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.

Ensaios em macroeconometria e finanças

This thesis is composed of three essays referent to the subjects of macroeconometrics and Önance. In each essay, which corresponds to one chapter, the objective is to investigate and analyze advanced econometric techniques, applied to relevant macroeconomic questions, such as the capital mobility hypothesis and the sustainability of public debt. A Önance topic regarding portfolio risk management is also investigated, through an econometric technique used to evaluate Value-at-Risk models. The Örst chapter investigates an intertemporal optimization model to analyze the current account. Based on Campbell & Shillerís (1987) approach, a Wald test is conducted to analyze a set of restrictions imposed to a VAR used to forecast the current account. The estimation is based on three di§erent procedures: OLS, SUR and the two-way error decomposition of Fuller & Battese (1974), due to the presence of global shocks. A note on Granger causality is also provided, which is shown to be a necessary condition to perform the Wald test with serious implications to the validation of the model. An empirical exercise for the G-7 countries is presented, and the results substantially change with the di§erent estimation techniques. A small Monte Carlo simulation is also presented to investigate the size and power of the Wald test based on the considered estimators. The second chapter presents a study about Öscal sustainability based on a quantile autoregression (QAR) model. A novel methodology to separate periods of nonstationarity from stationary ones is proposed, which allows one to identify trajectories of public debt that are not compatible with Öscal sustainability. Moreover, such trajectories are used to construct a debt ceiling, that is, the largest value of public debt that does not jeopardize long-run Öscal sustainability. An out-of-sample forecast of such a ceiling is also constructed, and can be used by policy makers interested in keeping the public debt on a sustainable path. An empirical exercise by using Brazilian data is conducted to show the applicability of the methodology. In the third chapter, an alternative backtest to evaluate the performance of Value-at-Risk (VaR) models is proposed. The econometric methodology allows one to directly test the overall performance of a VaR model, as well as identify periods of an increased risk exposure, which seems to be a novelty in the literature. Quantile regressions provide an appropriate environment to investigate VaR models, since they can naturally be viewed as a conditional quantile function of a given return series. An empirical exercise is conducted for daily S&P500 series, and a Monte Carlo simulation is also presented, revealing that the proposed test might exhibit more power in comparison to other backtests.

Prevendo inflação usando ridge regressions

Este estudo tem como objetivo analisar o desempenho de vários modelos econométricos ao prever Inflação . Iniciamos o trabalho utilizando como base de comparação para todos os modelos a tradicional curva de Phillips que usa a taxa de desemprego como variável explicativa para diferenças de preço. Dentre os modelos analisados temos univariados e bivariados, sendo estes últimos uma curva de Phillips alternativa já que apenas sustitui a variável desemprego por outra variável macroeconômica. Além destes modelos também comparamos o desempenho de previsão de modelos que usam como covariadas uma combinação das previsões dos modelos anteriores (univariados e bivariados). O resultado deste estudo aponta a combinação de modelos por "ridge regression" como uma técnica - dentre as analisadas para combinação de previsões - de menor erro de previsão sempre; sendo alcançado pela combinação da média em apenas um dos casos analisados. No entanto, a combinação de previsões não apresentou melhor resultado que algumas das covariadas testadas em modelos bivariados

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.

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.

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 .

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.

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.

Efeitos de abertura comercial sobre a evolução da produtividade industrial no Brasil

Este trabalho avalia a evolução da produtividade industrial brasileira — utilizando um painel de 16 setores da indústria de transformação no período 1985/97 — e o papel da abertura econômica neste processo. Os resultados mostram que a produtividade da indústria brasileira, seja ela medida pelo conceito de produtividade total dos fatores (PTF) ou de produtividade do trabalho, passou por duas fases distintas: de 1985 a 1990, há um processo de estagnação e de 1990 a 1997, a indústria passa a apresentar significativas taxas de crescimento. A abertura comercial, caracterizada por menores tarifas nominais e menores taxas de proteção efetiva, exerce um efeito positivo sobre o aumento da produtividade. Em todas as regressões do modelo — em que se utilizam técnicas de estimação em painéis — não se pode rejeitar a hipótese de que aumentos nas barreiras comerciais implicam menores taxas de crescimento da produtividade do trabalho e da PTF. Este resultado confirma a evidência internacional de que países mais abertos crescem mais rápido e desestimularia a adoção de políticas de restrição comercial como estratégia de desenvolvimento e de proteção à indústria nacional.

