Female labour force projections using microsimulation for six EU countries

Population ageing presents immediate economic and social challenges for the European Union (EU), as well as for other developed countries and even developing nations such as China. Compared to 1970, an average EU citizen now lives about ten years longer and works ten years less.¹ Furthermore, demographic change is accelerating: the old age dependency ratio (the ratio of people aged 65 years and over, to people aged 15–64 years), which is now below 30%, is expected to rise to approximately 50% by 2050.²

This explains the emphasis that policy makers put on increasing labour force participation rates, in particular for women, who have historically exhibited lower rates of participation than their male counterparts. Indeed, over the last two decades, EU strategies have focused on fostering a higher participation of women in the labour market. However, without social and labour market policies that help reconciliation of work and family responsibilities, increased female participation may produce a decline in the total fertility rate (Kohler, Billari, & Ortega, 2002), as women postpone childbearing in order either to enter the workforce or to avoid putting their professional careers at risk. Of particular relevance are family support policies, such as childcare services (Blau, 2001; Berlinski & Galiani, 2007) and paid parental leave (Pronzato, 2009), and policies directed at increasing part-time work opportunities (Paull, 2008). Paid parental leave and childcare services decrease the cost of child-rearing and help parents reconcile work and family life; the availability of flexible working-time arrangements and in particular the possibility to work part-time helps women to combine market work with traditional family responsibilities. While childcare services have an unambiguous positive effect on participation, both long-term leave and part time jobs can have the effect of detaching women from the labour market, penalising their working career and reducing disposable income, further hampering their empowerment. It is therefore an empirical issue to determine whether and under what circumstances a positive or a negative overall effect prevails.

The objective of this paper is to study the medium/long term implications for female participation and employment of demographic and behavioural dynamics as they are currently observed, with a focus on selected EU-Member States characterised by low female participation. Understanding these dynamics is instrumental to investigating the expected effects of different policies aimed at supporting better education, helping with family-work reconciliation, and delaying retirement. More specifically, we adopt Sweden as a benchmark, representative of the Nordic group of high participation countries, and study Italy, Spain and Hungary from the “long leave – low cash benefits” group, Greece from the “limited assistance” group and Ireland from the “short leave -low cash benefits” group.³

A recent surge in interest in the evolution of participation rates is related to the observed decline in U.S. labour force participation since the turn of the millennium (see Jacobs, 2015; Bullard, 2014; DiCecio, Engemann, Owyang, & Wheeler, 2008). While the focus of that literature has been mainly on participation rates for the (white) male population (Eberstadt, 2017), the methods used are the same we review in this paper. Hence, our suggestion to follow a microsimulation approach, which we substantiate in Section 4 below, can apply to that literature as well. Projecting the complex and intertwined dynamics forward in time is of course difficult. Most forecasting exercises, generally performed by governmental institutions at a national level, or by international organisations such as the International Labour Organization (ILO), OECD or the European Commission, focus therefore on only one aggregate outcome variable of interest (for example, female participation), assuming an exogenous evolution for its determinants. By contrast, in this paper we employ a dynamic microsimulation model (MSM) (Li & O’Donoghue, 2013), which challenges both assumptions underlying most official projection models (i) participation is estimated (and projected) at the individual level, and (ii) the model also evolves the determinants of participation, based on additional regression models estimated in the data. The advantage of the microsimulation approach is threefold. First, aggregation can be performed ex-post on any sub-population of interest. Second, by providing projections on a possibly large set of outcomes, dynamic microsimulations allow for a more comprehensive analysis of participation, and its complex relationship with other life course events. Third, by endogenizing the evolution of the determinants of participation, dynamic microsimulations allow for a more comprehensive quantification of the uncertainty surrounding the projections. We exploit these features by analysing education, household formation and dissolution, fertility decisions, labour force participation, employment outcomes, retirement decisions and ultimately death within the same model. Moreover, we provide projections for both men and women, starting from representative samples of the population in the base year, for each country.

The structure of this paper is as follows. First, we present the background against which we implement our model; then we motivate the choice of the EU Member States that we analyse (Section 3) and present the main features of the dynamic microsimulation approach that we adopt, vis-à-vis other approaches (Section 4). Sections 5 and 6 are devoted respectively to describing the model and our baseline parameterisation. Sources of uncertainty in the projections are discussed in Section 7, along with our approach to the issue. In Section 8 we discuss the long-term projections that the model generates, while in Section 9 we summarise and conclude. The paper is complemented by two appendices. Appendix A describes the MSM and the underlying estimates in more detail. Appendix B reports country tables for the baseline scenario of the MSM, which are referred to and discussed in the text.

