The IPANEMA project is devoted to the development of inference for non-, semi-parametric and high-dimensional structural economic models. It aims at producing reliable results that are based on inference on model that incorporate features of the unknown parameter/function that is coming from economic theory only. Non-parametric and semi-parametric inference for structural models usually gives rise to inverse problems. High-dimensional methods aim at computationally tractable model selection and inference in models with many more possible unknowns than observations when there is some parsimony or approximate parsimony. Parsimony can correspond to the fact that many coefficients are zero, that there are piecewise constant over time, the model is a discrete mixture of regression models, etc. Approximate parsimony corresponds to the case where the model can be well approximated by a parsimonious model. In that case, a high-dimensional method should select the best sub-model without knowing it in advance or using knowledge on the unknown. It should also account for the approximation error in the inference. Inverse problem techniques for non- and semi-parametric models have been introduced in structural econometrics since the beginning of the 2000’s. High-dimensional methods have been introduced in the econometrics in the last three years only. Though they already had a high impact in theoretical econometrics, we strongly believe that this is just the premises and that it will play an increasing role in empirical applications.
The group that we form through the IPANEMA proposal consists of specialists of inverse problems and high-dimensional estimation, of economists and statisticians interested in economics. The objectives of our proposal are twofold.
We will pursue the theoretical developments for inference based on non- and semi-parametric / high-dimensional structural economic models, as for instance: minimax theory, the development of data-driven methods for the choice of the regularization parameter that allow to achieve the minimax lower bounds, the construction of confidence sets -- possibly robust to identification -- and testing procedures, using bootstrap techniques or proper self-normalization, inference on functionals or in the presence of nuisance parameters (finite or infinite dimensional) - possibly under partial identification, and inference under shape restrictions. We will study structural models from various fields from economics including: evaluation of public policies, industrial organizations, labor economics, game theory, auctions and finance, among others. Importantly, we will consider both frequentist and Bayesian procedures. Interestingly, our group has strengths in both frequentist and Bayesian statistics. Bayesian procedures are appealing for designing data-driven methods and for incorporating economic restrictions. Incorporating prior knowledge can prove particularly useful when sample size is small. We also plan to go beyond cross-sections and propose methods for panel data or time series models. Handling dependence is very challenging and barely untouched for such models, even in the statistics literature.
The second objective of our proposal is to make our techniques: (1) easy to implement and (2) accessible. To handle point (1) we will bear attention on algorithmic issues. This is for example the motivation for the recent advances in the high-dimensional literature in comparison to earlier model selection methods. Algorithmic issues have been absent of econometrics until very recently and become increasingly important to handle rich new data configurations. Our proposal addresses point (2) through: systematic development of purely data-driven methods that achieve optimal theoretical bounds, carrying empirical applications, developing computer programs – written either in Matlab or in R - and making them accessible to the general public.
Project date: 01/09/2013 – 31/08/2017
Contact in TSE: Jean-Pierre FLORENS