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Review of the Evidence

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The Tobin Tax –

A Review of the Evidence

Neil McCulloch1

Grazia Pacillo
Institute of Development Studies

University of Sussex

23 March 2011

JEL Codes: G15, G18, H22, H27

The debate about the Tobin Tax, and other financial transaction taxes (FTT), gives rise to strong views both for and against. Unfortunately, little of the popular debate refers to the now considerable body of evidence about the impact of such taxes. This review attempts to synthesize what we know from the available theoretical and empirical literature about the impact of FTTs on volatility in financial markets. We also review the literature on how a Tobin Tax might be implemented, the amount of revenue that it might realistically produce, and the likely incidence of the tax. We conclude that, contrary to what is often assumed, a Tobin Tax is feasible and, if appropriately designed, could make a significant contribution to revenue without causing major distortions. However, it would be unlikely to reduce market volatility and could even increase it.


We are grateful to the participants of workshops at the Centre for the Study of Financial Innovation and the University of Göteborg for useful comments and suggestions. In addition, we received comments from a large number of authors and practitioners including: Viral Acharya, Dean Baker, Geert Bekaert, Francis Bismans, Zsolt Darvas, Randall Dodd, Paul De Grauwe, Lieven Denys, Thierry Foucault, Jeffrey Frankel, Ken Froot, Stephany Griffith-Jones, Harald Hau, Chris Heady, Thomas Hemmelgarn, Cars Hommes, Charles Jones, John Kay, Peter Kenen, Michael Kirchler, Thomas Palley, Robert Pollin, Helmut Reisen, Philip Saunders, Paul Spahn, Dietrich Stauffer, George Wang, Frank Westerhoff and Alan Winters. We are grateful to them all. Althea Rivea helped with the construction of our reference database and Stacey Townsend has also provided excellent and tireless administrative and research support – we are grateful to both. We gratefully acknowledge financial support from DFID for the research undertaken in this paper.

  1. Introduction

In 1972, in the Janeway Lectures at Princeton, James Tobin suggested that it might be a good idea to impose a currency transactions tax in order to enhance the efficacy of macroeconomic policy (Tobin 1974). He reiterated this view in his presidential address to the Eastern Economic Association in 1978 (Tobin 1978). The proposal did not get a good reception. As Tobin wrote ‘it did not make much of a ripple’ (Tobin in Ul-Haq et al. 1996). However, over the subsequent 30 years, every time there has been some form of financial or currency crisis, there is renewed discussion about whether the implementation of a Tobin Tax might be an appropriate policy response.

The Tobin Tax is an emotive issue. On the one hand such a tax is, as Tobin himself put it, ‘anathema to Central Bankers’. Many economists share an instinctive dislike for taxing transactions, often because they believe that such taxes reduce the efficiency of competitive markets and impose welfare costs. Bankers and other participants in financial markets are also often opposed because they regard it as unworkable or naïve. On the other hand, campaigning groups, politicians and economists frequently raise the issue of the Tobin Tax (and other similar financial transaction taxes), in reaction to major financial crises, due to its purported ability to stabilise markets. High volatility in the markets can be economically damaging, due to its negative impact on investment, and so if a Tobin Tax actually did stabilize markets this could be a significant benefit. Moreover, the fiscal difficulties created by the current crisis have led to renewed calls for the imposition of such a tax, both to boost tax revenues and as a means of extracting a larger contribution from the financial sector to fund a wide range of national and international public goods.2
Despite the long-standing debate on the issue, the arguments aired in the popular debate, by both proponents and opponents of the tax, are sometimes rather poorly grounded in evidence. This is surprising, because there is now a voluminous literature on the Tobin Tax. This includes extensive theoretical work, examining whether Tobin and Tobin-like taxes would stabilise markets in principle, simulations which explore how simple agents acting according to specified set of rules would react to the imposition of such a tax, as well as empirical work examining the actual impact upon markets and revenue when similar such taxes have been imposed in various countries. In addition, there is a comprehensive literature on potential ways in which such a tax might be implemented and the pitfalls, difficulties and possibilities associated with these differing modalities. In short, there is a great deal that we already know about the pros and cons of Tobin and Tobin-like taxes.
The aim of this paper is to lay out, in a disinterested fashion, the evidence currently available. Specifically we will attempt to review the evidence on four key questions:

  1. What is the impact of financial transaction taxes on volatility?

We will review the results arising from the main theoretical models that have been developed, as well as the findings from computational simulations. We then describe the findings from the empirical literature associated with similar kinds of transaction costs and taxes.

