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  • IV Regression Validity of Instruments, xtivreg 2, Overidentification, Hansen J Statistic

    Hi,

    I am using Stata 16IC and working with Panel Data. Currently I am doing a FE - IV Regression. I used the command:

    [xtivreg2 math4 (aexpp = lfound l96 l97 l98) $control $conyear, fe r endog(aexpp) ]

    Warning - singleton groups detected. 7 observation(s) not used.
    Warning - collinearities detected
    Vars dropped: y94 y98

    FIXED EFFECTS ESTIMATION
    ------------------------
    Number of groups = 543 Obs per group: min = 2
    avg = 4.0
    max = 4
    Warning - collinearities detected
    Vars dropped: y94 y98

    IV (2SLS) estimation
    --------------------

    Estimates efficient for homoskedasticity only
    Statistics robust to heteroskedasticity

    Number of obs = 2152
    F( 8, 1601) = 116.00
    Prob > F = 0.0000
    Total (centered) SS = 201356.9083 Centered R2 = 0.3787
    Total (uncentered) SS = 201356.9083 Uncentered R2 = 0.3787
    Residual SS = 125112.809 Root MSE = 8.818

    ------------------------------------------------------------------------------
    | Robust
    math4 | Coef. Std. Err. z P>|z| [95% Conf. Interval]
    -------------+----------------------------------------------------------------
    aexpp | 4.336699 21.96206 0.20 0.843 -38.70814 47.38154
    lunch | .454041 .3926596 1.16 0.248 -.3155577 1.22364
    lunchsq | -.0023254 .0043843 -0.53 0.596 -.0109185 .0062677
    lenrol | 76.45576 65.37296 1.17 0.242 -51.67288 204.5844
    lenrolsq | -5.676062 4.378242 -1.30 0.195 -14.25726 2.905134
    y94 | 0 (omitted)
    y95 | -12.75551 2.686937 -4.75 0.000 -18.02181 -7.489212
    y96 | -12.10136 1.165543 -10.38 0.000 -14.38578 -9.816936
    y97 | -14.68949 .6654535 -22.07 0.000 -15.99376 -13.38523
    y98 | 0 (omitted)

    ------------------------------------------------------------------------------
    Underidentification test (Kleibergen-Paap rk LM statistic): 80.417
    Chi-sq(4) P-val = 0.0000
    ------------------------------------------------------------------------------
    Weak identification test (Cragg-Donald Wald F statistic): 43.158
    (Kleibergen-Paap rk Wald F statistic): 25.287
    Stock-Yogo weak ID test critical values: 5% maximal IV relative bias 16.85
    10% maximal IV relative bias 10.27
    20% maximal IV relative bias 6.71
    30% maximal IV relative bias 5.34
    10% maximal IV size 24.58
    15% maximal IV size 13.96
    20% maximal IV size 10.26
    25% maximal IV size 8.31
    Source: Stock-Yogo (2005). Reproduced by permission.
    NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors.
    ------------------------------------------------------------------------------
    Hansen J statistic (overidentification test of all instruments): 14.831
    Chi-sq(3) P-val = 0.0020
    -endog- option:
    Endogeneity test of endogenous regressors: 0.014
    Chi-sq(1) P-val = 0.9062
    Regressors tested: aexpp
    ------------------------------------------------------------------------------
    Instrumented: aexpp
    Included instruments: lunch lunchsq lenrol lenrolsq y95 y96 y97
    Excluded instruments: lfound l96 l97 l98
    Dropped collinear: y94 y98
    ------------------------------------------------------------------------------

    I am not sure if I understand the results clearly:

    1) The Underidentification test checks whether the instruments are relevant for the potential endogenous regressor in the meaning that the instruments are correlated with the endogenous regressor. From the result I conclude, that my instruments are correlated with aexpp.

    2) The weak identification test checks whether the instruments are only weakly correlated with the endogenous regressors. Since the value of the statistic is large, I conclude the instruments appear to be strong.

    3) The Hansen J Statistic tests whether my instruments are valid, meaning whether they are correlated with the error term. Since the P-Value is 0.0020 I conclude, that the H0: Instruments are exogenous is not rejected.

    Can someone please check whether my interpretation is correct ?

    Thank you very much!

  • #2
    1) and 2) seem ok.

    Your conclusion in 3) is not correct: A p-value of 0.002 (less than any conventional significance level) means that you reject the null hypothesis of valid overidentification restrictions.
    https://twitter.com/Kripfganz

    Comment


    • #3
      Thank you very much for your answer!

      Yes absolutely, I misunderstood this.
      Can I conclude therefore that my instruments are relevant (Underidentification and weak identification test) but not exogenous?
      And that this will result in inconsistent FE IV estimates?

      Comment


      • #4
        Dear Lea Birm

        i'd like to ask you some questions if you do not mind

        * how can we choose our IVs ?? ( i mean based on what)* do i have to follow the 3 steps mentioned above to detect and solve the issue of endo ?

        kind regards

        Comment

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