Quantile Regression Under Misspecification With An Application To The U S Wage Structure

Quantile regression (QR) fits a linear model for conditional quantiles, just as ordinary least squares (OLS) fit a linear model for conditional means. An attractive feature of OLS is that it gives the minimum mean square error linear approximation to the conditional expectation function even when the linear model is misspecified. Empirical research using quantile regression with discrete covariates suggests that QR may have a similar property, but the exact nature of the linear approximation has remained elusive. In this paper, we show that QR can be interpreted as minimizing a weighted mean-squared error loss function for specification error. The weighting function is an average density of the dependent variable near the true conditional quantile. The weighted least squares interpretation of QR is used to derive an omitted variables bias formula and a partial quantile correlation concept, similar to the relationship between partial correlation and OLS. We also derive general asymptotic results for QR processes allowing for misspecification of the conditional quantile function, extending earlier results from a single quantile to the entire process. The approximation properties of QR are illustrated through an analysis of the wage structure and residual inequality in US census data for 1980, 1990, and 2000. The results suggest continued residual inequality growth in the 1990s, primarily in the upper half of the wage distribution and for college graduates. Keywords: residual inequality, income distribution, conditional quantiles. JEL Classifications: C13, C51, J31.

Quantile regression constitutes an ensemble of statistical techniques intended to estimate and draw inferences about conditional quantile functions. Median regression, as introduced in the 18th century by Boscovich and Laplace, is a special case. In contrast to conventional mean regression that minimizes sums of squared residuals, median regression minimizes sums of absolute residuals; quantile regression simply replaces symmetric absolute loss by asymmetric linear loss. Since its introduction in the 1970's by Koenker and Bassett, quantile regression has been gradually extended to a wide variety of data analytic settings including time series, survival analysis, and longitudinal data. By focusing attention on local slices of the conditional distribution of response variables it is capable of providing a more complete, more nuanced view of heterogeneous covariate effects. Applications of quantile regression can now be found throughout the sciences, including astrophysics, chemistry, ecology, economics, finance, genomics, medicine, and meteorology. Software for quantile regression is now widely available in all the major statistical computing environments. The objective of this volume is to provide a comprehensive review of recent developments of quantile regression methodology illustrating its applicability in a wide range of scientific settings. The intended audience of the volume is researchers and graduate students across a diverse set of disciplines.

The field of statistics not only affects all areas of scientific activity, but also many other matters such as public policy. It is branching rapidly into so many different subjects that a series of handbooks is the only way of comprehensively presenting the various aspects of statistical methodology, applications, and recent developments. The Handbook of Statistics is a series of self-contained reference books. Each volume is devoted to a particular topic in statistics, with Volume 30 dealing with time series. The series is addressed to the entire community of statisticians and scientists in various disciplines who use statistical methodology in their work. At the same time, special emphasis is placed on applications-oriented techniques, with the applied statistician in mind as the primary audience. Comprehensively presents the various aspects of statistical methodology Discusses a wide variety of diverse applications and recent developments Contributors are internationally renowened experts in their respective areas

'Handbook of Statistics' is a series of self-contained reference books. Each volume is devoted to a particular topic in statistics, with volume 30 dealing with time series.

Advances in Quantitative Analysis of Finance and Accounting (New Series) is an annual publication designed to disseminate developments in the quantitative analysis of finance and accounting. The publication is a forum for statistical and quantitative analyses of issues in finance and accounting as well as applications of quantitative methods to problems in financial management, financial accounting, and business management. The objective is to promote interaction between academic research in finance and accounting and applied research in the financial community and the accounting profession.

This festschrift includes papers authored by many collaborators, colleagues, and students of Professor Thomas P Hettmansperger, who worked in research in nonparametric statistics, rank statistics, robustness, and mixture models during a career that spanned nearly 40 years. It is a broad sample of peer-reviewed, cutting-edge research related to nonparametrics and mixture models.

