The purchasing power parity and the Russian ruble.

Bahmani-Oskooee, Mohsen ; Barry, Michael

The Purchasing Power Parity theory (PPP hereafter), formulated originally by Gustov Cassel (1916), asserts that exchange rate between two currencies is the ratio of two corresponding national price levels. Alternatively, once converted to the same currency, price levels between two countries should be equal. Authors have investigated the empirical validity of the PPP using different econometric methods and using data from developed as well as developing countries. The results are at best mixed. For example, using standard 2SLS and GLS while Frenkel (1981) showed that PPP failed to hold during 1970's, Davutyan and Pippinger (1985) concluded that indeed it held not only during 1920's, but also during 1970's. Even those who used most recent developments in econometric literature, have provided mixed results. For example, after introduction of unit root tests and cointegration analysis, most recent studies have adopted them in testing the PPP. Those who employed OLS based cointegration technique of Engle and Granger (1987) mostly reject the PPP. Examples include Taylor (1988), McNown and Wallace (1989), Karfakis and Moschos (1989), Layton and Stark (1990), Bahmani-Oskooee and Rhee (1992) and Bahmani-Oskooee (1993). However, those Like Mahdavi and Zhou (1994) who employ the Maximum-Likelihood based cointegration method of Johansen (1988), support the PPP. Fractional cointegration technique has been used by Diebold et. al. (1991) in support of the PAP.(1)

When PPP receives empirical support, it implies that there is a long-run and one to one relation between exchange rate and relative prices. It also identifies domestic inflation as a main source of depreciation of domestic currency, especially in high inflation countries. The transition of Eastern Europe and former Soviet Union from command to market economies has resulted in high rate of inflation and currency depreciation in many of these countries. Such transition has produced new set of data which could provide useful information in testing any theory in general and the PPP in particular.

Before the break up of the Soviet Union, the official currency of the Union, the ruble was subject to multiple exchange rate practices by the Union against the U.S. dollar. The exchange rates differed depending on the type of international transactions and type of the individuals. For example, in December 20, 1975 the Oligarchy-Kupon Ruble rate that stood at 4.60 rubles per dollar was only available to those who were considered elite or foreign diplomats. For Soviets travelling abroad, the rate was 6.28.(2) After the break up when the Commonwealth of Independent States was formed, all multiple rates were dropped in favor of an official rate for the Russian Ruble to be determined by auctions run by the Moscow Interbank Foreign Currency Exchange (MICEX). The central bank acted as an open market seller of the dollars to stabilize the exchange rate. The rate that stood at about 50 rubles per dollar in mid-1991, stood at about 4500 rubles per dollar in mid-1995.(3) The monthly data from March 1991 till May 1995 on the ruble/dollar exchange rate as well as the monthly price indexes in the U.S. and the Russia motivated us to test the PPP between the two old enemies, but new friends.

Section I outlines the formulation of PPP. Section II very briefly explains the cointegration technique and reports our empirical results. Section III concludes.

1. The PPP Formulation

In its simplest form, the absolute PPP theory states that the exchange rate between two currencies is nothing but the ratio of two corresponding price ratios. Let P denote the price level in Russia, [P.sub.U.S.], the price level in the United States, and EX the exchange rate (defined as number of rubles per dollar). The PPP theory could then be outlined as:

(1) [EX.sub.t] = [([P.sub.r]/[P.sub.u.s.]).sub.t]

or alternatively as

(2) [P.sub.rt] = [EX.sub.t] [multiplied by] [P.sub.u.s.t.]

While equation (1) is referred to as the PPP, equation (2) is referred to as the "Law of One Price". Thus, the PPP could be tested by making either equation subject to empirical test. To this end, we write both models in Log linear form as:

(3) Ln [Ex.sub.t] = a + b Ln [([P.sub.r]/[P.sub.u.s.]).sub.t] + [[Epsilon].sub.t]

and

(4) Ln [P.sub.rt] = c + d Ln ([Ex.sub.t] [multiplied by] [P.sub.u.s.t]) + [[micro].sub.t]

The test of the PPP amounts to establishing not only a long run equilibrium relation between the dependent and independent variables(1) in either model, but also verifying that the estimates of the slope coefficients are close to unity.

II. The Methodology

As indicated before, in testing the PPP, early studies employed old econometric methods such as OLS or 2SLS to estimate the PPP model. However, the existing evidence now suggests that like many other macro variables, the exchange rate data and national price levels data do contain unit roots or they are all non-stationary variables. The implication is that the standard t statistic can no longer be used to infer significance of estimated coefficients using non-stationary data. The cointegration technique tries to over come this issue. It basically concentrates on analyzing whether a linear combination of non-stationary variables is stationary. As a proxy for a linear combination among variables of a reduced form model, residuals are tested for their stationarity. In the OLS based cointegration approach introduced by Engle and Granger (1987) we first need to determine the degree of integration of each variable in a specific model (say equation 3 or 4). If two variables such as those in equation (3) or (4) are each integrated of order d, they would be cointegrated if in a simple OLS regression of one on the other, the residuals (as a proxy for a linear combination) are integrated at an order less than d. If however, we believe that feedback effects exist between exchange rate and relative prices, then we can employ Johansen's (1988) cointegration method which is based on maximum-likelihood estimation procedure. Johansen (1988) defines a distributed lag model of a vector of variables, X as

(5) [X.sub.t] = [[Pi].sub.1] [X.sub.t-1] + [[Pi].sub.2] [X.sub.t-2] + ...... + [[Pi].sub.k] [X.sub.t-k] + [[Epsilon].sub.t]

where X is a vector of N stationary variables. In case variables in X are non-stationary and achieve stationarity after being differenced once, equation (5) is rewritten in first difference form in a fashion similar to the Augmented Dickey Fuller (ADF) test as below:

(6) [Delta][X.sub.t] = [[Gamma].sub.1] [Delta][X.sub.t-1] + [[Gamma].sub.2] [Delta][X.sub.t-2] + ... + [[Gamma].sub.k-1] [Delta][X.sub.t-k+1] - [Pi][X.sub.t-k] + [[Epsilon].sub.t]

where

[[Gamma].sub.i] = - I + [[Pi].sub.1] + [[Pi].sub.2] + ... + [[Pi].sub.i] (i = 1, ...,k)

and

[Pi] = -(I - [[Pi].sub.1] - [[Pi].sub.2] - ... - [[Pi].sub.k]).

The long-run or cointegrating matrix is given by [Pi] which is an NxN matrix and includes number of r cointegrating vectors which is the rank of a. If we define two matrices [Alpha] and [Beta] (both Nxr) such that [Pi] = [Alpha][Beta'], the rows of [Beta] will form the r cointegrating vectors. Johansen and Juselius prove that one can test the hypothesis that there are at most r cointegrating vectors by calculating the two likelihood test statistics known as the trace and the [Lambda]-max tests.(4)

III. The Empirical Results

In this section we try to apply the two methods between the two variables of both equations (3) and (4). All data are monthly over May 1991-March 1995 period. While the Russian data come from the Russian Economic Trends (Different Issues), the U.S. data come from the International Financial Statistics.(5) To get some insight into the relation between [Ex.sub.t] and [([P.sub.r]/[P.sub.u.s.).sub.t] as well as between [P.sub.rt] and [Ex.sub.t] [multiplied by] [P.sub.u.s.t.] we plot them against each other in Figures 1 and 2.

[Figure 1-2 ILLUSTRATION OMITTED]

As can be seen, the two variables in either figure track each other very closely providing a graphical support for the PPP. However, to discover whether these relations are spurious or not, we apply the cointegration analysis. As indicated before, the first step is to determine the degree of integration of each variable. To this end, following many studies in the literature we rely upon the ADF test which includes a trend term.(6) The results of the ADF test applied to the level as well as to the first differenced variables are reported in Table 1.

