Taxing financial transactions in fundamentally heterogeneous markets

Economic Modelling 64 (2017) 322–333

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Economic Modelling journal homepage: www.elsevier.com/locate/econmod

Taxing financial transactions in fundamentally heterogeneous markets☆ a,⁎

Edoardo Gaffeo , Massimo Molinari a b

MARK

b

Department of Economics and Management, University of Trento, Via Inama 5, I-38100, Trento, Italy Department of Economics, University of Roma Tre, Italy

A R T I C L E I N F O

A BS T RAC T

JEL classification: C63 D53 G18

The recent global financial crisis has revived a long-standing debate on the desirability and feasibility of taxing financial activities to curb speculation and promote price stability. In this paper we apply agent-based computational techniques to explore this issue in a multi-market environment in which the processes driving the fundamental value of the securities traded in different jurisdictions are heterogeneous. A natural exemplification is to assume that security dealers have the opportunity to submit orders by choosing among stock markets at different stages of development. We argue that the proper policy objective to be pursued is not volatility in itself but price efficiency, that is, the volatility in excess of the discounted stream of subsequent dividends. In this case, a global coordination of tax rates is incentive-compatible, given that it minimizes the distortion associated with speculative trading, on the one hand, and it ensures that the loss of trading volume is lower if compared to the case of unilateral taxation on the other. Notwithstanding a fundamental heterogeneity of the markets involved, the optimal tax rate turns out to be symmetric provided that fundamental value trajectories are positively correlated.

Keywords: Agent-based models Financial transaction tax Heterogeneous traders

1. Introduction A key by-product of the 2007-08 global financial turmoil has been a profound rethinking of the set of policy responses that need to be deployed to curb systemic instability. Implicitly assuming that the stunning volatility and skyrocketing trading volume currently observed in securities markets might be the flip side of a disproportionate accumulation of risk by traders, in September 2009 the G-20 leaders brought back into the spotlight a renowned proposal long ago advanced by Keynes (1936) and Tobin (1972, 1978): to limit short-term speculative activities by means of Financial Transaction Taxes (FTTs) (IMF, 2010). Rephrasing Tobin, this amounts to throwing a few grains of sand in the well-greased wheel of financial markets, with the aim of constraining the negative impact that speculation exerts on systemic risk. Although the idea of taxing financial transactions has been extensively applied all around the world since the 1980s (Matheson, 2011), mixed evidence on the actual ability of FTTs to contain market volatility1 has spurred a highly animated debate. The long-standing stalemate experienced by EU governments in finalizing a harmonized

regional levy on financial transactions is paradigmatic of the objections commonly raised against this scheme, as well as of the major hindrances encountered on the road to an effective international coordination in its application (Kitromilides and Gonzáles, 2013).2 Critics argue that a FTT is disproportionately costly to administer; leads to a hazardous drop of transaction volume and market liquidity; slows down price discovery; and, as a final drawback, shrinks efficiency. Last but not least, any attempt to impose unilaterally a levy on domestic financial transactions in a world where capital can flow freely across borders will redirect buying and selling activities towards jurisdictions where exchanges are taxed at a lower rate, if at all. All these potential drawbacks were fully acknowledged by the original proposers of FTTs. In particular, Tobin (1972, 1978) suggested that any feasible international arrangement aimed at imposing an effective FTT should foresee the use of a (tiny) uniform tax rate, a position that we dub the Tobin conjecture since a formal proof of its validity is still lacking. Besides easing agreements by allowing negotiators to reason on a single number, the conjecture maintains that a common tax rate would yield the key benefit of sterilizing the crosscountry negative spillovers associated with the tax. Is this belief

☆ The authors gratefully acknowledge, without implications, excellent research assistance by Alessandro Asioli and helpful comments by Luca Riccetti, Roberto Tamborini and two anonymous referees. ⁎ Corresponding author. E-mail address: edoardo.gaff[email protected] (E. Gaffeo). 1 See Baltagi et al. (2006) and Hau (2006). 2 For an overview on the current state of the debate among EU members, see “Eurozone Financial Transaction Tax Plan Stalls, Says Minister” (http://www.wsj.com/articles/eurozonefinancial-transaction-tax-plan-stalls-says-minister-1457606638; last accessed on December 10th, 2016).

http://dx.doi.org/10.1016/j.econmod.2017.04.003 Received 11 July 2016; Received in revised form 4 April 2017; Accepted 5 April 2017 0264-9993/ © 2017 Elsevier B.V. All rights reserved.

Economic Modelling 64 (2017) 322–333

E. Gaffeo, M. Molinari

are positively correlated. This requirement for the Tobin conjecture to hold true is far from being restrictive in practical terms, given that it is fully consistent with the evidence showing that news affecting fundamentals on pivotal markets (like those of the U.S. and Japan) is transmitted, albeit with varying responses, even to geographically distant jurisdictions (Wongswan, 2006, 2009; Hausman and Wongswan, 2011). When a coordinated tax scheme is applied, the endogenous evolution of trading strategies across the population of agents generates a concave relationship between tax rates and market efficiency directly related to the market share of investors adopting fundamental forecasting rules. In fact, an international coordination in setting a common tax rate enables participants to achieve two results simultaneously: i) increase market efficiency globally; ii) individually maximize tax revenues in comparison to the case of a unilateral imposition. This implies that coordinating on a symmetric tax rate is an incentive-compatible solution even for heterogeneous jurisdictions as soon as information on fundamentals originating in one market is important for other markets. The rest of the paper is organized as follows. Section 2 presents the analytical structure of our modeling approach. Section 3 sets out simulation results showing the model's degree of accuracy in capturing several stylized facts of real financial markets, and an assessment of how alternative assumptions on the dynamics of the fundamental affects market outcomes. Section 4 studies the impact of FTTs in a multi-market fundamentally heterogeneous environment. Section 5 concludes.

confirmed when asset markets are structurally heterogeneous, so that the same tax rate can exert different impacts on asset valuation and trading volume? Our question is motivated by results recently emerged in two distinct streams of literature. First, a large body of econometric evidence has shown that international markets are indeed characterized by diverse dynamics due to differences in the speed with which news is incorporated into the present value of subsequent dividends (Andersen et al., 2007), informational efficiency (Griffin et al., 2010), risk-return profiles at different stages of development (Kohers et al., 2006), or the degree of macroeconomic volatility (Easterly et al., 2001). Second, research conducted with experimental methods has highlighted that alternative assumptions on the time path of the fundamental value of an asset generate significant differences in the degree of mispricing (Breaban and Noussair, 2014; Stöckl et al., 2015). A combined appraisal of these findings supports the view that any attempt to validate the Tobin conjecture should seriously take into account that international financial markets are characterized by a significant heterogeneity in the time path of intrinsic asset values, and that this heterogeneity is likely to have serious implications as regards market efficiency for any given tax rate. In order to address this issue, in what follows we employ agentbased modeling techniques. These involve simulating on a computer the dynamics of a stock market populated by a large number of interacting heterogeneous artificial traders (Hommes, 2006; LeBaron, 2006). Since these models are able to replicate many of the stylized facts characterizing financial market data with parsimonious analytical structures, the basic idea consists in using them as computer-based laboratories to conduct policy experiments, where alternative assumptions on trading strategies and market protocols can be tested in a controlled environment. Several papers have already applied this approach to assess the impact of FTTs on asset market outcomes,3 yielding three main conclusions. First, in a market in which traders can endogenously switch between technical and fundamental trading rules or remain entirely idle, the imposition of a FTT causes a reduction in volatility that depends on the proportion of chartists retreating from trading or switching to a fundamentalist strategy. Second, the drop in volatility is associated with the liquidity secured by the market microstructure, since liquidity is inversely related to the price responsiveness of any given order. Third, when agents are allowed to operate in several interconnected markets, unilaterally introducing a tax generates a negative spillover, in that the taxed market is stabilized at the expense of an increased volatility on the untaxed ones. Building on a prototypical small-type agent-based asset market model, the main novelty of this paper is that it studies how efficient price discovery is affected by alternative assumptions on the stochastic process driving the intrinsic value of the asset. In particular, we will admit the possibility that the fundamental value of the securities exchanged in different markets may vary along two dimensions: i) the speed with which any news is incorporated into intrinsic values; ii) the efficiency with which the additional items of information are priced in. Contrary to the received wisdom from the bounded rational heterogeneous agent literature (see e.g. Westerhoff, 2010), we show that price efficiency is significantly affected by the path of the fundamental, a result that corroborates the experimental evidence obtained in laboratory asset markets with distinct fundamental value regimes. Our augmented model is then used to test the Tobin conjecture. We find that the strategy of levying symmetric FTT rates is indeed optimal even after cross-market structural heterogeneity is taken into account, provided that the time paths for the fundamentals

2. The market environment The rationale for levying a Pigouvian tax on financial transactions must be grounded on some sort of market inefficiency. Observed price volatility in itself is not a sufficient argument, given that it may represent the optimal response of rational traders to news about the intrinsic value of the underlying asset. If this were the case, the main prescriptions of the efficient market hypothesis (EMH) would be entirely fulfilled and the tax would be merely distortionary. Since the pioneering work of Shiller (1981), however, a huge amount of empirical evidence has persuasively shown that stock prices move too much to be justified by subsequent changes in dividends; a feature which is today universally known as excess volatility. Accordingly, the proper purpose of FTTs should be to shrink the price volatility in excess of that associated with the path of the fundamental value. Fig. 1, taken from the background paper issued by the Economic Sciences Prize Committee of the Royal Swedish Academy of Sciences (2013) to celebrate the award of the Nobel Prize to Shiller himself, clearly illustrates the point. The solid line p traces the evolution of the S & P Composite Stock Price Index over the period 1871–1979, expressed in real terms and detrended by means of a long-run exponential growth factor. The dotted line p* is the present value of actual subsequent real detrended dividends, representing the optimal price forecast. The distance between the two lines is therefore a measure of the extent to which the market violates the EMH or, to put it differently, the degree of market inefficiency. It appears that the actual price dynamic is characterized by (i) severe bubbles and crashes with respect to its fundamental value, (ii) a slowly mean-reverting pattern, (iii) an underlying fundamental that varies as well, although at a much lower frequency. A persuasive explanation of the first two features – boom-and-bust dynamics and slow mean-reversion – can be obtained by means of an agent-based asset pricing model in which traders are allowed to switch among heterogeneous strategies from one trading period to the next. In a typical 2-type agent-based model, for instance, each trader can choose between a fundamentalist forecasting rule, according to which asset prices are expected to return to their fundamental value, and a chartist forecasting rule based on the assumption that prices move in trends. The probability of fundamental traders switching to technical

3 Key contributions are Westerhoff (2003), Ehrenstein et al. (2005), Westerhoff and Dieci (2006), Mannaro et al. (2008), Pellizzari and Westerhoff (2009), Demary (2010) and Fricke and Lux (2015).

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allowed to submit buy or sell orders for I marketable risky securities traded on as many separated markets. While orders can be submitted at most in one market at a time, roaming among markets from one trading period to the next is assumed to occur costlessly. Information on the fundamental values of the I risky assets is publicly available. Agents, however, have diverse beliefs on how useful these items of information are. In particular, after deciding the market in which s/he wants to operate, each trader can submit orders according to two different trading strategies – i.e. a fundamental rule predicting that the market price will eventually converge towards its fundamental, or a chartist rule exploiting price trends – or remain entirely idle. This implies that before a trading session starts the number of options available to each trader is (2I+1). The I prices registered after all orders have been executed define the profit obtained by each trader, who is now allowed to update his/her choices regarding both the market to visit and the trading strategy to follow during the subsequent periods. Operationally, in each market i∈I the net demand for the risky asset expressed by fundamentalists and chartists is given by: Fig. 1. Real stock prices and present value of subsequent dividends. Annual data for the S & P Composite Price Index over the time span 1871–1979.

