, where is the bargaining weight of vis a vis If the parties split their policy differences (i.e., M H. have equal bargaining weights), gets a transfer of . Empirically we may think of as the M relative seat share of in a coalition government with M H. The case of an coalition is more complicated because both and can tax and can also LM L M H, L tax So and must compromise on both dimensions. The policy vector is, but because there M. L M is no incentive by either or to tax beyond the point where additional taxation leads to L M H lower revenues, the former two policies lie on a line. The logic is illustrated in Figure 2, where each axis represents a tax rate in the policy space and where the optimal taxation of is H constrained to a linear combination of taxes preferred by and The optimal policies of and L M. L (defined above) are indicated by solid circles. M When and form a coalition, they must find a compromise that divide the difference between L M their preferred policies. If the compromise is a simple 50-50 split, half the taxes on will go to H L and the other half to and will only be taxed half the rate of that preferred by This is the M, M L. case illustrated in Figure 2. But this may not be a feasible outcome if has the option of allying with since should then M H, M be able get at least as much as it can get from (which is outside option). In the H M’s scenario above, that means that M must get , which is the middle of the solid line in Figure 2. Indeed, in any scenario with a binding outside constraint, the bargain must lie on LM this line. This implies that gets the same in an coalition as in an coalition. In general, M LM MH both and would be expected to get a share of the taxation of that equals their L M H “full” bargaining weigh: , is again the bargaining weight of relative to The net transfer rates from to and M L. H M L are then: . Figure E1. The Taxation Policy Space (Example: Coalition with 50-50 Split of Policy LM Differences). The policy vector is Note:
, where is the bargaining weight of M vis a vis H. If the parties split their policy differences (i.e., have equal bargaining weights), M gets a transfer of . Empirically we may think of as the relative seat share of M in a coalition government with H. The case of an LM coalition is more complicated because both L and M can tax H, and L can also tax M. So L and M must compromise on both dimensions. The policy vector is, but because there is no incentive by either L or M to tax H beyond the point where additional taxation leads to lower revenues, the former two policies lie on a line. The logic is illustrated in Figure 2, where each axis represents a tax rate in the policy space and where the optimal taxation of H is constrained to a linear combination of taxes preferred by L and M. The optimal policies of L and M (defined above) are indicated by solid circles. When L and M form a coalition, they must find a compromise that divide the difference between their preferred policies. If the compromise is a simple 50-50 split, half the taxes on H will go to L and the other half to M, and M will only be taxed half the rate of that preferred by L. This is the case illustrated in Figure 2. But this may not be a feasible outcome if M has the option of allying with H, since M should then be able get at least as much as it can get from H (which is M’s outside option). In the scenario above, that means that M must get , which is the middle of the solid line in Figure 2. Indeed, in any scenario with a binding outside constraint, the LM bargain must lie on this line. This implies that M gets the same in an LM coalition as in an MH coalition. In general, both L and M would be expected to get a share of the “full” taxation of H that equals their bargaining weigh: , is again the bargaining weight of M relative to L. The net transfer rates from H to M and L are then: . Figure E1. The Taxation Policy Space (Example: LM Coalition with 50-50 Split of Policy Differences). Note: The policy vector is
Elkjaer_Iversen_DPSA2018.docx