TABLE 1 The Calculated ADF Test Statistics For All Four Variables And their First Differences

Variable ADF Statistics # of Lags in
 the ADF Test

Ln EX -2.30 1
Ln ([P.sub.r]/[P.sub.u.s.]) -1.29 1
Ln [P.sub.r] -1.30 1
Ln EX.[P.sub.u.s.] -2.29 1

[Delta] Ln EX -4.67 1
[Delta] Ln ([P.sub.r]/[P.sub.u.s.]) -3.99 1
[Delta] Ln [P.sub.r] -3.98 1
[Delta] Ln EX.[P.sub.u.s.] -4.67 1

Notes: The Mackinnon (1991) critical value of the ADF statistic for 52 observations (when a trend term is included in the test) is -3.49 at the 5% level of significance and -3.17 at the 10% level of significance.

It is obvious from Table 1 that the calculated ADF statistics are less than the critical value only in the case of first differenced variables indicating that all four variables achieve stationarity after being differenced once. Therefore, all four variables are integrated of order one or I(1). What remains to be shown is that if the pair of variables in either equation, i.e., equations (3) and (4) are to be cointegrated, the residuals must be on a stationary process. These results are reported in Table 2.

TABLE 2

The calculated ADF test statistics for the residuals of cointegration equation and other statistics

 Cointegration
 Equation ADF [#lags] Slope [R.sup.2]

Ln EX=f[Ln[P.sub.r]/[P.sub.u.s.]] -4.04 [4] 0.27 0.97
Ln [P.sub.r]/[P.sub.u.s.] = Ln EX -2.83 [1] 0.79 0.97
Ln [P.sub.r] = Ln EX.[P.sub.u.s.] -4.04 [4] 0.27 0.97
Ln EX.[P.sub.u.s.] = Ln [P.sub.r] -2.83 [1] 0.79 0.97

Notes: The critical value of the ADF statistic from the Mackinnon (1991) table where a trend term is included in cointegration equation are -3.96 at the 5% level and -3.6 at the 10% level of significance.

From Table 2 we gather that the ADF statistic for the residuals of the first and third cointegration equations are less than the critical values (reported at the bottom of Table 2) rejecting the null of no cointegration. However, the slope coefficient in both cases are less than unity, indicating some imperfections in the PPP based on simple OLS estimation technique. What does Johansen's ML procedure yield?

In applying the Johansen's cointegration technique one has to decide about the order of lags in the VAR outlined by equation (6). Since the data are monthly, we employ the largest possible number of lags that the statistical package allows, i.e., eight. However, we tested the sensitivity of the results to the choice of lag orders with no significant changes in the results. The results of the trace and the [Lambda]-max tests with eight lags in the VAR are reported in Panel A of Table 3 and the estimate of cointegrating vector in Panel B of Table 3. Note that in reporting the estimates of cointegrating vectors it is a common practice to normalize the estimates by setting one of the coefficients at -1. We normalize one of the vectors on Ln EX and the other one on Ln [P.sub.r]

[TABULAR DATA NOT REPRODUCIBLE IN ASCII]

As can be seen, both models yield almost the same statistics, as was the case with the Engle-Granger OLS based cointegration technique. It is evidenced that the null of no cointegration, i.e., r = 0 is rejected by both the [Lambda]-max and the trace statistics due to the fact that both statistics are larger than their critical values. Thus, there must be at least one cointegrating vector in each case. However, the null of at most one vector cannot be rejected in favor of r = 2 since both statistics are less than their critical values. Thus, there is at most one cointegrating vector in each case. The estimates of these vectors are reported in Panel B. It is evident that in both cases the slope coefficient is very close to unity supporting the PPP. Therefore, we may conclude that the Johansen's ML procedure that incorporates the feedback effects between EX and [P.sub.r]/[P.sub.U.S.] or between Pr and EX.[PU.sub.U.S.] yields empirical results that are more supportive of the PPP than the OLS based cointegration method of Engle and Granger where the slope coefficient was much less than unity.

IV. SUMMARY AND CONCLUSION

Studies that have tested the empirical validity of the purchasing power parity theory (PPP), have employed readily available data from market economies of developed or developing countries. The transition of East European economies from command to market system as well as the break-up of the old Soviet Union into independent and free market states has been producing a new set of data that could shed new lights on some old economic theories. The PPP is no exception in this regard.