trading (and vice-versa) depends adaptively on the relative profitability that it secures. Although the EMH maintains that chartist strategies should not be profitable, and therefore bound to disappear very quickly, this is not necessarily true if the market is driven away from an efficient equilibrium for a significant amount of time. To understand why, suppose that in a given trading period a large number of traders adopt a chartist forecasting strategy. As the price increases due to the excess demand, being a chartist turns out to be increasingly profitable. It may then be rational for a fundamentalist to follow suit and become a chartist too, so that the chartists’ expectations may generate a selffulfilling prophecy in the form of a speculative bubble. As the price moves significantly away from its fundamental value, however, the prospective attractiveness of adopting a fundamentalist strategy increases, eventually leading to a mean-reverting market movement. With regard to the exogenous process forcing the evolution of the fundamental, the existing literature has to date considered only two alternatives – a constant value and a random walk – concluding that market outcomes remain basically unaffected as the modeler switches from one option to the other (Westerhoff, 2010). Inspired by this finding, all available extensions to a multi-market framework have invariably assumed that traders can post orders in two or more separate markets sharing a common fixed fundamental. The value added of this paper consists precisely in relaxing this assumption. This will serve two purposes. We shall first provide a detailed examination of how the volatility of the underlying fundamental impacts on the statistical features of observed market prices. After putting the role played by the dynamics of the fundamental in the right perspective, moreover, we shall address the issue of taxing financial transactions in fundamentally heterogeneous markets in order to test the Tobin conjecture of optimal uniform tax rates. Accordingly, in what follows we will make use of the chartistfundamentalist archetypal framework discussed at length in Hommes and Wagener (2009) and Chiarella et al. (2009), suitably amended to take cross-market heterogeneity in fundamentals into account. Our modelling choice yields two related advantages. First, it enables us take stock of the massive amount of work already done in exploring (i) the main features of nonlinear dynamic asset pricing models with evolutionary strategy switching, (ii) the impact of different parameter constellations on market outcomes, and (iii) the role of different assumptions on stochasticity in driving results. This in turn enables us to focus exclusively on the issue of cross-market heterogeneity in fundamentals and the related ability of FTTs to tame market inefficiency, without claiming to reinvent the wheel. Put briefly, the model works as follows. A large, fixed number of traders (ideally distributed as a continuum on the unit interval) N is

DtF , i = β F (Fti−Sti−1)+εtF , i

(1a)

DtC , i = β C (Sti−Sti−1)+εtC , i

(1b)

where β and β are positive reaction parameters capturing how strongly agents react to market signals. According to Eqs. (1a) and (1b), fundamentalists buy (sell) when the log price of the security Si is below (above) its fundamental log value Fi, while chartists buy (sell) when the price is increasing (decreasing). In order to capture withingroup heterogeneity in the intensity of reaction or the possibility of experimentation with slightly different trading rules, independent and normally distributed noise terms are added to each demand component, εF and εC. As shown in Hommes and Wagener (2009), these demand functions can be derived from the solution of a mean-variance portfolio optimization problem of a typical trader allocating her wealth between two assets – a risky asset and a risk-free one – under the assumptions of constant risk aversion, very short trading periods, and risk-free returns normalized to zero. Following Chiarella et al. (2009), the market clearing mechanism is modeled by assuming the existence of a market maker who takes offsetting long or short positions, with the aim of adjusting any excess of demand or supply. Accordingly, the log price Si at time (t+1) is determined by means of a log-linear impact function (Farmer and Joshi, 2002), which states how the asset price changes due to the buy and sell orders made by active traders: F

C

Sti+1 = Sti+α (WtF , i DtF , i +WtC , i DtC , i )+uti

(2)

where α is a positive adjustment coefficient measuring the speed of reaction of the market maker, WF,i and WC,i represent respectively the fractions of traders following fundamental and chartist strategies, while ui is a random term normally distributed with mean 0 and variance σ I,i, capturing possible frictions in the execution process. To be stressed is that in this framework α admits a dual interpretation. First, it tunes the market microstructure, since for α tending to infinity the clearing mechanism reduces to a Walrasian auctioneer. Second, it provides a measure of market liquidity: higher values of α make prices react vigorously to excess demand. Pellizzari and Westerhoff (2009) discuss the issue of how time-varying market liquidity interacts with the stabilizing impact of a transaction tax. They show that such a relationship turns out to be negative (i.e. a FTT destabilizes the market by decreasing liquidity) when market protocols force liquidity to evolve endogenously. In our setting, this occurs as we reach the limit for a Walrasian clearing mechanism. Therefore, as soon as the market maker provides a sufficient amount of liquidity to the market – i.e. as soon as α is not too high – we can confidently presume that a FTT can in principle reduce market volatility. Whether it can also increase efficiency is a matter subjected to careful scrutiny in what follows. In line with the evidence reported in e.g. Menkhoff and Taylor 324

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of cross-market heterogeneity additional to those associated with different values of the mean and variance of zi. Differences in the speed of reaction to news about the optimally forecasted present value of future dividends may be due to institutional factors affecting the quality and precision of the signals, or to differences in the cost of acquiring information. In any case, it is clear that all these factors vary with the stage of development of financial systems. In fact, the available cross-country empirical evidence provides convincing support for the hypothesis of large international dissimilarities in the information content of earnings announcements and other major news events, as well as in the promptness with which they are incorporated into the evaluation of securities (DeFond et al., 2007; Griffin et al., 2008).

(2007) and Gomber et al. (2017), traders stick neither to a particular trading strategy nor to a given market. Instead, they switch among rule/market combinations by comparing their past performances. At the end of any trading period t, agents compute the attractiveness (or fitness) of the trading rules as they are applied in each market i:

AtF , i = [exp (Sti )−exp (Sti−1)] DtF−2,i −τ i [exp (Sti )+exp (Sti−1)] DtF−2,i +δAtF−1,i

(3a)

AtC , i = [exp (Sti )−exp (Sti−1)] DtC−2,i −τ i [exp (Sti )+exp (Sti−1)] DtC−2,i +δAtC−1,i

(3b)

At0

(3c)

= 0.

