Productivity-Anchored Nonlinear Reversion in Long-Span Dollar Real Exchange Rates
Description
This dataset accompanies Taylor, Mark P., "Productivity-Anchored Nonlinear Reversion in Long-Span Dollar Real Exchange Rates" (2026). SSRN: https://ssrn.com/abstract=6880738 It provides five US-dollar bilateral real exchange rate panels — against sterling (1820–2022), the French franc (1820–1998), the Japanese yen (1875–2022), and the Australian (1823–2022) and Canadian (1873–2022) dollars — one sheet per pair, each listing the log real exchange rate q, the productivity differential pi, and a de facto fixed/floating regime indicator. The panels are assembled from established long-span sources and harmonised to a common annual format. The dollar–sterling and dollar–franc legs use the Lothian and Taylor (1996, 2008) dataset (wholesale price indices and real GDP per capita), spliced to IMF International Financial Statistics from 2001 and extended through 2022. The dollar–yen, dollar–Australian dollar, and dollar–Canadian dollar legs use the Global Macro Database (Müller, Xu, Lehbib and Chen, 2025): the implicit GDP deflator (nominal over real GDP), the local-currency-per-US-dollar nominal rate, and real GDP per capita; the deflator is preferred over the CPI. The franc is taken over its pre-euro sample, 1820–1998, so that no splicing across the monetary union is required. The Japanese real rate is de-interpolated at the war year 1945, the only internal gap in any series. The log real dollar exchange rate is q = s + p_US − p_i, and the Harrod–Balassa–Samuelson fundamental is the contemporaneous productivity differential pi = y_US − y_i, the difference in log real GDP per capita between the United States and the partner, with no moving-average smoothing or lag. The regime indicator is built from gold-standard chronologies together with the Obstfeld, Shambaugh and Taylor (2004) and Shambaugh (2004) classifications. Both q and pi are demeaned over each pair's estimation sample, normalising out the equilibrium constant; this is the form used in estimation. In the article these series are modelled jointly as a system of exponential smooth-transition autoregressions in the productivity-adjusted deviation z = q − βπ, each with regime-dependent innovation variance and a freely estimated cross-country innovation correlation matrix, fitted by full-information maximum likelihood on the unbalanced panel. The productivity slope is estimated freely where the joint likelihood identifies it and otherwise fixed or restricted to zero; transition delays are selected by maximum likelihood; the likelihood is optimised by multistart Nelder–Mead search. Inference uses parametric bootstrap p-values from 5,000 replications under the relevant null with the estimated correlation matrix imposed; adjustment speeds are summarised by generalized impulse-response half-lives by regime and shock size.
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Steps to reproduce
The five sterling bilateral panels were assembled from established sources and harmonised to a common annual format. For sterling–dollar and sterling–franc/euro, the Lothian and Taylor (1996, 2008) wholesale price series were ratio-spliced to IMF International Financial Statistics producer price indices at the 2001 overlap year and extended through 2022; the post-1998 franc rate was constructed as a synthetic continuation, S(FRF/GBP) = 6.55957 × S(EUR/GBP), using the irrevocable franc-per-euro conversion rate. For sterling–yen, sterling–Australian dollar, and sterling–Canadian dollar, nominal exchange rates and the implicit GDP deflator (nominal GDP divided by real GDP) were taken from the Global Macro Database (Mueller, Xu, Lehbib and Chen, 2025); the GDP deflator was preferred over the CPI because the latter's large non-traded component attenuates long-run mean-reversion estimates. From these inputs the log real sterling exchange rate was computed as q = s + p_UK − p_i, and the Harrod–Balassa–Samuelson fundamental d as a three-year trailing moving average of the UK-minus-partner log real GDP per capita differential. The de facto fixed/floating regime indicator was constructed from gold-standard chronologies together with the Obstfeld, Shambaugh and Taylor (2004) and Shambaugh (2004) classifications. Both q and d were then demeaned over each pair's estimation sample, so that the equilibrium constant is normalised out; this is the form stored in the deposited file. The estimates in the accompanying article were produced from these series by maximum likelihood. Each real exchange rate is modelled as an exponential smooth-transition autoregression in the HBS-adjusted deviation, with regime-dependent innovation variance (the fixed- and floating-regime variances concentrated out analytically). The likelihood was optimised by multistart Nelder–Mead simplex search to guard against local optima. Inference on the productivity coefficient uses the signed square-root likelihood-ratio statistic, asymptotically standard normal; inference on the transition parameter, which lies on a boundary under the null, uses parametric bootstrap p-values from 250 replications of the null random-walk-with-regime-variance model. The horizon regressions reported in Table 2 regress k-year changes in q on k-year changes in d, with Newey–West standard errors at lag k − 1, for k = 1 to 10. All computation was carried out in Python using the NumPy, SciPy, and pandas libraries. Full construction and estimation details are given in the paper.
Institutions
- Washington University in St. LouisMissouri, St Louis