New kinds of comparisons of the prices of tradables and nontradables

The received international economics view of the consequence of international trade is that it tends to equalize relative prices of tradable goods in different countries. This tendency is not strong enough to justify a literal belief in the law of one price, but it is an input into a variety of important economic propositions (e.g., the Balassa-Samuelson differential productivity hypothesis). This paper aims at an empirical verification of the price-equalizing effect of trade by comparing relative tradable and nontradable goods prices across countries using International Comparison Programme (ICP) benchmark price data. The differences between relative tradable and nontradable prices are examined in two different ways. The first of these involves a measure of the similarity of price structures in a pair of countries, and the second works with a decomposition developed by Nuxoll of the variance of the whole price structure into tradable and nontradable components. Analysis of the price-similarity and variance component estimates provides evidence that in fact the trade effects are clearly perceptible, if perhaps not as great as might have been expected. Heston and Summers: University of Pennsylvania; Aten: University of Illinois at Urbana; Nuxoll: Virginia Polytechnic Institute. Support for this investigation was provided by the World Bank. The research assistance of Taisir Anbar Colas and Valerie Mercer is gratefully acknowledged. New Kinds of Comparisons of the Prices of Tradables and Nontradables One important part of the received international economics view of the consequence of trade among countries is that it tends to equalize relative prices of tradable goods in different countries. This tendency may not be sufficiently strong to justify a literal belief in the law of one price, but it certainly is an input into a variety of important economic propositions. For example, the Balassa-Samuelson [1964] relies in part on this price-equalizing effect for some goods but not others. An empirical verification of the effect with existing final-expenditure data is not easy, but investigations based on the prices collected in the various International Comparison Programme (ICP) benchmark studies throw light on the phenomenon. We begin in Section I with a review of our previous work on the relationship between the prices of tradables and nontradables. In Sections II and III we develop two different ways not previously exploited of analyzing the differences between tradable and nontradable prices. The first of these involves a measure of the similarity of price structures in a pair of countries, and the second works with a decomposition developed by Nuxoll of the variance of the whole price structure into tradable and nontradable components. Section IV summarizes the results of this empirical exercise and points to directions for future work. I Background for the Present Investigation In Heston, Nuxoll, and Summers [1994], an attempt was made to distinguish between the average relative prices of tradable and nontradable goods. In the ICP the prices of individual goods are expressed relative to a numeraire country's currency unit. (The average of the prices of a group of goods is referred to here as a price parity to maintain consistency with the practice of using the term purchasing power parity (PPP) for the average price of all the goods of aggregate GDP, expressed per unit of the currency of the numeraire country. To make a country's tradable and nontradable price parities reflect relative prices, each of the price parities was divided by the country's overall PPP. ) First, we clarify what is meant by tradable and nontradable goods. The ICP works from the expenditure side. In the 1985 benchmark study, GDP was broken down into 139 basic headings of final-goods spending on Consumption (108), Investment (29), and Government (2), covering everything from various kinds of food, clothing, and shelter to machinery and construction to items of government services. It compares prices of identical or very similar goods and services across countries. For some goods, of course, such comparisons are very difficult and subject to considerable error. Determining which of the basic headings should be regarded as tradable and which nontradable is necessarily fairly subjective. In the absence of hard, specific information on what goods might potentially enter into international trade versus those that inevitably are absorbed domestically, the categories placed in the nontradable classification covered all services and construction. (Following Peter Hill [1977, 1987], a service is taken to be a nonstorable good and therefore unlikely to be traded; and because elements of construction are necessarily attached physically to some part of the domestic economy, they would not be traded.) All other categories were placed in the tradable classification. Annex A provides a description of the 1985 benchmark study categories classified as tradables (94) and nontradables (42). It should be emphasized that tradables in this definition are items that could be traded, though of course they are not necessarily in fact traded. (This is why the terms "tradable" and "nontradable" are preferred to "traded" and "non-traded") Our previous work focused first on averages of prices parities--remember, expressed relative to PPP--of tradables and nontradables. The relationship was explored between each of the price parities, and also the ratio of the two, and GDP per capita. (For example, the ratio of the two price parities was regressed against GDP per capita. As expected, the ratio varied inversely with income, and in a statistically significant way. More than that, the finding was replicated over the fifteen year period between 1970 and 1985, and for a number of different country combinations.) The work with average tradable and nontradable prices as related to GDP per capita was extended to the basic heading level also. The regressions involving these disaggregated data confirmed what was found with the average price-parity data. II Price-Similarity Indexes A. The Definition of a Price-Similarity Index In this note new ways of exploiting the ICP benchmark data are examined. A sharper alternative to average price parities is used in comparing countries. Consider the problem of judging how closely n relative prices match in two countries. A natural measure of the similarity of the price structures of the countries comes out of a consideration of the geometry associated with the n-dimensional price vectors of the two countries. Think of the plots of the two price vectors in ndimensional space. Each price vector defines a point, and the similarity of the price vectors can be measured by the size of the (two-dimensional) angle formed by the n-dimensional rays defined by the points. In fact, the cosine of the angle (call it PS, for price-similarity) rather than the angle itself, is a particularly convenient and transparent index of the degree of similarity of the price vectors. Partly, this is because PS is scaled so that it equals zero when the relative prices are as far apart as they can be (i.e., when the rays are orthogonal in the n-dimensional space) and it equals 1 when the relative prices are exactly the same (when the rays coincide). In addition, PSij, is defined by a familiar formula: