{smcl}
{* 16jul2007}{...}
{hline}
help for {hi:tobcm}{right: {hi:tobcm} }
{hline}

{title:Testing for normality after tobit estimation}

{p 8 16}{cmd:tobcm} [ {cmd:,} {cmdab:p:bs} {cmd:bsfile({it: filename})} 
{cmd:reps({it:#})}]

{title:Description}

{p} {cmd:tobcm} implements a conditional moment test for testing the null 
hypothesis that the disturbances in a tobit model have a normal distribution.
This test was derived by Skeels and Vella (1999), who built on work by Newey
(1985) and Tauchen (1985).  {cmd:tobcm} also implements the bootstrap method
described by Drukker (2002).

{title:Options}

{p 0 4}{cmdab:p:bs} specifies that the critical values should be obtained
from a parametric bootstrap as described by Drukker (2002).

{p 0 4}{cmd:bsfile({it:filename})} specifies the name of the file in which
the conditional moment statistics from the boostrap samples should be saved.

{p 0 4}{cmd:reps({it:#})} specifies the number of number of repetitions for
the bootstrap.

{cmd:Remarks}

{p} {cmd:tobcm} implements a conditional moment test for testing the null
hypothesis that the disturbances in a tobit model have a normal
distribution.  This test was derived by Skeels and Vella (1999), who built on
work by Newey (1985) and Tauchen (1985).  Along with several other studies,
Skeels and Vella (1999) found that using the asymptotic distribution of this
test produces severe size distortions, even in moderately large samples.
Drukker (2002) suggested using a parametric bootstrap to correct the size
distorion and showed that even with the bootstrap critical values, the test
still has reasonable power for samples greater than 500.  {cmd:tobcm} 
implements the bootstrap method described by Drukker (2002).


{p} {cmd:tobcm} can only be used after {helpb tobit}.  Furthermore, {cmd:tobcm}
can only be used be used for left-censored tobit models in which zero is the
censoring point.

{p} The output below gives an example of how to use {cmd:tobcm}, both with and
without the {cmd:pbs} option. 


{txt}
{com}. use moffit
{txt}
{com}. tobit hours  nwi ms age race clt6 educ, ll(0)

{txt}Tobit estimates                                   Number of obs   = {res}       610
                                                  {txt}LR chi2({res}6{txt})      = {res}     24.18
                                                  {txt}Prob > chi2     = {res}    0.0005
{txt}Log likelihood = {res}-1694.4825                       {txt}Pseudo R2       = {res}    0.0071

{txt}{hline 13}{c TT}{hline 64}
       hours {c |}      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
{hline 13}{c +}{hline 64}
         nwi {c |}  {res}-.0108405   .1754488    -0.06   0.951    -.3554044    .3337234
          {txt}ms {c |}  {res}-9.308479   3.902876    -2.39   0.017    -16.97333   -1.643622
         {txt}age {c |}  {res}-1.114833   .4674299    -2.39   0.017    -2.032818   -.1968478
        {txt}race {c |}  {res} 1.778366   3.726882     0.48   0.633    -5.540855    9.097587
        {txt}clt6 {c |}  {res}-6.346814   4.266223    -1.49   0.137    -14.72525    2.031617
        {txt}educ {c |}  {res} 2.017293   .5898988     3.42   0.001     .8587914    3.175795
       {txt}_cons {c |}  {res} 39.92167   22.07323     1.81   0.071    -3.427918    83.27127
{txt}{hline 13}{c +}{hline 64}
         _se {c |}  {res} 34.09747   1.611069           {txt}(Ancillary parameter)
{hline 13}{c BT}{hline 64}

  Obs. summary:  {res}      313{txt}  left-censored observations at hours<={res}0
                       297{txt}     uncensored observations

{com}. tobcm 

{txt}Conditional moment test against the null of normal errors

{col 5}CM{col 13}Prob > chi2
{res} 498.4408{col 15}0.00000
{txt}
{com}. tobcm, pbs reps(500)

{txt}Conditional moment test against the null of normal errors

{col 20}critical values
{col 5}CM{col 15}%10{col 25}%5{col 35}%1
{res} 498.4408{col 13}9.28122{col 22}12.901708{col 32}29.455544
{txt}

The next example illustrates that {cmd:tobcm} will not work after a tobit 
model that is left and right censored.

{com}. 
. tobit hours  nwi ms age race clt6 educ, ll(0) ul(50)

{txt}Tobit estimates                                   Number of obs   = {res}       610
                                                  {txt}LR chi2({res}6{txt})      = {res}     24.10
                                                  {txt}Prob > chi2     = {res}    0.0005
{txt}Log likelihood = {res}-1654.0428                       {txt}Pseudo R2       = {res}    0.0072

{txt}{hline 13}{c TT}{hline 64}
       hours {c |}      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
{hline 13}{c +}{hline 64}
         nwi {c |}  {res}-.0107371    .182306    -0.06   0.953    -.3687677    .3472934
          {txt}ms {c |}  {res}-9.837942   4.063255    -2.42   0.016    -17.81777   -1.858119
         {txt}age {c |}  {res}-1.093097   .4857082    -2.25   0.025    -2.046979   -.1392152
        {txt}race {c |}  {res} 1.931658   3.871081     0.50   0.618    -5.670755    9.534072
        {txt}clt6 {c |}  {res}-6.392259   4.428288    -1.44   0.149    -15.08897    2.304454
        {txt}educ {c |}  {res} 2.137241   .6149421     3.48   0.001     .9295563    3.344925
       {txt}_cons {c |}  {res} 37.84291   22.95145     1.65   0.100    -7.231417    82.91724
{txt}{hline 13}{c +}{hline 64}
         _se {c |}  {res} 35.33536   1.722316           {txt}(Ancillary parameter)
{hline 13}{c BT}{hline 64}

  Obs. summary:  {res}      313{txt}  left-censored observations at hours<={res}0
                       284{txt}     uncensored observations
                 {res}       13{txt} right-censored observations at hours>={res}50
{txt}
{com}. capture noi tobcm
{err}tobcm only works with lower limit of zero and no upper limit is specified
{txt}

The next example illustrates that {cmd:tobcm} will not work other commmands.

{com}. probit hours  nwi ms age race clt6 educ

{txt}Iteration 0:   log likelihood = {res}-422.60992
{txt}Iteration 1:   log likelihood = {res}-412.92441
{txt}Iteration 2:   log likelihood = {res}-412.91602

{txt}Probit estimates                                  Number of obs   = {res}       610
                                                  {txt}LR chi2({res}6{txt})      = {res}     19.39
                                                  {txt}Prob > chi2     = {res}    0.0036
{txt}Log likelihood = {res}-412.91602                       {txt}Pseudo R2       = {res}    0.0229

{txt}{hline 13}{c TT}{hline 64}
       hours {c |}      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
{hline 13}{c +}{hline 64}
         nwi {c |}  {res} .0030467   .0059293     0.51   0.607    -.0085745    .0146679
          {txt}ms {c |}  {res}-.2683211   .1341827    -2.00   0.046    -.5313143    -.005328
         {txt}age {c |}  {res}-.0328129   .0157792    -2.08   0.038    -.0637396   -.0018862
        {txt}race {c |}  {res} .1298931   .1260984     1.03   0.303    -.1172551    .3770414
        {txt}clt6 {c |}  {res}-.1508677   .1376471    -1.10   0.273    -.4206509    .1189156
        {txt}educ {c |}  {res} .0613806   .0197651     3.11   0.002     .0226417    .1001195
       {txt}_cons {c |}  {res} .9490395   .7468011     1.27   0.204    -.5146636    2.412743
{txt}{hline 13}{c BT}{hline 64}

{com}. capture noi tobcm
{err}tobcm only works after tobit
{txt}
{com}. capture log close
{smcl}
{com}{sf}{ul off}

{cmd:References}

{p 0 4}Drukker, D. M.  2002. Bootstrapping a conditional moments test for
normality after tobit estimation. The Stata Journal 2, Number 2: 125-139.

{p 0 4}Newey, W. 1985.  Maximum likelihood specification testing and
conditioanl moment tests. Econometrica 53: 1047-1073.

{p 0 4}Skeels, C. L., and F. Vella. 1999. A Monte Carlo investigation of the
sampling behavior of conditional moment tests in tobit and probit models.
Journal of Econometrics 92: 275-294.

{p 0 4}Tauchen, G. 1985. Diagnositic testing and evaluation of maximum
likelihood models. Journal of Econometrics 30: 415-443.