¹ See, for example, the review of Richard, M. Levich, “Empirical Studies of Exchange Rates: Price Behavior, Rate Determination and Market Efficiency,” in Ronald, W. Jones and Peter, B. Kenen, eds., Handbook of International Economics (Amsterdam, 1985), vol. 2, pp. 1020–36.Google Scholar

² Some investigators of gold-standard efficiency are blameless, because they wrote before Benoit Mandelbrot and Paul Samuelson developed the theory of asset-market efficiency in the mid-1960s, which Eugene Fama formalized more generally in 1970. See Eugene, F. Fama, “Efficient Capital Markets: A Review of Theory and Empirical Work,” Journal of Finance, 25 (05 1970), pp. 383–417.Google Scholar

³ There are exceptions. William Poole investigates the efficiency of earlier twentieth-century floating-rate experiences, while Oskar Morgenstern studies gold-standard efficiency in the interwar period as well as prior to World War I, and for France and Germany as well as for Britain and the United States.

⁴ Thus Levich notes: “With the establishment of floating exchange rates in the early 1970s (presumably dominated by free-market behavior), it was natural to begin the investigation of foreign exchange market efficiency.” To his credit, he goes on to write: “It is important to note that government intervention per se does not imply exchange market inefficiency” (Levich, , “Empirical Studies,” pp. 1020, 1024, fn. 39). However, he does not state that a gold standard can be efficient; nor does he acknowledge the literature on gold-standard efficiency.Google Scholar

⁵ Fama, , “Efficient Capital Markets,” p. 383.Google Scholar The best exposition of the theory of asset-market efficiency remains Fama, , “Efficient Capital Markets,” pp. 384–88;Google Scholar a formulation in terms of the foreign-exchange market is provided by Levich, , “Empirical Studies,” pp. 1022–25. Though technically correct, these treatments are too general and too mathematical to be fully understood by the nonspecialist. I hope to make the theory clear to the general reader by defining profit as true economic profit, making explicit the roles of arbitrageurs and speculators as the earners of this profit, and paying attention to the duration of the unit time period.Google Scholar

⁶ Inclusion of the risk premium or normal profit in cost is convenient pedagogically and does not detract from the generality of the analysis. Were one or both of these items excluded from cost, equilibrium profit would equal the risk premium or normal profit rather than zero.

⁷ There is the proviso of fast communication of information and instruction such as that offered by a telegraphic network for the domestic foreign-exchange market (utilized substantially in the United States by the late 1870s) and by oceanic cable for the international market (employed fully in the dollar-sterling market by the later 1880s). See Arthur, H. Cole, “Evolution of the Foreign-Exchange Market of the United States.” Journal of Economic and Business History, 1 (05 1929), pp. 414–16;Google Scholar and Edwin, J. Perkins, Financing Anglo-A Inerican Trade (Cambridge, MA. 1975), pp. 182–83.Google Scholar

⁸ For a brief history of usage of the various instruments and references to other literature on the topic, see Lawrence, H. Officer, “Integration in the American Foreign-Exchange Market, 1791–1900,” this JOURNAL, 45 (09 1985), pp. 559–60.Google Scholar

⁹ While overall cost is expressed as a percentage of the amount invested (see section above entitled “Definition of Exchange Market Efficiency”), it can just as well be interpreted as a percentage of the mint parity.

¹⁰ An Atlantic voyage of different duration from that expected could entail additional cost, but this applies to arbitrage using either exchange instrument (and for gold either exported or imported), and would be reflected in the risk-premium component of overall cost. (See subsection below entitled “Normal Profit, Risk Premium, and Estimated Gold Points,” under “The Data: Gold Points, 1890 to 1906”.)

¹¹ Of course, the gold point and the corresponding (identical) overall cost are specific to the exchange rate under consideration–cable or sight.

