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How stationarity contradicts intergenerational equity

Abstract

We show how the condition of stationarity may contradict intergenerational equity. By formalizing the intuition that less sensitivity remains for the continuation of the stream if sensitivity for the interests of the present is combined with stationarity, we point out conflicts (a) between stationarity and the requirement of not letting the present be dictatorial, and (b) between stationarity and equal treatment of generations. We use the results to interpret the non-stationarity of the Chichilnisky and Rank-discounted utilitarian social welfare functions. Non-stationarity combined with time invariance leads to time inconsistency. We illustrate how such non-stationary social welfare functions can be applied in the Ramsey model if time invariance is imposed.

References

  • Alcantud, J.C.R.: Inequality averse criteria for evaluating infinite utility streams: The impossibility of Weak Pareto. J. Econ. Theory 147, 353–363 (2012)

    Article  Google Scholar 

  • Asheim, G.B.: Individual and collective time-consistency. Rev. Econ. Stud. 64, 427–443 (1997)

    Article  Google Scholar 

  • Asheim, G.B., Ekeland, I.: Resource conservation across generations in a Ramsey-Chichilnisky model. Econ. Theory 61, 611–639 (2016)

    Article  Google Scholar 

  • Asheim, G.B., Mitra, T.: Sustainability and discounted utilitarianism in models of economic growth. Math. Soc. Sci. 59, 148–169 (2010)

    Article  Google Scholar 

  • Banerjee, K., Mitra, T.: On Wold’s approach to representation of preferences. J. Math. Econ. 79, 65–74 (2018)

    Article  Google Scholar 

  • Basu, K., Mitra, T.: Aggregating infinite utility streams with intergenerational equity: the impossibility of being Paretian. Econometrica 71, 1557–1563 (2003)

    Article  Google Scholar 

  • Basu, K., Mitra, T.: Utilitarianism for infinite utility streams: A new welfare criterion and its axiomatic characterization. J. Econ. Theory 133, 350–373 (2007)

    Article  Google Scholar 

  • Beals, R., Koopmans, T.C.: Maximizing stationary utility in a constant technology. SIAM J. Appl. Math. 17, 1001–1015 (1969)

    Article  Google Scholar 

  • Blackorby, C., Nissen, D., Primont, D., Russell, R.R.: Consistent intertemporal decision making. Rev. Econ. Stud. 40, 239–248 (1973)

    Article  Google Scholar 

  • Bossert, W., Sprumont, Y., Suzumura, K.: Ordering infinite utility streams. J. Econ. Theory 135, 579–589 (2007)

    Article  Google Scholar 

  • Chambers, C.: Intergenerational equity: sup, inf, lim sup, and lim inf. Soc. Choice Welfare 32, 243–252 (2009)

    Article  Google Scholar 

  • Chichilnisky, G.: An axiomatic approach to sustainable development. Soc. Choice Welfare 13, 231–257 (1996)

    Article  Google Scholar 

  • Crespo, J.A., Nuñez, C., Rincón-Zapatero, J.P.: On the impossibility of representing infinite utility streams. Econ. Theory 40, 47–56 (2009)

    Article  Google Scholar 

  • Diamond, P.: The evaluation of infinite utility streams. Econometrica 33, 170–177 (1965)

    Article  Google Scholar 

  • Dockner, E., Wagener, F.: Markov perfect Nash equilibria in models with a single capital stock. Econ. Theory 56, 585–625 (2014)

    Article  Google Scholar 

  • Dutta, B.: Some remarks on the ranking of infinite utility streams. In: Basu, K., Kanbur, R. (eds.) Arguments for a Better World: Essays in Honor of Amartya Sen, Volume I: Ethics, Welfare and Measurement, pp. 136–147. Oxford University Press, Oxford (2008)

    Chapter  Google Scholar 

  • Fleurbaey, M., Michel, P.: Intertemporal equity and the extension of the Ramsey criterion. J. Math. Econ. 39, 777–802 (2003)

