Let´s imagine that the only function of a Government were to redistribute income to make societies more equal. An easy way to measure the efficiency of each Government would be then to calculate the difference between the Gini index before taxes and subsidies and after.
It is fair to mention that not all Governments are of equal size, some are bigger than others and therefore more capable of redistribute income. To measure Government size a “% Government expenditure over GDP” variable might be used.
The following graph shows the relation between “% Government expenditure over GDP” (horizontal axis) and the reduction of the Gini variable (before and after taxes and subsidies) (vertical axis).
The residuals of the fitted values might be understood as the efficiency given the size of Government.
If all the assumptions of this piece are correct
Government would be the most efficient and the ’s the least. UK