nÃo hà / Esse trabalho teve por objetivo analisar a desigualdade de renda entre os municÃpios do estado do Piauà no perÃodo compreendido entre 1995 e 2007, no qual se testou, inicialmente, a validade da hipÃtese da curva de Kuznets e da convergÃncia da renda per capita. Em seguida fez-se uma anÃlise da desigualdade de renda a partir da decomposiÃÃo do Ãndice de Theil, considerando-se os fatores renda, gÃnero, raÃa, educaÃÃo e nÃvel de desenvolvimento. Concluiu-se que as condiÃÃes necessÃrias e suficientes de convergÃncia sÃo atendidas, bem como a hipÃtese do U-invertido da curva de Kuznets. Estima-se que o Piauà necessitaria de 27 anos para reduzir a desigualdade à metade entre seus municÃpios, a uma velocidade de convergÃncia de 0,2889. A desigualdade de gÃnero declinou ao longo do perÃodo e a educaÃÃo à a variÃvel que mais influencia a desigualdade no estado, seguida pela variÃvel inter-racial. O efeito da educaÃÃo sobre a desigualdade à significantemente realÃada quando a decomposiÃÃo distingue os municÃpios mais e menos desenvolvidos. / This dissertation aimed to analyze income inequality amongst the municipalities of the state of Piaui in the period 1995 â 2007 by testing, initially, the validity of the Kuznetsâ curve hypothesis and convergence of per capita income. Besides, it was analyzed a decomposition of Theil index based upon the factors: income, gender, race, education and development stage. It was concluded that the necessary and sufficient conditions of convergence are met, as well as the hypothesis of U-inverted of Kuznetsâ curve. It is estimated that the state of Piaui would need 27 years to reduce inequality in half between its municipalities, at a speed of convergence of 0.2889. Inequality due to gender declined along the period and education is the variable that most influences the income difference in the state, followed by the factor race. The effect of education on the inequality is significantly enhanced as municipalities are distinguished between those more and less developed.

Η παρούσα εργασία επικεντρώνεται στην αποτίμηση της μακροοικονομικής ετερογένειας μεταξύ Ευρωπαϊκών και μη Ευρωπαϊκών χωρών και στο να εκτιμήσει το κατά πόσο ο συγχρονισμός των οικονομικών κύκλων έχει μεταβληθεί με το χρόνο. Η μεθοδολογία είναι δομημένη με το εξής τρόπο. Πρώτον, συγκρίνουμε τις συσχετίσεις μεταξύ των χωρών για δύο περιόδους και δεύτερον, συγκρίνουμε τις τιμές του συντελεστή ανισότητας Theil για να σκιαγραφήσουμε την ετερογένεια μεταξύ αυτών των δύο περιόδων. Τέλος, παλινδρομούμε διάφορες μεταβλητές έτσι ώστε να καταλήξουμε ποιοι παράγοντες επιδρούν στον συσχετισμό και ποιοι επηρεάζουν την μείωση της ετερογένειας μεταξύ των χωρών που εξετάζουμε. / This paper focuses on assessing the macroeconomic heterogeneity among European and non European Countries and to account how does business cycle synchronization has changed over time. The methodology is structured in the following manner. First, we compare the correlations between the countries among two periods and second, we compare the values of the Theil Inequality coefficient to outline the heterogeneity between this two periods. Finally, we regress differently variables so as to conclude which factors affect the correlation and which affect the reduction of the heterogeneity among the countries we examine.

nÃo hà / Em virtude da importÃncia atribuÃda à educaÃÃo como um dos maiores condutores do crescimento, e à grande variaÃÃo de impactos decorrentes das diferentes polÃticas educacionais, a educaÃÃo bÃsica mantem-se um tema ativo na agenda de pesquisadores, na busca do desenvolvimento de pesquisas teÃricas e empÃricas, em alternativas abordagens de tratamento. A CiÃncia EconÃmica tem contribuÃdo significativamente com novas abordagens metodolÃgicas na relaÃÃo entre as ideias e a implementaÃÃo de anÃlises empÃricas, atravÃs do uso intensivo de modelos matemÃticos explicativos. Inspirado nisso, este trabalho espera contribuir para o debate atravÃs da formulaÃÃo de um modelo matemÃtico que busca solucionar alguns impasses incorridos nas anÃlises empÃricas. Tal modelo foi desenvolvido com base em pesquisas especializadas, que identificaram novos fatores explicativos da qualidade da educaÃÃo, corroboradas por duas anÃlises empÃricas. Inicialmente, investigou-se os fatores escolares relacionados à diferenÃa de desempenho das escolas pÃblicas brasileiras, medida atravÃs do Ãndice de Theil-L, a partir dos resultados observados na Prova Brasil de 2011. Em seguida, realizou-se uma avaliaÃÃo de impacto de uma polÃtica educacional especÃfica, para a qual se utilizou o mÃtodo de Controle SintÃtico, constatando a efetividade da polÃtica. A partir disso, hà a expectativa de que o modelo desenvolvido auxilie na discussÃo dos mecanismos que possibilitam polÃticas de educaÃÃo de maior impacto. / Due to the worldwide recognition of the importance attached to education as a major engine of growth, and the wide range of impacts carried out by the different educational policies, investigating basic education has been kept active on the agenda of researchers in the pursuit of the development of theoretical and empirical research, as well as alternative treatment approaches. Economic Science has contributed significantly to new methodological approaches in the relationship between ideas and implementation of empirical analysis, through extensive use of mathematical explanatory models. Inspired by this, this paper hopes to contribute to the debate by formulating a mathematical model that seeks to solve some deadlocks incurred in several empirical analyzes. This model was empirically applied through two distinct approaches, which identified new factors explaining the quality of education. Firstly, it was investigated the schooling factors that dictate the differences in the scores of the âProva Brazil of 2011â for public schools based upon the Theil-L index. Secondly, an impact evaluation of a specific educational policy was performed through a Synthetic Control Method, which pointed for the effectiveness of such policy. It is expected that the developed model contributes to the debate about alternative impact mechanisms caused by education policies.

