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The optimal quantity of debt

  • S. Rao Aiyagari
  • Ellen R. McGrattan

We describe a model for calculating the optimal quantity of debt and then apply it to the U.S. economy. The model consists of a large number of infinitely-lived households whose saving behavior is influenced by precautionary saving motives and borrowing constraints. This model incorporates a different role for government debt than the standard representative agent growth model and captures different trade-offs between the benefits and costs of varying its level. Government debt enhances the liquidity of households by providing additional assets for smoothing consumption (in addition to claims to capital) and effectively loosening borrowing constraints. By raising the interest rate, government debt makes assets less costly to hold and more effective in smoothing consumption. However, the implied taxes have wealth distribution, incentive, and insurance effects. Further, government debt crowds out capital (via higher interest rates) and lowers per capita consumption. Our quantitative analysis suggests that the crowding out effect is decisive for welfare. We also describe variations of the model which permit endogenous growth. It turns out that even with lump sum taxes and inelastic labor, government debt as well as government consumption have growth rate effects, thereby implying large welfare gains from reducing the level of debt.

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Paper provided by Federal Reserve Bank of Minneapolis in its series Working Papers with number 538.

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Date of creation: 1994
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Handle: RePEc:fip:fedmwp:538
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  1. Timothy J. Kehoe & David K. Levine & Michael Woodford, 1992. "The Optimum Quantity of Money Revisited," Levine's Working Paper Archive 2035, David K. Levine.
  2. Varian, Hal R., 1980. "Redistributive taxation as social insurance," Journal of Public Economics, Elsevier, vol. 14(1), pages 49-68, August.
  3. Lucas, Robert E, Jr, 1990. "Supply-Side Economics: An Analytical Review," Oxford Economic Papers, Oxford University Press, vol. 42(2), pages 293-316, April.
  4. Javier Diaz-Gimenez & Edward C. Prescott & Terry Fitzgerald & Fernando Alvarez, 1992. "Banking in computable general equilibrium economies," Staff Report 153, Federal Reserve Bank of Minneapolis.
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  6. Eaton, Jonathan & Rosen, Harvey S., 1980. "Labor supply, uncertainty, and efficient taxation," Journal of Public Economics, Elsevier, vol. 14(3), pages 365-374, December.
  7. Aiyagari, S Rao, 1994. "Uninsured Idiosyncratic Risk and Aggregate Saving," The Quarterly Journal of Economics, MIT Press, vol. 109(3), pages 659-84, August.
  8. Tauchen, George, 1986. "Finite state markov-chain approximations to univariate and vector autoregressions," Economics Letters, Elsevier, vol. 20(2), pages 177-181.
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  10. Mehrling, Perry, 1995. "A note on the optimum quantity of money," Journal of Mathematical Economics, Elsevier, vol. 24(3), pages 249-258.
  11. Bewley, Truman, 1983. "A Difficulty with the Optimum Quantity of Money," Econometrica, Econometric Society, vol. 51(5), pages 1485-504, September.
  12. Barro, Robert J., 1979. "On the Determination of the Public Debt," Scholarly Articles 3451400, Harvard University Department of Economics.
  13. Ellen R. McGrattan, 1993. "Solving the stochastic growth model with a finite element method," Staff Report 164, Federal Reserve Bank of Minneapolis.
  14. Jappelli, Tullio & Pagano, Marco, 1999. "The Welfare Effects of Liquidity Constraints," Oxford Economic Papers, Oxford University Press, vol. 51(3), pages 410-30, July.
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  16. Laitner, John, 1992. "Random earnings differences, lifetime liquidity constraints, and altruistic intergenerational transfers," Journal of Economic Theory, Elsevier, vol. 58(2), pages 135-170, December.
  17. Hansen, G.D. & Imrohoroglu, A., 1990. "The Role Of Unemployment Insurance In An Economy With Liquidity Constraints And Moral Hazard," Papers 21, California Los Angeles - Applied Econometrics.
  18. Laitner, John P, 1979. "Bequests, Golden-age Capital Accumulation and Government Debt," Economica, London School of Economics and Political Science, vol. 46(184), pages 403-14, November.
  19. S. Rao Aiyagari, 1994. "Macroeconomics with frictions," Quarterly Review, Federal Reserve Bank of Minneapolis, issue Sum, pages 24-40.
  20. Chamley, Christophe, 1986. "Optimal Taxation of Capital Income in General Equilibrium with Infinite Lives," Econometrica, Econometric Society, vol. 54(3), pages 607-22, May.
  21. Cukierman, Alex & Meltzer, Allan H, 1989. "A Political Theory of Government Debt and Deficits in a Neo-Ricardian Framework," American Economic Review, American Economic Association, vol. 79(4), pages 713-32, September.
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