"Indeed, using a multitude of sophisticated econometric strategies, Acemoglu et al. conclude “Democracy Does Cause Growth.” In their sample of 175 countries from 1960 to 2010, Acemoglu et al. find that democracies have a GDP per-capita about four times higher than nondemocracies ($2074 v. $8149). (This is uncorrected for time or other factors.) But how much of this difference is explained by democracy? Hardly any. Acemoglu et al. write:Maybe it is not that weak if we look at a longer time period. But first, we need to know what the annual growth rate in GDP would have been with and without democracy in those 25 years.
Our estimates imply that a country that transitions from nondemocracy to democracy achieves about 20 percent higher GDP per capita in the next 25 years than a country that remains a nondemocracy.In other words, if the average nondemocracy in their sample had transitioned to a democracy its GDP per capita would have increased from $2074 to $2489 in 25 years (i.e. this is the causal effect of democracy, ignoring other factors changing over time). Twenty percent is better than nothing and better than dictatorship but it’s weak tea."
If the country starts with a $1,000 per capita GDP and grows 2% annually for 25 years it will end up at $1,640.
What number is 20% higher than $1,640? $1,968. To get there after 25 years, the annual growth rate would have to be 2.746%. It might not seem like much, just an extra 0.746% per year. But what is the difference after 100 years instead of just 25?
Without democracy, the per capita GDP would be $7,244. With democracy, it would be $15,013. That is a very large difference.
This reminds me of the Rule of 72. If you want to know how long it will take a number to double, divide 72 by its annual growth rate.
For 2% it would be 36 years. But for 2.746% it will take about 26 years. The democracy will be 10 years ahead of the non-democracy.