Compared to the sample average, the inflation-adjusted dollar has performed strongly. It is unclear what this means – namely because the (real) dollar is statistically indistinguishable from the unit root process. The dollar could also strengthen based on historical patterns.
figure 1: Trade-weighted CPI-adjusted USD vs. a basket of currencies (blue) vs. a narrower basket of currencies (tan), Jan 2006 = 0. The NBER uses shades of grey to define the peak and trough dates of the recession. Fed series stitching; before 2006 trade in goods weights, after 2006 trade weights in goods and services. Source: Federal Reserve calculations via FRED, BIS, NBER and authors.
“Strong” relative to trend
A linear trend can be plotted through each series and the deviation from that trend can be calculated.This can, and does meet purchasing power parity (with measurement error) if the real exchange rate exhibits trend stationarity.For the BIS series (no rejecting unit root, trend stationary is), this is not desired, and for the Fed series ((no rejecting unit root, no rejecting trend stationarity boundary line) is ambiguous. See more discussion of the dangers when When variance stationarity is more likely, trend stationarity is assumed, in this postal.
In principle, if one has foreign price levels, one could estimate an error-corrected model that incorporates PPP, and different regression rates for prices and nominal exchange rates, which may have greater power (see Chin (2000) example on this method). I leave it to future research.
Assuming a steady trend (actual depreciation of 0.02% per year, not statistically significant), we find that July 2022 was overestimated by 17% (logarithmic), slightly higher than February 2002 (15%), but smaller than 1985 March (39%) was much smaller.
figure 2: The dollar is trending away from a trade-weighted CPI-adjusted value against a basket of currencies (blue). The NBER uses shades of grey to define the peak and trough dates of the recession. Fed series stitching; before 2006 trade in goods weights, after 2006 trade weights in goods and services. Source: Federal Reserve calculations via FRED, NBER and authors.
Of course, this is just one way of defining the strength of a currency.There are many ways to assess whether a currency is strong or overvalued – see discussion here Various methodsAnd the Penn effect/Big Mac parity here.
stronger vs. stronger
Another way to assess “strength” is to look at whether the dollar is rising or falling, because Engel and Hamilton (AER1990) did. (previous post here)
I collected data for the period 1973-2022 and estimated the Markov switching model. The dependent variable is the term change in dollar log value, sampled at the end of each term (ie, the last month of each term).
image 3: Semester/semester change in the log real value of USD against a basket of currencies, annualized (blue) and averaged 1973S2-2022S2 (dashed red line). The NBER uses shades of grey to define the peak and trough dates of the recession. Source: Federal Reserve Board, NBER, and author’s calculations.
Assuming a constant variance of the two regimes, I estimate that an ascending regime will actually appreciate by 3.4% per year, while the descending regime will actually depreciate by 2% per year.
Conditioned on being in state 1, the probability of remaining in state 1 (appreciation) is 85%; the probability of transitioning from regime 1 to regime 2 (depreciation) is 16%. The probability of staying in state 2 conditioned on being in state 2 is 87%; conversely, the probability of transitioning to state 1 in state 2 is 13%.
The smoothed state probability is shown in Figure 4:
Figure 4: Estimated smoothed state probabilities for State 1 (appreciation) and State 2 (depreciation) based on annual data from 1974-2022. The NBER uses shades of grey to define the peak and trough dates of the recession. Source: Federal Reserve Board, NBER, and author’s calculations.
Therefore, as of 2022S2, the US dollar may be in a state of appreciation. The expected duration is 3.2 years. In this case, the appreciation of the dollar still has some way to go. Having said that, using estimates of different frequencies yields different results. The ambiguity is not surprising. Engel (1994) It was found difficult to exploit the long swing feature in a way better than random walks.
