Tobit Model Decomposition (Marginal effects for probability of adoption and marginal effects for Intensity of adoption)

[tsegaye molla]

I am working on adoption study with non-adopter category and non-adopter category. How can I decompose marginal effects of Tobit model in to probability and intensity using stata 14? I am kindly looking for a command to decompose (Probability of adoption for non-adopter group and Intensity of adoption for adopter group).

[John Mullahy]

Perhaps something like this will work

tobit y x1 x2
/* probability */   margins, dydx(*) predict(pr(0,.))
/* intensity   */   margins, dydx(*) predict(e(0,.))

This assumes your LHS variable is in [0,∞).

[tsegaye molla]

Dear John Mullahy,

Thank you so much for your assistance.

One more please,

What you suggested works on Stata 14.

Can you still help me in the command to decompose separately Tobit into: Probability, Intensity, and total change (sum of the first two to be the total change in some papers) as illustrated here below:

[John Mullahy]

For total change I assume you mean with respect to the observed (censored) values of the outcome, e.g. E[y|x], where y≥0. For this:

tobit y x1 x2
/* probability */ margins, dydx(*) predict(pr(0,.))
/* intensity   */ margins, dydx(*) predict(e(0,.))
/* total       */ margins, dydx(*) predict(ystar(0,.))

The documentation for margins after tobit is perhaps a bit confusing since the notation y* is often used for the latent (uncensored) outcome. But using ystar(.) should give the proper response since it yields the same margins results as the more intuitive formulation

margins, dydx(*) expression(predict(pr(0,.))*predict(e(0,.)))

[tsegaye molla]

Dear John.,

I am on the right track following your intuitive direction.
probability and the intensity issue work.
But, for the total, I add the probability and intensity as:
margins, dydx(*) expression(predict(pr(0,.))+predict(e(0,.))) But, my TWO worries are: 1) margins, dydx(*) expression(predict(pr(0,.))*predict(e(0,.))) didn't yet bring exactly the sum of probability & intensity. E.g 0.01+0.327=0.337 as shown in this table. 2) margins, dydx(*) predict(ystar(0,.)) gives exactly same result with margins, dydx(*) predict(ystar(0,.)). Hence, I run this:
margins, dydx(*) expression(predict(pr(0,.))+predict(e(0,.))) and it gives me the exact sum of probability and intensity as shown in this table.

Can I go on with such command? I read extensively beyond your kind advice.
Thank you so much John.

[John Mullahy]

The overall marginal effect relies on a chain-rule result since E[y|x]=Pr(y>0|x)*E[y|x,y>0]. Thus:

dE[y|x]/dx = Pr(y>0|x)*dE[y|x,y>0]/dx + E[y|x,y>0]*dPr(y>0|x)/dx.

That is, the overall marginal effect is not just the sum of the two separate marginal effects.

[tsegaye molla]

Dear John Thank you very much for all your scholastic guidance. I was a bit disconnected to get back to you soon.

[Silas Ongudi]

Dear John, Please help me generate the IV Tobit mode decomposition. A reviewer has asked me to decompose my IV Tobit model as shown in Table 4 of Juarez's (2006) paper attached. The above codes seem to only give me answers to columns 2, 3, and 5. I am unable to reproduce columns, 5, 6, and 7.

As I can see from this paper,
column 2 is this code margins, dydx(*) predict(pr(0,.)));
column 3 : margins, dydx(*) predict(e(0,.)) and
column 4 :margins, dydx(*) expression(predict(pr(0,.))*predict(e(0,.)))

The question is now on other columns: 2nd part of Tobit decomposition
column 5 Pr(T>0)
column 6: dE(T|T>0)/dY
column 7: pr(T>0)*dE(T|T>0)/dY
column 8: dE(T)/dY

Please help