arXiv subjects

Alexandre Poirier

Publications and source records attributed to Alexandre Poirier.

22 records · Page 2Linked to original sources

arXiv2020

Salvaging Falsified Instrumental Variable Models

What should researchers do when their baseline model is refuted? We provide four constructive answers. First, researchers can measure the extent of falsification. To do this, we consider continuous relaxations of the baseline assumptions of concern. We then define the falsification frontier: The smallest relaxations of the baseline model which are not refuted. This frontier provides a quantitative measure of the extent of falsification. Second, researchers can present the identified set for the parameter of interest under the assumption that the true model lies somewhere on this frontier. We call this the falsification adaptive set. This set generalizes the standard baseline estimand to account for possible falsification. Third, researchers can present the identified set for a specific point on this frontier. Finally, as a sensitivity analysis, researchers can present identified sets for points beyond the frontier. To illustrate these four ways of salvaging falsified models, we study overidentifying restrictions in two instrumental variable models: a homogeneous effects linear model, and heterogeneous effect models with either binary or continuous outcomes. In the linear model, we consider the classical overidentifying restrictions implied when multiple instruments are observed. We generalize these conditions by considering continuous relaxations of the classical exclusion restrictions. By sufficiently weakening the assumptions, a falsified baseline model becomes non-falsified. We obtain analogous results in the heterogeneous effect models, where we derive identified sets for marginal distributions of potential outcomes, falsification frontiers, and falsification adaptive sets under continuous relaxations of the instrument exogeneity assumptions. We illustrate our results in four different empirical applications.

econ.EM↗

arXiv2019

Inference on Breakdown Frontiers

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 robustness of conclusions to relaxations of the baseline point identifying assumptions. We derive $\sqrt{N}$-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.

stat.ME↗

arXiv2018

Interpreting Quantile Independence

How should one assess the credibility of assumptions weaker than statistical independence, like quantile independence? In the context of identifying causal effects of a treatment variable, we argue that such deviations should be chosen based on the form of selection on unobservables they allow. For quantile independence, we characterize this form of treatment selection. Specifically, we show that quantile independence is equivalent to a constraint on the average value of either a latent propensity score (for a binary treatment) or the cdf of treatment given the unobservables (for a continuous treatment). In both cases, this average value constraint requires a kind of non-monotonic treatment selection. Using these results, we show that several common treatment selection models are incompatible with quantile independence. We introduce a class of assumptions which weakens quantile independence by removing the average value constraint, and therefore allows for monotonic treatment selection. In a potential outcomes model with a binary treatment, we derive identified sets for the ATT and QTT under both classes of assumptions. In a numerical example we show that the average value constraint inherent in quantile independence has substantial identifying power. Our results suggest that researchers should carefully consider the credibility of this non-monotonicity property when using quantile independence to weaken full independence.

econ.EM↗

arXiv2017

Identification of Treatment Effects under Conditional Partial Independence

Conditional independence of treatment assignment from potential outcomes is a commonly used but nonrefutable assumption. We derive identified sets for various treatment effect parameters under nonparametric deviations from this conditional independence assumption. These deviations are defined via a conditional treatment assignment probability, which makes it straightforward to interpret. Our results can be used to assess the robustness of empirical conclusions obtained under the baseline conditional independence assumption.

stat.ME↗