2. Estimates

1. Education

The Education module is comprised of two sub-modules: (i) Enrolment, and (ii) Achievement. The model is aligned to external forecasts with respect to the share of individuals with high education, in each country. This means that the simulation meets those aggregate targets exactly, and then distributes the educational achievements among those who exit education based on their individual characteristics.

1.1 Enrolment
The first process in the Education module determines whether students continue education. Then, if a student leaves education, his/her level of completed education is deermined, distinguishing between Low (International Standard Classification of Education –ISCED- 0, 1 and 2), Medium (ISCED 3 and 4) and High (ISCED 5 and 6) education. This automatically takes care of drop-outs, that is, individuals who exit education at a late age given their level of completed education. Exit from education is forced at age 30.
Enrolment is modelled as a function of gender, age, and region, and is estimated on students aged 18-29 (inclusive).

Probit Estimates of the probability of remaining in education, Education module. Population at risk: students aged 18-29.
Probit Estimates of the probability of remaining in education, Education module. Population at risk: students aged 18-29.

1.2 Achievements
Once an individual exits education, he or she is assigned an educational attainment. The model is a multinomial probit as a function of gender, age, and region; it is estimated on individuals aged 18-30 (inclusive) who made the transition from being a student (at time t-1) to not being a student (at time t).

Multinomial probit estimates of the probability of  having attained a specific educational level, Education module (base outcome is education = Medium). Population at risk: former students aged 18-30 who have just left education.


2. Household composition

The Household composition module is applied only to females, the reason being that family composition barely matters for the labour participation decisions of men. The module is comprised of two processes: (i) living in consensual union, and (ii) maternity.

2.1 Living in consensual union.
This process is estimated for all women aged 18-75 who are not in education, and describes both union formation and union dissolution (due to any cause: divorce, widowhood, etc.). To limit endogeneity concerns, the main explanatory variables enter the specification as lags: lagged labour market participation status (active or retired), lagged student status, and lagged maternity status (whether or not the woman has children aged three or below). Additional controls include age and education.


Probit estimates of the probability of  living in consensual union, Household composition module. Population at risk: females aged 18-75 who are not students.

2.2 Maternity
Females aged 18-45 (inclusive) enter the maternity module, where it is determined whether in the current year they have a new baby (the possibility of giving birth to siblings is not considered).The specification controls for three policy parameters: the amount of regional childcare spending per child, the amount of parental leave benefits (expressed in % of GDP), and the availability of part-time jobs. On leave benefits are regulated by a national law, and we can safely assume that they are exogenous (data come from the OECD Family database). As for childcare, we use a measure of public provision of childcare, which under the hypothesis that policy makers respond only sluggish to changes in the demand for childcare, can also be considered as exogenous. The data we use also come from the OECD Family database, and are available only at the national level. Finally, we use the share of part-time work among women in the 18-45 age range in the region as a proxy of the availability of part-time opportunities. Under the assumption that use of part-time in firms is mainly driven by social norms / managerial culture, this is also exogenous.

The specification also controls for one alignment variable: the overall (national) fertility rate. In the simulation, this is derived from the official demographic projections. Including it among the covariates takes care that the implicit fertility rate coming from the simulations tracks the official projections – indeed, our process becomes a model of differential alignment around the target given by the demographic projections, whereas fertility is allowed to vary across sub-groups, as defined by gender, age, region and the other explanatory factors. Table B.4 reports the estimation results. Any further differences between the overall fertility rate coming from the simulation and that defined by the demographic projections is adjusted by an additional alignment process.

To exploit cross-country variation in policy variables, the model is estimated on pool data for all countries, with regional dummies. Interaction between regional dummies and the variables of interest are used to permit differences in the returns of covariates across countries.


Pooled probit estimates of the probability of having a child, Household composition module. Population at risk: females aged 18-45 who are not students.

