HETEROGENOUS AGENTS AND INCOMPLETE MARKETS: AN EXPLORATION
Keywords:
Heterogenous agents, incomplete markets, Huggett economy, Krusell-Smith economy, Aiyagari model
Abstract
This paper will review the issue of heterogeneity of agents and incomplete markets in macroeconomics. Central idea of this paper is the notion that representative agent models were wrong turn for modern macroeconomics especially for general equilibrium model (some individuals are some are not liquidity constrained) and that central problems of macroeconomics cannot arise in representative agent models (debt, bankruptcy, asymmetric information) as has also being criticized by Stiglitz (2017).And finally main motivation for this paper were Achdou et al.(2022) who developed algorithm for “solving equilibria in Aiyagari–Bewley–Huggett economy” and Krusell-Smith (1998) comparison of economy behavior when incomplete markets (heterogeneous agents) and complete markets (representative agent) economy.
References
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5. Applebaum, D.(2004). Lèvy Procesess and Stochastic Calculus. Cambridge University Press, Cambrigde, UK.
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11. Auerbach, A. J. Kotlikoff, L. J. (1983). National Savings, Economic Welfare, and the Structure of Taxation. In M. Feldstein (Ed.), Behavioral Simulation Methods in Tax Policy Analysis, pp. 459–498. University of Chicago Press.
12. Bassetto, M. (1999). Optimal fiscal policy with heterogeneous agents. Report, Northwestern University. Available at http://www.nber.org/~bassetto/opttax.html. [678, 679]
13. Bellman R. (1954). Dynamic programming and a new formalism in the calculus of variations. Proc Natl Acad Sci U S A. 1954 Apr;40(4):231-5. doi: 10.1073/pnas.40.4.231. PMID: 16589462; PMCID: PMC527981.
14. Bellman, R. E. (1957). Dynamic Programming. Princeton, NJ.
15. Bellman, R.; Dreyfus, S. (1959). An Application of Dynamic Programming to the Determination of Optimal Satellite Trajectories. J. Br. Interplanet. Soc. 17: pp.78–83.
16. Benhabib, J., A. Bisin, S. Zhu (2015). The Wealth Distribution in Bewley Economies with Capital Income Risk, Journal of Economic Theory, 159(PA), 489{515.
17. Bernanke, B. S., Lown, C. S., & Friedman, B. M. (1991). The Credit Crunch. Brookings Papers on Economic Activity, 1991(2), 205–247. https://doi.org/10.2307/2534592
18. Bewley, T. (1986). Stationary monetary equilibrium with a continuum of independently fluctuating consumers. Contributions to mathematical economics in honor of Gérard Debreu, 79.
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21. Boppart,T.,Krusell,P.Mitman,K.(2018).Exploiting MIT shocks in heterogeneous-agent economies: the impulse response as a numerical derivative. Journal of Economic Dynamics and Control,Volume 89,pp. 68-92
22. Brito,D.L.,Hamilton,J.H.,Slutsky,S.M,Stiglitz,J.E.(1995).Randomization in optimal income tax schedules, Journal of Public Economics,Volume 56, Issue 2
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24. Diamond,P,Mirrlees,J.A.(1978).A model of social insurance with variable retirement, Journal of Public Economics,Volume 10, Issue 3, pp. 295-336
25. Fokker, A. D. (1914). Die mittlere Energie rotierender elektrischer Dipole im Strahlungsfeld. Ann. Phys. 348 (4. Folge 43):pp. 810–820.
26. Geanakoplos, J. (1990). An introduction to general equilibrium with incomplete asset markets. Journal of Mathematical Economics, 19(1-2), pp. 1–38.
27. Geanakoplos, J.D.; Polemarchakis, H.M. (1986). Existence, regularity and constrained suboptimality of competitive allocations when the asset structure is incomplete. In Hell, W.P.; Starr, R.M.; Starrett, D.A. (eds.). Uncertainty, information and communication: Essays in honor of K.J. Arrow. Vol. 3. Cambridge University Press. pp. 65–95. ISBN 9780521327046.
28. Greenwood, J., Hercowitz, Z., Krusell, P. (2000).The role of investment-specific technological change in the business cycle, European Economic Review, 44(1), pp.91-115.
29. Guerrieri, V., G. Lorenzoni, L. Straub, and I. Werning (2020). Macroeconomic Implications of COVID-19: Can Negative Supply Shocks Cause Demand Shortages? NBER Working Paper 26918.
30. Heathcote,J., Storesletten, K., Violante, G. L.(2009). Quantitative Macroeconomics with Heterogeneous Households. Annual Review of Economics, 1(1), pp.319–354. doi: 10.1146/annurev.economics.05
31. Hopenhayn, H. A. (1992). Entry, Exit, and firm Dynamics in Long Run Equilibrium. Econometrica, 60(5), 1127–1150. https://doi.org/10.2307/2951541
32. Huggett, M. (1993). The Risk-Free Rate in Heterogeneous-Agent Incomplete Insurance Economies, Journal of Economic Dynamics and Control 17, pp.953–969
33. Itô,K.(1951). On stochastic differential equations. Memoirs, American Mathematical Society 4,pp. 1–51. Online
34. Jacobsen.M(1996). Laplace and the Origin of the Ornstein-Uhlenbeck Process. Bernoulli, Vol. 2, No. 3. (Sept. 1996), pp. 271 – 286.
35. Johnson, David S., Jonathan A. Parker, and Nicholas S. Souleles.(2004).The Response of Consumer Spending to the Randomized Income Tax Rebates of 2001. Bureau of Labor Statistics, Princeton University, and University of Pennsylvania (February)
36. Judd, K. L. (1985). Short-Run Analysis of Fiscal Policy in a Simple Perfect Foresight Model.Journal of Political Economy 93, pp.298–319.
37. Kaplan, G., B. Moll, G. L. Violante (2018). Monetary Policy According to HANK. American Economic Review 108, pp.697–743.
38. Kolmogorov,A.(1931). Über die analytischen Methoden in der Wahrscheinlichkeitstheorie [On Analytical Methods in the Theory of Probability]. Mathematische Annalen (in German). 104 (1): 415–458 [pp. 448–451].
39. Krusell, P., A. A. Smith (1998).Income and Wealth Heterogeneity in the Macroeconomy,Journal of Political Economy, 106(5), pp.867-896.
40. Kydland, F. E., Prescott, E. C. (1982). Time to Build and Aggregate Fluctuations. Econometrica, 50(6), 1345–1370. https://doi.org/10.2307/1913386
41. Lucas, R.E., (1978). Asset prices in an exchange economy, Econometrica 46, 142991445
42. Lucas, RE. (1987). Models of Business Cycles. New York: Basil Blackwell.
43. Maliar, L. Maliar,S.Valli,F.(2010).Solving the incomplete markets model with aggregate uncertainty using the Krusell–Smith algorithm. Journal of Economic Dynamics and Control, Vol.34.Issue1, pp.42-49
44. Misra, K., and Surico, P. (2014). Consumption, income changes, and heterogeneity: Evidence from two fiscal stimulus programs. American Economic Journal: Macroeconomics 6, no. 4: pp.84-106.
45. Mukoyama,T.(2021).MIT shocks imply market incompleteness, Economics Letters,Volume 198
46. Piketty, T. (2014). Capital in the Twenty-First Century, Belknap Press, Cambridge, MA
47. Planck, M. (1917). Über einen Satz der statistischen Dynamik und seine Erweiterung in der Quantentheorie. Sitzungsberichte der Preussischen Akademie der Wissenschaften zu Berlin. 24: pp.324–341.
48. Pratt, John W. (1964). Risk Aversion in the Small and in the Large. Econometrica. 32 (1/2): pp.122–136.
49. Ragot, X., Grand, F. L. (2017). Optimal Fiscal Policy with Heterogeneous Agents and Aggregate Shocks, 2017 Meeting Papers 969, Society for Economic Dynamics.
50. Revuz,D. Yor, M. (2005). Continuous Martingales and Brownian Motion, Third Edition Corrected. Volume 293, Grundlehren der mathematischen Wissenschaften. Springer, Berlin, 2005.
51. Robbin, Joel W. (2010), Continuity and Uniform Continuity, UW-Madison Department of Mathematics
52. Rudin,W. (1987). Real & Complex Analysis. McGraw-Hill.
53. Stiglitz, J.E. (1982). Self-selection and Pareto efficient taxation, Journal of Public Economics 17, pp.213-240
54. Stiglitz, J.E. (2017). Where modern macroeconomics went wrong, NBER
55. Storesletten K, Telmer CI, Yaron A. (2001). The welfare cost of business cycles revisited: finite lives and cyclical variation in idiosyncratic risk. Eur. Econ. Rev. 45(7): pp.1311–1139
56. Taub, B., (1988). Efficiency in a pure currency economy with inflation, Economic Inquiry 26, pp.567-583
57. Weiss, L.W. (1976) The desirability of cheating incentives and randomness in the optimal income tax, Journal of Political Economy 89, pp.1343-1352.
Web sites:
1. Benjamin Moll Heterogeneous Agent Models in Continuous Time: https://benjaminmoll.com/codes/
2. Achdou, Y. Han, J. Lasry, J-M. Lions, P-L. Moll, B.(2022). Income and Wealth Distribution in Macroeconomics: A Continuous-Time Approach, The Review of Economic Studies,Volume 89,Issue 1,Pages 45-86
3. Aiyagari, S. R. (1994). Uninsured Idiosyncratic Risk and Aggregate Saving," The Quarterly Journal of Economics, 109(3), pp.659-84
4. Akerlof,G.A.(1978).The Economics of "Tagging" as Applied to the Optimal Income Tax, Welfare Programs, and Manpower Planning, The American Economic Review, Vol. 68, No. 1 (Mar., 1978), pp. 8-19
5. Applebaum, D.(2004). Lèvy Procesess and Stochastic Calculus. Cambridge University Press, Cambrigde, UK.
6. Arnott, R.J. Stiglitz, J.E (1988). Randomization with asymmetric information: A simplified exposition, RAND Journal of Economics 19, pp.344-362.
7. Arrow, J. (1951). An Extension of the Basic Theorems of Classical Welfare Economics. In J. Neyman (ed.), Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability (p./pp. 507--532), : University of California Press.
8. Arrow, K. (1953). The Role of Securities in the Optimal Allocation of Risk Bearing, Review of Economic Studies, 1964, 31,pp. 91-96.
9. Arrow, K. J. (1965). Aspects of the Theory of Risk Bearing. The Theory of Risk Aversion. Helsinki: Yrjo Jahnssonin Saatio. Reprinted in: Essays in the Theory of Risk Bearing, Markham Publ. Co., Chicago, 1971, pp.90–109.
10. Arrow, Kenneth J.; Debreu, Gérard (1954). Existence of an equilibrium for a competitive economy. Econometrica. The Econometric Society. 22 (3): 265–90. doi:10.2307/1907353. JSTOR 1907353
11. Auerbach, A. J. Kotlikoff, L. J. (1983). National Savings, Economic Welfare, and the Structure of Taxation. In M. Feldstein (Ed.), Behavioral Simulation Methods in Tax Policy Analysis, pp. 459–498. University of Chicago Press.
12. Bassetto, M. (1999). Optimal fiscal policy with heterogeneous agents. Report, Northwestern University. Available at http://www.nber.org/~bassetto/opttax.html. [678, 679]
13. Bellman R. (1954). Dynamic programming and a new formalism in the calculus of variations. Proc Natl Acad Sci U S A. 1954 Apr;40(4):231-5. doi: 10.1073/pnas.40.4.231. PMID: 16589462; PMCID: PMC527981.
