New Dynamic Public Finance. Mikhail Golosov (Yale, New Economic School, and NBER) Aleh Tsyvinski (Yale, New Economic School, and NBER)

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1 New Dynamic Public Finance Mikhail Golosov (Yale, New Economic School, and NBER) Aleh Tsyvinski (Yale, New Economic School, and NBER) New Dynamic Public Finance is a recent literature that analyzes taxation and social insurance policy in dynamic settings. Many of public finance and macroeconomics problems such as taxation of capital or Social Security and disability insurance are dynamic. When a taxation or insurance environment is static, a large body of Mirrlees taxation literature i showed how to design social insurance and taxation programs. The New Dynamic Public Finance literature extends the static Mirrlees framework to dynamic settings ii. The key tradeoff in such environments is the insurance incentives tradeoff: how to design social insurance or redistribution systems while ensuring necessary incentives to provide effort or work. In dynamic settings, the primary focus is the stochastic shocks that agents receive over time. There is an informational frictions these shocks are not directly observed by the government. Consider a simple example of such dynamic social insurance problem. An able worker can become disabled with some probability later in life. Moreover, it is relatively easy to claim disability. For example, one can pretend to be suffering from back pain which is very difficult to verify. A government wants to create an optimal disability insurance system. Such a system would provide adequate transfers to the truly disabled workers while discouraging fake disability applications. The decision of the worker whether to claim disability in the future is necessarily dynamic and will affect his choices today. For example, an able worker faced with a given transfer scheme can increase or decrease his savings. Such savings choices may increase or decrease his willingness to fake disability and claim disability benefits in the future. Intertemporal wedge and implicit tax on savings In our work with Narayana Kocherlakota we have shown one of the key general insights that holds in these dynamic settings when agents skills stochastically change it is optimal to introduce a positive distortion (an implicit tax) that implicitly discourages savings iii. This result holds for any stochastic process for skills (for example, for any persistence of the shocks) as long as there is some uncertainty about future individual shocks. A somewhat loose intuition for the implicit savings tax using the disability example above is as follows. Consider a system of disability transfers that gives a disabled worker, say, $1000. An able worker contemplates whether to work or to claim disability next period. If he fakes disability, he will for sure receive $1000. If he does not fake and claims disability only if he is truly disabled, he gets $1000 if he is disabled (with some probability) and a higher amount from work if he is able. The faker will then have higher savings, given this transfer system he knows that he will receive $1000 for sure and will not

2 work. A disability insurance scheme that introduces a tax on savings (for example, by asset testing, i.e., paying benefits only to those with assets low enough) will then help discourage fake applicants. The result on the positive intertemporal wedge or implicit tax does not necessarily mean that there has to be a positive capital tax, or that wedges are necessarily equal to taxes. Rather, the main point is that an optimal dynamic taxation or social insurance system has to necessarily take into account agents ability to save. In general, such accounting for agents savings implies that savings have to be discouraged. This contrasts with the Chamley Judd result iv, obtained in macroeconomic Ramsey settings, that capital should go untaxed in the long run. In the economy with heterogeneous unobservable skills that do not stochastically change over time, it is optimal to have a zero capital tax. v Implementation and Taxation of Savings. What kind of taxes does the optimal program imply? There are several papers studying implementation of the optimal programs. Our work on disability insurance shows that the optimum can be implemented by an asset tested program in which disability (or more, generally, retirement) benefits are paid only to agents who have assets below a specified limit vi. A possible implementation in general environments is one in which capital taxes are regressive vii. In a special case of the i.i.d. process for individual shocks, a non linear tax on wealth and income implements the optimum viii. In some models with habit formation the optimal allocation resembles a social security system in which taxes on wealth are linear, and taxes/transfers are history dependent only at retirement ix. All of these implementations have two key features: (1) taxes or transfers have to be conditioned on the amount of savings that agent accumulates, and (2) there is some degree of history dependency. Other taxes and social insurance problems This general framework allowed a variety of analyses of other dynamic taxes and social insurance problems. In an environment in which the utility of consumption is linear, labor taxes of all agents asymptotically converge to zero x. Optimal taxation of entrepreneurs has been studied xi. In that setup, an entrepreneur exerts unobservable effort that affects the rate of return of the project. The optimal implicit savings tax for the entrepreneurs can be either positive or negative. In a monetary model with heterogeneous agents with privately observed skills, the optimality of Friedman rule was proven, that is, the optimal inflationary tax is zero xii. In the economy in which all the skills do not stochastically change over time and in which there is aggregate uncertainty a labor tax smoothing result holds xiii. The analysis of estate taxation in an intergenerational dynastic model with dynamic private information shows that estate taxes should be progressive xiv. In a model of endogenous fertility with private information on productivity estate taxes are positive, and there are positive taxes on family size xv. Also optimal taxes on human capital have been studied. xvi Quantitative work In step with theoretical advances, several authors have carried out quantitative analyses on the size of wedges, taxes, and welfare gains from improving tax policy. The sizes and shapes of the optimal capital

3 and labor taxes were computed in a dynamic economy in the case of i.i.d. shocks to skills xvii. Moving to the other side of the spectrum, with permanent disability shocks, we showed that the welfare gains from improving disability insurance system might be large xviii. In a lifecycle version of a dynamic Mirrlees economy with publicly and privately observable shocks to individual labor productivity, a recent study estimates the fraction of labor productivity that is private information xix. It finds that for the model and data to be consistent, a large fraction of shocks to labor productivities must be private information. Another quantitative route is considering partial reforms. Rather than finding the full optimum, a variety of papers considered changes in the taxes or insurance systems that can improve upon the current system. One example is to consider the welfare gains from partial reforms that introduce optimal savings distortions but leave the labor allocations unchanged xx. Another important route of a partial tax reform in a dynamic setting is to compute the optimal tax schedule in a model where the tax function is restricted to a specific functional form but flexibly parameterized to allow for wide range of shapes, including progressive taxation, non discriminatory lump sum taxation, and various exemptions. xxi An interesting partial reform study determines welfare gains and optimal taxes in a calibrated model with age dependent taxes xxii. Private and public insurance An important aspect of designing optimal dynamic taxation and insurance is to allow for the possibility of private insurance and other frictions beyond unobservability of skills. We study an environment in which agents can trade unobservably on private markets xxiii. An example of this in the environment of the disability insurance considered above is that workers are able to borrow or lend with a market determined interest rate, and such transactions are not observable by the insurance agency. We show that when all market transactions are publicly observed, the optimal program can be implemented privately without any government intervention. However, if some of the financial transactions are not observable, private insurance is not efficient and has to be supplemented with public intervention. A recent interesting paper considers a dynamic Mirrleesian economy in which workers can sign insurance contracts with multiple firms (i.e., another friction non exclusivity of contracts is added) xxiv. The model endogenously divides the population into agents that are not monitored and have access to nonexclusive contracts and agents that have access to exclusive contracts. The authors use US household data and find that high school graduates satisfy the optimality conditions implied by the non exclusive contracts while college graduates behave according to the second group. Political economy and optimal taxation Another set of issues that this literature studies is that of the effect of the political economy on social insurance. The papers considered above assume that the policymaker is a fictitious benevolent social planner with full commitment. But in reality the social programs and taxation are run by politicians. In our work with Daron Acemoglu we study the optimal Mirrlees taxation problem in a dynamic economy but, in contrast to the exisiting approach, the policy is decided in a classical electoral accountability model of political economy xxv. Politicians are self interested (fully or partially) and cannot commit to promises. They can misuse the resources and the information they collect to generate rents.

4 An important technical result of our analysis is that a version of revelation principle works despite the commitment problems and the different interests of the government. Using this tool, we show that if the government is as patient as the agents, the best sustainable mechanism leads in the long run to allocation where the aggregate distortions arising from political economy disappear. In contrast, when the government is less patient than the citizens, there are positive aggregate political economy distortions even asymptotically. We also use this framework to compare centralized mechanisms operated by self interested rulers to anonymous markets xxvi. A related environment is that of the debt policy in dynamic settings with linear taxes and self interested politicians xxvii. A recent study of efficient nonlinear taxation of labor and capital in a dynamic Mirrleesian model incorporates political economy constraints in which policies are the outcome of democratic elections, and there is no commitment xxviii. Their main result is that the marginal tax on capital income is progressive, in the sense that richer agents face higher marginal tax rates. The properties of credible equilibria in dynamic settings with a lack of societal commitment are examined in another recent paper. xxix The authors isolate forces that promote and retard capital accumulation in these settings, derive the pattern of intertemporal wedges as well as provide an implementation result. Conclusion The literature on dynamic Mirrlees problems has already delivered many important results on a broad variety of social insurance and taxation issues in dynamic context. There are many interesting questions that lie ahead. On the theoretical part it is important to create a general algorithm that will allow to solve quantitatively a broader set of models, especially, ones with general persistent shocks which are empirically relevant. It is also important to bridge the gap with the more standard public finance literature much of which was done for the static framework xxx. i A seminal paper in this literature is J. Mirrlees, An Exploration in the Theory of Optimum Income Taxes, Review of Economic Studies, Vol. 38, No. 114, ii For surveys see M. Golosov, A. Tsyvinski, and I. Werning, New Dynamic Public Finance: A User s Guide, in NBER Macroeconomics Annual, D. Acemoglu, K. Rogoff, and M. Woodford ed., NBER, 2006 and N. Kocherlakota, The New Dynamic Public Finance, Princeton University Press, forthcoming iii The general proof is provided in M. Golosov, N. Kocherlakota and A. Tsyvinski, Optimal Indirect and Capital Taxation, Review of Economic Studies, Vol. 70, No. 3, For earlier results in more limited settings see P. Diamond and J. Mirrlees A Model of Social Insurance with Variable Retirement, Journal of Public Economics, Vol. 10, 1978 and W. Rogerson Repeated Moral Hazard Econometrica, 53, iv K.L. Judd, Redistributive Taxation in a Simple Perfect Foresight Model, Journal of Public Economics, Vol. 28, No. 1, 1985 and C. Chamley, Optimal Taxation of Capital Income in General Equilibrium with Infinite Lives, Econometrica, Vol. 54, No. 3, v I. Werning, Optimal Dynamic Taxation, Ph.D. Dissertation, The University of Chicago, 2002 and M. Golosov, N. Kocherlakota and A. Tsyvinski, Optimal Indirect and Capital Taxation, Review of Economic Studies, Vol. 70, No. 3, 2003.

5 vi M. Golosov and A. Tsyvinski, Designing Optimal Disability Insurance: A Case for Asset Testing, NBER Working Paper No , September 2004, and Journal of Political Economy, Vol. 114, No. 2, vii N. Kocherlakota, Zero Expected Wealth Taxes: A Mirrlees Approach to Dynamic Optimal Taxation, Econometrica, Vol. 73, No. 5, viii S. Albanesi and C. Sleet, Dynamic Optimal Taxation with Private Information, Review of Economic Studies, Vol. 73, No. 1, ix B. Grochulski and N. Kocherlakota, Nonseparable Preferences and Optimal Social Security Systems, NBER Working Paper No , September x M. Battaglini and S. Coate, Pareto Efficient Taxation with Stochastic Abilities, Journal of Public Economics, 2008, v. 92, iss. 3 4, pp xi S. Albanesi, Optimal Taxation of Entrepreneurial Capital with Private Information, CEPR Discussion Paper No. 5647, xii C. da Costa and I. Werning, On the Optimality of the Friedman Rule with Heterogeneous Agents and Nonlinear Income Taxation, Journal of Political Economy, Vol. 116, No. 1, xiii I. Werning, Optimal Fiscal Policy with Redistribution Quarterly Journal of Economics August 2007, Vol. 122, No. 3, Pages : xiv E. Farhi and I. Werning, Inequality, Social Discounting and Estate Taxation, NBER Working Paper No , June 2005 and Journal of Political Economy, Vol. 115, No. 3, xv R. Hosseini, L. Jones, and A. Shourideh, Risk Sharing, Inequality and Fertility, NBER Working Paper No , June xvi R. Bohacek and M. Kapicka, Optimal Human Capital Policies, Journal of Monetary Economics, Vol. 55, No. 1, 2008 and B. Grochulski and T. Piskorski "Risky Human Capital and Deferred Capital Income Taxation", Journal of Economic Theory (forthcoming). xvii S. Albanesi and C. Sleet, Dynamic Optimal Taxation with Private Information, Review of Economic Studies, Vol. 73, No. 1, xviii M. Golosov and A. Tsyvinski, Designing Optimal Disability Insurance: A Case for Asset Testing, NBER Working Paper No , September 2004, and Journal of Political Economy, Vol. 114, No. 2, xix L. Ales and P. Maziero, Accounting for private information, Mimeo, xx E. Farhi and I. Werning, Capital Taxation: Quantitative Explorations of the Inverse Euler Equation, xxi J.C. Conesa, S. Kitao and D. Krueger, Taxing Capital? Not a Bad Idea After All! NBER Working Paper No , January 2007, and American Economic Review, Vol. 99, No. 1, 2009 and J.C. Conesa and D. Krueger, On the Optimal Progressivity of the Income Tax Code, NBER Working Paper No , January 2005, and Journal of Monetary Economics, Vol. 53, No. 7, xxii M. Weinzierl, The Surprising Power of Age Dependent Taxation, Mimeo, Harvard University, 2008.

6 xxiii M. Golosov and A. Tsyvinski, Optimal Taxation with Endogenous Insurance Markets, NBER Working Paper No , March 2005, and The Quarterly Journal of Economics, Vol. 122, No. 2, xxiv L. Ales and P. Maziero, Non exclusive Dynamic Contracts, Competition and the Limits of Insurance, Mimeo, xxv D. Acemoglu, M. Golosov, and A. Tsyvinski Markets versus Governments: Political Economy of Mechanisms, NBER Working Paper No , 2006 and D. Acemoglu, M. Golosov, and A. Tsyvinski Political Economy of Mechanisms, Econometrica, Vol. 76, No. 3, 2008, and Dynamic Mirrlees Taxation under Political Economy Constraints, Review of Economic Studies, forthcoming, and Political Economy of Ramsey Taxation, NBER Working Paper No , August xxvi D. Acemoglu, M. Golosov, and A. Tsyvinski Markets versus Governments, Journal of Monetary Economics (2008), 55(1): xxvii P. Yared "Politicians, Taxes, and Debt," 2009, forthcoming in Review of Economic Studies. xxviii E. Farhi and I. Werning, The Political Economy of Non Linear Capital Taxation, Mimeo, xxix C. Sleet and S. Yeltekin Allocation and Taxation in Uncommitted Societies, Mimeo, xxx E. Saez, The Desirability of Commodity Taxation Under Non Linear Income Taxation and Heterogeneous Tastes, NBER Working Paper No. 8029, December 2000, and The Journal of Public Economics, Vol. 83, Vol. 2, 2002.