, and a net income of . taxation demanded by L is greater than for M since L wants to tax 2/3 of all income by , whereas M only taxes 1/3 of all income (again, H sets taxes equal to 0). This is the preference ordering assumed in Figure 1 in the main text. L’s optimal transfer as a share of the net income of M and H (L’s transfer rate) is identical to M’s optimal transfer rate from H: This completes the definition of preferences for each class. The next question is how political power shapes actual outcomes. If M and H share power the observed transfer ratio is a weighted average of the preferred levels by M and H: , is a weight that measures the political power of M over H (MH indicates that both M and H matter politically). we cannot observe we cannot identify , but we can test empirically whether the transfer rate,, responds to the relative income of M and H, as opposed to who are in government. If the democratic subversion thesis is correct, we should observe that , where are the observed relative pre-fisc incomes of M and H. In a model where the middle class is pivotal, as in the main text, the transfer rate is the preferred rate of M. As explained in the main text, but we can infer that in that case will be orthogonal to : . Note that this implication is stark because it means that even if top end inequality,rises, as it has in most countries, this should have no effect on the transfer rate, which will remain constant (ceteris paribus). Note also that this implication is contrary to the Meltzer-Richard model. The reason is that the M-R model implicitly assumes that the interests of L and M are aligned so that when M’s income falls its preference for taxation rises. As soon as taxes and benefits can be targeted, M always wants to tax as much as it can and spend the proceeds on itself. If government power matters (so the RDM applies) and M cannot govern on its own we need to derive the policy under different government coalitions. We assume such coalitions consist of at most two class parties. In the case of an MH coalition the bargain will lie between the optimal tax rate of M (which is ) and the optimal tax rate of H (which is 0):
, 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