¹² For use of forward cable, therefore, the gold-export point is endogenous (dependent on the actions of arbitrageurs). The reason for this unusual situation is that, for consistency with the other two techniques, the spot cable gold point is the focus. Were the forward cable gold point considered instead, the exchange rate (and arbitrage revenue) would be defined as the percentage deviation of the forward (rather than spot) cable rate from parity, and the forward-cable gold point would indeed be exogenous.

¹³ Note that the exchange rate (number of dollars per pound) below mint parity–and, in particular, below the gold-import point–implies a negative redefined exchange rate (percentage deviation from parity). “Increasing” the exchange rate refers to its algebraic value–for example, the rate moving from –3 to –2 percent, that is, from 3 to 2 percent below parity.

¹⁴ Compared to the demand bill, the sixty-day bill entailed an additional sixty days' interest loss for import arbitrage.

¹⁵ These studies are Oskar, Morgenstern, International Financial Transactions and Business Cycles (Princeton, 1959);Google ScholarTruman, A. Clark, “Violations of the Gold Points, 1890–1908,” Journal of Political Economy, 92 (10 1984), pp. 791–823;Google ScholarPablo, T. Spiller and Robert, O. Wood, “Arbitrage during the Dollar-Sterling Gold Standard, 1899–1908: An Econometric Approach,” Journal of Political Economy, 96 (08 1988), pp. 882–92.Google Scholar Also, Lawrence, H. Officer, “The Efficiency of the Dollar-Sterling Gold Standard, 1890–1908,” Journal of Political Economy, 94 (10 1986), pp. 1038–73, is devoted almost entirely to gold arbitrage via cable, with only pp. 1068–71 allocated to arbitrage via demand bills.Google Scholar

¹⁶ For example, confining attention to the 1875 to 1909 period, for gold-export points: Financial Review, 1875, p. 5. Commercial and Financial Chronicle, 01 28, 1882, p. 108. New York Times, 07 2, 1882, p.9; 12 27, 1885, p.7; 03 27, 1896, p.2 04 21, 1896, p. l; 06 28, 1896, p. 2; 04 27, 1897, p. 12; 06 2, 1899, p. 14; 06 9, 1899, p. 5; 06 13, 1899, p. 12; 06 17, 1899, p. 7; 12 16, 1899, p. 11; 03 7, 1909, p. 8. For gold-import points: Commercial and Financial Chronicle, 04 2, 1881, p. 358; 03 3, 1883, p. 232; 05 12, 1906, p. 1069. New York Times, 12 1, 1898, p.4. While I could find one reference to the cable rate alone in connection with a cited gold point (but unidentified by exchange instrument)–New York Times, 11 27, 1892, p. 5–it appears that the gold point nevertheless pertains to demand bills (the writer making the point that even the (higher) cable rate fell below the gold-export point). In several other articles in the New York Times a stated gold point, though unidentified, clearly is for demand bills, shown by comparison with the explicit demand-bill gold-point citations listed above.Google Scholar

¹⁷ New York Times, 08 9, 1895, p. 8; 06 28, 1896, p. 2.Google Scholar

¹⁸ Joseph, French Johnson, Money and Currency (Boston, 1905), pp. 88–91;Google ScholarGeorge, Clare, A Money-Market Primer (London, 1907), pp. 129–30.Google Scholar

¹⁹ Albert, Strauss, “Gold Movements and the Foreign Exchanges,” in The Currency Problem and the Present Financial Situation (New York, 1908), pp. 64–73, for the discussion of gold arbitrage using demand bills, and p. 73, for cable transfers.Google Scholar

²⁰ Charles, F. Dunbar (revised by Oliver, M. W. Sprague), The Theory and History of Banking (New York, 1929), pp. 110–13;Google ScholarIra, B. Cross, Domestic and Foreign Exchange (New York, 1923), pp. 386, 389–91;Google ScholarAlbert, C. Whitaker, Foreign Exchange (New York, 1920), pp. 519, 534, 536.Google Scholar

