**International Center for the Employment Prospective in Geosciences and Environment** (CIPEGE Center):

Elisabeth Verges (CNRS-Orleans), Christelle Garrouste (UO), E. Courtial (UO), Y. Toure (UO)

The purpose of the CIPEGE is to develop a strategy to enhance the employability of French graduates in a field that is both a key driver and a significant target of these new trends, namely Earth Sciences. The aim is to provide French universities with a predictive tool to adjust efficiently their skills’ supply capacity with the demand forecasts at the European level. By the end of 2014, the theoretical part of the CIPEGE tool had been successfully developed and is now validated. Encounters with influential industrials in the field of Earth sciences are planned in the second half of 2015 to present the theoretical tool and the preliminary results from the empirical estimations. These meetings will serve at validating the pertinence of the tool for industries and at fine-tuning the output parameters to be further estimated and reported from the estimation of the model.

Moreover, the interdisciplinary objective has been fully achieved with a successful partnership between the Laboratoire d’Economie d’Orléans (LEO) and the PRISME laboratory (specialized in automatics methods) of the university of Orléans. Finally, an agreement has been passed with the French Ministry of Higher Education and Research to extract annually all necessary student-based education data to estimate the transition paths probabilities from first year enrollement to graduation. A second agreement has been passed with Cambridge Econometrics to exploit their E3ME (Economics, Environment and Energy Model for Europe) model to estimate the matching model in Earth sciences for France, controlling for European supply and demand trends.

#### Results

The employability of French ES graduates is measured and forecasted using a labour market micro-econometrics model, controlling for European macroeconomic trends. The task of this WP is then to track the reference trajectory of the forecasted employability for the French graduates in Earth Sciences (ES). This objective can be viewed as a tracking problem from a control theory perspective. Among the existing advanced control laws, Model Predictive Control (MPC) is a mature control strategy well-adapted to deal with tracking problems (Alessio [2009], Camacho [2007]). Initially developed for linear systems in the 70s, MPC had extensively been studied for nonlinear systems with constraints and successfully been applied in numerous industrial domains (Alessio [2009], Qin [2003]). The MPC strategy is based on the receding horizon principle and is formulated as solving online a nonlinear optimization problem (Camacho [2007]). The success of MPC in several industrial sectors is due to the easy way to formulate the control objective in the time domain and also to the ability to handle constraints (Qin [2003]). A wide variety of applications has been reported in the literature but no application in labor economics exists to our knowledge. MPC is based on the direct use of an explicit model to predict the future behavior of a process. This model plays a crucial role in the MPC strategy. In our case, an econometric-based model is used to forecast the behavior of the process considered (the flow of ES graduates in France) over a finite prediction horizon.

Modeling

As stated above, the employability of French ES graduates is measured and forecasted using MPC, a labour market micro-econometrics model, controlling for European macroeconomic trends. In the context of CIPEGE tool, employability is defined as the capacity of a French Earth Sciences graduate to be employed at a fulfilling job that enables him or her to make use of the skills acquired during the training, given the demand trends of the relevant sectors of activity at the European level. The influence of international environmental and economic chocks on the demand for skills in ES is captured by the stock of unemployed ES graduates in France at current time t on the European market , which is estimated using an extended version of the energy-environment-economy model of Europe (E3ME), developed by Cambridge Econometrics, to forecast skills supply and demand in Europe (Wilson [2010]). All other parameters of the model are estimated using the 1990-2011 microdata collected by INSEE (French National Institute of Statistics and Economic Studies) through the Employment Survey.

In detail, the basic concepts of MPC are the explicit use of a model to predict the process behavior over a nite prediction horizon Np and the minimization of a cost function with respect to a sequence of Nc controls where Nc is the control horizon. At the current instant t (see Fig. 1), the process output is measured and the MPC algorithm computes a sequence of Nc control inputs by minimizing the tracking error (difference between the reference trajectory and the predicted model output) over Np. Only the first element of the obtained optimal control sequence is really applied to the process. At the next sampling time, the finite prediction horizon moves a step forward, the measurements are updated and the whole procedure is repeated.

