Essays in Econometrics

Abstract

In Chapter 1 we develop inference in high dimensional linear models with serially correlated errors. We examine the Lasso estimator under the assumption of strong mixing in the covariates and error processes. While the Lasso estimator performs poorly under such circumstances, we estimate via GLS Lasso the parameters of interest and extend the asymptotic properties of the Lasso under more general conditions. Our theoretical results indicate that the non-asymptotic bounds for stationary dependent processes are sharper. Further, we employ debiasing methods to perform inference uniformly on the parameters of interest. Monte Carlo results support the proposed estimator, as it has significant efficiency gains over traditional methods.

In Chapter 2 we examine the existence of heterogeneity within a group, in panels with latent grouping structure. The assumption of within group homogeneity is prevalent in this literature, implying that the formation of groups alleviates cross-sectional heterogeneity, regardless of the prior knowledge of groups. While the latter hypothesis makes inference powerful, it can be often restrictive. We allow for models with richer heterogeneity that can be found both in the cross-section and within a group, without imposing the simple assumption that all groups must be heterogeneous. We further contribute to the method proposed by Su et al. (2016), by showing that the model parameters can be consistently estimated and the groups, while unknown, can be identifiable in the presence of different types of heterogeneity. Within the same framework we consider the validity of assuming both cross-sectional and within group homogeneity, using testing procedures. Simulations demonstrate good finite-sample performance of the approach in both classification and estimation, while empirical applications across several datasets provide evidence of multiple clusters, as well as reject the hypothesis of within group homogeneity.

In Chapter 3 we study neural networks and their approximating power in panel data models. We provide asymptotic guarantees on deep feed-forward neural network estimation of the conditional mean, building on the work of Farrell et al. (2021), and explore latent patterns in the cross-section. We use the proposed estimators to forecast the progression of new COVID-19 cases across the G7 countries during the pandemic. We find significant forecasting gains over both linear panel and nonlinear time series models. Containment or lockdown policies, as instigated at the national-level by governments, are found to have out-of-sample predictive power for new COVID-19 cases. We illustrate how the use of partial derivatives can help open the “black-box” of neural networks and facilitate semi-structural analysis: school and workplace closures are found to have been effective policies at restricting the progression of the pandemic across the G7 countries. But our methods illustrate significant heterogeneity and time-variation in the effectiveness of specific containment policies.

Date of Award	1 Jun 2024
Original language	English
Awarding Institution	King's College London
Supervisor	George Kapetanios (Supervisor)