²¹ Paul, Einzig, International Gold Movements (London, 1931), p. 64.Google Scholar

²² See Cross, , Domestic and Foreign Exchange, p. 386.Google Scholar

²³ Whitaker, , Foreign Exchange, p. 534.Google Scholar

²⁴ There are three reasons for a wide spread. First, even though C. A. E. Goodhart, citing several authorities, can assert that “New York had a flourishing market, both in forward cable transfers … and in forward exchange bills,” he is forced to admit that “there are no statistics on forward exchange rates extant” (The New York Money Market and the Finance of Trade, 1900–1913 [Cambridge, MA, 1969], p. 57). Contemporary newspapers regularly published quotations on sight, sixty-day, and (spot) cable rates. Omission of forward rates indicates that the pre-1914 New York foreign-exchange market might have had a less active market for forward exchange than is generally supposed. Second, the ten-day forward contract required for gold arbitrage was quite distinct from the normal thirty-, sixty-, and ninety-day maturities of forward transactions of other market participants, suggesting a thin market for a ten-day contract. Third, the intermittent nature of gold arbitrage itself made for an often inactive market.Google Scholar

²⁵ Evidence exists for the House of Brown, a leading exchange dealer. See Perkins, , Financing, pp. 184, 291, fn. 24;Google Scholar and Edwin, J. Perkins, “Foreign Interest Rates in American Financial Markets: A Revised Series of Dollar-Sterling Exchange Rates, 1835–1900,” this JOURNAL, 38 (06 1978), pp. 406–7. Until 1879, demand bills also carried a discnminatorily high purchase price, but to a lesser degree than cables.Google Scholar

²⁶ “As the cable market is less active as a rule than the demand market, the cable rate is controlled by the demand quotation”…Thomas, York, International Exchange (New York, 1923), p. 105.Google Scholar

²⁷ Morgenstern, , International Financial Transactions, p. 241.Google Scholar

²⁸ As is done in the literature, reviewed below under the section entitled “Efficiency Concepts in the Literature.”

²⁹ William, H. White, “interest Rate Differences, Forward Exchange Mechanism, and Scope for Short-Term Capital Movements,” International Monetary Fund Staff Papers, 10 (11 1963), pp. 485–501.Google Scholar

³⁰ Ibid., p. 487.

³¹ Ibid., p. 489.

³² White's analog is that importers from the United Kingdom will gain, on average, by hedging (buying forward pounds) for a $2.78 to $2.80 forward rate and rejecting hedging in the $2.80 to $2.82 range, while exporters to the United Kingdom will gain, on average, by hedging (selling forward pounds) for a $2.80 to $2.82 forward rate and rejecting hedging in the $2.78 to $2.80 range. Ibid., p. 489.

³³ Of course other speculation, not specifically oriented to the gold standard, can take place even at $2.80, such as speculation on the seasonal pattern of the exchange rate, it is also possible that no funds would be committed, not just at $2.80 but also within a narrow band around $2.80, because of positive overall cost of speculation. However, the evidence for the pre-1914 American foreign-exchange market is that the exchange dealers themselves were speculators, thereby avoiding the transactions cost inherent in their bid-ask spread and making such a band extremely narrow. See Officer, , “Integration,” p. 578.Google Scholar

³⁴ In considering the demand for forward pounds by importers from the United Kingdom and the supply of forward pounds by exporters to the United Kingdom, White assumes that the demand and supply curves are mirror images of each other (resulting from balanced trade and identical hedging behavior by the importers and exporters). In fact, he graphs the case of linear curves with slopes of the same magnitude, whereupon the curves intersect–meaning zero net demand for forward pounds.–at the midpoint rate, $2.80. See White, , “Interest Rate Differences,” pp. 489–91.Google Scholar

