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Applied Econometrics
Econ 508 - Fall 2007

e-Tutorial 18: Censored Regression Models

Welcome. This time we focus on censored regression models. The idea is to apply the main concepts on Tobit models to the problem set 5. As usual, the main reference is Prof. Koenker's Lecture Notes.
 

Data

You can download your data from the Econ 508 web page (here) and save the file in your preferred directory (I'll save mine as "C:\weco.dat"). Then you open STATA and type:

infile  y sex dex lex kwit tenure censored using "C:\weco.dat"

Drop the first line of the data set containing missing values (due to the labels of variables).

Next you generate the variable lex squared:
gen lex2=lex^2

Then save the file in STATA format (I'll save mine as "C:\weco.dta").

I will use a subsample of the data set to demonstrate how to obtain the main results. My subsample contains only 257 observations, obtained from dropping lex==12. My results may differ from the original data set in PS5.
 

Question 4:

Part (a): (For my subsample

You need to use the Heckman two-step procedure to estimate the equation of productivity, using only non-quitters. For my subsample, the results will be as follows:

gen nonkwit=0
replace nonkwit=1 if kwit==0
probit  nonkwit sex dex lex lex2

Iteration 0:   log likelihood = -150.50058
Iteration 1:   log likelihood = -140.37588
Iteration 2:   log likelihood = -140.30471
Iteration 3:   log likelihood =  -140.3047
Probit estimates                                  Number of obs   =        257
                                                  LR chi2(4)      =      20.39
                                                  Prob > chi2     =     0.0004
Log likelihood =  -140.3047                       Pseudo R2       =     0.0677
------------------------------------------------------------------------------
 nonkwit |      Coef.   Std. Err.       z     P>|z|       [95% Conf. Interval]
---------+--------------------------------------------------------------------
     sex |  -.4195276   .1770855     -2.369   0.018      -.7666088   -.0724464
     dex |   .0447744   .0118068      3.792   0.000       .0216336    .0679153
     lex |   .3840883   .4376635      0.878   0.380      -.4737163    1.241893
    lex2 |  -.0149982   .0176316     -0.851   0.395      -.0495555     .019559
   _cons |  -3.528815   2.739516     -1.288   0.198      -8.898168    1.840538
------------------------------------------------------------------------------

predict xb, xb
gen smallphi=normd(xb)
gen largephi=normprob(xb)
gen lambda=smallphi/largephi
reg y sex dex lex lex2 lambda if nonkwit==1

  Source |       SS       df       MS                  Number of obs =     187
---------+------------------------------               F(  5,   181) =   27.21
   Model |  171.375875     5  34.2751749               Prob > F      =  0.0000
Residual |  228.009406   181  1.25972047               R-squared     =  0.4291
---------+------------------------------               Adj R-squared =  0.4133
   Total |   399.38528   186  2.14723269               Root MSE      =  1.1224

------------------------------------------------------------------------------
       y |      Coef.   Std. Err.       t     P>|t|       [95% Conf. Interval]
---------+--------------------------------------------------------------------
     sex |  -.7407524   .7180634     -1.032   0.304      -2.157604    .6760995
     dex |   .0886988   .0750953      1.181   0.239      -.0594761    .2368737
     lex |   .2145177   .7554096      0.284   0.777      -1.276024    1.705059
    lex2 |  -.0123412   .0298319     -0.414   0.680      -.0712041    .0465217
  lambda |  -1.702168     3.7428     -0.455   0.650      -9.087299    5.682964
   _cons |   11.01176   8.921278      1.234   0.219       -6.59132    28.61484
------------------------------------------------------------------------------

Then you can test for sample selectivity problems by checking the significance of lambda, as remarked in Lecture 17. Please indicate what model you should use after all, based on the sample selectivity test.
 

Part (b): (For my subsample)

The results from applying OLS to the full subsample are, as in question 1:

reg  y sex dex lex lex2

  Source |       SS       df       MS                  Number of obs =     257
---------+------------------------------               F(  4,   252) =   62.24
   Model |  286.582591     4  71.6456477               Prob > F      =  0.0000
Residual |  290.064441   252  1.15104937               R-squared     =  0.4970
---------+------------------------------               Adj R-squared =  0.4890
   Total |  576.647032   256  2.25252747               Root MSE      =  1.0729

------------------------------------------------------------------------------
       y |      Coef.   Std. Err.       t     P>|t|       [95% Conf. Interval]
---------+--------------------------------------------------------------------
     sex |  -1.039604   .1357226     -7.660   0.000        -1.3069   -.7723093
     dex |   .1248959   .0088647     14.089   0.000       .1074376    .1423542
     lex |   .6572255   .3479552      1.889   0.060      -.0280453    1.342496
    lex2 |  -.0292285    .013988     -2.090   0.038      -.0567767   -.0016802
   _cons |   5.952681   2.172383      2.740   0.007       1.674341    10.23102
------------------------------------------------------------------------------

And the results from applying the naive OLS to the restricted subsample of non-quitters are:

reg  y sex dex lex lex2 if nonkwit==1

  Source |       SS       df       MS                  Number of obs =     187
---------+------------------------------               F(  4,   182) =   34.11
   Model |  171.115328     4   42.778832               Prob > F      =  0.0000
Residual |  228.269953   182  1.25423051               R-squared     =  0.4284
---------+------------------------------               Adj R-squared =  0.4159
   Total |   399.38528   186  2.14723269               Root MSE      =  1.1199

------------------------------------------------------------------------------
       y |      Coef.   Std. Err.       t     P>|t|       [95% Conf. Interval]
---------+--------------------------------------------------------------------
     sex |  -1.058262   .1675522     -6.316   0.000      -1.388856   -.7276673
     dex |   .1224521   .0114198     10.723   0.000       .0999198    .1449843
     lex |   .4962791    .431264      1.151   0.251       -.354641    1.347199
    lex2 |   -.023397   .0172528     -1.356   0.177      -.0574383    .0106442
   _cons |   7.149452   2.726205      2.622   0.009       1.770421    12.52848
------------------------------------------------------------------------------

What can you conclude from them? Is there sample selectivity problem? Why?
 

 Last update: Nov 30, 2007