Wow. What a completely irresponsible study and summation of results.
To quote specifically from page 5 of the report:
When we restricted the sample to countries outside the former Soviet Union, we noted that greater progress in privatisation was associated with a neutral or favourable effect on mortality rates (emphasis mine) from 1991 to 2002, unlike in countries of the former Soviet Union
Which suggests that maybe, just maybe, privatization has nothing to do with the jump in mortality rates and that there are even larger historical and social processes at work here.
While the authors control for GDP, they don't control for *trends* in GDP. These economies (particularly Russia's) were collapsing before privatization occurred. I know they can't do a real counterfactual, but use some common sense for Christ's sake - GDP was already falling at something like 10% per year: absent privatization, would health outcomes have remained constant? Would they, fuck.
Controlling for the age of population might have been useful, too. Might the lack of a jump in death rates in the central asian republics have had something to do with the fact that their populations were younger rather than that they weren't privatising?