How do countries compete for mobile tax base when they lack precise information on how tax rates affect the tax base? We present a multi-period version of a classic tax competition model in which countries set source-based taxes under incomplete information on the tax base elasticity. This information, however, improves as they observe both their own and their neighbours' experiences. In contrast to the existing work on policy learning, we focus on learning in the presence of (fiscal) externalities. We show that, because learning can exacerbate this externality, the value of learning can be negative and, thus, learning may be too fast. Given that variance in tax policies enhances learning, this implies that, in the sequence of Markov perfect equilibria, tax rates can be too heterogeneous. Furthermore, we contribute to the empirical tax competition literature by showing that learning generates tax patterns that look as if countries react to each other even if there are no fiscal externalities. We conclude that the existing results typically taken as evidence of tax competition may be more nuanced than heretofore recognized.