Female labour force participation has generally increased in European countries over the last decades, passing the 70% watershed in 2013 (70.6% in 2014) in the 20–64 years age group; however, the gap with respect to male participation remains large, above 12 percentage points (ppt). Although a convergence process seems to be under way, heterogeneity among EU countries is still high (Figure 1). This is reflected in employment rates: the EU28 average in 2014 for females in the 20–64 years age group was only 63.5%, 11 ppt below the male employment rate (Figure 2). Only Sweden in 2014 had a female employment rate above 75%, thereby making a positive contribution towards the Europe 2020 target of an overall rate of 75%, unconditional on gender.

Figure 1

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Figure 2

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The European Commission (2000) proposed a Community framework strategy on gender equality for the period 2001–2005, which aimed, among other objectives, at strengthening the gender dimension in the European Employment Strategy. Equal employment opportunities and work-family balance are pointed out as priorities. This was followed by the European Pact for Gender Equality and the Roadmap for equality between women and men 2006–2010, updated in the Strategy for equality between women and men 2010–2015 (European Council, 2006; European Commission, 2006, 2011). In these documents, the European Commission proposed concrete actions for addressing a number of issues such as economic independence of women and equality in decision making. The Europe 2020 Strategy, by acknowledging that “policies to promote gender equality will be needed to increase labour force participation thus adding to growth and social cohesion”, sets among its targets for 2020 an overall employment rate of 75% across the population (see European Commission, 2010, p. 17). Furthermore, in the Social Investment Package, the European Commission (2013) reaffirmed the importance of fostering higher participation of women. According to this document, gender gaps in employment rates, as well as other gender disparities in the labour market, need to be reduced or eliminated in order to decrease the risk of social exclusion and poverty for women and to achieve inclusive growth. Access to early childhood education and care needs to be improved to foster both female employment and children’s life opportunities.

In addition to fostering equality, enhancing women’s access to employment can sustain economic growth, especially when considering population ageing and the expected labour supply shortages across the EU. According to the Organisation for Economic Co-operation and Development (OECD) (2008, 2012), narrowing the gap between male and female employment rates has accounted for half of the increase in Europe’s overall employment rate and a quarter of annual economic growth since 1995.

Notwithstanding the attention paid by policy makers, female labour force participation is still much lower than male participation and only slowly catching up in many countries. These differences are to some extent rooted in culture and social norms but they also reflect differences in the economic and demographic structure, as well as institutions and economic incentives. Figure 3 shows raw cross-country correlations between female participation rates and some key demographic and economic variables, at the EU level. Female participation appears to be only loosely related to population ageing, with if anything more participation in countries with an older population, and positively related to fertility rate, education, and the generosity of family policies. The large literature on the determinants of female labour force participation (see for instance Saurel-Cubizolles et al., 1999; Bratti, Del Bono, & Vuri, 2005; Attanasio, Low, & Sanchez-Marcos, 2008; Genre, Gomez-Salvador, & Lamo, 2010; Cipollone & D’Ippoliti, 2011) has investigated these relationships in a multivariate setting, stressing the role of composition effects (for example female participation is higher, on average, in countries with an older population because the share of students is lower and because the share of mothers with young children is also lower) and reverse causation (for example women can better afford having children if they have a job). The complexity of the relationship between demography and labour force participation also points to a crucial role of policies. Thévenon (2011) performs a principal component analysis aimed at identifying the most important characteristics of family policy packages in OECD countries. He finds two main components: one related to support allowing parents to combine work with childcare, and another related to the generosity of leave entitlements in terms of money and duration. Across the range of these two components, he notes that countries adopt one of five broad categories of family policy, of which the ‘Nordic’ family package, based on continuous, strong support for working parents, seems to be the most effective in promoting gender equality and female labour force participation and employment.

