The impact of a financial transaction tax on stylized facts of price returns-Evidence from the lab.

As the introduction of financial transaction taxes is increasingly discussed by political leaders we explore possible consequences such taxes could have on markets. Here we examine how "stylized facts", namely fat tails and volatility clustering, are affected by different tax regimes in laboratory experiments. We find that leptokurtosis of price returns is highest and clustered volatility is weakest in unilaterally taxed markets (where tax havens exist). Instead, tails are slimmest and volatility clustering is strongest in tax havens. When an encompassing financial transaction tax is levied, stylized facts hardly change compared to a scenario with no tax on all markets.

Introduction

In the wake of the financial crisis of 2007–2009 and the European debt crisis since 2010 the debate over the introduction of financial transaction taxes (FTT, a Tobin tax being the most prominent example for foreign exchange markets) got new impulses and new supporters. Especially in the EU, where chancellor Angela Merkel of Germany is the most outspoken advocate, the implementation of such a tax has become far from unthinkable. Whenever such major changes to markets are seriously considered it seems prudent to explore – as far as possible – consequences this could cause in affected markets. In this paper we do this by means of laboratory experiments. By exposing human traders to markets that mimic the key elements of the markets under consideration, we try to capture the main consequences that could result from this tax regime change.

The idea of a FTT has gained popularity as an instrument to reduce speculation and stabilize financial markets especially since the seminal work of Tobin (1978). Its originally intended effects include a decrease in volatility and an increase in market efficiency, as speculators (noise traders) are forced to reduce trading frequency. Scientific research on the impact of FTTs has mainly started in the 1990s with contributions by e.g. Stiglitz (1989), Summers and Summers (1989), Schwert and Seguin (1993), Jones and Seguin (1997), Subrahmanyam (1998), Dow and Rahi (2000), and Baltagi et al. (2006). There is broad consensus in the literature on some issues such as negative effects of a FTT on trading volume and market shares of taxed markets (compared to untaxed ones). Empirically, the decrease in trading volume is usually quite substantial when a financial transaction tax is introduced.1 Other issues, notably price volatility and market efficiency are still controversially and hotly debated. In general, studies which use agent-based models with either boundedly rational agents (i.e., chartist/fundamentalist approach) or with zero-intelligence traders mainly report lower price volatility as a reaction to the imposition of a FTT (e.g., Westerhoff, 2003; Ehrenstein et al., 2005; Westerhoff and Dieci, 2006). Instead, empirical studies either look at historical examples of FTTs or indirectly measure FTTs as increased transaction costs. They mainly report no or a positive relationship of transaction costs and price volatility when different types of FTTs were imposed (e.g., Aliber et al., 2003; Hau, 2006).

The effects of FTTs have also been investigated in the laboratory. Hanke et al. (2010) report increased volatility in small unilaterally taxed markets when tax havens exist. Due to a shift in liquidity, volatility decreases in the tax haven at the same time. Kirchler et al. (2012) investigate the impact of market microstructure on the effects of FTTs.2 Similarly to Hanke et al. (2010) they observe that volatility increases in unilaterally taxed markets without market makers, whereas it decreases when market makers provide permanent liquidity in unilaterally taxed markets. Importantly, both experimental studies report that an encompassing Tobin tax has no impact on volatility and market efficiency compared to a regime with no tax. Recently, a comprehensive survey on the impact and feasibility of the Tobin tax and FTTs has been published by McCulloch and Pacillo (2011). They review related scientific contributions since the 1970s and conclude that a Tobin tax is feasible and would generate substantial revenues without causing major distortions to market efficiency and price volatility. The latter is unlikely to decrease and could even increase.

In this paper we extend the body of literature by focusing on another implication of a FTT which has not been investigated so far—the impact of a FTT on so called “stylized facts” of price returns. As mentioned, the introduction of a FTT has effects on market liquidity, trading volume and price returns. In financial markets the distribution of the latter usually displays excess kurtosis (“fat tails” or leptokurtosis) and the time series is heteroscedastic (“volatility clustering”). These stylized facts are universal to financial markets and have been found in laboratory experiments as well.3 As the implementation of a FTT has an impact on price returns, it is possible that stylized facts are affected as well.

