# Mobility Index

From Open Risk Manual

## Contents

## Definition

**Mobility Index** is any scalar indicator of the relative rates of migration of entities between different states.

## Contexts

Mobility indexes are constructed and used in a wide variety of contexts, indicatively:

- Social Mobility (in terms of educational / professional status)
- Economic (Income or Wealth) Mobility
- Spatial Mobility
- Demographic Mobility (relocation of the permanent residence of people as measured for example by the Rank Mobility Index
- Credit Rating Mobility

## Construction

- The construction of a Mobility Index may involve first the construction of a Transition Matrix. This is typically required when the underlying Characteristic, feature, property or attribute has a continuous State Space which can be converted to a meaningful discrete space using variable bins.
- Given a transition matrix over successive periods one calculates a scalar indicator on the basis of changes in the matrix elements. Examples are listed below and documented in individual pages

## Formula

An index of mobility is defined as a continuous real function over the set of transition matrices ^{[1]}

## Special Cases

- Immobility
- Complete Mobility

## List of Mobility Indexes

- Prais-Bibby Index
- Bartholomew Index
- Sommers and Conlisk Index
- Shorrocks Index
- GMZ Index
- Jafry-Schuermann Index

## Issues and Challenges

- There is a broader use of the term
*index*to mean any quantitative indicator comparing two distributions (without any explicit presence of discrete states). This can be done e.g., on the basis of correlations or using a Concentration Index.

## References

- ↑ A. F. Shorrocks Source: Econometrica, Vol. 46, No. 5 (Sep., 1978)