Estimation and Inference in High-Dimensional Panel Data Models: Beyond the Linear Case

• Applicant: Professor Dr. Michael Vogt
• Subject Area: Statistics and Econometrics
• Term: since 2022
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 501082519

Nowadays, economic panel data sets are often high-dimensional: they comprise information on a wide variety of variables whose number may even exceed the sample size. Nevertheless, the literature on econometric methods for high-dimensional panels is quite limited. The main goal of the project is to develop estimation and inference methods for high-dimensional panel models with interactive fixed effects. So far, we have focused on the linear panel case in the project. Specifically, we have developed an estimation method for the linear case which can be regarded as a non-trivial extension of the very popular CCE (Common Correlated Effects) approach to high dimensions. For this reason, we refer to it as the HD-CCE approach. Very roughly speaking, we proceed as follows: we first construct a projection device based on principal components thresholding to (approximately) eliminate the unobserved factors from the model and then estimate the unknown parameters by applying lasso techniques to the projected model. To perform inference in high dimensions, we have further developed a desparsified version of our lasso-type estimator. We have derived asymptotic theory for our estimation and inference methods both in the large-T-case, where the time series length T tends to infinity, and in the small-T-case, where T is a fixed natural number. In particular, we have derived the convergence rate of our estimator and we have shown that its desparsified version is asymptotically normal under suitable regularity conditions. The aim of the renewal project is to go beyond the linear panel case, which is often too restrictive in practice. In applied work, it is very common to include not only the original regressors into the model but also certain nonlinear transformations of them (such as the first few monomials to capture quadratic or cubic effects). Hence, the regressors do not simply enter the model in a linear fashion. To take this into account, we consider a flexible additive framework where each regressor enters the model via an unknown (nonlinear) component function that may be modelled parametrically or nonparametrically. Whereas in the linear case, we can (approximately) eliminate the interactive fixed effects from both the covariates and the responses by a suitable data-driven projection, this is in general not possible any more in the additive case due to the nonlinearity of the component functions. As a consequence, substantially different arguments are needed to cope with this case. In the renewal project, we will extend our HD-CCE approach to the additive case and derive theory for this extended approach.

• DFG Programme: Research Grants
• International Connection: United Kingdom
• Cooperation Partner: Professor Oliver Linton, Ph.D.