Partial Independence in Nonseparable Models

Masten, Matthew A.; Poirier, Alexandre

doi:10.2139/ssrn.2797364

Cited by 2 publications

(2 citation statements)

References 60 publications

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“…This assumption implies that the endpoints y x (w) and y x (w) are point identified. We maintain Assumption A1.2 for simplicity, but it can be relaxed using similar derivations as in Masten and Poirier (2016). Assumption A1.3 is an overlap assumption.…”

Section: Supp(ymentioning

confidence: 99%

“…Thus one goal of future research is to explore this space of assumption relaxations, to understand their substantive interpretations, and to chart their implications for the robustness of empirical findings. In Masten and Poirier (2016) we have already compared three different measures of relaxation of the random assignment assumption, including the one used here. We further studied quantile independence, a common relaxation of random assignment, in Masten and Poirier (2018b).…”

Section: Breakdown Frontier Analysis For Other Models and Other Relaxmentioning

confidence: 99%

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Inference on breakdown frontiers

Masten

Poirier

2020

Self Cite

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Given a set of baseline assumptions, a breakdown frontier is the boundary between the set of assumptions which lead to a specific conclusion and those which do not. In a potential outcomes model with a binary treatment, we consider two conclusions: First, that ATE is at least a specific value (e.g., nonnegative) and second that the proportion of units who benefit from treatment is at least a specific value (e.g., at least 50%). For these conclusions, we derive the breakdown frontier for two kinds of assumptions: one which indexes relaxations of the baseline random assignment of treatment assumption, and one which indexes relaxations of the baseline rank invariance assumption. These classes of assumptions nest both the point identifying assumptions of random assignment and rank invariance and the opposite end of no constraints on treatment selection or the dependence structure between potential outcomes. This frontier provides a quantitative measure of the robustness of conclusions to relaxations of the baseline point identifying assumptions. We derive √ N-consistent sample analog estimators for these frontiers. We then provide two asymptotically valid bootstrap procedures for constructing lower uniform confidence bands for the breakdown frontier. As a measure of robustness, estimated breakdown frontiers and their corresponding confidence bands can be presented alongside traditional point estimates and confidence intervals obtained under point identifying assumptions. We illustrate this approach in an empirical application to the effect of child soldiering on wages. We find that sufficiently weak conclusions are robust to simultaneous failures of rank invariance and random assignment, while some stronger conclusions are fairly robust to failures of rank invariance but not necessarily to relaxations of random assignment.

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Section: Supp(ymentioning

confidence: 99%

Section: Breakdown Frontier Analysis For Other Models and Other Relaxmentioning

confidence: 99%

Inference on breakdown frontiers

Masten

Poirier

2020

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Choosing exogeneity assumptions in potential outcome models

Masten

Poirier

2023

The Econometrics Journal

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There are many kinds of exogeneity assumptions. How should researchers choose among them? When exogeneity is imposed on an unobservable like a potential outcome, we argue that the form of exogeneity should be chosen based on the kind of selection on unobservables it allows. Consequently, researchers can assess the plausibility of any exogeneity assumption by studying the distributions of treatment given the unobservables that are consistent with that assumption. We use this approach to study two common exogeneity assumptions: quantile and mean independence. We show that both assumptions require a kind of non-monotonic relationship between treatment and the potential outcomes. We discuss how to assess the plausibility of this kind of treatment selection. We also show how to define a new and weaker version of quantile independence that allows for monotonic selection on unobservables. We then show the implications of the choice of exogeneity assumption for identification. We apply these results in an empirical illustration of the effect of child soldiering on wages.

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Partial Independence in Nonseparable Models

Cited by 2 publications

References 60 publications

Inference on breakdown frontiers

Inference on breakdown frontiers

Choosing exogeneity assumptions in potential outcome models

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