In this paper we attempted to test the PPP between the Russian ruble and the U.S. dollar. By using monthly data over March 1991 March 1995 period and OLS based as well as ML based cointegration methods we were able to show that there exists a long-run equilibrium relation between the exchange rate and relative prices. However, it was only the ML based technique of Johansen that yielded a slope coefficient that was very close to unity providing relatively strong support for the PPP between the Russian ruble and the U.S. dollar.

TABLE 4 Monthly Data on Exchange Rate (EX, number of rubles per dollar), Russian Consumer Price Index (RCPI) and the United States Consumer Price Index (USCPI) over March 1991-May 1995 Period.

Date EX RCPI USCPI

1991.3 50.00000 118.00000 125.50000
1991.4 55.00000 194.00000 125.70000
1991.5 50.00000 199.00000 126.00000
1991.6 50.00000 202.00000 126.40000
1991.7 47.00000 203.00000 126.60000
1991.8 60.00000 204.00000 127.00000
1991.9 75.00000 206.00000 127.50000
1991.10 89.00000 213.00000 127.70000
1991.11 110.00000 232.00000 128.10001
1991.12 150.00000 261.00000 128.20000
1992.1 230.00000 899.00000 128.30000
1992.2 160.00000 1243.00000 128.80000
1992.3 150.00000 1613.00000 129.50000
1992.4 155.00000 1962.00000 129.60001
1992.5 145.00000 2197.00000 129.80000
1992.6 148.00000 2606.00000 130.30000
1992.7 170.00000 2893.00000 130.60001
1992.8 220.00000 3153.00000 130.89999
1992.9 320.00000 3531.00000 131.30000
1992.10 400.00000 4344.00000 131.80000
1992.11 450.00000 5473.00000 132.00000
1992.12 450.00000 6841.00000 131.89999
1993.1 600.00000 8606.00000 132.50000
1993.2 750.00000 0732.00000 133.00000
1993.3 780.00000 12889.00000 133.50000
1993.4 900.00000 15338.00000 133.80000
1993.5 1100.00000 18099.00000 134.00000
1993.6 1150.00000 21700.00000 134.20000
1993.7 1100.00000 26474.00000 134.20000
1993.8 1000.00000 33358.00000 134.60001
1993.9 1200.00000 41030.00000 134.89999
1993.10 1210.00000 49236.00000 135.39999
1993.11 1285.00000 57114.00000 135.50000
1993.12 1290.00000 64539.00000 135.50000
1994.1 1542.00000 76091.00000 135.89999
1994.2 1657.00000 84233.00000 136.30000
1994.3 1753.00000 90466.00000 136.80000
1994.4 1820.00000 98427.00000 136.92000
1994.5 1916.00000 105694.00000 137.03999
1994.6 1985.00000 112036.00000 137.53000
1994.7 2052.00000 117974.00000 137.89000
1994.8 2153.00000 123400.00000 138.37000
1994.9 2596.00000 133272.00000 138.74001
1994.10 3085.00000 153263.00000 138.86000
1994.11 3232.00000 176252.00000 139.10001
1994.12 3410.00000 205158.00000 139.10001
1995.1 4048.00000 242086.00000 139.59000
1995.2 4499.00000 268715.00000 140.20000
1995.3 4899.00000 292631.00000 140.67999
1995.4 5130.00000 317505.00000 141.17000
1995.5 4990.00000 342588.00000 141.41000

Sources: Data on EX and RCPI come from-different issues of Russian Economic Trends. Data on USCPI is from different issues of the International Financial Statistics of IMF.

Notes

(1.) For the most recent review article see Rogoff (1996).

(2.) For these and some other rates see World Currency Yearbook (1995), Russian section.

(3.) The policy is to maintain the exchange rate within a corridor of 4300-4900 rubles per dollar

(4.) Fortunately, all calculations are built into computer packages like MFIT3.0 by Pesaran and Pesaran (1991) that are employed in this paper.

(5.) All data are reported in Table 4.

(6.) For how to formulate and apply the ADF test see Bahmani-Oskooee (1993).

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