income of a country rises (Balassa, 1964). Choudri and Khan (2005) provide empirical evidence of the Balassa-Samuelson effect in developing countries.

The approach to estimating Balassa-Samuelson adjusted real exchange rates involves three steps.

First, using data from the WDI, we compute real exchange rates from 2000 to 2017 or 2018 (depending on availability of data) by dividing the purchasing power parity (PPP) conversion factor for each country by the official exchange rate to the US dollar for that country. The former is a measure of how much a basket of goods, which in the United States would cost one dollar, costs in the domestic currency of each country. Dividing the PPP conversion factor by the nominal exchange rate gives a measure of the domestic price level relative to the price level in the United States, computed at official exchange rates. A higher number denotes a more appreciated real exchange rate.

Second, to estimate the expected Balassa-Samuelson adjusted real exchange rates (henceforth BSA RER), we regress the log of the real exchange rate computed in step one on the log of per capita income in a cross-country regression involving 151 countries (countries with a population of less than half a million were omitted).<sup>4</sup> We run separate cross-country regressions for each of four sub-periods; 2000-04, 2005-09, 2010-14 and 2015-18. We obtained an intercept of between -2.2 and -2.7 for the four sub-periods and a coefficient on the log of GDP per capita of 0.18 to 0.21. The latter is similar to, although slightly lower than, the coefficient of 0.24 reported by Rodrik (2008). The coefficients are significant in each of the regressions. We then use these estimated coefficients to compute a fitted BSA RER for each country in each subperiod, which is an estimate of what the real exchange rate would be if the only determinant of it is the per capita income of the relevant country, relative to that of all other countries.

This fitted BSA RER is not the same as an “equilibrium real exchange rate” which would be consistent with long-run external balance and which would take into account other factors which affect the balance of payments, such as the terms of trade and sustainable capital flows and transfers, including remittances. A country may have an RER consistent with its fitted BSA RER but that does not guarantee that its balance of payments will be in short- or long-run equilibrium. But the BSA RER does provide a rough guide to estimating how competitive a country’s production of traded goods is in terms of its domestic costs relative to its productivity.

In the third step, we compute the under-valuation or over-valuation of the BSA RER for each sub-period for each country by subtracting the log of its fitted BSA RER from the log of its actual real exchange rate as computed in step one. If the actual real exchange rate is lower than

> 4 We also tried GDP per capita at Purchasing Power Parity (as in Johnson, Ostry and Subramanian, 2007) as the regressor but this regression had a poorer fit than the regression using GDP per capita, so we used the results from the latter to derive the fitted Balassa-Samuelson adjusted real exchange rates.

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