First note that expected accumulation of real wealth in natural units is:
We now hypothesize the forms of the savings functions in natural units per-unit real wealth. The per-unit-wealth functions depend upon the same arguments as the logarithmic functions but involve different coefficients, i.e.,
It is straightforward to verify that the coefficients of Te and Tx (when evaluated at the initial point) are related to those of lnTe and lnTx via β′e = ψe βe, γ′e = ψe γe, β′x = ψx βx, γ′x = ψx γx. In addition,
The next step is to equate Te and Tx with the appropriate components respectively, of total expected wealth accumulation. In order to preserve log-linearity of the model, it is convenient to assume a special form of the process governing the allocation of wealth between money accumulation and foreign asset accumulation. Specifically, the savings components Te Tx (in natural units) result in accumulation of money and foreign assets according to:
These processes are indeed special; however, other allocation processes would involve additional linearizations. Accordingly, the per unit wealth functions
Adams, C. and J. Greenwood, “Dual Exchange Rate Systems and Capital Controls: An Investigation,” Journal of International Economics, Vol. 18 (1985), pp. 43–63.
Aizenman, J., “Adjustment to Monetary Policy and Devaluation Under Two-Tier and Fixed Exchange Rate Regimes,” Journal of Development Economics, Vol. 18 (1985), pp. 153–169.
Argy, V. and M. Porter, “The Forward Exchange Market and the Effect of Domestic and External Disturbances under Alternative Exchange Rate Systems,” Staff Papers, International Monetary Fund, Vol. 19 (1972), pp. 503–532.
Bhandari, J.S., “Informational Regimes, Economic Disturbances and Exchange Rate Management,” in Exchange Rate Management Under Uncertainty, J.S. Bhandari ed., (Cambridge, Massachusetts: M.I.T. Press, 1985).
Bhandari, J.S., and B. Decaluwe, “A Stochastic Model of Incomplete Separation between Commercial and Financial Exchange Markets,” Journal of International Economics, Vol. 22 (1987), pp. 25–55.
Blanco, H., “The Variability of the Exchange Rates in Dual Exchange Rate Systems,” (1987). (Unpublished manuscript, Rice University).
Decaluwe, B., “Le Regime du double Marche des Changes: Theorie et Pratique, L’Experience de L’Union Economique Belgo-Luxembourgeoise,” Faculte Serie No. 122 (1975), Mecaprint, Bruxelles.
Decaluwe, B., and A. Steinherr, “A Portfolio Balance Model for Two-Tier Exchange Markets,” Economica, Vol. 1 (1976), pp. 111–125.
Delbecque, B., “Dual Exchange Rates Under Pegged Interest Rate and Balance of Payments Crisis,” (1988). (Unpublished manuscript, University of Pennsylvania).
Dornbusch, R., “Special Exchange Rates for Capital Account Transactions,” World Bank Economic Review, Vol. 1 (1) (1985), pp. 3–33.
Fleming, J.M., “Dual Exchange Rates for Current and Capital Transactions: A Theoretical Examination,” in his Essays in International Economics, (Cambridge, Massachusetts: Harvard University Press, 1971), pp. 246–325.
Flood, R., and N. Marion, “The Transmission of Disturbances under Alternative Exchange Rate Regimes with Optimal Indexing,” Quarterly Journal of Economics, Vol. 97 (1982), pp. 43–66.
Flood, R., and N. Marion, “Exchange Rate Regimes in Transition: Italy 1974,” Journal of International Money and Finance, Vol. 2 (1983), pp. 279–294.
Gardner, G., “Money, Prices and the Current Account in a Dual Exchange Rate Regime,” Journal of International Economics, Vol. 18 (1985), pp. 231–256.
Gros, D., “Dual Exchange Rates in the Presence of Incomplete Market Separation: Long-Run Effectivenss and Policy Implications,” Staff Papers, International Monetary Fund (Washington), Vol. 35/3 (1988), pp. 437–60.
