1. Theory of bid-ask spreads

The basic transactions cost in the interbank market is the bid-ask spread (Levich (1985)). Banks which are active in the market quote bid and offer prices at which they are prepared to deal with each other and with (large) customers. Around 10 to 15 percent of transactions reported by banks arise through dealings with nonbank customers, the rest through dealings with other banks, either directly or through brokers. The basic problem for the bank trader is to maximize trading profits without becoming overexposed to risk in any one currency. Since banks are committed to trading at the prices they quote, their positions are continually becoming unbalanced via trades with each other and with customers. As this happens they seek to square up their positions by further transactions, thus generating additional volume in the market. Finally, banks will actively take positions by trading at what they regard as favorable prices, expecting to close out the position later at a profit.

Allen (1977) and Booth (1984) have discussed the determination of bid-ask spreads in the foreign exchange market, while Demsetz (1968) and more recently Cohen et al. (1986) have discussed bid-ask spreads in securities markets. Both Allen and Booth assume the dealer is risk averse and analyze the problem as a type of portfolio choice. In Allen, the portfolio choice variables are the bid and ask prices, which are assumed to influence the probabilities of transacting at those prices. The relationship between prices and probabilities seems intuitively plausible but empirically difficult to estimate. In Booth, interaction between a risk-averse monopolistic dealer and risk averse customers leads to a bid-ask spread which depends only on differences in the exchange rate expectations of customers on the buying and selling sides of the market, implausibly independent of degrees of risk aversion and of exchange risk.

The following analysis assumes random buy and sell orders placed by liquidity traders “at the market” with a representative competitive risk-neutral dealer who then clears the market in deals with price-sensitive speculative traders. Let ${\tilde{\mathrm{Q}}}_{\mathrm{s}}$ and ${\tilde{\mathrm{Q}}}_{\mathrm{d}}$ be random sell and buy orders in a specific bilateral currency market from liquidity traders, each with mean liquidity traders, each with mean $\overline{\mathrm{Q}}$. Let P_b and P_a be the dealer’s posted bid and ask prices with mean $\overline{\mathrm{P}}$. ^2/ The actual price $\tilde{\mathrm{P}}$ at which the dealer can close out his position is determined after orders from liquidity traders have been received and accepted by interaction in the market with price-sensitive speculative traders who buy or sell at the actual price and expect to reverse their transaction later at the mean price. Therefore, the actual price is determined according to the equation

where $\begin{array}{c}\mathrm{b}\mathrm{\left(}\tilde{\mathrm{P}}\mathrm{-}\overline{\mathrm{P}}\mathrm{\right)}\end{array}$ and $\mathrm{-}\mathrm{a}\mathrm{\left(}\tilde{\mathrm{P}}\mathrm{-}\overline{\mathrm{P}}\mathrm{\right)}$ represent the price-sensitive traders’ supply and demand for foreign exchange, respectively. By taking the expected value of

(1), it can be seen that $\mathrm{E}\tilde{\mathrm{P}}=\overline{\mathrm{P}}$.

The representative dealer’s profit can then be defined as

If we define the spread t = P_a-P_b, then the expected value of the dealer’s profit is

Using (1) above, we can write (3) as

where σ²_p is the variance of $\tilde{\mathrm{P}}$ around $\overline{\mathrm{P}}$.

The assumption of competitive risk-neutral dealers will force expected profit to zero (or to a level just sufficient to cover dealer costs). As a result we find

The implication of this analysis is that spreads in the interbank market will vary directly with riskiness as measured by the variability of the exchange rate in the very short run and inversely with the expected volume of transactions in the market. Thus wider spreads will be expected in low volume markets and narrower spreads in markets where the authorities enforce narrow bands of short-term fluctuation, as in the EMS. Imperfect competition would be reflected in the addition of a margin c to equation (5), leading to wider spreads which would just tempt new entrants to reduce spreads to earn profits and gain market share. Where banks expect to have multiple relationships with customers, price competition via narrower spreads in the exchange market might be used to attract business that would bring profits in other areas.

The discussion so far relates to spreads quoted by bank dealers to customers. But Cohen et al. (1986) make clear that in securities markets observed market spreads will frequently be less than dealer spreads. Close observation of exchange market behavior confirms their conclusion. In active markets dealers will be constantly changing quotes with the arrival of new information and new orders from customers. Overlapping quotes from different dealers each using the same spread will create a narrower market spread during periods of significant market activity. Thus observed market spreads will also vary from (5) inversely with the current volume of transactions.

2. Estimation

As noted earlier, Boothe (1988) and Glassman (1987) have recently estimated the relationship between exchange rate spreads and volatility. Glassman examined daily spreads for bilateral dollar rates for six major currencies from 1975-83, finding a positive relationship with volatility, but mixed and confusing results for volume as measured by the volume of futures trading on the Chicago Mercantile Exchange. However, since futures contracts represent only 1.4 percent of the New York interbank market turnover, according to the March 1986 Federal Reserve Bank of New York survey, it is unlikely that futures volume is an accurate reflection of the total market volume. Boothe related weekly average spreads for seven currencies for 1980-81 to volatility and the interest differential as a measure of the expected change in the exchange rate, finding significant relationships in five out of seven cases.

While it is possible to replicate their work with daily and weekly data, the more significant challenge is to measure the effect of volume in combination with volatility. Unfortunately, accurate volume data are only available in surveys taken every three years by the Federal Reserve Bank of New York and other central banks. Therefore, I have calculated the annual average of the daily spread and the annual standard deviation of daily percentage changes for seven major currencies versus the dollar for the years in which the Federal Reserve Bank of New York conducted its survey of exchange market volume: 1980, 1983, and 1986. This provides 21 observations on the three key variables in equation (5). The spread is measured as the logarithm of the ratio of the asking price to the bid, the percentage change is measured by the logarithmic change in the middle rate, while volume is measured as share of the total market. The currencies are the deutsche mark, yen, pound sterling, French franc, Italian lira, Swiss franc, and Canadian dollar. Equation (6) below gives the results of regressing the spread (SPR) on the standard deviation of changes (SDCH), volume (VOL), and their ratio (SDCH/VOL), which according to equation (5) is the appropriate variable. ^3/

Analysis of the residuals from the above cross-section, time series regression shows that they have no remaining effects due to time or specific currency. While it would be nice to have more frequent observations on volume, it is impressive that it enters in the nonlinear form suggested by the theory. From equation (6), the elasticity of the spread is 0.675 with respect to volatility and -0.14 with respect to volume, at the sample mean.

This regression analysis has provided us with one key empirical link in the chain of relationship between transactions costs and vehicle currencies. We now turn to the other link.

1. Theory

Among the few attempts to model vehicle currencies, the work of Krugman (1980) and Chrystal (1984) stands out. Each assumes an underlying structure of payments based on transactions in goods and capital markets. Each assumes that transactions costs will be inversely proportional to volume in each bilateral currency market. Each then shows that a vehicle currency will emerge whenever indirect exchange costs through the vehicle are less than direct exchange costs between two nonvehicle currencies. Building on the structure of transactions costs derived above, this section modifies the approach of Chrystal, who used a model of uninformed traders based on the origin of currencies in barter exchange, following Jones (1976). In contrast, we use a model of liquidity traders who know exactly where to trade but who must rely on bank dealers and speculators to set the price at which they may trade.

We assume the bank is receiving orders from customers to buy currency j in exchange for currency i. The bank may offer to execute this transaction either directly or through a vehicle.

T = (t_ij) is a matrix of transactions costs or bid-ask spreads between currencies defined by equation (5) above. Assume

for some i,j ≠ n.

U = (u_ij) is a matrix of the fraction of customers entering on a given day who wish to exchange currency i for currency j directly. This is assumed to be independent of t_ij.

u = (u₁,….,u_n) is a vector of the row sums of U representing the fractions of customers wanting to purchase currency i directly.

q = (q₁,….,q_n) is a vector of shares of transactions in currency i taking account of both direct and vehicle use of each currency.

s is the fraction of direct currency exchanges occurring indirectly through the medium of currency n. The second transaction is assumed to take place on the same day, rather than on the next day as in Chrystal and Jones.

m is the number of individuals entering the market each day to make direct transactions, assumed constant for the purposes of this analysis. Each individual transaction is assumed to be of equal size, normalized to unity in terms of the numeraire.

