A note on endogeneity correction methods:¶
In the empirical part of their paper, CHS use two methods for endogeneity correction. Both require very strong assumptions on the scale of factors. Below I give an overview of the proposed endogeneity correction methods that can serve as a starting point for someone who wants to extend skillmodels in that direction:
In secton 4.2.4 CHS extend their basic model with a time invariant individual specific heterogeneity component, i.e. a fixed effect. The time invariance assumption can only be valid if the scale of all factors remains the same throughout the model. This is highly unlikely, unless age invariant measurements (as defined by Wiswall and Agostinelli) are available and used for normalization in all periods for all factors. With KLS transition functions the assumption of the factor scales remaining constant in all periods is highly unlikely (see: Why KLS functions don’t keep the scales constant). Moreover, this approach requires 3 adult outcomes. If you have a dataset with enough time invariant measurements and enough adult outcomes, this method is suitable for you and you could use the Fortran code by CHS as a starting point.
In 4.2.5 they make a endogeneity correction with time varying heterogeneity. However, this heterogeneity follows the same AR1 process in each period and relies on an estimated time invariant investment equation, so it also requires the factor scales to be constant. This might not be a good assumption in many applications. Moreover, this correction method relies on a exclusion restriction (Income is an argument of the investment function but not of the transition functions of other latent factors) or suitable functional form assumptions for identification.
To use this correction method in models where not enough age invariant measurements are available to ensure constant factor scales, one would have to replace the AR1 process by a linear transition function with different estimated parameters in each period and also estimate a different investment function in each period. I don’t know if this model is identified.
I don’t know if these methods could be used in the WA estimator.
Wiswall and Agostinelli use a simpler model of endegeneity of investments that could be used with both estimators. See section 6.1.2 of their paper.