Simulating migration in the Pensim2 dynamic microsimulation model

With mortality and fertility, migration is one of the demographic processes that determine the population within a country. Fertility and especially mortality are relatively slow moving processes as they reflect long-term trends in society and in the health status of society. Migration, the flows of people into and out of a location, however changes relatively quickly in response to change in economic circumstances and in policy as witnessed by the recent entry of the new-entrant states to the EU. As a result this process can add significant uncertainty as to the size of the population and to population projections.

Given the long-term impacts of demographic change, they have potentially major impacts on long-term policy instruments such as pension’s policy. Modelling demographic characteristics such as migration therefore is important within analytical programmes for evaluating and designing pension’s policy reform such as dynamic microsimulation models. Migrants can be seen as a contributor to reducing the dependency ratio and improving the sustainability of the pensions system in OECD countries (See Stølen, amd Texmon, 2007). These immigrants, given the typical age profile may reduce the ratio of retirement to working age. However they themselves will build up future pension entitlements. In addition if one’s focus is on trying to capture the financial cost of the pension system, also depending upon the design of the pension system, people may accumulate pension entitlement while working in a country and then be eligible for receipt of pensions while living overseas. As most dynamic microsimulation models have a single country focus, these people with pension entitlement are typically not covered in nationally focused microsimulation models.

This paper focuses in particular at modelling migration in a dynamic microsimulation model whose focus is on both the distributional impact of pension policy in the home country and on the overall fiscal cost of public pensions. Specifically we focus on incorporating migration in the UK model based at the Department of Work and Pensions, Pensim2. The purpose of the paper is to describe and evaluate a methodology for undertaking this task.

The scope of Pensim2 is Great Britain (GB), simulating the main public and private pension instruments in Britain as well as the demographic, labour market and income processes that influence pension entitlement, membership, contribution and benefits as well as other income sources of pensioners.

Migration while important from the point of view of population coverage is of particular relevance for the UK pension system. This is the case for a number of reasons.

• Firstly the pension system in Northern Ireland (NI), part of the UK, but not part of Pensim2 is the same as that of the rest of the UK and financed by the Treasury but administered by the Northern Ireland Civil Service. Migrants from NI to GB carry with them, transferable rights to a UK pension and as do GB migrants to NI.

• Non-national (or at least non-members of the UK national insurance system) migrants may carry with them entitlement or partial entitlement to foreign pensions, but this is beyond the scope of this paper. However if they work in the UK, they may build up eligibility for UK entitlement and their tax and contribution payments help to finance the pension and social security system.

• Returning emigrants similarly may have held rights overseas which is not relevant for the scope of this model or rights from previous residence in the UK, which is relevant.

• Similarly emigrants who accrue rights in Britain may result in overseas obligations – however the size of the obligation depends upon the country of residence as non-reciprocal countries, countries without a bilateral social security agreement will not be eligible for increments due to indexation in their pensions.

In this paper we focus on the methodological aspects of modelling migration in a dynamic microsimulation model. Heavy use of calibration is used in this analysis. As a result aggregate results are trivial as the population is precisely adjusted by the calibrated number of immigrants and emigrants. We therefore do not undertake an empirical analysis of migration. Rather this paper focuses on the description and analysis of the methodology of modelling migration. What is more interesting empirically is the impact migration has on pensions including the impact of migration on the economic dependency ratio and its consequences for pension sustainability and the welfare of pensioners. This analysis is beyond the scope this paper and thus this analysis is deferred until a later paper.

In this paper, we shall firstly overview recent trends in UK migration. In Section 3, we shall review what other dynamic microsimulation models have done to model migration. Section 4 overviews the Pensim2 dynamic microsimulation model. Section 5 describes the data available for the UK as well as the methodology used for modelling migration.

