Continuous national gross domestic product (GDP) time series for 195 countries: past observations (1850–2005) harmonized with future projections according to the Shared Socio-economic Pathways (2006–2100)

Gross domestic product (GDP) represents a widely used metric to compare economic development across time and space. GDP estimates have been routinely assembled only since the beginning of the second half of the 20th century, making comparisons with prior periods cumbersome or even impossible. In recent years various efforts have been put forward to re-estimate national GDP for specific years in the past centuries and even millennia, providing new insights into past economic development on a snapshot basis. In order to make this wealth of data utilizable across research disciplines, we here present a first continuous and consistent data set of GDP time series for 195 countries from 1850 to 2009, based mainly on data from the Maddison Project and other population and GDP sources. The GDP data are consistent with Penn World Tables v8.1 and future GDP projections from the Shared Socio-economic Pathways (SSPs), and are freely available at http://doi.org/10. 5880/pik.2017.003 (Geiger and Frieler, 2017). To ease usability, we additionally provide GDP per capita data and further supplementary and data description files in the online archive. We utilize various methods to handle missing data and discuss the advantages and limitations of our methodology. Despite known shortcomings this data set provides valuable input, e.g., for climate impact research, in order to consistently analyze economic impacts from pre-industrial times to the future.


Introduction
The concept of measuring and comparing economic activity within and across countries using the gross domestic product (GDP) is rather new in historic terms. Starting with some first attempts to quantify economic activity in the late 19th 5 century for certain countries, comprehensive regular assessments of GDP were only established in the second half of the 20th century. Since then GDP has become the standard indicator to assess nations' development, despite initial and more recent criticism concerning the incomplete representa-10 tion of a nation's state via GDP and the potential problematic comparison across countries (Speich Chasse, 2013).
Nonetheless and because of a lack of alternatives GDP has proven to be a useful measure to track the evolution of economic development within or across nations. Many 15 other development proxies, e.g., the level of education, life expectancy, the population's health status, and many others, have been shown to correlate well with a nation's GDP; see, e.g., Gennaioli and La Porta (2013). Similarly, a reduction in vulnerability (or an increase in resilience) to natural disasters 20 has also been shown to correlate well with a nation's GDP (Kousky, 2013), resulting in less mortality and in fewer damages relative to GDP. Most research in this field focuses only on the last decades where sufficient coverage of economic activity exists for most countries of the world. However, many 25 fields of research could benefit from a more comprehensive economic data set that covers a larger time horizon and a larger number of nations to gain a better understanding of 2 T. Geiger: TS3 Various global institutions (e.g., Worldbank, Organisation for Economic Co-operation and Development, OECD; International Monetary Fund, IMF) and research groups (e.g., Penn World Table) have therefore assembled global GDP data sets, most of which provide a comprehensive view 5 across space but lack data prior to the 1960s. In addition, there have been attempts to provide GDP or income (i.e., GDP per capita) estimates reaching further back in time based on proxies for specific periods; see, e.g., Baier et al. (2002), Mitchel (2003), Maddison (2007), and Bolt and 10 van Zanden (2014). However, these estimates only provide snapshots of economic activities for specific periods without continuous global coverage across time.
Here, we contribute to increasing the usability of historical economic time series by creating a continuous and com-15 plete income and GDP time series from 1850 to the present. We do so by combination of various data sources and methods to interpolate and extrapolate missing data points in a pragmatic but most sensible way. The Maddison Project Database (MPD) thereby constitutes the foundation of the 20 period mostly before 1960, while the Penn World Table (version 8.1) sets the basis for the more recent past. Our final GDP time series covers 195 countries (in their present constitution) from 1850 to 2009 and is consistent with GDP projections from the Shared Socio-economic Pathways (SSPs) 25 that extend the historical time series from 2010 to 2100.
The long record and complete coverage enhance the data set's usability. It has already been assigned as input data for the current climate change impact model runs within the global Inter-sectoral Impact Model Intercomparison Project 30 (ISIMIP2b, www.isimip.orgTS1) (Frieler et al., 2017), and has been used in a downscaling approach to provide spatially explicit economic information on the grid level (Geiger et al., 2017;Murakami and Yamagata, 2017) that can, e.g., be used to quantify economic values exposed to climate ex-35 tremes (Geiger et al., 2018). Despite various known shortcomings that are discussed in detail below, this new data set has broadened and will further broaden the applicability of historic estimates of economic activity and potentially feed back to foster increased research interest in the field of eco-40 nomic history and the improvement of the current data set.

