The law of one price: conditional convergence evidence from disaggregated data

Abstract

This article contributes to the literature on the Law of One Price (LOP) and absolute Purchasing Power Parity (PPP) in two ways. First, it uses a novel set of PPP data from the International Comparison Programme for OECD countries and 195 internationally comparable products from 1980 to 1996. Second, it derives and applies a test of conditional σ-convergence, which does not require long-time spans or high frequency data. Between 1990 and 1996 for 10 out of 23 countries, a significant reduction in the variance of the deviations from LOP is found for tradeables, but none in case of nontradeables. For the former, the deviations from LOP close out at half-lives between 2.2 and 6.3 years. However, there are also persistent country-specific deviations from LOP parities.

Acknowledgements

The authors are very grateful to Statistics Austria, EUROSTAT and, especially, to the OECD for supporting and enabling this project. We would like to thank Mark Nelson and Jeff Bergstrand for valuable comments and suggestions.

Notes

¹The Law of One Price (LOP) states that identical goods sold in different countries and/or locations should exhibit the same price expressed in common currency units, while Purchasing Power Parity (PPP) implies that similar baskets of goods should be identically priced once expressed in common units.

²In particular, the analysis of changes in relative prices (relative PPP) is not sufficient to show that international price differences cancel out over time in levels (absolute PPP). Here, we concentrate on LOP, i.e. absolute PPP. Recent contributions to relative PPP literature are Rogoff (1996), O’Connel (1998a, b), Cheung and Lai (2000a, b), Higgins and Zakrajsek (2000), Taylor (2001, 2002), Baum et al. (2001), Taylor and Peel (2000), Taylor and Peel (2001, 2002), Murray and Papell (2002), Taylor and Taylor (2004).

³See also Isard (1977), Giovannini (1988) and Knetter (1989, 1993) for early but influential contributions.

⁴In Egger and Pfaffermayr (2006), an even more general Wald-test on conditional σ-convergence is provided. As long as all explanatory variables are dummy variables as in our application, the here derived LR-test on conditional σ-convergence is sufficient.

⁵The final list of products narrowly specified for the 1996 OECD/EUROSTAT comparison covers over 2900 consumer goods and services, 34 occupations in government, education and health services, 186 equipment goods and 20 construction projects.

⁶The country sample consists of Germany, France, Italy, Netherlands, Belgium, Luxembourg, United Kingdom, Ireland, Denmark, Greece, Spain, Portugal, Austria, Switzerland, Finland, Iceland, Norway, Sweden, Turkey, Australia, New Zealand, Japan, Canada, USA. (Note, due to small changes in the classification, a few basic headings are not available in all of the rounds).

⁷For T approaching infinity, we have for b < 0, so that we observe σ-convergence if σ₁² > σ _v /( − 2b − b ²).

⁸If there is an infinite history of the process with a switch in the variance at period 1, the MA-representation implies that the starting value includes all previous errors up to period 1.

⁹See Crucini and Shintani (2004, p. 16): ‘In any case it seems fair to say that the absolute convergence hypothesis is flagrantly violated across international cities and at best weakly supported by the U.S. data. … Our results using absolute price data indicate that the resting point of most Law-of-One-Price deviations is not zero as implied by the theoretical proposition, even across cities within countries.’

¹⁰Engel and Rogers (1996, p. 1114) mention several reasons as to why deviations from absolute PPP might occur: (i) geographically segmented markets combined with market power (ii) productivity differences, (iii) differences in prices of nontradeable inputs due to wage differences and (iv) price differences of tradeable intermediates due to trade barriers. If a good is principally tradeable, the degree of trade barriers limits possible arbitrage and defines the width of the possible deviations from PPP. Parsley and Wei (1996) provide evidence for US cities that the lack of tradeability of goods and services is sufficient to drive a permanent wedge between prices at different locations even within the same country (see also O’Connel and Wei, 2002).

¹¹This assumption guarantees that, in contrast to the dynamic fixed effects model (Anderson and Hsiao, 1982; Hsiao, 2003), our estimate is consistent and unbiased. Note that the assumption of differing group effects can principally be tested for.