Welfare is often administered locally, but financed through grants from the central government. This raises the question how the central government can prevent local governments from spending more than necessary. Block grants are more efficient than matching grants, because the latter reduce the local governments' incentive to limit welfare spending. However, conventional block grant financing is less equitable, indeed, it may put a heavy burden on local governments in economically weak regions. This paper considers block grants which depend on exogenous spending need determinants, and are estimated from previous period welfare spending. This allocation method gives rise to perverse incentives by reducing the marginal costs of welfare spending. We derive the conditions for such a grant to be more efficient than a matching grant, and apply our results to the Netherlands, where such a grant exists since 2004. We conclude that the Dutch style grant is likely to be more efficient than a matching grant. As it is also more equitable, other countries might want to consider introducing a similar grant.