Data and methods
In the following we present our methodology that is used to create a continuous and consistent GDP time series for 195 countries based on national accounts data from the Penn 45 World Table (PWT), the MPD, World Development Indicators (WDI), the History Database of the Global Environment (HYDE), and projections from the SSPs. We will present the data sources first before we describe the consistent merging procedure across all sources, as additionally summarized in 50 Table 1. The PWTs comprise national accounts data maintained by scholars at the University of California and the University 55 of Groningen to measure real GDP across countries and over time. The database is successively updated and extended, with the latest release being PWT 9.0 (Feenstra et al., 2015), and provides the most extensive coverage for GDP reported in purchasing power parity (PPP) across time. We 60 here mostly rely on the PWT release 8. iiasa.ac.at/SspDb/dsd?Action=htmlpage&page=about. We here use the OECD GDP data set (Dellink et al., 2017) provided by the Inter-Sectoral Impact Model Intercomparison Project (ISIMIP), freely available at https://www. isimip.org/gettingstarted/availability-input-data-isimip2b/ 15 upon registration. This data set was directly provided by the OECD and is advantageous as it contains data on seven additional countries. Note that one of these additional countries (Aruba, ABW) was excluded due to data issues.
(The reported SSP GDP value for 2010 is a factor of 10 20 smaller than observational records.)

Maddison Project
The Maddison Project resembles a cooperative effort to assemble historical national accounts (Bolt and van Zanden, 2014), continuing the ground-breaking work by the late An-25 gus Maddison. The MPD is a freely available Excel spreadsheet (Maddison, 2016) that provides per capita income (in 1990 Geary-Khamis, G-K, dollars) for 184 countries and/or world regions between 1AD CE2 and 2010 in varying time intervals. Since 1800 data have been provided annually, con-30 taining however large fractions of missing values, in particular for the African continent, Western Asia and the former Soviet Union. The global missing value fraction is 61.8 % between 1800 and 2010. It steadily decreases to 51.7 % (36.9 %) when analyzing the data from 1850 (1900) onwards.

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After 1950, when national accounts data were starting to be routinely collected, the missing value fraction drops to 8 %. The data are nearly complete since 1990 (missing value fraction: 3.6 %). See Fig. 1 and the supplementary data in the DOI data archive (Geiger and Frieler, 2017). 40 We selected 1850 as the start year for our present work for two reasons: first, coverage is somehow better than in 1800, and second, we can rely on available data points between 1800 and 1849 for the purpose of interpolation rather than extrapolation.

Population data
Parts of the GDP data sets (PWT and WDI) also provide national population data to derive income. Whenever available we use the associated population estimates from the same source to derive income from GDP. However, to estimate na-  (1850,1900,1950), while the plot displays the actual number of available countries over the full period. Countries are displayed using their current borders. We only show data for those 160 countries that are explicitly named in the Maddison Project Database; country group estimates lacking national resolution are not shown (see Table 2 for details).
tional GDP from the income data generated within the MPD we use population estimates from the HYDE data set.

History Database of the Global Environment (HYDE)
HYDE is developed under the authority of the Netherlands Environmental Assessment Agency and provides (grid-55 ded) time series of population and land use for the last 12 000 years (Klein Goldewijk et al., 2010, 2011. HYDE provides national population data decennially up to 2000 and annually up to 2015. Where required we linearly interpolate the data to derive annual distributions. 60

Completing the Maddison Project Database
The MPD provides income data on a national and supranational level, where the supranational data represent population-weighted averages of national values (see Table 2). In addition, there exist three world region-specific 65 groups of small countries (groups of 14 small European countries, 21 Caribbean countries, and 24 South-East Asian countries) which lack national resolution; i.e., member countries are prescribed identical growth paths (see Table 2). In the following, each of the three country groups is treated like 70 an individual country with respect to replacement of missing data.
Generally, gap filling is first done on the supranational level and later gaps in national time series are filled by accounting for growth rates of either neighboring countries, the 75 4 T. Geiger: African total (AT) -associated supranational level, or the associated world region the country belongs to. In the following we present our gap-filling methodology, first general steps and then for each world region in detail, starting with regions with the least missing values.

Preparatory steps
As a first step we populate all missing data points in 1850, the initial year of our data product, by linear interpolation between the last available data point before 1850 and the first one after 1850, ensuring that it is not more distant in time 10 than 1870. Next, and if available, we generate annual data by linear interpolation of data points between 1850, 1860, and 1870. These preparatory steps reduce the missing value fraction from 51.7 to 48.5 %.

