Psychic Income, Taxes and the Allocation of Talent



Abstract

The efficiency consequences of taxation through its effect on occupational choice can be the opposite of the traditional labor supply effects that economists have focused on. Murphy et al. (1991) argue that some occupations may have positive, others negative, externalities. If occupations with positive externalities tend to be more enjoyable, then progressive taxation can have the efficiency benefit of encouraging talented, well-educated workers to go into more enjoyable, socially productive professions. I explore this mechanism and how social signalling, conformity, natural variation in the externalities of various professions and costly (rival) prestige can all play roles in generating it. I am working on gathering empirical data to test the effects of taxation on occupation choice. The argument suggests a number of directions for further research.

This paper is the theory section of an ongoing project with an empirical component, and even this part is extremely preliminary and incomplete.

The acquisition of wealth is no longer the driving force in our lives. We work to better ourselves, and the rest of humanity.

– Captain Jean Luc Picard describing the economy of the future in Star Trek: First Contact[1]

1 Introduction

Two dimensions of labor supply elasticity are commonly cited (Heckman, 1993): intensive and extensive. Workers may substitute along the intensive margin, deciding how long and hard to work, or along an extensive margin, choosing whether to work at all. This distinction can have important implications for optimal tax design, as demonstrated by Saez (2002). Recent empirical work, surveyed by Eissa and Liebman (1996) and Meyer and Rosenbaum (2001), suggests that traditional substitution along the intensive margin may be quite small. On the other hand, substitution along the extensive margin has been shown, for example by Pencavel (1986) and Blundell and MaCurdy (1999), to be quite important, at least among some groups. This work suggests that there may be margins other than the traditional intensive margin where substitution has important effects on the optimal design of tax policy. In this paper I consider the policy implications of such a third dimension, studied by economists in other contexts beginning with Roy (1951) but not commonly applied to tax design: occupational choice. I argue that responses of occupational choice to taxes may have very different, even opposite, implications for tax design from both the intensive and extensive margin. I am currently working to gather empirical evidence to test whether this margin may be quantitatively important.

My argument builds on the insight of Baumol (1990) and Murphy et al. (1991), as well as Landes (1969) before them, that not all occupations offering the same compensation have equal social value. Some occupations, such as law and finance, may involve substantial rent-seeking components while others, such as entrepreneurship and scientific research, may generate large positive externalities. The allocation of the scarce stock of high-ability, highly educated workers among these occupations may have important implications for economic efficiency and growth. Understanding the effect of policies on this allocation may therefore be important for policy design.

Of course, social value is not the only thing that varies across occupations. Some occupations are more enjoyable than others, but pay lower wages. When choosing among occupations, individuals often face a trade-off between psychic and material income. Casual observation suggests that, among potential occupations for graduates from top universities, psychic income is correlated with social value.Finance and law are viewed by many as stressful and lacking in tangible meaning. Science, academia, engineering and entrepreneurship are viewed more as more enjoyable, though less financially rewarding[2] , career paths. Such a correlation between social value and psychic income implies that the efficiency effects of taxation may be the reverse of what economists traditionally consider. High marginal rates to the rich may increase efficiency as they encourage talent to work in industries with higher positive externalities. Low tax rates for the poor and middle class may also augment economic output, as they help reduce income effects that would lead workers into lucrative, but unenjoyable and socially less productive occupations. This simple story may help explain the counterintuitive empirical finding, studied by Cullen and Gordon (2002), that higher and more progressive tax rates see to lead to increase entrepreneurship[3]. Thus entirely apart from its redistributive benefits, progressive taxation may be good for efficiency and aggregate output.

