Capitalized Productivity and the Dollar's Exorbitant… | Research

Working paper · SSRN 7251625 · Posted 13 Aug 2026 · 46 pages

Is the real exchange rate the present value of expected productivity differences, and is the dollar's privilege earned?

Anirban Majumdar · InnovationStrat Consulting, LLC · ORCID

Read the paper on SSRN ↗ Cite

Markets & asset pricingAdvisers & investorsResearchers & quantsJournalists

Key results

Across 22 economies over 1954-2019, relative productivity explains 58% of the cross-section of real exchange-rate levels, and the series are cointegrated.
The productivity gap forecasts future exchange-rate changes, with R-squared rising to 0.36 at eight years; a random walk still wins at one year.
US relative productivity explains 63% of the dollar's real premium; beside an observed convenience yield, productivity explains 45% and the yield adds 9 points.
All 231 cross pairs among non-US economies reproduce the anchor, with an elasticity of 0.37 and an R-squared of 0.60.
After 1999 the pair-spread half-life for euro pairs rises from 2.6 to 4.7 years; pairs outside the euro do not slow.

Summary

A currency priced like an asset

Textbooks usually explain an exchange rate the way they explain the price of wheat. Exporters, importers, tourists and fund managers all bring orders to the market, and the rate moves until those orders clear. We start somewhere else. A currency is also an asset, and asset prices look forward. Our central claim is that the real exchange rate equals the present discounted value of expected future productivity differences between two countries.

The model joins a Balassa-Samuelson real side to an asset-market condition. Solve it forward and one discount factor governs everything. Set that factor low and today's productivity sets today's rate, which is the old Balassa-Samuelson relation. Push it toward one, with productivity close to a random walk, and year-to-year changes in the rate become nearly unforecastable, as Engel and West found. Figure 1 shows how the model behaves.

Figure 1. Model mechanics. The real exchange rate response to a productivity innovation, for three discount factors. Left: a transitory (ρ=0.85) shock; low δ tracks the shock, high δ smooths it. Right: a permanent (unit-root) shock; the response is θ xt for every δ, so the rate inherits the random… — Figure 1. Model mechanics. The real exchange rate response to a productivity innovation, for three discount factors. Left: a transitory (ρ=0.85) shock; low δ tracks the shock, high δ smooths it. Right: a permanent (unit-root) shock; the response is θ xt for every δ, so the rate inherits the random walk (Corollary (cor:limits)).

Why does this help? It lets productivity anchor the level over decades while saying almost nothing about next quarter. One equation produces both facts.

What six decades of data say

Our main sample is Penn World Table data for 22 advanced economies over 1954-2019. Relative productivity explains 58% of the cross-country variation in real exchange-rate levels (Figure 2), with an elasticity of 0.344 for GDP per hour. In 59% of country pairs, an Engle-Granger test finds the two series cointegrated.

Figure 2. The real exchange rate rises with relative productivity across countries (PWT 10.01, 2019). Slope is the between estimator from Table (tab:balassa).

Forecasting is where readers will push back, and fairly so. The gap between the productivity-implied rate and the actual rate predicts future changes, and its R-squared climbs with the horizon until it reaches 0.36 at eight years. Figure 5 lays that profile beside a curve we derive from the gap's own persistence, without touching the predictive regressions; the two line up. Pooled across countries, the gap has a half-life of 6.0 years. Which side does the adjusting? When we split long changes between the exchange rate and productivity, the exchange rate moves toward the anchor and productivity behaves like a trend.

Figure 5. Slope βk (line, right axis) and R² (bars, left axis) of the long-horizon predictive regression rise with the horizon. The dashed curve is the model-consistent profile 1-ρ̂sk implied by the gap's own persistence, estimated without using the predictive regressions.

Out of sample, the claims get smaller

One year ahead, a random walk wins. Its advantage shows up as a Theil U of 1.061 for our model, and Figure 8 plots the race by horizon; since the theory itself predicts this outcome when the discount factor is near one, we do not count it against the model. Longer horizons go the other way. In a pooled real-time race the gap model pulls ahead from three years out, and at five years its Theil U is 0.933.

Figure 8. Out-of-sample Theil U by horizon. The random walk wins, as the δ→1 limit predicts.

