I'm currently performing some research, and need some help with the Heckman self selection correction that i want to use. the model is use for my research includes a dummy variable which is prone to self selection. to control for this i would like to use the Heckman model. is this applicable? second, i see some articles correct with the use of the Heckman model by including the lambda in the final model. while other articles calculate 2 different values for lambda dependent on the value of the dummy variable in the model. what is the reasoning behind this? does it have to do with the difference between controlling for sample selection and/or self-selection?
1) Yes it is applicable (pertinent) 2) Using the dummy as the dependent, you estimate the parameters of a probit. Then, you evaluate the probit (get the propensity scores) for treated and untreated units. Afterwards, you use the outcome variable as the dependent, and among the regressors you include the inverse Mills ratios (which you call lambda), which are a function of the propensity score. This because of the properties of the truncated normal distribution. You make this second step for treated units and untreated units. This is a selection model.
You might find usefull Heckman, Urzua, and Vytlacil .(2006). Understanding instrumental variables in models with essential heterogeneity. The Review of Economics and Statistics.