# Redistribution in a Model of Voting and Campaign Contributions

On Friday I attended a job market talk by recent Harvad PhD graduate Filipe Campante. Mr. Campante’s job market paper discussed how the equilibrium level of redistribution changes as inequality in a society increases.

The author sensibly assumes wealth is distributed in a according to a Pareto distribution. Individuals choose a tax level in order to maximize disposable wealth:

• wdi=(1-τ)wi+T
• T=τW-φ(τ)

The variable wi represents pre-tax wealth and wdi is after-tax wealth. The constant marginal tax rate is τ and the lump sum redistribution amount is T. The convex function φ(τ) represents economic or administrative costs to redistribution. Since the distribution of wealth is pareto, all individuals whose pre-tax wealth is above the mean wealth level, (W), will desire no redistribution (τ=0). Those with wealth below the mean will prefer taxes to be (1-wi/W). In equilibrium, the tax rate will be equal to the desired tax rate of the median voter. Since the wealth distribution is pareto, the median individual’s wealth level is below the mean wealth and thus some redistribution will take place.

Adding campaign contributions to the model

The central proposition Campante makes is that inequality will alter the traditional median voter predictions if we take into account campaign contributions. Consumers are assumed to vote or donate to political campaign because they gain utility from this action. This direct utility from civic participation is needed since a rational individual would realize that their vote has a measure 0 likelihood of changing the election’s outcome. Campante also gives evidence that any one individual’s contributions also will not change the outcome of the election. Some empirical findings are:

1. Contributions are typically very small and unable to change an election outcomes (the median contribution is around \$500)
2. Contributions are strongly related to personal income
3. Contributions are strongly related to other forms of political participation, such as turnout
4. Parties largely use contributions to increase the turnout of potential supporters

The author assumes contributions are proportional to income. Also, there are two parties: one for the rich (R) and one for the destitute (D). Party R favors less redistribution and party D favors more redistribution. A clever theoretical model is developed which finds that as inequality increases from complete equality, the society will favor more redistribution at first. This is due to the fact that when inequality increases, the median voter is relatively poorer and thus favors more redistribution (i.e.: an increase in τ). However, as inequality increases past a critical value, σ*, more and more wealth will fall into the hands of the supporters of party R. Party R will receive significantly more campaign contributions than Party D and thus the voter turnout for the supporters of Party R will be higher than the turnout for Party D. Thus, income redistribution, τ, will decrease as income inequality increases past the critical value σ*.

To summarize, when inequality increases there are two effects: 1) the median voter will prefer more and more redistribution and 2) Party R will receive a higher and higher percentage of the political contributions. Effect 1 dominates when inequality is relatively low and effect 2 dominates when inequality is relatively high.

Empirical Work

While the theoretical section of this paper is interesting, the empirical section is less significant. The author does not test whether redistribution increases with inequality—which is what the model proposes—but only whether campaign contributions increase with inequality. Campante finds that the amount, but not the number, of campaign contributions increases with inequality. This evidence is predicted by the theoretical model developed, but does not prove the theory since the regressions are based on campaign contributions and not redistribution levels.