Linking static and dynamic microsimulation models
By Matteo Richiardi (2020)
Linking a static tax-benefit model as EUROMOD to a dynamic microsimulation model is useful to reconstruct a budget constraint for each agent in the simulated population, in correspondence of any simulated behaviour and policy scenario. Agents can be individuals, in which case the main variable that EUROMOD can provide is household disposable income in correspondence to any level of labour supply of the household members. Agents can also be firms, in which case the main EUROMOD variable of interest would be total labour cost for each level of employment.
Given that the problem is in all effects a missing variable issue, it can be dealt with by using EUROMOD as a donor dataset to the dynamic microsimulation.
More precisely, EUROMOD is run prior to simulation, with the chosen tax & benefit parameters. This produces as many EUROMOD tables as the number of EUROMOD configurations (that is, if a policy change is envisaged in 2030, there will be two tables, one to be used up to 2030, and another one from 2030 onwards). For every given parameter configuration, EUROMOD computes, for each household in the EUROMOD sample, the corresponding disposable household income.
Moreover, for each individual in the EUROMOD sample, EUROMOD computes the total contributions paid by the firm, which added to the gross (market) wage constitute the total cost that the firm is incurring for employing the individual (this might be needed if the dynamic microsimulation also has a labour demand module).
Imputation is made by minimising the distance between the characteristics of the simulated household, for given levels of labour supply, and the characteristics of the EUROMOD household. A typical list of the characteristics to be matched is:
- Individual characteristics (for each partner): sex, age, health status, education, potential earnings (as estimated by a wage equation), work sector, number of hours worked.
- Household characteristics: region, number and age of kids.
Most of these variables are discrete, allowing for a perfect match.
The number of hours worked h_i is continuous (or discretised at integer steps) in the EUROMOD data (h_i^R), while it can be a discrete value in the simulated data (h_i^S). This is for instance the case if the dynamic microsimulation includes a discrete choice labour supply module. In this case, EUROMOD data need to be discretised to make it homogeneous with the simulation (~h_i^R): for instance, 0-4 hours will be considered as 0 hours, 5-14 hours as 10 hours, 15-24 hours as 20 hours, etc.
EUROMOD data contain information on gross or market income W_i^R (yem+yse in EUROMOD). To be compared to potential earnings (hourly wages) as computed in the simulation (w_i^S), it needs to be divided by the number of hours worked h_i^R (lhw in EUROMOD). Note that the recorded number of hours and not the reclassified number of hours should be used.
Hence, exact matching is in principle possible for all variables (included the reclassified number of hours worked), with the exception of unit wage, where minimum distance matching can be implemented. For instance, if there are 10 households in the EUROMOD data that match the discrete characteristics of the simulated household, the one with the closest unit wage to the simulated household will be used as a donor. As there are possibly two components in the household, the sum of the squared difference between the simulated and the EUROMOD unit wages for the two partners will be used as a measure of distance:
Exact matching will be relaxed if no households with the relevant characteristics are present in the EUROMOD sample.
EUROMOD donors are used, as already noted, to input disposable household income and total labour cost for the firm, for any given level of labour supply of the simulated household. In order to do this, the disposable household income and labour cost for the firm observed in EUROMOD need to be corrected to take into consideration the fact that matching in unit wages is not exact. As a first approximation we can compute the total gross-to-net conversion rate, dividing the disposable household income observed in the EUROMOD sample by the sum of the market wages of the two partners (the household index is omitted for ease of notation):
where Y is household disposable income, and W_M and W_F are respectively the gross (market) wages for the male and the female partners.
We then apply the conversion rate to the simulated total market income, for any given level of labour supply of the simulated household (the choice index is also omitted for ease of notation):
A corresponding labour cost for the firm is computed. First, the labour cost C_i^R for the EUROMOD donor is reconstructed (if the variable is not already present), by adding the social contributions paid by the firm to the gross wage. The labour cost is divided by the observed number of hours to obtain a unit labour cost:
The EUROMOD unit labour cost is then applied to the simulated number of hours supplied, to obtain the simulated labour cost*:
This adjusts for the difference between the EUROMOD hours and the simulated hours (due to discretisation of the simulated hours worked).
*Note that the simulated labour cost is also equal to:
