While it is not a slam dunk, there is pretty good empirical evidence that corruption and government expenses that are not tied to public infrastructure are not good for economic growth. This evidence comes largely from linear cross-country regressions of the kind that anybody with a little sense of theory or econometrics shudder. But sometimes this is done a little bit better.
Giorgio d'Agostino, John Dunne and Luca Pieroni take a simple growth model where government expenses are divided in public infrastructure, public consumption and military expense. Along with private capital, all three enter the production function for reasons that are not entirely clear, but we can let the data speak here. In addition, each expense is adorned with a multiplier that identifies how much is lost through corruption. The result is an equation for the growth rate that can be brought to the data, specifically a set of 53 African countries over 5 years. This is were things become iffy, as it is by now well-known that using panel data in growth regressions leads to very spurious results, especially when African data is considered. Using instruments and GMM will not help you much when data is of poor quality, especially from one year to the next. And taking lags of growth rates will make things even worse.
Results show coefficients "of the right signs" and a particularly strong interaction between corruption and military expenses. I am not sure I can believe these results given the above problems, but they make sense. And if one can extrapolate this African result to other countries, I would be especially worried for the US, where military expenses are always high and bribery of politicians is common and legal.