³⁵ This asymmetry of the gold points was recognized by both contemporary writers and later observers. See Clare, , A Money-Marker Primer, p. 129;Google ScholarWhitaker, , Foreign Exchange, pp. 437, 544; Cross, Domestic and Foreign Exchange, p. 392;Google Scholar and Paul, Einzig, The History of Foreign Exchange (London, 1970), p. 173. Theoretical studies of the gold standard and modern textbook treatments, however, invariably assume arbitrage costs to be the same in each direction, implying that mint parity is at the midpoint of the spread.Google Scholar

³⁶ Arbitrage and speculation of all kinds involving the foreign-exchange market are relevant, not just the arbitrage and speculation considered under “Arbitrage Specific to the Gold Standard” and “Speculation Specific to the Gold Standard.”

³⁷ It is assumed that marginal-utility-of-income functions are identical across economic actors and over time, and either that interpersonal comparisons of utility can be made or that compensatory transfers of real income can be effected. Quite analogously, other things being equal (that is, given a stable demand curve), the consumers of a commodity as a group enjoy greater utility (consumers' surplus) at a steady price than if the price vanes symmetrically between equally spaced higher and lower levels (whether in the form of price discrimination across consumers at a in time or via a uniform price changing over time), even though total consumption may be the same.

³⁸ These properties are conditional on a loss function pertaining only to exchange-market inefficiency as such. Given other criteria–such as real income, inflation, the balance of payments, or international reserves–an asymmetrical function could very well be warranted.

³⁹ The precise form of the exponential function is provided in the appendix.

⁴⁰ Alternatively, it may be assumed that exchange-rate speculation is absent and that a “law of large numbers” guarantees that over a sufficiently long time period the exchange rate takes on all values within the spread with equal probability.

⁴¹ See Huntington, A. T. and Robert, J. Mawhinney, Laws of the United States Concerning Money, Banking, and Loans, 1778–1909, S. Doc. 580, 61st Cong., 2d sess. (Washington, D.C., 1910), pp. 686, 696, 698;Google ScholarSayers, R. S., Bank of England Operations, 1890–1914 (London, 1936), p. 72;Google ScholarWhitaker, , Foreign Exchange, pp. 504–5.Google Scholar

⁴² See Sayers, , Bank of England Operations, p. 72; Huntington and Mawhinney, Laws, pp. 537, 685.Google Scholar

⁴³ For details of these policy actions over the 1890 to 1906 period, see the section entitled “The Data: Gold Points” and Tables 3–6.

⁴⁴ Therefore John Dutton's statement that “These … ‘gold devices’ had the effect of increasing the spread between the gold points” is the opposite of the truth (“The Bank of England and the Rules of the Game under the International Gold Standard: New Evidence,” in Michael, O. Bordo and Anna, J. Schwartz, eds., A Retrospective on the Classical Gold Standard, 1821–1931 [Chicago, 1984], p. 178).Google Scholar

⁴⁵ For a review and critique of these tests, see Levich, , “Empirical Studies,” pp. 1023–25, 1028–31.Google Scholar

⁴⁶ For a survey, see Levich, , “Empirical Studies,” pp. 1025–26, 1031–35. My attempt to test for interest-rate parity from 1880 to 1914 without forward-rate data is flawed, because the technique requires absolute confidence in the gold points–clearly absent in 1890 to 1897 (“Efficiency,” p. 1072; and “Selection of Sample Periods” below).Google Scholar

⁴⁷ The studies are Perkins, , Financing. pp. 28–29;Google ScholarLawrence, H. Officer, “Dollar-Sterling Mint Parity and Exchange Rates, 1791–1834.” this JOURNAL, 43 (09 1983), pp. 605, 608;Google ScholarMorgenstern, , International Financial Transactions, pp. 223–41;Google Scholar severely criticized by George, H. Borts, “Review of international Financial Transactions,” Journal of the American Statistical Association, 55 (03 1960), pp. 224–25;Google Scholar and Arthur, H. Cole, “Seasonal Variation in Sterling Exchange,” Journal of Economic and Business History, 2 (11 1929). pp. 203–18;Google ScholarMargaret, G. Myers, The New York Money Market (New York, 1931), pp. 75–76, 339–41, 344–45.Google Scholar

