I have two models, one with endogeneity correction (includes correction terms obtained using Heckman) and one without. The correction terms are significant in the second stage model, yet the AIC/BIC values of the model without the endogeneity correction is lower.
Significant correction terms suggest presence of endogeneity and hence the need to correct for the same. However, the AIC/BIC values suggest that correction is not required.
The model with the correction term makes more sense to me, but I would like to hear from the community about this anomaly and how do I justify using the model with the correction terms despite a higher AIC.
