Withholding-tax non-compliance: the case of cum-ex stock-market transactions

Buettner, Thiess; Holzmann, Carolin; Kreidl, Felix; Scholz, Hendrik Article — Published Version Withholding-tax non-compliance: the case of cum-ex stock-market transactions International Tax and Public Finance Provided in Cooperation with: Springer Nature Suggested Citation: Buettner, Thiess; Holzmann, Carolin; Kreidl, Felix; Scholz, Hendrik (2020) : Withholding-tax non-compliance: the case of cum-ex stock-market transactions, International Tax and Public Finance, ISSN 1573-6970, Springer US, New York, NY, Vol. 27, Iss. 6, pp. 1425-1452, https://doi.org/10.1007/s10797-020-09602-9 This Version is available at: https://hdl.handle.net/10419/288415 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. 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If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. https://creativecommons.org/licenses/by/4.0/ Vol.:(0123456789) International Tax and Public Finance (2020) 27:1425–1452 https://doi.org/10.1007/s10797-020-09602-9 1 3 Withholding‑tax non‑compliance: thecase ofcum‑ex stock‑market transactions ThiessBuettner1,2 · CarolinHolzmann1· FelixKreidl1· HendrikScholz1 Published online: 30 April 2020 © The Author(s) 2020 Abstract This paper explores withholding-tax non-compliance in the context of dividend taxation. It focuses on a specific type of stock-market transactions around ex-dividend dates, so-called “cum-ex” trades, which caused considerable revenue losses due to illegitimate tax refunds in Germany and other countries. We use a stylized model of the stock-market equilibrium to analyze the incentives of traders on the German stock market and find that cum-ex trades are only profitable for both buyer and seller in the presence of collusive tax fraud. Our empirical analysis of market data for publicly traded German stocks from 2009 to 2015 confirms that transaction numbers of stocks suitable for cum-ex trades show the expected increase shortly before exdividend dates in the period before the tax refunding was reformed. In line with the collusion hypothesis, effects on stock-market prices are not found. Keywords Tax compliance· Tax evasion· Withholding taxes· Collusion· Tax fraud· Tax refunding· Cum-ex trades· Ex-dividend date· Dividend taxes· Capital gains taxes JEL Classification H26· G12 Previous versions of the paper were circulated under the title “Stock Market Behavior on ExDividend Dates: The Case of Cum-ex Transactions in Germany.” Electronic supplementary material The online version of this article (https ://doi.org/10.1007/s1079 7-020-09602 -9) contains supplementary material, which is available to authorized users. * Thiess Buettner [email protected] Felix Kreidl [email protected] Hendrik Scholz [email protected] 1 FAU (Friedrich-Alexander-Universität Erlangen-Nürnberg), Nürnberg, Germany 2 CESifo, München, Germany 1426 T.Buettner et al. 1 3 1 Introduction Withholding taxes are a key instrument to ensure tax enforcement. Also taxation of dividends strongly relies on withholding taxes. In 2015, 23 out of 34 OECD countries levied withholding taxes on dividend income (Milanez 2017). The instrumental role of these taxes for enforcement is obvious in the debate on tax havens (Johannesen and Zucman 2014). In the EU, for instance, the EU Savings Directive requires countries to either engage in an automatic information exchange, or to levy a withholding tax on income of investors which are domiciled in other European countries (Johannesen 2014). A characteristic of withholding taxes is that the remitter is not the statutory bearer of the tax. This reduces the incentive to evade taxes since the remitter does not directly benefit from evasion. However, the use of withholding taxes shifts the risk of non-compliance to the remitter (Slemrod 2008), and it may happen that taxes are not withheld or not remitted to the tax authorities. A further problem arises since withholding taxes are typically associated with a refundable tax credit: If no taxes have been withheld, tax refunding results in negative taxes. As the infamous case of “missing trader” fraud under VAT shows, non-compliance of the remitter in combination with tax refunding can be highly problematic. Not only do illegitimate tax refunds reduce available public funds, they also exert important negative externalities such as distortions of competition, inequity and income transfers to organized crime (dela Feria 2018). Recently, withholding-tax non-compliance received public attention in the context of so-called “cum-ex” trades. This involves short trading around ex-dividend dates, where the stock is sold “cum-dividend” before the dividend date but delivered after, i.e., “ex-dividend”. Cum-ex trades are designed specifically to obtain refunds of withholding taxes on dividends even though the corresponding tax payment had not been remitted.1 These trades have been reported in various countries, including Germany, Austria and Switzerland (Special Investigation Committee 2017, 348) and, more recently, Denmark.2 The German case stands out both because of the magnitude of revenue losses and because of the length of the period during which these trades were possible. A tentative estimate of tax-revenue losses points at a stunning amount of 7.2 billion euros (Spengel etal. 2017) for the time period between 2005 and 2011 alone.3 One explanation for the massive volume of non-compliance in withholding dividend taxation is that traders searching for arbitrage opportunities simply exploited a tax loophole, or, more precisely, a technical defect in the way the withholding tax was being imposed and administered. This view has been featured in some media 1 Throughout the paper, the notion of cum-ex trades always refers to trades set up on purpose to obtain an illegitimate tax certificate. Accidental trades that take place around the ex-dividend date are not referred to as cum-ex trades. 2 See New York Times, October 5, 2018, “Where in the World Is Denmark’s $2 Billion?”. 3 See also Special Investigation Committee (2017), 471. 