To shed light on this issue we explore changes in leptokurtosis and volatility clustering in laboratory markets with different tax regimes. In each session two double auction markets for the same currency pair run simultaneously and a FTT is introduced in none, one, or both markets (i.e. no FTT on both markets; unilateral FTT, the other market being the tax haven; encompassing FTT). By using two simultaneously running markets we account for potential tax avoidance which allows us to analyze the impact of a FTT in unilaterally, and in comprehensively taxed markets, as well as in tax havens. Furthermore, we use two different microstructures that dominate real markets: (i) exchanges where market makers ensure permanent liquidity and (ii) over-the-counter markets where trading happens between individual parties without market makers. Some segments at real-world exchanges like at the CME and the LIFFE are examples of the former, while electronic trading platforms for currencies like EBS and Reuters3000 as well as the international money markets are examples of the latter. The choice of this specific setting is inspired by Pellizzari and Westerhoff (2009) which point out the high importance of market microstructure when a FTT is levied. If a FTT is imposed, they report a reduction in volatility in dealership markets where market makers provide permanent liquidity compared to a double-auction setting without market makers. Consequently, two treatments, Treatment “over the counter” () and Treatment “trading requirement” (), use the latter and Treatment “market maker” () is applied with the former market microstructure. There are no specific limitations or requirements to trade in Treatment , where each subject can post limit and market orders. With all other things being equal to Treatment half of the subjects have a trading requirement in Treatment , i.e. a minimum amount of trading they have to carry out in each period to avoid a penalty. Instead, in Treatment computerized market makers provide a constant liquidity flow, while human subjects can only post market orders, i.e. accept limit orders posted by market makers.

We find leptokurtosis of the distribution of returns under each tax regime. The following results hold for each treatment: (i) fat tails are largest and significantly larger in unilaterally taxed markets compared to most other tax regimes, while they are smallest in tax havens. Furthermore, (ii) we report clustered volatility under most tax regimes, most prominently in the tax havens. Instead, (iii) the autocorrelation function (ACF) of normalized absolute returns decays very quickly towards zero in unilaterally taxed markets, i.e. there are no volatility clusters in this tax regime. This finding is caused by the low trading frequency in unilaterally taxed markets since intervals of hectic trading, which are the main volatility clusters, almost never occur. Finally, (iv) we observe hardly any changes in leptokurtosis and volatility clustering when an encompassing FTT is applied in comparison to both markets being untaxed.

The importance of investigating price return distributions under different tax regimes is straightforward. For instance, the pricing of options and other structured products depends on the underlying distribution of returns. Fatter tails under a FTT mean more extreme tail events, e.g. large drops in asset prices. With extreme events becoming more likely options, similar derivatives and structured products that “insure” tail events, could become more expensive. Thus, we urge that any nation should tread carefully when contemplating the unilateral introduction of a FTT, as the costs for anyone trying to insure (with options and similar derivatives) would likely go up. A universal (encompassing) implementation of a FTT, however, would have hardly any negative effects on the fat tail and the volatility clustering property compared to the status quo. The latter implies that international coordination for implementing FTTs is a necessary condition to avoid distorting effects for the distribution of returns.

The remainder of the paper is structured as follows. Section 2 provides details on market design, experimental treatments, and experimental implementation. Section 3 outlines the econometric method. Section 4 presents the results from the experiments and Section 5 summarizes and concludes.

Design of the experiment

The framing we used for our experiments was trading in currencies (see instructions in Appendix), but it could be any asset. As a useful preliminary to understand the setup, we provide the following definitions: In this paper a phase is a sequence of five trading periods where a certain tax rate scenario is applied. Each market consists of two phases and is thus 10 periods long. A session consists of two markets (denoted LEFT and RIGHT and placed accordingly on the screen; see screenshots in Appendix), where traders can act on both markets simultaneously.4 A tax rate scenario defines when and on which markets within a session a two-way financial transaction tax (FTT) of 0.1% is implemented (possibilities: tax LEFT only; tax LEFT and RIGHT; no tax on both markets).5 Every treatment is associated with a specific market microstructure and within each treatment we model six different tax rate scenarios (see Table 1). We conduct two sessions of each tax rate scenario in Treatments and and four sessions in Treatment ).

