In implementing the IV design pattern **on the same data for the same problem**, we have used: - [[Statistical modeling of IV|a statistical model]] - [[(Double) Machine learning using IV|machine learning]] - [[IV the Bayesian way|Bayesian estimation]] We motivated the problem using the same [[Data and conceptual model|data and conceptual model]] and solved it using both `R` and `Python` (along with [[Naïve model in Stata|Stata]] for some robustness checks on the standard error). What have we learned so far? As long as the underlying conceptual model and the data are the same, the results are consistent across the board. However, we are able to mitigate the model misspecification error by using a doubly robust estimator as in [[(Double) Machine learning using IV]], especially when [[Model complexity|model complexity]] is high. We are also able to show the heterogeneity in the effect more clearly by modeling the [[IV the Bayesian way]] and using the many ways we can visualize the distributions of the posterior samples. The most important lesson is that methods don't matter so much when it comes to estimating causal effects; it's the conceptual model and related data and assumptions that matter. Estimating causal effects depends on the availability of data that support the conceptual model, and the methods serve only as tools to link the data to the results by making valid assumptions. > [!info]- Last updated: February 3, 2025