Figure 3

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We present long-term projections for a selection of EU Member States: Sweden (SE), Italy (IT), Spain (ES), Ireland (IE), Hungary (HU) and Greece (EL). Table 1 reports the participation subindex of the Gender Equality Index, computed by the European Institute for Gender Equality (2015) that considers both the gender gap, and the overall level of achievement. Sweden is the best performer, while the other countries included in our focus rank among the most problematic.⁴

We investigate the evolution of participation rates in the selected countries by means of a dynamic MSM. In dynamic microsimulations, each individual in a given initial population is evolved through time according to estimated transition probabilities. Different life course events are simulated (for example educational choices, entry in the labour market, household formation and dissolution, fertility, evolution of work careers, retirement, death) with specific MSMs having a focus on different dimensions (for example demography, work, family, etc.) and different subgroups of the population. This has an impact on model specification: for instance, if the focus is on the elderly, issues like retirement choices and disability must be considered in greater detail, while if the focus is on women in fertile years, the former processes can be more vague, while more attention needs to be paid to modelling household composition and its interaction with the working career of mothers. Because of its centrality in life, most MSMs have a labour participation/employment module: see Li and O’Donoghue (2013) for a review. Some are fairly complex models which require years and relatively large teams to build, and that could in theory provide projections on labour force participation with the required focus on the interaction between family choices and career. However, because they have a different primary interest (say, pensions), they do not provide published results on female labour force participation at early stages of the life cycle. Moreover, these large models are all country-specific, and exist only for a limited number of countries.

To the best of our knowledge, the only MSM in the literature with a focus on female labour force participation and its interaction with family life in a European context is Richiardi and Poggi (2014), estimated for Italy, which provides the basis for the model developed here. In addition to improvements in model specification, the new model presented here provides a first example of a multi-country dynamic microsimulation: the structure of the model is the same for all countries considered, and simulations only differ because of country-specific inputs, in terms of representative population samples, estimates and parameters. This feature allows us to obtain results for several countries which are directly comparable in terms of the assumptions and modelling choices made; moreover, it allows running “as if” scenarios, where inputs from one country are tested on a different country (we do so in our companion paper Richardson, Pacelli, & Richiardi, 2016). These benefits are achieved, without excessively complicating the model, by leaving two highly institution-dependent processes in the background: income determination and retirement decisions. While these processes are often the prime object of investigation in dynamic MSMs, our focus on labour force participation and employment, and in particular on participation decisions of women in childbearing years, permits us to treat them at a higher level of abstraction, without compromising the quality of the projections. On the other hand, issues such as household composition and its effects on labour force participation of mothers are considered in detail. Finally, the model can be interpreted as a first step towards a more general model for all EU member states, similarly to what EUROMOD (Sutherland & Figari, 2013) provides for tax-benefit microsimulations.⁵ In the next section we discuss in more details the pros and cons of the microsimulation approach with respect to what exists in the literature.

Houriet-Segard and Pasteels (2011) offer a review of the main methods used by governmental institutions around the world to forecast participation rates. Aside from judgmental (or qualitative) methods and simple time extrapolations from historical aggregate data, the most common methodologies are either regression models based on the correlation between participation rates and demographic, economic, and institutional factors, or cohort models.

According to the first approach, a regression model with a set of explanatory variables is fitted on observed (cross-sectional) labour force participation rates. Then, projections for the evolution of participation rates are made on the basis of scenarios for the future evolution of the explanatory variables, including demographic characteristics. According to the cohort model approach, future participation rates are predicted by estimating an age profile of the participation behaviour of the most recent cohorts, appropriately weighted to take into account the (exogenous) demographic evolution. Because cohort models are also based on regressions, in what follows we refer to Houriet-Segard and Pasteels’s regression models as cross-sectional models.

Cohort models are widely used at official agencies like the OECD and the European Commission: for instance, labour force projections in the 2015 Ageing Report are based on a cohort model (European Commission, 2014). In their basic form, cohort models analyse participation rates separately by age group and gender (see for instance Beaudry & Lemieux, 1999; Aaronson, Fallick, Figura, Pingle, & Wascher, 2006; Fallick & Pingle, 2007; Balleer, Gomez-Salvador, & Turunen, 2009). Controls include only aggregate variables, where aggregation is specific to the different gender and age groups: typically, the share of individuals with high/low education, the share of individuals living in different types of households (for example with/without a partner, with/without children), the share of individuals with disabilities, measures of earning potentials such as the (age-specific) gender wage gap, measures of (average) household wealth, measures for business cycle effects, and proxies for the relevant welfare programs, such as the availability of childcare for women in childbearing years, and the fraction of individuals eligible for early retirement in older cohorts. Because each gender-age subgroup provides one unit of observation, the identification of the effects of each determinant can be obtained only by exploiting its variation over time. Time invariant cohort effects are also included. Aggregation over the different gender-age categories is obtained by weighting the participation rates in each subgroup by the population size of that subgroup.

