Journal Article Arbitrage and the Forward Gold Premium: Reply Get access John H. Makin John H. Makin The University of Wisconsin — Milwaukee Search for other works by this author on: Oxford Academic Google Scholar The Quarterly Journal of Economics, Volume 88, Issue 3, August 1974, Pages 502–504, https://doi.org/10.2307/1881950 Published: 01 August 1974

I. Introduction, 349. — II. Swaps and Roosa Bonds as substitutes for conversion of dollars into gold, 349. — III. A portfolio behavior model for reserve assets, 351. — IV. Empirical results, 353. — V. Summary and conclusions, 355. — Appendix, 355.

THE hypothesis attributed to Fisher (1930) and more recently the innovative investigation by Fama (1975) have predisposed many economists to treat the expected rate of interest as a constant. At the very least, as a magnitude, the expected interest rate is appealingly viewed as being independent of monetary phenomena. The late 1970s and early 1980s have produced events which force reevaluation of the maintained hypothesis of constancy of the expected rate (hereafter referred to as the real rate). For example, from December 1980 to June 1981 the expected rate of inflation fell by 165 basis points from an annual rate of 10.51 % to an annual rate of 8.86%.' Over the same period 3 month Treasury bill rates continued to remain largely between 14% and 16% with average yields of 15.02% in December 1980 and 14.95% in June 1981. In order to reconcile such facts, one must either believe that security markets no longer fully reflect changes in anticipated inflation in nominal market rates, or that a large drop in anticipated inflation which is not accompanied by a drop of similar magnitude in nominal interest rates, is due to an offsetting rise in the rate.2 Statistical investigations regarding the possibility of movements in the rate have appeared with increasing frequency since publication of Fama's (1975) provocative article.3 Nelson and Schwert (1977) argued that Fama's test of the joint hypothesis of market efficiency and constancy of the rate was not sufficiently powerful and after applying more powerful tests concluded that the data permitted rejection of the hypothesis of constancy of the rate. Other investigations including those by Carlson (1977), Garbade and Wachtel (1978) and Levi and Makin (1979) have rejected the hypothesis of constancy of the rate while tending to support the hypothesis that market interest rates include an efficient inflationary premium. Tanzi (1980) has, along with others, emphasized the role of taxes in interest rate determination. More recently investigators have moved from merely testing the hypothesis of constancy of the rate to searching for an explanation for the rate movements suggested by a large body of statistical evidence. Mishkin (1981) and Fama and Gibbons (1982) have investigated the relationship between the rate and anticipated inflation suggested by Mundell (1963) and Tobin (1965).4 Levi and Makin (1979, 1981), Hartman (1981) and Hartman and Makin (1982) have considered effects of inflation uncertainty on the rate. Dwyer (1981) has found that the rate is independent of predictable changes in the supply. This paper derives a Fisher-type interest rate equation from a structural model similar to that employed by Sargent (1973) for other purposes. The primary differences involve inclusion of a government sector and a simple open economy specification along with introduction of a role for Received for publication February 22, 1982. Revision accepted for publication September 3, 1982. *University of Washington and National Bureau of Economic Research. This work was supported by the National Science Foundation under (irant No. SES-8112687. I would like to thank without implicating Charles Nelson, Richard Hartman and especially Andrew Criswell for excellent help in estimating the equations. An earlier version of this paper was presented at an FMME Conference at NBER where many useful suggestions were provided. ' This figure is based on Livingston survey data for 6 month horizon expectations regarding the consumer price index (CPI). The 12 month horizon figure for CPI also indicated a drop of 165 basis points while 6 and 12 month horizon numbers for WPI indicated drops of 192 and 174 basis points, respectively. Updated Livingston survey data are now compiled by the Federal Reserve Bank of Philadelphia. 2Summers (1982) has argued that nominal interest rates do not adjust by the full amount implied by the Fisher hypothesis modified to allow for marginal tax rates on interest earnings. His results based on both preand post-World War II data arise from equations which employ actual inflation rates in place of anticipated inflation and which generally do not include variables to control for movements in the expected rate. 3Even well before the investigations discussed here Irving Fisher himself reported, based on an investigation of market interest rates during the late 19th and early 20th centuries in London, New York, Berlin, Calcutta and Tokyo, that ' the rate of interest in terms of commodities is from seven to thirteen times as variable as the market rate of interest expressed in terms of money (Fisher (1930), p. 415). 4 Mishkin (198 1) found a significant negative impact upon the rate of a lagged actual (CPI) inflation rate taken as a proxy for anticipated inflation. An ARIMA (0, 1, 1) inflation model with a seasonal MAI term also provided an expected inflation proxy with a significant negative impact on the rate. Mishkin (1982) is discussed below.

