cointegration analysis of the black market and official exchange rates in india

HAMID BAGHESTANI The Economics Institute and University of Colorado

Boulder, Colorado

JOHN NOER The Center for Naval Analyses

Alexandria, Virginia

Cointegration Analysis of the Black Market and Official Exchange Rates in India*

The examination of stochastic properties of the black market and official exchange rates in India reveals that the series are cointegrated and, therefore, possess a long- run equilibrium relation. The black rate is found to be more sensitive to shocks, and at the same time, adjusts more quickly to departures from the long-run equilibrium relation. This is expected, since the policy-determined official rate was set by what seems to be a sluggish and/or arbitrary mechanism, and that the black had to largely respond and adjust to the exogenous shocks in order to maintain the long-run equilibrium relation.

1. Introduction India pursues policy-inhibiting international trade and foreign

exchange trading. Licenses are required for imports and for pur- chasing foreign exchange. Simultaneously, there exist illegal, liquid, readily accessible black foreign exchange markets. In the early 1970s, India effected a de facto devaluation by maintaining a relationship with the U.S. dollar when the dollar fell and floated after the de- mise of the Bretton Woods system of world-wide fixed exchange rates. Specifically, a crawling peg exchange rate has been adopted since 1973, by setting the official exchange rate (rupee per U.S. dollar) with reference to a basket of convertible floating currencies with unrevealed weights, fluctuating within a 5% band. With the foreign exchange and import licensing requirements relaxed some- what (Noer 1988), the dollar has been traded at a variable premium on the black foreign exchange market over the fluctuating official rate, with an average differential of 17% (see Figure 1).

One may hypothesize that India's official exchange rate may

*We would like to thank William Kaempfer, Robert McNown, and two anon- ymous referees of this journal for very helpful comments.

Journal of Macroeconomics, Fall 1993, Vol. 15, No. 4, pp. 709-721 Copyright © 1993 by Louisiana State University Press 0164-0704/93/$1.50

709

Hamid Baghestani and John Noer

22.5

20.5 ~ ; , ;

17.5 -- j~,/~t 15.0

#~ O#S%~S~ B tS S

12.5 | t !

1 0 . 0 . , , , . . . . - , , , , S t i I I • t I

"D" G I I ~ . 6 e

7 .5

5.0 l l l l l l i l l l=l l l I l i l l l=l i l l l i l l l i l lJl l l l l l i l l l i l i l i l l l=Jil i lJl i l l l lJl l 7 3 7 4 75 7 6 7 7 7 8 7 9 8 0 8 1 8 2 8 3 8 4 85 86 87 8 8 8 9 9 0

Figure la. Rupees per U.S. dollar: 1973:i-1990:ii

Official Rate (solid line): Mean = 10.717, Standard deviation = 2.798 Black Market rate (dotted line): Mean = 12.576, Standard deviation = 3.310

have had either an exogenous or endogenous dynamic relationship to the black rate, depending upon policy. The lack of an announced policy commitment combined with secret weights leaves open the possibility of discretionary policy reacting to excess demand, which could "endogenize" the official rate with respect to the black. Un- announced changes in the weights, or devaluations against the en- tire basket, are ways th.at the official rate might respond to the black rate. Alternately, if an arbitrary basket of foreign currencies is blindly adhered to, the result may be a pseudo-random non-market-clearing official rate either acting independently upon black markets, or unrelated to them.

'The purpose of this paper is to evaluate the dynamic relationship between the black market and official exchange rates using quarterly data for 1973:i-1990:ii. Section 2 will describe the market conditions in India and the data used in this study. Based on the evidence that the black market and official exchange rates are cointegrated, Section 3 will use the error correction model (ECM) estimates of the series to provide information on the relative respon-

710

40

30

25

17

10

0

Cointegration Analysis

i Illl l lJlll l l l l l l l l l l l lJlll l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l

7 3 7 4 7 5 7 6 7 7 7 8 7 9 8 0 8 1 8283 8 4 8 5 8 6 8 7 8 8 8 9 9 0

TIME Figure lb.

The spread as a percentage of the official exchange rate.

siveness of the black and official exchange rates to departures from the long-run equilibrium relation. Section 4 will interpret the em- pirical results and conclude the paper.

2. Market Conditions in India and the Data Two elements of fiscal policy drive a wedge between the pol-

icy-determined official exchange rate and the unregulated "'black" market exchange rate. One is taxes, and the other is license requirements. Generally, private Indian citizens wishing to buy foreign currency from the central bank for foreign travel have to pay a "foreign exchange conservation tax" of (typically) 15%, and have been subject to a quota enforced by licensing. Some certain com- mercial purchasers, however, were not subjected to the tax. The rationing of foreign currency by official limitations and delays in issuing licenses, at times, have been the binding constraint, re- suiting in a large black market premium. Other determinants of the

711


spread may be risk premia due to law enforcement activity, and uncertainty about the continuity of official policy. Foreign tourists, Indians unofficially repatriating overseas earnings, illegal exports, and under-invoicing of legal exports have been major sources of foreign exchange supply to the black market.

Contracts within the black market are not enforceable in the courts. Most black market transactions are spot physical transactions, or between parties well known to each other. Forward (fu- ture) markets are restricted on the official market, and license requirements prevent free entry into the official market. Therefore, there does not seem to be much reason to suppose that the black market for foreign exchange is less efficient than the official market, or less readily accessible, or even much riskier. Occasional localized "crackdowns" are often well anticipated, episodic in nature, and have temporary and minimal effect. The current prevailing spot black rate is well known throughout the marketplace, and is even published in the press. It is generally thought that typically more transactions occurred on the black market than on the official market during most of our study period.

In this study, the data on the official exchange rate (rupees per U.S. dollar) are obtained from various issues of International Financial Statistics. The data on the black market exchange rate, however, are obtained from Cowitt's Currency Yearbook and its predecessor, Pick's Currency Yearbook, an authoritative source of black rates and black market conditions for nearly all countries worldwide since the Second World War. The black data used here is for Bombay, historically and currently the center of India's un- official and official financial markets. While the black market premium varies from city to city in India due to transaction costs and the spot nature of the markets, Bombay is the reference market, with a high degree of liquidity and many dealers. The Bombay black market has operated without interruption since independence in 1947. As monetary policy and the rate of monetary creation by the Re- serve Bank of India is relatively stable, the floating black rate is relatively well-behaved compared to many other currencies of de- vel0ping countries (see Figure 1).

3. Testing for Unit Roots and Cointegration A time series, Xt, is said to be integrated of order d (Xt

I(d)) if it is a stationary series after differencing d times (Granger 1986). To establish the order of integration of the series, the test

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TABLE 1. Unit Root Test Results: 1973:i-1990:ii

Variable (X) ADF

B -1 .10 F - 0 . 2 7

AB -6.20*** AF -3.07**

NOTES: B and F are, respectively, the Indian black market and official rates in rupees per dollar. Numbers reported are the value of the calculated t-ratio on "b" in Equation (1) compared with the critical t-values from MacKinnon (1991).

*significant at the 10% level; **significant at the 5% level; ***significant at the 1% level.

provided by Dickey and Fuller (1981) is employed. The augmented Dickey-Fuller (ADF) equation,

m

Xt - X t - l = ao + alt + bXt-1 + E cj (Xt-j - Xt-j-1) q- et , (1) j=l

tests the null hypothesis of a unit root. The alternative hypothesis is that the series is an autoregressive order of m + 1, with m cho- sen to ensure that et is white noise. This test relies on rejecting the null hypothesis of a unit root (H0: b = 0) in favor of stationarity, which requires a negative and significant computed (non-normally distributed) t-ratio for b, using critical values from MacKinnon (1991). As a precondit ion for cointegration between the black market exchange rate (Bt) and the ottlcial exchange rate (Ft), the individual series are tested for a common order of integration. Based on the ADF test in Equat ion (1), Table 1 presents evidence that each series is integrated of order one for 1973:i-1990:ii. That is, the null hypothesis of a unit root is accepted for both B t and Ft , and is rejected in favor of stationarity for both A B t and A F t. In testing for a unit root in the first differences, the time t rend is excluded from the A D F test equations. All the A D F test equations include two lags or augmented terms (m = 2), with the adequacy of the lag length checked for serial correlation using the Lagrange multiplier ×2-statistics.

