A Positive Theory of Income Taxation Where Politicians Focus upon Swing and Core Voters

We construct an equilibrium model of party competition, in which parties are especially concerned with their core and swing voters, concerns which American political scientists have focused upon in their attempts to understand party behavior in general elections. Parties compete on a large policy space of possible income-tax policies. An element in this infinite-dimensional space is a function which maps pre-fisc income into post-fisc income. The only restrictions are that the function be continuous, and satisfy exogenously specified upper and lower bounds on its derivative, where it is differentiable. Only a fraction of each voter type will vote for each party, perhaps because of issues not modeled here or voter misperceptions of policies. Each party's policy makers comprise two factions, one concerned with maximizing the welfare of its constituency, or its core, the other with winning over swing voters. An equilibrium is a pair of parties (endogenously determined), and a pair of policies, one for each party, in which neither party can deviate to another policy which will be assented to by both its core and swing factions. Formally, this is a Nash equilibrium where each party possesses only a quasi-order over the policy space. We fully characterize the equilibria. There are many. In a specially important case, each party proposes a piece-wise linear tax schedule, and these schedules coincide for a possibly large interval of middle-income voters, while the left' party gives more to the poor and the ‘right’ party more to the rich. An empirical section uses the data of Piketty and Saez on taxation in the US during the twentieth century to assess the model's predictions. We argue that the model is roughly confirmed.