اولویت های تفکیک ناپذیر و سیستم های بهینه تأمین اجتماعی

In this paper, we consider economies in which agents are privately informed about their skills, which evolve stochastically over time. We require agents' preferences to be weakly separable between the lifetime paths of consumption and labor. However, we allow for intertemporal nonseparabilities in preferences like habit formation. In this environment, we derive a generalized version of the Inverse Euler Equation and use it to show that intertemporal wedges characterizing optimal allocations of consumption can be strictly negative. We also show that preference nonseparabilities imply that optimal differentiable asset income taxes are necessarily retrospective in nature. We show that under weak conditions, it is possible to implement a socially optimal allocation using a social security system in which taxes on wealth are linear, and taxes/transfers are history-dependent only at retirement. The average asset income tax in this system is zero.

In this paper, we consider a class of economies in which agents are privately informed about their skills and those skills might evolve stochastically over time. As in Golosov, Kocherlakota, and Tsyvinski (GKT) [3], we impose no restriction on the evolution of skills over time. GKT assume that preferences are additively separable between consumption and labor, and between consumption at different dates. We relax this assumption, and instead require only that prefer- ences over consumption sequences be weakly separable (not additively separable) from agents’ labor supplies. This assumption means that the marginal rate of substitution between consump- tion at any two dates is independent of the agent’s sequence of labor supplies. However, we allow for intertemporal nonseparabilities: the marginal rate of substitution between consumption at any two dates may depend on other consumptions. We restrict attention to economies in which agents must retire at some date S (but may live thereafter). Our goal is to study optimal allocations and tax systems in this setting with preference non- separabilities. We first derive a necessary optimality condition on the consumption allocation that generalizes the so-called Inverse Euler Equation of Rogerson [10] and GKT [3]. To do so, we use a variational argument that involves perturbations of consumption after the retirement date S ,as the standard variational argument perturbing consumption in any two consecutive periods cannot be used when preferences are nonseparable. In the separable case, GKT [3] use the Inverse Euler Equation to show that optimal allocations of consumption in dynamic private-skill economies are characterized by a positive intertemporal wedge: at every date and state, the marginal return on savings exceeds the shadow interest rate of every agent in the economy. We use the generalized version of this Euler equation to show that the same result does not hold when preferences are nonseparable: optimal intertemporal wedges can be negative. We show next that the complications arising from the nonseparability of preferences have important implications for the structure of the optimal tax systems that Albanesi and Sleet [1], Kocherlakota [8], and others studied in dynamic private-skill economies with additively separa- ble preferences. We use an illustrative example to show that with intertemporal nonseparabilities an optimal tax that is differentiable with respect to period t asset income must depend on labor income in future periods. This result means that an agent must pay his period t asset income taxes at some future date, after the tax authorities learn his labor income at that future date. Hence, optimal asset income taxes are necessarily retrospective . This finding leads us to consider a class of tax systems that we term social security systems . Agents pay a linear tax on labor income during their working lives. Then, during retirement, they receive a constant payment that is conditioned on their entire labor income history. As well, at the retirement date, agents pay taxes on their current and past asset income. These taxes are a linear function of past asset incomes; the tax rates are a possibly complicated function of the agents’ labor income histories. The social security systems that we study in this model are similar to the actual Social Secu- rity system in the United States. In the United States, as in the model, labor income is subject to a linear Social Security payroll tax. 1 In the United States, as in the model, the size of the benefit paid by the Social Security program in retirement is a complicated function of agents’ individual labor income histories. 2 There are only two important distinctions between our social security system and the actual Social Security system in the United States. First, in our social security systems, agents are allowed to borrow against their post-retirement transfers. There is no forced-saving element in our tax system. Second, agents must pay asset income taxes in pe- riod S . We assume that optimal incentive-feasible allocations are such that two agents with the same lifetime paths of labor income must have the same lifetime paths of consumption. Given an optimal allocation with this property, we can find a social security system that implements that allocation as an equilibrium. The social security system that implements an optimal allocation has the property that the average tax rate on period t asset income is zero. As well, in the optimal system, the aggregate amount of taxes collected on period t asset income is zero. We view our analysis as making two distinct contributions. First, GKT [3] initiated a literature on dynamic optimal taxation from a Mirrleesian approach. 3 However, GKT and the succeed- ing papers restrict attention to preferences that are additively separable between consumption and labor, and between consumption at different dates. 4 We relax these (severe) restrictions, obtain a generalized Euler equation, and show that optimal intertemporal wedges can be nega- tive. Second, we show that the resulting optimal tax system is necessarily retrospective in how it treats asset income. In addition, we show that optimal labor income taxes that agents face during their working years can have a simple structure. In our optimal system, agents face a period-by-period labor income tax rate that is independent of their age or their history of labor incomes. After retirement, agents receive transfers that depend in complicated ways on their histories of labor incomes. Thus, in our system, post-retirement transfers, but not pre-retirement taxes, depend on histories of labor incomes. In that, our tax system resembles the U.S. Social Security program. Our analysis shows that social security programs can be a powerful tool for implementation of socially optimal outcomes. We also demonstrate that the zero expected asset income tax result of Kocherlakota [8] holds with preference nonseparabilities. Our paper is not the first one to point out a role for retrospective taxes on capital income. Grochulski and Piskorski [6] demonstrate that retrospective taxation of capital income is nec- essary in a Mirrleesian economy with endogenous skills, in which the technology for skill accumulation requires input of physical resources and agents can privately divert these resources to ordinary consumption. In their model, retrospective taxes on capital income are necessary be- cause the government cannot observe agents’ individual consumption, and future observations of realized labor income carry information about past marginal rates of substitution. If individ- ual consumption were observable, retrospective capital income taxes would not be needed in their economy. In our model, we show that when preferences are time nonseparable, an optimal tax system must necessarily be retrospective, even when the government can observe individual consumption. Also, our analysis demonstrates how an optimal retrospective tax system can be implemented with a set of taxes and transfers closely resembling the structure of the U.S. Social Security System. Huggett and Parra [7] consider a social security system in the context of a Mirrleesian model. They, however, are interested in a quantitative evaluation of the possible inefficiency in the cur- rent U.S. Social Security system, and do not consider the question of implementation. In our paper, in contrast, we demonstrate how a (general) social security system can be used to imple- ment an optimal social insurance scheme in a Mirrleesian economy. Golosov and Tsyvinski [4] show how an optimal disability insurance scheme can be imple- mented with a tax system that is non-differentiable in capital. They consider the case of additively separable preferences, as well as a stochastic structure tailored to the question of optimal disabil- ity insurance. In our paper, we treat the case of preferences that are time nonseparable and weakly separable between consumption and leisure. Also, we consider a more general stochastic struc- ture for skill shocks. Our results can be viewed as demonstrating a much broader role for a social security system in the provision of social insurance than just the provision of insurance against disability. The structure of the paper is as follows. Section 2 lays out the environment we study. Section 3 obtains the generalized Euler equation for an optimal allocation of consumption and shows that the intertemporal wedge can be negative. Section 4 demonstrates that optimal differentiable capi- tal income taxes must be retrospective in our environment. Section 5 provides an implementation result. Section 5 provides a characterization of optimal asset income taxes. Section 6 concludes.

