APPSIM - Cohort component population projections to validate and align the dynamic microsimulation model APPSIM

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1 National Centre for Social and Economic Modelling University of Canberra APPSIM - Cohort component population projections to validate and align the dynamic microsimulation model APPSIM Sophie Pennec Working Paper 12 April 2009

2 About NATSEM The National Centre for Social and Economic Modelling was established on 1 January 1993 and supports its activities through research grants, commissioned research and longer term contracts for model maintenance and development with the federal departments of Families, Housing, Community Services and Indigenous Affairs; Education, Employment and Workplace Relations; Treasury; and Innovation, Industry, Science and Research. NATSEM aims to be a key contributor to social and economic policy debate and analysis by developing models of the highest quality, undertaking independent and impartial research, and supplying valued consultancy services. Policy changes often have to be made without sufficient information about either the current environment or the consequences of change. NATSEM specialises in analysing data and producing models so that decision makers have the best possible quantitative information on which to base their decisions. NATSEM has an international reputation as a centre of ecellence for analysing microdata and constructing microsimulation models. Such data and models commence with the records of real (but unidentifiable) Australians. Analysis typically begins by looking at either the characteristics or the impact of a policy change on an individual household, building up to the bigger picture by looking at many individual cases through the use of large datasets. It must be emphasised that NATSEM does not have views on policy. All opinions are the authors own and are not necessarily shared by NATSEM. Director: Ann Harding

3 ISSN ISBN NATSEM, University of Canberra 2009 National Centre for Social and Economic Modelling University of Canberra ACT 2601 Australia 170 Haydon Drive Bruce ACT 2617 Phone Fa natsem@natsem.canberra.edu.au Website

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5 microsimulation model APPSIM v Abstract This paper has been prepared as one in a series of papers associated with the development of the Australian Population and Policy Simulation Model (APPSIM). Dynamic microsimulation models, like any kind of model, need to be validated against some targets. The level of validation is highly dependent upon the use of the model. When population is concerned, the main validation figures used are official population projections but these projections are not always consistent with the approach in the model and the results of the microsimulation model are not directly comparable. This document describes the cohort component method used by the Australian Bureau of Statistics to produce their 2004 population projections and presents the transformations needed for the data to be comparable with the microsimulation output. We briefly discuss also how this approach can be used for a more dynamic alignment process that might be implemented in the future in the Australian dynamic microsimulation model APPSIM. Author note Dr Sophie Pennec is a researcher at the Institut national d études démographiques (INED the National Institute for Demographic Research) in France and is involved in the developing of the demographic modules within APPSIM through a series of visiting fellowships to NATSEM. Acknowledgments The author would like to acknowledge and thanks the French Embassy in Australia and the Academy of Social Sciences in Australia for their funding support through a series of FEAST grants. The APPSIM model is supported by the Australian Research Council (under grant LP ), and by the 13 research partners to the grant: Treasury; Broadband, Communications and the Digital Economy; Education, Employment and Workplace Relations; Health and Ageing; Innovation, Industry,

6 microsimulation model APPSIM vi Science and Research; Finance and Deregulation; Families, Housing, Community Services and Indigenous Affairs; Resources, Energy and Tourism; Immigration and Citizenship; Prime Minister and Cabinet; the Productivity Commission; Centrelink; and the Australian Bureau of Statistics. The author would like to thank the Australian Bureau of Statistics and, in particular, Michael Roden, for providing the data and assumptions about ABS population projections and for answering questions regarding some methodology issues. She would also like to thank Laurent Toulemon from INED; Heather Booth from ADSRI; and Bruce Bacon, Ann Harding and Linc Thurecht from NATSEM for their comments on an earlier draft and discussions about the contents of this paper. Special thanks are also due to Ann Harding for her patience in editing this document. Any errors in the processing of the data are of the author s responsibility. General caveat NATSEM research findings are generally based on estimated characteristics of the population. Such estimates are usually derived from the application of microsimulation modelling techniques to microdata based on sample surveys. These estimates may be different from the actual characteristics of the population because of sampling and nonsampling errors in the microdata and because of the assumptions underlying the modelling techniques. The microdata do not contain any information that enables identification of the individuals or families to which they refer. Abbreviations ABS ADSRI APPSIM CCM DMSM FEAST INED MSM NOM TFR Australian Bureau of Statistics Australian Demographic and Social Research Institute Australian Population and Policy Simulation Model Cohort component model Dynamic microsimulation model Forum for European-Australian Science and Technology Cooperation Institut national d études démographiques (National Institute for Demographic Research) Microsimulation model Net overseas migration Total fertility rate