The natural economist’s response to externalities in different professions is to subsidize income in some professions and tax others. While this clean solution is appealing, in this paper I analyze the effect of more traditional income taxation, assuming that such differential subsidies and taxes have not internalized the externalities. I take this approach for four reasons. First and most importantly, differential taxation of various occupations are simply not on the political agenda or likely to be in the near future. What economics says about whether income taxes should be more or less progressive is likely much more relevant for policy than an implausible recommendation for taxing some occupations and subsidizing others. Second and related, it is unlikely that any proposal for such targeted taxes and subsidies could ever make in through the political process, given the tremendous opposition it would arouse from workers in the targeted sector (for the case of taxes) and from the public (in the case of subsidies).Third, it may be that the correlation between psychic income and positive externalities is more robust than is the balance of externalities in any particular occupation. Given the slow pace of the political process and the dangers of throwing a flawed political process open to a new form of targeted taxation/subsidy, it may be best to stay away from such focused policies. Finally, the implications of externalities for tax design in the simple models I am consider are fairly obvious and well-understood; the effects of income tax are therefore more interesting to explore from a theoretical perspective.

Following this introduction, this paper is divided into five sections. Section 2 develops the basic version of the model, where there is an exogenous connection between psychic income and positive externalities. This is essentially a one-dimensional variant on the Roy model with general distributions, where individuals differ only in the extent to which they care about non-pecuniary benefits. I show that the income effects of taxation will tend to lead workers into the less socially productive sectors, while their substitution effects will lead them into the more productive sector. I then establish a few testable predictions about the effects of changes in taxes on wages and the allocation of work. On the normative side, I show that when only substitution effects exist, it is always beneficial to charge a positive tax, even in the absence of any redistributive motive or public goods. When taxes are lump-sum so that only income effects matter, I show that it is optimal not to tax away all the income of talented workers even if social welfare puts no weight on their utility because their resulting greed will lead them to inefficiently work in the more lucrative sector.

Section 3 explores two mechanisms that could generate the results of the basic model. In the first, largely inspired by B´enabou and Tirole (2006), individuals have pro-social motivation to work in a sector that generates positive externalities, but also a desire to signal to others that they are among the most pro-social. Even if actual pro-social motivation is small, large motives for social signalling lead to the same positive results as the model where psychic income is exogenous. If individuals vary primarily in how much they desire to socially signal, and this “conformism” is correlated with pro-sociality, the nworking in a sector with positive externalities can be a natural signal of desire for social signalling (ie concern for social relationships and perceptions, as in Bernheim (1994)). Regardless of the exact form,pro-sociality and desires for social signalling can reinforce one another in generating a correlation between virtuous and enjoyable occupations. However, negative signalling externalities from going into the pro-social sector somewhat weaken my earlier normative conclusions. In a second model, neither sector is inherently more enjoyable or more socially valuable. Some workers enjoy working one sectormore, others enjoy working in the other sector more. However, one sector captures a greater fraction of its social value than the other does, though its total social product (as a function of the number of workers it employs) is the same. This model generates exactly the same positive and normative results as simple model with an exogenous correlation between psychic income and positive externalities.

One objection to my basic model, which explore in section 4, is that it relies on the assumption that psychic income, unlike consumption goods, have no opportunity cost. Given that an important sources of psychic income in many of the relevant industries is prestige, which is often rival or requires the costly respect of peers and the public, this assumption may not be justified. Thus while prestigious industries generate positive externalities, at the margin it may be no externality exists because the cost of the prestige compensating the socially beneficial activity offsets its external benefits. I show that the validity of this critique depends on how the prestige of an industry responds to changes in the number of people working in that industry. If the prestige per-worker is constant, then it is true that only a marginal externality can justify a tax (though such an externality arises even if prestige is above its socially optimal level). If total prestige is constant in an industry, however, there are never any externalities on the margin, as a worker entering an industry is offset by another worker exiting that industry, impelled by the lost prestige. Nonetheless, tax increases are beneficial so long as there is not a grossly socially excessive amount of prestige allocated to the virtuous sector. Finally, in the case when prestige is determined socially optimally, jointly with taxes, raising taxes above their other wiseoptimal level is always beneficial, as it adds to the social planner’s leverage in allocating prestige. Thus costly prestige does not qualitatively change my argument, and in fact may provide further reasons for taxation.

Section 5 briefly outlines my plans for empirical worker to test the effects of taxation on occupational choice, using a data from a major US university and more macro-level data on the workforce and wages in sectors that draw highly educated individuals. Section 6 concludes by discussing directions for future research.

2 Basic Model

Consider the following variant on Roy (1951). There is a mass 1 of consumers who supply labor inelastically, but may work in either sector. Inelastic labor supply is intended to focus attention on the occupational choice mechanism rather than to suggest that the effects of taxation on labor supply are insignificant. Consumers’ utility functions are given by U (c) + βp, where c is the consumers’ consumption and p is an indicator for whether the consumer works in sector 2; thus sector 2 has positive psychic income associated with it. This can be viewed as workers having a heterogenous skill for producing psychic benefit for themselves in the different sectors; to keep things simple, I abstract away from different productive skills, assuming workers are identical along that dimension and in terms of their utility function for money income. U is assumed to be strictly increasing, twice continuously differentiable, weakly concave and unbounded (i.e. limc→∞ U (c) = ∞. β, which represents the weight the consumer places on psychic income, is distributed according to a cumulative distribution function G which is differentiable at all points but possibly the lower bound of its support, with corresponding density function g at all non-mass points. G has support

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where the first inequality follows by the positivity of the income effect, the second from the negativity of the substitution effect and the third from concavity of U and the fact that w1 > w2. Now note that

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Intuitively, absolute after-tax wage divergence would require a very large reallocation of workers to the more enjoyable sector in response to a rise in taxes. But to provide such a large incentive, after-tax wages would have to (absolutely) converge. Thus consumer optimization is inconsistent with absolute after-tax wage divergence as a result of a tax increase.

2.2 Linear utility, linear taxes (substitution effect)

Now I focus on the positive and normative consequences of the substitution effect. To do so, I now assume linear utility (i.e. U (c) = c). This is not, of course, meant to imply that I want to think about consumers as having no decreasing marginal utility or wealth. Rather it is a proxy for adjustments of marginal tax rates at high incomes, where the income effect is assumed to be small. Below linear utility also helps me abstract from distributional considerations in social welfare. In this case expression 2 reduces to

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Because taxes, as usual, dampen material greed when substitution effects dominate, they lead here to more workers going into the enjoyable sector, driving down pre-tax wages in that sector and driving up pre-tax wages in the other sector. The main argument I want to make is normative, rather than positive, however. To evaluate social welfare, now assume that all profits and taxes are divided evenly(lump sum) among all consumers. Note that this does not change any of the positive conclusions, because with linear utility there are no income effects. Furthermore, so that welfare will be finite assume that G is integrable in the sense that EG[β] is finite.

The main substantive assumption which drives my analysis is that there are positive externalities associated with work in sector 2. This represents a world where the most enjoyable professions (at least among those selected by well-educated, talented workers) are also those with the highest degree of positive (lowest degree of negative) externalities. Formally my assumption of positive externalities in sector 2 is that for every unit of (private) output produced in sector 2 there are A units of pure spillovers produced, which are distributed (like taxes and profits) evenly among all consumers. Social welfare is then given by total (social) output, plus total psychic income (again, assuming that β¯ is not at thebottom of the support of G).

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Proposition 4. For A > 0, the socially optimal tax τ * > 0. Furthermore τ * is strictly increasing in A. Proof. The proof of the first claim is given in the text. The proof of the second claim is identical, except that we must compare the value of expression 12 for A0 > A to its value of A.

It is socially optimal to subsidize (tax) activities that have positive (negative) externalities. Here I do not consider direct taxes or subsidies to work in the different sectors for the reasons discussed in the introduction, but effectively linear taxes on income in both sectors has the same effect: it encourages individuals to focus more on psychic income, leading them into the more enjoyable and socially beneficial sector and thereby correcting the market failure.