⁴⁸ See Davis, L. E. and Hughes, J. Rs. T., “A Dollar-Sterling Exchange, 1803–1895,” Economic History Review, 13 (08 1960), pp. 58–64;Google ScholarPerkins, , “Foreign Interest Rates,” pp. 410–15; Officer, “Dollar-Sterling Mint Parity,” pp. 603, 606–9; and Officer “Integration,” pp. 567–68.Google Scholar

⁴⁹ See Johnson, , Money and Currency, p. 90,Google Scholar fn. 1; Cole, , “Evolution,” pp. 405–6, 419–20;Google ScholarMyers, , New York Money Market, pp. 73–75, 342–43;Google ScholarEinzig, , History, pp. 172–73;Google Scholar and Officer, , “Integration,” pp. 561–62, 575–81.Google Scholar

⁵⁰ The applicable studies are Morgenstern, , International Financial Transactions, pp. 241–76,Google Scholar criticized by Borts, , “Review,” pp. 225–27;Google ScholarClark, , “Violations,” pp. 791–823;Google Scholar and Officer, , “Efficiency,” pp. 1038–73.Google Scholar The technique receives the implicit approval of Einzig, , History, pp. 194–95.Google Scholar

⁵¹ See Clark, , “Violations,” pp. 806–14, 817–18;Google Scholar and Officer, , “Efficiency,” pp. 1060–64.Google Scholar

⁵² See Spiller, and Wood, , “Arbitrage.”Google Scholar

⁵³ See Officer, , “Integration,” pp. 561–62, 575–82, and “Efficiency,” pp. 1070–71.Google Scholar

⁵⁴ Morgenstern, , International Financial Transactions;Google ScholarClark, , “Violations.”Google Scholar

⁵⁵ For these criticisms, see Borts, , “Review,” pp. 224–27; Davis and Hughes, “Dollar-Sterling Exchange,” pp. 63–64; and Officer, “Integration,” p. 559.Google Scholar

⁵⁶ Clark, , “Violations”;Google ScholarOfficer, , “Efficiency”;Google ScholarSpiller, and Wood, , “Arbitrage.” The only exception is my brief investigation of the 1881 to 1900 period, for which inferior data are employed (“Efficiency,” pp. 1070–71).Google Scholar

⁵⁷ For 1891, Clare, , Money–Money Primer, p. 130; for 1905,Google ScholarJohnson, , Money and Currency, pp. 90–91;Google Scholar for 1913, Einzig, , International Gold Movements, pp. 148–49,Google Scholar and Whitaker, , Foreign Exchange, pp. 524–33. The entire span of data information is contained in the sources to Tables 3–6.Google Scholar

⁵⁸ For an excellent summary account with extensive references to the literature, see Leland, B. Yeager, International Monetary Relations (New York, 1976), pp. 441–72.Google Scholar

⁵⁹ Alexander, D. Noyes, “The Treasury Reserve and the Bond Syndicate,” Political Science Quarterly, 10 (12 1895), p. 575, citing Bagehot.Google Scholar

⁶⁰ See Noyes, , “Treasury Reserve,” pp. 588, 592;Google ScholarAlexander, D. Noyes, Forty Years of American Finance (New York, 1909), pp. 162, 232–33;Google ScholarSprague, O. M. W., History of Crises under the National Banking System (Washington, D.C., 1910), pp. 141–42, 158, 179;Google ScholarMyers, , New York Money Market, p. 378;Google ScholarRendigs, Fels, American Business Cycles (Chapel Hill, 1959), pp. 167, 185–86, 191–95;Google ScholarMatthew, Simon, “The Hot Money Movement and the Private Exchange Pool Proposal of 1896,” this JOURNAL, 20 (03 1960), pp. 32–33;Google ScholarMilton, Friedman and Anna, J. Schwartz, A Monetary History of the United States, 1867–1960 (Princeton, 1963), pp. 104–13.Google Scholar