Europe 15
The preparatory steps completed the country-level data for most countries in Western Europe. These individual countrylevel data are then used to complete the time series for the supranational group of 12 Western European (WE) countries by population-weighted mean income using HYDE's 20 national population data, as growth rates from the WE time series are used to approximate missing values for the country group of 14 small CE4 European countries. Similarly, the United Kingdom's growth path is used to complete Ireland's time series.

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Next, gaps in the supranational group of seven Eastern Europe (EE) countries time series are linearly interpolated (including the time of World War 2) and then, starting in 1870, used to extrapolate individual country growth paths in Eastern Europe back to 1850. 30 Relative changes in the former Yugoslavia's time series are used to extrapolate their temporary constituents back to 1850, and to extrapolate Kosovo's income between 1991 and 2010. The same procedure is conducted for the constituents of the former Czechoslovakia.

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Relative EE changes prior to 1885 are used to complete the former USSR time series. The relative changes in the USSR time series are used to extrapolate income for all member countries of the USSR up to 1973USSR up to , and to interpolate between 1973USSR up to and 1990. The fraction of missing values in the entire 40 data set thus decreases to 34.4 %.

North America, Australia, and New Zealand
The preparatory steps were sufficient to fill the respective time series completely.

Latin America 45
Following the country grouping in the MPD, we generate a complete population-weighted average income time series for a group of eight large Latin American (LA) countries. To do so, Peru and Mexico's income is respectively extrapolated before 1870 and interpolated after 1870 based on the mean 50 growth of the seven remaining countries. Relative changes in the LA time series are applied to estimate the income of the remaining South American countries. The time series for the group of 21 Caribbean countries is linearly interpolated and then used to fill gaps in the remaining Caribbean and 55 Central American countries, except for Jamaica and Cuba, whose time series is sufficiently dense to be interpolated individually.
Finally, the fraction of missing values is reduced to 29.7 %.

Asia 60
Asia is separated into East and West Asia, reduced by the fraction that belonged to the former USSR. Where required relative income changes based on the linearly interpolated time series for a group of 16 Eastern Asian (EA) countries are used to extrapolate individual country 65 data before 1870. Furthermore, data gaps for selected countries with quite dense coverage (India, Japan, Indonesia (Java before 1880), Sri Lanka, and China) are filled by linear interpolation on an individual basis. Using a step-wise procedure, we fill the EA time series after 1870 with the population-70 weighted average income of all countries for which original data are available at any given time step. Relative changes in the EA time series are then used to fill gaps in all remaining Eastern and South-East Asian countries, in particular to complete the time series for the joint group of 24 South-East 75 Asian countries. However, missing values for Bangladesh and Pakistan are estimated based on India's relative changes. Thereby, the fraction of missing values is reduced to 24.3 %.
In a second step, Western Asian countries including the Gulf States are treated, where data availability is very lim-80 ited before 1950. Except for Turkey (former Ottoman Em-pire, complete data since 1923), relevant data points exist only for 1820, 1870, and 1913. To also include countries with completely missing data before 1950, we assume that the income of Israel is equal to West Bank/Gaza income in 1870 and 1913, and that the income of some Gulf States is equal 5 to Iran's income. For each country we linearly interpolate the data until 1913, and again until 1950, except for Kuwait, Qatar, and the UAE. For those three countries we estimate income growth to 1939 based on average income growth for all Western Asian (WA) countries and then linearly interpolate 10 each country individually between 1940 and 1950, thereby ensuring that sharp income rises only occur after the discovery of oil.
Upon completing Asian time series the fraction of missing values is reduced to 19.5 %.

Africa
The MPD contains only six countries with income data prior to 1950: Egypt, Tunisia, Morocco, Algeria, and South Africa/Cape Colony (all since 1820), and Ghana (since 1870). Therefore, the African total (AT) population-weighted 20 average income prior to 1950 is only defined by six countries. For historic and geographic reasons, we assume that those countries define the upper income limit when extrapolating the remaining countries back in time. So if a country's 1950 income is smaller than the six-country population-weighted 25 mean, the income fraction is used to define the scaled income in 1913; otherwise, it is set equal to the six-country mean in 1913. Missing data between 1913 and 1950 are then interpolated according to scaled AT relative changes, while the bare AT relative changes are used to extrapolate missing values 30 from 1913 to 1850.