2.3 General utility, lump sum taxes (income effect)

I now return to general concave utility functions to consider the positive and normative implications of income effects. To focus exclusively on income effects (and thereby illuminate the other side side of changes in tax progressivity) I consider lump-sum taxes. In particular, imagine that now instead of profits and spillovers being returned to consumers they are taken by the government. The government also has access to a lump sum tax on workers at rate t and seeks to maximize the total wealth appropriated by the state. This proxies for maximizing the welfare of other consumers (other than the talented workers I have been treating) who are assumed to get the bulk of non-wage income generated by work of the talented workers. When focusing on income effects, normative standards are much stickier; the analysis here is meant to focus on the notion of a social planner who aims to maximize production in the economy or economic growth, rather than efficiency in the stronger sense considered above.

If t is weakly lower than the wage earned by the worker, the worker must pay the tax; if t is greater than the wage earned by the worker, the worker pays her entire wage. Assuming that t < w2, equilibrium is now defined by a variant of equation 1

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3 Alternative mechanisms

I assumed above that the positive correlation between positive externalities and psychic income in occupations was exogenous. Here I consider two simple settings that generate such a correlation. The first draws heavily on B´enabou and Tirole (2006). Individuals have a small pro-social motivation to work in a sector that generates positive externalities, but they also have a large desire to signal to others that they are among the most pro-social. Because this social signalling generates negative externalities from going into the virtuous sector, it softens my earlier normative results. In the second, neither sector is inherently more enjoyable or more socially valuable. Some workers enjoy working one sector more, others enjoy working in the other sector more. However, one sector captures a greater fraction of its social value than the other does, though its total social product (as a function of the number of workers it employs) is the same. Both models generate essentially the same predictions as the basic model. The main purpose of these is to provide some foundation for my earlier assumption as well as to generate some additional (soft) comparative statics to help judge the plausibility of these justifications.

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this case the second sector is really a coordination device for signalling; in fact if δ is constant then work in the second sector is an arbitrary coordination device and work in the first sector could act to signal nearly as well. Here the main thing being signalled is desire to signal (i.e. concern for social perceptions), as in classic conformity models like Bernheim (1994). The coordination here on the second sector as signalling desire to conform is natural if the second sector is even vaguely viewed by the public as being more virtuous (see Appendix B for formally arguments for this refinement).

3. Finally the most straightforward case is one in which people who are more pro-social (in the sense of being altruistic) are also more sociable (in the sense of caring about public perceptions). In this case social (or self-) signalling simply reinforces the basic psychic income model.

In what follows, I focus on the equilibrium where working in sector 2 signals high α; when the variation in γ dominates the variation of γ other equilibria are possible. I ignore these because I view the sector2 signals high α as being more plausible. The basic reason is that, in the absence of signalling motivations, high α types would naturally sort into the pro-social sector; given that this continues to be the case if working in sector 2 is viewed as signalling high α, this equilibrium seems much more intuitive than one in which working in the anti-social sector signals pro-sociality. In Appendix B I provide two formal refinement arguments[9] for this selection, one elaborating this intuitive signalling argument (which is based on a stronger refinement than any standard in the signalling literature and which I call strong signal preservation) and one based on the evolutionary arguments of Kandori et al. (1993), Young (1993) and Ellison (2000). In this intuitive equilibrium, as in the simple model, there is a α¯ such that all consumers with α > α¯ work in sector 2. α¯ is now implicitly defined by

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consumers are interested in signalling some more general function of α essentially the same results would obtain, except that more care would need to be taken to ensure ξ satisfies the proper conditions.Intuitively, social signalling simply creates a different psychic benefit of working in sector 2, but changes nothing of substances about the positive conclusions of the simple model. The only additional insight the model gives is that one might expect the effects I am interested in to be operative in industries that are thought to be good signals of pro- (or anti-)social or other virtue (or vice) and where it is generally thought that working that sector represents a positive or negative social signal. However things are a bit more complicated on the normative side. While in the income effects only model nothing changes as social welfare does not include the utility of the talented, in the substitution effects model things can be quite different, as social signalling potentially introduces new externalities.

