This paper develops a model of search on the labour market with training. The model reveals how the tax system can restore the social optimum if the Hosio s condition is not satisfied in the private equilibrium. Furthermore, the effects are explored of a second-best reform from average to marginal taxes when a given amount of public revenue has to be raised. We find that (i) a marginal wage tax is less distortionary to raise revenue than is an average tax per job, provided that training is not distorted initially; (ii) this conclusion may reverse in the presence of training distortions; (iii) marginal wage taxes are less distortionary in economies characterized by commitment in wage bargaining, such as the European labour market. Hence, tax reforms that reduce the average tax per job and raise the marginal wage tax, such as an EITC or a negative income tax, are more attractive in Europe than in the US.