The trivial thing to do is to look at the list of countries sorted by GDP per capita.
At the top positions of the list on can find several good old oil-rich monarchies. Surely the source of the wealth for those countries is democracy.
One can find EU member states deep down in the middle of the list. Can a EU member state be non-democratic?
Now let's look at the very bottom of the list. How many countries there are not trying to be democracies? Not a single monarchy, princedom or a satrapy. They all are Republics.