This paper investigates properties of the second best allocation in a scal federal system in which both federal tax and intergovernmental grants are involved and the taxation is distortionary We extend the analysis of Boadway and Keen and Dahlby and Wilson by introducing both imperfect mobility and heterogeneous regions In contrast to the outcomes in the existing works we nd i the second best does not require the equalization of the conventional MCPFs between regions ii in order to replicate the second best matching grants based on either the local tax rates or tax revenues should be introduced to internalize the tax externality and iii federal tax policy is redundant once the intergovernmental grants are optimized The irrelevancy of the federal tax implies that optimal scal gap is indeterminate Therefore it will be argued that the standard framework of scal federal model in the literature does not provide a rationale for either decentralization or centralization of the tax system once the federal government is allowed to use sucient instruments of inter regional transfers