Table 1

Tax rate scenarios within each treatment.

Tax rate scenario	Periods 1–5		Periods 6–10
	LEFT (%)	RIGHT (%)	LEFT (%)	RIGHT (%)
0L	–	–	0.1	–
02	–	–	0.1	0.1
L0	0.1	–	–	–
L2	0.1	–	0.1	0.1
20	0.1	0.1	–	–
2L	0.1	0.1	0.1	–

Entries show the two-way tax rate (0.1% for each side) for taxed markets, dashes indicate the absence of taxes.

Market setup

In each session a different cohort of 16 (Treatments and ) or 8 (Treatment ) human subjects trade currency A for currency B on two markets (LEFT and RIGHT). Both markets are displayed on the trading screen at the same time and traders can be active on both markets simultaneously. Buying a currency on one market and selling it on the other is possible, as is buying on both markets or selling on both markets.

The fundamental value of A (expressed in units of B) is modeled as a geometric Brownian motion without driftwhere is the fundamental value in period k and is a normally distributed random variable with a mean of zero and a standard deviation of 5%. is set to 60. We draw one fundamental value path randomly (path I) and its counterpart mirrored at the unconditional expected value of is used as path II. For each tax rate scenario in each treatment two (four in Treatment ) sessions are run, half with path I, the other with path II.

We use a symmetric information structure where at the beginning of each period each subject receives a private signal (SIGNAL) on the fundamental value of currency A. This signal is the plus a noise term with a mean of zero and a standard deviation of 2.5%. To ensure that “the market” has an unbiased estimate of the FV estimation errors cancel out across subjects in each period.6

Initial endowments are 75 A and 1500 B for half of the subjects and 25 A and 4500 B for the other half. Given an initial fundamental value of 60 B per A each trader's initial wealth equals 6000 B. The holdings in A and B are carried over from one period to the next and short positions are possible up to 100 (6000) units of A (B). No interest is paid in either currency.

On the trading screen subjects are continuously informed about all open limit orders, their own holdings of both currencies, their trades in the current period, and their wealth. The latter is calculated as the sum of their B holdings and the value of their A holdings. A real-time chart provides subjects with the development of prices of both markets.

Each trading period ends after 4 min. Then subjects receive a summary of the trading activities of all previous periods in a “history screen” which is displayed for 10 s. It contains information on the closing prices, individual and total trading volumes and the amount of taxes paid in currency B (only if applicable) for each market. Furthermore, the holdings of A and B, trader's wealth, his estimate of the fundamental value (SIGNAL) and a chart of mean market prices of both markets are displayed (see screenshots in Appendix for more details).

Experimental procedure

Before trading starts subjects have 15 min to read written instructions. Questions are answered privately. Then the trading screen is explained and two trial periods are conducted which have no influence on the final payment. To avoid strategic behavior towards the end of the experiment, subjects are told that the experiment will end between periods 8 and 14 with equal probability.

Tax rate scenarios

Table 1 presents the tax rate scenarios used in each of the three treatments. The tax rate scenarios differ with respect to when and on which markets a (two-way) FTT of 0.1% of the transaction value (units of A traded multiplied by price in B) is levied.

In particular, each session consists of two phases of five periods each where a different tax rate scenario is implemented in each phase. Hence, the treatment abbreviations in Table 1 are to be read as follows: the numbers “0” and “2” specify whether no market (“0”) or both markets (“2”) are taxed. When only one market is taxed, we chose to tax only the left market (“L”) to reduce the number of possible scenarios. In this case the right market is referred to as tax haven. For instance, under tax rate scenario 2L the tax is introduced on both markets in the first five periods, but is levied only on the LEFT market in periods 6–10.7 Before the beginning of the first and the sixth period subjects are informed about the imposition of a tax with an announcement screen. This screen explains in detail which markets are taxed and provides a calculation example for taxation. Subjects do not get any information about the potential implementation of transaction taxes before the main experiment starts and they are not informed whether and when the tax regime is changed again. Once introduced, the tax rate is also placed on the trading screen.

