Exclusion restriction in heckprobit

[Sayoree Gooptu]

I am running heckprobit regression in stata. The outcome variable determines school choice - government=1 and private =0. The selection equation takes into account whether the child is currently attending education. I have added an exclusion restriction in the selection equation - headedu, which is a dummy variable.
headedu=1 if the household head has completed class 10
The reason I have included this is that a household with an educated head is more likely to send their child to school

On adding this, my main explanatory variable in the outcome equation is positive significant. However, the result changes when I use another exclusion restriction

bpl=1 if the children comes from the lowest consumption expenditure quantile. I justify this by saying that for very low income households, choice of attending school is a more serious concern than school choice.

It would be really helpful, if I get some clarification on what kind of restriction to use.

Thanks in advance

Sayoree Gooptu

[Maarten Buis]

So you need a variable that influences whether or not a child attends school, but does not influence whether or not that child attends a public or private school. That is obviously very very hard. If you have such a variable in your data, then heckprobit is a very powerful command. However, it is likely that your dataset does not have such a variable. If that is the case than heckprobit just cannot be used. Also see: https://www.statalist.org/forums/for...eniety-results

[Sayoree Gooptu]

Okay thanks a lot.

As an alternative specification, I was also wondering whether nested logit would work. However, since my main regressor 'price of private tuitions' is alternative invariant, I chose the other heckprobit method.

[Jeff Wooldridge]

This isn't directly related to your question, but your example is the kind that causes conceptual problems for me. You're including in your population children who are not currently in school, and so you are doing the following counterfactual: if the child were in school, would it be public or private? I suppose you're thinking of a future where, say, all children are forced to attend school? In Heckman's classic example, we are interested in the wage offer function for the entire population, but we only observe the wage offer for those working. This makes sense to me. Many other "selection" issues do not. Long ago I saw someone using selection corrections in health care cost equations to account for people who have passed away. Your example obviously isn't that extreme, but I wonder if you really want the answer to the question that heckprobit is supposed to provide. A case could be made for conditioning on attending school.

[Sayoree Gooptu]

Thank you for your response and suggestion, Professor Woolridge.

If I had only included in the sample, children attending some type of school, wouldn't that raise concerns about selection problems, if the decision of school choice and attendance are correlated?

As, I mentioned in my earlier reply, I was also considering nested logit. But since my main regressor is an alternate invariant one, I could not proceed.

[Jeff Wooldridge]

It can only be a "selection" problem once you have stated the population. If I say the analysis is for children currently enrolled in school then there can be none. You have to state very clearly what you hope to estimate from what population.

[Sayoree Gooptu]

I want to estimate school choice (government vs private) for the population. I have a population of students where there are both types - children attending and those not attending school. But the school choice information which I have is available only for those attending school. That is the reason I have decided on using a two stage regression (heckprobit).

However, I first conducted a basic probit regression only for those children who are currently attending schooling (eliminating those not attending school), since school choice data is availlable for them only. My outcome variable is
Y1=1 if the child attends government school and
Y1=0 if he/she attends private school.
After that, considering a possible sample selection problem, I have conducted a heckprobit regression including a selection equation, which accounts for whether or not the child is attending school. If the selection equation dependent variable is Y2, we have
Y2=1 if the child currently attends school and
Y2=0 if the child does not attend school.

Is my method correct?

[Maarten Buis]

Given your wording you seem mistake the sample for the population. The choice you need to make first is decide on what population interests you. Are these all children in your country born between yyyy and zzzz,or are they all children in your country who attend classes y till z? This is a choice you need to make before considering the data.

After you decide what your sample is, you look at the data: this is the sample. Then you look at the design of the sample and see if it is a sample from your chosen population, and if not, if you can fix it.

So what you have is irrelevant when deciding what population you want. You only look at your research question.