Durbin Wu Hausman Test

[John Marburg]

Hello,


i am struggling with interpreting results from Durbin-Wu Hausman Test for Pooled OLS and fixed effect model. I proceeded after the explanations of https://www.stata.com/support/faqs/s...-hausman-test/

1. The results of both equation suggest no endogeneity, if i done it right?

2. Does this mean that for these two equation the 2SLS is not allowed and would lead to wrong or distorted results?

3. Could a change of instrument, for example only using historic beta or shares turnover generate essential different results?

4. Is it useful to do this check before applying 2SLS method or should i evaluate endogeneity only after 2SLS?


Below my procedure and the results of the test command are displayed



Pooled OlS



reg SumHoldingsPct SharesTurnover DebtTotalAssets RD Marketcap Dividend SalesGrowth QuickRatio i.year i.industry i.country, robust cluster(industry)

predict ResidualsSumHoldingsPct, res

reg TobinsQ SumHoldingsPct DebtTotalAssets RD Marketcap Dividend SalesGrowth QuickRatio ResidualsSumHoldingsPct i.year i.industry i.country, robust cluster(industry)

test ResidualsSumHoldingsPct



( 1) ResidualsSumHoldingsPct = 0

F( 1, 7) = 1.43
Prob > F = 0.2708






Fixed effect Model


xtreg SumHoldingsPct SharesOutstand HistoricBeta SharesTurnover DebtTotalAssets RD Marketcap Dividend SalesGrowth QuickRatio i.year i.industry i.country, robust fe

predict ResidualsSumHoldingsPct, res

xtreg TobinsQ SumHoldingsPct DebtTotalAssets RD Marketcap Dividend SalesGrowth QuickRatio ResidualsSumHoldingsPct i.year i.industry i.country, robust fe

test ResidualsSumHoldingsPct



( 1) ResidualsSumHoldingsPct = 0

F( 1, 706) = 0.22
Prob > F = 0.6391

[Joro Kolev]

1. Yes, you have done it right, and the test suggests that SumHoldingsPct is exogenous in the TobinsQ equation.
2. You can do 2SLS, it will consistently estimate your equation. However this would be silly because you do not need to, and 2SLS is less efficient than OLS.
3. Yes, the test depends on the instrument you are using. You need to assume that your instrument is valid.
4. There is no prescribed timing and the computer does not break if you test for endogeneity before or after 2SLS.

[John Marburg]

Thank you for the response Joro. if have got an additional question in this context.

Is there a chance to apply an overidentification test in stata with the following command, because adding cluster specification and estat overid doesnt work together?
I also know that there is the ivreg2 command, but then my endogeneity test estat endogenous doesnt work anymore. My goal is to implement the first stage, overid and endogeneity test all together.


The referring equation

ivregress 2sls TobinsQ (SumHoldingsPct = SharesOutstand HistoricBeta SharesTurnover) DebtTotalAssets RD Marketcap Dividend CurrentRatio SalesGrowth QuickRatio i.year i.industry i.country, robust cluster(industry)

[Joro Kolev]

This is weird... I did not know that you cannot do -estat overid- after 2SLS with clustered variance... And I am not aware of any mechanical reason of why this should not be possible.

One solution is to revert to linear gmm, apparently Stata accepts -estat overid- post linear gmm with clustered variance. Here:

. sysuse auto, clear
(1978 Automobile Data)

. ivregress 2sls price (mpg = length weight), cluster(rep)

Instrumental variables (2SLS) regression          Number of obs   =         69
                                                  Wald chi2(1)    =       6.23
                                                  Prob > chi2     =     0.0125
                                                  R-squared       =     0.1816
                                                  Root MSE        =     2615.6

                                  (Std. Err. adjusted for 5 clusters in rep78)
------------------------------------------------------------------------------
             |               Robust
       price |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         mpg |  -306.8967   122.9083    -2.50   0.013    -547.7925   -66.00087
       _cons |   12679.83   2421.472     5.24   0.000     7933.832    17425.83
------------------------------------------------------------------------------
Instrumented:  mpg
Instruments:   length weight

. estat overid

  Test of overidentifying restrictions:


  robust tests of overidentifying restrictions after 2SLS
  estimation not available with cluster-robust standard errors
r(498);

. ivregress gmm price (mpg = length weight), cluster(rep)

Instrumental variables (GMM) regression           Number of obs   =         69
                                                  Wald chi2(1)    =      17.75
                                                  Prob > chi2     =     0.0000
                                                  R-squared       =     0.1989
GMM weight matrix: Cluster (rep78)                Root MSE        =     2587.8

                                  (Std. Err. adjusted for 5 clusters in rep78)
------------------------------------------------------------------------------
             |               Robust
       price |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         mpg |  -191.8927   45.54801    -4.21   0.000    -281.1652   -102.6203
       _cons |   10418.22   1043.445     9.98   0.000     8373.102    12463.33
------------------------------------------------------------------------------
Instrumented:  mpg
Instruments:   length weight

. estat overid

  Test of overidentifying restriction:

  Hansen's J chi2(1) = 1.35762 (p = 0.2440)

.

