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Essays in the Econometric Theory of Panel and Multidimensional Data

Freeman, Hugo Stuart Harold; (2023) Essays in the Econometric Theory of Panel and Multidimensional Data. Doctoral thesis (Ph.D), UCL (University College London). Green open access

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Abstract

This dissertation studies econometric models in the presence of unobserved heterogeneity when data is observed over multiple dimensions. Chapter~2 and 3 study this in the classic panel setting with two dimensions, which are usually individuals and time. Chapter~2 studies the setting where unobserved heterogeneity may enter non-linearly and nonseparably to the observed covariates. Established matrix completion methods and a group fixed-effect type estimator prove to approximate the model well. Chapter~3 studies the setting where unobserved heterogeneity enters linearly and separably, but is modelled as a generic functional transformation of unobserved characteristics. The factor model estimated with many factors approximates this form of unobserved heterogeneity well, and, like in Chapter~2, a group fixed-effects estimator also performs well in theory and in simulations. Chapter~4 studies this setting when three or more dimensions are observed in the data and restricts focus to the linear regression model. This chapter extends the notion of the group fixed-effects estimator to a nonparametric kernel style transformation that can be applied to any number of dimensions. The results in this chapter show that the current state-of-the-art factor model methods to approximate unobserved heterogeneity do not extend well to the setting with three or more dimensions. The results also show that the novel nonparametric kernel transformation proposed in this chapter control for unobserved heterogeneity sufficiently well to achieve the parametric rate of consistency under certain conditions.

Type: Thesis (Doctoral)
Qualification: Ph.D
Title: Essays in the Econometric Theory of Panel and Multidimensional Data
Open access status: An open access version is available from UCL Discovery
Language: English
Additional information: Copyright © The Author 2022. Original content in this thesis is licensed under the terms of the Creative Commons Attribution-NonCommercial 4.0 International (CC BY-NC 4.0) Licence (https://creativecommons.org/licenses/by-nc/4.0/). Any third-party copyright material present remains the property of its respective owner(s) and is licensed under its existing terms. Access may initially be restricted at the author’s request.
UCL classification: UCL
UCL > Provost and Vice Provost Offices > UCL SLASH
UCL > Provost and Vice Provost Offices > UCL SLASH > Faculty of S&HS
UCL > Provost and Vice Provost Offices > UCL SLASH > Faculty of S&HS > Dept of Economics
URI: https://discovery.ucl.ac.uk/id/eprint/10172491
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