How honest are the error bands? We built conformal bands around those forecasts, and at five years the 90% band covers 0.955 of outcomes. A betting test that can be read at any time, with no fixed sample size, agrees: wealth grows on the anchor signals, while a bet on the raw productivity level alone ends at 0.76.

The dollar's privilege, split in two

The United States borrows cheaply while the dollar stays strong, and the privilege literature reads that as a rent from demand for safe assets. In our model any economy expected to lead on productivity shows the same symptom. US relative productivity accounts for 0.63 of the time variation in the dollar's real premium over its trading partners (Figure 10). When we swap the residual for an observed convenience yield, the Aaa-Treasury spread, productivity alone explains 45% and the spread adds a further 9 points, with coefficients of 0.812 on productivity and 0.145 on the spread. Most of the privilege looks earned. A smaller part is rent.

Figure 10. The dollar's real premium over trading partners (solid), its productivity-justified component (dashed), and the residual ``pure privilege'' (shaded). Productivity accounts for R²=0.63 of the variation.

Taking the dollar out

Is this all a dollar story? To check, we formed all 231 cross pairs among the non-US economies, where anything specific to the United States cancels. The anchor survives: the elasticity is 0.37 with an R-squared of 0.60 (Figure 15), 43% of pairs are cointegrated, and the long-horizon predictability comes back.

Figure 15. The anchor without the dollar. Left: mean real exchange rate against mean relative productivity for all 231 cross pairs; the fitted elasticity of 0.37 matches the vs-US cross-section. Right: real-time out-of-sample Theil U of the pair gap model at each horizon (grey) against the… — Figure 15. The anchor without the dollar. Left: mean real exchange rate against mean relative productivity for all 231 cross pairs; the fitted elasticity of 0.37 matches the vs-US cross-section. Right: real-time out-of-sample Theil U of the pair gap model at each horizon (grey) against the oracle-location variant that knows the pair's full-sample mean (indigo); Clark–West statistics above each pair of bars.

Three further checks look at mechanism. After 1999 the half-life of the pair spread for euro pairs rises from 2.6 to 4.7 years, and pairs outside the union do not slow. Sectoral data show the traded-minus-non-traded productivity differential pricing the rate. And across 126 economies never used in estimation the ordering holds, though the slope flattens away from the technology frontier (Figure 16).

Figure 16. Mechanism and reach. Left: the levels relationship fit on 21 advanced economies (indigo, red line) and confronted with 126 unseen economies (grey; dashed line is the holdout refit). Right: half-life of the cross-pair spread before and after 1999, by euro membership; only the pairs that… — Figure 16. Mechanism and reach. Left: the levels relationship fit on 21 advanced economies (indigo, red line) and confronted with 126 unseen economies (grey; dashed line is the holdout refit). Right: half-life of the cross-pair spread before and after 1999, by euro membership; only the pairs that lost their nominal margin slowed.

Where trade flows fit, and what to be careful about

We keep the flow side of the market. A real appreciation lowers net exports afterward, with the Marshall-Lerner sign, and an undervalued currency's surplus erodes as the rate closes the gap. The trade balance forecasts nothing about the rate itself. On our reading the asset market sets the level and trade quantities adjust to it.

Some caution is due. The 0.36 at eight years is in sample. On a modern panel of BIS effective exchange rates the levels fit is weak, with a pooled coefficient of 0.013, even though the gap still forecasts changes there. We see the paper as a way to think about currency levels over decades, and as a reason not to read quarterly moves as news about fundamentals.

Who this is for: Researchers who model currencies, and journalists who write about why the dollar stays strong.

Figures

Figure 3. Real exchange rate q (solid) and productivity fundamental θ x (dashed) for four economies. The series track at low frequency.

Figure 4. Present-value-implied vs. actual real exchange rate.

Figure 6. Adjustment decomposition: k-year changes of the exchange rate (indigo) and of the productivity fundamental (red) regressed on the same gap θ xt-qt. The exchange rate does all the adjusting.

Figure 7. Left: distribution of per-country half-lives of the productivity gap. Right: per-country spread persistence against the DOLS long-run elasticity.

