Tim Besley at Vox has a theory about successful autocracies: the ones in which there is a "selectorate", a group of people who may depose the leader without risking the collapse of the regime, exhibit better economic growth rates than autocracies in which all the power is concentrated on a single individual.
In the absence of elections, it is important to focus on what incentive this group has to support leaders that foster good policies. As citizens, this group will tend to benefit from economic prosperity. But, equally they are likely to enjoy some trappings of power by having allied themselves with the leader. If deposing the leader threatens these benefits, they may be reluctant to do so. This leads us to predict that secure selectorates will tend to create performance-related incentives for their leaders and would be willing to remove the leader from office if he does not perform well. Selectorates whose own hold on power is closely tied to a specific leader are willing to preside over bad policy.
It makes sense to me that the ability to get rid of poorly performing leaders improves performance. Also, if there's no way for a peaceful transition of power, repeated power struggles can hurt a country's economic prospects.
Extension of this logic also reveals why democracy is not always able to achieve the best policy outcome. Effective democratic accountability requires that the salient issues on which elections are fought are those that promote general interests. Democratic accountability may founder when factional rather than general interests influence election outcomes.
Based on this theory I'd conclude that democracies should outperform autocracies. Electorates may be factional but they still have a more acute interest in a country's economic development than selectorates made up of oligarchs who can generally live in priviledge as long as they maintain their positions. However, when Beasley compares autocracies with democracies, he observes, "Successful autocracies outperform democracies at the top of the distribution. However, they perform worse at the bottom."
The problem here may be that countries aren't divided into autocracies and democracies randomly. That is, if you look at a list of the richest countries on earth, you'll notice a disproportionate number of democracies. If you look at a list of the poorest countries, you'll see a heck of a lot more autocracies. I would expect such differences to also affect growth rates. If we compared equally rich autocracies and democracies, would the differences become disappear or become more pronounced?