How Far Can We Push The "Law of One Price"?

May 1976

HOW FAR CAN WE PUSH THE "LAW OF ONE PRICE"? by

Peter Isard

NOTE: International Finance Discussion Papers are preliminary materials circulated to stimulate discussion and critical comment. References in publications to International Finance Discussion Papers (other than an acknowledgment by a writer that he has had access to unpublished material) should be cleared with the author or authors.

IFDP #84 a

Peter Isard* May 20, 1976

HOW FAR CAN WE PUSH THE "LAW OF ONE PRICE"?

1. Introduction and Summary

Students exposed to the pure theory of international - trade have been seduced by visions of an imaginary world with few goods, each typically produced by several countries but neverthe- - less homogeneous’. In the assumed absence of transport costs and trade restrictions, perfect commodity arbitrage insures that each good is uniformly priced (in common-currency units) throughout the world -- the "law of one price" prevails. Such simplification has facilitated the derivation of numerous theorems, many of which have in turn translated into useful insights about the real world. But the law of one price can

be pushed too far; and indeed, the conclusions of the new "global

1/

' monetarist" analysis of devaluation—’ rest on an invalid appli-

cation of this law.

*The views expressed herein are solely those of the author and do not necessarily represent the views of the Federal Reserve System. This paper has benefitted from the comments of a number of my colleagues, especially those of Jeffrey R. Shafer.

1/ The term "global monetarism" was coined by Marina V.N. Whitman, "Global Monetarism and the Monetary Approach to the Balance of Payments," Brookings Papers on Economic Activity, 3, 1975. Other published descriptions of this view, whose leading proponents are Arthur Laffer and Robert Mundell, are presented in Arthur B. Laffer, "The Bitter Fruits of Devaluation," The Wall Street Journal, Jan. 10, 1974; and Jude Wanniski, "The Mundell-Laffer Hypothesis - a new view of the world economy,"' The Public Interest, No. 39, Spring 1975.

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As a refutation of the global monetarist view, this paper presents evidence that exchange-rate changes substantially alter the relative dollar-equivalent prices of the most narrowlydefined domestic and foreign manufactured-goods for which prices can readily be matched. Moreover, these relative price effects seem to persist for at least several years and cannot be shrugged off as transitory. In other words, for manufactured goods selected from the most disaggregated commodity lists for which U.S. and foreign prices can be matched, the products of different countries exhibit relative price behavior which marks them as differentiated products, rather than near perfect substitutes. os Thus, devaluations may change relative prices sufficiently to have persistent effects on international trade volumes.2/

To clarify discussion it is useful to distinguish two contexts in which the law of one price is valid from a third context in which the law of one price does not hold. (1) Ina comparison of U.S., European and Japanese prices of various welldefined steel items (plate, galvanized sheet, cold-rolled sheet, and hot-rolled sheet) c.i.f. for delivery in a common port,

"27 The Mundell-Laffer hypothesis also grossly oversimplifies the wealth effects of devaluation and thereby mistreats a second channel through which devaluations can affect real variables.

See Peter Isard and Michael G. Porter, "The Analysis of Exchange

Rate Movements: Neutrality Results and The Role of Expectations," processed, October 1975.

-3-

Rosenberg3/ found that relative dollar prices charged by different countries were fairly constant over time and were not significantly affected by exchange-rate realignments. The dollar prices of primary commodities are also generally considered to be fairly

4/

independent of country of origin.—’ These are cases in which the products of different countries are close to identical, or nearperfect substitutes, so that any price disparities would be rapidly eliminated by commodity arbitrage. (2) In the absence of restrictions on commodity arbitrage, a product of any single country sold competitively in two different markets (foreign or domestic) would also obey the law of one price in the sense that its dollar-equivalent prices in the two markets could not differ by more than the cost of transportation between these markets.

