Endogeneity test

Discussion in 'Scientific Statistics Math' started by minimus, Dec 14, 2010.

  1. minimus

    minimus Guest


    I asked it before but could not get a response to my question that I state
    below. I would like to once again ask if someone would be willing to discuss
    with me my question...

    Thanks and kind regards.

    Let us consider the following equations:

    y = betazero + betaone x + u (1)
    x = alfaone z + e (2)

    Suppose x is endogenous in (1). Suppose z is an instrument for x in (2).
    If I understand it correctly, the logic of the endogeneity test goes as

    "x" has two components: "z" and "e".

    "z" is uncorrelated with "u". Hence, the only way "x" is correlated with "u"
    is if "e" is correlated with "u".

    Hence we cast the following equation, where n is an error term, and test if
    tetaone is 0:

    u = tetaone e + n (3)

    We do not observe u and e but could get the residuals from (1) and (2) and
    test this.
    But ok this does not work because residuals for u are by construction
    uncorrelated with x.

    Then we consider the following equation, where we predict e from equation
    (2) and test if tetaone is 0:

    y = betazero + betaone x + tetaone e + n (4)

    If it turns out that tetaone is not zero then we have endogeneity.

    Question 1:

    This last sentence is my problem. Why do I conclude that there is
    endogeneity if tetaone is not zero? The sort of logic I can think of is the
    following but it does not convince me:

    In equation (1) I replace "u" with "tetaone e + n". If it turns out that
    "tetaone" is significant, this will mean that we leave "e" in "u" in
    equation (1), which then means that "e" is part of "u"? But this does not
    tell me that e is a determinant of u. Ok I am confused here probably and
    don't quite know how I should look at the equations below.

    y = betazero + betaone x + u (1)
    y = betazero + betaone x + tetaone e + n (4)

    Question 2:

    From (2) we know that

    e = x - alfaone z

    I consider predicted e in (4). But (4) has the "x" variable and "e" is also
    defined by "x". Then x and predicted e will be perfectly correlated by
    construction right? Why is this not a problem in (4)?
    minimus, Dec 14, 2010
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  2. minimus

    Art Kendall Guest

    From your use of "endogenous" and "instrument" I speculated that this
    is an econometrics concept. perhaps you should look for an econometrics
    newsgroups or discussion list.
    I found many hits when I Googled "Hausman endogeneity test" e.g.,

    Art Kendall, Dec 14, 2010
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  3. minimus

    minimus Guest

    Yes, it is an econometrics concept but I could not find any other group
    whose name suggests to be more suitable for the question I am asking. For
    googling the term: No, that does not and will not help. I am asking a
    specific question about the test. I am not asking what the test is about.
    minimus, Dec 14, 2010
  4. minimus

    Bruce Weaver Guest

    Here are a couple possibilities.


    I'm not an econometrician, so do not recognize most of the mailing
    lists from that second link. I do recognize the Stata list though,
    and believe that Stata is pretty popular with folks who do
    econometrics. So you might try there.
    Bruce Weaver, Dec 14, 2010
  5. You might check the textbook by Davidson and MacKinnon.
    Richard Startz, Dec 15, 2010
  6. minimus

    minimus Guest

    Thanks. I will have a look at it.
    minimus, Dec 15, 2010
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