The Efficiency of a Currency Transaction Tax Bruno Jetin Maître de Conférences à l’Université Paris Nord, Centre d’Economie de l’Université Paris Nord (CEPN) Paper presented at the conference: “Taxing Currency transactions. From Feasibility to Implementation”, organised by Halifax Initiative, Vancouver, October 4-6, 2001.

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INTRODUCTION.

The paper deals with the efficacy of a small currency transaction tax (CTT) to curb speculation. It shows that a small transaction tax is sufficient to deter what could be called “ordinary” speculation providing that the exchange rate remains stable. When speculators have good reasons to anticipate even a modest (2%) depreciation of the exchange rate, a small CTT would prove insufficient.  We argue therefore that the rate of  the tax should be allowed to increase to much higher levels than was expected until now. This rationale apply particularly to developing countries where the instability of  the exchange rates is much higher than in rich countries.  We discuss the ability of a two tier tax in the P.B. SPAHN sense to respond to the problem.  We then turn to  the possibility to apply a high tax without paralysing the economy. Finally, we conclude that a CTT must be part of a broader strategy to regain control on finance. A CTT is only one tool inside the capital control box.

SECTION ONE: HOW MUCH EFFECTIVE ? 

There are at least four ways to calculate the efficacy of a CTT. They all rely on the central hypothesis that the exchange rate remains constant during the period of horizon. To begin with, let’s see what these four methods are, because the simplest and most often ones presented in the literature are not the most complete and accurate ones. Using the proper method, we shall see then what happens when we allow the exchange rate to fluctuate. We’ll see that the capacity of a small CTT to curb speculation is dramatically reduced.

The four methods to calculate the efficacy of the CTT when exchange rates are fixed.

The first and the simplest method considers a round trip between two currencies. For example euros would be changed in US dollars and after a period would be changed again in euros. It means that the rate of the tax has to be multiplied by 2. If the round trip is done once a day (240 days per year) we then multiply by 240, if it is done once a week, we multiply by 52, once a month by 12, etc… For example, a 1% tax levied on a monthly round trip would lead to an annualised  tax of 24% (1%*2*12 = 24%). The results are presented in table 1. A CTT looks very efficient as a small rate of 0,1% can impose a burden of 48% for daily transactions. But the efficacy is sharply decreasing. This is an expected result because the purpose of the CTT is to penalise short term capital flows without penalising the real economy, what is called by J. Tobin the “filtering effect”.

The second method considers an amount of money at the beginning of a period (Parlement Européen, 2000, p 14). Imagine that a traveller has a budget for his vacations and then goes from one country to another without spending his money. Each month he goes to another country, and changes his money (100 US $ to take a simple example)  and pay a fix banking fee, say 1%. At the end of January, he would have 98$ ((100- (100*2%)), at the end of February he would have 96,04$, etc… At the end of the year, he would have only 78,5 $, which means a annualised tax of 21,5% (against 24% in the first method). On a weekly basis, he would have only 35$ left which means a annualised tax of 65% (against 104% in the first method), etc…The same reasoning apply to a junior speculator I with 100 $ and who would make blank operations (no profit nor loss).  The results show a decreasing impact of the CTT.

The third method is used by G. Eichengreen and C. Wyplosz (1993) and is based on a compound interest formula :

1 + i^* = (1+ 2t/100)^p.              (1)

Where i^* is the annual foreign rate of interest, t is the rate of the CTT and p is the number of transactions per year. The interest of this formula is to show that the CTT must zero the profit of an investment abroad. If 1+ i^* < (1+ 2t/100)^p, then it is not interesting to invest abroad. At the minimum, the cost of the tax must be equal to the expected profit. Table 2 shows some results relative to the level of the tax. They show that the impact of the tax is much higher for daily and weekly round trips than in the first formula, but around the same for longer periods. If, for example the tax rate is 0,1%, then investing abroad must render a daily profit superior to 61,5% which is very high. But the effect is still decreasing sharply.

The fourth and more complete formula (Ministère des Finances 2000) derives from the third one but takes into account the domestic interest rate, i.

(1+i) ^1/p = (1-t)²*(1+i^*) ^1/p      (2)

Where 1/p is the duration of the investment measured as the number of years, or fractions of years, for which a foreign investment is held. If the investment is held for 1 year 1/p = 1. If it is held for 6 months, 1/p = ½, and p = 2 gives the number of transactions per year. If the investment is held one month, 1/p = 12, and the number of transactions per year is p = 12, etc…

In this case, the tax rate must zero the difference between the domestic and foreign interest rate which is closer to reality. If we take the hypothesis that the domestic interest rate is 4%, we can calculate the necessary level for the foreign interest rate i* which make profitable to invest abroad, relative to different tax rates levels and maturities. The formula, deriving from the previous one is the following:

  (3)

The results are shown in table n° 3.