Table 1 details recent trends in migration to the UK in relation to the origin and destination of immigrants and emigrants. In the early 1990’s the number of immigrants and emigrants was quite similar, with emigration exceeding immigration in 1992 and 1993. In the early to mid 1990’s both emigration and immigration declined or at least remained relatively static. In 1998, annual immigration increased by about 20%, while emigration did not exceed early 1990’s levels until 2000. These trends however have accelerated since this period, but with immigration accelerating at a more rapid pace. Between 1991 and 2006, emigration increased by over 60% while immigration increased by about 130%.

The composition of migration has also changed. About a third of immigrants to the UK in 1991 were British citizens, with about 15% from the EU and a quarter each from the commonwealth and other countries. While the return flow of British citizens has been relatively stable, the proportion of total immigration has declined to about 10%. Other than a period in the mid 1990’s, EU immigration remained stable until the entrance of the new member states of the EU in 2004, now accounting for about 45% of immigrants, although the in-flow from Eastern Europe was visible in the other countries since 1999. The in-flow from commonwealth countries also has more than doubled in the period. The rationale for migration has changed with only 39% of immigrants coming to the UK to work or study in 1991 compared with 68% in 2005, evidencing the economic rationale for migration and the potential volatility that may arise in different economic circumstances.

While emigration has increased, the pattern has not changed much with about 50% (but a declining proportion) of emigrants being British nationals. About 30% of emigrants are EU citizens. Overall there is a greater number of British nationals emigrating than immigrating with the gap reaching 126,000 in 2006. All other nationalities have positive net inflows, particularly in recent times for EU nationals. Most of the inflow and out-flow is concentrated in and around London, but there has been a slight trend since the mid 1990’s for greater dispersal across the country of immigrants.

In this section we review the methods used by existing dynamic microsimulation models, described in Table 2 drawing upon previous reviews of dynamic microsimulation models in O’Donoghue (2001), Spielauer (2002) and Pennec and Keegan (2007). There are a number of different possibilities in modelling migration. However because of the technicalities and/or focus on national populations, a number of models, especially dynamic cohort models such as LIFEMOD, HARDING and the LIAM cohort model but also dynamic population models such as SAGEMOD, INAHSIM (Inagaki, 2005) and Pensim2 (until now) did not include migration processes.

In order to maintain the correct population distribution, a model requires at a minimum net migration. This would adjust the population by the net change in migration (immigration minus emigration) each year. This is the method used by the CORSIM, DESTINIE and MOSART models Although requiring little extra external information, there are not that many computational gains from modelling migration in this way, as net migration can be positive or negative, thus requiring both immigration and emigration to be modelled. Also modelling net migration may bias the structure of the population as the number of foreign born may be too low as it will ignore the emigration. For example Pennec and Keegan (2007) identified that when modelling net migration, one may face a problem that while one may have information on immigrants and use this to model the population structure of net migrants, it may in fact be different to the population of emigrants.

Once a model contains decision to go down the route of modelling migration one needs to decide a number of issues

• the nationality;

• the unit of analysis;

• permanent residents;

• how to produce immigrants

Modelling the nationality of the individual is relevant for a number of reasons. Nationality may impact future labour market and demographic transitions, but also it may have an effect on pension membership as previous contributions may have been made previously. More precisely for the latter point it is national pension scheme membership that should be modelled. A number of models distinguish between national and nonnational migrants including DYNAMOD, LIAM, Lifepaths, NEDYMAS, Sverige and SESIM. SESIM and Lifepaths in addition model re-entry. SESIM uses data on overseas Swedish residents for this.

The unit of analysis relates to the decision making unit, which could vary from the household to the tax or benefit unit or the individual. In other words when migration is modelled do we move individuals by themselves or together with other individuals. We face a choice as to which unit will be modelled. Typically migration is modelled using the same unit of analysis as for other processes, typically the tax or benefit unit or household. This poses slight methodological issues as external control totals are typically only available at the individual level which is at a different level to the unit of analysis and so calibration routines need to be altered.

Some models such as Lifepaths exclude nonpermanent residents from their models. In the UK an increasing number of immigrants express a preference of staying for shorter periods with about half planning to stay 1–2 years. DYNAMOD distinguishes between different types of emigrants such as permanent (differentiated by skill level) and long-term migrants

Emigration tends to be modelled as a regression based upon characteristics such as age, sex, marital status nationality, residence and labour force status. While emigration is relatively easy to do as existing individuals are simulated to leave the model,¹ immigration requires the generation of new individuals, which creates the problem of how to maintain multi-dimensional characteristics of the population. A number of models such as Lifepaths and DESTINIE synthetically generate new individuals and assign individual characteristics, the main method used in dynamic microsimulation models is to clone individuals either from the existing population as in the case of DYNAMOD and DYNACAN or from specific immigrant pools such as LIAM and SVERIGE.

Pensim2 is a dynamic microsimulation model developed by the UK Department of Work and Pensions (See Drane, 2006). The model is a second generation model based upon a combination of administrative data (the LLMDB described below) and survey data (Family Resources Survey and British Household Panel Survey), combined using data fusion (See Redway, 2003). The coverage of the model is Great Britain, so the United Kingdom excluding Northern Ireland, whose pension system is managed by a different Ministry. Pudney (1992) describes the earlier Pensim model. The model is constructed using the GENESIS modelling framework, constructed in SAS, (See Edwards, 2004), which has been used to develop a suite of models within the DWP for benefit forecasting and labour market analysis.

Utilising the categorisation of O’Donoghue (2001), the model can be categorised as a

• Cross-sectional longitudinal model, projecting cross-section of the population forward in time

• Discrete time intervals, although containing episode data to be able to generate semi-continuous time episodes

• Closed model, where spouses are married within the sample. New children are imported into the model

• Aligned model, using extensive alignment of demographic and labour market characteristics

• Statistical, in that currently behaviour is not modelled endogenous to policy

The model contains detailed demographic, labour market and pension’s data. Tax-benefit policy is simulated via the DWP’s Policy Simulation Model (PSM). At present other income sources such as capital income and housing costs are modelled solely for pension age individuals. A key gap is in the maintenance of the actual GB population. The unit of analysis is the benefit unit. An evaluation of the processes contained with the model is described in Emmerson et al., (2004).

The model is fully operational, although subject to continuous updating and improvement and particularly used for pensions analysis. It formed the basis of the UK Pensions Commission Report (Turner et al., 2005) and the subsequent White Paper on Pensions.

Data and Methodology

In this section we consider how to model migration in the UK as part of Pensim2. The objective of the module is to

• Enable the model to reflect the population totals of the population projections of the Office for National Statistics

• Include sufficient information to be able to simulate the expenditure of the GB Pension model²

In making our modelling choices, we base our decision on the experience of other models internationally, highlighted above.

As there are few extra modelling components required to simulate immigration and emigration instead of net migration alone, unless one makes the assumption as the Norwegian MOSART model does that there is always positive inward net migration, we model these processes separately. This will help us to avoid producing biased population estimates due to the different characteristics of emigrants (mainly UK nationals) and immigrants (mainly non-UK nationals).

Fundamentally the modelling strategy is multistage see Figure 1. For both immigration and emigration, we have macro level processes known as alignment or calibration containing external control totals to model the number of migrants, or the how question and micro equations and processes to model what types of individuals migrate, the who question. As we are also interested in the population living overseas due to their eligibility for pensions, we must also model some of the processes relevant to their eligibility.

Figure 1

Download asset Open asset

Migration poses a number of challenges to a closed microsimulation model as:

• we have to bring the people into the population,

• we have to model processes where the external control totals have different units of analysis to the micro equations, and

• we may have to model a population living overseas.

In the following sections we discuss the choices and the decisions made in developing the model.

5.1 Control Totals

Key to our simulation of the number of migrants is appropriate control totals.³ Frequently, population projections publish only net migration totals, rather than the gross flows into and out of the country. One must then make an assumption as to how to disaggregate this net variable into these gross components. One possibility is to use historic ratios of emigration and immigration totals. However the question then is how to transform changes in the net migration totals to the gross migration totals. If net outward migration or net inward migration increases, then it may be reasonable to apply the ratio of the net migration to the gross migration totals to produce new estimated gross flows. However the difficulty occurs when the net migration total changes sign. In this case the ratio will be negative, having no sensible meaning in adjusting the gross control totals. Our solution is rather than concentrating on the level of the net totals, we focus on the absolute change in the net totals. Consider the following.

Net migration in baseline: NM₁ = I₁ − E₁.

Net migration in future year: NM₂ = I₂ − E₂.

We observe the following values: historic net migration (NM₁), historic inward migration (I₁) and historic outward migration (E₁) as well as the future assumed value of net migration (NM1). The change in net migration is also known:

(1) $∆NM= N{M}_2 - N{M}_1.$

One arbitrary assumption is to assume that the change in migration is borne in proportion to the original gross flows. Thus if ANM are positive then, immigration increases by

(2) $\frac{I_1}{I_1+E_1}\times \Delta NM$

(3) $\Delta I=\frac{I_1}{I_1+E_1}\times \Delta NM=I_2-I_1$

and emigration decreases by

(4) $\frac{E_1}{I_1+E_1}\times \Delta NM:$

(5) $\Delta E=\frac{E_1}{I_1+E_1}\times \Delta NM=E_2-E_1.$

If ΔM is negative then the gross flows decrease by these proportions. Therefore summing:

(6) $\Delta NM=\frac{I_1}{I_1+E_1}\times \Delta NM+\frac{E_1}{I_1+E_1}\times \Delta NM.$

Also

(7) $\Delta NM=\Delta I-\Delta E=(I_2-I_1)-(E_2-E_1)=(I_2-E_2)-(I_1-E_1)$

thus

(8) $(I_2-E_2)=(I_1-E_1)+\frac{I_1}{I_1+E_1}\times \Delta NM+\frac{E_1}{I_1+E_1}\times \Delta NM$

or

(9) $N{M}_2=I_1\times \left(1+\frac{\Delta NM}{I_1+E_1}\right)-E_1\times \left(1-\frac{\Delta NM}{I_1+E_1}\right)=I_1\times \left(1+k\right)-E_1\times \left(1-k\right)$

Thus we can express the future net migration in terms of known values, where

(10) $I_2=I_1+\frac{I_1}{I_1+E_1}\times \Delta NM=I_1\times \left(1+\frac{\Delta NM}{I_1+E_1}\right)=I_1\times \left(1+k\right)$

and

(11) $E_2=E_1-\frac{E_1}{I_1+E_1}\times \Delta NM=E_1\left(1-\frac{\Delta NM}{I_1+E_1}\right)=E_1\times (1-k).$

We face a choice in what we use for k. In Figure 2 we consider a number of different possibilities. In this graphic we consider the performance of our assumptions based upon a dataset that exhibited relatively small variations from 35,000 to 1,05,000 in the period 1991–1997, but increased rapidly to 1,50,000 to 2,25,000 in the 1998–2005 periods. In Figure 1, we consider in turn the assumption that (a) k depends upon the transition in the previous year, (b) that k depends upon the average transition over the period and (c) that k depends upon the value based upon 1991 transitions. We find that assumption (a) performs the best as the transitions year on year are smaller than over longer periods, while the average in (b) performs better than when k is based upon the 1991 transitions in (c). This is particularly noticeable in the 1998–2005 when there is greater volatility, but less important in the less volatile 1991–1997 period. This is not surprising as a sudden surge is likely to be as a result of either a large increase in immigration or emigration, due to an asymmetric shock such as immigration due to a war or entry of new states to the EU or emigration due to a downturn in the national economy. We would therefore argue for k based upon the shortest time, the lag order one.

(a) with 2 supplements see all

Download asset Open asset

Utilising ONS net migration projections and the disaggregation method described here, based on historical gross migration flows, we describe in Figure 3 the control totals used in the model for the total number of immigrants and emigrants.

Figure 3

Download asset Open asset

In this paper we developed a methodology for simulating migration in a dynamic microsimulation model. The method builds on methodologies used in other models, particularly in Sweden, Canada and Australia and focuses in particular on defining the algorithms used. We hope that these algorithms will prove useful to other model builders. Our migration module consisted of a number of parts. Firstly immigration was modelled using a sampling routine from an external sample of British and non-British migrants.

Emigrants were modelled utilising an emigration regression. Emigrants move into an external pool of emigrants who are then subjected to a sub-set of processes in order to be able to model pension expenditure amongst pensioners living abroad. Unlike the domestic pensioners, at present it is not possible to model the relative welfare of these pensioners as we neither model other family members and family formation, nor do we model other income sources. However the model is useful in capturing future liability for pensions paid to overseas pensioners and to assess the cost of pension reforms for this group.

One key gap in the model is migration between Northern Ireland which has a separate pension system and mainland GB. Given the transferability of eligibility for migrants between these different parts of the UK, this is an issue that will have to be dealt with in medium term improvements in the model.

Lastly once immigrants are introduced into the model, the question then remains what we do with them once they enter the model. Sulaheen and Shadforth (2006) and Haque et al. (2002) describe the situation of migrants in the UK, highlighting that immigrants tend to be younger, more like to be in work, but also likely to be both in the highest paid professions and the lowest paid professions, but less represented in the middle of the distribution. New immigrants are also more educated than older immigrants. Also there is quite a significant wage gap between immigrants and UK born. However for background information, it would be useful to have a handle on the extent to which migrant and non-migrant histories differ, even if only to provide some contextual background for simulations.

Incorporating this information would require the re-estimation of the entire labour market and demographic processes of the model and thus adjusting the other modules to account for alternative transitions for migrant and non-migrants is a very large task. Re-estimating existing models of labour market characteristics was beyond the scope of this project.

Therefore labour market processes for immigrants were not differentially simulated. Rather it was assumed that the difference in education and experience variables will account for the earnings and employment differential. However Duleep and Dowha (2008c) acknowledge that this approach from the point of view of simulating migrant earnings is problematical. It is likely to misrepresent the earnings profiles of migrants. They also recommend that in estimating models of migrant earnings, that separate equations should be estimated for migrants rather than simply including dummy variables in existing earnings regression models. This recommendation is likely to apply to other components of the labour market as well. Therefore it is hoped to improve this aspect in future developments of the model.

1. 1
   Microsimulation Modelling for Policy Analysis

   1. D. Chènard

   (2000)

   Individual alignment and group processing: an application to migration processes in DYNACAN, (eds), Microsimulation Modelling for Policy Analysis, Cambridge University Press, Cambridge.

   • Google Scholar
2. 2
   Pensim2: Analysing the Effect of Government Policy in the Long-term

   1. C. Drane

   (2006)

   Presentation to the, Pensions Policy Institute Modelling Seminar, http://www.pensionspolicyinstitute.org.uk/uploadeddocuments/Events/DWP_Presentation_at_PPI_Modelling_Seminar_06_2006.pdf, March, 3rd.

   • Google Scholar
3. 3
   Adding immigrants to microsimulation models

   1. H.O. Duleep
   2. Dowhan

   (2008a)

   Social Security Bulletin 68:51–66.

   • Google Scholar
4. 4
   Incorporating Immigrant Flows into Microsimulation Models Social Security Bulletin

   1. H.O. Duleep
   2. D.J. Dowha

   (2008)

   Incorporating Immigrant Flows into Microsimulation Models Social Security Bulletin, 68, 1.

   • Google Scholar
5. 5
   Research on immigrant earnings

   1. H.O. Duleep
   2. D.J. Dowha

   (2008c)

   Social Security Bulletin 68:31–50.

   • Google Scholar
6. 6
   GENESIS: SAS based computing environment for dynamic microsimulation models

   1. S. Edwards

   (2004)

   Mimeo: Department of Work and Pensions.

   • Google Scholar
7. 7
   An Assessment of Pensim2. IFS Working Paper W04/21

   1. C. Emmerson
   2. H. Reed
   3. A. Shephard

   (2004)

   An Assessment of Pensim2. IFS Working Paper W04/21.

   • Google Scholar
8. 8
   A Microsimulation Model for Projections of the Japanese Socioeconomic Structure (INAHSIM). IPSS Discussion Paper Series No.2005-03

   1. S. Inagaki

   (2005)

   A Microsimulation Model for Projections of the Japanese Socioeconomic Structure (INAHSIM). IPSS Discussion Paper Series No.2005-03.

   • Google Scholar
9. 9
   Brits Abroad

   1. IPPR

   (2006)

   London: Institute for Public Policy Research.

   • Google Scholar
10. 10
    Migrants in the UK: their characteristics and labour market outcomes and impacts

    1. R. Haque
    2. C. Dustmann
    3. F. Fabbri
    4. I. Preston
    5. J. Wadsworth
    6. Michael Shields and Stephen Wheatley Price

    (2002)

    RDS Occasional Paper No 82.

    • Google Scholar
11. 11
    Dynamic Microsimulation: A Survey

    1. C. O’Donoghue

    (2001)

    Brazilian Electronic Journal of Economics, 4, 2.

    • Google Scholar
12. 12
    APPSIM -Modelling Migration National Centre for Social and Economic Modelling (NATSEM). Working Paper No. 5

    1. S. Pennec
    2. M. Keegan

    (2007)

    APPSIM -Modelling Migration National Centre for Social and Economic Modelling (NATSEM). Working Paper No. 5, University of Canberra.

    • Google Scholar
13. 13
    Dept. of Applied Economics Microsimulation Unit Discussion

    1. S.E. Pudney

    (1992)

    Dynamic Simulation of Pensioner’s incomes: methodological issues and a model design for Great Britain, Dept. of Applied Economics Microsimulation Unit Discussion, paper no. MSPMU 9201, University of Cambridge.

    • Google Scholar
14. 14
    Data Fusion through Statistical Matching – Creating the Base Dataset for Pensim2

    1. H. Redway

    (2003)

    Presentation to the, Microsimulation Conference, Canberra, 2003, https://guard.canberra.edu.au/natsem/conference2003/papers/pdf/ppt_redway_h.pdf, March, 3rd.

    • Google Scholar
15. 15
    Immigrant characteristics and the supply potential of the economy

    1. J. Sulaheen
    2. C. Shadforth

    (2006)

    Q4, Quarterly Bulletin.

    • Google Scholar
16. 16
    Incorporating Immigration into Microsimulation Models

    1. M. Simpson

    (2009)

    Paper Presented to the, 2nd General Conference of the International Microsimulation Association, Ottawa.

    • Google Scholar
17. 17
    The Potential Dynamic of Microsimulation in Family Studies: A Review and Some Lessons for FAMSIM+. Working Paper 18-2002

    1. M. Spielauer

    (2002)

    The Potential Dynamic of Microsimulation in Family Studies: A Review and Some Lessons for FAMSIM+. Working Paper 18-2002.

    • Google Scholar
18. 18
    Effects from Higher Immigration on Demographic Development, Labour Supply and Pension Expenditures

    1. N.M. Stølen
    2. I. Texmon

    (2007)

    1st General Conference of the International Microsimulation Association.

    • Google Scholar
19. 19
    Pensions Commission, Second Report

    1. A Turner
    2. J Hills
    3. J Drake

    (2005)

    London: The Stationery Office.

    • Google Scholar

Author details

1. Cathal O’Donoghue

   Teagasc Rural Economy Research Centre, Athenry, Co. Galway, Ireland

   For correspondence

   cathal.odonoghue@nuigalway.ie

2. Howard Redway

   Department for Work and Pensions (DWP), United Kingdom

3. John Lennon

   Teagasc Rural Economy Research Centre Athenry, United Kingdom