areg vs. reg with group dummies

[Hannah Han]

Hi all,

I have searched through the forum, but I couldn't find a post with an answer I am looking for and this might be more of a simple econometrics question.

I am trying to evaluate a program that was implemented at the state level (the states were not randomly selected, unfortunately).
And since it was not randomized, I selected matching states based on state characteristics to serve as "counterfactual".

Now I have data on those "treatment" states as well as the matching states.

I want to control for state fixed-effects, but the problem arises because the treatment was assigned at the state level.

So obviously

areg outcome treatment $individual_level_controls, abs(state) cluster(state)

would not work as treatment gets absorbed by state fixed effects.

Question 1. However,

reg outcome treatment $individual_level_controls i.state, cluster(state)

seems to run fine. Why does this run? Shouldn't it give me the same result as the regression above? I do not think the coefficient on treatment variable would be valid in this case?

Question 2. How could I control for state-invariant unobservables? or could I at all?
Question 3. Should I just control for observable state characteristics and be happy with it?


Thank you very much for your time in advance.

[Carlo Lazzaro]

Hannah:
welcome to the list.
As per FAQ, please post not only what you typed, but also what Stata gave you back.
Eventually, some of the topics you're interested in are convered in Example 1 and 2 under -areg- entry in Stata .pdf manual.

[Hannah Han]

Carlo:

Thank you very much. I read the Example 1 and 2 as you mentioned, which helped a lot.

So this is what I get when I run areg

As expected, treatment variable gets omitted.

--

However, when I run reg with state dummies,

treatment variables does NOT get omitted.

So my questions stand the same; if areg is same as reg with dummies, why is treatment variable not omitted when I run reg?

(1) Is the coefficient of the treatment variable (of reg command) valid at all?

(2) How could I control for state-invariant unobservables? or could I at all?

(3) Should I just control for observable state characteristics and be happy with it?


Thank you!

[Clyde Schechter]

Unfortunately, I do not believe what you showed is is the actual complete output of -reg- with state indicators, because the output shows no results for those indicators! I think if you look carefully at the full output you will find that rather than omitting the treatment variable, Stata chose to omit one of the state indicators (in addition to the base value). That resolves the colinearity problem. You cannot control which variable Stata omits to break colinearity: it has its own algorithm hard coded. That is one of the reasons for using -areg- or -xtreg, fe- in these situations: Stata will preserve all of the fixed effects and omit some other variable.

With regard to questions 2 and 3, you cannot estimate a model that includes the state-level indicators and also includes a covariate that is constant within each state. That creates colinearity and Stata will omit something, either leaving you with no estimate for the covariate, or omitting one of the state-level indicators (meaning that you do not have true control of the fixed-effects). It doesn't matter whether it's observed or unobserved. The fixed-effects automatically adjust for all of these anyway.

If estimating the effects of observed state-level attributes on your outcome is one of the goals of your research, then you cannot accomplish it while absorbing or adjusting for the state-level indicators. You must use a different model instead. Among the possible considerations for this are a random effects model or a between-effects model.

[Clyde Schechter]

As an aside, having nothing to do with the questions you posed, the use of global macros is an unsafe programming practice and should be used only when there is no alternative. This is probably not one of those situations. You should store your list of covariates in a local macro. If you need to use the same list of covariates across several different analyses, then you can create a separate do-file that just creates that local macro, and then -include- that separate do-file in each of the analyses (see -help include-).

[Hannah Han]

Thank you very much for your comments, Clyde!