One can see that for low tax rates between 0,025% (equivalent to the ordinary transaction costs on the inter-bank market) and 0,1% (the most often mentioned rate in the literature), the CTT is efficient only for short maturities (daily or weekly transactions). But for monthly, 3 months and 6 months transactions, the difference between the domestic and foreign interest rates is too narrow (inferior to 2%) to be a disincentive to capital outflows. For rates in the 0,25%-0,5% range, the CTT becomes efficient for monthly and quarterly transactions, but it is only for rates superior or equal to 1% that a CTT tax gets efficient for 6 months and yearly time span as the interest differential becomes largely superior to 2%. To put it in another way, one may conclude from these data that a low CTT (minor than 1%) is not enough to curb speculation, except for very short time range, and that the monetary autonomy of the central  bank would be nearly inexistent. The threshold of 1% appears necessary to deter speculation on a yearly basis and give a substantial monetary autonomy to the central bank which can afford  a national interest rate 2% inferior to the foreign interest rate.

Unfortunately, these results are very dependant on the assumption that the exchange rates remains stable during the relevant period. If the exchange rate of the national currency depreciate, (i.e if the foreign currency in which an investment can be made appreciate), the efficiency of the CTT decrease sharply.

The impact of the fluctuations of the exchange rate on the efficacy of the CTT.

This one of the most serious critic addressed to the CTT. Preventing new financial crisis like the one experienced in the eighties and in the nineties is one of the justifications of the CTT. But a small tax (0,1%), and even a high one (1%) would be unable to deter serious speculation attacks (P. KENEN, 1995, P. DAVIDSON, 1997, J. HUFFSCHMID 1999, S. DE BRUNHOFF & B. JETIN, 2000, Ministère de l’Economie et des Finances (France), 2000, European Parliament, 2000).

Take the example of a 1% tax, which means 2% for a round trip. The second method of calculation of the impact of the tax on speculation on a annual basis would be : ((1+0,02)⁵² – 1 )* 100 = 180% (see table 2). It means that the burden of the tax is 180% and that a speculator must find a profit opportunity superior to 180% which looks rather difficult. But it would miss the point because this calculus does not take into account the  rationale of speculation.

P. KENEN puts it that way:  “Suppose that investors begin to anticipate a devaluation of 4% of the lira with a probability of 0,5% before the end of this week, the expected profit of a bet against the lira is 2%, which represents also a profit of 180% on an annual basis”. Granted that speculation is prone to herd behaviour, it is possible that, in some circumstances, the probability of a devaluation increase endogenously.

The previous example is based on the implicit assumption that there are no interest rate differentials between monetary investments in both countries, which is an over simplification of reality. If we take interest rates differentials into account, then the efficiency of the CTT is even smaller even for a small depreciation of the exchange rate (2%).

We can see it by including the anticipated variation of the exchange rate in equation (2).

(1+i) ^1/p = (1-t)²*(1+i^*) ^1/p (1 + e)           (4)

Where e is the anticipated variation of the exchange rate during the period of investment in the foreign asset. ( e > 0) means a depreciation of the domestic currency).

From equation (4) we can calculate the minimal foreign interest rate level for which an investment abroad is as profitable as a domestic investment.

          (5)

The results are presented in table 4, taking the hypothesis of a domestic interest rate i =  4% and a small depreciation of the exchange rate e = 2%.

If the tax rate is 0,1%, the most often quoted in the literature, the profitability of an investment abroad must be at least 68,1% to match the cost of the CTT when the exchange rate is stable, in the case of a daily round trip. But if a depreciation of 2% the exchange rate is anticipated, even a zero interest rate abroad would make a foreign investment profitable. When the investment is made once or twice a year, a low foreign interest rate is sufficient. A small CTT of 0,1% is therefore not efficient against speculation in case of small fluctuations of the exchange rate, but would affect  those who make exchange transactions once or twice a year. Would it be different with a rather high CTT of 1% ?

Unfortunately, the answer is no. The CTT is only efficient for daily round trip as the foreign interest rate must reach at least 11,7% to make an investment profitable. But, for a weekly round trip, the minimum level of  profitability which was 196% when the exchange rate was fixed, falls down to 5,6% if the currency in which the investment is made increase 2%. The difference between the domestic interest  rate (i) and the foreign interest rate (i*) is only 1,6% which is rather thin. The picture is worse for less frequent transactions because the interest rates differential is null.

 In case of an anticipated depreciation of 5% of the exchange rate, a CTT of 0,1% is not efficient at all. The CTT must reach at least 3% to become dissuasive.

What should be the level of the CTT in order to counteract the effect of an anticipated (or effective) devaluation when the interest rates differential is 2% ?

We can answer to this question by rearranging the terms of  equation (4) to express t, the level of the CTT, in function of the other parameters, i= 4%, i*= 6%, e = 1% to 10%.

          (5)

The results are shown in table n° 5.

For example, one can see that for a depreciation of the exchange rate of only 1%, the CTT rate must be around 0,5% if the round trips are daily, weekly or monthly ones, and between 0,7% and 1,4% if the round trips are made every 3 months, twice or once a year. This is a normal result because when the transactions are made very frequently, the taxpayer pays very often the tax and a small CTT rate will offset the gain of  the depreciation of the exchange rate. One can expects that a speculative attack will expect a significant depreciation of the exchange rate, say 5% or 10% in one month or three months. The Table n° 5 shows that if a country whose currency is attacked wants to keep its domestic interest rate 2% below the international level, it must raise the CTT at 2,5% if the anticipated depreciation of the forex is  5% in one month, and to 4,7% if the anticipated depreciation of the forex is 10%. These results are not sensitive to the levels of the interest rates. If i = 6% and i* = 5%, the required levels for the CTT rates are nearly the same until the one month horizon, but fall a bit for the longer horizons.

These results confirm the previous one. In case of even a small depreciation of the exchange rates, a small CTT  rate, inferior to 0,1% is too low to curb speculation efficiently. 1% appears to be the minimum to offset a short term speculation inferior or equal to the one  month horizon for an anticipated depreciation of the exchange rates of 2%. Fluctuations of 2% are said to be inferior to the monthly standard deviations between the main currencies ^([1]), and it is not rare that the fluctuations of the currencies of developing countries vis-à-vis the dollar are superior to 5%. In this case a CTT rate between 2,5% and 5,5% must be considered.

Clearly, a small CTT of the magnitude of the transaction costs on the interbank wholesale exchange market cannot perform the job. But is it possible to consider a high CTT rate ?

SECTION 2 : HOW TO RESOLVE THE PROBLEM ?

The problem is how to reach a high level of CTT without provoking the disappearance of the exchange market ? The answer will depend on who will pay effectively the CTT, the banks or their customers (multinational firms, pension funds, hedge funds, mutual funds, insurance companies, etc…) ? What are the existing transaction taxes of these economic agents ? Is their a cumulative effects of the CTT and how to figure it ?

It is said that the interbank commission fees are between 1 to 2 basis point (0,01% to 0,02%), and these figures are often taken as the relevant starting point to analyse the impact of the CTT on the volume and the structure of the exchange market. This transactions costs only cover the technical transactions costs between two banks. When banks sell currencies to their  (big) final customers, they charge around 0,1%. We think that taking these figures as the relevant references to judge the impact of the CTT is misleading. First, it is obvious that banks will try to shift at least a fraction of the CTT to their final customers. It is a bit like the VAT principle, but not exactly. Due to the fact that the banking sector is a competitive one, banks will have to take in charge a fraction of the CTT. Which one exactly it is difficult to say. Second, it follows that we have to consider the accumulated taxation along the whole chain of transactions: one customer order engenders between 4 to 5 transactions between banks before another final non bank customer is found. Third, these figures correspond to developed countries during “ordinary” periods. For developing countries and in periods of tension, the transactions costs are much higher because they include search costs and risk premia.

Like D. FELIX and R. SAU (1996) put it, the pre-tax transaction costs are higher than the ones frequently assumed in the literature based on the interbank commission fees of  0,01% to 0,02%. “The scope of transaction costs should, we believe, include the cost of carrying out the full array of financial exchanges needed to complete a primary transfer, as well as search cost and risk premia”. Hence the relevant pre-tax transactions costs are much higher than the interbank commission fees. This is why the authors pledged for a phased-in 0,25% tax in four years.

But even if the CTT level is fixed to 0,1%, its final effect on speculation would be higher than expected. This is due to what is called the “hot potato principle” to which the underlined part of the previous quotation refers : dealing banks typically engage in multiple follow-up trades with other dealing banks (4 or 5), after a primary foreign exchange trade has unbalanced the proportions of different currencies they want to maintain on their books. These follow-up exchanges fraction the initial transfer and restore the desired balance. “The fractions would likely, on average, to sum to more than one, so that the total impact of a 0,1% Tobin Tax would likely be superior to 0,2%. If the bank’s pre-tax charge to a hedge fund or multinational corporation were 0,05%, a 0,1% tax would raise the charge to an amount superior to 0,25%. For currency speculation, a similar cost would apply to the repatriated funds, which raises the cost of the speculative round trip from a pre-tax 0,1% to a post-tax  0,5%. For large volume-low margin covered interest rate arbitraging that’s a substantial deterrent; for open speculative attacks perhaps less so” (D. FELIX, 2001). In effect, Table n° 5 shows that a 0,5% CCT is efficient in case of  a depreciation of 1% for daily and weekly transactions (and for longer terms when the interest rates are equal).

