Now showing 1 - 4 of 4
  • Publication
    Shrinkage for Categorical Regressors
    (North-Holland, 2021-07)
    Heiler, Phillip
    ;
    This paper introduces a flexible regularization approach that reduces point estimation risk of group means stemming from e.g. categorical regressors, (quasi-)experimental data or panel data models. The loss function is penalized by adding weighted squared l2-norm differences between group location parameters and informative first stage estimates. Under quadratic loss, the penalized estimation problem has a simple interpretable closed-form solution that nests methods established in the literature on ridge regression, discretized support smoothing kernels and model averaging methods. We derive risk-optimal penalty parameters and propose a plug-in approach for estimation. The large sample properties are analyzed in an asymptotic local to zero framework by introducing a class of sequences for close and distant systems of locations that is sufficient for describing a large range of data generating processes. We provide the asymptotic distributions of the shrinkage estimators under different penalization schemes. The proposed plug-in estimator uniformly dominates the ordinary least squares estimator in terms of asymptotic risk if the number of groups is larger than three. Monte Carlo simulations reveal robust improvements over standard methods in finite samples. Real data examples of estimating time trends in a panel and a difference-in-differences study illustrate potential applications.
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  • Publication
    Comprehensive Causal Machine Learning
    Uncovering causal effects at various levels of granularity provides substantial value to decision makers. Comprehensive machine learning approaches to causal effect estimation allow to use a single causal machine learning approach for estimation and inference of causal mean effects for all levels of granularity. Focusing on selection-on-observables, this paper compares three such approaches, the modified causal forest (mcf), the generalized random forest (grf), and double machine learning (dml). It also provides proven theoretical guarantees for the mcf and compares the theoretical properties of the approaches. The findings indicate that dml-based methods excel for average treatment effects at the population level (ATE) and group level (GATE) with few groups, when selection into treatment is not too strong. However, for finer causal heterogeneity, explicitly outcome-centred forest-based approaches are superior. The mcf has three additional benefits: (i) It is the most robust estimator in cases when dml-based approaches underperform because of substantial selectivity; (ii) it is the best estimator for GATEs when the number of groups gets larger; and (iii), it is the only estimator that is internally consistent, in the sense that low-dimensional causal ATEs and GATEs are obtained as aggregates of finer-grained causal parameters.
  • Publication
    Comprehensive Causal Machine Learning
    Uncovering causal effects at various levels of granularity provides substantial value to decision makers. Comprehensive machine learning approaches to causal effect estimation allow to use a single causal machine learning approach for estimation and inference of causal mean effects for all levels of granularity. Focusing on selection-on-observables, this paper compares three such approaches, the modified causal forest (mcf), the generalized random forest (grf), and double machine learning (dml). It also provides proven theoretical guarantees for the mcf and compares the theoretical properties of the approaches. The findings indicate that dml-based methods excel for average treatment effects at the population level (ATE) and group level (GATE) with few groups, when selection into treatment is not too strong. However, for finer causal heterogeneity, explicitly outcome-centred forest-based approaches are superior. The mcf has three additional benefits: (i) It is the most robust estimator in cases when dml-based approaches underperform because of substantial selectivity; (ii) it is the best estimator for GATEs when the number of groups gets larger; and (iii), it is the only estimator that is internally consistent, in the sense that low-dimensional causal ATEs and GATEs are obtained as aggregates of finer-grained causal parameters.
  • Publication
    How well can Noncognitive Skills predict Unemployment? A Machine Learning Approach
    ( 2019-09-11) ;
    Pohlmeier, Winfried
    Presentation at the German Statistical Week 2019 in Trier