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  • After adding instruments in OLS, can significant estimates in OLS be changed?

    Hello,

    Based on the previous work by Papke and Wooldridge (2008), I am running both fixed effects model and fractional regression models using panel data (Basically, my dependent variable is a fractional response variable). Without considering instruments in both models, my key independent variable (assumed to be exogenous at the moment) turns out to be very significant with p-value less than 0.01. However, since my independent variable might suffer from potential endogeneity due to the theoretical reason in my field of research, I also did IV estimation using one single instrumental variable (average of the independent variable within the same industry; they are quite closely associated with the main independent variable according to the first stage result) for one potentially endogenous variable. I applied both 2SLS and control function approach (2SRI) as Papke and Wooldridge (2008) did, but I found that my independent variable became insignificant in the second stage after adding the instrumental variable.

    Based on the fact that weak IV test using estat firststage says my instrument is quite strong (F is way bigger than 10) and my independent variable appears to be exogenous according to the result of estat endogenous, would it be possible to conclude that my independent variable doesn't suffer from any endogeneity issue? I was wondering why the significant result of my independent variable in both fixed effects model and fractional regression models becomes insignificant after adding an instrumental variable even if weak IV test says my instrument is strong and actually my independent variable turns out to be exogenous. Thank you.



  • #2
    Don't think your exclusion is valid for several reasons, one of which it is correlated with the outcome too.

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    • #3
      Hello George,

      Thank you for the posting. Assuming that my dependent variable in the main model is called Y, potential endogenous variable is called X, and my instrumental variable is called Z, correlation between X and Z is about 0.5 and that between Y and Z is around 0.2. Do you think 0.2 is still too high? According to the first stage regression, X and Z are highly associated with each other. I have read through some papers in my field of studies, most of which were discussing the exclusion restriction just theoretically. They either mentioned the some figures of correlation or theoretical and practical background pertaining to why this instrument is reliable. Thank you for the comment.
      Last edited by Sean Park; 03 Jun 2023, 12:07.

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      • #4
        It's more of a theoretical issue than simple correlation. If X is correlated with Y, and Z with X, then Z will likely be correlated with Y. The key is that Z is not a direct determinant of Y--it's effect only goes through X. Here, you have mean(Xi) as instrument for X, which is likely directly related to Y.

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