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Growth and Distribution in a Model with Endogenous Time Peferences and Borrowing Constraints

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  • Kirill Borissov

Abstract

This paper proposes an AK-model with endogenous time preferences and borrowing constraints. It is assumed that the subjective discount factor of a household is an increasing function of its relative income. First we describe the structure of balanced-growth equilibrium paths, on which the population splits into two groups ? the rich and the poor. Then we study sliding equilibrium paths. They become balanced from some time onwards and eventually all the capital is owned by the household that is the richest at the initial state. Finally, we consider time consistent equilibrium paths and prove their existence.

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  • Kirill Borissov, 2011. "Growth and Distribution in a Model with Endogenous Time Peferences and Borrowing Constraints," DEGIT Conference Papers c016_073, DEGIT, Dynamics, Economic Growth, and International Trade.
    • Handle: RePEc:deg:conpap:c016_073
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    1. Romer, Paul M, 1986. "Increasing Returns and Long-run Growth," Journal of Political Economy, University of Chicago Press, vol. 94(5), pages 1002-1037, October.
    2. Tyson, Christopher J., 2008. "Management of a capital stock by Strotz's naive planner," Journal of Economic Dynamics and Control, Elsevier, vol. 32(7), pages 2214-2239, July.
    3. Leandro Siqueira Carvalho, 2010. "Poverty and Time Preference," Working Papers 759, RAND Corporation.
    4. Alesina, Alberto & Perotti, Roberto, 1996. "Income distribution, political instability, and investment," European Economic Review, Elsevier, vol. 40(6), pages 1203-1228, June.
    5. Schumacher, Ingmar, 2009. "Endogenous discounting via wealth, twin-peaks and the role of technology," Economics Letters, Elsevier, vol. 103(2), pages 78-80, May.
    6. R. H. Strotz, 1955. "Myopia and Inconsistency in Dynamic Utility Maximization," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 23(3), pages 165-180.
    7. Strulik, Holger, 2012. "Patience and prosperity," Journal of Economic Theory, Elsevier, vol. 147(1), pages 336-352.
    8. Erol, Selman & Le Van, Cuong & Saglam, Cagri, 2011. "Existence, optimality and dynamics of equilibria with endogenous time preference," Journal of Mathematical Economics, Elsevier, vol. 47(2), pages 170-179, March.
    9. Michel, Philippe, 1990. "Some Clarifications on the Transversality Condition," Econometrica, Econometric Society, vol. 58(3), pages 705-723, May.
    10. Pierre-Olivier Gourinchas & Jonathan A. Parker, 2002. "Consumption Over the Life Cycle," Econometrica, Econometric Society, vol. 70(1), pages 47-89, January.
    11. Jean-Pierre Drugeon, 1998. "A model with endogenously determined cycles, discounting and growth," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 12(2), pages 349-369.
    12. Alberto Alesina & Dani Rodrik, 1994. "Distributive Politics and Economic Growth," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 109(2), pages 465-490.
    13. Ken‐Ichi Hirose & Shinsuke Ikeda, 2008. "On Decreasing Marginal Impatience," The Japanese Economic Review, Japanese Economic Association, vol. 59(3), pages 259-274, September.
    14. Von Schlicht Ekkehart, 1975. "A Neoclassical Theory of Wealth Distribution," Journal of Economics and Statistics (Jahrbuecher fuer Nationaloekonomie und Statistik), De Gruyter, vol. 189(1-2), pages 78-96, January.
    15. Fwu‐Ranq Chang, 2009. "Optimal growth and impatience: A phase diagram analysis," International Journal of Economic Theory, The International Society for Economic Theory, vol. 5(2), pages 245-255, June.
    16. John D. Hey & Gianna Lotito, 2018. "Naive, resolute or sophisticated? A study of dynamic decision making," World Scientific Book Chapters, in: Experiments in Economics Decision Making and Markets, chapter 11, pages 275-299, World Scientific Publishing Co. Pte. Ltd..
    17. Kirill Borissov, 2013. "The Existence of Equilibrium Paths in an AK-model with Endogenous Time Preferences and Borrowing Constraints," EUSP Department of Economics Working Paper Series 2013/01, European University at St. Petersburg, Department of Economics.
    18. Shafer, Wayne & Sonnenschein, Hugo, 1975. "Equilibrium in abstract economies without ordered preferences," Journal of Mathematical Economics, Elsevier, vol. 2(3), pages 345-348, December.
    19. Cagetti, Marco, 2003. "Wealth Accumulation over the Life Cycle and Precautionary Savings," Journal of Business & Economic Statistics, American Statistical Association, vol. 21(3), pages 339-353, July.
    20. Glenn W. Harrison & Morten I. Lau & Melonie B. Williams, 2002. "Estimating Individual Discount Rates in Denmark: A Field Experiment," American Economic Review, American Economic Association, vol. 92(5), pages 1606-1617, December.
    21. Akerlof, George A, 1991. "Procrastination and Obedience," American Economic Review, American Economic Association, vol. 81(2), pages 1-19, May.
    22. Meng, Qinglai, 2006. "Impatience and equilibrium indeterminacy," Journal of Economic Dynamics and Control, Elsevier, vol. 30(12), pages 2671-2692, December.
    23. Leandro Carvalho, 2010. "Poverty and Time Preference," Working Papers WR-759, RAND Corporation.
    24. Mikhail Kaganovich, 1985. "Efficiency of Sliding Plans in a Linear Model with Time-Dependent Technology," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 52(4), pages 691-702.
