Estimation of the net migration by comparing two successive censuses
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ESTIMATION OF THE NET MIGRATION BY COMPARING TWO SUCCESSIVE CENSUSES. Michel POULAIN GéDAP UCL Belgium. The following methodology concerns the estimation of the net international migration. By definition this is the difference between immigration and emigration figures.

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Estimation of the net migration by comparing two successive censuses l.jpg

ESTIMATION OF THE NET MIGRATION BY COMPARING TWO SUCCESSIVE CENSUSES

Michel POULAIN

GéDAP UCL

Belgium


The following methodology concerns the estimation of the net international migration l.jpg

The following methodology concernsthe estimation of the net international migration.

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

Net migration is equal to zero for internal migrations.

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


Which statistical data are needed l.jpg

Which statistical data are needed?

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

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

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


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About the timing of census

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

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

The used data are recalculated figures for 1st January 1989 and 2000.


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About census reliability (1)

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

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


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About census reliability (2)

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


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About census reliability (3)

Let us take two concrete examples:

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

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


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About census reliability (5)

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

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

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


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About reliability of vital registration(1)

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

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


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About reliability of vital registration(2)

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

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

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


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Generally speaking…

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


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Basic steps for estimating net migration

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

Population at second census T 2 =

Population at first census T 1 + births (T1, T2) – deaths (T1, T2)

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


And accordingly n et migration t1 t2 l.jpg

And accordinglyNet migration (T1, T2)

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

Net migration (T1, T2) =

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

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


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For various reasons linked to over-coverage or under-coverage of some specific populations the real population stock at a given census would be accompanied by a confidence interval

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

< P real (T1)

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

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

< P real (T2)

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


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Accordingly we may assume that the real population figure in both censuses may beexpressed as follows:

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

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

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


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Coming back to the estimation of the net migration both censuses may be

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

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

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


Net migration by age l.jpg

Net migration by age both censuses may be

This equation allows estimating net migration for a given generation. As the age of a given generation will be different in the two censuses and if error is age dependant we cannot not agree that compensation will occur between the two error terms.


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In the best conditions both censuses may be

Let’s assume at that stage that the error terms may be neglected and that births and deaths figures by generation are well known


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The data from Estonia will be used as an illustrative example

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

31st March 2000.

The Estonian Statistical Office provided an appropriate estimation of the population on 1st January 1989 and 2000 based on both census enumerations and all changes in the population occurring between census and estimation times.


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Age structure for Estonia exampleat two last censuses


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Net migration for Estonia examplebetween two last censuses


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In depth analysis of results example

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

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

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


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In the case death statistics are not reliable or not available

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

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

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


The formula to estimate net migration census errors being ignored will become l.jpg

The formula to estimate net migration, census errors being ignored, will become:

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

- births (T1, T2)]

/(1/(1 – k/2))


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A final warning ignored, will become:

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

THANKS and let’s keep in touch if needed !