This paper tests whether OECD countries compete with each other over corporate taxes in order to attract investment. We develop two models: with …rm mobility, countries compete only over the statutory tax rate or the e¤ective average tax rate, while with capital mobility, countries compete only over the e¤ective marginal tax rate. We estimate the parameters of reaction functions using data from 21 countries between 1983 and 1999. We …nd evidence that countries compete over all three measures, but particularly over the statutory tax rate and the e¤ective average tax rate. This is consistent with a belief amongst governments that location choices by multinational firms are discrete. We also find evidence of concave reaction functions, consistent with the model outlined in the paper