Skip to main content

Probability Models for Mobility

  • Chapter
Probability in Social Science

Part of the book series: Mathematical Modeling ((MMO,volume 1a))

  • 207 Accesses

Abstract

We are a mobile society. Movement up the social ladder, movement among occupations and ranks in employment, movement from one residential location to another are all routine. It is not surprising that mobility has been studied at great length by social scientists, especially by sociologists, economists, and demographers. Many probability models have been introduced in an attempt to understand the possible dynamics of the observed transition process among social, occupational, income, or geographic states followed by subjects in studies of social, occupational, income, or geographic mobility. One seeks some reasonably concise set of assumptions of how people behave that will fit experimentally obtained mobility data. As we shall see, the simplest Markov chain model assuming a homogeneous population produces theoretical projections that deviate significantly from observed values. Much subsequent research was therefore focused on developing ways to accommodate population heterogeneity. Our aim here is to survey a small part of this work, following a line of research initiated by Blumen, Kogan, and McCarthy (BKM) [3] in their study of intragenerational labor mobility.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 54.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Bibliography

  1. Bartholomew, D. J., Stochastic Models for Social Processes, second edition, New York: Wiley-Interscience, 1974; third edition, 1982.

    Google Scholar 

  2. Bhat, U. N., Elements of Applied Stochastic Processes, New York: Wiley, 1972.

    MATH  Google Scholar 

  3. Blumen, I., M. Kogan, and P. J. McCarthy, The Industrial Mobility of Labor as a Probability Process, Ithaca: Cornell University Press, 1955. A selection from this book is reprinted under the title “Probability Models for Mobility,” pp.318–334 in Lazersfeld, P. F. and N. W. Henry (Eds.), Readings in Mathematical Social Science, Cambridge: M.I.T. Press, 1966.

    Google Scholar 

  4. Boudon, R., Mathematical Structures of Social Mobility, San Francisco: Jossey-Bass, 1973.

    Google Scholar 

  5. Brumelle, S. L. and Y. Gerchak, “A Stochastic Model Allowing Interaction Among Individuals and Its Behavior for Large Populations,” Journal of Mathematical Sociology, vol. 7 (1980), 73–90.

    Article  MathSciNet  MATH  Google Scholar 

  6. Chung, K. L., Markov Chains with Stationary Transition Probabilities, second edition, New York: Springer-Verlag, 1967.

    MATH  Google Scholar 

  7. Chung, K. L., Elementary Probability Theory with Stochastic Processes, New York: Springer-Verlag, 1979.

    MATH  Google Scholar 

  8. Conlisk, J., “Interactive Markov Chains,” Journal of Mathematical Sociology, vol. 4 (1976), 157–185.

    Article  MathSciNet  MATH  Google Scholar 

  9. Fararo, T. J., Mathematical Sociology, New York: Wiley, 1973.

    Google Scholar 

  10. Feller, W., An Introduction to Probability Theory and its Applications, vol. 1, third edition, New York: Wiley, 1968.

    MATH  Google Scholar 

  11. Gantmacher, F. R., The Theory of Matrices, New York: Chelsea, 1959.

    MATH  Google Scholar 

  12. Gaver, D. P. and G. L. Thompson, Programming and Probability Models in Operations Research, Monterey: Brooks-Cole, 1973.

    MATH  Google Scholar 

  13. Gilbert, G., “Semi-Markov Processes and Mobility: A Note,” Journal of Mathematical Sociology, vol. 3 (1973), 139–145.

    Article  MATH  Google Scholar 

  14. Ginsberg, R. B., “Semi-Markov Processes and Mobility,” Journal of Mathematical Sociology, vol. 1 (1971), 233–262.

    Article  MathSciNet  MATH  Google Scholar 

  15. Ginsberg, R. B., “Stochastic Models of Residential and Geographic Mobility for Heterogeneous Populations,” Environment and Planning, vol. 5 (1973), 113–124.

    Article  Google Scholar 

  16. Goodman, L. A., “Statistical Methods for the ‘Mover-Stayer’ Model,” Journal of the American Statistical Association, vol. 56 (1961), 841–868.

    Article  MathSciNet  Google Scholar 

  17. Henry, N. W., R. McGinnis, and H. W. Tegtmeyer, “A Finite Model of Mobility,” Journal of Mathematical Sociology, vol. 1 (1971), 107–118.

    Article  MATH  Google Scholar 

  18. Hodge, R. W., “Occupational Mobility as a Probability Process,” Demography, vol. 3 (1966), 19–34.

    Article  Google Scholar 

  19. Hoel, P., S. C. Port, and C. J. Stone, Introduction to Stochastic Processes, Boston: Houghton Mifflin, 1972.

    MATH  Google Scholar 

  20. Isaacson, D. L. and R. W. Madsen, Markov Chains: Theory and Applications, New York: Wiley, 1976.

    MATH  Google Scholar 

  21. Karlin, S., A First Course in Stochastic Processes, second edition, New York: Academic Press, 1975.

    MATH  Google Scholar 

  22. Kemeny, J. G. and J. L. Snell, Finite Markov Chains, New York: Springer- Verlag, 1976.

    MATH  Google Scholar 

  23. Konda, S. L. and S. Stewman, “An Opportunity Labor Demand Model and Markovian Labor Supply Models: Comparative Tests in an Organization,” American Sociological Review, vol. 45 (1980), 276–301.

    Article  Google Scholar 

  24. Land, K. D., “Duration of Residence and Prospective Migration: Further Evidence,” Demography, vol. 6 (1969), 133–140.

    Article  Google Scholar 

  25. Lehoczky, J. D., “Approximations for Interactive Markov Chains in Discrete and Continuous Time,” Journal of Mathematical Sociology, vol. 7 (1980), 139–157.

