Feature: Support ORIV Strategy to Handle Measurement Error in Covariates and Dependent Variables

[s3alfisc]

@dsliwka pointed me to this paper by Gillen et al on handling measurement error via IV: link. An ungated version of the paper can be found here.

To support the method via pyfixest, we would have to define a user-friendly API to run the following stacked instrumental variables regression

where $Y_a$ and $Y_b$ and $X_a$ and $X_b$ are two measurements of the same underlying construct.

One option would be to define an API as follows:

def oriv(*fmls, data, vcov=None, **options):
   # process data to get data_stacked and fml_stacked
   # then call pf.feols() to support all post-estimation procedures
   fit = pf.feols(fml = fml_stacked, data = data_stacled) 
   return fit

For more than one covariate with error, we would have to support multiple endogenous variables via GMM estimation, for which we should of course use gmm =) In this case, a larger update of the Feiv class would be required:

• The FixestFormula class would have to be reworked to support multiple endogenous variables
• The Feiv.fit() method would have to be adjusted to support GMM estimation.

Overall likely not a massive amount of work to support multiple endogeneous variables (?)