Methodological summary
Summary methodology of Population Now Casts
The method for computing Population Now Cast tries to factor in the most recent
information available on the behaviour of the demographic phenomena
determining current population figures and their structure by age.
Population Now Casts constitute a synthesising exercise which takes all the
demographic information available at the time into account: population censuses;
births and deaths accounted for in vital statistics; immigration and emigration
estimated from the latest population register changes, etc. These estimates are
considered the best possible approximation to the actual number of residents in
Spain, its Autonomous Communities and its provinces, with the information
available at a given time and, for this reason, they are currently used by the INE as
reference population statistics in all household surveys and to compute all types of
indicators.
The method for computing the statistics is based on the components method. The
application of this method follows the following scheme: based on the resident
population in a given geographic area and on the data observed for each basic
demographic component - mortality, fertility and migration – it seeks to estimate
the future population on the basis of certain assumptions about the future of these
three phenomena which determine its growth and age structure.
The forecasts for births, deaths and migrations relying on those assumptions are
subsequently compared to observed figures whenever new data become
available. Due to the sharp rise in immigration levels in recent years and the
uncertainty about the future evolution of these flows, the comparison between
projected figures and those which are being recorded in the now cast, generally
provisional or interim, are conducted at the end of each quarter.
Population figures, by province, sex and age, estimated from the 2001 Population
Census and dating back to 1 January 2002, make up the base population.1 For
each new estimate period, the base population for applying the component
method comprises the population figures by province, sex and age corresponding
to the Now Cast as of 1 January of the current year.
As the main basis of the forecast, the pattern of specific mortality and fertility rates
by age is observed, including the most recent information available. Based on the
flows observed in the continuous population register, the change in net foreign
inbound migration is determined as the difference between population changes
which inbound migratory movement assumes and those which assume an
outbound change. Domestic migratory flows are observed in a similar way.
The retrospective observation of the behaviour of fertility, mortality and inbound
and outbound flows using the most recent information available allows specific
rates of fertility and mortality by age to be forecast for the current year, as well as
an approximation of net inbound flows and domestic migrations for the same
period.
By applying survival probabilities to the base population by age as at 1 January of
the current year and to flows of births and immigrants for each year, we can
1
Censal populations of the three insular provinces are corrected by adding a total of 110,000 inhabitants,
40,000 of whom correspond to the Balearic Islands and 30,000 and 40,000 correspond to Santa Cruz de
Tenerife and Las Palmas, respectively.
generate the number of survivors broken down by age at the end of that year.
These probabilities are calculated from projected mortality tables.
Survivors from Autonomous Communities are adjusted to those from the national
total and those from provinces are adjusted to their respective Autonomous
Communities, so figures retain the required consistency. The resulting populations
are processed the same way.
Specifically, if I = sex, J = age and K = year, for the three geographic areas we
have:
- National total:
If j  1 , Pi , j ,k  ( Pi , j 1,k 1  PEX i , j 1,k 1 ) * Ti , j 1,k 1
where Pi , j ,k is the population figure of sex i, age j at 1 January of year k;
PEX i , j 1,k 1
is the net inbound foreign migration flow of sex i and age j-1 at 1
January of year k-1; and Ti , j 1,k 1 is the survival probability forecast for year k-1 for
an individual of sex i and age j-1 at 1 January of year k-1.
49
If j  0 , Pi ,0 ,k  (  ri  ( f j ,k 1  ( P2 , j ,k 1  P2 , j ,k ) / 2 )  PEX i ,1,k 1 )  Ti ,1,k 1
j 15
where Pi ,0 ,k is the population figure of sex i, less than 1 year old at 1 January of
year k; P2 , j ,k 1 being the population of women of age j at 1 January of year k-1; f j ,k 1
being the specific fertility rate projected for women of age j during year k-1; r1
being the estimate of the proportion of boys among births; r2  1  r1 being that for
girls; PEX i ,1,k 1 being the net inbound migration flow from overseas of children born
during year k-1; and Ti ,1,k 1 being the survival probability of children born of sex i
during year k-1.
