RDP 1999-12: Unemployment and Skills in Australia Appendix B: Steady-state Differences in Unemployment Rates

Our notation for a labour market transition is two lower case letters in italics (e.g. ne is a transition from not in the labour force to employment). For a labour market state we use a capital letter (e.g. U is unemployment). Since in equilibrium the flows into and out of each labour market state are equal, we can write:

U × ue + U × un = E × eu + N × nu (flows from unemployment = flows into unemployment)

E × en + E × en = U × ue + N × ne (flows from employment = flows into employment)

This also defines equilibrium for ‘not in the labour force’, since there are only three labour market states. To find the equilibrium unemployment rate as a function of the transition probabilities we solve the above inequalities simultaneously for the unemployment rate. This gives:

where ur is the unemployment rate.

A different but equivalent expression to this is given in Foster and Gregory (1982). They also calculate an expression for a four state system which includes part-time employment.

Table B1 shows the actual unemployment rates from SEUP from September 1994 to September 1996, the calculated equilibrium unemployment rates, and the actual unemployment rates from ABS Cat. No. 6227.0. The unemployment rates from SEUP are similar to those from the Transition from Education to Work survey, although there are some differences, reflecting the following factors.

1. The Transition from Education to Work survey is conducted annually in May, whereas the SEUP results are based on unemployment rates over the entire calendar year. Thus, there are some timing and seasonal differences between the two sets of results.
2. Results in the two surveys are obviously affected by sampling error. This is particularly true for the SEUP survey, which is based on a small sample of only 2,300 respondents.
3. There was a moderate non-response rate in the SEUP survey to the question ‘What is your highest level of educational attainment?’.
4. The SEUP survey is based on a sample of 15–59 year olds, compared with the Transition from Education to Work survey, which is based on 15–64 year olds.

Table B2 shows more detailed results for the contributions of various transition probabilities to the differences in unemployment rates between education groups.