Criticisms of endogenous growth models with flat rate taxes have highlighted two features that are not substantiated by the data. These models generally imply: (1) that economic growth must fall with the share of government expenditures in output across countries, and (2) that one-time shifts in marginal tax rates should instantaneously lead to similar shifts in output growth. In contrast, we show that allowing for heterogeneous households and progressive taxes into otherwise conventional linear growth models radically changes these predictions. In particular, economic growth does not have to fall, and may even increase, with the share of government expenditures in output across countries. Moreover, discrete permanent shifts in tax policy now lead to protracted transitions between balanced growth paths. Both of these findings hold whether or not government expenditures are thought to be productive and better conform to available empirical evidence.