[John Marburg]

Hello Joro,

i guess it depends on using the options robust and cluster together.


The error response is at follows:

"robust tests of overidentifying restrictions after 2SLS
estimation not available with cluster-robust standard errors"


So if anyone knows a solution to my question above i would be very pleased?

[Joro Kolev]

I showed you one solution in #4: revert to linear gmm instead of 2sls as in what I showed.

Another correct way how to do this is with the user written -ivreg2-:

. sysuse auto, clear
(1978 Automobile Data)

. ivreg2 price (mpg = length weight), cluster(rep) endog(mpg)

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

Estimates efficient for homoskedasticity only
Statistics robust to heteroskedasticity and clustering on rep78

Number of clusters (rep78) =         5                Number of obs =       69
                                                      F(  1,     4) =     4.91
                                                      Prob > F      =   0.0909
Total (centered) SS     =  576796958.9                Centered R2   =   0.1816
Total (uncentered) SS   =   3183192639                Uncentered R2 =   0.8517
Residual SS             =  472065626.4                Root MSE      =     2616

------------------------------------------------------------------------------
             |               Robust
       price |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         mpg |  -306.8967   122.9083    -2.50   0.013    -547.7925   -66.00087
       _cons |   12679.83   2421.472     5.24   0.000     7933.832    17425.83
------------------------------------------------------------------------------
Underidentification test (Kleibergen-Paap rk LM statistic):              3.439
                                                   Chi-sq(2) P-val =    0.1792
------------------------------------------------------------------------------
Weak identification test (Cragg-Donald Wald F statistic):               65.434
                         (Kleibergen-Paap rk Wald F statistic):         12.512
Stock-Yogo weak ID test critical values: 10% maximal IV size             19.93
                                         15% maximal IV size             11.59
                                         20% maximal IV size              8.75
                                         25% maximal IV size              7.25
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):         1.358
                                                   Chi-sq(1) P-val =    0.2440
-endog- option:
Endogeneity test of endogenous regressors:                               0.003
                                                   Chi-sq(1) P-val =    0.9567
Regressors tested:    mpg
------------------------------------------------------------------------------
Instrumented:         mpg
Excluded instruments: length weight
------------------------------------------------------------------------------

And one a bit dodgy way how to do this is to force the performance of non-robust test:

. ivregress 2sls price (mpg = length weight), cluster(rep)

Instrumental variables (2SLS) regression          Number of obs   =         69
                                                  Wald chi2(1)    =       6.23
                                                  Prob > chi2     =     0.0125
                                                  R-squared       =     0.1816
                                                  Root MSE        =     2615.6

                                  (Std. Err. adjusted for 5 clusters in rep78)
------------------------------------------------------------------------------
             |               Robust
       price |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         mpg |  -306.8967   122.9083    -2.50   0.013    -547.7925   -66.00087
       _cons |   12679.83   2421.472     5.24   0.000     7933.832    17425.83
------------------------------------------------------------------------------
Instrumented:  mpg
Instruments:   length weight

. estat overid, forcenonrobust

  Tests of overidentifying restrictions:

  Sargan chi2(1)         =  8.78068  (p = 0.0030)
  Basmann chi2(1)        =  9.62357  (p = 0.0019)

  robust tests of overidentifying restrictions after 2SLS
  estimation not available with cluster-robust standard errors

The last one is dodgy because the distribution theory behind these tests is for iid observations.

Yet another way is to see whether your clustering is really needed. If your clustered standard errors, and your only robust standard errors are more or less the same, you can estimate a robust only variance and perform appropriate test:

. ivregress 2sls price (mpg = length weight), robust

Instrumental variables (2SLS) regression          Number of obs   =         74
                                                  Wald chi2(1)    =      20.43
                                                  Prob > chi2     =     0.0000
                                                  R-squared       =     0.1963
                                                  Root MSE        =     2626.4

------------------------------------------------------------------------------
             |               Robust
       price |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         mpg |   -316.767   70.08472    -4.52   0.000    -454.1305   -179.4035
       _cons |   12911.54   1662.026     7.77   0.000     9654.026    16169.05
------------------------------------------------------------------------------
Instrumented:  mpg
Instruments:   length weight

. estat overid

  Test of overidentifying restrictions:

  Score chi2(1)          =  4.00719  (p = 0.0453)