Most of the empirical literature on tax competition has been using panel models in which each country's tax rate responds to a weighted average of other countries' tax rates, where weights are given. This approach imposes the reaction functions to be such that all tax rates are either strategic complements or strategic substitutes for all the countries. Moreover, it also requires that the intensity of the reactions of the countries to be proportional to the same set of given weights. Since no theoretical model relies on such restrictive assumptions, we regain flexibility in the empirical analysis by using Vector Autoregressive (VAR) models, where the sign and intensity of countries' reactions may be heterogeneous. Using a Monte Carlo exercise, we show that if the objects of interest are the reactions to shocks in the tax rates of the other countries and there is no a priori knowledge of the structure of the economy, it can be convenient to opt for a VAR rather than a panel setup. A Bayesian VAR model on real data shows that strategic complementarity between some countries may co-exist with strategic substitutability between other countries, a finding with potential policy implications on the debate on tax competition.