The Purchasing Power Parity Puzzle

Rogoff frames the puzzle as a reconciliation problem: real exchange rates are extremely volatile in the short run – “the one-month conditional volatility of real exchange rates… is of the same order of magnitude as the conditional volatility of nominal exchange rates” – yet “consensus estimates suggest… that the speed of convergence to PPP is extremely slow; deviations appear to damp out at a rate of roughly 15 percent per year.” It is a puzzle, not merely a failure, because the two facts pull in opposite directions: an explanation built on short-term nominal rigidities should produce fast reversion once prices adjust, while an explanation built on persistent real shocks should not generate this much short-run volatility in the first place.

Rogoff reports that “study after study has found that deviations from the law of one price are remarkably volatile across a surprisingly broad range of goods,” citing evidence from Isard (1977), Richardson (1978), and Giovannini (1988) on apparel, chemicals, paper, glass products and even “commodity manufactures” such as screws, nuts and bolts, where price differentials are “large, persistent, and to a significant extent simply reflect nominal exchange rate movements.” His Big Mac price table (1995 data) shows prices ranging “from $5.20 in Switzerland at the high end to $1.05 in China at the low end,” while gold prices across major markets stay within a fraction of a percent of each other – illustrating that the law of one price “does hold very well” for some highly traded commodities but that “commodities where the deviations… damp out very quickly are the exception rather than the rule.”

Engel and Rogers (1995), using fourteen categories of disaggregated consumer prices for 23 U.S. and Canadian cities, find that “even after controlling for distance, there remains a dramatic difference in relative price volatility when one compares two cities on opposite sides of the border versus two cities on the same side of the border,” an effect “equivalent to adding anywhere between 2,500 to 23,000 miles between cities.” Engel’s (1993) comparison of relative-price volatility for similar goods across the U.S.-Canada border versus dissimilar goods within either country similarly finds that, in over 2,000 pairwise comparisons, “the relative prices of very similar goods across the U.S. and Canada are much more volatile than the relative prices of very different goods within either country” – evidence Rogoff reads as a genuine border/segmentation effect, not simply a transportation-distance effect.

Froot, Kim and Rogoff’s (1995) study of grain and dairy prices in Holland and England from the fourteenth through the twentieth centuries finds that “the volatility of deviations from the law of one price, even among highly traded goods such as grains, has been remarkably stable over the centuries,” a result “quite robust to the choice of detrending methods.” Rogoff draws the inference that “any explanation of the PPP puzzle must not rely too heavily on institutional factors peculiar to the twentieth century” – ruling out, for instance, an explanation resting solely on the post-1973 shift to floating nominal exchange rates.

Early unit-root tests on post-1973 floating-rate data could not reject a random walk in real exchange rates, which Rogoff calls “something of an embarrassment” because “every reasonable theoretical model suggests that there should be at least some temporary component to PPP deviations,” given that long-run monetary neutrality implies monetary shocks’ real effects should eventually die out. Frankel argued the problem was low statistical power – if PPP deviations damp out slowly enough, “it may require many decades of data” to reject a unit root reliably – and, using annual dollar/pound data for 1869-1984, rejected the random walk with an estimated 14 percent annual decay rate, “implying a half-life for PPP deviations of 4.6 years.”

Across long-horizon studies (Abuaf and Jorion 1990, Glen 1992, Diebold-Husted-Rush 1991, Lothian and Taylor) and cross-country panel studies (Frankel and Rose 1995b), “the consensus among these studies on the half-life of PPP deviations is remarkable (three to five years).” Rogoff flags two caveats: first, these estimates typically “blend fixed and floating rate data,” whose econometric implications of pooling are unclear, though Lothian and Taylor’s Chow test cannot reject equal convergence rates before and after 1973; second, nearly all these exchange-rate pairs involve countries that have been high-income throughout the sample, so “this raises the question of whether PPP will hold across two countries with sharply differing growth experiences” – a question connected to the Balassa-Samuelson effect.

The Balassa-Samuelson hypothesis holds that rich countries have systematically higher exchange-rate-converted price levels than poor countries because rich countries are relatively more productive in the traded-goods sector specifically; a rise in traded-sector productivity raises wages economy-wide, and since non-traded producers must match those wages without a matching productivity gain, non-traded (and overall) prices rise, raising the real exchange rate. Rogoff reports “substantial empirical support for the Balassa-Samuelson hypothesis, especially in comparisons between very poor and very rich countries, and in time series data for a select number of countries, including especially Japan,” but notes that “whether traded goods productivity bias is of broader importance in explaining real exchange rates across industrialized countries remains a matter of some debate,” since industrialized countries also show long-run convergence to PPP “notwithstanding” the Balassa-Samuelson effect.

Current-account deficits are empirically correlated with long-run real depreciation over five-to-ten-year horizons (Obstfeld and Rogoff 1995a document this across fifteen OECD countries for 1981-1990), but Rogoff stresses “correlation does not imply causation,” since “virtually any correlation between the current account and the real exchange rate can be easily rationalized” theoretically. Government spending is also found to raise the real exchange rate (Froot and Rogoff 1991, among EMS countries) because it “tends to fall more heavily on nontraded goods,” but Rogoff argues any such demand effect “must be transitory” given sufficient long-run factor mobility. Overall, he concludes “the three modifications to PPP discussed… are useful in some circumstances but are not nearly robust or universal enough to fully supplant purchasing power parity as a theory of the long-run real exchange rate.”

Clarida and Gali (1994) estimate that monetary shocks account for roughly 45 percent of the forecast-error variance of the dollar-DM real rate and 34 percent for the yen-dollar rate over the floating-rate era; Rogers (1995), using 130 years of U.S.-U.K. data, finds real shocks account for roughly half the one-year forecast error. Rogoff treats this research as “promising but still at an early stage,” noting it is “difficult to justify identifying as a demand shift any shock with only a transitory effect on the real exchange rate, especially if the effect is highly persistent,” and that both studies rest on “the somewhat anachronistic Mundell-Fleming-Dornbusch IS-LM framework, rather than a modern sticky-price intertemporal model.”

Rogoff concludes that “international goods markets, though becoming more integrated all the time, remain quite segmented, with large trading frictions across a broad range of goods,” due to transportation costs, tariff and non-tariff barriers, information costs, and limited labor mobility, which together create “a large buffer within which nominal exchange rates can move without producing an immediate proportional response in relative domestic prices.” He calls this “not an entirely comfortable conclusion,” since it does not pin down a single mechanism, but states “for now there is no really satisfactory alternative explanation to the purchasing power parity puzzle” – international goods markets, in his words, are “highly integrated, but not yet nearly as integrated as domestic goods markets.”