Despite their popularity, machine learning predictions are sensitive to potential unobserved predictors. This paper proposes a general algorithm that assesses how the omission of an unobserved variable with high explanatory power could affect the predictions of the model. Moreover, the algorithm extends the usage of machine learning from pointwise predictions to inference and sensitivity analysis. In the application, we show how the framework can be applied to data with inherent uncertainty, such as students' scores in a standardized assessment on financial literacy. First, using Bayesian Additive Regression Trees (BART), we predict students' financial literacy scores (FLS) for a subgroup of students with missing FLS. Then, we assess the sensitivity of predictions by comparing the predictions and performance of models with and without a highly explanatory synthetic predictor. We find no significant difference in the predictions and performances of the augmented (i.e., the model with the synthetic predictor) and original model. This evidence sheds a light on the stability of the predictive model used in the application. The proposed methodology can be used, above and beyond our motivating empirical example, in a wide range of machine learning applications in social and health sciences.