The total demand for currency i on a given day is then mu_i if i = 1,….,n-1, and mu_n + ms if i = n. Since the total number of participants is m + ms, we find q_i related to u_i as

for i = 1,….,n-1 and

for i = n.

Equations (8) and (9) can be written in vector form as

where e_n = (0,0,….,0,1). Assuming that demanders and suppliers utilize the vehicle in the same proportions, we have for i,j ≠ n

Similarly, for j (or i) = n

We may now see how transactions costs are related to the use of vehicle currencies by substituting (11) and (12) into (5), which is repeated here in general form, with σ_ij as the variance of the exchange rate between currencies i and j.

Performing the substitution, for nonvehicle currencies, we have

and for vehicle currencies

Thus we have t_ij increasing in s and t_in decreasing in s.

To obtain an index of the relative magnitude of transactions costs via the vehicle compared to direct transactions costs, I define τ as the ratio of a weighted average of (15) relative to a weighted average of (14), using as weights the u_ij which by assumption are independent of t_ij.

From (14)-(16), we can write the supply function τ = Ø(s) as a convex decreasing function of s

with Ø < 0, Ø″ > 0.

The highest value of τ occurs at s = 0, τ_max = Ø(0). See Figure 1.

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Transactions Costs and Vehicle Currency Use

Citation: IMF Working Papers 1989, 096; 10.5089/9781451949902.001.A001

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The analysis is completed by specifying the demand function and a rule for the adjustment of s. The demand for vehicle use by traders is assumed to depend inversely on relative transactions costs according to

Thus as transactions costs through the vehicle fall, its use increases. In order for the analysis to be interesting, there must be some use of the vehicle, so I assume θ(τ_max) > 0.

In order to approximate a discrete process involving decisions by thousands of individual customers and hundreds of traders as a continuous function, I will assume that s is adjusted smoothly according to

For stability, we must have θ’ < 1/φ’. Figure 1 shows the case of an internal solution E for s^*, although the function θ(τ) need not be as regular as I have drawn it. Since s is bounded above by 1 - u_n, there will be a unique solution for s^* as long as the process starts from s = 0. The figure dramatically demonstrates the impact of economies of scale with increasing use of the vehicle, as increasing use reduces transactions costs further, inducing yet greater use of the vehicle.

This analysis of the interaction between transactions costs and vehicle use can be used to explore several issues discussed in the introduction to this paper. For example, consider the issues of changes in the degree of competition and changes in communication costs. Either imperfect competition or a level of operational communications costs can be represented in the form of a proportional markup c_ij > 1 multiplied into the right-hand side of (13). This means the numerator and denominator of (17) will contain multiplicative terms c_in and c_ij, respectively. Thus increased competition in the vehicle currency market will reduce markups c_in, shifting the Ø function down and raising s^*.

On the other hand, formation of a currency area such as the EMS outside the ambit of the vehicle will reduce exchange rate variability σ_ij for i,j ≠ n and therefore bid-ask spreads among the members. At the same time, variability against the vehicle σ_in may well increase, raising vehicle spreads t_in. Both factors will cause the Ø function to shift up, reducing the use of the vehicle.

The impact of falling communications costs depends on whether they affect the vehicle currency more or less than the nonvehicle currencies. It might be expected that communications costs among nonvehicle currencies c_ij would fall more than with the vehicle, since currencies which do not have extensive economies of scale might be expected to benefit more. The Ø function would then shift up, reducing the use of the vehicle.

2. Estimation

In order to evaluate the realism of the model depicted in Figure 1, we need to put empirical flesh on the bones of the theory constructed so far. The relationship of t_in to q_in has been estimated in equation (6) above, which at least provides insight into the general relationship of t_ij to q_ij. What remains to determine is the relationship of q_ij to u_ij and s (giving τ = Ø(s)) and the response of s to changes in t_ij (giving s = θ(τ)). Available data do not permit complete estimation of these relationships. However, utilizing and updating the data on currency denomination of trade in Page (1981) will allow us to construct two observations on the trade component of u_ij, for 1980 and 1987. Data on the currency composition of international bonds and bank loans will provide proxies for the capital flow components of u_ij.

Let us begin with the definition of u_ij, the share of customer transactions that are sales of currency i and purchases of currency j. Consider the following definitions.

