Accounting for U.S. Real Exchange Rate Changes
📄 Summarized from the full manuscript · Human-reviewed for faithfulness before publication
In brief
Why does the dollar's real value swing so much against other rich countries' currencies? One long-standing idea is that it's mainly non-traded goods -- haircuts, rent, local services -- getting relatively pricier or cheaper at home versus abroad. This 1999 paper tests that idea directly, using five different ways of separating traded from non-traded prices, at horizons from one month to thirty years. The answer is almost always no: traded-goods prices, which include the exchange rate itself, account for nearly all the movement, even over multi-decade periods and even when exchange rates are fixed. A detailed look at Japan's own service prices rules out one tempting alternative explanation.
What this paper finds — and why it matters
This 1999 Journal of Political Economy paper (NBER Working Paper 5394, 1995) by Charles Engel asks how much of the historical variation in the U.S. real exchange rate against other high-income countries can be attributed to relative-price movements in non-traded goods – the channel most open-economy models of the real exchange rate emphasize – versus movements in the relative price of traded goods, which includes the nominal exchange rate itself. Decomposing the mean-squared error, variance, and drift of the real exchange rate at horizons from one month to thirty years, using five separate measures of traded/non-traded prices built from consumer prices, OECD sectoral output prices, national-accounts consumption deflators, producer price indexes, and (for Japan) disaggregated corporate-services prices, Engel finds that the traded-goods component accounts for essentially all of the movement in the U.S. real exchange rate at every horizon, for almost every country pair and sample period examined – the share attributed to non-traded goods stays close to zero even over multi-decade horizons where sticky-price theories predict non-traded prices should dominate. The pattern holds whether nominal exchange rates are floating (1973-1995) or fixed (1962-1970), and it survives an explicit check for whether the traded-goods price indexes themselves are contaminated by non-tradable marketing and distribution costs: Japanese data on thirty-six categories of corporate-service prices show no systematic rise relative to the CPI that could explain the yen’s real appreciation. Canada, and under one producer-price-based measure a handful of European countries, are partial exceptions where the non-traded component matters more at long horizons, but the paper cautions this particular decomposition is highly sensitive to an arbitrary assumption about how to split the covariance between the two components. Engel concludes that whatever drives the dominant traded-goods component – a composition/terms-of-trade explanation, he finds, contributes “very little” – deviations from the law of one price for individual traded goods, rather than the relative price of non-traded to traded goods, is the more promising place to look.
Summary of a classic paper, AI-assisted and human-reviewed. See the linked original for the authoritative claims and full conditions.
Questions & answers
Q1. How does the paper decompose the real exchange rate into a traded-goods component and a non-traded-goods component?
The paper starts from a price index that is a geometric weighted average of traded and non-traded goods prices in each country, and shows that the log real exchange rate q_t can be written as the sum of two components: x_t, the log of the relative price of traded goods between the countries, and y_t, a weighted difference of the log of the relative price of non-traded to traded goods prices in each country (equation 1 and surrounding text). x_t includes the nominal exchange rate itself, while y_t = beta(p_N*-p_T*) - alpha(p_N-p_T), where alpha and beta are the non-traded-goods expenditure shares at home and abroad respectively.
Q2. What five measures of traded/non-traded goods prices does the paper construct, and over what country coverage?
The paper constructs five separate measures: (1) consumer price indexes (treating services and housing as non-traded, commodities as traded) for Canada, France, Germany, Italy, Japan and the U.S., monthly from January 1962 to March 1995; (2) OECD sectoral output prices, classifying most services as non-traded except transport/storage/communication, for up to seven countries relative to the U.S.; (3) national-accounts personal consumption expenditure deflators (goods versus services) for six countries, quarterly from 1970; (4) a cruder measure using the aggregate producer price index as the traded-goods proxy and CPI/PPI divergence as the non-traded component, across seventeen countries from 1972-1995; and (5) disaggregated Japanese corporate-services prices (thirty-six categories) used as a direct check on measure (4)’s assumptions.
Q3. What is the paper’s central empirical finding, and how robust is it across horizons?
The paper’s central finding is that “the non-traded component has accounted for almost none of the movements in the real exchange rate for the U.S. relative to high-income countries at any horizon” – with the exception of Canada and, under the PPI-based measure, a handful of European countries, “virtually 100% of the mean-squared error of real exchange rate changes for the U.S. are accounted for by movements in the traded goods component” at every horizon examined, from one month to as long as thirty years. This contradicts the expectation, from sticky-price theories, that the traded-goods component should matter mainly at short horizons and give way to the non-traded component at long horizons – using the output-price data, for instance, “there is no tendency for this component to become less important as the horizon lengthens.”
Q4. Does this pattern depend on whether nominal exchange rates are floating or fixed?