1427 1 3 Withholding-tax non-compliance: thecase ofcum-ex… reports4 and it is intuitive, since the traders’ quest for arbitrage opportunities can be seen as a sort of discovery process that detects all types of profitable transactions. An alternative explanation is that the profits associated with illegitimate tax refunds incentivized traders to pursue withholding-tax non-compliance as a deliberate act of tax fraud—buyers and sellers collude, set up deals designed to obtain illegitimate tax refunds, and conceal their trades from tax authorities. If the first explanation is correct, prevention of tax evasion ultimately requires governments to set up proper systems of taxation and administration which eliminate possibilities for tax arbitrage. Since identifying loopholes associated with transnational transactions is quite challenging, governments could introduce mandatory reporting by taxpayers and intermediaries of cross-border tax planning arrangements in order to improve compliance (e.g., Baker 2015). If the second explanation holds, however, despite already tight regulation and supervision of financial markets, tax authorities would need to take further action to make collusion of non-compliant traders more difficult. Against this background, this paper explores withholding-tax non-compliance involving illegitimate tax refunds in the context of dividend taxation. We analyze the incentives for traders in a stylized theoretical model of the stock-market equilibrium and derive empirical predictions with regard to market prices and transactions. The empirical analysis exploits the German experience as testing ground. More specifically, we test theoretical predictions using daily stock-exchange data for publicly traded German stocks from 2009 to 2015. Our identification strategy distinguishes between stocks with taxable dividends and stocks that pay tax-exempt dividends and compares developments of stock prices and trading volumes around ex-dividend dates before and after the change in the administration of the tax in January 2012. As we show in this paper, in a stock-market equilibrium characterized by elimination of arbitrage opportunities for German institutional investors, cum-ex trades are only profitable for both buyer and seller if they collude in tax non-compliance. Under collusion, trades should exert no effects on market prices but are reflected in transaction volumes. In accordance with the collusion hypothesis, the empirical results indicate that market-price effects are absent. Yet they confirm higher trading volumes shortly before the ex-dividend date in publicly available transaction data. However, not all stocks paying taxable dividends display the same increases in trading volumes, indicating that cum-ex trades focus on selected stocks. Our identification approach explicitly takes into account that excess trading around ex-dividend dates may arise for a variety of reasons and distinguishes between the specific effects associated with cum-ex trading and excess trading in general. A large body of literature in public economics has studied tax evasion and noted that it can be effectively reduced by controls such as withholding taxes and thirdparty reporting (e.g., Kleven etal. 2011; Slemrod and Gillitzer 2014). As noted by Slemrod (2008), however, despite the “paramount importance of withholding”, noncompliance under withholding taxation is rarely discussed. Yaniv (1988) provides a theoretical analysis that explores determinants of tax evasion under payroll taxation. 4 Cf. Der Spiegel, July 13, 2009, “Hase und Igel”. 1428 T.Buettner et al. 1 3 Allowing for collusion between employer and employee, Yaniv (1992) shows that tax evasion may actually increase rather than decrease under tax withholding. Madzharova (2013) argues that the corporate profit tax reduces the incentive for the employer to participate in such collusion. Kleven etal. (2016) provide an agency model, where collusion between employer and employee becomes less likely as firm size grows. Hence, firms have a role as “fiscal intermediaries” in facilitating revenue collection. To the best of our knowledge, this research paper is the first to deal with noncompliance in the context of withholding taxes on dividends. Revenue losses due to illegitimate tax refunds have so far mainlybeen discussed in the context of VAT (e.g., Keen and Smith 2006). Our paper also contributes to the literature on stockmarket effects of dividend and capital gains taxes (e.g., Elton and Gruber 1970; Kalay 1982; McDonald 2001; Klautke 2008). Haesner and Schanz (2013) explore the effects in the German case, noting high trading volumes around the ex-dividend dates. Whereas the literature has discussed various reasons for abnormal trading volumes around ex-dividend dates (e.g., Lakonishok and Vermaelen 1986; Karpoff and Walkling 1990; Michaely and Vila 1995; Dhaliwal and Li 2006; Akhmedov and Jakob 2010; Haesner and Schanz 2013; Hartzmark and Solomon 2013; Henry and Koski 2017), our paper shows that withholding-tax non-compliance offers a further explanation. The paper proceeds as follows. Section2 gives background information on cumex trading. Section3 provides a theoretical discussion of cum-ex trading in a stockmarket equilibrium and discusses empirical implications. Section 4 describes the data. Section5 develops the empirical methodology. Section6 presents the empirical results and Sect.7 concludes. 2 Dividend tax withholding andcum‑ex trading inGermany Dividends (D) of corporations located in Germany are subject to a withholding-tax rate ( 𝜏w ) of 26.4%.5 Under the rules in place until 2011 (see Fig.1), the withholding tax ( 𝜏w ⋅ D ) was remitted by the dividend-paying corporation, and the shareholder’s depository bank was responsible for issuing the tax certificate that entitles fully taxable German investors to a tax credit or a tax refund. The withholding tax is fully credited against any income taxes.6 If taxes filed under the income tax are less than the amounted credited for the certified withholding tax, the tax payer receives the net excess in cash. The fact that the party remitting was not the same as the party issuing the tax certificate facilitated withholding-tax non-compliance: Using so-called cum-ex 5 The withholding-tax burden of 26.4% consists of a 25% dividend tax plus 5.5% solidarity surcharge: (25 ×1.055)% = 26.375% . 