Dividend payout ratio follows a Tweedie distribution: international evidence

Dividend policy is still a largely discussed issue in corporate finance literature. One of the main indicators used in analysing the dividend policy is the dividend payout ratio. Using a database consisting of 12,085 companies operating in 73 countries, for the period 2008– 2014, the authors found that the dividend payout ratio follows a Tweedie distribution, and not a normal one. This distribution is stable over time for the entire analysed period. In addition, it describes the case of almost all the countries included in the sample. Thus, a better estimation of the probability that dividend payout ratio is lower or higher than a benchmark can be provided. Also, an analysis of dividend policy, distinctly considering payer versus non-payer companies, can offer additional important information for both practitioners and academics. JEL G35 C01 C51 C55


Introduction
Figure 1: Dividend payout ratio for the companies included in the sample, in the period 2008-2014. All companies' financials were collected from the Thomson Research Worldscope database. DPR is computed as: .
be fitted at best by a Tweedie distribution (Tweedie 1984). Moreover, this distribution is stable in time for the entire analysed period. In addition, it describes the case of almost all the countries included in the sample and the most part of the years (some more detailed statistics are provided in Appendix 1). As far as we know, finding the distribution for DPR is a new contribution for financial literature. The distribution depicted in Figure 1 suggests that dividend policy is mainly an issue of "to be or not to be" a dividend payer, some authors suggesting the decrease in dividend payments in time (Fama and French 2001, Fatemi and Bildik 2012, Kuo et al. 2013, which can be modelled through the propensity to pay dividends (Fama and French 2001, Denis and Osobov 2008, von Eije and Megginson 2008, Fatemi and Bildik 2012, Kuo et al. 2013, Banyi and Kahle 2014, Floyd et al. 2015, Jiang et al. 2017. As practical implication, a proper analysis of DPR should consider both components of the distribution -the 0 inflated component and the distribution for DPR > 0. However, as Figure 1 suggests, this is not a 0% / 100% dividend payout ratio policy! An analysis concerned only about the decision to pay or not to pay dividend can miss some important information. The most appropriate distribution for modelling DPR is not the normal (Gaussian) one, but the less used Tweedie distribution, proposed by Maurice Tweedie (1984). Using a better fit for the distribution, a better estimation of the probability that the event to occur (e.g., DPR to be lower or higher than a benchmark) can be provided. This result can be useful for instance in the context of international portfolio management, especially if the investments are made in a large number of companies (with minority participations), and when forecasting of the future collected dividends is of interest.
One important contribution, comparative to previous research, is the large number of countries considered (73). For instance, the database used by La Porta et al. (2000) includes 33 countries, the one of Ferris et al. (2009) 25, etc. Our sample is geographically diverse, including countries from Africa, North and South Americas, Asia, Australia, and Europe. From here, a large diversity regarding the cultural values, but also legal systems (our sample includes common law, but also civil law countries) can be noticed.
The remainder of our paper is structured as follows. Some related studies are discussed in Section 2. Section 3 presents the methodology. Section 4 describes the data. Section 5 presents and examines the results. In Section 6, we conclude.

2
Theoretical background. Modelling dividend policy through dividend payout ratio Different indicators are used for modelling dividend policy, in various contexts (see Table 1).