Series: INEQ Working Paper Series

Support for the use of progress monitoring results for high-stakes decisions is emerging in the literature, but few studies support the reliability of the measures for this level of decision-making. What little research exists is limited to oral reading fluency measures, and their reliability for progress monitoring (PM) is not supported. This dissertation explored methods rarely applied in the literature for summarizing and analyzing progress monitoring results for medium- to high-stakes decisions. The study was conducted using extant data from 92 "low performing" third graders who were progress monitored using mathematics concept and application measures. The results for the participants in this study identified 1) the number of weeks needed to reliably assess growth on the measure; 2) if slopes differed when results were analyzed with parametric or nonparametric analyses; 3) the reliability of growth; and 4) the extent to which the group did or did not meet parametric assumptions inherent in the ordinary least square regression model. The results indicate reliable growth from static scores can be obtained in as few as 10 weeks of progress monitoring. It was also found that within this dataset, growth through parametric and nonparametric analyses was similar. These findings are limited to the dataset analyzed in this study but provide promising methods not widely known among practitioners and rarely applied in the PM literature.

The aim of this study is to examine the impact of the South Eastern Anatolia Project (GAP) on the inter-regional inequality between the GAP region and the rest of Turkey. Cross-sectional analyses are carried out for the years of 1990 and 2000, that is, before the project is put into effect and 10 years after of its implementation. Although this thesis is ultimately concerned with the inter-regional inequality, the within and the total-region inequality are also discussed. Moreover, since not only the economic, infrastructure and service related variables, but also the sociodemographic variables are included in the analyses, it is a comprehensive evaluation, and the results provide current information about the success of the GAP. In this study, Theil&#039 / s inequality index is used as it provides the property of additive decomposability, which allows us to analyze the magnitudes and trends in inequality among regions and within regions as well as total inequality. The indicators include 17 socio-demographic, 12 economic, and 10 infrastructure and service related variables, i.e., total of 39 independent variables. Although the GAP region performed an improvement in absolute terms for most of the variables, the findings show that the inequality between the GAP region and the rest of Turkey increased for more than half of the variables during the last decade. These variables are mostly related to demography (i.e., infant mortality rate, fertility rate, etc.), health services, and GDP p.c.. On the other hand, the between-region inequality decreased for the variables related to infrastructure, urbanization, educational level (i.e., literacy and schooling ratios in primary education), and nonagricultural labor force.

This dissertation examines the robust regression methods. The primary purpose of this work is to propose an extension, derivation and summary (including computational algorithm) for Theil-Sen's regression estimates (or in some literature also referred to as Passing-Bablok's regression method) for multi-dimensional space and compare this method to other robust regression methods. The combination of these two objectives is the primary and the original contribution of the dissertation. Based on the available literature it is unknown if anyone has discussed this problem in greater depth and solved it in total. Therefore this work provides a summary overview of the issue and offers a new alternative of this multidimensional, nonparametric, robust regression method. Secondary goals include a clear summary of other robust methods, a summary of findings related to these robust regression methods, robust methods compared with each other placing emphasis on the comparison with the proposed Theil-Sen's regression estimates method and with the least squares method. The summary also includes individual mathematical context and interchangeability of the proposed methods. These secondary objectives are also another benefit of this dissertation in the field of robust regression problems; this is especially important to gain a unified view of the problems of robust regression methods and estimates in general.

The ordinary least squares (OLS) is one of the most widely used methods for modelling the functional relationship between variables. However, this estimation procedure counts on some assumptions and the violation of these assumptions may lead to nonrobust estimates. In this study, the simple linear regression model is investigated for conditions in which the distribution of the error terms is Generalised Logistic. Some robust and nonparametric methods such as modified maximum likelihood (MML), least absolute deviations (LAD), Winsorized least squares, least trimmed squares (LTS), Theil and weighted Theil are compared via computer simulation. In order to evaluate the estimator performance, mean, variance, bias, mean square error (MSE) and relative mean square error (RMSE) are computed.