Eqs. (3a)–(3c) are based on four assumptions. First, due to market timing – orders submitted in period (t–2) are executed at time (t–1) – profits depend on the price return between (t–1) and t. Second, if a positive transaction tax rate τ is levied, traders incur a cost which is registered when positions change. Third, agents have a memory of the past attractiveness of the rule, where δ is a parameter which measures how quickly agents discount this item of information. Fourth, the fitness associated with inaction is set to 0, a choice commonly made in this class of models. Note that this last assumption is consistent with the presence of a region of no transaction around the optimal portfolio allocation, which is increasing with the level of proportional transaction costs (Constantinides, 1986). The market dynamics can be fully derived as we define how agents make use of the attractiveness associated with each option to select where to submit orders in the following period, as well as the trading strategy for executing them. A standard approach (Brock and Hommes, 1997, 1998) is to assume that the fraction of traders choosing a certain option is determined through a multinomial logit model (Manski and McFadden, 1981), in which the weights W depend positively on the fitness of a strategy as it is applied in a given market:

WtF , i =

WtC , i =

3. Results The key features of the environment sketched above are explored by resorting to agent-based simulations. In this section we focus on the ability of the model to capture several stylized facts concerning financial markets in an extremely parsimonious framework. We will first assess the case of closed heterogeneous markets (autarky), and then study what happens when traders are allowed to frictionlessly choose the market in which their buy or sell orders are submitted (openness). The issue of how FTTs affect market outcomes is left to the next section. Table 1 reports the parameters’ constellation for benchmark simulations. Since the purpose of this paper is merely theoretical, no serious attempt to calibrate the model has been made. In fact, we use values employed in similar exercises by Westerhoff and Dieci (2006) and Westerhoff (2010). Interestingly, these values have been shown to be consistent with the presence of an asymptotically stable steady state for the multi-dimensional discrete-time dynamical system (1a)–(4c), as tax rates are set to zero and all stochastic disturbances are suppressed (Westerhoff and Dieci, 2006). Assuming that the typical trading period is one day, each simulation covers a time span of approximately twenty years. For ease of exposition we consider just two markets which differ in the speed and resonance with which new information is incorporated into fundamentals. An extension to three markets will be discussed in Section 4. In particular, in the first market the probability that any news regarding subsequent dividends is disseminated and processed by agents is equal to 6% per day. This amounts to an average of 15 variations per year. In the second market, news arrives with a probability of 2.4% per day, meaning that the fundamental jumps on average 6 times per year. Likewise, when a jump occurs, the volatility of the fundamental in Market 1 is two times that of Market 2, capturing

exp (γAtF , i ) I ∑i =1 exp (γAtF , i )

I

+ ∑i =1 exp (γAtC , i ) + exp (0)

(4a)

exp (γAtC , i ) I ∑i =1 exp (γAtF , i )

Wt0=1 −

I

I

+ ∑i =1 exp (γAtC , i ) + exp (0)

(4b)

I

∑i =1 WtF ,i− ∑i =1 WtC,i

(4c)

The parameter γ≥0 measures the sensitivity of traders in selecting the most attractive option. If γ=0 all agents are divided evenly among the market/strategy options, while if γ→+∞ all agents select the option with the best performance. Since by construction the weights sum up to one, in what follows we embrace a frequentist approach: the fraction of traders adopting a given strategy at any point of time is simply assumed to be equal to the probability of that same strategy being chosen. This allows us to get rid of one parameter when the model is taken to the computer – i.e. the overall population size N. As already emphasized, the novelty of our model concerns the process driving fundamental values. The cursory evidence reported in Fig. 1 suggests that a plausible candidate should be characterized by smooth and irregular movements, with short intervals in which the value remains almost constant. To capture these features, the fundamental of the asset traded in market i is assumed to evolve according to a jumping random walk:

Fti

=

Fti−1+(1ϕ )i zti

Table 1 Parameter setting for benchmark simulations.

(5)

where zi is a normally distributed random term, and 1ϕ is the indicator function:

Parameter

Description

Value

T I α

σ1I

Trading days per simulation Number of markets Market impact factor of demand Noise in price formation in Market 1

5000 2 1 0.01

σ2I

Noise in price formation in Market 2

0.01

βF

Aggressiveness of fundamentalists

0.05

βC

Aggressiveness of chartists

0.065

σεF

Noise in fundamentalist demand

0.01

σεC

Noise in chartist demand

0.05 0.06

ϕ1

Probability of fundamental's jumping in Market 1

ϕ2

Probability of fundamental's jumping in Market 2

0.024

(6)

σz1

Noise of fundamental dynamics in Market 1

0.06

with ϕ being a well-defined probability. The role of ϕ is that of tuning the speed with which new information is incorporated into the fundamental value of the stock, and allows us to introduce a source

σz2 δ γ

Noise of fundamental dynamics in Market 2

0.03

Memory in updating attractiveness Sensitivity in selecting options

0.975 300

(1ϕ

)i

⎧ 1 w. p. ϕi =⎨ w. p. 1 − ϕi ⎩0

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Fig. 2. Numerical simulation of the model with parameters as in Table 1, except for I=1. The values for σIi , σzi and ϕ i are those for Market 1.

absence of linear serial dependence – the autocorrelation function of absolute returns (dotted line) is significant and slowly decaying over many time lags, a typical signature of volatility clustering. The overall system dynamics are driven by the evolutionary competition between trading strategies, which translates into an endogenous evolution of adoption frequencies. Periods characterized by bursts in volatility and large market mispricing are associated with the preponderance of chartist traders, while mean-reverting movements are caused by the action of fundamentalists. Since the price return volatility is given by 2 2 V = (W F )2 (σεF ) +(W C )2 (σεC ) , its path is dependent on how the market is divided between fundamentalists and chartists, and its value would change even if the noise in their respective demand were equal. Notable results emerge when we allow the jumping random process guiding the fundamental value to diverge across markets. The upper line of Fig. 3 reports a comparison between the performance registered in two closed, fundamentally heterogeneous markets, obtained by averaging market prices across 5000 Montecarlo repetitions. In addition to Market 1, we consider a closed jurisdiction in which new information on future dividends arrives less frequently and impacts less widely on the optimal forecasts of agents (Market 2 in Table 1). It appears that the process for the fundamental matters for the statistical properties of the market price and – as we will argue below – the degree of market efficiency; a feature which to our knowledge has never been explored before. Consider first that the stochastic processes generating fundamentals are by construction weakly non-stationary (with standard deviations increasing with t ), and that the variance of the random term for the fundamental value in the first market is two times that for the second one. Unsurprisingly, both features are inherited by actual prices. In spite of this, the sample means of price volatility and kurtosis