Many U.S. manufactured goods do not have near-perfect substitutes on the lists of products manufactured abroad, however, and in this third context the law of one price is denied as an empirical proposition. Agricultural tilling machinery produced in the United States, for example, is apparently not a close

substitute for agricultural tilling machinery produced in Germany.

3/ Laurence C. Rosenberg, "The Impact of the Smithsonian and February, 1973 Devaluations on Imports: A Case Study of Steel Imports," in Peter B. Clark, Dennis Logue and Richard J. Sweeney, eds., The Effects of Exchange Rate Adjustments (U.S. Department of the Treasury, forthcoming, 1976).

4/ This may not be the case when sellers of primary commodities have monopoly power and/or enter into long-term marketing agreements with their customers, as do U.S. copper producers, for example. a

-~-4-

More generally, the most disaggregated groupings of manufactured goods for which both U.S. and German prices are readily available are dominated by products for which German dollar price indexes diverge over time from U.S. dollar price indexes2/ in a manner that is strongly correlated with exchange-rate movements, This divergence is evident in comparisons of U.S. wholesale transactions prices and German export transactions prices for various 2 and 3-digit sectors of the WPI industry breakdown (Section 2), in comparisons of U.S. and German export transactions prices for various 4 and 5-digit SITC machinery categories (Section 3), and in comparisons of U.S. export unit values with unit values of U.S. imports from Canada, Germany and Japan for various 7-digit Schedule A and B commodity groups (Section 4).

The denial of the law of one price in this context -at the most disaggregated product level for which price data can be readily matched -- provides a strong presumption that it is impossible to assemble available data into aggregate price indexes which can be expected to obey the law of one price (except, perhaps, when product coverage is restricted to primary

commodities). Obversely, the notion that aggregate indexes of

5/ This divergence should come as no surprise to anyone familiar with the work of Irving B. Kravis and Robert E. Lipsey, Price Competitiveness in World Trade, National Bureau of Economic Research, Studies in International Economic Relations No. 6,

New York, 1971.

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export or tradeable-goods prices will exhibit purchasing power parity -- i.e., that relative home-currency prices of different countries will stay in line with exchange rates -- cannot validly

lean on the law of one price for support.

2. Comparative Movements of U.S. and German Industrial Prices

The adjustment mechanism alleged to police the law of one price is commodity arbitrage. Under free trade, if products were marketed competitively, commodity arbitrage would prevent disparities between the f.0.b. transactions prices associated with export and domestic sales of the same product -- i.e., export and wholesale transactions prices would be equal f.o.b. International tests of the law of one price would be insensitive to whether the comparisons were between international wholesale prices, export prices, or a mix of both.

Discriminating monopolies and tariffs, subsidies, or other trade restrictions create disparities between export and wholesale prices. Provided that trade restrictions do not change substantially during the data period, however, international comparisons of any mix of export and wholesale prices can validly test the law of one price by focussing on whether any initial disparities change substantially over time. Evidence that disparities between the common-currency prices of different countries are systematically correlated with exchange rates, rather than randomly fluctuating over time, is a strong denial of

the law of one price for the products being compared.

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The United States, Germany and Japan publish data on export transactions prices. The coverage of U.S. data is restricted mainly to various 4 and 5-digit-SITC machinery items, collected only once a year (in June) prior to 1974 and 4 times a year beginning in 1974, German and Japanese data are available monthly for a broad list of items; but for many items Japanese ‘prices are sticky. These considerations have led us to first compare nonthly time series of U.S. wholesale prices and German export prices for a variety of industries over the 1968-75 period, and to then compare June data on U.S. and German export prices for various machinery categories over the 1970-75 period .2/

The first set of industry price comparisons is described by Figure 1 and Tables 1 and 2. The exchange rate is measured

in dollars per mark (1970=100) ,2/ and relative price indexes are

6/ The first comparison extends a similar study of the 1968- 73 period, described by Peter Isard, "The Price Effects of Exchange Rate Changes," in Peter B. Clark, Dennis Logue and Richard J. Sweeney, eds., The Effects of Exchange Rate Adjustments (U.S. Department of the Treasury, forthcoming, 1976). This comparison focuses on 2 and 3-digit sectors of the 8-digit WPI industry breakdown, and does not consider the most narrowlydefined industries for which price comparison is possible. The comparisons of machinery export prices (Section 3) and U.S. import and export unit values (Section 4), however, are restricted to the most narrowly-defined products for which such prices can readily be compared.

