Table 2 Comparison of Regression, IPTW, and 2SLS under Unobserved Confounding
Regression | IPTW | 2SLS | |
|---|---|---|---|
Mechanism | Hold constant variables \(\leftrightarrow\) Block paths on DAG | Balance groups via overweighting “rare” individuals \(\leftrightarrow\) Eliminate arrows in DAG via independence | Identify treatment from variation independent from unobserved confounding \(\leftrightarrow\) Create a new DAG with no backdoor paths for treatment |
Consistency Assumptions | |||
\(\bullet\) SUTVA | \(\bullet\) SUTVA | \(\bullet\) SUTVA | |
\(\bullet\) No unmeasured confounders | \(\bullet\) No unmeasured confounders | \(\bullet\) IVs are predictive of treatment assignment | |
\(\bullet\) Positivity | \(\bullet\) Positivity and No Near-Violations | \(\bullet\) IVs are as good as randomized | |
\(\bullet\) Does not directly affect outcome | |||
\(\bullet\) (For ATE) no treatment effect heterogeneity | |||
\(\bullet\) (For LATE) monotonicity | |||
Considerations | |||
\(\bullet\) Inconsistency amplification with inclusion of IVs | \(\bullet\) Inconsistency amplification with inclusion of IVs | \(\bullet\) Inefficiency compared to confounder methods | |
\(\bullet\) Treatment effect heterogeneity: conditional effect \(\ne\) marginal effect | \(\bullet\) Fitting propensity score model mistaken for prediction task | \(\bullet\) Validity possibly contingent on unobserved confounders | |
\(\bullet\) With higher dimensionality, difficult to interpret positivity violations | \(\bullet\) Treatment effect heterogeneity: LATE \(\ne\) ATE | ||
\(\bullet\) Balancing on observed confounders does not imply balance on unobserved confounders | \(\bullet\) LATE difficult to interpret for many IVs, weak IVs, and inclusion of covariates | ||
\(\bullet\) Treatment effect heterogeneity: estimates marginal effect | \(\bullet\) Weak IVs: increased finite bias and increased sensitivity to validity violations |