Second, although we do not consider such models in this book, we can imagine a situation in which agents undertake investments in human capital, and the poor are credit-constrained and underinvest relative to the optimal amount. Then, redistributive taxation - even without public-good provision - by increasing the post-tax incomes of the poor may contribute to aggregate human-capital investments and improve the allocation of resources (Galor and Zeira 1993; Benabou 2000; Acemoglu and Robinson 2000a, 2002). Moreover, as we show later, democracy may in fact be more efficient than nondemocracy even when there are taxes raised in democracy. This is because nondemocracies may allocate resources to socially wasteful activities such as repression to stay in power, and the costs of taxation may well be less than the costs of repression.
4.3 Targeted Transfers
The model of redistributive politics we have analyzed so far places many restrictions on the form of fiscal policy. For instance, all agents receive the same amount of redistribution. As we suggested previously, allowing for completely arbitrary forms of redistribution quickly leads to a situation in which collective choices are not determinate. However, it is possible to introduce more complicated forms of redistribution without losing the determinateness of social choices, and the comparison of economies with different structures of taxation yields interesting results.
Most relevant in this context is an extension of the two-group model to allow for targeted transfers - that is, different levels of transfers for the rich and the poor. More concretely, after tax revenues have been collected, they may be redistributed in the form of a lump-sum transfer T, that only goes to rich people, or a transfer Tp that only goes to poor people. This implies that the government budget constraint is now:
(4.12)
The indirect utility of a poor person, in general, is:
This problem has a three-dimensional policy space because voting will be over the tax rate τ and the two transfers Tp and T, but where one of these variables can be determined residually from the government budget constraint. This is why we condition the indirect-utility function V(yP | τ, Tp) on only two of these variables with Tr following from (4.12). Because the policy space is now two-dimensional, the MVT does not apply. However, collective choices are determinate and the equilibrium policy will still be that preferred by the poor. The poor are more numerous and all prefer the same policy because targeted transfers, like lump-sum transfers, do not allow the formation of a coalition of the rich and a subset of the poor to overturn the majority formed by the poor.
To characterize the equilibrium, we can again think of the model as a game in which two political parties propose policy platforms. The unique Nash equilibrium involves both parties offering the ideal point of the poor. To see what this ideal point is, note that a poor agent clearly does not wish to redistribute to the rich; hence, Tr = 0. Hence, the intuitive outcome is that the poor choose τ to maximize:
with first-order condition, yp( 1 - δ) =gives an ideal point of (τpT, )where rpT > 0. Here, we use the superscript T to indicate that rpT is the tax rate preferred by a poor agent when targeted transfers are allowed. Similarly,andare the preferred levels of transfers of a poor agent. Substituting for yp, we see that tpT satisfies the equation:
(4.13)
and becauseTrpT = 0 from the government budget constraint, we have=
The first important implication of this analysis is that the equilibrium tax rate in democracy with targeted transfers,is greater than the tax rate without targeted transfers, τp’, given by (4.11). Mathematically, this follows from the fact that θ > (θ — δ)/(1 — δ). The intuitive reason for this is also simple: without targeted transfers, because redistribution goes both to the poor and the rich, each dollar of tax revenue creates lower net benefit for the poor than in the presence of targeted transfers.and τp converge when δ → 0; that is, when the fraction of the rich in the population becomes negligible. This is natural; in this case, there are so few rich agents that whether they obtain some of the transfers is inconsequential.
More important than the comparison of the tax rates is the comparative statics ofIt can be seen that those are identical to the results obtained in the model without targeted transfers. In particular, greater inequality again increases taxes.
It is instructive to examine the burden of taxation on the elite in this model, which is now:
Obviously, BurdenT(τ) > Burden(τ), where Burden(τ) was the burden of taxation defined in the previous subsection when there were no targeted transfers. Hence, the introduction of targeted transfers increases the burden of democracy on the rich. Moreover, as before, higher inequality increases this burden at unchanged tax rates.
An important implication of this result is that targeted transfers increase the degree of conflict in society. In particular, because with targeted transfers democracy charges higher taxes and redistributes the proceeds only to the poor, the rich are worse off than in democracy without targeted transfers. Furthermore, for similar reasons, nondemocracy is now worse for the poor. This is because, as discussed in Chapter 2, we can think of nondemocracy as the rule of an elite who we associate with the rich. In particular, and as we now show, in nondemocracy when targeted transfers are available, the rich elite would prefer to set positive taxes and redistribute the proceeds to themselves. In particular, their ideal point would be a vector(withfollowing from (4.12)), wheresatisfies the first-order condition — yrδ + (1 —= 0ifτrT > 0or — yrδ + (1 -< 0 andt’T = 0. Unlike in the model without targeted transfers, the first-order condition for the rich does have an interior solution, withimplicitly defined by the equation:
(4.14)
which has a solution for someHence, introducing targeted transfers makes nondemocracy better for the rich and worse for the poor.
The increased degree of conflict in society with targeted transfers has the effect of making different regimes more unstable - in particular, making democratic consolidation more difficult.
4.4 Alternative Political Identities
In the previous subsection, we allowed transfers to go to some subset of society, the poor or the rich. More generally, we are interested in what a democratic political equilibrium looks like when voting takes place not along the lines of poor versus rich but rather perhaps along the lines of ethnicity or another politically salient characteristic. There are few analytical studies in which researchers have tried to understand when socioeconomic class rather than something else, such as ethnicity, might be important for politics (Roemer 1998; Austen-Smith and Wallerstein 2003). Our aim is not to develop a general model but rather to illustrate how democratic politics might work when other identities are salient and how this influences the comparative statics - for example, with respect to inequality, of the democratic equilibrium. In subsequent chapters, we use this model to discuss how our theory of the creation and consolidation of democracy works when political identities differ.
Consider, then, a model of pure income redistribution with rich and poor people but where people are also part of two other groups perhaps based on religion, culture, or ethnicity, which we call X and Z. Thus, some members of type X are relatively poor and some are relatively rich, and the same is true for type Z. To capture in a simple way the idea that politics is not poor versus rich but rather type X versus type Z, we assume that income is taxed proportionately at rate r as usual but that it can be redistributed either as a transfer to type X, denoted TX, or as a transfer to type Z, denoted TZ. Let there be EX type Xs and and j = X, Z for the subpopulations. Throughout, we assume that δx > ½ so that type Xs are in a majority and letbe the income of type i = p, r in group j = X, Z.
The government budget constraint is:
where average income is defined as:
where the total population size is again 1. To be more specific about incomes, we assume that group X gets a fraction 1 — α of total income and group Z gets a. Thus,Income is distributed within the groups in the following way: 8rxyrx=so thatis the fraction of the income that a
ccrues to the rich in group X. Similarly, we haveWe assume:
It is straightforward to calculate the ideal points of the four types of agents. Both poor and rich type X agents prefer Tz = 0 and both may prefer Tx > 0. However, poor type Xs prefer more redistribution than rich type Xs. To see this, note that the preferred tax rates of poor and rich type Xs (conditional on Tz = 0), denotedandsatisfy the first-order conditions (with complementary slackness):
(4.15)
As usual, a priori we do not know if the solutions are interior or at a corner. The first-order condition for a rich agent can imply a positive tax rate whenIntuitively, in this model, redistribution is not from the rich to the poor but from one type of agent to another. Therefore, even rich people may benefit from this type of redistribution. If both tax ratesand -r” are interior, thenfollows from (4.15) so that the poor members of group X prefer higher tax rates and more redistribution. The ideal points of group Z are also easy to understand. All members of group Z prefer Tx = 0 and both may also prefer Tz > 0, but poor members of Z prefer higher taxes and more redistribution than rich members of the group.
We now formulate a game to determine the tax rate in democracy. If we formulate the model as we have done so far in this chapter, where all issues are voted on simultaneously, then because the model has a three-dimensional policy space, it may not possess a Nash equilibrium. To circumvent this problem in a simple way, we formulate the game by assuming that the tax rate and the transfers are voted on sequentially. The timing of the game is as follows:
1. All citizens vote over the tax rate to be levied on income, r.
2. Given this tax rate, voting takes place over Tx or Tz, the form of the transfers to be used to redistribute income.
We solve this game by backward induction and show that there is always a unique subgame perfect Nash equilibrium. We focus on two types of equilibria. In the first, when> ½, so that poor type Xs form an absolute majority, there is a unique equilibrium of this model that has the property that the equilibrium policy ispreferred by the poor type Xs.
In the second,< ½, so that poor type Xs do not form an absolute majority, there is a unique equilibrium of this model that has the property that the equilibrium policy ispreferred by the rich type Xs.
To see why these are equilibria, we start by considering the first case. Solving by backward induction at the second stage, because δX > ½, it is clear that a proposal to redistribute income only to Xs (i.e., propose Tx > 0 and Tz = 0) will defeat a proposal to redistribute to Zs or to redistribute to both Xs and Zs. That this is the unique equilibrium follows immediately from the fact that Xs are in a majority. Next, given that only TX will be used to redistribute, in the first stage of the game all agents have single-peaked preferences with respect to r. The ideal point of all type Zs, given that subsequently Tz = 0, is T = 0. The ideal points of poorer and richer members of X areandas previously shown. When> ½, poor Xs form an absolute majority and, hence, the median voter is a poor type X. Because only Tx will subsequently be used to redistribute income, the MVT applies and the tax rate determined at the first stage of the game must be the ideal one for poor type Xs,Therefore, in this case, there is a unique subgame perfect Nash equilibrium, which we denote
In the second case, where poor Xs are not an absolute majority, the difference is that the median voter is now a rich type X. Hence, the MVT implies thatwill be the tax rate determined at the first stage. Therefore, in this case, there is a unique subgame perfect Nash equilibriumx))y/8X).