7/ For December 1968 - September 1969 the exchange rate is

set 4 per cent above the actual spot rate to reflect the effective exchange rate for German exports under the 4 per cent export tax levied between late November 1968 and the mark revaluation in October 1969.

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German mark prices multiplied by the exchange rate and divided by U.S. dollar prices (and then converted to 1970=100). Industry definitions are described in the data appendix. The Figure presents strong evidence that relative dollar prices of apparel and paper products have not fluctuated about constant levels during the 8-year data period under examination, but rather have ' been influenced heavily by exchange rate movements. Interpreted casually, the Figure suggests that the relative price of apparel is explained almost entirely by the exchange rate, whereas the relative price of paper products adjusts almost entirely to exchange rate changes in the short-run while moving back slowly toward its initial level over time.

In Tables 1 and 2 we have divided the sample period into 8 three-month periods, during each of which the exchange rate was fairly stable. Table 1 compares movements in exchange rates and relative prices during the succesive intervals between these 8 periods, while Table 2 shows cumulative charges. The first “interval in Table 1 starts at the beginning of the data period and ends just prior to the German revaluation in October 1969. The second interval includes this revaluation and ends just prior to the start of the German float in May 1971. The third interval spans the German float, the Smithsonian Agreement in December 1971, and the three quarters following the Smithsonian yet prior to

the early signs of the pressures that brought the realignment

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in February 1973. The fourth interval includes the realignments of first-quarter 1973 and the float ing period thereafter, ending when the mark was at its peak in Summer 1973. The fifth interval ends a year later, after the mark had fallen to a trough in January 1974, risen to a new peak in May, and then depreciated to a Summer 1974 trough. The sixth interval ends with the mark at its next peak in Spring 1975. The seventh interval spans the dollar appreciation in the second half of 1975.

For most of these intervals, changes in the exchange rate are paralleled fairly closely by movements in 5 af the 9 relative price indexes -- those for apparel, metalworking machinery, electrical industrial equipment, home electronic equipment, and glass products -- although relative prices of metalworking machinery and home electronic equipment show "unexplained" upward shifts in the first two intervals while the relative price of glass products shows "unexplained" downward shifts. The relative price of paper products moves up proportionately less (or down proportionately more) than the exchange rate in 6 out of 7 intervals; while relative prices of industrial chemicals, agricultural chemicals and plastic materials parallel exchange rates fairly closely for the first half of the sample period and then fall sharply during the second half.

The conclusions drawn from this informal analysis are

(1) that exchange rate movements are associated with substantial

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‘short-run changes in relative dollar price indexes for all industrial categories considered here, and (2) that in most

cases a major share of the short-run relative price change persists for at least several years. Careful econometric studies of data for a longer sample period might indeed find that the relative price changes associated with any particular exchange rate movement are completely offset over long periods of time. But in reality exchange rates are rarely stable over long periods of time. Thus, for practical purposes, products at this level

of disaggregation are not sufficiently close substitutes to preclude substantial and persistant changes in relative common-

currency prices.

3. Comparative Movements of U.S. and German Export Prices for Selected Machinery Categories

U.S. and German export transactions prices for various 4 and 5-digit SITC machinery categories allow relative price comparisons at a finer level of commodity disaggregation than the industry groups considered above. Prior to 1974, U.S. data are collected only once a year, in June. Table 3 compares relative prices for six machinery categories with the exchange rate in June of each year during the 1970-75 period. (See the data appendix for product descriptions.) The conclusions of

the previous section extend to this finer level of disaggregation.

