Fan, YanqinRivero, Jorge Andres2024-09-092024-09-092024-09-092024Rivero_washington_0250E_26681.pdfhttps://hdl.handle.net/1773/51898Thesis (Ph.D.)--University of Washington, 2024This dissertation contributes to two major research areas: multivariate analysis of eco- nomic inequality and panel data methodology. The focus is on extending popular es- tablished approaches while retaining the features responsible for their enduring appeal. I achieve this by applying optimal transport theory directly to develop inequality or- derings based on Lorenz curves, and indirectly to relax structure imposed in traditional fixed effects models. The first chapter offers a brief introduction on optimal transport. In the second chapter, we propose a multivariate extension of the Lorenz curve based on multivariate rearrangements of optimal transport theory. We define a vector Lorenz map as the integral of the vector quantile map associated with a multivariate resource allocation. Each component of the Lorenz map is the cumulative share of each resource, as in the traditional univariate case. The pointwise ordering of such Lorenz maps defines a new multivariate majorization order, which is equivalent to preference by any social planner with inequality averse multivariate rank dependent social evaluation functional. We define a family of multi-attribute Gini index and complete ordering based on the Lorenz map. We propose the level sets of an Inverse Lorenz Function as a practical tool to visualize and compare inequality in two dimensions, and apply it to income-wealth inequality in the United States between 1989 and 2022. In the third chapter, I extend the linear grouped fixed effects (GFE) panel model to allow for heteroskedasticity from a discrete latent group variable. Key features of GFE are preserved, such as individuals belonging to one of a finite number of groups and group membership is unrestricted and estimated. Ignoring group heteroskedasticity is shown to lead to poor classification, which causes significant finite-sample bias. I intro- duce the “weighted grouped fixed effects” (WGFE) estimator that minimizes a weighted average of group sum of squared residuals. I establish pNT-consistency and normal- ity under a concept of group separation based on second moments. A test of group heteroskedasticity is proposed. A fast computation procedure is provided. Simulations show that WGFE outperforms alternatives that exclude second moment information. I demonstrate this approach by revisiting studies on the effect of unionization on earnings and the link between income and democratization. In the fourth chapter, I reexamine the Rational Addiction model by introducing the type fixed effects (TFE) panel model. The TFE model incorporates heterogeneous coeffi- cients and time-varying patterns of heterogeneity, which reflect differences in preferences and the addiction process. The model assumes the existence of a latent, time-invariant continuous variable referred to as a “type”, which drives the heterogeneity in the pa- rameters. Smoothness of the parameters as functions of the type is key to identification, allowing individuals of similar types to have similar parameter values. Correlation be- tween the parameters, covariates, and instruments stem from type heterogeneity. I pro- pose the type fixed effects generalized method of moments (TFE-GMM) estimator and establish consistency. I provide fast computation procedures based on a stochastic gra- dient descent algorithm. Simulations demonstrate good performance of this estimator. Using yearly household cigarette purchase data to estimate the model shows that most households follow cyclical consumption patterns and insensitivity to prices changes, giving support to educational interventions to curb smoking.application/pdfen-USCC BYcigarette demanddiscrete heterogeneityfixed effectsmultidimensional inequalityoptimal transportpanel dataEconomicsStatisticsEconomicsThesis