The Parallel Market for Foreign Exchange in an Oil Exporting Economy
The Case of Iran, 1978-1990

This paper provides a model for the determination of the parallel market exchange rate premium in a country where oil export earnings accrue directly to the government, and foreign exchange is centrally allocated for the importation of specific goods. Next, it studies the parallel market for foreign exchange In the Islamic Republic of Iran during the period 1978-90. The paper then examines the various time series properties of parallel market exchange rate in Iran, and the evidence of the role of oil and non-oil exports in the determination of the parallel market premium.

## Abstract

This paper provides a model for the determination of the parallel market exchange rate premium in a country where oil export earnings accrue directly to the government, and foreign exchange is centrally allocated for the importation of specific goods. Next, it studies the parallel market for foreign exchange In the Islamic Republic of Iran during the period 1978-90. The paper then examines the various time series properties of parallel market exchange rate in Iran, and the evidence of the role of oil and non-oil exports in the determination of the parallel market premium.

## I. Introduction

The purpose of this paper is to develop a theoretical model for the determination of the parallel market exchange rate premium in an oil exporting economy where oil revenues accrue directly to the government. Furthermore, it attempts to analyze empirically developments in the parallel market premium for the U.S. dollar in Iran during the period 1978-1990, up to the major reform of the exchange system in January 1991.

### APPENDIX II: Mathematical Details

#### The Steady State Values of the Model

The steady state value of the parallel market premium was provided in the text. The equilibrium value for the real exchange rate, ρ, and the steady state values for holdings of foreign currency, f, and money, m, are given below:

$\begin{array}{cc}{\rho }^{*}=\left[\frac{\left(1-\alpha \right)\left(1-\phi \right){q}_{x}}{\alpha \left(1-\theta \right){q}_{n}-\left(1-\alpha \theta \right){g}_{n}}\right],& \left(A-1\right)\end{array}$
$\begin{array}{cc}{f}^{*}=\frac{\phi {q}_{x}\left(1-\lambda \right)}{\alpha \theta \omega },& \left(A-2\right)\end{array}$
$\begin{array}{cc}{m}^{*}=\frac{{\lambda \phi }^{\alpha \theta }{q}_{x}^{\alpha }{\left(1-\phi \right)}^{\alpha \left(1-\theta \right)}{\left({q}_{n}-{g}_{n}\right)}^{1-\alpha }}{{\left(\alpha \theta \right)}^{\alpha \theta }\omega {\left(1-\alpha \right)}^{1-\alpha }{\left[\alpha \left(1-\theta \right)-\left(1-\alpha \right)\left(\frac{{g}_{n}}{{q}_{n}-{g}_{n}}\right)\right]}^{\alpha \left(1-\theta \right)}}& \left(A-3\right)\end{array}$

#### Stability Analysis

The dynamical system given by equations (7), (11), and (12) linearized around its steady state values is:

$\left(\begin{array}{c}\begin{array}{c}\stackrel{˙}{d}\\ \stackrel{˙}{f}\end{array}\\ \stackrel{˙}{m}\end{array}\right)=J\left(\begin{array}{c}\begin{array}{c}d-{d}^{*}\\ f-{f}^{*}\end{array}\\ m-{m}^{*}\end{array}\right),$

where J is the Jacobian matrix the elements of which, omitting the argument of the function λ(0), are given below:

${J}_{11}=\frac{-\lambda \left(1-\lambda \right)\left(1-\alpha \theta \right)}{{\lambda }^{\prime }}>0,$
${J}_{12}=\frac{-\lambda \left(1-\lambda \right){d}^{*}}{{\lambda }^{\prime }{f}^{*}}>0,$
${J}_{13}=\frac{{\left(1-\lambda \right)}^{2}}{{\lambda }^{\prime }{f}^{*}{\rho }^{*\left(\alpha -1\right)}{d}^{*\left(1-\alpha \theta \right)}}<0,$
${J}_{21}=-\left(\alpha \theta -1\right)\alpha \theta \omega {m}^{*}{\rho }^{1-\alpha }{d}^{*\left(\alpha \theta -2\right)}>0,$
${J}_{22}=-\alpha \theta \omega <0,$
${J}_{23}=-\alpha \theta \omega {\rho }^{1-\alpha }{d}^{*\alpha \theta -1}<0,$
${J}_{31}=-\alpha {\rho }^{\alpha -1}{d}^{*-\alpha \theta -1}\left[\theta \left(1-\phi \right)+\left(1-\theta \right)\omega {f}^{*}{d}^{*-1}+\theta {g}_{n}{\rho }^{-1}\right]<0,$
${J}_{32}=-\alpha \left(1-\theta \right)\omega {\rho }^{\alpha -1}{d}^{*1-\alpha \theta }<0,$
${J}_{33}=-\alpha \left(1-\theta \right)\omega <0.$

The characteristic equation for the above system is:

${\mu }^{3}+{a}_{1}{\mu }^{2}+{a}_{2}\mu +{a}_{3}=0,$

where:

