Long Swings in the Dollar: Are They in the Data and Do Markets Know It?

Summary

Engel and Hamilton (1990) model the dollar exchange rate as a stochastic segmented trend — a two-state Markov-switching mean process — and ask two questions. First (statistical): do the persistent multi-year swings in the DM/dollar (Deutsche Mark), franc/dollar, and pound/dollar represent a genuine departure from a random walk? Second (economic): if the swings are real, do currency markets know about them — i.e., do interest rate differentials correctly predict them via uncovered interest parity (UIP)? The answer to the first question is yes: the segmented-trends model significantly beats the random walk in- and out-of-sample for all three currencies. The answer to the second question is no: interest rate differentials have essentially no predictive content for regime transitions, and the sign of the interest differential during dollar appreciation episodes is often the wrong sign for UIP.

Key Claims

Stochastic segmented trends: $\Delta y_t = \mu_{s_t} + \sigma_{s_t}\varepsilon_t$ where $s_t \in \{1,2\}$ follows a first-order Markov chain with transition probabilities $p_{11} = P(s_t=1|s_{t-1}=1)$ and $p_{22} = P(s_t=2|s_{t-1}=2)$ . State 1 = dollar depreciating ( $\mu_1 < 0$ ), state 2 = dollar appreciating ( $\mu_2 > 0$ ).
German mark estimates (quarterly, 1973 Q3–1983 Q4): $\hat\mu_1 = -1.25\%$ /qtr, $\hat\mu_2 = +3.3\%$ /qtr; $\hat{p}_{11} = 0.922$ , $\hat{p}_{22} = 0.850$ ; implied mean durations ≈ 13 and 7 quarters. France and UK yield qualitatively similar estimates with persistent regimes.
Non-standard testing: Under the null $\mu_1 = \mu_2$ , the transition probabilities $p_{11}$ , $p_{22}$ are unidentified (nuisance parameters disappear under the null), so standard asymptotics break down. Engel and Hamilton use Wald tests on overidentifying moment conditions. The random walk null is rejected for all three currencies at the 5% level (Table 2).
Forecasting superiority (Tables 3–4): In-sample mean squared error (MSE) improvement over the random walk is 9–14% at 4-quarter horizon for Germany and France; similar gains in post-sample period 1984–1987. The smoothed regime probabilities (Hamilton filter output) closely track the actual trajectory of dollar appreciation and depreciation.
UIP implication: Under uncovered interest parity, $i_t - i_t^* = E_t[\Delta y_{t+1}]$ , the expected depreciation given the current regime probability. During state-2 episodes (dollar appreciation), UIP requires U.S. interest rates to be higher than foreign rates.
UIP failure — univariate test: In practice, U.S. interest rates were often lower than foreign rates during the 1980s dollar appreciation. The forward premium was the wrong sign, ruling out UIP as an explanation.
UIP failure — bivariate model: A bivariate system of $(\Delta y_t, i_t - i_t^*)$ is estimated allowing interest differentials to be informative about regimes. Interest differentials have essentially no predictive power for regime transitions. The bivariate model does not improve on the univariate model in identifying or predicting regime switches.
Peso problem caveat: Rational agents who expected a large unrealized depreciation with small probability would exhibit systematic ex-post forward rate forecast errors without being irrational. But the wrong sign of interest differentials during dollar appreciation is hard to reconcile even with this story.
Connection to Meese-Rogoff (1983): The random walk's out-of-sample dominance over structural exchange rate models (Meese-Rogoff 1983) is not contradicted: a highly persistent Markov-switching process with $p_{11}, p_{22} \approx 0.9$ looks nearly like a random walk over short horizons, so structural models that miss the regime process will fail to beat the random walk at 1–4 quarter horizons.

Concepts Introduced or Extended

Entities Mentioned

Quotes

"We find strong evidence that the process generating exchange rates differs significantly from a random walk."

"We find very little evidence that markets know about the long swings."

My Take

A landmark paper both methodologically and empirically. The pairing of "yes, the swings are in the data" with "no, markets don't know about them" is striking: there is statistically predictable structure in exchange rates, but it is not arbitraged away through interest differentials. The non-standard testing problem (unidentified nuisance parameters under the null) is handled carefully via moment conditions; later work by Hansen (1992) and Garcia (1998) would develop general likelihood-ratio tests for Markov-switching models. The UIP failure finding here anticipates the broader "exchange rate disconnect" literature. One limitation: the estimation sample is short (about 40 quarters per currency), making the parameter estimates for $\mu_2$ especially imprecise.