Do you have any evidence of that at all? Because I have evidence showing the opposite: eg China has an estimated public sector value of between 29% and 50%[1] and it is generally regarded as a high-growth economy (6.5%+ growth(, while somewhere like Greece (22% public sector, 0% growth) isn't.
In-fact, eyeballing that table doesn't show much apparent correlation at all. There are high-growth, high-public sector countries, high-growth, low public sector countries, low public sector, low growth AND low public sector high growth countries.
[1] https://en.wikipedia.org/wiki/List_of_countries_by_public_se...
China has substantially lower levels of social welfare spending. Its healthcare spending as a percentage of GDP is 5.5% for example [2].
Labour regulations are also much less onerous. You can use IQ tests to filter candidates for example, which would be extremely illegal in the West.
[1] http://ime.bg/uploads/335309_OptimalSizeOfGovernment.pdf
[2] http://data.worldbank.org/indicator/SH.XPD.TOTL.ZS?locations...
How are you measuring progress there? If you mean economic growth then now might be a good time to point out that correlation does now imply causation. Otherwise perhaps increasing life expectancy also causes a larger public sector? ;)