At least in recent times, democracy did boost economic growth, according to a 2017 study:
based on a panel data of 144 countries observed for 1980–2014 show that democracy
had a robust positive impact on economic growth. Credit guarantee is one of the most
significant positive links between economic growth and democracy. The marginal effects
of credit guarantee and foreign direct investment inflows are stronger in democratic
countries than they are in non-democratic ones. In order to check the robustness of these
results, a dynamic model constructed with a flexible adjustment speed and a target level of
GDP is also tested. The results of this dynamic model also support the positive impacts of
democracy on economic growth.
Apparently investors are more willing to invest in democracies. Of course, there's only one China, so they'll invest there too. But if you're a small country...
And even considering the more mixed results of older studies, some positive effects were derived (in 2008 meta-analysis):
Despite a sizeable theoretical and empirical literature, no firm conclusions have been drawn regarding the impact of political
democracy on economic growth. This article challenges the consensus of an inconclusive relationship through a quantitative
assessment of the democracy-growth literature. It applies meta-regression analysis to the population of 483 estimates derived
from 84 studies on democracy and growth. Using traditional meta-analysis estimators, the bootstrap, and Fixed and Random
Effects meta-regression models, it derives several robust conclusions. Taking all the available published evidence together, it
concludes that democracy does not have a direct impact on economic growth. However, democracy has robust, significant,
and positive indirect effects through higher human capital, lower inflation, lower political instability, and higher levels of
economic freedom. Democracies may also be associated with larger governments and less free international trade. There also
appear to be country- and region-specific democracy-growth effects. Overall, democracy’s net effect on the economy does not
seem to be detrimental.
And as you probably expect (in this last paper):
Real-world factors appear to be important. The coefficient on Latin America is positive and statistically significant. That is, partial correlations from studies that
include Latin American countries in their samples are
larger than those that use OECD without Latin American
observations (OECD is the base region). In addition, studies report lower democracy-growth effects when Asian
countries are included in their datasets.
These conclusions are not universally accepted though. There's 2016 IADB paper which disagrees in the following sense: if you exclude all former-Socialist countries (because their economic data before 1990 cannot be trusted) and if you also exclude all countries in which transition to democracy happened (according to experts) primarily due to the poor economic situation (e.g. Benin and many of the other African transitions, or Latin America due to the 1980s debt crisis), then what's left is a sample where the transition to democracy happened "exogenously" (e.g. Spain after the death of Franco) and in these exogenously democratized countries no improvement in GDP growth due to a democratic transition is observed. However, even for these exogenously democratized countries they found some non-economic benefits, e.g. an improvement in "Physical integrity rights index (measured by the degree of torture, extrajudicial killing, political imprisonment, and disappearance indicators)" and "Empowerment rights index (measured by indices regarding freedom
of speech, freedom of assembly and association, workers' rights, electoral self-determination, freedom
of religion, and citizens' freedom to leave and return to their country as well as to travel within their own country)".
I should also mention that this IADB paper seems largely intended to debuk a paper of Acemoglu et al. (draft in 2014, peer-reviewed published in 2019) which not making this separation of democratization events in endo- and exogenous ones just concluded that democratization events increased the GDP growth rate for the time frame 1960-2010.
Another interesting nuance paper (2015), using data that goes back to 1820, basically finds that
prior to 1960, democratizations were not confounded by the influx of [foreign] aid and were
not associated with accelerated rates of economic growth.
To reach this conclusion this paper excluded (controlled for) Marshall Plan recipients (which was pre-1960).