We present a multi-period model in which countries set source-based taxes without having precise information how their and their neighbours' tax rates affect the tax base. Countries can learn from past experience and from observing their neighbours' outcomes and/or tax policy choices. We consider the sequence of Markov perfect equilibria and show that the beliefs become more precise over time and, eventually, correct. The precision of beliefs in a given period increases in the number of observed countries. In equilibrium, tax rates are inefficiently low if the value of learning is positive and the pace of learning increases in the level of tax rates (because higher tax rates trigger larger tax base effects which helps learning); in the presence of fiscal externalities, tax rates are too homogeneous (because variance in tax policies enhances learning). If, due to fiscal externalities, the value of learning is negative, the opposite may be true. From the viewpoint of empirical measurement, the model generates time patterns that look as if countries react to each other even if there are no fiscal externalities. We conclude that the existing evidence may therefore be inconclusive with regard to the existence of tax competition.