The Premium in Black Foreign Exchange Markets

The Premium in Black Foreign Exchange Markets

The Premium in Black Foreign Exchange Markets: Evidence from Developing Economies Yochanan Shachmurove, The City College of The City University of New...

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The Premium in Black Foreign Exchange Markets: Evidence from Developing Economies Yochanan Shachmurove, The City College of The City University of New York and The University of Pennsylvania This paper examines the determinants of the premia between the black and official exchange rates using monthly data for 17 developing countries. The premium is hypothesized to be positively influenced by the official depreciation-adjusted interest rate differential and dollar value of domestic assets. It is hypothesized to be negatively influenced by the official real exchange rate, exports, and a seasonal factor associated with tourism. The countries studied are: Bangladesh, Brazil, Fiji, Gambia, Ghana, Guyana, Hungary, Ireland, Jamaica, Kenya, Nepal, Nigeria, Philippines, Somalia, South Africa, Uganda, and the former Yugoslavia. In general, the results are very supportive of the model. It is found that the interest rate differential and assets positively influence the premium, as is expected. The official real exchange rate is found to negatively influence the premium.  1999 Society for Policy Modeling. Published by Elsevier Science Inc.

1. INTRODUCTION This paper develops a model with which to explain the effects of various economic factors on the black market exchange-rate premium. This study is targeted at the behavior of the black market foreign exchange in developing countries using monthly data from 1985 to 1989. The vast majority of black markets in foreign exchange are in the developing countries. The empirical investigation is based on a model developed by Dornbusch, Dantas, Pechman, Rocha, and Simo˜es (1983). The central and most interesting feature of the model is the interaction of stock and flow conditions in determining both the premium on the black dollar and the stock Address correspondence to Professor Yochanan Shachmurove, Department of Economics, University of Pennsylvania, 3718 Locust Walk, Philadelphia, PA 19104-6297. I would like to thank Robert Alwine for excellent research assistance and the Schweger Fund for partial financial support. Received October 1996; final draft accepted March 1997. Journal of Policy Modeling 21(1):1–39 (1999)  1999 Society for Policy Modeling Published by Elsevier Science Inc.

0161-8938/99/$–see front matter PII S0161-8938(97)00091-4

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of black money. It is proposed that the black market premium is determined by the official real exchange rate, the official depreciation-adjusted interest rate differential, the level of exports, and a seasonal factor associated with tourism. These factors are interesting to examine because they may provide a foothold for governments of developing countries in trying to restrict activities in the black market. Black money affects public revenues, degenerates the investable surplus, delimits the national productivity, drains the balance of payments, and distorts equity and equality concepts of economic distribution. The black market exchange rates in the following 17 developing countries are studied. Bangladesh, Brazil, Fiji, Gambia, Ghana, Guyana, Hungary, Ireland, Jamaica, Kenya, Nepal, Nigeria, Philippines, Somalia, South Africa, Uganda, and (the former) Yugoslavia. Despite the increasing trend toward globalizing the world economy, many developing countries are still living in a chaotic constellation of limitations and controls over foreign currency holdings and transactions and a wide array of black market of currencies. (Chow, Kellman, and Shachmurove, 1994, 1998; Adams and Shachmurove, 1997; Friedman and Shachmurove, 1997; Shachmurove, 1998). Many developing countries’ currencies have so called “legislation for monetary protection,” usually limiting the amount of foreign exchange an individual is allowed to hold. Such currency regulations lead to unofficial, parallel, or illegal transactions in foreign currencies. A parallel, or a black market, is an illegal structure that is created in response to government intervention that produces excess supply or demand for a product. When the price of foreign currency is set below the market clearing rate, an excess demand is usually generated for acquiring foreign currency. The government has the choice of either devaluating the currency or maintaining strict controls over exchange, such as setting quotas on the purchase of foreign exchange. Such currency controls are designed by governments to limit the use of foreign exchange in transactions. The United States’ dollar used to be the only preferred currency on the black market. When the dollar was removed from the gold standard in August 1971, it lost its dominance, and other currencies became popular as vehicle currencies in foreign currency black markets throughout the world. The increased demand for such monies as the German Mark and the Swiss Franc reduces the

THE PREMIUM IN BLACK FOREIGN EXCHANGE MARKETS

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premia for the U.S. Dollar. Nonetheless, the U.S. dollar is still the primary currency traded in most of the globe’s black markets, serving as a “pass-through” vehicle to precious metals such as gold, energy uses such as oil, and other monetary units such as the Japanese yen, the German mark, and the Swiss franc. (Ajayi, Mehdian, and Shachmurove, 1996). Only 17 countries have currencies that are free from internal black market exchange.1 Most other currencies have legislation that limits the foreign exchange available, which only serves to generate illegal transactions. Controls over monetary exchange only increase the risk and encourage evasion. The restrictions promote the diversion of scarce money from the official channels to be distributed later in the illegal channels. As long as the risk is tolerable, there are high incentives to sell on the black market to reap the profits. The commodity is purchased at a lower price, but is then sold illegally at a higher price on the market because of the demand generated from shortages. The more inefficient a country’s reserves or financial capacities, the greater the likelihood of a vigorously organized black market. The stringent regulations or punishments only serve to increase the premium between the black and the official foreign exchange rates. If a large proportion of foreign exchange transactions are conducted in this manner, the devaluation of official rates can affect consumer prices as well as the entire economy. Legislative controls and rationing that attempt to fight black markets often contribute instead to higher activities in the black market for foreign exchange. The enforcement of governmental policies, price ceilings, and restrictions on foreign currency help increase scarcity, which in turn, encourages accumulation for later illegal transactions. Attempts by governments are usually ineffective unless they are also accompanied by increases in productivity, price stability, and availability of goods. Without careful monitoring of these actions, transactions in the black market are going to persist, despite government interventions. The designing of monetary policy in each country depends on the official economy. This economy involves open transactions financed through identifiable sources and generates income within the parameters of government rules and regulations. In addition 1 The countries are Bahrain, Djibouti, Hong Kong, Kuwait, Lebanon, Malaysia, Netherlands, Oman, Panama, Qatar, Saudi Arabia, Seychelles, Singapore, United Arab Emirates, the United Kingdom, and the United States (World Currency Yearbook, 1989).

