Harry Haupt

Cross-validating fit and predictive accuracy of nonlinear quantile regressions

The paper proposes a cross-validation method to address the question of specification search in a multiple nonlinear quantile regression framework. Linear parametric, spline-based partially linear and kernel-based fully nonparametric specifications are contrasted as competitors using cross-validated weighted L 1-norm based goodness-of-fit and prediction error criteria. The aim is to provide a fair comparison with respect to estimation accuracy and/or predictive ability for different semi- and nonparametric specification paradigms. This is challenging as the model dimension cannot be estimated for all competitors and the meta-parameters such as kernel bandwidths, spline knot numbers and polynomial degrees are difficult to compare. General issues of specification comparability and automated data-driven meta-parameter selection are discussed. The proposed method further allows us to assess the balance between fit and model complexity. An extensive Monte Carlo study and an application to a well-known data set provide empirical illustration of the method.

Assessing parametric misspecification and heterogeneity in growth regression

A fully nonparametric analysis is applied to address the problems of nonlinearity and heterogeneity in classical growth regression models using original data from seminal contributions in this field. Nonparametric specification tests and in-sample goodness-of-fit measures, as well as cross-validation based out-of-sample measures provide considerable evidence for parametric misspecification and a superior performance of a nonparametric model, despite the small sample size. In contrast to recent contributions identifying heterogeneity as the primal source of misspecification, a formal and graphical analysis does not reveal evidence for heterogeneity in a parametric and nonparametric quantile regression framework.

Statistical validation of functional form in multiple regression using R

In applied statistical research the practitioner frequently faces the problem that there is neither clear guidance from grounds of theoretical reasoning nor empirical (meta) evidence on the choice of functional form of a tentative regression model. Thus, parametric modeling resulting in a parametric benchmark model may easily miss important features of the data. Using recently advanced nonparametric regression methods we illustrate two powerful techniques to validate a parametric benchmark model. We discuss an empirical example using a well-known data set and provide R code snippets for the implementation of simulations and examples.

A Nonparametric Approach to Modeling Cross-Section Dependence in Panel Data: Smart Regions in Germany

In addition to intuitively plausible dependence structures in the time series dimension, in many applications it is reasonable to assume that there are contagion, spill-over, and repercussion effects among cross-sectional units. Modeling those structures in the systematic part of a panel regression requires both information on the underlying sources that drive the dependence and their respective range. The range allows one to define a neighborhood for each unit, a crucial concept for common methods in spatial statistics and econometrics. Furthermore, specification of a parametric regression function requires knowledge of the specific functional form of the spatial associations. However, lacking information on the sources usually leads to accepting misspecification and to including spatial error component or factor structures. As recent research reveals, the consequences of misspecification in both strategies are troubling in many cases. This paper proposes a data-driven nonparametric method for determining neighborhood as a first step. Second step nonparametric panel regressions have several benefits: (i) they allow one to test for misclassification of cross-sectional units to a wrong neighborhood in the first step; (ii) estimation is accomplished using data beyond the respective neighborhood, thus imposing less structure than parametric methods; (iii) neighborhood/location effects can be directly estimated in analogy to spatial statistics; (iv) no assumptions on functional form are required. The proposed method is illustrated with an empirical analysis of spatio-temporal patterns of high-skilled employees across German regions.

The role of sorting portfolios in asset-pricing models

This article investigates the role of sorting portfolios in evaluating asset-pricing models. With the rising number of empirical studies about asset-pricing models, the comparability of these effects suffers from (1) different aggregational levels of firm returns, (2) different models, i.e. Capital Asset-Pricing Model (CAPM) versus the Fama and French model and (3) time-varying factor risk loadings. We find that β-sorting improves the performance of the CAPM, while portfolios built according to size and book-to-market equity (BE/ME) enhance the Fama and French model. However, the success of the three-factor model is not restricted to its factor-mimicking portfolios. For all analysed types of portfolios the Fama and French three-factor model turns out to be superior to the CAPM, both statistically and economically. Applying a quantile regression-based analysis, we also find support that the ‘independent and identically distributed’ (i.i.d.)-assumption empirically holds in these asset-pricing models, but the role of the unspecified part (α) changes when looking at the tails of the return distribution. The validity of our empirical results is supported by careful specification tests.

Dynamic effects of user- and marketer-generated content on consumer purchase behavior: Modeling the hierarchical structure of social media websites

Abstract User- and marketer-generated content items on social media platforms are supposed to have an impact on economic target variables, such as variables measuring consumers purchase behavior. The position of each content item – and thus the impact on economic variables – changes with newly appearing items. We propose a hierarchy score to capture the dynamics of the content items on social media platforms. In order to mimic the reduced visibility of earlier content items, our hierarchy score computes the position of content items based on the number of text line equivalents of content items above a particular item. Employing the proposed hierarchy score in a dynamic regression framework for data of a large online store yields improved estimates and predictions compared to a variety of other models.