Nonlinearity and Harrod–Balassa–Samuelson Effects in Real Exchange Rates over the Past Two Centuries
Description
This dataset accompanies Taylor (2026), "Nonlinearity and Harrod–Balassa–Samuelson Effects in Real Exchange Rates over the Past Two Centuries." The research question is whether the nonlinear mean reversion and productivity-anchored long-run equilibrium documented by Lothian and Taylor (2008) for sterling–dollar and sterling–franc survive an extension of the data to 2022 and generalise to other sterling bilateral real exchange rates over two centuries. The data support an affirmative answer. Estimated on these series, an exponential smooth-transition (ESTAR) model with a Harrod–Balassa–Samuelson (HBS) productivity term shows nonlinear adjustment in all five pairs and a statistically significant HBS effect in four of the five — the exception being sterling–franc/euro, where the productivity coefficient is small and insignificant and is restricted to zero, as in the original study. The HBS slopes are largest where cross-country productivity differentials have been largest and most persistent. The dataset comprises two files. Taylor2026_estimation_series.csv is the estimation-ready annual panel underlying Tables 1 and 2: five sterling bilateral real exchange rates — against the US dollar, French franc/euro, Japanese yen, Australian dollar, and Canadian dollar — at annual frequency over 1819–2022, in wide format with one row per year. For each pair it reports the log real sterling exchange rate (q = s + p_UK − p_i), demeaned over the estimation sample; the HBS fundamental (d), a three-year trailing moving average of the UK-minus-partner log real GDP per capita differential, also demeaned; and a de facto fixed-regime indicator (fix; 1 = fixed, 0 = floating). Cells are blank in years before a pair's sample begins. The series were assembled from established sources. Sterling–dollar and sterling–franc/euro extend the Lothian and Taylor (1996, 2008) data, spliced to IMF International Financial Statistics producer price indices at the 2001 overlap and continued to 2022 (the post-1998 franc rate constructed at the irrevocable euro conversion rate). The yen, Australian dollar, and Canadian dollar series are from the Global Macro Database (Mueller, Xu, Lehbib and Chen, 2025), using the implicit GDP deflator. The fixed/floating classification follows gold-standard chronologies with Obstfeld, Shambaugh and Taylor (2004) and Shambaugh (2004). To interpret and reuse the data: q and d are already demeaned, so an estimated equilibrium constant is normalised out; the series reproduce the maximum-likelihood ESTAR–HBS estimates in Table 1 and the horizon regressions in Table 2 directly. README_estimation_series.txt documents the variable scheme, per-pair sample windows and estimation sample sizes (T = 203, 203, 146, 199, 149), construction details, and full source references.
Files
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