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to the official economy, many countries, particularly developing ones, have developed a parallel economy. This parallel economy, or black market, emerges through the manipulation of the economic forces of supply and demand for both currency and commodities. A black market also emerges when trade and industry create an artificial situation of scarcity or glut, and in the process, amass high returns on their investments by profiteering. As a result of profiteering activity, the black market generates unreported income and wealth that escape detection by official statistics (Culbertson, 1975; Ray, 1981; Nowak, 1985; Manasian et al., 1987; Roemer and Jones, 1991; Beghestani and Noer, 1993; Argy, 1994; Ethier, 1995; Krugman and Obstfeld, 1997). Gupta (1981) attributes much of the strength of the black market to the resale of officially allocated foreign exchange holdings and to the incentive to under invoice and smuggle exports. He argues that an increase in the black market rate, given the official exchange rate, creates an incentive for residents abroad to channel their remittances through the black market. This raises their private receipts in terms of home currency and deprives the central bank of this foreign exchange. Economists studying black market activity in developing countries advocate that it is best to keep the black market premium rate as low as possible (Gupta, 1981). By influencing the determinants of the black market exchange rate, developing countries can keep the black market premium rate low and increase their official foreign exchange currency holdings. The paper is organized as follows. Section II presents the model for the premium on the black dollar. Section III introduces the data. Section IV details the empirical results. Section V summarizes. 2. THE MODEL The model is based on that of Dornbusch et al. (1983). The black market is treated in a partial-equilibrium, stock, and flow framework. The interest rate on the home currency, the U.S. interest rate, the official exchange rate, and the domestic currency value of nondollar assets are taken as given. The stock demand for black dollars arises as the result of portfolio diversification and the flow market arises as the result of international trade, both reported and unreported.

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2.1 The Stock Demand for Black Dollars The stock demand for black dollars is posited to be positively related to wealth and the official depreciation-adjusted interest rate. Equilibrium in the stock market for dollars must meet the condition that supply equal demand. Using the notation of Dornbusch et al., this relation may be expressed as follows: EB 5 u(i* 1 d 2 i)(A 1 EB)

u9 . 0.

(1)

Thus, EB represents the supply of black dollars and u is a positive function of u (i* 1 d 2 i) (A 1 EB) where E represents the black market exchange rate, B the stock of black dollars, i* the interest rate on U.S. dollars, d the rate of depreciation of the home currency in the black market, i the interest rate on the home currency, and A represents the value of nondollar assets. As stated above, demand is posited to be positively related to wealth and to the depreciation-adjusted interest rate, or yield. The stock market equilibrium condition can be written alternatively in terms of the black market premium, actually 1 plus the premium, and the ratio of black dollars to wealth. The premium is defined as X 5 E/E, where E represents the official exchange rate. Dividing Equation 1 by wealth: XB/(XB 1 A) 5 u(i* 1 d 2 i),

(2)

where the dollar value of domestic assets, A ; A/E, is taken as exogenous. The rate of depreciation of the black dollar, d, is taken as given. The rate of change of the premium is denoted by X/X and is equal to the difference between the rate of depreciation the official and black exchange rate, or formally: X/X ; d 2 d.

(3)

Substituting Equation 3 into the stock market equilibrium condition, Equation 2, and inverting equation in such a way that X/X will be on the left-hand side of the equation, one can express the relationship between the stock of black dollars, the premium, and the rate of change of the premium as follows: X/X 5 G(XB/A) 2 (i* 1 d 2 i),

G9 . 0

(4)

where (XB/A) denotes the relative supply of black dollars. From Equation 4, the dynamic relationship between the above variables is given. Equilibrium in the stock market for black dollars requires

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that an increase in the relative supply of black dollars occur along with an increase in the relative yield via either an increase in the premium or an increase in the official depreciation-adjusted interest rate differential, (i* 1 d 2 i). On the other hand, an increase in the official depreciation-adjusted interest rate differential will cause an excess demand for black dollars that must be offset either by a decrease in demand due to a lowering premium or through an increase in supply due to a higher premium (Kocagil and Shachmurove, 1998). 2.2 The Flow Market for Black Dollars The demand in the flow market is the product of both import smugglers and tourism out of the country, and supply is the product of export smugglers and tourism into the country. Following Phylaktis (1992), it is assumed that the flow demand for black dollars is positively related to wealth. The current account of the black market is posited to be a function of the premium, the official real exchange rate, and exports: b 5 f(X, e, exports, [A 1 EB]).

(5)

fx . 0, fe . 0, fexports . 0, and f [A 2 EB] . 0 and e represents the official real exchange rate. Substituting A ; A/E into Equation 5, the dynamic relationship between b, B, exports, and X is obtained for a given value of e and A as follows: b 5 f(X, e, exports, [A 1 EB]).

(6)

An increase in the black market premium is expected to reduce underinvoicing and tourism abroad by domestic tourists. Due to the accompanying fall in the relative value of home currency assets, there will also be a decrease in wealth. At the same time, there is an increase in the supply of black dollars to export smugglers, or overinvoicers. Taken together, the two effects result in a current account surplus. Equilibrium is regained through an increase in the stock of black dollars, B, which increases wealth and thus the demand for black dollars in the flow market. A depreciation of the official real exchange rate is expected to increase net inflows, as it makes domestic goods more competitive, and thus increases exports and reduces the supply of black dollars to smugglers and tourists.

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Figure 1.

These relationships are demonstrated graphically in Figures 1, 2, and 3. In Figure 1, a balanced current account is represented by the upward sloping b 5 0 schedule, while the X 5 0 schedule represents the points at which the premium is constant. As can be seen from Equation 4, the X 5 0 schedule is a rectangular parabola. The X 5 0 schedule is drawn for a given (i* 1 d 2 I) and e. Points to the right of b 5 0 represent a premium that is

Figure 2.

