Eigenvalue immobility measures for Markov chains¹

Conlisk was supported on this project by National Science Foundation grant SOC74–15238. Helpful comments were provided by a referee.

Two eigenvalue measures of immobility are proposed for social processes described by a Markov chain. One is the second largest eigenvalue modulus of the chain's transition matrix. The other is the second largest eigenvalue modulus of a closely related transition matrix. The two eigenvalue measures are compared to each other and to correlation and regression‐to‐the‐mean measures. In illustrative applications to intergenerational occupational mobility, the eigenvectors corresponding to the eigenvalue measures are found to be good proxies for occupational status rankings for a number of countries, thus reinforcing a pattern noted by Klatsky and Hodge and by Duncan‐Jones.

Notes

Conlisk was supported on this project by National Science Foundation grant SOC74–15238. Helpful comments were provided by a referee.