⁶¹ Friedman, and Schwartz, , Monetary History, p. 105.Google Scholar

⁶² In the 1890s, however, the bankers were no public-spirited agents but rather were motivated by self-interest. Their provision of gold to the Treasury in 1895 involved the purchase of government bonds at 104½12; (4½12; percent above face value) at a time when comparable bonds were being transacted at 113½, and the bonds were marketed by the syndicate at 112¼14; eleven days after the purchase. In four days of bargaining (in writing, by dispatch), the syndicate maintained a tough bargaining stance and won its terms. Either the bankers were prepared to see the gold standard fall, or they were confident that the government would not let it fall (that is, would accept the terms of the syndicate). As Noyes notes: “It was, however, perfectly plain that the administration had no choice but to accept the syndicate's proposition or suspend government specie payments” (“Treasury Reserve,” p. 592).

⁶³ The proximate source is Andrew, A. Piatt, Statistics for the United States 1867–1909, S. Doc. 570, 61st Cong., 2d sess. (Washington, D.C., 1910), PP. 189–205. Obvious misprints or misrecordings are corrected and daily ranges are replaced by their midpoints.Google Scholar

⁶⁴ As noted in the source, the data to 1895 are “posted rates” and from 1896 are “actual rates”. Actual rates were wholesale rates, applying to large-scale transactions; posted rates were formal prices announced by the exchange dealers “as maxima, and employed only for casual business and for small dealings in exchange”. The upward bias of posted rates is minimal, however, for they “ran only fractionally higher” than actual rates. See Cole, , “Seasonal Variation”, P. 214.Google Scholar Indeed, data on posted and actual rates for the 1870 to 1900 period are conjoined and used systematically by Perkins, (“Foreign Interest Rates”, PP. 393, 408–9, 413–15)Google Scholar with no noticeable breaks in the series. (Perkins fails to show awareness of the differential character of his exchange-rate series; a full description is in Cole, , “Seasonal Variation”, pp. 214–15.)Google Scholar

⁶⁵ The source is Board of Governors of the Federal Reserve System, Banking and Monetary Statistics, 1941–1970 (Washington, D.C., 1976), PP. 1046–47.Google Scholar

⁶⁶ “The rate for cable transfers is the basic spot rate in the market…” (Alan, R. Holmes and Francis, H. Schott, The New York Foreign Exchange Market [New York, 1965], P. 34).Google Scholar “The Bank of England, as agent for Her Majesty's Treasury, fulfills its IMF obligation on exchange rate fluctuations by being committed to deal in spot telegraphic transfers for U.S. dollars at the limits of 2.78 and 2.82, respectively” (The Bank of England, “The Foreign Exchange Market in Great Britain”, in Robert, Z. Aliber, ed., The International Market for Foreign Exchange [New York, 1969], p. 90).Google Scholar

⁶⁷ Ideally, the exchange rate would be the midpoint of dealers' bid-ask prices. So for each period the series is an overestimate.

⁶⁸ See fn. 85.

⁶⁹ In “Integration”, pp. 568–74, I construct specie points for the 1790s and 1820s, when the United States was effectively on a silver standard; but, with the underlying data so limited, heroic assumptions are required to generate cost components. In “Violations”, pp. 797–98, 804–5, Clark develops arbitrage interest costs for 1890 to 1908 from first principles, but does not do the same for direct costs. While in “Efficiency”, (pp. 1042–57)I combine Clark's interest costs with direct costs estimated from components, serious problems remain. First, the underlying exchange-rate concept is the cable rather than sight rate. Second, interest cost is marred by Clark's cavalier use of interest-rate parity to eliminate the exchange risk from export arbitrage (see Officer, , “Efficiency”, pp. 1069–70). Third, the dominant arbitrageur group is misidentified and an inappropriate interest-rate series used (see subsection below entitled “Interest Cost: Import Arbitrage”). Fourth, the direct-cost estimates are based on observations for only 44 and 16 months for U.S. export and import arbitrage, respectively, for a sample period of 228 months.Google Scholar

⁷⁰ See Whitaker, , Foreign Exchange, pp. 497, 502.Google Scholar

⁷¹ Obtained by converting the British mint price of 77s. 10½d. per ounce 11002F;12th fine to the American. 9002F;10th. fineness equivalence.

