Choosing Wisely: Evaluating Latent Factor Models in the Presence of Contaminated Instrumental Variable with Differing Strength

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Causal inference methods are widely used in empirical research; however, there is a paucity of evidence on the properties of shared latent factor estimators in the presence of contaminated instrumental variable (IV) when strong IV may not be available. We present a theoretical formulation to depict how the strength of an IV and the degree of contamination simultaneously determine the optimal choice of estimator. We perform Monte Carlo simulations with four outcome variables and an endogenous treatment variable, with sample sizes varying between 500 and 1000, and for 1000 iterations, to compare the finite sample properties of the OLS, 2SLS, shared latent factor (SLF), and shared latent factor with IV (SLF+IV) estimators. Finally, we demonstrate the applicability of the proposed estimators to study the causal impact of obesity on different health indicators: diastolic blood pressure, systolic blood pressure, blood glucose level and hemoglobin level, using data from the 2019-21 Round 5 of the National Family Health Survey (NFHS-5) from India. Our simulation results indicate that, for a given strength of the IV, there exists a threshold degree of contamination, such that the SLF+IV estimator has a lower (greater) bias than the SLF estimator when the degree of contamination lies below (above) that threshold. Similarly, we find that for a given degree of contamination of the IV, there exists a threshold strength of the IV, such that the SLF+IV has a lower (greater) bias than the SLF estimator if the strength of the IV lies above (below) that threshold. The empirical results suggest that obesity is significantly associated with higher diastolic and systolic readings, a higher blood sugar level, and a higher haemoglobin level in the blood.