A Tractable Overlapping Generations Structure for Quantitative DSGE Models

Kollmann, Robert (2022): A Tractable Overlapping Generations Structure for Quantitative DSGE Models.

Abstract

This paper develops a novel tractable overlapping generations (OLG) structure that is suitable for use in rich quantitative dynamic stochastic general equilibrium (DSGE) models. The OLG structure assumes that newborn agents receive a wealth transfer such that that their equilibrium consumption represents a time-invariant share of aggregate consumption. Under efficient risk sharing across contemporaneous cohorts, this implies that aggregate consumption obeys a (quasi-)Euler equation that is isomorphic to the Euler equation of an infinitely-lived representative agent. As a result, DSGE models, with the proposed OLG structure, can be solved as conveniently as standard DSGE models with infinitely-lived representative agents. The great tractability of the OLG structure here constitutes an important advantage over conventional OLG models, especially when agents are long-lived. While highly tractable, the present OLG structure maintains key predictions of standard OLG models, namely the possibility of low (even negative) real interest rates and of equilibrium indeterminacy.

• Item Type: MPRA Paper
• Language: English
• Keywords: overlapping generations; dynamic stochastic general equilibrium models; Euler equation; subjective discount factor; transversality condition; multiple equilibria.
• Subjects: C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling; E - Macroeconomics and Monetary Economics > E1 - General Aggregative Models; E - Macroeconomics and Monetary Economics > E3 - Prices, Business Fluctuations, and Cycles

References

Albonico, Alice, Guido Ascari and Alessandro Gobbi, 2021. The Public Debt Multiplier. Journal of Economic Dynamics & Control 132, Article 104204

Allais, Maurice, 1947. Economie et Intérêt. Paris: Imprimerie Nationale.

Auerbach, Alan and Laurence Kotlikoff, 1987. Dynamic Fiscal Policy. Cambridge University Press.

Blanchard, Olivier and Charles Kahn, 1980. The Solution of Linear Difference Models under Rational Expectations. Econometrica 48, 1305-1311.

Blanchard, Olivier, 1985. Debt, Deficits and Finite Horizons, Journal of Political Economy 93, 223-247.

Carvalho, Carlos, Andrea Ferrero and Fernanda Nechio, 2016. Demographics and Real Interest Rates: Inspecting the Mechanism. European Economic Review 88, 208-226.

d’Albis, Hippolyte, Carole Bonnet, Xavier Chojnicki, Najat El Mekkaoui, Angela Greulich, Jérôme Hubert and Julien Navaux, 2019. Financing the Consumption of the Young and Old in France. Population and Development Review 45, 103-132.

Devereux, Michael B., 2011. Fiscal Deficits, Debt, and Monetary Policy in a Liquidity Trap. In: Monetary Policy under Financial Turbulence (L. Céspedes, R. Chang and D. Saraiva, eds.). Central Bank of Chile. 369-410.

Eichenbaum, Martin, Lars Peter Hansen and Kenneth Singleton, 1988. A Time Series Analysis of Representative Agent Models of Consumption and Leisure Choice Under Uncertainty. Quarterly Journal of Economics 103, 51-78.

Galí, Jordi, 2015. Monetary Policy, Inflation, and the Business Cycle (2nd ed.). Princeton University Press.

Guesnerie, Roger and Michael Woodford, 1992. Endogenous Fluctuations. In: Advances in Economic Theory: Sixth World Congress (J.-J. Laffont, ed.). Cambridge University Press, Vol. II. 289-412.

King, Robert and Sergio Rebelo, 1999. Resuscitating Real Business Cycles. In: Handbook of Macroeconomics (J. Taylor and M. Woodford, eds.), Elsevier, Vol. 1B, 927-1007.

Kollmann, Robert, 2021a. Liquidity Traps in a World Economy. Journal of Economic Dynamics & Control 132, Article 104206.

Kollmann, Robert, 2021b. Liquidity Traps in a Monetary Union. Oxford Economic Papers 73, 1581-1603.

Kollmann, Robert, 2021c. Effects of Covid-19 on Euro Area GDP and Inflation: Demand vs. Supply Disturbances. International Economics and Economic Policy 18, 475-492.

Kollmann, Robert, 2022. Speculative Bubbles and Aggregate Boom Bust Cycles. Working Paper, Université Libre de Bruxelles.

Mc Morrow, Kieran and Werner Roeger, 2004. The Economic and Financial Market Consequences of Global Ageing. Springer Verlag.

Niepelt, Dirk, 2019. Macroeconomic Analysis. MIT Press.

Papetti, Andrea, 2021. Demographics and the Natural Real Interest Rate: Historical and Projected Paths for the Euro Area. Journal of Economic Dynamics & Control 132, Article 104209.

Saito, Makoto, 2001. An Empirical Investigation of Intergenerational Consumption Distribution: Comparison among Japan, the United States, and the United Kingdom. In: Aging Issues in the United States and Japan (S. Ogura, T. Tachibanaki and D. Wise, eds.). University of Chicago Press, pp.135-167.

Samuelson, Paul, 1958. An Exact Consumption-Loan Model of Interest With and Without the Social Contrivance of Money. Journal of Political Economy 66, 467-482.

Weil, Philippe, 2008. Overlapping Generations: The First Jubilee. Journal of Economic Perspectives 22, 115-134.

Wieland, V., E. Afanasyeva, M. Kuete and J. Yoo, 2016. New Methods for Macro-Financial Model Comparison and Policy Analysis. In: Handbook of Macroeconomics (J. Taylor and H. Uhlig. eds.), Elsevier, Vol. 2, 1574-1319.