Subject 1: Economic Impact of Ageing


Subject: Economic Impact of Ageing


Duration: 3 years, Le Mans (France)



  • X. Fairise
Professor of Economics

GAINS-TEPP (FR-CNRS 3435), Le Mans University

Institut du Risque et de l’Assurance du Mans

  • A. Popier

ass. Pr of Mathematics

LMM, Le Mans University




The aging of the population in most developed countries has a considerable impact on the savings choices of economic agents. The current system of social protection, and more specifically the PAYG system, risks becoming unsustainable in the context of a weak economic growth characterized by secular stagnation. The scenario of secular stagnation, if it is not certain, has to be considered. To ensure a complementary retirement, economic agents will be encouraged to increase their savings and more specifically to make long-term investments, providing additional income at the time of retirement. This increase in private household savings is likely to generate low interest rates over the long term. This raises questions the ability of central banks to use monetary policy, via lower interest rates, to stimulate the economy in the event of a major recession.


The aim of the thesis is to construct general equilibrium models taking into account 1) different demographic scenarios, 2) changes in public debt, and 3) integrating different institutional characteristics of European economies (imperfections in labor markets and goods). The next step is to assess the ability of monetary policies to stabilize the economy.

A second step will consist in proposing complementary or substitution, budgetary or fiscal policies and in giving a quantitative evaluation.


The study will be conducted with dynamic models of general equilibrium in continuous time and will use the methodology developed by Achdou et al. (2017). It will be necessary to highlight the different demographic scenarios and to model the agents' savings choices with possible consideration of wealth inequalities (heterogeneous agents). It will then be a question of modeling monetary policy (Taylor's rule) and of considering various budgetary and fiscal instruments to correct excess savings. The aim is also to produce analytical results allowing to characterize in particular the saving behaviors of the agents or the asymptotic distribution of the richness of the agents.




  • Kaplan, G., Moll, B., and Violante, G. «Monetary Policy According to HANK», Mimeo, 2017.
  • Carvalho, C., Ferrero, A. and Nechio, F. «Demographics and Real Interest Rates: Inspecting the Mechanism», FEDERAL RESERVE BANK OF SAN FRANCISCO WORKING PAPER SERIES, Working Paper 2016-05.
  • Carvalho, C. and Ferrero, A. «Monetary Policy and the Demographic Transition», Mimeo, 2012.
  • De Nardi, M., Imrohoroglu, S., and Sargent, T., « Project US Demographics and Social Security », Review of Economic Dynamics, 1999.
  • Achdou, Y.., Han, J., Lasry, J_M., Lions, J-M.,and  Moll,B. « Income and Wealth Distribution in Macroeconomics: A Continuous-Time Approach, » NBER Working Papers 23732, National Bureau of Economic Research, Inc, 2017


For any extra informations: xavier.fairise @


Download the file «diffusion_english_ageing.pdf» (412.3 KB)

Subject 2Online estimation of state space models, with applications in Economics and Finance.


Duration: 3 years, Le Mans (France)



F. Karamé

Professor of Economics

GAINS-TEPP (FR-CNRS 3435), Le Mans University

Institut du Risque et de l’Assurance du Mans

DynareTeam (Cepremap)

A. Brouste

Professor of Mathematics

LMM, Le Mans University




In Economics as in many other disciplines, one often use state-space models, ie that contain unobserved variables (solved DSGE models for instance). These representations are difficult to estimate because they are concerned by all the usual numerical problems related to estimation (size, slow calculations, local solutions, ...).


The one-step online approach has the double advantage of circumventing the usual numerical problems and providing efficient estimators. Nevertheless, these properties have been obtained for rather simple models and can not therefore be applied directly to more complex models such as state-space models.


The aim of the thesis is to extend this online estimation method to state-space models. An efficient and fast estimation of these models represents an important breakthrough, especially if it can be implemented transparently for a user. The developed method will also be implemented to macroeconomic or financial issues, using more complex and better specified models.


The thesis will include three objectives:



1. Generalize the properties of the estimators of the one-step online estimation method obtained for simple models in the case of state-space models. This first contribution will be original insofar as the one-step online method has never been applied to this category of models. In particular, we are interested in linear Gaussian model-state models and Markovian regime switching models, which are currently very popular and useful in the economic literature. The ease of implementation of this approach should ensure an international and multi-disciplinary interest in this method. Indeed, estimating such models currently requires very large computation times and multiple robustness exercises before using the estimated model.


2. Apply this method to economic or financial issues using better specified models. The second originality of our approach is that once the limit of the practical implementation of the estimation has been pushed back, it will be possible to improve the current models.



3. Extend the online method to non-Gaussian nonlinear models.



  • Doucet, A., N. de Freitas & N. Gordon, 2001, Sequential Monte Carlo Methods in Practice, New-York Springer.
  • Gasparyan, S.B. and Y.A. Kutoyants, 2015, An example of one-step MLE-process in volatility estimation problem, Izvestiya Natsionalnoi Akademii Nauk, Armenia : Matematika, 50(3), 71-76.
  • Gordon N., D. Salmond, A. Smith, 1993, Novel Approach to Nonlinear and Non-Gaussian Bayesian State Estimation, IEEE Proceedings-F, 107-113.
  • Hamilton J.D., 1989, A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle, Econometrica, 57(2), 357-384.
  • Kalman, R.E., 1960, A New Approach to Linear Filtering and Prediction Problems, Transactions of the ASME-Journal of Basic Engineering, 82, 35-45.
  • Kantas N., A. Doucet, S. Singh, J. Maciejowski, N. Chopin, 2015, On Particle Methods for Parameter Estimation in State-Space Models, Statistical Science, 30(3), 328-3510.
  • Krishnamurthy V. and T. Rydén, 1998, Consistent estimation in linear and non-linear autoregressive models with Markov regime, Journal of Time Series Analysis, 19, 291-307.
  • Kutoyants, Y.A. and A. Motrunich, 2016, On multi-step MLE-process for Markov sequences, Metrika, 79(6), 705-724.
  • Le Cam L., 1956, On the asymptotic theory of estimation and testing hypothesis, In: Proceedings of 3rd Berkeley Symposium I, 355-368.
  • Moulines E. R. Douc and T. Rydén, 2004, Asymptotic properties of the maximum likelihood estimator in autoregressive models with Markov regime, The Annals of Statistics, 32(5), 2254-2304.
  • Veretennikov A., 1998, On parameter estimation for ergodic Markov chains with unbounded loss functions, miméo.


For any extra information:


Download the file «diffusion_english_online.pdf» (434.5 KB)

How to apply

The application, including the usual supporting documents such as :

  • Your CV,
  • A description of your MASTER courses, with your results, projects and master dissertation,
  • Letters of recommendation.

Before June 30th 2019 23h59

For more informations:

  • About subject n°1 : xavier.fairise @
  • About subject n°2 : . (frederic.karame @

Pre-selected candidates will be auditioned in le Mans on July 9th 2019.

To apply, please send all informations please follow the website of Doctoral School EDGE.