Though cohort models are more sophisticated than cross-sectional models, they basically share common assumptions: (i) both modelling approaches are aggregate, meaning that the units of analysis are groups of individuals, and (ii) the evolution of the explanatory variables is external to the model. The difference lies in the level of aggregation, which in cohort models is taken down to individuals born broadly in the same period (typically, a 5-year or a 10-year window). Participation rates for different cohorts are then aggregated using population weights, while no weighting takes place in cross-sectional models. The results of the two approaches become similar once a full set of demographic characteristics is included among the covariates in cross-sectional models.

This group-level analysis however suffers from what is known as “ecological fallacy” (Robinson, 1950). The ecological fallacy arises when aggregate data are used to infer about the individual level parameters. Many investigators have shown that the aggregate and the individual-level coefficients seldom agree in either magnitude or direction. For instance, it is possible that the individual probability to participate is higher for the majority of individuals in group A, but group B displays a higher aggregate participation rate.⁶ Also, a characteristic might negatively impact participation rate at the individual level but display a positive association at the aggregate level.⁷ Avoiding the ecological fallacy is important if one wants to learn about the channels through which the determinants of participation work. This is particularly important when it comes to evaluating or devising policies aimed at fostering participation.

The most sophisticated cohort models get around the ecological fallacy problem by increasing the number of cells (individual characteristics), for instance taking into account differences in skills and family structure. As the number of conditioning variables increases, the approach converges to a microeconometric approach where the estimates are performed at the individual level. Still, the evolution of the weighting variables (for example skills and family structure) for the different groups/individuals is exogenous to the model.⁸

This is the strategy used, for instance, by Aaronson, Davis, and Hu (2012) and Aaronson, et al. (2014), who estimate the probability of being in the labour force at the individual level, separately by gender and age groups in order to allow the cohort effects and other controls to flexibly vary across age, gender, and education. They control for age, year of birth (i.e. cohort), race, education, the business cycle, plus include additional conditioning variables for specific demographic groups, like the real state minimum wage and the ratio of the average youth hourly wage to average adult hourly wage for the younger age groups, indicators for being married with children and married with a young child for the middle age groups, and gender-specific life expectancies for the older age groups.

As in the microeconometric approaches described above, in the dynamic microsimulation approach (Li & O’Donoghue, 2013) participation is also estimated (and projected) at the individual level. Indeed, the specification of the participation equation in a MSM can be identical to that of an individual-based, microeconometric cohort model. However, the latter are single-equation models, where the outcome of interest (say, the participation rate) is estimated on the basis of individual characteristics — to reiterate, these are just age and gender in the simplest macro-based models, while more individual controls are included in the most sophisticated micro-based models. These individual characteristics define the cells of interest. Aggregate participation rates are recovered as a weighted average of the participation rates in the different cells, using population shares as weights. These weights are then evolved over time based on external scenarios (for example demographic projections). By contrast, in MSMs there are more equations, explaining the evolution, at a micro level, of more variables, including the demographic and economic variables used as controls in the participation equation. Hence, MSMs allow to project participation rates considering the likely evolution of their determinants, at a micro level.⁹

In dynamic MSMs, each process is estimated at an individual level and feeds back into the other processes in the simulation. For instance, educational choices are simulated and predict, for every individual in the simulation, a level of education at any point in life. This level of education is then taken into account in the simulation of the (individual-specific) probability of entering a consensual union, participating in the labour market, etc. With K processes considered, the general form of a MSM is

where the outcome y_k for each process k is simulated for every individual i and time-step t based on the previous individual outcomes of all processes, additional individual characteristics Xi,t and scenario and policy parameters P_t.¹⁰

The advantage of the microsimulation approach is threefold. First, aggregation can be performed ex-post on any sub-population of interest (provided it can be identified using the variables included in the model). For instance, we could study the participation rate of mothers with at least one child aged three years old. In contrast, in a cohort model the analysis is restricted to the predefined cells (often, gender and age only). This advantage obviously fades away as the number of characteristics that are allowed to influence the participation rate (the number of cells) increases. Microsimulations are in this respect no different from micro-based cohort models.

Second, and most important, the model provides projections on a possibly large set of outcomes, and not only on one variable. This is valuable even if we are interested in just one outcome y1 (say, labour force participation): the model produces conditional forecasts of y1 given the evolution of other determinants y2, …, y_K, plus projections for the likely evolution of those determinants. In contrast, a cohort model provides projections for y1 under the assumption that all the variables which do not define groups remains constant, and conditional on external projections for the evolution of the variables that define groups (the weighting variables).

The third advantage is a consequence of the multi-process nature of dynamic microsimulations and relates to uncertainty assessment. Microsimulations allow an integrated assessment of the uncertainty surrounding the projections, based on the uncertainty of the underlying estimates for all the different processes that compose the model. On the other hand, uncertainty of the projections, even in the most sophisticated cohort models, can only come from the uncertainty surrounding the estimates of the single equation (for example participation). As this is generally not considered, uncertainty assessment in this type of models often boils down to running multiple scenarios about the exogenous evolution of the weights attributed to the different cells, but the choice of these scenarios, and their likelihood, remains outside the scope of the model. Unfortunately, uncertainty analysis is also generally neglected in dynamic microsimulation modelling, so that the advantages of an integrated assessment remain unexploited. An explicit and formal assessment of the uncertainty around our baseline projections is an innovative feature of our analysis. We elaborate on this point in Section 7.

Obviously, in the face of the benefits outlined above, there is a price to pay for the integrated microsimulation approach, in terms of (i) higher model complexity, and (ii) increased data requirements. If the sub-populations of interest are defined only in terms of exogenous variables such as gender and the age structure —considering, at a first approximation, the age structure as exogenous— the extra burden of a MSM might not be worth the costs. On the other hand, if the sub-populations of interest are defined in terms of clearly endogenous variables such as family composition, microsimulations offer a better and more comprehensive theoretical framework.

The MSM, based on Richiardi and Poggi (2014) and Leombruni and Richiardi (2006), receives as an input a representative sample of the population in each country, drawn from the 2012 wave of EU-SILC¹¹ data —the last available wave at the time the model was implemented— plus the estimated coefficients and tables for the scenario parameters. The microsimulation is composed of four different modules: (i) Demography, (ii) Education, (iii) Household composition, and (iv) Labour market. Each module is in turn composed of different processes, or sub-modules as plotted in Figure 4 (more details on the specification of each module are given in Appendix A).

Figure 4

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The model simulates the following state variables of the individuals: age, gender, region, educational attainment, labour market status (student, employed, unemployed, retired or other inactive), cohabitation status (for females only) and number and age of children (for females only). Table 2 lists all the equations estimated in the model, identifying outcome variables and determinants (the estimates, together with filtering conditions, are reported in Appendix A). In choosing the specifications for the different equations, we looked at the ‘usual suspects’ identified in the literature (see Del Boca & Wetzels, 2007; and Boeri, Burda, & Kramarz, 2008 for surveys), while taking two considerations into account. First, specifications are kept as lean as possible in order to limit the number of non-significant coefficients, which would increase the variance in the simulated outcomes once the uncertainty of the coefficients is taken into account (more on this in Section 7). Second, specifications are general enough to adapt to the different country characteristics. The equations are estimated on the 2005–2011 waves of the EU-SILC longitudinal panel, the maximum number of waves available at the time.

Causal relations can be highlighted as follows: the education module determines whether the individual continues as a full-time student or if s/he leaves education in t; this depends on age and gender, that is, on demographic characteristics only. If s/he leaves education, the household composition module determines —for women only— whether they move to cohabitation and whether they have a child; this depends on status at t-1, education, age and on having children already. Finally, men and women enter the labour market module where they decide first if they participate and then if they are actually employed, conditional on their family composition, education, and status at t-1. Then they age and go back to the household composition module or to the education module, depending on whether they have left full-time education in the past or not. Everything is conditional on Region of residence.

Inclusion of the lagged dependent variable in most processes is of course problematic: the effects of true persistence, as captured by the lagged status, are estimated with error (typically, overestimated) in presence of unobserved heterogeneity (UH), as discussed in Richiardi and Poggi (2014). Fully accounting for UH is however complicated, especially when the available data have a short longitudinal component, as in the EU-SILC. It is possible to show that including the lagged dependent variable, with high predictive power, and neglecting UH is optimal when one is interested in cross-sectional averages, as in our forecasting exercise —see Richiardi (2012). Clearly, using the MSM for analysing individual trajectories would require more caution in the treatment of UH, and possibly also the inclusion of more lags in the specification of the different processes.

Individuals effectively enter the simulation at age 17, the first age observed in EU-SILC data. The initial population is then evolved forward in time from 2013 to 2050 according to the estimated coefficients and the scenario parameters. Time is discrete, with one period corresponding to one year: correspondingly, all models are discrete choice models (either probit or multinomial probit) with the outcome variable being the probability of occurrence of a given event/transition. In each period, agents first go through the Demographic module, which deals with evolving the population structure by age, gender and area, based on Eurostat official demographic projections. Then, individuals above an individual-specific age threshold retire. Retired individuals remain in the simulation until they die but nothing else happens to them, except the ageing process. As in Richiardi and Poggi (2014), alignment of the population to the official statistics is made by randomly removing individuals from their age-gender cell when the concentration of the cell is higher than in the demographic projections for the specific year, or randomly cloning individuals when the concentration is lower. Students enter the Education module. If they remain in education, nothing else happens to them until the next period. If they exit education, they join the ranks of potentially active individuals. Females enter the Household composition module, where it is determined whether they form or remain in a union and whether they give birth to a child. Then, they join males in the Labour market module, where participation and employment are finally determined.

We now discuss the most important assumptions in the construction of the model, which, as in any model, is based on a number of simplifications.

Retirement

Given that the primary focus of the microsimulation exercise is not on the elderly, individual behaviour with respect to retirement decisions is kept as simple as possible, while preserving individual heterogeneity. When individuals first enter the simulation, they draw a percentile in the distribution of retirement age. This determines a time-specific individual threshold for retirement (the threshold follows the evolution over time of the average retirement age). In each year, individuals check whether their age is above their (time-specific) threshold: if this is the case, they retire. This approach allows to abstract from the details of the specific pension reforms implemented in each country and is motivated by the observation that the average age of retirement changes shows a high degree of persistence, as depicted in Figure 5 and Figure 6 (the within-country variance remains substantially constant).

Figure 5

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Figure 6

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The model has the following scenario and policy parameters (Table 3):

Uncertainty regarding a model’s projections can arise from a variety of reasons (Bilcke, Beutels, Brisson, & Jit, 2011; Creedy, Kalb, & Kew, 2007). In particular, sources of uncertainty are generally distinguished in (i) input data, for instance due to sampling errors in the initial population, (ii) model structure, that is the validity of the general modelling approach used (also called “methodological uncertainty”), (iii) model specification, which concerns the choice of the covariates and the functional forms used, and in particular the crucial assumption that any regularity observed in the data will not break up in the future, (iv) model parameters, pointing to the imprecision of the estimates and/or externally provided parameters, and finally (v) Monte Carlo variation of the model output, which originates from the fact that the simulated aggregate quantities are also imprecise estimates of the theoretical aggregate quantities that the model implicitly defines. None of the above sources of uncertainty is generally considered in microsimulation studies, although this is recognised and criticised (see for instance Goedemé, Van den Bosch, Salanauskaite, & Verbist, 2013). However, “[t]he calculation of confidence intervals around model results that account for all sources of error remains a major challenge” (Mitton, Sutherland, & Weeks, 2000, p. 4).¹⁸