The equilibrium of this game does not depend on the timing of play. To see this, consider the following game in which we reversed the order in which the policies are voted on:
1. All citizens vote on the type of transfers, Tx or Tz, to be used to redistribute income.
2. Given the form of income transfer to be used, all citizens vote on the rate of income tax, τ.
We can again see that there is a unique subgame perfect equilibrium, identical to the one we calculated previously. Begin at the end of the game where, given that either Tx or Tz has been chosen, individuals vote on τ. In the subgame where Tx has been chosen, all agents again have single-peaked preferences over τ. Thus, when> ½, the median voter is a poor member of X and the equilibrium tax rate chosen isWhen< ½, the median voter is a rich member of X and the equilibrium tax rate chosen isIn the subgame where Tz has been chosen, because type Xs do not benefit from any redistribution, the ideal point of all Xs must be to set a tax rate of zero. Because type Xs are a majority, the equilibrium must have τ= 0 because the median voter is a type X. Now, moving back to the first stage of the game, since Xs are in a majority, the outcome is that income will be redistributed only according to Tx. From this, we see that the unique subgame perfect equilibrium is identical to the one we analyzed before.
For our present purposes, the most interesting features of these equilibria are the comparative statics with respect to inequality. In both types of equilibria, an increase in inter-group inequality, in the sense that the income of type Xs falls relative to the income of type Zs, holding inequality within group Z constant, leads to higher tax rates and greater redistribution. If there is an increase in Zs income share, holdingy constant, then bothyX andyX will fall and both poor and rich type Xs favor higher taxes. To see this, we use the definitions of income and substitute them into (4.15):
where we assumed for notational simplicity that both first-order conditions have interior solutions. An increase in the share of income accruing to the Zs increases α, which increases bothandthat is:
that is, an increase in α increases the tax rate. Similarly,.
However, such a change in income distribution does not map easily into the standard measures such as the Gini coefficient. Moreover, if there is a change in inequality that redistributes within groups (e.g.,increases [so thatfalls and yX rises]), then the comparative statics are different in the two equilibria. In the first, taxes will increase, whereas in the second, they will decrease.
It is worth pausing at this point to discuss the empirical evidence on the relationship between inequality and redistribution. Our model predicts that greater inequality between groups will lead to greater inter-group redistribution in democracy. However, because political identities do not always form along the lines of class, it does not imply that an increase in inequality- as conventionally measured by the Gini coefficient or the share of labor in national income - will lead to more measured redistribution. The empirical literature reflects this; for example, Perotti (1996) noted following the papers of Alesina and Rodrik (1994) and Persson and Tabellini (1994) that tax revenues and transfers as a fraction of GDP are not higher in more unequal societies.
Nevertheless, so far, this relationship has not been investigated with a careful research design. One obvious pitfall is that of reverse causality. Although Sweden is an equal country today, what we are observing is the result of seventy years of aggressive income redistribution and egalitarian policies (e.g., in the labor market). Indeed, existing historical evidence suggests that inequality has fallen dramatically during the last hundred years in Sweden.
There are also many potential omitted variables that could bias the relationship between inequality and redistribution, even in the absence of reverse causality. Stated simply, many of the institutional and potentially cultural determinants of redistribution are likely to be correlated with inequality. For example, Sweden is a more homogeneous society than either Brazil or the United States, and many have argued that the homogeneity of the population is a key factor determining the level of redistribution (Alesina, Glaeser, and Sacerdote 2001; Alesina and Glaeser 2004). Moreover, there may well be much more of a “taste for redistribution” in Sweden given that for most of the last seventy years, the country has been governed by socialists with a highly egalitarian social philosophy.
5. Democracy and Political Equality
Although the MVT is at the heart of this book and much positive political economy, there are, of course, many other th
eoretical approaches to modeling democratic politics. A useful way of thinking about these theories is that they imply different distributions of power in the society. The median-voter model is the simplest and perhaps the most naive setup in which each person has one vote. In the two-group model, numbers win and the citizens get what they want.
Nevertheless, as previously mentioned, in reality some people’s preferences are “worth” more than others. There are many ways in which this can happen. First, preferences may be defined not just over income but people may also care about ideological positions associated with different political parties. Voters who are less ideological are more willing to vote according to the policies offered by different parties. Such voters, often called swing voters, therefore tend to be more responsive to policies and, as a result, the parties tailor their policies to them. To take an extreme situation, imagine that poor people are very ideological and prefer to vote for socialist parties, whatever policy the party offers. In this case, policy does not reflect the preferences of the poor because right-wing parties can never persuade the poor to vote for them; socialist parties already have their vote and, therefore, can design their policies to attract the votes of other groups, perhaps the rich. These ideas stem from the work on the probabilistic voting model by Lindbeck and Weibull (1987), Coughlin (1992), and Dixit and Londregan ( 1996, 1998). In this model, the preferences of all agents influence the equilibrium policy in democracy; the more a group tends to consist of swing voters, the more their preferences will count. Thus, for instance, if the rich are less ideological than the poor, it gives them considerable power in democracy even though they are in a numerical minority.
Economic Origins of Dictatorship and Democracy Page 17