Real exchange rate misalignment—the sustained departure of the actual real exchange rate from its equilibrium value—has been a recurring policy problem in many developing countries. Overvaluation of the real exchange rate has had undesirable effects on net exports and growth in some countries, while undervaluation has created problems for monetary control and inflation in others. Getting the real exchange rate “right” in a world in which the fundamental structural determinants of the equilibrium real exchange rate are constantly changing remains one of the most important goals of economic policy in developing countries.
The problems associated with real exchange rate misalignment have led policymakers in developing countries to try to reduce the degree of overvaluation or undervaluation of their currencies by appropriate policies for the nominal exchange rate. The idea behind such policies is that the transition from, for example, a situation of overvaluation to one of real exchange rate equilibrium can be long and drawn out, particularly if institutional factors—such as wage- and price-setting behavior—are unfavorable. Under these circumstances, a change in the nominal exchange rate (a devaluation) can help to reestablish equilibrium more quickly and thereby mitigate some of the costs associated with the transition.
A well-known problem associated with the implementation of such policies is that the extent of real exchange rate misalignment—and in some cases even its sign—may be difficult to gauge. This is because information about the extent of misalignment requires knowledge of the level of the equilibrium real exchange rate, which depends both on structural factors (including trade and industrial policies, the degree of capital mobility, and the terms of trade) and on macroeconomic factors, such as the level and composition of government spending and taxation as well as the international macroeconomic environment. The problem of real exchange rate misalignment thus lies at the heart of both macro-economic and structural policy in developing countries.
In practice, the problem of estimating the extent of real exchange rate misalignment has been addressed in a variety of ways. One approach has been to determine some base period in which the actual and equilibrium real exchange rates were equal and then attempt to determine the extent by which the equilibrium real rate has changed as a result of changes in its fundamental structural determinants, so that a comparison can be made with the path of the actual real exchange rate.1 This approach, however, has not been used as frequently as one might think, probably because the effects of exogenous and policy-induced shocks on the equilibrium real exchange rate depend on structural relationships in the economy about which policymakers are likely to have insufficient information.
An alternative approach, which is simpler and more direct, involves using information from the parallel market to gauge the extent of real exchange rate misalignment.2 The existence of a premium on foreign exchange in the free market is taken to indicate an excess demand for foreign exchange at the official exchange rate, which in turn is interpreted as arising from an overvaluation of the domestic currency at the prevailing official exchange rate.
This intuition is buttressed by models in the literature in which the premium and the degree of misalignment both respond endogenously to some shock, such as an increase in the stock of credit. For example, models in the currency-substitution tradition (Calvo and Rodríguez (1977)) have been used by Edwards (1989) and Kamin (1993) to analyze the effects of unsustainable financial policies on the parallel market premium and the divergence of the real exchange rate from its long-run equilibrium value. The robust finding from these models is that, along the adjustment path, overvalued real exchange rates are associated with high premia. One interpretation of this relationship views the equilibrium exchange rate as a weighted average of the free rate and the official rate. Consequently, in many developing countries, exchange rate policy is designed to reduce the gap between the two rates by depreciating the official exchange rate (see, for example, Aghevli, Khan, and Montiel (1991)). In effect, the misalignment of the official rate is contained by targeting the premium at a reduced level.3
This view of the relationship between the premium and real exchange rate misalignment has some empirical support. For example, studies of a number of devaluation episodes (see Edwards (1989) and Kamin (1993)) find that the parallel market premium often rises very rapidly in the period immediately preceding a major devaluation, and then falls off just after the devaluation. A positive correlation between the premium and the extent of underlying real exchange rate overvaluation is suggested by such cases.
Nonetheless, from an analytical standpoint, the case for treating the size of the parallel market premium as an indicator of the magnitude of real exchange rate misalignment seems far from obvious. Both the premium on foreign exchange in the free market and the real exchange rate in the official market are endogenous variables with complex macroeconomic roles. As such, the correlation between them should depend on the sources of shocks impinging on the economy. Moreover, the parallel market premium is an asset price, which can be expected to exhibit much greater volatility than the official real exchange rate, in particular by responding to transitory shocks that leave the equilibrium real exchange rate unaffected. The very different time series properties of the two variables raise some doubts about the reliability of the premium as an indicator of real exchange rate misalignment.