Figure 9. Left: net exports after a unit log real appreciation (local projections; shaded band is ±2 Driscoll–Kraay standard errors). Right: the gap's direct effect on future trade balances next to the composed chain, the exchange-rate response times the net-export response.

Figure 11. Decomposing the dollar's real premium into a productivity-only fit (dashed) and the additional contribution of the observed Aaa-Treasury convenience yield (shaded). Productivity dominates; the measured convenience yield adds a minority band.

Figure 12. Left: monthly BIS real effective exchange rates swing at high frequency. Right: yet the productivity gap forecasts their future changes, with R² rising in the horizon, the same signature as the PWT panel, on independent data.

Figure 13. Honest bands and what they contain. Left: empirical coverage of the conformal bands at k=5 by forecast decade, against the nominal levels (dashed). Right: pooled five-year-ahead gap-model forecasts against realized outcomes, with the fitted line in red and the 45-degree line in black.

Figure 14. The betting ledger. Left: wealth paths for one-year bets on the cross-sectional association between each signal and next year's real-exchange-rate change (log scale; the dotted line at 20 is the threshold for anytime-valid p<0.05). Right: final wealth from non-overlapping five-year bets… — Figure 14. The betting ledger. Left: wealth paths for one-year bets on the cross-sectional association between each signal and next year's real-exchange-rate change (log scale; the dotted line at 20 is the threshold for anytime-valid p<0.05). Right: final wealth from non-overlapping five-year bets, averaged over the five phases.

Tables

Table 1. Data and sources. All series are public and downloaded by the reproducible pipeline.
Object	Source	Coverage
Real exchange rate qi (price level of GDP, US=1)	PWT 10.01 plgdpo	22 countries, 1954–2019
Labour productivity Y/H (output-side, chained PPP)	PWT 10.01 rgdpo/(emp·avh)	annual
Total factor productivity (within-country)	PWT 10.01 rtfpna	annual
Human capital index	PWT 10.01 hc	annual
Real effective exchange rates (robustness)	BIS via FRED	8 economies, 1994–2026
GDP per capita (robustness)	World Bank via FRED	10 economies, 1960–2024
Panel observations	1421 country–year cells

Table 2. Balassa–Samuelson elasticities. Dependent variable: log real exchange rate versus the US, q. Four estimators × three productivity proxies. Driscoll–Kraay and clustered t-statistics.
	Between (long run)			Pooled (DK SE)		Country FE		Two-way FE
Productivity proxy	β	t	R²	β	t	β	t	β	t
GDP per hour	0.344	6.5	0.58	0.361	15.7	0.381	4.4	-0.018	-0.2
Total factor productivity	-0.190	-0.5	0.02	0.278	2.6	0.756	4.4	-0.008	-0.0
Human capital	0.690	5.2	0.38	0.642	9.0	0.322	0.9	-0.344	-1.2

Table 3. Integration and cointegration of real exchange rates and productivity. Panel of 22 economies, 1954–2019.
Statistic	Value
Series with a unit root in levels (ADF, 10%)	77%
Series stationary in first differences (ADF, 10%)	100%
Country pairs cointegrated (Engle–Granger, 10%)	59%
DOLS long-run elasticity (median)	0.513
DOLS long-run elasticity (mean)	0.696
Panel combination (Fisher / Maddala–Wu, χ²2N)
joint no-cointegration null (Engle–Granger)	126.4 [p<0.001]
joint non-stationarity null of spread q-θ x	104.2 [p<0.001]

Table 4. Long-horizon predictability (Mark-1995 design). Dependent variable: k-year change qt+k-qt; regressor: productivity gap θ xt-qt. Clustered t-statistics.
Horizon k (yr)	βk	t-stat	R²	N
1	0.085	8.0	0.046	1399
2	0.211	8.3	0.112	1377
3	0.323	8.7	0.172	1355
4	0.422	9.1	0.224	1333
5	0.513	9.6	0.273	1311
8	0.650	11.9	0.359	1245