6 This holds regardless of whether the buyer is subject to the personal income tax or to the corporate income tax. 1429 1 3 Withholding-tax non-compliance: thecase ofcum-ex… trades, tax refunds were generated even though no taxes were remitted.7 Numerous instances of non-compliance have been detected. The Special Investigation Committee, set up by the German Federal Parliament to investigate cum-ex trading, reports 570 suspicious cases for the time period between 2009 and 2011 (cf. Special Investigation Committee 2017, 370).8 To illustrate the institutional arrangement, we first consider the case where an owner of a stock sells the stock 2 days before the ex-dividend date.9 The German stock-market guidelines require the settlement of a regular trade to be within 2 days after the date of the transaction.10 Hence, with a sale 2 days before the ex-dividend date, the stock may be delivered on the ex-dividend date. In this case, the buyer will not receive the net-of-tax dividend payment from the corporation ( 1−𝜏 w) ⋅ D , but rather the seller of the stock will. In order to ensure correct dividend distribution, a dividend settlement is carried out. The settlement involves a corresponding compensation of the buyer, which is charged to the seller’s account. Thus, the net-of-tax dividend is effectively transferred to the buyer. The settlement also ensures that the buyer, not the seller, receives a withholding-tax certificate. As a consequence of the settlement, the buyer receives a “three-part delivery” of the stock: First, the seller delivers the stock ex-dividend. Second, the buyer receives the dividend compensation ( 1−𝜏 w) ⋅ D . Third, the buyer’s depository bank issues the withholding-tax certificate that entitles the buyer to a tax refund in the amount of 𝜏w ⋅ D . This procedure is in accordance with the basic aim of the withholding tax: A tax on dividends is withheld and a tax certificate is issued that entitles the shareholder to a tax credit or refund depending on whether or not taxes are imposed at a later stage. In the above case, the seller actually owns the stock before the sale. In the case of cum-ex trades, however, the seller (in the following, the cum-ex seller) does not own the stock and conducts a so-called short sale. Figure2 depicts such a trade. The cum-ex seller instigates the trade through a short sale of a stock cum-dividend at price PCUM 2 days before the ex-dividend date. This ensures that a delivery on the ex-dividend date and, thus, ex-dividend is in accordance with the stock-market guidelines.11 Due to the delivery ex-dividend, the trade triggers the dividend settlement process. Similar to the above case, the cum-ex buyer receives the stock exdividend, a compensation equal to the dividend net of the withholding tax as well as a certificate that entitles the cum-ex buyer to a tax credit. The compensation is 7 This practice is not confined to Germany. Interestingly, the Special Investigation Committee of the German Federal Parliament cites a confidential internal report by a bank domiciled outside Germany noting that similar flaws in the administration of the withholding tax exist also in Belgium, France, Italy, Netherlands, Spain, and Switzerland (Special Investigation Committee 2017, 348). 8 For an assessment of the illegality of cum-ex trades in Germany see Spengel and Eisgruber (2015) as well as Special Investigation Committee (2017), 378. 9 For the following, cf. Spengel (2016). 10 See §7 I Boerse Frankfurt (2008). 11 German stock-exchange rules require no coverage of the short sale provided delivery is completed on the second day after the date of the transaction (§7 I Boerse Frankfurt 2008), i.e., cum-ex transactions require no stock borrowing. The cum-ex seller covers the short sale by purchasing the stock from a third party on the ex-dividend date upon immediate delivery and concurrently forward the stock to the cum-ex buyer. 1430 T.Buettner et al. 1 3 charged to the account of the cum-ex seller. However, the buyer’s depository bank does not consider the short-sale nature of the transaction and ignores the fact that the original owner has received not only the net-of-tax dividend but also a withholdingtax certificate. As a consequence, the second certificate de facto entitles the buyer to a refund of taxes that were actually never remitted. In 2007, the government changed the rules for the dividend withholding tax in order to stop illegitimate tax refunding. To this end, the depository bank of the cumex seller has been made responsible for collecting a tax equivalent to 𝜏w ⋅ D from the cum-ex seller (Special Investigation Committee 2017, 161). However, cum-ex sellers with a foreign depository bank were de facto exempted from this rule. Only those cum-ex trades were prevented from generating an illegitimate tax credit that involved cum-ex sellers with domestic accounts. Transnational cum-ex trades could still lead to illegitimate tax refunds.12 Finally, effective in January 2012, the rules for collecting the withholding tax were changed. Since 2012, not the corporations but the banks withhold and remit dividend taxes and are responsible for issuing certificates that entitle the investor to a tax refund. Hence, the party remitting the dividend tax is now the same as the party issuing the tax certificate. 3 Theoretical analysis This section provides a theoretical analysis of the incentives for cum-ex trading. We derive stock-market equilibrium conditions to determine the expected price/drop ratio (PDR), i.e., the price drop on the ex-dividend date in relation to the dividend of a stock. On the ex-dividend date, the owner of the stock is no longer entitled to receive the current dividend. This causes a “technical” drop in the expected price of the stock at the ex-dividend date. Following the literature (Elton and Gruber 1970; Fig. 1 Dividend tax withholding until 2011. Note D is the dividend and the withholding-tax rate is 𝜏w . 12 As a consequence, cum-ex trades with illegitimate tax credits turned international. See Wall Street Journal, October 29, 2014, “European probe widens into tax manoeuvre—Germany-led investigation has recently broadened to involve tax authorities and prosecutors in other countries.” 