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      name:  <unnamed>
       log:  U:\projects\misc\stata_lf_programs\tobit\tobit_expected_value.txt
  log type:  text
 opened on:  31 Oct 2014, 13:25:58

. 
. version 13.1

. clear all

. set more off

. set seed 1234567

. set obs 10000
obs was 0, now 10000

. 
. 
. * Simulate data
. gen x = rnormal(5, 2)

. gen y = -4 + 1*x + rnormal(0,1)

. gen yt = max(0, y) 

. sum yt y

    Variable |       Obs        Mean    Std. Dev.       Min        Max
-------------+--------------------------------------------------------
          yt |     10000    1.452821    1.594159          0   8.417286
           y |     10000    .9556056    2.225627  -7.519608   8.417286

. 
. * Esimate Tobit model (i.e. latent variable). Should match above DGP
. tobit y x, ll(0)

Tobit regression                                  Number of obs   =      10000
                                                  LR chi2(1)      =   13626.10
                                                  Prob > chi2     =     0.0000
Log likelihood = -10811.579                       Pseudo R2       =     0.3866

------------------------------------------------------------------------------
           y |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
           x |   .9963011   .0070562   141.20   0.000     .9824695    1.010133
       _cons |  -3.967395   .0413477   -95.95   0.000    -4.048445   -3.886345
-------------+----------------------------------------------------------------
      /sigma |   .9913134   .0086852                      .9742886    1.008338
------------------------------------------------------------------------------
  Obs. summary:       3332  left-censored observations at y<=0
                      6668     uncensored observations
                         0 right-censored observations

. 
. * Predictions based on latent variable
. predict yhat
(option xb assumed; fitted values)

. 
. * Censored predictions
. predict yhatstar, ystar(0,.)

. 
. sum yhat*

    Variable |       Obs        Mean    Std. Dev.       Min        Max
-------------+--------------------------------------------------------
        yhat |     10000    .9682756    1.972654  -6.852201   8.662807
    yhatstar |     10000    1.449505    1.399097   3.29e-13   8.662807

. 
. * Do it "by hand"
. gen sigma = _b[sigma:_cons]

. gen myhatstar = normal(yhat/sigma)*(yhat+sigma* ///
>                          normalden(-yhat/sigma)/normal(yhat/sigma))

. 
. * The wrong way of getting predictions
. gen ystarwrong = max(0, yhat)

.                                                                                         
>   
. * Compare
. sum y yhat yt yhatstar  myhatstar ystarwrong

    Variable |       Obs        Mean    Std. Dev.       Min        Max
-------------+--------------------------------------------------------
           y |     10000    .9556056    2.225627  -7.519608   8.417286
        yhat |     10000    .9682756    1.972654  -6.852201   8.662807
          yt |     10000    1.452821    1.594159          0   8.417286
    yhatstar |     10000    1.449505    1.399097   3.29e-13   8.662807
   myhatstar |     10000    1.449505    1.399097   3.29e-13   8.662807
-------------+--------------------------------------------------------
  ystarwrong |     10000    1.365353    1.457802          0   8.662807

. 
. log close
      name:  <unnamed>
       log:  U:\projects\misc\stata_lf_programs\tobit\tobit_expected_value.txt
  log type:  text
 closed on:  31 Oct 2014, 13:25:58
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