Of course, each of these indicators expresses something else, but all of them can be used in analysing dividend policy. Two indicators are extensively used in studies on dividend policy, respectively dividend payout ratio (DPR) and the propensity to pay dividends (hereafter, PPD). They are somehow related, in the sense that PPD can be modelled as a particular case of DPR. Thus, PPD can be defined as: PPD = DPR if DPR = 0, and PPD = 1 if DPR > 0. DPR is defined as the ratio between net dividend paid to shareholders and net earnings (for instance, DPR in the year t, as a ratio between dividend per share and earnings per share, both recorded in the year t) and calculated only if the company records profit, and not loss (La Porta et al. 2000, Fidrmuc andJacob 2010). Dividend is considered usually as total cash dividend paid to common and preferred shareholders (La Porta et al. 2000, Fidrmuc andJacob 2010). 3 DPR can be considered as explaining the interest of the shareholders for receiving dividends (or, in some cases, the interest of managers to protect the shareholders' interests). Share repurchases can be considered as an alternative to dividend payments (La Porta et al. 2000, von Eije and Megginson 2008, Fidrmuc and Jacob 2010, Banyi and Kahle 2014, Baker and Weigand 2015, and some studies correct DPR for accounting for this type of shareholders' remuneration (e.g., Renneboog and Trojanowski 2007, Floyd et al 2015, Ye et al. 2019. However, share repurchases imply the termination of the role as shareholder for the receiver of the payment, and this is why it should be analyzed independently by dividend payments. Undoubtedly, as most of the financial indicators, DPR has certain limits. Net earnings depend on the countries' accounting conventions and are not always comparable from one country to another, being also easily manipulated by "accounting tricks". Also, "diversion of _________________________ 3 In some cases, supplementary adjustments are made. For instance, "Earnings are measured after taxes and interest but before extraordinary items" (e.g., La Porta et al. 2000, Faccio et al. 2001 Lintner (1956), Holder et al. (1998), La Porta et al. (2000, Faccio et al. (2001), Aivazian et al. (2003), Renneboog and Trojanowski (2007), Fidrmuc and Jacob (2010), Fatemi and Bildik (2012), Floyd et al. (2015), He et al. (2017), Jiang et al. (2017), Chen et al. (2017), Yaseen and Dragotă (2019), Ye et al. (2019), Yaseen (2019) Propensity to pay dividends (dummy variable, reflecting the quality of dividend payer / non-payer) Fama and French (2001), Denis andOsobov (2008), von Eije andMegginson (2008), Bena and Hanousek (2008), Ferris et al. (2009), Fatemi andBildik (2012), Kuo et al. (2013), Banyi and Kahle (2014) Dividend payments (total amount paid as dividend) Lintner (1956), Renneboog and Trojanowski (2007) resources may occur before earnings are reported" (in this case, dividend payout ratio "overestimates the share of true earnings that is paid as dividends" (La Porta et al. 2000). 4 It can be stated that DPR is also a classical, traditional indicator. It expresses the share of profit paid to shareholders. In this vision, profit is somehow considered having "a cash flow essence". As signalling theory notices (Bhattacharya 1979, Kalay 1980, in practice, one company can record profits, but having not enough cash for paying dividends. Also, if one company pays dividends from previous years earnings (from reserves), DPR can be higher than 100%. This nonsynchronicity between dividends (an amount paid from the cash existent in one financial exercise) and net earnings (the result in previous year) can complicate also the financial interpretation of DPR.
_________________________ 4 These problems are solved somehow using dividend-to-sales or dividend-to-cash flow ratios (La Porta et al. 2000, Faccio et al. 2001, Fidrmuc and Jacob 2010. However, these indicators do not reflect a portion from net earnings paid as dividend, dividends being defined as a part of the earnings distributed to shareholders. DPR does not reflect a return (like dividend yield); it is a share of profit paid to shareholders. If dividends and retained earnings are considered as expressing opposite interests (see the literature regarding minority shareholders' protection, e.g., La Porta et al. 2000), DPR would reflect a higher interest for one issue or another or, maybe, a power in negotiation. However, the interpretation of the indicator should be made cautiously. If one company records 100 monetary units (m.u.) as earnings and pays 50 m.u. as dividends, it records only a 50% DPR, comparatively with another, which pays 100% as dividends from its 1 m.u. earnings. Looking only to DPR, the second one seems to be more oriented to shareholders; however, it does not mean that its shareholders would be more satisfied.
DPR is used as dependent variable in regressions (La Porta et al. 2000, Fidrmuc and Jacob 2010, Jiang et al 2017. Different factors are considered as determinants of DPR, some of them -financial (e.g., size, return of assets, leverage, sales growth, in Based on empirical evidences, different papers found that the presence of non-paying dividends companies is significant (Fama and French 2001, von Eije and Megginson 2008, Fatemi and Bildik 2012, Kuo et al. 2013. Maybe for this reason, many papers prefer to analyse the propensity to pay dividends and its determinants, along with dividend payout ratio or not (e.g., Denis and Osobov 2008, von Eije and Megginson 2008, Fatemi and Bildik 2012, Kuo et al. 2013, Banyi and Kahle 2014, Jiang et al. 2017, Ye et al. 2019) (see also Table 1). Even PPD is a less sensitive indicator, it has the same purpose as DPR in reflecting the company's interest for paying dividends for shareholders.
