Instrumental Variables- Choosing between 2SLS, GMM2S and LIML

[Tripti Nash]

Hi,

How can I find out which among 2SLS, GMM2S and LIML is most efficient? Like Hausman test helps to decide between fixed and random effects, is there any way I can find the most efficient estimation among these three? I understand that each one of the estimator is suited for specific condition. I am using 2SLS, GMM2S and LIML as follows:

ivreg2 q (owncn= int assetturnover) deta size risk age, robust endog (owncn)
estimates store sls
ivreg2 q (owncn= int assetturnover) deta size risk age, robust gmm2s endog (owncn)
estimates store gmm
ivreg2 q (owncn= int assetturnover) deta size risk age, robust liml endog (owncn)
estimates store lim

and I wish to compare the stored estimates. How can I do so?

Also, are my commands written correctly?

Thanks

[Emad Shehata]

You can use Hausman test as follows:

* Example generated by -dataex-. To install: ssc install dataex
clear
input float(y1 y2 x1 x2) int(x3 x4)
 89.1  99.6  96.7   101  12  28
 99.2 102.6  98.1 100.1  15  35
   99 125.6   100   100  17  37
  100 130.1 104.9  90.6  22  42
111.6 135.6 104.9  86.5  36  47
122.2 142.2 109.5  89.7  45  51
117.6 157.6 110.8  90.6  66  56
121.1 125.2 112.3  82.8  89  60
  136   136 109.3  70.1  99  65
154.2 154.2 105.3  65.4 118  69
153.6 153.6 101.7  61.3 134  74
158.5 155.5  95.4  62.5 151  78
140.6 140.7  96.4  63.6 167  83
136.2 176.2  97.6  52.6 184  87
  168 185.8 102.4  59.7 200  92
154.3 186.3 101.6  59.5 217  96
  149   189 103.8  61.3 233 101
end

 ivregress 2sls y1 x1 (y2= x2 x3 x4) , small robust
 estimates store tsls
 ivregress gmm  y1 x1 (y2= x2 x3 x4) , small robust
 estimates store gmm
 hausman tsls gmm , sigmamore force

and the code for (ivreg2) is

 ivreg2 y1 x1 (y2= x2 x3 x4) , small robust
 estimates store tsls
 ivreg2 y1 x1 (y2= x2 x3 x4) , small robust gmm2s
 estimates store gmm
 hausman tsls gmm , sigmamore force

  hausman tsls gmm , sigmamore force

                 ---- Coefficients ----
             |      (b)          (B)            (b-B)     sqrt(diag(V_b-V_B))
             |      tsls         gmm         Difference          S.E.
-------------+----------------------------------------------------------------
          y2 |    .8692534     .8644736        .0047798        .0499991
          x1 |   -.4368934    -.3387199       -.0981735         .343353
------------------------------------------------------------------------------
                       b = consistent under Ho and Ha; obtained from ivregress
        B = inconsistent under Ha, efficient under Ho; obtained from ivregress

    Test:  Ho:  difference in coefficients not systematic

                  chi2(2) = (b-B)'[(V_b-V_B)^(-1)](b-B)
                          =        0.33
                Prob>chi2 =      0.8487

[Tripti Nash]

Thanks Emad, the hausman test between 2SLS and GMM works fine.

But, when I run hausman test between 2SLS and LIML, I get the following output:

hausman sls lim, sigmamore force

Test: Ho: difference in coefficients not systematic

chi2(15) = (b-B)'[(V_b-V_B)^(-1)](b-B)
= 0.25
Prob>chi2 = 1.0000
(V_b-V_B is not positive definite)


I am not sure how to interpret this result when "(V_b-V_B is not positive definite)". Does it still mean that 2SLS is preferred because it is atleast consistent?

[Emad Shehata]

Because the results are very similar and have nearly no difference