- Autonomous Communities:
If j  1 , Pi , j ,k ,h  ( Pi , j 1,k 1,h  PEi , j 1,k 1,h  PSi , j 1,k 1,h  PEX i , j 1,k 1,h ) * Ti , j 1,k 1,h
where Pi , j ,k ,h the population figure of sex i, age j, in Autonomous Community h at 1
January of year k; PEi , j 1,k 1,h the inbound migration flow during year k-1 in
Autonomous Community h, from the rest of Spain, of sex i and age j-1 at 1
January of year k-1; PSi , j 1,k 1,h outbound migration flow during year k-1 of
Autonomous Community h, to the rest of Spain, of sex i and age j-1 at 1 January
of year k-1; PEX i , j 1,k 1,h the net inbound migration during year k-1 in Autonomous
Community h, from overseas, of sex i and age j-1 at 1 January of year k-1; and
Ti , j 1,k 1,h is the survival probability forecast for year k-1, for an individual residing in
Autonomous Community h, of sex i and age j-1 at 1 January of year k-1.
If j  0
49
Pi ,0 ,k ,h  (  r i  ( f j ,k 1,h  ( P2 , j ,k 1,h  P2 , j ,k ,h ) / 2 )  PE i ,1,k 1,h  PS i ,1,k 1,h  PEX i ,1,k 1,h )  Ti ,1,k 1,h
j 15
where Pi ,0 ,k ,h is the population figure of sex i, less than 1 year old at 1 January of
year k, in Autonomous Community h; P2 ,k 1 ,k ,h being the population of women of age
j at 1 January of year k-1, in Autonomous Community h; f j ,k 1,h being the specific
fertility rate projected for women resident in Autonomous Community h, of age j
during year k-1; r1 being the estimate of the proportion of boys among total births;
r2  1  r1 being the estimate of the proportion of girls in the total for births;
PE i ,1,k 1,h being the inbound migration flow in Autonomous Community h from the
rest of Spain, born during year k-1; PSi ,1,k 1,h being the outbound migration flow,
from Autonomous Community h to the rest of Spain, of sex i born during year k-1;
PEX i ,1,k 1,h being the net inbound migation flow in Autonomous Community h of sex
i, born during the year k-1, from abroad; and Ti,-1,k-1 being the survival probability of
children born of sex i during year k-1.
- Provinces:
If j  1 , Pi , j ,k ,h ,l  ( Pi , j 1,k 1,h ,l  PPVi , j 1,k 1,h ,l  PEX i , j 1,k ,lh ) * Ti , j 1,k 1,h ,l
where Pi , j , k , h ,l is the population figure of sex i, age j, in province I of Autonomous
Community h at 1 January of year k; PPVi , j 1,k 1,h ,l the net inbound migration flow
during year k-1 in province I of Autonomous Community h, from the rest of Spain,
of sex i and age j-1 at 1 January of year k-1; PEX i , j 1,k 1,h ,h the net inbound
migration flow during year k-1 in province I of Autonomous Community h, from
abroad, of sex i and age j-1 at 1 January of year k-1; and Ti , j 1,k 1,h is the survival
probability forecast for year k-1, for an individual residing in Autonomous
Community h, in province I, of sex i and age j-1 at 1 January of year k-1.
If j  0 Pi ,0 ,h ,l  (( ri  Pi ,1,h ,l  PPVi ,1,k 1,h ,l  PEX i ,1,k ,h ,l )  Ti ,1,k 1,h
where Pi , 0 , k , h ,l is the population resident in province l of Autonomous Community
P
h, of sex i less than 1 year of age at 1 January of year k; i ,1,h ,l being the estimate
of the number of births during year k-1, in province l of Autonomous Community h;
r1 being the estimate of the proportion of boys in the total for births; r2  1  r1 the
PPV
i , j 1 ,k 1 ,h ,l
estimate of the proportion of girls in the total for births;
being the net
incoming migration flow of sex i, born during year k-1, in province l of Autonomous
PEX i ,1,k 1,h ,l
Community h, from the rest of Spain;
the net inbound migration flow for
sex i, born during year k-1, in province l of Autonomous Community h, from
Ti ,1,k 1,h
abroad; and
being the survival probability of children born of sex i during k1 in Autonomous Community h.
Lastly, we should add that the estimated population figures for day 1 of each
quarter of year k-1 are generated by linear interpolation for those corresponding to
the current population now cast at 1 January of year k-1 and that projected and the
end of each quarter for 1 January of year k, using the latest available
demographical information. And, the estimated population figures for intermediate
dates of the quarter are generated by linear interpolation between those
corresponding to the first day of the same and of the following quarter.