The Known Unknowns of Historical GDP Estimates

The Known Unknowns of Historical GDP Estimates

February 2, 2022

Originally published at

Joe Francis

One of my favourite graphs in recent writing on economic history might seem obscure. Reproduced below, it is found on page 28 of the working paper underlying the latest update of the Maddison Project database of historical GDP estimates. It shows the various estimates of British GDP per capita relative to US GDP per capita from 1770 to 1950. For me, this is interesting  because it illustrates how little we know about levels of GDP in the past.

Source: Bolt et al (2018, p. 28).

To recap, there are two main ways to measure historical GDP. The first method, pioneered by Angus Maddison, is to extrapolate back from recent estimates of GDP per capita at purchasing power parity (PPP) using constant-price indices of GDP per capita. The second benchmark method is to estimate past levels of GDP per capita in nominal values, then adjust them for differences in international price levels.

In a world of perfectly accurate historical statistics, both the backwards extrapolation and benchmark estimates would produce the same results. Yet Figure 4 shows that not to be the case.

The red line in Figure 4 shows the backwards extrapolation of the UK/US GDP per capita from the previous iteration of the Maddison Project database. According to this measure, British GDP per capita was considerably higher than US GDP per capita for most of the nineteenth century, before they converged from 1870 until the First World War, when the United States overtook Britain. The problem with this narrative is that it is contradicted by the various benchmark estimates, represented by the coloured dots, which tend to show British GDP per capita below US GDP per capita. The Maddison Project’s solution is to adjust the GDP per capita estimates for both countries so that they meet Mariane Ward and John Devereux’s (2018) benchmark estimates for 1872 and 1910. The result, shown by the blue line, suggests that the United Kingdom and United States enjoyed the same level of GDP per capita until circa 1870, when the United States pulled away. Once more, however, there is a problem: the authors of the Maddison Project update have ignored Ward and Devereux’s (2005, 2006) earlier, more comprehensive benchmark estimates of UK and US GDP per capita. If they are included in the graph, as I have approximately done by drawing them on with the blue dots below, they suggest a third narrative: Britain catching up to the United States from 1830 to 1870, but then falling away again. More estimates thus yield another, quite different narrative.

Such uncertainty about relative UK/US GDP per capita is particularly problematic because they are two of the countries with the most data. If we cannot even say what the relative GDP per capita of these two countries was in the first half of the nineteenth century, what are we to make of recent estimates of – heaven forbid – China’s GDP per capita in the tenth century (Broadberry, Guan, & Li 2018)?

The graph in the recent Maddison Project working paper is so interesting, then, because it shows that the relative GDP levels of the United Kingdom and the United States – the two countries with the best data – should be considered a known unknown. On the one hand, this is good news for economic historians because it means that there is still plenty for them to do producing new and (hopefully) improved historical GDP estimates. Yet it is also highly problematic: If we have not even been able to produce reliable historical GDP statistics for the United Kingdom and the United States, it may prove impossible to produce them for most other countries. As such, relative levels of GDP in the past may end up being considered a known unknowable.


Broadberry, S., H. Guan, and D.D. Li (2018) ‘China, Europe, and the Great Divergence: A Study in Historical National Accounting, 980–1850‘, Journal of Economic History, 78:4, pp. 955-1000.

Bolt, J., R. Inklaar, H. de Jong, & J. Luiten van Zanden (2018) ‘Rebasing “Maddison”: New Income Comparisons and the Shape of Long-Run Economic Development‘, GGDC Research Memorandum 174, University of Groningen.

Ward, M., & J. Devereux (2018), ‘Prices and Quantities in Historical Income Comparisons –New Income Comparisons for the late Nineteenth and Early Twentieth Century‘, Maddison-Project Working Paper WP-9.

––––––– (2006), ‘Relative British and American Income Levels during the First Industrial Revolution‘, Research in Economic History, 23, pp. 249-86.

––––––– (2005) ‘Measuring British Decline: Direct versus Long-Span Income Measures‘, Journal of Economic History, 63:3, pp. 826-51.