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Figure 3.

so high as to cause a surplus in the stock of dollars. Points to the left, on the other hand, represent shortage conditions as the result of a low premium. Point A represents the point of market equilibrium, as indicated by the arrows on the unique trajectory Q. As the stock of black dollars rises over time, the rate of depreciation of the black dollar decreases relative to that of the official rate. Figure 2 shows the effects of a shock to the stock market via a change in the interest rate differential. A reduction in the differential, by making domestic assets more attractive, results in a demand-side shift out of the black market as people shift their money to the official market. Figure 3 pictures the reaction to the flow market to changes in the real official exchange rate. A real depreciation in the domestic currency leads to increased flow into the black market as the black market rate becomes relatively more attractive. The increased flow into the black market causes a shift to the left in the current account balance, b 5 0. 3. DATA The developing countries examined in this paper are: Bangladesh, Brazil, Fiji, Gambia, Ghana, Guyana, Hungary, Ireland, Jamaica, Kenya, Nepal, Nigeria, Philippines, Somalia, South Africa, Uganda, and Yugoslavia. The monthly data starts January

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Table 1: Black Market Premiums for the U.S. Dollar (Based on Official Rate at the End of December 1988) Bangladesh Brazil Fiji Gambia Ghana Guyana Hungary Ireland Jamaica Kenya Nepal Nigeria Philippines Somalia South Africa Uganda Yugoslavia

318% 57% 13% 36% 36% 430% 56% 2% 22% 13% 61% 87% 3% 48% 5% 261% 17%

1985 and ends December 1989. The data is from the World Currency Yearbook of various years (Cowitt, 1992). The premium, vis-a-vis the Official Rate of a currency are based on the unofficial and/or illegal prices paid for the U.S. dollar in the trading centers of the above-mentioned countries. The CPI is based on data of the CPI for both the United States and the developing countries. The CPI is the monthly price level of the various countries measured in terms of U.S. dollars.2 The consumer price indexes are found in the Prices section of the International Financial Statistics (International Monetary Funds, 1985–1992). They are compiled from reported versions of national indexes. Most countries listed in the International Financial Statistics (IFS) compile their consumer price indexes according to the Laspeyres formula that utilizes weights and selections of items based on consumption patterns. The interest rates used are the Deposit Interest Rates and they are found in the interest rate section of the IFS. They include rates offered to resident consumers for demand, savings, and time deposits. The IFS also publishes the exports data measured in 2 Summers and Heston (1988) provide yearly, but not monthly, purchasing power parity price levels estimates.

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Table 2: Statistics for Black, Official and Premium Dollar Exchange Rates Mean Bangladesh BEX OFFEX PB Brazil BEX OFFEX PB Fiji BEX OFFEX BP Gambia BEX OFFEX PB Ghana BEX OFFEX PB Guyana BEX OFFEX PB Hungary BEX OFFEX PB Ireland BEX OFFEX PB Jamaica BEX OFFEX PB Kenya BEX OFFEX PB Nepal BEX OFFEX PB

Std error

Minimum

91.56 30.74 60.99

22.15 1.59 20.8

37.3 26 10.3

400.49 55851.75 261629.29

806.35 68735.98 70132.99

0.77 1.29 20.5

Maximum

Median

128 32.27 96

96.88 31 65.69

4 88.04 2278936

3300 278940 2591.67

37.05 22391.73 242201.78

0.12 0.17 0.28

0.57 1.07 20.94

0.96 1.53 20.13

0.8 1.29 20.38

0.16 6.44 26.11

0.05 1.43 1.45

0.1 3.37 27.68

0.28 8.32 23.09

0.13 6.99 26.77

209.56 155.28 68.87

59.04 80.63 24.32

120 50 17.73

339 303.03 129.99

215 149.93 67.89

44.91 11.15 36.18

10.57 9.63 9.11

19 4.15 14.7

58 33 47.7

50 10 40

64.7 50.48 15.28

7.69 5.17 4.48

51.2 43.58 6.72

87 62.9 29.46

62.4 48.24 14.29

1.37 0.74 0.62

0.18 0.11 0.3

0.91 0.6 20.16

1.6 1.07 1

1.42 0.7 0.72

6.49 5.55 0.99

0.3 0.24 0.31

5.55 5.04 0.31

7.4 6.48 1.92

6.48 5.48 0.99

19.09 17.51 2.03

2.78 1.8 2.01

14.85 16 21.19

24.5 21.86 6.48

18.9 16.6 2.4

27.26 22.46 5.44

7.19 3.09 5.22

19.9 17.3 21.5

46 28.6 18.7

24.75 21.85 4 (Continued)

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Table 2: Continued

Nigeria BEX OFFEX PB Philippines BEX OFFEX PB Somalia BEX OFFEX PB South Africa BEX OFFEX PB Uganda BEX OFFEX PB Yugoslavia BEX OFFEX PB

Mean

Std error

Minimum

Maximum

0.2 3.75 23.14

0.07 2.37 2.2

0.07 0.83 27.49

0.32 7.65 20.55

0.19 4.04 23.76

21.41 20.52 1.07

1.7 1.13 0.99

16.9 18.36 21.57

24 22.44 3.54

22 20.59 0.99

230.65 179.99 102.36

197.11 191.49 97.32

0.41 2.3 21.85

0.05 0.27 0.29

0.29 1.9 22.45

221.08 81.22 161.95

224.71 94.06 165.11

5.9 5.5 0.35

2359.31 0.74 2359.1

3778.8 1.96 3778.45

238 0.02 237.98

40 36 4

Median

800 929.5 426

153.5 100 70

0.52 2.79 21.41

0.41 2.26 21.8

625 370 460

121.25 60 95.5

18000 11.82 17998.26

705 0.07 704.94

millions of U.S. dollars. The official exchange rates measured by the IFS are expressed in U.S. dollars per national currency unit. This model uses the ae series official exchange rates, which denote end of the period exchange rates. Table 1 presents the black market premia for the U.S. dollar based on the official rate at the end of December 1988. The premia range from 2 percent in Ireland to 430 percent for Guyana in that period. Table 2 presents some summary statistics for each of the black, official, and premium dollar exchange rates. It is clear from the table that different countries have very different patterns of black and official dollar exchange rates. These patterns are visualized in Figures 4–20 where the black, official, and the premium exchange rate for each country are presented as a function of time. The left y-axis measures the black and the official exchange rates with respect to the U.S. dollar. The premium as a function of time is measured on the right y-axis. It is of particular interest

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Figure 4.

to ascertain whether the model presented above is capable of explaining the premium as a function of the variables introduced above. The cross-sectional data is pooled and estimated by OLS (White, 1980; Brown and Maital, 1981; Hayashi and Sims, 1983). Dummy variables are constructed to represent the 17 developing countries used in this paper. Dummy variables are also constructed to represent a seasonal factor and time dimension. The seasonal factor is estimated in two ways. First, an 11-month dummy variable is constructed to capture monthly tourist movements either into or out of the country in question. Second, a bimonthly dummy variable is constructed to capture the effects of tourist movements by season, either high or low tourist travel season. The time-dimension dummy variables are constructed to capture the fluctuation in the premium for the years of 1985, 1986, 1987, and 1988. 4. EMPIRICAL RESULTS As can be seen in Table 3, the empirical results are very supportive of the model. The first set of results, called Model 1, is obtained by testing the premium against the dollar value of the domestic assets, the real exchange rate, the interest rate differential, exports, Rho, and the country dummy variables. In this set of results, every variable tested is found to be significant at the 5 percent level and of the expected sign. the R-squared and adjusted R-squared are over 0.99. The country dummy variables show that in each of the 17 countries, the premium is declining.

