Appendix: The Unified Floating Exchange Rate Model
Under a unified system the price of traded goods reflect the uniform exchange rate, denoted by x. The price level is thus given by
The condition for equilibrium in the nontraded goods market becomes
Since international reserves are constant under a uniform floating exchange rate, the change in the real quantity of domestic money is given by
The change in private sector holdings of foreign money is equal to
The other conditions for steady state equilibrium are indicated by equations (9), representing money market equilibrium, and (A.2), representing nontraded goods market equilibrium. The steady state relative price between traded and nontraded goods can be obtained from equations (A.2) and (A.6),
Therefore, the relative price between traded and nontraded goods is the same as in the reserves rationing model. Using (A.7) in equation (A.6), gives
Kharas, Homi, and Brian Pinto, “Exchange Rate Rules, Black Market Premia, and Fiscal Deficits: The Bolivian Hyperinflation”, The Review of Economic Studies, Vol. 56 (1989), pp. 435–448.
Kiguel, Miguel A., and J. Saul Lizondo, “Adoption and Abandonment of Dual Exchange Rate Systems,” Revista de Analisis Economico, Vol. 5 (1990), pp. 3–23.
Lizondo, J. Saul (1987a), “Exchange Rate Differential and Balance of Payments Under Dual Exchange Markets,” Journal of Development Economics, Vol. 26 (1987), pp. 37–53.
Lizondo, J. Saul (1987b), “Unification of Dual Exchange Markets,” Journal of International Economics, Vol. 22 (1987), pp. 57–77.
Lizondo, J. Saul, “Multiple Exchange Rates and Black Market Exchange Rates: A Nontechnical Survey of Theoretical Results,” University of Tucuman (unpublished, 1990).
Nowak, Michael, “Quantitative Control and Unofficial Markets in Foreign Exchange: A Theoretical Framework” Staff Papers (International Monetary Fund: Washington), Vol. 31 (1984), pp. 404–31.
Pinto, Brian, “Fiscal Deficits, Inflation, and Parallel Exchange Markets in Ghana: Monetarism in the Tropics?,” World Bank CPD Discussion Paper No. 1985-43 (1986).
Pinto, Brian, , “Black Markets for Foreign Exchange, Real Exchange Rates and Inflation,” Journal of International Economics, forthcoming 1990.
For a description of the exchange regime of a particular country see International Monetary Fund (1990).
Most models assume that the official market clears through changes in international reserves. However, Nowak (1984) argued that in some cases it is more appropriate to assume a rationing mechanism in the official market. This assumption was later used by Pinto (1986, 1990) to examine the experience of African countries, and by Kharas and Pinto (1989) to discuss the Bolivian experience.
There is a variety of models of dual exchange markets in the literature, with differing implications regarding the effects of various economic policies. The discussion in this paper is confined to one particular type of model. For a survey of theoretical results from different models see Lizondo (1990).
The basic model used here was developed in Lizondo (1987a, 1987b) for examining a dual exchange market economy with an official market that clears through changes in international reserves. This model was later modified and extended to examine an economy with an official market subject to rationing by Pinto (1986, 1990) and Kharas and Pinto (1989). The analysis here replicates various of the results presented in those papers, but it also expands the discussion in some directions. One of the basic differences is that the present paper includes private sector and public sector expenditure on both traded and nontraded goods. In contrast, Lizondo (1987a, 1987b) and Pinto (1986) assume that all goods are traded, while Pinto (1990) and Kharas and Pinto (1989) assume that the private sector consumes only nontraded goods and the public sector spends only on traded goods. The assumption in this paper, besides allowing for a discussion of the effects of changes in public sector expenditure on nontraded goods, has some implications that differ from those in the other papers, as will be noted where relevant. Also, this paper examines the effects of adopting a rationing scheme in a dual economy that operated without rationing.
The exchange rate is defined as the amount of domestic currency equivalent to one unit of foreign currency.
The model does not include overinvoicing and underinvoicing of transactions, so the private sector is assumed to comply with the official allocation between markets.
The implications of the model would be essentially the same if the demand for money is assumed to depend also on the level of wealth, as in Lizondo (1987a), Pinto (1986, 1990), and Kharas and Pinto (1989). However, the simpler formulation used in this paper permits a sharper comparison across regimes.
Expected and actual rates of depreciation are taken to be equivalent since the discussion is centered on the steady state results.
With the real exchange rate defined this way, an increase in p indicates a real appreciation, while a decline in p indicates a real depreciation, of the official exchange rate. The discussion focuses on the behavior of the real exchange rate defined by using the nominal official exchange rate because this is one of the variables typically examined when assessing the adequacy of official exchange rate policy. In any case, the behavior of the real exchange rate defined by using the nominal free exchange rate (pn/b) - ps1, is also indicated in the paper.
The expression for private sector consumption of nontraded goods is obtained by dividing nominal private sector expenditure on nontraded goods (1-α) ω (M+bf), on the price of nontraded goods, and rearranging terms. Similar reasoning applies to private sector consumption of traded goods.
The definition of steady state equilibrium must be interpreted in a broad sense in the reserves adjustment model. A situation of balance of payments deficit is not sustainable in the long run, and thus cannot be a steady state equilibrium in the strict sense. Policies will eventually have to be modified, or the exchange rate system will have to be abandoned. However, a situation in which all real variables other than international reserves remain constant, seems the closest possible approximation to the strict steady state equilibrium used as base for comparison in the other exchange regimes. This qualification must be kept in mind when interpreting the results regarding the “steady state” effects of the various policies.
