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This paper evaluates the effects of being an only child in a family on psychological health, leveraging data on the One-Child Policy in China. We use an instrumental variable approach to address the potential unmeasured confounding between the fertility decision and psychological health, where the instrumental variable is an index on the intensity of the implementation of the One-Child Policy. We establish an analytical link between the local instrumental variable approach and principal stratification to accommodate the continuous instrumental variable. Within the principal stratification framework, we postulate a Bayesian hierarchical model to infer various causal estimands of policy interest while adjusting for the clustering data structure. We apply the method to the data from the China Family Panel Studies and find small but statistically significant negative effects of being an only child on self-reported psychological health for some subpopulations. Our analysis reveals treatment effect heterogeneity with respect to both observed and unobserved characteristics. In particular, urban males suffer the most from being only children, and the negative effect has larger magnitude if the families were more resistant to the One-Child Policy. We also conduct sensitivity analysis to assess the key instrumental variable assumption. 

Estimating causal effects under exogeneity hinges on two key assumptions: unconfoundedness and overlap. Researchers often argue that unconfoundedness is more plausible when more covariates are included in the analysis. Less discussed is the fact that covariate overlap is more difficult to satisfy in this setting. In this paper, we explore the implications of overlap in observational studies with high-dimensional covariates and formalize curse-of-dimensionality argument, suggesting that these assumptions are stronger than investigators likely realize. Our key innovation is to explore how strict overlap restricts global discrepancies between the covariate distributions in the treated and control populations. Exploiting results from information theory, we derive explicit bounds on the average imbalance in covariate means under strict overlap and show that these bounds become more restrictive as the dimension grows large. We discuss how these implications interact with assumptions and procedures commonly deployed in observational causal inference, including sparsity and trimming. 

Summary It is important to draw causal inference from observational studies, but this becomes challenging if the confounders have missing values. Generally, causal effects are not identifiable if the confounders are missing not at random. In this article we propose a novel framework for nonparametric identification of causal effects with confounders subject to an outcome-independent missingness, which means that the missing data mechanism is independent of the outcome, given the treatment and possibly missing confounders. We then propose a nonparametric two-stage least squares estimator and a parametric estimator for causal effects. 

Abstract The Pandora Software Development Kit and algorithm libraries provide pattern-recognition logic essential to the reconstruction of particle interactions in liquid argon time projection chamber detectors. Pandora is the primary event reconstruction software used at ProtoDUNE-SP, a prototype for the Deep Underground Neutrino Experiment far detector. ProtoDUNE-SP, located at CERN, is exposed to a charged-particle test beam. This paper gives an overview of the Pandora reconstruction algorithms and how they have been tailored for use at ProtoDUNE-SP. In complex events with numerous cosmic-ray and beam background particles, the simulated reconstruction and identification efficiency for triggered test-beam particles is above 80% for the majority of particle type and beam momentum combinations. Specifically, simulated 1 GeV/ c charged pions and protons are correctly reconstructed and identified with efficiencies of 86.1 $$\pm 0.6$$ ± 0.6 % and 84.1 $$\pm 0.6$$ ± 0.6 %, respectively. The efficiencies measured for test-beam data are shown to be within 5% of those predicted by the simulation.