Page 39 - Contributed Paper Session (CPS) - Volume 3

CPS1941 Jang S.
Our model allows obviously to overcome the drawbacks of Nagin’s model.
The standard deviation of the uncertainty can vary across groups and the
trajectories depend in a nonlinear way on the covariates. Since our model is
just a generalization of Nagin’s finite mixture model, a lot of its main features
and properties remain the same as in Nagin’s model.

4. A data example
For the following example, we use Luxembourg administrative data
originating from the General Inspectorate of Social Security, IGSS (Inspection
gnrale de la scurit sociale). The data have previously been described and
exploited with Nagin's basic model by Guigou, Lovat and Schiltz (2010, 2012).
The file contains the salaries of all employees of the Luxembourg private sector
who started their work in Luxembourg between 1980 and 1990 at an age of
less than 30 years. This choice was made to eliminate people with a long career
in another country before moving to Luxembourg. The main variables are the
net annual taxable salary, measured in constant (2006 equivalent) euros,
gender, age at first employment, residentship and nationality, sector of
activity, marital status and the years of birth of the children. The file consists
of 1303010 salary lines corresponding to 85049 employees, capped at
7577 EUR (2006 equivalent euros) per month.
We will not present here an exhaustive analysis of the whole dataset, but
an illustration of the possibilities of our generalized mixture model and its
differences from Nagin's model. We concentrate on the first 20 years of the
careers of the employees who started working in Luxembourg in 1987, giving
us a sample of 1716 employees. We compute typical salary trajectories for
them, taking into account the gender of the employees, as well as their
dependancy from the GDP of the country. Let us first highlight the differences
with respect to Nagin's extended model.
Figure 1 shows a three group solution modeled by Nagin's generalized
model representing the salary of employees in Luxembourg during the first 20
years of their professional career. We see that for the low salary group women
and men are gaining exactly the same salary (with the consequence that there
appears just one salary trajectory for the two lower salary groups on the graph
instead of two) whereas in the middle and high salary groups, men earn more
than women. Due to the limitations of the model, the evolution of the salaries
seems to be exactly the same for men and women; their salary trajectories are
strictly parallel.

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