March 21, 2013
One of the reasons that many proponents give for supporting a financial transactions tax (FTT) is that it will reduce trading volume in financial markets. This can be considered good for two reasons.
First it may reduce the likelihood of erratic fluctuations that have no basis in the fundamentals like the flash crash in the spring of 2010. The existence of a huge amount of rapidly traded assets can create this sort of sudden divergence from fundamental driven prices. Reducing trading volume may reduce the probability of similar occurrences.
The other reason that a reduction in trading volume is desirable is that it would reduce the amount of resources wasted in the financial sector. The labor and capital absorbed in trading are resources that could in principle be used productivity elsewhere in the economy. If greater trading volume does not in some way result in the better allocation of capital then we should be pleased to the extent that an FTT reduces trading volume in various markets.
For this reason, a paper published by the CATO Institute last summer showing that a FTT would lead to a sharp decline in the trading of futures should not be seen as negative from the standpoint of proponents of FTTs. Unfortunately, the paper did not accurately measure the decline in trading volume that would result from a tax, leading to an overstatement of the actual decline that would be implied with the tax rate and elasticities assumed in the paper. This mistake wrongly leads the paper to conclude that several major future markets would disappear even with a low tax rate. When a correct calculation is done, it can be shown that this is not true.
The paper’s mistake is a simple one. Elasticities are usually calculated as point elasticities, which relate the change in quantity that would result from a small change in price. For most questions we ask, where we consider price changes that are relatively small (say under 20 percent) using a point elasticity will give us a reasonably good approximation of the change in quantity that would result from the change in price being considered.
However for large changes of the type considered in this paper (all the changes in the price of transactions resulting from the FTT are far more than 100 percent of the current cost of transactions) it is necessary to be more careful in the calculation.
The correct measure of elasticity to apply would be an arc elasticity. This relates the change in quantity over the average of the old and new quantity to the change in price over the average of the old and new price.
Elasticity = (D Q/ ((Q1 +Q2)/2)) / (DP/ ((P1+P2)/2)
Where Q1 is the pre-tax quantity, Q2 is the post-tax quantity, P1 is the pre-tax price of the transaction, and P2 is the post-tax price of the transaction.
The change in quantity is D Q and the change in price is D P
This formula generates considerably smaller decline in trading volume than the ones calculated in the Wang and Yau paper.
This can be seen by taking the example of a 0.02 percent tax on S&P 500 futures highlighted in the paper. The paper assumes that the current transactions cost of a S&P future is $14.80. It calculates that the 0.02 percent tax on a future, with an average price of $283,981 in 2010 would increase transactions costs by $56.80, or 383.8 percent of the pre-tax transactions cost. The paper relies on prior work that estimates an elasticity of trading in the S&P 500 futures market -0.81. Applying the point estimate method to calculate the change in trading volume it multiples the percentage change in price times elasticity, which gives:
D Q = 383.8% * (-0.81) = -310.9%
In other words, this completely eliminates the market since trading volume declines by more than 100 percent.
However, if we applied an arc elasticity then the percentage change in would be -69.3 percent (see appendix for this calculation): This is of course a very large drop in trading volume, but would still leave a market with annual trading of $670 billion, down from a pre-tax market volume of over $2 trillion.
In fact, if the correct methodology was applied to the other futures contracts shown in Table 2 in the paper, it is unlikely that any markets would actually disappear as a result of a 0.02 percent tax. (The paper doesn’t show current trading costs for other markets, so it is not possible to be certain this is the case.)
With elasticities that are less than one, it is impossible for any price increase to completely eliminate the market. Even when elasticities are slightly above 1, it would take an extraordinarily large increase in prices to completely eliminate a market.
This should not be surprising if we step back and consider the issue for a moment. If a tax of 0.02 percent would eliminate the market this means that the value of trades in this market is less than 0.02 percent of the price of futures contract being traded. While this is likely true for many of the trades in the market, it is unlikely to be true for all of the trades.
Futures contracts do serve an economic purpose and it is unlikely that the actors in the market who are buying contracts for their actual purpose (e.g. farmers wanting insurance on crop prices or airlines wanting insurance on jet fuel costs) would abandon the market completely if the price of the contract were to rise by 0.02 percent of the nominal value of the contract. In fact, since many of these futures markets have existed for many decades, when transactions costs were far higher than they would be now even with a 0.02 percent transactions tax, it is not plausible that this tax would eliminate the market.
