Optimal tax theory: the journey from the negative income tax to the earned income tax credit.

• Author: Hamilton, Jonathan H.
• Position: 2009 Presidential Address

1. Introduction

   As a Yale undergraduate in the 1970s, it was nearly impossible not to be aware of the contrasting views of Milton Friedman and James Tobin on macroeconomic policy. At the same time, Professors Friedman and Tobin were among the most prominent economists supporting proposals for a "Negative Income Tax" (NIT). Many graduate students I knew placed great importance on the fact that Friedman and Tobin were in agreement on this issue. "If they agree on this, it must be the right policy" is a fair summary of their views. Because the Yale graduate students did not accept Friedman's views on monetary policy, it was certainly fascinating to see them hold Friedman's support for any policy in such high esteem. Then again, Milton Friedman was such a passionate advocate for many policies--the students may just have been overcome with joy to have Milton on their side for once. More likely, the graduate students still shared the public's common misconception that economists agree on very little. As most of us know, we agree on quite a bit--it is with noneconomists that we agree on fewer issues in the realm of economic policy.

   Not only was Milton Friedman a passionate advocate, in many cases, he was a successful one. Rent control policies now meet considerable skepticism. School vouchers find support from many different groups. In contrast, the NIT is not an ideal toward which many continue to strive. I wish to explore what we've learned in economic theory that might explain why society has not come to share Friedman and Tobin's views on this issue.

   First, we need to recall the alternatives at the time. The Aid to Families with Dependent Children (AFDC) program in the 1950s made no provisions for two-parent households. When a recipient entered the labor force, she faced a 100% marginal tax rate on earnings because benefits were reduced dollar-for-dollar with wages. (1)

   Tobin (1965) argued that welfare gave recipients incentive to withdraw from the labor force and gave fathers incentives to desert their families. Tobin, Pechman, and Mieszkowski (1967, p. 1) also found the "numerous indignities by the procedures employed to enforce the means test..." an objectionable feature of the existing system. They also sought a system of uniform benefits across the nation (states chose benefit levels at the time).

   Friedman's support for the NIT had other motivations. First, he pushed for a program to replace all existing programs (including Social Security and many other forms of income maintenance). Consistent with his passion for liberty, he sought a system that "treats [the] indigent as responsible individuals, not incompetent wards of the state" (Friedman 1968, p. 211). Furthermore, he argued that "if social workers are hired on government funds they should devote their energies to helping the indigent, not spying on them" (p. 205). (2)

   During the Nixon Administration, the Family Assistance Plan was actively considered in welfare reform discussions. At the same time, the NIT experiments were conducted to determine the incentive effects and costs of these proposals.

   In 1975, the Earned Income Tax Credit was introduced. Initially, the benefit was quite small, and only a small number of individuals received it. By 2000, after several expansions of the program, it supported 55 million people (Moffitt 2003).

   In 1996, President Clinton and a Republican Congress agreed on a major welfare reform bill, which included work requirements (although some waivers and exceptions do exist). With lifetime limits on benefits, this really did "end welfare as we knew it."

   What I will discuss here is what we have learned in economic theory about income redistribution since Friedman and Tobin, some policy innovations in the U.S. and elsewhere, and I hope to shed light on how and why the public and policy makers have come to regard the NIT as not ideal.

2. The Optimal Income Tax

   The 1996 Nobel Memorial Prize in Economics was unique in one way the two men who shared the prize were not coauthors or scholars pursuing different lines of inquiry. William Vickery in 1945 posed a problem, and James Mirrlees solved it in 1971 (Vickery 1945; Mirrlees 1971). The essential insight is that the optimal income distribution question is one of asymmetric information. Ideally, one's tax payment depends on one's earning ability. However, the tax authority only observes earned income, and earnings depend on choices that the tax schedule affects. Mirrlees's breakthrough is often called the Revelation Principle. The tax authority does not know each person's ability, but it develops a tax schedule for which each person would truthfully reveal his or her type.

   With a continuous ability distribution (as Vickery and Mirrlees considered), the mathematics constrain us to consider individuals who differ only in ability but share a common utility function. Stiglitz (1982) introduced the discrete ability distribution version, and Brito et al. (1990) relaxed many of the restrictive assumptions.