A set of nonstat ionary t ime series are cointegrated ff there exists a linear combination of them that is itself stationary. For ex- ample, let

Bt = a + f~ Ft + u t , (2)

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H a m i d B a g h e s t a n i a n d J o h n N o e r

T A B L E 2. C o i n t e g r a t i o n T e s t Resu l t s : 1 9 7 3 : i - 1 9 9 0 : i i

D e p . Vat . C O N S T . B F R 2 D W A D F

B 0 .192 - - 1 .154 0 .944 1.40 - 5 . 5 7 9 * * * F 0 .426 0 .818 - - 0 .944 1.33 - 5 . 3 3 1 " * *

NOTES: DW is the cointegrating regression Durbin-Watson statistic. The reported Augmented Dickey-Fuller (ADF) statistics on the residual series of the re- spective cointegrating regressions are compared with the critical values from MacKinnon (1991).

t h e n Bt a n d Ft are d e f i n e d to b e c o i n t e g r a t e d , if ut is s t a t i o n a r y , ut I(0). I n t h e s a m e m a n n e r , for t h e two se r i e s to b e c o i n t e g r a t e d ,

vt, t h e e r r o r t e r m f rom t h e r e v e r s e c o i n t e g r a t i n g e q u a t i o n , s h o u l d b e s t a t i ona ry . T a b l e 2 r e p o r t s t h e o r d i n a r y l eas t s q u a r e s (OLS) r e g r e s s i o n e s t i m a t e s o f b o t h n o r m a l i z a t i o n s a n d t h e A D F t e s t sta- t i s t ics on t h e r e s p e c t i v e r e s i d u a l se r i e s . T h e r e s i d u a l s e r i e s f rom each n o r m a l i z a t i o n a p p e a r to b e s t a t i o n a r y , w i t h t h e A D F t e s t sta- t i s t ics c o m p a r e d to M a c K i n n o n ' s (1991) c r i t i ca l va lue s . T h e A D F t e s t e q u a t i o n s for c o i n t e g r a t i o n e x c l u d e b o t h t h e i n t e r c e p t a n d a t i m e t r e n d , s ince such d e t e r m i n i s t i c c o m p o n e n t s fail to b e s ta t i s - t i ca l ly s ign i f ican t . T h e s e t e s t e q u a t i o n s , h o w e v e r , i n c l u d e o n e lag o r a u g m e n t e d t e r m , w i t h t h e a d e q u a c y o f t h e lag l e n g t h c h e c k e d for se r ia l c o r r e l a t i o n u s i n g t h e L a g r a n g e m u l t i p l i e r ×2-stat is t ics . Ac- c o r d i n g l y , Bt a n d Ft a r e c o i n t e g r a t e d , i m p l y i n g t ha t t h e s e r i e s pos - sess an e q u i l i b r i u m r e l a t i o n in t h e fo rm of B = 0 .192 + 1 . 1 5 4 F to w h i c h t h e y c o n v e r g e in t h e l o n g - r u n . l

~As an additional check on the robustness of the unit root results, we also apply the test provided by Phillips (1987), Phillips and Perron (1988), and Perron (1988). This test is based on a nonparametric correction to account for serially correlated and heterogeneously distributed innovations in the series. Based on the following equation,

X, = Ix + ~ (t - T/2) + (xX,_t + "q, ,

which tests the null hypothesis of a unit root (Ho: 6t = 1); the calculated test statistics are -0.56 and -0.70 for Bt and Ft, respectively. Again, we fail to reject the null hypothesis of a unit root for both Bt and Ff. The truncation lag parameter is set to five. Our conclusion is not sensitive to other values assigned for the truncation lag parameter. The Phillips-Perron approach is also used to test for cointegration by checking the stationarity of the residual series from the cointegrating regressions in Table 2. With the intercept and time trend excluded from the test equations, the calculated test statistics are found to be -5.06 and -4.93 for ut and vt, respectively, indicating that Bt and Ft are eointegrated.

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Cointegrat ion Analys is

Following the Granger representation theorem (Engle and Granger 1987), for the cointegrated series Bt and Ft, there exists an ECM of the form

ABt = ~n + Z ~/1, ABt_, + Z ~12j AFt-i -- kl u,_, + el , , i j

el, ~ IN(0, (r~,), (3)

AFt = 5zz + Z ~/3, AF,_, + Z ~lAj AB,_j - hzv,-i + e2,, i j

e2, ~ IN(0, (r,~), (4)

where i begins at one, and j begins at zero in order for the series to be related within a s t ruc tura l ECM (Engle and Yoo 1991). The ECM embodies both the short-run dynamics and the long-run equilibrium relation of the series. When the system is at rest, all differences vanish, and the long-run equilibrium relation holds. In other words, Equation (3) specifies the short-run convergence process of B t to the equilibrium relation with convergence being assured when h~ is between zero and one. Similarly, Equation (4) specifies the short-run convergence process of F t to the equilibrium relation with convergence being assured when h2 is between zero and one.

The ECM, which initially includes five lag differences for both Bt and Ft, is estimated using OLS. Excluding the insignificant lag differences, the ECM is then reestimated, with the results reported in columns 1 and 2 of Table 3. The corresponding two stage least squares (TSLS) estimates, ~ which purge the simultaneous-equation bias, are reported in columns 3 and 4. These estimates, which are very similar to the OLS estimates, pass a series of diagnostic tests, including serial correlation (based on the inspection of the autocor- relation functions of the residuals as well as the reported insignificant Lagrange multiplier ×%statistics at the 10% or lower level) and

2The instrumental variables used consist of the predetermined variables included in the model in addition to the rank of AFt for the black rate equation and the rank of ABt for the official rate equation. The use of rank variables as instrumental variables was suggested by Durbin (1954) in dealing with measuring errors in ex- planatory variables. Their use here is to increase the efficiency of the TSLS estimates (Baghestani 1991).

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H a m i d Baghes tan i a n d J o h n N o e r

omit ted variables such as a t ime t rend and o ther lags. In addition, based on the cusum of squares test of stability deve loped by Brown, Durbin, and Evans (1975), the TSLS estimates of the E C M are stable in terms of parameters over the estimation period at the 10% or lower level of significance. 3 This p roper ty fails to hold when using monthly instead of quarter ly data. Specifically, our results (not repor ted here) suggest that the month ly time series of the black and oflqcial rates are still cointegrated, but they do not provide an ECM that is stable in terms of parameters . This, in addition to Hakkio and Rush's (1991, 571) argument that cointegration is a long- run concept and hence requires long spans of data, may justify the use of quarter ly rather than monthly data in our study.

Since the short-run dynamics of the series within the E C M is contemporaneously specified, a positive exogenous shock in Bt raises Ft, which in turn produces fur ther rises in both B t and Ft within the immediate period. Using the TSLS parameter estimates on AFt (= 1.544) and on ABt (= 0.156) repor ted in columns 3 and 4 of Table 3, our calculations indicate that a 1-unit (defined as one rupee per U.S. dollar) positive exogenous shock in Bt produces a further increase of 0.317 units in Bt, result ing in a total increase of 0.205 units in Ft within the immedia te quarter. Similarly, a 1-unit positive exogenous shock in Ft results in a fur ther increase of 0.317 units in F t simultaneously with an increase of 2.034 units in B, within the immedia te quarter.