1431 1 3 Withholding-tax non-compliance: thecase ofcum-ex… Kalay 1982; McDonald 2001), we use a costly–arbitrage framework to derive conditions under which risk-neutral investors fail to find arbitrage opportunities—neither buying the stock cum-dividend and selling it ex-dividend (long–arbitrage strategy) nor shorting cum-dividend and closing the short position ex-dividend (short–arbitrage strategy) result in a profit. 3.1 Stock‑market equilibrium On the stock market, investors who consider selling the stock meet investors who consider buying the stock. Selling and buying on the stock market each come at transaction cost c. Taxation is taken into account by two tax rates, a dividend tax 𝜏d and a tax on realized capital gains 𝜏g . In view of the tax conditions faced by a fully taxable institutional investor in Germany, which is the testing ground for the empirical analysis, we simplify the exposition and assume that both tax rates are equal to the withholding-tax rate 𝜏w=𝜏g=𝜏d .13 Consider first an investor following a long-arbitrage strategy, who is buying a stock cum-dividend at the price PCUM and selling the stock ex-dividend at the price PEX . The expected return is (1−𝜏w) ⋅ (E[PEX ]−PCUM −2c)+(1−𝜏w) ⋅ D .14 The long-arbitrage strategy yields an expected return that is smaller than or equal to zero if the expected PDR exceeds or equals a certain threshold, formally, P CUM −E[P EX ] D ≥1− 2c D . An alternative strategy is short arbitrage. This consists of short selling a stock cum-dividend, such that the net dividend is forgone, and purchasing and returning the stock ex-dividend. This strategy yields an expected return of Fig. 2 Cum-ex trades until 2011. Note D is the dividend. The withholding-tax rate is 𝜏w . PCUM denotes the stock price cum-dividend 13 Under the tax law implemented in 2009, this condition applies if the marginal investor is a fully taxable German investor (e.g., Haesner and Schanz 2013). 14 In accordance with the literature, we assume that the transaction cost is deductible from the capital gains tax base. In the German case, this deduction may or may not be possible. Since the results are not affected by the tax treatment of the transaction cost, we stick to the conventional formulation of the problem. 1432 T.Buettner et al. 1 3 (1−𝜏w) ⋅ (PCUM −E[PEX ]−2c)−(1−𝜏w) ⋅ D . The expected return is non-positive, if P CUM −E[P EX ] D ≤1+ 2c D . The two inequalities allow us to derive a condition that ensures the absence of profitable arbitrage trading opportunities for common investors around ex-dividend dates. This holds if the PDR is within the interval 3.2 Cum‑ex trading In this subsection, we explore the incentives for cum-ex trading in a market equilibrium where the PDR is in accordance with inequality (1). In the first step, we analyze the profit opportunities of short seller and buyer separately in the stock-market equilibrium without illegitimate tax refund.15 In the next step, we explore the profit opportunities if the buyer receives an illegitimate tax refund. In a third step, we explore the profit opportunities under collusion. 3.2.1 The shortseller The stock is sold cum-dividend at the price PCUM and delivered at the ex-dividend date, when it is traded at price PEX . The transaction cost is 2c. The short seller is obliged to pay a compensation in the amount of the net-of-tax dividend (1−𝜏w) ⋅ D to the buyer. The short seller’s expected profit from the trade is: The short seller holds the short position in the stock until the ex-dividend date. Hence, the larger the price drop, the more favorable is the price development from the short seller’s perspective. Given inequality (1), the maximum expected price drop in the stock-market equilibrium is PCUM −E[PEX ]=D+2c . In this case, the short seller earns a profit in the amount of 𝜏w ⋅ D . More generally, Therefore, in the stock-market equilibrium described by inequality (1), provided the transaction cost is small, a trade would result in a positive profit for the short seller. Importantly, this holds only with taxable dividends, where 𝜏w>0 . In the special case of tax-exempt dividends ( 𝜏w =0 ), the short seller never obtains a positive profit, as −4c ≤ ΠS ≤ 0 . (1) 1 −2c D ≤ P CUM −E[P EX ] D ≤1+2c D . (2) ΠS=(PCUM −E[PEX ]−2c)−(1−𝜏w) ⋅ D (3) 𝜏w ⋅D −4 c≤ ΠS ≤ 𝜏w ⋅D . 15 Without loss of generality we abstract in the following from the taxation of the profits of traders and focus on the gross earnings of short seller and buyer. 1439 1 3 Withholding-tax non-compliance: thecase ofcum-ex… from the constant during the cum-ex period. 𝛽1 and B1 measure the average difference between taxable and non-taxable dividend paying stocks on ordinary trading days in all years and in the cum-ex period, respectively. The key parameters of interest are Ω−2 and Ω−1 . They indicate whether stocks suited for cum-ex trades do, in fact, show increased transactions on the 2 days before the ex-dividend date—in the time period during which illegitimate tax credits were obtained. More precisely, they capture the difference in trading volumes between stocks with taxable and stocks with tax-exempt dividends on the 2 days before the ex-dividend date in the cum-ex period compared to the post period. As discussed above, we expect to find stocks with taxable dividends in the cumex period to show higher trading numbers on the last 2 days before the ex-dividend date, i.e., Ω−2>0 and Ω−1>0 . Specification (9) tests for differences in the trading numbers of stocks with taxable dividends in the cum-experiod only on the last 2 days before the dividend date and not on other days before or after. The analysis below provides test statistics showing that this restriction is confirmed by the data. To estimate Eq. (9), we apply pooled OLS as well as panel regressions with dividend-event effects. These effects are specific to each dividend event and, in contrast to company-specific effects, capture differences in the dividend policy of a company over time. This is important, since the basic regression does not include the determinants of the dividend policy and, hence, might be biased due to confounding effects. By including event-specific random and fixed effects we also provide results which capture or even condition on all possible determinants of the decision regarding the dividend policy.24 This includes also shocks associated with