Does voting for an inefficient government make sense?

Given a distribution of skills and interest in public service in the labor force, would it be best if the public-minded workers go into government or to the private sector? Essentially, this is what Esteban Jaimovich and Juan Pablo Rud ask. If the better ones go private, then the unmotivated ones go into government and wreak havoc: they seek rents, hire more public (low-skilled) employees, thus inflating their wages and depressing the returns of the most skilled private workers, which lessens their incentives to do better in terms of entrepreurship. Jaimovich and Rud also claim that this outcome is actually preferred by the (low-skilled) working class, because of the higher wage. They also support the outcomes of their model with observations from the data.

While it seems obvious that a government with more public-minded officials is better, the point about the wage inflation in the market for low-skilled workers is interesting. It also highlights once more that a good mechanism for the self-selection of workers into public and private jobs is essential. If public wages and side benefits (bribes included) are such that public-minded workers are better off going private, the whole economy suffers. That means, you need to pay civil servants well, but not necessarily better than private workers. But at least, remove incentives to complement wages with bribes.