⁷² The Bank always accepted Treasury bars at their stamped fineness. See New York Times, 0117, 1895, p. 3; 01 19, 1895, p. 9; 11 23, 1895, p. 1;Google Scholar and Whitaker, , Foreign Exchange, p. 505.Google Scholar

⁷³ Estimates of the four components of the marginal costs for 1890 to 1906 are provided in Tables 3–5.

⁷⁴ This is 10002F;9th the mint price of $18.60465+ per ounce of gold 9002F;10th fine.

⁷⁵ See Whitaker, , Foreign Exchange, p. 496.Google Scholar Abrasion of sovereigns was much greater than that of exported U.S. coin (see Table 5) because, at $4.86656, the sovereign corresponded closest in value to the half-eagle ($5.00), the lowest-denomination coin exported. Arbitrageurs sought double-eagles–on the principle that the fewer the coins for a given value shipment, the less the abrasion–but the Treasury would provide only a mixture of denominations (half-eagle to double-eagle) in proportion to the stock at hand. See New York Times, 03 19, 1891, p. 3; 03 20, 1891, p.8.Google Scholar

⁷⁶ See Johnson, , Money and Currency, pp. 88–91;Google ScholarStrauss, , “Gold Movements”, pp. 64–68;Google ScholarWhitaker, , Foreign Exchange, pp. 518–39;Google ScholarCross, , Domestic and Foreign Exchange, pp. 383–95.Google Scholar

⁷⁷ See Einzig, , International Gold Movements, p. 82.Google Scholar

⁷⁸ Cross, , Domestic and Foreign Exchange, p. 383.Google Scholar

⁷⁹ See Whitaker, , Foreign Exchange, p. 537;Google ScholarCross, , Domestic and Foreign Exchange, p. 392;Google ScholarMyers, , New York Money Market, pp. 76, 349–50;Google ScholarEinzig, , History, pp. 178–79, 243–44.Google Scholar Why a market for dollar drafts in London failed to develop is not entirely clear. The answer provided in the above literature is twofold. First, there was the long and powerful tradition, going back to colonial times, of financing trade with bills drawn on Britain. Second, British importers and exporters were themselves unwilling to transact in dollars (or other foreign currency) until after World War 1. All the while the balance-of-payments strength of the United States was growing, along with resentment of foreign-exchange dependence on London. Net monetary gold flows–the balance of payments–were negative from 1889 to 1905 but positive for all years but one from 1906 to 1913. The balance on goods and services (U.S. net foreign investment) was negative in 12 of the 15 years from 1881 to 1905 and positive continuously thereafter to the 1970s. (The data source is U.S. Bureau of the Census, Historical Statistics of the United States: Colonial Times to 1970, Part 2 [Washington, D.C., 1975], pp. 867–68.)Google Scholar Attempts on the part of New York to rid itself of dependence on sterling drafts were made, but failed prior to World War I because of domestic political considerations. See Myers, , New York Money Market, pp. 349–50.Google Scholar

⁸⁰ See Johnson, , Money and Currency, pp. 88–91;Google ScholarStrauss, , “Gold Movements,” pp. 64–65;Google ScholarCole, , “Evolution”, pp. 408, 420–21;Google ScholarWhitaker, , Foreign Exchange, p. 519.Google Scholar