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Note that there is now an additional externality, going in the opposite direction. A marginal worker moving from sector 1 to 2 harms both workers in sector 1 and sector 2, while helping the moving worker.Intuitively, workers in sector 1 lose the most pro-social worker who was giving them positive external benefits and workers in sector 2 gain the least pro-social worker, bringing negative externalities to them. Thus if the size of γ outweighs the positive production externalities of moving into sector 2, a tax on material income could be harmful rather than beneficial. On the other hand if the production externality is large, then a tax can still be beneficial. Thus a substantial social signalling motive being part of generating the correlation between positive production externalities and psychic income does,at least so far as it is taken into account in welfare calculations, weaken the case for taxation. This implies that if one considers social signalling motivations to be important in generating the correlation above, one should be cautious about the normative implications. The following proposition formally expresses this result.

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Proof. See Appendix C.

In the case when γ is not constant, the exact same result[10] obtains except that γ must be replaced with γ¯ ≡ E γ(α) .

3.2 Heterogenous psychic income

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This model really just provides another way of interpreting the assumptions underlying my basic model above. However, it does suggest one potential way of empirically identifying industries where my argument may be relevant. If college majors better reect individuals’ preferences about the psychic benefits they gain from various occupations, then one would based on this model expect that after a fall in taxes workers who majored in, say, civil engineering would go more heavily into, say, law or _nance. By observing the \draw” of professions out of not directly related majors, one may be able to identify, under this model, which industries are attracting socially too many workers. Similarly, we might consider the draw of professions across traditional geographic boundaries to be associated with negative social externalities.

4 Costly prestige

One objection to my basic model and its justifying variants is that they rely on the assumption that psychic income, unlike consumption goods, have no opportunity cost. Given that an important sources of psychic income in many of the relevant industries is prestige13, this assumption may not be justified. In particular, prestige is often rival or requires the (costly) attention or respect of peers or the public. This may mean that while prestigious industries generate positive externalities, at the margin no externality exists because the cost of the prestige compensating the socially beneficial activity offsets its external benefits. In this section I examine this reasoning. The extent to which it is valid depends on how the prestige of an industry responds to changes in the number of people working in that industry. If the prestige per-worker is constant, then it is true that only a marginal externality can justify a tax (though such an externality arises even if prestige is above its socially optimal level). If total prestige is constant in an industry, however, there are never any externalities on the margin, as a worker entering an industry is o_set by another worker exiting that industry, impelled by the lost prestige. Nonetheless, taxes increases will generally be beneficial, even in cases when the prestige allocated to sector 2 is socially super-optimal. Finally, in the case when prestige is determined socially optimally, jointly with taxes, raising taxes above their otherwise optimal level is always beneficial, as it adds to the social planner’s leverage in allocating prestige. The most realistic case likely lies somewhere along this spectrum. My basic argument is that, unless one believes the extreme case where prestige in an industry is completely non-rival14, the lack of positive externalities on the margin does not undermine the argument that correlation between psychic income and external monetary benefits of occupations give weigh in favor of raising taxes.

To keep things simple and focus on the main argument, I jump directly to focus on substitution effects only. I also assume that all consumers are identical in their desire for prestige, primarily to abstract away from screening problems and other complicating features that arises in determining social welfare when consumers have heterogeneous preferences for prestige. Formally, I assume that consumers’ utility is given by c + _, where _ is the level of prestige attached to their profession. I now consider the three cases discussed above.

