Speaker: Eric Gautier, Université Toulouse Capitole

Title: Inference on slopes in linear panel data models with approximately low rank unobservables

Fixed effects allow to estimate the coefficients of a “long linear regression” with missing regressors in a panel data context, avoiding the use of instrumental variables. It is usual to rely on certain transformations such as the “within” transform to annihilate the fixed effects and rely on a least squares procedure. We consider the case where the fixed effects are replaced by a N*T matrix (N is the sample size and T the number of time periods) which can be well approximated by a low-rank matrix. We allow for interactive fixed effects (Bai, Econometrica 2009) with unknown rank and for a certain amount of misspecification. The method involves estimation of annihilators which play the role of the within transform for more restrictive unobservables. The use of two estimated annihilators allows for weaker assumptions to justify the procedure to make inference on the slopes.  We present two approaches to do so. One relies on a self-tuned nuclear norm penalization and the second one involves a data driven truncated singular value decomposition of certain stacked matrices (see https://arxiv.org/abs/1904.09192 and https://arxiv.org/abs/2010.01837). The second approach is particularly appealing to handle linear models with more than two indices.

His research is in nonparametric and high-dimensional modeling of multiple sources of unobserved heterogeneity and endogeneity, as well as stochastic partial differential equations.

Host: Guðmundur Stefán Guðmundsson

Organisers: Luke Taylor and Leopoldo Catania.