Targeted Maximum Likelihood Estimation for Causal Inference With Observational Data-The Example of Private Tutoring

State-of-the-art causal inference methods for observational data promise to relax assumptions threatening valid causal inference. Targeted maximum likelihood estimation (TMLE), for example, is a template for constructing doubly robust, semiparametric, efficient substitution estimators, providing consistent estimates if the outcome or treatment model is correctly specified. Compared to standard approaches, it reduces the risk of misspecification bias by allowing (nonparametric) machine-learning techniques, including super learning, to estimate the relevant components of the data distribution. We briefly introduce TMLE and demonstrate its use by estimating the effects of private tutoring in mathematics during Year 7 on mathematics proficiency and grades using observational data from starting cohort 3 of the National Education Panel Study ($N=$ 4,167). We contrast TMLE estimates to those from ordinary least squares, the parametric G-formula, and the augmented inverse-probability weighted estimator. Our findings reveal close agreement between methods for end-of-year grades. However, variations emerge when examining mathematics proficiency as the outcome, highlighting that substantive conclusions may depend on the analytical approach. The results underscore the significance of employing advanced causal inference methods, such as TMLE, when navigating the complexities of observational data and highlight the nuanced impact of methodological choices on the interpretation of study outcomes.