Christophe Gaillac will defend his thesis on economics next Wednesday, March 3, 2021 at 03:30 PM, by Zoom meeting.
Title: Some Problems Related to Random Coefficients Models and Data Combination in Economics
Supervisor : Eric Gautier
To attend the public lecture, please contact Eric Gautier
- Marine Carrasco, researcher at University of Montréal
- Enno Mammen, researcher at University of Heidelberg
- Karine Van Der Straeten, Senior researcher CNRS, TSE
- Jean-Pierre Florens, Emeritus professor, University of Toulouse 1 Capitole - TSE
- Eric Gautier, Professor, University of Toulouse 1 Capitole - TSE
Among the elements explaining the behaviour of economic agents, there are heterogeneous characteristics which are unobserved by the economist. They can be modelled as random vectors. For example, in a linear model where the coefficients are random, the dependent variable can be affected differently by the regressor according to the individuals: the parents’ income might have different effects on student’s achievements, for reasons which are unobserved. Thus, the first three chapters of this PhD thesis study some random coefficients models, with multiple sources of unobserved heterogeneity. Here, it is crucial to weaken the assumptions used for identification and estimation to be credible in applications.
The second part of the thesis, chapters three and four, consider some data combination problems. Data combination leverages two different datasets which cannot be matched at the individual level to learn about features of the joint distribution. This allows to test the researchers’ working assumptions, like the rational expectations hypothesis, without collecting a full dataset. Here, the third chapter, addressing the ecological inference problem with an application to electoral studies, relates two parts of the thesis: it is both a data combination problem and a system of random coefficients equations.
Finally, the fifth chapter analyzes the properties of the singular value decomposition (SVD) of an operator intervening in the inverse problem of the second chapter. This SVD is also particularly well suited to perform stable analytic continuation, which means recovering an analytic function on its domain of definition when it is observed with error on an interval.