One of the seminal empirical exchange rate papers is Charles Engel‘s and Jim Hamilton‘s “Long swings in the exchange rate: are they in the data and do markets know it?” (AER, 1990). Think about it – while one often can’t reject the null hypothesis of a random walk in the exchange rate (using typically low-powered tests), the typical floating exchange rate sure doesn’t look like a random walk. What does a Markov switching model applied to the US broad trade-weighted real value of the US dollar (instead of bilateral against Deutsche mark, French franc, British pound).

A switching model estimated over the 1973Q1-2022Q3 period indicates the dollar falls 4.1% during depreciation regimes and rises 5.8% during appreciation regimes. Figure 1 displays on top panel the log real dollar value, and in the middle (bottom) panel, the probability of being a depreciating (appreciating) regime. [Markov switching model, 2 regimes, same variance in two regimes.]

Figure 1: Top panel, log real value of broad trade weighted dollar (black), 2006M01=0; Middle panel: probability of being in depreciating regime (blue), NBER peak-to-trough recession dates shaded gray; Bottom panel: probability of being in appreciating regime (blue). Red dashed line at 50%. Probabilities are smoothed and filtered. Source: Federal Reserve Board (goods export weighted through 2015, goods and services export weighted 2016 and onward), NBER, and author’s calculations.

Using a 50% threshold, the dollar has been in an appreciating regime since 2021Q2. The probability of staying in an appreciating regime when in an appreciating regime is 81%, while the probability of transitioning to a depreciating regime from an appreciating regime is only 15%.

The expected duration of regime 2 (appreciating) is 5.23 quarters. If the appreciating regime has been in place since 2021Q2, then a switch to depreciation would not be surprising. However, the model I’ve estimated does not ascribe a higher likelihood to a switch the longer one is in a given regime.

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