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EMP – A Note on Empiricism and Foreign Exchange Markets
EMP1 Empiricism and purchasing power parity
Purchasing power parity (PPP), in its absolute form, maintains that, in competitive markets free of transportation costs and official barriers to trade, such as tariffs, identical goods sold in different countries must sell for the same price where their prices are expressed in terms of the same currency – this is the law of one price. A study by Isard (1977) compared the movements of dollar prices of West German goods relative to their US equivalents for specific tradable goods. His results showed persistent violation of the law of one price. He concluded that ‘the law of one price is flagrantly and systematically violated by empirical data’; he went on to say that ‘these relative price effects seem to persist for at least several years and cannot be shrugged off as transitory’. Isard’s judgement is echoed by McKinnon (1979) who observed that: ‘substantial and continually changing deviations from PPP are commonplace. For individual tradable commodities, violations of the law of one price can be striking.’ Despite this conclusion, McKinnon is defensive lest he throws out the baby with the bathwater. He observes that ‘until a more robust theory replaces it, I shall assume that purchasing power parity among tradable goods tends to hold in the long run in the absence of overt impediments to trade among countries with convertible currencies’.
Purchasing power parity, in its relative forms, maintains that changes in relative prices of a basket of similar goods among countries determine changes in exchange rates. This form of theory reflects that postulated by Cassal (1921), namely that the exchange rate between two currencies in the medium term simply reflects the ratio of prices of a representative basket of goods, both domestic and foreign, in two countries.
The history of empirical work on purchasing power parity has followed a pattern. Prior to the 1980s, there were many and various tests of Cassal’s medium-term model. Generally, these found that purchasing power parity held as a long-run phenomenon. Indeed, dynamic exchange rate models, as developed, for example, by Dornbusch (1976) and Mussa (1982), began to rely on purchasing power parity as a long-term condition for equilibrium of foreign exchange rates. In the 1980s, much research challenged this view. The orientation of tests moved towards whether the real effective exchange rate follows a random walk. The findings of these studies are by no means unanimous.
Reverting to Cassal’s medium-term model, the consensus of a large number of studies confirms his view – for example, Yeager (1958), Balassa (1964), Treuherz (1969), Aliber (1975a, b) and Aliber and Stickney (1975). Some of these are worth mentioning in more detail.
Treuherz (1969) investigated the relationship between annual inflation rates and devaluation percentages against the US dollar for five South American countries – Argentina, Brazil, Chile, Colombia and Peru – for the fourteen-year period from 1954 to 1967. While Treuherz’s results showed that the relationship between the two variables was weak for any individual year on its own, he found an almost perfect relationship between changes in internal purchasing power and the external value of the currency when using averages beyond four years.
Aliber and Stickney (1975) tracked inflation rates, as measured by consumer price indices, and exchange rates for forty-eight countries over the period 1960 to 1971. Like Treuherz, their results are that for individual years there may be substantial deviations from PPP but, as a long-run phenomenon, PPP holds up well. Their investigation shows deviations from PPP to be far greater for developing countries compared to industrialized countries. The authors note that the use of different measures of inflation, such as wholesale price indices, GDP deflators and so on, would have little effect on their findings.
Gailliot (1970) carried out a long-run test of PPP in its relative form using data covering 1900 to 1967 for the United States, Canada, the United Kingdom, France, West Germany, Italy, Japan and Switzerland. His results support PPP as a long-run relationship – even though his study covered a vast number of shocks to the economies of countries examined.
One of those shocks was the German hyperinflation of the early 1920s. This period provided the database for an investigation of the US dollar/mark relationship for 1920 to 1923. Frenkel (1977) found that actual and expected changes in price levels over this period accounted for in excess of 99 per cent of the exchange rate movement. In a not dissimilar empirical exercise based upon the hyperinflation of Germany and Poland during the 1920s, Huang (1984) found that PPP held as expected.
Generally speaking, international finance specialists in the mid-1970s took the view that, empirically, the key determinant of long-run exchange rate movement was relative purchasing power. Indeed, Hodgson and Phelps (1975) concluded that, based upon a statistical model involving exchange rate movements and prior inflation differentials, it takes some eighteen months for PPP corrections to flow through. Folks and Stansell (1975) came to the conclusion that rates moved very rapidly towards PPP equilibrium. Their study, based upon data drawn from the highly inflationary, flexible exchange rate period from 1920 to 1924, concluded that there was only a minimal lag between inflation differentials and exchange rate movements. The authors of this research believe that their finding is consistent with the efficient market view that because relative inflation rates are publicly available data, they should immediately be incorporated into exchange rates. Undoubtedly, however, the experience of the massive inflation in the 1920s was exceptional, and we should be wary about applying these conclusions today. Drawing on more recent evidence for European countries, Thygesen (1977) found that it took five to six years for inflation differentials for the United Kingdom and Italy to come through in terms of restoration of PPP equilibrium. Thygesen observed that three-quarters of this movement was achieved within two years.
