My colleague argues to use a Heckman Model in the following case (Agricultural economics):
I have a random sample of farmers (n) of the general population N. In n some observations apply a given technique to improve agricultural productivity whereas others don't. If they use this technique, they can choose to apply it on any given amount of area on their farm. I would like to test whether a given policy change influenced their choice to apply this technique and the subsequent amount of area where this technique is applied, once the choice was positive.
Without deeper econometric knowledge I would use a probit/or logit model to estimate the influence of the policy on choice and a separate OLS to estimate the influence of the policy on the total amount of area where this technique is applied. My colleague, however, argues that estimating a normal OLS might suffer from bias because of variables that determine the set of "technology adopters" in the first place.
My intuition tells me that I can just use these potentially relevant variables as controls in the OLS which will single out their effect. Furthermore, literature suggest, that Heckman is applied to the case where I have a non-random sample where those who are not selected are omitted from the sample in the first place (selection bias). The classical example is the one of incidental truncation where we do not observe the dependent variable y because of the outcome of another variable x. An often cited example is the wage offer function from labor economics where wages are only observed for the workforce and a model of e.g. education on wage suffers from bias (see Wooldrige, 2009. p.606ff).
Certo et al (2016) discuss the usage of Heckman models and argue:
"The first step in implementing a Heckman model involves considering the potential for sample selection bias. As we noted previously, our literature review suggests that scholars often conflate sample selection bias with endogeneity from other sources. A simple rule helps to distinguish between these two alternatives: If the dependent variable is observed for only a subsample of a larger population (e.g., wages for working women, stock market reactions to acquisition announcements, etc.), sample selection is a potential problem. In such cases, Heckman models (i.e., Stata’s “-heckman-”) may help to resolve potential sample selection bias. In contrast, if the dependent variable is available for all observations (e.g., ROI of acquirers versus nonacquirers), then sample selection is likely not an issue. Instead, in such cases the independent variable is likely endogenous, which would require either two-stage least squares (i.e., Stata’s “-ivreg-”) or treatment effects models (i.e., Stata’s “-etregress-”)"
Can anybody highlight me whether I am overseeing something essential here? Also alternative solutions to model my stated problem would be very welcome.