3The cusum of squares test of stability is based on a standardized one-step-ahead prediction of errors, w, from recursive regressions and is designed to test the null hypothesis that the regression parameters vector of the recursive regressions are identical. The cusum of squares test statistic is

r T

r = k + l . . . . . T,

where k is the number of regression parameters, and T is the number of obser- vations of the last estimation period (1974:iii-1990:ii). The expected value of Sr under the null hypothesis of parameter stability is (r - k)/(T - k). One accepts this null hypothesis if the absolute deviation of Sr (for all r) from its expected value falls below the critical values given in Durbin (1969). The maximum absolute deviation of Sr from its expected value for the TSLS estimates of the black rate equation is 0.1615, which is below the 10% critical value (= 0.1753, for T = 64 and k = 6). This value for the TSLS estimates of the official rate equation is 0.1213, which is, again, below the 10% critical value (= 0.1741, for T = 64 and k = 5). These findings indicate that the ECM model is stable in terms of parameters at the 10% or lower level of significance.

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Furthermore, based on the TSLS estimates of the ECM in Table 3, in the short-run the change in the black rate adjusts to departures from the equilibrium relation (measured by ut = Bt

- 0.192 - 1.154Ft from Table 2) with a parameter estimate of 0.688. This indicates that 68.8% of the adjustment towards the equilibrium relation occurs within a quarter through changes in the black. Sim- ilarly, in the short run the change in the official rate adjusts to departures from the equilibrium relation (measured by vt = Ft

- 0.426 - 0.818Bt from Table 2) with a parameter estimate of 0.201. This indicates that 20.1% of the adjustment towards the equilibrium relation occurs within a quarter through changes in the official rate.

4. I n t e r p r e t a t i o n s and C o n c l u d i n g R e m a r k s The interpretation of our results is as follows: The Indian black

and official exchange rates are found to be cointegrated and, therefore, possess a long-run equilibrium relation. This is consistent with Booth and Mustafa (1991), who also have found cointegration between the Turkish black and official exchange rates for both Ger- man marks and U.S. dollars.

As implied by the first cointegrating regression estimates reported in row 1 of Table 2, in the long-run the black rate is ap- proximately 15.4% above the official rate. 4 Since, for most of the study period, authorized individuals wishing to purchase foreign exchange in the official market were required to pay a 15% foreign exchange conservation tax, this finding implies that in the long-run the black rate was quite close to the tax adjusted official "effective" rate, a selling rate for dollars. Policy measures such as taxes, quotas and licenses imposed by the Reserve Bank of India, therefore, were simply "'tax equivalents of quotas," which have driven a tax-like wedge between the black and official rates. The exchange rate regime which creates a disparity between the two rates is simply a tax-like distortion imposed on one bifurcated market. Unlike our results, Booth and Mustafa's findings indicate that in the long run such a disparity does not exist between the Turkish black and official rates due to

~Using the TSLS estimates of an unrestricted ECM (which replaces the error correction term with Bt-~ and Ft-0 and the TSLS estimates of an alternative ECM which instead embodies the spread between the black and official rates as the error correction term, we have tested the null hypothesis that ~3 in Equation (2) is unity. This hypothesis is rejected, indicating that there is a disparity between the two

rates in the long run.

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TABLE 3. ECMs of the Black Market and Official Exchange Rates: 1973:i-1990:ii

OLS TSLS

Dep. Var.: AB AF AB AF

CONST. -0.001 (0.01) 0.049 (i.28) 0.009 (0.0S) 0.048 (1.26) AB 0.154 (4.14) 0.156 (3.91) aB(- i ) an(-2) aB(-3) 0.160 (1.56) 0.158 (1.55) aB(-4) aB(-5) 0.224 (2.02) 0.220 (1.98) AF 1.633 (4.90) 1.544 (4.40) AF(-1) -0.754 (2.21) 0.298 (2.82)-0.728 (2.13) 0.299 (2.83) aF(-2) AF(-3) 0.206 (2.00) 0.206 (1.99) AF(-4) aF(-5) u(-1) -0.096 (5.05) -0.688 (5.56) v(-1) -0.199 (3.70) -0.201 (3.67) or 0.755236 0.255437 0.755702 0.255443 X~ 5.38 4.60 7.94 7.19