One missing link between considering averages DPR and propensity to pay dividends in modelling dividend policy can be somehow intuited. On the one hand, the use of the average DPR can be misleading, as long as DPR is 0% in many cases. An average DPR should be interpreted cautiously; it is as if you would say that in average you feel all right if one part of you is kept in frozen water and the other one in boiling water. On the other hand, neglecting the distribution of DPR in the absence of DPR = 0 (considering 1% DPR to be as such important as a 100% DPR) can determine missing some information.
For all these reasons, finding if probability distribution of DPR can be modelled can provide a useful result for both academics and practitioners. Finding the probability distribution for one variable is studied in literature (e.g., Clauset et al. 2009). In general, in is accepted that the selection procedure is following some subsequent steps, respectively (Clauset et al. 2009): (1) choose a suitable theoretical model; (2) estimate the model parameters; (3) determine the significance level and use a goodness-of-fit test in order to determine the most appropriate theoretical distribution. As far as we know, finding the distribution for DPR is a new contribution for financial literature. _________________________

Methodology
Our methodology is focused on finding the most appropriate distribution for DPR. In order to fit the probability distribution for DPR, we follow the methodology recommended by Clauset et al. (2009), and we applied it for the analysed variable. Thus, the fitting problem can be split in three main tasks (Clauset et al. 2009). First, we have chosen a suitable theoretical model. Descriptive statistics like histogram and skewness are useful in this step. Based on the shape of the empirical distribution, we have decided to estimate a range of theoretical distribution that may fit the data: Tweedie, Scaled Tweedie, Lognormal, Burr, Weibull, Inverse Gaussian, Exponential, Generalized Pareto Distribution, Pareto and Gamma distribution. The Tweedie distribution, as a model for zero-inflated data (see Gilchrist and Drinkwater, 1999), has been previously used in other areas, such as healthcare data (Kurz 2017), modelling insurance claims (Renshaw 1994;Jørgensen et al. 1994), etc.
Secondly, we have estimated the model parameters. In order to estimate the parameters of the theoretical distributions, the Maximum Likelihood method was used.
Finally, we have determined the significance level and we have used a goodness-of-fit test in order to determine the most appropriate theoretical distribution. For finding the most appropriate distribution for the data, we have used the Anderson-Darling test (Anderson and Darling 1954). This is one alternative used to test and to find the distribution of experimental data that follows a theoretical distribution. The conclusion of the Anderson-Darling test is usually drawn by comparing the obtained statistics with the available critical value. This test is one of the most frequent tests used to find the best distribution for the data, generally called "goodness-of-fit tests" (Pearson 1895, Anderson and Darling 1954, Stephens 1974, Jäntschi and Bolboacă 2018. This methodology has the advantage of allowing a more sensitive test (Scholz and Stephens 1987). By minimizing the statistics obtained from the Anderson Darling test, we have chosen the most appropriate distribution for our data.

Data
All companies' financials were collected from the Thomson Research Worldscope database. 6 We have included in our database only those countries with minimum 10 companies available for the entire period (for this reason, we have excluded from the initial database some countries). In addition, we have not considered the financial institutions because of the difference in the accounting standards for financial reporting, as La Porta et al. (2000), Fidrmuc and Jacob (2010) Porta et al. 2000, Fidrmuc andJacob 2010). The inclusion of this kind of data is incoherent with the financial logic of the indicator -dividend payout ratio is defined as a share of profit paid to shareholders. Another criterion for the imported data from Thomson Research Worldscope was that dividend DPR ≥ 0 (to eliminate possible negative dividend payout ratio) (Jiang et al. 2017). We considered dividends, but not other forms of shareholders' remuneration (such as shares repurchases) (as Floyd et al. 2015, among others) (due to data availability, but also because share repurchases determine the end of the quality of company's shareholder for their receiver). Also, have considered only cash dividends, and no other "cosmetically" (non-cash) operations (e.g., dividends in stocks).
The final database consists of 12,085 companies operating in 73 countries in the period 2008-2014. As such, our database covers a crisis, but also a post-crisis period. The data are winsorized to 2% and DPR is limited to 100%. 9 We have considered each company as being a different and sole company, in the case of a group of companies, which activates in more than one country. 10 Appendix 2 presents the descriptive statistics for DPR for the analysed countries. The number of companies per country is constant for the entire period analysed and the average number of companies per country is 168. Table 2 provides much more details about the process of building the final sample. Appendix 1 presents DPR distributions for the countries included in our sample, for the period 2008-2014. In almost all of the cases (53 countries from 73, respectively 72.6% from the total population), DPR distribution is zero inflated (the modal value of the distribution equals 0). 11 One issue that can complicate the picture is the existence in some countries of the mandatory dividend, respectively a legal requirement that a fraction of earnings to be paid as dividend. 12 The results (somehow surprising) confirm the same distribution even for the cases of the countries with regulated dividend payment. The mode for DPR for Brazil, Greece, Peru, Philippines and Venezuela is zero, and the percent of companies that do not pay dividends in Chile is important (44%). 13 Table 3 provides the descriptive statistics for DPR. As observation, a look only to the mean (and to the median) of the population can be misleading. The mode is 0% and a closer look to the distribution of the variable confirms that, for the entire population, but also for the majority of the countries, the distribution of DPR is a zero-inflated distribution -the mode being 0, with the corresponding probability significantly higher than the other probabilities. This phenomenon is documented also by many other studies (Fama and French 2001, Denis and Osobov 2008, von Eije and Megginson 2008, Fatemi and Bildik 2012, Kuo et al. 2013.  Porta et al. (2000) exclude these countries from their analysis from the beginning. However, they mention that "they nevertheless appear, in the data, to have lower payouts than required by the law. A possible reason for this is that the accounting earnings reported to the authorities for the purpose of compliance with mandatory dividend rules are lower than the earnings reported to the shareholders which we use in our analysis". La Porta et al. (2000) use the March 1996 edition of the WorldScope Database, "which presents information on the (typically) largest firms in 46 countries". According to Fidrmuc and Jacob (2010), such requirements are present in Brazil, Chile, Greece, Peru, and the Philippines. Huang et al. (2015) mention in this category Brazil, Chile, Colombia, Greece, and Venezuela. The differences can be related not only to the countries included in the database, but also to the moment of analysis.
13 Colombia is not included in our database.

Results
Analysing visually the histogram of distribution, it can be easily observed that it is a zeroinflated distribution (see also Appendix 3 By minimizing the statistics obtained from the Anderson Darling test, we have chosen the Tweedie Distribution as being the most appropriate distribution for our data (see Table 4). Figure 2 explains graphically this choice. Figure 2 depicts the empirical distribution function of DPR versus the estimated Tweedie Cumulative Distribution Function. It can be observed that the estimated Tweedie distribution fits the best the empirical distribution of DPR, out the selected probability density functions. Figure 3 fits the empirical distribution with the Tweedie distribution. Figure 4 shows the conditional probability density function estimates for Tweedie distribution against the empirical distribution: Tweedie distribution is a good choice in approximating the real distribution.
Tweedie distribution (Tweedie 1984) is included in the class of exponential dispersion models. Some familiar distributions are special cases of the Tweedie distribution (e.g., normal, Poisson, compound Poisson gamma distribution, etc.) (Kurz 2017). They have positive mass at zero, but are otherwise continuous. Tweedie distribution is a special case of exponential dispersion models, a class of models used to describe error distributions for the generalized linear model.
If Y is a Tweedie random variable, then the mean and the variance are , where  is the dispersion parameter and p is an extra parameter that controls the variance of the distribution. The Tweedie distribution is not defined when p is between 0 and 1. In practice, the most interesting range is from 1 to 2, in which the Tweedie distribution gradually loses its mass at 0 as it shifts from a Poisson distribution to a gamma distribution. For p>1, the Tweedie probability density function (pdf) has the following form:   where N ~ Poisson (λ) and X i ~ gamma (α, θ) are i.i.d. gamma random variables with shape parameter α and scale parameter θ. The correspondence between these parameters and the parameters of the Tweedie distribution is the following: (2) The Scaled Tweedie distribution (denoted here STweedie (θ, λ, p)) is a version of the Tweedie distribution, corresponding to a compound Poisson-gamma distribution with gamma scale parameter θ, Poisson parameter λ, and the index parameter p such as 2 1 p p     (Dunn and Smyth 2005). The correspondence between the parameters of the STweedie (θ, λ, p) distribution and the Tweedie (μ,, p) distribution is the following: (3) The Tweedie distribution has nonnegative support and can have a discrete mass at zero, making it useful to model responses that are a mixture of zeros and positive values, just like the empirical distribution of DPR (see Figures 1-4). Hence, we will describe the behaviour of DPR using the Tweedie distribution.
We have estimated the parameters of the Tweedie distribution for the complete database, using numerical method for the maximum likelihood estimator of extra parameter of variance, mean and dispersion parameter. A detailed description of the method is given in Gilchrist and Drinkwater (1999). This method has been implemented in SAS 9.3 and we have used the proc severity procedure for this. The results of the estimation are presented in Table 5.
By analysing the parameters of the estimated Tweedie distribution, several conclusions can be drawn. Firstly, the value of extra parameter controlling for variance is significantly different from zero, as it would be the case if DPR follows a Gaussian distribution. Moreover, 1<p<2, so the distribution of dividend payout ratio is in fact a compound Poisson-gamma distribution. 14 A compound Poisson random variable Y is the sum of N independent gamma random variables where N follows a Poisson distribution and N and the gamma random variates are independent. The distribution of DPR is stable in time, the parameters of the yearly Tweedie distribution being significant and in line with the values estimated for the entire time-period (see Table 6).
For the majority of countries in our sample, DPR follows either a Tweedie distribution or a Scaled Tweedie (STweedie) distribution. This may be a sign of systematic behaviour, regardless of country. The exceptions are Côte d'Ivoire, Luxembourg and Latvia. In the map below, the distribution for each country is presented (see Figure 5). In Appendix 4, the estimated parameters of the Tweedie and Scaled Tweedie distribution by country are shown.
The finding that the Dividend Payout Ratio follows a Tweedie distribution can be have practical applications; for example, one can use the fitted distribution in order to have better estimates of the probability that a certain event will occur (e.g., DPR to be lower or higher than a benchmark).

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14 This is the most used case in practice, when the Tweedie random variable can be generated from a Poisson gamma distribution (see Smyth 1996).

Conclusions
Dividend policy is still a largely discussed issue in corporate finance literature. For its analysis, dividend payout ratio has certain advantages and is extensively used. Using a database consisting of 12,085 companies operating in 73 countries, for the period 2008-2014, we found that this indicator does not follow a normal distribution, but a zero-inflated one. The most appropriate distribution for modelling dividend payout ratio is the Tweedie distribution (Tweedie 1984) and its version Scaled Tweedie Distribution (Dunn and Smyth 2005). Thus, a better estimation of the probability that dividend payout ratio is lower or higher than a benchmark can be provided. Also, an analysis of dividend policy, distinctly considering payer versus non-payer companies, can offer additional important information for practitioners and, also, for academics. The use of the average levels of dividend payout ratio can determine misleading results. As far as we know, finding the distribution for DPR is a new contribution for financial literature. Another contribution, comparative to previous research, is the large number of countries considered (73) and covering a crisis and a post-crisis period (2008)(2009)(2010)(2011)(2012)(2013)(2014). Our sample included countries from Africa, North and South Americas, Asia, Australia, and Europe. From here, conclusions are validated for countries with a large diversity regarding the cultural values, but also legal systems (our sample includes common law, but also civil law countries).
This outcome could be useful in the future research where a more appropriate distribution could be used for modelling the influencing factors of the DPR. Based on our knowledge, our paper is the first one that tried to investigate which would be the most appropriate distribution function for DPR. Our result can be useful in the context of international portfolio management, especially when we discuss about investments made in a large number of companies (with minority participations), and when forecasting of the future collected dividends is of interest.
As a limitation of the study, our analysis and results are made on only one financial indicator that describe dividend policy -dividend payout ratio. One interesting extension can be made analyzing other indicators reflecting the dividend policy, too. Also, accounting rules are different from country to country (Chui et al. 2002;Dragotă et al. 2018) and from sector to sector (Short et al 2002). Fiscal systems are also different and they can have an impact on financial decisions (Chui et al. 2002, Dragotă et al. 2018, including dividend policy (Short et al 2002, Fidrmuc andJacob 2010). These issues can have an impact on earnings (La Porta et al. 2000), and, from here, on dividend payout ratio. It can be suspected that the situation from Table A.3.1 can be related to the capital market development (see market capitalization as proxy). However, from the first 10 countries ranked function of market capitalization, 15 four present a zero-inflated distribution (US, China, Canada, India). Considering the value of stocks traded as percent in GDP, 16 six present a zero-inflated distribution. 17 One interesting future direction for analysis is to consider some cultural determinants for explaining this zero-inflated distribution for DPR. These similarities can be explained by similar cultural dimensions or people behaviour. For example, similar harmony index (Yaseen and Dragotă, 2019) or similar life standards (Yaseen, 2019) in those countries may lead to similar decisions regarding paying dividends or not.