Advertisement

A Dynamic Analysis of Schelling’s Binary Corruption Model: A Competitive Equilibrium Approach

  • Jonathan P. Caulkins
  • Gustav FeichtingerEmail author
  • Dieter Grass
  • Richard F. Hartl
  • Peter M. Kort
  • Andreas J. Novak
  • Andrea Seidl
  • Franz Wirl
Article

Abstract

Schelling (in Micromotives and Macrobehavior, Norton, New York, 1978) suggested a simple binary choice model to explain the variation of corruption levels across societies. His basic idea was that the expected profitability of engaging in corruption depends on its prevalence. The key result of the so-called Schelling diagram is the existence of multiple equilibria and a tipping point. The present paper puts Schelling’s essentially static approach into an intertemporal setting. We show how the existence of an unstable interior steady state leads to thresholds such that history alone or history in addition to expectations (or coordination) is necessary to determine the long-run outcome. In contrast to the related literature, which classifies these two cases according to whether the unstable equilibrium is a node or a focus, the actual differentiation is more subtle because even a node can lead to an overlap of solution paths such that the initial conditions alone are insufficient to uniquely determine the competitive equilibrium. Another insight is that a (transiently) cycling competitive equilibrium can dominate the direct and monotonic route to a steady state, even if the direct route is feasible.

Keywords

Corruption Schelling diagram Intertemporal competitive equilibria Thresholds History versus expectations 

Notes

Acknowledgements

The authors like to thank Marjorie Carlson, two referees, and the editor for their helpful comments. This research was supported by the Austrian Science Fund (FWF) under Grant P21410-G16 and P23084-N13.

References

  1. 1.
    Krugman, P.: History versus expectations. Q. J. Econ. 106(2), 651–667 (1991) CrossRefGoogle Scholar
  2. 2.
    Andvig, J.C., Moene, K.O.: How corruption may corrupt. J. Econ. Behav. Organ. 13(1), 63–76 (1990) CrossRefGoogle Scholar
  3. 3.
    Friedrich, C.J.: The Pathology of Politics, Violence, Betrayal, Corruption, Secrecy, and Propaganda. Harper & Row, New York (1972) Google Scholar
  4. 4.
    Popper, K.R.: The Open Society and Its Enemies, vol. 1. The Spell of Plato. Routledge, London (1966) Google Scholar
  5. 5.
    Lui, F.T.: A dynamic model of corruption deterrence. J. Public Econ. 31(2), 215–236 (1986) CrossRefGoogle Scholar
  6. 6.
    Rose-Ackerman, S.: The economics of corruption. J. Public Econ. 4, 187–203 (1975) CrossRefGoogle Scholar
  7. 7.
    Rose-Ackerman, S.: Corruption: A Study in Political Economy. Academic Press, New York (1978) Google Scholar
  8. 8.
    Rose-Ackerman, S.: The law and economics of bribery and extortion. Ann. Rev. Law Soc. Sci. 6, 217–238 (2010) CrossRefGoogle Scholar
  9. 9.
    Schelling, T.: Hockey helmets, concealed weapons, and daylight saving: a study of binary choices with externalities. J. Confl. Resolut. 17(3), 381–428 (1973) CrossRefGoogle Scholar
  10. 10.
    Schelling, T.C.: Micromotives and Macrobehavior. Norton, New York (1978) Google Scholar
  11. 11.
    Shleifer, A., Vishny, R.W.: Corrupt. Q. J. Econ. 108(3), 599–617 (1993) CrossRefGoogle Scholar
  12. 12.
    Feichtinger, G., Wirl, F.: On the stability and potential cyclicity of corruption within governments subject to popularity constraints. Math. Soc. Sci. 28(2), 113–131 (1994) zbMATHMathSciNetCrossRefGoogle Scholar
  13. 13.
    Dong, B., Torgler, B.: Democracy, property rights, income equality, and corruption. Fondazione Eni Enrico Mattei Working Papers 559 (2011) Google Scholar
  14. 14.
    Caulkins, J.P., Feichtinger, G., Grass, D., Hartl, R.F., Kort, P.M., Novak, A., Seidl, A.: Leading bureaucracies to the tipping point: an alternative model of multiple stable equilibrium levels of corruption. Eur. J. Oper. Res. 225(3), 541–546 (2013) MathSciNetCrossRefGoogle Scholar
  15. 15.
    Andvig, J.C.: The economics of corruption: a survey. Stud. Econ. 43(1), 57–94 (1991) Google Scholar
  16. 16.
    Glaeser, E.L., Sacerdote, B.I., Scheinkman, J.A.: The social multiplier. J. Eur. Econ. Assoc. 1(2–3), 345–353 (2003) CrossRefGoogle Scholar
  17. 17.
    Glaeser, E.L., Sacerdote, B.I., Scheinkman, J.A.: Crime and social interactions. Q. J. Econ. 111(2), 507–548 (1996) CrossRefGoogle Scholar
  18. 18.
    Dong, B., Torgler, B.: Corruption and social interaction: evidence from China. J. Policy Model. 34(6), 932–947 (2012) CrossRefGoogle Scholar
  19. 19.
    Aidt, T.S.: Economic analysis of corruption: a survey. Econ. J. 113(491), F632–F652 (2003) CrossRefGoogle Scholar
  20. 20.
    Wirl, F.: Socio-economic typologies of bureaucratic corruption and implications. J. Evol. Econ. 8(2), 199–220 (1998) CrossRefGoogle Scholar
  21. 21.
    Epstein, J.M.: Modeling civil violence: an agent-based computational approach. Proc. Natl. Acad. Sci. USA 99, 7243–7250 (2002) CrossRefGoogle Scholar
  22. 22.
    Feichtinger, G., Rinaldi, S., Wirl, F.: Corruption dynamics in democratic systems. Complexity 5(3), 53–64 (1998) Google Scholar
  23. 23.
    Wirl, F., Feichtinger, G.: History versus expectations: increasing returns or social influence? J. Socio-Econ. 35(5), 877–888 (2006) CrossRefGoogle Scholar
  24. 24.
    Fukao, K., Benabou, R.: History versus expectations: a comment. Q. J. Econ. 108(2), 535–542 (1993) CrossRefGoogle Scholar
  25. 25.
    Liski, M.: Thin versus thick CO2 market. J. Environ. Econ. Manag. 41(3), 295–311 (2001) MathSciNetCrossRefGoogle Scholar
  26. 26.
    Sethi, S.P., Thompson, G.L.: Optimal Control Theory Applications to Management Science and Economics, 2nd edn. Kluwer Academic, Boston (2000) zbMATHGoogle Scholar
  27. 27.
    Grass, D., Caulkins, J.P., Feichtinger, G., Tragler, G., Behrens, D.A.: Optimal Control of Nonlinear Processes: With Applications in Drugs, Corruption and Terror. Springer, Heidelberg (2008) CrossRefGoogle Scholar
  28. 28.
    Karp, L., Thierry, P.: Indeterminacy with environmental and labor dynamics. Struct. Chang. Econ. Dyn. 18(1), 100–119 (2007) CrossRefGoogle Scholar
  29. 29.
    Wirl, F.: Conditions for indeterminacy and thresholds in neoclassical growth models. J. Econ. 102, 193–215 (2011) zbMATHCrossRefGoogle Scholar
  30. 30.
    Kuran, T.: Sparks and prairie fires: a theory of unanticipated political revolution. Public Choice 61(1), 41–74 (1989) CrossRefGoogle Scholar
  31. 31.
    Wirl, F.: Social interactions within a dynamic competitive economy. J. Optim. Theory Appl. 133(3), 385–400 (2007) zbMATHMathSciNetCrossRefGoogle Scholar
  32. 32.
    Hartl, R.F.: A simple proof of the monotonicity of the state trajectories in autonomous control problems. J. Econ. Theory 40(1), 211–215 (1987) MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Jonathan P. Caulkins
    • 1
  • Gustav Feichtinger
    • 2
    • 3
    Email author
  • Dieter Grass
    • 2
  • Richard F. Hartl
    • 4
  • Peter M. Kort
    • 5
    • 6
  • Andreas J. Novak
    • 4
  • Andrea Seidl
    • 2
    • 3
  • Franz Wirl
    • 4
  1. 1.H. John Heinz III CollegeCarnegie Mellon UniversityPittsburghUSA
  2. 2.Department for Operations Research and Control Systems, Institute for Mathematical Methods in EconomicsVienna University of TechnologyViennaAustria
  3. 3.Wittgenstein Centre for Demography and Global Human Capital (IIASA,VID/OEAW,WU)Vienna Institute of Demography/Austrian Academy of SciencesViennaAustria
  4. 4.Department of Business AdministrationUniversity of ViennaViennaAustria
  5. 5.Department of Econometrics and Operations Research & CentERTilburg UniversityTilburgThe Netherlands
  6. 6.Department of EconomicsUniversity of AntwerpAntwerpBelgium

Personalised recommendations