This project focuses on the exercise of comparing coefficients across regression specifications, broadly known as robustness checks, a very popular tool in applied economic research. The econometric literature has proposed to formalize this coefficient stability exercise in linear models by turning robustness checks into a robustness test. Unfortunately, for available procedures, a rejection in their proposed test may be due to either a failure in the notion of robustness or to a failure of the linearity of the model, making the robustness test non-specific. I bypass this difficulty by proposing a semi-parametric test based on linear sieve estimators that allows for non-linearity and is specific to testing the coefficient stability.
Supplementary notes can be added here, including code and math.