Back Matter
Author: Mr. S. E Oppers


  • Baliño, T. and C. Enoch (1997), Currency Board Arrangements: Issues and Experiences, IMF Occasional Paper No. 151 (Washington: International Monetary Fund).

    • Search Google Scholar
    • Export Citation
  • Berg, A. and E. Borensztein (2000), “The Pros and Cons of Full Dollarization,” IMF Working Paper No. WP/00/50.

  • Eichengreen, B., P. Masson, et al. (1998), Exit Strategies: Policy Option for Countries Seeking Greater Exchange Rate Flexibility, IMF Occasional Paper No. 168 (Washington: International Monetary Fund).

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Flood, R. and P. Garber (1983), A Model of Stochastic Process Switching, Econometrica 51, 537-551.

  • Froot, K. and M. Obstfeld (1991), Exchange-Rate Dynamics Under Stochastic Regime Shifts: A Unified Approach, Journal of International Economics 31, 203-229.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Krugman, P. (1991), “Target zones and exchange rate dynamics,” Quarterly Journal of Economics, 106, 669-682.

  • Laughlin, J. L., 1968 [1885, 1896], The History of Bimetallism in the United States (New York, NY: Greenwood Press).

  • Mundell, R.A. (1961), “A Theory of Optimum Currency Areas,” American Economic Review, 51, 657-665.

  • Mussa, M., P. Masson, et al. (2000), Exchange Rate Regimes in an Increasingly Integrated World Economy, IMF Occasional Paper No. 193 (Washington, International Monetary Fund).

    • Search Google Scholar
    • Export Citation
  • Oppers, S.E. (2000), “A Model of the Bimetallic System,” Journal of Monetary Economics, 46, 517-533.

Appendix I

Appendix I: a Model of a Dual Currency Board

We can model the dual currency board using the log-linear model of the exchange rate originally used by Flood and Garber (1983) and subsequently adopted by the target-zone literature (e.g., in Flood, Rose and Mathieson (1991), Froot and Obstfeld (1991), and Krugman (1991)). Assume, for simplicity, that there are only three “countries” in our world, the United States, the euro area, and the CB country. The United States and the euro area each have their own currency, and the CB country’s ducat is fully backed by either dollars or euros.

Thus, we can model the international monetary system by only considering the dollar and euro realms, with

article image

Lowercase denotes natural logs, except for the interest rate.

m$  p$=a$+β$y$+γ$i$+v$(1)
m  p=a+βy+γi+v(2)
i=i$ Et(dx)/dt(3)

Equations (1) and (2) are money demand relationships for the dollar and euro realms, while equation (3) indicates that uncovered interest parity holds. Equation (4) assumes PPP.

The dual currency board is incorporated into the model by apportioning the CB country’s economy to the dollar and euro realms as follows:

y=ln(YEUR+ (1 λ)YCB)(6)

In this setup, y$ and y represent the proportions of world output that are “covered” by the dollar and euro money supplies. Thus, y$ includes all of YUS and part of YCB, where the share of YCB that is apportioned to the dollar area depends on the share of dollars in the CB’s reserves.

To summarize the model conveniently, we can combine (1) through (4) to get:

x=w+k+γ Et(dx)/dt(7)

where k = (m$ - m) - (a$ - a) - (v$ - v), and w = β ln(YEUR + (1 - λ)YCB) - β$ ln(YUS + λYCB). The system knows three basic states. In the first, λ = 1 and all of the CB’s reserves are held in dollars. The exchange rate between the dollar and the euro, x, is above x¯, the cross rate implicit in the dual currency board. The ducat is effectively pegged to the dollar. In the second state, λ=0 and all of the CB’s reserves are held in euros; x is below x¯ and the ducat is effectively pegged to the euro.

In the intermediate state, λ is between 0 and 1, with dollars and euros both present in the CB’s reserves. In this case, the cross rate between the two reserve currencies is momentarily fixed (x=x¯), and its instantaneous expected change is zero. Thus, x¯=w+k. Any effects on x of changes in fundamentals k are offset by a change in the composition of the CB’s reserves; an increase in, say, the dollar money supply would prompt an incipient fall in the value of the dollar, creating an arbitrage opportunity. Arbitrageurs would buy dollars in the exchange market for less than 1 euro, but sell them at the CB (using the ducat as an intermediary) for exactly 1 euro, making a profit. Their actions increase the amount of dollars held by the CB and decrease its holdings of euros. At the same time, the associated demand for dollars and supply of euros generated in the exchange market would tend to push the market exchange rate x towards the implicit cross rate of the dual currency board x¯. This type of arbitrage would continue until x was again exactly equal to x¯.11 In the model, an increase in k would spark arbitrage that would cause λ to rise, thereby decreasing y and increasing y$; the resulting fall in w offsets exactly the initial increase in k. On balance, a larger share of world output will be covered by dollars, prices will rise proportionally in the dollar and euro areas, and the market exchange rate between the dollar and the euro will remain unchanged.

