Purchasing power parity under fixed and flexible exchange rates

Journal of International

PURCHASING

Economics 8 (1978) 247-276. Q North-Holland

Publishing Company

POWER PARITY UNDER FIXED AND FLEXIBLE EXCHANGE RATES Hans GENBERG*

Graduate Insti: :te of International Studits, Geneva, Switzerland Received June 1977, revised version received December 197!‘ The relationship between exc-Ldnge rates and relative price levels in a sample of fourteen countries is studied for periods of fixed and of floating e>;change rates. In comparing tho deviations of the exchange rates from their purchasing power. parity levels in the two casts it turns out that both the average siie of the divergencies and their duration are smaller under the fixed rate psariod 1957-66 than under the recent period of floating rates. The adjustable %?eg years of the late sixties fall in between. Evidence is also found which indicates a bias in purcbaskg power parity calculations using consumer price indexes, and the hypothesis that purchasing power parity relationships shifted as a result of changef, in relative prices occuring at the end of 1973 car not be mjected. The findings are re’ated to the empirical literature on the internatic,nal tr~nsmissio:n of inflation and to recent comparisons of exchange rates and relative inflat ion rat es.

5. Ilatrodllctioll

T?re purchasing power parity (PPP) relationship is a relevant #concept under kjoth fixedi and flexible exchange rates, It. has been used as an explanation of both the international transmission of inflation and of movements in a freely floating exchange rate. Yet, there exist important differences in the PPP r,elation. hip under one as compared to the other exchange rate regime. The t.ime pro.‘les of short-run deviations from thr; PPP path can provide useful irtformaticln about the reasons for these different es. They also suggest hypothesis concerning tile sources of the transmission of economic disturbances between countries under the two systems. For these reasons, this paper will be concerned with. the application of PPP theory to both type: of exchange rate arrangements. A substantial part of the empirical evidence will be used to compare exchange rates and relative price level movements in the two cases., The remainder of the gaper is divided into three mtin parts. The first is concerneci with the transmission of inflation under fixed exchange rates and its implications for the purchasing power parity relationship. After a very brief review of the relevant theory it contains a fair!y extensive urvey of the eulpirical evidence which is used, together wi some additional new evidence, to derive *IIelpful ~commenis from Rudiger Dombusch and Michael Pa&in on an earlier draft are gratefully acknowledged.

248

H. G&erg, PBP: Exchange rates

some implications for what should ‘be expected from PPP theory mde.r flexible exchange rartes. Part 3 of the paper is concerned directly with PPP under floating rates. The theoretical discussion is again kept to a minimum and the focus is on the present&ion of empirical results and on a comparison and evalua.tion of other recent empirical st,ud&. The topic concerned with the determinants of shortnm deviations from PPP i:s also introduced. The final part of the paper offers some general conclusions of the analysis, draws attention to a numlber of unsettled issues and policy implications, ;md provides suggestions for future research. 3.

Transmission of ihfiatioxnunder fixed exchange rates

Discussions of the transmission of inflation naturally start wit.h a p+e increase abrmoadand then try to identify the channel by which domesitic prices are affected.. The: most common such channel is probably that suggested by the arbitrage hypothe:sis. This hypothesis, which is also referred to as the traded goods mode:1 UI the law of ane price, simply states that the price of a hoanogeneous ,=ommoldity must be the same in all countries provided the market for this commodity is internationally integrated.2 A price increase abroad will, oa this hypothesis, lead to an immediate increase in the domestic price xvithout even the need fiar flows of goods to occur. Such flows constitute an Integral pz::^tof a channel of transmission under which an increase in the foreign price of imports ieads to a temporary deterioration of the terms of trade, an increased flow of exports as consumers and producers react to altered relative prices, and finally increased export prices and a return of the terms of trade to its initial level either as exporters meet the augmented demand directly by increasing prices c: as tlhe higher rate of prcriuction hits capacity constraints and leads to cost and ,price increases.. The third route by which an observed price change abroad would get trsnsmi~tted is through the expectations of domestic firms and househlslds which, by anticipating the future transmission, will act so as to bid up prices today. The practlice of starting out the analysis of transmission with an exogenelo’ns price changl:: abroad .may be misleading. Factors which generate inflation abroad may themselves tend to get transmitted and thus create domestic ‘A large literature n.ow exists on xhe theory of the international transmission of inflat ion. 4rticlw of a survey type are, for instance, OECD (1973), Selant (1977), Sweeney a-Id Willet (14X More speciiic are Branion (1977) and Swoboda (1977). See also the references listed in these p-;ers. 2‘Integra&’ 51--:.:!L ’oe interpreted broadly, and includes conditions on infurmation and transaction costs in pkrticukr. Provisos relating to transportation costs, tariffs, etc. are Aso recognized by this hypothesis.

H. Genberg, PPP: Exchange rates

249

mflation ~norz or iess simultaneously. The issue of the generation of inflation should not be separated from that of the transmission. Among the proximate causes of; nflatiorxit is monetiryimpulses which have received the most attention in the recent international transmission literature. This may be justied on the basis of empirical evidence ‘,,ut, as we shall see, there is also strong evidence that direct measures of excess demand in goods and labor markets move in harmony across countries which may be taken as evidence of the functioning of other conduits. The mos$ common of these is of course the well-known foreign trade multiplier mechanism. But also here it would appear zhat the formation of expectation could play an important role if fGr instance domestic exporters make plans for the supply of goods and the demand for factors of production on the basis of their judgement not only of the current but also of the future state of demand in their export markets. 2.2. Empirical evidence 2.21. Okaggregated price hdexes. The closest one citn get to the ideal conditions for the pure arbitrage model is probably by co.nparing price quotations on the major commodity exchanges. Here it is possible to narrow &wn differences in quality and specification to a minimum, information on price and quality is readily and chc-aply available, and cornpetition ensures that no extraordinary profits are made on a consistent basis. If changes in prices of comparable commodities on these commodity exchanges did not conform to the predictions implied by she traded goods hypoth.esis we could probably stop right away and deciare the transmission mechatissrr. via arbitrage rejected by the data. Fortunately it turns out that this ver;) weak test of the traded goods hlypothesis does support the notion of integratec. woAdwide markets in these narrowly defined prod.ucts. Genberg (1975) use(q data published in the InternationalFinancialStathtics on whole-sale prices .5,r cacao, copper, copra, jute, rubber, and tin to compare quarterly price ch:.nges in eight different lacations in the ~~orld. The results cast no doubt on the appropriateness of the arbitrage hypothesis for these commodities. When we turn to slightly less ideal conditiorz for the arbitrage model there is more room for scepticism. Isard (1974), Kravis and Lip.;ey (1977), and Bordo and Choudhri (1976) all present evidence based on rc:M\ely narrowly defined commodity groups which cnlls into question the la,w of one 9rice.3 Isard compared monthly indexes clf German export priz, Japanese export prices and U.S. wholes.ale prices for eleven different commodity classifications for the period Jan. 1968 to Nov. 1973. His results, subjec,. to some qualifications to be mentioned ‘below, are c?uite clear on one point; t 2ere is substantial flexi%ard Emas entitled a revise price 1’.

H. Genberg, PPP: Exchange rates

250

bility of relative export prices between countries. This implies a rcjecticn of the hypothesis that exports of Germany, Japan, and the TJnited States are s’uch close substitutes that their relative prices do not change. As to the sec:ond plaint which Isard addresses, the evidence, as I interpret it, is less unambignous. Ilsard compares relative export prices, measured in U.S. dollars, with the relevant exchange rate and finds a pcsitivt: relationship when Germany and Japan are compared w,th the United States. This means that if the dollar is devalued relative to the mark or the yen, Gemian or Japanese exports become relatively more expensive than U.S. exports (as proxied by the WPI). When Germany is compared with Japan, however, the relationship is the opposite. One may inerefore question Ylsard’sassertion that ‘th.e evidence suggests tha.t exchange rate changes do have substantial permanent effec+c on these relative dollar yrrce indexes.’ It appeal s that this conclusion first of all is sensitive to the choice of countries for the ct)::lparison. Secondly it may be more justified to speak of exchange rate changes having ‘substantial prolonged effects’ rather than ‘substantial permanent effects.’ Kravis and Lipsey use yearly data on export prices of machinery and equipment (SITC 7) for the United States and export prices of manufacturing products in Germany to test a number of hypotlzeses relevant far the present discussion. Referring to their earlier work [Kravis and Lipsey (1971)] they first show that ‘prices may differ substantially for competitive products exported by different countries .’ This finding reinforces that of Isard which implied a relatively low degree of substituta’bility between countries’ exptirts and a high degree flexibility of’ the terms of trade. Kravis and Lipsey also present regression results shelving thilt changes in the DM/$ exchange rate has affected the price of U.S. expo,ts re.lative to the domestic price of the same commodity group and their data imply that the relative price of U.S. and German exports is also altered. The duration of these effects is hard to ascertain but it seems to be substantial. Bordo and Choudhry carry out two types of statistical tests with quarterly data, spanning 19tiS/II to 1974/N, on price indexes for eighteen industry groups in the United States and Canada, First they estimate an equation of the type dlOg

Pi -- &+Jl

dlOgP[+Az

dlog e+A, Alogp-t-u,

where Pi = the Canadian price of the output of the ith industry in $ Can., pif = the U.S. price of the output of the ith industry in $ I J.S., e = the exchange rate. $ Can. per $ U.S., P = the Canadian implicit GNP price deflator. The :-esults, which in general are not sensitive to a classi ‘~2tion into a trJdec aI; L a ncniraded Izategory, show the estimates of *4, to bl: : her of the wrong

Ii. Ge&wg, PPP: Exdzange U&J

251

sign (negative) or significantly different from zero. 4, on the other hand is often positive and significant. The arbitrage model again seems at variance with the data since it jmplies that A1 = 1 and A3 = (:. Part of the explanation for the negative result for the coefficient on the exchange rate may be due to the small variance of this variable during the samp e period, a point which Bordo and Choudhry recognize, but the sig.tificant e:fect of the general price level is unmistakable. The second test the authors carry out involves findin ; a time series representation of the ratio PJ(e P{) and studying the properties of this time series. The arbitrage hypothesis of course jmplies that this ratio should be unity and one might want to find out first of all if the data support:s this hype-&esis as far as the average value is concerned. 3f so it would be of in:erest to try and estimate how protracted the deviations from this value have been. The evidence, again, is not very favorable to the arbitrage model. For several industry groups the time series representation of the ratio is not stationary implying no tendency for it to t%nd to a constant value. For others, the ratio does E=em to oscillate about a constant mean, but the conl’ergence to that mean is very slow. For only one industry group is the mean time lag less than one year. The implications of the difference between the results based on prices on the commodity exchanges and the data on more agyegate
252

H. Genberg, PPP: Exchange votes

ing the duration of the effect of changes in exchange rates on relative prices should be high on the agenda for research on commodity price behavior. If the caveats I have: raised turn out to be not important then the conclusion of this section must either be that the transmission of inflation (Jr the estatdishment of purchasing power parity is something which takes quite a long time or that direct goods arbitrage plays a relatively minor role in t%s process, 2.2.2. Transmission ofgeneral price irljlation (i) Dispersion and cowergence

of in$?at!on rates. Purchasin power parity under fixed exchange rates implies that inflation rates must, subject to certain reservations,4 be eqtu. in all countries of an integrated world economy. By computing the variance of inflation rates across countries at a point in time one could test this proposition were it not for the difficulty in determining what constitutes a ‘small varianc,e. Genberg (1977b) computed the principal components of the price levels (and rates of inflation) of 21 GECD countries. In a period of absolutely fixed cxchangc rates the first principal component could explain 97.5 % of the variance of the 21 different price levels and 38.2 % cf the variance of the yearly inflation rate:;. These percentages were shown to compare favorably with similar figures based on computations carried out on the 21 commodity categories making up the U.S. consumer price index [Hester (1973)].’ Another standard of reference that has been used is the variation in the rate of inflation within a country as me;lsured by regional consumer price indexes [Genberg (1975), Pattison (1976), V.Wbe1 (1976)]. The upshot of these comparisons seems to be that the variation between countries is higher than the variaj.rlce within countries when the computations are carried out at single points in time.” As noted by Vaubel this standard of reference may be rrnrealistically stringent when one takes into consideration differences in methads of index construction between countries, differences in the levels and ehangcs in indirect tales, differences in governmentally administered prices, etc. A final way to analyze cross-country variation in inflation rates ma;; be to try to determine if there has been a convergence of inflation rates in tbe Jiense that standard deviations, have followed a downward trend since tlx war. Farkin (1977a) argues, by Inspecting a time series plot of standard &via .;ons of yearly inflation rates. in the Group of Ten countries during the pc-riod 1950-75, that the Ziffermce between coa:ltries was considerably smallr+r in

4See for instance Swoboda (1977). Q is interesting to note that calculations of principal components of interest rate .mries drawn from six west European countries plus the United States does not pr-Auce higher explained percentages than those based on price indexes despite the alleged higher international Integration of capital zmarkets as comparei to goods markets ISee Logue, Salant. and Sw~zney (I 976). J 6Genberg’s results which do not show hi her CrOss-COUntry varintlce depend upoil J c%YSSification of quarters into high, medium, and low in& ‘ioo pertods. This could possibly &id to biases, and may be the reason for the different conclusion.

His chart indicates further that there seems year the standard deviations is, w%ch wilt be investigated ue tQ (6i hW% rSdtt?d ill) this date. The simprest ki

wcr idea under fiaredexchan

el which captures

rates is

(2) whem Ps stands for tkc price level in country i and Pf +tnds f+r an appropriate measure of the foreign price level. The systematic part of equations ( f ) and (2)

t of as representing a long-run purchasing power parity constraint the properties of the error terms woul~:ldescribe the nature of om it. Par the long+=unconstraint to TXsatisfied it is necessary 0, and fir = 1 Furthermore, evidence of serial correIation ce term in equation (1) would indicate that there may be prctracted short-run divergencies fpom PPP. Serial correlation in equation (2) Woitld mean not only that a country’s price level may be different from its PPP level but that the divergence may increase uring several coMcutive ob~rvation periods. 7a) estimated equations (1) and (2) for ten European countries ta on consumer price indexes span&r 1955-1970. Neglecting the results and relatively minor differen s between the countries the results confirmed the I run version of the rchasing power parity atraint in that the es~rn~ of the coetfkients cvnforrled to the a priori

254

H. Get&erg, PPP: Exchange rates

lag involved in the reestablishment of purchasing power par@] after 8 skxk was on the average two years for the countries involved in the regress;3ns.g Suggestive as they are about the degree of validity of the puxhltsing power parity hypothesis under fixed exchange rates, the above results based only cr11 comparisons of domestic and foreign price indexes are incomplete in several respects. First of all they do not contain any information on the reasons for the divergences from PPP. Secondly, they do not address the question ot w mechanism brings relative prices into line, and thirdly they are silent on the issue of how far from its PPP level a country’s price level can get and the consequences of getting there for the balance of payments, the level of emgloymt:nt, domestic relative prices, etc. The first two of these questions have been investigated directly or indirectly in a number of studies which aim to estimate individual countries’ price equations. Cross and Laidler (1976) ;md Laidler (1976) set out to test a model in which the rate of inflation in a given country is determined by the expected rate of inflation and a measure of excess demand for goods and services is the economy. Influences from abroad are assumed to enter the determination of domestic inflation through the formation of price expectations, it is specified that domestic agents base their expectations partly on the rate of inflation in the rest of the worid. On balance the evidence implies that the rate of inflation in a country with a fixed exchange rc?te will converge over time to that in the rest of the world. This follows from the estimates of the coefficient on the expectations variable which is not signiticantly differen:. f:om unity, and the fact that. the foreign inhation rate seems t 0 play an important role in expectations formation. The convergence process i,c.estimated to be rather slow, however, the mean time !ag, between a change in the foreign inflation rate and its incorporation in domestic price expectations, varying between two and five years depending on the country. Remembering that t!zse time lags refer to the convergence of inflation rates an;f not price I;vels, these estimates can only be consistent with the evidence drawn from Genberg’s e&mates of equation (2) if the transmission of inflation is carried out to a large extent by the excess demand variables in the Cross and. La.idler mcdei. A spot check of this hypothesis using data provided by Cross and Laidler, reveals that for at least one country (Sweden) it is correct since the co-relation coefficient between excess demand in the Woild as a whobe and excess demand in Swede:n is 0.82.” gThe mean time lag ib defined here as the length of time it takes for approximately 6:; YL of an initial divergence from PPP to disappear. The distribution among countries of the rn~~n lag is: Austria 2.0, Belgium 3.0, Germany 1.0, Italy 3.2, Luxembourg 1.6, Netherlands 0.8, Norway 0, Portugal 4.4, Sweden 2.0, and Switzerland 2.1 years. ‘%:To and Saidi {19’74;\also find e-;idenc,: of rapid transmission of excess Anand in 1-5~ labor market. Their ‘results suggest that nnovc:t:on~ in the U.S. unemploj meat rate rend to be transmitted on almost a one-to-one ba~;is to Cawdian employment, and that this linkage: i? independent of the ruling exchange rste regime.’ Tb transmission is furthermore shown to be contemporaneous.

ets,captnred

directly by a term red by the rate of than at these either enter di Ieence domestic prices through a mclrk up proc intermediate goods.’ 2 The pact of fiscal and monetary po!icy impulses ~~~~tivc~~ and the symbol x stands for various other measures of excess demand in the domestic economy. The enlpirical counterparts are usw 11: taken to be either the deviation of current ouqxt from trend or potential output, tie uremployment rate, or the difference between ;he unemployment canGvacancy rates. No attempt will be made here to review in detail tht: differences and similaritie- between the empirical estimates obtained in-.$: *Iany Jountry studies in whch a form of (3) has been estin?a:z!. Only the gere * 4 thrust of these findings will be retamed in order to establish more cl :arly by Hk3t mechanism purchasing po\ver parity gets established if it IrAdeeddoes. First of all it is noteworthy that the &mates of rr, the coe&ient on the import price variable, is almost universally below zmity and ofteu by a large marqin svhen yearly data are rvsed. This suggests either that fo impulses take longer n a year to have a substantial eff&$ on the dom c economy or that ot variables constitute gested a large part of the transmission mechanism. This has already been asures in the discussion of the work of Cross and Laidler. The excess demand y ok,en si~i~~ant explanatory factors. This is sometimes summarized by x are t thare is substantial scope for inflation rates to diverge ioterpreted to lean even under fixed exchau c rates. As already noted, this dock not follow if cycles in real czsnomic r.ivity are ~y~chr~~i~~d ir~tc~ation~~~~ because then excess demand in any particular cc~~~~~~yis merely tt reflection of ~~n~r~li~c~ CXCYSS demand the world over. As long as the MNIICCof t excess demand is is to took at the not specified, a more appropriate test of domestic ~ut~~~ effects ctf monetary and fiscal policy tools under the control of do makers. Here the interesting result emerges that, at least for the llSee, for instance, the ern~jri~~iy oriented c~nt~but~o~ in K~a~ss annd $a~~~~ 41947), ~s~~a~~e~ (1977). ~Tlni ~~~7~~,K~rt~~~ ’ ?ll~e coefficient (I~ dczs therefore not measure the strength of the purchasing pow% parity relationship since the relationship between our import price index and geneA price level indexes abroad is not taken into account. I &ail elaborate on this point below.

256

H. Genher,y, PPP: I jcckmgera,tes

[Korteweg (197513 and to some extent fur Switzerland wasserfallen (:977)], fiscal policy impulses have little or ndb ef?ect on inflation and that monetary impulses have their strongest and most ,i,~ificant effect when they are measured by the rate of change in the worLJ money sfock rather than the domestic money stock. This is corrsistent with a monetarist hypothesis that the main determinant of general inflation is excessive monetary expansion. The latter should ho:vever be measured by the rate of change in some worid a.ggregate money- stock under fixed exchatnge ractes because internationai trade, financial, and expectational linkages distribute disturbances rapidly throughout the world. ecLgnomy. This line of reasoning should clearly not be carried too far, and them is evi’dence that it is not entirely satisfactory. This evidence emerges when the variabit to be explained in tbe regression model is not the rate of inflation itself but rather the rate of change in the ratio of domestic to foreign prices cr alternatively the ratio of non-traded to traded goods. Both Blejer (1977) working with Mexican data and Myhrman (1976) analyzing Sweden find that domestic monetary policy has some influence in this case. The quantitative importance of their results is di3icult. to determine from their reported results but Blejer states that domestic monetary policy will havle relevant effects for a period of about three yes rs.’ 3 Before turning to simultaneous models which incorporafs ;a number of possible transmission mechanisms in ‘structural’ equations, it :is useful to take up a CIASSof models which has become popular recently and which constitute a move towards multi-equation systems. This class of model .which is represented in the work of Goldstein (1974) and Calmfors (1977) anong others contain both a price equation and a wage equation and allows for some limited interaction between the two. In Calmfors’ rt:presentation the chain of causation can be described as follows.1 4 Foreign factors are the main determinants of prices in the sector of the economy producing traded goods. Wages in this sector are determined partly ‘by current otrtput prices adjusted for the level of labor productivity and partly by excess demand in the labor lnarket. The tradable goods sector is furtheimore considered to be a wage leader in the sense that wages in other sectors of the economy passively follow those set there. Prices of non-traded goods are determined by a mark-up process over unit labor cost in. this sector. The general price level is finally made a function of the prices of both traded and nont:;rded goclds which implies that the reduced form expression for the dumestic price level will contain a distributed lag function of the price of ,tradeables and of excess demand in the labor market. 1“It is interesting and imp0rtan.tt:, not ice that both jBlejer and Myhrman find that monetary policy has a stronger effect on tke balar,as of paymtrlts than it does on the relative price of nonir Aed goods. ’ W-ie reader kmi~ ..tr n :&I ’ ” the so called Scandinzv,an model of inflation I:,Qukrust (‘1975), Edgrer; Faxen, Ohdr ::I~(19731 will notire that Calr&rs uses the same general structure and chain of cauzatlon but adds an excess demand variat:!e in the wage equations.

H. Genberg, PPP: Exchange rates

257

This is essentially identical to the price equation discussed above (eq. (3)) so the limitations, with respect to its usefulness for purchasing power parity comparisons, pointed out there apply to the wage-price models as well. If excess demands are transmitted rapidly between coun.tries, then any difference in inflation rates betbveen two economies is entirely due to differenaces in the length of the causal chain in each country and not the absolute length itseEl Thus it may be perfec’bly consistent to observe a long lag between r;hanges in import prices and the reaction of domestic prices and wages and at the same time observe purchasing power parity holding with respect to general price levlel indexes. In order to be able to infer anything more about PPP from equations which include goods, labor, and money market excess demand variables than from simple cross-country comparisons of price levels or inflation rates we must thus inquire about the intercountry transmission mechanisms of these excess demands themselves. An attempt to survey all tht: relevant empirical evidence on this issue would take us too far from the main track off this paper so we conclude this section with some observations based on evidence obtained from a limited number of multi-equation models of open economies. An advantage of simultaneous equation models in the present context is that they make it poslsible to isolate the various transmission mechanisms which work to spread infiationary impulses across countries. In order that proper account is taken of the interrelationships it is desirable that the eqluations be estimated simultaneously because only then can the interactions be reflected in the parameter estimates. l?ecent work using a full information maximum likelihood technique for estimating differential equation systems have produced quite interesting insights with respect to the international linkages afYecting an open economy. The models of the U.K. economy by Jonson (1976) and Knight and Wymer (1975), those of Germany and France in Sassanpour and lsLet PrA be the general price level in country A at time t and suppose

where L is the lag operator, PT is the world price of traded goods, and XA stands for excess demand and other variables affecting country A’s price level. For country 3 we have PrB = g,(L)P,T-tg2(L)XtB+stB,

which if subtracted from the above gives PSA = PfBf [f,(L)-g,(L)]P,~+.h(L)X,A-ggz(L)J

r~+cld---EtB*

If the excess demand variables are highly correlated so that XzA Y XtB, then the difference b::tween F 4 aild PB is seen to be dsle entirely to differences in the lag functions ,fi and gl describing :the response to world-wide price shocks or to differences between fi attd adz, the time pattern of response tc excess demand. Equation (1) can be thought of as an. approximation to she last equation ~i~~ve where PT and X have been replaced by their time series. repremntation. On the present ,nterpretation the terms U, in (1) would be a function of both fl(L)-gn(k)aad f2(L)-g&C), andthe clc?jer to zero these differences are the closer U, would be tc pure white noise.

258

H. Genbeb-g,PPP: Excknge rates

Sheen (19771, of Australia in. Jonson, Moses and Wymer (1976), and of Austria Bauagartner (1976) are all fairly standard macro-models AS far as longer run equilibrium properties are concerned a>ld their short-run dynamics is governed by adjustment functions in differential equation form. The Iprice equations in these mod&, which are of main interest here, are generally specified as (3) above with both foreign price? and various forms of d.omestic excess demand and policy variables included as explanatory v~izblts. It is therefore interesting that the direct influence of foreign ,nrices almost always loses in significance when estimated in these mcltiequatio:l structures compared to the single equation models The more elaborated the model the smaller the importance of this term. Transmission of foreign impulses is instead carried by other means such as relative price effects in import and export functions, variations of exports due to foreign income changes, and the repercussions on the domestic money supply of balance of payments disequilibria. These traditional transmission mechanisms are always found to be working in the pro,per direction and the corresponding coefficients generally have high degrees of statistical significance. It is noteworthy for the discussion of PPP under flexible exchange rates that the balance of payments process distributing monetary disturbances is the quickest of the three, in some cases disbursing the major part of a monetary impulse to foreign countries within one to two quarters whereas the effect on prices and incomes and therefore on exporl:s and imports is sprearl over a longer time period. An evaluation cf the empirical relevance of the PPP concept on the basis of the structural models is unfortunately difficult for two reasons. The :brst is the neglect of price expectations 5 la Cross and Laidler in. the price equation. The signiticanse of this variable in single equation contexts may carry over to large models and if so it may have an important bearing on the relevance of PPP under flexible exchange rates. The second shortcoming of almost all simuhaneous models it that they tl-eat foreign prices as parametric.16 A typical experiment is thus to trace the effect of a once and for all increase in this parameter on. say, the domestic price level and then make statements about the lag in the transmission of inflation based on this. We have already pointed out the error in this procedure :n connection with rhe discassion of the meaning of the coefficient of the forcigar price variable in equation (3). The proper procedure for the analysis of the speed of the transmission pralcesses is to start with a foreign disturbance such as an increase in the ex.ogcneous source component of the foreign monetary base and to determine the timing of its influence OE both foreign and domestic prices.l” Differences in the behaviour

in

’ 6Thisshortco:ningis of course present in single-equation modeis also. ’ ‘Welliuell and Maxwell (1974) carry out exactlv this exercise in linked simulations rll”the RDX2 model of ranada .and the MPS model o”f the bjs, Unfortunately, their publhhed results are not in the form that they can be used to shed muc’h light on the PPP issue considered here.

H. Genberg, PPP:Exchmge

rates

259

of the two countries’ price levels can now be traced to different adjustment speeds following a common exogeneous impulse as shown in footnote 15 above. 2.3. Summary of the evidence ,fiom fixed exchange rates and its implications for purchasing power parity underfloating rates 2.3.1. Price index comparisons. In attempting to evaluate the evidence on purchasing power parity under fixed exchange rates that has been surveyed in the previous section one must once again face up to the difficult question of how closely price levels must conform to their PPP paths in order for the theory to bc accepted. The answer will undoubtedly depend on to what use the PPP theory is put which means that no absolute standard is likely to be found. This in turn implies that my interpretation of the evidence, an1 probably that of the reader, is going to be influenced to some extent by our predispositions to the theory. On the basis mainly of direct comparisons of price ievels and rates of inflation in industrial economies I would argue that there exist strong forces tihich keep price levels from deviating substantially and for extended periods from the paths dictated by PPP under fixed exchange rates. Table 1 gives some information about the average size of deviations from PPP and the distribution of these deviations for a number of countries and time periods. The figures in ~01s. l-3 of the table are based on the estimated residuals of regression equations of the type

log (eg*P;r/P,.,)

= a+bt+u,,

where the superscript ‘eff’ indicates that effective exchange rates and foreign price levels are used. The equation hypothesizes that the natural logarithm of the ratio of the effcvtive foreign price level, converted to domest:ie currency units by the effective exchange rate, to the domestic price level is equal to a constant plus a time trend. As will be explained in more detail below, the i;onstant term is included in order to adjust for differences in base peri’ods among countries’ price indexes. The trend term is intended to capture the effect on relative prices of diverging structural developments in each country. The consumer price index in each country was the measure of the price levels and export shares were used as weights in the effective rate calculations.‘8 The time unit was one year. In table 1 the average of the absolute values of the residuals from (4) are given for the fourteen countries in the sample and for three time periods, 1957-1966, 1967-1972, and 1973-1976. The first period was one in which exchange rate changes were relatively rare, being confined to those of France (1957 and 1958) and of Germany and t e Nether;.ands (1960’” 1*A more detailed description of the data can be obtain&

upon requestfrom the author.

i gCanada of course had a flexibleexchazqe rate from 1959 to 1962.

, PPP: Exchange rrltes

ationfromPPP o,f1.2‘4 the

degree of ‘=c?rrespond.ience _rtgerates to PPP is the seatest for this time period. ix yeats of adjustable but net floati;zg exchange rates witnessed and revaluations culminating in the reaEgnment s coated with the Smithsonian agreement in 1971, The &’ the average residual reflects tbio increased tendenc,y among use exchange rate changes to cure balance of pzy_mnenta future referenct: the still larger residuals mlhen Myfloating rates is included. Table 1 deviations from purchasing power parity.= (21 1957-72 W-I___-

(31 1957-76

t.7 3.1 1.5 1‘3 I.8 3.0 2.1 2.3 I.0

3.8 3.8 2.0 2.1 2.0 3.0 2.7 5.8 1.7

A:: ::;

2.9 1.4 3.3 5.8

2.2

3.8

1.9

3.2

(41 1960-66

(5) 1960-72 --.-

05) 1960-74

0.8

2.0

2.5

1.1 1.8 1.4 1.1 1.3 1.3

1.3 1.6 2.2 I:: 1:9

1.4 2.2 2.4 25, 2.0 2.2

1.3

1.7

2.1

residuals from equation :(4) in the text. fi’~,n tabk 8 in Vaukl(l979.

looked upon frolm another perspec:tive. ich the observatjons liie inside a band PPP patb it turns out that in order to include ‘90% +20/, around PPP in 7 % for the fuli twentyaverage price level change untries in the sample the ervations does lend substa~tja~ increase

1%Get&erg, PPP: Exchanqcrates

261

Turning to the length of the time interval during which deviations from PPP persist, the comparisons in Genberg (1977a) suggested a mean time lag between a disturbance and its correction of about two years on the average, This finding was based on a very simple model which can be described by equations (5~(7). PPP, = PPP;+a

(PPP,_r-PFP;_1)+u,,

(5)

PPP, = log {A?,/et -Pi),

(6)

PPP,* = constant,

(7)

w’here, as before, P, e, and lPf stand for the domestic price level, the exchange rate, and the foreign p&e level respectively, and where the disturbince term ti is a?,sumed to be serially uncorrelated. These equations implg f.hat a proportion 1 -a of any current deviation from PPP will be removed durilng the next time period. If it is assumed that PPl?: = a+&, the mean time lags turn out to be somewhfrt shorter. For the ten year period 1957-1966 the mean time lag is slightly 13verone year or the average, a lit& less when bilateral data are used, a little more with multilateral comparisonsXO When the turbulent years 1967-1972 are included, however, the time lags increase to 2-2+ years Given the increased frequency with which ‘artificial’ changes in exchange rates took place during this period, the increased time lags could be interpreted as showing the slower speed of the arbitrage and relative p?.ice mechanisms of transmission, relative to the balance of payments mechanisl,:?. Finally, an a.verage mean time lag of 2&-3+ years indicates that deviations from purchasing power parity are even more protracted when the last four years of floating are taken into account. The reliability and mea,ning of this result wiil be discussed be.low. 2.3.2. The transmission.,wechanism. We hcevcfound evidence of the significance of all the traditional transmission mechan-sms working to ensure purchasing power parity under fixed exchange rates. The issue is therefore no longer whether or not they are important, but it instead concerns the speed with which they work. On this empirical evidence is spottier but a somewhat impressionistic picture still emerges. For the industrialized worJd, with which we are concerned here, there is no doubt that the transmission of monetary disturbances between countries is the fastest. The degree of capital market integrH.ion is high enough to spread a substantial, part of national monetary policy irlitiatives to trading partners within a period of one to two quarters. Measures of excess demands or supplies in goods markets are also highly correlateli contemporar,cously. This may be an indication of the rapid. function2ODetailed results by cousiry are available upon request.

262

Ii_ Genberg, PPP: Exchange rates

ing of the trade multiplier mechanism, a manifestation of the significance of expectational factors in transmitting real disturbances, or. finally, a mere reflection of the close relationship between monetary conditions in countries linked tog&m by integrated capital markets as already discussed above. T;ie arbitrage mechanism, and the mechanism relying on changes in the terms of’ trade to influence export and import volumes and hence prices, is much slower accord.ing to the empirical findings surveyed here and should perhaps be measured in years rather than in quarters. The last factor, and for our discussion of PPP under floating rates may be thl’: most important, is also the one about which the least can be ascertained. Tii e reference is to expectational factors working either directly on price formation by ‘way of price expectations of price setters, or indirectly via expectations of changes in foreign real excess demands as suggested above, or through the zn ticipated effects of policy changes abroad. The first of these three possibilities was shown to be important in the work of Cross and Laidler (1976) and their results (and. those of Laidler (1976)) indicate that the mechanism can be very a quick one. The second and third channels of transmission have not as yet been sy:;tematically iuvestigated for several countries but the findings of Saidi and Barro (1976) indicate that the anticipated growth rate of the Canadian money ~@y is strongly afTected by the contemporaneous anticipated growth rate .,f the U.S. money supp!j r when the exchange rate is fixed. 2.3.3. hplications f3r PPP ivnderfloating rates. Bat zd on the evidzzce from the fixed rate period jt can be argued that monetary ‘isturbances will lead to substantially larger deviations from PPP under floating rates than under fixed rates. This fo8110wsfrom findings indicating ,rhat the b; lance of payml:nts is quickly affizcted by monetary policy measures whereas price levei in@lences are subject to longer lags. With the exchange ra’te free to rnox= the rapid barlanceof-payments effects will be absorbed by the exchange rate whicn wili be pushed away from its PPP path. Over time relative price level movements will restore the relationship but this would occur only slightly faster than under fixed rates. Turning to aggregate demand disturbances of a real nature th.e :?sult in Barre and Saidi 0976), indicating that changes in the U.S. unlznployment rate get transmit& r.;ne-for-one to Canada within one year even during Jperiods of a floating Canad:ian dollar, is important. For it implies that a.n aggregate demand disturbance in an economy would not have a substantial effect on the PPP relationship. Tine exchange rate would not be likely to move :nuch since the disturbance would hit both economies a.nd, in so far as the state oraggregate and influenced price settiag, the ratio of the two countries’ price: levels nly to the ext5nf that a gi:zn aggregate demand impulse had ct in the two economies. In sny case the deviaiinn from PPP rent in size or timing from what it ,wo*Jd have been under fixed rates.

H. Get&erg,PPP: Exchangerates

263

The above arguments have abstracted from the issue of the formation of expectations under rloating rates and its implication for PPP. On this question there is relatively little empirical evidence to date.. /,n interesting argument by Parkin (1977b) even implies that the last four gears may be of only limited usefulness for empirical work on expectations formation under floating rates.2’ He considers the possibility that economic agents may continue for some period to form expectations on the basis of the stmcture relevant under fixed rates. Only after some time do they learn how a floatina rate economy functions. If this is indeed the case, then a part of the recent period of floating must be considered atypical in the sense that it does not reflect the behavior of a truly flexible rate system. 2 2 Purchasing power parity comparisons for this period may reflect partly the legacy of fixed exchange rates so the pattern of deviation from PPP may change as time passes. ‘With this caveat in mind I now turn to a discussion of more direct evidence drawn from, data from the current floating rate period. 3. Purchasing power parity mder flaating rates: The recent experience 3.1. Preliminary observations: Choice of index and base period, monetary v. real disturbances, bilateral x multilateral comparisons, etc.

Since there already exists alL excellent review article of the PPP theory of exchange rates [Officer (19’?6aj], only some brief additional comments need to be made here, The first concerns the choice of index and base period for relative PPP calculations. I take the -/iew that purchasing power parity is a macroeconomic concept and as such should be measured by a relatively broadly based index. I also follow the recent literature on exchange-r&e det8ermination which emphasizes price expect:\tions rather than cost competitiveness as sources of fluctuations of exchange rates. F~J these reasons I will work exclusively with consumer prize indexes ?n the empirical investigation reported on below despite their recognized shorlcomings from the point of view of international comparability [Vannereau (1375)]. The GNP defator may have been mort appropriate in this respect but only a Yewcountries publish quarterly series for this variable. Ideally the choice of base period for relative PPP rslculations should be one dining which absolute p;;rc,hasing powel p rrity h&. IJsing: a base period for which this was not the CAt;t can cause seri us problems of interpre;ation in empirical studies. A findi1.g that the change in the excha.nge ralte between 21Se.eBlackhur!;t (I 976) :for a si; tihr arg~mxent. 22Note that the argument is di!Zrent from one which would see the recent periou as unrepresentative because it has bee; characte:‘zed by considerable management of exchange rates on the part of moneiary a&hor:tb:s. Thi factor is however also very important both for its OWI sake and for the itifiuance rt may have on the mechanism by which agents learn about the working of the floating rate economy.,

264

H. Genberg, PPP: Exchmge rates

two periods was only a fraction of the relative change in ,tbe price levels of two countries could constitute positive evidence of a dynanGg movement towards purchasing power parity if the base period exchange rate was not eqitai to its PPP equivalent. On the other hand, if the results showed the exchange riate: offsetting perfectly movements i2 the price levels we might wrongly infer tilla!: PPP was being maintained when in fact slow adjustments were keepirxg the: exchange rate aw;y from its l?PP path. In the regression work preser%ed in this paper I have chosen to deal with this problem by, in a sense, letting the: data chmse the base period. By making the assumption, admittedly not un-, objectionable, that PPP held on the average during the particular sample: period being studied, I could let a constant term determine the appropriate: base period.23 One of the more .persistent criticisms of PPP theory emphasizes changes? in relative prices as a major reason why practical application of the theory will be of limited value. Officer (1976b) dealt extensively with a particillar version. of this kind of argument, the productivity bias hypothesis. In summa:iz:ing his empirical results Officer concluded that this hypothesis ‘lacks a firm emyirica!l foundatiozb sugge!sGngthat the general acceptano: of the hypothesis is nilwar*. ranted’ (p. 575). Althea versions of this general line of argument may be fi)rrnuU. Med. One which most readi!y come:s to mind would rel!y un asymmetries on the demand side rather than on the supply side to generate changes over time in the prices of n{ontraded goods relative tc trayed goods. Since this isrue is of considerable importance for PPP calculations I shall provide some indirect evidence on this question below. Relative price changes of dxmmodities whose prices (adjusted for exchange rates variations) are continuousiy kept in line internationally by arbi? rage mtiy cause problems which for measurement purposes are quite serious. ‘They stem from cross-country differences iu weights attached to these comano&& in national CPls. For the recent period of floating this source of error m~;r be particularly relevant given the iarge variations in the relativ’lzprices c4 primarq’ commodities surrounding the oil pnce increases inidated in 1973. In reviewing the existing empiricak work and interpreting my own the artificial modiP;,ca:ior;l of the PPP rela:ionship possibly introduced by this factor will be kept in mind Finally it shoti. be kept in mind that most of my results will be based on movements in elective exchange rate although differences which emerge from bilateral calculations will be brougbt up on occasion. 3.2. Some empiricid results In this section I shall investigate

r&es and their corresponding 2%ee section ?.3.I. ;br a

the relationship between the exchange purchasing power F,a.rity levels for the set of’

mart: delziled description of the specification being rekrred to.

f~u?
The coefEcient in this equation will be estimated for time periods covering both fixed and flexible exchange rates. a.r,d comparisons between the pericids will be carried out. As mentioned in section 3.1, the constant a’is included to let the data determine the appropriaie base year under the hypothesis that PPP held on average over the sample period. The time trend is included as a proxy for those factors which may produce a bias in PPP calculations. The properties of the error term will 6;1z:eindications as to the nature of departures from purchasing power parity. Table 1 already contains some information obtained from OLS estimation of (8). It shows the increase in the absolute percentage deviations from PPP (measured as X-ti-bt> as we move from the relatively fixed rate period 1957-1966 to the adjustable peg period 1967-1972 and finally to the floating rate period. The figures underlying the first three columns of ta’ble 1 indicate that the average absolute deviation increased from. 1.3 % in 1957-1966 to 2.2 % in 1967-1972 and finally to 4.1 I’/ in 1973-1976.25 In section 2.3.1, I presented estimaP:s of the speed of adjustment towards PPP based on the serial correlation properties of the error term in the estimated equation. Contrary to what a:-pears to ba common expectations [see for instance Kemp (1976)J the:re is an ueiiI&takea.bk: lengthening of the time lags dkring th.e years of flexible exchange razz: 5:comp,ired to either of the two earlier subperiods. This finding may be the restlit: of essentially spurious factors to be investigated below, but if it holds up, ow discussion in part 2 implies th;it the disturbances which have moved exchanifk. rates off their PPP pathha in trae past four years, and the adjustment mecham-ms which bring them back, ha.ve been more akin to the processes at work in c evaluations and revaluatrons under an adjustable 24Henceforth the expression cm the left hand side will be refe%d to as Xl,,. 25The corresponding figures bahzd on cols. 4-6 are 1.3 % far 196&196k, 2.1% for 1967-1972, md 4.7 % for 1972-l 974.

H. Genberg, APP: Ljcchange r&es

266

peg system than to’ the seemingly smoother morzetary, income and expect ations mechanisms working under fixed rates. This in turn may be relevant fix the issue of whether changes in exchange rates tend to bri.ag about adjustment in relative price levels or vice versa.

_--

Table 2 Estimates of coeflicien;s ‘~2,be trend.* _,_ --__Y Multilatiral comparisons _----p

Country ---A

- 0.00367 (15.74) 0.00314 (13.34) -0.00161 (11.65) 0.00036 (2.53) -0.00375 (25.56) 0.00180 (9.77) -0.00190 (9.54) 0.00134 (4.13) -0.00355 (33.61) - 0.00305 (17.99) - 0.00104 (11.38) - 0.00285 (8.36) 0.00109 (5.58) - 0.00888 (35.87)

U.S. U.K. Austria. Belgium Dcarnark France Germany Italy Netherlands Norway Sweden S%itzerland Canada Japan _--_

Bihtteral coInjxUisons with the U.S.

-0.00104 (3.88) -0.00651 (16.45) -0.00467 (11.8X) -0.00779 (23.225) - 0.00290 (7.8!$) - 0.00626 (15.2~1) .-0.00310 (13.21) - 0.00783 (17.64) -0.00718 (19.94) -0.OOS60 (24.92)1 -0.&704 (12.74) O.OOOtM (0.00) -0 0J023 (30.42) ---P--P

aNotes: The estirrmtes are based on quarterly data spanning 1957/I-1976/IV. The Durbin-Watson stat&z indicated the presence of first-order serial correlation HI all equations which should not a&c;: the point esthnates but should bias the standard errors towards zero. Figures in parentheses are t-values.

Moving on TV the estimates Cf the coefficient on the time trend we notice f 3t it is significanlly diRerent from zero fol, all cou&ks in the t Ige rate compxisons and for all but ant: (Canads) In bilateral c~~~pa~sons with the United States. This suggests that. there exist:, indeed a

i!. Gertberg,PPP: Exchattge rafes

267

hias in PPP measured by CPIs and an import task must be to explain the sources of this bias. The productivity bias hypothesis has been cluestioned on em,pirical grounds by Officer (1976b). Two alternatives w.ill be investigated here based on demand rather than supply considerations. Suppose that nontraded goods are such that their income e1asticit.y of demand is ‘higher than unity and that their share of governr i nt expenditures is larger than their share of private expenditures. Then, assuming unbiased growth on the production side, the relative price of nontraded goods will rise as income grows and as expenditures arc rle-distributed towards the gozrnment. Assuming further that the response of relative prices to these factors is the same across :ountries, and that income elasticities of demand and (maybe unrealistically) the weight of nontraded in the CPI do not differ significantly between countries it can be shown that the trend term in (8) should satisfy (91, where both kl and kz are expected to be positive :

b = ko+k, (EG-g,)+kz kihd~

(9)

T&le 3 OLS estimation of equation (9). Standard country

kz

U.S.

1.27 ((2.38)

U.S. (Japan excluded from the sample)

1.34 (1.16)

(KZ)

Japan

(1.37 1S3)

0.08 (1.26)

82

d.f.

0.24

11

0.16

10

0.20

11

In the derivation of this equa?ion the foreign and domestic rates of growth of real per capita income, g,” and g,, as well as the growth rates of the ratio of government expenditures f~ GNP, gGfand gG, are assumed to be csns!aiit. Table 3 contains estrmatcs oi the parameters in this equation based cn the trend estimates in column 2 in table 2 and on data on real GNY, populatirjn, nominal GNP, and governmnt expenditures taken from IFS.26 The results are not spectacular as far as the explanatory power of l,.heequation is concerned but they do suggest that there ma!’ be come validity in the hypothesis that the relative price of non-traded goods depends positively on the 1eve1of income. The share of government expenctitures in. GNP does not appear to afEe& relative prices however. In order to check the robustness of these z6Lines Wax, 99x1,99a, and 91f, respectively. The yowtb rates were computed compounded annual rat : ?f powth linking 1957 with 1974. The end year was chosen @iflack of data for 1971, and 1976.

as the

because

research might usefully be directed at investigating altcrn;%k functional forms and removing some of the more restrictive assumptions of &he underlying theory. In the meantime the evidence of a bias in PPP calculationz:; based on CPYs wllP have to rely mainly on the significance of the trend terms reported in table 2. S,o far our results have tended to show a marked inferiority of the purchasing power parity reiationship during the flexible exchange rate years as compared to the earlier years of fixed or adjustable exchange rates. Not only have the devia. tions from PF3 tended to be larger but the speed of adjustment towards PPP seems to have declined. As we shall see shortly, these findings may give the impression of being at variance with several recent studiies of the relationship between exchange rates and relative rates of inflation under the current float. Thz imply that PPP has been maintained rather well during this period. Since most of these studies do not provide comparison with the fixed exchange rate period it may just be that the problem of not having a standard of reference against which to measure the results for the current period influences the interpretation of, the results. 27 It may nevertheless be that by their exclusive: focus on the recent years they have automatically overcome a difficulty which. a study of longer time span must deal with. I am referring to the possibility that there has bezn a shift in PPP rdationships, as measured by CPIs, d~ueto changes in relative prices of traded goods combined with intercountry differetlces; ia the weights they are accorded in national indexes. The obvious candidate: for n:ch a relative price change would be the increase in oil prices ir, late 1973. Th2 existence of a shift in F’PP relatiomhips may be investigated by means of adding a dummy variable to equation (9) for the affected. peri.!d. In our case this was assumed ito be tbe three years 1974-19716.The c:oelRcient of the added variable turned cut significant for all but one country ~ICI the 1:yp&esis, of a shift in 1974 cannot be rejected without further ct:vidc:nce:..The modified, specification also led to a substantial reduction of the size of the deviations from PJPP as well as in the length of the adjustment lags. The averagr: absolute errors t\ermereduced to 3.1% for the 1973-76 period. They fell also for the earlier periods, however so the association of the flexible rade period Gth the largest deviations from PPP is still valid. The persistence of the errors was ou the other hand reduced to such INIextent .hat it is now comparalble to the fixed rate period. ‘The meail time lag was reduced for all countries, and the aterage fell. from 14.3 to 5.6 quarters. Ir 1:husappears that the inclusion of a shift variable makes PPP comparisons show results that are more in agreement with many econom+.ts’

Scoriclusions future

“‘Kemp (1976) actuall,’ does Elmpare the 1970-1973 period with the 1973-76 yeaE; and ~tids a better performan& of I’PP in th.: latter. This is, in my opinion, not an appropriate mu-ison sim_ tba 1970-73 period csrrtains several discrete parity changes which, I have i~~~~~~,produce relaiivcly long=las:;ng kviations from PPP which is not representatfn: of a :i!xod r:[email protected] period.

H. Gederg, PPP: Exchange rates

269

a qriori expectations. 2R &fore _ the hypothesis is accepted, however, further tests will have to be made. First of all the size of.+; coeficient of the shift variable needs to be checked against what the above theoretical arguments would pr edict. This could be done by investigatin;: in some detail the weighting patterns in each count:y’s CPI. Other outside evidence needs to be examined and other methods of ,:stimating the existence of a shift should be explored. 3.3. Comparison with o,ther studies One issue deliberately not investigated in the elmpiricaB work of the previous section concerned the sensitivity of the results ,:o the choice of CPIs as a measure of prices in each country ,.It is therefor? interesring to see what other investigators have found in this respect. The evide:lce appears t 3 be inconclusive. IMy reading of King’s (1976) and Kemp’s (KY2) results wit;1 respect to the LL’.S.and its main trading partners indicates that the CPI is a better measure than the WPI on balance. The WPI gives a higher correlation between re1ativ.e inflation rates and changes in the exchange rates but the (1Pi is suge;lor when it comes to the value of the slope coeticient in a regression of the change of the exchange rate on the relative rates of inflation. OPTICA (1977) leans towar& the WPI as the better measure mainly because of its higher explanaiory power. Aliber’s (1976) r :sults are consistent with this view in that he shows that deviations from PPP are smaller for WPIs than for CPIs. Cost indexes such as wages and unit labor cost consistently give less satisfactory results than either of the price indexes. Turning to the comparisons between fixed and flexible rate periods, both Aliber (1976; and Wihlborg (1976) argue that deviafons from PPP have increased under flexible rates. Wihlborg adds however that deviations during periods of unreliably pegged exchange rates - associated with changes in par values - are as large as under floating rates implying that exchange risk is no bigger under the latter system. ” The same conclusion emerges from the OPTICA report.” Both the OPTICA report and King note that the adherence of exchange rates to PPP increases substantially when th,: obsf::rvation peri;.:d is lengthened. In the latter’s pooled cross-country and time series study (14 trading partners of theunited States over the period 1973/11--1975/l1: the coefficient of determina2*Note however that accepting the i;lea of shifts in PPP 1evels makes PPP ;alculations lose much of their simplicity and may lead IO very r’:ifficuItprolJems in designing target zones end surveillance rules based on PPP. Using different price indel.es, for instance WPIs. is not lY.ely to be a solution to these problems. 2’It is in this manner that we have already interpreted :
iX Genberg, PPP: Exchmge

2743

rales

tion increases sharply as annual or biannual changes are used instead of quarterly or semi-annual.3X Ind.eed it is only for the former two time periods that ihie slope coefficient is significantly different from zero at the 95 “/(; level. From this short review, it seems clear that on common ismsuesmy research and others’ yield essentially the same conclusions despite differences in empirical methods. Questions concerning the choice of base period and the possibility of shifts in PPP relationships have not been addressed1 in previous research on the recent floating rate period so comparisons with my resui ts are impossible. The hypothesis that there exist systematic biases in PPP com;parisons have not been tested on recent data. either apart from in the work of Officer (197Sb). My results here are consistent with those he obtains when he re,sresses the change in the CPI/WPI ratio on changes in GDP per capita from 1953-1973 (see his tab!e 13). Given his otherwise negative results concerning the productivity bias hypothesis, my interpretation of this result in terms of deimand factors may be justified. 3.4. Sources’ ofsitort+un deviationsfrom PPP As a matter of pu.re arithmetic it is possible to explain deviations from PPP in terms of movements of Gther the exchange rate or the relative price levels between two countries, because by definition

A log (eP/P)

= A log e i-d log (P/P).

