University of Groningen - Master’s Thesis EORAS
Life expectancy and population projections by age, gender and
level of educational attainment for the Netherlands for 2014-2060
Author: V. Haring - S2165635
University of Groningen - Master’s Thesis EORAS
Life expectancy and population projections by age, gender and
level of educational attainment for the Netherlands for 2014-2060
Author: V. Haring - S2165635
August 14, 2017
Abstract
Contents
1. Introduction 5
2. Description of the data 9
2.1. Different datasets with the component education . . . 9
2.1.1. Censuses . . . 9
2.1.2. Dutch Labor Force Survey . . . 9
2.1.3. Educational Attainment File . . . 9
2.2. Mortality by level of educational attainment . . . 10
2.3. Definitions . . . 10
3. The model 11 3.1. Base population . . . 11
3.2. Mortality rates . . . 11
3.2.1. Determination of mortality rates by educational level . . . 12
3.2.2. Forecasting of mortality rates by education level . . . 13
3.2.3. Standard mortality rates . . . 15
3.2.4. Convert mortality rates by five-year age groups to mortality rates by single age . . . 16
3.3. Fertility rates . . . 16
3.4. Migration rates . . . 16
3.5. Educational transition rates . . . 17
3.6. Population projections: Cohort-component model . . . 18
4. Results 21 4.1. Past trends in life expectancy . . . 21
4.2. Life expectancy projections . . . 22
4.3. Population projections with mortality rates by level of educational attainment . 24 4.4. Population projections with standard mortality rates . . . 28
5. Comparison with other papers 31 5.1. Comparision Van Baal et al. (2016) . . . 31
5.2. Comparision K.C. et al. (2013) . . . 32
6. Conclusion 35
A. Appendix: the increment weight 38
1. Introduction
Nowadays, people become increasingly older. In the Netherlands, the life expectancy at birth has increased from 71 years in 1950 to 81 years in 2015. In the twentieth century, deaths due to infectious and parasitic diseases decreased, due to the introduction of the national vaccination program by the government in 1957. Moreover, there have been improvements in the technology used in health care, which has caused a decrease in infant mortality and cardiovascular deaths, among other things (Mathers et al., 2015). Furthermore, people’s wealth has grown, which has caused better living standards, such as more nutritious diets and clean drinking water (NIH, 2011). Finally, the use of tobacco has also decreased, especially among males (Stoeldraijer et al., 2012) and highly educated persons (Statistics Netherlands, 2017). The expectation is that the life expectancy will continue to increase in the upcoming years.
Because of the increasing life expectancy, the proportion of elderly increased. In 1950, 770.5 thousand persons in the Netherlands were 65 years or older (7.7% of the Dutch population). Decades later, in 2015, the number of persons of 65 years or older has increased to 3 million (17.8% of the Dutch population). Another reason for the aging of the Dutch population is that the number of children born has decreased over the past years. In 1950, the average number of children born per woman was 3.1. This was after the second world war and people from this generation are generally known as the babyboomers. In the 70s, the average number of children born per woman declined rapidly to 1.6 and it stayed around this level until today1. The conse-quence is that there are not only more elderly because of the increasing life expectancy, but also younger generations consisting of relatively less persons. As a result, the proportion of elderly with respect to the people in the working age (old-age dependency ratio) increased from 14,0% in 1950 to 29,9% in 2015. The continuing increase in life expectancy and the expectation that the average number of children born will stay below the replacement level, will result in a further increase of the old-age dependency ratio in the future.
A structural problem of aging is the affordability of pensions. One of the imposed solutions in the Netherlands to ensure the future pensions are affordable is increasing the retirement age gradually from 65 years to 67 years. From 2022 onwards, the retirement age is linked to the life expectancy, which can cause a further increase of the retirement age if the life expectancy increases. Unfortunately, this does not solve the entire problem. The old-age dependency ra-tio will still increase when the retirement age is linked to the future life expectancy. Another consequence of an aging population is the increasing demand for special services for elderly, like nursing homes and care for the elderly. Hence, the composition of the population and their needs are changing, now and in the future, and therefore, it is really important to make an accurate and detailed population projection of the future.
In this paper, we are going to make forecasts of the life expectancy in the Netherlands by age, gender and level of educational attainment. The education-specific mortality rates will be esti-mated using an extended Li-Lee model (Van Baal et al., 2016) and then they will be forecasted using ARIMA models. A demographic multi-state cohort-component model can be used to pro-duce the population projections by five-year age groups, gender and four levels of educational attainment for the years 2014-2060.
Nowadays, population projections are made in the Netherlands (Van Duin and Stoeldraijer, 2014) and in other countries. For the underlying assumptions of mortality there have also been
1
significant developments in forecasting (Booth and Tickle, 2008). Although there have been ex-ceptions, most approaches are based on time-series extrapolation models such as the Lee-Carter model (Lee, 2000). These models have been used to project the life expectancy by age and gender and are used as input for the population projections. One important factor that is often neglected in mortality forecasting and population projections is educational attainment. However, mortal-ity (and also fertilmortal-ity and migration; a topic for future research) and - as a consequence - the number of elderly within the population is strongly affected by education.
One of the reasons for the relation between education and mortality is that there is a large and persistent association between education and health (Ross and Wu, 1995). Education is related to income and occupational choices. In general, people with more money can pay for medical care more easily. Even though the Netherlands has social insurance, this is still relevant due to the obligatory deductible and sometimes voluntary deductible. Moreover, due to education, there are differences in information and cognition (Fletcher and Frisvold, 2012). People with higher education will know more about healthier food and disease prevention. For example, higher educated people will know more often that unhealthy food might lead to obesity and they know what is healthy and what is not. Moreover, they have the resources to buy healthy food, because generally healthy food is more expensive. Hence, the empirical research (Lleras-Muney, 2004) has shown that higher educated persons will usually live longer as a result of a better health and thus have a higher life expectancy. This is known as differential mortality in the literature. Another reason for the relation between education and mortality is that if citizens become more informed and active voters, this will have a positive effect on other citizens through improving the quality of the democratic process. Milligan et al. (2004) relate educational attainment to several measures of political interest and involvement in the UK and the US and they find that higher educational attainment generally leads to more political involvement. Hence, people who are more involved tend to make a better environment for themselves and one could argue that they live longer. Furthermore, research shows that higher levels of education are associated with a lower likelihood of criminal activity. Lochner and Moretti (2004) find that US high school graduation has a significant negative effect on the incarceration probability for both blacks and whites. The biggest impacts of graduation are associated with murder, assault, and motor vehi-cle theft. A comprehensive national study for Norway conducted by researchers at IIASA and Statistics Norway (Skardhamar and Skirbekk, 2013) finds that people with criminal records die younger than those without one. For the Netherlands, Groot and Maassen-van den Brink (2010) show that the probability of committing crimes like shop lifting, vandalism and threat, assault and injury decreases with years of education. Nieuwbeerta and Piquero (2008) examine the rela-tion between criminal conduct and mortality rates in the Netherlands and the results show that criminal conduct increases the chance of premature death due to both natural and unnatural causes.
Another interesting point is that the percentage of higher educated people, who attained college or university, in the Netherlands is growing. Between 2003 and 2012, this percentage increased from 22% to 28% for people aged between 15 and 65 years. At the same time, the percent-age of lower educated persons (who only attained primary education, lower general secondary education, higher general secondary education class 1-3, pre-university education class 1-3 or intermediate vocational education level 1) decreased from 36% in 2003 to 30% in 2012 2. In other words, there is a shift of more or less 6 percent point from the lower educated persons to
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the higher educated persons. A possible result of this shift is that the labor force participation can increase (Loichinger and Prskawetz, 2016). Because of this shift in education levels and the differences in life expectancy between lower and higher educated persons, it is very important to take educational attainment into account in population projections. In doing so, it could improve the accuracy of the population projections and provide more detail about the future population. Moreover, predictions for health care demand might get better and it might show whether an increase in retirement age is justified.