NOTES: The error correction terms u and v are, respectively, the residuals from the cointegrating regressions in rows 1 and 2 of Table 2. Absolute values of t-ratios are given in parentheses. ~r is the standard error of regression. ×~ is the Lagrange multiplier ehi-squared statistic, which detects serial correlation up to eight lags (Johnston 1984, 319-21).

perhaps the absence of taxes or a more liberal approach pursued by the government of Turkey.

Based on the TSLS estimates of the ECM in Table 3, within the immediate quarter, the black rate responds strongly to an exogenous shock in the official rate, while the responsiveness of the official rate to an exogenous shock in the black rate is relatively sluggish. In addition, in the short run the response of the black rate to departures from the long-run equilibrium relation is more than three and a half times larger than the response of the official rate. The black rate does provide some feedback to the official rate. For the most part, however, the official acts on the black, and the black bears most of the burden of short-run adjustment to eliminate deviations from the long-run equilibrium relation. Such findings are

718


expected, since the official rate was set by pegging against a perhaps arbitrary basket of convertible currencies, a system which omits important economic information. More generally, both the official rate and the measures generating the distortion were set by what seems to be a sluggish and/or arbitrary mechanism. Quite natu- rally, therefore, it was the black rate that had to largely respond and adjust to the policy shocks as well as the shocks in the demand for and the supply of the foreign exchange to maintain the equilibrium relationship, with the fluctuations in the spread re- flecting the market-clearing process. These results are in line with Booth and Mustafa, who showed that the Turkish black rate had a far larger volatility than the policy-determined official rate. s In general, if the official rate were set by a highly responsive market- clearing mechanism such as an open auction, the official rate would adjust immediately and fully, generating a different out- come.

In conclusion, our findings may suggest that a crawling peg monetary regime using a floating basket is not much different a procedure from, say, a fixed peg against a single currency, if that peg cannot he maintained without a black market springing up; that is, a crawling peg monetary regime can behave more like a fixed rate than a floating rate, even if it tends to move around.

Furthermore, our findings for India reject the view that the official rate is irrelevant, merely a government bookkeeping con- vention, and unrelated to the black market which might be as- sumed to be the market-clearing rate. In the case of India, we also reject the alternative view that the black market is simply an insignificant peripheral market for illegal transactions, operating in the shadow of the official market.

Received: December 1991 Final version: December 1992

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Relationship." Journal o f Industr ial Economics 39 (1991): 671- 82.

SThe structural ECM parameter estimates presented in Table 3 should not be compared with the reduced form ECM parameter estimates in Booth and Mustafa (1991). However, one should note that the structural ECM parameter estimates, unlike the reduced-form ECM parameter estimates, are directly interpretable.

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Booth, Geoffrey G., and Chowdhury Mustafa. "Long-term Dynam- ics of Black and Official Exchange Rates." Journal of Interna- tional Money and Finance 10 (1991): 392-405.

Brown, R. L., J. Durbin, and J. M. Evans• "Techniques for Testing the Constancy of Regression Relationship over Time." Journal of the Royal Statistical Society 37, Series B (1975): 149-92.

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• "Tests for Serial Correlation in Regression Analysis Based on the Peridogram of Least Squares Relationship." Biometrika 56 (1969): 1-15.

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MacKinnon, James G. "Critical Values for Cointegration Tests." In Long-run Economic Relationships, edited by Robert F. Engle and Clive W. J. Granger, 267-76. Oxford: Oxford University Press, 1991.

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Phillips, Peter C. B. "Time Series Regression with a Unit Root." Econometrica 55 (1987): 277-301.

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cointegration analysis of the black market and official exchange rates in india

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