THE PREMIUM IN BLACK FOREIGN EXCHANGE MARKETS

Figure 5.

Figure 6.

Figure 7.

13

14

Figure 8.

Figure 9.

Figure 10.

Y. Shachmurove

THE PREMIUM IN BLACK FOREIGN EXCHANGE MARKETS

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Figure 11.

The second set of results, called Model 2, shown in Table 3, is obtained by testing the premium against the dollar value of the domestic assets, the real exchange rate, the interest rate differential, exports, Rho, the country dummy variables, and the time dummy variables. Each of the results, with the exception of the time-dummy variables, is significant at the 10 percent level. The coefficients of country dummy variables are, again, all negative demonstrating a declining premium. The third set of results, called Model 3, shown in Table 3, is obtained by testing the premium against the same variables in the first with the addition of the time dummy variable and the 11month seasonal dummy variables. It is found that the dollar value

Figure 12.

16

Figure 13.

Figure 14.

Figure 15.

Y. Shachmurove

THE PREMIUM IN BLACK FOREIGN EXCHANGE MARKETS

Figure 16.

Figure 17.

Figure 18.

17

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Figure 19.

of domestic assets, the real exchange rate, the interest rate differential, and Rho are found to be significant at the 10 percent level. Each of the country variables is significant at 5 percent and negative. Unexpectedly, the time and seasonal variables are not found to be significant. Nonetheless, the R-squared and adjusted R-squared values are above 0.99. The fourth set of results is obtained from the same variables as the second with the addition of the bimonthly seasonal factor in place of the 11-month factor. The country variables are each significant at 5 percent and negative. The dollar value of domestic assets, the real exchange rate, the interest rate differential, and Rho are all significant at the 10 percent level. In Appendix 1 two additional sets of results are presented. First, the results of the premium tested against the dollar value

Figure 20.

Model 1 Coefficient T-statistic Model 2 Coefficient T-statistic Model 3 Coefficient T-statistic Model 4 Coefficient T-statistic 0.336171 4.095847 0.338 4.093 0.337 4.100

2780.4917 21.774593 2790.186 21.781 2806.317 21.824

0.000 2.803 0.000 2.850

7731.867 17.267 7743.748 17.391

(i* 1 d 2 i)

7757.125 0.00 17.54434 2.906188

e

0.344 4.337

0.000 2.924

A 2809.407 21.980

7681.293 17.699

Constant

Table 3: Regression Results

20.110 21.626

20.108 21.587

20.135746 22.070552

20.126 22.006

Exports

0.324 8.970

0.326 8.980

0.325456 9.049065

0.333 9.333

Rho

27828.606 217.879

27808.155 217.755

27826.098 217.9443

27735.934 217.939

Bangladesh

27461.650 216.753

27445.739 216.633

27403.191 216.70685

27340.035 216.642

Brazil

(Continued)

27329.110 213.579

27318.297 213.512

27341.212 213.66091

27235.770 214.007

Fiji

THE PREMIUM IN BLACK FOREIGN EXCHANGE MARKETS 19

Model 1 Coefficient T-statistic Model 2 Coefficient T-statistic Model 3 Coefficient T-statistic Model 4 Coefficient T-statistic

27666.936 217.579

Nepal

27649.476 217.650

Nigeria

27704.896 217.156

27686.320 217.043 27921.149 217.952

27906.185 217.830 27657.586 217.436

27640.133 217.315 27685.155 217.039

27667.108 216.929

27749.850 217.482

27758.400 217.481

27739.018 217.363

(Continued)

27752.130 217.578

27733.882 217.461

27767.289 217.608

27657.151 217.573

Kenya

27695.661 217.066

27592.658 217.184

Jamaica

27730.624 217.364

27545.914 217.387

Ireland

27747.615 217.487

27847.297 218.060

Hungary

27677.422 216.955

27612.218 217.288

Guyana

27747.288 27757.472 27741.877 217.54464 217.54786 217.61909

27674.863 217.679

Ghana

27696.393 27764.053 27704.468 27935.994 27625.859 27684.923 217.13593 217.66865 217.22158 218.07208 217.42688 217.10568

27604.116 217.213

Gambia

Table 3: Continued

20 Y. Shachmurove

Model 1 Coefficient T-statistic Model 2 Coefficient T-statistic Model 3 Coefficient T-statistic Model 4 Coefficient T-statistic 27746.970 217.462

27836.903 218.012

27785.165 217.839

27767.278 217.716

27743.192 217.51767

27755.591 217.83423 27726.914 217.340

27666.220 217.800

S. Africa

27663.612 217.506

Somalia

27817.345 217.887

7826.922 218.05642

27732.438 218.046

Phillippines

Table 3: Continued

— —

1985

27802.058 216.669

27782.978 216.543 14.824 0.393

16.172 0.426

27797.243 11.75963 216.70618 0.331696

27714.569 216.720

Uganda

21.564 20.043

21.365 20.037

22.58002 20.074219

— —

1986

43.132 1.247

43.351 1.250

44.22624 1.339731

— —

1987

5.821 0.172

6.288 0.185

— —

49.713 1.064

— —

— —

Jan

(Continued)

8.186367 0.252267

— —

1988

THE PREMIUM IN BLACK FOREIGN EXCHANGE MARKETS 21

Model 1 Coefficient T-statistic Model 2 Coefficient T-statistic Model 3 Coefficient T-statistic Model 4 Coefficient T-statistic — — 4.537 0.106 — —

— — 25.674 0.584 — —

Mar

— —

Feb

— —

Table 3: Continued

— —

230.664 20.708

28.445 20.195 — —

— —

— —

May

— —

— —

Apr

— —

25.863 20.137

— —

— —

Jun

— —

27.530 20.167

— —

— —

Jul

— —

59.395 1.309

— —

— —

Aug

— —

2.440 0.054

— —

— —

Sept

(Continued)

— —

18.656 0.412

— —

— —

Oct

22 Y. Shachmurove

— — — — — — 44.367 1.354

— — 217.318 20.382 — —

J/F

— —

Nov

6.379 0.206

— —

— —

— —

M/A

— — 34.288 1.063

29.884 20.319

— —

— —

J/A

— —

— —

— —

M/J

Note: A represents the dollar value of domestic assets. e represents the official real exchange rate. (i* 1 d 1 i) represents the official depreciation-adjusted interest rate differential. Rho represents the first-order difference in the black market premium. Jan represents January, Feb represents February, and so forth through November. J/F represents January and February. M/A represents March and April. M/J represents May and June. J/A represents July and August. S/O represents September and October. RS represents R-squared. ARS represents Adjusted R-squared.