The asymmetric behavior of the U.S public debt

Our main goal in this paper was to measure how e¢ cient is risk sharing between countries. In order to do so, we have used a international risk sharIn this paper we re-analyze the question of the U.S. public debt sustainability by using a quantile autoregression model. This modeling allows for testing whether the behavior of U.S. public debt is asymmetric or not. Our results provide evidence of a band of sustainability. Outside this band, the U.S. public debt is unsustainable. We also nd scal policy to be adequate in the sense that occasional episodes in which the public debt moves out of the band do not pose a threat to long run sustainability.

Consumption smoothing in Latin America: an empirical assessment of present value models

The study aims to assess the empirical adherence of the permanent income theory and the consumption smoothing view in Latin America. Two present value models are considered, one describing household behavior and the other open economy macroeconomics. Following the methodology developed in Campbell and Schiller (1987), Bivariate Vector Autoregressions are estimated for the saving ratio and the real growth rate of income concerning the household behavior model and for the current account and the change in national cash ‡ow regarding the open economy model. The countries in the sample are considered separately in the estimation process (individual system estimation) as well as jointly (joint system estimation). Ordinary Least Squares (OLS) and Seemingly Unrelated Regressions (SURE) estimates of the coe¢cients are generated. Wald Tests are then conducted to verify if the VAR coe¢cient estimates are in conformity with those predicted by the theory. While the empirical results are sensitive to the estimation method and discount factors used, there is only weak evidence in favor of the permanent income theory and consumption smoothing view in the group of countries analyzed.

Transporte aéreo doméstico: uma análise econômica para o período recente

Esta dissertação visa investigar a estrutura de custos do setor aéreo doméstico brasileiro. A fim de realizar essa investigação com maior detalhamento, faz-se, respectivamente, nos capítulos 1 e 2, descrições histórica e econômica desse setor. Essa investigação permitirá dar uma resposta a polêmica sobre a quantidade de empresas que esse setor comporta; além disso, fornecerá indicações de políticas públicas, para que se possa fazer uma melhor avaliação de possíveis mudanças no comportamento das empresas aéreas existentes.

Sources of comparative advantages in Brazil

Based on the Heckscher-Ohlin-Vanek model, this paper investigates relative factor abundance in Brazil, as revealed by its international trade. We study two different time periods: one characterized by high trade barriers (1980 to 1985) and the trade liberalization period (1990 to 1995). Two alternative methodologies are used: the estimation of factor intensity regressions on net exports and the direct computation of factor content in net exports. In the factor intensity regression, we incorporate technological changes that might have occurred over time, and those turned out to be significant. Both methods yield the same results: the Brazilian international trade reveals relative abundance in capital, land and unskilled labor, and scarcity in skilled labor, with qualitatively equivalent results for the two time periods studied.

The impact of public capital and public investment on economic growth: an empirical investigation

in this anicle we measure the impact of public sector capital and investment on economic growth. Initially, traditional growth accounting regressions are run for a cross-country data set. A simple endogenous growth model is then constructed in order to take into account the determinants of labor, private capital and public capital. In both cases, public capital is a separate argument of the production function. An additional data-set constructed with quarterly American data was used in the estimations of the growth mode!. The results indicate lhat public capital and public investment play a significant role in determining growth rates and have a significant impact on capital and labor returns. Furthermore, the impact of public investment on productivity growth was found to be positive and always significant for bolh samples. Hence. in a fully optimizing modelo we confmn previous results in the literature that lhe failure of public investment to keep pace with output growlh during the Seventies and Eighties may have played a major role in the slowdown of lhe productivity growth in the period. Anolher main outcome concems the output elasticity wilh respect to public capital. The coefficiem estimates are always positive and significant but magnitudes depend on each of lhe two data set used.