Appendix A: The temporal disaggregation approach of quarterly GDP data for East Germany
This appendix describes the estimation of quarterly gross domestic product (GDP) for East Germany (Fig. 4). The quarterly series is provided on the Web site of the Halle Institute for Economic Research (IWH).Footnote 12
The IWH has regularly provided GDP estimates for East Germany (excluding Berlin) based on quarterly gross value added until 2015. (See Konjunktur-barometer-Ost.) From 2016 onwards, the calculation is carried out using interpolation methods based on annual regional GDP data as well as quarterly regional indicators.
The most important data sources are the publications of the working group “Regional Accounts” and official employment statistics. Based on gross value added calculations, recent GDP figures are only available at annual frequency and are published with a delay of three months after the end of the reference period.Footnote 13 Updates for the first half of a year are published in the summer of the corresponding year. Official quarterly data have not been published since 1999.
Therefore, following the guidelines of the European Statistical System (ESS) (2018), temporal disaggregation, benchmarking and reconciliation methods are used. The use of temporal disaggregation techniques allows the conversion of a lower-frequency time series into a higher-frequency time series, i.e., from annual to quarterly data. Based on the official annual data for the German regions (East and West), quarterly data are disaggregated using regional quarterly indicators. Deviations from previous publications by the IWH can arise due to the fact that the national accounts of the states are revised up to 5 years into the past.
For the years 1991–1994, corresponding statistics of the Federal Statistical Office (so-called Schienenhefte) were used as source, in which quarterly figures for the gross domestic product were published for the states.Footnote 14 The distribution of current annual values for the gross domestic product is made using the quarterly shares of these former official values. For the period 1995–2015, the IWH uses its own quarterly series, which were determined on the basis of a bottom-up approach (IWH Konjunkturbarometer). Starting in 2016, appropriate regional indicators that best reflect the quarterly trend of East German gross domestic product are used to break down the quarters. This approach is described in more detail below.
For temporal disaggregation, it is useful to select a number of appropriate higher-frequency indicators that cover at least the same period as the annual indicator. Indicators should be timely available and not too volatile. In addition, indicators should have a high correlation with the original target variable when converted to the low frequency. Nevertheless, the selection of possible indicators is hampered by the lack of official regional statistics at monthly and/or quarterly frequency and by considerable delay in publication.
In a first step, various eligible indicators were identified. However, the use of all variables in the temporal disaggregation process is not recommended as it may also increase the risk of collinearity. Empirical evidence has shown that the joint use of both output indicators (e.g. turnover) and input indicators (such as employees) is particularly well suited for disaggregation of GDP in East Germany. Due to high correlation with GDP, monthly data on employees subject to social security contributions and turnover in the manufacturing sector, as well as the quarterly figures for the production index in the manufacturing have been selected. Together, these economic indicators can well reflect the underlying dynamics in East Germany.
Standard temporal disaggregation methods are usually only applicable to one target series and do not consider relationships between multiple time series. However, the use of various indicators may result in an inconsistent picture of the time-disaggregated series, although the annual data are consistent. Therefore, reconciliation methods aim to use a plurality of time series at the same time to disaggregate the target series, without losing consistency. For this approach, the IWH uses the ECOTRIM package provided by EUROSTAT, which includes the multivariate Chow and Lin method (Chow and Lin 1971) and other temporal disaggregation options for time series.
By using the X-12-ARIMA procedure, we can finally adjust the data for seasonal and calendar irregularities in Germany. As we perform benchmarking first and then do seasonal adjustment, we end up with small differences in the annual alignment, which are compensated by an annual sum adjustment factor.
See Tables 4, 5, 6 and Figs. 5, 6.