Model 1 Coefficient T-statistic Model 2 Coefficient T-statistic Model 3 Coefficient T-statistic Model 4 Coefficient T-statistic

Table 3: Continued

18.807 0.587

— —

— —

— —

S/O

707

707

707

707

Obs

0.994

0.994

0.993678

0.994

RS

0.993

0.993

0.993446

0.993

ARS

THE PREMIUM IN BLACK FOREIGN EXCHANGE MARKETS 23

24

Y. Shachmurove

of domestic assets, the real exchange rate, the interest rate differential, and Rho are included. Second, the results of the premium tested against the above variables and the time dummy variables are included. The results summarized in Appendix 1 all have R-squared and adjusted R-squared values of over 0.99, even though the significance of the coefficients is not as supportive, as in the cases of the results presented in Table 3. In Appendices 2 and 3 the model is tested with adjustments for the different sizes of the economies examined and the results are summarized (Shachmurove, 1985; Shachmurove and Spiegel, 1995). In this paper the developing countries examined have economies of vastly differing sizes. Thus, to adjust for the variations in the size of the economies examined, the assets, A, and exports variables are divided by the gross domestic product (GDP) of the country in question in Appendix 2 and the population of the country in question in Appendix 3. The results obtained from these adjustments are similar to those in Table 3. In Appendix 2, the results found for the GDP-adjusted dollar value of domestic assets, interest rate differential, Rho, and the country dummy variables are supportive of the model. However, the results presented in Appendix 2 demonstrate that the real exchange rate and GDP-adjusted exports are not significant. The results presented in Appendix 3 demonstrate that the populationadjusted assets, real exchange rate, and population-adjusted exports are not significant, but that the interest rate differential, Rho, the country dummy variables, the month of January in Model 5 and January/February in Model 6 are significant at the 10 percent level. 5. CONCLUSION This paper develops a model with which to explain the effects of various economic factors on the black market exchange rate premium. It uses monthly data beginning in 1985 and ending in 1989. The empirical results are very supportive of the model and agree with the findings of Dornbusch et al. (1983). R-squared and adjusted R-squared values are all above 0.99. It is found that the interest rate differential and assets positively influence the premium as is expected. The official real exchange rate is found to negatively influence the premium. Unexpectedly, neither the

THE PREMIUM IN BLACK FOREIGN EXCHANGE MARKETS

25

seasonal factors nor the time dummy variables are found to significantly affect the premium. It is very interesting that the coefficient values of the country dummy variables are all negative. This suggests that the premium in all of these countries is decreasing. These results are important because they provide a starting point for governments to control the level of black market activity. Developing countries appear to be the most disastrously affected by black market activity. This may be due to a strong distrust in the ability of the free market to regulate supply and demand in these countries. In addition, third-world governments heavily embed foreign sector regulations into their planned programs. However, the most important reason for the harmful impact of high black market activity on developing nations is the flight of much needed capital abroad. Developing countries can stem the tide of foreign currency out of the country through appropriate economic policy. A proper policy, in light of the findings of this paper, would tend to reduce the incentives of the population to resort to black market activities, and thus to contribute more to the official economy. By implementing policies that monitor and/ or affect the variables examined in this study, governments in developing countries can control the level of black market activity and lessen its negative impact on the development of their economies. REFERENCES Adams, F.G., and Shachmurove Y. (1997) Trade and Development Patterns in the East Asian Economies. Adian Economic Journal 11:345–360. Ajayi, R.A., Mehdian S.M., and Shachmurove, Y. (1996) Stock Return Differentials as Predictors of Exchange Rates: An Empirical Investigation. The Journal of Business and Economic Studies 3:45–52. Argy, V. (1994) International Macroeconomics: Theory and Policy. London: Rutledge. Baghestani, H., and Noer, J. (1993) Cointegration Analysis of the Black Market and Official Exchange Rates in India. Journal of Macroeconomics 15:709–720. Brown, B., and Maital, S. (1981) What Do Economists Know? An Empirical Study of Experts’ Expectations. Econometrica 49:1287–1294. Chow, P., Kellman M., and Shachmurove Y. (1999) A Test of the Linder Hypothesis in Pacific Newly Industrialized Countries Trade. Applied Economics, (in press). Chow, P., Kellman M., and Shachmurove Y. (1994) East Asian Newly Industrialized Countries Manufactured Intra-Industry Trade 1965–1990. Journal of Asian Economics 5:335–348. Cowitt, P.P. (1992) 1988–1989 World Currency Yearbook. Brooklyn, NY: International Currency Analysis, Inc. Culbertson, W.P., Jr. (1975) Purchasing Power Parity and the Black Exchange Rates. Economic Inquiry 13:287–296.