Under the reserves rationing model, public sector expenditure on traded goods contributes to monetary expansion because the central bank must buy the necessary foreign exchange from the private sector in exchange for domestic money. In contrast, under the reserves adjustment model there is no monetary expansion because the central bank provides the necessary foreign exchange from its own reserves.
This assumes yn > [1 + (1-α)/(1-u)α] gn. Other things constant, an increase in the spread produces two opposing effects on the real value of monetary expansion. On the one hand, monetary expansion declines due to a decline in the real value of exports, and an increase in the real value of private sector imports channeled through the official market. On the other hand, monetary expansion increases due to an increase in the real value of public sector expenditure on nontraded goods. It is assumed that the two factors leading to a lower monetary expansion dominate.
In all the discussion it is assumed that s ≥ 1.
The condition for (ds/dgn) > 0 is v(l+α) > uα.
The real exchange rate defined by using the nominal free exchange rate is equal to ps-1 - A. Therefore, among the policies examines above, the only one to affects the real exchange rate thus defined is a change in public sector expenditure on nontraded goods. An increase in this type of expenditure causes a real appreciation.
The reserves adjustment model in Lizondo (1987a) assumes all goods to be traded, so there is no discussion about effects on the real exchange rate.
The condition for (ds/dgt) > 0 is yt > α (gt + p gn), while the condition (dp/dgt) > 0 is yt > gt + α (gt + p gn). Therefore, although both variables may move in either direction, it is change in reserves has to reflects not possible for the spread to decline and the real exchange rate to appreciate at the same time.
The condition for (ds/dgn) > 0 is (yn-gn) (yt-gt)+αgn yt>gt yn.
The real exchange rate defined by using the nominal free exchange rate is equal to B. Therefore, an increase in public sector expenditures on nontraded goods, or a reduction in public sector expenditure on traded goods, causes the real exchange rate thus defined to appreciate.
In contrast to the results derived here, in Pinto (1990), and in Kharas and Pinto (1989), the real exchange rate defined by using the official exchange rate always moves in the same direction as the spread while the real exchange rate defined by using free exchange rate always moves in the opposite direction. Those results are due to some particular assumptions regarding production and smuggling technology, demand conditions play no role. In contrast, the results in this paper are mainly due to demand factors, since output is assumed to be fixed and smuggling nonexistent.
For the reserves adjustment model, the evolution of the real quantity of money is given by (8). If the central bank were to charge e* for foreign exchange sold to the rest of the public sector (different from e, charged to the private sector) equation (6) would be replaced by (6’) D - e*gt+pngn-Pt. Equation (7) would also be modified to account for the fact that the domestic currency value of the change in reserves has to reflect e*, instead of e, for the transactions of the public sector. These two modifications leave equation (8) unchanged. The same reasoning applies for the reserves rationing model, where the evolution of the real quantity of money is given by (16). If the central bank were to charge e* to the rest of the public sector, the change in domestic credit would be given by (6’). In addition, although international reserves remain constant in terms of foreign exchange, they would change by gt (e-e*) in terms of domestic currency, since the central bank would be buying gt of foreign exchange at e, and selling it at e*. These modifications in the behavior of domestic credit and reserves offset each other, so that equation (16) remains valid.
For economies with one official exchange rate, for both private and public sector transactions, the “accounting” deficit mentioned above is the same as the “official” deficit included in equations (13) and (20). Clearly, in this case the accounting deficit has implications for the behavior of the economy. However, for economies with two official exchange rates, one for private and another one for public sector transactions, the “accounting” deficit mentioned above must be distinguished from the deficit included in equations (13) and (20). The latter, which is the relevant one for the behavior of the economy, must be interpreted in this case as the deficit calculated by valuing public sector expenditure on traded goods at the official exchange rate applied to private sector transactions.
Since the spread and the real exchange rate are not affected, the one-to-one effect of a change in public sector expenditure on traded goods on the balance of payments can be derived directly from equation (12).
This discussion is based on equation (20), which can also be written as (20’) mπ= gt (pt/P) s-1 + gn (pn/P) - t, where pt denotes the domestic currency price of traded goods, which in the rationing regime is equal to the free exchange rate b.
From (25), an increase in public sector imports increases B-1, which is the relative price of traded with respect to nontraded goods.
The possibility of an overall negative effect on the deficit, and therefore a resulting decline in the spread, does not arise in Kharas and Pinto (1989) due to their assumptions that the public sector spends only on traded goods.
See the appendix.
It is assumed that the size of the deficit is such that it can be financed by the inflation tax at some finite rate of inflation. Otherwise there is no steady state solution.
This trade-off between the implicit exchange tax and the inflation tax was first stressed by Pinto (1986).
The values of u and v.
This relationship between the spread and the required inflation tax revenue does not necessarily hold in models where all current transactions are channeled through the official market. In those models, the spread is partly determined by private sector holdings of foreign money, which remains constant at the level outstanding at the time of adoption of the dual system because private sector net capital flows are necessarily zero. See Kiguel and Lizondo (1990).
If the central bank were to buy and sell foreign exchange in both markets, the calculation of profits and losses must take into account the average buying and the average selling exchange rate. Denoting those rates by eb and es, respectively, and the market rate by em, central bank profits are equal to X(em-eb+Z(es-em), where X and Z represent respectively central bank purchases and sales of foreign exchange to the private sector. If the central bank intervenes only in the official market, eb-es-e, thereby resulting in central bank profits equal to (X-Z)(em-e), which is the definition used above.
From (29) and (30), and remembering the assumption that relative prices are the same for both regimes, the condition r=0 implies that sr=su, where sa is the spread in the reserves adjustment regime, and sr is the resulting spread in the reserves rationing regime.