In our case, source (i) should be limited, due to the use of the sampling weights provided in the EU-SILC data. Sources (ii)–(iii) are left unexplored, and we make the common assumption that the model is well specified. Measures of fit for each estimated equation are reported in Appendix A, and they are generally appropriate. Monte Carlo variation of the model outcome (source v) can be brought down to negligible by appropriately scaling up the simulated population size.¹⁹ The remaining source of uncertainty that needs to be addressed is therefore parameter uncertainty, stemming from sampling errors in estimation (source iv). There are two approaches that can be used to deal with this uncertainty (Creedy et al., 2007). The first is what we might label “brute force” and prescribes to bootstrap the coefficients of the estimated equations from a multivariate normal distribution (in the case of probit or multinomial probit regressions) with mean equal to the point estimate, and variance-covariance matrix equal to the estimated variance-covariance. Bootstrapping needs to be performed only once, at the beginning of the simulation: the entire simulation is then performed with the bootstrapped values of the coefficients. The second approach provides an approximation by assuming from the onset a normal distribution for the resulting confidence intervals, requiring many fewer draws from the parameter distribution. We follow the first approach and draw 1,000 sets of parameter values from their estimated multivariate distribution, for each country in the baseline scenario. Then, for every simulation time, we provide confidence intervals based on a kernel density estimation of the resulting distribution. The results, together with some additional remarks on the uncontrolled sources of uncertainty and the scope of the microsimulation exercise, will be presented in Section 8.3. Here, we only stress once again that the objective of dynamic microsimulation modelling is not forecasting per se, but rather the identification of the forces that are at work at the individual level, and the analysis of how these forces interact in shaping the particular societal outcome of interest. The projections should therefore be considered ceteris paribus exercises with respect to all the dynamics that are not explicitly modelled, and for which an assessment of the uncertainty must rely on external knowledge.

In this paper, we have presented a dynamic MSM of educational choices, household formation and labour market outcomes (participation and employment), that we have then applied to derive medium- and long-term projections for a selection of EU member states characterised by low labour force participation rates (Italy, Spain, Greece, Hungary and Ireland, in decreasing order of population), with a high-participation benchmark represented by Sweden.

The microsimulation approach has several advantages over simpler and more common methodologies. Most importantly, it produces forecasts not only on the outcomes of interest (participation and employment in our case) but also on their determinants (for example educational attainments, household composition). Related to this, it allows a more comprehensive assessment of the uncertainty around the projections, given that the evolution of the determinants is endogenous to the model rather than being exogenously provided, though this is very rarely done in microsimulation modelling. Finally, having the individual rather than a group of individuals as the basic unit of analysis allows to study the dynamics of any sub-population of interest (provided it can be identified using the variables included in the model), rather than being constrained by an ex ante choice of a (generally limited) set of characteristics.

From a methodological perspective, two features of our study are noteworthy. First, the model is, to the best of our knowledge, the first dynamic microsimulation exercised to be applied simultaneously to a number of different countries, providing homogenous results which can be directly compared. Second, we offer a thorough discussion of the uncertainty surrounding our projections, quantifying both the sample size required to keep Monte Carlo variation sufficiently low, and the effects of sampling errors in the estimation of the underlying equations.

Results of the baseline scenario identify a general trend of increasing participation rates towards the very high Swedish levels, which accelerates in the 20–64 population after 2030 when older cohorts are finally replaced by younger cohorts with higher participation rates. The only exception to this general pattern is Hungary, where participation rates of mothers are particularly low and, given the recent trends as observed in the EU-SILC data, are not projected to increase. However, Sweden will not be joined by any other country in our sample in meeting the Europe 2020 target of a 75% overall employment rate by 2020, though Ireland will be close. According to the projections, the 75% target will be approached only at the end of the simulation period, by 2050, in all countries with the exception of Hungary, whose employment rate is projected to increase only to slightly more than 70%.

These projections are not too dissimilar from other forecasting exercises in the literature. In particular, we reach the same conclusions of the 2015 Ageing Report (European Commission, 2015), in the aggregate, with respect to Greece, Spain and Hungary, while we are less pessimistic than the 2015 Ageing Report with regards to Italy and Ireland. However, our microsimulation approach permits a finer disaggregation of the results, which turns out to be crucial in understanding the dynamic causal mechanisms at work, as explored further in our companion paper (Richardson et al., 2016).

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Author details

1. Ross Richardson

   Institute for New Economic Thinking at the Oxford Martin School, United Kingdom

   For correspondence

   r.richardson05@alumni.imperial.ac.uk

2. Lia Pacelli

   Universita’ di Torino and LABORatorio Revelli, Italy

   For correspondence

   lia.pacelli@unito.it

3. Ambra Poggi

   University of Milan-Bicocca and LABORatorio Revelli, Italy

   For correspondence

   ambra.poggi@unimib.it

4. Matteo Richiardi

   Institute for New Economic Thinking at the Oxford Martin School and Nuffield College, Italy

   For correspondence

   matteo.richiardi@spi.ox.ac.uk