When confronted with China's recent brilliant growth rates, a cynic might say China had an unfair advantage: it had room to grow. That is, it's easy to grow your GDP at 6.46% annually since 1980 if you start out with a per capita income of US$305.46. Labor is cheap, you have no legacy infrastructure to deal with, and your exports are extremely competitive. Of course, this begs the question that there are lots of countries with low PCI, and not all of them grow at such robust rates - but let's come back to that. I was also once challenged by a European that the U.S. grew slightly faster than Europe not because of any decision we've made to embrace free markets, but because of our good land and wide open spaces which are cheaper to develop. Because of population density rather than PCI, we have room to grow.
This interested me, so I pulled together some IMF and UN figures for 179 countries and territories; most growth rates are annualized since 1980. First let's look at population density's relationship to income growth, if any (source for population and area data here and here resp.) For viewability purposes, the scatter plot below excludes the 11 most densely populated countries/territories (Singapore, Hong Kong, Malta, Bangladesh, Bahrain, Maldives, Taiwan, Mauritius, Barbados, Korea, and Lebanon, all > 400 people/km^2).
The red circle contains 18 countries, all of which have had at least 10% annual growth since 1992: Armenia, Kazakhstan, Estonia, Latvia, Lithuania, Turkmenistan, Bosnia and Herzegovina, Equatorial Guinea, Russia, Azerbaijan, Belarus, Tajikistan, Cambodia, Ukraine, Slovakia, Moldova, Czech Republic, and Croatia (Bosnia-Herzegovina data since 1994, Equatorial Guinea data since 1980, Cambodia data since 1986). There's a trend there: of these 18 countries, fully 17 transitioned from a closed communist in the last decade; 16 of 18 were Soviet satellites. The trend on display is the effect of markets, not low population density. Not the effect I was looking to call out, but interesting that it's so apparent here.
It's worth pointing out that, for the 12 countries that grew at greater than 15%, the average density was 45/km^2; for the rest that grew at less than 15%, the average population density was 218/km^2. The same statistics using 10% as the break point are 62/km^2 for 18 countries >10% growth and 222 for the rest. Breaking the other way, the 58 countries with greater than 120 people/km^2 density grew at 4.15%; the rest that have less than 120 people/km^2 grew at 4.34%. There does seem to be some effect. (These figures include the 11 densest countries taken out of the scatter plot.)
The picture for growth rate and PCI could fool you into thinking it's some sort of normal distribution, but it's not. PCI is taken from 1999 for all countries because it was the first year that IMF had data for all 179 countries.
Interestingly, the vast majority of high-PCI countries have a middle-road growth rate of around 5%. Low PCI countries are more widely distributed. The 18 countries with growth above 10% have average PCI of US$1,836.08; those with growth less than 10%, US$6,505.82. Then again, the 32 countries with negative growth rates clocked in at average PCI US$1,703.99, vs. positive growers at US$6,979.31. Breaking the other way, those with 1999 PCI below US$5,000 had average growth of 4.17% (131 countries), while those above US$5,000 PCI had average growth of 4.55%. Of course, again the low PCI, high growth countries were all ex-communist but one. Who are the low PCI low-growth countries (i.e. < $5,000 PCI and negative growth)? Georgia, Congo-Zaire, Ghana, Mongolia, Yemen, Niger, Sierra Leone, Burundi, Eritrea, Madagascar, Papua New Guinea, Nigeria, Ivory Coast, Gambia, Solomon Islands, Namibia, Zambia, Myanmar, Malawi, Paraguay, Syria, Togo, Uganda, Ethiopia, Suriname, Guyana, Rwanda, and Guinea. This is a grab-bag, but many of the countries were victims of civil wars (10 of 28) and a few resource-cursed ones.
There is a weak inverse correlation between growth and both population density and per capita income, although it is swamped by the signal from the post-communist states. The lesson here? Those states were left with strong institutions, which visibly benefit them (particularly in the case of the growth-PCI comparison). So perhaps it's true: China's low initial PCI and its strong institutions, as well as the U.S.'s open spaces, are both advantages to growth.