  1. Is a Financial Transaction Tax feasible?

A key concern running through the debate is whether it is actually feasible to implement such taxes in a way that would prevent significant avoidance. Three key questions arise here. First, what instruments should be taxed (and would market actors simply be able to substitute non-taxed instruments for taxed ones to avoid the tax). Second, at what point in the payment system (i.e. trading, clearing or settlement) and on what resource (e.g. registration, brokerage) should the tax be imposed? Third, what should the scope of the tax be? i.e. should it cover domestic assets or also foreign assets; domestic market actors or also foreign actors; transactions taking place in the domestic market or also those taking place abroad? Related to this, is the issue of whether market actors can circumvent the tax by migrating their business, or at least their trades, to untaxed centres, and, whether it would therefore be necessary to get agreement among all, or a large number of key countries for the tax to be effective.

  1. How much money would a FTT collect?

The answer to this question is clearly determined by the answers to the feasibility questions above. We outline the large range of estimates in the literature of the revenue that would be collected and attempt to explain how the figures produced depend on the coverage of instruments, actors and countries and the rates applied. We also examine the existing estimates of the elasticity of trade volume with respect to the tax and the effect that this has on the revenue figures obtained. Finally, we conduct a meta-analysis of the revenue collection potential using the median estimates from the literature.3

  1. What would be the incidence of the Tobin Tax?

Unfortunately, the analytical and empirical literature on the incidence of a Tobin Tax is rather sparse. Nonetheless, we examine the merits of the various positions taken and draw on the literature on the incidence of other taxes in an attempt to come to a reasoned judgment about the likely incidence of the tax.
Given the range of terms used to describe financial transaction taxes, it is useful to define the scope of our review. We are interested in financial transaction taxes which affect the wholesale market. We do not consider non-financial transaction taxes (e.g. taxes on the exchange or trade in goods or services); nor do we explore non-transaction taxes on financial assets (e.g. capital gains tax, or the recently proposed Financial Assets Tax). Moreover, we do not consider transaction taxes that are oriented to the retail market e.g. bank debit taxes. Even with these restrictions, our definition is broad, covering taxes on the exchange of the entire range of financial securities, including bonds, shares, and foreign exchange as well as the spot, forward, swaps, futures and options markets for these assets. When referring to this full range of transaction taxes we use the term Financial Transaction Taxes (FTT). When referring only to transaction taxes on foreign exchange we will use the term Tobin Tax, since Tobin’s original idea only related to the taxation of foreign exchange transactions. However, we broaden Tobin’s original concept to include all forms of transaction tax on the foreign exchange market, including forward, futures and options, not merely those pertaining to the spot market.

  1. The Impact of FTTs on Volatility

Tobin’s original proposal was focused on reducing the volatility of markets.4 His reasoning, and that used subsequently in much of the debate, was that very short-term transactions are more likely to be destabilising than long-term transactions based on market fundamentals. A tax on each transaction represents a much higher tax rate for short term than for long term investments, hence discouraging the former. As he puts it:

Most disappointing and surprising, critics seemed to miss what I regarded as the essential property of the transaction tax –the beauty part- that this simple, one-parameter tax would automatically penalize short-horizon round trips, while negligibly affecting the incentives for commodity trade and long-term capital investments. A 0.2 per cent tax on a round trip to another currency costs 48 per cent a year if transacted every business day, 10 per cent if every week, 2.4 per cent if every month. But it is a trivial charge on commodity trade or long-term foreign investments.

(Tobin in Ul Haq et al. 1996, p.xi)

If it is true that short term transactions induce more volatility than long term trades, the tax should reduce overall market volatility.
The assumptions underlying this reasoning have been subject to comprehensive scrutiny in both the theoretical and empirical literature. We start by briefly reviewing the traditional theoretical work on the topic in the tradition of Keynes and Friedman. The opposing views about the impact of speculation on volatility arising from the traditional literature gave rise to a closer focus in theoretical models on the microstructure of these markets and the characteristics of traders (Frankel and Rose 1994). These models depart from traditional assumptions of fully rational agents. Rather market actors are assumed to have bounded rationality, making decisions according to ‘rules of thumb’ which may not necessarily be optimal. In addition, these Heterogenous Agent Models (HAM) take into account the fact that market actors may have different interests, capabilities, and access to funding. A further group of models adopt the HAM approach but allow interaction between the various agents in ways that can affect aggregate variables (Westerhoff 2003; Westerhoff and Dieci 2006).
A second group of theoretical studies focus on zero intelligence atomistic models based on percolation theory (Cont and Bouchaud, 2000). These models reproduce excess volatility and fat tails in the distribution of returns, through herding behaviour in the population of traders (e.g. Ehrenstein et al 2005; Mannaro et al. 2008). This class of models, though neglecting any notion of optimising behaviour, has the virtue of taking into account the discrete nature of traders, whereas in the heterogeneous agent approach only the effect of the aggregate demand of different types of traders matters (Bianconi et al. 2009).
We then review game theoretical approaches to modeling the impact of Tobin-like taxes on volatility (Bianconi et al. 2009; Kaiser et al. 2007). All three of these approaches are better than traditional models in reproducing the ‘stylized facts’ of real financial markets (Cont 2001) such as excess volatility, the fat tailed distribution of returns and volatility clustering.
Finally, we provide a brief review of papers which, whilst adopting one of the theoretical frameworks above, have undertaken simulations or laboratory experiments to test whether the theory holds in such a setting.
After reviewing the theoretical literature, we turn to the empirical literature. Since a Tobin Tax, as originally envisaged has never been implemented, the empirical evidence of the impact of a transaction tax in the foreign exchange market is much more sparse than the theoretical literature. However, numerous countries have implemented a variety of financial transaction taxes (see IMF (2010) for a recent review). We therefore draw on the empirical literature assessing the impact of these taxes on volatility. We conclude with an overall assessment of the evidence about the impact of FTTs on volatility from both the theoretical and empirical literature.

    1. Theoretical Models

Traditional theoretical debates
Tobin’s proposal for a financial transaction tax was by no means the first. Keynes famously argued that:
Speculators may do no harm as bubbles on a steady stream of enterprise. But the situation is serious when enterprise becomes the bubble on a whirlpool of speculation.

(Keynes 1936:159)

His solution, was to propose a transaction tax on equity trades, on the assumption that short-term trades are likely to be more destabilising to financial markets than longer term trades. Indeed this is the underlying rationale behind the arguments of a very large number papers supporting financial transaction taxes.5
However, this view was famously challenged by Friedman (1953), who argued that speculation cannot be destabilising in general since, if it were, the actors involved would lose money:
People who argue that speculation is generally destabilizing seldom realize that this is largely equivalent to saying that speculators lose money, since speculation can be destabilizing in general only if speculators on the average sell when the currency is low in price and buy when it is high.

(Friedman 1953: 175)

This strand of the literature therefore argues that speculative opportunities occur when the market is inefficient, and that rational arbitrage trading on unexploited profit opportunities is effective in clearing markets and stabilising prices, bringing them down to their fundamental values (Fama 1965). As is well known, the theoretical basis for the view that taxes reduce efficiency and impose welfare costs depends on a particular set of assumptions about the market which may not hold. For example, Stiglitz (1989) showed that markets are not necessarily efficient when there are externalities or asymmetric information. More generally, Greenwald and Stiglitz (1986), showed that whenever markets are incomplete and/or information is imperfect, tax interventions may be Pareto improving.

Beyond traditional theoretical approaches
Traditional models of financial markets tend to assume optimising agents with rational expectations about future events (i.e. that forecasts are perfectly consistent with the realisation of the events so that agents do not make consistent mistakes.) However, such models do not explain many of the characteristics that are observed in real financial markets such as excess liquidity (i.e. excessive trading activity due to speculative trade), excess price volatility, fat tailed distributions of returns (i.e. a much higher probability of very large positive and negative changes) and volatility clustering (i.e. switches between periods of high and low volatility).
To try and account for these, a new generation of theoretical models looked at the ‘microstructure’ of financial markets. These models typically assume that market actors are not perfectly rational, but rather apply rules-of-thumb when making decisions to buy or sell, based on whatever information they have at their disposal. They also assume that there are different types of market actors. As a result these models are known as Heterogenous Agent Models.

Heterogeneous Agent Models6
Models which assume rational traders with complete information face a fundamental difficulty because theory would suggest that, in these circumstances, there should be no trade. This is because a trader with superior private information about an asset should not be able to benefit from his information, because other rational traders, seeing the first trader trying to buy, would anticipate that he must have positive information about the asset and will therefore not be willing to sell the asset to him (Milgrom and Stokey 1982). Heterogenous Agent Models (HAMs) attempt to find a solution to this problem by assuming that traders are different from one another, and that they are boundedly rational.7 Agents do not have complete information about the market because gathering the necessary information is very costly, and because there is fundamental uncertainty about what the ‘correct fundamentals’ are (Keynes 1936). As a result they use a range of rules-of-thumb to set their strategies.
HAMs in financial markets typically assume the existence of at least two different types of traders: ‘fundamentalists’, who base their expectations about future asset prices and their trading strategies on market fundamentals and economic factors, such as market dividends, earnings, macroeconomic growth, exchange rates, etc; and ‘chartists’ or ‘noise traders’ who base expectations and trading strategies on historical patterns. The latter employ a variety of ‘technical trading rules’ based on moving averages – buying when the short run moving average crosses the long run moving average from below and selling when the opposite occurs (Schulmeister 2009). In such a set up, the volatility of the market is driven by the share of market traders that are noise traders (who increase volatility) relative to the share that are fundamentalists (who reduce it).8
De Long et al. (1990a and 1990b) formalised such a model in which fundamentalists are called ‘sophisticated traders’ and the chartists are ‘noise traders’. The noise traders use signals from technical analysis, economic consultants and stock brokers to set their portfolio, irrationally (in the model) believing that these sources contain correct information. Sophisticated traders exploit this misperception, buying when noise traders depress prices and selling when prices are inflated. Thus sophisticated traders pursue a contrarian strategy, pushing prices towards their fundamental values. One advantage of these models is that they give more realistic outcomes in terms of the stylised facts of these markets, such as excess volatility (De Grauwe and Grimaldi 2006).
Frankel and Froot (1990a and 1990b) apply such a model to the exchange rate markets, and extend it by adding another agent: the portfolio managers. As before, chartists use moving averages to trade, taking only the past exchange rate into account, but it is the portfolio managers who actually buy and sell foreign assets. They form their expectations as a weighted average of the forecasts of fundamentalists and chartists, adapting the weight over time in the direction that would have yielded a perfect forecast (Hommes 2006). Simulation of this model shows that exchange rates may exhibit temporary bubbles during which the weight that portfolio managers place on the forecasts of fundamentalists is negative, inducing (in this model) an increase in the exchange rate. However, when the exchange rate goes too far away from its fundamental value, portfolio managers increase the weight given to fundamentalists thereby accelerating a depreciation. Frankel and Froot (1990a and 1990b) therefore show that, when the behavior of portfolio managers is driven by bounded rationality, it is possible for exchange rate markets to exhibit significant temporary deviations from market fundamentals.
Haberer (2004) describes the effect of a transaction tax in a perfectly efficient market and in an inefficient market – where efficiency is defined as the ability of the market to incorporate news. The efficient market is composed by fully rational agents with complete information about the structure of the model and the behaviour of relevant fundamentals. In this market, all market participants are homogenous and new information causes the price to change towards a new equilibrium through an approximation path.9 Greater liquidity in this market helps prices to reach the new equilibrium and reduces volatility. The inefficient market, by contrast, is composed of heterogeneous participants (fundamentalists, who do not contribute to excess volatility; and chartists, who do) with different expectations and forecasting techniques. In this market, higher liquidity due to speculation increases volatility. Taking the two markets together, Haberer therefore suggests that there may be a U shaped relationship between liquidity and excess volatility. At low levels of market volume, greater liquidity reduces excess volatility. However, after a certain point, the confusion caused by speculation creates a positive relationship between liquidity and excess volatility. This suggests that a transaction tax in a low liquidity market would increase volatility, but in highly liquid markets such a tax may reduce volatility by reducing the incentives for speculative trading.10
Shi and Xu (2009), augmenting Jeanne and Rose’s (2002) study on the effect of a transaction tax on ‘noise trading’, analysed the effect of a Tobin tax on exchange rate volatility. Again, the idea is that exchange rate volatility is caused by changes in the relative share of fundamentalist and noise traders. A transaction tax might reduce exchange rate volatility by reducing the number of noise traders. They analysed entry costs for both informed (fundamentalists) and noise (chartists) traders after the introduction of a transaction tax in a general equilibrium model. A key assumption is that informed traders' unconditional expectation of excess return depends on the ‘noise component’ i.e. the ratio of noise entrants to informed entrants, but that this does not influence noise traders' expectations. An increase in the noise component increases market volatility. It also changes the risk premium and the gross benefit of entry, but in a different way for informed and noise traders because of the asymmetry in their expectations.

