# Predicted probabilities - Tobit/probit - differences

For long I have been a silent reader of your forum, but now I have to ask you for your expertise, as I haven't found an answer to my question yet.

Short to my back story: My aim is to calculate the predicted probabilities that a country receives development aid from a donor with Stata14. The models under evaluation are the tobit (xttobit) and the probit. The supervisor of my thesis suggested the use of the Tobit, as the dependent variable (USD value of aid flows in year t) contains roughly 35% zeroes. However, is there actually an advantage of the Tobit over the Probit if i just want the probabilities to receive aid?

In see the point of the Tobit model, if I want to calculates estimates of E(Y*) but not for estimates of Pr(0 < y < +∞).

Best, Jules

• I decided to change my focus on the marginal effect of E(y* | x ), as it seems that the Tobit estimator is not perfectly suited for calculating the probabilities of receiving aid Pr(0 < y < +∞), as David already stated: > "The estimated probability that a country gets aid might have little relationship to how much aid a country gets." Thanks again for your comment. – Jules Watson Jun 8 '17 at 22:10

The tobit and probit methods are quite different models; they should not be seen as slightly different variations of each other.

The probit method, as you have noted, only uses information about whether or not a country received aid. It uses no information whatever about the amount of aid.

The tobit method uses information about how much aid a country receives and incorporates the characteristics of countries that receive no aid.

The estimated parameters have no relationship, in principle, when most of the observations have an observed positive value of the dependent variable. Even when a small proportion of the observations have a positive value the estimates of the coefficients can be quite different.

The estimated probability that a country gets aid might have little relationship to how much aid a country gets.

The two models estimate quite different things, an amount of aid and the occurence or nonoccurence of any aid whatever. These might depend on different independent variables or depend on them in different ways.

It is clear that the two methods are designed to meet different objectives. Decide what your purpose is and you have the answer to what methods you need.