Heckman application to non-censored data

[Alison El Ayadi]

Hello everyone - I am looking to apply the heckman selection model to a situation where we anticipate sample selection by sociodemographic characteristics (Mother_age_group i.Mother_Edu_Group i.Husband_Occu_group WorkoutsideHome Hindu FirstBirth i.wealthquin i.districtcode) but not due to censoring/lack of observed data.Specifically, I am interested in understanding the relationship between StayingOut6 (binary predictor) and Deliver_PrivateFac (binary outcome), while acknowledging the potential patterning of sociodemographic char on StayingOut6 (binary predictor).

I have modeled this using SEM but am responding to a reviewer who wants a heckman model for this analysis, thus have been reviewing this model. but don't have prior experience with it. When I run the following code:

heckman Deliver_PrivateFac StayingOut6 .Mother_age_group i.Mother_Edu_Group i.Husband_Occu_group WorkoutsideHome Hindu FirstBirth i.wealthquin i.districtcode, twostep select(StayingOut6 i.Mother_age_group i.Mother_Edu_Group i.Husband_Occu_group WorkoutsideHome Hindu FirstBirth i.wealthquin i.districtcode)

I get the error: "Depend variable never censored because of selection: model would simplify to OLS regression".

I wonder: how would I modify the procedure to provide the assessment that I want - or am I/the reviewer misunderstanding the heckman model and is it only applied where selection is due to censoring/missing data?

Thanks so much for any advice, and I am happy to provide any further details.

[Maxence Morlet]

The classical example for the use of Heckman is studying the impact of education on female wages. One only observes a positive wage for females if they work, and this observability is not random, i.e. females do not randomly decide to work. So researchers typically use a Heckman model in this context, with a selection equation to predict (using probit) female's probability to work, and then the outcome equation evaluating the impact of education on wages. Finally, you will need an exclusion restriction: a factor that affects females' probability to work, but not their wage levels. Classically, in the literature, this is the number of children they have.

For Heckman models, observability should be dictated by nonrandom selection. If the selection and outcome equations are identical, Heckman collapses down to Tobit (Johnston and DiNardo, 1997).

Basically, the whole point of Heckman models is to generate an inverse Mills ratio and account for non-random observability of the dependent variable.

Hope this helps!

[Hong Il Yoo]

Alison El Ayadi: I think you'll be able to get a more helpful response from one of us on this forum if you could tell us more about what your reviewer's request is. Did they elaborate on the sample selection issue they had in mind in the context of your research?

Based on your summary, I assume that you always know the value of -Deliver_PrivateFac- regardless of whether -StayingOut6- is equal to one or zero. Also, the selection indicator you're trying to use, -StayingOut6-, is one of regressors in your outcome equation. Thus, there is no sample selection (aka incidental truncation) problem that is relevant to -heckman-. You'd have had a selection problem relevant to -heckman- if -StayingOut6- was not one of your regressors & you knew the value of -Deliver_PrivateFac- only if -StayingOut6- took a particular value.

[Alison El Ayadi]

Thanks so much for this feedback. The sample selection issue is as follows: our main question of interest is whether predictor (StayingOut6 in original post) influences outcome (Delivery_PrivateFac in original post). The reviewer is concerned that both the predictor and the outcome may be influenced by sociodemographic characteristics, in distinct ways, and believed that the Heckman selection model would be the appropriate way to pull these differential impacts apart while being able to estimate the true (with assumptions) relationship between predictor and outcome. All of our data are observed which suggests that the Heckman model is not appropriate, and the SEM approach that I implemented was an appropriate way to model these (also propensity score would have worked).

[Maxence Morlet]

Have you got panel data?

Do you have a potential instrumental variable you could use?

Is the endogenous regressor binary?

[Maxence Morlet]

Given the relatively limited information we have, Heckman is really not adequate here, your reviewer is probably not an econometrician...