Real GDP per capita is a fairly standard proxy for the “level of development” in the context of Wagner’s hypothesis. It might not be appropriate to use nominal GDP per capita. For the government share, it seems better to take the current-price ratio which indicates what fraction of the current output is used for government activities. The deflators for GDP and government spending are different and “real” government-share may not be a good indicator of the resource-use by the government during the current year.
The variables used do not have the same units, which may clog the analysis of the paper. Specifically, real GDP per capita is measured in 2005 dollars while the share of government consumption on GDP is measured in current prices. Either both should be in real terms or both in current prices, but not as is currently the case.