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OCR for page 495
D
United Nations
Estimates and Projections
The urban/rural growth rate difference, or URGD, is the centerpiece of the method
developed by the United Nations Population Division to estimate and project ur-
ban populations. In its initial formulation, however, the United Nations method
did not exploit the full implications of equation (B.7) in Appendix B. Here we
first discuss the extrapolation method as it was presented by the United Nations
(1974: 29), and then show how the refinements later introduced by the United
Nations ( 1980: 10-1 1 ) exploited the equation.
With data at two points in time, say, t—1 and t, the urban/rural growth rate
difference can be approximated by
URGDt_i = in——in t ~ .
Rt Rt_i
Taking the growth rate difference to be constant at URGD = d and expressing
the urban/rural balance in t as a function of a base year balance, we may write
_ _ Uo edt
Rt Ro
To convert the urban/rural balance at time t into an expression for the level of
urbanization, we make use of the relation
Ut/Rt
l+Ut/Rt'
and obtain, after substitution,
p (UO/RO)edt
ant 1 + (Uo /Ro j edit
495
Jo -
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496
CITIES TRANSFORMED
With SO _ in (Uo/Ro), the level of urbanization can be written in a standard logit
form,
em+ ~
1 + e~o+d t
(D.1)
This is the essence of the so-called "United Nations method" for estimating the
level of urbanization from data on a country's urban and rural populations at two
points in time. ~
In the format of World Urbanization Prospects, estimates (and projections) are
published for 5-year intervals beginning in 1950. To produce these estimates, the
United Nations uses equation (D.1) to interpolate between censuses and to pro-
vide reasonable guesses of urban proportions between 1950 and the first national
census available after that date (United Nations, 1998b: 33~.
The weak point of the United Nations method emerges when it is employed
to generate forward projections of urbanization levels. The method assumes con-
stancy in the URGD, and this is an untenable assumption in medium- and long-
term projections. The simple analytic model of Appendix B shows that, with
other things held constant, the URGD should decline with urbanization. Refer-
ring to equation (B.7), we see that as the urban/rural balance Ut_~/Rt_i rises,
a reduction in the growth rate difference must result, except in the unlikely case
in which both mr,~' and m~`,r are zero. Noting this, the United Nations (1980:
10-11) sought and found in the empirical record supporting evidence for URGD
decline.
Since 1980, therefore, the United Nations has incorporated in its projections
a function that ensures a progressive decline in growth rate differences over the
course of each country's projection. The United Nations (1998b: 33-4) gives a
concise summary of the function, which is based on a simple regression model
estimated on data from all countries, whether developing or developed, with more
than 2 million inhabitants in 1995 (a total of 113 countries). The function has
the effect of slowing the projected rate at which countries with high levels of ur-
banization approach the upper limit of unity, but it also induces somewhat faster
projected urbanization for countries with low levels of urbanization (United Na-
tions, 1980: 11~. Note also that whereas the United Nations estimates of urban
population are based only on country-specific census data, the projections of ur-
ban population use both country-specific and cross-country data, with the latter
including developed as well as developing countries.
The United Nations method for estimating and projecting the population of
individual cities is, in broad outline, little more than an application of the URGD
method to different data. Rather than working with the urban/rural balance Ut/Rt,
however, the method considers a city's population in relation to the national total
less the population of the city in question.2 Let i denote the city whose population
iNote that the maximum urbanization level implied by the equation is unity.
2The approach is a revised version of a method set forth earlier by the United Nations (1974), in
which each city's population was examined in relation to the total urban population of the country,
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UNITED NATIONS ESTIMATES AND PROJECTIONS
497
is being estimated and projected, and let Ui,~ be its population in year t. The
estimation exercise for city i begins with
ui't
At—Ui,t
(D.2)
and the population of city i is then estimated from the differences in growth rates
of numerator and denominator found in the most recently available intercensal
period. The method is applied independently, city by city within a country, to all
those cities whose populations are to be estimated (United Nations 1980: 44-47,
1998b: 35).