From the late 1970s and onwards, an empirically based argument has raged. Does PPP hold, even in the long run? Using various indices to account for inflation differentials, Kravis and Lipsey (1978) found that PPP held more closely for traded goods than for non-traded items, but departures from PPP were substantial, even over long periods and even for traded goods. Similarly, Krugman (1978) found against PPP. In tests of the floating periods of the inter-war years and the 1970s, he concludes that ‘there is . . . evidence that there is more to exchange rates than PPP. This evidence is that the deviations from PPP are larger, fairly persistent, and seem to be larger in countries with unstable monetary policies.’
This lack of support for PPP is reinforced by Edison (1985). Using monthly changes in the US dollar/sterling exchange rate over the period from 1973 to 1979, she tested how well three models fared in terms of predicting rates. First, a monetary model was used; then the Dornbusch overshooting model was used; and finally a combined monetary/portfolio balance model was tested. Edison concluded that exchange rate behaviour over the period concerned was inconsistent with PPP. Beginning from 1973, de Grauwe (1988) also found against PPP. Plotting real exchange rates for the US dollar against both the German mark and the Japanese yen for the period 1972 to 1986, real exchange rates were found not to hold and fluctuations were substantial.
Not all recent studies reject PPP. Using average quarterly data for the US dollar/Swiss franc exchange rate from 1973 to 1977, Driskill (1981) found evidence of overshooting in the face of monetary shocks. Such monetary disturbances during a particular quarter caused an overshoot to the extent of a factor of 2. Furthermore, any subsequent tendencies towards correction were found to be irregular. Defining long run as a period of two to three years, Driskill found some evidence to support PPP holding over this time span. However, this study covered a very narrow range of exchange rates. This finding is, to some extent, supported by Everett, George and Blumberg (1980), who have achieved more than a random degree of success in forecasting long-run exchange rate movements based on restoration of PPP. Rush and Husted (1985) have also found long-run support for PPP in Japan, Canada and various European countries. And Manzur (1990), looking at a wide spectrum of exchange rates, investigated currency movements with inflation – due allowance being given in respect of trade weighting. He found that PPP cannot be rejected over the long term but is convincingly found not to hold in the short run. Manzur’s evidence suggests that PPP, based on a weighted basket of currencies, tends to reassert itself over a period of about five years.
A new development in testing long-run economic relationships has emerged over the recent past. This is the co-integration technique. Its development and application for the analysis of time series have been associated with Granger (1986) and Engle and Granger (1987). Many economic time series have a long-term change in the mean level – they may show a trend up or down over time in a non-stationary fashion – but groups of variables may be inclined to drift together. If this is the case and there is an inclination for some linear relationship to hold between a group of variables over a long period of time, then co-integration analysis will help to determine this relationship.
Many economic theories are concerned with equilibrium relationships, but the equilibrium relationship may not hold at all times. The distinction is made between the short run and the long run, with deviations from equilibrium in the short run but, in general, the equilibrium relationship holding in the long run. The co-integration techniques applied to time series analysis may provide a formal framework for testing equilibrium relationships of this kind. Co-integration analysis can be used to test the validity of an economic theory, if the theory involves groups of variables that trend up and down over time in a non-stationary fashion.
The PPP relationship is a classic example of an economic theory under which certain variables should not tend to diverge from one another without limit. There have been various recent tests using the co-integration methodology. Taylor (1988) tested nominal exchange rates and relative manufacturing prices for five major countries – the United Kingdom, West Germany, France, Canada and Japan. The PPP hypothesis was tested over the floating exchange rate period since the demise of the Bretton Woods system. The results found little evidence of PPP holding. Taylor was unable to reject the hypothesis that the nominal exchange rates and prices for the different countries tended to drift apart without bound. But Taylor and McMahon (1988), using co-integration techniques, found that, in general, long-run PPP held among the US dollar, the UK pound, the German mark and the French franc during the 1920s. The single exception to this was the dollar/sterling relationship. In an even more rigorous examination, Taylor (1992) looked further at the long-run PPP relationship for the dollar/sterling exchange rate during the 1920s. This time, a stable equilibrium relationship for the exchange rate was found. Taylor argued that the tests used earlier lacked power and the wrong conclusion had been drawn in the earlier analysis.