If λ is either 0 or 1, this arbitrage mechanism cannot operate and x is free to “float.” The existence of the dual currency board still has an effect on x, however, akin to the “target-zone” effect under a target-zone system. In essence, x¯ is a regulating barrier for x, whose path is affected by the anticipation of the CB’s reserves of dollars (or euros, as the case may be) released onto the market when x reaches x¯. The target-zone effects—which influence all variables in the model, including price levels and interest rates—can be easily computed if it is assumed that fundamentals k follow a continuous-time random walk (see Oppers, 2000, for the complete solution to the model applied to the bimetallic system).


I would like to thank Tamim Bayoumi for providing initial ideas on how my previous research on bimetallism could be applied to currency boards, and for subsequent helpful comments and discussions. I am also indebted to Michael Bordo, Eduardo Borensztein, Barry Eichengreen, and Sergio Leite for helpful comments on earlier drafts. Any errors are my responsibility.


Under bimetallism, concurrent circulation of gold and silver coins was rarely achieved, since relatively small changes in the relative price of gold and silver—induced, say, by a change in their relative supply—would induce bimetallic arbitrage that would quickly replace the “good” (appreciating) money with the “bad” (depreciating) money through the operation of Gresham’s Law. Thus, countries went through periods when only coins of one metal remained in circulation, punctuated by periodic remintings of the entire money supply, as they saw their pegs change from gold to silver or vice versa (for a description of the workings of the system, see Oppers, 2000).


The model can easily be extended to incorporate a tri-polar world with the dollar, the euro and the yen, and with other countries operating currency boards at possibly different conversion rates. See below for details.


This suggests a rule for the composition of reserves upon implementation of the dual currency board: only the currency that is overvalued in the CB system should be present in reserves. If any of the undervalued currency were to be present, a run on this part of reserves would ensue and the CB would suffer capital losses as these reserves were sold to the public at less than their market value. The only situation in which both currencies can be present in reserves is that in which the CB is implemented with an implicit cross rate that is exactly equal to that prevailing in the market.


It is true that upon the dollar’s appreciation, the total value of the CB’s reserve holdings would be lower measured in dollars, but that is not the unit of account of the CB, nor the country’s fiscal accounts. But there is a symmetry here as well: when the exchange rate is above 1 dollar per euro, and all reserves are in dollars, their total value in dollars may be $10 billion, but measured in euros, their value would be below €10 billion.


While the dual currency board’s effect on the average level of the real exchange rate is clearly downward, its effect on the variability of the real exchange rate is ambiguous, depending on the trade shares of the various currencies and their covariance against the domestic currency, as well as each other.


One could also envisage a “basket” currency board with the domestic currency backed by a fixed amount of a number of reserve currencies to approximate the direction of trade. While such a system could further enhance stability of the real exchange rate, it would lack the transparency and simplicity of the dual currency board. The value of the domestic currency would no longer have a clear benchmark and the implementation of the convertibility guarantee would be cumbersome, either requiring the public to transact with the CB in a number of different foreign currencies simultaneously (likely involving significant transaction costs) or the CB authorities to actively manage the relative composition of reserves, leaving them exposed to potential trading losses. Also, movements in cross rates may move the basket weights away from the trade weights; it would be unclear how to effectuate any periodic reweightings that may be desirable.


While the system is symmetric, holders of dollars do not hold an option to buy euros, since the CB does not own any euros when the ducat is effectively pegged to the dollar. It is as if the option has not been written yet. There is nevertheless a symmetry in the system: when the ducat is effectively pegged to the euro, dollar holders would own a call option on the euro, and the dollar interest rate would be relatively lower.


The technical side of these differences is explored in detail in Oppers (2000) for the case of 19th century bimetallism; since the dual CB can be modeled analogously (see Appendix I below), the technical results of that paper hold without modification.


In a further extension, the dual CB system could provide global currency stabilizing effects if other countries adopted dual-currency currency boards using dollars and yen or yen and euros. Note however, that because there are only (n-1) independent cross rates, a peripheral country cannot independently choose a yen-euro system of currency-board cross rates if dollar-euro and dollar-yen dual currency boards are already in existence.


Any costs associated with the arbitrage would allow the market cross rate to deviate from the implicit cross rate of the CB by some margin before arbitrage would start taking place. This margin is akin to the “gold points” under a gold standard.

Dual Currency Boards: A Proposal for Currency Stability
Author: Mr. S. E Oppers