Abstract

In this article, I derive a simple formula for approximating the ultimate size of a population that undergoes a gradual transition to replacement fertility. I model the fertility transition by specifying a linear frontier on the Lexis surface across which a change in fertility is instantaneous. Gradual transitions result from variations in the slope of this frontier. This framework can be used to reproduce and understand previous studies of population momentum and gradual transitions.

The text of this article is only available as a PDF.

References

Bos, E., Vu, M.T., Levin, A., & Bulatao, R.A. (
1992
).
World Population Projections, 1992–1993
.
Baltimore
:
John Hopkins University Press
.
Bos, E., Vu, M.T., Massiah, E., & Bulatao, R.A. (
1994
).
World Population Projections 1994-95: Estimates and Projections With Related Demographic Statistics
.
Baltimore
:
Johns Hopkins University Press
.
Feller, W. (
1971
).
An Introduction to Probability Theory and Its Applications
. 2nd ed.
New York
:
John Wiley and Sons
.
Frauenthal, J.C. (
1975
).
Birth Trajectory Under Changing Fertility Conditions
.
Demography
,
12
,
447
54
. 10.2307/2060827
Goldstein, J.R., & Schlag, W. (
1999
).
Longer Life and Population Growth
.
Population and Development Review
,
25
,
741
47
. 10.1111/j.1728-4457.1999.00741.x
Goldstein, J.R. and G. Stecklov. 2001. “The Virtues of Simplicity: Long Run Population Forecasting Without Computers.” Unpublished manuscript. Office of Population Research, Princeton University.
Kendall, M.G. (
1952
).
The Advanced Theory of Statistics
. 5th ed.
New York
:
Hafner Publishing
.
Keyfitz, N. (
1971
).
On the Momentum of Population Growth
.
Demography
,
8
,
71
80
. 10.2307/2060339
Keyfitz, N., & Flieger, W. (
1990
).
World Population Growth and Aging
.
Chicago
:
University of Chicago Press
.
Li, N., & Tuljapurkar, S. (
1999
).
Population Momentum for Gradual Demographic Transitions
.
Population Studies
,
53
,
255
62
. 10.1080/00324720308078
Li, N. (
2000
).
The Solution of Time-Dependent Population Models
.
Mathematical Population Studies
,
74
,
311
29
. 10.1080/08898480009525464
Mitra, S. (
1976
).
Influence of Instantaneous Fertility Decline to Replacement Level on Population Growth: An Alternative Model
.
Demography
,
13
,
513
19
. 10.2307/2060507
Ryder, N. (
1975
).
Notes on Stationary Populations
.
Population Index
,
41
(
1
),
3
28
. 10.2307/2734140
Schoen, R., & Kim, Y.J. (
1998
).
Momentum Under a Gradual Approach to Zero Growth
.
Population Studies
,
52
,
295
99
. 10.1080/0032472031000150476
Long-Range World Population Projections: Two Centuries of Population Growth 1950–2150
. (
1992
).
New York
:
United Nations
.