14. Bellman, R. E. (1957). Dynamic Programming. Princeton, NJ.
15. Bellman, R.; Dreyfus, S. (1959). An Application of Dynamic Programming to the Determination of Optimal Satellite Trajectories. J. Br. Interplanet. Soc. 17: pp.78–83.
16. Benhabib, J., A. Bisin, S. Zhu (2015). The Wealth Distribution in Bewley Economies with Capital Income Risk, Journal of Economic Theory, 159(PA), 489{515.
17. Bernanke, B. S., Lown, C. S., & Friedman, B. M. (1991). The Credit Crunch. Brookings Papers on Economic Activity, 1991(2), 205–247. https://doi.org/10.2307/2534592
18. Bewley, T. (1986). Stationary monetary equilibrium with a continuum of independently fluctuating consumers. Contributions to mathematical economics in honor of Gérard Debreu, 79.
19. Bewley, T., (1980). The optimum quantity of money, in: J. Kareken and N. Wallace, eds., Models of monetary economies (Federal Reserve Bank of Minneapolis, Minneapolis, MN).
20. Boar, C. V. Midrigan (2020). Efficient Redistribution. mimeo. New York University.
21. Boppart,T.,Krusell,P.Mitman,K.(2018).Exploiting MIT shocks in heterogeneous-agent economies: the impulse response as a numerical derivative. Journal of Economic Dynamics and Control,Volume 89,pp. 68-92
22. Brito,D.L.,Hamilton,J.H.,Slutsky,S.M,Stiglitz,J.E.(1995).Randomization in optimal income tax schedules, Journal of Public Economics,Volume 56, Issue 2
23. Chien, Y., Wen, Y. (2020). Optimal Ramsey Taxation in Heterogeneous Agent Economies with Quasi-Linear Preferences, Working Papers 2019-007D, Federal Reserve Bank of St. Louis.
24. Diamond,P,Mirrlees,J.A.(1978).A model of social insurance with variable retirement, Journal of Public Economics,Volume 10, Issue 3, pp. 295-336
25. Fokker, A. D. (1914). Die mittlere Energie rotierender elektrischer Dipole im Strahlungsfeld. Ann. Phys. 348 (4. Folge 43):pp. 810–820.
26. Geanakoplos, J. (1990). An introduction to general equilibrium with incomplete asset markets. Journal of Mathematical Economics, 19(1-2), pp. 1–38.
27. Geanakoplos, J.D.; Polemarchakis, H.M. (1986). Existence, regularity and constrained suboptimality of competitive allocations when the asset structure is incomplete. In Hell, W.P.; Starr, R.M.; Starrett, D.A. (eds.). Uncertainty, information and communication: Essays in honor of K.J. Arrow. Vol. 3. Cambridge University Press. pp. 65–95. ISBN 9780521327046.
28. Greenwood, J., Hercowitz, Z., Krusell, P. (2000).The role of investment-specific technological change in the business cycle, European Economic Review, 44(1), pp.91-115.
29. Guerrieri, V., G. Lorenzoni, L. Straub, and I. Werning (2020). Macroeconomic Implications of COVID-19: Can Negative Supply Shocks Cause Demand Shortages? NBER Working Paper 26918.
30. Heathcote,J., Storesletten, K., Violante, G. L.(2009). Quantitative Macroeconomics with Heterogeneous Households. Annual Review of Economics, 1(1), pp.319–354. doi: 10.1146/annurev.economics.05
31. Hopenhayn, H. A. (1992). Entry, Exit, and firm Dynamics in Long Run Equilibrium. Econometrica, 60(5), 1127–1150. https://doi.org/10.2307/2951541
32. Huggett, M. (1993). The Risk-Free Rate in Heterogeneous-Agent Incomplete Insurance Economies, Journal of Economic Dynamics and Control 17, pp.953–969
33. Itô,K.(1951). On stochastic differential equations. Memoirs, American Mathematical Society 4,pp. 1–51. Online
34. Jacobsen.M(1996). Laplace and the Origin of the Ornstein-Uhlenbeck Process. Bernoulli, Vol. 2, No. 3. (Sept. 1996), pp. 271 – 286.
35. Johnson, David S., Jonathan A. Parker, and Nicholas S. Souleles.(2004).The Response of Consumer Spending to the Randomized Income Tax Rebates of 2001. Bureau of Labor Statistics, Princeton University, and University of Pennsylvania (February)
36. Judd, K. L. (1985). Short-Run Analysis of Fiscal Policy in a Simple Perfect Foresight Model.Journal of Political Economy 93, pp.298–319.
37. Kaplan, G., B. Moll, G. L. Violante (2018). Monetary Policy According to HANK. American Economic Review 108, pp.697–743.
38. Kolmogorov,A.(1931). Über die analytischen Methoden in der Wahrscheinlichkeitstheorie [On Analytical Methods in the Theory of Probability]. Mathematische Annalen (in German). 104 (1): 415–458 [pp. 448–451].
39. Krusell, P., A. A. Smith (1998).Income and Wealth Heterogeneity in the Macroeconomy,Journal of Political Economy, 106(5), pp.867-896.
40. Kydland, F. E., Prescott, E. C. (1982). Time to Build and Aggregate Fluctuations. Econometrica, 50(6), 1345–1370. https://doi.org/10.2307/1913386
41. Lucas, R.E., (1978). Asset prices in an exchange economy, Econometrica 46, 142991445
42. Lucas, RE. (1987). Models of Business Cycles. New York: Basil Blackwell.
43. Maliar, L. Maliar,S.Valli,F.(2010).Solving the incomplete markets model with aggregate uncertainty using the Krusell–Smith algorithm. Journal of Economic Dynamics and Control, Vol.34.Issue1, pp.42-49
44. Misra, K., and Surico, P. (2014). Consumption, income changes, and heterogeneity: Evidence from two fiscal stimulus programs. American Economic Journal: Macroeconomics 6, no. 4: pp.84-106.
45. Mukoyama,T.(2021).MIT shocks imply market incompleteness, Economics Letters,Volume 198
46. Piketty, T. (2014). Capital in the Twenty-First Century, Belknap Press, Cambridge, MA
47. Planck, M. (1917). Über einen Satz der statistischen Dynamik und seine Erweiterung in der Quantentheorie. Sitzungsberichte der Preussischen Akademie der Wissenschaften zu Berlin. 24: pp.324–341.
48. Pratt, John W. (1964). Risk Aversion in the Small and in the Large. Econometrica. 32 (1/2): pp.122–136.
49. Ragot, X., Grand, F. L. (2017). Optimal Fiscal Policy with Heterogeneous Agents and Aggregate Shocks, 2017 Meeting Papers 969, Society for Economic Dynamics.
50. Revuz,D. Yor, M. (2005). Continuous Martingales and Brownian Motion, Third Edition Corrected. Volume 293, Grundlehren der mathematischen Wissenschaften. Springer, Berlin, 2005.
51. Robbin, Joel W. (2010), Continuity and Uniform Continuity, UW-Madison Department of Mathematics
52. Rudin,W. (1987). Real & Complex Analysis. McGraw-Hill.
53. Stiglitz, J.E. (1982). Self-selection and Pareto efficient taxation, Journal of Public Economics 17, pp.213-240
54. Stiglitz, J.E. (2017). Where modern macroeconomics went wrong, NBER
55. Storesletten K, Telmer CI, Yaron A. (2001). The welfare cost of business cycles revisited: finite lives and cyclical variation in idiosyncratic risk. Eur. Econ. Rev. 45(7): pp.1311–1139
56. Taub, B., (1988). Efficiency in a pure currency economy with inflation, Economic Inquiry 26, pp.567-583
57. Weiss, L.W. (1976) The desirability of cheating incentives and randomness in the optimal income tax, Journal of Political Economy 89, pp.1343-1352.
Web sites:
1. Benjamin Moll Heterogeneous Agent Models in Continuous Time: https://benjaminmoll.com/codes/
Published
2022-12-23
Section
Articles
