Equilibrium policy Party P =1, 2 in a coalition government sets rP and gJ,
J = P, so as to maximize (2.4), subject to (3.2), (2.1) and (2.2), and for a given
value of future seats RP . Since both parties in the coalition government agree
over spending benefiting the groups not represented in government, it is irrelevant
who sets it; we thus let either of P =1, 2 optimize with regards to gJ,J6=1, 2.
Moreover, the policymaking incentives are identical independently of whether the
opposition consists of on or two parties (in the previous section we could omit the
back subscript N from policy outcomes, because they are the same irrespective
of N, given the type of government).
The resulting optimality conditions for spending imply:11
J = ½ H-1I1 ] if J = 1,2 (3 3)
gC = Hg-1[1], if J =3,4 . (3.3)
Retrospective voting induces opportunistic politicians to enact a suboptimal allo-
cation of local public goods, relative to the choices of a social planner. The groups
represented in government have an advantage, and spending on the local public
good benefiting them exceeds the social optimum: gCJ >gJ = Hg-1(1), J =1, 2.
Intuitively, the disproportionate electoral response by its own voters induces each
party in government to give them more weight. Since coalition members chose
local public goods unilaterally, we have a common-pool problem: the necessary
financing comes out of taxes levied on all groups, and the electoral losses from
this are also borne by the coalition partner. This leads both parties in govern-
ment to overspend on their constituencies. Conversely, the economic groups not
represented in government (J =3, 4) receive the efficient amount of public goods
although they pay higher than optimal taxes. Intuitively, the parties in govern-
ment agree to give less weight to groups 3 and 4 because electoral support in these
groups is less sensitive to their welfare compared to one’s “own” constituency.
It remains to determine the rents extracted by each party. In deciding on rP ,
party P trades off the direct gain of higher rents today against the loss of a lower
expected seat share (recall that the future value of office is taken as given by the
party). The optimum condition can be written:
1+ RP .∙ =o . (3.4)
11In deriving (3.3), we use (2.1) and (2.2) which imply that ddVgIr" = Hg(gJ) — 1/4 for I = J,
and dV-r = -1/4 for I = J.
14