ESTIMATION ESTIMATION OF THE NET MIGRATION OF THE NET MIGRATION

BY COMPARING BY COMPARING TWO SUCCESSIVE CENSUSESTWO SUCCESSIVE CENSUSES

Michel POULAINMichel POULAIN

GéDAP UCLGéDAP UCLBelgiumBelgium

The following methodology The following methodology concernsconcerns the estimation of the estimation of

the net international the net international migration.migration.

• By definition this is the difference By definition this is the difference between immigration and between immigration and emigration figures. emigration figures.

• Net migration is equal to zero for Net migration is equal to zero for internal migrations.internal migrations.

• If data on international If data on international immigrations is available and immigrations is available and enough reliable, then the enough reliable, then the international emigration figure international emigration figure may be estimated by difference may be estimated by difference between the international between the international immigration figure and the net immigration figure and the net migration estimation EMI migration estimation EMI = IMMI – (IMMI-EMI).= IMMI – (IMMI-EMI).

Which statistical dataWhich statistical data are needed? are needed?

• Population by sex and year of Population by sex and year of birth at national level at the time birth at national level at the time of first census.of first census.

• Population by sex and year of Population by sex and year of birth at national level at the time birth at national level at the time of second census.of second census.

• Number of births and deaths by Number of births and deaths by sex and year of birth for the sex and year of birth for the intercensal period (the date of intercensal period (the date of occurrence of death is not needed occurrence of death is not needed for this calculation).for this calculation).

About the timing of censusAbout the timing of census

The date of census is not usually 1 The date of census is not usually 1 January (or 31 December), but January (or 31 December), but recalculated figures for official recalculated figures for official population estimates often have population estimates often have to be provided for these particular to be provided for these particular dates each year. dates each year.

We will present a concrete example We will present a concrete example on Estonia where the two last on Estonia where the two last censuses where carried out on censuses where carried out on 12ve January 1989 and 31st 12ve January 1989 and 31st March 2000.March 2000.

The used data are recalculated The used data are recalculated figures for 1st January 1989 and figures for 1st January 1989 and 2000.2000.

About census reliability (1)About census reliability (1)

The reliability of Census data must be The reliability of Census data must be examined carefully before starting examined carefully before starting the estimation of the net the estimation of the net migrationmigration

In fact, census errors may have a In fact, census errors may have a substantial impact on estimated substantial impact on estimated net migration figures and net migration figures and therefore under-coverage or therefore under-coverage or double-counts by age and sex are double-counts by age and sex are useful information for carrying out useful information for carrying out our estimations.our estimations.

About census reliability (2)About census reliability (2)

First, it is essential to identify which specific First, it is essential to identify which specific populations that were not concerned by populations that were not concerned by either or both censuses such as army, either or both censuses such as army, refugees, asylum seekers, short-term refugees, asylum seekers, short-term immigrants etc. More generally there immigrants etc. More generally there will be some problems if census will be some problems if census enumeration rules vary from one enumeration rules vary from one census to the next or if the census rules census to the next or if the census rules do not match those followed in vital do not match those followed in vital registration as regards the population at registration as regards the population at risk. risk.

About census reliability (3)About census reliability (3)

Let us take two concrete Let us take two concrete examples:examples:

• The second census considers refugees The second census considers refugees but the first did not, while no but the first did not, while no immigration has been registered for immigration has been registered for these refugees. In this situation there these refugees. In this situation there are two possibilities to make everything are two possibilities to make everything consistent: either not to consider consistent: either not to consider refugees in the second census or to refugees in the second census or to include them ex post in immigration include them ex post in immigration figures.figures.

• The first census included some army The first census included some army personnel but the second does not, personnel but the second does not, while these persons were not recorded while these persons were not recorded in emigration statistics. in emigration statistics.

About census reliability (5)About census reliability (5)

• So far we may consider under-coverage So far we may consider under-coverage arising quasi-randomly or relating to a arising quasi-randomly or relating to a non-covered specific population. non-covered specific population.

• We have also to face another possible We have also to face another possible source of error: untrue responses to source of error: untrue responses to census questions and more specifically census questions and more specifically to census questions relate to age or to census questions relate to age or data of birth. This may result in age data of birth. This may result in age exaggeration by the oldest or some exaggeration by the oldest or some attraction towards specific ages. attraction towards specific ages.