The fact that trading volume would tumble as a result of the tax is likely consistent with how most supporters of FTTs would view its impact. The FTT would eliminate a large amount of short-term and speculative trading, while still allowing a large enough volume of trading for the markets to serve their purpose. In this case, the tax on this single futures contract (which has one of the lowest trading volumes of the futures contracts shown in Table 2 of the paper) would still raise $135 million a year in revenue each year and almost $2.0 billion in the 10-year budget window.
The incidence of this tax falls overwhelmingly on the financial industry, even in this case where we have assumed that 100 percent of the tax is passed on to traders in the form of higher costs. Previously traders had been paying $114 million a year in transactions costs on S&P 500 contracts, according to the estimates in the paper. After the implementation of the tax they would be spending $168 million a year, including the tax. This means that the government would be collecting $133 million annually while traders were only seeing their costs rise by $54 million, as shown in Table 1.
The situation would look even better from the standpoint of traders if we assume that a modest portion of the tax (e.g. 10 percent) was eventually passed on to the financial sector in the form of lower fees per transaction. This seems plausible since the sharp drop in demand for services from the sector is likely to lead to some decline in the wages and prices in the sector. In this case the reduction in trading volume would be slightly less, with volume falling to $710 billion a year. The tax would then $142 million a year, or more than $2.1 billion over the 10-year budget horizon. However in this case, because the fees charged by the intermediaries had fallen, the amount spent on trading would be just $161 million a year, just $47 million more than before the tax was put into place. In this case, financial intermediaries would bear 64 percent of the incidence of the tax ($91 billion/ $142 billion).
|The Case of S&P 500 Futures||
(trillions of dollars)
(millions of dollars)
(millions of dollars)
|After-tax — 100 percent pass through||0.7||34.8||133.0||167.8||59.6%|
|After-tax 90-percent pass through||0.7||23.0||141.7||164.7||64.2%|
Source: Author’s calculations, see text.
The trading that is eliminated can be viewed as a waste of resources. The resources released by the reduction in trading volume will then be available for use in productive sectors of the economy.
It is worth noting that situation would look better from the standpoint of traders for assets where the demand is more elastic, since this means that the same percentage tax increase would result in a larger decline in trading volume. The estimate of elasticity for S&P 500 contracts is lower than all the other estimated elasticities that appear in the Wang and Yau paper, except for home heating oil. (The elasticity on future contracts for home heating oil is estimated at -0.80, compared to 0.81 for S&P 500 future contracts.) This means that a larger portion of the tax would be borne by financial intermediaries for these other contracts.
A modest financial transactions tax will lead to a sharp falloff in trading volume for many types of financial instruments. However it is unlikely to eliminate markets altogether except in cases where the instrument provided very little value to the economy. The decline in trading volume is one of the goals of the tax both since it may reduce volatility in financial markets and reduce the amount of resources consumed by the sector, freeing them up for productive uses elsewhere in the economy. The greater the elasticity of demand in a market, the larger the portion of the tax that will be borne by the financial sector rather than end users. In almost all cases, the financial sector is likely to bear the vast majority of the burden of the tax resulting in considerably lower wages and profits in the sector.
Working with the numbers from the article, we have:
%DP = $56.80/ (($71.60 +$14.80)/2)
= $56.80/ $43.20
We then have to relate this 131.5 percent change in price to the change in quantity using the elasticity estimate of -0.81. This means that the change in quantity will be -0.81 * 131.5 percent or -106.5 percent of the average of the old and new quantities:
DQ = -106% *((Q1 +Q2)/2)
= -106%*(( Q1 +Q1 +DQ) /2), since Q2 = Q1 +DQ
= -106% * ((2Q1/2) +DQ/2)
= -106% *Q1 – (106%*DQ)/2
153% * DQ = -106% *Q1
DQ = -(106%/153%)*Q1 = -69.3% * Q1
 Wang, George and Jat Yau, 2012. “Would a Financial Transactions Tax Affect Financial Market Activity? Insights from the Futures Market, “ Washington, DC: Cato Institute, available at http://www.cato.org/sites/cato.org/files/pubs/pdf/PA702.pdf.
 This calculation assumes that 100 percent of the tax is passed on to traders. This is likely not to be true.
 The product of the elasticity and the percentage change in price would have to exceed 2 for a market to be completely eliminated by a tax.