Summary
Using all the steps described above, all missing values are filled and a complete time series (1850-2010) is obtained for all countries listed within the MPD. This time series, reported 35 in 1990 G-K dollars and matched with IS03 country codes, can be found in the DOI data archive (Geiger and Frieler, 2017). Note that for some countries the reporting period ends in 2008; no extrapolation was done thereafter as more reliable data from other sources are available for this period. To test for robustness the conversion factors are calculated for not only the earliest reporting year of PWT8.1, but also for each of the first 5 years. If the five individual conversion factors significantly vary (fraction of standard deviation of 65 the first five conversion factors and the first conversion factor larger than the iteratively derived threshold of 4 %), we use the 5-year mean conversion factor instead. In total, 78 out of 195 countries require a mean conversion factor, while overlapping time series for 14 countries are so short that a mean 70 conversion factor cannot be determined. All conversion factors and the base year of matching are available in the Supplement as well as supplementary data in the DOI archive (Geiger and Frieler, 2017). Figure 2 provides an illustration of the conversion factors, here shown as conversion rates in 75 percent to highlight the symmetrical scattering around the cross-country median, which is larger than unity, as expected, due to the transformation forward in time between 1990 and 2005. The statistical distribution of conversion rates is shown for all 195 countries (left boxplot in Fig. 2), all 36 countries 80 that do not appear specifically in the MPD but as country groups only ("no Maddison" boxplot in Fig. 2; see also Table 2), and separately for six different world regions. The outliers ARE (United Arab Emirates), BRN (Brunei), and SOM (Somalia) are explicitly stated in Fig. 2, making their respec-85 tive converted time series before 1970 and 2010 rather uncertain. A large fraction of relatively large conversion rates stems from those countries with no individual resolution in the MPD ("no Maddison" boxplot in Fig. 2) that are matched to PWT8.1 data using the respective country group data; see 90 Table 2. In contrast to the other world regions, Europe and South America show rather small variations in conversion rates that are in line with the relatively dense data coverage within the MPD.
Additional countries that are reported in the SSPs but not 95 in PWT8.1 are included based on data first from PWT9.0 and second from WDI, except for El Salvador (SLV) and Zimbabwe (ZWE), where PWT9.0 data are chosen in place of the available PWT8.1 due to known issues in the data set; see https://www.rug.nl/ggdc/docs/what_is_new_in_pwt_ 100 81.pdf for details. Conversion of PWT9.0 data between 2011 PPP USD and 2005 PPP USD values is conducted by us-6 T. Geiger: ticipated changes due to the global financial crisis (SSP products were produced many years prior to the financial crisis), we opted for this smooth procedure consistent with other Figure 3. Base year dependent relative change in 5-year runningmean conversion factors for all 181 countries (gray lines) for which a 5-year mean can be determined. The cross-country mean (reddashed) and the median (blue-solid) conversion factor increase by 28.2 and 8.4 % between 1954 and 2005, respectively. SSP-informed data sources to avoid large unphysical kinks in the time series. Users that require more recent observa-30 tional data are advised to rely on the underlying data sources directly. An illustrative example of the matching procedure for four selected countries is displayed in Fig. 4; the matching result for all 195 countries is shown in Fig. S1 in the Supplement.

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As mentioned above, there are several reasons why we use the earliest year of data availability for PWT8.1 data as a base year for conversion, one of which being insufficient coverage for many countries in the MPD. While this is a sensible decision for most countries where conversion factors 40 do not fluctuate rapidly over time, it can lead to distortions for some countries as, e.g., hyperinflation, economic crisis, or rapid economic growth may produce different conversion factors in different base years. In general, using earlier years for matching results in more conservative estimates of past 45 income because mean and median conversion factors across countries grow with time; see Fig. 3. Figure 3 also illustrates that changes in country-specific conversion factors over time cluster at relatively low values, while some countries show larger deviations and fluctuations 50 from the mean development. Table 3 therefore provides a more detailed sensitivity analysis for 181 countries for which at least 5 years of overlapping data exist. For more than 70 % of the countries the change in conversion factors is smaller than 50 %, while almost 14 % of the countries show changes 55 larger than 100 %. This sensitivity check provides useful information about the uncertainty of past income estimates: users should keep in mind that income estimates are inherently uncertain not only due to reporting issues and lack of data, but also due to currency conversion and their respective 60 change over time. Country-specific conversion factors over time are provided for selected countries in Fig. 4 and for all countries in Fig. S1.
In a next step we multiply income and population time series to obtain GDP time series. As for the income matching 65 between historical observations and SSP projections, population estimates are truncated in 2005 and linearly interpo-  Fig. 4 corresponds to income deviations only, it also reflects GDP differences well as the SSP income projections are the main source of deviations, mostly due to the 10 already mentioned fact that SSP simulations were completed before the financial crisis in 2008. However, Zimbabwe shows a large discrepancy of about 70 % that is caused by differences in both income and population estimates. When using Zimbabwe's time series for historical analysis only, we  All data sets are provided in "csv" format and are freely available at https://doi.org/10.5880/pik.2017.003. Please also consult the data description file for additional information on the data set.