7 microsimulation model APPSIM vii Contents 1 Cohort component method of population projection Survival of people already in the population at the beginning of the projection period Determination of migrants Survival of new migrants Fertility 1.5 Survival of the newborn Deaths 15 2 Brief overview of ABS population assumptions for the 2004 revision Mortality Fertility Migration Overseas arrivals Overseas departures 18 3 APPSIM and its alignment to macro data 18 4 Cohort component method for microsimulation alignment From age period rates to age-period cohort rates Mortality and deaths Fertility and births Migration Implementation of the age-period-cohort component model Results and comparison with the ABS cohort component model 27

8 microsimulation model APPSIM 8 This paper has been prepared as one of a series associated with the development of the Australian Population and Policy Simulation Model (APPSIM). The APPSIM dynamic population microsimulation model is being developed as part of an Australian Research Council (ARC) Linkage grant (LP ), and will be used by Commonwealth government policy makers and other analysts to assess the social and fiscal policy implications of Australia s ageing population. Rather than simply creating aggregate economic and social projections (as nondynamic microsimulation models do), APPSIM will project the lives of approimately one percent of the Australian population, including such life events as birth, education, marriage, employment, earnings, taation, wealth generation, housing, migration, disability, use of health care and aged care services, retirement and death. Because APPSIM will model individuals, it can be used to project the distributional effects of future policy, as well as aggregate effects (NATSEM 2006 cited in Pennec and Keegan, 2007). One of the issues that has received much attention during the past decade is the need to align summed micro estimates to benchmark data sources that are regarded as reliable within a country such as official population projections (Anderson 2001). This topic in the contet of APPSIM is more fully developed in another paper (Bacon and Pennec 2007). One proposal where demographics are concerned is to link a cohort component model to the microsimulation model. Our idea is not only to align the microsimulation results to the official results but to built a cohort component model that take into account certain specificities of microsimulation like (1) the events are determined according to age at the beginning of the simulation step that could not be equal to age at the event; (2) rates are not applied to the mean population but to the population as it is when this event is calculated. This approach leads to a real consistency of the macro and micro levels. It gives better consistency for those who want to use some other scenario; for eample, even if the user wants to increase fertility only, this affects the number of deaths, so this method recalculates all events involved. Once the population macro model is developed, as long as rates by age and se are available for a variable, it is quite easy to derive benchmarks that are consistent with the population to be used for aligning the microsimulation model.

9 microsimulation model APPSIM 9 This paper aims at presenting how to adjust ABS population projections to suit the required alignment to macro data of dynamic microsimulation models such as APPSIM. From these population projections, any other simple projections based on age-se-specific prevalence rates can be easily derived, for eample, education or labour force participation. One of the models is the traditional cohort component method, the one used by ABS. The second follows some specificities of the approach retained by microsimulation such as (a) simulating each event one after the other and on the population as it is after the previous event (not a mean population), or (b) using a different definition of age. The results of these models are useful to check, align and benchmark a dynamic microsimulation model that needs to be aligned to a specific set of aggregates, for eample, an ABS population projection. The first section of this note introduces the cohort component method used by ABS to produce their population projections. In the second section, the assumptions chosen by ABS for their 2004 revision of population projections are described. The third section gives some insights into the use of this macro demographic model for aligning/testing a microsimulation model such as APPSIM. The final section shows how to create a macro demographic/cohort component model that reflects the microsimulation approach. 1 Cohort component method of population projection The cohort component method is the most commonly used method for simple population projections. For more comple projections, more comple and datahungry methods have to be applied, such as multi-state models or microsimulation. The cohort-component method begins with a base population, usually categorised by age and se. This base population evolves through the years by applying assumptions regarding mortality, fertility and migration. This procedure gives, for every year of the projection, a distribution of the population by age and se. This method can be applied to any geographical level. It is applied at the sub-national level with constraints, such as that the sum of projected sub-national levels must be equal to the projected total for the overall country/region.

