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Math Help - Setting up Regression

  1. #1
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    Setting up Regression

    I'm working on a project for school and struggling to set up the regression properly. I have data that is taken every year from all 50 states, GDP. I want to run a regression that looks at the growth of GDP based on that state's income tax. The table below should give you an idea how I have it set up now. Is this the best way to do it? It seems excessive to have 49 dummy variables but I'm unsure of a better way to set it up while including state. Also, for year, is it best to put in the actual year, or just go sequentially with 1's, 2's etc?
    GDP Year Recession Tax Alaska Alabama California
    3.4 2001 1 3 1 0 0
    4.1 2001 1 4 0 1 0
    3.8 2001 1 2.1 0 0 1
    3.5 2002 0 3 1 0 0
    4.2 2002 0 4 0 1 0
    4.0 2002 0 2.4 0 0 1
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  2. #2
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    Re: Setting up Regression

    I would set up just a few variables:
    Dependent variable, Y: growth in state GDP
    independent variables:
    X1: National GDP (controls for all exogenous variables)
    X2: state tax rate
    enter all your data for all 50 states for all available years (could be 500 observations for 10 years!). Y (state growth) = a1 + b1*National growth + b2*state tax rate. Coefficient b2 becomes the effect of the tax rate!
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  3. #3
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    Re: Setting up Regression

    Thanks for the reply.

    So with the national GDP you don't see a need to include some sort of State variable in the regression?
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  4. #4
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    Re: Setting up Regression

    The state variable is already there! It is the tax rate. According to your hypothesis, two states with the SAME tax rate would have the SAME economic growth (more or less than the national average.)
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  5. #5
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    Re: Setting up Regression

    Actually, I might rethink that last post! There are other variables that would make a state perform better or worse than average (right to work, education level, etc.) Dummy variables would help capture those effects, sharpening the tax effect. I'd run it both ways and see what happens. I might also include a sales tax variable. And finally, watch out for lag effects.
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