Shi and Xu find that, when the entry decisions of all traders are endogenous, three equilibria are possible. In the first equilibrium, the noise component is one i.e. there are the same number of noise and informed entrants, so all traders form their expectations in the same way. As a result, an increase in entry costs due to a transaction tax leads them to leave the market in pairs. The ‘asymmetric expectation effect’ therefore disappears and the gross benefits of entry are only affected by market depth (i.e. the sum of informed and noise traders). Hence a transaction tax only reduces market depth and does not affect volatility, since it does not influence the composition of traders. The second equilibrium occurs when the noise component is different from one. If entry costs are increased due to the tax, the asymmetry in expectations causes a larger reduction in the gross benefits of entry for informed traders’ than for noise traders’. This, in turn, affects the composition of traders, increasing the noise component and, thereby, volatility. The third equilibrium occurs when the entry cost is sufficiently high to prevent the entry of noise traders. In this case, the introduction or increase of a transaction tax has no effect on volatility. Thus a Tobin tax will have an effect on volatility only if there are entry costs and if its imposition changes the share of noise traders in the market. Moreover, in Shi and Xu’s model, the imposition of a Tobin tax does not reduce volatility, but may increase it depending on the ratio of noise to informed entrants.11

Bloomfield et al. (2009) raise the same issue in an experimental context. They show that a uniform tax on noise traders and sophisticated traders has little effect on volatility. A recent paper by Foucault et al. (2010) suggests that the reason for this is that the tax affects both types of traders uniformly. They simulate a policy change in France that makes the cost of equity trading higher for retail investors (who are often regarded as noise traders) than for other investors and show that this would significantly reduce the volatility of stocks.
Hau (1998) also develops a theoretical model on the relationship between taxes and volatility. His model allows for endogenous entry of traders subject to heterogenous expectational errors. Entry of a marginal trader into the market has two effects: it increases the capacity of the market to absorb exogenous supply risk, and at the same time it adds noise and endogenous trading risk. The competitive entry equilibrium is characterized by excessive market entry and excessively volatile prices. A positive tax on entrants can decrease trader participation and volatility while increasing market efficiency.

The models described above assume stochastic interaction between agents, who are assumed not to be able to influence aggregate variables. This assumption is questioned by HAM interaction models, which support the idea that even weak interactions between individuals can lead to large movements in aggregate variables. Follmer (1974) considers an exchange economy with random preferences based on a probability law which depends on the agents’ environment. Using results on interacting particle systems from physics, he shows that even short range interactions may propagate through the economy and lead to aggregate uncertainty causing a breakdown of price equilibria (Hommes 2006).

Kirman (1991) formalised a ‘local interaction model’ comprising two sub–models: a model of opinion formation through a stochastic model of recruitment and an equilibrium model of the foreign exchange rate. The model of opinion formation argues that there is individual behavioural asymmetry when facing symmetric events.12 Applied to financial markets, Kirman assumes that agents have to form opinions about the next period price of a risky asset, and they can choose between an optimistic and a pessimistic view. The fractions of fundamentalists and chartists in the market are thus derived from a stochastic model of recruitment and then used in the foreign exchange rate model. Agents’ expectations are influenced by random meetings with other agents. Agents have to decide to invest in two different assets: a safe asset, namely domestic currency, paying a fixed interest rate ; and a risky asset in the form of foreign currency paying an uncertain dividend. As usual, the equilibrium exchange rate is found where the aggregate demand for currency equals aggregate supply. If the market is dominated by fundamentalists, the exchange rate is stable and is pushed towards its fundamental value, causing low volatility. If noise traders dominate the market, the exchange rate is either driven by a stable but near unit root process, or by an unstable process when chartists think that the movement in the exchange rate will be greater than the risk free asset return, leading to high volatility. In this way, local interaction models capture one of the most important stylised facts of financial markets, namely volatility clustering, in which the exchange rate switches irregularly between phases of high and low volatility.
Lux and Marchesi (1999, 2000) also attempt to derive a model capable of explaining the stylised facts of financial markets (e.g. asset prices follow a unit root process; asset returns are unpredictable with almost no autocorrelation; return distribution has fat tail; volatility clustering).13 They analyse the probability of traders switching from chartist to fundamentalist trading strategies as well as from an optimistic chartist strategy to a pessimistic one and vice versa. The equilibrium price is derived based on the composition of traders in the market and a market opinion index, which captures the average opinion among chartists. Volatility arises through the interaction of, and switching between, fundamentalist and chartist trading strategies. Periods of high volatility are associated with an increase in the number of chartists in a market with a balanced distribution of pessimistic and optimistic views.14
Another set of models have looked at the implications of imposing Tobin taxes on volatility when there is more than one market (e.g. London and New York). Westerhoff (2003) and Westerhoff and Dieci (2006) developed a simulation model of heterogeneous interactive agents in which rational agents apply technical and fundamental analyses for trading in two different markets. The technical analysis is based on past price trends, whereas fundamental analysis predicts a convergence towards fundamentals. The agents have several options, which are chosen depending on their relative fitness, where the fitness is given as a weighted average of current and past profits. Their model shows that even the imposition of a low tax rate of 0.25 percent in one market reduces distortions and volatility in the taxed market, whereas the untaxed market experiences stronger bubbles and crashes and higher volatility than before. Their model therefore supports Tobin’s hypothesis that imposing a tax will reduce volatility. Moreover, they conclude that ‘there is no reason for regulators of a market not to impose such a tax – at least the own market will benefit’, because ‘if the agents have to pay a uniform levy in both markets, chartism declines in favor of fundamentalism in both markets and thus both markets display lower price fluctuations and deviations from fundamentals’. This also suggests that regulators in the untaxed, more volatile market may see it in their interests to also impose the tax in order to compete for investors with a longer term horizon.
Finally, the market microstructure may influence the impact of a FTT (Honohan and Yoder 2009). For example, broker markets may react differently from dealer markets, and products characteristics might also influence the impact of taxation. Mende and Menkhoff (2003) suggest that asset managers are, most probably, the group with the heaviest influence on shorter-term exchange rate movements. They argue that there is no tax rate that could both influence their behaviour and simultaneously maintain the desired high level of liquidity, therefore concluding that no uniform proportional Tobin tax can achieve its objectives.
A recent model by Pellizzari, P. and Westerhoff, F. (2009) shows how the effectiveness of transaction taxes can depend on the market microstructure. In their model, heterogeneous traders use a blend of technical and fundamental trading strategies to determine their orders; they may also become inactive if the profitability of trading decreases. They find that, in a continuous double auction market15, the imposition of a transaction tax is not likely to stabilize financial markets since a reduction in market liquidity amplifies the average price impact of a given order. However, in a dealership market, abundant liquidity is provided by specialists and thus a transaction tax may reduce volatility by crowding out speculative orders.