Over the past five years, there has been a great deal of work on optimal asset taxation when agents are privately informed about skills. This work has typically restricted agents’ preferences to be additively separable between consumption at different dates, and between consumption and leisure. Both restrictions are severe ones. In this paper, we relax these restrictions considerably, and require only that preferences be weakly separable between consumption paths and labor paths. This class of preferences includes, for example, the possibility that preferences exhibit habit formation with respect to consumption. We show that intertemporal nonseparabilities matter. We demonstrate that if a tax system is differentiable with respect to asset income, and implements a social optimum, then the taxes on period t asset income must depend on period t  labor income, where t  >t . Given this result, it is natural to look at tax systems in which period t asset income is taxed only at the time of retirement. We restrict attention to what we term social security systems . In these systems, labor income before retirement is taxed at a time-independent rate. At retirement, agents’ asset income is taxed linearly, but at a rate that depends on their full labor income history. After retirement, agents receive history-dependent constant transfers. We prove that, because of the weak separability of preferences, the taxes on asset income average to zero across all agents (as in Kocherlakota [8]). Asset income taxes are purely redistributive. In our analysis, the only form of uncertainty is idiosyncratic labor productivity risk. In the real world, there are many other forms of risk, including age of death and health shocks. We could readily extend our analysis to account for these forms of risk, as long as there is no private information associated with them. For example, with uncertain lifetimes, we could implement an optimal allocation by embedding an annuity feature into our social security system. One criticism of the implementations used in Albanesi and Sleet [1] and especially Kocher- lakota [8] is that they are too complex relative to capital and labor income taxes used in practice. In this paper, even though preferences are time nonseparable, all redistribution and insurance is embedded in the calculations of taxes and transfers at retirement. These calculations are admit- tedly complex. But there is no real sense that they are any more complex than the calculations that the Social Security Administration currently does to determine post-retirement benefits. We believe that social security systems can be useful for implementation in many other dynamic settings.