{smcl}
{com}{sf}{ul off}{txt}{.-}
       log:  {res}C:\Documents and Settings\jli2\My Documents\Log\MLE_log\tobit_165.smcl
  {txt}log type:  {res}smcl
 {txt}opened on:  {res}29 Sep 2004, 20:09:46
{txt}
{com}. * tobit model, see wooldridge page 546. exercise 16.5
. use http://fmwww.bc.edu/ec-p/data/wooldridge/FRINGE
{txt}
{com}. * run OLS regression
. regress hrbens exper age educ tenure married male white nrtheast nrthcen south union

      {txt}Source {c |}       SS       df       MS              Number of obs ={res}     616
{txt}{hline 13}{char +}{hline 30}           F( 11,   604) ={res}   32.50
    {txt}   Model {char |} {res} 101.132288    11  9.19384436           {txt}Prob > F      = {res} 0.0000
    {txt}Residual {char |} {res} 170.839786   604  .282847328           {txt}R-squared     = {res} 0.3718
{txt}{hline 13}{char +}{hline 30}           Adj R-squared = {res} 0.3604
    {txt}   Total {char |} {res} 271.972074   615  .442231015           {txt}Root MSE      = {res} .53183

{txt}{hline 13}{c TT}{hline 64}
      hrbens {c |}      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
{hline 13}{char +}{hline 64}
       exper {c |}  {res} .0029862   .0043435     0.69   0.492     -.005544    .0115164
{txt}         age {c |}  {res}-.0022495   .0041162    -0.55   0.585    -.0103333    .0058343
{txt}        educ {c |}  {res}  .082204   .0083783     9.81   0.000     .0657498    .0986582
{txt}      tenure {c |}  {res} .0281931   .0035481     7.95   0.000      .021225    .0351612
{txt}     married {c |}  {res} .0899016   .0510187     1.76   0.079     -.010294    .1900971
{txt}        male {c |}  {res}  .251898   .0523598     4.81   0.000     .1490686    .3547274
{txt}       white {c |}  {res}  .098923   .0746602     1.32   0.186    -.0477021    .2455481
{txt}    nrtheast {c |}  {res}-.0834306   .0737578    -1.13   0.258    -.2282836    .0614223
{txt}     nrthcen {c |}  {res}-.0492621   .0678666    -0.73   0.468    -.1825451     .084021
{txt}       south {c |}  {res}-.0284978   .0673714    -0.42   0.672    -.1608084    .1038129
{txt}       union {c |}  {res} .3768401   .0499022     7.55   0.000     .2788372    .4748429
{txt}       _cons {c |}  {res}-.6999244   .1772515    -3.95   0.000    -1.048028   -.3518203
{txt}{hline 13}{c BT}{hline 64}

{com}. * run canned "tobit" model
. tobit hrbens exper age educ tenure married male white nrtheast nrthcen south union, ll

{txt}Tobit estimates                                   Number of obs   = {res}       616
                                                  {txt}LR chi2({res}11{txt})     = {res}    283.86
                                                  {txt}Prob > chi2     = {res}    0.0000
{txt}Log likelihood = {res}-519.66616                       {txt}Pseudo R2       = {res}    0.2145

{txt}{hline 13}{c TT}{hline 64}
      hrbens {c |}      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
{hline 13}{c +}{hline 64}
       exper {c |}  {res} .0040631   .0046627     0.87   0.384    -.0050939    .0132201
         {txt}age {c |}  {res}-.0025859   .0044362    -0.58   0.560    -.0112981    .0061263
        {txt}educ {c |}  {res} .0869168   .0088168     9.86   0.000     .0696015    .1042321
      {txt}tenure {c |}  {res} .0287099   .0037237     7.71   0.000      .021397    .0360227
     {txt}married {c |}  {res} .1027574   .0538339     1.91   0.057    -.0029666    .2084814
        {txt}male {c |}  {res} .2556765   .0551672     4.63   0.000     .1473341     .364019
       {txt}white {c |}  {res} .0994408    .078604     1.27   0.206     -.054929    .2538105
    {txt}nrtheast {c |}  {res}-.0778461   .0775035    -1.00   0.316    -.2300547    .0743625
     {txt}nrthcen {c |}  {res}-.0489422   .0713965    -0.69   0.493    -.1891572    .0912729
       {txt}south {c |}  {res}-.0246854   .0709243    -0.35   0.728    -.1639731    .1146022
       {txt}union {c |}  {res} .4033519   .0522697     7.72   0.000     .3006999    .5060039
       {txt}_cons {c |}  {res}-.8137158   .1880725    -4.33   0.000     -1.18307   -.4443616
{txt}{hline 13}{c +}{hline 64}
         _se {c |}  {res} .5551027   .0165773           {txt}(Ancillary parameter)
{hline 13}{c BT}{hline 64}

