one This The seminal empirical exchange rate paper was Charles Engel‘sand Jim Hamiltonof “Long-Term Fluctuations in Exchange Rates: Are They in the Data? Does the Market Know?” (AER1990). Think about it – while one generally cannot reject the null hypothesis of a random walk of exchange rates (usually using a low power test), a typical floating exchange rate certainly does not Look Like a random walk. What Markov transformation model applies to U.S. broad trade-weighted dollar real values (not bilateral vs. Deutsche Mark, French Franc, GBP).
The conversion model, estimated between the first quarter of 1973 and the third quarter of 2022, shows that the dollar fell 4.1% during depreciation and rose 5.8% during appreciation. Figure 1 shows the log real dollar value in the top panel and the probability of the depreciation (appreciation) mechanism in the middle (bottom) panel. [Markov switching model, 2 regimes, same variance in two regimes.]
figure 1: Top panel, log of broad trade-weighted dollar real value (black), 2006M01=0; middle panel: probability of depreciation (blue), peak-to-trough dates of NBER recession, shaded gray; bottom panel: appreciating state Probability (blue). Red dotted line at 50%. The probabilities are smoothed and filtered. Sources: Federal Reserve Board (2015 merchandise exports weighted, 2016 and beyond merchandise and services exports weighted), NBER, and author’s calculations.
Using the 50% threshold, the dollar has been appreciating since Q2 2021. The probability of staying in an appreciating state in an appreciating state is 81%, while the probability of transitioning from an appreciating state to a depreciating state is only 15%.
The expected duration of regime 2 (appreciation) is 5.23 quarters. If the appreciation mechanism has been in place since the second quarter of 2021, it would not be surprising to turn to depreciation. However, my estimated model does not attribute the likelihood of switching to longer switching times in a given state.