Examples of previous research accounting for the effect of education on mortality are K.C. and Lentzner (2010) and Van Baal et al. (2016). However, K.C. and Lentzner (2010) assumed changes in projected overall mortality rates only due to compositional changes. Van Baal et al. (2016) did make life expectancy projections whereby the death rates differ by level of education. They used the Dutch Labor Force Survey (DLFS) linked to the municipal population registers as their data source, which is sample data and thus contains only information on a limited part of the population.
In 1999, Filmer and Ahuja (1999) projected levels of educational attainment through the year 2020 by using the United Nations Educational, Scientific, and Cultural Organization’s projec-tions of enrollment and the International Labour Organization’s projecprojec-tions of population by sex and two broad age groups (6-24 and 25+). K.C. et al. (2010) made population projections by level of educational attainment, age, and sex for 120 countries for 2005-2050. In 2013 they made improvements and documented them in a new paper (K.C. et al., 2013). For the Netherlands, they used the Census of 2001 of Eurostat as dataset and due to the fact that they made projec-tions for 195 countries, the assumpprojec-tions were very general. For example, K.C. et al. (2013) used 2010 as base year, while we can use 2014 as base year, which make the projections more accurate and up-to-date. Furthermore, K.C. et al. (2013) used six education categories, including the categories of “No Education” and “Incomplete primary”. For the Netherlands, these categories are not very relevant, because it is compulsory to go to school until the age of 18. Therefore, we will skip those two categories. Concluding, the previous research is lacking recent and accurate datasets, specific assumptions for the Netherlands, small age groups and mortality differentials by educational attainment.
We improve on previous research by taking five-year age groups, calculating mortality differen-tials and using more comprehensive and accurate data. Five-year age groups are chosen to give more detail to the projections. It is important to distinguish between age groups, because they will show different life expectancies. The 65+ group is most interesting, because from this age, the mortality rates continue to increase. Moreover, using mortality differentials yield also more detail. We make not only projections by gender and age, but also by level of educational at-tainment, because the component education influences the mortality rates and in a consequence also the life expectancy. Because of this, we can distinguish between high and low educated persons and see the differences in life expectancy between them. Furthermore, comprehensive and accurate data is important to make reliable life expectancy and population projections. The EAF, which we use, is more up-to-date then the Census of 2001 and the DLFS, so we use more recent data. Moreover, the Census and DLFS are register based, but the component education is on a sample basis. For the EAF yields that all variables are register based and registers are of good quality.
2. Description of the data
To make projections by level of educational attainment we would like to have as much information as possible about the education level of the Dutch population. Since 1950, births and deaths are recorded by age and gender in the Netherlands. Information about the level of educational attainment is available in the Netherlands since 1987 and that is pretty unique. The Netherlands is far ahead when it comes to the use of register data. While many countries still use individual census questionnaires successfully, the last complete enumeration in the Netherlands was in 1971 (Statistics Netherlands, 2014). In this section, we will describe the different data sources that are available, make some assumptions about the data and determine which data source we will use to make population projections by age, gender and level of educational attainment.
2.1. Different datasets with the component education
2.1.1. Censuses
In the Netherlands, we have a register-based census, which is produced by combining existing register and sample survey data. In the 2011 Census, only two variables were not taken from a register: ‘occupation’ and ‘educational attainment’. Records from the Dutch Labor Force Survey (DLFS) in a three year period around the enumeration date (1 January 2011) were used to estimate these two variables. If one has a series of at least two censuses (held every ten year), which are both considered to be fairly reliable and give the total population by age, sex and level of educational attainment, one can quite easily calculate census survival ratios. The advantage is that the registers are of good quality. The disadvantage is that for the variable educational attainment only sample information is available. This means that the census survival ratios can be wrong due to (repeatedly) scaling of the variable educational attainment. Moreover, surveys tend to underestimate lower educational categories and overestimate higher educational categories, since persons in the high educational categories are more inclined to participate in surveys than persons in the low educational categories. This results in a bias towards a higher level of education.
2.1.2. Dutch Labor Force Survey
The data of the Dutch Labor Force Survey (DLFS) is based on a random sample available from 1987, which means that we have 28 years of data with information on educational attainment. However, linking persons who participated in the DLFS to the death registry is only possible since 1996. Hence, we only have 19 years of historical data left with information on educational attainment. The DLFS has the same advantages and disadvantages as the census. The only difference is that the DLFS is held yearly, while the census is held once every ten years.
2.1.3. Educational Attainment File
data is available from 1999 until 2014 and the current method is used since 2006. This means that we have 16 years of historical data with information on educational attainment. The EAF is a consistent dataset and therefore, this dataset is used to make the population projections by age, gender and level of educational attainment.
2.2. Mortality by level of educational attainment
To calculate the mortality rates of the historical period, we use the EAF linked to the death registry from 1999 to 2014. For example, the reference date of the EAF 1999 is 24th of September 1999. The death registry from 1st October 1999 until 30th September 2000 is linked to the EAF 1999. We assume that under the age of 25, the mortality rates are not distinguished by level of education, which means that the rates are the same for each education group. Before the age of 25, the mortality rate is very low and at that age, the educational attainment is already determined for most persons. Moreover, for the calculation of the mortality rates, five-year age groups will be made. Persons who are 80 years or older are put together in one age group, called 80+, since we do not have enough data of these age groups to model them separately. To calculate the mortality rates by level of education, the total number of deaths and the total population by age, gender and level of educational attainment should be known. Unfortunately, this data is unavailable, but an estimation of the total population and number of deaths is possible by weighting the EAF, as described in Section 3.2.1.
2.3. Definitions
Data of the Netherlands are collected, which gives the total population and mortality by: • Sex,
• Single age (0 to 99 years) and five-year age groups (0, 1-4, 5-9, ..., 75-79, 80+) respectively, • Four educational attainment categories based on SOI (Standard Education Classification),
which is determined by Statistics Netherlands: 1. Low: Primary education (elementary school);
2. Mid-low: VMBO (lower general secondary education), HAVO class 1-3 (higher general secondary education), VWO class 1-3 (pre-university education) and MBO level 1 (intermediate vocational education);
3. Mid-high: HAVO class 4-5, VWO class 4-6 and MBO level 2, 3 and 4; 4. High: HBO (college) and university.
3. The model
To make population projections we need a base population of the year 2014, mortality rates, fertility rates and migration rates, all by age, gender and level of educational attainment. Moreover, we need educational transition rates, which determine to which educational cate-gory a certain person transitions every year. The following parameters are used in this section: 100 ages x = 0, ..., 99; 18 age groups xg = 0, 1-4, 5-9, ..., 75-79, 80+; different time intervals tp1= 1999, ..., 2014, tp2= 1970, ..., 2014 and tf = 2014, ..., 2059; 2 genders g = male and f emale and 4 educational levels e = high, mid-high, mid-low and low. In this section, we will explain how these different rates are calculated.
3.1. Base population
The base population is constructed from the EAF 2014. The EAF is weighted (as described in the Appendix), such that it represents the whole population of the Netherlands. The base population is as follows:
P (x, 2014, g, e) = PEAF(x, 2014, g, e) · wP(x, 2014, g) = PEAF(x, 2014, g, e) · P (x, 2014, g)
PEAF(x, 2014, g),
where P (x, 2014, g, e) and P (x, 2014, g) are the Dutch populations in 2014 by age x, gender g with and without level of educational attainment e respectively. PEAF(x, 2014, g, e) and PEAF(x, 2014, g) are the populations from the EAF in 2014 by age x, gender g with and without level of educational attainment e respectively. Finally, wP(x, 2014, g) is the increment weight for the population (calculated in the Appendix). The base population is used to apply the mor-tality, fertility, migration and educational transition rates on, to estimate the population of the Netherlands in 2015-2060 by age, gender and educational attainment.
3.2. Mortality rates
Research shows that there is a large and positive correlation between education and health and that education has a causal impact on mortality (Lleras-Muney, 2004). Therefore, it is important to differentiate the mortality rates by level of education. The mortality rates mEAF(xg, tp1, g, e) of the EAF by age group, year, gender and educational group are estimated as follows:
mEAF(xg, tp1, g, e) = RR(xg, tp1, g, e) ·
mEAF(xg, tp1, g) P
eRR(xg, tp1, g, e) · p(xg, tp1, g, e) ,
where p(xg, tp1, g, e) denotes the proportion in the population of a particular age group xg, year tp1, gender g and educational group e, m
EAF
(xg, tp1, g) denotes the mortality rates of the EAF by age group xg, year tp1 and gender g and
RR(xg, tp1, g, e) =
mEAF(xg, tp1, g, e) mEAF(xg, tp1, g, eR),
where RR(xg, tp1, g, e) is the mortality rate of educational group e relative to the mortality rate of the reference educational group eR, by age group xg, year tp1, gender g. To estimate RR(xg, tp1, g, e), a Poisson regression model with the exposure as offset is used:
where E(D|xg, tp1, g, e) equals the expected number of deaths conditional on age group xg, year tp1, gender g and educational class e, X is a 768 × 39 matrix, which denotes predictor variables and θ is a 39-dimensional vector of coefficients that needs to be estimated. The predictor vari-ables consist of age dummies, year dummies and educational class dummies and of interactions of the educational class dummies with age and year variables, both continuous.
A weighting strategy has already been applied to make the EAF representative for the Dutch population. This way, the results of the file represent the entire Dutch population and the selected subpopulations. The records from the registers and the population aged 0 to 14 years get an increment weight of one. Most records from the DLFS have an increment weight unequal to one and they are determined with a special method invented by Linder et al. (2011, chapter 3). 3.2.1. Determination of mortality rates by educational level
After an analysis of the EAF, it turns out that the number of survivors and deceased in the EAF is not really representative for the whole population. The number of deaths in this dataset is very low, especially in the earlier years. There are several explanations for this. For the EAF 1999, the register data until 1999 is used. However, the DLFS from 1996 until 2005 is used, because if someone has a certain education level in 2005, attained before 1999, we know the education level of this person in 1999 as well. However, we also know for sure that this person will not die in the period 1999-2005 and that the amount of surviving persons is overestimated. For the EAF 2014, the register data until 2014 and the DLFS from 1996 until 2015 is used, which makes the above problem almost irrelevant for this year. Another explanation is that the elderly are poorly represented in the register data and in the DLFS. The register data exists since 1999 and most elderly attained their education level already before 1999. Moreover, persons over 65 years are no longer in the labor force and therefore occur less in the DLFS. However, persons who were for example 64 years old in 1999 became 80 years old in 2014. Hence, EAF 2014 will contain more elderly than the EAF 1999.
The problem of overestimating the survivors, as described above, can be solved by using a different weighting strategy (see the Appendix for the details). The increment weight that is used to increment the population in the EAF w(xg, tp1, g) is given by:
w(xg, tp1, g) =
mStatline(xg, tp1, g) mEAF(xg, tp1, g)
, (1)
where mStatline(xg, tp1, g) is the mortality rate in year tp1 of the Dutch population by age group xg and gender g (based on data from Statline) and m
EAF
(xg, tp1, g) is the mortality rate in year tp1 of the population of the EAF by age group xg and gender g.
attainment group e: m(xg, tp1, g, e) = m EAF (xg, tp1, g, e) · w(xg, tp1, g) = RR(xg, tp1, g, e) · mEAF(xg, tp1, g) P eRR(xg, tp1, g, e) · p(xg, tp1, g, e) ·m Statline (xg, tp1, g) mEAF(xg, tp1, g) = RR(xg, tp1, g, e) · mStatline(xg, tp1, g) P eRR(xg, tp1, g, e) · p(xg, tp1, g, e) .
3.2.2. Forecasting of mortality rates by education level
After obtaining the estimates of the mortality rates by age group, gender and level of educational attainment for the entire Dutch population, we can use these to forecast the mortality rates, us-ing the extended Li-Lee model based on the Lee-Carter and Li-Lee model.
The Lee-Carter model (Lee and Carter, 1992) was invented by Ronald D. Lee and Lawrence R. Carter in 1999 to forecast the mortality rates stratified by age group. They used three sets of parameters: age-specific constants, a time-varying index and interaction terms between time and age in the following model:
logm xg, tp2 = α xg + β1 xg κ1 tp2 + ε xg, tp2 , (2) where m xg, tp2 is the mortality rate for age group xg at time tp2. The α xg parameters indicate the time-average log mortality rate stratified by age group, κ1 tp2
is a time trend in mortality that is shared by all age groups, β1 xg
denotes which mortality rates decline rapidly and which decline slowly in response to changes in κ1 tp2 and ε xg, tp2 is the error term, which is independently and identically distributed (i.i.d) with mean 0 and variance σ2ε and reflects particular age-specific historical influences not captured by the model. A Singular Value Decomposition (SVD) method is used to find a least squares solution when applied to the logarithms of the rates after the averages over time of the (log) age-specific mortality rates have been subtracted logm xg, tp2 − α xg. Hence, we minimize the following objective function: X xg,tp2 ε xg, tp22 = X xg,tp2 logm xg, tp2 − α xg − β1 xg κ1 tp2 2 .
Equation (2) cannot be fitted by ordinary regression methods, because there are no observed regressors; on the right hand side of equation (2) we only have parameters to be estimated and the unknown index κ1 tp2. The following constraints are imposed on the parameters so that a unique solution can be determined: P
xgβ1(xg) = 1 and
P
tp2κ1(tp2) = 0.
The SVD provides a convenient way for breaking up a matrix, containing data we are interested in, into simpler, meaningful pieces. The formula of the SVD is given by:
A = U DVT,
diagonal. In our case,
A = logm xg, tp2 − α xg , U = β1 xg ,
DVT = κ1 tp2 .
This technique is used to estimate the κ tp2 parameters for each year. Forecasts of κ1 tp2 are made by using a random walk with drift parameters. These forecasts are inserted into equation (2) to obtain forecasts of mortality rates m xg, tp2.
Nan Li and Ronald D. Lee (Li and Lee, 2005) reason that mortality patterns and trajectories in closely related populations are likely to be similar in some respects, and differences are unlikely to increase in the long run. It should therefore be possible to improve the mortality forecasts for individual population by taking into account the patterns in a larger group. The Li-Lee model is defined as follows:
logm xg, tp2, g = α xg, g + β1 xg κ1 tp2 + β2 xg, g κ2 tp2, g + ε xg, tp2, g , (3) where m xg, tp2, g is the mortality rate at age group xg, time tp2 and subgroup g (for example different genders or different countries). The α xg, g parameters again indicate the time-average log mortality rate stratified by age group and subgroup, κ1 tp2 is the common time trend in mortality that is shared by all age groups and subgroups and β1 xg denotes the common age interaction with the common time trend. The κ2 tp2, g parameters indicate the subgroup spe-cific time trend and β2 xg, g denotes the subgroup specific age interactions with the subgroup specific time trend. The error term ε xg, tp2, g is i.i.d. with mean 0 and variance σ
2 ε. After fitting the model, κ2 tp2, g is forecasted using a mean-reverting process (AR(1) for example), which assumes that the forecasts of κ2 tp2, g will approach κ2 tp2, g and it prevents a strong divergence.