  Obs. summary:  {res}       41{txt}  left-censored observations at hrbens<={res}0
                       575{txt}     uncensored observations

{com}. * the difference between tobit and OLS is small, why?
. * user-defined MLE procedure
. program drop _all
{txt}
{com}. program define tobit_165
{txt}  1{com}. args lnf theta1 theta2
{txt}  2{com}. quietly replace `lnf'=ln(norm(-`theta1'/sqrt(`theta2'))) if $ML_y1==0
{txt}  3{com}. quietly replace `lnf'=-0.5*ln(`theta2')-($ML_y1-`theta1')^2/(2*`theta2') if $ML_y1!=0
{txt}  4{com}. end
{txt}
{com}. ml model lf tobit_165 (hrbens = exper age educ tenure married male white nrtheast nrthcen south union) ()
{txt}
{com}. ml maximize

{txt}initial:       log likelihood = {res}    -<inf>{txt}  (could not be evaluated)
feasible:      log likelihood = {res}-224.43978
{txt}rescale:       log likelihood = {res}-193.47444
{txt}rescale eq:    log likelihood = {res}-140.95815
{txt}Iteration 0:   log likelihood = {res}-140.95815{txt}  
Iteration 1:   log likelihood = {res}-40.265962{txt}  
Iteration 2:   log likelihood = {res}  2.516603{txt}  (not concave)
Iteration 3:   log likelihood = {res} 6.0557566{txt}  (not concave)
Iteration 4:   log likelihood = {res} 7.9079098{txt}  (not concave)
Iteration 5:   log likelihood = {res} 8.3157337{txt}  
Iteration 6:   log likelihood = {res} 8.6986728{txt}  
Iteration 7:   log likelihood = {res} 8.7234839{txt}  
Iteration 8:   log likelihood = {res} 8.7234948{txt}  
Iteration 9:   log likelihood = {res} 8.7234948{txt}  

{col 51}Number of obs{col 67}= {res}       616
{col 51}{txt}Wald chi2({res}11{txt}){col 67}= {res}    355.32
{txt}Log likelihood = {res} 8.7234948{col 51}{txt}Prob > chi2{col 67}= {res}    0.0000

{txt}{hline 13}{c TT}{hline 64}
      hrbens {c |}      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
{hline 13}{c +}{hline 64}
{res}eq1          {txt}{c |}
       exper {c |}  {res} .0040631   .0046628     0.87   0.384    -.0050758     .013202
         {txt}age {c |}  {res}-.0025859   .0044363    -0.58   0.560    -.0112809    .0061091
        {txt}educ {c |}  {res} .0869168    .008817     9.86   0.000     .0696357    .1041979
      {txt}tenure {c |}  {res} .0287099   .0037238     7.71   0.000     .0214114    .0360083
     {txt}married {c |}  {res} .1027574   .0538353     1.91   0.056     -.002758    .2082727
        {txt}male {c |}  {res} .2556765   .0551687     4.63   0.000     .1475479    .3638051
       {txt}white {c |}  {res} .0994408   .0786061     1.27   0.206    -.0546243    .2535058
    {txt}nrtheast {c |}  {res}-.0778461   .0775056    -1.00   0.315    -.2297543    .0740621
     {txt}nrthcen {c |}  {res}-.0489422   .0713984    -0.69   0.493    -.1888805    .0909961
       {txt}south {c |}  {res}-.0246854   .0709261    -0.35   0.728    -.1636981    .1143272
       {txt}union {c |}  {res} .4033519   .0522711     7.72   0.000     .3009025    .5058013
       {txt}_cons {c |}  {res}-.8137158   .1880775    -4.33   0.000    -1.182341   -.4450907
{txt}{hline 13}{c +}{hline 64}
{res}eq2          {txt}{c |}
       _cons {c |}  {res}  .308139   .0184054    16.74   0.000     .2720651     .344213
{txt}{hline 13}{c BT}{hline 64}

{com}. * we get the same result as that of canned command
. log close
       {txt}log:  {res}C:\Documents and Settings\jli2\My Documents\Log\MLE_log\tobit_165.smcl
  {txt}log type:  {res}smcl
 {txt}closed on:  {res}29 Sep 2004, 20:13:50
{txt}{.-}
{smcl}
{txt}{sf}{ul off}