Document Type : Research Article


RANEPA, Moscow, Russian Federation


Modern research often requires the use of economic models with multiple agents that interact over time. In this paper we research overlapping generations models, hereinafter OLG. In these models, the phenomenon of the multiplicity of long-term equilibrium may arise. This fact proves to be important for the theoretical justification of some economic effects, such as the collapse of the market and others. However, there is little theoretical research on the possibility of multiple equilibria in these models. At the same time, the works that exist are devoted to models with only few periods. This is due to the fact that the complexity of algorithms that calculate all long-term equilibria grows too fast with realistically selected lifespan values. However, solutions of some OLG models after the introduction of additional variables can become polynomial systems. Thus it is possible to represent many long-term equilibria as an algebraic variety. In particular, the Gr¨obner basis method became popular. However, this approach can only be used effectively when there are few variables. In this paper we consider the task of finding long-term equilibrium in overlapping generations models with many periods. We offer an algorithm for finding the system’s solutions and use it to investigate the presence of multiple solutions in realistically calibrated models with long-lived agents. We also examine these models for multiple equilibria using the Monte Carlo method and replicate previously known results using a new algorithm.


[1] Altig A.,Auerbach A.,Kotlikoff L., 2001, Simulating fundamental tax reform in the United
States American Economic Review, 91 (3), 574-595.
[2] Auerbach A.,Kotlikoff L., 1987, Evaluating fiscal policy with a dynamic simulation model,
The American Economic Review, 77(2) 49-55.
[3] Auerbach A.,Kotlikoff L., National savings, economic welfare, and the structure of taxation,
1983, Behavioral simulation methods in tax policy analysis, 459-498
[4] Basak S.,Cass D.,Manuel J.,Pavlova A., 2006, Multiplicity in General Financial Equilibrium
with Portfolio Constraints, Institute for Economic Research (PIER) Working Paper Series.
[5] Basiri A.,Riahi M”
Kubler F.,Rahmany S., 2023, Efficient Calculation of All Steady States
in Large-Scale Overlapping Generations Models, Journal of Mathematics and Modeling in
[6] Becker T.,Weispfenning V., 2012, Gr¨obner bases: a computational approach to commutative
algebra, Springer Science & Business Media, 141.
[7] Bovenberg L.,Heijdra B. 1998, Environmental tax policy and intergenerational distribution,
Journal of Public Economics, 67, 1-24.
[8] Carvalho O., 2017, A simple recursive algorithm to find all real roots of a polynomial, Researchgate.
[9] Fried S”
Novan K.,Peterman W., 2018, The distributional effects of a carbon tax on current
and future generations, Review of Economic Dynamics, 30, 30-46.
[10] Hong H.,Stein J., 2003, Differences of Opinion, Short-Sales Constraints, and Market Crashes,
Review of Financial Studies, 16, 487-525.
[11] Kehoe, T.,Levine D., 1990, The economics of indeterminacy in overlapping generations models, Journal of Public Economics, 42, 219-243.
[12] Kotlikoff L.,Kubler F.,Polbin A.,Sachs J.,Scheidegger S., 2021, Making carbon taxation a
generational win win, International Economic Review, 62(1), 3-46.
[13] Kotlikoff L.,Smetters K.,Walliser J., 2007, Mitigating America’s demographic dilemma by
pre-funding social security, Journal of monetary Economics, 54, 247-266.
[14] Kubler F.,Schmedders K., 2010, Tackling multiplicity of equilibria with Gr¨obner bases, Operations research, 58(4-part2), 1037-1050.
[15] Kubler F.,Schmedders K., 2010, Uniqueness of steady states in models with overlapping
generations, Journal of the European Economic Association, 8(2-3), 635-644.
[16] Summers L., 1981, Capital Taxation and Accumulation in a Life Cycle Growth Model, The
American Economic Review, 71, 533-544.