Working Paper: NBER ID: w30302
Authors: Victor Chernozhukov; Carlos Cinelli; Whitney Newey; Amit Sharma; Vasilis Syrgkanis
Abstract: We derive general, yet simple, sharp bounds on the size of the omitted variable bias for a broad class of causal parameters that can be identified as linear functionals of the conditional expectation function of the outcome. Such functionals encompass many of the traditional targets of investigation in causal inference studies, such as, for example, (weighted) average of potential outcomes, average treatment effects (including subgroup effects, such as the effect on the treated), (weighted) average derivatives, and policy effects from shifts in covariate distribution -- all for general, nonparametric causal models. Our construction relies on the Riesz-Frechet representation of the target functional. Specifically, we show how the bound on the bias depends only on the additional variation that the latent variables create both in the outcome and in the Riesz representer for the parameter of interest. Moreover, in many important cases (e.g, average treatment effects and avearage derivatives) the bound is shown to depend on easily interpretable quantities that measure the explanatory power of the omitted variables. Therefore, simple plausibility judgments on the maximum explanatory power of omitted variables (in explaining treatment and outcome variation) are sufficient to place overall bounds on the size of the bias. Furthermore, we use debiased machine learning to provide flexible and efficient statistical inference on learnable components of the bounds. Finally, empirical examples demonstrate the usefulness of the approach.
Keywords: sensitivity analysis; short regression; long regression; omitted variable bias; omitted confounders; causal models; machine learning; confidence bounds
JEL Codes: C14; C21; C31
Edges that are evidenced by causal inference methods are in orange, and the rest are in light blue.
| Cause | Effect |
|---|---|
| Omitted Variable Bias (OVB) (C20) | Estimated Causal Parameters (C51) |
| Bias in estimating Average Treatment Effect (ATE) (C22) | Covariance between regression errors and errors from Riesz representers (C21) |
| Omitted Confounders (C20) | Distortion of inferred causal relationships (C22) |
| Squared Bias (C46) | Product of additional variations from omitted confounders (C29) |
| Omitted Variables (C29) | Outcome and treatment regressions (C22) |
| Explanatory power of omitted variables (C20) | Bounds on bias (C46) |
| 401k eligibility (L26) | Financial assets (G19) |