PAUL DE GRAUWE (2000), a strong opponent of the Tobin Tax, using a microstructure model developed by A. LYONS (1999) reach the same kind of  conclusion and but with stronger results. He thinks that the impact of a 0,1% ^([2]) would be much higher. He takes the example of a speculator who buys dollars and sells euros to a dealing bank. The first dealer obtaining the euros will want to unload them, but not the full amount. Because of the drop of the price of the euro, the dealer has an incentive to hold a fraction of these cheap euros. Suppose, he holds 5%. He then unloads the other 95% to another dealer, who has the same incentive to hold  a fraction and to unload the rest….after five dealers, the rest is unloaded to another speculator willing to take a reverse position. The chain of taxes (assuming a Tobin Tax of  0,1%) will be :

100*0,001 [1 + 0,95 + 0,95 ² + 0,95 ³ + 0,95 ⁴] = 0,45%

This means that the last bank buying the rest of the euros would be taxed at a rate of 0,45%. If the bank’s pre-tax charge to a hedge fund or multinational corporation is still 0,05%, the final charge for a one way trip is 0,45% + 0,1% = 0,55%, and a for a round trip, 1,1%. This level of taxation is sufficient to curb speculation on a monthly  basis in case of a depreciation of the exchange rate of 2%, and when domestic interest rate is below 2% the foreign interest rate (see Table n° 5). ( If dealing banks sell 100% of  the euros, the final speculator would pay 0,5% + 0,1% = 0,65% for a one way trip, and 1,3% for a round trip).

The same reasoning shows that a CTT of 0,5% leads to an accumulated taxation of 2,3% for the last dealing bank, 2,8% for the speculator for a one way trip and 5,6% for a round trip. This last figure corresponds to a depreciation of the foreign exchange of 10% (see Table n° 5).

In synthesis, the multiplying effect of the CTT on the whole chain of exchange transactions allows a small rate, say 0,1% to be efficient against a small speculative attack leading to a 2% depreciation of the exchange rate, and a higher  rate of 0,5% to compensate a depreciation of 10% of the exchange rate. 

Are these rates so high that the market could shrink too much and lead to its disappearance ?

Yes, if it is demonstrated that the banks wont shift the burden of the tax to the final customers. In this case, the foreign exchange market would evolve from a price-driven market to an order-driven markets like the ones that exist in the stock markets. It is not proved that  markets driven by orders are less liquid, and less efficient for spreading risks.

No, if it is accepted that part or the total of the tax will be passed along to the final customers. In this case, banks are not fully taxed even if the rate is set to 0,5%. There would be some shortening of the multi-dealer chain and a some centralisation of the market without a total transformation of the structure of the market.

How to implement a CTT rate of at least 0,1% ?

There are basically two possibilities.

1)     The first one is to implement a variable CTT with a build-in mechanism. The rate would be a function of the depreciation (or appreciation ) rate of the foreign exchange. The more stable the exchange rate, the smaller the rate of the CTT. The  higher the depreciation of the exchange rate, the higher  the CTT rate. It would be a strong disincentive to speculate, especially if it is announced in advance. Is it unconceivable to imagine a variable tax ? Is it illegal ? Impracticable  ? We don’t think so. In France there exists a variable tax on petrol. The tax rate increase when the price of petrol decrease, and decrease when the price of petrol decrease. In our case, it would be more simple. The tax would increase with the anticipated price of the foreign currencies signalised by the forward exchange rate. J.R. BRETON (1998) has made a proposal in this sense.

2)     The second possibility is the proposal of a two-tier tax (P.B. SPAHN, 1995, p 31). But we think that to be effective against speculation, the “normal rate” or the “underlying transaction tax” should be set at least at 0,1%. Otherwise, the surcharge would be activated very often, or maybe always, because the a zero tax or a tax of 1 to 2 basis points would be so small that the ceiling or the floor would be reached to easily. (remember that a depreciation of 2% the forex is only matched by a CTT of 0,1%, if the multiplying effect is taken into account, see table n° 5). This is especially true for developing countries where the fluctuations of the forex are much higher. 

CONCLUSION.

We have try to establish that the supporters of the CTT must not be to shy if they want to curb effectively speculation and generate new resources for development. We don’t think that a tax rate of 1 to 5 basis points is appropriate to reach this goals, even in developed countries. If the tax is too “market friendly” the danger is that the market can swallow it to easily. We would have demonstrated its inefficacy, and this is not what we want.

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