Experimental treatments

In total we ran 48 sessions; 12 each of Treatments and with 16 human subjects each, and 24 sessions of Treatment , each with 8 humans and 2 computerized agents.8 This results in 96 markets in total (one LEFT and one RIGHT market in each session). All 576 subjects were business or economics students at the University of Innsbruck, recruited with ORSEE (Greiner, 2004).9 Sessions were computerized (using zTree 3.2.8 by Fischbacher, 2007) and lasted about 90 min.

Treatment 1: over-the-counter—

Subjects trade in a continuous double auction market and can post limit and market orders. Limit orders (bids and asks) are executed according to price and then time priority.10 Market orders have priority over limit orders and are always executed instantaneously.11 The order books are open which means that limit orders are visible to all subjects at the same time. Any order size and the partial execution of limit orders is possible as long as the endowments in A and B are above −100 and −6000, respectively. The cancellation of orders is not possible. Order books are emptied, i.e. all orders deleted, before the beginning of a new period. All this is public knowledge.

Treatment 2: trading requirements—

The market setup of Treatment is an exact replication of Treatment with the only difference that eight of the 16 traders have a trading requirement of 1000 units of B (roughly 17% of their initial wealth) per period. Four of the traders have to fulfill this volume requirement on the LEFT market, the other four on the RIGHT market. If a trader does not fulfill his trading requirement in a given period a penalty of 500 B was deducted from his account. The remaining eight traders have no trading requirement. With this treatment we capture the real-world situation that some traders cannot freely switch between FX-markets or have to trade for bona-fide commercial reasons. Both treatments, and , mimic real-world FX trading platforms like EBS and Reuters3000.

Treatment 3: market makers–

There are no trading requirements in Treatment , but this treatment deviates from Treatment in one crucial aspect: all limit orders are provided by artificial market makers. Subjects can thus only place market orders, i.e. accept limit orders set by the market makers. To achieve a constant liquidity inflow we implement one computerized market maker in each market (similar to Pellizzari and Westerhoff, 2009).12 Every several seconds (see process and parameters below) a market maker places both a bid and an ask at time t

Here denotes the last transaction price at time t in period k and is the absolute value of a standard normally distributed random variable. With this setting, market makers react to changes in demand and supply by human traders. For instance, if prices go up (through excess demand), market makers increase their bids and asks. Note that market makers do not process any fundamental information. Thus price levels and market efficiency are driven only by the actions of the human subjects. In real markets market makers usually try to keep their long- and short-positions balanced, i.e. have a net exposure of zero. We therefore add a parameter to ensure that the market maker has a tendency to keep his net holdings in A close to his initial endowment of zero. is calculated as with denoting the holdings in currency A at time t of period k.13 To achieve comparability to the other two treatments, the parameters of the market makers are derived from Treatment .14 With this treatment we mimic trading on market maker driven markets like in some segments of the CME and LIFFE.

Econometric method

To avoid idiosyncratic effects of individual sessions we follow the approach of Plerou et al. (1999) and Kirchler and Huber (2009) by normalizing log-returns (). First we calculate the log-returns,where m indicates market and i stands for the individual transaction (tick). In a next step we normalize the log-returns by their mean () and standard deviation () in each session s

Consequently, this normalization of returns (normalized returns, ) and of absolute returns (normalized absolute returns, ) allows pooling data of different markets (see the discussion in Plerou et al., 1999).

As excess kurtosis of the distribution of returns (absolute returns) is an ambiguous concept, it is common practice to calculate exponents of empirical power laws as measures for the “fatness” of tails (see Hill, 1975). In the applied economics literature the tail exponent for the 10%, 5%, and 2.5% tail of the distribution of absolute returns are usually calculated. To arrive at these Hill estimators the returns have to be put in descending order and the last x% are selected as the “x% tail”

Eq. (6) outlines the formula for computing the Hill estimator with m being the number of observations located in the corresponding tail of the distribution, j indicating observations of the tail, and n representing the total number of absolute returns. One can see that the lower the tail exponent , the fatter are the tails of the distribution.

Volatility clustering, the heteroscedasticity of a distribution, is measured and depicted by the autocorrelation function (ACF) of absolute returns. Persistent positive ACF points to volatility clustering, while a quick decay of the ACF to zero shows the absence of volatility clusters.

