Abstract
Considering linear dynamic panel data models with fixed effects, existing outlier–robust estimators based on the median ratio of two consecutive pairs of first-differenced data are extended to higher-order differencing. The estimation procedure is thus based on many pairwise differences and their ratios and is designed to combine high precision and good robust properties. In particular, the proposed two-step GMM estimator based on the corresponding moment equations relies on an innovative weighting scheme reflecting both the variance and bias of those moment equations, where the bias is assumed to stem from data contamination. To estimate the bias, the influence function is derived and evaluated. The robust properties of the estimator are characterized both under contamination by independent additive outliers and the patches of additive outliers. The proposed estimator is additionally compared with existing methods by means of Monte Carlo simulations.
Highlights
Dynamic panel data models with fixed effects have been used in many empirical applications in economics; see Bun and Sarafidis (2015) and Harris et al (2008) for an overview of the methodology and applications
Considering linear dynamic panel data models with fixed effects, existing outlier–robust estimators based on the median ratio of two consecutive pairs of firstdifferenced data are extended to higher-order differencing
We address this by proposing a data-driven weighting and selection of the median ratios of differenced data since the traditional strategy used in the robust statistics—using an initial robust estimator to detect outlying observations, and after removing them, applying an efficient non-robust estimator (c.f., Gervini and Yohai 2002)—is not feasible in this context
Summary
Dynamic panel data models with fixed effects have been used in many empirical applications in economics; see Bun and Sarafidis (2015) and Harris et al (2008) for an overview of the methodology and applications. Our aim is to extend these median-based estimators of Dhaene and Zhu (2017) and Aquaro and Cížek (2014) by employing multiple pairwise difference transformations in such a way that the resulting estimator is robust and exhibits good finitesample performance in data without outliers. Higher-order differences have not been previously used since (1) they can result in a substantial increase in bias in the presence of particular types of outliers and (2) their number grows quadratically with the number of time periods, which can lead to additional biases due to weak identification or outliers We address this by proposing a data-driven weighting and selection of the median ratios of differenced data since the traditional strategy used in the robust statistics—using an initial robust estimator to detect outlying observations, and after removing them, applying an efficient non-robust estimator (c.f., Gervini and Yohai 2002)—is not feasible in this context. The existing and proposed methods are compared by means of Monte Carlo simulations in Sect. 4 and the proofs can be found in the “Appendix”
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