Heckman leads to different results with twostep vs mannual

[Zainab Iftikhar]

Hi Everyone!

I am running a heckman regression, using PSID data, as follows to generate wage margins by age and college/non-college for a sample of women

Code:
heckman lnlabinc i.year##coll i.age##coll, select(morg i.year##coll i.age##coll) twostep //ML doesn't converge

where lnlabinc is the log wage, coll is the dummy for college grads and I have year and age fixed effects. The selection variable is "morg", which takes the value 1 if the household has mortgage. I then run the following command to get the margins

code: margins coll#age, asbalanced nose

I then plot them and get the graph below.


I then run the regression on the same sample in two steps, first running a probit regression (emp is the dummy that takes the value 1 if the person is employed)

code:
probit emp i.year##coll i.age##coll i.morg
predict xb, xb

predict phat, pr

gen imr = normalden(xb)/phat

label variable imr "inverse Mills ratio"

Then a wage regression

code:
reg lnlabinc i.year##coll i.age##coll imr

Then the margins

code: margins coll#age, asbalanced nose

I plot the margins and the results are not at all comparable with what I get from a two step Heckman. The plot with probit and linear regression make more sense as they are close to what I get without controlling for imr. I do not understand why the results are so different. I would highly appreciate any help.


Thank you very much.