the Euro crisis.25 From an econometric perspective, biases may also arise due to confounding announcement effects. However, because of the decision process involving the boards and the shareholders assembly, the announcement of the dividend by the HDAX firms is typically made before the actual ex-dividend date. Information about the dividend, including whether it is taken from the capital reserves, is therefore given in the period around the ex-dividend date. We also estimate an enriched form of a random-effects model that allows us to study potential heterogeneity in cum-ex trading between dividend events. This so-called mixed linear model allows for random intercepts for each dividend event and event-specific cum-ex effects. These effects capture event-specific deviations from the average cum-ex effects ( Ω−2,i and Ω−1,i ). Besides analyzing the number of stocks traded, we also explore the effects of cum-ex trading on the ex-dividend date price drop. To this end, we focus on the price drop between dividend date and ex-dividend date for all dividend events. Formally, we use the following cross-sectional specification: (10) PD i =𝛾 1 Div i +𝛾 2 Div i⋅ I i +Γ 1 Div i⋅ T i +Γ 2 Div i⋅ I i⋅ Ti +𝛽 0 +𝛽 1Ii + B0Ti + B1Ii ⋅ Ti + ui 24 Note that the event-specific effects nest also stock-specific effects. 25 In fact, the data display a general decline in the numbers of stock traded. Removing the 10 days around the ex-dividend dates, the average daily number of stocks traded in the estimation sample is 1101907, 901900, 1070403, 928000, 800838, 773031, 819035 in the years from 2009 to 2015. 1440 T.Buettner et al. 1 3 The dependent variable, PDi , is the drop in the stock price from the dividend date (day −1 ) to the ex-dividend date (day 0) in euros for each dividend event.26 The dividend, Divi , is the dividend in euros. As above, Ii is a binary indicator that equals unity in the case of taxable dividends and zero in the case of withholding-tax-free dividends. Ti is unity for dividend payments in the cum-ex period from January 2009 to December 2011 and otherwise zero. ui is an error term. The baseline price/drop is captured by 𝛾1 . 𝛾2 tests for differences between taxable and tax-exempt dividends. Γ1 captures differences in PDRs in the cum-ex period compared to the post period. To study the effect of cum-ex trading on stock prices, we are interested in the coefficient Γ2 which captures differences in the PDR of stocks paying taxable dividends during the cum-ex period compared to the post period. Due to collusion between cum-ex seller and buyer, we do not expect an effect of cum-ex trading on stock prices and, hence, Γ2=0 . 𝛽1 , B0 and B1 allow for deviations from the constant for the two groups and time periods. 6 Empirical results 6.1 Numbers ofstocks traded Descriptive evidence on the time pattern of trades is provided in Fig.3. It depicts the daily average total number of stocks traded for a 131-day window around stocks’ ex-dividend dates (ex-dividend dates normalized to zero) as reported in the XETRA data. The trading volumes are separately shown for stocks with taxable dividends (black lines) and stocks with tax-free dividends (gray lines), both for the cum-ex period (solid lines) and the post period (dashed lines). In the case of taxable dividends for the cum-ex period, the figure shows that the average total number of stocks traded increases substantially by approximately 200% in the last 2 days before the ex-dividend date and immediately drops back to normal levels after the ex-dividend date. Interestingly, this pattern arises in the cum-ex period and not in the post period. No noticeable increases are indicated for events with tax-exempt dividends. Table1 presents results for the parameters of interest obtained from various alternative specifications following Eq. (9). It reports estimates for the 2 days before the ex-dividend date in the cum-ex period ( Ω−2 , Ω−1 ) and the baseline effects for these days ( 𝜔 −2 , 𝜔 −1 ) for taxable dividends. Table A.2 in Appendix provides the estimation results also for all other parameters. Column (1) reports estimates from a simple OLS specification. The point estimates of 0.487 and 0.238 indicate increases in the number of stocks traded on days −2 and −1 in the cum-ex period. A joint test of the cum-ex effects indicates that the absence of higher trading numbers can be rejected 26 To prevent bias due to market developments, we adjust the cum-price by the expected daily return according to Elton etal. (2005). The expected daily return is estimated using a market model. The estimation period covers a time window of 131 days around the ex-dividend date, where 10 days before and 10 days after the ex-dividend date are excluded. 1441 1 3 Withholding-tax non-compliance: thecase ofcum-ex… at a 10% level of significance. However, the effects on the 2 days before the ex-dividend date are imprecisely estimated with large standard errors. Column (2) of Table 1 reports coefficients resulting from an event-level fixedeffects estimation. This specification reports significant effects. The point estimates of 0.256 and 0.324 indicate increases in the number of stocks traded on days −2 and −1 , respectively. Column (3) shows results from a random-effects regression. Though the estimates of the parameters of interest in columns (2) and (3) are almost identical, a formal Hausman test27 rejects the null hypothesis that random effects estimates are consistent for all estimated parameters. Hence, we follow Mundlak (1978) and allow for some correlation between unobserved factors and regressors. More specifically, we extend the regression equation with the averages of the timevarying variables (Mundlak terms) in the random-effects specification. Column (4) shows that the results are not affected. Fig. 3 Daily average total number of stocks traded (XETRA data, 2009–2015). Note This figure depicts the daily average total number of stocks traded as reported in the XETRA data. Dividends paid from current profits are subject to withholding tax (taxable dividends) and, therefore, suitable for cum-ex trading. Dividends from capital reserves are withholding-tax free (tax-free dividends) and, thus, not suitable for cum-ex trading. The trading volumes are separately presented for stocks with taxable dividends (black lines) and stocks with tax-free dividends (gray lines), both for the cum-ex period from 2009 to 2011 (solid lines) and the post period from 2012 to 2015 (dashed lines). The vertical dashed lines mark a 2-day window prior to the ex-dividend date. The vertical solid lines mark the 21-day trading window around the ex-dividend date. Data source: Thomson Reuters EIKON. 