ε_ji is the share of i’s exports denominated in currency j, assumed independent of transactions costs (Σ_j ε_ij = 1).

μ_ij is the share of i’s imports denominated in currency j, assumed independent of transactions costs (Σ_jμ_ij = 1).

X_i is i’s share of total world exports, measured in some numeraire currency (ΣX_i = 1).

M_i is i’s share of total world imports (equal to world exports), measured in numeraire currency (ΣM_i = 1).

v_ij is the share of trade transactions that represent purchases of currency j and sales of currency i.

k_ij is the share of total capital flows that represent purchases of currency j and sales of currency i.

We may now relate v_ij, the share of trade transactions involving sales of i and purchases of j, to the denomination and trade shares as follows. To begin with, exporters from j are selling currency i and importers into i are buying currency j. Note that the matrix V = [v_ij] is not symmetric. Therefore the trade component v_ij is

Let α represent the share of trade transactions in total customer transactions and 1-α the share of capital flows. Then

a. Trade flows

Appendix Tables A.1 to A.4 provide data on ε_ij and μ_ij for the years 1980 and 1987, while International Financial Statistics provides data for X_j and M_i, permitting the construction of Tables 1 and 2 below containing estimates of the trade component v_ij for the respective years. The OPEC import shares μ_7j M₇ are added to the elements of the first row of V representing sales of dollars and purchases of other currencies. The parenthetical diagonal entries in the tables represent the percentage of world trade that constitutes exports or imports from the home country denominated in the home currency and are included for completeness, even though they do not involve foreign exchange. According to Table 1, for example, in 1980 U.S. exports and imports denominated in dollars constituted 22.57 percent of world trade.

Table 1.

Currency Use in Trade, 1980

(In percent)

Source: Appendix Tables A.1 and A.3.

Table 1.

Currency Use in Trade, 1980

(In percent)

Sell/Buy	Dollar	Deutsche Mark	Yen	Pound Sterling	French Franc	Italian Lira
Dollar	(22.57)	1.95	4.67	1.72	1.41	1.36
Deutsche mark	3.31	(12.53)	0.28	0.47	0.89	0.57
Yen	6.76	0.10	(2.20)	0.06	—	—
Pound	1.84	0.69	0.08	(6.67)	0.49	—
French franc	2.41	1.17	0.07	0.38	(6.18)	0.54
Italian lira	2.33	0.73		0.26	0.47	(2.41)

Source: Appendix Tables A.1 and A.3.

View Table

Table 1.

Currency Use in Trade, 1980

(In percent)

Sell/Buy	Dollar	Deutsche Mark	Yen	Pound Sterling	French Franc	Italian Lira
Dollar	(22.57)	1.95	4.67	1.72	1.41	1.36
Deutsche mark	3.31	(12.53)	0.28	0.47	0.89	0.57
Yen	6.76	0.10	(2.20)	0.06	—	—
Pound	1.84	0.69	0.08	(6.67)	0.49	—
French franc	2.41	1.17	0.07	0.38	(6.18)	0.54
Italian lira	2.33	0.73		0.26	0.47	(2.41)

Source: Appendix Tables A.1 and A.3.

Table 2.

Currency Use in Trade, 1987

(In percent)

Source: Appendix Tables A.2 and A.4.

Table 2.

Currency Use in Trade, 1987

(In percent)

Sell/Buy	Dollar	Deutsche Mark	Yen	Pound Sterling	French Franc	Italian Lira
Dollar	(24.23)	3.14	6.99	1.80	1.38	1.33
Deutsche mark	2.30	(15.16)	0.43	0.41	1.01	1.03
Yen	5.37	0.18	(3.94)	0.06	0.09	—
Pound	1.39	1.19	0.23	(6.69)	0.74	0.13
French franc	1.34	1.32	0.08	0.30	(6.93)	0.73
Italian lira	1.56	1.20		0.26	0.71	(3.26)

Source: Appendix Tables A.2 and A.4.

View Table

Table 2.

