Semiparametric Least Square (SLS) - Ichimura

[Max Resende]

TDear StataList colleagues,

I have been trying to build a semiparametric model for high school dropout based on Ichimura (1993). But there are a few things that i haven't figure it out yet.

I made a bseline mode and this is what I got

. sls transitioning menino branco rural lnpib_pc i_funcionarios_razao prof_idade if i<=100064
initial:       SSq(b) =  896.97362
alternative:   SSq(b) =  896.98122
rescale:       SSq(b) =  896.97362
SLS 0:   SSq(b) =  896.97362  (not concave)
SLS 1:   SSq(b) =   894.3267  (not concave)
SLS 2:   SSq(b) =  893.73212  (not concave)
SLS 3:   SSq(b) =  891.03668  (not concave)
SLS 4:   SSq(b) =  890.79053  (not concave)
SLS 5:   SSq(b) =  890.77715  (not concave)
  pilot bandwidth
  90.46624046
SLS 0:   SSq(b) =  893.42571  (not concave)
SLS 1:   SSq(b) =  884.68644  (not concave)
SLS 2:   SSq(b) =  884.38933  (not concave)
SLS 3:   SSq(b) =  882.48653  
SLS 4:   SSq(b) =  872.16431  (not concave)
SLS 5:   SSq(b) =  869.41449  (not concave)
SLS 6:   SSq(b) =  866.57781  
SLS 7:   SSq(b) =  860.83147  (not concave)
SLS 8:   SSq(b) =  860.59351  
SLS 9:   SSq(b) =  860.19257  (not concave)
SLS 10:  SSq(b) =  860.16003  (not concave)
SLS 11:  SSq(b) =  860.15529  (not concave)
SLS 12:  SSq(b) =  860.14491  
SLS 13:  SSq(b) =  860.14046  
SLS 14:  SSq(b) =  860.13996  
SLS 15:  SSq(b) =  860.13943  
SLS 16:  SSq(b) =  860.13937  
SLS 17:  SSq(b) =  860.13935  
                                                      Number of obs =     5461
                                                      root MSE      =   .39687
--------------------------------------------------------------------------------------
       transitioning |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
---------------------+----------------------------------------------------------------
Index                |
              branco |  -846.1087   43.70445   -19.36   0.000    -931.7679   -760.4496
               rural |  -7490.569   374.1025   -20.02   0.000    -8223.797   -6757.342
            lnpib_pc |   15266.43   760.6964    20.07   0.000     13775.49    16757.37
i_funcionarios_razao |   1418.522   70.88002    20.01   0.000       1279.6    1557.444
          prof_idade |  -349.8687   17.34921   -20.17   0.000    -383.8725   -315.8649
              menino |          1  (offset)
--------------------------------------------------------------------------------------

These are my questions:

1) What does it means

initial:       SSq(b) =  896.97362
alternative:   SSq(b) =  896.98122
rescale:       SSq(b) =  896.97362
root MSE      =   .39687
pilot bandwidth
  90.46624046 - this is the kernel h?

2) How can i find out the nonparametric equation, g(.)? I know how to generate the index.

I look it up on https://ideas.repec.org/c/boc/bocode/s457927.html, but i had no luck.

Thank you all,

Max

[Max Resende]

is
pilot bandwidth 90.46624046 my kernel density bandwith?

[Marcos Almeida]

Since you said you "had no luck" in finding core information, you may start by taking a look at the help files.

This is a user-written program, whose author is Michael Barker (actually, you are supposed to provide this information, according to the FAQ advice).

I have no experience with - sls - but there is some information in the help files that may interest you particularly:

pilot specifies that the pilot bandwith calculation be used for the entire estimation procedure. The pilot bandwidth is a plug-in estimate that follows the Silverman rule-of-thumb. For actual bandwidth values, I used values given in lecture notes by Bruce E. Hansen. The default procedure first goes through several iterations using the pilot bandwidth, then minimizes bandwidth simultaneously with the squared error objective function. This option follows the same procedure, but constrains the bandwidth to the final pilot bandwidth estimate during the simultaneous minimization procedure.

Also here:

sls performs semi-parametric estimation as described in Ichimura's 1993 paper. Kernel density estimates are calculated using a gaussian kernel. The bandwidth parameter is estimated using a two-step procedure. First, the index parameters are estimated using a plug-in optimal bandwidth estimate. The bandwidth and index parameter estimates from this preliminary estimation are used to construct bounds on the final bandwidth estimate. The final optimal bandwidth parameter is estimated simultaneously with the index parameters. The bandwidth parameter is chosen as the minimizer of the squared error objective function, as described in Hardle, Hall, & Ichimura, 1993.

Hopefully that helps.

[Max Resende]

Thank you MArcos for your help,

I have read that help lots of times, but sometimes you just don't see whats is in front of oyu.

So my kernel bandwith will be 90.46624046;

But what about SSq(b):
Will it be the value for squared error objective function in each interaction?

Max

[Max Resende]

Another question, dear friends:

Doesn anyone know how can I interpret the values of the index? And how can I plot the kernel estimate?

Hope someone can help me!!!

Max