10 microsimulation model APPSIM 10 The method is quite simple to implement. The most important elements of this eercise are the assumptions of changes of each component - mortality, fertility and migration. The implementation of the method follows si steps: 1. Survival of people already in the population at the beginning of the projection period 2. Determination of migrants 3. Survival of new migrants 4. Fertility 5. Survival of the newborn 6. Number of deaths derived from previous calculations. 1.1 Survival of people already in the population at the beginning of the projection period The number of surviving persons is determined by applying probabilities of survival by age and se to the base population (parallelogram with vertical base), that is the population distributed by age and se at the beginning of the projection period. In Australia, the projection period is the financial year and begins on 1 July.

11 microsimulation model APPSIM 11 Figure 1: Leis diagram of survival P +1 (t+1) +1 P (t) 1/1 1/7 1/1 1/7 1/1 1/7 t t+1 P + 1( t + 1) = P ( t)* S with t + 1) P ( t) : population age at the date1/7/t S t + 1) = survival ratio (or probability to survive) at age during the period 1/7/t and 1/7/t Determination of migrants We assume that the net overseas migration in the assumption is the number of net migrants from 1/7/t to 30/6/t+1. This number represents migrants by age at arrival or departure (square of the leis diagram - Figure 2)). What we need for projection purposes is the number of migrants that were aged at the beginning of the projection period (parallelogram with vertical base composed by triangles A+B), rather than those age at their arrival/departure (square composed by triangles A+C). From this graph we can see that some migrants arrive while they are still age (triangle A) and some arrive after their birthday and therefore are of age +1 (triangle B). Overseas migrants are assumed to arrive or leave, on average, half way through the projection year so we can assume that half of the migrants aged at their arrival/departure were of age at the beginning of the projection period (half of B+C) and half of those age +1 (half of A+D) at their arrival/departure were also of age at the beginning of the projection period.

12 microsimulation model APPSIM 12 Figure 2: Leis diagram for migrants D +1 B A 1/1 1/7 1/1 1/7 1/1 1/7 t t+1 C OM with OM OM ' OM ' t + 1) = 0.5*[ OM ' t + 1) t + 1) + 1 t + 1) ( t) + OM '( + 1 ( t)] : overseas net migrants during t and t : overseas net migrants during t and t : overseas net migrants during t and t + 1of age at beginning of projection period (A + B) + 1of age during t and t + 1(A + C) + 1of age + 1during t and t + 1(B + D) 1.3 Survival of new migrants Like those already in the population, migrants face a statistical probability of death. Migrants are assumed to stay half the projection year within the population (so they are facing half the probability of dying of those staying during all the projection year). Survival of migrants is done by applying to migrants who were age at the beginning of the projection period, the probability of survival of those age., as follows From my understanding, ABS applies the survival rate of age to migrants of age and survival rate +1 to those aged +1 while I apply the survival rate of age to both. The ABS methodology differs in that I assume that the survival rate applies to all persons age at the beginning of the projection period (parallelogram A+B). As mortality level is low and linear, both methods give very similar results.

13 microsimulation model APPSIM 13 OM with OM ( t + 1) = [[ OM ' t + 1) + OM ' t + 1)]* S t + 1)]/ 2 t + 1) : surviving net migrants of age at the end of the projection period OM ' t + 1) : net migrants of age at their arrival/departure + 1 S t + 1) = survival ratio (or probability to survive) for the period t and t + 1 of persons of age at the beginning of the projection period 1.4 Fertility Once the mortality and migration are done, the projection of fertility is performed by applying the calendar fertility rates to the women of reproductive age (15-49 years old). Then, to obtain the number of births, it is necessary to derive a financial year average from the calendar year rates. This is undertaken as follows: (1) the number of births for year t is determined by applying the fertility rate of calendar year t to the mean number of women of reproductive age in t (assumed to be the population at 1 July, which is also the population at the beginning of the projection period). (2) the number of births for year t+1 is determined by applying the fertility rate of calendar year t+1 to the mean number of women of reproductive age in t+1 (assumed to be the population at 1 July t+1, which is also the population at the end of projection period). (3) a mean of these two figures is calculated to determine the number of births during the projection period, that is, 1/7/t et 1/7/t+1. B t + 1) W ( t) 49 B t + 1) = [ ( W ( t) * ASFR t + 1) + ( W ( t + 1) * ASFR ( t + 1, t + 2)]/ 2 15 with : births of : population of women aged occuring during the period t and t + 1 women age during the period t and t + 1 ASFR t + 1) = Age - specific fertility rate at age during the period t and t + 1