Zero intelligence agent models
Another approach to modeling the behaviour of financial markets is through the use of ‘zero intelligence’ (ZI) models – so called because they assume that market traders in the aggregate, behave probabilistically rather than being driven by any intelligent maximising behaviour. Agents in these models place orders to buy and sell at random depending on the current price. Only the institutions (e.g. the auction process) in these models have some kind of intelligence since they let prices converge to equilibria. The idea behind this approach is that modeling market behaviour using minimally intelligent agents provides a good benchmark of the effect of the market institutions, since it shows what sorts of behaviour arise purely because of these institutions and not due to any intelligent or strategic behaviour on the part of the agents. It may well be that market institutions shape agents behaviour so much that some properties of their behaviour depend more on the structure of these institutions than on any rationality on their part.16
ZI models are therefore much simpler than models assuming full rationality because they do not try to derive the properties of the market from assumptions of utility maximising rational individual agents. Rather, the ZI models study the flow of liquidity in and out the market and its interaction with price formation. Interestingly, ZI models and models based on the rationality paradigm can give rise to quite different explanations for volatility. For example Hasbrouck and Saar (2002), using a rational optimising model, find a positive link between the ratio of market and limit orders and volatility. They explain that this is because, when prices are more volatile, market orders become more attractive to risk averse rational agents (because, unlike limit orders, they entail an immediate transaction) and so the fraction of market orders increases. However, Farmer et al. (2004), using a ZI model, show that the same relationship can be explained without any rational optimising behavior. They show that a ZI model can exhibit a positive relationship between volatility and the ratio of market and limit orders due to the reduction of liquidity induced by the increase in market orders (since market traders are liquidity demanders), and that it is this reduction in liquidity that increases volatility.
Ehrenstein et al. (2005) used a ZI model to evaluate the impact of a Tobin tax on volatility, market distortions and government revenue, varying the size of the tax from 0 to 1 per cent. In this model, the introduction of a Tobin tax also brings about a reduction in volatility, as long as the tax rate is not so high as to significantly reduce market liquidity.
However, Mannaro et al. (2008) using a similar approach obtains a different result. They use a multi-agent simulation model to analyze the effects of introducing a transaction tax on one, and then on two related stock markets. The market consists of four kinds of traders (Raberto et al. 2003): Random traders, who trade at random; Fundamentalists, who pursue the ‘fundamental’ value; and Chartists, who are either Momentum traders (following the market trend) or Contrarian traders (who go against the market trend). Each trader is modeled as an autonomous agent, with a limited stock portfolio and cash. When there are two stock markets, at each simulation step the trader decides in which market to operate by evaluating an attraction function for both markets.

Mannaro et al. find that the imposition of a tax in a single market of between 0.1per cent and 0.5 per cent of transaction costs increases price volatility, as long as there are noise traders in the market. When there are two markets, volatility is higher as traders switch from one market to the other to try and reduce their risk. In this case, the taxed market is generally more volatile than the untaxed one because the tax reduces trading volume and market liquidity.

Game theoretical approaches
It is also possible to use game theory to assess the impact of a Tobin Tax on volatility. For example, the Grand Canonical Minority Game model has also been used to analyse the effect of the imposition of a Tobin Tax in the exchange rate market.17 It is a stylised representation of the financial markets, which are depicted as an ecology of different types of agent, speculators and institutional traders, interacting in an ‘information food chain’ (Bianconi et al. 2009). As in previous models, it captures the interplay between commercial traders and financial speculators, with the latter group assumed to be responsible for both excess volatility and market efficiency. There are two types of agents. The first is commercial traders. They trade no matter what, so that the imposition of a tax cannot affect their choice. The second type of agent is financial speculators, who trade only if the perceived market profit exceeds a given threshold. The speculators’ keep scores of the success of their previous strategies and adapt them accordingly. The main objective of each agent is to be in the minority, i.e. to place a bid which has the opposite sign of the aggregate bid of all agents.
Bianconi et al. (2009) analyse the impact of the imposition of a Tobin tax on the volatility of the exchange rate in a GCMG model. The first effect of the tax is to increase the profit threshold for speculators, discouraging them from trading. More generally, the effect of the tax depends on how close the market is to a critical zone of information efficiency. If it is far from this zone, the tax has mild effect on volatility and information efficiency. If the market is within the critical zone and volatility is high, only a sufficiently large tax will have an impact on volatility. Moreover, the impact on volatility is found to be very dependent of the market size. Since volatility decreases with the size of market, the effect of a Tobin tax is much stronger in a small market than a bigger one. Finally, in a market in which the composition of agents is evolving, a tax can reduce volatility only if the rate of change in the composition of agents is slow.

