Model structure
SimPaths is a family of models for individual and household life course events, all sharing common components. The framework is designed to project life histories through time, building up a detailed picture of career paths, family (inter)relations, health, and financial circumstances. It builds upon standardised assumptions and data sources, which facilitates adaptation to alternative countries – versions currently exist for the UK and Italy, and are under development for Hungary, Poland and Greece. Careful attention is paid to model validation, and sensitivity of projections to key assumptions. The modular nature of the SimPaths framework is designed to facilitate analysis of alternative assumptions concerning the tax and benefit system, sensitivity to parameter estimates and alternative approaches for projecting labour/leisure and consumption/savings decisions. Projections for a workhorse model parameterised to the UK context are reported, which closely reflect observed data throughout a validation window between the Financial crisis (2011) and the Covid-19 pandemic (2019).
SimPaths is a fully open-source structural dynamic microsimulation framework, designed to facilitate experimentation with alternative model assumptions. It is coded in Java using the JAS-mine core and JAS-mine GUI simulation libraries. SimPaths models are currently estimated for the United Kingdom and Italy, and are under development for Hungary, Poland, and Greece.
SimPaths implements a hierarchical architecture where individuals are organised in benefit units (for fiscal purposes), and benefit units are organised in households. The model projects data at yearly intervals, reflecting the yearly frequency of the survey data used to estimate model parameters. The model is composed of eleven modules:
- Ageing
- Education
- Health
- Family composition
- Social care
- Investment income
- Labour income
- Disposable income
- Consumption
- Mental health
- Statistical display
Each module is composed of one or more processes; for example, the ageing module contains ageing, mortality, child maturation, and population alignment processes. Empirical specification of dynamic processes makes extensive use of cross-module characteristics (state variables). A graphical representation of the simulated modules is shown below:
The first simulated process in each period increments the age of each simulated person by one year. Any dependent child that reaches an exogenously assumed “age of independence” (18 years-of-age in the parameterisation for the UK) is extracted from their parental benefit unit and allocated to a new benefit unit. Individuals are then subject to a risk of death, based on age, gender and year specific probabilities that are commonly reported as components of official population projections. Death is simulated at the individual level but omitting single parent benefit units (to avoid the creation of orphans).
Population alignment is performed to adjust the number of simulated individuals to national population projections by age, gender, region, and year. Alignment proceeds from the youngest to the oldest age described by national population projections. Each age is considered in two discrete steps. First, within each age-gender-region-year subgroup, the simulated number of individuals is compared against the associated population projection. Regions with too few simulated individuals (relative to the respective target) are partitioned from those with too many. Net “domestic migration” is then projected by moving individuals from regions with too many simulated people to those with too few, until all options for (net) domestic migration are exhausted. All migratory flows are simulated at the benefit unit level, with reference to the youngest benefit unit member.
Following domestic migration, remaining disparities between simulated and target population sizes are adjusted to reflect international immigration (if the simulated population is too small), or emigration and death (if the simulated population is too large). Like domestic migration, international migration is simulated net of opposing flows and at the benefit unit level with reference to the youngest benefit unit member. Death is simulated in preference to international emigration for population alignment for all ages above an exogenously imposed threshold (65 for the UK).
Except for the distinction between age, gender, region, and year, all transitions simulated for population alignment are randomly distributed. This means that the model does not reflect, for example, the higher incidence of international emigration among prior international immigrants. Furthermore, the model projects international immigration by cloning existing benefit units without taking into consideration any systematic disparities between the domestic and migrant populations, including with regard to their respective financial circumstances.
Individuals who have recently attained the assumed age of independence and were moved to separate benefit units are evaluated to determine if they leave their parental home. Any individual still in education is assumed to remain a member of their parental household. For mature children not in education, the probability of leaving their parental home is based on a probit model conditional on gender, age, level of education, lagged employment status, lagged household income quintile, region, and year (to reflect observed time trends). Mature children who are projected to remain in their parental homes may leave in any subsequent year.