• For specific age attraction some For specific age attraction some smoothing correction methods may be smoothing correction methods may be used, but none will be appropriate to used, but none will be appropriate to correct age exaggeration. correct age exaggeration.

About reliability of vital About reliability of vital

registrationregistration (1)(1)

Information is also needed about the Information is also needed about the reliability and coverage of all reliability and coverage of all recorded demographic events recorded demographic events (births, deaths, international (births, deaths, international immigration and international immigration and international emigration). emigration).

Birth and death registration are both Birth and death registration are both usually considered as broadly usually considered as broadly reliable, and limited errors in the reliable, and limited errors in the associated statistical data associated statistical data collection process will usually collection process will usually have no impact on the estimation have no impact on the estimation of the net migration. of the net migration.

About reliability of vital About reliability of vital

registrationregistration (2)(2)

However, we have to take care of two However, we have to take care of two specific points:specific points:

1.1. Do vital statistics data cover all Do vital statistics data cover all years during the intercensal years during the intercensal period, including the few months period, including the few months between exact census dates and between exact census dates and the time of official annual the time of official annual population figure release?population figure release?

2.2. Do the vital statistics include all Do the vital statistics include all specific groups of population, specific groups of population, following the same rules as following the same rules as census enumeration?census enumeration?

Generally speaking…Generally speaking…

It is essential that both censuses and It is essential that both censuses and vital statistics relate to the same vital statistics relate to the same population. If all exclude the same population. If all exclude the same specific group(s) there will be no specific group(s) there will be no negative impact on the method. negative impact on the method. However if a specific group is However if a specific group is missing in one data source, it is missing in one data source, it is probably easier to eliminate the probably easier to eliminate the same group from the other data same group from the other data source than to try to adjust the source than to try to adjust the data source from which it is data source from which it is excluded.excluded.

Basic steps for estimatingBasic steps for estimating net migration net migration

The basic equation to explicit the The basic equation to explicit the population change is the population change is the following : following :

Population at second census T 2 =Population at second census T 2 =Population at first census T 1 + Population at first census T 1 +

births (T1, T2) – deaths (T1, T2)births (T1, T2) – deaths (T1, T2) + immigrations (T1, T2) – + immigrations (T1, T2) –

emigrations (T1, T2)emigrations (T1, T2)

And accordinglyAnd accordingly

NNet migration (T1, T2)et migration (T1, T2)

= immigrations (T1, T2) – emigrations (T1, = immigrations (T1, T2) – emigrations (T1, T2)T2)

Net migration (T1, T2) = Net migration (T1, T2) =

Population at second census T 2 - Population at second census T 2 - Population at first census T 1 Population at first census T 1

- births (T1, T2) + deaths (T1, T2)- births (T1, T2) + deaths (T1, T2)

For various reasons linked to over-For various reasons linked to over-coverage or under-coverage of some coverage or under-coverage of some

specific populations the real population specific populations the real population stock at a given censusstock at a given census

would be accompanied by a confidence would be accompanied by a confidence

intervalinterval

P observed (T1) – Over-estimation (T1) P observed (T1) – Over-estimation (T1)

< < P real (T1)P real (T1)

< P observed (T1) + Under-estimation < P observed (T1) + Under-estimation (T1)(T1)

P observed (T2) – Over-estimation (T2) P observed (T2) – Over-estimation (T2)

< < P real (T2)P real (T2)

< P observed (T2) + Under-estimation < P observed (T2) + Under-estimation (T2)(T2)

Accordingly we may assume Accordingly we may assume that the real population that the real population

figure in both censuses may figure in both censuses may bebe expressed as follows:expressed as follows:

P real (T1) = P observed (T1) + Error term P real (T1) = P observed (T1) + Error term (T1)(T1)

P real (T2) = P observed (T2) + Error term P real (T2) = P observed (T2) + Error term (T2)(T2)

where error terms may be positive or negative where error terms may be positive or negative depending if we are facing under-coverage depending if we are facing under-coverage (positive error) or over-coverage (negative (positive error) or over-coverage (negative error).error).

Coming back to the Coming back to the estimation of the net estimation of the net

migrationmigration

Net migration (T1, T2) = P real (T2) - P real (T1) Net migration (T1, T2) = P real (T2) - P real (T1)

- births (T1, T2) + deaths (T1, T2)- births (T1, T2) + deaths (T1, T2)

Net migration (T1, T2) = P observed Net migration (T1, T2) = P observed (T2) + Error term (T2) - P observed (T2) + Error term (T2) - P observed (T1) - Error term (T1) - births (T1, (T1) - Error term (T1) - births (T1,

T2) + deaths (T1, T2)T2) + deaths (T1, T2)

Net migration by ageNet migration by age

This equation allows estimating net This equation allows estimating net migration for a given generation. As migration for a given generation. As the age of a given generation will be the age of a given generation will be different in the two censuses and if different in the two censuses and if

error is age dependant we cannot not error is age dependant we cannot not agree that compensation will occur agree that compensation will occur

between the two error terms. between the two error terms.

In the best conditionsIn the best conditions

Let’s assume at that stage that the error Let’s assume at that stage that the error terms may be terms may be neglected neglected and that and that

births and deaths figures by generation births and deaths figures by generation are are well knownwell known

The data from Estonia will be The data from Estonia will be used as an illustrative used as an illustrative

exampleexample

The two last censuses have been organised The two last censuses have been organised respectively on 12ve January 1989 and respectively on 12ve January 1989 and

31st March 2000.31st March 2000. The Estonian Statistical Office provided an The Estonian Statistical Office provided an

appropriate estimation of the population appropriate estimation of the population on 1st January 1989 and 2000 based on on 1st January 1989 and 2000 based on

both census enumerations and all both census enumerations and all changes in the population occurring changes in the population occurring

between census and estimation times.between census and estimation times.

Age structure for Estonia Age structure for Estonia at two last censusesat two last censuses

-

5 000

10 000

15 000

20 000

25 000

30 000

1999

1995

1991

1987

1983

1979

1975

1971

1967

1963

1959

1955

1951

1947

1943

1939

1935

1931

1927

1923

1919

1915

1911

1907

1903

1899

Population on January 1st 89based of 89 census

Observed population onJanuary 1st 2000 according2000 census

Net migration for Estonia Net migration for Estonia between two last censusesbetween two last censuses

-5 000

-4 000

-3 000

-2 000

-1 000

-

1 000

1999

1995

1991

1987

1983

1979

1975

1971

1967

1963

1959

1955

1951

1947

1943

1939

1935

1931

1927

1923

1919

1915

1911

1907

1903

Calculated Netmigration

In depth analysis of resultsIn depth analysis of results

• We are expecting to find a very well We are expecting to find a very well smoothed curve without any accident, peak smoothed curve without any accident, peak or hole. If such an accident appears, there or hole. If such an accident appears, there should be a direct and evident explanation should be a direct and evident explanation in terms of specific migration flow.in terms of specific migration flow.

• This explanation should fit at the same time This explanation should fit at the same time with the specific age in concern and the with the specific age in concern and the amplitude of the accident. amplitude of the accident.

• If such a direct explanation does not exist If such a direct explanation does not exist possible under- or over-estimations in both possible under- or over-estimations in both censuses have to be reconsidered.censuses have to be reconsidered.

In the case death statistics are In the case death statistics are not reliable or not availablenot reliable or not available

• In this case we will used an In this case we will used an appropriate life table where the appropriate life table where the probability probability kk to die between the two to die between the two censuses may be estimated censuses may be estimated

• On this base the number of deaths On this base the number of deaths may be estimated as follows:may be estimated as follows:

Deaths (T1, T2) = Deaths (T1, T2) = kk. [P (T1) + . [P (T1) + (Net migration)/2](Net migration)/2]

The formula to estimate net The formula to estimate net migration, census errors migration, census errors

being ignored, will become:being ignored, will become:

Net migration (T1,T2) Net migration (T1,T2) = [P(T2) - P(T1) (1-k) = [P(T2) - P(T1) (1-k)

- births (T1, T2)] - births (T1, T2)]

/(1/(1 – k/2))/(1/(1 – k/2))

A final warningA final warning

Net migration is the difference Net migration is the difference between agregate numbers of between agregate numbers of immigrations and emigrations by age immigrations and emigrations by age and sex but people immigrating are and sex but people immigrating are never similar to those emigrating as never similar to those emigrating as they are reacting to clearly different they are reacting to clearly different stimuli…stimuli…

THANKS and let’s keep in touch if THANKS and let’s keep in touch if needed !needed !