Much of the foreign direct investment worldwide is affected by one of more than 3000 bilateral tax treaties. There is an agreement that dividend and interest payments respond to these tax treaties' provisions, but evidence is scarce as to the magnitude of this response. We aim to fill in this gap for as many countries as possible by estimating the elasticities of dividend and interest income with respect to withholding tax rates, and the associated revenue foregone, exploiting the best available cross-country datasets. We collect information on withholding tax rates from the International Bureau of Fiscal Documentation; this includes information on EU directives, which imply zero withholding rates among all the EU member states and Switzerland, in addition to standard bilateral tax treaties. We combine this detailed information on withholding tax rates with foreign direct investment data from the International Monetary Fund, which we use to approximate bilateral dividend and interest flows; this results in a large panel data set of around 65,000 annual country-pair observations. While also observing heterogeneity in elasticities across countries, we estimate dividend flows to be highly elastic in a cross-country regression: a 1% increase in the applicable withholding tax is associated with a 2.3% - 2.6% decrease in dividend flows. We apply the elasticities to estimate potential tax revenue foregone. We estimate the largest annual revenue foregone for the United States (2.3 - 2.9 billion USD) and Canada (1.4 - 3.2 billion USD), while the investor country behind the largest revenue foregone is the Netherlands (2.9 - 3.3 billion USD). We arrive at somewhat lower and less robust estimates for interest income. Although our headline revenue estimates are, as expected, lower than static estimates that do not reflect elasticities, we nevertheless show that the revenue foregone of tax treaties remain non-negligible for some countries.