Guidotti, P., and C. Vegh, “Macroeconomic Interdependence Under Capital Controls: A Two-Country Model of Dual Exchange Rates,” I.M.F. Working Paper, No. WP/88/74 (1988).
Kiguel, M. and J. Lizondo, “Adoption and Abandonment of Dual Exchange Rate Systems,” (1986). (Unpublished manuscript, The World Bank).
Lanyi, A., “Separate Exchange Markets for Capital and Current Transactions,” Staff Papers, International Monetary Fund (Washington), Vol. 22 (1975), pp. 714–749.
Lizondo, S., “Exchange Rate Differential and Balance of Payments under Dual Exchange Markets,” Journal of Development Economics, (1987), pp. 37–53.
Marion, N., “Insulation Properties of a Two-Tier Exchange Market in a Portfolio Balance Model”, Economica, Vol. 48 (1981), pp. 61–70.
Obstfeld, M., “Capital Controls, the Dual Exchange Rate and Devaluation,” Journal of International Economics, Vol. 20 (1986), pp. 1–20.
Pinto, B., “Black Market Premia, Exchange Rate Unification and Inflation in Sub-Saharan Africa,” (1987). (Unpublished manuscript, the World Bank).
Swoboda, A., “The Dual Exchange Rate Sysem and Monetary Independence,” in National Monetary Policies and the International Financial System, R.Z. Aliber, ed. (Chicago: University of Chicago Press, 1974), pp. 258–270.
The author acknowledges helpful comments by Mohsin Khan and Carlos Vegh on an earlier draft. All remaining errors are the sole responsibility of the author.
Additional details may be obtained from the Annual Report.
An earlier strand of literature includes Argy and Porter (1972), Fleming (1971), Decaluwe (1974), Decaluwe and Steinherr (1976) and Swoboda (1974). A somewhat later group of papers include Flood (1978), Marion (1981), Flood and Marion (1982, 1983), among others. To a large extent, the later literature may be viewed as an extension of models of earlier vintage with the replacement of static or adaptive expectations by the now-popular rational expectations hypothesis. Another distinction is that the newer models tend to be dynamic and/or stochastic as opposed to the generally static models of the earlier period. The most recent papers cited in the main text continue the examination of the same type of issues as previously (for example, efficacy of various policies, insulation from external disturbances etc.); however, the types of models utilized are more sophisticated in the sense of being of an optimizing nature rather than of the ad hoc type that characterized the earlier work.
Underinvoicing or overinvoicing of exports/imports may also occur quite apart from the maintenance of dual exchange rates; for example, if trade tariffs or subsidies are present.
A limited number of capital account transactions are often required to be settled in the commercial market in some countries. However, these items usually involve certain types of public sector capital account items and their empirical significance appears to be very limited; see also Lanyi (1975) in this regard.
This modification is not without costs however, in that the resulting model is of a short-run nature.
All parameters are defined positively in what follows.
If contemporaneous wage indexation were incorporated, then as shown by Flood and Marion (1982) among others, the form of the supply function is not altered. However, the slope parameter b is now given by b = (a/(1-a)(1-θ) where θ is the degree of contemporaneous wage indexation.
Technically, α represents the value share of trade transactions settled at the commercial exchange rate to the total value of trade transactions. However, provided that the initial spread between the two exchange rates is small, α can also approximate the relevant real share, i.e., α ≈ Te°/(Te + Tx)°, where Te° and Tx° denote initial volumes of transactions settled in the commercial and financial markets respectively.
At this stage it is useful to recall that owing to the one-good nature of the model, the trade surplus (Tt > 0) is synonymous with total exports. Throughout this paper, we assume without consequence, that the domestic economy is a net exporter (so that aggregate savings are positive). If the country in question were a net importer (i.e., Tt < 0), then equation (5) is replaced by a function that associates the trade deficit (negatively) with income. Our results are not altered by this modification.