As is the case when urban totals are projected, the projections of city popu-
lation must rely upon additional research judgments. The United Nations (1980)
introduced a method for keeping the projected growth rates of large cities within
reasonable bounds. In this study, the United Nations noted a U-shaped relation-
ship between city size and city growth rates, with the highest growth rates evident
in small (under 500,000 population) and very large (over 4 million population)
cities. At the time of the study, however, there were relatively few very large
cities in developing countries, and the United Nations concluded that the relation-
ship between city size and growth rates was predominantly negative. City size
was found to be only a weak predictor of city growth, however, with the raw cor-
relation between city growth rates and the log of city size being only—0.083.
The United Nations (1998b: 36) revisited the issue, again using both developed
and developing countries, and confirmed what had been seen earlier: a weakly
negative relationship between city size and growth.3
Although mindful of the thin empirical justification, the United Nations has
judged it sensible to embed a negative relationship between city size and growth
in its city population projections. As explained by the United Nations (1998b), the
method relies upon the results of a cross-country regression, estimated using the
sample of 113 developed and developing countries described above (which con-
tains some 1,982 cities). The dependent variable of the regression is the difference
in growth rates between the city and the country's total urban population (rather
than the total population used in the denominator of equation (D.2)); the explana-
tory variable is the log of initial city size. This regression produces a predicted
value for the city-urban growth rate difference given the size of the city.
rather than the national total. The growth rate of city i is of course linked to the growth rate of the
country's urban population the linkage is obvious in countries where the urban sector is dominated
by a few large cities. Hence in the approach favored by the United Nations (1974: 46-47), the city
projections were to be made iteratively, beginning with the country's largest city and the projected
urban total, and at each subsequent step removing from the denominator of the equation (an expression
analogous to equation (D.2)) those cities whose populations had already been projected.
Tin view of this low bivariate correlation, it is surprising that in the multivariate regressions reported
by Preston (1979: Table 2) and Brockerhoff (1999: Table 4), where one might have expected a weak
city size effect to disappear altogether, city size remains negatively and significantly associated with
the rate of city growth.
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498
CITIES TRANSFORMED
Consider a projection of the population of city i in year t, which relies on the
size projected for that city in year t—1. The projection for t relies in large part
on the URGD for city i in the most recent intercensal period, but the projected
value is modified to reflect the regression equation described above, which is mul-
tiplied by a year-specific weight. The sequence of weights is chosen so as to force
the projected city-urban growth difference toward the relationship implied by the
regression equation. The United Nations (1980: 45-47) gives a lucid account of
this procedure.
We would not want to leave the impression that these city estimates and pro-
jections are little more than a mechanical extrapolation of assumptions. United
Nations researchers have long recognized the possibility of errors and have at-
tempted to take them into account. The United Nations (1974: 45, 48) warned
of the possibility of considerable error if the city projection method were to be
applied mechanically and urged that the results of the exercise be carefully scruti-
nized. Recently, the United Nations (1998b: 36) conceded that, even with a damp-
ening function in place, when the city population projections are aggregated to the
country level, they can show a tendency to grow more rapidly than the country's
total projected urban population. This is not, in itself, evidence of an inconsis-
tency between the two types of projections recall that small urban areas do not
usually have their populations estimated and projected. But care must obviously
be taken to ensure that the total of the projected city populations does not exceed
the total projected for all urban areas.
When the aggregate of the city-specific projections happens to grow more
rapidly than the projected urban total (the United Nations, 1998b: 36, suggests
that this situation is common), yet another adjustment is applied to bring the pro-
jected rates of city growth more in line with that of the urban total. Each city's
growth rate is reduced by the same amount in such a way that, over the full course
of a projection, the projected city total can never exceed the projected urban to-
tal. Finally, additional adjustments are made in cases of negative estimated or
projected city growth rates; in the final adjusted estimates and projections, such
negative growth rates are generally replaced by zero growth rates (or so it appears,
to judge from the United Nations, 1998b: 36~.
The result of all this is a complicated algorithm whose success in estimating
and projecting city populations is far from being assured. Although the United
Nations has been careful to describe the main features of the methods it applies, it
has not fully developed the demographic justification for its projection adjust-
ments, nor has it presented a clear rationale for commingling developed- and
developing-country population data in these projections. The consequence is that
the United Nations' city population projections are linked across countries and
over time in ways that are difficult to defend. Criticisms of this nature can also be
leveled at the projections of total urban populations, although where these projec-
tions are concerned, the adjustments are fewer and somewhat better justified.
Representative terms from entire chapter:
urban population
