RDP 2025-09: Forecasts of Period-average Exchange Rates: Insights from Real-time Daily Data Appendix B: Inputs into Bilateral RER and EER Calculations

Section 3 describes how we constructed real-time vintages of bilateral RERs and REERs. This appendix provides detail on each of the inputs into these calculations: daily NERs; daily CPI levels; and trade weights.

B.1 Daily nominal exchange rates

B.1.1 IMF nominal exchange rates

We use daily NERs from an internal IMF database called ‘Global Data Source’. They are expressed in ‘USD per units of national currency’, and were available for 165 countries. The earliest observation was 1 January 1993 and the latest was 21 October 2022.^[10] These data provide a single time series for each country. Where a country has adopted a new currency during the sample period, the exchange rates of the two currencies are spliced together so that EDNA does not contain a level shift when the new currency is adopted.^[11]

B.1.2 Splicing on Eikon nominal exchange rates

The IMF NERs start on 1 January 1993 for some countries, and later for others. For many countries, Eikon NERs are available from an earlier date. For many countries, we splice the Eikon NERs onto the IMF NERs, resulting in a longer time series of NERs, and increasing the estimation sample for our models.

We perform the splicing in stages.

1. For each country with an IMF NER, we identify the currency they used before the start of the IMF NERs. This is needed because each Eikon NER series refers to a currency, while each IMF NER series refers to a country.
2. Check if Eikon has data on the currency of interest. This is not the case for some discontinued currencies.
3. Check if the Eikon NERs start earlier than the IMF NERs. This is not the case for currencies introduced relatively recently.
4. Check that the Eikon and IMF NERs are the same during any period when both series are available. If they are not the same, it would suggest that we have identified the currency incorrectly, or that the Eikon and IMF NERs are not comparable for some other reason.
5. Splice the series if the previous checks are met. We use the IMF series on each day it is available, and the Eikon series otherwise.

Using the above process, we are able to splice Eikon and IMF NERs for 51 countries (Table B1).

To determine which exchange rate each country used before the start of the IMF data, we rely on the IMF annual reports on exchange arrangements and exchange restrictions (AREAER). This dataset lists the currency that each country used in each year as early as 1999. We assume that a country did not introduce a new currency before 1999 if it did not withdraw a currency before 2004. We allow for this five-year gap between introducing and withdrawing a currency because countries sometimes introduce a new currency and withdraw the old one a few years later.^[12] We determine if the country withdrew a currency before 2002 using the list of discontinued currencies that accompanies the ISO-4217 standard for currency codes.^[13]

There are 11 countries where splicing was not possible because the Eikon and IMF NERs differ during an overlapping period. This check could, in principle, detect cases where the country's currency has been identified incorrectly. However, the series tend to be broadly similar, suggesting that the currency has been identified correctly, but Eikon and IMF provide different exchange rates for the same currency, such as a black market rate versus an official rate.

B.2 Monthly consumer price index levels

B.2.1 World Bank dataset of monthly CPI levels

The World Bank CPI dataset provides a variety of inflation measures for a large set of countries since 1970. We use the monthly headline CPI indices. These are available for 171 countries in total, though individual countries drop in and out of the sample. The dataset is described in Ha, Kose and Ohnsorge (2021). As the authors do not specify whether the dataset is seasonally adjusted, we assume that it is not seasonally adjusted. As such, any seasonal pattern in the CPI index levels will translate into a seasonal pattern in the RERs. Our main estimates rely on these not seasonally adjusted CPIs.

By restricting ourselves to the monthly dataset, we exclude countries for which only quarterly indices were available at the time of our analysis. However, these tend to be the countries that also have shorter histories of nominal exchange rates, with the notable exceptions of Australia and New Zealand.

B.2.2 Constructing real-time vintages of monthly CPIs

To construct real-time vintages of monthly CPIs, we need to determine the latest CPI outcomes known to forecasters at the time of their forecast. To determine this, we need to know the ‘publication lag’, which is the number of months it takes for the statistical agency to publish a country's CPI after the relevant month.

We estimate the publication lag using the World Bank dataset. Typically, the World Bank dataset reports the latest CPI outcome available when they compiled the dataset. We know the dataset was compiled in January 2023.^[14] The latest month for which data are available varies by country (Table B2). For many countries, the latest observation is December 2022, so the publication lag is estimated to be one month. Similarly, for countries where the latest observation is November 2022, October 2022 or September 2022, we estimate the publication lag to be two, three or four months respectively.

There are some countries where the latest observation is even earlier than September 2022. Taken at face value, this suggest a publication lag of five months or more, which seems implausible. In some of these countries, such as Ghana, the latest observation in the World Bank dataset is not actually the latest outcome published by the statistical agency. In other countries, such as Afghanistan, the statistical agency has suspended its CPI. This means the latest observation is far in the past, but prior to the suspension of the CPI series, the publication lag may have been much shorter. We take the pragmatic approach of setting the publication lag to four months wherever the latest observation was before September 2022.

To construct the real-time CPI vintages for a country, we extract subsets of the latest vintage of CPI outcomes using our estimated publication lag. Each CPI vintage is intended to contain the data available at the end of a specified month. For example, the July 2020 vintage of Belarusian CPI is intended to contain CPI available at the end of July 2020. Since Belarus's publication lag is two months, we make this vintage by extracting Belarusian CPI levels up to May 2020.

