The New Palgrave Dictionary of Economics

2018 Edition
| Editors: Macmillan Publishers Ltd

Stable Population Theory

  • Shripad Tuljapurkar
Reference work entry


A population’s age structure and growth are determined by rates of fertility, mortality and migration. Stable population theory provides a widely useful mathematical framework, described here, that connects a fixed set of rates to the population dynamics they generate. This theory makes it possible to trace causes and consequences of population change, to establish methods for estimating rates, and to make projections of future population. Much of the power of stable theory rests on the fact that the key features of population dynamics with fixed rates can be generalized, as discussed here, to rates that vary over time.


Continuous and discrete time models Dependency ratio Economic demography Fertility Forecasting Generation times International migration Markov processes Mortality Population growth Population momentum Population projections Stable population theory Stochastic stable theory 

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  1. Arthur, W.B., and T.J. Espenshade. 1988. Immigration policy and immigrants’ ages. Population and Development Review 14: 315–326.CrossRefGoogle Scholar
  2. Caswell, H. 2001. Matrix population models: Construction, analysis and interpretation. 2nd ed. Sunderland: Sinauer.Google Scholar
  3. Coale, A.J. 1972. The growth and structure of human populations: A mathematical investigation. Princeton: Princeton University Press.Google Scholar
  4. Cohen, J.E. 1976. Ergodicity of age structure in populations with Markovian vital rates, I: Countable states. Journal of the American Statistical Association 71: 335–339.CrossRefGoogle Scholar
  5. Feichtinger, G., and G. Steinmann. 1992. Immigration into a population with fertility below replacement level – the case of Germany. Population Studies 46: 275–284.CrossRefGoogle Scholar
  6. Feller, W. 1941. On the integral equation of renewal theory. Annals of Mathematical Statistics 12: 243–267.CrossRefGoogle Scholar
  7. Feller, W. 1971. An introduction to probability theory and its applications. Vol. 2. 2nd ed. New York: Wiley.Google Scholar
  8. Fisher, R.A. 1930. The genetical theory of natural selection. Oxford: Clarendon Press.CrossRefGoogle Scholar
  9. Keyfitz, N.C. 1971. On the momentum of population growth. Demography 8: 71–80.CrossRefGoogle Scholar
  10. Keyfitz, N.C. 1977. Introduction to the mathematics of population – With revisions. New York: Addison-Wesley.Google Scholar
  11. Lee, R.D. 1994. The formal demography of population aging, transfers, and the economic life cycle. In The demography of aging, ed. L. Martin and S. Preston. Washington, DC: National Academy Press.Google Scholar
  12. Lee, R., and S. Tuljapurkar. 2000. Population forecasting for fiscal planning: Issues and innovations. In Demography and fiscal policy, ed. A. Auerbach and R. Lee. Cambridge: Cambridge University Press.Google Scholar
  13. Leslie, P.H. 1945. On the use of matrices in certain population mathematics. Biometrika 33: 183–212.CrossRefGoogle Scholar
  14. Li, N., and S. Tuljapurkar. 1999. Population momentum. Population Studies 53: 255–262.CrossRefGoogle Scholar
  15. Lopez, A. 1961. Problems in stable population theory. Princeton: Office of Population Research.Google Scholar
  16. Lopez, A. 1967. Asymptotic properties of a human age distribution under a continuous net maternity function. Demography 4: 680–687.CrossRefGoogle Scholar
  17. Lotka, A.J. 1939. A contribution to the theory of self-renewing aggregates, with special reference to industrial replacement. Annals of Mathematical Statistics 10: 1–25.CrossRefGoogle Scholar
  18. Preston, S.H., P. Heuveline, and M. Guillot. 2000. Demography: Measuring and modeling population processes. Malden: Blackwell.Google Scholar
  19. Sharpe, F.R., and A.J. Lotka. 1911. A problem in age-distribution. Philosophical Magazine 21: 435–438.Google Scholar
  20. Tuljapurkar, S. 1982. Population dynamics in variable environments. IV: Weak ergodicity in the Lotka equation. Journal of Mathematical Biology 14: 221–230.CrossRefGoogle Scholar
  21. Tuljapurkar, S. 1990. Population dynamics in variable environments. Berlin: Springer Verlag.CrossRefGoogle Scholar
  22. Vassiliou, P.-C.G. 1997. The evolution of the theory of non-homogeneous Markov systems. Applied Stochastic Models and Data Analysis 13: 159–176.CrossRefGoogle Scholar

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© Macmillan Publishers Ltd. 2018

Authors and Affiliations

  • Shripad Tuljapurkar
    • 1
  1. 1.