   Let us start with a simple model. Two types of individuals differ in earning ability (wages), with [w.sub.1]

   [V.sup.i](C, Y) [equivalent to] U(C, Y/[w.sub.i]).

   Because wages differ, the utility functions differ. Stiglitz (1982) discusses the usefulness of considering the information-constrained Pareto frontier, so let us write our problem as follows:

   [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

   The first constraint is the Pareto constraint, and the second is the revenue constraint. These last two constraints are the self-selection (or incentive compatibility) constraints--each individual prefers the bundle intended for her to the bundle intended for the other type.

   When the tax authority redistributes toward the low-ability type, the solution has the following properties (see Figure 1):

1. Type 1's marginal rate of substitution (MRS) between C and Y is less than 1.

2. Type 2's MRS is equal to 1.

   Type 2 thus has a marginal tax rate equal to zero, while type 1 has a bundle that is distorted by the tax schedule. (3) All the tax paid by type 2 is effectively a lump-sum tax. In contrast, type 1's labor supply is less than what he would choose if given the transfer in lump-sum form. The distortion is to prevent type 2 from mimicking type 1. Notice that the role of the tax wedge differs from a linear income tax--the distortion serves to collect money from someone else, not to raise money directly.

   [FIGURE 1 OMITTED]

   One problem jumps out--our tax system looks nothing like this. Sadka (1976) shows that the highest ability type faces a zero marginal tax rate in the continuous case. However, Diamond (1998) shows that optimal tax rates may be quite high near the top of the income distribution. There are also results on when the marginal tax rate at the bottom of the earning schedule equals zero, but the conditions are unlikely to hold in practice (Brito and Oakland 1977; Seade 1977).

   However, many individual redistributive programs fit the model better. Many programs have income cutoffs for eligibility that may reduce the labor supply of the recipients, while nonrecipients simply support the programs through the normal tax system. Let's explore further by expanding our model.

   With discrete types, we can solve the model in more general settings than with a continuous ability distribution. One result continues to hold--the taxpayer who pays the largest tax faces a zero marginal tax rate because no one will envy his bundle in a constrained efficient allocation. (4) Now relax the assumption that all taxpayers have the same utility function over consumption and labor effort (a two-characteristic model presents many mathematical complexities with continuous distributions, but it is straightforward with discrete distributions).

   Assume that there are three consumer types:

   Type a has a low wage and a high disutility of labor; Type b has a high wage and a high disutility of labor; and Type c has a high wage and a low disutility of labor. [FIGURE 2 OMITTED]

   To keep things simple, assume that utility is additive in consumption and labor supply: [U.sup.i](C, L) = v(C) - [g.sub.i]t(L). The function t(L) is the same for all consumers, but [g.sub.i] is a constant that differs across types (so that we have a multiplicative shift on the disutility of hours). We can keep things simple by further assuming that [w.sub.1] [g.sub.2], where [g.sub.1] multiplies a's and b's disutilities of labor and [g.sub.2] multiplies c's disutility of labor.

   Thus, the utility functions of the three types in terms of C and Y are as follows:

   [V.sup.a](C, Y) = v(C) - [g.sub.1]t(Y/[w.sub.1]),

   [V.sup.b](C, Y) = v(C) - [g.sub.1]t(Y/[w.sub.2]),

   [V.sup.c](C, Y) = v(C) - [g.sub.2]t(Y/[w.sub.2]),

   In some applications, we need to worry whether differences in the disutility of labor arise from disability or taste for leisure. (5) Here, I want to focus on taste for leisure as what certainly distinguishes group b from group c. Figure 2 displays one possibility for the optimal allocation chosen by the tax authority. Note that groups a and b differ only on one dimension, and groups b and c differ only on one dimension. An allocation where c envies b and b envies a is the normal case--the only way to have c envy a at the optimum is for a and b to get the same bundle. What we can't tell without more structure is whether type b is taxed or subsidized.

   The work disincentive for type a does not discourage type b particularly strongly because of the difference in earning abilities. What would discourage type b individuals from mimicking type a is having to work as much as type a workers, in contrast to having to earn the same amount of money income.

   I want to use this model to illustrate a key point. With self-selection constraints, anything that weakens the constraints can lead to a more efficient outcome. The solution in Figure 2 simply uses the conventional approach. What else might be considered? Certainly, it is at least...