Heteroskedasticity-Robust Inference in Finite Samples

Since the advent of heteroskedasticity-robust standard errors, several papers have proposed adjustments to the original White formulation. We replicate earlier findings that each of these adjusted estimators performs quite poorly in finite samples. We propose a class of alternative heteroskedasticity-robust tests of linear hypotheses based on an Edgeworth expansions of the test statistic distribution. Our preferred test outperforms existing methods in both size and power for low, moderate, and severe levels of heteroskedasticity.

Cuban immigrants in the United States: what determines their earnings distribution?

Este artículo analiza la distribución de ingresos condicionales de los inmigrantes cubanos en los Estados Unidos usando OLS y analizando una Regresión Cuantílica. Los datos usados en este estudio fueron tomados del American Community Survey (ACS) de los Estados Unidos y fueron suministrados por IPUMS (2011). Los resultados muestran que incrementos en los ingresos asociados a diferentes características socioeconómicas tales como: el sexo, estado civil, etnia, manejo del idioma inglés y educación varían entre las diferentes distribuciones de ingresos.In this paper the conditional earnings distribution of Cuban immigrants in the U.S. using OLS and Quantile Regression is analyzed. The data used in the study come from the 2011 American Community Survey (ACS) in the U.S. provided by IPUMS (2011). The results show that increments in earnings associated with different socioeconomic characteristics such as: sex, marital status, ethnicity, proficiency in English and education vary across the earnings distribution.Este artigo analisa a distribuição de ingressos condicionais dos imigrantes cubanos nos Estados Unidos usando OLS e analisando uma Regressão Quantílica. Os dados usados neste estudo foram tomados do American Community Survey (ACS) dos Estados Unidos e foram subministrados por IPUMS (2011). Os resultados mostram que incrementos nos ingressos associados a diferentes características socioeconômicas tais como: o sexo, estado civil, etnia, manejo do idioma inglês e educação variam entre as diferentes distribuições de ingressos

Heteroskedasticity-robust inference in finite samples

Since the advent of heteroskedasticity-robust standard errors, several papers have proposed adjustments to the original White formulation. We replicate earlier findings that each of these adjusted estimators performs quite poorly in finite samples. We propose a class of alternative heteroskedasticity-robust tests of linear hypotheses based on an Edgeworth expansion of the test statistic distribution. Our preferred test outperforms existing methods in both size and power for low, moderate, and severe levels of heteroskedasticity.National Science Foundation (U.S.). Graduate Research Fellowship (Grant 0645960

Object-oriented Computation of Sandwich Estimators

Sandwich covariance matrix estimators are a popular tool in applied regression modeling for performing inference that is robust to certain types of model misspecification. Suitable implementations are available in the R system for statistical computing for certain model fitting functions only (in particular lm()), but not for other standard regression functions, such as glm(), nls(), or survreg(). Therefore, conceptual tools and their translation to computational tools in the package sandwich are discussed, enabling the computation of sandwich estimators in general parametric models. Object orientation can be achieved by providing a few extractor functions' most importantly for the empirical estimating functions' from which various types of sandwich estimators can be computed.

FDR Control in the Presence of an Unknown Correlation Structure

The false discovery rate (FDR, Benjamini and Hochberg 1995) is a powerful approach to multiple testing. However, the original approach developed by Benjamini and Hochberg (1995) applies only to independent tests. Yekutieli (2008) showed that a modification of the Benjamini-Hochberg (BH) approach can be used in the presence of dependent tests and labelled his procedure as separate subsets BH (ssBH). However, Yekutieli (2008) left the practical specification of the subsets of p values largely unresolved. In this paper we propose a modification of the ssBH procedure based on a selection of the subsets that guarantees that the dependence properties needed to control the FDR are satisfied. We label this new procedure as the separate pairs BH (spBH). An extensive Monte Carlo analysis is presented that compares the properties of the BH and spBH procedures.Multiple testing, False discovery rate, Copulas

Econometric Computing with HC and HAC Covariance Matrix Estimators

Data described by econometric models typically contains autocorrelation and/or heteroskedasticity of unknown form and for inference in such models it is essential to use covariance matrix estimators that can consistently estimate the covariance of the model parameters. Hence, suitable heteroskedasticity consistent (HC) and heteroskedasticity and autocorrelation consistent (HAC) estimators have been receiving attention in the econometric literature over the last 20 years. To apply these estimators in practice, an implementation is needed that preferably translates the conceptual properties of the underlying theoretical frameworks into computational tools. In this paper, such an implementation in the package sandwich in the R system for statistical computing is described and it is shown how the suggested functions provide reusable components that build on readily existing functionality and how they can be integrated easily into new inferential procedures or applications. The toolbox contained in sandwich is extremely flexible and comprehensive, including specific functions for the most important HC and HAC estimators from the econometric literature. Several real-world data sets are used to illustrate how the functionality can be integrated into applications.

A Minimax Bias Estimator for OLS Variances under Heteroskedasticity

Analytic evaluation of heteroskedasticity consistent covariance matrix estimates (HCCME) is difficult because of the complexity of the formulae currently available. We obtain new analytic formulae for the bias of a class of estimators of the covariance matrix of OLS in a standard linear regression model. These formulae provide substantial insight into the properties and performance characteristics of these estimators. In particular, we find a new estimator which minimizes the maximum possible bias and improves substantially on the standard Eicker-White estimate

Application of robust residuals in matrices of consistent covariance

The estimation of the parameters, by the linear regression model, is made by the method of ordinary least squares (OLS). This method provides estimates unbiased, consistent and efficient. However, under heteroscedasticity, the OLS estimators become inefficient and the common estimator of their covariance matrix is not consistent. Heteroskedasticity consistent covariance matrix estimator (HCCME) were proposed to solve the heteroscedastic problem in linear regression. In this work, four types of robust residuals were applied in the HC3, HC4, HC4m and HC5 estimators to evaluate their performances. We also present an empirical application that uses real data.A estimação dos parâmetros, pelo modelo de regressão linear, é feita pelo método dos mínimos quadrados ordinários (OLS). Este método fornece estimativas não-viesadas, consistentes e eficientes. No entanto, sob heterocedasticidade, os estimadores OLS tornam-se ineficientes e o estimador comum de sua matriz de covariância não é consistente. Foram propostos estimadores de matrizes de covariância consistentes sob heterocedasticidade (HCCME) para resolver o problema heteroscedástico na regressão linear. Neste trabalho, quatro tipos de resíduos robustos foram aplicados às matrizes HC3, HC4, HC4m e HC5 para avaliar seus desempenhos. Também apresentamos uma aplicação empírica que usa dados reais