To forecast the mortality rates by age, gender and level of educational attainment, it is appro-priate to use the extended Li-Lee model (Van Baal et al., 2016). Instead of modelling only one subgroup, Van Baal et al. (2016) included a second subgroup. This way, we can not only forecast the mortality rates by age group and gender, but also add the subgroup education, which results in the following model:
logm xg, tp1, g, e = α xg, g, e + β1 xg κ1 tp1 + β2 xg, g κ2 tp1, g
(4) + β3 xg, g, e κ3 tp1, g, e + ε xg, tp1, g, e ,
where m xg, tp1, g, e is the mortality rate at age group xg, time tp1, gender g and level of edu-cational attainment e. The α xg, g, e parameters again indicate the time-average log mortality rate stratified by age group, gender and level of educational attainment, κ1 tp1 is the common time trend in mortality that is shared by all age groups, genders and levels of educational at-tainment and β1 xg denotes the common age interaction with the common time trend. The κ2 tp1, g
parameters indicate the gender specific time trend and β2 xg, g
denotes the gen-der specific age interactions with the gengen-der specific time trend. The κ3 tp1, g, e parameters indicate the gender and education specific time trend and β3 xg, g, e denotes the gender and education specific age interactions with the gender and education specific time trend. Finally ε xg, tp1, g, e is the error term, which is i.i.d. with mean 0 and variance σ
The extended Li-Lee model in equation (4) can be estimated in a stepwise manner. First, the α xg, g, e parameters can be calculated by taking the time-average of the log mortality rates. Secondly, the β1 xg and κ1 tp2 are estimated using the Lee-Carter model. Thirdly, β2 xg, g
and κ2 tp2, g
can be estimated using the SVD by plugging in the estimates of β1 xg
and κ1 tp2 into equation (3):
logm xg, tp2, g − α xg, g − ˆβ1 xg ˆκ1 tp2 = β2 xg, g κ2 tp2, g + ε xg, tp2, g . Finally, β3 xg, g, e and κ3 tp1, g, e can be estimated using the SVD by plugging in the estimates of β1 xg, κ1 tp1, β2 xg, g and κ2 tp1, g in equation (4):
logm xg, tp1, g, e − α xg, g, e − ˆβ1 xg ˆκ1 tp1 − ˆβ2 xg, g ˆκ2 tp1, g = β3 xg, g, e κ3 tp1, g, e + ε xg, tp1, g, e .
For the first two steps, mortality rates from 1970 until 2014 are used. However, for the last step, mortality rates from 1999 until 2014 were used, since there was no more data available.
Estimating the extended Li-Lee model yields eleven series of time-dependent κ parameters. To get the future mortality rates, the κ parameters need to be forcasted and substituted into equation (4). To forecast the κ parameters, optimal ARIMA models are selected by comparing the AIC values of different models. Table 1 displays the ARIMA models that are used to forecast the different parameters. Substituting the forecasted values into equation (4) yields the forecasted educational mortality rates by age group, gender and level of educational attainment.
Table 1: Chosen ARIMA models
κ parameter Chosen ARIMA Model
κ1 tp2
ARIMA(1,1,0) with drift κ2 tp2, men ARIMA(0,1,2) κ2 tp2, women ARIMA(0,1,0) κ3 tp1, men, low ARIMA(0,1,0) κ3 tp1, men, mid − low
ARIMA(0,1,0) κ3 tp1, men, mid − high
ARIMA(1,0,0) with non-zero mean κ3 tp1, men, high
ARIMA(0,1,0) κ3 tp1, women, low
ARIMA(0,0,0) with non-zero mean κ3 tp1, women, mid − low
ARIMA(0,1,0) κ3 tp1, women, mid − high
ARIMA(0,1,0) κ3 tp1, women, high
ARIMA(0,1,0)
3.2.3. Standard mortality rates
In order to make a comparison, we need to calculate mortality rates where we do not take the component education into account. Therefore, mortality rates m(xg, tp2, g) stratified only by age group xg and gender are calculated as follows:
Then, the Lee-Carter and Li-Lee models are applied, yielding three κ parameters. These κ parameters are forecasted with ARIMA models, as we did in Section 3.2. Filling in the forecasted κV parameters in equation (3) yields the forecasted standard mortality rates by age group and gender.
3.2.4. Convert mortality rates by five-year age groups to mortality rates by single age To make population projections by gender, age and level of educational attainment, we need to convert the mortality rates by five-year age groups to mortality rates by single age. Mortality rates stratified only by age and gender of the past are used to make a profile per age group. These profiles are applied on the mortality rates by five-year age groups to make mortality rates by single age. The only difficulty was the age group 80+, because the profile made for this age group was related to the ages 80-84. Therefore, the estimated mortality rate at the age of 84 divided by the mortality rate at age 84 of the past is used as a rate to estimate the mortality rates for the ages 85 until 100.
3.3. Fertility rates
Nowadays, women do not get as many children as a few decades ago. The average number of children born per woman decreased from 3.1 in 1950 to 1.65 in 2015. This decrease is caused by the fact that women get older when they get their first child and they just get fewer children, due to accepted birth control. In 1970, the average age by getting a first child was 24, while it has increased to 29 in 2015. Main reasons for this are that people want to enjoy their freedom longer, they want to have a adequate partner and they first want to make a career and gain some working experience (Doorten and Struijs, 2007). There are also differences between higher and lower educated persons. Kravdal and Rindfuss (2008) show that, in all cohorts, better-educated women have later first births and remain childless more often than the less educated. This means that we should differentiate the fertility rates by level of educational attainment. However, for the projection of the older population is this less important. Forecasting the fertility rates stratified by level of education is beyond the scope of this paper and fertility rates stratified by age and gender will be used from Van Duin et al. (2015). These fertility rates are applied on the female population between the ages of 15 and 50 years stratified by level of educational attainment.
3.4. Migration rates
Migration has increased the past few years, mostly due to the wars in the Middle East and labor migration from Eastern Europe. In 1995, 96 thousand people immigrated and 63 thousand emigrated in the Netherlands. This increased to 204.5 thousand immigrants and 127 thousand emigrants in 20153. Whether these numbers differ between educational groups is unclear. Some research (White et al., 1995; Yang and Guo, 1999) says that migration is higher for higher educated persons, while other papers (Taylor, 1987; Quinn and Rubb, 2005) say the opposite. Again others (Adams Jr, 1993; Curran and Rivero-Fuentes, 2003) say that it makes no difference. However, for the projection of the older population is this less important and therefore is it beyond the scope of this paper to calculate migration rates by level of educational attainment, but it would be an appropriate topic for future research. In this paper, immigration numbers and emigration rates stratified by age and gender are used from Van Duin et al. (2015). The proportion of immigrants in each education group is the same as the proportion of the population in each education group. So the immigration numbers are divided over the four education groups
3
proportional to the size of the population per educational group. The emigration rates are applied to the population stratified by age, gender and level of educational attainment.
3.5. Educational transition rates
Making a projection by level of educational attainment means that persons can transition from one educational category to another. A constant enrollment ratio (CER) scenario is used to calculate educational transition rates. This scenario assumes that the proportion making each educational transition remains constant over time. The policy goals for education of the young generation have already been achieved, so it is reasonable to assume that the proportion highly educated persons will not increase any further. First, some assumptions are made:
1. Transitions from one educational category to another can only go in one direction. For example, a person can go from the mid-high category to the high category, but not the other way around. This means that if someone is in the highest category, this person will be there the rest of his or her life.
2. Transitions from one educational category to another have to follow a predefined sequence, so it is not allowed to skip a category. For example, a person can go from the mid-low category to the mid-high category, but not from the mid-low to the high category. 3. From the age of 30 onwards, the educational category of a person remains the same. 4. From the age of 0 up to and including the age of 13, all persons are in the low category,
meaning that they have primary school as highest obtained level of education.
5. From the age of 14 up to and including the age of 16, all persons are in the low or mid-low category.
6. From the age of 17 up to and including the age of 20, all persons are in the low, mid-low or mid-high category.
7. From the age of 21 up to and including the age of 29, persons can be in all 4 categories. To calculate transition rates, a population P is needed from two successive years, say t and t + 1, for t = 2009, ..., 2014, age x = 0, 1, ..., 99, genders g = male and f emale and 4 educational levels e = high (4), mid-high (3), mid-low (2) and low (1). Proportions of these populations are taken to calculate the rates. Then we define:
P (x, t, g, e) = population proportion in year t with age x, gender g and level of educational attainment e. q(x, t, g, e1, e2) = transition rate from year t, age x, gender g and level of educational attainment e1
to year t + 1 age x + 1, gender g and level of educational attainment e2.
Assumptions 1 and 2 imply that
We can calculate the transition rates q(x, t, g, 3, 4) and q(x, t, g, 3, 3) as follows: P (x + 1, t + 1, g, 4) = q(x, t, g, 4, 4) · P (x, t, g, 4) + q(x, t, g, 3, 4) · P (x, t, g, 3) = P (x, t, g, 4) + q(x, t, g, 3, 4) · P (x, t, g, 3). Hence, q(x, t, g, 3, 4) = P (x + 1, t + 1, g, 4) − P (x, t, g, 4) P (x, t, g, 3) , and q(x, t, g, 3, 3) = 1 − q(x, t, g, 3, 4) = 1 −P (x + 1, t + 1, g, 4) − P (x, t, g, 4) P (x, t, g, 3) . Similarly, the other transitions rates are given by:
q(x, t, g, 2, 3) =P (x + 1, t + 1, g, 3) − P (x, t, g, 3) P (x, t, g, 2) , q(x, t, g, 2, 2) = 1 −P (x + 1, t + 1, g, 3) − P (x, t, g, 3) P (x, t, g, 2) , q(x, t, g, 1, 2) =P (x + 1, t + 1, g, 2) − P (x, t, g, 2) P (x, t, g, 1) , q(x, t, g, 1, 1) = 1 −P (x + 1, t + 1, g, 2) − P (x, t, g, 2) P (x, t, g, 1) .
The transition rates are calculated and averaged over the years 2009-2014. The calculated tran-sition rates are used for all future years, so we assume that these remain constant over time.
3.6. Population projections: Cohort-component model
The population projection is calculated with a cohort component model, which does the following. There exists a base population by age, gender and level of educational attainment in 2014. We apply the mortality rates (Section 3.2), fertility rates (Section 3.3), migration rates (Section 3.4) and transition rates (Section 3.5) to it and a new population is calculated for a year later. Doing this for each age group and gender for every year yields a projection of the population by age, gender and level of educational attainment. In formula:
P (x, tf+ 1, g, e) = q(x − 1, tf, g, e, e)P (x − 1, tf, g, e) (5) + Ie6=1·q(x − 1, tf, g, e − 1, e)P (x − 1, tf, g, e − 1)
where
P (x, tf, g, e) = the population in year tf at age x, gender g and educational level e,
q(x, tf, g, e − 1, e) = the transition rate from year tf, age x, gender g and level of educational attainment e − 1 to year tf+ 1 age x + 1, gender g and level of educational attainment e,
q(x, tf, g, e, e) = the transition rate from year tf, age x, gender g and level of educational attainment e to year tf+ 1 age x + 1, gender g and level of educational attainment e,
Ie6=1= an indicator function, which equals 1 if e 6= 1 and 0 otherwise, Ix=0= an indicator function, which equals 1 if x = 0 and 0 otherwise,
Im(x, tf, g, e) = the number of immigrants in year tf at age x, gender g and educational level e, Em(x, tf, g, e) = the number of emigrants in year tf at age x, gender g and educational level e,
D(x, tf, g, e) = the number of deceased in year tf at age x, gender g and educational level e, B(tf) = the number of births in year tf,
s = the sex-ratio, giving the percentage of males and females born. Furthermore, the emigration probability em(x, tf, g, e) is equal to
em(x, tf, g, e) = 1 Em(x, tf, g, e) 2P (x − 1, tf, g, e) + P (x, tf− 1, g, e) + Em(x, tf, g, e) = 2Em(x, tf, g, e) P (x − 1, tf, g, e) + P (x, tf− 1, g, e) + Em(x, tf, g, e) ⇐⇒ Em(x, tf, g, e) =P (x − 1, tf, g, e) + P (x, tf− 1, g, e) em(x, tf, g, e) 2 − em(x, tf, g, e) . Similarly, we have D(x, tf, g, e) =P (x − 1, tf, g, e) + P (x, tf− 1, g, e) m(x, tf, g, e) 2 − m(x, tf, g, e). We define B(tf) = 50 X x=15 P (x − 1, tf, f emale) + P (x, tf+ 1, f emale) 2 · f (x, tf),
f (x, tf) = the fertility rate in year tf at age x, M+(x, tf, g, e) = 1 + m(x, tf, g, e) 2 − m(x, tf, g, e) + em(x, tf, g, e) 2 − em(x, tf, g, e) , M−(x, tf, g, e) = 1 − m(x, tf, g, e) 2 − m(x, tf, g, e) − em(x, tf, g, e) 2 − em(x, tf, g, e) .
Recall that newborns (x = 0) start in the lowest education category (e = 1). Hence, for x = 0 and e = 1, we have: P (0, tf, g, 1) = s · B(tf) + Im(0, tf, g, 1) · 1 M+(0, tf, g, 1) .
4. Results
In this section we will look at life expectancies and projections (of different subgroups) of the population. Special attention will be given to the age group 65+ for several reasons. Until 2012, the retirement age in the Netherlands was 65 and it is important to know how many years the 65+ group has left after retirement. Secondly, their generation (especially the women) were low educated, which will change in the future. Finally, elderly have more health expenditures and deaths occur more often in the 65+ group.
4.1. Past trends in life expectancy
Figure 1 shows the life expectancy at birth for men and women, calculated from the EAF. The life expectancy experienced a major increase in the past few decades. Nowadays, the life expectancy at birth for men and women is 79.73 and 83.13 respectively. We can see that the life expectancy of women is higher than that of men. However, the life expectancy of men increased more than for women, which means that the gap between men and women has become smaller.
Figure 1: The life expectancy at age 0 for men and women from 1999 to 2014
From Figure 1 and 2 we can see that the life expectancy has grown significantly from 2000 until 2010. However, the growth stagnated after this period and even decreased in 2011. Since this pattern is visible in the overall life expectancy, it also affects life expectancies by level of educational attainment due to the use of the extended Li-Lee model.
(a) The life expectancy at age 0 (b) The life expectancy at age 65
Figure 2: Plots of life expectancy by level of educational attainment for men and women from 1999 to 2014
4.2. Life expectancy projections
(a) The life expectancy at age 0 (b) The life expectancy at age 65
Figure 3: Plots of life expectancy by level of educational attainment for men and women from 1999 to 2060
(a) The life expectancy at age 0 for men (b) The life expectancy at age 0 for women
(c) The life expectancy at age 65 for men (d) The life expectancy at age 65 for women
Figure 4: Plots of life expectancy per education group for men and women for 2014 and 2060
4.3. Population projections with mortality rates by level of educational
attainment
(a) Population in 2014 (b) Projected population in 2060
Figure 5: Observed and projected population of the Netherlands in millions by age, gender and educational attainment calculated from the EAF
Figure 6 shows the projected Dutch population over the years and the distribution of the educa-tional categories. From Figure 6a, we see that the Dutch population increases to approximately 18 million in 2060. The low educational group is relatively big, because the youth is also included. Figure 6b shows that the proportion of the population who are in the lowest two categories will decrease in the upcoming years, while the proportion in the population who are in the high-est category increases. This means that the population of the Netherlands will become higher educated in the future.
(a) Population in millions (b) Population proportion in %
Figure 6: The observed and projected population of the Netherlands by education level, 1999-2060
the Dutch population aged 15-65, which gives a better view of the working population. In 2060, the percentage of lower educated people in the Netherlands will have decreased to 18% and the percentage of higher educated people in the Netherlands will increase to 36%, which is a bit low. This is due to the fact that persons aged 15-25 are still attaining education. If we look at persons aged 30-65, the percentage low educated people in 2060 is 11% and the percentage high educated people in 2060 is 43%.
(a) Population in millions (b) Population proportion in %
(a) Population in millions (b) Population proportion in %
(a) Population in millions of men (b) Population proportion in % of men
(c) Population in millions of women (d) Population proportion in % of women
Figure 9: The population of the Netherlands aged 65+ by gender and education level, 2014-2060
4.4. Population projections with standard mortality rates
Table 2: Observed and projected population of the Netherlands in millions in 2000-2060 with differential and with standard mortality rates
Mortality rates Year Low Mid-low Mid-high High Total
Differential 2000 4.81 3.23 5.15 2.57 15.76 2010 4.81 2.93 5.13 3.70 16.57 2020 4.38 2.76 5.98 4.28 17.40 2025 4.21 2.62 6.23 4.64 17.69 2030 4.10 2.49 6.40 4.94 17.92 2035 4.03 2.37 6.51 5.19 18.09 2040 3.90 2.29 6.60 5.39 18.19 2045 3.74 2.21 6.69 5.56 18.20 2050 3.57 2.13 6.75 5.71 18.17 2055 3.45 2.06 6.79 5.83 18.13 2060 3.41 1.99 6.82 5.92 18.13 Standard 2000 4.81 3.23 5.15 2.57 15.76 2010 4.81 2.93 5.13 3.70 16.57 2020 4.40 2.77 5.97 4.25 17.39 2025 4.24 2.64 6.22 4.58 17.68 2030 4.13 2.51 6.38 4.86 17.89 2035 4.06 2.40 6.48 5.09 18.04 2040 3.94 2.32 6.58 5.27 18.11 2045 3.77 2.24 6.66 5.42 18.10 2050 3.60 2.16 6.72 5.56 18.05 2055 3.48 2.09 6.76 5.67 17.99 2060 3.42 2.02 6.78 5.75 17.98
Figure 11 shows the population of the Netherlands in millions by age, gender and educational attainment in 2060 using differential mortality rates and using standard mortality rates. The colored boxes are not delineated and represents the population using differential mortality rates. The black delineated boxes are the population of the Netherlands in millions by age, gender and educational attainment in 2060 using standard mortality rates. It is interesting to see that especially from the age of 65 there are small differences. From this age we see that the colored boxes (not delineated) expand beyond the black delineated boxes. For example, the 95+ female population in 2060 exists of 42,086 high educated persons using differential mortality rates (the light pink in the right corner of Figure 11), while using standard mortality rates, the 95+ female population in 2060 exists of 28,757 high educated persons (the black delineated box in the right corner of Figure 11). This means that we expect more people using the mortality differentials than by using the standard mortality rates, which is in accordance with Figure 10. Moreover, the “additional” persons are light in color, as we can see in Figure 11, which means that these persons are high educated, which is in accordance with Figure 5b. Hence, using differential mortality rates yields a larger and smarter population.
5. Comparison with other papers
In this section, we make a comparison with two other papers, Van Baal et al. (2016) and K.C. et al. (2013), to see what the differences are in the approach and to explain the differences in the results.
5.1. Comparision Van Baal et al. (2016)
Van Baal et al. (2016) present an approach to forecast life expectancy for different educational groups within a population. They used the DLFS as a dataset, while the EAF is used in our paper to forecast the life expectancy. Moreover, Van Baal et al. (2016) classified the educational attainment in three categories: low: primary education, middle: pre-vocational education and high: secondary education and tertiary education. In our paper, the third education category (high) is divided into two categories.
The life expectancy at age 65 for men and women stratified by education in 1996, 2012 and 2042, calculated by Van Baal et al. (2016) (reference paper) and our paper, is shown in Table 3. Both the overall life expectancy for men and women is lower in the reference paper than in our paper, while we use the same dataset to calculate this. The difference arises from the fact that we forecast the mortality rates by age groups, while Van Baal et al. (2016) forecast the mortality rates by single age. The disadvantage of forecasting the mortality rates by single age is that the groups for the older ages get really small, because there is not many data available for the older ages. When you use age groups, there will be a bit more data per age group then there will be per single age and more data give more consistent results. It can be the case that there is only one person for a certain age and forecasts depending on data of one person is not really reliable. Therefore, we chose to forecast using age groups, instead of single ages. Since the life expectancies of the low, middle and high education groups follow the trend of the overall life expectancy, the life expectancies of the different education groups of the reference paper will also be lower than the life expectancies of the different education groups of our paper.
Table 3: Life expectancy at age 65 for men and women stratified by education in 1996, 2012 and 2042 for Van Baal et al. (2016) and our paper
Gender Education 1996 1996 2012 2012 2042 2042
Van Baal Our Van Baal Our Van Baal Our
et al. (2016) paper et al. (2016) paper et al. (2016) paper
Men Overall 15.1 15.7 18.3 19.1 21.1 22.2 High 16.2 - 19.2 19.9 22.8 22.8 Middle 14.5 - 17.7 18.4 21.5 21.5 Low 13.5 - 15.9 17.8 17.9 21.1 Women Overall 19.6 20.3 21.4 22.1 23.8 24.6 High 21.1 - 22.9 23.1 25.2 25.6 Middle 20.0 - 21.8 21.9 24.2 24.3 Low 18.5 - 19.6 21.3 20.7 24.2
groups, i.e. for middle educated men this difference is equal to 0.7 years in 2012. We expect that the life expectancy for low educated men will grow with 3.3 years, a similar growth as for the other two education groups. Van Baal et al. (2016) expects that it will increase with 2.0 years, much less than the other two education groups. Hence, the difference in life expectancy between the lower educated and middle/higher educated will become even larger according to Van Baal et al. (2016). Furthermore, the differences in growth between the reference paper and our paper are bigger for men than for women.
Table 4: Difference in life expectancy between 2012 and 2042 for Van Baal et al. (2016) and own calculations
Gender Education Van Baal et al. (2016) Own calculations
Men Overall +2.8 +3.1 High +3.6 +2.9 Middle +3.8 +3.1 Low +2.0 +3.3 Women Overall +2.4 +2.5 High +2.3 +2.5 Middle +2.4 +2.4 Low +1.1 +2.9
5.2. Comparision K.C. et al. (2013)
K.C. et al. (2013) (reference paper) describe the baseline data and summarize the methodol-ogy that underlies the projections presented for 195 countries of the world by age, gender and educational attainment, based on detailed data on education for 171 countries. For the Nether-lands, they used the Census (Eurostat) 2001 as dataset to make the population projections, while we used the EAF 2014, which is more accurate. They assumed six educational categories: no education, incomplete primary, completed primary, lower secondary, upper secondary and post secondary. In our paper, the first two categories (no education and incomplete primary) are not included, because that almost never occurs in the Netherlands. Furthermore, K.C. et al. (2013) only look at persons older than 15 years old, while we make projections for all ages. However, we assumed that until the age of 25, the mortality rates are the same for every education group. Another difference between our paper and the reference paper is that they do take fertility and migration differentials into account in the population projections, while we do not. Besides they use another method to calculate the mortality differentials. Their mortality assumptions are based on a combination of a statistical model and country-specific expert assessment, while our assumptions are only based on a statistical model.
the Netherlands, while we did not. That explains the difference in life expectancy at birth for women between the reference paper and our paper.
Table 5: Life expectancy at birth for women of K.C. et al. (2013) and own calculations Year K.C. et al. (2013) Own calculations
2005 82.2 83.1 2010 83.1 84.1 2015 84.0 84.8 2020 85.0 85.4 2025 86.0 86.0 2030 87.0 86.6 2035 88.0 87.1 2040 89.0 87.6 2045 90.1 88.1 2050 91.1 88.6 2055 92.2 89.1 2060 93.3 89.4
Table 6 shows the proportion distribution by education among age group 30-34, 65+ and 80+ in 2010, 2030 and 2060, calculated by the GET and CER scenario of the reference paper and the CER scenario of our paper. The GET scenario assumes that the educational expansion will converge on an expansion trajectory based on the historical global trend. The CER scenario assumes that the proportion making each educational transition remains constant over time. For the 65+ group and the 80+ group we see almost no differences in the outcomes between the GET and CER scenario of the reference paper, probably because the elderly attained their education levels when they were younger. The scenarios do not play a big role for these ages. For the age group 30-34, there are differences. With the GET scenario, the low education groups are decreasing, while the high education groups are increasing. For the CER scenario in the reference paper it is the other way around and also we expects that the proportion of persons in the highest education group is smaller in 2030 and 2060 than it is in 2010.
Table 6: Proportion distribution by education among age group 30-34, 65+ and 80+ in 2010, 2030 and 2060 for the GET and CER scenario of K.C. et al. (2013) and the CER scenario of our paper
GET scenario CER scenario CER scenario
K.C. et al. (2013) K.C. et al. (2013) Our paper
Age group Education Level 2010 2030 2060 2010 2030 2060 2010 2030 2060
6. Conclusion
The life expectancy of Dutch persons has been increasing for years and the expectation is that it will continue to increase. This means that also the proportion of elderly in society is growing, which causes problems for the affordability of pensions and an increase in the demand for health care for the elderly. It is thus very important to make a good and reliable population projection to get more detail about the future population.
Several studies (Lleras-Muney, 2004; Ross and Wu, 1995) show that there is a positive relation between mortality and education. High educated elderly will remain longer in good condition. Furthermore, the increase in education in recent years will result in more higher educated elderly in the near future. This means that the health care cost for higher educated persons will not be very high and the demand for health care will probably have a less rapid increase than we might think. It is therefore very important to include education in a mortality and population forecast. Moreover, for the policy about retirement age it is also important to know the education levels of the persons, because higher educated persons often have less physical jobs than low educated persons and could be able to work longer. Hence, a population projection stratified by level of educational attainment gives a better overview of the future population and their needs. This paper provided a projection of the life expectancy and population for the years 2015-2060 including educational attainment. Furthermore, register data of the Netherlands is used, giving a better estimate of the population by educational attainment than previous papers, which are based on census or survey data.
The extended Li-Lee model is used to forecast mortality rates by five-year age groups, gender and four levels of educational attainment. The extended Li-Lee model distinguishes between overall, gender specific and education specific trends in mortality and forecasts educational differences in a coherent fashion. The forecasted mortality rates and a cohort-component model are used to make the population projections by age, gender and level of educational attainment.
The results in this paper show that there are differences in life expectancy between males and females and between high and low educated persons. Furthermore, the composition of the pop-ulation will change. The group of low educated persons will almost disappear and the group of high educated persons will increase. Moreover, we see that the group of high educated women aged 65+ is larger than the group of high educated men aged 65+ in 2060. These results are important to know to make better adjustments for the elderly in the future.
References
Adams Jr, R. H. (1993). The economic and demographic determinants of international migration in rural egypt. The Journal of Development Studies 30 (1), 146–167.
van Baal, P., F. Peters, J. Mackenback, and W. Nusselder (2016). Forecasting differences in life expectancy by education. Population Studies 70 (2), 201–216.
Booth, H. and L. Tickle (2008). Mortality modelling and forecasting: A review of methods. Annals of Actuarial Science 3 (1-2), 3–43.
Curran, S. R. and E. Rivero-Fuentes (2003). Engendering migrant networks: The case of mexican migration. Demography 40 (2), 289–307.
Doorten, I. and A. Struijs (2007). Postponement of parenthood [in dutch]. Demos 23 (3), 1–4. van Duin, C. and L. Stoeldraijer (2014, December). Population projection 2014 - 2060: growth
due to migration [in dutch]. Publication on the website of Statistics Netherlands.
van Duin, C., L. Stoeldraijer, H. Nicolaas, J. Ooijevaar, and A. Sprangers (2015, December). Core projections 2015 - 2060: High population growth on the short-term [in dutch]. Publication on the website of Statistics Netherlands.
Filmer, D. and V. Ahuja (1999). Educational Attainment in Developing Countries: New Esti-mates and Projections Disaggregated by Gender. The World Bank.
Fletcher, J.M. and D.E. Frisvold (2012). Higher education and health investments: Does more schooling affect preventive health care use? Journal of Human Capital 3 (2), 144–176. Groot, W. and H. Maassen-van den Brink (2010). The effects of education on crime. Applied
Economics 42 (3), 279–280.
K.C., S., B. Barakat, A. Goujon, V. Skirbekk, W. Sanderson, and W. Lutz (2010). Projections of populations by evel of educational attainment, age, and sex for 120 countries for 2005-2050. Demographic Research 22 (15), 383–472.
K.C., S. and H. Lentzner (2010). The effect of education on adult mortality and disability: A global perspective. Vienna Yearbook of Population Research, 201–235.
K.C., S., M. Potancokov, Bauer R., A. Goujon, and E. Striessnig (2013, October). Summary of data, assumptions and methods for new wittgenstein centre for demography and global human capital (wic) population projections by age, sex and level of education for 195 countries to 2100. Iiasa interim report, IIASA, Laxenburg, Austria.
Kravdal, O. and R.R. Rindfuss (2008). Changing relationships between education and fertility: A study of women and men born 1940 to 1964. American Sociological Review 73 (5), 854–873. Lee, R.D. (2000). The lee-carter method for forecasting mortality, with various extensions and
applications. North American Actuarial Journal 4 (1), 80–93.
Lee, R.D. and L.R. Carter (1992). Modeling and forecasting u. s. mortality. Journal of the American Statistical Association 87 (419), 659–671.
Linder, F., D. van Roon, and B. Bakker (2011). Combining data from administrative sources and sample surveys; the single-variable case. case study: Educational attainment. In Report on WP4 Case studies. Statistics Netherlands.
Lleras-Muney, A. (2004). The relationship between education and adult mortality in the united states. The Review of Economic Studies 72 (1), 189–221.
Lochner, L. and E. Moretti (2004). The effect of education on crime: Evidence from prison inmates, arrests, and self-reports. American Economic Review 94 (1), 155–189.
Loichinger, E. and A. Prskawetz (2016, August). Changes in economic activity: The role of age and education. Iiasa working paper, IIASA, Laxenburg, Austria.
Mathers, C.D., G.A. Stevens, T. Boerma, R.A. White, and M.I. Tobias (2015). Causes of international increases in older age life expectancy. The Lancet 385 (9967), 540–548.
Milligan, K., E. Moretti, and P. Oreopoulos (2004). Does education improve citizenship? evidence from the united states and the united kingdom. Journal of Public Economics 88 (9-10), 1667– 1695.
Nieuwbeerta, P. and A.R. Piquero (2008). Mortality rates and causes of death of convicted dutch criminals 25 years later. Journal of Research in Crime and Delinquency 45 (3), 256–286. NIH (2011). Global Health and Aging, Volume 11. National Institute of Aging and National
Institute of Health.
Quinn, M. A. and S. Rubb (2005). The importance of education-occupation matching in migra-tion decisions. Demography 42 (1), 153–167.
Ross, C.E. and C. Wu (1995). The links between education and health. American Sociological Review 60 (5), 719–745.
Skardhamar, T. and V. Skirbekk (2013). Relative mortality among criminals in norway and the relation to drug and alcohol related offenses. Plos One 8 (11), 1–6.
Statistics Netherlands (2014). Dutch census 2011 - analysis and methodology.
Statistics Netherlands (2017, May). Especially highly educated persons smoke less [in dutch]. Stoeldraijer, L., C. van Duin, and F. Janssen (2012, December). Population projection 2012
-2060: model and assumptions concerning mortality [in dutch]. Publication on the website of Statistics Netherlands.
Taylor, J. E. (1987). Undocumented mexicous migration and the returns to households in rural mexico. American Journal of Agricultural Economics 69 (3), 626–638.
White, M. J., L. Moreno, and S. Guo (1995). The interrelation of fertility and geographic mobility in peru: a hazards model analysis. International Migration Review , 492–514.
A. Appendix: the increment weight
To calculate the mortality rates by age group, gender and level of educational attainment, the total population by age group, gender and level of educational attainment and total number of deaths should be known. Unfortunately, this is not the case, but an estimation of this population is possible by weighting the EAF. This file has increment weights, however, we can not use these, because the population of a certain year is constructed from several DLFS years, as stated in Section 2.1.3. Due to this fact, the amount of deceased will be underestimated in the EAF. Therefore, we will use another weighting strategy.
The mortality rate m xg, tp1, g, e of the Dutch population in year tp1 by age group xg, gender g and level of educational attainment e is defined as follows:
m xg, tp1, g, e = D xg, tp1, g, e
P xg, tp1, g, e , (7)
where D xg, tp1, g, e
equals the number of deceased by age group xg, gender g and level of educational attainment e at 31 December of year tp1 and P xg, tp1, g, e equals the population by age group xg, gender g and level of educational attainment e at 1 January of year tp1 . The mortality rate, based on the EAF (for details see Section 3.2.1), is given by:
mEAF(xg, tp1, g, e) = RR(xg, tp1, g, e) ×
mEAF(xg, tp1, g) P
eRR(xg, tp1, g, e) × p(xg, tp1, g, e) .
We will calculate the increment weights by:
1. incrementing the EAF population by age group xg, gender g and level of educational attainment e to the total Dutch population with the same characteristics. This increment weight will be indicated by wP(xg, tp1, g);
2. incrementing the EAF deceased by age group xg, gender g and level of educational attain-ment e to the total Dutch population with the same characteristics. This increattain-ment weight will be indicated by wD(xg, tp1, g).
Furthermore, we assume that the increment weight is equal for records with the same age group xg and gender g in year tp1. Furthermore, we assume that the increment weight is the same for every level of educational attainment.
The incremented Dutch population by year tp1, age group xg, gender g and level of educational attainment e is written by:
P (xg, tp1, g, e) = wP(xg, g, tp1) · P EAF
(xg, tp1, g, e). (8) Similarly, for the deceased we have:
D(xg, tp1, g, e) = wD(xg, g, tp1) · D EAF
The total deceased in year tp1, D(xg, tp1, g), of the Dutch population is just the sum of the deceased over all the educational attainment levels:
D(xg, tp1, g) = X e D(xg, tp1, g, e) =X e wD(xg, tp1, g) · D EAF (xg, tp1, g, e) = wD(xg, tp1, g) · X e DEAF(xg, tp1, g, e). Similarly, we have: P (xg, tp1, g) = wP(xg, tp1, g) · X e PEAF(xg, tp1, g, e).
This results in the following increment weights: wD(xg, tp1, g) = D(xg, tp1, g) DEAF(xg, tp1, g) , wP(xg, tp1, g) = P (xg, tp1, g) PEAF(xg, tp1, g) .
Substituting wP(xg, tp1, g) into equation (8), wD(xg, tp1, g) in equation (9) and using equation (7) yields: m(xg, tp1, g, e) = D(xg, tp1, g, e) P (xg, tp1, g, e =wD(xg, g, tp1) · D EAF (xg, tp1, g, e) wP(xg, g, tp1) · P EAF (xg, tp1, g, e) =D EAF (xg, tp1, g, e) PEAF(xg, tp1, g, e) · D(xg,tp1,g) DEAF(xg,tp1,g) P (xg,tp1,g) PEAF(xg,tp1,g) =D EAF (xg, tp1, g, e) PEAF(xg, tp1, g, e) · D(xg,tp1,g) P (xg,tp1,g) DEAF(xg,tp1,g) PEAF(xg,tp1,g) = mEAF(x, t, g, e) ·m Statline (x, t, g) mEAF(x, t, g) ,
where mStatline(xg, tp1, g) is the mortality rate of the Dutch population by year tp1, age group xg and gender g (based on data from Statline) and m
EAF
(xg, tp1, g) is the mortality rate of the population of the EAF by year tp1 age group xg and gender g. Hence, the increment weight w(xg, tp1, g) is equal to:
w(xg, tp1, g) =
B. Appendix: the cohort-component model
Equation (5) in Section 3.6 can be rewritten as follows:
P (x, tf+ 1, g, e) = q(x − 1, tf, g, e, e)P (x − 1, tf, g, e) + Ie6=1·q(x − 1, tf, g, e − 1, e)P (x − 1, tf, g, e − 1) + Im(x, tf, g, e) − Em(x, tf, g, e) − D(x, tf, g, e) + Ix=0· sB(tf)
= q(x − 1, tf, g, e, e)P (x − 1, tf, g, e) + Ie6=1·q(x − 1, tf, g, e − 1, e)P (x − 1, tf, g, e − 1) −
q(x − 1, tf, g, e, e)P (x − 1, tf, g, e) + Ie6=1·q(x − 1, tf, g, e − 1, e)P (x − 1, tf, g, e − 1) + P (x, tf+ 1, g, e) em(x, t f, g, e) 2 − em(x, tf, g, e) −
q(x − 1, tf, g, e, e)P (x − 1, tf, g, e) + Ie6=1·q(x − 1, tf, g, e − 1, e)P (x − 1, tf, g, e − 1) + P (x, tf+ 1, g, e) m(x, t f, g, e) 2 − m(x, tf, g, e) + Im(x, tf, g, e) + Ix=0· sB(tf). Rewriting yields P (x, tf+ 1, g, e) 1 + em(x, tf, g, e) 2 − em(x, tf, g, e) + m(x, tf, g, e) 2 − m(x, tf, g, e) =hq(x − 1, tf, g, e, e)P (x − 1, tf, g, e) + Ie6=1·q(x − 1, tf, g, e − 1, e)P (x − 1, tf, g, e − 1) i 1 − em(x, tf, g, e) 2 − em(x, tf, g, e) − m(x, tf, g, e) 2 − m(x, tf, g, e) + Im(x, tf, g, e) + Ix=0· sB(tf). Rewriting again gives equation (6): P (x, tf+ 1, g, e) =
h