Laboratory Experiments
Closely related to the above theoretical papers, is an emerging literature that attempts to test these theories directly, by constructing laboratory experiments or simulated marketplaces. An early example of this is the work of Noussair et al. (1998). They use a continuous double auction model to explore the impact of a FTT on market efficiency and the volume of trade. They show that, despite the imposition of a small fixed transaction tax18, prices are still driven towards their equilibrium level, although with reductions in market efficiency and turnover.
Similarly, Hanke et al. (2010) simulates two continuous double auction markets, denoted LEFT and RIGHT, on which a foreign currency (Taler) can be traded for the home currency (Gulden). They analyse the effect of the imposition of a transaction tax (0.5 per cent of the transaction value) on one and then on both markets. In order to examine the persistence of the impacts, they also consider a scenario where the tax is abolished again, after its introduction. Where the tax is imposed only on one market, they find that volatility in the taxed market decreases when the market is large and liquid, but increases when the market is small and illiquid. Moreover, volatility on the untaxed market is reduced significantly as a consequence of an increase in liquidity as traders shift to the untaxed market. If a Tobin tax is introduced simultaneously on both markets, overall trading volume is reduced and price volatility remains unchanged. Finally, they argue that the effects of a Tobin tax, once introduced on a market, cannot be completely undone by abolishing the tax later on, since the pre–tax level of trading activity would not be restored.
Kaiser et al. (2007) describe a game theoretical approach applied to an asset market both with and without the introduction of a Tobin tax. The game was set up with two steps. In the first step, agents define their bid and ask prices. Market prices are then created, with the ask price as the lowest stated by agents and bid price as the highest. In the second step, each agent decides whether to buy or sell or to refrain from trade. When a tax is introduced, it is paid by the agent who initiates the trade and is a percentage of the bid or ask price. In addition, the tax’s height was varied to analyse the elasticity of volatility with respect to the tax. In the final period the assets each agent holds are converted into money.
Using this framework Kaiser et al. (2007) carried out experiments on 96 subjects, mostly students from the University of Bonn. They analysed 6 sessions for the taxed scenario and 6 sessions for the untaxed one, each session lasting two hours. In general they found that the Tobin Tax reduced volatility, relative to the untaxed market.19 However, a tax rate above 2 percent increased volatility drastically in their experiment, although the statistical evidence is not strong enough to give a definitive conclusion on this.
Cipriani and Guarino (2008) also elaborate a theoretical and experimental paper on the negative effects of transaction costs, such as a Tobin tax, on price discovery. In their model, informed and uninformed traders trade in sequence with a market maker, and pay a cost to trade. They show that, eventually, all informed traders decide not to trade when transaction costs are imposed, independently of their private information, i.e. an ‘informational cascade’ occurs. When they replicated their financial market in the laboratory, they found that informational cascades occur when the theory suggests that they should.
As the above discussion makes clear, there are a wide range of theoretical models with different assumptions and different results. Table 1 provides a summary of the conclusions from the key theoretical papers on the topic. Most, but not all, studies conclude that a small Tobin tax would reduce volatility, but many models also suggest that great care should be taken in choosing the size of the tax since, if it is too large, the reductions in market trading and liquidity could result in an increase rather than a reduction in volatility (Song and Jungxi 2005).
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