⁸¹ Myers, , New York Money Market, pp. 274–75.Google Scholar

⁸² The source is Andrew, , Statistics, pp. 119–35.Google Scholar In contrast, Clark takes (from the same source) the average call-loan rate at the stock exchange, a series less specific to the New York banks. Further, both Clark and I misidentify the primary arbitrageurs, Clark, (“Violations”, pp. 793–94, 801–3) computing arbitrage profits for “American citizen[s]”, and “British subjects” on an equal basis, and I (“Efficiency”, pp. 1041–42, 1057) asserting that the arbitrageurs in the market with the lower interest rate dominated.Google Scholar

⁸³ This figure is the average of annual observations, each observation calculated as the average of weekly rates for the year, with the midpoint taken when the weekly figure is a range. Averaging interest expense over the entire period from 1890 to 1906 would be absurd in a gold-point violations or gold flow approach. The model of gold-standard efficiency developed here, however, requires that only the average hypothetical and average actual loss from inefficiency be computed–and only the period-average gold-import point and period-average gold-export point are necessary to calculate average hypothetical loss. See above, the subsection entitled “Experienced versus Hypothetical Loss” under “A General Model of Gold-Standard Efficiency”.

⁸⁴ For details on the Shaw plan, see Andrew, A. Piatt, “The Treasury and the Banks under Secretary Shaw”, Quarterly Journal of Economics, 21 (08 1907), pp. 543–48;CrossRefGoogle ScholarMyers, , New York Money Market, pp. 343, 386–87;Google ScholarFriedman, and Schwartz, , Monetary History, pp. 155–56.Google Scholar

⁸⁵ The figure twenty-one-days' interest loss for demand-bill import arbitrage is given by Clare, , Money-Market Primer, p. 130, referring to 1891002F;92.Google Scholar An estimate of twenty days is provided by Whitaker, , Foreign Exchange, p. 534,Google Scholar and Cross, , Domestic and Foreign Exchange, p. 390.Google Scholar In contrast, the figure of fifteen days offered by Strauss, (“Gold Movements”, p. 67) is clearly an underestimate.Google Scholar

⁸⁶ A range of six to nine days is mentioned by Sayers, (Bank of England Operations, p. 92), and nine days was the approximate duration of a one-way voyage between New York and London.Google Scholar

⁸⁷ See Sayers, , Bank of England Operations, pp. 83–96.Google Scholar

⁸⁸ Source of the London rate is National Monetary Commission, Statistics for Great Britain, Germany, and France, 1867–1909, S. Doc. 578, 61st Cong., 2d sess. (Washington, D.C., 1910), pp. 53–60. The compared monthly figures are averages of weekly rates.Google Scholar

⁸⁹ Some contemporary gold-standard writers were well aware of the necessity to include normal profit and risk premium in arbitrageurs' overall cost (see the references in Officer, “Efficiency”, pp. 1052–53);Google Scholar but modern investigators such as Clark and modem authors of textbooks and treatises ignore these items (an admirable exception is Yeager, , International Monetary Relations, p. 20).Google Scholar

⁹⁰ See The Economist, 12 22, 1951, p. 1538.Google Scholar

⁹¹ For this subsection and the two subsequent ones, the corresponding subsections of “Experienced versus Hypothetical Loss” under “A General Model of Gold-Standard Efficiency” may be consulted.

⁹² See the Appendix.

⁹³ Intuitively, the first equality defines the expected value of u as the sum (integral) of all values of u in the interval [0, z_x], that is, all positive value of u, divided by the width of the interval (z_x – 0). (Because the function u is symmetrical, only the interval [0, z_x] need be considered.) The second equality provides the formula to calculate E(u002F;z_x).

⁹⁴ Intuitively, the average value of u(z) over [0, z_x] may be approximated by u(z_x002F;2), which correctly yields z_x002F;2 for the identity loss function. For the other u functions, however, this approximation is an underestimate (for example, z_x2/4 rather than z_x2/3 for the square loss function), because the functions increase at increasing rates.