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Machinery items at the 4 and 5-digit SITC level of disaggregation are not sufficiently close substitutes to preclude substantial

and persistent changes in relative common-currency prices.

4. Comparisons of U.S. Export Unit Values with Unit Values of U.S. Imports from Canada, Germany and Japan

U.S. export price data are available at a still finer level of product disaggregation in the form of unit value indexes for 7-digit Schedule-B export commodities. These export unit values can be compared with 7-digit Schedule-A import unit values for products distinguished by country of origin. 8/9/ Unlike the process of collecting transactions price data, however, the process of collecting unit value information does not hold constant the mix of items within each commodity group whose prices are sampled. Thus, on the one hand, there is no strong presumption that the law of one price will be more evident in these unit value data than it is in the export and wholesale price data previously examined for less-disaggregated commodity groups. But on the other hand, there is no presumption that shifts in commodity composition will generate "noise" in relative export and import unit values that is strongly correlated with exchange-

rate movements.

8/ The Schedule-A and Schedule-B classifications differ, but a reasonably close matching is possible at the 7-digit level.

9/ It is not appropriate to dismiss this comparison on the grounds that countries rarely export the exact same products that they import. The relevant issue is whether products selected from disaggregated lists of U.S. manufactured goods have close (not exact) substitutes on lists of goods manufactured abroad, and this is an

empirical question which should be addressed in each of the few contexts for which matching data are available.

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Because our only access to these unit value data was by hand copying, we limited our sample size to 5 commodity groups and constructed unit values on a quarterly basis, rather than monthly, from first-quarter 1968 through first-quarter 1975. Our focus is on unit values of exports to all import ing-areas combined and unit values of imports from three selected countries: Canada, Germany and Japan. The 5 commodity groups are soaps, tires (pneumatic passenger car), wall paper, ceramic tile (floor and wall), and steel bars. (See the data appendix for detailed definitions of commodity groups.) Export unit values are generally f.a.s. at the U.S. port of export, based on the transactions price, including inland freight, insurance and other charges incurred in placing the merchandise alongside the carrier at the U.S. port of exportation. Import unit values are c.i.f. beginning in 1974; prior to 1974 c.i.f. values are not available and import value is defined generally as "the market value in the foreign country."

These unit value data fluctuate so erratically that it is difficult to reach any conclusions about the law of one price by looking casually at plots analogous to Figure 1, or at information analogous to that provided in Tables 1-3. Accordingly we have relied on regression analysis to determine if any part of the variation in ratios of import unit values to export unit

values is redated systematically to fluctuations in exchange rates.

~16- Our notation is:

t = index of quarterly time periods

R, = ratio of U.S. import unit value by country-oforigin to U.S. export unit value, in period t

St = exchange rate in period t: the U.S. dollar price of one unit of the currency of the country-oforigin of U.S. imports.

D_ = dummy variable: 0 from 1968 Ql to 1973 Q4; 1 from 1974 Ql to 1975 Ql

where D, is introduced to adjust for the shift in first-quarter

1974 in the method of valuing imports.

The first regression hypothesis that we tested is (1) Re = 4) + ay Sp tag Dp, tee + pep]

which allows for first-order autocorrelation. We also tested

the hypothesis

(2) ARe = by AS + bo ADt + UE + Our]

10/

which allows for a different pattern of serial correlation.— In each case we used the Cochrane-Orcutt procedure. The empirical results argued in favor of hypothesis (1) on two counts: the Durbin- Watson statistics were closer to 2.0 for 6 out of 11 pairs of

10/ Other patterns of serial correlation are more difficult to take into account and have been implicitly assumed not to exist.