14 microsimulation model APPSIM 14 Figure 3: Leis diagram for projection of fertility +1 W (t) W (t+1) 1/1 1/7 1/1 1/7 1/1 1/7 t t Survival of the newborn Newborns face a probability of death from their birth to the end of the projection year (that is, the following 30 June). To determine those who will survive from birth to the net projection period, a survival rate is applied to all newborns. For the migrants of age 0, we assume that half the migrants aged 0 belong to the triangle C and therefore face the survival rate from birth to net projection period 2. 2 This is potentially the same concern as in Footnote 1. To be consistent, I apply the survival rate from birth to net projection period both to births occurring during the projection period and to half the migrants aged 0. ABS applies the survival rate from birth to net projection to the births, but the survival rate at age 0 to all migrants arriving at age 0. Following a discussion with Laurent Toulemon (INED), it may be appropriate to do so if most migrants at age 0 are older than one month. Most of the over-mortality included in the survival ratio from birth to net projection period is the over-mortality within the first month after birth. If newborn migrants are older than one month, then applying the survival ratio at age 0 for all migrants aged 0, as ABS does, could be quite sensible.

15 microsimulation model APPSIM 15 Figure 4: Leis diagram for mortality of the newborn 1 P 0 (t) A C P 0 (t+1) 0 Births 1/1 1/7 1/1 1/7 1/1 1/7 t t+1 P ( t + 1) = [ B( t, t + 1) + 0.5* OM ]* S t + 1) 0 with P ( t + 1) 0 : population age 0 at the date1/7/t + 1 OM t + 1) : net overseas migrants aged 0 at arrival during period t and t S t + 1) = survival ratio (or probability to survive) from birth to net projection period b b 1.6 Deaths Deaths at age that is, the number of deaths of persons age at the time of death are derived from the previous calculations. For those aged over 1 year old, it is assumed that the deaths are linearly distributed during the projection period. Therefore the number of deaths at age is half the deaths of persons aged at the beginning of the projection period and half the deaths of persons aged -1 at the beginning of the projection period. For the first year of life it is not possible to assume the linear distribution of deaths during the projection period. D D D ' = 0.5[( P ( t) + OM t + 1)]* (1 S )) + ( P 1( t) + OM 1( t, t + 1)]* (1 S 1 0' 1' = 0.7 * B = 0.3* P ( t) * S 0 t + 1) * S 0 N + 0.3* P ( t) * S + 0.5* P ( t) * S ))]

16 microsimulation model APPSIM 16 2 Brief overview of ABS population assumptions for the 2004 revision This section gives a summary of the assumptions employed by ABS for their population projections. It is not the purpose of this paper to discuss these assumptions or the method used to produce the projections. For the overall set of projections, see ABS Mortality For the mortality component, assumptions are made about future levels of life epectancy at birth for males and females. Two assumptions have been made medium assumption: life epectancy at birth will reach 84.9 years for males and 88.0 years for females by and remain constant thereafter. Under this assumption life epectancy at birth will increase by 0.40 years per year for males and 0.30 years per year for females until , then by 0.30 years per year for males and 0.25 years per year for females until , after which mortality improvement will gradually decline until ; and high assumption: life epectancy at birth will reach 92.7 years for males and 95.1 years for females by and remain constant thereafter. Under this assumption male and female life epectancy at birth will increase by 0.40 years per year for males and 0.30 years per year for females until , then by 0.30 years per year for males and 0.25 years per year for females until For both assumptions, the change in age-se-specific death rates derived from mortality data is assumed to continue until Thereafter the age-specific death rates are scaled to conform to the assumed life epectancy at birth for future years.

17 microsimulation model APPSIM Fertility For the fertility component, assumptions are made about future total fertility rates (TFRs), age-specific fertility rates and the se ratio at birth. Three assumptions have been made about Australia's future TFR, from a value of 1.77 in 2004 (ABS, 2004)- high assumption: the TFR will increase to 1.9 births per woman by 2018, and remain constant thereafter; medium assumption: the TFR will decline to 1.7 births per woman by 2018, and remain constant thereafter; and low assumption: the TFR will decline to 1.5 births per woman by 2018, and remain constant thereafter. Under all three scenarios the trend towards older ages of mothers at birth of children is assumed to continue to 2018, and then remain constant. The se ratio at birth is assumed to be male births per 100 female births for all years. 2.3 Migration Three assumptions have been made about Australia's future levels of net overseas migration (NOM) - high assumption: annual NOM gain will increase to people per year by and remain constant thereafter; medium assumption: annual NOM gain will be constant at people per year throughout the projection period; low assumption: annual NOM gain will decline to people per year by and remain constant thereafter. A zero net overseas migration assumption has been included to facilitate analysis of the impact of overseas migration on Australia's future population. Two behavioural assumptions have also been made: (1) migrants arrive throughout the year so they spend on average half the year on Australian soil; (2) migrants have the same mortality and fertility behaviour as the overall Australian resident population.

18 microsimulation model APPSIM Overseas Arrivals The assumptions regarding overseas arrivals are - high assumption: increase from arrivals in 2005 to in 2008 and then remain constant; medium assumption : arrivals per year throughout the projection period; low assumption: from arrivals in 2005 to in 2008 and then remain constant Overseas Departures high assumption: from departures in 2005 to in 2008 and then remain constant; medium assumption : departures per year throughout the projection period; low assumption: departures in 2005 to in 2008 and then remain constant. 3 APPSIM and its alignment to macro data As already mentioned and described elsewhere (Bacon and Pennec 2007), a linkage between individual behaviour and macro aggregates was envisaged for APPSIM. As microsimulation techniques use a sample of the population and most of demographic events are determined by stochastic draw, the sum of individual behaviours does not always give eactly the aggregates produced by eternal sources such as cohort component models. Most microsimulation models align their results to official population projections by aligning against the number of deaths, births and migrants. A more sophisticated approach is to link the microsimulation model with a cohort component model that replicates the official projections (or any type of projections that users of the model wish to rely on). One idea for the macro model for APPSIM is that, instead of

19 microsimulation model APPSIM 19 benchmarking from different sources using different base populations (which can lead to distortion and bias), it should be possible to have a consistent macro projection. There are a range of reasons for supporting such a linkage instead of just introducing the results of projections as benchmarks - If we want to have an up-to-date model, it is important to run the model using the most recent data and rates. Having a cohort model gives this opportunity to rerun the projections with updated data. This is particularly relevant when population projections are issued only every 5 or 10 years (or if new data shows that the assumption chosen for one event is not the right one). For eample, if the fertility assumption is good but mortality decreases more quickly than foreseen, it is possible to rerun the macro model with these updated assumptions. This allows the microsimulation model to align with more pertinent benchmarks. It helps to have consistent benchmarks. For eample, if for any reason the labour force participation projections used as benchmarks are calculated on a different, or not updated, population structure, or are not available, having such a macro model is very helpful. It can give estimates that are consistent with our population. We can think of population projections being carried out more often than education ones. If we have the rates that give the probabilities by age and se and some other simple variables, we can estimate an aggregate to align with. For eample, let us assume that the latest education projections issued in 2006 are run against the 2004 population projections. In 2007 a new set of population projections are issued. To be as consistent as possible, we have to keep the 2004 population-based education projections for the benchmark. But it means a loss of accuracy because the distribution of population is distorted compared to the current population. This is particularly annoying if a noticeable change has been observed, for eample, an increase in fertility. It means also that the model looks slightly old. On the other hand, if we use the new population, we apply the aggregates of education for 2007 that have been estimated against a different population structure and therefore the benchmarks are not the correct ones for the new population. Having a macro model such as the one described here can avoid all these drawbacks and help the microsimulation model to be aligned to the most up-to-date and consistent data. It is easier for the user of the model to alter the projections according to new assumptions. A macro level model uses more user-friendly indicators than a microsimulation model. So if the changes in the assumptions are not

20 microsimulation model APPSIM 20 markedly different, they can be changed at the macro level and the changes will be done during the alignment to new data. From a theoretical point of view, such a model is very helpful to understand the errors introduced by the order of events chosen in a microsimulation model. Microsimulation models (ecept those using continuous time) consider events one after the other - and therefore make some combinations of events impossible. For eample, if we apply fertility to the surviving women, (that is, fertility after mortality), we miss births by women who died soon after giving birth. If we run fertility first, we may increase the number of orphans, as we apply full fertility to a group of women that stayed only a part of the year in our population. In a macro model, fertility is applied to the mean of the population (that is, the average of the population before and after mortality) to take into account the two events (fertility and mortality) occurring during the same period of time. These are regarded as competing events. In Australia, as in many countries, rates used in the cohort component model are age-period rates for fertility and migration and age-cohort-period rates for mortality. The logic of microsimulation models is age-cohort-period rates. It is possible to transform age-period rates into age-cohort-period rates and therefore to have a macro model that can reconstitute the way the microsimulation model works, which will provide a very consistent binomial between both macro and micro level. The model can be used to display the discrepancies between official cohort component models that use mean population to estimate fertility and the cohort component models using only age cohort rates that use population after the previous event. For eample, cohort component models estimate fertility by averaging the rates at year t to the population at the beginning of the projection year t and the rates at year t+1 to the population at the end of the projection. The age cohort model applies the mean of the rate in t and t+1 to the surviving population (that is, the population at the end of projection period).

21 microsimulation model APPSIM 21 4 Cohort component method for microsimulation alignment This section gives the differences induced in the cohort component method when applying some of the specificities of microsimulation. The two main specificities are: (1) use age at the beginning of the projection step and not age at the event for all events; (2) consider each event as independent that is, each event is simulated/calculated one after the other one and based on the population obtained after the previous calculation. For eample, fertility is based on the population alive before the event that is, minus all those who will die during the projection period; while with the more traditional method, fertility is based on an average of the population. As mortality is quite low at reproductive ages, this methodological difference will not lead to many discrepancies. 4.1 From age-period rates to age-period cohort rates Mortality and deaths The mortality rates or survival ratios that are the complement to one of mortality rates do not need any transformation; they are already age-period cohort mortality rates. While with age-period component projection, a transformation is needed to determine the number of deaths by age, here the number of death of those aged at the beginning of the period is the one given by the age-period cohort mortality rates Fertility and births ABS uses for its fertility rates the probabilities of giving birth at age X. For our projection we need the probabilities of women age X at the beginning of the projection period. How to reconcile rates using age at beginning of period and rates using age at the event? First of all, we will consider that age at the beginning of projection period is lower by half a year compared to age at the event. A simple assumption for the calculation of rate at age at the beginning of the period from those at age at event is to consider that the rates follow a linear trend. In that case, the age-period cohort fertility rate for persons aged at the beginning of

22 microsimulation model APPSIM 22 the projection period is determined by the mean of the age-specific fertility rate of age at year t and age-specific rate of age +1 at year t+1. [ ASFR' t + 1) + ASFR+ 1' t + 1)] ASFR t + 1) = 2 with ASFR t + 1) : age - specific cohort fertility rate at age during the period t and t + 1 ASFR t + 1) = age - specific period fertility rate at age during the period t and t + 1 ' Figure 5: Leis diagram for age-specific fertility rates As fertility rates do not follow a linear trend, Gérard Calot (1984) proposed a transformation that better follows the trend of the age-specific fertility rate curve ASFR t + 1) = [ ASFR' ( t + 1, t + 2) + ASFR 1' t + 1)] [ ASFR 2' t + 1) + ASFR+ 1' t + 1)] with ASFR t + 1) : ' age - specific cohort fertility rate at age during the period t and t ASFR t + 1) = age - specific period fertility rate at age during the period t and t Births are determined by applying the rate by age at the beginning of the projection period to women of that age at the beginning of the period.

23 microsimulation model APPSIM 23 B t + 1) = 49 = 15 W ( t) * ASFR t + 1) Figure 6 gives the ABS age-specific period rates and the age-specific cohort rates determined according to the above-mentioned method. As epected, both sets of rates follows a very similar shape but the level of the rates are different and rates at beginning of the period at age sit between the rate at age of event -1 and. Using this approach, the total number of births obtained with the microsimulation is very close to the number obtained with the cohort component method. Figure 6: Differences in fertility between age at event and age at beginning of period Fertility 2004 Fertility MSM Note: mark is at age for the curve fertility 2004 and at age -1/2 for the curve fertility MSM With this second method, the number of births obtained is closer to the one obtained with the traditional approach Migration We want to obtain the number of migrants (immigrants and emigrants are transformed in the same way) by age at 1 July, using the number of migrants by age

24 microsimulation model APPSIM 24 during the period. Let us assume that migrations follow a linear pattern, that is, migrants arrive or leave throughout the year without any seasonality. This allow us to consider that half of migrants aged at migration would have been age at the beginning of the projection period (year). The other half of migrants at age had their birthday between the beginning of the projection period and their migration to Australia. They would have been aged -1 at the beginning of the projection period. So, of the migrants belonging to the cohort aged at the beginning of projection year, half are migrants aged at migration and half are migrants aged +1 at migration. Figure 7: Comparison of net migrations in the ABS cohort component model and in the microsimulation approach net migrations net migrations MSM Note: Mark is at age for the curve migrations 2004 and at age -1/2 for the migrations in the MSM Here again, the number of net migrations both with the ABS cohort component method and the approach used for the microsimulation gives similar results both in the distribution of migrations (shape of the curve) and in the total number of migrants.

25 microsimulation model APPSIM Implementation of the age-period cohort component model Cohort component models determine the number of births by applying the fertility rate to the mean population at t and t+1, in order to take into account the fact that some women who will die during the period may have had a baby before dying. In the same way migrants fertility and mortality rates are lower, to take into account that they stayed within the population for only a part of the projection period (usually the assumption is made that they stay half a year on average). The microsimulation approach is different in two ways at least. One is the fact that one event is determined or estimated after the other the population facing the new event is the one resulting from the previous population. The second is known as the competing event problem. Let us illustrate these two differences with the eample of mortality and fertility. (1) If we consider mortality before fertility, we apply survival ratios to the initial population and then to survivors only do we apply fertility rates. This implies that those who die during the projection year cannot give birth. This in turn means that the number of births is lower than if calculated with the traditional cohort component method. The difference is equal to the number of deaths of women multiplied by half the fertility rate (by age) - half the fertility rate because we assume that the dead person will have lived on average half the year before dying and therefore faced the fertility rate for half a year. (2) If we consider fertility before mortality, we apply fertility to the initial population and then we apply mortality rates. This implies that those who die during the projection year are capable of giving birth, that is, they have the same fertility rate as those who do not die in the period. This means that the number of births is higher than with the traditional cohort component method. The difference relates to the number of births attributed to women who died during the period. Women who die will have lived on average half the year (assuming a linear distribution of deaths during the period). Therefore we give them the same probability of giving birth as if they were living the entire year and not half the year. The order of the variables is not neutral as, if we model first mortality, a person statistically selected to die cannot emigrate nor have a child later on. The order of the modules must thus reflect a logical interaction pattern and the probabilities of each event must be conditional probabilities taking into account the implications of the order.

26 microsimulation model APPSIM 26 In microsimulation models, each event is modelled in a more or less independent way. While projections run using a cohort component method use the average population and not the population at the beginning of the projection step for events such as fertility (so as to be able to take into account the fact that more than one event can arise during the year), in microsimulation each event arises independently. If death is the first event then, for eample, any women selected to die will not be able to give birth. We impose a causality in the model that has to be taken into account in the estimate at least when the probability that both events arise during the same period of time is not negligible. The order proposed here is first, immigration, then mortality, fertility and emigration. With this order, we can take into account - Immigrants are alive when they arrive but can die or have children as soon as they arrive on the Australian soil; Mortality before fertility: this assumption reduces the number of orphans at birth; but in a country like Australia it is fortunately quite a rare event to have the death of a woman in the year of the birth of her child. These two events are estimated independently that is, the risk of mortality is not dependant upon whether a person will have a baby. Therefore this is a less risky assumption in many respects, as estimating births after mortality will reduce orphanhood in the first year of life but the error will not be great and we assume this error to be better than the reverse. The other reason for using this order is that the data used to determine the fertility estimates are based on surviving women. Emigrants are alive at the moment of their departure but could have had a child just prior to emigration. This order presents a drawback related to the fertility and mortality of migrants. If we assume, like all projections, that immigrants and emigrants stay on average half the projection period in the country, then death and fertility rates of migrants are half those who stay the whole year in the country. While it is possible to have a variable distinguishing immigrants and applying half the rates to them, it is not possible to do the same for emigrants because we do not know who they are when fertility and mortality calculations are performed. This can lead to a small increase in mortality and fertility.

27 microsimulation model APPSIM 27 It is possible to avoid this problem by using the following method 3. Let us consider that half the immigrants will arrive at the beginning of the period and half of them will arrive at the end of the projection period. Those arriving at the beginning of the projection period will face the whole year of events such as death and births, while those arriving at the end of the period will not face any such events. We calculate in the same way for emigrants that is, we consider that half of them will leave the country at the beginning of the projection period and therefore will not face any other events in the country, while the other half of the emigrants will leave at the end of the period and will face the events during the whole year. This shortcut is possible with the assumption that they stay on average half the period; instead of all the immigrants and emigrants facing the events with half the probabilities because they stay half the year in the population, we will have half the immigrants and emigrants with the full rate. Implementation 1. Determining migrants; 2. Altering the population just after the beginning of the period by adding half the immigrants and removing half the emigrants; 3. Applying mortality rates; 4. Applying fertility rates to surviving women aged 15 to 49; and 5. Adding the second half of immigrants and removing the second half of emigrants Results and comparison with the ABS cohort component model The following table shows that the discrepancies between the results of the ABS population projection (with the traditional cohort component method) and the results using a cohort component method with some alterations as described to suit the microsimulation model. The differences between both approaches are minor. The differences are what was epected and mean that in a country like Australia the constraints of microsimulation do not significantly affect the results. In a country or 3 The author would like to thank Laurent Toulemon for this very pertinent suggestion.

28 microsimulation model APPSIM 28 population with a higher level of mortality at reproductive age or with a chaotic age structure, the method would give more discrepancies and techniques to take into account these competing effects should then be envisaged. Table 1: Results of simulation using cohort component model and the cohort component model that considers each event as independent Population CCM 20,323,721 21,4722,82 23,662,576 25,603,272 MSM-CCM 20,323,699 21,472,012 23,661,729 25,601,826 Difference (number) ,446 Births CCM 254, , , ,669 MSM-CCM 254, , , ,614 Difference (number) Deaths CCM 131, , , ,017 MSM-CCM 131, , , ,040 Difference (number)

29 microsimulation model APPSIM 29 Conclusion This paper presents how to use the rates used in the ABS cohort component population projections to run a cohort component model consistent with the microsimulation model approach The main difference lies in the definition of age at event as compared with age at the beginning of the projection period.. This shows that it is a valid approach to have a macro model that is consistent with the microsimulation approach and therefore the alignment can be done on consistent macro results. References ABS, 2004, Births, Australia, ABS 2006, Population projections Australia, 2004 to 2101, , reissue, 3222, 149 pp. Calot, G., 1984, La mesure des tau en démographie. Age en année revolu ou âge atteint dans l année, incidence du choi de la definition, application à la fécondité générale (France, ), Paris, INED and PUF, 322 pp, (Travau et documents, cahier 104). Henry, L. 1968, Projection de population, INED, 115 pp. Pennec, S. and Keegan, M. 2007, APPSIM - Modelling migration, NATSEM/Canberra, 26 pp. (Online Working Paper WP 5). Pennec, S. and Bacon, B. 2007, APPSIM - Modelling Mortality and Fertility, NATSEM/Canberra, 52 pp. (NATSEM Online Working Paper; WP 7). Bacon, B. and Pennec, S. 2007, Validation of micro-macro linkage in APPSIM, mimeo, 35 pp.