Empirically, parallel market premia tend to be a good deal more variable than real exchange rates in developing countries and can easily reach levels of several hundred percent without discernible changes in the underlying extent of real exchange rate misalignment. Furthermore, the sign of the correlation between the parallel market premium and the official real exchange rate seems to vary from country to country and time period to time period.4 For example, in the study cited previously, Kamin (1993) found that in about a third of the devaluation episodes he studied, the premium actually fell before an exchange rate correction. This certainly calls into question the presumption that there is a robust correlation between real exchange rate misalignment and the parallel market premium that is independent of the nature of the underlying shocks and the structure of the economy.
The purpose of this paper is to explore these issues in the context of a fully optimizing model of a developing country that simultaneously determines the degree of misalignment of the real exchange rate and the premium in the parallel market. The paper’s objective is to assess the reliability of the premium as an indicator of exchange rate misalignment by answering the following questions: Letting e and
This paper is organized as follows. First, we set up the model by describing the consumer’s optimization problem and then discussing the equilibrium and solution of the model. We then proceed to demonstrate the central point of the paper, that adjustment in an economy (modeled along fairly standard lines) to even a simple shock (consisting in this case of a permanent productivity shock) can be rather complex. We show, in particular, that while the adjustment of the real exchange rate to its new long-run equilibrium is monotonic, that of the parallel market premium is not, implying that neither the sign nor the magnitude of the premium is informative about the extent of misalignment in this case. We end by summarizing the main conclusions.
The purpose of this appendix is to show that in response to a positive productivity shock, the premium must jump down on impact and that the adjustment of the economy to such a shock must be as presented in Figure 1. Figure 3 plots the stock of foreign securities F on the horizontal axis and the parallel market premium (plus unity) b on the vertical axis. The slope of the Ḟ = 0 locus (which is drawn relative to the new post-shock steady-state equilibrium at B) is equal to –F4/F1 which is negative (equation (31)).16 From equations (38) and (41), we can derive the slopes of the dominant and nondominant eigenvectors:
where, by the fact that λ1 < λ2 < 0, the dominant eigenvector is more steeply sloped than the nondominant eigenvector, and both are more steeply sloped than the Ḟ = 0 locus, as drawn in Figure 3. As mentioned previously, unless the initial steady-state values of the two state variables place the economy on the dominant eigenvector, the path followed by the economy in Figure 3 eventually converges to the slope of the nondominant eigenvector.
The question, as in Figure 1, is where the economy jumps on impact along the line perpendicular to point F = 0, which is the new (and old) steady-state value of F. There are two possibilities, labeled I and II in Figure 3. Under path I, the premium jumps up on impact, and, given the arrows of motion drawn relative to the Ḟ = 0 locus, the premium must approach its steady-state level from below. Under path II, the premium jumps down on impact and, given the arrows of motion, must approach the steady state at B from above.
It may be recalled from Figure 1 that whether b jumps up or down on impact it must approach the steady state from above. But this rules out path I in Figure 3 since, in this case, b approaches the steady state from below. Therefore, b must jump down on impact, and the economy must follow the path indicated in Figure 1 (with the dynamics of the individual variables as drawn in Figure 2) and likewise path II in Figure 3.
Aghevli, Bijan B., Mohsin S. Khan, and Peter J. Montiel, Exchange Rate Policy in Developing Countries: Some Analytical Issues, Occasional Paper No. 78 (Washington: International Monetary Fund, 1991).
Bhandari, Jagdeep S., and Carlos A. Végh, “Dual Exchange Markets Under Incomplete Separation: An Optimizing Model,” Staff Papers, International Monetary Fund, Vol. 37 (March 1990), pp. 146–67.
Calvo, Guillermo A., and Carlos A. Rodríguez, “A Model of Exchange Rate Determination Under Currency Substitution and Rational Expectations,” Journal of Political Economy, Vol. 85 (1977), pp. 617–25.
