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.

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.

Extreme poverty and development: the role of state in the assurance of minimal existence conditions

This paper follows the idea of Amartya Sen, Nobel Prize of economic, about the role of State in the assurance of minimal existence condition, and aim to answer how countries of Latin America (specifically Brazil) and countries of Europe (specifically United Kingdom) deal with the assurance of this minimal existence conditions. According to Amartya Sen’s view, development must be seen as a process of expanding substantive freedoms, such expansion being the primary purpose of each society and the main mean of development. Substantive freedoms can be considered as basic capabilities allocated to individuals whereby they are entitled to be architects of their own lives, providing them conditions to “live as they wish”. These basic capabilities are divided by Amartya Sen in 5 (five) kinds of substantive freedoms, but for this article’s purpose, we will consider just one of this 5 (five) kinds, specifically the Protective Safety capability. Protective Safety capability may be defined as the assurance of basic means of survival for individuals who are in extreme poverty, at risk of starvation or hypothermia, or even impending famine. Among the means available that could be used to avoid such situations are the possibility of supplemental income to the needy, distributing food and clothing to the needy, supply of energy and water, among others. But how countries deal whit this protective safety? Aiming to answer this question, we selected the problem of “fuel poverty” and how Brazil and United Kingdom solve it (if they solve), in order to assess how the solution found impacts development. The analysis and the comparison between these countries will allow an answer to the question proposed.

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.

Extreme observations and diversification in Latin American emerging equity markets

In this paper, we focus on the tails of the unconditional distribution of Latin American emerging markets stock returns. We explore their implications for portfolio diversification according to the safety tirst principIe, tirst proposed by Roy (1952). We tind that the Latin American emerging markets have signiticantly fatter tails than industrial markets. especially, the lower tail of the distrihution. We consider the implication of the safety tirst principIe for a U .S. investor who creates a diversitied portfolio using Latin American stock markets. We tind that a U.S. investor gains by adding Latin American equity markets to her purely domestic portfolio. For different parameter specitications. we finu a more realistic asset allocation than the one suggested by the Iiterature haseu on the traditional mean-variance framework.

Bayesian analysis of extreme events with threshold estimation

The aim of this paper is to analyze extremal events using Generalized Pareto Distributions (GPD), considering explicitly the uncertainty about the threshold. Current practice empirically determines this quantity and proceeds by estimating the GPD parameters based on data beyond it, discarding all the information available be10w the threshold. We introduce a mixture model that combines a parametric form for the center and a GPD for the tail of the distributions and uses all observations for inference about the unknown parameters from both distributions, the threshold inc1uded. Prior distribution for the parameters are indirectly obtained through experts quantiles elicitation. Posterior inference is available through Markov Chain Monte Carlo (MCMC) methods. Simulations are carried out in order to analyze the performance of our proposed mode1 under a wide range of scenarios. Those scenarios approximate realistic situations found in the literature. We also apply the proposed model to a real dataset, Nasdaq 100, an index of the financiai market that presents many extreme events. Important issues such as predictive analysis and model selection are considered along with possible modeling extensions.

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.