Price level convergence and purchasing power divergence

• DOI: http://doi.org/10.1111/infi.12118
• Author: Nikolas A. Müller‐Plantenberg,Maria Eleftheriou
• Published date: 01 March 2018
• Date: 01 March 2018

DOI: 10.1111/infi.12118

ORIGINAL ARTICLE

Price level convergence and purchasing

power divergence

Maria Eleftheriou

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Nikolas A. Müller-Plantenberg

Department of Economic Theory and

Economic History, Faculty of Economics

and Business Administration, Universidad

Autónoma de Madrid, Madrid, Spain

Correspondence

Nikolas A. Müller-Plantenberg,

Department of Economic Theory and

Economic History, Faculty of Economics

and Business Administration, Universidad

Autónoma de Madrid, Madrid 28049,

Spain.

Email: nikolas.mullerpl@uam.es

Abstract

We construct four large data sets of bilateral real exchange

rates based on traded good prices (food and clothing,

respectively) and broader price indices (consumer price

index, CPI, and wholesale price index, WPI).On these data

sets, we run non-parametric regressions to examine how the

real exchange rate, the price differential, and the nominal

exchange rate reactto an overvalued real exchange rate over

time. In line with the theory we develop, our regressions

show the following: First, real exchange rates are mean-

reverting. Second, prices converge. Third, price conver-

gence implies purchasing power divergence and thus does

not contribute to real exchange rate convergence. Indeed,

when price adjustment is fast (as for our traded good price

data sets), we even observe diverging nominal exchange

rates. Our findings suggestthat movements both away from

and towards PPP may be less related to traded good price

movements than is commonly thought.

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INTRODUCTION

The idea of this paper is best conveyed by means of an example. Suppose a country's real exchange

rate is 100% above purchasing power parity (PPP). In other words, if Qis the real exchange rate, Q

equals two rather than one. Assume further that there are no transport costs or other impediments to

good market arbitrage. Then, according to the PPP theory, the ratio of domestic to foreign prices

should quickly fall by a factor of two to 50% its initial level. As a consequence, PPP would be

restored.

The stated argument for why deviations from PPP should be temporary is simple and compelling.

Yet as this paper seeks to demonstrate, it overlooks one very important point. For imagine that domestic

traded good prices really become twice as cheap. In this event, the domestic currency's purchasing

International Finance. 2018;21:71–91. wileyonlinelibrary.com/journal/infi © 2017 John Wiley & Sons Ltd

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power in terms of traded goods would rise by a factor of two, making a large nominal appreciation

likely. Indeed, if the nominal exchange rate was flexible, it could rise by as much as 100%, leaving the

real exchange rate at exactly its original level.

The objective of this paper is to study empirically the reactions of the real exchange rate and

its components—the nominal exchange rate on the one hand and the price level differential on the

other—to deviations of the real exchange rate from its long-run trend. We estimate these reactions

by means of non-parametric regressions, so as to allow for the non-linearities that can arise, for

instance, due to the existence of transportation costs. As required in non-parametric regression

analysis, we employ very large data sets of bilateral real exchange rates, nominal exchange rates,

and good price differentials.

In the theoretical part of this paper, we derive formal hypotheses on how the nominal

exchange rate and the price level differential should react to deviations of the real exchange rate

from PPP. It should be stressed that our hypotheses can both be corroborated or rejected by the

data.

After all, there are three possible outcomes. The first outcome is that the mean convergence of the

real exchange rate occurs in the presence of a nominal exchange rate divergence that is compensated by

an even greater convergence of traded good prices. Our theoretical analysis leads us to conclude that

this outcome is likely to occur when price adjustment is fast, as rapidly converging prices will be

associated with a divergence of the purchasing powers of the respective currencies. And, indeed, in the

empirical part of this paper we are able to corroborate this conclusion using data of price indices of

highly traded goods (food and clothing, respectively).

The second possible outcome is that both the nominal exchange rate and the good price

differential converge in response to deviations from PPP. Our theoretical model suggests that

this outcome is to be expected in cases where price adjustment is slow. Under this scenario, the

purchasing power divergence will still be at work, yet the nominal exchange rate is

predominantly driven by forces that are unrelated to price fluctuations, forces for which,

following Müller-Plantenberg (2017a, 2017b), we use the term ‘currency market pressure’.As

it turns out, currency market pressure is mean-reverting, so that the reversion of the real

exchange rate to PPP is driven by both the price differential and the nominal exchange rate. In

the empirical part of this paper, we use the consumer price index (CPI) and the wholesale price

index (WPI) as examples of slowly adjusting price levels and find that with both data sets our

regressions confirm our conjecture of a simultaneous convergence of the price level differential

and the nominal exchange rate.

Finally, the third outcome is that the nominal exchange rate converges in response to deviations

from PPP whereas the traded good price differential does not. This outcome contradicts not only our

hypotheses, but the PPP hypothesis itself, and it is thus not surprising that we find no empirical

evidence for it in the data.

The reader may ask at this point why in the introductory example deviations from PPP arise in the

first place. Although this is an important question, it is not of central concern here. Nevertheless, in the

theoretical part of this paper we will provide a tentative answer, arguing that balance of payments flows

could be an important driving force behind real exchange rate fluctuations.

The paper is structured as follows. Section 2 reviews the relevant literature. Section 3 presents the

theoretical model and formulates the hypotheses for the empirical part of the paper. Section 4 gives

details on how the real exchange rate data sets are constructed. Section 5 explains how non-parametric

regressions are carried out to estimate the reactions of the good price differential and the nominal

exchange rate to deviations of the real exchange rate from PPP. Section 6 presents the empirical results.

Finally, section 7 provides conclusions.

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