Instead of constructing our own real-time vintages from World Bank data, we could have used the real-time vintages of data from the OECD's Main Economic Indicators, both those provided on the OECD website and those compiled by the Dallas Fed. This would avoid the need to estimate the publication lags, removing one source of error in our estimates. We decided against this for two reasons. Firstly, some vintages are missing.^[15] Second, the OECD vintages are only available for 35 countries, most of which use the euro or have a floating exchange rate, limiting our ability to evaluate forecasts for real exchange rates governed by other exchange rate regimes.

B.2.3 Extrapolating monthly CPI levels

The CPI vintage for a particular month contains the data available at the end of that month. We will use that CPI vintage to compute an RER up to the end of the month. Hence, we need to extrapolate the CPI data from the latest observation to the end of the specified month. For example, given the July 2020 Belarusian vintage, we need to extrapolate from the latest observation of May 2020 to the end of July 2020. The number of months by which we need to extrapolate the series is the publication lag, so it varies from one to four months depending on the country.

Our approach is to use linear extrapolation. That is, we compute the rate of change for the log CPI from the second-latest month to the latest month, and then extrapolate that forward as far as needed. Since this interpolation does not affect the actual outcomes, just the inputs we provide to our forecasting methods, the quality of our approach to extrapolation should ultimately be judged by the performance of the forecasts.

B.3 Trade weights

An effective exchange rate of a country aggregates together information about that country's trading partners. To do this, we need the weights that each country places on its trading partners. We use the trade weights produced by the IMF. The IMF has produced eight sets of weights, each referring to a different time period, ranging from 1979–1989 to 2016–2018 (Table B3). The weights are available for almost all countries, and are available on request to the IMF. For a given reporting country (i.e. the country whose EER is being calculated), the number of partners with weights varies. For example, in 1979–1989, China has weights for 20 partners, while Iraq only has weights for 11 partners. We use the IMF weights because they cover a longer time period and a larger number of countries than alternative sources of weights, such as those published by the BIS. The IMF's method for computing these weights is described in Bayoumi et al (2006).

When constructing real-time vintages of REERs, we assume that the set of trade weights for a period only become available with a five-year delay. Historically, the delay between the end of a weight reference period and the IMF publishing new weights has varied over time. We assume a five-year delay to approximate the IMF's current practice. For example, the January 2000 vintage is the first to have access to the 1990–1995 weights.^[16] As the weights are published with a lag, the REERs for the latest days must be calculated with the weights for an earlier period. For example, in the January 2022 vintage, the daily REERs from 1 January 2019 to 31 January 2022 must be computed with the 2016–2018 weights, as these are the latest available at the time.^[17]

Ideally, our real-time vintages of REERs would not only account for the fact that each set of weights is published with a lag, but would also account for the fact that a given set of weights are revised over time. For example, in March 2019 the IMF revised the weights for 2004–2006, which had been published some time ago (International Monetary Fund 2019). Unfortunately, previous vintages of weights are not available, so it is not possible to account for this.

Although our real-time vintages of REERs take into account the tendency of the IMF to publish weights with a lag, they don't take into account the tendency of the IMF to revise the weights over time.

Footnotes

The Global Data Source database contains two similar series: ‘EDNA’ and ‘EDNA_EER’. For some countries, EDNA_EER only reports exchange rates on trading days, and reports n/a on other days. EDNA reports rates on all days, because on weekends and public holidays it carries forward the observation from the last trading day. The two series are otherwise identical. We use EDNA_EER, but since we carry forward the observation from the last trading day this is equivalent to using EDNA. [10]

For example, the EDNA data contains a single series for Austria from 1 January 1993 onwards, even though Austria switched from the Austrian schilling to the euro on 1 January 1999. For days before the adoption of a new currency, EDNA reports the schilling/US dollar exchange rate. From 1 January 1999, EDNA starts at the schilling/US dollar rate and is then grown based on the euro/US dollar exchange rate. Splicing exchange rates in this way avoids a jump in EDNA, which avoids a jump in RERs or REERs. [11]

For example, the IMF AREAER dataset lists France as using the euro in all years from 1999 onwards. If a gap was not allowed, one would erroneously conclude that France had not introduced any new currency before the end of 1999, and hence that before 1999 it had always used the currency the IMF lists it as using in 1999, which was the euro. Similarly, in 1998 Russia replaced the old Russian ruble (ISO code RUR) with the new Russian ruble (ISO code RUB), but the old Russian ruble is listed as being withdrawn in 2004. [12]

Available at <https://www.six-group.com/en/products-services/financial-information/data-standards.html>. [13]

We use the January 2023 vintage of the dataset. The webpage for the dataset says it was last updated on 2 February 2023. Either the dataset was made available on this date, or it was made available slightly earlier than the webpage was updated in some other way on 2 February 2023. [14]

The Dallas Fed provides vintages up to 1998:Q4, while the OECD website provides vintages from January 2000 onwards, so neither provides vintages for 1999. Additionally, the vintages that the OECD website lists as relating to April 2021, January 2020 and August 2017 are actually duplicates of the vintages for other months. [15]

The aim of our paper is to provide evidence on how useful different methods of temporal aggregation would be if adopted today. For that purpose it is better to provide the forecasting models with data that mimics the delays we expect to see in the future, which is achieved by choosing a five-year delay. If we instead constructed the vintages using the longer delays that were used historically, our results would be less informative to forecasters choosing a temporal aggregation method today. [16]

The IMF follows the same practice. For this reason, they refer to the ‘2016–2018’ weights as the ‘2016–Latest’ weights. We use the term ‘2016–2018’ weights to emphasise that these weights are based only on trade data for these three years, and will eventually be followed by weights for later periods, such as ‘2019–2021’. [17]