In their paper, NOUS member Tim Krieger and Daniel Meierrieks examine the effect of population size on government size for a panel of 130 countries for the period between 1970 and 2014. They show that previous analyses of the nexus between population size and government size are incorrectly specified and fail to consider the influence of cross-sectional dependence, non-stationarity, and cointegration. Using a panel time-series approach that adequately accounts for these issues, they find that population size has a positive long-run effect on government size. This finding suggests that effects of population size that increase government size (primarily due to the costs of heterogeneity, congestion, crime, and conflict) dominate effects that reduce government size (primarily due to scale economies).
The full paper is available here.