The dissertation consists of three chapters that study topics related to structural change, spatial and network data. The first chapter considers the problem of testing for a structural change in the spatial lag parameter in a panel model. We propose a likelihood ratio test of the null hypothesis of no change against the alternative hypothesis of a single change. The limiting distribution of the test is derived under the null hypothesis when the number of time periods is large. We also propose a break-date estimator to determine the location of the change point following evidence against the null hypothesis. We present Monte Carlo evidence to show that the proposed procedure performs well in finite samples. We use US state budget data to investigate changes in budget spillovers and the interdependence of fiscal policy within US states. The second chapter proposes a theory of cross-country migration in the form of labor mobility based on regional and sectoral productivity shocks in a multi-country, multi-sector setting. The productivity model when applied to US state data explains both the nominal and relative flow of workers across the U.S. well, which is taken as the frictionless benchmark. On the other hand, when applied to Europe the model explains the relative flow network well, but predicts a higher nominal flow. This missing mass of migrants is explained by socio-cultural-political barriers. We use dyadic regressions to assess the effects of institutional and cultural "distance" between countries in explaining the "European immobility puzzle". The third chapter shows that the "iron-law" of convergence (2\%) still holds for the world. We document a structural break in Africa's convergence rate and argue that Africa was not converging before 2000. The world convergence rate before 2000 was driven by Asian and Latin American countries. We show that recent institutional and infrastructural developments have led the African countries on the path of "catching up". We use Least-Absolute-Shrinkage-and-Selection-Operator (LASSO) to select the variables and a double selection method to estimate the treatment effect in a partially linear model. We compare LASSO variable selections with those obtained using Gradient-Boosting-Method (GBM) and Random Forest.