Abstract
This paper considers a class of growth models with idiosyncratic human capital risk and private information about individual effort choices (moral hazard). Households are infinitely-lived and have preferences that allow for a time-additive expected utility representation with a one-period utility function that is additive over consumption and effort as well as logarithmic over consumption. Human capital investment is risky due to idiosyncratic shocks that follow a Markov process with transition probabilities that depend on effort choices. The production process is represented by an aggregate production function that uses physical capital and human capital as input factors. We show that constrained optimal allocations are simple in the sense that individual effort levels and individual consumption growth rates are history-independent. Further, constrained optimal allocations are the solutions to a recursive social planner problem that is simple in the sense that exogenous shocks are the only state variables. We also show that constrained optimal allocations can be decentralized as competitive equilibrium allocations of a market economy with a simple tax- and transfer scheme. Finally, it is always optimal to subsidize human capital investment in the market economy.
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Abraham, A., Koehne, S., Pavoni, N.: On the first-order condition approach in principal–agent models with hidden borrowing and lending. J. Econ. Theory 146, 1331–1361 (2011)
Aiyagari, R.: Optimal capital income taxation with incomplete markets, borrowing constraints, and constant discounting. J. Polit. Econ. 103, 1158–1175 (1995)
Atkeson, A., Lucas, R.: On efficient distribution with private information. Rev. Econ. Stud. 59, 487–504 (1992)
Becker, R., Boyd, J.: Capital Theory, Equilibrium Analysis and Recursive Utility. Blackwell Publishers, Hoboken (1997)
Constantinides, G., Duffie, D.: Asset pricing with heterogeneous consumers. J. Polit. Econ. 104, 219–240 (1996)
Da Costa, C., Maestri, L.: The risk properties of human capital and the design of government policy. Eur. Econ. Rev. 51, 695–713 (2007)
Davila, J., Hong, J., Krusell, P., Rios-Rull, V.: Constrained efficiency in the neoclassical growth model with uninsurable idiosyncratic shocks. Econometrica 80, 2431–2467 (2012)
Diamond, P., Mirrlees, J.: Optimal taxation and public production: production efficiency. Am. Econ. Rev. 61, 8–27 (1971)
Farhi, E., Werning, I.: Inequality and social discounting. J. Polit. Econ. 115, 365–402 (2007)
Fudenberg, D., Holmstrom, B., Milgrom, P.: Short-term contracts and long-term agency relationships. J. Econ. Theory 51, 1–31 (1990)
Geanakoplos, J., Polemarchakis, H.: Existence, regularity and constrained suboptimality of competitive allocations when the asset market is incomplete. In: Arrow, K.J., Heller, W., Starret, D., Starr, R. (eds.) Essays in Honour. Cambridge University Press, Cambridge (1986)
Golosov, M., Kocherlakota, N., Tsyvinski, A.: Optimal indirect and capital taxation. Rev. Econ. Stud. 70, 569–587 (2003)
Gottardi, P., Kajii, A., Nakajima, T.: Optimal taxation and debt with uninsurable risks to human capital accumulation. Am. Econ. Rev. 105, 3443–3470 (2015)
Grochulskia, B., Piskorskib, T.: Risky human capital and deferred capital income taxation. J. Econ. Theory 145, 908–943 (2010)
Hahn, G., Yannelis, N.: Efficiency and incentive compatibility in differential information economies. Econ. Theor. 10, 383–411 (1997)
Heckman, J., Lochner, L., Taber, C.: Explaining rising wage inequality: explanations with a dynamic general equilibrium model of labor earnings with heterogeneous agents. Rev. Econ. Dyn. 1, 1–58 (1998)
Holmstrom, B., Milgrom, P.: Aggregation and linearity in the provision of intertemporal incentives. Econometrica 55, 303–328 (1987)
Hopenhayn, H., Nicolini, P.: Optimal unemployment insurance. J. Polit. Econ. 105, 412–438 (1997)
Huggett, M., Ventura, G., Yaron, A.: Sources of lifetime inequality. Am. Econ. Rev. 101, 2921–2954 (2011)
Jones, L., Manuelli, R.: A convex model of equilibrium growth: theory and policy application. J. Polit. Econ. 98, 1008–1038 (1990)
Krebs, T.: Human capital risk and economic growth. Quart. J. Econ. 118, 709–744 (2003)
Krebs, T.: Recursive equilibrium in endogenous growth models with incomplete markets. Econ. Theor. 29, 505–523 (2006)
Laffont, J., Martimort, D.: Theory of Incentives: The Principal-Agent Model. Princeton University Press, Princeton (2002)
Ljungqvist, L., Sargent, T.: Recursive Macroeconomic Theory, 4th edn. MIT Press, Cambridge (2018)
Mirrlees, J.: An exploration in the theory of optimal income taxation. Rev. Econ. Stud. 38, 175–208 (1971)
Pavoni, N., Violante, G.: Optimal welfare-to-work programs. Rev. Econ. Stud. 74, 283–318 (2007)
Phelan, C.: Opportunity and social mobility. Rev. Econ. Stud. 73, 487–504 (2006)
Phelan, C., Townsend, R.: Computing multi-period, information-constrained optima. Rev. Econ. Stud. 58, 853–881 (1991)
Rebelo, S.: Long-run policy analysis and long-run growth. J. Polit. Econ. 99, 500–521 (1991)
Rogerson, W.: Repeated moral hazard. Econometrica 53, 69–76 (1985)
Rogerson, W.: The first-order conditions approach to principal-agent problems. Econometrica 53, 1357–1368 (1985)
Rustichini, A.: Lagrange multipliers in incentive-constrained problems. J. Math. Econ. 29, 365–380 (1998)
Sannikov, Y.: A continuous-time version of the principal-agent problem. Rev. Econ. Stud. 75, 957–984 (2008)
Spear, S., Srivastava, S.: On repeated moral hazard with discounting. Rev. Econ. Stud. 54, 599–617 (1987)
Stantcheva, S.: Optimal taxation and human capital policies over the life-cycle. J. Polit. Econ. 125, 1931–1990 (2017)
Stantcheva, S.: Dynamic taxation. Ann. Rev. Econ. 12, 801–831 (2020)
Stokey, N., Lucas, R., Prescott, E.: Recursive Methods in Economic Dynamics. Harvard University Press (1989)
Toda, A.: Incomplete market dynamics and cross-sectional distributions. J. Econ. Theory 154, 310–348 (2014)
Toda, A.: Asset prices and efficiency in a Krebs economy. Rev. Econ. Dyn. 18, 957–978 (2015)
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We thank participants at various seminars, an associate editor, and two referees for helpful comments. Tom Krebs thanks the German Science Foundation for financial support.
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Krebs, T., Scheffel, M. Optimal allocations in growth models with private information. Econ Theory 78, 125–154 (2024). https://doi.org/10.1007/s00199-023-01527-8
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DOI: https://doi.org/10.1007/s00199-023-01527-8