The central theme of this thesis is the development of econometric methods for panel data models. It is comprised of two main chapters: `Shrinkage Estimation of Network Spillovers with Factor Structured Errors' and `Fixed T Estimation of Dynamic Panel Data Models with Interactive Fixed Effects'. The first of these chapters explores the estimation of a panel data model with cross-sectional interaction, which assumes there are different sources of information available on a network, represented in the form of multiple weights matrices. A penalised quasi-maximum likelihood estimator is proposed which aims to alleviate the risk of network misspecification, by shrinking the coefficients of irrelevant weights matrices to exactly zero. Moreover, controlling for unobserved factors in estimation provides a safeguard against the misspecification that might arise from unobserved heterogeneity. The estimator is shown to be consistent and selection consistent as both n and T tend to infinity, and its limiting distribution is characterised. The method is applied to study the prevalence of network spillovers in determining growth rates across countries. The second of these chapters explores the estimation of a dynamic linear panel data model with interactive fixed effects, and in which one dimension of the panel, typically time, may be fixed. By exploiting the invariance properties of this model, a new estimation approach is introduced which reduces the model to a lower dimension, and in doing so, removes the incidental parameter problem from the cross-section. In the simplest case, transforming the model and then applying the principal component estimator of Bai (2009) yields root-n consistent estimates with T fixed. Moreover, with T fixed, the estimator is asymptotically unbiased in the presence of cross-sectional dependence, serial dependence and with the inclusion of dynamic regressors. The properties of the estimator with large n and large T are also studied, where many of these results carry over in the case in which n is growing sufficiently fast relative to T.