Given its formulation in an optimization problem, MPC is well suited to take into account constraints. It is the most effective way to satisfy all kinds of constraints (on states, inputs or outputs) by adding them explicitly to the optimization problem.

The reference trajectory: testing and calibrating the model

This reference has been determined off-line by estimating model parameters using E3ME outputs and French microdata (INSEE Employment Survey). The following figure (see Fig. 2) describes the future general trend of employability in ES in France at level j = 3, i.e Bachelor degree.

The internal model uses data from a student tracking survey collected by the Students’ Life Observatory (OVE), which describes the transition trajectories of Master graduates 3 years after graduation, by degree field; university administrative records of the number of intakes and graduates, per year; data from ES Master programmes’ curricula; and complementary data from the report by Varet [2008]. The data collected are represented on Fig. 3. As explained above, the reference trajectory is calculated using INSEE and E3ME data. The inputs are obtained from the OVE data and the administrative data. As can be seen, the trajectory of the measured employability is very nonlinear.

According to the same modeling procedure described above, the state-space representation of the employability model at Master degree level can be calculated as well. Due to the fact that parallel admissions are possible in the second year of the Master, the number of graduated students at level j = 5 is impacted by the number of students enrolled at level j = 4 and j = 5, at time t. Thanks to an identication procedure, we obtained a model which matches the process with a relative error of 9:33% (see Fig. 4).

Predictive Control

The econometric model-based predictive control developed here is implemented. The simulation was performed

under various conditions. The future tracking errors are more and more weighted in order to give importance to the final objective, i.e. the desired employability at the end of the prediction horizon, and this, at each sampling time. The reference employability is obtained applying our model, using again INSEE and E3ME data. Several simulations were carried out according to different horizons of control and prediction. The prediction horizon Np = 5 seems to be the best compromise between the tracking accuracy, the intrinsic dynamic (the current control will impact the employability of Master degree graduates in at least five years) and the stability of the controlled system. We can see (see Fig. 5) that the process output tracks the reference trajectory by remaining within the range of uncertainty. The number of students enrolled is more relevant and gives a very interesting information to university and policy makers.

These simulations show that the approach of predictive control for economics purposes is feasible and leads to useful results from a social, educational and economic point of view.

Conclusion

For the first time, Model Predictive Control was combined with an econometric model of employability. The MPC enables to take into account disturbances and modeling errors through an internal model control, which complements eciently the error correction model (ECM) implemented in the econometric model used to measure the reference trajectory. Moreover, combining the econometrics approach and the MPC yields a predictive tool where the control inputs are held exogenous to the optimization process, which makes it possible to test an unlimited range of possible interventions. The calculated control inputs can then serve as potential action-tools for policy makers. Furthermore, because this approach is very flexible, it can easily be adapted to other disciplines (chemistry, medicine, …) but also to other countries, provide that the input data (ie INSEE type) are available. Hence, the statistical capacity (in terms of error control), the economic relevance (in terms of control inputs formulation) and the unlimited potentialities for application expansions of the CIPEGE tool, makes it an attractive and valuable decision tool for universities and policy makers.

References

A. Alessio , A. Bemporad Nonlinear Model Predictive Control. Lecture Notes in Control and Information Sciences, vol 384, 2009.

E. Camacho and C. Bordons. Nonlinear Model Predictive Control: An Introductory Review. Assessment and Future Directions of Nonlinear Model Predictive Control, LNCIS 358. Berlin: Springer-Verlag Berlin Heidelberg, pages 1{16, 2007.

S.J. Qin, T. A. Badgwell. A survey of industrial model predictive control technology. Control Engineering Practice, vol11, pages 733{764, 2003.

J. Varet. Prospective de l’emploi dans le domaine des geosciences a l’horizon 2020. Orleans: BRGM, 2008.

R.A. Wilson et al. Skills supply and demand in Europe: medium-term forecast up to 2020. Thessaloniki: Cedefop, 2010.