The Index measures the degree to which each of the present-day countries was the site of nation-states, kingdoms, or empires every half-a-century since the first century.
Louis Putterman and his colleagues have compiled the data in the following way. For each of half a century from the year of 1 AD to 1950, each present-day country is coded on (1) whether there is a government above the tribal level; (2) whether this government is foreign or locally based; (3) how much of the territory was ruled by this government. These three aspects of the state history are then aggregated (see this document for detail).
Downloadable from Putterman's website.
Version 1 is used by Bockstette, Chanda, and Putterman (2002), which find that the Index is correlated with measures of political stability and institutional quality, with income per capita, and with the rate of economic growth between 1960 and 1995.
Version 2 is used by Chanda and Putterman (2006).
Version 3 is used by Putterman and Weil (2010).
Used also by Bardhan (2005).