the assumption that in the former new items of information are processed more efficiently and priced more quickly. It follows that the first market is fundamentally more volatile than the second one. Besides their noisier demand, chartists are assumed to be more aggressive in submitting orders than fundamentalists. This feature is consistent with recent estimates of the model obtained by means of the method of simulated moments (Franke and Westerhoff, 2017). Fig. 2 presents results for a representative simulation run, as we assume that traders can operate in one market only (in this case Market 1, i.e. the more fundamentally volatile one). All the following findings have been extensively reported in the literature dealing with the chartist-fundamentalist approach. We cover them as a quick reminder of the ability of small-type agent-based computational models to capture a wide range of stylized facts on real markets within an extremely parsimonious framework, on the one hand, and as a benchmark against which to measure the impact of alternative assumptions on the stochastic process driving the fundamental on the other. The time series for the log price (continuous line in the upper-left panel) exhibits a typical bubbles-and-crashes dynamic and excess volatility, meaning that the occurrence of positive and negative large returns cannot be generally explained solely by the arrival of news on the market. In particular, the volatility of market prices is much higher (around 3 times) than that of the fundamental (dotted line). Returns are characterized by a heavy-tailed (leptokurtic) distribution, with an excess kurtosis around K ∼7. As shown in the semi-logarithmic histogram plot, furthermore, the tails display an approximately exponential decay, a result in line with the evidence reported in various studies employing daily data (see e.g. Ding et al., 1993). While the sample autocorrelation function of returns (continuous line in the left panel of the third line) is insignificant at all lags – indicating the

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Fig. 3. Comparison between two closed markets characterized by different stochastic processes for fundamentals. Parameters are those of Table 1. Plots in the first line report averages over 5000 Montecarlo repetitions with ± 2 standard deviations around the mean. The bottom line reports the distribution of market distortion in the two markets over Montecarlo repetitions.

systematically higher for Market 1, while a KS test rejects the null that the two distortion distributions were generated by a common probability density function at the 1% significance level. It follows that both the average market inefficiency, as well as the probability of experiencing longer spells of excess volatility, are positively correlated with the instability of fundamentals. Limiting the comparison between fundamentally heterogeneous markets to the phenomenological properties of market prices – typically, the price volatility and the leptokurtosis of returns – might misleadingly convey the impression that structural differences in the frequency of news arrival and the speed with which this is incorporated into the present value of subsequent dividends do not matter in driving market performances. Indeed, the underlying dynamics of fundamentals, which are strictly related to the effectiveness with which traders collect and process items of information to form a consensus on the right valuation of stocks, impinges on their ability to keep the market price at its fair value. Markets characterized by a structurally higher volatility of fundamentals are therefore structurally more inefficient, because the excess volatility caused by the destabilizing speculative activity of chartist traders is magnified. Since the rationale for non-distortive FTTs is that they restrain market inefficiency, policymakers interested in setting tax rates according to an optimal taxation principle should take this issue into serious account. According to the chartist-fundamentalist approach, the crucial source of market inefficiency is the inability of agents to coordinate their trading activities so that market prices incorporate any news about future profitability in a comprehensive and timely manner. Decades-long empirical research in finance has made it possible to identify two stylized facts which are strictly associated with such a violation of the EMH (Shleifer, 2000). The first, called ‘underreaction’, states that prices tend to underreact to news announcements and keep trending for several weeks after the news is released. The second, called ‘overreaction’, states that over longer time spans of three to five years prices first overreact to correlated patterns of news, and then revert to the mean. Note that combining the two phenomena should yield a hump-shaped response of prices to innovations in the fundamental. This is precisely what we obtain in our simulations. Fig. 4 reports

Table 2 Key statistics for returns in the two markets, as traders operate under autarky and openness, respectively. Figures in chevrons are averages over 5000 Montecarlo repetitions. Market 1

Market 2

Autarky

〈V〉 〈K〉 〈D〉 σD SkD

0.0176 6.6768 0.1396 0.0279 1.1261

0.0177 6.6898 0.1256 0.0272 0.9930

Openness

〈V〉 〈K〉 〈D〉 σD SkD

0.0132 8.4448 0.1390 0.0223 0.9628

0.0130 8.5553 0.1143 0.0216 0.9926

of returns (〈V〉 and 〈K〉 in the upper part of Table 2, respectively) obtained by averaging across Montecarlo repetitions are basically unaffected by differences in the data generating process of fundamentals. The most interesting aspect emerges when we consider how the non-stationarity of market prices and fundamentals affect market efficiency, expressed in terms of excess volatility. A metric commonly used to measure it is a distortion index defined as follows:

Di =

1 T

T

∑ t =1

Sti−Fti .

(7)

The index is bounded below by 0, while increasing values of D signal higher amounts of market inefficiency. Visual inspection of the bottom line of Fig. 3 – where we plot the values of D obtained in 5000 Montecarlo repetitions – suggests that the distortion index is in both cases skewly distributed to the right, but the moments of the two distributions are quantitatively different. In fact, the mean, the standard deviation, and especially the skewness of the distribution (〈D〉, σD and SkD in the upper part of Table 2, respectively) are 327

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Underreaction is more pronounced on Market 1, where the market price trends up for more than 50 weeks after a unitary shock to the fundamental. However, the peak of the price response function is higher and its mean-reversion faster on Market 2, signaling that in this case overreaction is relatively stronger. Once again, heterogeneity in the process governing the evolution of fundamental values matters for market outcomes and the degree of inefficiency. What happens to the price dynamics if barriers to trading mobility are removed? In order to answer this question, we allow traders to move freely across the two fundamentally heterogeneous markets. Montecarlo simulations show that in this case the average volatility of prices decreases in both jurisdictions if compared to the autarky scenario – a finding in line with the empirical evidence reported in Bekaert and Harvey (1997) – while the average kurtosis of returns increases steadily (bottom part of Table 2). The openness of markets is thus associated with a generalized stronger incidence of extreme returns. This is accompanied by a better performance in discovering the right price in Market 2, while the average of the distortion index in the fundamentally more volatile Market 1 remains basically unaffected. Although the skewness turns out to be equalized across the two distortion distributions, therefore, movements towards a closer inte-

Fig. 4. Impulse-response functions of market prices to a one unit shock to fundamentals.

