Inefficiency Traps in New Democracies

The effect of democracy on nations' development is still debated both within and outside academia.
The existence itself of an academic debate proves that there isn't a unique and definitive answer, and hence that democracy might sometimes fail in fostering development. Indeed, if this was not the case, an open debate would not be there and everyone attempting to study the issue would end up with evidence of a positive relation.
In this work, I describe a mechanism that might cause a country to remain stuck with bad institutions and under development and which passes through democracy.
The idea is simple: if a country is spending in a too inefficient way when democracy is introduced, citizens might find convenient to stick with bad institutions even if they have the chance to vote for some more efficient candidate.
To understand the mechanism consider two main channels through which efficiency affects citizens: first, a more efficient government is able to distribute more public good, wasting fewer resources. At the same time, though, a more efficient government is more effective in the collection of taxes.
If the initial level of efficiency is too low, then, the positive effect will be more than compensated by the negative effect (for individuals) of reduced evasion capability. In practice, a marginal increase in efficiency may cause individuals to pay more money in the form of taxes to the government, for an amount that is higher than the one they get back as public good. Hence, the country might be stuck in a bad equilibrium with a highly inefficient government, with no incentives to fight corruption.
The basic idea of the trap is that negative initial conditions may cause democratization to fail in fostering efficiency, and hence redistribution and development.
My model predicts different outcomes depending on the initial conditions of the country: if efficiency of public spending is too low when democracy is introduced, the burden of taxation might become higher than the benefit from democratic redistribution. In this setting, increasing efficiency of the government may be harmful to individuals who thus prefer inefficient and corrupt politicians. This causes the country to be stuck with bad institutions, ending up in a trap of inefficiency. The model does not have direct predictions on growth and development; nonetheless, the negative relation between corruption and growth is well established in the literature.
I build a model of risk-neutral, profit-maximizing individuals whose choice variable is tax evasion, constrained by a concave enforcement technology. I find a threshold level of efficiency of public spending, which depends upon the country's initial endowments (geography and individuals' preferences) which determine whether individuals would prefer more efficiency. If the country starts from an efficiency level which is below this cut-off, then a marginal increase in efficiency is harmful to the median voter. Hence, fighting corruption is not beneficial to anyone in this situation.
I also identify a lower bound for efficiency, below which increasing efficiency is always positive for citizens. This is due to the fact that there exists a minimum level of state capacity that is desirable for anyone. Indeed, when efficiency is close to zero, there is no public good provision and hence no defense, no police and no justice (no-anarchy condition). Such state-capacity lower bound is not constant across nations: geographic endowments may matter in the long-run, as the density of population, the shape of the territory and climate can affect the cost of ``controlling'' a country.
To sum up, a nation is stuck in an ``inefficiency trap'' as long as its government efficiency level is in between the lower bound and the cutoff. A sudden jump in efficiency (over the threshold) would bring the country out of the trap since above the cut-off efficiency starts having a positive effect on citizens again.