${a}_{1}={J}_{11}+{J}_{22}+{J}_{33}\gtrless 0,$
$\begin{array}{c}{a}_{2}=\left({J}_{11}{J}_{22}\right)+\left({J}_{11}{J}_{33}\right)+\left({J}_{23}{J}_{33}\right)-\left({J}_{23}{J}_{32}\right)\\ -\left({J}_{12}{J}_{21}\right)-\left({J}_{13}{J}_{31}\right)<0,\end{array}$
$\begin{array}{c}{a}_{3}=-\left({J}_{11}{J}_{22}{J}_{33}\right)-\left({J}_{12}{J}_{23}{J}_{31}\right)-\left({J}_{13}{J}_{21}{J}_{32}\right)+\left({J}_{11}{J}_{23}{J}_{32}\right)\\ +\left({J}_{12}{J}_{21}{J}_{33}\right)+\left({J}_{13}{J}_{22}{J}_{31}\right)<0.\end{array}$

The signs of the eigenvalues of the dynamical system could be obtained by using the following relationship among the roots of the system: 1/

a1=-(μ1+μ2+μ3),

a2 = μ1μ2+μ1μ3+μ2μ3,

a3 = -μ1μ2μ3.

Given that the determinant of the system, a3, is negative, at least one root must be negative. Furthermore, the total number of roots is three and, hence, the remaining two roots must be of the same sign. The negative sign of a2 implies that the other two roots must be positive. Therefore, the system displays saddlepath stability.

### APPENDIX III: Variable Definitions and Data Sources #### References

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1/

I am thankful for discussions with and comments from P.R. Agenor, P. Cashin, M. El-Erian, H. Golriz, Z. Iqbal, A. Leijonhufvud, S. Lizondo, and M.H. Pesaran.

1/

With the exception of only a few years, Iran also had a parallel market for foreign exchange from 1930 to 1960. For discussions of Iran’s foreign exchange system prior to and since the 1979 revolution, see Amuzegar (1977), Behdad (1988), Central Bank of Iran (1979), Khosropour (1956), Lautenschlager (1986), Mazarei (1995b), and Pesaran (1992).

2/

The parallel market premium is defined as the ratio of the parallel market rate to the basic official exchange rate, minus one. See Appendix III for definition of variables and sources of data used.

1/

The evolution of the Iranian foreign exchange system in the post-revolutionary period is discussed in more detail in Appendix I. It should be noted that Iran has not been the only oil exporter that has had a-parallel market for foreign exchange. A number of other oil producers, including Algeria, Indonesia, Libya, Nigeria, and Venezuela, have at times had such a market. Parallel markets have come about in these countries as a result of balance of payments difficulties caused by a decline in oil revenues, or simply as a result of government policies aimed at restricting capital flight or certain types of imports.

2/

The model presented here is akin to the reserve adjustment version of Lizondo’s model.

3/

Pinto (1987) discusses the parallel market exchange rate in Nigeria, an oil exporter, but does not provide a formal model. For general discussions of parallel markets for foreign exchange, see Agénor (1990), Dornbusch (1986a), and Edwards (1989).

1/

While Iran has actually had a system of numerous exchange rates, the model developed in this paper will contain only two rates. For a theoretical discussion of systems with more than two exchange rates, see Dornbusch (1986b).

2/

As Agénor (1995) argues, illegal trade and leakages are, however, likely to affect the dynamics of parallel market exchange rate.

3/

Another difference between the model presented here and the one in Lizondo (1991) is that in Lizondo’s framework there exists a range of goods which are exported either at the official or the parallel market rate. In our model, however, there is only one non-oil export, but the authorities determine the surrender requirement rate on these exports.

4/

Hence, gm = β H.

1/

While the parameter β has been fixed in this model, it could conceivably be related to variables such as the total foreign exchange earnings of the country. Under such a setup, the value of this parameter would rise as total foreign exchange receipts increase, thereby allowing the fiscal authority to sell a smaller portion of its receipts to the central bank.

2/

The maximum real amount of foreign exchange (in terms of imported goods) that the foreign exchange board can obtain is [(1-β)H + (1-ϕ)qx]/pm. Given the assumption of unitary import prices, this is equal to [(1-β)H + (1-ϕ)qx].

3/

It should be remembered that we have assumed that our hypothetical economy can not borrow funds on the international capital markets. Consequently, the above framework suggests a tight relationship between a country’s foreign exchange earnings and its official imports. Faini, Pritchett, and Clavijo (1988), Hemphill (1974), and Moran (1988) provide general discussions of the effect of foreign exchange earnings on the imports of the developing countries. Evidence of the strong influence of foreign exchange receipts on Iran’s imports is provided in Mazarei (1995a).

4/

An alternative modelling strategy would be to assume that the authorities limit the amount of imports in general, with or without regard to the particular type of goods being imported.

1/

More accurately, the premium should be defined as (b/e)-1. Throughout the remainder of this paper the ratio (b/e) is referred to as the parallel market premium.

1/

The expression for the private sector consumption of goods traded in the free market is obtained by dividing nominal wealth by the domestic prices of the goods traded on the parallel market, b. It should be recalled that the foreign price of the import and non-oil export goods have been set equal to one.