Currency Use in Trade, 1987

(In percent)

Sell/Buy	Dollar	Deutsche Mark	Yen	Pound Sterling	French Franc	Italian Lira
Dollar	(24.23)	3.14	6.99	1.80	1.38	1.33
Deutsche mark	2.30	(15.16)	0.43	0.41	1.01	1.03
Yen	5.37	0.18	(3.94)	0.06	0.09	—
Pound	1.39	1.19	0.23	(6.69)	0.74	0.13
French franc	1.34	1.32	0.08	0.30	(6.93)	0.73
Italian lira	1.56	1.20		0.26	0.71	(3.26)

Source: Appendix Tables A.2 and A.4.

What is particularly notable about the tables is the sum of the top row and left-hand column, representing foreign exchange transactions directly involving the dollar. In 1980 such transactions constituted 27.77 percent of world trade. By contrast, the sum of the elements in the remainder of the matrix, the inner 5x5 submatrix constituting transactions not involving the dollar, amounted to only 7.17 percent of world trade in 1980. Under these conditions, it is easy to understand why transactions costs in bilateral dollar/foreign currency markets have encouraged the use of the dollar as a vehicle currency.

On the other hand, comparing 1987 to 1980, the nondollar share has risen from 7.17 percent to 10.10 percent, while the dollar share has fallen from 27.77 percent to 26.60 percent. Of the 2.93 percentage point increase in the nondollar exchange market, 1.87 points, or 64 percent, is attributable to increased use of the deutsche mark. Another 0.70 points, or 24 percent, is due to increased use of the French franc (omitting franc/mark transactions). The yen, by contrast, has hardly increased its role in world trade at all, except through transactions also involving the dollar.

b. Capital flows

Let us now consider calculation of the capital flows k_ij. Assume that the capital flows are denominated in the same proportions as the stocks of international bonds and bank loans outstanding. Data on the currency denomination of bonds and bank loans, shown in Appendix Tables A.5 and A.6, can be used to construct estimates of the weighted average share k = (k₁,…,k₄) of bonds and bank loans outstanding denominated in the four major currencies in 1982 and 1987 (except 1983 data on bank loans from the Bank for International Settlements have been used). I assume that trading in these assets is proportional to the existing stocks and that cross-trading between currency i and currency j is proportional to the product of their respective shares in total assets. Thus given a vector k of asset shares, I form a matrix K = k’k representing the shares of trade in asset markets involving sales of currency i and purchases of j. The results for 1982 and 1987 are shown in Tables 3 and 4. An alternative calculation has also been performed using the new issue and flow data shown in Tables A.7 and A.8. The resulting vectors of asset shares are k₈₁ = (67.77, 8.57, 5.15, 2.86) and k₈₇ = (44.36, 8.65, 25.0, 4.85).

Table 3.

Currency Use in Capital Flows, 1982

(In percent)

Source: Appendix Tables A.5 and A.6.

Table 3.

Currency Use in Capital Flows, 1982

(In percent)

Sell\Buy	Dollar	Deutsche Mark	Yen	Pound
Dollar	48.44	7.41	2.42	1.59
Deutsche mark	7.41	1.13	0.37	0.24
Yen	2.42	0.37	0.12	0.07
Pound	1.59	0.12	0.07	0.05

Source: Appendix Tables A.5 and A.6.

View Table

Table 3.

Currency Use in Capital Flows, 1982

(In percent)

Sell\Buy	Dollar	Deutsche Mark	Yen	Pound
Dollar	48.44	7.41	2.42	1.59
Deutsche mark	7.41	1.13	0.37	0.24
Yen	2.42	0.37	0.12	0.07
Pound	1.59	0.12	0.07	0.05

Source: Appendix Tables A.5 and A.6.

Table 4.

Currency Use in Capital Flows, 1987

(In percent)

Source: Appendix Tables A.5 and A.6.

Table 4.

Currency Use in Capital Flows, 1987

(In percent)

Sell\Buy	Dollar	Deutsche Mark	Yen	Pound
Dollar	28.60	7.31	7.51	2.34
Deutsche mark	7.31	1.87	1.92	0.60
Yen	7.51	1.92	1.97	0.62
Pound	2.34	0.60	0.62	0.19

Source: Appendix Tables A.5 and A.6.

View Table

Table 4.

Currency Use in Capital Flows, 1987

(In percent)

Sell\Buy	Dollar	Deutsche Mark	Yen	Pound
Dollar	28.60	7.31	7.51	2.34
Deutsche mark	7.31	1.87	1.92	0.60
Yen	7.51	1.92	1.97	0.62
Pound	2.34	0.60	0.62	0.19

Source: Appendix Tables A.5 and A.6.