(W

Various measures exist for determining how much of the variation in the 1.h.s. of (10) can be sscribed to variations in the exchange rate and in the relative price levels respectively. Table 4 contains figures based on two such measures. The first, Kf p is calculated as

-$i & =

d log e;sign (A log (#/P),)

1-1

(11)

and measures the pro:portion of the average absolute change in eP*/P which is tracable to variations in e.32 The second measure is x’” 2

_ Clrv (A

-

.I

log e, A log (eF/P)) var (Kg (ePf/P))

’

(12)

3’In the rzg-ession equation the peicsntage rate of change of bilateral exchange rates is regressed on the corrt:s?onding lclative inflation rates. 3ZKle need xt Se between zero and one but the sum of (;I1) and a similar coefficient ca.lxrlaied on the bas.zr ~>1’ changees in ,PJ/F Jnust add up to unity.

H. Get&erg, PPP: Exchangt~ rates

271

which again has the propeny that Ki+ Kz”” = 1 where K{‘lp ir calculated as in (12) except with A log (Pf/P> instead of A log e. The third matrix in table 4 contains simple correlation coefficients between A !og e and A log (e.Pf/.P). In this table the sample perio is 1973/I-1976/IV and the observation periold is one quarter. The figures which are based on bilateral comparisons show Table 4 Sources of deviations from PP?: 1973/2-1976/N. U.S.

U.K.

France

Germany

Italy

Sweden Switz.

0.87 1.02 0.96 0.90 0.97 1.03 1.38

1.22 0.915 0.75 0.91 1.09 0.80

1.02 1.19 1.01 1.23 0.57

1.14 0.59 0.93 0.81

1.31 1.21 0.86

1.15 0.82

0.76

0.85 1.03 0.97 1.06 1.06 0.98 0.89

0.95 0.89 0.89 0.85 0.75 0.76

1.M 1.07 1.00 0.99 0.86

0.80 0.87 0.94

1.09 1.os 0.90

0.84 0.87

0.86

0.96 0.92 0.94 0.94

c .94 c.94 c.94

0.87 0.89

0.87

Japan

i%K1e

Ui.

France GernWly Italy Sweden Lcultzerland Japan

0) Kz= T1.S.

U.K. France Germany Italy Sweden Switzerland Japan

0.99

g)sCorr (d log e, A log (eP*/P)) u:Ii

France Germany Italy Sweden Switzerland Japan -~-

0.91 0.99 0.99 0.95 0.98 0.98 0.91

0.91 0.94 0.86 0.37 0.Y3 0.78 --

0.97 0.96 0.94 0.93 0.94 -

-_

-__

unmistakably that the exchan!ge rate has been thl: ovzrwheimicgly dominant source of short-run fluctuetions in the ratio of e to P/k’* in the: last four years. This can be contrasted wi:h the conclusions whicl emerge when the 1957-66 period is used for the computations. Table 5 shows t’rat for these years variations of the exchange rate within the marSins played a relatively minor role. It is interesting to note that.+ Car those ‘ountries whit h altered tilezr par valves (France and Germany) the figures tend to look sim Jar to those fc A the Roaiing rate years. This may suggest that as far as deviatio.1~ from BPP are concerned,

It Ge&rg,

272

PPP: Exchange rates

exchange rates in the recent periods have behaved like changes in par values under an adju.stable peg system. .%ter having established that short-run deviations from PYP can be associated +th movements in the exchange rate there remains to provide an explanation of -&at factor ‘jr factors are the main determinants of the latter. This task is rtf ~XFS~ well beyond the scope of this paper, but a review of the emerging ~*mpirical evidence may be found in the excellent survey by Schadler (1977). Table 5 Sources of deviations from PPP: 195?/1-1966iJ.V. .---. IJS.

U.K.

France

Germany

FlZOCe Germany Jti!y Sweden Sw:tzerla: Id Japan

0.07 0.65 0.30 -0.04 0.06 0.09 0.01

0.59 0.33 0.07 0.09 0.15 u.09

0.66 0.70 0.59 0.71 0.55

0.14 0.18 0.38 0.16

(bj Kz= U.S. U.K. FrWMX Germany Italy Sweden Switzerland Japan

0.10 1.11 0.49 -003 0 18 O.l( 0.01

0.98 0.51 0.06 0.18 0.21 0.11

1.02 1.12 1.06 1.c2 0.89

0.41 0.37 0.46 0.20

0.85 0.72 0.23 0.48 0.61 0.34

0.86 0.86 0.83 0.82. 0.70

0.65 0.73 0.78 0.51

Italy

Sweden Switz.

Japan

f.$&=

u:8.

0.05 0.19 0.M

0.10 0.05

0.06

0.20 0.08

0.11

0.52 0.27

0.38

.

0.31 0.14 0.02

g)s2x-r (A log e, d {eP*/P)) Uk. FmZIE Geranxty Italy Sweden Switzerland Jartan

.

0.37 0.88 0.76 -0.24 0.50 0.52 0.05

0.37 0.49 0.06

Celecludiug remarks

It seems clear that PW is mainly a longer run phenolmenon in the sense that it should be expect& to agree with data on price levels and exchange rates only as an average olier several quarters. In times of only moderate &fIerertces in inflation rates bei ween cour&-ies - less than iO% per an;lum, say - this kies &it structural c iinge which alters internal relative prices or leads to

H. dertberg, PPP: Exchange rates

273

modifications in the output mix in the export s..nd import competing, sectors must be allowed for in measurements of PPP levels. I have presented evidence pointing to the significance lof this effect at least when CPIs are used. Other price or cost indexes should also be investigated with this issue in mind. A bias due to structural change could F---zcily b: incorporated into nlost uses of the PPP relationship ifit were reasonably stead! pand predictable. lily evidence indicates that actual e:xchange rates are not likely- to be far off their PPP levels if a simple adjustment for structural c’ .ange is al lowed for. On the other hand serious problems could arise if a true: bias were i;,mored in the design of target zones or surveillance indicators for exchange rites based on PPP. A similar difficulty, which is probably harder to handle, appears if PPP relationships, measured by commonly used indexes, tend to :;hift with change:; in relative prices of traded goods :IS it appearis that they do based on the preliminary estimates presented here,. Turning to shorter rug questions the evidence, suggests rather strongly that deviations from PPP are both smaller and less prc longed under fixed rates than under flexible rates, at least the kind of flexible rate s that we have had recently. 33 Apparently the disturbances impinging on the I’PP relationstip are different as between the two systems. Short-run variations in exchange rates under floating do not get offset by movements in relative r;rice levels. The reason for this must be looked for in theorizing about the determination of exchange rate levels in the short run.,, -More detailed time series evidence on PPP may be of some help in this rega.rd by pointing to em lirical regularifcs which have to be explained by the theory. As a final note of caution I would 1ia.e to emphasize that four years is quite a short period on which to base empirical results. Added to this 2s the ‘q*unrepresentative of the possibility that the recent period of flexible raies iv likely future behavior of excha.nge rates as both governments and private agents may adapt their behavior in response to increased knowledge about the new economic structure. Empirical research sh oultl therefore continue, not only by testing new hypothesis and estimating nevc models but also by examining older theories and relationships in light of new dilta as it is generated. 33The reason why this &ding may seem surprisiug is in my alpinion a result of a misplaced emphasis in conventional analysis on overvarucd vnd undervalued currencies, rather than mappropriate (for external balance) monetary and fi, ~31pclicy, as the main sources of balance oi pay’ments or bafance of trade deficils and surplus~.

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274

Ii. Gettberg, PPP: Exchange rates

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H. Genberg, PP?: Emhang e rates

Kb,

27’5

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