Hausman specification test 2sls vs 3sls in stata 18.0

[Jose Tavares]

Dear all
How to perfomer Hausman specification test 2sls vs 3sls in stata 18.0.
Someone can help with comand,
Best regards
José tavares

[George Ford]

help ivreg2

word search for Hausman.

[Andrew Musau]

Not sure that you can estimate a 3sls model with ivreg2 from SSC. There are two issues: Stata's reg3 command and the hausman command do not have options for robust standard errors. These are needed for a large number of empirical analyses. If you can ignore this, here is how you can implement the test. This is based on Kmenta's (1986) dataset, also discussed at https://cran.r-project.org/web/packa.../systemfit.pdf (p. 27).

In this example, the test statistic had 7 degrees of freedom, implying that the Hausman test includes the constants from 2sls and 3sls in the test. Stata's results are equivalent to those obtained here.

* Example generated by -dataex-. For more info, type help dataex
clear
input float(consump price income farmPrice) byte trend
 98.485 100.323  87.4    98  1
 99.187 104.264  97.6  99.1  2
102.163 103.435  96.7  99.1  3
101.504 104.506  98.2  98.1  4
 104.24  98.001  99.8 110.8  5
103.243  99.456 100.5 108.2  6
103.993 101.066 103.2 105.6  7
   99.9 104.763 107.8 109.8  8
 100.35  96.446  96.6 108.7  9
 102.82  91.228  88.9 100.6 10
 95.435  93.085  75.1    81 11
 92.424  98.801  76.9  68.6 12
 94.535 102.908  84.6  70.9 13
 98.757  98.756  90.6  81.4 14
105.797  95.119 103.1 102.3 15
100.225  98.451 105.1   105 16
103.522  86.498  96.4 110.5 17
 99.929 104.016 104.4  92.5 18
105.223 105.769 110.7  89.3 19
106.232  113.49 127.1    93 20
end
label var consump "food consumption per capita"
label var price "ratio of food prices to general consumer prices"
label var income "disposable income in constant dollars"
label var farmPrice "ratio of preceding year's prices received by farmers to general consumer prices"
label var trend "time trend in years"

global demand "(qDemand: consump price income)"
global supply "(qSupply: consump price farmPrice trend)"
reg3 $demand $supply, endog(consump price) 2sls
est sto _2sls
reg3 $demand $supply, endog(consump price) 3sls
hausman _2sls ., alleq cons

Res.:

. reg3 $demand $supply, endog(consump price) 2sls

Two-stage least-squares regression
------------------------------------------------------------------------------
Equation             Obs   Params         RMSE  "R-squared"         F      P>F
------------------------------------------------------------------------------
qDemand               20        2      1.96632      0.7548      23.81   0.0000
qSupply               20        3     2.457555      0.6396      10.70   0.0000
------------------------------------------------------------------------------

------------------------------------------------------------------------------
             | Coefficient  Std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
qDemand      |
       price |  -.2435564   .0964843    -2.52   0.017    -.4398551   -.0472577
      income |   .3139917   .0469436     6.69   0.000     .2184842    .4094993
       _cons |    94.6333   7.920836    11.95   0.000     78.51824    110.7484
-------------+----------------------------------------------------------------
qSupply      |
       price |   .2400757   .0999338     2.40   0.022     .0367588    .4433927
   farmPrice |   .2556056   .0472501     5.41   0.000     .1594747    .3517366
       trend |   .2529243   .0996551     2.54   0.016     .0501745     .455674
       _cons |   49.53245   12.01052     4.12   0.000     25.09686    73.96805
------------------------------------------------------------------------------
Note: Small-sample degrees-of-freedom adjustment applied when estimating
      covariance matrix of residuals.
Endogenous: consump price
Exogenous:  income farmPrice trend

.
. est sto _2sls

.
. reg3 $demand $supply, endog(consump price) 3sls

Three-stage least-squares regression
------------------------------------------------------------------------------
Equation             Obs   Params         RMSE  "R-squared"      chi2   P>chi2
------------------------------------------------------------------------------
qDemand               20        2     1.812857      0.7548      56.02   0.0000
qSupply               20        3     2.315341      0.6001      38.20   0.0000
------------------------------------------------------------------------------

------------------------------------------------------------------------------
             | Coefficient  Std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
qDemand      |
       price |  -.2435564   .0889541    -2.74   0.006    -.4179033   -.0692096
      income |   .3139917   .0432799     7.25   0.000     .2291647    .3988188
       _cons |    94.6333    7.30265    12.96   0.000     80.32037    108.9462
-------------+----------------------------------------------------------------
qSupply      |
       price |   .2289322   .0891504     2.57   0.010     .0542006    .4036637
   farmPrice |   .2289775   .0393492     5.82   0.000     .1518544    .3061006
       trend |   .3579074   .0651942     5.49   0.000      .230129    .4856857
       _cons |   52.11765   10.63775     4.90   0.000     31.26804    72.96726
------------------------------------------------------------------------------
Endogenous: consump price
Exogenous:  income farmPrice trend

.
. hausman _2sls ., alleq cons

                 ---- Coefficients ----
             |      (b)          (B)            (b-B)     sqrt(diag(V_b-V_B))
             |     _2sls          .          Difference       Std. err.
-------------+----------------------------------------------------------------
qDemand      |
       price |   -.2435564    -.2435564       -7.11e-15        .0373682
      income |    .3139917     .3139917        7.11e-14        .0181812
       _cons |     94.6333      94.6333       -1.09e-11        3.067726
-------------+----------------------------------------------------------------
qSupply      |
       price |    .2400757     .2289322        .0111436        .0451551
   farmPrice |    .2556056     .2289775        .0266282        .0261573
       trend |    .2529243     .3579074       -.1049831        .0753714
       _cons |    49.53245     52.11765       -2.585195        5.575921
------------------------------------------------------------------------------
                           b = Consistent under H0 and Ha; obtained from reg3.
            B = Inconsistent under Ha, efficient under H0; obtained from reg3.

Test of H0: Difference in coefficients not systematic

   chi2(7) = (b-B)'[(V_b-V_B)^(-1)](b-B)
            =   2.28
Prob > chi2 = 0.9426

[Jose Tavares]

thank you so much

[Jose Tavares]

Thanks, it works ok.. Nice advice. I Just running the model.
Works perfectly.
Thank you once again
Best regards