    Article  MathSciNet  MATH  Google Scholar 

  26. Mahoney, T. A. and G. T. Milkovich, “The Internal Labor Market as a Stochastic Process,” in Bartholomew, D. J. and A. R. Smith (Eds.), Manpower and Management Science, Lexington, Mass.: Heath, 1971.

    Google Scholar 

  27. Maki, D. P. and M. Thompson, Mathematical Models and Applications, Englewood Cliffs: Prentice-Hall, 1973.

    Google Scholar 

  28. Mayer, T. F., “Models of Intra-generational Mobility,” pp.308–357 in Berger, J., M. Zelditch, and B. Anderson (Eds.), Sociological Theories in Progress, New York: Houghton Mifflin, 1972.

    Google Scholar 

  29. McCall, J. J., Income Mobility, Racial Discrimination, and Economic Growth, Lexington, Mass.: Heath, 1973.

    Google Scholar 

  30. McFarland, D., “Intragenerational Social Mobility as a Markov Process: Including a Time-Stationary Markovian Model that Explains Observed Declines in Mobility Rates over Time,” American Sociological Review, vol. 35 (1970), 463–476.

    Article  Google Scholar 

  31. McGinnis, R., “A Stochastic Model of Social Mobility,” American Sociological Review, vol. 33 (1968), 712–721.

    Article  Google Scholar 

  32. Morrison, P. A., “Duration of Residence and Prospective Migration: The Evaluation of a Stochastic Model,” Demography, vol. 4 (1967), 554–561.

    Article  Google Scholar 

  33. Myers, G. C., R. McGinnis, and G. Masnick, “The Duration of Residence Approach to a Dynamic Stochastic Model of Internal Migration: A Test of the Axiom of Cumulative Inertia,” Eugenics Quarterly, vol. 14 (1967), 121–126.

    Google Scholar 

  34. Prais, S. J., “Measuring Social Mobility,” Journal of the Royal Statistical Society, Series A, vol. 118 (1955), 56–66.

    Article  Google Scholar 

  35. Prais, S. J., “The Formal Theory of Social Mobility,” Population Studies, vol. 9 (1955), 72–81.

    Article  Google Scholar 

  36. Pullum, T., Measuring Occupational Mobility, New York: Elsevier, 1975.

    Google Scholar 

  37. Pyke, R., “Markov Renewal Processes: Definitions and Preliminary Properties,” Annals of Mathematical Statistics, vol. 32 (1961), 1231–1242.

    Article  MathSciNet  MATH  Google Scholar 

  38. Ross, S. M., Applied Probability Models with Optimization Applications, San Francisco: Holden-Day, 1970.

    MATH  Google Scholar 

  39. Sandefur, G. D., “Organizational Boundaries and Upward Job Shifts,” Social Science Research, vol. 10 (1981), 67–82.

    Article  Google Scholar 

  40. Schinnar, A. P. and S. Stewman, “A Class of Markov Models of Social Mobility with Duration Memory Patterns,” Journal of Mathematical Sociology, vol. 6 (1978), 61–86.

    Article  MathSciNet  Google Scholar 

  41. Singer, B. and S. Spilerman, “Social Mobility Models for Heterogeneous Populations,” pp.356–401 in Costner, H. L. (Ed.), Sociological Methodology 1973–1974, San Francisco: Jossey-Bass, 1974.

    Google Scholar 

  42. Singer, B. and S. Spilerman, “The Representation of Social Processes by Markov Models,” American Journal of Sociology, vol. 82 (1976), 1–54.

    Article  Google Scholar 

  43. Snell, J. L., Introduction to Probability Theory with Computing, Englewood Cliffs: Prentice-Hall, 1975.

    MATH  Google Scholar 

  44. Sorensen, A. B., “The Structure of Intragenerational Mobility,” American Sociological Review, vol. 40 (1975), 456–471.

    Article  Google Scholar 

  45. Spilerman, S., “Extensions of the Mover-Stayer Model,” American Journal of Sociology, vol. 78 (1972), 599–626.

    Article  Google Scholar 

  46. Spilerman, S., “The Analysis of Mobility Processes by the Introduction of Independent Variables into a Markov Chain,” American Sociological Review, vol. 37 (1972), 277–294.

    Article  Google Scholar 

  47. Stewman, S., “Two Markov Models of Open System Occupational Mobility: Underlying Conceptualizations and Empirical Tests,” American Sociological Review, vol. 40 (1975), 298–321.

    Article  Google Scholar 

  48. Stewman, S., “Markov Models of Occupational Mobility: Theoretical Development and Empirical Support. Part 1: Careers, Part 2: Continuously Operative Job Systems,” Journal of Mathematical Sociology, vol. 4 (1976), 201–245, 247–278.

    Article  MathSciNet  MATH  Google Scholar 

  49. Tuma, N. B., “Rewards, Resources, and the Rate of Mobility: A Nonstationary Multivariate Stochastic Model,” American Sociological Review, vol. 41 (1976), 338–360.

    Article  Google Scholar 

  50. White, H., Chains of Opportunity: System Models of Mobility in Organizations, Cambridge, Mass.: Harvard University Press, 1970.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 1983 Birkhäuser Boston, Inc.

About this chapter

Cite this chapter

Goldberg, S. (1983). Probability Models for Mobility. In: Probability in Social Science. Mathematical Modeling, vol 1a. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-5616-8_6

Download citation

  • DOI: https://doi.org/10.1007/978-1-4612-5616-8_6

  • Publisher Name: Birkhäuser Boston

  • Print ISBN: 978-1-4612-5618-2

  • Online ISBN: 978-1-4612-5616-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics