Abstract This paper investigates the tax responsiveness of multinational firms’ investment decisions in foreign countries, distinguishing firms that are able to avoid taxes (avoiders) from those that are not (non-avoiders). From a theoretical point of view, the tax responsiveness of firms crucially depends on this distinction. Empirically, however, a firm's ability to avoid profit taxes is inherently unobservable to the researcher. To address this problem, we use a finite mixture modeling approach which allows us to distinguish avoiders from non-avoiders stochastically from a mixture of distributions of the two types of firms. Using panel data on the universe of foreign affiliates of German multinational firms over the years 1999–2010, we find that investments of tax avoiders do not respond to host-country profit taxes at all, while those of non-avoiders do. About 11% of the affiliates are estimated to be able to avoid taxes. These investments account for about 58% of the stock of foreign fixed assets held by German multinational firms abroad. A one-percentage-point increase in the statutory corporate profit tax rate of a host country is found to reduce the fixed assets of non-avoiders in that host country by 0.81%.