The education module determines transitions into and out of student status. Students are assumed not to work and therefore do not enter the labour supply module. Individuals who leave education have their level of education re-evaluated and can become employed.
Individuals leave continuous full-time education during an exogenously assumed age band (16 to 29 for the UK). The probability of leaving continuous full-time education within this age band is described by a probit model conditional on gender, age, mother’s education level, father’s education level, region, and year.
Individuals who are not in education may re-enter education within another exogenously assumed age band (16 to 45 for the UK). In this case, the probability of re-entering education is described by a probit model conditional on gender, age, lagged level of education, lagged employment status, lagged number of children in the household, lagged number of children aged 0-2 in the household, mother’s and father’s education levels, region, and year.
Students are considered not to work. Those who return to education can leave again in any subsequent year.
Individuals who cease to be students are assigned a level of education based on an ordered probit model that conditions on gender, age, mother’s and father’s education level, region, and year. The education level of individuals who exit student status after re-entering education may remain unchanged or increase but cannot decrease.
The health module projects an individual’s health status, comprising both self-rated general health and mental health metrics (based on a clinically validated measure of psychological distress using a Likert scale and a caseness indicator), and determines whether an individual is long-term sick or disabled (in which case, he/she is not at risk of work and may require social care).
Physical health status is projected on a discrete 5-point scale, designed to reflect self-reported survey responses (between “poor” and “excellent” health). Physical health dynamics are based on an ordered probit, distinguishing those still in continuous education. For continuing full-time students, the ordered probit conditions on gender, age, lagged benefit unit income quintile, lagged physical health status, region, and year. The same variables are considered for individuals who have left continuous education, with the addition of education level, lagged employment status, and lagged benefit unit composition.
Any individual aged 16 and above who is not in continuous education can become long-term sick or disabled. The probability of being long-term sick or disabled is described by a probit equation defined with respect to lagged disability status, prevailing and lagged physical health status, gender, age, education, income quintile, and lagged family demographics.
In each simulation cycle, a baseline level of psychological distress for individuals aged 16 and over is determined using the 12-item General Health Questionnaire (GHQ-12). Two indicators of psychological distress are computed: a Likert score, between 0 and 36, estimated using a linear regression model; and a dichotomous indicator of the presence of potentially clinically significant common mental disorders is obtained using a logistic regression model. Both specifications are conditional on the lagged number of dependent children, lagged health status, lagged mental health, gender, age, level of education, household composition, region, and year.
The baseline measures of the level and caseness of psychological distress described above are modified by the effects of economic transitions and non-economic exposure to the Covid-19 pandemic. Fixed effects regressions are used to estimate the direct impact of transitions from employment to non-employment, non-employment to employment, non-employment to long-term non-employment, non-poverty to poverty, poverty to non-poverty, and poverty to long-term poverty, as well as changes in growth rate of household income, a decrease in household income, and non-economic effect of the exposure to Covid-19 pandemic in years 2020 and 2021. The effects of economic transitions are estimated on pre-pandemic data to ensure validity in other periods. The non-economic effects of the pandemic are estimated using a multilevel mixed-effects generalized linear model.
The family composition module is the principal source of interactions between simulated agents in the model. The module projects the formation and dissolution of cohabiting relationships and fertility. Where a relationship forms, then spouses are selected via a matching process that is designed to reflect correlations between partners’ characteristics observed in survey data. The proportion of the population in a cohabiting relationship is, by default, aligned to the population aggregate in the years for which observational data is available, to account for changes in household structure introduced by the population alignment.
Females in couples can give birth to a (single) child in each simulated year, as determined by a process that depends on a range of characteristics including age and presence of children of different ages in the household. In case of divergence from the officially projected number of newborns, fertility rates are adapted by an alignment process to match population projections for new-born children distinguished by gender, region, and year.
Individuals aged 18 and over who do not have a partner may decide to enter a partnership based on the outcome of a probit model. For students, the probit conditions on gender, age, lagged household income quintile, lagged number of (all) dependent children, lagged number of children aged 0-2, lagged self-rated health status, region, and year. For non-students, the probit conditions on the same set of variables as for students, expanded to include level of education and lagged employment status.
Individuals who enter a partnership are matched using either a parametric or non-parametric process, focussing exclusively on opposite-sex relationships. In the (default) parametric matching process, the model searches through the pools of males and females identified as cohabiting in each simulated period to minimise the distance between individual expectations, in terms of partner’s ideal earnings potential and age, and individual characteristics of each individual in the matching pool. The matching procedure prioritises matching individuals within regions, but if the sufficient quantity and / or quality of matches cannot be achieved, matching is performed nationally. In contrast, the non-parametric process uses an iterative proportional fitting procedure to replicate the distribution of matches observed in survey data between different types of individuals, where a type is defined as a combination of gender, region, education level, and age.
Partnership dissolution is modelled at the benefit unit level with the probability described by a probit model conditional on female partner’s age, level of education, lagged personal gross non-benefit income, lagged number of (all) children, lagged number of children aged 0-2, lagged self-rated health status, lagged level of education of the spouse, lagged self-rated health status of the spouse, lagged difference between own and spouse’s gross, non-benefit income, lagged duration of partnership in years, lagged difference between own and spouse’s age, lagged household composition, lagged own and spouse’s employment status, region, and year.
The matching processes for new relationships outlined above fails to identify matches for all individuals flagged as entering a partnership by the related probit equations. This tends to bias the simulated population, resulting in an under-representation of partner couples. An alignment process is consequently used to match the rate of incidence of partner couples to survey targets. The alignment process works by adjusting the intercept of the probit relationships governing relationship formation, increasing the intercepts where the incidence of couples is too low.
Females aged 18 to 44 can give birth to a child whenever they are identified in a partnership. The probability of giving birth is described by a probit model conditional on a woman’s age, benefit unit income quintile, lagged number of children, lagged number of children aged 0-2, lagged health status of the woman, lagged partnership status for those in continuous education. For those not in continuous education, the probability of giving birth is described by a probit model conditional on a woman’s age, the fertility rate of the UK population, benefit unit income quintile, lagged number of children, lagged number of children aged 0-2, lagged health status of the woman, lagged partnership status, lagged labour market activity status, level of education, and region. The inclusion of the overall fertility rate allows the model to capture fertility projections for future years, whereas the overall change in projected fertility is distributed across individuals according to their observable characteristics.
The number of projected births is aligned to the number of newborns supplied by the official projections used for population alignment. The alignment procedure randomly samples fertile women and adjusts the outcome of the fertility process until the target number of newborns has been met.
The social care module projects provision and receipt of social care activities for people in need of help due to poor health or advanced age. The module is designed to distinguish between formal and informal social care, and the social relationships associated with informal care. The social care module accounts for the time cost incurred by care providers with respect to informal care, and the financial cost incurred by care receivers with respect to formal care.
The model distinguishes between individuals aged above and below an age threshold when projecting receipt of social care. This reflects the relatively high prevalence of social care received by older people, for whom more detailed information is often reported by publicly available data sources.
For individuals aged above an exogenously defined threshold (65 years in the UK), the model begins by considering whether an individual is in need of care. This is simulated as a probit equation that varies by gender, education, relationship status, whether care was needed in the preceding year, self-reported health, and age. The probability of receiving care is projected using a similar set of explanatory variables. Where an individual is identified as receiving care, a multinomial logit equation is used to determine if the individual receives: i) only informal care; ii) formal and informal care; or iii) only formal care. This multinomial logit varies by education, relationship status, and age band in addition to a lag dependent variable.
For individuals projected to receive informal care, a multi-level model is used to distinguish between alternative care providers. The first level considers whether a partner provides informal care, for individuals with partners. For individuals who receive social care from their partner, the second level uses a multinomial logit to consider whether they also receive care from a daughter, a son, or someone else (other). For individuals in receipt of informal care who do not have a partner caring for them, another multinomial logit is used to select from six potential alternatives that allow for up to two carers from “daughter”, “son”, and “other”. Log-linear equations are then used to project the number of hours of care received from each identified carer. Finally, hours of formal care are converted into a cost, based on the year-specific mean hourly wages for all social care workers.
Receipt of social care among individuals under the exogenously assumed age threshold is simulated using a more stylised approach to that described for older people, reflecting the less detailed data available for parameterisation. In this case, the model focusses exclusively on informal social care for individuals simulated to be long-term sick or disabled. At the time an individual is projected to enter a disabled state, a probit equation is used to identify whether the individual receives informal social care. This identification is assumed to persist for as long as the person remains disabled.
If an individual under age 65 is identified as receiving social care, then the time of care received is described by a log-linear equation.
The model is adapted to project provision of social care by informal sector providers; the characteristics of formal sector providers of social care are beyond the current scope of the model. The approach adopted for simulating receipt of social care described above identifies the incidence and hours of informal social care that individuals are projected to receive. In the case of people over the assumed age threshold, it also identifies the relationship between those in receipt of informal social care and their informal care providers, and the persistence of those care relationships. These details consequently provide much of the information necessary to simulate provision of informal social care, in addition to the receipt of care.
Nevertheless, the data sources for starting populations considered for SimPaths – with the notable exception of partners – generally omit social links that are implied to exist between informal social care providers and those receiving care. Specifically, links between adult children and their parents, and the wider social networks that often supply informal social care services are generally not recorded. The method that is used to project informal provision of social care is designed to accommodate limitations of the simulated data in a way that broadly reflects projection of social care receipt discussed above.
Specifically, the model distinguishes between four population subgroups with respect to provision of informal social care: (i) no provision; (ii) provision only to a partner; (iii) provision to a partner and someone else; and (iv) provision but only to non-partners. For people who are identified as supplying informal care to their partner via the process described above, a probit equation is used to distinguish between alternatives (ii: provision only to partner) and (iii: provision to a partner and someone else). Similarly, for the remainder of the population, another probit equation is used to distinguish between alternatives (i) and (iv). A log linear equation is then used to project number of hours of care provided, given the classification of who care is provided to.
The investment income module projects income from investment returns and (private) pensions. The approach taken to project these measures of income depends upon the model variant considered for analysis. Where consumption/savings decisions are simulated using a structural behavioural framework, then asset income is projected based on accrued asset values and exogenously projected rates of return. Alternatively, computational burden of model projections can be economised by proxying non-labour income without explicitly projecting asset holdings.
Simulation of retirement varies slightly depending on the accommodation of forward-looking expectations. In both cases, retirement is possible for any adult above an assumed age threshold (50 in the parametrisation for the UK). When forward-looking expectations are implicit, entry to retirement is based on a probit model that controls for gender, age, education, lagged employment status, lagged (benefit unit) income quintile, lagged disability status, indicator to distinguish individuals in excess of state pension age (accounting for changes in the state pension age), region, and year. For couples, characteristics of the spouse (employment status, reaching retirement age) also affect the probability of retirement. When forward-looking expectations are explicit, then entry to retirement is considered to be a control variable. Retired individuals may receive pension income.
When wealth is implicit in the model, then private pension income is projected using a linear regression model that conditions on age, level of education, lagged household composition, lagged health status, lagged private pension income, region, and year for individuals who continue in retirement. For individuals entering retirement, the probability of receiving private pension income is first determined using a logit model that conditions on having reached the state pension age, level of education, lagged employment status, lagged household composition, lagged health status, lagged hourly wage potential, region, and year. The amount of pension income is projected using a linear regression model conditional on the same observed characteristics.
When the simulation projects wealth explicitly, then an assumed fraction of benefit unit wealth at the time of retirement is converted into a life annuity, or joint-life annuity for adult couples. Annuity rates in the model are actuarily fair, given (cohort specific) mortality rates and an assumed internal rate of return.