27 We employ a heteroskedasticand cluster-robust version of the Hausman test as suggested in the literature (e.g., Arellano 1993; Wooldridge 2002). 1442 T.Buettner et al. 1 3 Across the different panel model specifications (columns (2) to (4)), the point estimates consistently indicate that the number of stocks traded is increased by cumex trading on day −2 by around 29% (point estimates of the regression of 0.256 to 0.258) and on day −1 by 38% (point estimate 0.324) during the cum-ex period.28 Apart from the cum-ex period, we do not find any statistically significant effects Table 1 Regression results: number of stocks traded around ex-dividend date The dependent variable is the natural logarithm of the traded number of stocks as reported in the XETRA data. The sample includes all German stocks that are constituents of the HDAX index between 2009 and 2015. It includes 103,386 observations for 806 dividend events by 155 firms. Due to missing values not all 829 dividend events in the data are included. D i ,d takes a value of unity on day d before or after the ex-dividend date. Ii is a binary indicator that equals unity in the case of taxable dividends and zero in the case of withholding-tax-free dividends. Ti is a binary indicator that takes value unity for observations during the cum-ex period from January 2009 to December 2011, and zero in the post period, i.e., in the years 2012 to 2015. Regression coefficients result from pooled OLS regressions (column (1), fixed-effects (column (2)) and random-effects regressions (columns (3) to (5)). Specification (5) allows for event-specific deviations from the average cum-ex effect on days −2 and −1 (random slopes). The variances of the random intercept and slope effects are reported at the bottom of the table. The employed estimation method, ordinary least squares, without (OLS) and with fixed effects (OLS(FE)), generalized least squares (GLS(RE)) with random effects, or mixed effects maximum likelihood (ML(ME)), and the use of Mundlak terms in random effects regressions are noted in the table. Cluster-robust standard errors (clustered at dividend-event level) are in parentheses. Asterisks denote statistical significance at the 0.01 (***) and 0.10 (*) levels (1) (2) (3) (4) (5) Cum-ex period Di,−2∗Ii∗Ti 0.487 0.256* 0.258* 0.258* 0.253 (0.30) (0.15) (0.16) (0.16) (0.15) D i, − 1 ∗I i ∗Ti 0.238 0.324*** 0.324*** 0.324*** 0.316*** (0.15) (0.11) (0.11) (0.11) (0.11) Baseline effects D i ,−2∗Ii 0.018 −0.021 −0.021 −0.021 −0.021 (0.08) (0.07) (0.07) (0.07) (0.08) D i ,−1∗Ii 0.061 0.054 0.054 0.054 0.054 (0.07) (0.07) (0.07) (0.07) (0.08) Estimation method OLS OLS(FE) GLS(RE) GLS(RE) ML(ME) Mundlak terms – – – Yes Yes P value cum-ex effects 0.10 0.01 0.01 0.01 0.01 P value other days 0.83 0.25 0.24 0.24 0.24 Variances random effects Random effect D i ,−2∗I i ∗Ti – – – – 0.102 Random effect D i ,−1∗I i ∗Ti – – – – 0.273 Random intercept – – – – 5.288 28 In the log-linear model, the predicted cum-ex effect on trading numbers based on the point estimate (in %) is defined as ( exp{  Ω d }−1)⋅ 100 . 1443 1 3 Withholding-tax non-compliance: thecase ofcum-ex… in the trading numbers around the ex-dividend date, and the point estimates for the baseline effects are close to zero. In accordance with the theoretical predictions, thebasic specification (9) tests for cum-ex effects only on the last 2 days before the ex-dividend date. As reported in Table1, joint tests enable us to reject deviations from the baseline time pattern on other days within the 21 days time window around the ex-dividend date at reasonable levels of significance (see P value other days). Compared with the large spike in the total number of stocks traded in Fig. 3 which points to a 200% increase, the magnitudes of the point estimates of the cumex effects (29% and 38% on days −2 and −1 , see above) seem rather small. A possible explanation for the difference between the descriptive evidence and the model results is that not each stock with taxable dividends is used for cum-ex trading, as the basic specification implicitly assumes. Following the theoretical analysis, it makes sense to argue that the costs of non-compliance and collusion as well as the value of the tax refund vary between dividend events. As a result, cum-ex effects will be heterogeneous. To study the heterogeneity in cum-ex effects between different events, we estimate an enriched random-effects model that incorporates event-specific random effects for days −2 and −1 . Column (5) of Table1 reports results. The mean cum-ex effects of this model,  Ω−2 and  Ω−1 , are similar to the above results. Figure4 shows the empirical distribution of the predicted cum-ex effects in % for days −2 and −1 .29 The figure reports the distribution of the cum-ex effects based on the point estimate of the mean cum-ex effect  Ωd and the event-specific predictions of the random day effect  Ωd,i . It shows that there is substantial variation in cum-ex effects between events. In particular, the distributions are skewed and show long tails on the right-hand side. This indicates that there are some dividend events where the number of trades increases by muchmore than suggested by the average cum-ex effects. In fact, some events are predicted to show an increase in the number of stocks traded by more than 100%. On day −1 , we even find increases of more than 200%. While the above results are obtained using XETRA data which captures the majority of transactions on the XETRA trading venue, over-the-counter trades are not covered. To see whether similar patterns can be found specifically for these types of transactions, we ran a set of regressions using XETRA-OTC data. The results are reported in Table 2. Across specifications, the results point to a strong increase in transactions before the ex-dividend date. Unlike with the XETRA data, no effect is found 2 days before and excess trading is concentrated on the last day before the ex-dividend date. Interestingly, the magnitude of this effect is much stronger than above: The point estimates indicate an increase of 304% on the last day before the ex-dividend date. Strong heterogeneity is also found in this case. Using a mixed effects model, the average effects are similar, but the results point to substantial variances. 