Edwards, Sebastian, Real Exchange Rates, Devaluation, and Adjustment: Exchange Rate Policy in the Developing Countries (Cambridge, Mass.: MIT Press, 1989).
Kamin, Steven B., “Devaluation, Exchange Controls, and Black Markets for Foreign Exchange in Developing Countries,” Journal of Development Economics, Vol. 40 (1993), pp. 151–69.
Khan, Mohsin S., and Jonathan D. Ostry, “Response of the Equilibrium Real Exchange Rate to Real Disturbances in Developing Countries,” World Development, Vol. 20 (1992), pp. 1325–34.
Kharas, Homi, and Brian Pinto, “Exchange Rate Rules, Black Market Premia, and Fiscal Deficits: The Bolivian Hyperinflation,” Review of Economic Studies, Vol. 56 (1989), pp. 435–48.
Lizondo, J. Saul, and Peter J. Montiel, “Fiscal Policy and the Dynamics of Devaluation for a Small Country with Optimizing Agents” (unpublished; Washington: International Monetary Fund, 1991).
Quirk, Peter J., and others, Floating Exchange Rates in Developing Countries: Experience with Auction and Interbank Markets, Occasional Paper No. 53 (Washington: International Monetary Fund, 1987).
On the use of the premium as an indicator of real exchange rate misalignment in developing countnes, see Quirk and others (1987).
The first optimizing model of dual rates with leakages is Bhandari and Végh (1990). The main differences between their paper and ours relate to the goods structure and the economy’s access to world capital markets.
The production side of the economy is described in the following section.
Clearly, β is the expenditure share of nontraded goods.
Essentially, this assumption pins down the stock of foreign securities in the steady state.
To simplify the analysis, it is assumed that the output (productivity) shock affects only the tradables sector. This implies that the productivity shock does not enter into equation (16) below, which relates the equilibrium real exchange rate to the level of total expenditure.
In any period, the effective price of consumption is equal to 1 + αR, which is the sum of its market price (unity) and the opportunity cost (αR) of holding, the a units of money needed to purchase a unit of the good. The consumption rate of interest, which is the true intertemporal price of consumption, is equal to the interest rate R less the rate of change of the effective price of consumption,
In this case, we could think of the model as comprising an exportables and a nontradables sector on the supply side and importables and nontradables on the demand side. Also, it should be noted that the analysis of a negative shock would be completely symmetric to that presented below for a positive shock.
Specifically from equation (32), it can be shown that as λ goes to –∞ then lim P(λ) > 0 and P(Z3) < 0. From these two facts, it follows that λ1 < Z3 < λ2 < 0. The signs of the slopes in equations (42) and (43) follow directly.
It is interesting to note that the qualitative path followed by the economy in response to a real shock (an improvement in productivity) is the same as that followed in response to a nominal shock (for example, an exogenous change in the stock of money). Figure 1 is again illustrative. Suppose the initial steady state is B in Figure 1 and that there is an exogenous decrease in the stock of money. Since the model exhibits neutrality in the steady state, the new long-run equilibrium will be identical to the initial equilibrium: the new steady state is also point B in Figure 1. On impact, though, a decrease in the nominal money stock implies a decrease in expenditure in terms of traded goods (that is, a decrease in Z), since the official exchange rate is fixed and the cash-in-advance constraint must hold. Thus, on impact, the economy must move to a point along the perpendicular rising from Z0 in Figure 1. But then, as shown in the Appendix, the dynamic path followed by the economy must be as drawn in Figure 1—in particular, the premium must jump down on impact. Thus, the economy begins at point B, jumps to point C, and then follows the arrowed curve back to point B. Clearly, therefore, a nominal shock is capable of generating the same type of nonmonotonicity in the adjustment of the premium as the productivity shock does.
An alternative to looking at the premium at a point in time is to look at its average behavior over some period of time. Whether this yields a more reliable indicator depends on how long the economy spends in each phase of the adjustment path and on how long after the shock an assessment is made.