4.1 Constant per-person prestige

I assume that the prestige attached to professions is determined exogenously, though I focus on comparing various (endogenous) benchmarks for prestige. Despite the level of prestige attached to professions being exogenous, prestige is costly to produce, either because it is rival or because it requires valuable public attention. In particular, to continue to keep things simple, one unit of prestige for one consumer requires a lump sum tax uniformly on all consumers of size C > 1; thus prestige is an inefficient form of consumption qua consumption and can only be beneficial to provide incentives for going into one industry or another.

In what follows I only consider cases in which positive prestige is assigned to industry 2 and no prestige is assigned to industry 1. These cases are intuitive and other arrangements are inefficient in an uninteresting way: namely they involve the wasting of resources on inefficient prestige consumption that has no or negative incentive effects. From here on, I let l1 be the fraction of workers.

At equilibrium, all of the (identical) workers must be inefficient between working in the two sectors.

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Intuitively when the total industry prestige is fixed, one individual taking prestige denies it to another individual. Thus one worker moving into sector 2 has no external costs or benefits, as he simply switches places with another worker currently in sector 2. Nonetheless a rise taxation is beneficial because it appreciates the value of the prestige assigned to sector 2, encouraging more workers to go into that sector and thereby improving productive efficiency. Intuitively this may be true even if more prestige than is socially optimal has been allocated to sector 2, because the socially optimal level of prestige must balance the costs of producing prestige with the benefits of moving workers into sector 2. Taxation helps overcome this trade-o_ by impelling more workers into sector 2 for any given level of prestige.

4.3 Socially optimal prestige

Now I suppose that prestige and taxes are jointly determined socially optimally. That is, when the social planner running the government decides whether to raise taxes above their current level, she takes into account that prestige will be adjusted according in a socially optimal fashion. The following result shows that taking this model, without any modification to take into account other factors effecting the socially optimal tax rate, to its logical extreme yields a strange result, somewhat related to Proposition 10.

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5 Plans for empirical work

I am looking for two data sets. The _rst would be from a university on and would track the occupations

chosen by students. The second would be more macroeconomic and would track aggregates on occupational choices and wages at a national level. I plan to use these data sets to test the positive predictions of the theory. In this section, I brief discuss what I hope these data sets will contain and how I hope to use them to test my theory.

I hope to obtain a data set from a major US university (I am starting to talk to Princeton) tracking occupational choices and hopefully start salaries of jobs for students with different majors. Ideally the data set would also allow me to track occupational after the initial choice, in case individuals first job is not representative of their long-term career path. I would then look at changes in occupational choices around major changes in tax rates, such as the early eighties, the mid-eighties, the early nineties and the early 2000’s. I would look to test the predictions of my theory about occupational choice and changes in relative pre- and post-tax wages of various sectors. This data set would focus on the demographic I am targeting (talented individuals) as well as allowing me to test changes in the draw” of certain professions from unrelated majors (or from other areas of the country), as discussed in subsection 3.2, to help identify which occupations I should be focusing on. Along these lines it might even be interesting to measure the response of physical mobility for work to changes in taxes. I suspect that my main focus would be to label as \sector 1-like” industries _nance, law and accounting and label as \sector 2-like” academia, medicine, engineering and scientific research. Depending on the richness of the data set, I might be able to test the effects in changes in taxes in individuals’ home countries for foreign students, if there is a substantial contingent from a particular foreign country. Ideally I would get data from more than one university, perhaps in more than one country. The latter enrichment would allow a broader set of experiments to test the reaction of occupational choice to changes in taxes. It might also be interesting to not just track undergraduates, but also, for example, law students and whether they go into corporate or public-interest law.

I also hope to obtain a more macro-level data set on the evolution of occupational choice among highly educated individuals over time. This would hopefully give me a clearer picture of changes in wages. I would again try to identify around major tax changes, ideally with data from many countries.

It might also be interesting, though likely beyond the scope of my current project, to get some sense of the prestige associated with various occupations, say in terms of their press mentions.

6 Conclusion and extensions

Economists have extensively studied labor supply responses to taxation and regulation. If occupational choice responses, particularly among highly educated workers, to these policies are large, I argue that this may have important implications for tax policy that go in a direction opposite to conventional economic wisdom. Given that this paper can supply at best suggestive evidence about this elasticity and that my arguments depend on unmeasured covariance’s between social value of occupations and the psychic income associated with it, this paper offers many avenues for future research. I conclude by brief discussing a few of these.

First, clearly my empirical estimates of the responses of occupational choice to changes in taxation are both entirely reduced-form and poorly identified. In order to get a clear sense of the importance of occupational substitution, as well as to estimate policy relevant elasticities, more careful structural modeling as well as more sophisticated identification strategies will be necessary.

A more complex, long-term direction for future research is trying to understand and measure the externalities generated by particular occupations. For example, one might try to study the social value of lawyers17. Should one expect that lawyers who help _rms comply with laws are compensated more or less than the social value of that compliance? How much social value, in terms of the quality of legal outcomes, does a good defense lawyer bring relative to the value of that lawyer to her client? Answer such questions will require a sophisticated combination of theoretical modeling and empirical measurement. In terms of publicans theory, my argument here takes occupational substitution in isolation and does not give a clear picture about how concerns about occupational substitution should interact with broader goals in optimal tax design. A more careful, broad theoretical analysis of the implications of career substitution, especially with more than two occupations and varying levels of education/ability might yield a much more thorough understanding of how the issues raised here should a_ect tax design.

Such an analysis would of course incorporate distributional concerns that I abstracted from here both by assuming linear utility in most of my analysis, but more importantly by considering an economy with only the talented, highly educated workers I focused on, rather than also including other, presumably less well-o_ workers. In a more sophisticated model, the mechanism described above might have important distributional consequences. If the externalities produced by highly educated (and likely well-o_, even if working in virtuous occupations) workers largely bene_t (or harm) the poor and middle class, then this may provide a further reason why progressive taxation may lead to lower inequality. Furthermore if the poor and middle class also face trade-o_s (though this seems less likely than for high ability workers) between enjoyable carers with positive externalities and less enjoyable, and many of these externalities a_ect the rich, than a similar mechanism at the bottom of the income distribution could reinforce these conclusions.

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probabilities of each player playing any particular action and therefore there are no o_-equilibrium-path beliefs.

To argue against these counterintuitive equilibria, I use two strategies. The first argument corresponds closely to the intuition that makes the equilibrium developed in subsection 3.1 intuitive and the intuition behind standard signalling re_nements: if, in the absence of signaling motives, high _ is monotonically related to desire to be in sector 2 and there exists an equilibrium where being in sector 2 signals high _, this equilibrium seems more intuitive than one in which being in sector 2 signals low _. As shown below, the intuitive equilibrium is the unique equilibrium in the _rst class. While this argument cannot be justi_ed by any signalling re_nement I am aware of, it seems to be based on a similar logic and perhaps can be generalized to form a strong re_nement in monotonic signalling games.

The second argument relies on the evolutionary arguments of Kandori et al. (1993), Young (1993) and Ellison (2000). Suppose there is a populations of players playing a game with two equilibria that are asymptotically stable under some dynamics that gradually lead the population of players to optimize. Now suppose that, starting at equilibrium 1, a shock that changes the behavior of a small number of players can place the population (under the dynamics) into the basin of attraction of the other equilibrium, so that they dynamics after the shock converge to equilibrium 2. Furthermore suppose that, starting at equilibrium 2, the smallest shock that in the corresponding way moves the population to equilibrium 1 is larger than the small shock causing a move from equilibrium 1 to equilibrium 2. Then equilibrium 2 seems a more stable (plausible) equilibrium. My second argument is essentially that, starting an an unintuitive equilibrium, all that needs to happen to lead the population to evolve towards the intuitive equilibrium is that enough high type players move to sector 2 so that the average rank of consumers working in sector 2 is higher than the average rank of consumers working sector 1. On the other hand to move from the intuitive equilibrium to an unintuitive equilibrium enough high _ workers have to move from sector 2 to sector 1 so that the di_erence in the sector 1-average rank is su_ciently greater than the sector 2-average rank to outweigh the natural tendency of high _ workers to go into sector 2. Thus an Ellison-Kandori-Mailath-Rob-Young (EKMRY)-type argument suggests that the intuitive equilibrium may be more stable or plausible.