The fact that fertility (and mortality) rates are exogenously given (those embedded in the projections) is potentially annoying given our focus on female labour supply: policies aimed at providing services to women of childbearing age – childcare for instance – which are meant to sustain labour force participation, might also foster an increase in maternity, which feedbacks negatively into labour supply. The alternative is having a fully-fledged microfounded demographic module, which is outside of the scope of the present model. To get around this problem in a simple way, we allow flags to be switched on when a new baby is born, without new individuals actually entering the simulated population. The model can then be run either by aligning the number of flags switched on to the number of new babies born each year according to the official demographic projections, which ensures internal consistency of the model at the cost of treating fertility rates as exogenous, or without alignment – that is, allowing women to have more children than the numbers predicted by the official projections.


3. Labour market

The labour market module is comprised of three processes: (i) retirement, (ii) participation, and (iii) employment. Each process is estimated separately for men and women.

3.1 Retirement.
A differential  between the mean retirement age and an individual retirement age is drawn, for each simulated individual, when he or she reaches the age of 45 – which we consider as the minimum retirement age – from a normal distribution with mean 0 and a standard deviation equal to that observed in the EU-SILC data.  Then, we specify in the scenario parameters the evolution of the mean retirement age, by gender (as a default, we simply extrapolate linearly from the data). Finally, at each simulation time we compute an individual retirement threshold equal to mean retirement age plus the individual differential. Individuals retire if their age is above the threshold. The table below reports the estimated mean and standard deviation of retirement age:


Distribution of retirement age.

3.2 Labour force participation.
Labour force participation is estimated separately for men and women, conditional on not being retired nor a student. Female participation rates are also estimated separately for women with children aged 3 or under, women with children age 4-12, and women without children or with grown-up children. The specification for females with very young children (0-3 years old) closely resembles that for maternity, without the fertility rate and with the addition of a 0-1 indicator for the crisis (2009 and beyond). In the simulations, the coefficient of this variable is a scenario parameter to model the dynamics of the recovery. As a default, it is decreased linearly up to 2020 (2030 for Greece), when we assume that the effects of the crisis will be over. The specification for females with children aged 4-12 does not include the family related policy variables, but still includes the availability of part time. The specification for women without children or with older children also does not include the availability of part-time. The model is estimated on pooled data for all countries, with country interactions introduced when appropriate (this explains why some coefficients are equal for all countries, while other differ).

Probit estimates of the probability of being active, Labour market module. Population at risk: females aged 18-74 who are not students nor retired.

The model for males is simpler, as it does not include neither family related policy variables, nor the availability of part time, nor cohabitation status.

Probit estimates of the probability of being active, Labour market module. Population at risk: males aged 18-74 who are not students nor retired.

3.3 Employment
Employment is modelled conditional on being active, and is based on a common specification for both females and males. It features the usual set of explanatory variables, with the exclusion of family composition. Because the microsimulation is a model of labour supply rather than labour demand, the aggregate unemployment rate (which is the result of the interaction between labour supply and labour demand) is aligned to a scenario parameter, which is allowed to vary over the time: as a default value, it is considered that the overall unemployment rate will linearly decrease to its pre-crisis level (computed as the average unemployment rate in the 2005-2007 period). The overall unemployment rate also enters the equation as a control variable, making the employment process a model of differential employment (analogously to the maternity process).

Probit estimates of the probability of being employed, Labour market module.. Population at risk: active people aged 18-74.


4. Individuals aged 17

Individuals enter the simulation at age 17 without a previous history, and as such they cannot enter the modules described above. Therefore, the status of individuals aged 17 is assigned with a simple probabilistic model, which specifies the probability of being a student, the probability of being active, given that an individual is not a student, and the probability of being employed, given an individual is active. Individuals who are not student are assigned an education level based on specific probabilities. The evolution of these probabilities is exogenously controlled by the user.

Distribution of states for individuals aged 17.


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Estimates performed by Ambra Poggi (University of Milan Bicocca)


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