My dissertation consists of three chapters that focus on panel data models in econometrics and under high dimensionality; that is, both the number of individuals and the number of time periods are large. This high dimensionality is widely applicable in practice, as economists increasingly face large dimensional data sets. This dissertation contributes to the methodology and techniques that deal with large data sets. All the models studied in the three chapters contain a factor structure, which provides various ways to extract information from large data sets. Chapter 1 and Chapter 2 use the factor structure to capture the comovement of economic variables, where the factors represent the common shocks and the factor loadings represent the heterogeneous responses to these shocks. Common shocks are widely present in the real world, for example, global financial shocks, macroeconomic shocks and energy price shocks. In applications where common shocks exist, failing to capture these common shocks would lead to biased estimation. Factor models provide a way to capture these common shocks. In contrast to Chapter 1 and Chapter 2, Chapter 3 directly focuses on the factor model with the loadings being constrained, in order to reduce the number of parameters to be estimated. In addition to the common shocks effect, Chapter 1 considers two other effects: spatial effects and simultaneous effects. The spatial effect is present in models where dependent variables are spatially interacted and spatial weights are specified based on location and distance, in a geographic space or in more general economic, social or network spaces. The simultaneous effect comes from the endogeneity of the dependent variables in a simultaneous equations system, and it is important in many structural economic models. A model including all these three effects would be useful in various fields. In estimation, all the three chapters propose quasi-maximum likelihood (QML) based estimation methods and further study the asymptotic properties of these estimators by providing a full inferential theory, which includes consistency, convergence rate and limiting distribution. Moreover, I conduct Monte-Carlo simulations to investigate the finite sample performance of these proposed estimators. Specifically, Chapter 1 considers a simultaneous spatial panel data model with common shocks. Chapter 2 studies a panel data model with heterogenous coefficients and common shocks. Chapter 3 studies a high dimensional constrained factor model. In Chapter 1, I consider a simultaneous spatial panel data model, jointly modeling three effects: simultaneous effects, spatial effects and common shock effects. This joint modeling and consideration of cross-sectional heteroskedasticity result in a large number of incidental parameters. I propose two estimation approaches, a QML method and an iterative generalized principal components (IGPC) method. I develop full inferential theories for the two estimation approaches and study the trade-off between the model specifications and their respective asymptotic properties. I further investigate the finite sample performance of both methods using Monte-Carlo simulations. I find that both methods perform well and that the simulation results corroborate the inferential theories. Some extensions of the model are considered. Finally, I apply the model to analyze the relationship between trade and GDP using a panel data over time and across countries. Chapter 2 investigates efficient estimation of heterogeneous coefficients in panel data models with common shocks, which have been a particular focus of recent theoretical and empirical literature. It proposes a new two-step method to estimate the heterogeneous coefficients. In the first step, a QML method is first conducted to estimate the loadings and idiosyncratic variances. The second step estimates the heterogeneous coefficients by using the structural relations implied by the model and replacing the unknown parameters with their QML estimates. Further, Chapter 2 establishes the asymptotic theory of the estimator, including consistency, asymptotic representation, and limiting distribution. The two-step estimator is asymptotically efficient in the sense that it has the same limiting distribution as the infeasible generalized least squares (GLS) estimator. Intensive Monte-Carlo simulations show that the proposed estimator performs robustly in a variety of data setups. Chapter 3 documents the estimation and inferential theory of high dimensional constrained factor models. Factor models have been widely used in practice. However, an undesirable feature of a high dimensional factor model is that the model has too many parameters. An effective way to address this issue, proposed in Tsai and Tsay (2010), is to decompose the loadings matrix by a high-dimensional known matrix multiplying with a low-dimensional unknown matrix, which Tsai and Tsay (2010) name the constrained factor models. Chapter 3 proposes a QML method to estimate the model and develops the asymptotic properties of its estimators. A new statistic is proposed for testing the null hypothesis of constrained factor models against the alternative of standard factor models. Partially constrained factor models are also investigated. Monte-Carlo simulations confirm the theoretical results and show that the QML estimators and the proposed new statistic perform well in finite samples. Chapter 3 also considers the extension to an approximate constrained factor model where the idiosyncratic errors are allowed to be weakly dependent processes.

A survey for the different variational principles and their corresponding finite element model formulations is given. New triangular finite elements for the analysis of stiffened panels are suggested. The derivation of the stiffness matrix for these elements is based on the hybrid stress model. The boundary deflections for these elements are assumed linear. These elements are different in two aspects, the degree of the internal stress polynomials and the number and location of the stiffeners. Numerical studies are carried out and results are compared to the theoretical solutions given by Kuhn as well as to results of the compatible model. Convergence of the stress in stiffeners to the actual solution through mesh refinement is studied. Jumps in the stiffener stresses given by the new elements exist. The use of special Lagrangian elements at the interelement boundaries to eliminate some of these jumps is studied.

The first chapter compares two types of univariate endogenous one-break unit root tests, namely the Dickey-Fuller (DF) type and the Schmidt-Phillips Lagrange Multiplier (LM) type tests. To investigate the small-sample properties of these tests, they are applied to the Nelson-Plosser macroeconomic time series with bootstrapped critical values used for unit root inference. Simulation results show that breaks under the null for the observed data are of sufficient magnitude to lead to size distortion for the DF-type tests, whereas the LM-type tests generally exhibit satisfactory size performance and possess the invariance property. Furthermore, in implementing the LM-type tests, the one that uses the minimum sum of squared residuals break selection method demonstrates better performance over the one that employs the minimum statistic break selection method. / The second chapter proposes LM type panel unit root test procedures with structural changes based on the group mean and combination test approaches. The proposed test procedures allow for breaks under both the null and alternative, and capture heterogeneity due to individual specific characteristics. The same set of distributions of the underlying individual LM statistics can be utilized to compute the panel statistics for the cases with no breaks and with intercept breaks as a result of the invariance property. Simulation results demonstrate that the inverse normal test exhibits the best overall finite-sample properties measured in terms of size and power. When break dates are unknown, the minimum sum of squared residuals break selection method is preferred. The bootstrap approach is suggested to account for cross-sectional dependence. / The third chapter studies panel cointegration tests dealing with two manifestations of structural changes, viz. breaks in the cointegrating relationship and breaks in the trend functions of time series. The importance of accounting for these breaks is highlighted using a simulation study. Finite-sample properties of the Gregory-Hansen (GH) type and LM type tests incorporating breaks in the cointegrating relationship are assessed. Two variants of the LM type tests are further examined in the presence of cross-sectional dependence taking on a factor structure. In the course of test comparison, some modifications are also suggested. A novel test procedure, based on the LM approach, is devised when trend functions of time series are subjected to breaks. Unlike existing tests, this procedure permits unknown breaks under both the null and alternative that can differ in locations among the variables under study. / This thesis investigates panel unit root and cointegration tests with structural changes that are generalizations of their univariate counterparts. Small-sample properties of two well-established univariate test procedures are first assessed using the bootstrap approach. Extensions of these procedures in the panel framework are then examined. / "February 2008." / Adviser: Win Lin Chou. / Source: Dissertation Abstracts International, Volume: 69-08, Section: A, page: 3266. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2008. / Includes bibliographical references (p. 298-305). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. Ann Arbor, MI : ProQuest dissertations and theses, [201-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstracts in English and Chinese. / School code: 1307.

Thesis (Ph. D.)--University of Missouri-Columbia, 2007. / The entire dissertation/thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file (which also appears in the research.pdf); a non-technical general description, or public abstract, appears in the public.pdf file. Title from title screen of research.pdf file (viewed on November 27, 2007) Vita. Includes bibliographical references.

Thesis (Ph. D.)--University of Texas at Austin, 2002. / Vita. Includes bibliographical references. Available also from UMI Company.

Thesis (Ph.D.)--Northwestern University, 1990. / Includes bibliographical references.

It is anticipated that there will be a shortage of 1.1 million college-educated workers in California by 2030 (Johnson, Bohn, & Cuellar Mejia, 2016). Within this context, the California State University (CSU) is the principal source of skilled workers in the state, producing more career-ready candidates than any other single institution (“California State University 2018 Fact Book“, n.d.). This study examined the relationship between student retention rates and institutional expenditures across the different functional categories of instruction, student services, academic support, and instructional support at the CSU. With the exception of student grants and scholarships, these selected expenditures represent the system’s four largest individual expense categories. This study also sought to reveal the existence of similarities between institutions across the CSU based on institutional characteristics that emerged from the literature as predictors of student success including faculty composition, socioeconomic status of student population, and institutional selectivity (Bailey, Calcagno, Jenkins, Kienzl, & Leinbach, 2005; Ehrenberg & Zhang, 2005a, 2005b; Gansemer-Topf & Schuh (2006); Terenzini, Cabrera, & Bernal, 2001; Titus, 2006b). The sample utilized in this study is the entire population of the CSU, which is comprised of 23 campuses. Data for this study were drawn from the IPEDS database, managed by the National Center for Education Statistics (NCES). This quantitative, non-experimental, correlational study used panel data analysis to determine if the selected institutional expenditures influence retention rates and also to examine the extent to which institutional expenditures contribute to the prediction of retention rate. Multidimensional Scaling (MDS) cluster analysis was performed for exploratory purposes and to reveal groups with similar institutional characteristics. This study found that instructional, academic support, and institutional support expenditures were positively correlated with student retention rates. This finding suggests that increases in both dollar amounts and proportion of expenditures allocated to each functional category would result in higher retention rates. However, there was an exception: student services expenditures were found to be negatively correlated with student retentions rates, implying that allocating funds to student services activities would not result in higher student retention. This study also found that the CSU institutions can be grouped in six different clusters based on similarities of institutional characteristics, suggesting that the criteria to allocate funds from the CSU system to individual campuses should account for these differences to effectively support student success.

Thesis (Ph. D.)--Ohio State University, 2006. / Title from first page of PDF file. Includes bibliographical references.

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Thesis advisor: Ina V. S. Mullis / TIMSS and PIRLS assess representative samples of students at regular intervals, measuring trends in student achievement and student contexts for learning. Because individual students are not tracked over time, analysis of international large-scale assessment data is usually conducted cross-sectionally. Gustafsson (2007) proposed examining the data longitudinally by analyzing relationships between country-level trends in background constructs and trends in student achievement. Through longitudinal analysis of international large-scale assessment data, it becomes possible to mitigate some of the confounding factors in the analysis. This dissertation extends this country-level approach to subpopulations within countries. Adapting a pseudo-panel approach from the econometrics literature (Deaton, 1985), the proposed approach creates subpopulations by grouping students based on demographic characteristics, such as gender or parental education. Following grouping, the subpopulations with the same demographic characteristics are linked across cycles and the aggregated subpopulation means are treated as panel data and analyzed through longitudinal data analysis techniques. As demonstrated herein the primary advantages of the subpopulation approach are that it allows for analysis of subgroup differences, and it captures within-country relationships in the data that are not possible to analyze at country level. Illustrative analysis examines the relationship between early literacy activities and PIRLS reading achievement using PIRLS 2001 and PIRLS 2011 data. Results from the subpopulation approach are compared with student-level and country-level cross-sectional results as well as country-level longitudinal results. In addition, within-country analysis examines the subpopulation-level relationship between early literacy activities and PIRLS reading achievement, multiple group analysis compares regression coefficient estimates between boys and girls and across parental education subgroups, and mediation analysis examines the extent that partaking in early literacy activities can explain differences between boys and girls in PIRLS reading achievement. / Thesis (PhD) — Boston College, 2017. / Submitted to: Boston College. Lynch School of Education. / Discipline: Educational Research, Measurement and Evaluation.