When wealth is not projected by the model, then the incidence of capital income among the simulated population aged 16 and over is based on probabilities described by a logit regression equation that varies by age, lagged health, lagged gross employment and capital income, region and year. For individuals not in continuous education, the list of explanatory variables for the logit equation also includes education status, lagged employment status, and lagged household composition.
For individuals simulated to be in receipt of capital income, the amount of capital income is described by linear regression models that condition on gender, age, lagged health status, lagged gross employment income, lagged capital income, region, and year for individual in continuous education. Individuals not in continuous education are also distinguished by their level of education, lagged employment status, and lagged household composition.
When wealth is explicitly projected by the model, then capital income is the product of net asset holdings and an assumed rate of return. The rate of return varies by year, and by the value of benefit unit net wealth, w_{i,t}, as described by:
where
The labour income module projects potential (hourly) wage rates for each simulated adult in each year and their associated labour activity. Given potential wage rates, hours of paid employment by all adult members of a benefit unit are generated. Labour (gross) income is then determined by multiplying hours worked by the wage rate.
Hourly wage rates are simulated for each adult in the model based on Heckman-corrected regressions stratified by gender and lagged employment status (distinguishing between employed and not-employed individuals) that include as explanatory variables, part-time employment identifiers, age, education, student status, parental education, relationship status, presence of children, health, and region. For individuals observed in employment in the previous year, lagged (log) hourly wage rates are also included as an explanatory variable.
Two alternative methods for projecting employment decisions can be considered by the model. These alternatives are both designed to reflect the influence of financial incentives on behaviour and are distinguished by whether they reflect forward-looking expectations.
The default specification of SimPaths projects labour supply using a non-forward-looking random utility model. The method projects labour supply as though employment decisions are made to maximise within-period benefit unit utility over a discrete set of labour/income alternatives (by default, 5 alternatives for individuals, and 25 for couples). Given any labour alternative, labour income is computed by combining hours of work with the respective hourly wage rate. The utility of the benefit unit is calculated using a quadratic utility function and takes as arguments benefit unit disposable income and the number of hours worked by adult members.
The model can also be directed to project labour and discretionary consumption to reflect forward-looking expectations for behavioural incentives. As for the implicit expectations case, the unit of analysis is the benefit unit. Incentives are translated into behaviour via an assumed intertemporal utility function. By default, the model adopts a nested constant elasticity of substitution (CES) utility function.
Each adult is considered to have three alternative labour supply options, corresponding to full-time, part-time and non-employment. Labour supply and discretionary consumption are projected as though they maximise the assumed utility function, subject to a hard constraint on net wealth and assumed agent expectations. Expectations are “substantively rational” in the sense that uncertainty is characterised by the random draws that underly dynamic projection of modelled characteristics. As no analytical solution to this problem exists, numerical solution methods are employed.
The model proceeds in two discrete steps. The first step involves solution of the lifetime decision problem for any potential combination of agent specific characteristics, with solutions stored in a look-up table. The second step uses the look-up table as the basis for projecting labour supply and discretionary consumption.
When the default specification of SimPaths for projecting labour supply is used, the estimated utility of single men, single women, and couples is adjusted to align the aggregate employment rate to the employment rate observed in the data in the validation period. The final adjustment value is used in the subsequent periods, for which no data is available. This procedure accounts for the existence of unemployment in the real economy and the fact that labour supply decisions simulated using the random utility model assume no constraints on labour demand in the economy.
Disposable income is simulated by matching each simulated benefit unit in each projected period with a donor benefit unit reported by a tax-benefit reference database, following the procedure described by van de Ven et al. (2022). The database stores details of taxes and benefits alongside associated demographic and private income characteristics for a sample of benefit units. This database could be populated from a wide range of sources. The approach was originally formulated to draw upon output data derived from the UK version of EUROMOD (UKMOD), and then extended to accommodate projections from any EUROMOD country.
The matching procedure for benefit units applies coarsened exact matching over a number of discrete-valued characteristics, followed by nearest-neighbour matching on a set of continuous variables. The nearest neighbour matching is performed with respect to Mahalanobis distance measures evaluated over multiple continuous valued characteristics.