Table 5. Long-horizon predictability: robust inference. tclu clusters by country; tDK is Driscoll–Kraay with k+2 lags; boot p is the moving-block bootstrap p-value of βk under the no-predictability null (1,000 draws); the year-effects columns absorb common time variation; the floating-era columns re-estimate on 1973–2019.
	Full sample 1954–2019				Year effects		Floating era 1973+		R²
k	βk	tclu	tDK	boot p	βk	t	βk	tDK	full	1973+
1	0.085	8.0	4.5	<0.001	0.067	4.4	0.096	3.2	0.05	0.04
2	0.211	8.3	5.3	<0.001	0.144	4.5	0.251	4.5	0.11	0.11
3	0.323	8.7	5.3	<0.001	0.207	4.6	0.388	4.8	0.17	0.17
4	0.422	9.1	5.4	<0.001	0.259	4.8	0.511	5.2	0.22	0.23
5	0.513	9.6	5.7	<0.001	0.288	5.1	0.635	6.5	0.27	0.28
8	0.650	11.9	6.4	<0.001	0.371	6.1	0.717	9.4	0.36	0.35

Table 6. Productivity vs. pure PPP mean reversion (within-country). Dependent variable: qt+k-qt. ``PPP only'' regresses on the country-demeaned -qt; the next columns add the country-demeaned productivity level xt. Clustered t-statistics.
	PPP only	+ productivity level xt
Horizon k (yr)	R²	βx	t	Δ R²	R² joint
1	0.058	0.019	2.0	0.003	0.061
2	0.131	0.060	3.2	0.013	0.144
3	0.198	0.096	3.4	0.021	0.219
4	0.258	0.127	3.5	0.028	0.285
5	0.318	0.151	3.5	0.031	0.349
8	0.440	0.154	3.3	0.026	0.465

Table 7. Speed of adjustment and level robustness. Top: pooled and cross-country distribution of the spread persistence and half-life. Bottom: the between Balassa–Samuelson elasticity with a government-consumption (demand-side) control and on the floating era only.
Quantity	Value
Pooled spread persistence ρ̂s (AR(1))	0.890
Pooled half-life of the gap (years)	6.0
Median country half-life (years)	6.4
Interquartile range of country half-lives (years)	3.4–7.2
Median country ρi	0.897
Between elasticity with gov.-share control (t)	0.332 (6.0)
Between elasticity, floating era 1973+ (t)	0.454 (8.7)
R² between, floating era	0.63

Table 8. Recursive out-of-sample horse race against a random walk. Theil U<1 would favour the model; U>1 favours the random walk.
Horizon k (yr)	RMSE model	RMSE RW	Theil U	DM stat
1	0.102	0.096	1.061	-3.97
4	0.245	0.211	1.159	-2.86
8	0.418	0.248	1.686	-2.48
12	0.591	0.243	2.432	-2.85

Table 9. The flow side. Panel A: local projections of net exports (share of GDP) on a real appreciation. Panel B: forecasting qt+k-qt with the trade balance, alone and jointly with the productivity gap. Panel C: the gap forecasts subsequent trade-balance changes. Country-demeaned; Driscoll–Kraay t-statistics with k+2 lags.
Panel A. Net exports respond to the real exchange rate: tbt+k-tbt-1 on Δ qt
k	βk	(tDK)	R²	N
0	-0.090	(-4.2)	0.073	1399
1	-0.121	(-4.4)	0.066	1377
2	-0.117	(-4.4)	0.047	1355
3	-0.116	(-4.3)	0.037	1333
4	-0.114	(-4.2)	0.030	1311
5	-0.098	(-3.8)	0.018	1289
Panel B. Does the trade balance forecast the exchange rate? qt+k-qt regressed on:
	tbt alone		tbt and the gap θ xt-qt jointly
k	βtb	(tDK)	βtb	(t)	βgap	(t)
1	0.026	(0.6)	-0.022	(-0.5)	0.108	(4.4)
3	0.023	(0.2)	-0.158	(-1.2)	0.414	(4.8)
5	-0.054	(-0.3)	-0.334	(-2.1)	0.666	(4.8)
8	-0.120	(-0.6)	-0.474	(-3.4)	0.843	(5.4)
Panel C. The gap forecasts trade-balance adjustment: tbt+k-tbt on θ xt-qt
k	β	(tDK)	R²
1	-0.014	(-3.0)	0.008
3	-0.050	(-4.5)	0.043
5	-0.084	(-5.3)	0.081

Table 10. Competing fundamentals. Panel A: between-country regressions of the average real exchange rate on each candidate, alone and jointly with productivity (HC1 t-statistics). Panel B: within-country long-horizon regressions at k=8, each candidate added to PPP reversion.
Panel A. Between-country levels: q̄i on each candidate, alone and with productivity
	alone			jointly with productivity
Candidate	β	(t)	R²	βz	(t)	βprod	(t)
Labour productivity	0.344	(6.5)	0.58	–
Human capital	0.690	(5.2)	0.38	0.315	(2.1)	0.275	(5.0)
Government share	2.421	(1.6)	0.20	2.139	(3.3)	0.332	(6.0)
Trade balance	1.236	(1.7)	0.12	0.386	(0.9)	0.329	(6.3)
Terms of trade	0.230	(0.3)	0.01	0.654	(1.4)	0.360	(5.6)
Panel B. Within-country, k=8: qt+8-qt on PPP reversion -qt plus each candidate
Candidate	βz	(t)	Δ R²	(joint t)
Labour productivity	0.154	(3.3)	0.026	(5.7)
Human capital	-0.126	(-0.4)	0.001	(-3.0)
Government share	0.984	(1.8)	0.012	(1.2)
Trade balance	-0.029	(-0.4)	0.000	(-3.9)
Terms of trade	0.322	(2.1)	0.013	(1.3)
All five candidates jointly with PPP reversion: R²=0.52 against 0.44 for PPP alone; clustered t-statistics; N=1,421 country-years.

Table 11. Theories of the exchange rate and their verdicts in this dataset.
Theory family	Observable implication here	Verdict in this panel
PPP (Cassel)	q reverts to a country constant	Holds slowly (half-life ≈6 yr); anchor drifts (T4c)
Balassa–Samuelson / productivity	productivity prices levels, forecasts q	Both confirmed; survives every rival (T1, T4, T10)
Monetary (flex- and sticky-price)	monetary fundamentals anchor q	Absorbed: machinery inherited, anchor replaced; overshooting lives in ut
Portfolio balance / current account	trade balance forecasts q	Rejected: t of 0.2–0.6 (T9, Panel B)
Elasticities / Marshall–Lerner	appreciation lowers net exports	Confirmed: β≈-0.12, t≈4 (T9, Panel A)
J-curve	perverse impact response	Not visible at annual frequency; medium-run sign correct
Intertemporal / NOEM	consumption smoothing shapes tb dynamics	Consistent: surpluses erode as gap closes (T9, Panel C)
Financial / UIP-wedge	disconnect from a valuation shock	Complementary: ut is the wedge; it decays to the productivity anchor
Risk premia (habit, LRR, disasters)	wedge from preferences	Not separately identified; bounded by the measured CY split (T6b, T6d)
Safe assets / convenience yield	dollar premium from Treasury demand	Present and measured: adds 9–11 points of R² (T6b, T6d)
Commodity / terms of trade	terms of trade price q	Rejected in this panel: R²=0.01 alone, nothing jointly (T10)

Table 12. Decomposing the dollar's exorbitant privilege. The productivity share is the R² of the dollar's real premium on US relative productivity.
Quantity	Value
Productivity share of real-exchange-rate level variance (panel)	0.36
US labour-productivity lead over sample mean (log)	0.46
Dollar time series, 1954–2019:
slope on US relative productivity β	0.61
t-statistic (HAC)	8.5
R² (productivity-justified share of dollar premium)	0.63
residual ``pure privilege'' share	0.37

Table 13. The privilege split with a measured convenience yield. Dependent variable: the dollar's real premium over trading partners. HAC t-statistics.
Dollar real premium regressed on:	Coef. (t)
US relative productivity	0.812 (6.2)
Observed convenience yield (Aaa-Treasury)	0.145 (2.5)
R², productivity only	0.45
R², joint (productivity + convenience yield)	0.54
Incremental R² from convenience yield	0.09
Sample	58 yrs (1962–2019)

Table 14. Privilege-regression robustness: persistence defenses and a credit-risk-purged convenience yield.
Specification	Estimate
A. Persistence defenses (dollar premium on US rel. productivity)
Engle–Granger cointegration ADF p-value	0.10
slope in first differences (HAC t)	0.82 (1.8)
slope in levels, HAC(8) t	0.61 (7.5)
B. Credit-risk-purged convenience yield (1962–2019)
productivity slope, 3-variable (HAC t)	0.80 (6.5)
Aaa-Treasury slope, 3-variable (HAC t)	0.15 (2.6)
Baa-Aaa credit-spread slope (HAC t)	-0.05 (-1.0)
productivity slope with credit-purged CY (HAC t)	0.81 (6.8)
incremental R² of the purged convenience yield	0.11

Table 15. Modern BIS real-effective-rate panel (8 economies, 1994–2025). Panel A: contemporaneous levels. Panel B: long-horizon predictability from the productivity gap. Clustered t-statistics.
Panel A. Contemporaneous levels (REER on relative productivity)
Estimator	β	t
Pooled (clustered)	0.013	0.7
Country fixed effects	0.272	0.6
Panel B. Long-horizon predictability (REER change on productivity gap)
Horizon k (yr)	βk	t	R²	N
1	0.117	2.7	0.053	241
3	0.467	4.4	0.221	225
5	0.658	3.9	0.321	209
7	0.828	4.6	0.430	193

Table 16. Pooled real-time out-of-sample forecasts of qt+k-qt (origins 1975 to 2019-k). U is the ratio of each model's RMSE to the random walk's; the out-of-sample R² follows (campbellthompson2008); Clark–West statistics test the nested pairs; the DM column compares the gap and PPP models directly (positive favours PPP).
	RMSE ratio to random walk U				OOS	Clark–West t			DM
k	PPP	gap	PPP+prod	GBM	R²gap	PPP\|RW	gap\|RW	full\|PPP	gap-PPP	N
1	1.002	1.004	1.024	1.068	-0.008	0.68	0.92	-0.39	0.16	945
3	0.981	0.978	1.054	1.132	0.043	1.87	2.44	0.05	-0.14	901
5	0.939	0.933	1.055	1.095	0.129	3.50	4.29	0.25	-0.20	857
8	0.833	0.853	0.990	1.038	0.273	9.45	6.03	0.32	0.55	791
10	0.812	0.860	0.934	1.105	0.261	5.74	5.34	0.97	1.32	747

Table 17. Empirical coverage of the weighted split-conformal bands around the gap model's out-of-sample forecasts. Width is the mean band width in log points; the decade column is the range of 90% coverage across forecast decades.
	nominal 80%		nominal 90%		90% by decade
k	coverage	width	coverage	width	range	N
1	0.811	0.26	0.915	0.35	0.84–0.96	906
3	0.850	0.54	0.938	0.66	0.83–0.99	822
5	0.882	0.65	0.955	0.82	0.90–0.99	738
8	0.820	0.58	0.935	0.73	0.86–0.98	611
10	0.838	0.63	0.943	0.79	0.91–0.97	525

Table 18. Anytime-valid e-processes: betting wealth by signal. Under the no-association null expected wealth never exceeds one at any stopping time, so large final wealth is sequential evidence and its reciprocal bounds an anytime p-value.
		1-year bets		5-year bets
Signal	mean τt	final E	anytime p	final E	years
Productivity gap θ x - q	0.073	2.28	0.44	1.52	35
PPP reversion -q	0.087	3.03	0.33	1.68	35
Productivity level x	-0.012	0.76	0.85	0.88	35
Human capital	0.018	1.15	0.69	1.04	35
Trade balance / GDP	-0.011	0.78	0.95	0.92	35
Betting period 1984–2018; mixture over λ ∈ [0.05, 0.75].
The 5-year column averages five phase-shifted non-overlapping streams.

