countries; industry; incorporation period; public limited companies and size of the industrial group the subsidiary belongs to. The dotted lines delimit the 95 % confidence bands. Standard errors are clustered, with clusters defined by the subsidiary-parent country pairs and computed by cluster bootstrapping.

5 Conclusions

This article has applied panel data quantile regression analysis to examine the determinants of the capital structure of European foreign-owned subsidiaries. It has compared the unconditional quantile partial effects estimated using both the correlated random effects and the fixed effects estimation approaches. The analysis has shown that business taxation affects a subsidiary’s capital structure in a heterogeneous manner. In particular, tax changes mainly impact the lower quantiles of the distribution, leaving the higher levels of leverage unaffected. The results are also in line with the static version of the POT as they show that a higher ROA reduces leverage at all the quantiles of the marginal distribution, although with varying intensity.

Thus, if policymakers aim to understand how a generalized increase in subsidiary tax rates influences the overall leverage distribution, they must recognize that tax changes affect the lower quantiles much more than the higher ones. In other terms, an increase in tax rates shifts the leverage distribution toward higher values and makes it more concentrated. The opposite holds true for a tax rate cut. This heterogeneity may stem from companies with higher leverage levels facing borrowing constraints, which limit their ability to fully exploit the tax benefits of further debt financing.

A similar effect occurs with a generalized decrease in parent company tax rates. Lower taxation at the parent level increases the lower quantiles of subsidiary leverage, and vice versa. To fully evaluate the implications of their policies, policymakers should carefully consider the characteristics of companies operating within their jurisdiction. Furthermore, they should acknowledge that any tax measure influencing ROA negatively impacts leverage, although the magnitude of this effect varies across the distribution of firms’ leverage.

There are several ways to improve our analysis. For example, we could leverage the worldwide coverage of databases like Orbis to consider also non-European firms and benefit of the International Tax Institutions dataset (ITI, https://www.rsit-uni-tuebingen.de/data/) to update the analysis. Furthermore, the use of dynamic quantile regression models could better capture the stickiness of the capital structure adjustment process of firms. Finally, we have only considered the identity of the global ultimate owner in 2018. Further insights can be gained by taking into account ownership changes that occur over time.