The default set of discrete value characteristics considered for matching includes age of the benefit unit reference person, relationship status, numbers of children by age, hours of work by each adult member, disability status, and informal social care provision. Similarly, the default set of continuous value matching characteristics includes original (pre-tax and benefit) income, second income (to allow for income splitting withing couples), and formal childcare costs.
Having matched a simulated benefit unit to a donor, disposable income is imputed via one of two methods. For benefit units with original income above a “poverty threshold”, disposable income is imputed by multiplying original income of the simulated benefit unit by the ratio of disposable to original income of the donor unit. For benefit units below the considered poverty threshold, disposable income is set equal to the (growth adjusted) disposable income of the donor.
Finally, adjustments to account for public subsidies for the costs of (formal) social care are evaluated separately from the database approach described above, based on internally programmed functions. This is done because public subsidies for social care are not always included in database sources (e.g. tax-benefit models) considered for analysis.
Given disposable income and household demographics, the consumption module projects measures of benefit unit expenditure. Where the model projects wealth, then a simple accounting identity is used to track the evolution of benefit unit assets through time. A regression-based homeownership process predicts if the primary residence is owned by either of the responsible adults in a benefit unit, in which case the benefit unit is considered to own its home.
The model can project two forms of non-discretionary benefit unit expenditure: formal social care costs and formal childcare costs. Social care costs are projected based on projections of hours of formal social care received and assumed hourly wage rates for social care workers.
Childcare costs are projected using a double-hurdle model, characterised by a probit function describing the incidence of formal childcare costs and a linear least-squares regression equation describing the value of childcare costs when these are incurred. Both equations include the same set of explanatory variables describing the number and age of dependent children in a benefit unit, the relationship status and employment status of adults in the benefit unit, whether any adult in the benefit unit is higher educated, region, and year.
The model can be directed to project employment and discretionary consumption jointly to reflect forward-looking expectations for behavioural incentives. The projection of discretionary consumption varies depending on whether forward-looking expectations are chosen to be explicit or implicit within a simulation.
By default, yearly equivalised disposable income is calculated by adjusting disposable income to account for benefit unit demographic composition via the modified OECD scale. Equivalised consumption is set equal to equivalised disposable income for retired individuals, and to disposable income adjusted by a fixed discount factor to account for an implicit savings rate otherwise. The assumed savings rate, in turn, influences simulated capital income.
When expectation are explicit, the model evaluates solutions to the lifetime decision problem in the form of a look-up table when directed to reflect forward-looking expectations for behavioural incentives. In the case of discretionary consumption, the look-up table stores the ratio of consumption to “cash on hand”, where cash on hand is the sum of net wealth, disposable income, and available lines of credit. This ratio has the advantage that it is bounded between zero and one, which facilitates the computational routines and consideration of selected policy counterfactuals.
Net wealth is the key transition mechanism that balances intertemporal behavioural incentives when forward-looking expectations are treated explicitly by the model. In this case, dynamic evolution of wealth in most periods is described by the accounting identity:
where
Although net wealth is not disaggregated in the model, the incidence of home ownership is reflected, as this is used as an input to for projection of psychological distress. Home ownership is evaluated at the benefit unit level, by considering if at least one of the adult occupants is classified as a homeowner. At the individual level, home ownership is determined using a probit regression model conditional on gender, age, lagged employment status, education level, lagged self-rated health, lagged benefit unit income quintile, lagged gross personal non-employment non-benefit income, region, lagged household composition, lagged spouse’s employment status, and a time trend.
A secondary subjective-wellbeing process adjusts estimates obtained by the primary process to account for the effect of exposure to labour market transitions, such as moving in and out of employment and/or poverty.
At the end of each simulated year, SimPaths generates a series of year specific summary statistics. All of these statistics are saved for post-simulation analysis, with a subset of results also reported graphically as the simulation proceeds.
Review the detailed model parameters.
Refer to the technical description of SimPaths classes.