Population Projections Revisited:
Moving beyond convenient assumptions on fertility, mortality and migration
Part 1:
Revis...
1. Introduction: Background, Objectives and Structure
Demographic structures have a major bearing on the financial sustain...
demographic projections need to be taken with a grain of salt and reconsidered, and in what
direction such assumptions may...
childbearing age) population and assumptions on the dynamics of the sex ratio at birth. The new
birth cohort is updated fo...
extrapolation of past projection errors, or based on expert opinion used to assess the future
uncertainty.
In what follows...
This differentiation by groups has been a main characteristic of UN projections over recent decades.
While the key assumpt...
Figure 1. Total fertility trajectories for the world and development groups, 1950-2100
(medium variant)
In addition to the...
• To construct projections of female life expectancy at birth for a country, the Bayesian
Hierarchical Model was used to g...
Migration Projections:
The UN population team acknowledges very frankly that migration flows are difficult to predict as
t...
b. World Bank Population Projections
The (annual) population data and projections by the World Bank from 1960 till 2050 fo...
of 1.83. This is not the case for most other countries and the average of all 31 countries of the EEA.
For the average of ...
Figure 4: Eurostat Demographic Projections 2013: Projected Life Expectancy in EEA countries
Male Female
Source: Eurostat 2...
 For Portugal and Spain the migration balances after the recovery remain very small
(Portugal) or modest (Spain), amount ...
homogéneas posibles9
en relación a los diferentes fenómenos demográficos (ver en Cuadrado
(2014) un análisis de la evoluci...
Figura 5a&b: Fertility rates for national and foreign population by age groups
Fuente: INE (2014a)
La evolución del indica...
Proyección de la mortalidad
La proyección de la incidencia de la mortalidad en España se realiza a partir de la extrapolac...
Figura 7a&b. Tasas de mortalidad observadas y proyectadas (2014-2063)
a. Hombres b. Mujeres
Fuente: elaboración propia en ...
Como puede observarse, se espera un incremento de la esperanza de vida tanto para los hombres
como para las mujeres a lo l...
Tabla 3 Figura 9
Fuente: INE (2104c)
Finalmente el saldo migratorio por edades observado en el periodo 2009-2013 y proyect...
bianual: las Proyecciones de Población. Un resumen de las principales cifras derivadas de las mismas
queda reflejado en el...
Alternative assumptions regarding future levels of fertility and mortality are encompassed in
pessimistic (pessimista), mo...
Figure 12 summarizes this information and exhibits the observed and forecasted values (in the three
variants) for the tota...
levels. The classical age-period (AP) Lee-Carter (LC) model was first introduced by Lee and Carter
(1992), combining a dem...
Source: Author's preparation based on INE (2014)
Alternative scenarios have also been devised using an extension of the tr...
Source: Author's preparation based on INE (2014)
Population projections for Portugal
Table 5: Population projections and m...
developments is little understandable and conjectured to be wrong. Third and combining elements
of the prior two component...
Based on this modelling idea Hertzer, Strulik and Vollmer (2012) develop an econometric
specification that allows the test...
whether and when such a convergence is taking place, what the key drivers are (morality reduction
or also other and econom...
Using the idea of different regimes (clubs) and applying it to fertility transition Strulik and Vollmer
(2015) were able t...
high and low scenarios and a specified path.18
The main advantage of expert opinion methods is the
possibility to incorpor...
of the crucial factors that have influenced mortality improvements over the past century are the
access to primary medical...
c. The economic and other explanations of migration development
The investigation of migration flows to and from a country...
Source: Eurostat 2011: Figure 1.
This subsection will briefly (i) explore the conjectured economic and non-economic determ...
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Population projections

Pension systems and reforms are critically influenced by demographic developments that are increasingly compared across countries to identify common issues and trends. For demographic projections researchers across the world rely on those produced by the United Nations; for Europe the demographic projections by Eurostat form the basis of the periodic aging report by the EU Commission. While these projections are technically well done the underlying assumptions for the demographic drivers – fertility, mortality and migration – in the central variants are limited and are largely flawed. Worse, they risk offering a wrong picture about the likely future developments and the relevant alternatives. This paper investigates the assumptions of the demographic drivers by UN and Eurostat, compares it with those by national projections in Portugal and Spain, and offers a review of alternative, recent and cutting edge approaches to project demographic drivers that go beyond the use of past demographic developments. They suggest that economic and other socio-economic developments have a main bearing on future trends in fertility, mortality and migration. And they support the assessment that the UN/Eurostat projected re-increase in fertility rates may not take place, that the increase in life expectancy may be much larger, that the future flows of net migrants to EU countries may be much higher and rising. The resulting overall underestimation of population aging has a bearing on the financial sustainability of the pension systems and reform choices, a topic to be explored in the next papers.
Published on: Mar 4, 2016
Published in: Economy & Finance      
Source: www.slideshare.net


Transcripts - Population projections

  • 1. Population Projections Revisited: Moving beyond convenient assumptions on fertility, mortality and migration Part 1: Revisiting the Projection’ Assumptions on Demographic Drivers by International Organization, National Institutes, and Academic Literature Mercedes Ayuso1 , Jose Maria Bravo2 , and Robert Holzmann3 Barcelona/Kuala Lumpur/ Évora, Final Draft, as of February 25, 2015 Foro de Expertos del Instituto de Pensiones BBVA Abstract Pension systems and reforms are critically influenced by demographic developments that are increasingly compared across countries to identify common issues and trends. For demographic projections researchers across the world rely on those produced by the United Nations; for Europe the demographic projections by Eurostat form the basis of the periodic aging report by the EU Commission. While these projections are technically well done the underlying assumptions for the demographic drivers – fertility, mortality and migration – in the central variants are limited and are largely flawed. Worse, they risk offering a wrong picture about the likely future developments and the relevant alternatives. This paper investigates the assumptions of the demographic drivers by UN and Eurostat, compares it with those by national projections in Portugal and Spain, and offers a review of alternative, recent and cutting edge approaches to project demographic drivers that go beyond the use of past demographic developments. They suggest that economic and other socio- economic developments have a main bearing on future trends in fertility, mortality and migration. And they support the assessment that the UN/Eurostat projected re-increase in fertility rates may not take place, that the increase in life expectancy may be much larger, that the future flows of net migrants to EU countries may be much higher and rising. The resulting overall underestimation of population aging has a bearing on the financial sustainability of the pension systems and reform choices, a topic to be explored in the next papers. 1 Full professor for Actuarial Statistics at University of Barcelona (Department of Econometrics, Statistics and Spanish Economy, Riskcenter-UB); Director of the Master in Actuarial Science at University of Barcelona. 2 Professor of Economics at University of Évora; Guest Professor at Nova University of Lisbon - ISEGI and at Université Paris-Dauphine (Paris IX); Coordinator of ORBio - Observatory of Biometrical Risk of Portuguese of Insured Population, Portuguese Insurers Association. 3 Professor of Economics and Chair, Old-age Financial Protection, University of Malaya (Kuala Lumpur); Honorary Professor, Centre of Excellence in Population Ageing Research, University of New South Wales (Sydney); Research Fellow of IZA (Bonn) and CESifo (Munich), and Fellow of the Austrian Academy of Science (Vienna). 1
  • 2. 1. Introduction: Background, Objectives and Structure Demographic structures have a major bearing on the financial sustainability of pension schemes whether unfunded or funded, and demographic projections provide an important signaling tool for policy makers and the population at large on the need to adjust pension programs accordingly. A critical benchmark for policy reform pressure are demographic and financial sustainability projections in other countries as moving in a herd makes policy makers and countries more comfortable. To this end policy researchers and policy makers rely world-wide and in Europe typically on the demographic projections by the UN. These projections are technically well done and accessible via the internet but have a main problem – the underlying assumptions for the 8 published variants are limited and are largely flawed. Worse, they risk offering a wrong picture about the likely future development and the relevant alternatives. Very briefly: The main fertility variant assumes a long- term convergence of countries toward replacement level (for those currently below and above). This may be politically expedient but is in contrasts to scientific results on the determinants of fertility over the last 100+ years. The alternative variants tend to be too optimistic: Too high increases in fertility for the rich countries, too high reduction for the poorest ones. The main mortality assumption is too pessimistic about future progress (the only alternative variant is constant mortality). And the main migration assumption is a migration balance between countries broadly reflecting recent levels that converge as of 2050 toward zero (!) at the end of the projection period in 2100 (the only alternative variant is no migration at all). Against this background this publication project has three objectives and proceeds in three parts, i.e. papers. Part 1 and this paper presents the demographic assumptions by international organizations, in particular the United Nations, Eurostat for European Countries, and Portuguese and Spanish National Statistical offices for their country’ population projections. These assumptions and underlying concepts are compared and evaluated against the broader economic/empirical literature that explains the demographic drivers - fertility, mortality and migration - not only through self- contained demographic models but economic drivers such as income level, income dynamics and income gaps. Part 2 and the next paper will explore the effects of differences in driver assumptions on demographic outcomes, in particular median age, old-age share and demographic old-age dependency ratio with retrospective and prospective old-age definition. In a first stage the paper will have to rely on and exploit existing demographic projections to offer results. In a second stage it may be possible und useful, at least for Portugal and Spain, to engage with forecast institution to derive new population projections and results. Part 3 and the final paper will assess the implications of more realistic demographic assumptions and outcomes on the key policy areas, i.e. family policy, labor market policy and pension system reform. To this end we may present (a) the policy approaches for and trade-off between family policy and migration policy, and the experience of countries; (b) the labor market implications of different scenarios and policies for different scenarios to address them; and (c) the implication of the demographic scenarios for pension policy and the demands/ requirements on pension systems and their reforms. Conclusions and proposals for next step are provided at the end. This paper reviews the assumptions by the UN and other international organizations on fertility, mortality and migration in comparison to the recent academic literature on past drivers and future trends as well as national (and European) developments and forecasts. This should allow an assessment to what extend the assumptions and in consequence the existing cross-country 2
  • 3. demographic projections need to be taken with a grain of salt and reconsidered, and in what direction such assumptions may be directed. To this end, the structure of this paper is as follows: Section 2 presents the assumptions on the key demographic drivers – fertility, life expectancy and net migration - underlying the existing country projections by international organizations (UN, World Bank), by Eurostat for the EU countries, and by the key Spanish and Portuguese demographic research institutions, explores the communalities and differences, and briefly surveys the quoted literature that has been used to this end, if available. Section 3 reviews and presents alternative recent academic literature that uses long-term data sets to determine empirically trends and drivers of past developments as well as their economic determinants. The latter aspect is typically missing in population projections undertaken by demographers. The information of both sub-sections set should form the background for an assessment and suggestions in what direction assumptions for revised demographic projections should be developed (presented in Section 4). The final Section 5 offers brief summary and first directions for other two parts/papers. 2. The assumptions on demographic drivers in institutional forecasts To assess the challenges that future demographic changes represent to age-related expenditure programs so as to shed light on the economic challenges that policy-makers will have to face, it is essential to consider the age-structure of the population today and how it will evolve in coming decades. The dynamics of a given population depends on its initial age-age structure and on key demographic determinants, namely: (i) total and age-specific fertility rates; (ii) age-specific mortality rates and (iii) the level and age composition of net migration. Official population projections are normally prepared by national statistical offices for their own countries (such as for Portugal and Spain) that in some cases may cover all countries (such as by the US Census Bureau), supranational institutions (such as EUROSTAT for the European Union), international organizations (in particular United Nations, to some extend World Bank) and sporadically some international research institutes (such as IIASA – International Institute for Applied System Analyses). The long-term population projections provide an indication of the timing and scale of demographic changes that would result from a combination of expert-based assumptions and statistical modelling of demographic determinants in a "no-policy change" scenario. To a certain extent, they are helpful in highlighting the immediate and future policy challenges posed for governments by long term trends of the demographic drivers. Population projections are computational procedures to calculate population size and structure at some future moment based on its initial figures, together with a specification of how change takes place during the interim period. These projections are produced using a cohort-component method and are based on assumptions about demographic drivers of change (future births, deaths, and net international migration). The computational procedure begins with an estimated base population, consistent with the most recent census data. First, components of population change (mortality, fertility, and net international migration) are projected based on time series analysis of historical trends and the adoption of stochastic methods. Next, for each passing year, the population is aged one year and the new age categories are updated using the projected survival rates and age and sex specific levels of net international migration for that year. A new birth cohort is then added to form the population under one year of age by applying projected age-specific fertility rates to the average female (of 3
  • 4. childbearing age) population and assumptions on the dynamics of the sex ratio at birth. The new birth cohort is updated for the effects of mortality and net international migration. Formally, the cohort-component method is based on the demographic balancing equation for each sex and cohort nttnttnttntttnt EIDNPP +++++ −+−+= ,,,,, (1) where Pt and Pt+n denote, respectively, the population at time t and t+n, Nt,t+n is the number of birth between t and t+n, Dt,t+n represents the number of deaths between t and t+n; It,t+n and Et,t+n denote, respectively the number of international immigrants and emigrant between t and t+n. The period n considered is typically one year for national population projections but for data and other reasons it is typically 5 years in large-scale international projections. The drivers of the population dynamics – births, death, and migration – are calculated on assumptions related to the existing population structure through the application of fertility rates per female age group (say 15 to 45), mortality rates and migration rates to all age groups and by gender. And it is these future projected rates by age group and gender – for fertility, mortality and migration – and their surrounding assumptions and models the population projections are built. And it is the assumptions and models about these rates this paper is about.4 The way in which these deterministic projection variants are being constructed has been questioned due to its insufficient theoretical foundations and to the lack of information on the assumptions used to establish the different paths for the future levels of the demographic components. Because of this, in the 1990s a number of papers argued for the need to move away from variant- style projections to probabilistic ones (see, e.g., Lee and Tuljapurkar 1994; Lutz 1996; Bongaarts and Bulatao 2000). From the methodological point of view, the advantages seem to be clear: probabilistic projections specify the likelihood that a particular future population value will occur given a set of assumptions about the underlying probability distributions. On the other hand, with variant projections the user has no idea how likely they are. This means that users have to trust that the experts have provided them with plausible scenarios representing the “most likely” (the central projection) and the variants (the high and low population projections). In both cases, the quality of the forecasts depends on the quality of the input data, on the projection models and on the assumptions made. Despite the advantages of a probabilistic approach, nearly all national statistical offices in the world (including the Portuguese and the Spanish) still rely on deterministic variant projections to accomodate uncertainty. Uncertainty in population projections come from four main sources: the projection model(s), parameter estimates, expert judgments and historical data. Uncertainty can also be based on the results of past projections. Uncertainty in projections can be ignored, described using various plausible scenarios or quantified using probabilities. The deterministic scenarios can be data-driven, i.e., based on simple mathematical extrapolations of past trends, or expert-driven, that is, relying mainly on expert judgment. Similarly, stochastic (probabilistic) projections can be based on time series analysis or 4 Applying the same projected rates to different starting population structures leads to a different dynamics for many decades. For this reason is the initial population structure often considered as a 4 th demographic driver in demographic discussions. 4
  • 5. extrapolation of past projection errors, or based on expert opinion used to assess the future uncertainty. In what follows we provide details about the methods used to project fertility rates, mortality rates, and future levels of net international migration in international and national population projections and the way they address the uncertainty in these projections. a. UN Population Projections The key institution for comparable demographic projections across countries is the United Nations, with the Population Division of the Department of Economics and Social affairs in charge of the demographic scenarios developed. All other international organizations use this data or make institution-specific minor adjustments around their medium (normal) projection, such as the World Bank. For this reason the UN demographic projections have such an importance in the pension world and such a wide use in policy and research. The assumptions and projections are subject to an elaborate participatory process and well documented. 5 This comprehensive process may explain why assumption and projections are little questioned and subject to external critique. The projections prepared by the United Nations Population Division are based on a theoretical framework known as demographic transition (see, for example, Chesnais 1992). Over the course of the demographic transition, populations move from a regime of high mortality and high fertility to a regime of low mortality and low fertility. Over time rapid population growth takes place because mortality decline typically begins before fertility decline: as death rates fall but birth rates remain high, the number of births exceeds the number of deaths and population therefore grows. The countries that are still in the beginning or in the middle of the demographic transition are expected to complete their transitions over the next several decades. Both fertility and mortality levels in these countries are assumed to decline. For the countries that have already completed their demographic transitions, mortality is still assumed to be declining but fertility is expected to fluctuate around or below a level of about two children per woman. For the countries with natural growth close to zero (i.e., when the number of deaths is close to equal to the number of births), future population trajectories are to a greater extent influenced by assumptions about future migration in or out of the countries. Future population trajectories therefore depend on assumptions about future trends in fertility, mortality and migration. In addition, the current population age structure influences future growth by actually affecting the overall number of births, deaths and migrations that are implied by fertility, mortality and migration rates. All four demographic components can have a significant impact, positive or negative, on future population growth (UN 2014M). Fertility Projections: Against the background of the demographic transition model, the UN defines three groups of countries in transition for which special modeling techniques are applied and assumptions made: Group 1: High-fertility countries: Countries that until 2010 had no fertility reduction or only an incipient decline; Group 2: Medium-fertility countries: Countries where fertility has been declining but whose estimated level is above the replacement level of 2.1 children per woman in 2005-2010; Group 3: Low-fertility countries: Countries with total fertility at or below the replacement level of 2.1 children per woman in 2005-2010. 5 See http://esa.un.org/wpp/ 5
  • 6. This differentiation by groups has been a main characteristic of UN projections over recent decades. While the key assumptions for all countries within a group were originally identical they become somewhat more differentiated over time. E.g. since the last (2010) projection, the 2012 takes somewhat account that in Group 1 that in some countries the fertility decline has not happened as envisaged or even increased. For Group 3 (which includes Portugal and Spain), the original assumption was a re-increase in the total fertility rate to replacement rate of 2.1 children per woman. In the 2010 projection this common convergence rate within the projection period was somewhat reduced. The 2012 projection allows for some differentiation across countries according differences in trends with an average for Western Europe by 2100 of 1.90 (UN 2012, Vol. II, p. 27). Overall, a mechanical statistical approach against the background of the transition model is applied to forecast the future fertility rates of countries. It has a (nowadays slightly) differentiated convergence path with somewhat different levels at the end of the projection period in 2100, with the convergence path driven and estimated by most recent data.6 The ultimate maximum convergence level for low fertility countries is still left at 2.1. Stronger differentiation in the convergence path based on most recent data is also introduced for the convergence from above for group 1 and 2 but the assumption of a below reproduction level final convergence is retained. Figure 1 exhibits the convergence paths for the World (i.e. average of all countries) and the main country groupings by the United Nations: More developed countries that have essentially all a convergence from a above; less developed countries where the fertility is mostly in full decline but that includes also countries with rates below replacement level (such as Sri Lanka); and the least developed countries where there are countries (in Africa) where fertility decline has not yet started or have known recently reverses. The broad but not full alignment of transition stage with broad economic development level indicates that there are differences in speed and convergence levels that are not well captured in the current statistical approach of projection that uses only historical demographic information. Furthermore, there may be other considerations that speak for differences in the convergence levels in the short and long run, a point that will be taken-up later in the paper. 6 Group 3 convergence is modelled with a first order auto-regressive time series model (AR(1)) in a Bayesian hierarchical framework. See UN (2014a) for more technical details. 6
  • 7. Figure 1. Total fertility trajectories for the world and development groups, 1950-2100 (medium variant) In addition to the medium variant 4 other fertility paths are projected in scenario calculations: a low fertility variant that subtracts 0.5 (children) in each year from the medium fertility level of a country; the high fertility variant adds 0.5; a constant fertility variant that keeps fertility at the level of the period 2005/10 throughput the whole projection period; and an instant replacement fertility variant that selects the fertility level in such a way that would keep the population constant assuming no change in mortality and net migration. Mortality/life-expectancy Projections: The 2012 projections use new approaches to project improvements in mortality and thus longevity in countries. In summary, the key elements of these projections are as follows: • The projections differentiate between countries without and with HIV epidemics (the latter are not discussed here). • The standard mortality projection assumption used for the 2012 Revision introduced two innovations: (1) future values of female life expectancy at birth are now based on a probabilistic projection model of life expectancy at birth (modelled as a random walk with drift where the drift is determined by a Bayesian Hierarchical Model), and (2) future male life expectancies at birth take into account the correlation between female and male life expectancies and the empirical regularity that life expectancy is typically higher for females than for males. • The life expectancy estimation use the empirically documented improvements of female life expectancy at birth as the starting position, taking account of the almost linear gains over decades that can be differentiated by the reached levels of life-expectancy across countries. • For all countries undergoing mortality transition, the pace of improvement in life expectancy at birth is decomposed into a systematic decline and random distortion terms. 7
  • 8. • To construct projections of female life expectancy at birth for a country, the Bayesian Hierarchical Model was used to generate 1,450,00022 double-logistic curves for each country, representing the uncertainty in the double-logistic gain function. A 1/14 sample of double-logistic curves is then used to calculate over 100,000 life expectancy projections for each country. The median of these 100,000 trajectories is used as the standard mortality projection in the World Population Prospects. • To construct projections of male life expectancy at birth, the gender gap autoregressive model was then used in conjunction with probabilistic projections of female life expectancy at birth to generate 100,000 trajectories for each country, representing the uncertainty in the future gap between female and male life expectancy projections. • The sample of gender gap trajectories was then used to calculate over 100,000 male life expectancy projections for each country. The median of these projections was used as the standard mortality projection in the World Population Prospects. • Once the path of future expectation of life was determined, mortality rates by five-year age group and sex that are consistent with the expectation of life at birth for each quinquennium were calculated. This quite sophisticated statistical approach signals the difficulty of modeling and estimating future changes (i.e. improvements) in life expectancy. In the past such improvements have essentially always been underestimated, i.e. actual life expectancy increased faster than the projected one. This new modelling and estimation approach attempts to overcome this weakness while having a globally applicable framework. Whether this will do justice to high-income countries will need to be seen. There, essentially most and soon all of the future gains in life expectancy at birth will happen after retirement as mortality till this age is already very low. However, the modelling of such gains is fraught with uncertainties as sparse data on mortality rates for the highest age groups indicate flattening or even decreases; it is unclear whether these are temporary and cohort specific phenomena or a general trend (taken up again later in the paper). Figure 2 highlights the projected life expectancy for the world and the three UN development regions. As visible, for the world the projections assume an further increase but with slowing pace that is driven by low and least developed regions and their slowing progress in improvement (also due to HIV epidemics). In contrast, for more developed regions the projections foresee an almost linear improvement that is much more in line with past experience. Yet further under-estimations given past developments are still not excluded. There are no other mortality/longevity variants to the presented medium (or most probable) variant. Figure 2. Life expectancy at birth for the world and development groups, 1950-2100 8
  • 9. Migration Projections: The UN population team acknowledges very frankly that migration flows are difficult to predict as they depend on economic, political, demographic, and increasingly (again) environmental developments that are difficult to foresee and even more difficult to put into numbers, also because they have to be symmetrical between countries. The UN projections allow for differentiation between migrants (voluntary) and refugees (involuntary), as well as by gender and by age groups. The latter differentiation is critical as it has main effects on population dynamics, if sustained, but it is also most difficult to get data for disaggregation. The UN projects only the net migration flows between countries (i.e. immigration minus emigration) and these flows have to be symmetrical in size and structure (by age groups and gender) between countries. Only two scenarios are considered: Normal migration assumption, and zero (net) migration assumption. Under the normal migration assumption, the future path of international migration is set on the basis of past international migration estimates and consideration of the policy stance of each country with regard to future international migration flows. Projected levels of net migration are generally kept constant over the next decades. After 2050, it is assumed that net migration would gradually decline and reach zero by 2100. This assumption is very unlikely to be realized but it proved impossible to predict the levels of immigration or emigration within each country of the world for such a far horizon. Sending countries of today may become receiving countries and vice versa (UN 2014M). Under the zero migration assumption, for each country, international migration is set to zero starting in 2010-2015. Table 1 present the average annual figures of migrants per decade by development group and major areas for the period 1950/60 to 2000/10 (actual) and 2010/20 to 2050/60 (projected); thereafter this figures are assumed to reach linearly zero by 2090/2100. Table 1. Average annual number of migrants per decade by development group and major area, 1950-2050 9
  • 10. b. World Bank Population Projections The (annual) population data and projections by the World Bank from 1960 till 2050 for almost 200 countries are largely based on those of the UN medium (normal) variants, with own projections for some (small) countries for which UN data and projections are not available; see World Bank web site. The main data sources of the World Bank’s demographic estimates and projections include the United Nations Population Division’s World Population Prospects; census reports and other statistical publications from national statistical offices; household surveys conducted by national agencies, ICF International, UNICEF, and the U.S. Centers for Disease Control and Prevention; Eurostat, Demographic Statistics; U.S. Bureau of the Census, International Database; United Nations Statistical Division’s Population and Vital Statistics Report (various years); and Secretariat of the Pacific Community, Statistics and Demography Programme (see World Bank, w/o year). Population projection is conducted up to 2050. The base year of the population projections is mid- 2010. For those countries with the 2010 population estimates that are from United Nations Population Division’s World Population Prospects, United Nations population projections of medium fertility are directly taken (rounded to nearest 1000). For other countries, projection software PROJPC is used to project the populations, with five-year period assumptions of mortality, fertility and migration data from the United Nations Population Division’s World Population Prospects of medium fertility. c. Eurostat population projections Eurostat undertakes and publishes historical demographic data and undertakes demographic projections for all of its 28 member countries as well as the other 4 members of the European Economic Area (see EU Commission website). The most recent population projection EUROPOP2013 is also the basis for the 2015 Ageing Report that undertakes the most recent assessment of demographic, economic and reform developments and the implications for public expenditure programs, in particular pensions, health and education. The 2015 Ageing Report itself is still pending but the Report on the underlying assumptions and projections has recently been released (EU Commission 2014). While the way actual demographic data, including information on the collection of data and from which sources is well documented, there is little easily accessible information on the web about the methodology and assumptions of its most recent demographic projections. The Ageing Report (page 26) refers in a footnote 1 to a forthcoming description of EUROPOP2013 that seem to be still in preparation. Yet the assumed paths for the demographic drivers can be downloaded, turned into charts and interpreted: Figure 3 presents the projected total fertility rates (TFR) for the 31 countries of the European Economic Area for the period 2013 till 2080.7 As visible, the projections for each country follow a moderately differentiated convergence approach. In general, the lower the initial TFR, the stronger the increase is assumed (i.e. β convergence is assumed, discussed in Section 3); for the few countries above some unknown convergence level such as France, Iceland, and Ireland a convergence from above takes place. However, for some Central and East European countries that had economic transition determined lower TFR levels it is assumed that their convergence speed will be faster. For some countries, such as Romania, it is assumed that the convergence ends already in 2060 with a TFR 7 The European Economic Area (EEA) consists of the 28 EU countries plus Iceland, Norway, Switzerland (incl. Lichtenstein). 10
  • 11. of 1.83. This is not the case for most other countries and the average of all 31 countries of the EEA. For the average of EEA countries the TTF rate increases broadly by 0.02 children as of the middle of the projection period and is 1.79 in 2080. Portugal and Spain share with Slovakia the privilege of having the lowest TFR in the EEA as starting position. The projections assume that their rates rise fast but remain for the total projection period at the bottom and in the same order; the TFR in 2080 for Portugal and Spain amount to 1.60 and 162, respectively, compared to the initial level in 2013 of 1.27 and 1.32, respectively. Figure 3: Eurostat Demographic Projections 2013: Projected Total Fertility Rates in EEA countries Source: Eurostat 2014 In addition to a low TFR variant Eurostat calculates a low and a high variant. The low variant differs from the medium variant in 2080 by 0.11 (Romania) to 0.5 (Iceland) children. In similar magnitudes but in the reverse order and sign are the differences between medium and high variant: The higher the level, the small the differences. Figure 4 present the male and female life expectancy in the medium variant. A number of conclusions stand out:  For both male and female the projections assume a strong further increase in life expectancy with, however, decreasing pace.  The projections assume β convergence leading to a stronger increase for the laggards both for male and for female population.  The marked gap between male and female life expectancy remains, albeit with some reductions.  The difference between male and female is particularly stark in the economic transition economies of Central and Eastern Europe, and in consequence the projected stark improvements there for the male population.  The male life expectancy in Portugal is at the lower end of the old EU countries, and remains there; that of Spain is among the top and also remains there.  The female life expectancy of Spain starts and ends as the highest of all 31 EEA countries, only rivaled by Iceland and France; that of Portugal is in the good old EU average. 1.25 1.35 1.45 1.55 1.65 1.75 1.85 1.95 2.05 2.15 2013 2020 2030 2040 2050 2060 2070 2080 TotalFertilityRate Belgium Bulgaria Czech Republic Denmark Germany Estonia Ireland Greece Spain France Croatia Italy Cyprus Latvia Lithuania Luxembourg Hungary Malta Netherlands Austria Poland Portugal Romania Slovenia Slovakia Finland Sweden United Kingdom Iceland Norway Switzerland 11
  • 12. Figure 4: Eurostat Demographic Projections 2013: Projected Life Expectancy in EEA countries Male Female Source: Eurostat 2014 Eurostat calculates also a high fertility variant. The difference to the medium variant in 2060 amounts to 2.4 years (male) and 2.3 years (female), respectively. The difference for the countries ranges for males from 1.1 years (Italy and Spain) to 5.7 years (Latvia and Lithuania), and for females from 0.9 years (Italy and Spain) to 4.8 years (Romania) and 5.0 years (Bulgaria). In line with a β convergence hypothesis, the differences across countries are typically the stronger the lower the initial life expediency is. Eurostat is not explicit about the assumptions and methodology on net migration that comprises both EEA internal migration as well as EEA external migration. The data available for the medium migration variant present the net migration balance for all 31 EEA countries. Table 2 presents the data and invites to the following observations:  The base year 2013 is characterized by a number of particularities: fallout of crisis, in particular for Greece, Ireland, Protugal and Spain; economic transition travails plus fall-out, in particular the Baltic and Balkan countries; and refugee inflow, in particular Italy.8  The projection assume that these particularities are worked out within the next 2-3 decades so that by 2040 all EEA countries have again a positive migration balance  After 2040, however, and till the end of the projection period it assumed that net migration balances will broadly be reduced to lower levels.  For the EEA as a whole the assumed reduction in the migration balances between 2040 and 2080 amount to 40 percent. 8 The negative sign for Germany must be an error as Germany is now among the most migrant receiving countries in the world. 68.0 70.0 72.0 74.0 76.0 78.0 80.0 82.0 84.0 86.0 88.0 90.0 92.0 2013 2020 2030 2040 2050 2060 2070 2080 Belgium Bulgaria CzechRepublic Denmark Germany Estonia Ireland Greece Spain France Croatia Italy Cyprus Latvia Lithuania Luxembourg Hungary Malta Netherlands Austria Poland Portugal Romania Slovenia Slovakia Finland Sweden UnitedKingdom Iceland Norway Switzerland 68.0 70.0 72.0 74.0 76.0 78.0 80.0 82.0 84.0 86.0 88.0 90.0 92.0 2013 2020 2030 2040 2050 2060 2070 2080 12
  • 13.  For Portugal and Spain the migration balances after the recovery remain very small (Portugal) or modest (Spain), amount to much less than 1% of population. Table 2: Eurostat Demographic Projections 2013: Projected Migration Balance in EEA countries Source: Eurostat 2014 d. Spanish Population Projections: National Institute of Statistics/ Instituto Nacional de Estadística El cálculo de predicciones sobre el comportamiento de variables demográficas es una de las labores fundamentales de los organismos oficiales de estadística. Es el caso del Instituto Nacional de Estadística (INE) que se encarga de realizar las proyecciones de población de España, incluyendo proyecciones de fecundidad, mortalidad y migración exterior. ¿Cómo realiza el INE las proyecciones de los diferentes componentes que permiten proyectar el comportamiento de la población en su globalidad? Veamos a continuación un resumen de las Notas Metodológicas elaboradas por dicho organismo y que acompañan a las proyecciones realizadas más recientemente para la población española. Determinación de la población inicial en España en un momento t (magnitud stock) En primer lugar, a la hora de realizar predicciones, se debe determinar de la manera más precisa posible la población en el momento inicial, o tP . Es la magnitud stock de la ecuación (1), dado que recoge la cuantificación del fenómeno en un momento concreto del tiempo, y en España suele obtenerse a partir de registros estadísticos de población. Las diferencias observadas entre diferentes registros, como censos y padrones, puede afectar a las proyecciones realizadas, siendo uno de los objetivos prioritarios de los organismos oficiales avanzar en la obtención de cifras lo más 2013 2020 2030 2040 2050 2060 2070 2080 Belgium 61 192 80 214 80 903 69 764 46 801 42 120 37 432 32 760 Bulgaria -2 901 -5 827 -5 841 5 323 3 660 623 1 249 1 594 Czech Repu -1 297 28 042 35 777 40 736 25 480 21 240 19 088 17 597 Denmark 21 196 18 929 19 936 16 263 10 492 10 035 8 394 7 347 Germany (un -1 126 999 228 679 220 234 142 591 119 267 97 891 83 133 78 895 Estonia -2 699 -3 700 -2 189 640 567 8 199 255 Ireland -32 413 -30 303 -12 140 4 819 16 731 15 063 13 394 11 719 Greece -15 889 -22 262 -10 003 1 258 7 340 4 695 5 390 4 264 Spain -310 916 -79 009 87 513 225 207 305 561 275 002 244 449 213 888 France 52 775 90 186 91 239 83 988 74 229 66 807 59 383 51 953 Croatia 2 281 2 415 3 528 4 580 5 709 4 750 4 048 3 784 Italy 1 135 522 348 082 382 425 335 911 214 822 196 417 181 859 157 990 Cyprus -575 -627 2 794 6 016 8 834 7 945 7 061 6 181 Latvia -10 085 -14 308 -9 895 933 737 -1 4 235 Lithuania -16 802 -37 393 -21 066 964 396 5 5 156 Luxembourg 10 523 11 720 11 175 9 072 5 394 4 858 4 326 3 782 Hungary 8 089 24 302 20 936 24 176 15 315 14 014 11 615 10 151 Malta 1 617 1 565 1 468 1 422 1 336 1 146 1 002 893 Netherlands 22 064 24 163 23 537 12 995 8 949 9 257 8 019 6 668 Austria 55 540 51 343 51 904 41 918 27 179 24 758 21 568 19 546 Poland -15 583 2 947 -903 25 433 29 474 11 566 9 344 12 158 Portugal -40 275 285 9 218 11 944 8 284 7 932 8 018 5 733 Romania -9 245 405 -24 656 11 626 7 092 2 397 3 153 3 663 Slovenia 782 4 076 4 639 5 460 5 417 4 462 3 968 3 753 Slovakia 2 037 2 982 2 464 4 668 4 718 2 403 2 282 2 176 Finland 17 158 22 047 21 743 17 682 9 603 8 864 7 702 7 011 Sweden 65 779 55 256 55 993 49 117 34 666 31 195 27 735 24 267 United Kingd 165 003 172 091 203 324 209 284 190 246 171 229 152 197 133 177 Iceland 1 635 5 224 403 566 513 439 379 Norway 39 205 53 390 51 824 42 335 24 905 22 413 19 926 17 438 Switzerland 85 233 73 177 72 073 62 396 44 115 39 709 35 289 30 875 161 952 1 102 872 1 368 178 1 468 924 1 257 885 1 099 316 981 671 870 288 13
  • 14. homogéneas posibles9 en relación a los diferentes fenómenos demográficos (ver en Cuadrado (2014) un análisis de la evolución reciente y proyecciones de población en España). Para las últimas proyecciones publicadas en Octubre de 2014, Proyecciones de la población de España 2014-2064, la población de partida a 1 de enero de 2014 utilizada por el INE está constituida por las Cifras de Población Provisionales en dicha fecha.10 En la Proyección de la Población de España a Largo Plazo (2012-2052) la población de partida se obtuvo de los Estimaciones de Población Actual a 1 de enero de 2012 (INE, 2012). Una vez establecida la población stock de partida, y a partir del estudio retrospectivo de los fenómenos demográficos flujo (véase, nacimientos, defunciones, emigraciones e inmigraciones) se establecen hipótesis sobre la incidencia de los mismos en cada año del periodo para el que se realizan las proyecciones, teniendo en cuenta las tasas de fecundidad, mortalidad, y movimientos migratorios para cada generación (y género, dado que suele hacerse de manera independiente para hombres y mujeres). Cabe señalar que desde 2014 se han establecido hipótesis diferenciadas según nacionalidad española o extranjera para aquellos fenómenos demográficos en que resulte conveniente hacerlo, como el análisis de las tasas de fecundidad. Ello ha obligado a establecer hipótesis sobre el comportamiento esperado del número de personas que adquieren la nacionalidad española. No ocurría lo mismo en las proyecciones del 2012, en las que se utilizaban las tasas estimadas de fecundidad globalmente consideradas. Proyección de la fecundidad El INE estima la evolución de la fecundidad11 de las mujeres residentes en España para cada año del periodo de proyección teniendo en cuenta la modelización de las tasas específicas de fecundidad por edad observadas durante los últimos diez años, realizando una extrapolación de las mismas en base a dicha modelización. Desde el año 2014, como comentábamos anteriormente, se ha introducido la modelización de la fecundidad según la nacionalidad de la madre, dado el distinto comportamiento de las mujeres españolas y extranjeras que ya analizábamos en Ayuso y Holzmann (2014a). En primer lugar se modeliza la serie retrospectiva de las tasas de fecundidad por edad y nacionalidad utilizando la serie anual de resultados de los Indicadores Demográficos Básicos12 (para las últimas proyecciones, la serie 2004-2013)13 . Las tasas de fecundidad observadas para cada edad x se ajustan según una función log-lineal en el tiempo (2), realizándose la estimación de los parámetros por el método de Mínimos Cuadrados Ordinarios. )ln(,,, zbaf nxnx t nx += con t=2014,…, 2063; x=15,…, 49 y z=3,4… (2) En segundo lugar, una vez realizada la estimación del modelo log-lineal especificado, se realiza la proyección de las tasas específicas de fecundidad en base al mismo por año de nacimiento de la madre en cada año del periodo 2014-2063 (o 2012-2051, en el caso de las proyecciones de 2012). La Figura 5a&b muestra los valores observados y proyectados para las tasas de fecundidad por edad y nacionalidad de la madre a partir de las proyecciones de 2014, recientemente publicadas por el INE. 9 Los censos son recuentos exhaustivos de población que recogen toda la población que tenga fijada su residencia habitual en España (incluida la población extranjera). Los padrones son registros administrativos donde constan todos los vecinos que tienen su residencia habitual en un municipio en cuestión. 10 Ver INE, 2014b, Anuario Estadístico de España, para una descripción completa de las diferentes operaciones estadísticas llevada a cabo por la Administración General del Estado. En junio de 2013 el INE comienza a publicar las Cifras de Población, con el objetivo de proporcionar semestralmente una medición cuantitativa de la población residente en España a escala provincial. En su cálculo parte del Censo de Población de 2011 e incorpora los resultados de mortalidad, fecundidad y migración que se van produciendo. 11 Recordemos que la tasa de fecundidad proporciona el número de nacidos vivos por cada 1.000 mujeres de edades comprendidas entre los 15 y 49 años en un determinado año (Ayuso y Holzmann, 2014a, sección 2). 12 http://www.ine.es/jaxi/menu.do?type=pcaxis&path=/t20/p318/&file=inebase 13 Para las proyecciones del 2012, la serie de tasas de fecundidad correspondientes al periodo 2002-2011. 14
  • 15. Figura 5a&b: Fertility rates for national and foreign population by age groups Fuente: INE (2014a) La evolución del indicador coyuntural de fecundidad según datos observados y proyectados, y teniendo en cuenta la nacionalidad de la madre, aparece en la figura 6. Como puede observarse, y a diferencia de las proyecciones realizadas para 2012-2052 (ver INE, 2012, donde se observaba una tendencia creciente en el número esperado de hijos por mujer, hasta 1.55 en 2050) ahora se proyecta un decrecimiento en la tasa de fecundidad, muy acentuada para las mujeres de nacionalidad extranjera. El número medio de hijos por mujer se espera que esté ligeramente por encima de 1.20 en 2050, según las nuevas proyecciones. Figura 6 Fuente: INE (2014a) 15
  • 16. Proyección de la mortalidad La proyección de la incidencia de la mortalidad en España se realiza a partir de la extrapolación de las probabilidades de muerte a cada edad, ajustadas mediante un modelo exponencial de las trayectorias suavizadas de las mismas en función del tiempo, y diferenciando por sexo s: t xs xsxs eq ,, , ˆ βα + = con x=0,…,99. (3) Los parámetros correspondientes pueden estimarse por MCO sobre los modelos lineales obtenidos de la transformación logarítmica de (3). Las proyecciones de mortalidad observadas y proyectadas según las cifras de proyección de 2014 aparecen en las figuras 7a y 7b diferenciando por género. Los gráficos ponen de manifiesto un decrecimiento en las tasas de mortalidad proyectadas, fundamentalmente en las edades más jóvenes e intermedias, pero también, aunque menos acentuado, en las avanzadas. 16
  • 17. Figura 7a&b. Tasas de mortalidad observadas y proyectadas (2014-2063) a. Hombres b. Mujeres Fuente: elaboración propia en base a INE (2014) A partir de las tasas anuales de mortalidad proyectadas se pueden obtener las diferentes funciones biométricas de la tabla de mortalidad, entre las que se encuentra la función de fallecimiento, que nos proporciona el número de fallecimientos entre dos periodos determinados (anuales o de duración superior al año). Los datos obtenidos nos permiten también proyectar el comportamiento de la esperanza de vida al nacer para hombres y mujeres (eje izquierdo, figura 8), así como la brecha de género entre hombres y mujeres (eje derecho, figura 8). Figura 8. Esperanza de vida al nacer observada y proyectada (2014-2063) Hombres y mujeres, y brecha de género Fuente: elaboración propia en base a INE (2014) ,0 ,1 ,2 ,3 ,4 ,5 ,6 ,7 ,77 ,79 ,81 ,83 ,85 ,87 ,89 ,91 ,93 ,95 ,97 2007 2010 2013 2016 2019 2022 2025 2028 2031 2034 2037 2040 2043 2046 2049 2052 2055 2058 2061 Brechadegénero(Mujeres-Hombres) Esperanzadevidaalnacimiento Proyección Hombres Observado Hombres Proyección Mujeres Observado Mujeres Brecha de género 0,000001 0,00001 0,0001 0,001 0,01 0,1 1 0 10 20 30 40 50 60 70 80 90 100 2001 2011 2031 2041 2051 2061 0,000001 0,00001 0,0001 0,001 0,01 0,1 1 0 9 18 27 36 45 54 63 72 81 90 99 2001 2011 2031 2041 2051 2061 17
  • 18. Como puede observarse, se espera un incremento de la esperanza de vida tanto para los hombres como para las mujeres a lo largo del periodo de proyección. En 2050 se espera que las mujeres vivan en término medio 92.4 años en España, alcanzando los 93.9 años en 2060. Para los hombres, el número medio de años de vida proyectado es de 88.6 y 90.4 años, en 2050 y 2060, respectivamente. La brecha de género entre hombres y mujeres se espera que se vaya reduciendo, pasando de 6.4 años de diferencia en 2007 a 3.8 en 2050 y 3.5 en 2060. Proyección de la migración exterior El INE distingue en la formulación y análisis de las hipótesis de inmigración exterior entre la entrada de población española y extranjera, teniendo en cuenta su diferente naturaleza y razones que pueden justificarla. Los datos sobre inmigración exterior se introducen en la proyección considerando su intensidad global para españoles y extranjeros del año corriente, que se mantiene constante para todo el periodo proyectivo, repartiéndose por sexo y generación con datos promedio de los últimos seis años (en el caso de las últimas proyecciones, las correspondientes al periodo 2008-2013, Estadística de Migraciones14 ). Las distribuciones promedio se mantienen constantes a lo largo del periodo de proyección. Al igual que con la inmigración, el INE diferencia en el análisis de la emigración exterior la correspondiente a población española y población extranjera, de nuevo, teniendo en cuenta la diferente naturaleza de la misma. En el cálculo de proyecciones se tienen en cuenta las tasas de emigración por generación para cada sexo y nacionalidad. De este modo, para cada nacionalidad, las tasas de emigración exterior por cada generación, para cada sexo, de un determinado año se calculan teniendo en cuenta el denominado Índice Sintético de Emigración Exterior (ISE, que mide la intensidad de la emigración en el año corriente), un diferencial por género, y una distribución por generaciones de dicha intensidad (calendario por generación). En el caso de las últimas proyecciones se utilizan en su cálculo las observaciones obtenidas de la Estadística de Migraciones en el periodo 2008-2013. El ISE utilizado se supone constante para todo el periodo de proyección (a modo de ejemplo el ISE en septiembre de 2014 es de 0.20 para la población española, y de 6.11 para la población extranjera). Asimismo, el diferencial por sexo para la intensidad de emigración al exterior de cada nacionalidad, y el calendario de emigración por generación o año de nacimiento, para cada sexo y nacionalidad, también se establecen constantes para todo el periodo proyectivo. Todos ellos, tal y como hemos comentado, calculados en las últimas proyecciones en base al periodo 2008-2013. Siguiendo un proceso análogo al presentado para la emigración exterior el INE proyecta desde 2014 el número de adquisiciones de nacionalidad española. Las proyecciones de migración exterior observadas entre 2009-2013 y proyectadas 2014-2063 aparecen en la tabla 3 y en la figura 9. En las mismas puede observarse un saldo migratorio proyectado negativo hasta 2018 (mayor número de emigraciones que de inmigraciones), que cambia de signo a partir de dicha fecha. No obstante es necesario remarcar que el número de inmigraciones proyectado se supone constante para todo el periodo de proyección. 14 http://www.ine.es/jaxi/menu.do?type=pcaxis&path=%2Ft20%2Fp277&file=inebase&L=0 18
  • 19. Tabla 3 Figura 9 Fuente: INE (2104c) Finalmente el saldo migratorio por edades observado en el periodo 2009-2013 y proyectado para los años 2031 y 2061 aparece en la figura 10. Como puede observarse el número de emigraciones ha ido aumentando respecto al número de inmigraciones en el periodo 2009-2013, provocando saldos migratorios negativos cada vez más acentuados, fundamentalmente en la franja asociada al mercado laboral (20-60 años, aproximadamente). Las proyecciones realizadas muestran recuperaciones en dicha franja de edad, aunque fundamentalmente para las edades más jóvenes, entre los 20 y 25 años. Figura 10. Saldo migratorio por edad observado y proyectado (2009-2061) Fuente: elaboración propia en base a INE (2014) Para concluir este apartado señalar que el INE elaboraba desde el año 2008 las Proyecciones de Población a Corto Plazo para España y sus Comunidades Autónomas y Provincias en los 10 años siguientes, y cada tres años unas Proyecciones de Población a Largo Plazo para España en los 40 años siguientes. A partir de 2014 ambas operaciones han quedado integradas en una sola de carácter -14000 -12000 -10000 -8000 -6000 -4000 -2000 0 2000 4000 6000 8000 0 6 12 18 24 30 36 42 48 54 60 66 72 78 84 90 96 Saldomigratorio Edad 2009 2010 2011 2012 2013 2031 2061 19
  • 20. bianual: las Proyecciones de Población. Un resumen de las principales cifras derivadas de las mismas queda reflejado en el Tabla 4. Tabla 4. Proyecciones de Población 2014-2064 Población residente en España Año 2014 Año 2029 Año 2064 Población a 1 de enero 46.507.760 45.484.907 40.883.832 Fenómenos demográficos Año 2014 Año 2028 Año 2063 Nacimientos 408.901 299.279 229.434 Defunciones 395.196 411.392 559.857 Inmigraciones del extranjero 332.522 332.522 332.522 Emigraciones al extranjero 417.191 288.152 245.903 Saldo vegetativo 13.705 -112.113 -330,423 Saldo migratorio -84.669 44.370 86.619 Fuente: Datos proyecciones 2014-2064 (INE, 28/10/2014) f. Portuguese Population Projections: Statistics Portugal/ Instituto Nacional de Estatística The official population data and projections are periodically provided by Statistics Portugal/ Instituto Nacional de Estatística. The latest and recently 2012-2060 population projections (INE 2014) takes the annual provisional estimates of resident population on December 31, 2012 as the starting population. As other national statistical offices they continue preferring deterministic scenario projections over probabilistic ones. The most recent projection exercise of 2014 comprises four alternative scenarios for the dynamics of the resident population (low - baixo, medium - tendencial, high - elevado, zero migration - sem migrações), resulting from the combination of different paths for the future levels of fertility, mortality and international migration. Figure 11 illustrates this approach. Figure 11 – Alternative population projection scenarios for Portugal Source: Authors’ preparation based on Statistics Portugal. Hip. Mortalidade moderada optimista Hip. Fecundidade moderada optimista pessimista Hip. Migrações S.M. positivos S. M. negativos Sem migrações CENÁRIOS tendencial baixo elevado sem migrações 20
  • 21. Alternative assumptions regarding future levels of fertility and mortality are encompassed in pessimistic (pessimista), moderate (moderada) and optimistic (optimista) variants. Alternative assumption for future levels of international migration comprise a negative (S.M. negativos), a positive (S.M. positivos) and a zero (Sem migrações) net migration scenarios. In what follows we provide details about the methods used to project fertility rates, mortality rates, and future levels of net international migration in Portugal and the way in uncertainty is addressed in population projections. Projecting Fertility: In Portugal, the methodology used by the official Statistics bureau to project the number of births is based on the analysis of time series fertility data, assumptions regarding the dynamics of the Total Fertility Rate (TFR), assumptions on the mean age at birth of a child, sex ration assumptions, fertility and family surveys and statistical modeling. Age-specific fertility rates (ASFRs) are modelled using the approach proposed by Schmertmann (2003, 2005). The model describes the shape of the ASFR schedule in terms of the ages at which the graphical schedule reaches certain characteristic points, specifically α , the youngest age at which fertility rises above zero, P , the age at which fertility reaches its peak level, and H , the youngest age above P at which fertility falls to half of its peak level. Age-specific fertility rates ( )f x between age α and an upper age β (e.g., age 49) are modelled through a piecewise quadratic spline function. ( ) ( ), 14,...,50f x R x xφ= = ( ) [ ] 4 2 0 , ( ) 0, , k k k x t x x x θ α β φ α β + =  − ≤ ≤ =   ∉ ∑ , (2) where R is a scalar, “knots” 0 1 4...t t t< < < fall in the interval [ ],α β , 0t α= (the lowest age of childbearing), and ( ) ( )max ;0k kx t x t+ − ≡ − . To reduce the number of parameters the knot positions are determined from the index ages, and certain mathematical restrictions are impose so that the spline function mimics common features of ASFR schedules. The ( )f x function is continuous, with quadratic subsections joined at knot values and yields a closed-form expression for TFR: ( ) ( ) ( ) 4 3 03 k k k R TFR f x dx R x dx t β β α α φ θ β = = = = −∑∫ ∫ (3) In preparing the fertility assumptions for Portugal, the results from the fertility and family survey conducted in 2013 (Inquérito à Fecundidade IFEC2013, INE 2013) were taken into consideration. Survey results provide an in-depth analysis of fertility decisions, particularly as the number of actual children (observed fertility), the number of children that families think they will have (expected final fertility), and the number of children that they would have given certain demographic and socioeconomic developments (desired fertility). Three alternative assumptions regarding future levels of fertility have been defined. The pessimistic (low variant) hypothesis assumes TFR will roughly stabilize at around 1.30 children per woman (the observed TFR in 2012 was 1.28). The optimistic variant assumes a gradual recovery of TFR, reaching 1.80 children per woman in 2060. This assumption takes into account the results provided by IFEC2013, according to which the "expected final fertility" (actual and expected average number of children) of 18-49 years old women living in Portugal assumed this value. The medium variant assumes a moderate recovery of fertility levels, with and expected TFR of 1.55 children per woman in 2060. 21
  • 22. Figure 12 summarizes this information and exhibits the observed and forecasted values (in the three variants) for the total fertility rate in Portugal in the period 1992-2060. In Figure 13 we represent the forecasted age-specific fertility schedules for selected years considering the central scenario. Figure 12: Total Fertility Rate, Portugal, 1992-2060 (observed and projected) Source: Authors’ preparation based on INE (2014) Figure 13: Age-Specific fertility schedule, Portugal, selected years (central variant) Source: Author's preparation based on INE (2014) Projecting Mortality and Longevity In addressing the mortality component of population projections, two alternative hypotheses have been considered: (i) a medium hypothesis, which assumes that recent observed trends in mortality will continue into the future, with nationwide life expectancy at birth increasing to 84.21 (89.88) years for the male (female) population by 2060; (ii) an optimistic hypothesis, which assumes a more marked increase in the longevity prospects for the Portuguese populating, with life expectancy at birth increasing to 86.44 (92.15) years for the male (female) population by 2060. The projection of mortality is made using the Poisson-Lee-Carter (PLC) log-bilinear methodology (Brouhns et al., 2002) in conjunction with relational models (Brass, 1971) for subnational population 1,30 1,55 1,22 1,80 1,00 1,10 1,20 1,30 1,40 1,50 1,60 1,70 1,80 1,90 2,00 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 2012 2014 2016 2018 2020 2022 2024 2026 2028 2030 2032 2034 2036 2038 2040 2042 2044 2046 2048 2050 2052 2054 2056 2058 2060 Observed Low variant Central variant high variant 0,000 0,020 0,040 0,060 0,080 0,100 0,120 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 2012 2020 2030 2040 2050 2060 22
  • 23. levels. The classical age-period (AP) Lee-Carter (LC) model was first introduced by Lee and Carter (1992), combining a demographic model for the mortality rate, dependent only on factors related to age and period, describing the historical change in mortality, a method for fitting the model and a time series (Box-Jenkins) method for modelling and forecasting the time-varying parameter. From this forecast of the general level of mortality, the actual age-specific rates are derived using the estimated age effects.15 The PLC log-bilinear methodology assumes that the number of deaths by age and calendar year, ,x tD , follows a Poisson distribution with parameter , ,x t x tEµ ( ), , ,~x t x t x tD Poisson Eµ (3) with ( ), expx t x x tkµ α β= + (4) where ,x tE denotes the exposure-to-risk at age x during year t , ,x tµ is the mortality force at age x during calendar year t . Parameter vector xα represents the general shape of the mortality schedule in the sample period, vector xβ represents the age-specific patterns of mortality change and vector tk denotes time-varying trend. Parameter estimates are obtained through maximum-likelihood methods using an unidimensional Newton-Raphson type iterative algorithm (Goodman, 1979). Initial parameter estimates are subjected to two constraints to ensure model identification. Box-Jenkins techniques are used to estimate and forecast tk within an ARIMA(p, d, q) times series model. To project mortality rates for the oldest-old ( 85x ≥ ), INE uses a log-quadratic model proposed by Denuit & Goderniaux (2005). Forecasts of age-specific mortality rates are derived using the estimated age effects and the forecasted time-varying component. From this, life table biometric functions and other mortality and longevity markers can be calculated. Figure 14 exhibits the observed and forecasted life expectancy at birth for both the male and female Portuguese populations in the period 2012-2060, in both the moderate (central) projection scenario and in a more optimistic scenario. Figure 14: Observed and forecasted life expectancy at birth, Portugal, 1992-2060 15 The main statistical tool of Lee & Carter (1992) is least-squares estimation via singular value decomposition of the matrix of the log age-specific observed forces of mortality. This implicitly means that the errors are assumed to be homoskedastic, which is quite unrealistic: the logarithm of the observed force of mortality is much more variable at older ages than at younger ages because of the much smaller absolute number of deaths at older ages. Another drawback of the Lee-Carter methodology is that the required data have to fill a rectangular matrix because of singular value decomposition. In addition, estimated prediction intervals are quite narrow. 23
  • 24. Source: Author's preparation based on INE (2014) Alternative scenarios have also been devised using an extension of the traditional PLC log-bilinear methodology but considering a limit life table (Bravo, 2007, 2010). To forecast regional level mortality rates, a Brass-type relational model has been adopted considering logit transformations of crude rates. Forecasting international net migration In addressing the international net migration component of population projections, three alternative hypotheses have been considered by Statistics Portugal for the period 2012-2060 (Figure 15): i) A pessimistic hypothesis, which assumes negative annual international migration balances throughout the whole projection period, starting with the estimated values for the base year and converging in 2035 to the average 2010-2012 period observed figures; ii) An optimistic hypothesis, which assumes a gradual recovery of international annual migration balances shifting to positive values in 2020, starting with the estimated values for the base year and converging in 2035 to the average of net migration estimates observed in the period 1991-2012; iii) A zero net migration hypothesis, which admits the absence of international migration, which despite its improbability allows evaluating the influence of migration on population dynamics. Annual international migration balances are distributed by age and sex using assumptions on the age structure of migration flows, considering the latest observed patterns. Figure 15: Observed and forecasted international net migration, Portugal, 1992-2060 77,11 83,18 84,21 89,88 86,44 92,15 65,0 70,0 75,0 80,0 85,0 90,0 95,0 1991 1993 1995 1997 1999 2001 2003 2005 2007 2009 2011 2013 2015 2017 2019 2021 2023 2025 2027 2029 2031 2033 2035 2037 2039 2041 2043 2045 2047 2049 2051 2053 2055 2057 2059 Observed - male Observed female moderate variant male moderate variant - female optimistic variant - male optimistic variant - female 24
  • 25. Source: Author's preparation based on INE (2014) Population projections for Portugal Table 5: Population projections and markers, Portugal & NUTS II Male Female Male Female Scenario 1 Low 1,30 84,2 89,9 - 19 289 6 346 726 90,1 Scenario 2 Central 1,55 84,2 89,9 19 493 8 575 339 67,0 Scenario 3 High 1,80 86,4 92,2 19 493 9 223 617 70,9 Scenario 4 Zero migration (central) 1,55 84,2 89,9 7 856 281 73,0 Scenario 1 Low 1,25 84,0 89,7 - 7 989 2 110 746 100,3 Scenario 2 Central 1,51 84,0 89,7 3 852 2 788 256 74,5 Scenario 3 High 1,76 86,3 92,1 3 852 3 014 128 78,7 Scenario 4 Zero migration (central) 1,51 84,0 89,7 2 723 769 77,5 Scenario 1 Low 1,25 84,5 90,1 - 3 773 1 258 379 100,0 Scenario 2 Central 1,51 84,5 90,1 3 941 1 709 950 72,7 Scenario 3 High 1,76 86,7 92,4 3 941 1 844 314 76,7 Scenario 4 Zero migration (central) 1,51 84,5 90,1 1 581 791 79,2 Scenario 1 Low 1,40 83,7 89,6 - 5 142 1 909 196 77,5 Scenario 2 Central 1,66 83,7 89,6 7 670 2 642 332 58,1 Scenario 3 High 1,86 86,0 91,9 7 670 2 818 302 61,7 Scenario 4 Zero migration (central) 1,66 83,7 89,6 2 285 386 65,1 Scenario 1 Low 1,30 84,0 89,5 - 1 363 398 218 94,2 Scenario 2 Central 1,56 84,0 89,5 976 536 737 69,6 Scenario 3 High 1,81 86,2 91,9 976 579 674 73,7 Scenario 4 Zero migration (central) 1,56 84,0 89,5 511 401 74,1 Scenario 1 Low 1,35 83,8 90,1 - 290 319 930 75,8 Scenario 2 Central 1,61 83,8 90,1 2 139 454 489 56,4 Scenario 3 High 1,86 86,0 92,3 2 139 486 967 59,7 Scenario 4 Zero migration (central) 1,61 83,8 90,1 345 651 68,7 Scenario 1 Low 1,32 80,7 87,5 - 324 189 159 70,8 Scenario 2 Central 1,58 80,7 87,5 277 224 170 60,5 Scenario 3 High 1,83 83,3 90,0 277 242 713 64,1 Scenario 4 Zero migration (central) 1,58 80,7 87,5 213 909 63,0 Scenario 1 Low 1,19 81,3 87,5 - 408 161 098 89,2 Scenario 2 Central 1,45 81,3 87,5 638 219 405 65,7 Scenario 3 High 1,70 83,8 89,9 638 237 519 69,4 Scenario 4 Zero migration (central) 1,45 81,3 87,5 194 374 73,3 Old-age dependency ratio 2012 2060 2012 2060 2012 2060 2013 2060 2013 Total Fertility Rate Life Expectancy at birth Net migration Population 2060 Portugal 1,28 77,1 83,2 - 37 352 10 487 289 29,4 Portugal & NUTS II Scenarios/Components 25,5 Centro 1,19 77,4 83,4 - 8 139 2 298 938 34,6 Norte 1,15 76,8 82,9 - 16 863 3 666 234 30,0 Alentejo 1,33 76,7 82,6 - 1 910 748 699 38,2 Lisboa 1,51 76,4 82,8 - 8 599 2 818 388 30,7 R. A. Açores 1,34 72,7 80,0 - 133 247 549 18,7 Algarve 1,43 76,5 83,4 - 942 444 390 21,1R. A. Madeira 1,08 73,3 80,3 - 766 263 091 Source: Authors’ preparation based on INE (2014) 3. The population drivers beyond demography: What data analyses and economics have to say! Common characteristics in the assumptions for the three demographic drivers were the base for all projections presented in the prior Section: First, a convergence vision driven by the demographic transition model (fertility rates), a conjectured vision that age-specific mortality rates across will somehow become more similar but with decreasing speed, and convenience assumption that migration balances will be reduced or even disappear. Second, data used to estimate parameters for the projected developments of the three demographic drivers are exclusively of demographic nature – for individual countries but also for multi-country projections. While autoregressive approaches have their charm and convenience, in particular when high-frequency data is at hand (such as in financial markets), leaving out any economic explanation of the drivers for past and projected future -60000 -40000 -20000 0 20000 40000 60000 80000 1991 1993 1995 1997 1999 2001 2003 2005 2007 2009 2011 2013 2015 2017 2019 2021 2023 2025 2027 2029 2031 2033 2035 2037 2039 2041 2043 2045 2047 2049 2051 2053 2055 2057 2059 "estimates" "pessimistic scenario" "optimistic scenario" "zero migration scenario" 25
  • 26. developments is little understandable and conjectured to be wrong. Third and combining elements of the prior two components: Moving away from unconditional convergence (i.e. a common state) is suggested by the data; but as in economic (country) convergence without additional explanatory variables (and storyline), the projections are not credible. And there is economic and other research out there to offer both. This Section reviews key economic variables that may be productively applied to assist demographic projections and presents some of the reviewed recent literature. As this is a first stab on the topic, the review will be selective, i.e. incomplete. Yet it will offer some gist in which direction future research and demographic projections should go. a. The economic and other explanations of fertility development This sub-section on fertility development focuses on three issues: (i) what is the role of income compared to mortality development in explaining the direction of fertility development?; (ii) is there a convergence of countries toward common fertility levels?, and (iii) what converging (total) fertility rate(s) do emerge from recent large-scale econometric analyses? (i) Theories of demographic transition and the explanation on fertility development focus typically on either on the impact of the mortality or on the impact of income levels and economic growth. Demographers tend to emphasize, not surprisingly, the mortality channel while economists tend to emphasize the income channel broadly understood (i.e. rising income per capita serving as a proxy for technological change and productivity growth, see Herzer et al. 2012). The most prominent explanations for the mortality channel offered by demographers are physiological mechanisms (such as the link between breast feeding and fecundity) and the concept of the ideal family size (implying a wish for the replacement of the deceased children). These channels establish a negative association between fertility and mortality which is, however, insufficient to explain demographic transition understood as a secular decline of net fertility, i.e. of the surviving children per family and thus the secular decline in population growth. In order to establish the mortality channel as a sufficient for demographic transitions several refinements of the demographic driven theory have been proposed, including the precautionary child-bearing of risk-adverse parents or more complex theories around the interaction between extrinsic survival conditions and child health, and the impact of adult longevity in fertility (Herzer et al. 2012). For an economic theory of demographic transition the basic challenge is to explain the negative association between income and fertility without abandoning the assumption of children as “normal goods”. A common element of economic theories is that the positive income effect (more income increases the demand for children) is dominated by a negative substitution effect (more income increases the price/opportunity costs of children and reduces the demand). Examples for such explanation include two theories proposed by Garry Becker: One based on time allocation and the assumption that children are more time-intensive than other consumption goods (Becker 1965); the other is based on a quantity/quality trade-off and the substitution of fertility with expenditure on children as income rises (Becker and Lewis 1973). With the rise of the unified growth theory (see Galor 2005, 2011), the economic analysis of fertility has been framed in a dynamic context that rejects simple causality and allows for endogeneity from and to the main drivers of fertility. With this approach the focus has shifted away from the association between fertility and income levels (across countries) toward the association between fertility change and income growth (within countries and over time). Moreover, the time cost idea and the child quality trade-off have been refined. Yet a common element of these income based theories is that without further assumptions mortality plays no role in explaining fertility decisions. If added it is netted out in the standard model framework. A way to introduce a role for mortality is to abandon the assumption of homothetic utility in the model framework (Doepke 2005). 26
  • 27. Based on this modelling idea Hertzer, Strulik and Vollmer (2012) develop an econometric specification that allows the testing of the long run relationship between fertility, mortality and economic development ititittit egdpmortafert +++= )log(21 ββ [2] Where i=1,2,…,N and t=1,2,…,T are country and time indices, fertit is fertility measured by the crude birth rate ( births per thousand population), mortit stands for mortality, measured in crude death rate (death per thousand population), and log(gdpit) is the GDP per capita measure in logs. Using data over a 100 year period from 1900 to 1999 packed in 5 years averages for a mix of 20 developed and countries across the globe, panel co-integration techniques, dynamic OLS, and a battery of cutting-edge statistical tests, they are able establish with high confidence the co- integrating relationship between fertility, mortality and income, test the robustness of the estimates and investigate the direction of the causality. Using a shorter data set (1950-1999) but for 119 countries they could also ascertain the coefficients are stable between the data sets and for a split between developed and developing countries (Table 6). Table 6: DOLS Estimates of the Long-Run Effects on Fertility mortit log(gdpit) No of countries in sample 20 countries 1900-1999 0.378** (7.40) -7.246** (-10.18) 20 Developed countries 0.623** (6.25) -4.757** (-8.22) 12 Developing countries 0.470** (5.45) -4.021** (-3.50) 8 119 countries 1950-1999 0.420** (13.74) -5.829** (-11.46) 119 Developed countries 0.502** (5.96) -5.567** (-4.03) 16 Developing countries 0.487** (10.45) -4.987** (-9.83) 103 Source: Hertzer, Strulik and Vollmer (2012), based on tables 2, 3 and 4 Table 6 indicates highly and surprisingly stable coefficients across data sets and sub-samples. For the full 20 country data sample the coefficient of fertility with respect to morality is estimated to be positive and 0.378 (implying that in the long run a one standard deviation increase in the mortality variable is associated with an increase in the fertility variable equal to 25 percent of a standard deviation of this variable), while the coefficient of fertility with respect to log per capita income is negative and -5.246 (indicating a reduction by 42 percent of a standard deviation of the mortality variable by an increase of one standard deviation in the income variable). These results imply that an increase of GDP per capita by $1.000 and a decrease of the mortality rate by 0.5 percentage points both decrease the fertility rate by about 0.19 percentage points. These estimates further imply that a reduction of the mortality rate by 0.5 percentage points is associated with an increase of the population growth rate by 0.31 percentage points (0.5 minus 0.19) holding GDP constant. This allows the conclusion that declining mortality is insufficient to explain the declining population growth observed along the path of transition. More generally, the results of this first macro-study with data for a full century and cutting-edge estimation techniques strongly suggest that (1) declining mortality leads to declining fertility; (2) growth in income per capita leads to declining fertility; (3) declining fertility is insufficient to explain the secular decline on population growth over the last century; and (4) fertility changes are both causes and consequences of economic development. But the observed linearity of the last century cannot continue as fertility and mortality are bounded to be non-negative and cannot continue to fall indefinitely with forever rising income. We return to this below. (ii) A key assumption of the UN population projection is the convergence of all countries toward broadly the same (total) fertility rate. A main research topic over decades has been to establish 27
  • 28. whether and when such a convergence is taking place, what the key drivers are (morality reduction or also other and economic development’s, discussed above), how the convergence differs between groups of countries, and what characteristics it has. The demographic convergence investigations in recent years have profited and borrowed from a similar economic literature on economic growth convergence. The access to better and more diversified data across the world has helped to this end. Cutting through a rich discussion of the topic, here are the critical issues and recent results: First, the world was and is still separated into a low fertility regime and a high fertility regime. The twin peaks of fertility rates across countries have been shifting over time, the composition has changed, and the second peak of high fertility is reduced but not yet vanished. Figure 16 shows the changing shape between the period 1950-1955 and 2000-2005. In the first period the first peak comprised some 1/3 of the countries with low fertility and the second peak 2/3 of the countries with high fertility; in the second period size of the composition is broadly reversed.16 Figure 16: Cross-Country Distribution of Fertility Rates 1950-1955 vs. 2000-2005 Source: Strulik and Vollmer (2015) Second, when discussing convergence the literature on economic growth has developed two testing concepts called β- and σ-convergence (Barro and Sala-i-Martin 1992). These concepts can easily be adapted to analyze fertility transition: β-convergence applies if countries of initial high fertility experience a stronger decline than countries of initial low fertility; σ-convergence if the cross-country dispersion (measured by the standard deviation of fertility), for a group of countries declines over time. β-convergence implies a tendency for σ–convergence but is not sufficient. In turn, decreasing dispersion does not necessarily entail β-convergence. Relatedly, the concept of club convergence with regard to economic growth can also be applied to fertility developments. 16 The data in the graph is based on a methodology which is invariant to strictly monotonic transformation thus robust against arbitrary presentation choices (See Holzmann et al. 2007) 28
  • 29. Using the idea of different regimes (clubs) and applying it to fertility transition Strulik and Vollmer (2015) were able to establish statistically that from 1950 to 2005 there exist two distinct fertility distributions: a high-fertility regime and a low-fertility regime. Here are their specific main results:  Within both regimes fertility is falling over time starting from a much higher initial level in the high fertility regime  They observe σ–convergence across the world and within the low fertility regime but not in the high fertility regime  They observe β-convergence in the low fertility regime but not in the high fertility regime  The high fertility regime is not a convergence club and, in consequence, countries in this regime cannot be conceptualized as belonging to a “high fertility” trap.  The heterogeneity in the high fertility regime and the experience with fertility decline of other countries that moved to the low fertility regime suggests in the past suggest country specific transitions that cannot be forecasted. (iii) A critical question for countries in the low fertility regime is about the final level of convergence and the likely reversal towards higher levels once lower levels are reached. Demographers have for a long time argued for an innate tendency for fertility to move toward replacement. While some temporary corrections have been observed in some countries, they are mostly due to differences in fertility rates of newly arrived migrants and an observed tendency to downward adjust fertility after some residency. The papers presented in this section do not offer any hope for reversal and return toward replacement rate (or even its neighborhood). The estimates by Strulik and Vollmer (2015) allow an assessment via the β-convergence and predicted equilibrium. It suggests that for the low fertility regime that the transition is still ongoing at unchanged speed, with a predicted equilibrium level of 1.12. Such a fertility level is only slightly more than half of the replacement level and such rates and below already experience in some parts of the world such as Shanghai. The estimates by Herzer et al. 2012 using the same 119 countries shorter data base as well as a 20 country longer data base suggest that their linear model of fertility is during the observation periods not questioned. Hence further falling mortality (where progress is limited) and further increasing income (that is potentially unlimited) suggests a further and unlimited decrease in the fertility rate. As it is bounded from below at one moment the linear relationship will disappear but this does not seem to be tomorrow. b. The economic and other explanations of mortality/life expectancy development How mortality rates are changing over time, and in particular the increase observed in life expectancy, has been a topic of considerable academic and professional debate across the world over recent decades. The rise in the cost of providing for pensions, insurance and healthcare at older ages, determined by the rapid improvements in life expectancy, led life companies, pension schemes, individuals and governments to give more importance to how these costs will be met in the future. In response to the increasing role of longevity risk and the demand for more accurate projections of future mortality rates, a vast literature on mortality forecasting has been produced during the last decade. Mortality forecasting methods can be divided into four major categories: expectation methods, extrapolative methods, explanatory methods and process-based methods.17 The expectation method is based on expert opinions. For instance, expert judgement is used to specify a given forecast or scenario for a mortality/longevity measure (e.g. life expectancy, mortality rates, age-specific mortality reduction factors, target life table), often accompanied by alternative 17 For an extensive literature review on the methods used for modelling and forecasting mortality see, for instance, Booth and Tickle (2008). 29
  • 30. high and low scenarios and a specified path.18 The main advantage of expert opinion methods is the possibility to incorporate (qualitative and quantitative) demographic, epidemiological and other relevant knowledge about future longevity prospects. The main drawback refers to its subjectivity and potential for (upward/downward) bias. Traditional extrapolative methods assume that future trends (e.g., in life expectancy) will essentially be a continuation of the past, i.e., they rely on the basic notion that the conditions which led to changing mortality rates in the past will continue to have a similar impact in the future. Advances in medicine or the emergence of new diseases that have a significantly different impact than those in the past could undermine the validity of the results of an extrapolative projection. In general, these models focus on the long term observed mortality patterns, and extract some latent factors from historical data, summarizing trends in mortality rates along a period or cohort dimension. Single and multifactor time series methods are commonly used in extrapolative forecasting, since they have the advantage of being stochastic and enable the calculation of the probabilistic prediction interval for the forecast value. The Lee and Carter (1992) model provided the seminal approach to mortality modelling using a principal components analysis of mortality data with one common factor. Subsequently, a number of innovations have been developed, including modelling the cohort effect (Renshaw & Haberman, 2006), adding a second period effect (Cairns et al., 2006), using a state space framework (Pedroza, 2006), using functional principal components analysis (Hyndman and Ullah, 2007), using Bayesian methods to smooth over time, age and country (Girosi and King, 2008) and adding additional factors for varying mortality improvement rates across ages (Plat, 2009). Most of the models used in demographic and actuarial practice lie in this category. Explanatory methods make use of expert medical knowledge and information on economic, behavioural and environmental changes (e.g., changes in lifetime smoking patterns) over time and try to explain and forecast mortality based on structural or causal epidemiological models of a set of causes of death involving disease processes and known risk factors. This type of model requires not only a determination of appropriate explanatory variables, but also their prediction, which might not be any simpler than predicting mortality directly. Although the explanatory approach to forecasting mortality is still in its infancy, in that the relationships between risk factors and mortality are still imperfectly understood, making their use in forecasting difficulty, they are a valuable instrument in simulating the effect on morbidity and mortality of policy changes (e.g., health policies) affecting the risk factors. In some cases, an explanatory model is used in conjunction with expert opinion methods, for instance, in the specification of future scenarios for the medical breakthroughs in the treatment of a given disease. Process‐based methods focus on the factors that determine deaths and attempt to model mortality rates from a bio‐medical perspective. This class includes the cause‐of‐death‐type of models. The main difficulty with these models is that they generally assume independence among the causes of death, while in reality the different causes can be interrelated. In practice, the unreliability of cause- of-death reporting at older ages where most deaths occur, and the fact that cause-reduction may have minimal effect on overall mortality means that limited value can generally be gained from decomposition by cause of death. There are many possible explanations for recent declines in mortality rates and life expectancy increases. Literature typically specifies future mortality improvement assumptions against a number of dimensions: gender, age, period, cohort. A large number of factors can in theory influence the rate of mortality improvement, many of those, however, are not independent of each other. Literature generally classifies changes into technological, medical, environmental and societal categories. Some 18 Examples of the use of this methodology in the actuarial context and official statistical offices can be found, for instance, in Continuous Mortality Investigation Bureau (1990, 1999), Wong-Fupuy & Haberman (2004) and Bravo (2008). 30
  • 31. of the crucial factors that have influenced mortality improvements over the past century are the access to primary medical care for the general population, the discovery and general availability of antibiotics and immunizations, the access to clean water supply and sanitation, and the rapid rate of growth in the general standard of living. Using mortality as a proxy of health conditions is a common approach in trying to understanding the determinants of mortality. For instance, Auster et al. (1969) used the following health production model: i i i i i i im c Z X HC E uα β γ δ= + + + + + (1) where im are logged (standardised) mortality rates, iZ socio-economic status (income, education), iX lifestyle inputs (alcohol, tobacco), iHC are healthcare inputs (drugs, doctors, hospital capital stock), iE captures environmental variables (urbanization, industrialization) and iu is a random term. The increase in per-capita income allows people to spend more not only on health (doctors, medicine, hospital care) but also on non-health inputs that benefit health (e.g., better housing, more nutritious food, better clothing, gym membership).19 Crucial to future life expectancy developments are the choices that individuals make in relation to their health. Lifestyle factors such as smoking (Leon, 2011), obesity and nutrition (Cutler et al., 2009), amount and type of physical activity and drugs (including alcohol) consumption (Miller and Frech, 2000) are all recognised as significant risk factors. The role of advances in medical technology is critical in understanding the secular trends in mortality. Much of the decline in adult mortality in the second half of the twentieth century has been attributed to cardiovascular disease treatment (new drugs, new surgical procedures and specialised equipment). Factors that may influence future mortality improvements include the development and application of new diagnostic, surgical, and life‐sustaining techniques, the rate of future increases in health spending and the efficiency of that spending relative to mortality improvement. Other factors considered are environmental air pollution, pharmaceutical expenditure (Miller and Frech, 2000) and crime (Thornton et al., 2002), the incidence of violence and suicide, the isolation and treatment of causes of disease (e.g., genetic breakthroughs), the emergence of new forms of disease and the evolution of existing ones, the extent to which people assume responsibility for their own health, education regarding health, and changes in our perception of the value of life. In recent years several OECD countries have taken steps to increase the retirement age in order to address the sustainability problems of pension systems. Usually, workers and their representatives strongly oppose such reforms, claiming that workers who spent their whole life working in physically demanding jobs should be allowed to retire early to avoid emerging health problems. If we all agree that leaving a pernicious work environment contributes to improve health, the overall consequences of early retirement on health could go in the opposite direction. In fact, retirement is associated with less cognitive and physical activity as well as with changes in daily routines and lifestyles that are potentially associated with unhealthy behaviour. For some countries, there is empirical evidence that shows that a reduction in the retirement age causes a significant increase in the risk of premature death (e.g, Kuhn et al., 2010). These results mean that early retirement does not only adversely affect government budgets but might also unintentionally increasing individuals’ mortality risk. This conclusion has a major implication for pension reforms since labour-market policies aiming to keep older individuals at work not only contribute to the sustainability of pension systems but also raise individuals’ welfare by prolonging their lives. 19 For a recent investigation on the relation between trends in mortality decrease and economic growth see Niu and Melenbergb (2014). 31
  • 32. c. The economic and other explanations of migration development The investigation of migration flows to and from a country is quite likely the area where most of the economic and non-economic research has taken place and this over many decades or even two centuries (see Chiswick and Miller 2015). More recently and with the advent of re-increased migration flows and new and better data the migration literature has blossomed supporting some older conjectures and introducing a number of new spins. The traditional main questions on the determinants of migration between countries – who migrates and why, and the impact within receiving and sending countries are still in the forefront of analyses supplemented by more recently emerging issues such as size and role of remittances and portability of social benefits across international borders. As of 2013, there are estimated some 232 million individuals living outside their home country, amounting to over 3.1 percent of world population with rising tendency.20 From 1990 to 2013 the number of international migrants increased by 77 million or 50 percent (UN 2013). Most of this international migration happens in the South-South and South-North Corridor leaving behind the North-North corridor movements in recent decades; the North-South corridor has been stagnant in absolute numbers (See Figure 17).21 Figure 17: Numbers of international migrants by origin and destination, 1990-2013 (millions) Source: United Nations, Department of Economic and Social Affairs (2013). Trends in International Migrant Stock: The 2013 Revision-Migrants by Destination and Origin (United Nations database, POP/DB/MIG/Stock/Rev.2013/Origin). For European countries it is the South-North and the North-North corridors that have the greatest importance. The North-North corridor includes the EU-internal/European Economic Area migration that has gained importance with the full mobility from the member countries of Central and Eastern Europe. Most future net migration can be expected from the South-North corridor in view of the economic, demographic and other differences in developments. Already nowadays is the change in the demographic structure of the EU dominated by net-migration flows and thus dwarfing or compensating the low or negative natural demographic balances of birth and death (see Ayuso and Holzmann 2014a, and Figure 18). Figure 18. Population Change by Component, EU 27, 1961-2009 (in 000’) 20 This number is estimated on foreign born or else foreign citizens. It does typically not include refugees or which it is assumed that they will return to the home country at a moment of time. 21 The internal migration in large countries is quite likely of much larger in absolute numbers. Alone in China is the number of migrant workers living outside their local residency permits estimated at some 250 million. 32
  • 33. Source: Eurostat 2011: Figure 1. This subsection will briefly (i) explore the conjectured economic and non-economic determinants of (bi-lateral) migration flows; (ii) highlight the results of empirical studies from OECD-type economies; and (iii) outline how these results can be used to project future net-migration flows in the world and in particular for EU countries. (i) The economic and non-economic determinants of (bi-lateral) migration flows. Migration is quite likely the oldest and most important risk management instrument in mankind’s history. While the main determinants may have somewhat shifted over time from escaping wars to getting jobs, the main driver for migration remains essentially unchanged and an application of the human capital model: migration is risk management instrument to protect and further one’s human capital and contribute one’s well-being.22 A traditional and still largely valid conceptualization of migration flows between countries is the push and pulls approach. There are forces that push individuals outside their country, and forces that drag them in, the most important ones being those of demographic, economic and political nature and reflect imbalances and thus arbitrage possibilities for migrants (see Holzmann and Muenz 2006):  Demographic imbalances between countries/regions with high and low (or even negative) demographic balance (i.e. births and deaths) are the first main determinant for migration flows. More refined, it is imbalance at the entry to the labor market that matters most as this is also the age when individuals have most to win and least to loose from going abroad. The mere quantitative side is, of course, closely linked with unemployment and with wages levels but is a determinant of its own. Fertility in Europe is low and the population despite increasing longevity projected to decrease without migration. This is in contrast to the MNA and SSA region where fertility will remain well above replacement rate. This leads to projected population gap by 2060 of 100 million in the EU and a surplus of 150 million in MNA and 1.500 million in SSA.  Economic imbalances are another main migration determinant and include the access to a good job, the wage level it pays, etc, all of which are closely linked to the GDP per capita. Economic indicators clearly show two things: the large gap between Europe and neighboring world regions, but also considerable heterogeneity within these regions. For example, the maximum ratio of per capita income between the richest European and 22 For a human capital inspired economic approach to explain the determinants if international migration, see for example Bodvarrsson & Van den Berg (2013); for a development science inspired approach that stresses capabilities and aspirations of migrants, see de Haas (2011) and the related project International Migration Institute (university of Oxford); for the risk management approach, see Holzmann & Jorgensen (2001). 33

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