« 17 - 11/

commodities and countries-of-origin,—

12/

statistics were consistently higher .—

while corrected-R2

Table 4 presents the regression results for hypothesis (1). Ratios of German dollar prices to U.S. dollar prices, and ratios of Japanese dollar prices to U.S. dollar prices, are seen to be significantly and positively dependent on U.S. dollar prices of the mark and yen, respectively, for almost all commodity groups under consideration. A similar finding does not emerge in the Canadian case, perhaps because the exchange rate between the U.S. and Canadian dollars showed little variance and no abrupt changes during the sample period. The significance of exchange rate levels in the German and Japanese cases, however, suggests again that substantial changes in exchange rates typically have substantial and persistent effects on the relative common-currency prices of closely-matched manufactures produced in different countries. ~~ 11/ Four of the 15 pairs were discarded because U.S. imports from the country-of-origin were zero or negligible, so that unit

values could not be computed, in one or more quarters of the sample period.

12/ It is worth noting, however, that b; was judged to be

significantly greater than zero with at least 95 per cent confidence in 5 of the 11 estimates of equation (2).

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Table 4, Regression Results for Hypothesis (1 2 | ; a, ay ay ) R D.W. CANADA tires -4.16 .0588 -.317 859 .737 2.33 - ,832 1.16 -1.15 8.87 wallpaper -.406 .0118 361 . 186 .656 1.89 -~ .462 1.31 4.50 1.00 steel bars .852 -.00292 .418 .0930 .553 1.94 935 -.312 4.82 -494 GERMANY soap .726 .0938 -.791 ~120 .148 1.60 .607 2.35 -1.35 ~641 _tires | - .0828 .0437 -.142 .758 .728 1.66 -.152 2.72 - 816 6.15 wallpaper 316.0264. —--.0401 -.0974 163. —:1,96 885 2,21 -.223 -.518 JAPAN soap -.582 15.49 .921 .113 .N674 1.87

(-.137) (1.12) (.740) (.604)

tires - .940 6,28 244 461 .869 2.11 (-2.90) (6.04) (2.95) (2.75)

eee en a

wallpaper -.720 6.79 1.07 153 .901 2.04

(-1.83) (5.30) (9.40) (.817)

ceramic tile ~0242 2.32 -428 125 .693 1.74 (.0826) (2.43) (4.99) (.665)

steel bars .183 1.39 .148 .908 -672 2.42

(.825) (1.95) (2371) (3.12)

Note: Numbers in parentheses are t-values. Critical values for the one-tailed t-test are 1.71 (95 per cent confidence) and 2.48 (99 per cent confidence).

-.19 -

DATA APPENDIX A.) U.S. and German Transactions Prices for Selected Industries

U.S. wholesale price indexes were taken from various issues of the Monthly Labor Review (U.S. Department of Labor, Bureau of Labor Statistics). In most cases these are constructed from f.o.b. prices at production or central marketing point. Weights are based on value of shipments data from the 1963 industrial censuses.+

German export price indexes were taken from Preise Lohne Wirtschaftrechnungen Reihe 1: Preise und Preisindices fur Aussenhandelsguter (Statistiches Bundesamt Wiesbaden, various annual and monthly issues). Prices are generally collected on an f.o.b. basis and in all cases are duty free. Weights are based on German export values.

Foreign exchange rates for the Deutschemark vis-a-vis the dollar were taken from various issues of the Federal Reserve Bulletin, computed as monthly averages of noon buying rates in New York for spot cable transfers.

The 9 industries, their respective titles in the U.S. and German data sources, their U.S. wholesale price codes in parentheses, and other relevant specifics are as follows:

1. Apparel (03-5); Bekleidung (zusammen). ~~ 1/ For a more complete description, see U.S. Department of

Labor, Bureau of Labor Statistics, BLS Handbook of Methods, Bulletin 1711, 1971, Chpt. 11.

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2. ‘Industrial chemicals (06-1); weighted average of Anorganische and Organische Grundstoffe und Chemikalien. The weights used to combine the German series were .4250 (inorganic) and .5750 (organic), based on the relative weights. of these items in the U.S. wholesale price index.2/

3. Agricultural chemicals and chemical products (06-5); ‘Dungemittel und Schadlingsbekampfungsmittel.

4, ‘Plastic resins and meterials (06-6); Kunststoffe.