This research studies the relationships in Electric Energy Consumption, Carbon Dioxide Emission and Theil Index in Brazil. The period of analysis includes annual data from 1980 to 2011 in a total of 31 observations. The series presented order of integration equal one with the presence of cointegration thus to measure these influences we used a vector error correction model (VEC). By Function Impulse Response (FIR) and Variance Decomposition Analysis (ADV) we observed how each variable behaves to an abrupt change. To analyze the behavior of variables, methods of vector autoregressive (VAR) and residues control charts were used. The VAR modeling revealed that there is a significant interrelationship among the variables under study, thus showing that there is a short-term relationship between these variables. As for the residues control chart to individual measures, a problem in the original variables was avoided tha were the the autocorrelation, and showed that all variables had a period of instability and also enabled the identification of this period. The emission of carbon dioxide and Theil Index are determining factors in the explanation of environmental impacts as well as the development of the country. The variance decomposition indicates that the carbon dioxide emission is primarily responsible for mainly caused damage to the environment. / Esta pesquisa estudou as relações existentes no Consumo de Energia Elétrica, Emissão de Dióxido de Carbono e Índice de Theil no Brasil. O período de análise se refere a dados anuais de 1980 a 2011 perfazendo um total de 31 observações do Brasil. As séries apresentaram ordem de integração igual a um com a presença de cointegração, assim, para mensurar essas influências foi utilizado um modelo de Vetor de Correção de Erros (VEC). Por meio da Função Impulso Resposta (FIR) e Análise de Decomposição da Variância (ADV) foi possível verificar como cada variável se comporta a uma mudança abrupta. Para analisar o comportamento das variáveis, foram utilizadas as metodologias de vetores auto regressivos (VAR) e gráficos de controle de resíduos. Já a modelagem VAR revelou que há um inter-relacionamento significativo entre as variáveis em estudo, mostrando assim que há uma relação de curto prazo entre estas variáveis. Quanto aos gráficos de controle de medidas individuais aos resíduos, contornou-se um problema presente nas variáveis originais que era o de autocorrelação, e mostrou-se que todas as variáveis apresentaram um período de instabilidade o que também possibilitou a identificação deste período. A Emissão de Dióxido de Carbono e o Índice de Theil são fatores determinantes na explicação dos impactos ambientais, assim como no desenvolvimento do país. A decomposição da variância indica que a Emissão de Dióxido de Carbono é o principal responsável pelos danos causados principalmente ao meio ambiente.

Utiliza-se o método de decomposições do índice Theil-L para encontrar determinantes da desigualdade de desempenho escolar das crianças da 4ª série do ensino fundamental do estado de São Paulo. Os dados de proficiência dos alunos em português e matemática são extraídos da Prova Brasil 2005 e combinados com os dados do Censo Escolar 2005. A análise das contribuições brutas e marginais geradas por meio do índice Theil L mostra que variáveis comumente utilizadas como medidas de background sócioeconômico dos alunos explicam pouco da desigualdade das notas, menos de 2%. Ao mesmo tempo, as contribuições brutas e marginais apontam para a importância significativa das escolas, que explicam 14,58% da desigualdade de desempenho dos alunos em matemática e 13,27% do desempenho dos alunos em português. A única variável que explica significativamente a desigualdade entre as escolas é o município, 14,56% da desigualdade em matemática e 13,98% em português. As demais variáveis quando consideradas isoladamente, respondem por menos de 2,5% da desigualdade. Quando tomadas em grupos, seu poder explicativo aumenta. As variáveis de infraestrutura escolar explicam 18,68% da desigualdade entre as escolas em português e 20% da desigualdade em matemática. As variáveis referentes ao background dos colegas respondem respectivamente por 8,79 e 9,40%. Conclui-se que o impacto das diferentes variáveis no desempenho dos alunos se dá por meio de sua interação mais do que pelo efeito de variáveis específicas. Reitera-se também a importância de se entender o impacto dos insumos escolares para compreender a proficiência dos alunos. O trabalho aponta ainda o efeito que os municípios têm sobre as escolas e oferece base para uma melhor compreensão posterior desse fenômeno. / This research uses the method of Theil-L decomposition to find determinants of the inequality among students scores of the 4th grade of the fundamental school in the state of São Paulo. The data is provided by a combination of Prova Brasil 2005 standardized tests and the Censo Escolar 2005. The analysis of the gross and marginal contributions measured by the Theil-L indez indicates that the variables normally used for students social and economic background give few explanation about the total inequality measured. The analysis of the decompositions also shows that schools play a main role in the inequalities among students, explaining 14,58% of the students inequality in math and 13,27% in Portuguese. The only single variable that shows an important impact in the score inequalities among schools is the municipality, 14,56% for math and 13,98% for Portuguese. The other variables have no impact over 2,5% when considered solely. By the other side, when these variables are considered in groups, there is a gain in explanation. The school infra-structure explain 18,68% of the inequality among schools in Portuguese and 20% of the inequality in math. The variables about the peers background are responsible for 8,79 and 9,40% respectively. It is concluded that the impact of differents variables in students learning are more due to their interaction, than by their direct effects. It is reinforced the importance of a better understanding of school variables to understand children apprenticeship as shown by part of the literature. This research points to the importance of municipalities for schools and gives a basis for further discussion on this matter.