The volume aims at providing an outlet for some of the best papers presented at the 15th Annual Conference of the African Econometric Society, which is one of the “chapters” of the International Econometric Society. Many of these papers represent the state of the art in financial econometrics and applied econometric modeling, and some also provide useful simulations that shed light on the models' ability to generate meaningful scenarios for forecasting and policy analysis. Contents:Financial Econometrics and International Finance:Modeling Interest Rates Using Reducible Stochastic Differential Equations: A Copula-Based Multivariate Approach (Ruijun Bu, Ludovic Giet, Kaddour Hadri and Michel Lubrano)Financial Risk Management Using Asymmetric Heavy-Tailed Distributions and Nonlinear Dependence Structures of Asset Returns Under Discontinuous Dynamics (Alaa El-Shazly)Time-Varying Dependence in the Term Structure of Interest Rates: A Copula-Based Approach (Diaa Noureldin)Nonlinear Filtering and Market Implied Rating for a Jump-Diffusion Structural Model of Credit Risk (Alaa El-Shazly)Time-Varying Optimal Weights for International Asset Allocation in African and South Asian Markets (Dalia El-Edel)Econometric Theory and Methods:Econometric Methods for Ordered Responses: Some Recent Developments (Franco Peracchi)Which Quantile is the Most Informative? Maximum Likelihood, Maximum Entropy and Quantile Regression (Anil K Bera, Antonio F Galvao Jr, Gabriel V Montes-Rojas and Sung Y Park)The Experimetrics of Fairness (Anna Conte and Peter G Moffatt)Uniform in Bandwidth Tests of Specification for Conditional Moment Restrictions Models (Pascal Lavergne and Pierre E Nguimkeu)Joint LM Test for Homoscedasticity in a Two-Way Error Components Model (Eugene Kouassi, Joel Sango, J M Bosson Brou and Kern O Kymn)An Approximation to the Distribution of the Pooled Estimator When the Time Series Equation is One of a Complete System (William M Mikhail and Ghazal A Ghazal)Monetary, Labor and Environmental Applications:Monetary Policy and the Role of the Exchange Rate in Egypt (Tarek A Moursi and Mai El-Mossallamy)International Migration, Remittances and Household Poverty Status in Egypt (Rania Roushdy, Ragui Assaad and Ali Rashed)Determinants of Job Quality and Wages of the Working Poor: Evidence From 1998–2006 Egypt Labor Market Panel Survey (Mona Said)A Contract-Theoretic Model of Conservation Agreements (Heidi Gjertsen, Theodore Groves, David A Miller, Eduard Niesten, Dale Squires and Joel Watson)Household Environment and Child Health in Egypt (Mahmoud Hailat and Franco Peracchi)Modeling the Relationship between Natural Resource Abundance, Economic Growth, and the Environment: A Cross-Country Study (Hala Abou-Ali and Yasmine M Abdelfattah)Global Cement Industry: Competitive and Institutional Frameworks (Tarek H Selim and Ahmed S Salem)On the Occurrence of Ponzi Schemes in Presence of Credit Restrictions Penalizing Default (A Seghir)Is Targeted Advertising Always Beneficial? (Nada Ben Elhadj-Ben Brahim, Rim Lahmandi-Ayed and Didier Laussel) Readership: Graduate students and researchers in the fields of econometrics, economic theory, applied econometrics. Keywords:Financial Econometrics;Applied Econometrics;Econometric Theory and MethodsKey Features:Contains original contributions to economic theory, financial econometrics and applied econometrics

The book ‘Economic Trends and Sustainable Environmental Assessment’ attempts to x-ray the economic and socioeconomic activities, and cultural or behavioural aspects from the concept of sustainability by employing several related research scenarios spanning the micro-, meso-, and macro-level approaches. Given the increasing awareness of the importance of social, economic, environmental, and even now human sustainability aspects to a sustainable global (present) future, the relevance of the dimensions of Sustainable Development Goals (SDGs) need to be consistently examined. For instance, decades of climate-related disasters which have increasingly endangered humans are the reason for ongoing advanced advocacy, policy, and research towards achieving an environmentally sustainable or net zero emission (NZE) future. Thus, considering the illustration of the theoretical and practical dimensions of the connectedness of the economic and socioeconomic aspects with environmental dimensions, this book should hugely benefit students, researchers, and policymakers to further understand and solve some of the world’s lingering challenges.