Hippolyte BOUCHER 's PhD Thesis, April 19th, 2023

April 19, 2023 Research

  Hippolyte BOUCHER will defend his thesis on Wednesday 19 April at 16:00 (Auditorium 3)
« Essays on Specification Testing and Model Selection in Instrumental Variable Models »
Supervisor Professor Pascal LAVERGNE

To attend the conference, please contact the secretariat Christelle Fotso Tatchum

Memberships are:

Abstract :

This thesis contains four chapters on specification testing and model selection in instrumental variable models. Instrumental variables (IVs) have become a major tool in the social sciences and in the evaluation of public policies as they allow researchers to estimate causal effects of endogenous variables on outcomes without bias (for instance due to omitted variables) by projecting said endogenous variables on the IVs. For this strategy to work the IVs must be valid, in other words they must be exogenous and relevant. Thus, in this thesis, I design tests and methods to choose IV models in order to estimate the true causal effect of one variable on another. Its contribution is important because the statistics and econometrics literature has mainly focused on choosing the best model to perform prediction and finding the best causal model in simpler cases (linear model, binary classifier) without IVs.

The first chapter is called "A Pivotal Nonparametric Test for Identification-Robust Inference in Linear IV Models" and is largely based on the ideas developped in Antoine and Lavergne (2022). In it, I develop a nonparametric specification for linear IV models which allows, after inversion, to perform inference on the causal homogenous effect of one or more endogenous variables. This test has three notable characteristics: It is robust to weak IVs, it also captures all the information contained in the relation between the IVs and the endogenous variables, and it is pivotal so that the inference procedure is very easy to apply.

The second chapter is called "Testing and Relaxing Distributional Assumptions on Random Coefficients in Demand Models" and is co-authored with Gökçe Gökkoca and Max Lesellier. In this chapter, we consider a demand model for differentiated goods with IVs and random coefficient and propose a validity test and a selection method for the distribution of said random coefficients. These new tools are a significant contribution because any counterfactual analysis depends on the validity of the specification of the random coefficients.

The third chapter is called "Selecting Strong and Exogenous Instruments via Structural Error Criteria". In it, I consider the linear IV model with homogenous effect and allow some of the IVs to be invalid (they can be weak and / or endogenous). In practice, this model is very common and the choice of IVs is arbitrary which is why I propose a data-driven method to select the good IVs. I coin three criteria which consistently select the subset of IVs which is valid. These methods are based on out-of-sample validation, in practice cross-validation, thus this chapter is a contribution to econometrics and statistics literature on causal model selection.

The fourth and last chapter is the vignette of the library "SpeTestNP" developed on R in collaboration with Pascal Lavergne. This R package performs nonparametric tests of parametric specifications. Five heteroskedasticity-robust tests are available: Bierens (1982), Zheng (1996), Escanciano (2006), Lavergne and Patilea (2008), and Lavergne and Patilea (2012). Specific bandwidth and kernel methods can be chosen along with many other options. Allows parallel computing to quickly compute p-values based on the bootstrap.