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  • Sargan-Hansen test with a single IV(just-identified case)?

    Hi to everyone,

    I was wondering if Sargan -Hansen test could be used in the case of a single IV in the extent instrumental variable regression (ivreg2) , or there is an alternative for testing exogeneity of an instrument. Below are the tests from my ivreg2 regression. All of them support the model, except for the Sargan-Hansen test..

    Code:
    -----------------------------------------------------------------------------
    Underidentification test (Kleibergen-Paap rk LM statistic):            392.487
                                                       Chi-sq(1) P-val =    0.0000
    ------------------------------------------------------------------------------
    Weak identification test (Kleibergen-Paap rk Wald F statistic):       7515.033
    Stock-Yogo weak ID test critical values: 10% maximal IV size             16.38
                                             15% maximal IV size              8.96
                                             20% maximal IV size              6.66
                                             25% maximal IV size              5.53
    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):         0.000
                                                     (equation exactly identified)
    -endog- option:
    Endogeneity test of endogenous regressors:                              77.328
                                                       Chi-sq(1) P-val =    0.0000
    Regressors tested:    lnl
    ------------------------------------------------------------------------------
    Instrumented:         lnl
    Included instruments: lnk lnm ln_K_l1 ln_M_l1 km_l1 k2_l1 m2_l1 k2m_l1 km2_l1
                          k3_l1 m3_l1 ln_M_l2
    Excluded instruments: ln_L_b_l1
    ------------------------------------------------------------------------------
    (0 real changes made)
    
    Estimating confidence sets over 100 grid points
    ----+--- 1 ---+--- 2 ---+--- 3 ---+--- 4 ---+--- 5 
    ..................................................    50
    ..................................................   100
    
    Weak instrument robust tests and confidence sets for linear IV
    H0: beta[lnrev:lnl] = 0
    ------------------------------------------------------------------------------
     Test |       Statistic         p-value |  Conf. level        Conf. Set       
    ------+---------------------------------+-------------------------------------
       AR | chi2(1)   =    39.67     0.0000 |      95%       [ .066825, .121308]  
    ------+---------------------------------+-------------------------------------
     Wald | chi2(1)   =    44.88     0.0000 |      95%       [ .066547, .121586]  
    ------------------------------------------------------------------------------
    Confidence sets estimated for 100 points in [ .039027, .149106].
    Number of obs N = 6752.
    Method = lagrange multiplier (LM).
    Tests robust to heteroskedasticity and clustering on id (N_clust=1265).
    Wald statistic in last row is based on ivreg2 estimation and is not robust to weak
    instruments.
    Thank you in advance any help.

  • #2
    The Sargan/Hansen test is a test of the overidentifying restrictions. As the name says, it cannot be used in the just-identified case.
    https://twitter.com/Kripfganz

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    • #3
      Mina,

      Further to Sebastian useful information, please also note that the Hansen/Sargan test is not a test for the exogeneity of an instrument. As Sebastian said, it is a test of the validity of overidentifying restrictions.

      Best wishes,

      Joao

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      • #4
        Thank you.

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        • #5
          I have a proble with the interpretation of this output in stata. Can I say that I reject HO because the p-value is <0,05 ? What about the second table ? Can I say that I keep less than 5% of the OLS bias ?
          Attached Files

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