Hi, I am preparing for an Honour Thesis right now and I need to be directed on
(1) Appropriateness of my model
(2) The right syntax to be used



I am working on the topic of Intergenerational Income Mobility, which the ideal model is as follows:

log Ys = α+ β1log Yf + β2multiple characteristics of child + β3age+ β4age2+ ui

Where Y refer to the earnings of the son denoted by s and the earning of the father denoted by f at age 40. The datasets that I have are unfortunately annual data, so I used the TS2SLS method as proposed, by multiple researches.

To achieve this I modelled

log Yf = γ + δ1age + δ2age2 + δ3multiple characteristics of father + vi to estimate δ2, δ1,γ and δ3 to generate log Yf at the age of 40 with characteristics found in another dataset, as these are characteristics described by the child.

Then I will use the predicted log Yf (hat) and substitute into the main equation and normalise the son's age to 40 and estimate β1.

However, I do not know how to transfer the standard errors over into the reduced form equation, if I were to regress step by step.

Can I know what are the proposed commands or syntax in STATA which I could use? I saw bootstrapping, but I am unsure of how bootstrapping might map the standard errors from the first stage into the second stage.

Thank you!