McNown and Wallace (1990) examined PPP data to determine whether exchange rate adjusted price levels between the United States, Japan, the United Kingdom and Canada formed a co-integrated system. During the fixed rate sub-period, the Japanese and possibly the Canadian wholesale price indices were found to form co-integrated systems with the United States. With the possible exception of Canada, co-integration was rejected for the recent period of flexible exchange rates. In the period from 1957 to 1986, evidence of co-integration was only found for the United States and Japan. No evidence of co-integration was found for any period for Great Britain. Johnson (1990) explored the PPP relationship between Canada and the United States using co-integration techniques. He found strongly in favour of a PPP relationship, particularly over the period 1950–1986; this is in keeping with the findings of McNown and Wallace.
Phylaktis (1992) used co-integration techniques to test the PPP hypothesis between Greece, the United States, France and the United Kingdom for a short period in the 1920s. The evidence supports PPP for the Greek drachma and the US dollar, as well as for the French franc and the UK pound.
Using data for Australia, New Zealand and the United Kingdom, Richards (1993) used co-integration techniques to determine whether a PPP equilibrium was apparent. The tests were carried out over the period from 1948 to 1992. She found some support for long-run PPP having held between New Zealand and the United Kingdom but generally rejected the PPP relationship for the three countries tested.
Another area of interest in recent investigations of PPP has been concerned with testing whether or not the real exchange rate follows a random walk. Important investigations by Roll (1979), by Pigott and Sweeney (1985), by Adler and Lehmann (1983) and by Hakkio (1986) have not been able to reject the hypothesis that real exchange rates do follow a random walk. If this is so, Abuaf and Jorion (1990) conclude that ‘the random walk . . . has the disturbing implication that shocks to the real exchange rate are never reversed, which clearly implies that there is no tendency for PPP to hold in the long run’. By contrast, if PPP were to hold, we would experience a mean-reverting process. At least one of the above researchers, Hakkio (1986), is sufficiently doubtful to state that ‘though the hypothesis that the exchange rate follows a random walk cannot be rejected, not much weight should be put on this conclusion’. Both Pippinger (1986) and Levi (1996) refer to a number of weaknesses in the statistical tests used in evaluating PPP.
Not all random walk tests have come out against PPP. Work undertaken by Cumby and Obstfeld (1984) and Cumby and Huizinga (1988) on expected exchange rate changes and relative inflation rates found that real exchange rate changes were somewhat predictable. Investigating the behaviour of long-run real exchange rates, Huizinga (1987) found a tendency – albeit statistically insignificant – towards reversion to the mean. Abuaf and Jorion (1990), studying exchange rate data for six European Union countries plus Canada, Japan, Norway and Switzerland for the period from 1973 to 1987, and applying more sophisticated statistical techniques than heretofore, concluded that ‘the empirical results . . . cast doubt on the hypothesis that the real exchange rate follows a random walk’. They found clear evidence of a tendency for real exchange rates to revert to their central value. Interestingly, they also conclude that ‘a 50 per cent over-appreciation of a currency with respect to PPP would take between 3 and 5 years to be cut in half. Similarly, analyzing annual data over the period 1900–1972 reveals that a period of 3 years is needed for such a reversal.’
If there were a tendency for the real exchange rate to return to its initial value, then it may reasonably be argued that PPP holds in the long run. The tendency for a time series to revert to its mean – mean reversion – is characteristic of a stationary time series. A random walk is an example of a non-stationary time series because it hold no tendency to return to its starting, or any other, value. Meese and Rogoff (1988) and Mark (1990) have been unable to reject the possibility that the real exchange rates evolve as a random walk without any mean reverting properties.
FIGURE EMP.1 ABOUT HERE
Mark (1995) also provides strong evidence that the long-run path of the exchange rate can be accurately gauged from knowledge of the current level of the rate relative to its equilibrium value in a monetary model. The adjustment path corresponds broadly to the overshooting path described in Figure EMP.1. In fact, Mark’s results confirm this hypothesis. Mark found that his model explains between 50 and 75 per cent of the variation in the US dollar’s exchange rate against the mark, the Swiss franc and the yen over three and four year horizons. But Obstfeld (1995), studying exchange rate changes and inflation over a 20 year period (1973–1993) in the modern floating currency era, has concluded that the long-run variation in exchange rate changes across countries is largely dependent on differences in rates of inflation.
The most complex problem in testing the empirical validity of PPP is that the real exchange rate itself need not be constant. Real variables, such as real income and real interest rates, may change permanently if there is a permanent real disturbance. The real exchange rate might also change on a permanent basis if a real shock affected one country but not its trading partners. That the long-run path of real exchange rates is constant is a convenient assumption. It might plausibly be based on the assumption that while real shocks occur, they affect all countries more or less equally, leaving long-run real exchange rates unchanged. However, for nations that experience country-specific real shocks, such as the discovery of significant new oil resources or the abandonment of distorting market practices, a change in the long-run real exchange rate remains a possibility – see Edison (1987). But evidence of the long run mean reverting behaviour of the real exchange rate is extensive. And this is consistent with PPP working well in the longer term.