Montecarlo averages of the impulse-response functions obtained by estimating a vector autoregression model of market prices and fundamental values for Market 1 and Market 2, respectively.

Fig. 5. Numerical simulation of the open-market model with parameters as in Table 1 and no taxation.

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gration of financial markets and broader opportunities of diversification imply an enlargement in the asymmetry of cross-market efficient price discovery. To our knowledge, this finding has been largely neglected so far. A huge body of literature has rightly pointed out that any move towards the greater integration of financial markets should imply that assets with identical risk should command the same expected return, irrespective of where they are traded. We argue that this insight should be complemented with a focus on the impact of integration on excess volatility, which represents a signature of the market inefficiency due to mispricing. Our results suggest that unless the integration process involves greater synchronization in the evolution of fundamentals, the gain in efficiency stemming from the opening of domestic asset markets to foreign investors is larger for jurisdictions in which the incorporation of news on fundamentals is smoother and the macroeconomic environment is more stable – that is, for more fundamentally stable markets. Moving on from the results discussed in this Section, the next one explores whether the fundamental heterogeneity of asset markets has any consequence when an attempt is made to regulate them through the imposition of taxes.

simulation run. It is only when we reach this stage of analysis that it clearly appears that traders are in fact operating in two heterogeneous markets. Pricing inefficiency is stronger in the most fundamentally volatile jurisdiction – where distortion exceeds that of Market 2 by 27% – and this feature is echoed also in transaction volumes, which are on average 32% higher. Both features underpin the economic rationale for FTTs to act as Pigouvian taxes aimed at discouraging activities with negative side effects (Stiglitz, 1989). The excess volatility stemming from the interplay between traders believing that the market price should be anchored to its fundamental value and traders speculating on trends implies that the latter exert a negative externality on the former by generating positive feedbacks. This in turn creates a wedge between private and social returns, suggesting that the price distortion index (7) may be conceived as the proper social welfare criterion that policymakers should employ in determining the optimal level of taxation. This point has been already stressed from a different perspective in the literature exploring the nexus between mispricing in asset markets and firms’ investment policy (Stein, 1996; Polk and Sapienza, 2004). While the correct magnitude of actual price volatility is a target very difficult to identify – given that it should be related to the unobservable risk tolerance of the traders – a better alignment between the market price and its fundamental value proves to be socially valuable for two reasons that do not require the elicitation of individuals’ preferences. First, more informative securities prices provide a better alignment of the incentives of shareholders and managers, thus helping to solve the typical problem of corporate governance. Second, when the market price reflects its fundamental value, the management of a firm can correctly assess its cost of capital, and use this item of information as guidance in planning the appropriate level of investment. The simple fact that both informational outputs are likely to be small for a truly efficient capital market (Bresnahan et al., 1992) is irrelevant for the case in point. When market outcomes are driven by a process of evolutionary selection among many different interacting trading strategies – that is, the EMH is violated – the maximization of social welfare is achieved by minimizing the volatility in excess of that implied by the dynamic evolution of the securities’ fundamental value, not that of the actual volatility of prices. Although the price distortion criterion has the additional advantage of being neutral with respect to the potential use of revenues, any consideration about optimality must also take into account how the level of the tax rate impacts on the tax base, that is, on the trading volume. Simply stated, levying an optimal tax that forces a market to remain steadily at its fundamental value by annihilating exchanges is basically useless. Note that the rationale for this statement is different from the one usually put forward by detractors of FTTs, who argue that the major adverse consequence of the tax is the decrease of market liquidity associated with lower volumes. In fact, in our framework the two issues are detached, owing to the presence of a market-maker who provides a sufficient amount of liquidity irrespective of the fraction of traders actively engaged in the market (see Eq. (2)). The plausibility of this assumption is corroborated by a huge amount of research on actual market microstructure suggesting that the presence of a market-maker is a pervasive feature of organized asset markets (O’Hara, 1995; Madhavan, 2000). Deprived of the liquidity issue, the volume of trading can be seen as a way to quantify other key economic functions performed by a capital market, i.e. those of expanding the choice set of agents through exchanges, and of assisting firms to exploit diverse sources of financing for valuable projects by helping them to raise equity capital (Schwartz et al., 2015). The decision of a policymaker to levy a tax on financial transactions therefore implies striking a balance between two different instances of efficiency, i.e. the one associated with efficient price discovery, and the one related to the additional functions of resource allocation performed by financial markets. The second and third columns of Table 3 provide an illustration of what happens when only one market at a time is taxed (Market 1 and

4. Taxation The open market framework analyzed at the end of Section 3 is now employed to evaluate the usefulness of levying FTTs. Our treatment moves through several steps. First, we assess the effects of taxing one market at a time. Besides exploring what happens to the price dynamics in the taxed market and the spillover effects on the untaxed one, we focus on the trading volume and market price efficiency. We shall argue that the social welfare impact of a tax on financial transactions should be correctly measured along these two margins, instead of being exclusively associated with a reduction in volatility. Second, we consider the case of a simultaneous application of FTTs on both markets. Finally, we look for optimal tax rates, where optimality is expressed in terms of the minimum amount of excess volatility associated with the trading patterns of market participants over and above the incorporation of fundamental news. In order to assess the robustness of our results, we extend the analysis to the case of a third market whose regulatory authority has to gauge the right tax rate when an agreement on the other two markets has already been reached. A benchmark simulation run without taxation is represented in Fig. 5. All the stylized facts recalled above are largely confirmed. A simple visual inspection of the two series for price returns – as well as the sample autocorrelations for returns and absolute returns – suggests that there is no significant difference between the underlying datagenerating processes, although the fundamentals behave quite dissimilarly. In both cases, market outcomes are characterized by a boomand-bust dynamic, cluster volatility, uncorrelated returns, and absolute returns displaying a significant positive auto-correlation for many lags. The first column of Table 3 reports the time averages of daily trading volume and price distortion in the two interconnected markets over the Table 3 Trading volume and distortion for different choices of the tax rate.