I then take a weighted average of the v_ij and k_ij to represent u_ij. As weights I use (0.15 and 0.85) and, alternatively (0.50, 0.50). Given these data on u_ij, we need only to examine data on t_ij to evaluate the relevance of the model. Unfortunately, because of the dominance of the dollar in foreign exchange markets, most readily available bid-ask quotations are for bilateral dollar/foreign currency rates t_in. However, I have been able to obtain daily average bid-ask quotations from Frankfurt in terms of the deutsche mark, from Paris in terms of the French franc, and end-of-month quotations from London in terms of the Pound sterling, as well as daily average quotations from New York in terms of the dollar, for both 1980 and 1987. These data are shown in Tables 5 and 6. What is immediately evident from the tables is the clear superiority of the bilateral dollar spreads by comparison with the mark, pound, and franc bilateral spreads. Also apparent is the sharp fall in the pound spreads by 1987, due to the increased competition in London financial markets following the end of foreign exchange controls in 1980.

Table 5.

Daily Average Bid-Ask Spreads, 1980

(In percent, in terms of domestic currency)

Sources: New York data from Data Resources Inc., Frankfurt, London, and Paris data from Statistiches Beihefte zu den Monachtsberichten der Deutschen Bundesbank, Reihe 5: Die Wahrungen Welt.

^1/Average of month-end data.

Table 5.

Daily Average Bid-Ask Spreads, 1980

(In percent, in terms of domestic currency)

Market	Dollar	Deutsche Mark	Yen	Pound	French Franc	Italian Lira
New York	—	0.044	0.060	0.047	0.049	0.060
Frankfurt	0.44	—	0.37	0.33	0.37	0.47
London 1/	0.73	0.97	1.65	—	0.63	0.57
Paris 1/	0.26	0.25	0.31	0.22	—	0.26

Sources: New York data from Data Resources Inc., Frankfurt, London, and Paris data from Statistiches Beihefte zu den Monachtsberichten der Deutschen Bundesbank, Reihe 5: Die Wahrungen Welt.

^1/Average of month-end data.

View Table

Table 5.

Daily Average Bid-Ask Spreads, 1980

(In percent, in terms of domestic currency)

Market	Dollar	Deutsche Mark	Yen	Pound	French Franc	Italian Lira
New York	—	0.044	0.060	0.047	0.049	0.060
Frankfurt	0.44	—	0.37	0.33	0.37	0.47
London 1/	0.73	0.97	1.65	—	0.63	0.57
Paris 1/	0.26	0.25	0.31	0.22	—	0.26

Sources: New York data from Data Resources Inc., Frankfurt, London, and Paris data from Statistiches Beihefte zu den Monachtsberichten der Deutschen Bundesbank, Reihe 5: Die Wahrungen Welt.

^1/Average of month-end data.

Table 6.

Daily Average Bid-Ask Spreads, 1987

(In percent, in terms of domestic currency)

Sources: Same as Table 5, except daily average Paris data from Data Resources, Inc.

^1/Average of month-end data.

Table 6.

Daily Average Bid-Ask Spreads, 1987

(In percent, in terms of domestic currency)

Market	Dollar	Duetsche Mark	Yen	Pound	French Franc	Italian Lira
New York	—	0.054	0.047	0.050	0.053	0.080
Frankfurt	0.44	—	0.24	0.48	0.54	0.72
London 1/	0.061	0.34	0.051	—	0.097	0.047
Paris	0.20	0.18	0.19	0.20	—	0.19

Sources: Same as Table 5, except daily average Paris data from Data Resources, Inc.

^1/Average of month-end data.

View Table

Table 6.

Daily Average Bid-Ask Spreads, 1987

(In percent, in terms of domestic currency)

Market	Dollar	Duetsche Mark	Yen	Pound	French Franc	Italian Lira
New York	—	0.054	0.047	0.050	0.053	0.080
Frankfurt	0.44	—	0.24	0.48	0.54	0.72
London 1/	0.061	0.34	0.051	—	0.097	0.047
Paris	0.20	0.18	0.19	0.20	—	0.19

Sources: Same as Table 5, except daily average Paris data from Data Resources, Inc.

