DESCRIPTION OF THE KANTOR DEMO-TOOL

 

1.-Accounting identities

 

The Kantor Demo-tool is an Excel spreadsheet designed to produce transparent and easy population projections for non-professional users.

 

The population stock (P) in a given moment (t) is the result of two components: vegetative growth and migration flow. The vegetative growth is the net result of births (B) minus deaths (D), while the migration flow is the net of immigration (I) minus emigration (E). Given these definitions, the following identity holds:

 

The vegetative dynamics of a population is strongly dependent on its age structure, because both birth and death rates are strongly age-dependent.  A population pyramid is a graph showing the population in a given geographical area (vg. a country) in a given year [1: a  note on sex ratios]. The Kantor Demo-tool is designed to project population pyramids (stocks-by-age), using two flow-by-age curves: the mortality and fertility curves. For demographically open countries, a migration curve should be provided in addition.

 

The fertility (mortality) curve is an age-indexed curve, showing the number of births (deaths) in a given age group. The essential difference between the two curves is that the deaths reduce population in the age group where they happen (the individual itself is removed), while births increase population in the age group “zero years”.

 

Let be the  Pit population of age i in a given year t, fit, mit the fertility and mortality  rate of the age group i in the year t, and let be nmit the net migration flow (positive or negative) in the group i in year t. Then the following accounting identities hold:

 

 

Given a population pyramid for a given year, this identity can be used to produce population projections as long as mortality, fertility and migration dynamics are provided.

 

The spreadsheet “Population_stock” run these two equations across projection years, using fertility (spreadsheet “Fertility”), mortality (spreadsheet “Mortality”) and migration curves (spreadsheet “Migration”). The population stock in the first year comes from the age pyramid of Holland in 2005 (data for Algeria are also included in the spreadsheet “Stock en 0”). Our population range is 0-95 years old. The fertility time span is supposed to be 15-49 years old.

 

2.-Modeling Flows: mortality and migration net flows

 

The UN “Replacement Migration” report provides a model (derived with US, Canada and Australia data) for the population pyramid of migrants. This population pyramid is implemented in the spreadsheet “Migration Builder”. If the reader fills the yellow row with the yearly number of migrants, the spreadsheet will produce an age breakdown of the given net migration flow of the year. These data are added in the “Population_stock” spreadsheet, as a flow contributing to the evolution of the population pyramid. Migration data for the EU-15 are provided in the EU Statistical Yearbook (pag. 53).

 

The age mortality curve comes from data of Holland (2005). Actuarial tables can also be used. The mortality curve is supposed in our model to be fixed (it is the same for all projection years). The user can build her own improved model of future mortality.

 

3. Modeling Flows: the Convex Fertility Model

 

There is an extensive literature linking socio-demographic and macro-economic variables with fertility curves. But these models are not specially useful for projection purposes, because social determinants are often harder to project than fertility itself. On the other hand, the structure of fertility rates can be fitted from past trends and international comparison.

 

The Population Division of the UN Department of Economic and Social Affairs,  produces every five years “The World Fertility Report”, where fertility curves (spreadsheet “II.2”) for an ample range of countries are provided. The age groups are five year long, and the provided data are the number of births by 1000 women in the age group every year. Total fertility (children by woman in the five years) is the number of births, multiplied by the five years length of the group and divided by 1000.

 

 

 

 

In the graph above, fertility rates in terms of number of children per woman in the age group are provided (original data x 5/1000). The area below the curve is the total fertility rate (children per woman in all her fertile life span):

 

 

The fertility rate is fully determined by the fertility curve, but many different fertility curves can produce the same fertility rate (there is an infinite number of curves that leave the same area below themselves). On the other hand, the shape of fertility curves is more or less uniform: They tend to be single-peaked, to have a peak in the 25-29 group, and the countries with high fertility rates are the ones with more the most precocious mothers.

 

Then, the Fertility Convex Model is a fitting model that constructs a fertility curve for every fertility rate, based on a convex combination of two chosen fertility curves.

 

Let be θEgypt , θGermany the fertility rates for Egypt and Germany (considered as extreme representative cases), and fEgypt(i) ,fGermany(i) their fertility curves. Let be θ the fertility rate of a given country. Then there is a unique  α  such that:

 

α is:

 

 


 fθ(i), the fertility curve is constructed as the linear combination:

 

 

When θ in [θEgypt , θGermany], the combination is convex (giving the name to the model).

 

Lets take θUSA=2,13 and compare the synthetic curve with the real US data:

 

 

The “Fertility” spreadsheet is linked to the “Fertility_builder” spreadsheet. If a fertility rate path in the yellow colored row is provided, the spreadsheet builds the corresponding fertility curves. That is, “Fertility_builder” turns a fertility rate path into a fertility curves path, using the convex combination model. If the user is interested in a different model, she can write her own “Fertility builder” and link it to the “Fertility” spreadsheet.

 

Additionally, the spreadsheet “Stock en 0” provides an annualizer, in order to turn 5-year population pyramids into yearly ones. The 5-year pyramid is fed (in the yellow colored range) and a yearly pyramid is given back under the title “pyramids annualizer”. This allows the user to use the 5-year population pyramids provided in the UN Population Statistics, for the demographic analysis of given countries.

 

For European Union data (2005) the European Comission publishes the following report: population in Europe 2005.

 

 

[1: a note on sex ratios]: the Kantor Demo-tool supposes that natural sex ratios (close to 1:1) hold for all age groups and years. The population in the spreadsheet is total (male+female), and the equilibrium fertility rate is 2.0 (the population is in equilibrium when every couple replaces itself with two children).  A different approach would be to project only female population: under that methodology only female babies/adults are taken into account, and the equilibrium fertility rate is 1.0 (the population is in equilibrium when every woman replaces herself with a daughter).

 

Disclaimer: the Kantor demo-tool is for free, but we expect users to quote and link it in any application. The Excel sheet is given as is, with no guarantee attached. The user should check and understand it by herself. This is a beta version that can be improved.