Econometrics F Test Dummy Variables Help

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The discussion revolves around using econometric methods to test the null hypothesis of coefficient constancy across different racial subsamples in a wage regression model. The user seeks clarification on whether to run a regression including all independent variables and two dummy variables for race, while avoiding the dummy variable trap, and then compare it to a regression without race variables. They inquire about conducting an F test for joint restrictions using various SSR methods. Another participant expresses a similar concern and asks if any helpful responses were received. The conversation highlights the need for guidance on appropriate econometric testing methods for dummy variables.
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Hello,

I am fairly new to econometrics and have an assignment that I would like some clarification with.

My regression involves regressing wage on various variables including dummy variables for white, black and asian. I have run separate regressions using subsamples for specific races so far.

I am then asked to suggest a model that allows one to test the nul hypothesis of coefficient constancy across the three subsamples and carry out
the test using the appropriate F statistic.

I think this is the correct strategy, however I would greatly appreciate if someone could clarify this:

1. Run the regression of y on all of the independent variables and 2 of the races (to avoid dummy variable trap)
2. Run the regression of y on all of the indepedent variables apart from the races.

Do an F test for joint restrictions using SSRr, SSRur or R^2 restricted and R^2 unrestricted.

I would greatly appreciate if someone could let me know if this is the correct method or if I need to do some kind of chow test. Could both methods be acceptable?

Thanks!

All the best.
 
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Hi I'm facing exactly the same issue, did you get any reply/inspiration regarding your issue ?
 
The standard _A " operator" maps a Null Hypothesis Ho into a decision set { Do not reject:=1 and reject :=0}. In this sense ( HA)_A , makes no sense. Since H0, HA aren't exhaustive, can we find an alternative operator, _A' , so that ( H_A)_A' makes sense? Isn't Pearson Neyman related to this? Hope I'm making sense. Edit: I was motivated by a superficial similarity of the idea with double transposition of matrices M, with ## (M^{T})^{T}=M##, and just wanted to see if it made sense to talk...

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