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Chaos and Unpredictability in Dynamic Social Problems

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  • Marco Battaglini

Abstract

We study a dynamic model of environmental protection in which the level of pollution is a state variable that strategically links policy making periods. Policymakers are forward looking but politically motivated: they have heterogeneous preferences and do not fully internalize the cost of pollution. This type of political economy model is often reduced to a "modified" planner's problem, and yields predictions that are qualitatively similar to a planner's constrained optimum, albeit with a bias: too much pollution in the steady state (or, in other applications, too little investment in public goods, too much public debt, etc.). We highlight conditions under which this reduction is not possible, and the dynamic time inconsistency generated by the political process is responsible for a new type of distortion. Under these conditions, there are equilibria in which, for a generic economy and generic initial conditions, the state evolves in complex cycles, or unpredictable chaotic dynamics. Depending on the fundamentals of the economy, these equilibria may generate ergodic distributions that consistently overshoot the planner's steady state of pollution, or that fluctuate around it.

Suggested Citation

  • Marco Battaglini, 2021. "Chaos and Unpredictability in Dynamic Social Problems," NBER Working Papers 28347, National Bureau of Economic Research, Inc.
  • Handle: RePEc:nbr:nberwo:28347
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    1. Leslie M. Marx & Steven A. Matthews, 2000. "Dynamic Voluntary Contribution to a Public Project," Review of Economic Studies, Oxford University Press, vol. 67(2), pages 327-358.
    2. Marco Battaglini & Stephen Coate, 2008. "A Dynamic Theory of Public Spending, Taxation, and Debt," American Economic Review, American Economic Association, vol. 98(1), pages 201-236, March.
    3. Baumol, William J & Benhabib, Jess, 1989. "Chaos: Significance, Mechanism, and Economic Applications," Journal of Economic Perspectives, American Economic Association, vol. 3(1), pages 77-105, Winter.
    4. Gale, David, 1973. "Pure exchange equilibrium of dynamic economic models," Journal of Economic Theory, Elsevier, vol. 6(1), pages 12-36, February.
    5. Alberto Alesina, 1988. "Macroeconomics and Politics," NBER Chapters, in: NBER Macroeconomics Annual 1988, Volume 3, pages 13-62, National Bureau of Economic Research, Inc.
    6. Francois Melese & William Transue, 1987. "Unscrambling Chaos through Thick and Thin: An Explanation," The Quarterly Journal of Economics, Oxford University Press, vol. 102(1), pages 171-171.
    7. Jinhui H. Bai & Roger Lagunoff, 2011. "On the Faustian Dynamics of Policy and Political Power," Review of Economic Studies, Oxford University Press, vol. 78(1), pages 17-48.
    8. Fershtman, Chaim & Nitzan, Shmuel, 1991. "Dynamic voluntary provision of public goods," European Economic Review, Elsevier, vol. 35(5), pages 1057-1067, July.
    9. E. S. Phelps & R. A. Pollak, 1968. "On Second-Best National Saving and Game-Equilibrium Growth," Review of Economic Studies, Oxford University Press, vol. 35(2), pages 185-199.
    10. Chatterjee, Satyajit & Eyigungor, Burcu, 2016. "Continuous Markov equilibria with quasi-geometric discounting," Journal of Economic Theory, Elsevier, vol. 163(C), pages 467-494.
    11. Rodrigo Harrison & Roger Lagunoff, 2017. "Dynamic Mechanism Design For A Global Commons," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 58(3), pages 751-782, August.
    12. Marco Battaglini & Salvatore Nunnari & Thomas R. Palfrey, 2014. "Dynamic Free Riding with Irreversible Investments," American Economic Review, American Economic Association, vol. 104(9), pages 2858-2871, September.
    13. Reichlin, Pietro, 1986. "Equilibrium cycles in an overlapping generations economy with production," Journal of Economic Theory, Elsevier, vol. 40(1), pages 89-102, October.
    14. David Levhari & Leonard J. Mirman, 1980. "The Great Fish War: An Example Using a Dynamic Cournot-Nash Solution," Bell Journal of Economics, The RAND Corporation, vol. 11(1), pages 322-334, Spring.
    15. Alexandre Scheinkman, Jose, 1976. "On optimal steady states of n-sector growth models when utility is discounted," Journal of Economic Theory, Elsevier, vol. 12(1), pages 11-30, February.
    16. ,, 2014. "A dynamic theory of electoral competition," Theoretical Economics, Econometric Society, vol. 9(2), May.
    17. Rodrigo Harrison & Roger Lagunoff, 2017. "Dynamic Mechanism Design For A Global Commons," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 58, pages 751-782, August.
    18. Marco Battaglini & Bård Harstad, 2016. "Participation and Duration of Environmental Agreements," Journal of Political Economy, University of Chicago Press, vol. 124(1), pages 160-204.
    19. Day, Richard H. & Shafer, Wayne, 1987. "Ergodic fluctuations in deterministic economic models," Journal of Economic Behavior & Organization, Elsevier, vol. 8(3), pages 339-361, September.
    20. Benhabib, Jess & Day, Richard H., 1982. "A characterization of erratic dynamics in, the overlapping generations model," Journal of Economic Dynamics and Control, Elsevier, vol. 4(1), pages 37-55, November.
    21. Bård Harstad, 2012. "Buy Coal! A Case for Supply-Side Environmental Policy," Journal of Political Economy, University of Chicago Press, vol. 120(1), pages 77-115.
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    1. Deng, Liuchun & Khan, M. Ali & Mitra, Tapan, 2022. "Continuous unimodal maps in economic dynamics: On easily verifiable conditions for topological chaos," Journal of Economic Theory, Elsevier, vol. 201(C).

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    More about this item

    JEL classification:

    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
    • D72 - Microeconomics - - Analysis of Collective Decision-Making - - - Political Processes: Rent-seeking, Lobbying, Elections, Legislatures, and Voting Behavior
    • D78 - Microeconomics - - Analysis of Collective Decision-Making - - - Positive Analysis of Policy Formulation and Implementation
    • H23 - Public Economics - - Taxation, Subsidies, and Revenue - - - Externalities; Redistributive Effects; Environmental Taxes and Subsidies
    • Q50 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Environmental Economics - - - General

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