If a real wealth effect is included in the consumption (savings) function, then the total trade surplus (or savings) responds negatively to an increase in real wealth, i.e. (5) would be replaced by
If the wealth effect were included in (5), then an increase in total real wealth increases both Te and Tx.
These conditions can be derived by recalling that T = Te + Tx and that α = [Te/(Te + Tx)]°, where the superscript ‘°’ refers to an arbitrary linearization point.
This expression may be derived by a procedure similar to that in Flood and Marion (1982), extended to incorporate leakage.
Note that the principal on foreign securities is always acquired (by assumption) at the financial exchange rate. However, interest proceeds (a current account item) may be repatriated via either market. It is not difficult (in principle) to model leakage from the financial to the commercial market: essentially, this requires the use of a suitably defined aggregate financial rate in the definition of wealth. As pointed out earlier however, the empirical significance of such cross transactions is minimal compared with leakage from the commercial to the financial market (as incorporated in this paper).
The banking sector is suppressed in this model, i.e. reserves accumulation is equivalent to money accumulation.
Strictly speaking, reserve accumulation corresponds to the commercially-settled trade balance plus the commercially-settled component of the service account. The service account component has been disregarded in the following accumulation equations on the grounds of maintaining analytical tractability.
Details as to the derivation of these accumulation equations are provided in the Appendix.
Formally, Et-1, ēt = ē, i.e., Et-1, νt = 0.
In reality of course, certain variables (for example, financial market variables) are more readily observable than others (eg. real sector variables). In addition, domestic variables may be more easily observed (by domestic agents) than foreign variables. These issues (relating to differential information availability) are not treated here; see however, Bhandari (1985).
An anticipated devaluation of the commercial exchange rate is fully neutral in that the price level and the financial exchange rate increase equiproportionately with no effect upon output.
At this juncture it should be noted that in the long-run, commercial devaluation—anticipated or unanticipated-leads to equiproportionate financial depreciation, thereby leaving the spread unaffected. It is clear therefore, that permanent re-unification cannot be achieved by attempting to eliminate the spread via commercial devaluation. Rather, the abolition of dual rate markets requires the judicious use of policy instruments in addition to the commercial exchange rate. This point has also been noted by other authors, for example, Lizondo (1987). It should also be noted that the persistence of a long-run spread is attributable to the presence of officially authorized cross-transactions. Thus, in models wherein only fraudulent cross-transactions are incorporated, the spread is necessarily arbitraged away in the long-run (see for example, Gros 1987)).
Plausible parameter values are for example,
d1 (ratio of money to wealth) = .80,
λ (interest rate semi-elasticity of money demand) = 10,
Φ (income elasticity of money demand) = 1,
b (slope of supply curve) = 3,
βe (income elasticity of commercially-settled trade balance) = .50,
ψe (ratio of commercial trade surplus to real wealth) = .10,
γe (elasticity of commercial trade balance with respect to the spread) = 1, and
α, ω (leakage parameters) = .50.
For these parameter values, the expression Ω = - 9.17. The negativity of Ω is assured despite any other plausible parameter configuration unless γe is extremely large. With the above parameters, γe would need to be approximately 90 before ft can turn positive. It is apparent, therefore, that in the most usual case Ω is expected to be negative.
A high value of γe implies low penalty costs associated with cross-transactions. This may occur for example, if enforcement of exchange regulations is extremely lax or if private cross transactions are of a permissive character. Permissive cross-transactions have in fact, been authorized in the past by the BLEU by granting certain traders an “option” to transact in the exchange market of their choice (subject to certain mandatory eligibility requirements).
By contrast a change in Q is a systematic change in the allocation of current account transactions between the two exchange markets that is attributable to administrative fiat.
As noted previously, these effects are contingent upon reasonable values of the underlying parameters such that Ω is negative. A sufficiently high value of γe however, could lead to Ω being positive, in which case all the qualitative results are reversed.