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Technical Notes
Population Projections
for Cities and Municipalities

To project population of cities and municipalities, the ratio method, rather than the cohort component method, was utilized because of the unavailability of data on fertility, mortality and migration at the city/municipality level.

The ratio method of estimating the future population of cities and municipalities makes use of the levels and trends in the ratios of the population of cities and municipalities to the population of their respective provinces observed in previous censuses. These ratios are then projected on the assumption that after some time stability will be attained.

In the present application, all cities and municipalities comprising a province were classified according to the trend of their ratios as observed in the 1970, 1980, 1990 and 1995 censuses. The four classifications are the following:

Type I - cities/municipalities that showed unidirectional trend in their ratios (either increasing or decreasing) throughout the observation period.

Type II - cities/municipalities that had unidirectional trends only during the last two intercensal periods.

Type III - cities/municipalities that had unidirectional trends only during the first two intercensal period.

Type IV - cities/municipalities with erratic trends.
For each type of city/municipality, the initial rates (r) at which the ratios will change were computed as follows:

1.      For a type I city/municipality, the initial rate of change is equal to the geometric mean of the observed annual rates of change of the ratios for the three intercensal periods.

2.      For a type II city/municipality, the initial rate of change is equal to the geometric mean of the observed annual rates of change of the ratios during the last two intercensal periods.

where I (x) =  1 if  r80-90 > 0  and r90-95 > 0
                  =  -1 otherwise

3.      For a type III city/municipality, the initial rate of change is equal to the geometric mean of the observed annual rates of change of the ratios of the first two intercensal periods.

  where I (x) =  1 if  r70-80 > 0 and r80-90 > 0
                    =  -1 otherwise

4.   For a type IV city/municipality, the initial rate of change is equal to one half the annual rate of change in the ratios of the last intercensal period.

It was assumed that for all cities/municipalities, r would gradually reduce so that they would all become zero around 95 years from the base year, which is 1995.  Based on this assumption, a schedule of ratios was derived for each projection year using the following formula:

or

where:        =  ratio of the population of the city/municipality to that of the province in 1995

                   =  ratio of the population of the city/municipality to that of the province   for the kth year from 1995, and

                  =  initial rate of change in the ratios.

Projected ratios are finally adjusted such that the ratios of all cities/municipalities comprising a province sum up to 1.0.
  
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