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

• Author: Strauss, Jack
• Position: Purchasing power parity hypothesis

1. 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.

2. 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...