Compared to a sample average, the inflation-adjusted dollar is strong. It’s not clear what that means — namely because the (real) dollar is not statistically distinguishable from a unit root process. The dollar is also likely to get stronger, based on historical patterns.

Figure 1: Trade weighted CPI adjusted value of USD against a broad basket of currencies (blue), and against a narrow basked of currencies (tan), both in logs, 2006M01=0. NBER defined peak-to-trough recession dates shaded gray. Fed series spliced; pre-2006 is goods trade weights, 2006 onward is goods and services trade weights. Source: Federal Reserve via FRED, BIS, NBER, and author’s calculation. 

“Strong” Relative to Trend

One could draw a linear trend through each of the series, and calculate the deviation from this trend. This would ok, and indeed consistent with purchasing power parity (with measurement error) if the real rate exhibited trend stationarity. One would not want to do this for the BIS series (unit root is not rejected, trend stationary is), while is ambiguous for the Fed series ((unit root not rejected, trend stationarity borderline not rejected). See more discussion of the hazards of assuming trend stationarity when difference stationarity is more likely, in this post.

In principle, if one had the foreign price level, one could estimate an error correction model incorporating PPP, and different reversion rates for prices and nominal exchange rates, that might have more power (see Chinn (2000) for an example of this methodology). I leave that for future research.

Taking a leap of faith, assuming trend stationarity (with 0.02% real depreciation per annum, not statistically significant), one finds a 17% (log terms) overvaluation in July 2022, slightly higher than that in February 2002 (15%), but much smaller than that in March 1985 (39%).

Figure 2:Deviation from trend of trade weighted CPI adjusted value of USD against a broad basket of currencies (blue). NBER defined peak-to-trough recession dates shaded gray. Fed series spliced; pre-2006 is goods trade weights, 2006 onward is goods and services trade weights. Source: Federal Reserve via FRED, NBER, and author’s calculation. 

Of course, this is only one way of defining currency strength. There are numerous ways to assess whether a currency is strong, or overvalued – see discussion here of various approaches, and for Penn effect/Big Mac Parity here.

Stronger vs. Strong

Another way of evaluating “strength” is to see whether the dollar is on an upswing or downswing, as Engel and Hamilton (AER, 1990) did. (Previous post here)

I take data over the 1973-2022 period, and estimate a Markov Switching model. The dependent variable is the semester-on-semester change in the log value of the dollar, sampled at the end of each semester (i.e., last month of each semester).

Figure 3: Semester/semester change in log real value of US dollar against broad basket of currencies, annualized (blue) and average over 1973S2-2022S2 (red dashed line). NBER defined peak-to-trough recession dates shaded gray. Source: Federal Reserve Board, NBER, and author’s calculations.

Assuming a constant variance over two regimes, I estimate an upswing regime with real appreciation of 3.4% per annum and downswing regime with real depreciation of 2% per annum.

The probability of staying in regime 1 (appreciation) conditional on being in regime 1 is 85%; the probability of transitioning to regime 2 (depreciation) from regime 1 is 16%. The probability of staying in regime 2 conditional on being in regime 2 is 87%; in contrast, the probability of transitioning into regime 1 when in regime 2 is 13%.

The smoothed regime probabilities are presented in Figure 4:

Figure 4: Smoothed regime probabilities for regime 1 (appreciation) and regime 2 (depreciation) estimated on annual data, 1974-2022. NBER defined peak-to-trough recession dates shaded gray. Source: Federal Reserve Board, NBER, and author’s calculations.

Hence, as of 2022S2, the US dollar was likely in appreciation regime. The expected duration is 3.2 years. In this case, the dollar appreciation still has some time to run. That being said, estimates using different frequencies will yield different results. The ambiguity is not unexpected; Engel (1994) found that it was hard to exploit the long swing characteristic in such a way as to outperform a random walk.

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