To arrive at statistical results for testing the fat-tail and volatility clustering properties of returns, we set up the following panel regression model:

Here, is a generic placeholder for the dependent variables, m indicates cross-section (market) and p phase (sequence of five consecutive periods in which a certain tax regime is applied). equals 1 when both markets are taxed, zero otherwise. defines unilaterally taxed markets with the other market being untaxed and is a binary dummy for the untaxed market when the other market is taxed. With Wald-coefficient tests we measure differences between the coefficients (tax regimes). We apply clustered standard errors on a session level to allow for correlation within sessions and independence of observations between sessions. As main dependent variables the Hill Estimator for the 10%-tail () and the coefficients of the autocorrelation function (ACF) of normalized absolute returns () for each market m and phase p are used. We refrain from estimating Eq. (7) with the Hill estimators of the 5% and 2.5% tail, since sample size in individual markets, especially under tax regime is too small.

Results

To provide a first idea of return dynamics Fig. 1 gives an overview over the development of normalized returns as a function of trading time for three representative sessions of the “L2”-type. One can see more pronounced clusters of volatility when an encompassing FTT is applied (i.e., in the second half of each market) and in the tax haven (i.e., market RIGHT in the first half of each market). Instead, hardly any clusters in volatility are visible in unilaterally taxed markets (i.e., market LEFT in the first half of each market).

Fig. 1

Normalized returns as a function of trading time (in s) of representative sessions (“L2”: in market LEFT until period 6 followed by until the end of the experiment) in treatments (top left), (top right), and (bottom).

Leptokurtosis

To test whether normalized returns are distributed Gaussian in each market and phase, we run both the Kolmogorov–Smirnov and the Jarque–Bera test. For each subsample we reject the null hypothesis of Gaussian-distributed normalized returns on the 1%-level with both tests.

To provide a visual impression of the impact of tax regime on the distribution of price changes, Fig. 2 plots the empirical cumulative distribution function (ECDF) of normalized absolute returns () for each tax regime of the aggregate data set.15 One can see large outliers under each tax regime, as the probability of large price changes in the experiments is much higher than would be expected by a normal distribution with same mean and standard deviation (solid line). Importantly, a FTT has a strong impact on the fatness of the tails of the distribution. Unilaterally taxed markets (bottom left) exhibit much fatter tails than markets under the other tax regimes. It is also worth mentioning that this pattern holds for each treatment separately.16

Fig. 2

Empirical cumulative distribution function (ECDF) of normalized absolute returns of the four tax regimes. The dots represent the ECDF and the solid lines approximate a normal distribution with same mean and variance. Tax regimes: : both markets untaxed; : this market taxed, but other market untaxed; : both markets taxed; : this market untaxed, but other market taxed. For better clarity the graphs only show the tails of the distribution (plots in Appendix provide the entire distribution).

Additionally, Fig. 3 shows the average Hill estimator of the 10% tail of normalized absolute returns for each treatment and tax regime (HILL_10). To arrive at these values, the mean of the individual observations of each market and phase is calculated. One can see that the average Hill estimators range from 2.3 to 4.3. There is also a clear tendency of tails being fattest in unilaterally taxed markets and of tails being thinnest in tax havens. These estimates, with lower values denoting fatter tails, are perfectly in line with empirically observed data which provide values between 2 and 6 (see Voit, 2003).

Fig. 3

Averages of the 10% Hill Estimator for each treatment and tax regime. Tax regimes: : both markets untaxed; : this market taxed, but other market untaxed; : both markets taxed; : this market untaxed, but other market taxed.

Table 2 shows the statistical tests according to Eq. (7).17 On aggregate, tails are fattest in unilaterally taxed markets () and significantly larger compared to both the tax haven () and when both markets are untaxed (). While the effect is strongest in Treatment , it is also evident in the other treatments.18

Table 2

Panel regression for the 10% tail of the Hill estimator ().