Volume Mkt 1 Volume Mkt 2 Volume Total D Mkt 1 D Mkt 2 D Total

τ1=τ2=0

τ1=0.25%; τ2=0

τ1=0; τ2=0.25%

τ1=τ2=0.25%

1.2742

0.2552

1.6595

0.4147

0.9617

1.4097

0.2277

0.4110

2.2359 0.1474 0.1158 0.2632

1.6650 0.0734 0.1259 0.1993

1.8871 0.1569 0.0847 0.2416

0.8257 0.0597 0.0563 0.1160

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Fig. 6. Total distortion and fractions of chartists, inactives and fundamentalists operating in both markets for different levels of taxation. In the second row the two horizontal axes are inverted.

trading volume. In the absence of any consideration on liquidity, the externality exerted across borders through unilateral taxation is positive as soon as we concede that a greater volume of trading activity can be conceived as a proxy for the stock market's ability to furnish a larger amount of real services. Note that in the aggregate the burden in terms of wasted trading volume is lower when the tax is levied on the jurisdiction with a less volatile fundamental. The sign of the externalities generated by the just-described unilateral imposition of a FTT is entirely in accordance with the evidence reported by comparable computational studies (Westerhoff and Dieci, 2006; Mannaro et al., 2008). If traders are allowed to move freely across fundamentally heterogeneous markets, however, which one is effectively taxed matters. Systemic informational efficiency is higher when the tax is levied on the more fundamentally volatile market. In turn, the loss in terms of volumes is lower when the opposite holds true. This raises the question of whether a multilateral agreement is not only feasible but also desirable. This issue can be addressed by inspecting the fourth column of Table 3, which illustrates the case in which both markets are taxed with a common tax rate of 25 basis points. Coordination proves to be beneficial for price discovery because the aggregate distortion is the lowest among the four scenarios under scrutiny. Interestingly, the final outcome in terms of informational efficiency is now enhanced in both

Market 2, respectively). Comparability of results is ensured through use of the same seed as employed in the simulation of Fig. 4. As a reference, we assume that the public authority sets the tax rate at 25 basis points. As expected, it appears that the unilateral imposition of a FTT determines a substantial decrease of trading volume in the taxed market. This comes with a significant enhancement of price efficiency, measured by the excess volatility over and above the dynamics of the fundamental. At the same time, however, the untaxed market is negatively affected, since its distortion increases. Measured in terms of the welfare criterion (7), the final result of a unilateral imposition is positive for the system as a whole because the total distortion is in both cases lower than it would be in the absence of taxation. It is also evident that the spillovers impinged upon the untaxed market by the migration of trend-chasing activity from the taxed one are less damaging when the tax is levied on the more fundamentally volatile jurisdiction – if considered once again from a systemic perspective. In this case, the total amount of distortion decreases by 24% in comparison to the benchmark unregulated situation, while the gain of systemic efficiency when the opposite case applies is limited to a mere 8%. The trade-off in terms of spillovers between informational efficiency and the interference of FTTs on the other economic functions served by the stock market becomes apparent when we complete the picture by conducting a comparison between the two experiments with a focus on 330

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jurisdictions compared to what would happen if taxation were unilaterally imposed. In strategic terms, as soon as the two public authorities are interested in maximizing pricing efficiency, coordination is a strictly dominant strategy for both of them. But the result changes if the main objective is to minimize the loss of trading volume. In this case, the only equilibrium admitted by the game is the no-tax solution. We argue that a proper ordering of the two welfare targets could make a coordination agreement incentive-compatible. If we assume that policymakers are primarily concerned with avoiding excess volatility, and only in subordination to this goal do they aim to limit volume losses, the coordinating equilibrium is not only self-enforcing in the first place, but it also allows an increase of domestic trading volume when compared to the scenarios with unilateral taxation. The general lesson to be learned is that in levying FTTs careful crafting of the agenda for negotiations is of key importance for securing a coordinated approach. The agreement is self-enforcing if the policy goals are prioritized correctly by all participants. The primary welfare criterion should be that of enhancing the ability of financial markets to stay in line with fundamental values, that is, to avoid excess volatility. Any other objective, such that of limiting the loss of trading volume, should be considered as a derivative. The next issue to analyze is whether the agreement should entail as an optimal choice that of a common tax rate, a condition that we have called the Tobin conjecture. The upper-left panel of Fig. 6 reports the level of aggregate distortion as the tax rates in both jurisdictions are increased from 0 to 50 basis points, obtained by averaging outcomes over 1000 Montecarlo repetitions. The surface we obtain is convex, and the minimum level of distortion is reached for a slightly asymmetric combination corresponding to a tax rate of 27 basis points in Market 1 and 30 basis points in Market 2. The reason for this result can be grasped by looking at the other three panels of Fig. 6, where we plot the average fractions of traders adopting alternative trading strategies in correspondence to the different tax rates. To enable easier interpretation, the two horizontal axes of the charts in the lower row are inverted. As the tax rate is increased, the chartists exit the market in a monotonic fashion, signaling that the FTT curbs speculative activity by forcing trendchaser agents to abstain from trading (lower-left panel) or to switch to fundamental trading. In turn, the surface representing the average fraction of fundamentalists (lower-right panel) is concave, signaling that excessive tax rates make fundamental trading unprofitable too. Thus, the global maximum level of efficiency in terms of minimized excess volatility is reached for a combination of tax rates that maximizes the presence of fundamental activity. The magnitude of optimal tax rates is in line with what is observed in real applications (Matheson, 2011). Fig. 7 reports the trading volume obtained in the two markets for

Fig. 8. Optimal tax rates for increasing mean-preserving spreads of fundamentals’ volatility.

different combinations of the tax rates. The brighter surface refers to Market 1, and the darker one to Market 2. As already observed with regard to Table 3, a harmonized application of the tax makes it possible – for any given rate – to obtain higher volumes in comparison to what occurs with a unilateral imposition. The two externalities tend to offset each other as the two jurisdictions coordinate on a symmetric solution. In order to investigate how the heterogeneity of fundamentals’ processes affects our results, similar Montecarlo experiments have been repeated for ten different scenarios organized in terms of increasing (mean-preserving) spreads for the two parameters ruling their dynamics, that is, ϕ and σ. Fig. 8 reports the optimal tax rates in both markets under two different treatments. In the first treatment, consistently with what we have assumed so far, the stochastic processes ruling fundamental values are autonomous. In line with the empirical evidence showing that macroeconomic news in core countries is largely transmitted across markets (Wongswan, 2006; 2009; Hausman and Wongswan, 2011), in the second treatment we assume that the sequences for the fundamental are drawn from correlated probability distributions, where the coefficient of correlation has been set at 0.8. There is a clear difference between the two treatments. In the uncorrelated case (triangles), as the heterogeneity between fundamentals increases, the combination of tax rates minimizing total distortion tends to spread out. Interestingly, this comes in a somewhat counterintuitive fashion. Larger heterogeneity calls for lower tax rates in the more fundamentally volatile market, while higher tax rates are optimal in the market with a smoother fundamental. The reason for this result can be grasped by looking again at the surface reported in the upperleft panel of Fig. 6. The speed with which the aggregate distortion frontier decreases is greater along the axis which measures the tax rate applied to the more volatile market. In other words, the marginal benefit associated with an additional basis point of taxation is higher in Market 1, meaning that the optimal solution is reached sooner than in Market 2. By contrast, as soon as the processes are correlated, optimal combinations are invariably organized along the 45° line. This is precisely the Tobin conjecture. The optimal uniform tax rate is decreasing with an increase in the degree of heterogeneity of fundamentals. As a final robustness check, we performed an experiment in which the same two-market open system parametrized according to the values reported in Table 1 was augmented with a third market whose fundamental was characterized by ϕ=0.09 and σ=0.07. As a starting point, we assumed that the original two markets were correlated, and an agreement on a common tax rate had already been reached. In the absence of the third market, the optimal uniform rate was in this case 27 basis points. We then calculated the total distortion obtained when a FTT was levied also in Market 3, attaining a convex surface in line with

Fig. 7. Trading volume in the two markets for different combinations of tax rates.

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the one reported in the upper-left panel of Fig. 6. When the fundamental on the third market was uncorrelated with those of the two coordinated jurisdictions, the minimum distortion was reached for the following combination: 25 basis points inside the coordinated zone, and 20 basis points in Market 3. Again, the optimal solution called for a lower rate in the more fundamentally volatile market. If all fundamental processes were correlated, however, the lowest aggregate emerged for a uniform tax rate equal to 20 basis points. 5. Conclusions FTTs are Pigouvian taxes. This means that the use of such a policy option must be firmly grounded on an exact definition of the kind of externality that it aims to offset. In this paper we have started from recognizing that the existence of speculative activity in financial markets is not an evil in itself, arguing instead that the main reason for limiting its incidence is that this could help traders to trade at the securities fundamental value. In other words, the proper target for levying FTTs is the volatility in excess of the discounted stream of subsequent dividends, and not the observed one. Indeed, the price volatility measured in diverse markets might be similar even if the degree of market inefficiency varies substantially. The latter is associated with the process driving the evolution of fundamental values, which is in turn related to the speed with which news is incorporated into estimates of fair prices, risk-return profiles, and macroeconomic volatility. Since all these factors vary substantially across countries, it seems interesting to ask whether this kind of cross-market heterogeneity plays any role in easing or hindering internationally coordinated actions in taxing financial markets. In this paper, a fairly standard agent-based pricing model in the chartist-fundamentalist tradition has been enriched by assuming that fundamental values vary according to jumping random processes with different jump frequencies and volatilities. The analysis has allowed us to draw two main conclusions. First, global coordination to tax financial markets is feasible, given that the multilateral imposition of a FTT is incentive-compatible provided that the policy target is correctly set as the minimization of both domestic and systemic price distortions. Second, the optimal tax rate is uniform across jurisdictions even if markets are characterized by fundamental heterogeneity, provided that the stochastic processes guiding the evolution of fundamentals are correlated. The main message that ensues from our analysis is that for the Tobin conjecture to hold true the simple removal of barriers to capital mobility is not enough. An additional requirement is that the integration among countries signing an international agreement to tax financial transactions with a uniform tax rate also includes the real part of the economy, i.e. trade flows. The increasing synchronization of business cycles is in fact a prerequisite for news to spread with impacts of similar sign across jurisdictions, leading to a significant correlation of fundamentals. Given these results, future research should be devoted to validating the class of agent-based models discussed in this paper with real data, in order to provide precise policy advice on the effective rate to be agreed upon by the governments involved in an international agreement aimed at taxing financial markets. From this point of view, several approaches can be fruitfully employed. In addition to the method of simulated moments proposed by Franke and Westerhoff (2017), a particularly promising approach is the gradient-based method suggested by Recchioni et al. (2015). References Andersen, T., Bollerslev, T., Diebold, F., Vega, C., 2007. Real-time price discovery in global stock. Bond and foreign exchange markets. J. Int. Econ. 73, 251–277. Baltagi, B., Li, D., Li, Q., 2006. Transaction tax and stock market behavior: evidence from and emerging market. Empir. Econ. 31, 393–408. Bekaert, G., Harvey, C., 1997. Emerging equity market volatility. J. Financ. Econ. 43, 29–77.

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