    25. SCHUMACHER, Ingmar, 2006. "On optimality, endogenous discounting and wealth accumulation," LIDAM Discussion Papers CORE 2006103, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    26. Hongyi Li & Heng‐fu Zou, 1998. "Income Inequality is not Harmful for Growth: Theory and Evidence," Review of Development Economics, Wiley Blackwell, vol. 2(3), pages 318-334, October.
    27. Partridge, Mark D, 1997. "Is Inequality Harmful for Growth? Comment," American Economic Review, American Economic Association, vol. 87(5), pages 1019-1032, December.
    28. Carroll, Christopher D & Overland, Jody & Weil, David N, 1997. "Comparison Utility in a Growth Model," Journal of Economic Growth, Springer, vol. 2(4), pages 339-367, December.
    29. Kirill Borissov, 2013. "The Existence of Equilibrium Paths in an AK-model with Endogenous Time Preferences and Borrowing Constraints," EUSP Department of Economics Working Paper Series Ec-01/13, European University at St. Petersburg, Department of Economics.
    30. Borissov, Kirill, 2002. "Indeterminate steady-state equilibria in a one-sector model," Economics Letters, Elsevier, vol. 77(1), pages 125-130, September.
    31. Samwick, Andrew A., 1998. "Discount rate heterogeneity and social security reform," Journal of Development Economics, Elsevier, vol. 57(1), pages 117-146, October.
    32. Bleaney, Michael & Nishiyama, Akira, 2004. "Income inequality and growth--does the relationship vary with the income level?," Economics Letters, Elsevier, vol. 84(3), pages 349-355, September.
    33. Pollak, Robert A, 1978. "Endogenous Tastes in Demand and Welfare Analysis," American Economic Review, American Economic Association, vol. 68(2), pages 374-379, May.
    34. Kirill Borissov & Stéphane Lambrecht, 2009. "Growth and distribution in an AK-model with endogenous impatience," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 39(1), pages 93-112, April.
    35. Bewley, Truman, 1982. "An integration of equilibrium theory and turnpike theory," Journal of Mathematical Economics, Elsevier, vol. 10(2-3), pages 233-267, September.
    36. Becker, Robert A. & Foias, Ciprian, 1987. "A characterization of Ramsey equilibrium," Journal of Economic Theory, Elsevier, vol. 41(1), pages 173-184, February.
    37. Persson, Torsten & Tabellini, Guido, 1994. "Is Inequality Harmful for Growth?," American Economic Review, American Economic Association, vol. 84(3), pages 600-621, June.
    38. Chen, Been-Lon, 2003. "An inverted-U relationship between inequality and long-run growth," Economics Letters, Elsevier, vol. 78(2), pages 205-212, February.
    39. Epstein, Larry G & Hynes, J Allan, 1983. "The Rate of Time Preference and Dynamic Economic Analysis," Journal of Political Economy, University of Chicago Press, vol. 91(4), pages 611-635, August.
    40. Perotti, Roberto, 1996. "Growth, Income Distribution, and Democracy: What the Data Say," Journal of Economic Growth, Springer, vol. 1(2), pages 149-187, June.
    41. Bourguignon, Francois, 1981. "Pareto Superiority of Unegalitarian Equilibria in Stiglitz' Model of Wealth Distribution with Convex Saving Function," Econometrica, Econometric Society, vol. 49(6), pages 1469-1475, November.
    42. Olivier Jean Blanchard & Stanley Fischer, 1989. "Lectures on Macroeconomics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262022834, April.
    43. Lawrance, Emily C, 1991. "Poverty and the Rate of Time Preference: Evidence from Panel Data," Journal of Political Economy, University of Chicago Press, vol. 99(1), pages 54-77, February.
    44. Barro, Robert J, 2000. "Inequality and Growth in a Panel of Countries," Journal of Economic Growth, Springer, vol. 5(1), pages 5-32, March.
    45. Michael Stern, 2006. "Endogenous time preference and optimal growth," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 29(1), pages 49-70, September.
    46. Thaler, Richard H, 1994. "Psychology and Savings Policies," American Economic Review, American Economic Association, vol. 84(2), pages 186-192, May.
    47. Das, Mausumi, 2003. "Optimal growth with decreasing marginal impatience," Journal of Economic Dynamics and Control, Elsevier, vol. 27(10), pages 1881-1898, August.
    48. John D. Hey & Luca Panaccione, 2018. "Dynamic decision making: what do people do?," World Scientific Book Chapters, in: Experiments in Economics Decision Making and Markets, chapter 10, pages 235-273, World Scientific Publishing Co. Pte. Ltd..
    49. repec:bla:rdevec:v:2:y:1998:i:3:p:318-34 is not listed on IDEAS
    50. Kristin J. Forbes, 2000. "A Reassessment of the Relationship between Inequality and Growth," American Economic Review, American Economic Association, vol. 90(4), pages 869-887, September.
    51. Nicholas S. Souleles, 1999. "The Response of Household Consumption to Income Tax Refunds," American Economic Review, American Economic Association, vol. 89(4), pages 947-958, September.
    52. S. M. Goldman, 1968. "Optimal Growth and Continual Planning Revision," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 35(2), pages 145-154.
    53. Lusardi, Annamaria, 1996. "Permanent Income, Current Income, and Consumption: Evidence from Two Panel Data Sets," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(1), pages 81-90, January.
    54. Robert A. Becker, 1980. "On the Long-Run Steady State in a Simple Dynamic Model of Equilibrium with Heterogeneous Households," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 95(2), pages 375-382.
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    Cited by:

    1. Borissov, Kirill & Hashimzade, Nigar, 2022. "Fiscal policy and inequality in a model with endogenous positional concerns," Journal of Mathematical Economics, Elsevier, vol. 103(C).
    2. Ken-Ichi Hirose & Shinsuke Ikeda, 2015. "Decreasing Marginal Impatience and Capital Accumulation in a Two-Country World Economy," Metroeconomica, Wiley Blackwell, vol. 66(3), pages 474-507, July.
    3. Kirill Borissov & Mikhail Pakhnin & Ronald Wendner, 2020. "Naive Agents with Quasi-hyperbolic Discounting and Perfect Foresight," EUSP Department of Economics Working Paper Series 2020/03, European University at St. Petersburg, Department of Economics.
    4. Borissov, Kirill & Pakhnin, Mikhail & Wendner, Ronald, 2021. "The Neoclassical Growth Model with Time-Inconsistent Decision Making and Perfect Foresight," MPRA Paper 108336, University Library of Munich, Germany.
    5. Borissov, Kirill & Pakhnin, Mikhail & Wendner, Ronald, 2024. "General equilibrium and dynamic inconsistency," Journal of Mathematical Economics, Elsevier, vol. 114(C).
    6. Borissov, K. & Pakhnin, M., 2018. "A Division of Society into the Rich and the Poor: Some Approaches to Modeling," Journal of the New Economic Association, New Economic Association, vol. 40(4), pages 32-59.
    7. Kirill Borissov & Mikhail Pakhnin & Ronald Wendner, 2024. "Present-Biased Envy, Inequality, and Growth," CESifo Working Paper Series 11090, CESifo.
    8. Borissov, Kirill, 2016. "The Rich And The Poor In A Simple Model Of Growth And Distribution," Macroeconomic Dynamics, Cambridge University Press, vol. 20(7), pages 1934-1952, October.
    9. Borissov, Kirill & Pakhnin, Mikhail & Wendner, Ronald, 2024. "General equilibrium and dynamic inconsistency," Journal of Mathematical Economics, Elsevier, vol. 114(C).

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    More about this item

    Keywords

    AK-model; Income Distribution; Endogenous Time Preferences;
    All these keywords.

    JEL classification:

    • D90 - Microeconomics - - Micro-Based Behavioral Economics - - - General
    • O41 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - One, Two, and Multisector Growth Models

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