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[∗] This paper was written while I was visiting at the Becker Center on Chicago Price Theory at the University of Chicago and I am grateful to the Center for their support. Ed Glaeser, James Heckman, AlexKaufman, Steve Levitt, Kevin Murphy, Josh Schwartzstein, Jesse Shapiro, Andrei Shleifer and Heidi Williams provided helpful comments. As always, I am grateful most of all to my advisers Roland Benabou,Hyun Shin and especially Jos´e Scheinkman for their support and advice on this and other projects.

E. Glen Weyl[†][† ]Bendheim Center for Finance, Department of Economics, Princeton University, 26 Prospect Avenue, Princeton, NJ 08540: eweyl@princeton.edu.

[1] Frakes (1996).

[2] While it may seem that entrepreneurship fits a bit less into this category, empirical research indicates entrepreneurship is not very lucrative and entry may plausibly be driven by psychic income; see Hamilton (1999). As mentioned below, this provides a simple story for why increased taxation and tax progressivity could encourage more entrepreneurship.

[3] But note that empirical evidence on this topic is not clear: Gentry and Hubbard (2000) find results that largely contradict Cullen and Gordon (2002).

Psychic Income, Taxes and the Allocation of Talent_html_m56a2f737

[6 ]Note that social welfare is well-defined by the assumption that EG [β] is finite.

[7]These cases are also emphasized in, and provided some superficial empirical support by, the sociology literature on values and occupational choice, see Schwartzweller (1960). Furthermore, the other cases differ only in the minor way that equilibrium will sometimes require individuals with low α entering the socially beneficial sector. I am working in collaboration with Joshua Schwartzstein on more completely  characterizing games of this form.

[8 ]Of course self-signalling requires some failure of perfect memory, along the lines of B´enabou and Tirole (2004).

[9] As discussed in the appendix, I am working with Josh Schwartzstein to elaborate the connection between these two argument so as to both lay an evolutionary foundation for standard signalling refinements and use this foundation to extend them to contexts where standard refinements have no bite.

[11] Note that, in this model done properly, externalities, not simply psychic income, would be worker-sector dependent. I am therefore thinking about breaking this mechanism off into a separate subsection in a future draft.

Psychic Income, Taxes and the Allocation of Talent_html_m707b12f9

[12]This interpretation is eshed out in more detail in an analogous result, Proposition ??.

[13]This critique was brought to my attention by Jesse Shapiro.

[14]I suspect that if prestige per-person in an industry increases in the number working in that industry, it might be that positive externalities of going into an industry could exist, even when taxes are not justified. However, I consider this case less interesting for a few reasons. First, it seems very likely that prestige within an industry is rival, rather than increasing per-person in the size of the industry. Second, an industry with such dynamics might exhibit multiple equilibria (fads) which I do not think play a large role in occupational choice. Finally, and most importantly, this case does not seem to be in the spirit of the critique laid out above.

[15]Note that this is a strictly weaker condition than that required above, in that it loses the +1 term on the right hand side inside the parentheses.

[16]I do not formally establish this result in this draft, as the technical conditions necessary to get the second order conditions to work out correctly are messy. I am considering adding this perhaps in a technical appendix to the paper.

[17]I am currently working on a project studying the social value of arbitrage activities. This is at a very early stage, but preliminary work is available in Weyl (2007).

Assistant Professor in the Department of Economics and in the College, University of Chicago, USA