26

Y. Shachmurove

Dornbusch, R., Dantas, D.V., Pechman, C., Rezende Rocha, R., and Simo˜es, D. (1983) The Black Market for Dollars in Brazil. The Quarterly Journal of Economics, February:25–40. Ethier, W.J. (1995) Modern International Economics, 3rd ed. New York: W.W. Norton. Friedman, J., and Shachmurove, Y. (1997) Co-Movements of Major European Community Stock Markets: A Vector Autoregression Analysis. Global Finance Journal 8:257– 277. Gupta, S. (1981) Black Market Exchange Rates. Tubingen: Mohr. Hayashi, F., and Sims, C.A. (1983) Nearly efficient estimation of time series models with predetermined, but not exogenous, instruments. Econometrica 51:783–798. International Monetary Fund. International Financial Statistics, 1985–1992. Kocagil A.E., and Shachmurove Y. (1998) Return-Volume Dynamics in Futures Markets. The Journal of Futures Markets 18:399–426. Krugman, P.R., and Obstfeld, M. (1994) International Economics: Theory and Policy, 4th ed. Readings, MA: Addison-Wesley. Manasian, D., Leigh, B., Bernier, L., Ingersoll, R., Pilarski, L., Reed, C., Mollett, P., and Skole, R. (1987) Europe’s booming black economy. International Management 42:24–30. Nowak, M. (1985) Black Markets in foreign exchange. Finance And Development 22:20–23. Phylaktis, K. (1992) Purchasing Power Parity and Cointegration: The Greek Evidence from the 1920s. Journal of International Money and Finance 11:502–513. Ray, S.K. (1981) Economics of the Black Market. Boulder, CO: Westview Press. Roemer, M., and Jones, C. (1991) Markets in Developing Countries. San Francisco: ICS Press. Shachmurove, Y. (1985) Changes in the Dependence of State Employment on National Employment in the Last Decade: Some Evidence. Indiana Business Review 60:8–13. Shachmurove, Y. (1998) Portfolio Analysis of South American Stock Markets. Applied Financial Economics 8:315–327. Shachmurove, Y., and Spiegel U. (1995) On Nations’ Size and Transportation Costs. Review of International Economics 3:235–243. Summers, R., and Heston, A. (1988) A New Set of International Comparisons of Real Product and Price Levels Estimates for 130 Countries, 1950–1985. Review of Income and Wealth 34:1–25. White, H. (1980) A Heteroskedasticity-Consistent Covariance Matrix Estimator and Direct Test for Heteroskedasticity. Econometrica 48:817–838. World Currency Yearbook. (1984–1989), Brooklyn, NY: International Currency Analysis, Inc.

0.000 1.446

213.954 20.414

Model 1 Coefficient T-statistic Model 2 Coefficient T-statistic — — — —

— — — —

Gambia

Ghana

0.000 1.411

A

3.128 0.207

Appendix 1: Continued

Model 1 Coefficient T-statistic Model 2 Coefficient T-statistic

Constant

— —

— —

Guyana

242.780 20.570

240.961 20.548

e

Appendix 1: Additional Regression Results

— —

— —

Hungary

20.004 20.046

0.005 0.059

(i* 1 d 2 i)

— —

— —

Ireland

20.019 20.829

20.019 20.795

Exports

— —

— —

Jamaica

0.991 196.450

0.991 198.656

Rho

— —

— —

Kenya

— —

— —

Bangladesh

— —

— —

Nepal

— —

— —

Brazil

(Continued)

— —

— —

Nigeria

(Continued)

— —

— —

Fiji

THE PREMIUM IN BLACK FOREIGN EXCHANGE MARKETS 27

— — — —

— —

Model 1 Coefficient T-statistic Model 2 Coefficient T-statistic

Mar

Somalia

— —

— — — —

— — — —

Feb

Appendix 1: Continued

Model 1 Coefficient T-statistic Model 2 Coefficient T-statistic

Phillippines

Appendix 1: Continued

— —

— —

Apr

— —

— —

S. Africa

— —

— —

May

— —

— —

Uganda

— —

— —

Jun

19.983 0.504

— —

1985

— —

— —

Jul

23.253 0.596

— —

1986

— —

— —

Aug

13.102 0.332

— —

1987

— —

— —

Sept

20.815 0.532

— —

1988

(Continued)

— —

— —

Oct

(Continued)

— —

— —

Jan

28 Y. Shachmurove

— — — —

— — — —

J/F

— —

— —

M/A

— —

— —

M/J

— —

— —

J/A

ARS represents Adjusted R-squared.

RS represents R-squared.

S/O represents September and October.

J/A represents July and August.

M/J represents May and June.

M/A represents March and April.

J/F represents January and February.

Jan represents January, Feb represents February, and so forth through November.

Rho represents the first order difference in the black market premium.

e represents the official real exchange rate. (i* 1 d 1 i) represents the official depreciation-adjusted interest rate differential.

Note: A represents the dollar value of domestic assets.

Model 1 Coefficient T-statistic Model 2 Coefficient T-statistic

Nov

Appendix 1: Continued

— —

— —

S/O

707

707

Obs

0.990

0.990

RS

0.990

0.990

ARS

THE PREMIUM IN BLACK FOREIGN EXCHANGE MARKETS 29

30

Y. Shachmurove

Appendix 2: GDP-Adjusted Regression Results A

e

(i* 1 d 2 i)

Exports

5.862 0.385

0.000 20.171

213.370 20.183

0.020 0.079

0.000 20.013

2.356 0.071

20.000 20.167

213.846 20.189

0.026 0.102

0.000 20.012

7710.788 18.395

0.000 0.056

11.312 0.046

0.547 2.626

0.004 0.715

7793.307 18.416

20.000 20.072

69.309 0.274

0.541 2.564

0.003 0.639

7772.057 18.212

20.000 20.040

67.664 0.266

0.570 2.682

0.004 0.747

7802.352 18.368

20.000 20.007

62.881 0.248

0.562 2.647

0.004 0.720

Constant Model 1 Coefficient T-statistic Model 2 Coefficient T-statistic Model 3 Coefficient T-statistic Model 4 Coefficient T-statistic Model 5 Coefficient T-statistic Model 6 Coefficient T-statistic

(Continued)

Appendix 2: Continued

Model 1 Coefficient T-statistic Model 2 Coefficient T-statistic Model 3 Coefficient T-statistic Model 4 Coefficient T-statistic Model 5 Coefficient T-statistic Model 6 Coefficient T-statistic

Rho

Bangladesh

Brazil

Fiji

Gambia

0.997 216.677

— —

— —

— —

— —

0.997 214.540

— —

— —

— —

— —

0.352 9.975

27719.08 216.810

27683.484 217.570

27717.789 217.614

27708.228 218.346

0.345 9.689

27776.315 216.709

27748.140 217.614

7831.557 217.620

27795.274 218.406

0.346 9.663

27770.991 216.565

27746.069 217.510

27819.159 217.489

27783.380 218.256

0.343 9.613

27814.868 216.734

27781.648 217.658

27853.786 217.628

27820.284 218.418 (Continued)

THE PREMIUM IN BLACK FOREIGN EXCHANGE MARKETS

31

Appendix 2: Continued

Model 1 Coefficient T-statistic Model 2 Coefficient T-statistic Model 3 Coefficient T-statistic Model 4 Coefficient T-statistic Model 5 Coefficient T-statistic Model 6 Coefficient T-statistic