^1/Average of month-end data.

We are now in a position to calculate estimates of τ. We first calculate u_ij = 0.15*v_ij + 0.85*k_ij for 1980 and 1987, based on Tables 1 to 4. The numerator of τ in equation (16) can then be calculated from the first row and column of the matrix U and the first row of Table 5 for 1980 (corresponding elements of U and Table 6 for 1987). The denominator terms involving the deutsche mark, pound sterling and French franc can be calculated from the relevant nondollar row and column elements of U, multiplied by the corresponding elements of Table 5 for 1980 (and correspondingly for 1987). The results of this calculation give τ = 1.3213 in 1980 and τ = 1.3837 in 1987, which is a 4.7 percent increase in τ. A calculation with equal weights for trade and capital flows gives a 6.4 percent rise in τ from 0.8387 to 0.8921. Thus the calculations appear to show a modest, but unambiguous rise in τ, the weighted average ratio of dollar transactions costs to nondollar transactions costs. These results are consistent with an upward shift in the Ø function. An alternative calculation using new issue data for capital flows shows an 18.56 percent increase in τ from 1.1804 to 1.3995 with a 15/85 weighting for capital flows and a 10.1 percent increase from 0.8086 to 0.8904 with a 50/50 weighting. Given wide variations in the currency denomination of new issues, I regard the results based on stocks as more reliable. We may then ask if τ has risen, has s fallen?

Total exchange market turnover q_ij including indirect vehicle currency use and endogenously determined flows in the foreign exchange market itself can be observed only in the periodic market surveys reported in Table 7. From these data it is apparent that almost all transactions involve the vehicle currency, with only London showing a small 3 percent share for cross-currency transactions not involving the vehicle. However, the cross-currency share in New York is almost certainly understated in Table 7, because of failure to ask the correct questions.

Table 7.

The Currency Composition of Banks’ Foreign Exchange Market Turnover

Sources: Federal Reserve Bank of New York; Bank of England Quarterly Bulletin (1986), pp. 379-382; and Kinyu Zaisei Jijou (September 1986) pp. 38-39.

Table 7.

The Currency Composition of Banks’ Foreign Exchange Market Turnover

Percent	New York			London March 1986	Tokyo March 1986
	March 1980	April 1983	March 1986
Deutsche mark	31.7	32.5	34.2	28	10.4
Yen	10.2	22.0	23.0	14	77.0
Sterling	22.8	16.6	18.6	30	3.4
Swiss franc	10.1	12.2	9.7	9	5.6
French franc	6.9	4.4	3.6	4	0.3
Canadian dollar	12.3	7.5	5.2	2	—
Other currency	6.0	4.6	5.8	10	3.3
Cross currency	—	0.2	—	3	—

Sources: Federal Reserve Bank of New York; Bank of England Quarterly Bulletin (1986), pp. 379-382; and Kinyu Zaisei Jijou (September 1986) pp. 38-39.

View Table

Table 7.

The Currency Composition of Banks’ Foreign Exchange Market Turnover

Percent	New York			London March 1986	Tokyo March 1986
	March 1980	April 1983	March 1986
Deutsche mark	31.7	32.5	34.2	28	10.4
Yen	10.2	22.0	23.0	14	77.0
Sterling	22.8	16.6	18.6	30	3.4
Swiss franc	10.1	12.2	9.7	9	5.6
French franc	6.9	4.4	3.6	4	0.3
Canadian dollar	12.3	7.5	5.2	2	—
Other currency	6.0	4.6	5.8	10	3.3
Cross currency	—	0.2	—	3	—

Sources: Federal Reserve Bank of New York; Bank of England Quarterly Bulletin (1986), pp. 379-382; and Kinyu Zaisei Jijou (September 1986) pp. 38-39.

The data in Table 7 are not inconsistent with a small decline in s occurring over the period 1980-86. In 1980 s must have been less than the value of 1 - u_n = 0.88, based on Tables 1 and 3, with trade weighted at 15 percent. If we take the 3 percent London estimate for nondollar transactions as representative, it suggests that s may have fallen something like three percentage points. This is what would be expected to happen if the Ø function shifted upwards while the θ function remained unchanged. Of course the small magnitude of these effects suggest that we should treat these results with caution.