This paper critically examines a number of maintained hypotheses that are necessarily being tested along with the basic notion derived from the rational expectations (RE) formulation of Lucas (1972) (19 73) that only unanticipated money matters. The trend stationary representation of secular real output of Lucas and others is replaced by a difference stationary representation found by Nelson and Plosser (1980) to be consistent with U. S. historical data. The impact of inflation uncertainty on real activity is considered. Attention is paid to possible mis-measurement of agents' ex ante -- anticipated money growth. It is found that three alternative measures of anticipated money growth produce a stable impact on growth of output and employment. Contemporaneous and lagged values of unanticipated money growth have no significant additional explanatory power in the presence of any one of the three measures of anticipated money growth. Beyond this, it is impossible to reject the hypothesis that the initial positive real impact of anticipated money is not temporary. Inflation uncertainty is found to act as a significant depressant of real economic activity in the presence of all tested combinations of anticipated and unanticipated money growth.

over this business would depend upon the size of the advantage and the rate with which the advantage becomes recognized. The apparent parabolic growth path displayed by Eurodollar deposits so far is consistent with theories of the early stages of a new product. The path of Eurodollar expansion can be formulated as a cumulative response to a gradually recognized cost advantage. Such factors as the stringencies of Regulation Q ceilings on interest rates and the exchange controls can be viewed as sources of the residual variation from the growth path.

T HIS study considers the market for Eurodollar deposits as a structural system with determinate demand and supply relationships. It is important at the outset to distinguish the stock demand for Euro-dollar deposits, which we shall be investigating here, from the flow demand for Euro-dollar credit. Machlup (1970) points out that the demand for Euro-dollar credit is a demand for a flow of funds to borrowers who, in turn, plan to pay out the funds they have borrowed. The demand for Euro-dollar deposit balances is, on the other hand, a demand for money, or near-money, to hold. We shall be concentrating upon the factors affecting the demand for a stock of Eurodollar deposits to hold.1 Since we shall not be taking the stock of Euro-dollar deposits in existence at a point in time as exogenously given, we shall also be identifying an equation to determine the stock of Euro-dollar balances supplied by Euro-dollar issuing institutions (hereafter Euro-banks). This will be based on an identifiable stock of reserves held by Euro-banks. Briefly, the procedure and results are as follows. Quarterly data from 1964-III through 1970-IV are employed to obtain parameter estimates for scale and substitution arguments in a stock demand function for Euro-dollar deposit balances as well as to obtain an estimated equation for the stock of dollar claims produced by Euro-banks. The empirical results suggest that a stable stock-demand function for Euro-dollar deposit balances exists along with a stable stock-supply function for Eurodollar deposits. The results also suggest that about 40 per cent of the growth of Euro-dollar deposits in the 1964-III 1970-IV period was due to the multiple deposit expansion process.

This paper is directed to the goldexchange world which existed before the advent of the two-tier gold market in March 1968. It considers the choice between dollars and gold as international reserves and views the economic forces underlying the substitution of dollars for gold as significant in determining the viability of a dollar-exchange standard. Gold and dollars are both viewed as nonsterile assets with an expected return on gold and a certain return on dollars. In the case of dollars and gold, gold is often labelled as the sterile asset. This is incorrect since a substantial and variable forward dollar premium on gold futures has been paid in an active Zurich market, indicating a positive expected return on gold. This market quoted a price of gold six months forward, in terms of an annual premium on the market price, from 1961 to 1968. An individual willing to pay a premium in order to purchase sterile gold at about $35 an ounce six months in the future indicates that he attaches a positive probability to the chance of a rise in the dollar price of gold. Otherwise, why forego the opportunity to invest in interest-yielding assets? The average premium, from the second quarter of 1961 through the first quarter of 1968 was 6.39 percent. The forward premium on gold as an index of the expected return on gold is a crucial factor, in the empirical analysis below, of the choice by central banks between dollars and gold. It proves to be a significant independent variable. If we restrict consideration to short-term dollar liabilities (ninety days) then we have an asset (dollars) with a certain positive return (neglecting capital gains on ninetyday dollar assets) compared with an asset (gold) with an expected positive return. The choice between dollars and gold is cast in terms of independent, utilitymaximizing portfolio behavior. This is contrary to the view expressed by Fritz Machlup among others, that the holdings of reserves by officials are entirely politically determined:

Helmut A. Hagemann has provided a useful analysis of reserve policies of central banks in his recent article in this Review. However, I am afraid that the unavailability of data has led him into wishful thinking about the value of the dependent variables in his exercise. I refer specifically to the use of (FIR)j, foreign exchange of country i, relative to total reserves of country i as a proxy for (D/R) i;1 dollar-denominated foreign exchange of country i, relative to total reserves of country i. Let us consider what distortions may arise from using (FIR), where (DIR)i ought to be. Let: