{"id":218,"date":"2025-04-10T07:57:56","date_gmt":"2025-04-10T07:57:56","guid":{"rendered":"https:\/\/www.endogeneity.net\/?page_id=218"},"modified":"2026-04-07T07:03:21","modified_gmt":"2026-04-07T07:03:21","slug":"evaluating-endogeneity","status":"publish","type":"page","link":"https:\/\/www.endogeneity.net\/?page_id=218","title":{"rendered":"Sensitivity Analysis"},"content":{"rendered":"

Sensitivity Analysis<\/strong><\/span><\/p>\n

After addressing plausible confounding through rich controls and fixed effects, accounting for latent heterogeneity, and mitigating simultaneity and measurement error, researchers must assess whether meaningful endogeneity concerns remain. Because no statistical test can directly detect endogeneity, this assessment relies on sensitivity analysis.<\/p>\n

The Core Idea<\/strong><\/p>\n

A common endogeneity critique is that an estimated effect may be driven by an unobserved confound. Sensitivity analysis as developed by Frank (2000) reframes this critique as a quantitative question: how strong would an unobserved confound need to be to change the conclusion?<\/span>
\n
\nRather than debating whether bias exists, the approach asks how much bias would be required to push an estimate below a specified threshold, whether that threshold reflects statistical significance or managerial relevance.<\/span><\/p>\n

An Example<\/strong><\/p>\n

Consider a retailer that deploys personalized coupons through its app. Estimated spending increases following coupon exposure, but a critic argues that higher-propensity customers were more likely to receive the coupon, rendering the estimated lift non-causal. The sensitivity analysis does not try to settle this debate directly. Instead, it asks: how strong would that unobserved propensity need to be to make the estimated coupon effect disappear?<\/p>\n

Impact Threshold for a Confounding Variable (ITCV)<\/strong><\/p>\n

The ITCV quantifies the minimum strength an unobserved confound would need, in partial-correlation terms, conditional on observed controls \u2014 to overturn a focal inference.<\/p>\n

The key insight is that an unobserved confound threatens inference only if it is related to both the predictor and the outcome. The ITCV captures this as the product of these two partial correlations. If no observed control variable in the model exerts an influence of comparable magnitude, an unobserved confound of the required strength is less plausible.<\/p>\n

Beyond Inflated Effects<\/strong><\/em><\/p>\n

The ITCV is most directly informative when confounding inflates an estimated effect, raising Type I error concerns. But the same logic applies to suppression, situations where confounding masks a true effect. By redefining the inference threshold relative to a substantively meaningful benchmark, researchers can assess how much bias would be required to sustain an incorrect conclusion that an effect is negligible or nonexistent.<\/p>\n

Supported model types:<\/span><\/em><\/p>\n