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In conclusion, we provide a continuous time series for per capita income and GDP between 1850 and 2009 for 195 countries. The foundation of our work is the income data set maintained by the Maddison Project, which is completed using various interpolation and extrapolation techniques and 40 harmonized with economic data from the Penn World Tables. The main objective is to provide a continuous economic time series that is readily applicable across disciplines and by nonexperts in the field. The methodology applied is rather simple and comes with several limitations and caveats.

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As we do not devise new historic economic figures ourselves, we are bound to existing data only that areCE5 combined with various techniques to replace missing values. Our main assumption is that geographically close countries have observed similar growth paths over the last 150-200 years, 50 such that we can use neighboring (groups of) countries to estimate missing data. This assumption strongly depends on many political, economical, and societal aspects (e.g., the economic system, the membership in alliances, the occurrence of wars, the colonial background, and many more) 55 that, however, were not considered in our work. While rather exhaustive data exist for Western European countries, these limitations might be less of a problem than for most African countries. As a consequence, one should treat the data with care and allow for uncertainties, in particular where data cov-60 erage is limited or almost non-existent. Another limitation arises due to different units: the original MPD is measured in 1990 GK USD, while all other data sets use PPP equivalents in either 2005 or 2011 USD. The required PPP transformation can lead to underestimation or 65 overestimation of economic figures, in particular further back in time. As mentioned above for Brunei (discovery of fossil fuels) and Somalia (ethnic conflict and civil war), large conversion factors are due to rapid changes in a country's income over a short period of time that can deteriorate the PPP 70 conversion. However, as currently there exists no reliable solution to circumvent this conversion problem, one has to interpret transformed data with caution. For example, countries that mainly depend on fossil-fuel exports had rapid income jumps in the not so distant past that can overestimate their 75 income before oil discovery. For this reason we also provide the interpolated MPD in original 1990 GK USD. In addition to this, the choice of a specific base year for currency conversion introduces additional uncertainty about past estimates. For several reasons discussed above, we here systematically 80 rely on a conversion factor defined at the earliest possible time. While this provides a rather conservative estimate of historical income in general, a different base year for conversion can yield large differences for some countries, as our sensitivity assessment has shown.

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Another problem arises due to shifting national borders, and the formation of new and disappearance of old nations: the data sets only reflect the current political map defined by the list of countries available in the PWT8.1 database. To circumvent but not fully exclude this problem, we work with per capita income time series until the very last moment that are then multiplied by historical population data to gen-5 erate GDP estimates. The income data are here provided as well such that the inclined user can generate GDP time series for a different political map himself. For consistency reasons population and income estimates are selected from identical sources, except for the MPD, where HYDE data are used.
However, when merging different time series, inconsistencies arise due to different country definitions, e.g., as is the case for countries in the former Yugoslavia or for the transition between historical data and SSP projections. To reduce the inconsistencies to a minimum we rely on the country definitions in PWT8.1 and adjust the other sources to it. Regarding the former Yugoslavia, we split the population estimates for missing time periods for SCG (Serbia and Montenegro) into Serbian (SER) and Montenegrin (MNE) parts based on reported population ratios from 1990. Further, the population 20 of Kosovo (KSV) was added to Serbia (SER) to match with the PWT's estimates. A similar procedure was followed for the respective population of Israel (ISR) and Palestine (PSE) prior to 1950 and 1969, respectively: reported population ratios were used to estimate a single country's population fur-25 ther back in time. No further adjustment was necessary for the other world regions.
Furthermore and as mentioned above, historical population estimates are unavailable for some small countries, making the GDP time series incomplete. 30 Despite these shortcomings and uncertainties, this new data set will broaden the applicability of historic estimates of economic activity, e.g., in the field of climate impact research in order to facilitate impact simulations on centennial timescales (Frieler et al., 2017). It further provides the op-35 portunity to generate gridded GDP distributions for the past based on recent downscaling initiatives (Geiger et al., 2017;Murakami and Yamagata, 2017). Moreover, the increased research interest in past GDP data will provide valuable feedback to the historians and economists working in this field 40 and might stimulate further advances. These advances are expected to improve this current data set further.
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