Implementing the Latent Instrumental Variables Approach
The latent instrumental variables approach addresses omitted variables, simultaneity, and measurement error with the assumption that the distributional properties remove the endogenous part of the predictor (Ebbes et al. 2005; Gui et al. 2023). Nonnormality of predictor and normality of residual are required. In a combined estimation, a discrete, unobserved, latent instrumental variable decomposes the variance of the predictor into exogenous and endogenous parts, and the predictor is replaced with the exogenous and endogenous part.
The rEndo package can be used to implement a latent instrumental variable with two categories in R (https://cran.r-project.org/web/packages/REndo/index.html), without additional control variables in the model..
#load the rEndo package
library (rEndo)
#estimate the latent instrumental variables -corrected regression
model_LIV <- latentIV(Outcome ~ Predictor, data = Dataset)
The functionality of the rEndo package is not directly available in Stata.
References
Ebbes, Peter, Michel Wedel, Ulf Böckenholt, and Ton Steerneman (2005), “Solving and Testing for Regressor-Error (In)Dependence when no Instrumental Variables are available: With New Evidence for the Effect of Education on Income,” Quantitative Marketing and Economics, 3, 365-392.
Gui, Raluca, Markus Meierer, Patrik Schilter, and René Algesheimer (2023), “REndo: An R Package to Address Endogeneity Without External Instrumental Variables,” Journal of Statistical Software, 107(3), 1–43.