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  • IV estimation for ordinal variable

    Dear stata users,

    I am new to this forum, so first of all I hope I am meeting the requirements of being a good participant. I already scanned the existing posts for my following question but could not find a thread which adressed my question.

    I am facing a problem with endogeneitey in calculations of an OLS I am running. I analyze the relation between the implementation of a managerial accounting system and the stock performance on events. The implementation of the managerial accounting system is measured by a ordinal variable ranging from 0 (no implementation at all) to 5 (very sophisticated implementation). As I now want to make sure there is no problem of reverse causality I intend to run the usual 2sls procedure. Independently of the instrument I am going to use, I was wondering how to define the first stage. Do I have to run an "ologit" regression in the first stage to then run an ordinary OLS in the second stage? And if yes, is there a way to account for an ordinally scaled endgoneous variable within ivreg? Unfurtunately results between the "manual" two stage procedure and the ivreg command were not that similar, so I obviously did a mistake on at least one of them.

    I would be more than happy if you could help me out somehow as I want to make sure that in the end I am not running "forbidden regressions" or conduct some other servere mistakes. Thank you very much in advance for helping me out!


  • #2
    You'll increase the chances of a helpful answer if you follow the FAQ on asking questions - provide Stata code in code delimiters, Stata output, and sample data using dataex.
    Your question is a bit hard to understand.
    You may be able to estimate this precisely using cmp or GSEM.
    The "manual" two stage procedure is not estimating the same first stage as the ivreg. You're seeing the difference between predictions from ologit and regress in the first stage (and also some corrections for the instrument in ivreg that are not in your manual approach). I've been told that ivreg is consistent for a binary endogenous variable, but I don't know whether that generalizes to a five category ordinal variable.


    • #3
      Sven: It's easy to extend Procedure 21.1 in my 2010 MIT Press book. In fact, if I ever get the 3rd edition finished, this will appear as a problem at the end of the chapter. It has come up before.

      Let the 0 outcome be the base case. Then define dummy variables d1, d2, ..., d5 for the different implementation levels. Let w be the implementation level itself.

      In the first stage, use ordered probit of w on all exogenous variables, including your instrument or instruments. Then you have to take some care to compute P(w = j) for j = 1,2, ..., 5 after the OP. The formulas for these probabilities are easy to find, and Stata should compute them after oprobit (although I've never done that).

      Then, in the equation

      y = b0 + x*b1 + a1*d1 + a2*d2 + ... + a5*d5 + u.

      use the fitted probabilities as IVs for d1, d2, ..., d5. Of course, elements of x act as their own IVs.

      I think this will do it. z1, ..., zm are the IVs:

      oprobit w x1 x2 ... xk z1 ... zm
      predict d0h d1h d2h d3h d4h d5h
      ivregress 2sls y x1 ... xk (d1 d2 d3 d4 d5 = d1h d2h d3h d4h d5h), robust
      This assumes that you have at least one strong instrument that affects w in the oprobit. The Wald statistic should be at least 10 (extrapolating from the linear case).

      Hope this helps.