Ghana

Guyana

Hungary

Ireland

Jamaica

— —

— —

— —

— —

— —

— —

— —

— —

— —

— —

27709.456 217.997

27705.218 218.346

27711.270 218.109

27711.117 218.352

27705.081 218.343

27780.083 218.019

27791.933 218.405

27791.625 218.173

27795.155 218.414

27792.825 218.401

27771.114 217.865

27780.701 218.257

27769.000 217.995

27783.595 218.263

27780.779 218.252

27811.477 218.039

27817.782 218.420

27801.636 218.152

27820.663 218.426

27817.660 218.413 (Continued)

Appendix 2: Continued

Model 1 Coefficient T-statistic Model 2 Coefficient T-statistic Model 3 Coefficient T-statistic Model 4 Coefficient T-statistic Model 5 Coefficient T-statistic Model 6 Coefficient T-statistic

Kenya

Nepal

Nigeria

Philippines

S. Africa

— —

— —

— —

— —

— —

— —

— —

— —

— —

— —

27708.628 218.352

27710.435 218.351

27710.690 218.301

27708.970 218.319

27710.624 218.223

27792.342 218.413

27793.784 218.413

27802.716 218.354

27799.858 218.374

27807.111 218.268

27780.636 218.263

27782.193 218.262

27790.764 218.207

27787.692 218.225

27794.987 218.124

27817.781 218.426

27819.339 218.425

27827.233 218.366

27824.159 218.385

27831.103 218.280 (Continued)

32

Y. Shachmurove

Appendix 2: Continued

Model 1 Coefficient T-statistic Model 2 Coefficient T-statistic Model 3 Coefficient T-statistic Model 4 Coefficient T-statistic Model 5 Coefficient T-statistic Model 6 Coefficient T-statistic

Somalia

Uganda

1985

1986

1987

— —

— —

— —

— —

— —

— —

— —

4.344 0.110

7.117 0.186

27705.774 218.267

27699.931 217.190

— —

— —

27776.720 218.329

27778.288 217.249

28.722 20.250

215.443 20.457

26.149 0.803

27765.482 218.178

27766.654 217.099

23.506 20.095

215.943 20.451

25.332 0.746

27803.668 218.346

27812.749 217.288

26.470 20.176

216.270 20.461

24.949 0.735

22.319 20.060 — —

(Continued)

Appendix 2: Continued

Model 1 Coefficient T-statistic Model 2 Coefficient T-statistic Model 3 Coefficient T-statistic Model 4 Coefficient T-statistic Model 5 Coefficient T-statistic Model 6 Coefficient T-statistic

1988

Jan

Feb

Mar

Apr

— —

— —

— —

— —

— —

6.885 0.178

— —

— —

— —

— —

— —

— —

— —

— —

— —

26.601 20.205

— —

— —

— —

— —

27.131 20.213

74.901 1.678

20.520 0.490

23.344 20.080

211.626 20.277

28.096 20.242

— —

— —

— —

— — (Continued)

THE PREMIUM IN BLACK FOREIGN EXCHANGE MARKETS

33

Appendix 2: Continued

Model 1 Coefficient T-statistic Model 2 Coefficient T-statistic Model 3 Coefficient T-statistic Model 4 Coefficient T-statistic Model 5 Coefficient T-statistic Model 6 Coefficient T-statistic

May

Jun

Jul

Aug

Sep

— —

— —

— —

— —

— —

— —

— —

— —

— —

— —

— —

— —

— —

— —

— —

— —

— —

— —

— —

— —

216.430 20.391

25.512 20.133

26.781 20.155

65.909 1.512

2.993 0.069

— —

— —

— —

— —

— — (Continued)

Appendix 2: Continued

Model 1 Coefficient T-statistic Model 2 Coefficient T-statistic Model 3 Coefficient T-statistic Model 4 Coefficient T-statistic Model 5 Coefficient T-statistic Model 6 Coefficient T-statistic

Oct

Nov

J/F

M/A

M/J

— —

— —

— —

— —

— —

— —

— —

— —

— —

— —

— —

— —

— —

— —

— —

— —

— —

— —

— —

— —

19.756 0.450

216.633 20.379

— —

— —

— —

— —

— —

52.279 1.682

0.532 0.018

22.984 20.099 (Continued)

34

Y. Shachmurove

Appendix 2: Continued

Model 1 Coefficient T-statistic Model 2 Coefficient T-statistic Model 3 Coefficient T-statistic Model 4 Coefficient T-statistic Model 5 Coefficient T-statistic Model 6 Coefficient T-statistic

J/A

S/O

Obs

RS

ARS

— —

— —

701

0.990

0.990

— —

— —

701

0.990

0.990

— —

— —

701

0.993

0.993

— —

— —

701

0.993

0.993

— —

— —

701

0.993

0.993

37.655 1.210

19.337 0.621

701

0.993

0.993

Note: A represents the dollar value of population-adjusted domestic assets. e represents the official real exchange rate. (i* 1 d 1 i) represents the official depreciation-adjusted interest rate differential. Rho represents the first order difference in the black market premium. Jan represents January, Feb represents February, and so forth through November. J/F represents January and February. M/A represents March and April. M/J represents May and June. J/A represents July and August. S/O represents September and October. RS represents R-squared. ARS represents Adjusted R-squared.

THE PREMIUM IN BLACK FOREIGN EXCHANGE MARKETS

35

Appendix 3: Population-Adjusted Regression Results A

e

(i* 1 d 2 i)

Exports

23.446 20.225

0.000 1.770

2100.131 21.143

0.011 0.131

20.251 21.417

217.080 20.503

0.000 1.760

2100.743 21.145

0.005 0.060

20.248 21.396

7630.838 17.618

0.000 2.372

2233.437 20.855

0.371 4.725

20.309 20.876

7710.438 17.607

0.000 2.342

2192.329 20.678

0.373 4.651

20.346 20.940

7701.697 17.397

0.000 2.174

2181.813 20.638

0.373 4.638

20.197 20.525

7715.596 17.520

0.000 2.204

2189.086 20.665

0.373 4.645

20.226 20.604

Constant Model 1 Coefficient T-statistic Model 2 Coefficient T-statistic Model 3 Coefficient T-statistic Model 4 Coefficient T-statistic Model 5 Coefficient T-statistic Model 6 Coefficient T-statistic

(Continued)

Appendix 3: Continued

Model 1 Coefficient T-statistic Model 2 Coefficient T-statistic Model 3 Coefficient T-statistic Model 4 Coefficient T-statistic Model 5 Coefficient T-statistic Model 6 Coefficient T-statistic

Rho

Bangladesh

Brazil

Fiji

Gambia

0.989 182.456

— —

— —

— —

— —

0.989 181.385

— —

— —

— —

— —

0.336 9.386

27638.907 217.627

27547.964 217.489

27655.212 216.969

27621.035 217.529

0.329 9.118

27721.088 217.668

27620.570 217.538

27759.766 216.939

27706.829 217.557

0.329 9.050

27727.929 217.537

27633.454 217.424

27768.702 216.835

27714.855 217.432

0.327 9.046

27746.692 217.656

27651.603 217.541

27783.828 216.933

27732.915 217.547 (Continued)

36

Y. Shachmurove

Appendix 3: Continued

Model 1 Coefficient T-statistic Model 2 Coefficient T-statistic Model 3 Coefficient T-statistic Model 4 Coefficient T-statistic Model 5 Coefficient T-statistic Model 6 Coefficient T-statistic

Ghana

Guyana

Hungary

Ireland

Jamaica

— —

— —

— —

— —

— —

— —

— —

— —

— —

— —

27635.591 217.627

27739.220 218.116

27913.227 218.248

27784.247 217.724

27649.718 217.707

27717.605 217.669

27825.148 218.161

27995.532 218.305

27856.925 217.756

27735.527 217.741

27725.089 217.539

27828.675 218.023

27974.903 218.109

27900.744 217.706

27744.160 217.617

27743.732 217.658

27847.621 218.149

27990.535 218.236

27911.564 217.804

27761.954 217.733 (Continued)

Appendix 3: Continued

Model 1 Coefficient T-statistic Model 2 Coefficient T-statistic Model 3 Coefficient T-statistic Model 4 Coefficient T-statistic Model 5 Coefficient T-statistic Model 6 Coefficient T-statistic

Kenya

Nepal

Nigeria

Philippines

S. Africa

— —

— —

— —

— —

— —

— —

— —

— —

— —

— —

27631.880 217.595

27634.378 217.598

27618.233 217.458

27659.489 217.712

27742.176 217.983

27715.325 217.631

27717.700 217.636

27707.624 217.475

27749.619 217.743

27834.412 218.012

27722.857 217.503

27724.784 217.506

27715.806 217.353

27754.439 217.609

27839.576 217.885

27741.315 217.621

27743.358 217.624

27733.345 217.465

27772.784 217.727

27856.956 218.003 (Continued)

THE PREMIUM IN BLACK FOREIGN EXCHANGE MARKETS

37

Appendix 3: Continued

Model 1 Coefficient T-statistic Model 2 Coefficient T-statistic Model 3 Coefficient T-statistic Model 4 Coefficient T-statistic Model 5 Coefficient T-statistic Model 6 Coefficient T-statistic

Somalia

Uganda

1985

1986

1987

— —

— —

— —

— —

— —

— —

— —

16.380 0.414

27628.972 17.509

27669.301 216.682

— —

— —

— —

27699.880 217.549

27750.340 216.737

2.093 0.060

217.208 20.506

28.688 0.872

27709.582 217.426

27763.339 216.630

8.497 0.228

214.649 20.410

29.755 0.863

27728.471 217.546

27779.725 216.749

6.575 0.178

215.465 20.433

29.141 0.847

17.029 0.437

8.982 0.228

(Continued)

Appendix 3: Continued

Model 1 Coefficient T-statistic Model 2 Coefficient T-statistic Model 3 Coefficient T-statistic Model 4 Coefficient T-statistic Model 5 Coefficient T-statistic Model 6 Coefficient T-statistic

1988

Jan

Feb

Mar

Apr

— —

— —

— —

— —

— —

— —

— —

— —

— —

— —

— —

— —

— —

— —

22.661 20.082

— —

— —

— —

— —

22.995 20.089

58.202 1.260

36.993 0.856

8.631 0.202

20.309 20.007

23.612 20.107

— —

— —

— —

— —

18.636 0.477

(Continued)

38

Y. Shachmurove

Appendix 3: Continued

Model 1 Coefficient T-statistic Model 2 Coefficient T-statistic Model 3 Coefficient T-statistic Model 4 Coefficient T-statistic Model 5 Coefficient T-statistic Model 6 Coefficient T-statistic

May

Jun

Jul

Aug

Sep

— —

— —

— —

— —

— —

— —

— —

— —

— —

— —

— —

— —

— —

— —

— —

— —

— —

— —

— —

— —

223.164 20.536

5.806 0.136

20.326 20.007

70.540 1.561

10.463 0.233

— —

— —

— —

— —

— — (Continued)

Appendix 3: Continued

Model 1 Coefficient T-statistic Model 2 Coefficient T-statistic Model 3 Coefficient T-statistic Model 4 Coefficient T-statistic Model 5 Coefficient T-statistic Model 6 Coefficient T-statistic

Oct

Nov

J/F

M/A

M/J

— —

— —

— —

— —

— —

— —

— —

— —

— —

— —

— —

— —

— —

— —

— —

— —

— —

— —

— —

— —

211.954 20.263

— —

— —

— —

— —

51.669 1.602

9.792 0.316

22.857 20.092

24.336 0.536 — —

(Continued)

THE PREMIUM IN BLACK FOREIGN EXCHANGE MARKETS

39

Appendix 3: Continued

Model 1 Coefficient T-statistic Model 2 Coefficient T-statistic Model 3 Coefficient T-statistic Model 4 Coefficient T-statistic Model 5 Coefficient T-statistic Model 6 Coefficient T-statistic

J/A

S/O

Obs

RS

ARS

— —

— —

707

0.990

0.990

— —

— —

707

0.990

0.990

— —

— —

707

0.994

0.993

— —

— —

707

0.994

0.993

— —

— —

707

0.994

0.993

40.751 1.264

23.085 0.718

707

0.994

0.993

Note: A represents the dollar value of population-adjusted domestic assets. e represents the official real exchange rate. (i* 1 d 1 i) represents the official depreciation-adjusted interest rate differential. Rho represents the first order difference in the black market premium. Jan represents January, Feb represents February, and so forth through November. J/F represents January and February. M/A represents March and April. M/J represents May and June. J/A represents July and August. S/O represents September and October. RS represents R-squared. ARS represents Adjusted R-squared.