A recent interesting paper Moeller-Zapata, Grieve, Basu and O’Neal (2023) Compare local instrumental variables (LIV) with two-stage least squares (2SLS) with IV.
Local instrumental variable (LIV) methods use continuous/multivalued instrumental variables (IV) to generate consistent estimates of the mean treatment effect (ATE) and the conditional mean treatment effect (CATE). There is little evidence of how the LIV method works based on the strength of the IV or varying sample sizes. Our simulation study examines the performance of the LIV method and the two-stage least squares (2SLS) method at different sample sizes and IV strengths. We considered four scenarios of ‘heterogeneity’: homogeneity, apparent heterogeneity (overmeasured covariate), intrinsic heterogeneity (not measured), and a combination of explicit and intrinsic heterogeneity. In all cases, the estimates reported by LIV have low bias even at the smallest sample sizes, provided the tool is sufficiently powerful. LIV provides estimates of ATE and CATE with lower levels of bias and root mean square error compared to 2SLS. Due to the small sample size, both methods require stronger IVs to ensure low bias. We considered both approaches in our evaluation of emergency surgery (ES) for three acute gastrointestinal conditions. While 2SLS found no difference in the effectiveness of ES across subgroups, LIV reported that frail patients had poorer outcomes after ES. In the setting of moderate-intensity serial IV, the LIV method was better suited than 2SLS for estimating policy-relevant treatment effect parameters.
LIV may seem superior, but the key is not only to have a powerful tool, but that tool must be multi-valued (i.e. non-binary) and have sufficient support.Empirical applications are for ESORT (Emergency Surgery or Not) Study Emergency surgery to check for three gastrointestinal disorders: acute appendicitis, gallstone disease, and abdominal wall hernias. Compared to 2SLS, LIV is less biased, especially at small sample sizes, and as shown in the figure below, using root mean square error (RMSE), LIV also provides more precise estimates, especially at sample sizes lesser cases. This is true even in the presence of heterogeneity.
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