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Teachers and the birth rate

The demographic dynamics of a service population


A theoretical model is developed in which the market for teachers is linked to the time path of fertility in the general population. The model is simple in its components but when the components are combined they form a complex long-memory dynamic system. Simulation experiments are carried out to investigate the effects of changes in fertility rates on supply/requirements imbalances in the teachers' market, the median age of teachers, and other variables. The model (and by implication, the real-world system) is found to be highly volatile in response to fertility variations.

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a :

sex proportion of newly trained teachers (males a 1, females a 2 = 1−a 1)

B :

live births (males B 1, females B 2)

d :

death rate

E :

number of early retirements

e :

early retirement rate

F :

total fertility rate

f :

age-specific fertility rate

h :

subscript for age (in seniority-based and early retirement summations)

i :

subscript for sex (males i = 1, females i = 2)

j :

subscript for age


minimum age of students

k :

age of attainment of teacher qualifications

k * :

maximum age of employment for teachers

L :

teacher labour force (persons employable as teachers, whether or not currently employed)

L * :

number of employed teachers

M :

median age of general population 22–64 years of age

M :

median age of employed teachers

N :

general population

N :

population with teacher qualifications of age k * or less

q :

teacher entry rate (ratio of newly trained teachers to general population of age k)

q :

minimum allowable value of q

R :

number of teachers required to service student population

r :

teacher retention ratio (ratio of teacher labour force to population with teacher qualifications)

r :

retention ratio for newly trained teachers (assumed constant)

S :

number of students

t :

subscript for time (year)

U :

number of teachers unemployed (i.e., unemployed as teachers)

u :

rate of unemployment of teachers

Ū :

underutilization of teacher labour force (labour force minus requirements)

ū :

rate of underutilization of teacher labour force

X :

unsatisfied teacher requirements (excess of requirements over labour force)

x :

proportion of teacher requirements unsatisfied

Z :

number of newly trained teachers that would be needed to equate teacher labour force with requirements

z :

ratio of Z to general population of age k

a :

parameter representing natural reduction of teacher retention ratio

γ :

parameter representing rate of adjustment of training system to teacher requirements in a given year

δ :

parameter in function that determines γ

gq :

required teacher/student ratio for students of given age

λ :

parameter in function that determines γ

π :

educational participation rate (ratio of students to population of given age)

σ :

sex ratio at birth (ratio of male to female live births)

ϕ :

ratio of age-specific to total fertility rate


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Additional information

This study was supported by a grant from the Social Sciences and Humanities Research Council of Canada. The authors are grateful for the able research assistance provided by Guy Brockington and Renqun Wang and for the helpful comments of the referees.

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Denton, F.T., Feaver, C.H. & Spencer, B.G. Teachers and the birth rate. J Popul Econ 7, 307–329 (1994).

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  • Dynamic System
  • General Population
  • Birth Rate
  • Theoretical Model
  • Simulation Experiment