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Stata Data Analysis Examples
Tobit Analysis with Robust Standard Errors

Example with Robust Standard Errors

This page is a continuation of Example 3 from the Tobit Models data analysis example. The issue addressed here is how to do a tobit analysis with robust standard errors since there is no robust option in the Stata tobit command. The trick is to make use of the intreg command which does allow for robust standard errors.

After we read in the dataset we will reconfigure the data so that it will work with intreg. The intreg command requires two values of the response variable for each observation. In this case we will call them lapt and uapt. For those cases in which the response is not censored both lapt and uapt are set to the same value. When a response is right-censored uapt is set to missing and when the response is left-censored lapt is set to missing. There are no left-censored responses in this example.

use http://www.ats.ucla.edu/stat/stata/dae/tobitex, clear

generate lapt = apt

generate uapt = apt

replace uapt = . if lapt == 800

intreg lapt uapt read math public, robust

Fitting constant-only model:

Iteration 0:   log pseudolikelihood = -1147.6099  
Iteration 1:   log pseudolikelihood = -1146.7615  
Iteration 2:   log pseudolikelihood = -1146.7608  
Iteration 3:   log pseudolikelihood = -1146.7608  

Fitting full model:

Iteration 0:   log pseudolikelihood = -1073.2252  
Iteration 1:   log pseudolikelihood = -1072.2471  
Iteration 2:   log pseudolikelihood = -1072.2469  
Iteration 3:   log pseudolikelihood = -1072.2469  

Interval regression                               Number of obs   =        200
                                                  Wald chi2(3)    =     254.97
Log pseudolikelihood = -1072.2469                 Prob > chi2     =     0.0000

------------------------------------------------------------------------------
             |               Robust
             |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
        read |   3.681712   .6931961     5.31   0.000     2.323072    5.040351
        math |   4.557839   .7449784     6.12   0.000     3.097708     6.01797
      public |    62.1633    10.6758     5.82   0.000     41.23912    83.08748
       _cons |   188.3943   30.38885     6.20   0.000     128.8332    247.9553
-------------+----------------------------------------------------------------
    /lnsigma |   4.299086   .0512244    83.93   0.000     4.198688    4.399484
-------------+----------------------------------------------------------------
       sigma |   73.63244   3.771777                      66.59888    81.40882
------------------------------------------------------------------------------

  Observation summary:         0  left-censored observations
                             185     uncensored observations
                              15 right-censored observations
                               0       interval observations

You should compare these results with the results using the tobit command. Because the point estimates are the same and because all of the predictors are still significant with the robust stand errors, the interpretation and write-up of the analysis will be the same as the Tobit Models example.

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