No: the paper finds essentially the same decomposition under the floating-rate period (1973-1995) and the fixed-rate period (1962-1970) for the CPI and output-price measures – “in both cases, at all horizons, nearly all of the movement in the real exchange rate comes from movements in the traded goods component.” The paper connects this to Froot, Kim and Rogoff’s (1995) finding, using 700 years of data, that “the volatility of deviations from the law of one price is no greater in the 20th century under floating exchange rates than it was in previous centuries when the exchange rate was essentially fixed.”
Q5. Why does the sizable rise in Japan’s relative price of non-traded goods since 1970 explain so little of the yen’s real appreciation?
The paper gives four specific reasons: the roughly 40% rise in Japan’s relative non-traded-goods price is small next to the 180% CPI-based real appreciation of the yen over the period; there are no large downswings in Japan’s relative non-traded price even though the yen has had episodes of dramatic real depreciation; the effect is scaled down in the real-exchange-rate formula by Japan’s non-traded expenditure share, calculated at about .31; and – “the most important reason” – the non-traded component y_t is a relative relative price, so it “subtracts off” the U.S.’s own relative price of non-traded goods, and “the relative price of non-tradables in the U.S. has closely mirrored the relative price of non-tradables in Japan,” so the two largely cancel.
Q6. How does the paper test, and reject, the hypothesis that the main finding is an artifact of hidden non-traded “marketing” costs inside the traded-goods price measures?
If the traded-goods price index itself contains an unmeasured non-tradable marketing/distribution component, the paper’s method would understate the true importance of non-traded prices; to check this directly for Japan, it examines actual price data for thirty-six categories of Japanese corporate services (finance, real estate, transport, etc.) since January 1985, and finds that “most of these prices fall relative to the CPI,” with only six of the thirty-six rising noticeably, and that “the index for all corporate services holds steady relative to the CPI over the entire period.” Even under an arbitrary algebraic correction that assumes marketing services make up two-thirds of the measured traded-goods price (which the paper judges a likely overcorrection), “x_t accounts for a large share of the MSE at all horizons for most of the currencies.”
Q7. What exceptions to the main finding does the paper report, and how does it qualify them?
Canada is a partial, mild exception across several measures, where the traded-goods share dips to roughly 50-60% around a 15-16 year horizon before rising again (though the paper notes “very few observations are used” at these horizons); under the crude PPI-based measure specifically, three countries – Germany, the Netherlands and Canada – show the sticky-price-consistent pattern of non-traded goods dominating at long horizons, while results for ten other countries are mixed. The paper explicitly cautions that this PPI-based decomposition “depend[s] heavily on our choice of attributing exactly half of the co-movements” between the two components to each, and “we must not take the decompositions presented in this section too seriously.”
Q8. In what sense does the paper describe its own numbers as “accounting numbers” rather than statistics, and why does that framing matter for interpreting the results?
The paper explicitly frames its results as a historical decomposition rather than an inference about an underlying population: “The numbers presented here should be thought of as accounting numbers, not as statistics. The numbers do not represent sample measures of some underlying population parameters,” drawing an analogy to calculating the actual average height of the people in a room (a fact about them) rather than estimating the average height of humans in general (a population parameter) – the goal is to say how much of the U.S. real exchange rate’s actual historical movement over the past 20-30 years is attributable to y_t, not to estimate a stable structural share.
Q9. What does the paper conclude about where the explanation for traded-goods-price movements should be sought instead?
Having shown that the traded-goods component x_t, not relative non-traded prices, drives nearly all real-exchange-rate movement, the paper reports that an explicit test of one candidate explanation – terms-of-trade composition effects, where traded-goods sub-indexes carry different weights across countries – “explains very little,” because “the weights of the sub-categories in the overall price index are not too different across countries.” The paper instead points toward deviations from the law of one price for individual traded goods (pricing-to-market, market segmentation) as the more promising direction, while stressing this remains an open question: “the evidence of this paper suggests that the relative price of non-traded goods has little import for understanding U.S. real exchange rate movements,” leaving what does drive x_t for future research. The paper also notes its scope is limited to high-income countries, since “the behavior of real exchange rates for low-income countries might be very different.”
Key terms in this paper
Definitions below follow the paper's own usage.
- Traded-goods component (x_t)
- the part of the log real exchange rate equal to the nominal exchange rate plus the log relative price of traded goods between the two countries -- the component the paper finds accounts for "virtually 100%" of U.S. real exchange rate movement at nearly every horizon studied.
- Non-traded-goods component (y_t)
- the part of the log real exchange rate attributable to each country's relative price of non-traded to traded goods, weighted by each country's non-traded expenditure share and differenced across countries -- a "relative relative price" that the paper shows is distinct from, and much smaller than, the within-country relative price of non-traded to traded goods on its own.
- Accounting numbers (as distinct from statistics)
- the paper's own characterization of its reported decomposition shares -- a measure of how much of the actual, historical movement of the U.S. real exchange rate is attributable to each component, not "sample measures of some underlying population parameters," analogous to measuring the actual average height of people in a specific room rather than estimating a population average.