	Aggregate	OTC	TR	MM
FTT_unilateral	−0.442⁎⁎ (−2.063)	−0.340 (−0.584)	−0.192 (−0.387)	−0.608⁎⁎⁎ (−2.721)
FTT_encompassing	−0.175 (−0.954)	−0.020 (−0.041)	−0.262 (−0.819)	−0.201 (−0.950)
Tax_haven	0.460 (0.958)	1.664 (0.914)	0.417 (0.955)	−0.116 (−0.542)
c	2.931⁎⁎⁎ (22.715)	2.662⁎⁎⁎ (8.491)	2.689⁎⁎⁎ (9.847)	3.180⁎⁎⁎ (22.925)
N	192	48	48	96

Top panel. Independent variables: , this market taxed, but other market untaxed; , both markets taxed; , this market untaxed, but other market taxed. t-Values of a double-sided test are given in parentheses. Clustered standard errors to allow for correlation within sessions and independence of observations between sessions are applied (“vce (cluster varname)” method in STATA).

⁎, ⁎⁎ and ⁎⁎⁎ represent the 10%, 5% and the 1% significance levels.

Bottom panel. Pairwise Wald-tests: Chi2-values and p-values (in parenthesis) are provided.

The reason for the very fat tails in unilaterally taxed markets in Treatments and is that human subjects post fewer limit orders and that volume is very low which makes large price changes (outliers) more likely. Table 3 provides evidence on this liquidity and volume issue by using the same panel regression methodology as in Eq. (7) for the number of limit orders posted () and for trading volume (). While there are no differences in in Treatment where the computerized market makers post limit orders irrespective of tax regimes, we see clear effects, i.e. significantly fewer limit orders in unilaterally taxed markets of Treatments and compared to both markets being untaxed (−47% and −30%, respectively). Consequently, is lowest in unilaterally taxed markets and highest in the tax haven in both treatments. Therefore, in Treatments and price outliers happen more easily under tax regime which drives the value of the Hill Estimator down.

Table 3

Panel regression for limit orders (; top panel) and trading volume (; bottom panel).

	Aggregate	OTC	TR	MM
LO
FTT_unilateral	−41⁎⁎⁎ (−4.513)	−90⁎⁎⁎ (−6.302)	−59⁎⁎⁎ (−6.421)	−10 (−1.069)
FTT_encompassing	3 (0.515)	5 (0.389)	7 (0.568)	1 (0.143)
Tax_haven	28⁎⁎⁎ (2.966)	77⁎⁎⁎ (6.517)	58⁎⁎⁎ (4.918)	−7 (−0.682)
c	292⁎⁎⁎ (19.775)	190⁎⁎⁎ (37.210)	200⁎⁎⁎ (22.008)	389⁎⁎⁎ (93.426)
N	192	48	48	96
VOLUME
FTT_unilateral	−334⁎⁎⁎ (−5.597)	−498⁎⁎⁎ (−3.133)	−318⁎⁎⁎ (−3.441)	−259⁎⁎⁎ (−3.875)
FTT_encompassing	−39 (−0.547)	77 (0.362)	−17 (−0.138)	−110 (−1.522)
Tax_haven	267⁎⁎⁎ (3.796)	563⁎⁎⁎ (4.360)	465⁎⁎⁎ (3.344)	22 (0.330)
c	807⁎⁎⁎ (16.028)	820⁎⁎⁎ (7.337)	943⁎⁎⁎ (8.571)	733⁎⁎⁎(11.377)
N	192	48	48	96

Independent variables: , this market taxed, but other market untaxed; , both markets taxed; , this market untaxed, but other market taxed. t-Values of a double-sided test are given in parentheses. Clustered standard errors to allow for correlation within sessions and independence of observations between sessions are applied (“vce (cluster varname)” method in STATA).

⁎, ⁎⁎ and ⁎⁎⁎ represent the 10%, 5% and the 1% significance levels.

In Treatment the reason for the fatter tails in unilaterally taxed markets is different: while we also observe significantly fewer transactions, volatility measured by the standard deviation of normalized absolute returns is lowest which is in contrast to the other treatments. Market makers keep liquidity constant and, as fewer limit orders are accepted due to the unilateral imposition of the tax, order books become highly liquid. Hence, the price impact of market orders is reduced as gaps between limit orders are narrowed. In the bottom panel of Fig. 4 the lower volatility under in Treatment is evident as a lower mean, median, and standard deviation of normalized absolute returns.19 We further observe that the share of returns of zero (i.e. unchanged prices) among all returns in unilaterally taxed markets in Treatment is 26.5% and thus higher than in any other tax regime. While the lower overall volatility level is evident, the ratio of standard deviation to the mean of normalized absolute returns is 1.5 in unilaterally taxed markets, compared to 1.2 in the other three tax regimes. Thus, in addition to more low and zero-returns we also observe relatively more outliers (which drives up standard deviation) in unilaterally taxed markets than in any other tax regime of Treatment .20

Fig. 4

Mean, standard deviation, and median of normalized absolute returns conditional on tax regime and treatment. Tax regimes: : both markets untaxed; : this market taxed, but other market untaxed; : both markets taxed; : this market untaxed, but other market taxed.

Volatility clustering

To explore the extent of volatility clustering in a market it is the established method to look at the autocorrelation function of absolute returns, as persistent positive correlations hint at clusters in volatility. In a first step, the ACF-coefficient of normalized absolute returns for lag l and market phase p of market m is calculated. Then, to arrive at , we compute the mean coefficient value for each tax regime and lag l.

Fig. 5 provides a graphical overview of volatility clustering on aggregate and for each treatment separately by showing the autocorrelation function (ACF) of normalized absolute returns () conditional on tax regime. Additionally, Table 4 presents statistical tests according to Eq. (7).21 On aggregate, one can see a clear pattern of volatility clustering being strongest in the tax havens (). Compared to other tax regimes the ACF of normalized absolute returns is highest for each lag and decays only from 0.27 at lag one to 0.08 at lag ten. The second- and third-highest autocorrelations at each lag are present when both markets are untaxed () and in markets with an encompassing FTT (), respectively. In contrast to the tax havens, the ACF of unilaterally taxed markets () quickly decays and is significantly smaller than the ACF of most of the other tax regimes at each lag. We attribute this again to the lowered trading frequency in unilaterally taxed markets in all treatments: with fewer transactions times of hectic trading with several transactions per second, which are the main volatility clusters in our markets, almost never occur and thus autocorrelation of absolute returns is much lower.22 The regressions for limit orders () and trading volume () in Table 3 and the analysis of the average waiting time between consecutive trades (WTT) per phase p corroborate this line of argumentation. With an average WTT of 13.5 s trading frequency is very low in unilaterally taxed markets compared to tax havens with an average WTT of 4.9 s. Unsurprisingly, the WTT of tax regimes (7.6) and (6.5) are in between.23

Fig. 5

Autocorrelation function (ACF) of normalized absolute returns for the aggregate data (top left) and for each treatment separately. Tax regimes: : both markets untaxed; : this market taxed, but other market untaxed; : both markets taxed; : this market untaxed, but other market taxed.

Table 4

Panel regression of the autocorrelation function (ACF) of normalized absolute returns () for lags 1–5 of the aggregate data set.

	lag 1	lag 2	lag 3	lag 4	lag 5
FTT_unilateral	−0.005 (−0.121)	−0.075⁎⁎⁎ (−2.802)	−0.097⁎⁎⁎ (−4.027)	−0.054⁎⁎ (−2.527)	−0.016 (−0.568)
FTT_encompassing	−0.004 (−0.161)	−0.015 (−0.744)	−0.021 (−1.030)	−0.032⁎⁎ (−2.167)	−0.015 (−0.937)
Tax_haven	0.050⁎ (1.958)	0.032 (1.113)	0.032 (1.269)	0.065⁎⁎⁎ (2.799)	0.076⁎⁎⁎ (3.085)
c	0.216⁎⁎⁎ (12.428)	0.156⁎⁎⁎ (11.641)	0.125⁎⁎⁎ (8.213)	0.098⁎⁎⁎ (8.191)	0.084⁎⁎⁎ (5.863)
N	185	185	185	185	185

Top panel. Independent variables: , this market taxed, but other market untaxed; , both markets taxed; , this market untaxed, but other market taxed. t-values of a double-sided test are given in parentheses. Clustered standard errors to allow for correlation within sessions and independence of observations between sessions are applied (“vce(cluster varname)” method in STATA).

⁎, ⁎⁎ and ⁎⁎⁎ represent the 10%, 5% and the 1% significance levels.

Bottom panel. Pairwise Wald-Tests: Chi2-values and p-values (in parenthesis) are provided.

Conclusion

In this paper we have presented data from laboratory experiments to study the impact of a financial transaction tax (FTT) on stylized facts of price returns. In particular, a FTT was introduced in none, one or both of two simultaneously running double auction markets for the same currency pair. We set up three treatments to get a broader picture of differences between tax regimes in different market microstructures with different parameters.

We found that the distribution of normalized absolute returns is fat-tailed under each tax regime. The following results hold for each treatment separately: (i) fat tails were largest and significantly bigger in unilaterally taxed markets compared to most other tax regimes. As usually observed in real-world markets we also found clustered volatility in untaxed markets and in markets with an encompassing FTT, while the clusters disappeared in unilaterally taxed markets. In particular, (ii) tax havens showed the strongest volatility clusters since the autocorrelation function (ACF) was highest at each lag compared to the other tax regimes. In contrast, (iii) the ACF of normalized absolute returns decayed very quickly towards zero in unilaterally taxed markets in each treatment. This finding can be attributed to the low trading frequency in unilaterally taxed markets, since times of hectic trading, which are the main volatility clusters in our markets, almost never occur. Notably, (iv) we observed hardly any changes in both variables when an encompassing FTT was applied compared to both markets being untaxed.

To address the question whether human behavior or the market microstructure (or a combination of both) causes these differences in stylized facts is difficult with this setting (see Bottazzi et al., 2006; Anufriev and Panchenko, 2009 for related studies). However, we observe very similar dynamics in stylized facts conditional on tax regime across different market microstructures. Therefore we indirectly infer that human behavior mainly drives the results, as they react similarly to tax regimes irrespective of the market microstructure applied.

The results presented here are not only relevant for scientists, interested in specific statistical properties of returns. Especially investors, regulators, and politicians should also care: Fatter tails under a FTT mean more extreme tail events, e.g. large drops in asset prices. A measure for the fatness of tails should thus be a key variable in risk management and changes of this variable should be taken into account by risk managers and regulators. Similarly, the pricing of options and structured products depends on the underlying distribution of returns. With extreme events becoming more likely options, similar derivatives and structured products that “insure” tail events, become more expensive. Volatility clustering, though sometimes considered “bad” when right in the middle of such a cluster, allows to predict future volatility to a certain (small) degree. The lack of volatility clusters – as evident in our unilaterally taxed markets – thus means that financial professionals lose the little forecasting power they had with respect to volatility. Thus, we urge that any nation should tread carefully when contemplating the unilateral introduction of a FTT, as the costs for anyone trying to insure (with options and similar derivatives) would likely go up, while predictability of future volatility, small as it was, would decrease. Instead, a universal (encompassing) implementation of a FTT would have hardly any negative effects on the fat tail and the volatility clustering property compared to the current status quo. The latter implies that international coordination for implementing FTTs is a necessary condition to avoid distorting effects for the distribution of returns.

Table A1

Robustness check for the fat tail property of normalized absolute returns: Pairwise Mann–Whitney U-tests for the 10% tail of the Hill estimator ().

	FTT_unilateral	FTT_encompassing	Tax_haven
Aggregate
no_FTT	2.145⁎⁎ (0.032)	0.586 (0.558)	−1.034 (0.301)
FTT_unilateral		−1.718⁎ (0.086)	−2.672⁎⁎⁎ (0.008)
FTT_encompassing			−1.710⁎ (0.087)
OTC
no_FTT	0.857 (0.391)	0.000 (1.000)	−0.551 (0.582)
FTT_unilateral		−0.612 (0.540)	−1.050 (0.294)
FTT_encompassing			−0.674 (0.500)
TR
no_FTT	0.919 (0.358)	0.754 (0.451)	−0.857 (0.391)
FTT_unilateral		−0.429 (0.668)	−1.365 (0.172)
FTT_encompassing			−1.531 (0.126)
MM
no_FTT	2.296⁎⁎ (0.022)	0.524 (0.601)	−0.372 (0.710)
FTT_unilateral		−1.903⁎ (0.057)	−2.450⁎⁎ (0.014)
FTT_encompassing			−1.094 (0.274)

⁎, ⁎⁎ and ⁎⁎⁎ represent the 10%, 5% and the 1% significance levels.

The numbers represent z-values and p-values (in parenthesis) of a double-sided Mann–Whitney U-test.