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I have a problem regarding causation and effect. I have a linear model $ wage=\beta_0+\beta_1educ+\beta_2female+\beta_3hourseworked+errorterm$ When I need to estimate the causal effect for educated people on wages, I have chosen a subpopulation educ==1 (educated people) and made a regression in stata. The used commands are reg wages educ female hourseworked

From this regression I obtain 0 for the educated people, and it says that it is omitted. How can I find the causal effect of educated people on wages, when I have this problem?

I have tried to remove the intercept, from which I get an estimate causal effect of education, but is it correct just to remove the intercept?

Do I have to think about endogeneity - omitted variables - instruments?

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    $\begingroup$ You run a regression on only the sub-population with education =1? Doesn't that mean that you have no variation in education in the resulting regression? $\endgroup$ – BKay Jan 23 '16 at 16:11
  • $\begingroup$ That is exactly what it means. There is absolutely no variability in that regressor- basically making it a constant. Your regression is conditioning on the fact that people are educated $\endgroup$ – ChinG Jan 23 '16 at 16:49
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Yes, you have to worry about the difference between correlation and causality. In these situations, it helps to try to force a case of ommited variable bias.

In this case "talent" or "effort" is unobserved. Both this might make people more likely to pick up additional education, and also be more successful at their jobs.

Or family background: If your parents are high achievers, they might induce you to take more education, and they also are well-linked to ensure you get a well-paid job.

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  • $\begingroup$ But I don't have data for the omitted variables. I only have data for wages, educ, female, hoursworked. But if I sayd that talent or effort, or for example family background is the omitted variable, how do I then estimate the causal effect of educ on wages? I'm a bit confused about how to go on. $\endgroup$ – aa_x Jan 23 '16 at 14:15
  • $\begingroup$ @aa_x I suggest you digg into handbooks or lecture notes on identification. Without a natural experiment, or a case study (where you conduct an experiment), you usually have little chance of convincing academics of having found a causal relationship -- in most cases. Unless you really happen to have that magical dataset that allows you to control for anything people might worry about - and people worry about a lot. $\endgroup$ – FooBar Jan 23 '16 at 14:17
  • $\begingroup$ Okay, but is it possible for me to find an estimate of educ on wages by considering this omitted value problem in practice? Furthermore I have to use a sample selection model to correct for this sample issue problem, that I'm dealing with. I've stated that I'm only focussing on the educated population and not on the whole population (where the uneducated are included). I though about a Tobit or Heckit model, but can you help me with explanaining which of those will be preffered to my problem? $\endgroup$ – aa_x Jan 23 '16 at 14:23

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