5. Pulp, paper and allied products (09); Papier und Pappewaren.

6. Metal-working machinery and equipment (11-3); Metallbearbeitungsmaschinen (zusammen).

7. Electrical machinery and equipment (11-7); weighted average of Gerate und Einrichtungen (a) zur Elektrizitatserzeugung and (b) zur Elektrizititsverteilung. The weights used to combine the German series were (a) .4983 and (b) .5017, based on the relative weights assigned to items (a) 11-73 plus 11-74 and (b) 11-71 plus 11-75 in the U.S. wholesale price index.3/

8. Home electronic equipment. (12-5); Rundfunk - Fernseh - phonotechn. Gerate und Einrichtungen.

9. Flat glass plus Glass containers (13-11 plus 13-8);

Glas und Glaswaren (zusammen).

2/ Source: U.S. Department of Labor, Bureau of Labor Statistics Wholesale Prices and Price Indexes: Supplement 1972, Feb. 1973, Table 4.

3/ Source: Ibid.

3

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B.) U.S. and German Export Prices for Selected Machinery Categories

U.S. export price indexes for 4 and 5-digit SITC categories of machinery are taken from quarterly news releases by the Division of International Prices of the Bureau of Labor Statistics, U.S. Department of Labor. German export price indexes and exchange rates are from sources described in part A.

The machinery categories listed in Table 3 have the following representations in the U.S. and German data sources:

1. U.S.: Internal Combustion Engines Other Than for Aircraft (SITC 711.5); Germany, Internal Combustion Engines for Motor Vehicles and Motorcycles (Verbrennungsmotoren fur Kraftwagen und Kraftrader).

2. U.S.: Calculating Machines, Accounting Machines and Similar Machines Incorporating a Calculating Device (SITC 714.2); Germany: Adding and Calculating and Accounting Machines (Rechen und Buchungsmachinen) .

3. U.S.: Machine Tools for Working Metals (SITC 715.1); Germany: Metalworking Machinery (Metalbearbeitungsmachinen).

4. U.S.: Pumps, Excluding Centrifuges (SITC 719.2 excl. 719.23); Germany: Pumps and Compression Equipment (Pumpen und Druckluftgerate und dgl.).

5. U.S.: Forklift Trucks (SITC 719.32); Germany: cranes and Lifting Gear (Krane und Hebezeuge).

6. U.S.: Argricultural Machinery and Appliances for Preparing and Cultivating the Soil (SITC 712.1); Germany: Soil

Tilling Equipment (Ackerschlepper).

~ 22+

C.) Unit Values of U.S. Exports and Imports

Sources: U.S. Department of Commerce, Bureau of the Census, "U.S. Exports: Schedule B Commodity by Country” (FT 410 publications, various issues) and "U.S. General Imports: Schedule A Commodity by Country" (FT 135 publications, various issues). Data on dollar values and physical quantities were gathered -cumulative, January to date -- for March, June, September and December of each year, from which quarterly values and quantities were derived and quarterly unit values then computed. The five commodity categories and their 7-digit Schedule B and Schedule A codes are:

1. Exports of "soap, bulk" (5541010); imports of "soaps, including soap powers, but not synthetic detergents" (5541000).

2. Exports of "tires, passenger car and motorcycle, pneumatic" (6291010); imports of "tires, pneumatic, passenger car, new” (6291015).

3. Exports of "wallpaper" (6419700); imports of "wallpaper" (6419700).

4. Exports of "non-refractory ceramic floor and wall tiles" (6624610); imports of "tile, ceramic floor and wall, except masaic, glazed" (6624750).

5. Exports of "carbon steel bars and rods and hollow drill steel, cold finished, n.e.c." (6732440); imports of steel

bars, not alloyed, cold formed (6732440).