    Article  Google Scholar 

  • Halevy, Y.: Time consistency: stationarity and time invariance. Econometrica 83, 335–352 (2015)

    Article  Google Scholar 

  • Jackson, M.O., Yariv, P.: Collective dynamic choice: The necessity of time inconsistency. AEJ: Microecon 7, 150–178 (2015)

  • Jonsson, A., Voorneveld, M.: The limit of discounted utilitarianism. Luleå University of Technology and Stockholm School of Economics, Mimeo (2015)

    Google Scholar 

  • Jonsson, A., Voorneveld, M.: The limit of discounted utilitarianism. Theor. Econ. 13, 19–37 (2018)

    Article  Google Scholar 

  • Koopmans, T.C.: Stationary ordinal utility and impatience. Econometrica 28, 287–309 (1960)

    Article  Google Scholar 

  • Lauwers, L.: Ordering infinite utility streams comes at the cost of a non-Ramsey set. J. Math. Econ. 46, 32–37 (2010)

    Article  Google Scholar 

  • Millner, A., Heal, G.: Time consistency and time invariance in collective intertemporal choice. J. Econ. Theory 176, 158–169 (2018)

    Article  Google Scholar 

  • Mitra, T., Ozbek, M.K.: On representation of monotone preference orders in a sequence space. Soc. Choice Welfare 41, 473–487 (2013)

    Article  Google Scholar 

  • Mitra, T., Sorger, G.: Extinction in common property resource models: an analytically tractable example. Econ. Theory 57, 41–57 (2014)

    Article  Google Scholar 

  • Pollak, R.A.: Consistent planning. Rev. Econ. Stud. 35, 201–208 (1968)

    Article  Google Scholar 

  • Ramsey, F.: A mathematical theory of saving. Econ. J. 38, 543–59 (1928)

    Article  Google Scholar 

  • Sakai, T.: Limit representations of intergenerational equity. Soc. Choice Welfare 47, 481–500 (2016)

    Article  Google Scholar 

  • Sorger, G.: Markov-perfect Nash equilibria in a class of resource games. Econ. Theory 11, 79–100 (1998)

    Article  Google Scholar 

  • Zame, W.R.: Can intergenerational equity be operationalized? Theor. Econ. 2, 187–202 (2007)

    Google Scholar 

  • Zuber, S., Asheim, G.B.: Justifying social discounting: the rank-discounted utilitarian approach. J. Econ. Theory 147, 1572–1601 (2012)

    Article  Google Scholar 

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Acknowledgements

Open Access funding provided by University of Oslo (incl Oslo University Hospital)

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Correspondence to Geir B. Asheim.

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Tapan Mitra passed away on 3 February 2019. Through his work he seamlessly combined authority and grace. He remains a valuable source of inspiration to his co-authors. We thank two anonymous referees, Walter Bossert, Claude d’Aspremont, Marc Fleurbaey, Sean Horan, Adam Jonsson, Paolo Piacquadio, and other seminar participants in Lund, Marseille, Montréal, Oslo, Taipei, Tokyo, and Tucson for helpful comments. This paper is part of the research activities at the Centre for the Study of Equality, Social Organization, and Performance (ESOP) at the Department of Economics at the University of Oslo. Asheim’s research has benefitted from stays at IMéRA–Marseille, CIREQ–Montréal, and Paris School of Economics. An earlier version of this paper was circulated under the title “The necessity of time inconsistency for intergenerational equity”.

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Asheim, G.B., Banerjee, K. & Mitra, T. How stationarity contradicts intergenerational equity. Econ Theory 72, 423–444 (2021). https://doi.org/10.1007/s00199-020-01296-8

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Keywords

  • Intergenerational equity
  • Stationarity
  • Time inconsistency

JEL Classification

  • D63
  • D71
  • Q01