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Heckman correction method + endogenous explanatory variables

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Heckman correction method + endogenous explanatory variables

Hello All;

I had previously posted this question in SAS statistical procedures and did not get any answer, maybe because that was the wrong place to ask this question. So, I re-post it here:

Lets say you want to analyze the effects of hours spent on watching TV (variable name: TV) on the productivity (Var=prod), assuming that you have a good measure of productivity and also a bunch of other control variables (C).

I have the data on productivity, hours of watching TV and the control variables for a sample in which half of it, does not have a TV and thus can not watch TV. However, for these observations, I still have the productivity values. Let's also assume that the TV variable is endogenous and is affected by some instrumental variables.

I wonder if I have to use Heckman sample correction method? I have read about it and in all of the examples, the Dependent Variable of the censored observations were missing, in my case, the dependent variable is available for all of the observations. Shall I just correct for endogeneity of hours spent on watching TV by some instrumental variables and analyze the whole population? then I will have a whole bunch of observations that have a value of 0 for the hours spent on TV. there are two methods that I can think of. They are:

1-  Just focus the  analysis on the observations for which the hours spent on TV is nonzero and use Heckman method to correct for sample selection bias. If I do so, then how can I also adjust for the endogeneity of explanatory variable (TV) in the same heckman model? If I implement this method and ignore the observations in which TV=0, then I am eliminating a lot of information from my analysis which as a general rule, is not the best thing to do. How does this affect my estimations?

2- analyze the whole population and not just the ones with nonzero values of hours watched TV. If I do so, then do I only need to correct for endogeneity of TV variable and not worry about sample selection bias?

Which method do you recommend?

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