29 The event-specific prediction of the cum-ex effect on day d in % is ( exp{  Ω d +  Ω d,i }−1)⋅ 100 . 1444 T.Buettner et al. 1 3 6.2 Ex‑dividend date price/drop ratios Having explored effects on the number of stocks traded, this section reports tests of the theoretical prediction that, due to collusion, cum-ex trades do not affect stockmarket prices. Descriptive evidence on the PDRs is provided in Fig.5. It reports kernel-based estimates of the distribution of price/drop-ratios in the cum-ex period separately for stocks with dividends subject to withholding taxes and for those with tax-exempt dividends. Both distributions are largely overlapping with mean PDRs close to one. This suggests that cum-ex trading has had little effect on the PDRs, as the distributions are clearly centered around unity. Regression results following Eq. (10) are provided in Table3. With regard to the actual magnitude of the PDR, it is interesting to note that the point estimates suggest a PDR of around unity. Provided the marginal trader is a fully taxable German institutional investor, this is consistent with the standard arbitrage equilibrium outlined in Sect.3. In fact, statistical testing does not allow us to reject a unit PDR (see P values noted at the bottom of the table). More importantly, however, the interaction terms with taxable dividends in the cum-ex period are very small and not significantly different from zero. Thus, our empirical results do not enable us to reject the theoretical prediction that collusive cum-ex trades have no stock-market price effects on the ex-dividend date. Fig. 4 Prediction of event-specific cum-ex effects. Note The graphs depict kernel-based estimates of the distributions of predicted event-specific cum-ex effects for days −1 (solid line) and −2 (dashed line) obtained by the mixed-linear model (see column (5) in Table 1). The event-specific prediction of the cum-ex effect in % is ( exp{  Ωd+  Ωd , i}−1)⋅ 100 . Epanechnikov kernel densities 1445 1 3 Withholding-tax non-compliance: thecase ofcum-ex… 6.3 Robustness checks The above findings for the number of stocks traded are obtained using a difference-in-difference approach. Hence, the estimates distinguish between treatment and control groups based on the difference in the number of stocks traded between taxable dividends and tax-exempt dividends and distinguishing events that take place within and after the cum-ex period. Therefore, general increases in trading volumes around ex-dividend dates are removed from the estimates. But depending on the motives of trading around ex-dividend dates other than cum-ex trading, composition of treatment and control groups might differ, which Table 2 Regression results: number of stocks traded via XETRA-OTC around ex-dividend date The dependent variable is the natural logarithm of the traded number of stocks as reported in the XETRA-OTC data. The sample includes all German stocks that are constituents of the HDAX index between 2009 and 2015. It includes 103,386 observations for 806 dividend events by 155 firms. Due to missing values not all 829 dividend events in the data are included. D i , d takes a value of unity on day d before or after the ex-dividend date. Ii is a binary indicator that equals unity in the case of taxable dividends and zero in the case of withholding-tax-free dividends. Ti is a binary indicator that takes value unity for observations during the cum-ex period from January 2009 to December 2011, and zero in the post period, i.e., in the years 2012 to 2015. Regression coefficients result from pooled OLS regressions (column (1)), fixed-effects (column (2)) and random-effects regressions (columns (3) to (5)). Specification (5) allows for event-specific deviations from the average cum-ex effect on days −2 and −1 (random slopes). The variances of the random intercept and slope effects are reported at the bottom of the table. The employed estimation method, ordinary least squares, without (OLS) and with fixed effects (OLS(FE)), generalized least squares (GLS(RE)) with random effects, or mixed effects maximum likelihood (ML(ME)), and the use of Mundlak terms in random effects regressions are noted in the table. Cluster-robust standard errors (clustered at dividend-event level) are in parentheses. Asterisks denote statistical significance at the 0.01 (***) levels (1) (2) (3) (4) (5) Cum-ex period Di,−2∗Ii∗Ti −0.008 0.109 0.107 0.107 0.070 (0.36) (0.34) (0.34) (0.34) (0.34) D i, − 1 ∗I i ∗Ti 1.408*** 1.397*** 1.396*** 1.396*** 1.320*** (0.41) (0.39) (0.39) (0.39) (0.39) Baseline effects D i ,−2∗Ii 0.164 0.133 0.133 0.133 0.133 (0.21) (0.20) (0.20) (0.20) (0.20) D i ,−1∗Ii 0.268 0.354 0.352 0.352 0.352 (0.26) (0.25) (0.25) (0.25) (0.25) Estimation method OLS OLS(FE) GLS(RE) GLS(RE) ML(ME) Mundlak terms – – – Yes Yes P value cum-ex effects 0.00 0.00 0.00 0.00 0.00 P value other days 0.02 0.00 0.00 0.00 0.00 Variances random effects Random effect D i ,−2∗I i ∗Ti – – – – 1.479 Random effect D i ,−1∗I i ∗Ti – – – – 3.986 Random intercept – – – – 4.101 1446 T.Buettner et al. 1 3 could result in biased estimates. In fact, the literature on trading around ex-dividend dates suggests that the volume of transactions might be positively related to the dividend yield (e.g., Karpoff and Walkling 1990; Michaely and Vila 1995; Haesner and Schanz 2013; Henry and Koski 2017). The literature also discusses the role of transaction costs for the trading volume around ex-dividend dates (e.g., Lakonishok and Vermaelen 1986; Karpoff and Walkling 1990; Haesner and Schanz 2013). As a robustness check, therefore, we introduce as an additional control variable the dividend yield of the respective event. Moreover, since the transaction cost might vary with this indicator, we also include the market capitalization of the respective