Can Sticky Price Models Generate Volatile and Persistent Real Exchange Rates?

Decomposing the variance of the log real exchange rate into a traded-goods component and a nontraded-relative-price component using disaggregated OECD price data for the United States and an 11-country European aggregate (1973-1998), the paper finds var(log q) = 3.64 = 4.10 + 0.076 - 0.54, implying that “the maximum portion of the variance of the real exchange rate attributable to variability in the nontraded goods relative price is only about 2%” (Sec. 1.B, p. 7). This finding, corroborated using wholesale price indices to check that distribution/retailing costs are not driving the result, justifies the paper’s decision to build a model with price-discriminating monopolists and abstract entirely from nontraded goods.

Competitive final-goods producers in each country combine home and foreign intermediate goods (an Armington/Dixit-Stiglitz aggregator, eq. 1) purchased from monopolistically-competitive intermediate-goods producers who can price-discriminate across countries, set prices in the local currency of each market, and set those prices in a staggered fashion for N periods at a time (following Calvo 1983); capital accumulation with convex adjustment costs is included so the model can also match the relative volatility of consumption and investment to output (Sec. 2, pp. 8-14). Asset markets are complete, so the real exchange rate equals the ratio of the two countries’ marginal utilities of consumption (eq. 14/18) – a relationship that becomes central to the paper’s main anomaly.

Log-linearizing the real exchange rate gives q-hat is approximately equal to A times (c-hat minus c-hat) plus smaller terms in relative money and relative leisure, where A is approximately the coefficient of relative risk aversion; with the paper’s benchmark preferences A = 4.96 (set via the curvature parameter sigma = 5), which is needed to reproduce the data’s real-exchange-rate-to-output volatility ratio of 4.36* (Sec. 4, eq. 18, pp. 19-20, Figure 3). The autocorrelation of the real exchange rate is essentially unaffected by varying sigma, since persistence instead comes from price-stickiness.

With the benchmark N=4 quarters of price-stickiness (per Taylor 1999), the model generates a nominal exchange rate 4.32 times as volatile as output and a real exchange rate 4.27 times as volatile (close to the data’s 4.67 and 4.36), with autocorrelations of 0.69 and 0.62 respectively – less persistent than the data’s 0.86 and 0.83 (Sec. 4, Table 5, p. 20). The paper shows the autocorrelation of the real exchange rate is “essentially determined by” the autocorrelation of relative consumption, and that without substantial price-stickiness (N=1), both would be negative rather than positive (Sec. 4, Figure 4, p. 21). Replacing flexible labor markets with four-quarter sticky nominal wages (Sec. 6A) improves persistence only marginally (autocorrelation rising from 0.62 to 0.69).

Because asset markets are complete, the real exchange rate is tied by eq. (14)/(18) to the ratio of marginal utilities of consumption across the two countries, which under the benchmark separable-in-leisure preferences implies a model correlation between the real exchange rate and relative consumption of 1; in the data, this correlation is -0.35 for the US-Europe aggregate, and ranges from -0.48 to 0.24 across five individual European country pairs (France, Germany, Italy, the UK, and the US) – “we refer to this large discrepancy as the consumption-real exchange rate anomaly” (Sec. 4, Table 6, pp. 23-24, Sec. 6B, Table 7). The paper stresses this proportionality between the real exchange rate and relative marginal utilities holds in ANY complete-markets model, “regardless of the frictions in the goods and labor markets like sticky prices, sticky wages, shipping costs, and so on” (Introduction, p. 4) – meaning no further goods- or labor-market friction can fix it.

Replacing the full set of contingent bonds with a single noncontingent nominal bond (so that the real-exchange-rate/marginal-utility relationship holds only in expected first differences, eq. 32-33, rather than in levels) leaves the statistics for both volatility and persistence “virtually identical to those for the benchmark economy with complete markets” – “while adding incomplete markets theoretically could help eliminate the consumption-real exchange rate anomaly, quantitatively it does not” (Sec. 6B, pp. 32-33).

Adding external habit persistence (replacing consumption c with c minus d times lagged aggregate consumption in the utility function, eq. 34) and checking what habit parameter d would be needed to match the US-Europe data’s actual correlation between the real exchange rate and the habit-adjusted consumption differential, the paper finds the correlation attains a maximum of only -0.19 as d ranges up to 1 (versus the theoretically required value of 1), and concludes “this popular version of the habit persistence approach is not particularly promising” (Sec. 6B, pp. 34-35).

Raising the export share of output from the benchmark 1.6% (matching actual US-Europe bilateral trade) to 15% (matching total US trade with the rest of the world) “produces little change overall” (Sec. 5A, pp. 22-23). Switching to a commonly-used nonseparable utility specification consistent with balanced growth causes real exchange rates to “vary hardly at all,” because movements in employment then offset movements in consumption in determining the marginal utility of consumption – the covariance between relative consumption and relative employment is far larger in this version of the model (1.41) than in the data (0.37) (Sec. 5B, pp. 23-24). Adding technology and government-spending shocks on top of monetary shocks changes most statistics “little,” with the main exception that investment volatility relative to output rises closer to the data’s level (Sec. 5C, pp. 25-26).

“We have developed a general equilibrium, sticky price model which can generate real exchange rates that are appropriately volatile and quite persistent, though not quite persistent enough,” requiring preferences separable in leisure, high risk aversion, and at least a year of price-stickiness; but “the main failing of our model is the consumption-real exchange rate anomaly,” which the paper traces to the assumption of complete (or simply-incomplete) asset markets common to essentially the entire international business cycle literature, real and nominal alike (Sec. 7, Conclusion, pp. 35-36). The authors conclude that “to attempt to eliminate it, future research should focus on incorporating richer forms of asset market frictions,” rather than further goods- or labor-market frictions.