Table 19. Per-country VECM on (q,θ x): Johansen trace statistics, error-correction loadings, and the weak-exogeneity verdict.
	Johansen	coint.	αq		αf		f weakly
Country	trace	(5%)	coef.	(t)	coef.	(t)	exogenous
AUS	12.4	no	-0.125	(-2.8)	0.003	(0.5)	yes
AUT	9.7	no	-0.124	(-2.3)	0.003	(0.5)	yes
BEL	25.9	yes	-0.259	(-3.0)	0.031	(3.0)	no
CAN	15.5	no	-0.109	(-2.8)	-0.014	(-1.6)	yes
CHE	5.5	no	-0.046	(-1.9)	-0.000	(-0.0)	yes
DEU	15.4	no	-0.075	(-1.5)	0.012	(2.2)	no
DNK	7.3	no	-0.109	(-2.3)	0.000	(0.0)	yes
ESP	20.3	yes	-0.147	(-2.9)	0.015	(2.8)	no
FIN	15.9	yes	-0.202	(-3.3)	0.008	(1.0)	yes
FRA	25.3	yes	-0.112	(-2.2)	0.017	(3.6)	no
GBR	14.5	no	-0.221	(-3.2)	0.010	(1.3)	yes
GRC	23.1	yes	-0.164	(-2.4)	-0.024	(-2.1)	no
IRL	8.1	no	-0.098	(-2.4)	0.013	(1.8)	yes
ISL	20.4	yes	-0.395	(-4.0)	0.030	(1.9)	yes
ITA	21.0	yes	-0.200	(-2.7)	0.023	(2.5)	no
JPN	20.4	yes	-0.078	(-1.1)	0.021	(3.7)	no
KOR	21.0	yes	-0.413	(-4.7)	-0.021	(-1.7)	yes
NLD	17.0	yes	-0.152	(-2.2)	0.025	(2.8)	no
NOR	9.0	no	-0.127	(-2.6)	0.020	(1.2)	yes
NZL	20.1	yes	-0.285	(-3.9)	0.008	(0.8)	yes
PRT	18.8	yes	-0.289	(-3.7)	0.019	(1.5)	yes
SWE	10.6	no	-0.134	(-2.7)	-0.006	(-1.4)	yes
Shares: cointegrated 55%; q error-corrects (negative, \|t\|>1.96) 86%; f weakly exogenous 64%.
Medians: αq=-0.141 (t=-2.7), αf=0.011 (t=1.3).

Table 20. The cross-pair falsification panel: all 231 pairs among the 22 non-US economies, every dollar-specific factor differenced out. Panel A inference is a delete-one-country jackknife (22 replicates), since the pair means are linear combinations of 22 country means. Panel B pools all pairs with Driscoll–Kraay standard errors (lag k+2), robust to the mechanical cross-pair dependence from shared countries.
Panel A. Levels and cointegration: β=0.367 (jackknife t=5.5), R²=0.60,
231 pairs, 14,615 pair-years; Engle–Granger cointegration in 43% of pairs.
Panel B. Long-horizon predictability of the pair gap
	levels			within pair
k	β	(tDK)	R²	β	(tDK)	R²	N
1	0.067	(6.2)	0.044	0.097	(6.0)	0.062	14,384
3	0.207	(10.3)	0.130	0.299	(10.8)	0.185	13,922
5	0.286	(12.2)	0.180	0.416	(12.4)	0.256	13,460
8	0.368	(10.5)	0.236	0.534	(13.7)	0.329	12,767
Panel C. Real-time out-of-sample race (RMSE ratio to random walk)
	real time		oracle location		Clark–West t
k	PPP	gap	PPP	gap	PPP\|RW	gap\|RW	N
1	1.004	1.008	0.970	0.976	2.37	2.60	9,689
3	1.017	1.028	0.902	0.919	3.77	4.30	9,227
5	1.064	1.082	0.865	0.890	4.04	4.07	8,765
8	1.129	1.148	0.829	0.862	3.83	4.42	8,072
E-process (one-year bets, 49 years): gap E=2.44, PPP E=2.79.
Oracle location = full-sample pair means, slopes still real-time.