stock (before the event). The dividend yield and market capitalization of the respective stock at the dividend event may also be related to the profitability, risks and costs associated with cum-ex trades. For instance, it seems possible that cum-ex trades are concentrated on high-dividend-yield events and on stocks with large market capitalization. Therefore, in the robustness checks, we also include interaction terms between these indicators and the cum-ex effects associated with the last 2 days before the ex-dividend date. The results of these robustness checks are provided in Appendix. Table A.3 reports the estimates of the interaction terms between the dividend yield and the two indicators capturing the cum-ex effects.30 While the results support a positive effect Fig. 5 Price/Drop Ratios, cum-ex period (2009–2011). Note The graphs depict kernel-based estimates of the distributions of PDRs of both stocks with taxable dividends (solid line) and withholding-tax-exempt dividends (dashed line) in the cum-ex period. Epanechnikov kernel densities 30 Note that we have scaled the dividend yield such that it captures the deviation from the sample average. 1447 1 3 Withholding-tax non-compliance: thecase ofcum-ex… of the interaction, the point estimates for the basic cum-ex effect turn out to be very similar to the above findings. TableA.3 reports the estimates of the interaction terms between the market capitalization and the two indicators capturing the cum-ex effects.31 Again, we find a positive effect of the interaction, but the point estimates for the basic cum-ex effect turn out to be very similar to the above findings. 6.4 Implied tax‑revenue loss To compute the implied magnitude of revenue losses, we use the point estimates of the parameters of Eq. (9) based on XETRA data. The tax-revenue loss in euros caused by cum-ex trading for a dividend event i is estimated according to: Table 3 Regression results: ex-dividend date price/drop ratios The dependent variable, PDi , is the drop in the stock price from the dividend date (day −1 ) to the ex-dividend date (day 0) in euros as reported in the XETRA data. The sample includes all dividend payments of German stocks that are constituents of the HDAX index between 2009 and 2015. Due to missing values not all 829 dividend events in the data are included. Dividends paid from current profits are subject to withholding tax (taxable dividend, Ii=1 ), dividends from capital reserves are tax exempt ( Ii=0 ). Ti is unity for dividend payments in the cum-ex period from January 2009 to December 2011 and zero in the post period from January 2012 to December 2015. P(Divi < 1) provides P values for testing whether the slope parameter for the dividend is less than 1. Regression coefficients result from OLS regressions (1) and OLS regressions with year dummies (2). Cluster-robust standard errors (clustered at the stock-level) are presented in parentheses. Asterisks denote statistical significance at the 0.01 (***) and 0.10 (*) levels (1) (2) Dividend, Divi 0.977*** (0.07) 0.994*** (0.07) Taxable dividend, Ii 0.159 (0.16) 0.172 (0.16) Cum-ex period, Ti −0.109* (0.06) 0.042 (0.19) Divi∗Ii∗Ti 0.001 (0.23) 0.031 (0.24) Divi∗Ti 0.236* (0.14) 0.206 (0.16) Divi∗Ii −0.175 (0.15) −0.192 (0.15) Ii∗Ti −0.211 (0.22) −0.235 (0.22) Constant −0.015 (0.04) −0.067 (0.15) P( Div i < 1) 0.350 0.466 N 811 811 31 We have scaled this indicator such that it measures the percent deviation from the average market capitalization based on the sample average. 1448 T.Buettner et al. 1 3 Ni,d is the observed number of stocks traded d days before the dividend event. Divi is the dividend (in euros) per stock associated with event i. 𝜏w is the withholding-tax rate of 26.4% levied on the dividend. If we allow for heterogeneity in cum-ex trading and incorporate event-specific cum-ex effects, the tax-revenue loss in euros caused by cum-ex trading on the 2 days prior to the ex-dividend date for the dividend event i is: For both measures of the revenue loss associated with a specific dividend event, the total tax loss from cum-ex trading in our sample of stocks that occurred during the cum-ex period is where the sum is taken over all dividend events with taxable dividends in the period between 2009 and 2011. If we rely on the random-effects estimates and use Eq.(11) to evaluate expression (13), we obtain a point estimate of the total tax-revenue loss based on XETRA trading activity of about 167 million euros between 2009 and 2011. Allowing for event-specific cum-ex effects by using Eq. (12), the predicted tax-revenue loss is estimated at about 640 million euros. This higher figure suggests that cum-ex trades focus on events with higher dividends and/or on stocks with a higher number of stocks traded. These estimates for the revenue losses are based on the empirical findings obtained using the XETRA data. The analysis of XETRA-OTC data also points to cum-ex effects on the number of stocks traded. Using the same methodology we can also compute the revenue losses associated with the cum-ex effects found in the XETRA-OTC data. Even though the effect on the number of stocks traded is found to be much stronger, the baseline number of stocks traded in this dataset is small. Hence, the predicted tax-revenue losses from cum-ex trading via OTC on the XETRA platform are roughly similar to the tax-revenue losses predicted for other types of trades on this platform. More specifically, the corresponding figures point to a loss of 274 million euros between 2009 and 2011, based on the random-effects estimates. If we employ the alternative method, which takes account of event-specific cum-ex effects, we obtain a figure suggesting that cum-ex trades using XETRAOTC amount to a tax-revenue loss of 445 million euros. Including XETRA-OTC our estimates point to a revenue loss of 1.085 billion euros. While XETRA data cover approximately 60% of the regular trading activity of German stocks (Gomber 2015), it is unlikely that our data also capture 60% of cum-ex trading. Since it might be much more prevalent on other platforms, the (11) Loss i= −1 ∑ d=−2 ( exp{  Ωd}−1 exp{ Ω d } ) ⋅Ni,d⋅𝜏w⋅Div i (12) Loss i= −1 ∑ d=−2 ( exp{  Ωd+  Ωd,i}−1 exp{ Ω d + Ω d,i } ) ⋅Ni,d⋅𝜏w⋅Div i (13) Total Loss = ∑ i Lossi ,