# Real exchange rates, PPP and the relative price of nontraded goods.

I. Introduction

The purchasing power parity hypothesis (PPP) states that nominal exchange rates move with differences in relative prices between economies. The theory has received considerable attention in the economic literature since Cassell [6], and is the foundation of many long-run theoretical hypotheses in international finance; yet, its empirical validity remains in question. Many tests of PPP focus on the stationarity of the real exchange rate, the nominal exchange rate adjusted for changes in price levels between economies. If domestic and foreign price levels and the nominal exchange rate are integrated, then cointegration between these variables implies the existence of both a long-run equilibrium relationship and PPP. The residual, the real exchange rate, then follows a stationary process. The paper uses the multivariate cointegration methodology of Johansen [16] and Johansen and Juselius [17; 18] to examine the source of real exchange rate nonstationarity. Is the nonstationarity due to shifts in the domestic and foreign price of nontradeables or productivity differentials between traded and nontraded sectors? Or is the nonstationarity a possible outcome of difficulties in intercountry comparisons of prices movements associated with construction of these price indices?

Most research finds the real exchange rate follows a nonstationary process due to the presence of a unit root [8; 12; 1; 9; 19; 27]. However, the existence of a variable trend in the real exchange rate does not imply the absence of a long-run relationship between relative prices levels and nominal exchange rates for two reasons. First, a long-run relationship between price levels and nominal exchange rates may exist but not the one-for-one relationship implicit in the calculation of real exchange rates due to measurement differences in the construction of price indices between economies. Second, PPP violations may occur due to the presence of permanent productivity innovations which affect the relative price of nontradeables. If these shocks are not represented by measurable variables, a cointegrating relationship will not exist.

The paper constructs traded and nontraded GDP price indices and productivity rates for 14 OECD economies, and tests: (1) if the variable trend (the nonstationary process) in the real exchange rate is due to permanent innovations in relative price of domestic and foreign nontradeables; (2) if long-run PPP violations are due to permanent movements in the relative price of nontradeables; (3) if the nonstationarity in the real exchange rate is due to permanent innovations in domestic and foreign productivity differentials between the traded and nontraded sectors; (4) if the variable trend in the relative price of nontradeables is due to permanent innovations in productivity between sectors. Lastly, the paper constructs a cointegrating error correction model using the estimated long-run parameter coefficients from the Johansen procedure and estimates the short-run and speed of adjustment of real exchange rates to innovations in the relative price of nontradeables.

The contents of the paper are as follows: section II presents a brief model, which outlines the role of the relative price of nontradeables and productivity differentials on real exchange rate determination and PPP violations; section III presents the testing methodology; section IV contains data descriptions and results; section V concludes with a summary of the evidence.

II. The Model

One measure of competitiveness economists and firms use to explain trade patterns are movements in the real exchange rate. An appreciating real exchange rate adversely affects the competitive position of a firm or country, since the price of its products have risen relative to the foreign economy. If price differences between economies become large, arbitrage opportunities should occur to prevent unbounded price movements; thus, the existence of profitable opportunities for trade should ensure the existence of a long-run cointegrating equilibrium. In this case, PPP holds and the real exchange rate follows a stationary process.

The presence of nontraded goods in the economy implies the prices of these goods may diverge substantially without an effective arbitrage mechanism to ensure price equality or co-movement. In this case, increases in the foreign price of nontraded goods will not be matched by equivalent domestic price increases; hence, no cointegrating relationship is expected between domestic and foreign nontraded goods prices. Since innovations in these price indices affect real exchange rates, it is important to model their role:

p = (1 - [Alpha])[p.sub.T] + [Alpha][p.sub.NT], (1)

[Mathematical Expression Omitted],

where p is the logarithm of the general price level, * denotes the foreign economy, [p.sub.T] and [p.sub.NT] represent the logarithms of the traded and nontraded goods price levels, and [Alpha] and [Beta] are the shares of the nontraded goods sector in the domestic and foreign economy, respectively [9]. Throughout the paper, all lower case variables are expressed in logarithms. If relative PPP holds for traded goods, then:

[Mathematical Expression Omitted],

where e is the logarithm of the nominal exchange rate and represents the price of foreign currency in terms of domestic currency units, and k is a constant which may differ from zero due to tariffs, quotas, distribution costs, etc. If absolute PPP holds, k = 0.

The real exchange rate, q, is the nominal exchange rate deflated by the domestic and foreign price levels, and represents the real price of a foreign basket relative to a domestic one:

q = e + [p.sup.*] - p. (4)

Note an explicit relationship exists between equations (3) and (4), PPP and the real exchange rate. The constant k determines the level for the real exchange rate. Deviations from relative PPP imply movements in real exchange rates. If these deviations are permanent, PPP fails in the long-run and real exchange rates are nonstationary.(1) Real exchange rates can be expressed as a function of the price of traded and nontraded goods by substituting (1), (2) and (3) into (4):

[Mathematical Expression Omitted], or

[Mathematical Expression Omitted],

where [z.sub.NT] is the logged, relative price of nontraded goods, [p.sub.NT] - [p.sub.T]. An increase in the relative price of domestic nontradeables imply a real appreciation of the domestic currency, represented by a fall in q, the real price of the foreign currency. To obtain PPP as a function of the relative price of nontradeables, substitute (5a) into (4):

[Mathematical Expression Omitted],

where P and [P.sup.*] are the domestic and foreign price levels. Throughout the paper, capital letters denote levels. If traded and nontraded prices contain a unit root, and no cointegrating relationship exists between them, the relative price of nontradeables will contain a unit root. This variable trend is predicted to be cointegrated with real exchange rates and cause PPP violations; i.e., the failure of a long-run relationship between housing and car prices implies permanent changes in the relative price of nontradeables, real exchange rates and PPP.

Permanent changes in the relative price of nontradeables can be explained by changes in productivity between traded and nontraded goods and services [2; 16; 28; 22].(2) If labor is mobile across sectors, wage equalization will occur. In a one-factor model, competition causes firms to equate prices to reflect unit labor costs, nominal wages adjusted for productivity:

[P.sub.T] = W/[A.sub.T], [P.sub.NT] = W/[A.sub.NT],

[Mathematical Expression Omitted],

where W is the nominal wage, and [A.sub.T] and [A.sub.NT] represent productivity in the traded and nontraded goods, respectively. The relative price of nontradeables can be expressed as:

[P.sub.NT]/[P.sub.T] = [A.sub.T]/[A.sub.NT],

[Mathematical Expression Omitted],

or, in logarithms,

[z.sub.NT] = ln([A.sub.T]/[A.sub.NT]),

[Mathematical Expression Omitted].

Substitution of (8a) into (5a) yields the real exchange rate expressed as a function of productivity:

[Mathematical Expression Omitted],

where the parentheses terms will be referred to as the domestic and foreign productivity differentials. If these differentials (or ratios) are constant or subject to temporary, mean-reverting innovations, the relative price of nontradeables and real exchange rate are constant or follow a stationary process. If the productivity differentials contain a variable trend, the price of nontradeables and real exchange rate follow a random walk. A cointegrating relationship should then exist between innovations in productivity differentials and real exchange rates.

III. Methodology

The paper uses the multivariate cointegration methodology proposed by Johansen [17] and Johansen and Juselius [18; 19]. The Johansen maximum likelihood approach allows testing in a multi-variate framework and avoids some of the drawbacks of the Engle-Granger [13] cointegration methodology. In contrast to the Engle-Granger procedure, Johansen's maximum likelihood method considers the error structure of the data processes allows for interactions in the determination of the relevant economic variables and is independent of the choice of the endogenous variable. Most importantly, the Johansen method allows explicit testing of parameter estimates and rank restrictions using likelihood ratio tests that employ Chi-Square statistics [18; 19].(3)

In addition, Monte Carlo simulations find the augmented Dickey-Fuller (ADF) [10] and the Phillips [26] [Z.sub.[Alpha]] tests have lower power against interesting alternative hypotheses than the Johansen test [7]. The ADF and Phillips [Z.sub.[Alpha]] tests do not reject the false hypothesis of no cointegration as often as the Johansen test; thus, the Johansen test possesses significant power advantages over standard residual-based tests. This implies that a long-run equilibrium may exist in the data but the ADF and Phillips test may not detect the "true" cointegrating relationship. The results may indicate that the Johansen procedure, based on full system estimation, eliminates the simultaneous equation bias and raises efficiency relative to single equation methods [7].

The Johansen procedure consists of a maximum likelihood estimation of a VAR model that includes both levels and differences of the relevant variables:

D[X.sub.t] = [[Theta].sub.1]D[X.sub.t-1] + [[Theta].sub.k-1]D[X.sub.t-(k-1)] + [Gamma] [X.sub.t-k] + [[Epsilon].sub.t], (10)

where D is the difference operator, and [[Theta].sub.i], i = 1, ... k - 1 and [[Gamma].sub.i], i = 1, ... k, are the matrices of coefficients on the differenced and level variables, respectively. Equation (10) resembles a traditional first difference VAR model except for the term [Gamma] [X.sub.t-k]. The Johansen method determines whether the coefficient matrix [Gamma] contains information about the long-run properties of the model. There are three possibilities. If the rank of this matrix is zero, (r = 0) no cointegrating or long-run relationship in levels exists among any linear combination of the variables, and equation (10) reduces to a VAR model in first differences. If r = 1, only one linearly independent cointegrating equilibrium exists that yields a stationary process; when r [greater than] 1, there exists more than one cointegrating relationship. If the r = p (p is the number of variables in the VAR), then a trivial form of cointegration exists, where all the variables are stationary.

The Johansen tests determine the rank of equations (5a), (6), (9) and (8a) by testing the following vectors:

[Mathematical Expression Omitted],

[Mathematical Expression Omitted],

[Mathematical Expression Omitted],

[[z.sub.NT] [A.sub.T]/[A.sub.NT]], (14)

where all terms are in logarithms (i.e., [A.sub.T]/[A.sub.NT] and P/[P.sup.*] represent ln([A.sub.T]/[A.sub.NT]) and ln(P/[P.sup.*]), respectively). If a stationary linear combination of vector (11) (or vector (12)) is rank one, a single long-run equilibrium relationship exists between the relative price of nontradeables in the domestic and foreign economies and the real exchange rate (or between nominal exchange rates and relative prices). If a stationary linear combination of vector (13) is rank one, then a long-run relationship exists between productivity differentials and real exchange rates; in this case, permanent innovations in the real exchange rate can be attributed to changes in productivity between the traded and nontraded sectors in the domestic and foreign economy.

If a stationary linear combination of vector (14) is rank one, then a long-run relationship exists between the relative price of nontradeables and productivity differentials, where the variable trend in the productivity differentials is linked to permanent innovations in the relative prices between sectors. If a stationary linear combination exists for all vectors, permanent innovations in real exchange rates are linked to innovations in the relative price of nontraded goods, which are linked to productivity differentials. In this case, productivity differentials can explain permanent movements in real exchange rates and PPP violations.

The hypothesis that a stationary linear combination of the vector arises solely from the relationship between domestic and foreign productivity, independent of the real exchange rate, is tested by imposing the restriction [0 a b] on the vector [Mathematical Expression Omitted]. This likelihood ratio test (equivalent to [H.sub.6] in Johansen and Juselius [18] examines whether any stationary linear combination of the subset [Mathematical Expression Omitted] exists; H(r): [Lambda] = [Alpha][Beta][prime]. The test concerns restrictions on the space spanned by [Beta], often referred to as the cointegrating space, where [Beta] is the p times r matrix of cointegrating vectors and [Alpha] is a suitable matrix of the same dimension. If this restriction is rejected, the hypothesis that a stationary linear combination arises solely from the relationship between the domestic and foreign relative prices of nontradeables is rejected. In this case, the real exchange rate follows a stationary process allowing for innovations in the relative price of nontradeables in the domestic and foreign economies.

Several interesting hypotheses restrictions can be tested for vector (12). First, the restriction [1 - 1 0 0] tests whether nominal exchange rates and relative prices move one-for-one and form a cointegrating vector. Second, the restriction [Beta]1+[Beta]2 = 0, where [Beta]'s are given by [[Beta]1 [Beta]2 [Beta]3 [Beta]4], tests if nominal exchange rates and relative prices move one-for-one, allowing for movements in the domestic and foreign relative price of nontradeables. Third, the restriction [a b 0] verifies whether any stationary linear combination of nominal exchange rates and relative prices exists, excluding changes in the relative prices of nontradeables. If we reject restriction one, but not restriction three, nominal exchange rates and relative prices form a stationary non proportional (non one-for-one) linear combination. This may be due to measurement error.

For vector (13), the restriction test [0 a b] verifies whether a stationary linear combination of the vector arises from the productivity differentials. Rejection of the restriction implies that a cointegrating relationship exists between the real exchange rate and productivity; thus, violations in long-run PPP can be explained by permanent innovations in productivity differentials.

IV. Results

Data Descriptions

The current study constructs traded and nontraded GDP deflators and productivity for the G7 for the period 1960-1990 using OECD data from the International Sectoral Database.(4) The sector breakdowns follow the International Standard Industrial Classifications (ISIC) currently used in the OECD National Accounts (ANA) publication. Following the work of the OECD [24], the open or traded goods sectors comprise only manufacturing and the nontraded goods or closed sectors are the service sectors comprising: (1) electricity, gas and water, (2) construction, (3) wholesale and retail trade, restaurants and hotels, (4) transport, storage and communications, (5) financial services and insurance, (6) community, social and personal services and (7) government services. Agriculture and mining are considered neither open (traded) nor closed (nontraded), since intercountry trade is partially hindered in some economies by large tariffs and informal barriers; thus, these sectors are excluded from the sample [24].

The GDP price deflators are constructed by dividing the nominal GDP for the traded (nontraded) by the real GDP for that sector. Traded (nontraded) productivity data are obtained by dividing the OECD's figures for GDP in constant prices for the open (closed) sector by total labor employment for that sector, yielding labor productivity or real output per worker. Nominal exchange rates and price levels are obtained from the Citibase tapes. Nominal exchange rates are bilateral rates against Germany; results with France yielded similar results.(5) The U.S. was not chosen as the benchmark, since several authors have noted the U.S. exchange rate behaved erratically in the 1980s, and hence would not have been an appropriate base [5; 21]. Additionally, the U.S. price/exchange rate relationship may be more subject to hysterisis than other economies, which may bias the results [3; 20].

The use of annual data contrasts with other research which adopts monthly data from the early 1970s to late 1980s [1; 9; 19; 7; 23]. Although these studies have considerably higher degrees of freedom, Hendry [15] points out that increasing the sample size by simple time disaggregation from years to months is not likely to reveal long term relationships. Frenkel [14] maintains that PPP requires at least ten years to be established. Pippenger maintains that the use of high frequency data (for example monthly data) over a short horizon may not be able to detect convergence that takes this much time [27].(6)

[TABULAR DATA FOR TABLE I OMITTED]

Table I presents stationarity tests for the relevant variables using Augmented Dickey Fuller tests assuming a constant, one difference and a time trend. The following logarithmic variables are tested: nominal exchange rates, e, real exchange rates, q, relative price of nontradeables, [z.sub.NT], relative prices, ln(P/[P.sup.*]), and productivity differentials, ln([A.sub.T]/[A.sub.NT]). Bilateral comparisons use Germany as the benchmark. Tests fail to reject at the 5% level the null hypothesis of a unit root for all the series. (Alternative specifications concerning the difference variable or time trend yield similar results). The null hypothesis is rejected when the series is differenced (not reported). This implies the variables are integrated of order one. The next step is to determine if the variable trend in the real exchange rates results from the variable trend in the relative price of nontradeables in the domestic and foreign economies.

Real Exchange Rates and Relative Prices

Table II presents Johansen cointegration tests of real exchange rates with the relative price of nontradeables, [Mathematical Expression Omitted]. The VAR lag length is chosen using the Akaike criterion and depending on the economy, range from one to two years. The Schwartz criterion yields similar lag lengths. Rank results in column three assume a trend in the variables and in the data generating process, since plots of the data suggest strong time trends. Results in column three indicate that the null hypothesis of no cointegrating relationship between real exchange rates and the relative price of nontradeables can be rejected in ten of the thirteen economies at the 10%. Only in the U.S., Japan, [TABULAR DATA FOR TABLE II OMITTED] and Norway can we not reject the null hypothesis of nonstationary. The U.S. and Japan are the least open (export plus imports as a percentage of GDP) of the economies considered. Norway's trade and exchange rate is heavily influenced by the price of oil and its export, and thus may have also experienced a shift in the terms of trade.

Likelihood ratio tests for reduced rank in column four test the hypothesis that the stationarity arises solely from a linear combination of the relative prices. Chi-Square statistics reject the restriction, [0 a b], at the 1% confidence level in nine of the tested economies. The test statistics are not presented for the vectors where no stationarity exists, since the test statistics are not asymptotically valid. Hence, the cointegrating relationship can not be explained simply by the relationship between domestic and foreign productivity differentials, but instead by the existence of an equilibrium relationship between real exchange rates and productivity differentials.

The individual significance of the domestic and foreign relative price of nontradeables are presented in columns five and six, respectively. Chi-Square statistics pertain to the following restrictions: [Beta]2 = 0, and [Beta]3 = 0, where the [Beta]'s are given by [[Beta]1 [Beta]2 [Beta]3] for vector [Mathematical Expression Omitted]. Rejection of the restriction implies that the domestic or foreign relative price of nontradeables exert a significant influence on the real exchange rate. For all economies (except France), at least one of the relative prices is significant at the 5% level; hence, individually, the relative price of nontradeables serve as significant determinants of the real exchange rate.

Lastly, we test the hypothesis that the relative price of domestic and foreign nontradeables have equal, but opposite signs. This hypothesis implies real exchange rates can be influenced by the difference between the two relative price indexes. Failure to reject implies that the tested vector can be collapsed into [q d[z.sub.NT]], where d is the difference between the relative price of nontradeables in the domestic and foreign economy. For the economies of Canada, Finland, France, Italy, the Netherlands and Sweden, this restriction can not be rejected; hence the real exchange rate is significantly influenced by the difference in the relative prices of nontradeables in these economies vis-vis Germany. In the economies of Australia, Belgium, Denmark and the U.K., the parameter estimates of the domestic and foreign nontradeable prices are significantly different from each other and thus can not be adequately summarized by their difference. The vector can not be collapsed into the real exchange rate and the differenced variable.

PPP and the Relative Price of Nontradeables

Table III presents Johansen cointegration results for PPP and the relative price of nontradeables. In twelve of thirteen economies, a stationary linear combination of the vector exists. Column four examines whether this stationary exists solely as a result of the relative price of nontradeables; we reject this assumption in all cases.(7) Thus, PPP exists allowing for shifts in the relative price of nontradeables in these economies. Columns four, five and six test different hypotheses concerning PPP. In all cases, we can reject at the 5% confidence level the restriction [1 -1 0 0]; thus, the strict version of PPP, involving one-for-one changes in nominal exchange rates and relative prices and no shifts of relative nontradeable prices is rejected.

In the economies of Australia, Belgium, Canada, France, Sweden and Japan, we reject the hypothesis that any stationary linear combination of nominal exchange rates and relative prices exists. In these economies, movements in relative prices of nontradeables are significant determinants [TABULAR DATA FOR TABLE III OMITTED] of PPP violations; without their inclusion, PPP fails. In Finland, Italy, U.S. and U.K., a stationary linear combination of PPP exists. Lastly, we test the assumption that PPP moves one-for-one allowing for movements in relative prices of nontradeables. This restriction is rejected in most economies, implying that measurement errors may exist in comparing relative prices and nominal exchange rates. Accordingly, the results support the conclusions arrived in the previous section: the relative price of nontradeables is a significant determinant of nominal exchange rates and relative prices, and can explain PPP violations. One additional finding is nominal exchange rates and relative prices may be linked, but not proportionally. Thus, a source of real exchange rate nonstationarity may be due to difficulties in intercountry comparisons or measurements of prices.

Real Exchange Rates and Productivity

Table IV presents Johansen cointegration results for productivity and real exchange rates. Column three presents stationarity results for the vector [Mathematical Expression Omitted]. In nine of the thirteen economies, we reject at the 10% confidence level no stationary linear combination. No long-run cointegrating relationship exists between productivity differentials and real exchange rates in Japan and the three Scandinavian economies, Norway, Sweden and Finland. Likelihood ratio tests in column five reject in eight of the nine economies that the stationary linear combination of the vector arises solely from the productivity differentials. Columns six and seven test the individual significance of productivity differentials; in the tested economies, at least one of the differentials is significant at the 5% confidence level. Therefore, in most economies (except the Scandinavian region and Japan), a long-run cointegrating relationship exists between real exchange rates and productivity differentials.

In column four, we test the cointegrating relationship between the relative price of nontradeables and the productivity differential. In seven of the thirteen economies, we reject no long-run relationship between these variables; thus, in only half the countries does a long-run equilibrium exist between productivity and relative prices. In Canada, the U.K. and the U.S., a cointegrating relationship exists between real exchange rates and both relative prices and productivity, but not [TABULAR DATA FOR TABLE IV OMITTED] [TABULAR DATA FOR TABLE V OMITTED] between relative prices and productivity. This implies that the productivity differentials affect real exchange rates, but not through the relative price channel.(8)

Error Correction Model

Table V presents a cointegrating error correction model that estimates the short-run and speed of adjustment of real exchange rates to innovations in the price of nontradeables. To minimize the standard errors, a seemingly unrelated regressor (SUR) procedure is employed. The error correction term is estimated using the Johansen long-run parameter estimates discussed above; i.e., the residuals from the long-run estimation of the vector [Mathematical Expression Omitted] are saved and lagged one period. For the three economies where the errors are nonstationary (Japan, Norway and the U.S.), these residuals are not used, and the model is simply presented in differences. Since the variables are in log levels, differences yield growth rates, which have readily interpretable coefficients. When autocorrelation exists, lagged differences of the relative price of nontradeables and the real exchange rate are used to eliminate this problem; insignificant variables are subsequently dropped from the equation.

In most of the economies, changes in the relative prices of nontraded goods significantly influence the real exchange rate. The predicted impact of the domestic relative price of nontradeables is negative since increases in the domestic price of nontraded goods with respect to traded goods are expected to appreciate the real exchange rate. By similar logic, the predicted impact of the foreign relative price of nontradeables is an increase in [q.sub.t]. For most economies, the parameter coefficients possess the correct sign. The speed of adjustment is significant in seven of the ten economies and on average is .3, indicating approximately a three year adjustment.

V. Conclusion

The real exchange rates are an important determinant in international trading patterns. A variable trend in real exchange rate may imply both a failure of purchasing power parity and a permanent change in international competitiveness. The observed nonstationary process of the real exchange rate may be due to changes in the relative price levels of traded and nontraded goods as a result of differing productivity rates in these sectors. The issue of international competitiveness and the hypothesis of purchasing power parity should only hold for traded goods; no arbitrage or trading opportunities are available for nontraded goods. But since the real exchange rate is measured as the nominal exchange rate adjusted for changes in the general price level, permanent changes in the price ratio of nontraded to traded goods may account for the variable trend in the real exchange rate and the failure of PPP.

The paper constructs indices for price and productivity for traded and nontraded goods for 14 OECD economies for 1960-1990. Using Johansen maximum likelihood cointegration tests, we show that in most economies the source of the variable trend in the real exchange rate and permanent PPP violations are due to permanent shifts in relative prices of nontradeables and productivity differentials; hence, in the long-run, the permanent deviations in PPP and real exchange rates can be explained by permanent movements in the relative price of nontradeables and domestic and foreign productivity differentials between the traded and nontraded sector. A second source of nonstationarity in the real exchange rate may be due to construction of this variable. Johansen hypotheses tests reveal that nominal exchange rates and relative prices form a stationary long-run linear combination, but not the one-for-one which theory predicts in the absence of measurement errors.

The paper estimates a cointegrating error correction model using the Johansen long-run parameter estimates; the error correction model indicates that the relative price of nontradeables significantly influences the real exchange rate in the short-run. Positive innovations in the domestic (foreign) relative price of nontradeables appreciate (depreciate) the real exchange rate. For most economies, equilibrium adjustment is approximately three years.

Thus, the paper shows that the nonstationary process of the real exchange rate and permanent PPP violations are caused by permanent innovations in the relative price of nontradeables. Productivity differentials between economies explain permanent shifts in real exchange rates, thus explaining the origin of the PPP violations. Changes in relative prices are significant determinants of real exchange rates in the short and long-run.

1. One qualification should be added here. "Since the observed price levels are imperfect proxies at best for the theoretical price variables, the usual symmetry and proportionality restrictions under PPP are not necessarily consistent with empirical data [7, 183]." This implies that prices and nominal exchange rates may be moving together, but not one-for-one, and hence no arbitrage opportunities exist. The implication of measurement errors implies that a stationary non one-for-one linear of (3) may cause nonstationary real exchange rates by construction.

2. Alternative explanations to movements in the relative price of nontradeables that rely on nominal movements due to devaluations or money can be found in Officer [27] and Dornbusch [11] or differing capital/labor ratios in Balassa [2].

3. An alternative cointegration method is fractional integration. This method is a less restrictive type technique than the Johansen method, but requires a large numbers of observations, and hence was inappropriate in this text.

4. The following time periods are available: 1) 1960-1990 for France, Germany, Belgium, Norway, U.K., U.S. and Finland, 2) 1962-1989 for Canada, 3) 1967-1990 for Denmark, and 4) 1970-1990 for Australia, Sweden, Netherlands, Italy and Japan.

5. Bilateral rates were used to avoid issues of multilateral aggregates, and whether the results are sensitive to shifting weights, or to the omission of relevant countries in the multilateral aggregate. Further, bilateral rates avoid the complex issue of whether there is an aggregation restriction on the statistical properties of a multilateral aggregate. For instance, a weighted sum of a nonstationary and stationary series is a nonstationary series, and hence the exchange rate would be very sensitive to the index. Also, a multilateral index would then be related to the index of other economies. The author thanks the referee for these comments.

6. Additionally, disaggregation may obscure the long-run picture because the monthly variation in productivity is small compared to the monthly variability of nominal and real exchange rates. Nominal exchange rates possess high volatility since they are determined by supply and demand conditions in the foreign exchange market and respond to news like asset prices.

7. No Chi-Square restrictions exists for Italy and the Netherlands since all the variables are stationary; i.e., r = 4 can not be rejected. Hence, we reject the restrictions of the stationarity arising solely from the relative price of nontradeables, since PPP must form a stationary linear combination.

8. Comparisons between Table II and IV show that productivity differentials, and not relative prices explain real exchanges rates movements for the U.S., and that relative prices, not productivity differentials, explain real exchange rate movements for Sweden. Possible explanations for these occurrences are that relative wages or unit labor costs between sectors may be influencing real exchange rates; in this case, equation (7) is violated due to different wages between sectors, and (12) omits an important explanatory variable, unit labor costs.

References

1. Abauf, Niso and Phillippe Jorion, "Purchasing Power Parity during the Recent Float." Journal of Finance, March 1990, 157-74.

2. Balassa, Bela, "The Purchasing Power Parity Doctrine: A Reappraisal." Journal of Political Economy, December 1964, 584-96.

3. Baldwin, Richard, "Hysteresis in Import Prices: the Beachhead Effect." American Economic Review, September 1988, 773-85.

4. Bhagwati, Jagdish, "Why Are Services Cheaper in the Poor Countries?" Economic Journal, June 1984, 279-86.

5. Branson, William. "Causes of Appreciation and Volatility of the Dollar," in The Recent Developments, Outlook, and Policy Options. Kansas City: Federal Reserve Bank of Kansas City, 1985, pp. 33-52.

6. Cassel, G., "The Present Situation of the Foreign Exchanges." Economic Journal, 1916, 62-65.

7. Cheung, Yin-Wong and Kon Lai, "Long-run Purchasing Power Parity during the Recent Float." Journal of International Economics, 1993, 181-92.

8. Corbae, Dean and Sam Ouliaris, "Cointegration and Tests of Purchasing Power Parity." Review of Economics and Statistics, August 1988. 508-11.

9. Couglin, Cletus and Kees Koedijk, "What Do We Know about Long-run Real Exchange Rate?" Federal Reserve Bank of St. Louis, January/February 1990, 36-48.

10. Dickey, David and Wayne Fuller. "Distribution of the Estimators for Autoregressive Time Series with a Unit Root. Journal of American Statistical Association, June 1979, 427-31.

11. Dornbusch, Rutiger. "Devaluation, Money and Nontraded Goods." Exchange Rates and Inflation. Cambridge, Mass.: MIT Press. 1994.

12. Enders, Walter, "ARIMA and Cointegration Tests of PPP under Fixed and Flexible Exchange Rate Regimes." Review of Economics and Statistics, August 1988, 504-508.

13. Engle, Robert and C. W. J. Granger, "Cointegration and Error Correction: Representation, Estimation and Testing." Econometrica, March 1987, 251-76.

14. Frenkel, Jeffrey. "International Capital Bobility and Crowding-out in the U.S. Economy: "Imperfect Integration of Financial Markets or of Goods Markets," in How Open is the U.S. Economy?, edited by Ruth Hafer. Lexington. Mass: Lexington Books, 1986, pp. 33-67.

15. Hendry, David, "Econometric Modelling with Cointegrated Variables: An Overview." Oxford Bulletin of Economics and Statistics, August 1986, 201-12.

16. Hseih, David, "The Determination of the Real Exchange Rate." Journal of International Economics, May 1982, 355-62.

16. Johansen, Soren, "Statistical Analysis of Cointegration Vectors." Journal of Economic Dynamics and Control, June-September 1988, 231-54.

17. ----- and Katerina Juselius. "Maximum Likelihood Estimation and Inference on Cointegration - With Applications to the Demand for Money." Oxford Bulletin of Statistics, May 1990, 169-210.

18. ----- and -----, "Testing Structural Hypotheses in Multivariate Cointegration Analysis of the PPP and the UIP for UK." Journal of Econometrics, May 1992, 211-44.

19. Kim, Yoonbai, "Purchasing Power Parity in the Long Run: A Cointegration Approach." Journal of Money, Credit and Banking, November 1990, 491-503.

20. Krugman, Paul. "Pricing to Market when the Exchange Rate Changes," in Real-Financial Linkages among Open Economies, edited by Sven Arndt and J. David Richardson. Cambridge: MIT Press, 1985, pp. 49-70.

21. ----- and Richard Baldwin, "The Persistence of the U.S. Trade Deficit." Brookings Papers on Economic Activity, 1987, 1-56.

22. Krugman, Paul and Maurice Obstfeld. International Economics, Third Edition, New York: Harper-Collins, 1994. Pp. 422-23.

23. Kugler, Peter and Carlos Lenz, "Multivariate Cointegration Analysis and the Long-run Validity of PPP." Review of Economics and Statistics, January 1990, 180-84.

24. Meyer-zu-Schlochtern, F. J. M. "An International Sectoral Data Base for Thirteen OECD Countries." Organization for Economic Co-operation and Development, Economics and Statistics, Department Working Paper, 1988.

25. Officer, Lawrence. Purchasing Power Parity and Exchange Bates. Greenwich, Conn.: JAI Press, 1984.

26. Phillips, Peter C. B., "Time-Series Regression with a Unit Root. Econometrica, March 1987, 277-301.

27. Pippenger, Michael, "Cointegration Tests of Purchasing Power Parity: the Case of Swiss Exchange Rates." Journal of International Money and Finance, January 1993, 46-61.

28. Samuelson, Paul, "Theoretical Notes on Trade Problems." Review of Economics and Statistics, May 1964, 145-54.

The purchasing power parity hypothesis (PPP) states that nominal exchange rates move with differences in relative prices between economies. The theory has received considerable attention in the economic literature since Cassell [6], and is the foundation of many long-run theoretical hypotheses in international finance; yet, its empirical validity remains in question. Many tests of PPP focus on the stationarity of the real exchange rate, the nominal exchange rate adjusted for changes in price levels between economies. If domestic and foreign price levels and the nominal exchange rate are integrated, then cointegration between these variables implies the existence of both a long-run equilibrium relationship and PPP. The residual, the real exchange rate, then follows a stationary process. The paper uses the multivariate cointegration methodology of Johansen [16] and Johansen and Juselius [17; 18] to examine the source of real exchange rate nonstationarity. Is the nonstationarity due to shifts in the domestic and foreign price of nontradeables or productivity differentials between traded and nontraded sectors? Or is the nonstationarity a possible outcome of difficulties in intercountry comparisons of prices movements associated with construction of these price indices?

Most research finds the real exchange rate follows a nonstationary process due to the presence of a unit root [8; 12; 1; 9; 19; 27]. However, the existence of a variable trend in the real exchange rate does not imply the absence of a long-run relationship between relative prices levels and nominal exchange rates for two reasons. First, a long-run relationship between price levels and nominal exchange rates may exist but not the one-for-one relationship implicit in the calculation of real exchange rates due to measurement differences in the construction of price indices between economies. Second, PPP violations may occur due to the presence of permanent productivity innovations which affect the relative price of nontradeables. If these shocks are not represented by measurable variables, a cointegrating relationship will not exist.

The paper constructs traded and nontraded GDP price indices and productivity rates for 14 OECD economies, and tests: (1) if the variable trend (the nonstationary process) in the real exchange rate is due to permanent innovations in relative price of domestic and foreign nontradeables; (2) if long-run PPP violations are due to permanent movements in the relative price of nontradeables; (3) if the nonstationarity in the real exchange rate is due to permanent innovations in domestic and foreign productivity differentials between the traded and nontraded sectors; (4) if the variable trend in the relative price of nontradeables is due to permanent innovations in productivity between sectors. Lastly, the paper constructs a cointegrating error correction model using the estimated long-run parameter coefficients from the Johansen procedure and estimates the short-run and speed of adjustment of real exchange rates to innovations in the relative price of nontradeables.

The contents of the paper are as follows: section II presents a brief model, which outlines the role of the relative price of nontradeables and productivity differentials on real exchange rate determination and PPP violations; section III presents the testing methodology; section IV contains data descriptions and results; section V concludes with a summary of the evidence.

II. The Model

One measure of competitiveness economists and firms use to explain trade patterns are movements in the real exchange rate. An appreciating real exchange rate adversely affects the competitive position of a firm or country, since the price of its products have risen relative to the foreign economy. If price differences between economies become large, arbitrage opportunities should occur to prevent unbounded price movements; thus, the existence of profitable opportunities for trade should ensure the existence of a long-run cointegrating equilibrium. In this case, PPP holds and the real exchange rate follows a stationary process.

The presence of nontraded goods in the economy implies the prices of these goods may diverge substantially without an effective arbitrage mechanism to ensure price equality or co-movement. In this case, increases in the foreign price of nontraded goods will not be matched by equivalent domestic price increases; hence, no cointegrating relationship is expected between domestic and foreign nontraded goods prices. Since innovations in these price indices affect real exchange rates, it is important to model their role:

p = (1 - [Alpha])[p.sub.T] + [Alpha][p.sub.NT], (1)

[Mathematical Expression Omitted],

where p is the logarithm of the general price level, * denotes the foreign economy, [p.sub.T] and [p.sub.NT] represent the logarithms of the traded and nontraded goods price levels, and [Alpha] and [Beta] are the shares of the nontraded goods sector in the domestic and foreign economy, respectively [9]. Throughout the paper, all lower case variables are expressed in logarithms. If relative PPP holds for traded goods, then:

[Mathematical Expression Omitted],

where e is the logarithm of the nominal exchange rate and represents the price of foreign currency in terms of domestic currency units, and k is a constant which may differ from zero due to tariffs, quotas, distribution costs, etc. If absolute PPP holds, k = 0.

The real exchange rate, q, is the nominal exchange rate deflated by the domestic and foreign price levels, and represents the real price of a foreign basket relative to a domestic one:

q = e + [p.sup.*] - p. (4)

Note an explicit relationship exists between equations (3) and (4), PPP and the real exchange rate. The constant k determines the level for the real exchange rate. Deviations from relative PPP imply movements in real exchange rates. If these deviations are permanent, PPP fails in the long-run and real exchange rates are nonstationary.(1) Real exchange rates can be expressed as a function of the price of traded and nontraded goods by substituting (1), (2) and (3) into (4):

[Mathematical Expression Omitted], or

[Mathematical Expression Omitted],

where [z.sub.NT] is the logged, relative price of nontraded goods, [p.sub.NT] - [p.sub.T]. An increase in the relative price of domestic nontradeables imply a real appreciation of the domestic currency, represented by a fall in q, the real price of the foreign currency. To obtain PPP as a function of the relative price of nontradeables, substitute (5a) into (4):

[Mathematical Expression Omitted],

where P and [P.sup.*] are the domestic and foreign price levels. Throughout the paper, capital letters denote levels. If traded and nontraded prices contain a unit root, and no cointegrating relationship exists between them, the relative price of nontradeables will contain a unit root. This variable trend is predicted to be cointegrated with real exchange rates and cause PPP violations; i.e., the failure of a long-run relationship between housing and car prices implies permanent changes in the relative price of nontradeables, real exchange rates and PPP.

Permanent changes in the relative price of nontradeables can be explained by changes in productivity between traded and nontraded goods and services [2; 16; 28; 22].(2) If labor is mobile across sectors, wage equalization will occur. In a one-factor model, competition causes firms to equate prices to reflect unit labor costs, nominal wages adjusted for productivity:

[P.sub.T] = W/[A.sub.T], [P.sub.NT] = W/[A.sub.NT],

[Mathematical Expression Omitted],

where W is the nominal wage, and [A.sub.T] and [A.sub.NT] represent productivity in the traded and nontraded goods, respectively. The relative price of nontradeables can be expressed as:

[P.sub.NT]/[P.sub.T] = [A.sub.T]/[A.sub.NT],

[Mathematical Expression Omitted],

or, in logarithms,

[z.sub.NT] = ln([A.sub.T]/[A.sub.NT]),

[Mathematical Expression Omitted].

Substitution of (8a) into (5a) yields the real exchange rate expressed as a function of productivity:

[Mathematical Expression Omitted],

where the parentheses terms will be referred to as the domestic and foreign productivity differentials. If these differentials (or ratios) are constant or subject to temporary, mean-reverting innovations, the relative price of nontradeables and real exchange rate are constant or follow a stationary process. If the productivity differentials contain a variable trend, the price of nontradeables and real exchange rate follow a random walk. A cointegrating relationship should then exist between innovations in productivity differentials and real exchange rates.

III. Methodology

The paper uses the multivariate cointegration methodology proposed by Johansen [17] and Johansen and Juselius [18; 19]. The Johansen maximum likelihood approach allows testing in a multi-variate framework and avoids some of the drawbacks of the Engle-Granger [13] cointegration methodology. In contrast to the Engle-Granger procedure, Johansen's maximum likelihood method considers the error structure of the data processes allows for interactions in the determination of the relevant economic variables and is independent of the choice of the endogenous variable. Most importantly, the Johansen method allows explicit testing of parameter estimates and rank restrictions using likelihood ratio tests that employ Chi-Square statistics [18; 19].(3)

In addition, Monte Carlo simulations find the augmented Dickey-Fuller (ADF) [10] and the Phillips [26] [Z.sub.[Alpha]] tests have lower power against interesting alternative hypotheses than the Johansen test [7]. The ADF and Phillips [Z.sub.[Alpha]] tests do not reject the false hypothesis of no cointegration as often as the Johansen test; thus, the Johansen test possesses significant power advantages over standard residual-based tests. This implies that a long-run equilibrium may exist in the data but the ADF and Phillips test may not detect the "true" cointegrating relationship. The results may indicate that the Johansen procedure, based on full system estimation, eliminates the simultaneous equation bias and raises efficiency relative to single equation methods [7].

The Johansen procedure consists of a maximum likelihood estimation of a VAR model that includes both levels and differences of the relevant variables:

D[X.sub.t] = [[Theta].sub.1]D[X.sub.t-1] + [[Theta].sub.k-1]D[X.sub.t-(k-1)] + [Gamma] [X.sub.t-k] + [[Epsilon].sub.t], (10)

where D is the difference operator, and [[Theta].sub.i], i = 1, ... k - 1 and [[Gamma].sub.i], i = 1, ... k, are the matrices of coefficients on the differenced and level variables, respectively. Equation (10) resembles a traditional first difference VAR model except for the term [Gamma] [X.sub.t-k]. The Johansen method determines whether the coefficient matrix [Gamma] contains information about the long-run properties of the model. There are three possibilities. If the rank of this matrix is zero, (r = 0) no cointegrating or long-run relationship in levels exists among any linear combination of the variables, and equation (10) reduces to a VAR model in first differences. If r = 1, only one linearly independent cointegrating equilibrium exists that yields a stationary process; when r [greater than] 1, there exists more than one cointegrating relationship. If the r = p (p is the number of variables in the VAR), then a trivial form of cointegration exists, where all the variables are stationary.

The Johansen tests determine the rank of equations (5a), (6), (9) and (8a) by testing the following vectors:

[Mathematical Expression Omitted],

[Mathematical Expression Omitted],

[Mathematical Expression Omitted],

[[z.sub.NT] [A.sub.T]/[A.sub.NT]], (14)

where all terms are in logarithms (i.e., [A.sub.T]/[A.sub.NT] and P/[P.sup.*] represent ln([A.sub.T]/[A.sub.NT]) and ln(P/[P.sup.*]), respectively). If a stationary linear combination of vector (11) (or vector (12)) is rank one, a single long-run equilibrium relationship exists between the relative price of nontradeables in the domestic and foreign economies and the real exchange rate (or between nominal exchange rates and relative prices). If a stationary linear combination of vector (13) is rank one, then a long-run relationship exists between productivity differentials and real exchange rates; in this case, permanent innovations in the real exchange rate can be attributed to changes in productivity between the traded and nontraded sectors in the domestic and foreign economy.

If a stationary linear combination of vector (14) is rank one, then a long-run relationship exists between the relative price of nontradeables and productivity differentials, where the variable trend in the productivity differentials is linked to permanent innovations in the relative prices between sectors. If a stationary linear combination exists for all vectors, permanent innovations in real exchange rates are linked to innovations in the relative price of nontraded goods, which are linked to productivity differentials. In this case, productivity differentials can explain permanent movements in real exchange rates and PPP violations.

The hypothesis that a stationary linear combination of the vector arises solely from the relationship between domestic and foreign productivity, independent of the real exchange rate, is tested by imposing the restriction [0 a b] on the vector [Mathematical Expression Omitted]. This likelihood ratio test (equivalent to [H.sub.6] in Johansen and Juselius [18] examines whether any stationary linear combination of the subset [Mathematical Expression Omitted] exists; H(r): [Lambda] = [Alpha][Beta][prime]. The test concerns restrictions on the space spanned by [Beta], often referred to as the cointegrating space, where [Beta] is the p times r matrix of cointegrating vectors and [Alpha] is a suitable matrix of the same dimension. If this restriction is rejected, the hypothesis that a stationary linear combination arises solely from the relationship between the domestic and foreign relative prices of nontradeables is rejected. In this case, the real exchange rate follows a stationary process allowing for innovations in the relative price of nontradeables in the domestic and foreign economies.

Several interesting hypotheses restrictions can be tested for vector (12). First, the restriction [1 - 1 0 0] tests whether nominal exchange rates and relative prices move one-for-one and form a cointegrating vector. Second, the restriction [Beta]1+[Beta]2 = 0, where [Beta]'s are given by [[Beta]1 [Beta]2 [Beta]3 [Beta]4], tests if nominal exchange rates and relative prices move one-for-one, allowing for movements in the domestic and foreign relative price of nontradeables. Third, the restriction [a b 0] verifies whether any stationary linear combination of nominal exchange rates and relative prices exists, excluding changes in the relative prices of nontradeables. If we reject restriction one, but not restriction three, nominal exchange rates and relative prices form a stationary non proportional (non one-for-one) linear combination. This may be due to measurement error.

For vector (13), the restriction test [0 a b] verifies whether a stationary linear combination of the vector arises from the productivity differentials. Rejection of the restriction implies that a cointegrating relationship exists between the real exchange rate and productivity; thus, violations in long-run PPP can be explained by permanent innovations in productivity differentials.

IV. Results

Data Descriptions

The current study constructs traded and nontraded GDP deflators and productivity for the G7 for the period 1960-1990 using OECD data from the International Sectoral Database.(4) The sector breakdowns follow the International Standard Industrial Classifications (ISIC) currently used in the OECD National Accounts (ANA) publication. Following the work of the OECD [24], the open or traded goods sectors comprise only manufacturing and the nontraded goods or closed sectors are the service sectors comprising: (1) electricity, gas and water, (2) construction, (3) wholesale and retail trade, restaurants and hotels, (4) transport, storage and communications, (5) financial services and insurance, (6) community, social and personal services and (7) government services. Agriculture and mining are considered neither open (traded) nor closed (nontraded), since intercountry trade is partially hindered in some economies by large tariffs and informal barriers; thus, these sectors are excluded from the sample [24].

The GDP price deflators are constructed by dividing the nominal GDP for the traded (nontraded) by the real GDP for that sector. Traded (nontraded) productivity data are obtained by dividing the OECD's figures for GDP in constant prices for the open (closed) sector by total labor employment for that sector, yielding labor productivity or real output per worker. Nominal exchange rates and price levels are obtained from the Citibase tapes. Nominal exchange rates are bilateral rates against Germany; results with France yielded similar results.(5) The U.S. was not chosen as the benchmark, since several authors have noted the U.S. exchange rate behaved erratically in the 1980s, and hence would not have been an appropriate base [5; 21]. Additionally, the U.S. price/exchange rate relationship may be more subject to hysterisis than other economies, which may bias the results [3; 20].

The use of annual data contrasts with other research which adopts monthly data from the early 1970s to late 1980s [1; 9; 19; 7; 23]. Although these studies have considerably higher degrees of freedom, Hendry [15] points out that increasing the sample size by simple time disaggregation from years to months is not likely to reveal long term relationships. Frenkel [14] maintains that PPP requires at least ten years to be established. Pippenger maintains that the use of high frequency data (for example monthly data) over a short horizon may not be able to detect convergence that takes this much time [27].(6)

[TABULAR DATA FOR TABLE I OMITTED]

Table I presents stationarity tests for the relevant variables using Augmented Dickey Fuller tests assuming a constant, one difference and a time trend. The following logarithmic variables are tested: nominal exchange rates, e, real exchange rates, q, relative price of nontradeables, [z.sub.NT], relative prices, ln(P/[P.sup.*]), and productivity differentials, ln([A.sub.T]/[A.sub.NT]). Bilateral comparisons use Germany as the benchmark. Tests fail to reject at the 5% level the null hypothesis of a unit root for all the series. (Alternative specifications concerning the difference variable or time trend yield similar results). The null hypothesis is rejected when the series is differenced (not reported). This implies the variables are integrated of order one. The next step is to determine if the variable trend in the real exchange rates results from the variable trend in the relative price of nontradeables in the domestic and foreign economies.

Real Exchange Rates and Relative Prices

Table II presents Johansen cointegration tests of real exchange rates with the relative price of nontradeables, [Mathematical Expression Omitted]. The VAR lag length is chosen using the Akaike criterion and depending on the economy, range from one to two years. The Schwartz criterion yields similar lag lengths. Rank results in column three assume a trend in the variables and in the data generating process, since plots of the data suggest strong time trends. Results in column three indicate that the null hypothesis of no cointegrating relationship between real exchange rates and the relative price of nontradeables can be rejected in ten of the thirteen economies at the 10%. Only in the U.S., Japan, [TABULAR DATA FOR TABLE II OMITTED] and Norway can we not reject the null hypothesis of nonstationary. The U.S. and Japan are the least open (export plus imports as a percentage of GDP) of the economies considered. Norway's trade and exchange rate is heavily influenced by the price of oil and its export, and thus may have also experienced a shift in the terms of trade.

Likelihood ratio tests for reduced rank in column four test the hypothesis that the stationarity arises solely from a linear combination of the relative prices. Chi-Square statistics reject the restriction, [0 a b], at the 1% confidence level in nine of the tested economies. The test statistics are not presented for the vectors where no stationarity exists, since the test statistics are not asymptotically valid. Hence, the cointegrating relationship can not be explained simply by the relationship between domestic and foreign productivity differentials, but instead by the existence of an equilibrium relationship between real exchange rates and productivity differentials.

The individual significance of the domestic and foreign relative price of nontradeables are presented in columns five and six, respectively. Chi-Square statistics pertain to the following restrictions: [Beta]2 = 0, and [Beta]3 = 0, where the [Beta]'s are given by [[Beta]1 [Beta]2 [Beta]3] for vector [Mathematical Expression Omitted]. Rejection of the restriction implies that the domestic or foreign relative price of nontradeables exert a significant influence on the real exchange rate. For all economies (except France), at least one of the relative prices is significant at the 5% level; hence, individually, the relative price of nontradeables serve as significant determinants of the real exchange rate.

Lastly, we test the hypothesis that the relative price of domestic and foreign nontradeables have equal, but opposite signs. This hypothesis implies real exchange rates can be influenced by the difference between the two relative price indexes. Failure to reject implies that the tested vector can be collapsed into [q d[z.sub.NT]], where d is the difference between the relative price of nontradeables in the domestic and foreign economy. For the economies of Canada, Finland, France, Italy, the Netherlands and Sweden, this restriction can not be rejected; hence the real exchange rate is significantly influenced by the difference in the relative prices of nontradeables in these economies vis-vis Germany. In the economies of Australia, Belgium, Denmark and the U.K., the parameter estimates of the domestic and foreign nontradeable prices are significantly different from each other and thus can not be adequately summarized by their difference. The vector can not be collapsed into the real exchange rate and the differenced variable.

PPP and the Relative Price of Nontradeables

Table III presents Johansen cointegration results for PPP and the relative price of nontradeables. In twelve of thirteen economies, a stationary linear combination of the vector exists. Column four examines whether this stationary exists solely as a result of the relative price of nontradeables; we reject this assumption in all cases.(7) Thus, PPP exists allowing for shifts in the relative price of nontradeables in these economies. Columns four, five and six test different hypotheses concerning PPP. In all cases, we can reject at the 5% confidence level the restriction [1 -1 0 0]; thus, the strict version of PPP, involving one-for-one changes in nominal exchange rates and relative prices and no shifts of relative nontradeable prices is rejected.

In the economies of Australia, Belgium, Canada, France, Sweden and Japan, we reject the hypothesis that any stationary linear combination of nominal exchange rates and relative prices exists. In these economies, movements in relative prices of nontradeables are significant determinants [TABULAR DATA FOR TABLE III OMITTED] of PPP violations; without their inclusion, PPP fails. In Finland, Italy, U.S. and U.K., a stationary linear combination of PPP exists. Lastly, we test the assumption that PPP moves one-for-one allowing for movements in relative prices of nontradeables. This restriction is rejected in most economies, implying that measurement errors may exist in comparing relative prices and nominal exchange rates. Accordingly, the results support the conclusions arrived in the previous section: the relative price of nontradeables is a significant determinant of nominal exchange rates and relative prices, and can explain PPP violations. One additional finding is nominal exchange rates and relative prices may be linked, but not proportionally. Thus, a source of real exchange rate nonstationarity may be due to difficulties in intercountry comparisons or measurements of prices.

Real Exchange Rates and Productivity

Table IV presents Johansen cointegration results for productivity and real exchange rates. Column three presents stationarity results for the vector [Mathematical Expression Omitted]. In nine of the thirteen economies, we reject at the 10% confidence level no stationary linear combination. No long-run cointegrating relationship exists between productivity differentials and real exchange rates in Japan and the three Scandinavian economies, Norway, Sweden and Finland. Likelihood ratio tests in column five reject in eight of the nine economies that the stationary linear combination of the vector arises solely from the productivity differentials. Columns six and seven test the individual significance of productivity differentials; in the tested economies, at least one of the differentials is significant at the 5% confidence level. Therefore, in most economies (except the Scandinavian region and Japan), a long-run cointegrating relationship exists between real exchange rates and productivity differentials.

In column four, we test the cointegrating relationship between the relative price of nontradeables and the productivity differential. In seven of the thirteen economies, we reject no long-run relationship between these variables; thus, in only half the countries does a long-run equilibrium exist between productivity and relative prices. In Canada, the U.K. and the U.S., a cointegrating relationship exists between real exchange rates and both relative prices and productivity, but not [TABULAR DATA FOR TABLE IV OMITTED] [TABULAR DATA FOR TABLE V OMITTED] between relative prices and productivity. This implies that the productivity differentials affect real exchange rates, but not through the relative price channel.(8)

Error Correction Model

Table V presents a cointegrating error correction model that estimates the short-run and speed of adjustment of real exchange rates to innovations in the price of nontradeables. To minimize the standard errors, a seemingly unrelated regressor (SUR) procedure is employed. The error correction term is estimated using the Johansen long-run parameter estimates discussed above; i.e., the residuals from the long-run estimation of the vector [Mathematical Expression Omitted] are saved and lagged one period. For the three economies where the errors are nonstationary (Japan, Norway and the U.S.), these residuals are not used, and the model is simply presented in differences. Since the variables are in log levels, differences yield growth rates, which have readily interpretable coefficients. When autocorrelation exists, lagged differences of the relative price of nontradeables and the real exchange rate are used to eliminate this problem; insignificant variables are subsequently dropped from the equation.

In most of the economies, changes in the relative prices of nontraded goods significantly influence the real exchange rate. The predicted impact of the domestic relative price of nontradeables is negative since increases in the domestic price of nontraded goods with respect to traded goods are expected to appreciate the real exchange rate. By similar logic, the predicted impact of the foreign relative price of nontradeables is an increase in [q.sub.t]. For most economies, the parameter coefficients possess the correct sign. The speed of adjustment is significant in seven of the ten economies and on average is .3, indicating approximately a three year adjustment.

V. Conclusion

The real exchange rates are an important determinant in international trading patterns. A variable trend in real exchange rate may imply both a failure of purchasing power parity and a permanent change in international competitiveness. The observed nonstationary process of the real exchange rate may be due to changes in the relative price levels of traded and nontraded goods as a result of differing productivity rates in these sectors. The issue of international competitiveness and the hypothesis of purchasing power parity should only hold for traded goods; no arbitrage or trading opportunities are available for nontraded goods. But since the real exchange rate is measured as the nominal exchange rate adjusted for changes in the general price level, permanent changes in the price ratio of nontraded to traded goods may account for the variable trend in the real exchange rate and the failure of PPP.

The paper constructs indices for price and productivity for traded and nontraded goods for 14 OECD economies for 1960-1990. Using Johansen maximum likelihood cointegration tests, we show that in most economies the source of the variable trend in the real exchange rate and permanent PPP violations are due to permanent shifts in relative prices of nontradeables and productivity differentials; hence, in the long-run, the permanent deviations in PPP and real exchange rates can be explained by permanent movements in the relative price of nontradeables and domestic and foreign productivity differentials between the traded and nontraded sector. A second source of nonstationarity in the real exchange rate may be due to construction of this variable. Johansen hypotheses tests reveal that nominal exchange rates and relative prices form a stationary long-run linear combination, but not the one-for-one which theory predicts in the absence of measurement errors.

The paper estimates a cointegrating error correction model using the Johansen long-run parameter estimates; the error correction model indicates that the relative price of nontradeables significantly influences the real exchange rate in the short-run. Positive innovations in the domestic (foreign) relative price of nontradeables appreciate (depreciate) the real exchange rate. For most economies, equilibrium adjustment is approximately three years.

Thus, the paper shows that the nonstationary process of the real exchange rate and permanent PPP violations are caused by permanent innovations in the relative price of nontradeables. Productivity differentials between economies explain permanent shifts in real exchange rates, thus explaining the origin of the PPP violations. Changes in relative prices are significant determinants of real exchange rates in the short and long-run.

1. One qualification should be added here. "Since the observed price levels are imperfect proxies at best for the theoretical price variables, the usual symmetry and proportionality restrictions under PPP are not necessarily consistent with empirical data [7, 183]." This implies that prices and nominal exchange rates may be moving together, but not one-for-one, and hence no arbitrage opportunities exist. The implication of measurement errors implies that a stationary non one-for-one linear of (3) may cause nonstationary real exchange rates by construction.

2. Alternative explanations to movements in the relative price of nontradeables that rely on nominal movements due to devaluations or money can be found in Officer [27] and Dornbusch [11] or differing capital/labor ratios in Balassa [2].

3. An alternative cointegration method is fractional integration. This method is a less restrictive type technique than the Johansen method, but requires a large numbers of observations, and hence was inappropriate in this text.

4. The following time periods are available: 1) 1960-1990 for France, Germany, Belgium, Norway, U.K., U.S. and Finland, 2) 1962-1989 for Canada, 3) 1967-1990 for Denmark, and 4) 1970-1990 for Australia, Sweden, Netherlands, Italy and Japan.

5. Bilateral rates were used to avoid issues of multilateral aggregates, and whether the results are sensitive to shifting weights, or to the omission of relevant countries in the multilateral aggregate. Further, bilateral rates avoid the complex issue of whether there is an aggregation restriction on the statistical properties of a multilateral aggregate. For instance, a weighted sum of a nonstationary and stationary series is a nonstationary series, and hence the exchange rate would be very sensitive to the index. Also, a multilateral index would then be related to the index of other economies. The author thanks the referee for these comments.

6. Additionally, disaggregation may obscure the long-run picture because the monthly variation in productivity is small compared to the monthly variability of nominal and real exchange rates. Nominal exchange rates possess high volatility since they are determined by supply and demand conditions in the foreign exchange market and respond to news like asset prices.

7. No Chi-Square restrictions exists for Italy and the Netherlands since all the variables are stationary; i.e., r = 4 can not be rejected. Hence, we reject the restrictions of the stationarity arising solely from the relative price of nontradeables, since PPP must form a stationary linear combination.

8. Comparisons between Table II and IV show that productivity differentials, and not relative prices explain real exchanges rates movements for the U.S., and that relative prices, not productivity differentials, explain real exchange rate movements for Sweden. Possible explanations for these occurrences are that relative wages or unit labor costs between sectors may be influencing real exchange rates; in this case, equation (7) is violated due to different wages between sectors, and (12) omits an important explanatory variable, unit labor costs.

References

1. Abauf, Niso and Phillippe Jorion, "Purchasing Power Parity during the Recent Float." Journal of Finance, March 1990, 157-74.

2. Balassa, Bela, "The Purchasing Power Parity Doctrine: A Reappraisal." Journal of Political Economy, December 1964, 584-96.

3. Baldwin, Richard, "Hysteresis in Import Prices: the Beachhead Effect." American Economic Review, September 1988, 773-85.

4. Bhagwati, Jagdish, "Why Are Services Cheaper in the Poor Countries?" Economic Journal, June 1984, 279-86.

5. Branson, William. "Causes of Appreciation and Volatility of the Dollar," in The Recent Developments, Outlook, and Policy Options. Kansas City: Federal Reserve Bank of Kansas City, 1985, pp. 33-52.

6. Cassel, G., "The Present Situation of the Foreign Exchanges." Economic Journal, 1916, 62-65.

7. Cheung, Yin-Wong and Kon Lai, "Long-run Purchasing Power Parity during the Recent Float." Journal of International Economics, 1993, 181-92.

8. Corbae, Dean and Sam Ouliaris, "Cointegration and Tests of Purchasing Power Parity." Review of Economics and Statistics, August 1988. 508-11.

9. Couglin, Cletus and Kees Koedijk, "What Do We Know about Long-run Real Exchange Rate?" Federal Reserve Bank of St. Louis, January/February 1990, 36-48.

10. Dickey, David and Wayne Fuller. "Distribution of the Estimators for Autoregressive Time Series with a Unit Root. Journal of American Statistical Association, June 1979, 427-31.

11. Dornbusch, Rutiger. "Devaluation, Money and Nontraded Goods." Exchange Rates and Inflation. Cambridge, Mass.: MIT Press. 1994.

12. Enders, Walter, "ARIMA and Cointegration Tests of PPP under Fixed and Flexible Exchange Rate Regimes." Review of Economics and Statistics, August 1988, 504-508.

13. Engle, Robert and C. W. J. Granger, "Cointegration and Error Correction: Representation, Estimation and Testing." Econometrica, March 1987, 251-76.

14. Frenkel, Jeffrey. "International Capital Bobility and Crowding-out in the U.S. Economy: "Imperfect Integration of Financial Markets or of Goods Markets," in How Open is the U.S. Economy?, edited by Ruth Hafer. Lexington. Mass: Lexington Books, 1986, pp. 33-67.

15. Hendry, David, "Econometric Modelling with Cointegrated Variables: An Overview." Oxford Bulletin of Economics and Statistics, August 1986, 201-12.

16. Hseih, David, "The Determination of the Real Exchange Rate." Journal of International Economics, May 1982, 355-62.

16. Johansen, Soren, "Statistical Analysis of Cointegration Vectors." Journal of Economic Dynamics and Control, June-September 1988, 231-54.

17. ----- and Katerina Juselius. "Maximum Likelihood Estimation and Inference on Cointegration - With Applications to the Demand for Money." Oxford Bulletin of Statistics, May 1990, 169-210.

18. ----- and -----, "Testing Structural Hypotheses in Multivariate Cointegration Analysis of the PPP and the UIP for UK." Journal of Econometrics, May 1992, 211-44.

19. Kim, Yoonbai, "Purchasing Power Parity in the Long Run: A Cointegration Approach." Journal of Money, Credit and Banking, November 1990, 491-503.

20. Krugman, Paul. "Pricing to Market when the Exchange Rate Changes," in Real-Financial Linkages among Open Economies, edited by Sven Arndt and J. David Richardson. Cambridge: MIT Press, 1985, pp. 49-70.

21. ----- and Richard Baldwin, "The Persistence of the U.S. Trade Deficit." Brookings Papers on Economic Activity, 1987, 1-56.

22. Krugman, Paul and Maurice Obstfeld. International Economics, Third Edition, New York: Harper-Collins, 1994. Pp. 422-23.

23. Kugler, Peter and Carlos Lenz, "Multivariate Cointegration Analysis and the Long-run Validity of PPP." Review of Economics and Statistics, January 1990, 180-84.

24. Meyer-zu-Schlochtern, F. J. M. "An International Sectoral Data Base for Thirteen OECD Countries." Organization for Economic Co-operation and Development, Economics and Statistics, Department Working Paper, 1988.

25. Officer, Lawrence. Purchasing Power Parity and Exchange Bates. Greenwich, Conn.: JAI Press, 1984.

26. Phillips, Peter C. B., "Time-Series Regression with a Unit Root. Econometrica, March 1987, 277-301.

27. Pippenger, Michael, "Cointegration Tests of Purchasing Power Parity: the Case of Swiss Exchange Rates." Journal of International Money and Finance, January 1993, 46-61.

28. Samuelson, Paul, "Theoretical Notes on Trade Problems." Review of Economics and Statistics, May 1964, 145-54.

Printer friendly Cite/link Email Feedback | |

Title Annotation: | purchasing power parity hypothesis |
---|---|

Author: | Strauss, Jack |

Publication: | Southern Economic Journal |

Date: | Apr 1, 1995 |

Words: | 5816 |

Previous Article: | A general theory of professional sports leagues. |

Next Article: | The macroeconomic dynamics of tariffs: a symmetric two-country analysis. |

Topics: |