A study on time-varying quantile and its applications

This Thesis is the result of my Master Degree studies at the Graduate School of Economics, Getúlio Vargas Foundation, from January 2004 to August 2006. am indebted to my Thesis Advisor, Professor Luiz Renato Lima, who introduced me to the Econometrics' world. In this Thesis, we study time-varying quantile process and we develop two applications, which are presented here as Part and Part II. Each of these parts was transformed in paper. Both papers were submitted. Part shows that asymmetric persistence induces ARCH effects, but the LMARCH test has power against it. On the other hand, the test for asymmetric dynamics proposed by Koenker and Xiao (2004) has correct size under the presence of ARCH errors. These results suggest that the LM-ARCH and the Koenker-Xiao tests may be used in applied research as complementary tools. In the Part II, we compare four different Value-at-Risk (VaR) methodologies through Monte Cario experiments. Our results indicate that the method based on quantile regression with ARCH effect dominates other methods that require distributional assumption. In particular, we show that the non-robust method ologies have higher probability to predict VaRs with too many violations. We illustrate our findings with an empirical exercise in which we estimate VaR for returns of São Paulo stock exchange index, IBOVESPA, during periods of market turmoil. Our results indicate that the robust method based on quantile regression presents the least number of violations.

Evaluating Value-at-Risk models via Quantile regressions

This paper is concerned with evaluating value at risk estimates. It is well known that using only binary variables to do this sacrifices too much information. However, most of the specification tests (also called backtests) avaliable in the literature, such as Christoffersen (1998) and Engle and Maganelli (2004) are based on such variables. In this paper we propose a new backtest that does not realy solely on binary variable. It is show that the new backtest provides a sufficiant condition to assess the performance of a quantile model whereas the existing ones do not. The proposed methodology allows us to identify periods of an increased risk exposure based on a quantile regression model (Koenker & Xiao, 2002). Our theorical findings are corroborated through a monte Carlo simulation and an empirical exercise with daily S&P500 time series.

The firm size wage premium : a quantile analysis

Empirical evidence shows that larger firms pay higher wages than smaller ones. This wage premium is called the firm size wage effect. The firm size effect on wages may be attributed to many factors, as differentials on productivity, efficiency wage, to prevent union formation, or rent sharing. The present study uses quantile regression to investigate the finn size wage effect. By offering insight into who benefits from the wage premi um, quantile regression helps eliminate and refine possible explanations. Estimated results are consistent with the hypothesis that the higher wages paid by large firms can be explained by the difference in monitoring costs that large firms face. Results also suggest that more highly skilled workers are more often found at larger firms .

Comparing value-at-risk methodologies

In this paper, we compare four different Value-at-Risk (V aR) methodologies through Monte Carlo experiments. Our results indicate that the method based on quantile regression with ARCH effect dominates other methods that require distributional assumption. In particular, we show that the non-robust methodologies have higher probability to predict V aRs with too many violations. We illustrate our findings with an empirical exercise in which we estimate V aR for returns of S˜ao Paulo stock exchange index, IBOVESPA, during periods of market turmoil. Our results indicate that the robust method based on quantile regression presents the least number of violations.

Podem os baixos salários ser apontados como uma das fontes de corrupção no setor público?: um estudo sobre os diferenciais de salário público/privado nos governos estaduais brasileiros

Na literatura econômica, encontramos o argumento de que as políticas salariais que resultem em uma remuneração inferior no setor público podem funcionar como um estímulo ao corrupt behavior por parte do funcionalismo público. No Brasil, a existência de fracos controles administrativos e a baixa punição corroboram para validade desta relação sem, porém existirem indícios de que o salário pago no setor público seja inferior ao praticado no setor privado. Diante disso, este trabalho tem como objetivo testar a dinâmica dos salários pagos pelos governos estaduais brasileiros de forma a verificar se o nível de remuneração praticado, comparativamente ao setor privado, pode ser apontado como um dos fatores que causem a corrupção no país. Para o desenvolvimento da pesquisa empírica, trabalhamos com os micro dados da PNAD para os vinte e seis estados brasileiros e o Distrito Federal entre os anos de 1995 a 2004. Os resultados foram calculados utilizando a técnica de Oaxaca (1973) onde foi estimada a existência de um diferencial de salários público privado. A estimativa dos diferenciais foi realizada para a media dos salários e também para diferentes coortes de renda através do emprego de Quantile Regression sendo que, de forma geral foi detectada a presença prêmios nos salários do funcionalismo público estadual em praticamente todas as regiões brasileiras. Com base nos resultados encontrados, este trabalho conclui que, dada sua inexistência não há indícios de que os baixos salários no setor público possam ser apontados como causa da corrupção nos governos estaduais brasileiros.

Discriminação salarial por cor e gênero revisitada: uma abordagem de decomposição contrafactual utilizando regressões quantílicas

A desigualdade salarial, especialmente a resultante da discriminação contra negros e mulheres no mercado de trabalho, é um componente importante da elevada concentração de renda da economia brasileira. Ao contrário da grande maioria dos trabalhos já desenvolvidos nesta área, este trabalho não adota a hipótese de que os efeitos de atributos determinantes do salário são constantes e idênticos para os indivíduos ao longo da distribuição de renda. São estimadas as estruturas salariais para cada percentil da distribuição salarial para homens brancos, homens negros, mulheres brancas e mulheres negras utilizando a técnica de decomposição contrafactual por regressões quantílicas, proposta por Koenker e Bassett (1978) e desenvolvida por Machado e Mata (2004). Isto proporciona uma compreensão mais detalhada e abrangente dos fatores que determinam a remuneração do trabalho para diferentes níveis de renda e fornece uma medida mais completa do grau de discriminação contra os negros e mulheres no mercado de trabalho ao longo da distribuição salarial. Para os três grupos, a discriminação é crescente em relação à posição na distribuição salarial, indicando a dificuldade de se atingir posições melhor remuneradas no mercado de trabalho por parte de mulheres e negros. A discriminação afeta principalmente as mulheres negras, seguidas das mulheres brancas e dos homens negros. Para os homens negros, a discriminação é baixa entre os mais pobres e cresce nos níveis mais altos da distribuição. As mulheres brancas sofrem ao longo de toda a distribuição com maior efeito entre os 15% mais ricos. As mulheres negras sofrem com a discriminação por cor e gênero, estando assim na pior situação entre os grupos. A remuneração da educação estimada para os quatro grupos indica ganhos crescentes conforme a posição na distribuição salarial ampliando a desigualdade salarial intra-grupo, adicionalmente, observa-se uma desvalorização da educação dos negros de ambos os sexos na determinação salarial e que as mulheres sofrem algum tipo de discriminação no que diz respeito à educação apenas nos níveis salariais mais elevados. Os ganhos salariais obtidos com a equalização da escolaridade e formalização entre os grupos discriminados e os homens brancos indicam que, no caso da educação, homens e mulheres negros teriam ganhos ao longo de toda a distribuição, com ênfase entre os mais ricos. Para a formalização, a população nos decis inferiores da distribuição salarial seria a principal beneficiada.

The distribution of male wages in Brazil

This paper examines the evolution of wage inequality in Brazil in the 1980s and 1990s . It tries to investigate the role played by changing economic returns to education and to experience over this period together with the evolution of within-group inequality. It applies a quantile regression approach on grouped data to the Brazilian case. Results using repeated cross-sections of a Brazilian annual household survey indicate that : i) Male wage dispersion remained basically constant overall in the 1980's and 1990' s but has increased substantially within education and age groups. ii) Returns to experience increased significantly over this period, with the rise concentrated on the iliterate/primary school group iii) Returns to college education have risen over time, whereas return to intermediate and high-school education have fallen iv) The apparent rise in within-group inequality seems to be the result of a fall in real wages, since the difference in wage leveIs has dec1ined substantially over the period, especially within the high-educated sample. v) Returns to experience rise with education. vi) Returns to education rise over the life-cycle. vii) Wage inequality increases over the life-cycle. The next step i~ this research will try to conciliate all these stylised facts.

Do borrowing constraints decrease intergenerational mobility? evidence from Brazil

In this paper, we find evidence that suggests that borrowing constraints may be an important determinant of intergenerational mobility in Brazil. This result contrasts sharply with studies for developed countries, such as Canada and the US, where credit constraints do not seem to play an important role in generating persistence of inequality. Moreover, we find that the social mobility is lower in Brazil in comparison with developed countries. We follow the methodology proposed by Grawe (2001), which uses quantile regression, and obtain two results. First, the degree of intergenerational persistence is greater for the upper quantiles. Second, the degree of intergenerational persistence declines with income at least for the upper quantiles. Both findings are compatible with the presence of borrowing constraints affecting the degree of intergenerational persistence, as predicted by the theory.

Debt ceiling and fiscal sustainability in Brazil: a quantile autoregression approach

In this paper we investigate fiscal sustainability by using a quantile autoregression (QAR) model. We propose a novel methodology to separate periods of nonstationarity from stationary ones, which allows us to identify various trajectories of public debt that are compatible with fiscal sustainability. We use such trajectories to construct a debt ceiling, that is, the largest value of public debt that does not jeopardize long-run fiscal sustainability. We make out-of-sample forecast of such a ceiling and show how it could be used by Policy makers interested in keeping the public debt on a sustainable path. We illustrate the applicability of our results using Brazilian data.

Electoral rules, political competition and fiscal spending: regression discontinuity evidence from brazilian municipalities

We exploit a discontinuity in Brazilian municipal election rules to investigate whether political competition has a causal impact on policy choices. In municipalities with less than 200,000 voters mayors are elected with a plurality of the vote. In municipalities with more than 200,000 voters a run-off election takes place among the top two candidates if neither achieves a majority of the votes. At a first stage, we show that the possibility of runoff increases political competition. At a second stage, we use the discontinuity as a source of exogenous variation to infer causality from political competition to fiscal policy. Our second stage results suggest that political competition induces more investment and less current spending, particularly personnel expenses. Furthermore, the impact of political competition is larger when incumbents can run for reelection, suggesting incentives matter insofar as incumbents can themselves remain in office.

Wald tests for IV regression with weak instruments

This dissertation deals with the problem of making inference when there is weak identification in models of instrumental variables regression. More specifically we are interested in one-sided hypothesis testing for the coefficient of the endogenous variable when the instruments are weak. The focus is on the conditional tests based on likelihood ratio, score and Wald statistics. Theoretical and numerical work shows that the conditional t-test based on the two-stage least square (2SLS) estimator performs well even when instruments are weakly correlated with the endogenous variable. The conditional approach correct uniformly its size and when the population F-statistic is as small as two, its power is near the power envelopes for similar and non-similar tests. This finding is surprising considering the bad performance of the two-sided conditional t-tests found in Andrews, Moreira and Stock (2007). Given this counter intuitive result, we propose novel two-sided t-tests which are approximately unbiased and can perform as well as the conditional likelihood ratio (CLR) test of Moreira (2003).

Conditional labour supply, quantile functions in Brazil

The estimation of labor supply elasticities has been an important issue m the economic literature. Yet all works have estimated conditional mean labor supply functions only. The objective of this paper is to obtain more information on labor supply, by estimating the conditional quantile labor supply function. vI/e use a sample of prime age urban males employees in Brazil. Two stage estimators are used as the net wage and virtual income are found to be endogenous to the model. Contrary to previous works using conditional mean estimators, it is found that labor supply elasticities vary significantly and asymmetrically across hours of work. vVhile the income and wage elasticities at the standard work week are zero, for those working longer hours the elasticities are negative.

Improved combinations of parametric and nonparametric Regression estimators

This paper provides a systematic and unified treatment of the developments in the area of kernel estimation in econometrics and statistics. Both the estimation and hypothesis testing issues are discussed for the nonparametric and semiparametric regression models. A discussion on the choice of windowwidth is also presented.

Efficient semiparametric estimation of quantile treatment effects

This paper presents calculations of semiparametric efficiency bounds for quantile treatment effects parameters when se1ection to treatment is based on observable characteristics. The paper also presents three estimation procedures forthese parameters, alI ofwhich have two steps: a nonparametric estimation and a computation ofthe difference between the solutions of two distinct minimization problems. Root-N consistency, asymptotic normality, and the achievement ofthe semiparametric efficiency bound is shown for one ofthe three estimators. In the final part ofthe paper, an empirical application to a job training program reveals the importance of heterogeneous treatment effects, showing that for this program the effects are concentrated in the upper quantiles ofthe earnings distribution.