1/

The lack of responsiveness of the money supply in a petroleum exporting economy, where oil revenues accrue to the government, to movements in oil revenues is discussed in Dailami (1979) and Morgan (1979).

2/

This follows from the general feature of our model that if oil export earnings are spent abroad, they would not affect the money supply. A shift in the parameter β leads to a reduction in government imports, but has no effect on private sector imports (assuming that θ does not depend on H). A decline in β reduces the growth rate of domestic credit (equation 9) and increases, by the same amount, the accumulation of reserves (equation 10). As a result, there is no impact on the money supply or any other variable in the model.

3/

This formulation abstracts from one of the interesting aspects of the Iranian parallel market experience, namely, the central bank’s conducting of foreign exchange operations in the parallel market, which could bring about discrete changes in the parallel market exchange rate. The purpose of these open market operations was to raise revenues for the government and to influence the movements of the parallel market exchange rate.

1/

It is necessary to point out that in our model the steady state might be one in which international reserves are increasing or declining permanently. Such a decline in international reserves is indeed likely to invoke a Krugman-type balance of payments problem. One remedy to this problem is to modify the formulation of government finances to include a nondistortionary lump sum tax to cover the budget deficit so that the need for an increase in credit to the government is eliminated.

2/

Equation (13) in the text is obtained by dividing nominal wealth, W = M + bf, by the price of the nontraded good, Pn.

3/

Here, as in Lizondo (1991), it is assumed that ${q}_{n}>\left(1+\frac{1-\alpha }{\alpha \left(1-\theta \right)}\right){g}_{n}$ at all times.

1/

Proofs of these results are not provided here, but are available upon request.

2/

Changes in the price and quantity of oil have the same impact in our model. In a more comprehensive model which allows for foreign borrowing by the government and exhaustibility of oil, price and quantity changes could have very different effects on the parallel market premium.

1/

A pervasive issue in discussions of exchange rates is the distribution of the changes in the exchange rate. Various studies, such as Hodrick (1987), suggest that the distribution of exchange rate changes departs from normality. Among other consequences, this would have implications for the interpretation of statistical results, including autocorrelation tests, which are reported later in the paper. The non-normality of the distribution of changes in the rial/dollar parallel market rate was tested using the Jarque-Bera test. (See Bera and Jarque (1980)). The Jarque-Bera test statistic, JB, is given by:

$JB=n\left[\frac{{b}_{1}}{6}+\frac{{\left({b}_{2}-3\right)}^{2}}{24}\right],$

where (b1)1/2 and b2 are, respectively, measures of skewness and kurtosis of the distribution. The Jarque-Bera test statistic has a χ2 distribution with two degrees of freedom. The value of the test statistic for the rial/dollar parallel market rate, computed using the information provided in Table 1 based on 156 observations, was equal to 661.44. Hence, the hypothesis of normality of the parallel market exchange rate was rejected. Lilliefors’ version of the Kolmogorov-Smirnov test was also used to test for a possible departure of the observed distribution of the rate of growth of the parallel market rate from normality, and the null hypothesis of normality was rejected at the 1 percent level of significance. The Kolmogorov-Smirnov test is described in Daniel (1990).

2/

See Dickey and Fuller (1979, 1981).

1/

The above results should be interpreted with the low power of unit root tests in mind.

2/

Indeed, these results should be considered with caution since the Box-Ljung test for the significance of the autocorrelation function depends on the assumption of normality of the time series being studied. It should be recalled that the normality test reported in section 3.1.1 indicated that the rate of change in the parallel market exchange rate does not have a normal distribution.

3/

For a discussion of runs analysis see Wallis and Roberts (1956). Applications of it to official and black market exchange rates are provided by Cornell and Dietrich (1978), and Gupta (1981), respectively.

1/

These results were insensitive to the use of the median instead of the mean.

1/

Given that the official exchange rate remained largely stable throughout the period under study, the parallel market premium and exchange rate should have similar time series properties.

1/

All variables are recorded on the end-of-the-month basis. However, the parallel market premium is measured according to the Gregorian calendar, while all other variables are recorded according to the Iranian calendar. The Iranian calendar month runs from the twenty-first day of one Gregorian month to the twentieth day of the next month. Different weighted averaging schemes were tried in order to make the series compatible, but did not improve the empirical results.

2/

In order to examine the possibility of a long-run relationship between the parallel market premium and monetary factors, the existence of a cointegration relationship between the premium and the broad measure of money in real terms was tested using the Johansen procedure [Johansen (1988), and Johansen and Juselius (1990)]. Such a relationship could be established only at the α = 10 percent level of confidence. Similar results were obtained when testing for the presence of a cointegration relationship between the parallel market premium and nominal stock of money.

1/

It should be noted that prior to 1991 export surrender requirements were not always enforced.

2/

Although the exchange system was unified at the rate of Rls. 1,540 per U.S. dollar, a sizable amount of imports of essential goods and some current account transactions continued at the former basic official rate.

The Parallel Market for Foreign Exchange in an Oil Exporting Economy: The Case of Iran, 1978-1990