I am aware that because of externalities or public goods (or for other reasons) there can be no allocative efficiency on the market. I am also aware that policy makers' subjective judgement of the situation on the market (if market outcomes are distributed "fair") can be considered as equity in economics.
I wanted to empirically check if government spending can potentially increase efficiency or equity (as I think it should). I took labor productivity (a percentage of GDP) as a measure for efficiency and Gini index in disposable income as a measure for equity. While I am quite convinced with my measure of equity, as Gini tells me about the inequality of income distribution - I am not entirely sure about labor productivity. I am curious if I could choose better statistics to measure either efficiency or equity?
In my results I got that government spending on environment is positively correlated with increase in efficiency in only about 30% cases and in equity in about 50% cases. This seems a little bit counter-intuitive as environment seemed like a textbook example where there is a negative externality, so the firms maximizing their profits based on private costs tend to overproduce - and that the government intervention in that case is justified. So that I thought after the intervention, there should be increase in allocative efficiency, right? But it is a case in only around 30% of cases. What could be a reason for that?
Similarly, government spending on health. To my contention, it should increase both, equity and efficiency - but from what I've got it seems to be true in about 20% of cases. Why would that be a case?
Is it because of the measures I chose? Or my logic was simply wrong and government spending on environment causes efficiency to decrease and on health cases both, efficiency and equity, to decrease?