Table 21. Mechanism and reach. Panel A: cross pairs grouped by euro membership; between-pair inference by delete-one-country jackknife; half-lives from the pooled AR(1) of the pair spread (floating era vs post-entry); error-correction slope of the 3-year change on the pair gap, Driscoll–Kraay t. Panel B: country-fixed-effects regressions of q on GGDC sectoral productivity differentials. Panel C: the levels elasticity fit on advanced economies only (per-worker productivity, 1990–2019 means) and confronted with 126 unseen economies.
Panel A. The euro experiment: cross pairs by membership, post-1999 window
		between levels			half-life (yrs)		EC slope, k=3
Pair group	pairs	β	(tJK)	R²	pre	post	β	(tDK)
both in euro	55	0.279	(3.7)	0.53	2.6	4.7	0.083	(1.6)
one in euro	121	0.331	(2.7)	0.33	2.5	2.6	0.247	(3.1)
neither in euro	55	0.332	(0.8)	0.38	3.4	2.7	0.331	(6.1)
Panel B. The sectoral mechanism: 9 countries vs US, 1954–2010, country fixed effects, N=434
Regression	β1	(tDK)	β2	(tDK)	R²
traded xT and non-traded xN	0.268	(2.8)	0.634	(4.9)	0.51
dual xT-xN	0.600	(5.3)	–		0.24
dual, manufacturing only	0.015	(0.1)	–		0.00
dual gap forecasts qt+5-qt	0.602	(4.5)	–		0.35
Panel C. Out-of-country holdout: elasticity fit on advanced economies only, 1990–2019 means
	N	slope	R²	corr	act. on pred.	holdout slope by tercile (low/mid/high)
advanced (fit)	21	0.491	0.33
holdout, all	126	0.141		0.45	0.29	0.04	0.12	0.20

Abstract

We treat the real exchange rate as a forward-looking asset price, the present discounted value of expected future cross-country productivity differentials, rather than the price clearing a contemporaneous currency flow. A two-country model combines a Balassa-Samuelson real side with an asset-market condition; the rate solves forward to a present value of expected productivity, nesting Balassa-Samuelson and the Engel-West disconnect as limits of one discount factor. A productivity leader funds itself cheaply while its currency is strong, the textbook symptom of "exorbitant privilege"; here it is the rational capitalization of anticipated productivity, earned rather than exorbitant. On Penn World Table data for 22 economies, 1954-2019, productivity explains 58% of the cross-section of real exchange-rate levels, the series are cointegrated, the productivity gap forecasts future changes with R-squared rising to 0.36 at eight years, and US relative productivity explains 63% of the dollar's real premium, a measured convenience yield adding about ten points: the privilege is mostly earned, with a minority rent. The forecasting claim is held to modern predictive-inference standards. A pooled real-time out-of-sample race beats the random walk from three years out; conformal bands hold their promised coverage; an anytime-valid e-process ranks the anchor signals above every rival; and error-correction loadings make the exchange rate the adjusting variable, productivity the trend. All 231 cross pairs among the non-US economies, where everything dollar-specific differences out, reproduce the anchor (elasticity 0.37, R-squared 0.60). Mechanism tests agree: the pair-spread half-life doubles after 1999 for euro pairs only, the sectoral traded-minus-non-traded differential prices the rate and forecasts it, and across 126 unseen economies the ordering survives while the slope flattens off the frontier. Marshall-Lerner holds on the flow side; the trade balance forecasts nothing.

Keywords: exchange rate, productivity, Balassa-Samuelson, present value, exorbitant privilege, convenience yield, out-of-sample forecasting, conformal prediction, anytime-valid inference, Penn World Table, cointegration, long-horizon predictability

How to cite

Majumdar, A. (2026). Capitalized Productivity and the Dollar's Exorbitant Privilege: The Real Exchange Rate as an Asset Price. SSRN Working Paper No. 7251625. https://ssrn.com/abstract=7251625

@techreport{majumdar_exchange_rate_productivity,
  author={Majumdar, Anirban},
  title={Capitalized Productivity and the Dollar's Exorbitant Privilege: The Real Exchange Rate as an Asset Price},
  institution={SSRN},
  number={7251625},
  year={2026},
  url={https://ssrn.com/abstract=7251625}}

Educational only. Not investment, tax, or legal advice, and not an offer of advisory services. InnovationStrat Wealth, LLC is not yet registered as an investment adviser. Questions about a paper? Use the contact form. · ← All papers

Capitalized Productivity and the Dollar's Exorbitant Privilege: The Real Exchange Rate as an Asset Price