Blinder-Oaxaca decomposition for probit model

[Will Murphy]

Hello,

I have assessed online materials available for the decomposition of both linear and non-linear models but am not quite understanding the correct code to use in the current context.

I have obtained results for the average predicted probabilities (of being employed (emp = 1 if employed, 0= otherwise)) of non-disabled (DISTYPE = 4) and work-limited disabled (DISTYPE =1) via:

 probit emp DISTYPE SEX ETH AGES1 URESMC1 HDPCH191 IND1 MARSTA1 HIQUAL81 REGWKR1 SKSBN911 FTPTWK1, nolog 

margins, at(DISTYPE=(1 4)) vsquish

I believe the following format is adequate:

 fairlie depvar indepvars [if] [in] [weight], by(groupvar) [ options ]

But I am struggling how to integrate these results (the average predicted probabilities for both groups) to decompose the differences in observed characteristics and the 'unexplained' gap, for male and female?

Any help would be greatly appreciated.

[Dung Le]

Hello,

I have assessed online materials available for the decomposition of both linear and non-linear models but am not quite understanding the correct code to use in the current context.

I have obtained results for the average predicted probabilities (of being employed (emp = 1 if employed, 0= otherwise)) of non-disabled (DISTYPE = 4) and work-limited disabled (DISTYPE =1) via:

 probit emp DISTYPE SEX ETH AGES1 URESMC1 HDPCH191 IND1 MARSTA1 HIQUAL81 REGWKR1 SKSBN911 FTPTWK1, nolog

margins, at(DISTYPE=(1 4)) vsquish

I believe the following format is adequate:

 fairlie depvar indepvars [if] [in] [weight], by(groupvar) [ options ]

But I am struggling how to integrate these results (the average predicted probabilities for both groups) to decompose the differences in observed characteristics and the 'unexplained' gap, for male and female?

Any help would be greatly appreciated.

Hi Murphy,

Have you tries users-written command Oaxaca by Ben Jann or mvdcmp by Powers and colleagues? The Oaxaca can do both linear and non-linear models, while the mvdcmp gives you another option to deal with non-linear models.

Best regards,

Dung Le

[Will Murphy]

Hi Murphy,

Have you tries users-written command Oaxaca by Ben Jann or mvdcmp by Powers and colleagues? The Oaxaca can do both linear and non-linear models, while the mvdcmp gives you another option to deal with non-linear models.

Best regards,

Dung Le

Thank you for the reply- I am trying to replicate a literature that uses Oaxaca for probit so I think the former is definitely the approach, however the code suggested by online resources such as Ben Jann I can't really understand

[Will Murphy]

I assumed using command 'fairlie' was the non-linear (e.g probit) Oaxaca decomposition method

[Will Murphy]

To clarify the problem at hand following some alterations: I have obtained the difference in average predicted probabilities in female (FEMALE = 0 if male, =1 if female) employment between the Non-Disabled (ND = 1 if non-disabled, 0 = if otherwise) and Work-limited Disabled (WLD =1 if so, =0 if not) via:

(N.B: FEMALE = 1 if female, 0 if male
: ND = 1 if non-disabled, 0 if otherwise
:WLD = 1 if work-limited disabled, 0 if otherwise )

 by FEMALE, sort: probit emp WLD ND ETH AGES1 URESMC1 HDPCH191 IND1 MARSTA1 HIQUAL81 REGWKR1 SKSBN911 FTPTWK1, nolog
 
margins, at (WLD = 1) at (ND = 1) post

lincom _b[2._at] - _b[1._at]

I was wondering how I can decompose this difference into explained (due to characteristics) and unexplained (due to parameters)?

Thank you.

[FernandoRios]

That is exactly what Oaxaca does:

use http://fmwww.bc.edu/RePEc/bocode/o/oaxaca.dta
 oaxaca married educ exper age , probit by(female)

HTH
Fernando

[Will Murphy]

That is exactly what Oaxaca does:

use http://fmwww.bc.edu/RePEc/bocode/o/oaxaca.dta
oaxaca married educ exper age , probit by(female)

HTH
Fernando

Thank you very much. Could I just clarify, if I was to do:

 oaxaca emp WLD ND ETH AGES1 URESMC1 HDPCH191 IND1 MARSTA1 HIQUAL81 REGWKR1 SKSBN911 FTPTWK1, probit by(FEMALE)

Would this take into account the difference in average predicted probability generated in #5?

[FernandoRios]

One way to see that oaxaca is doing what you want is to also run this code:

. qui:probit married educ exper age if female==0
. margins
. qui:probit married educ exper age if female==1
. margins

[Will Murphy]

One way to see that oaxaca is doing what you want is to also run this code:

. qui:probit married educ exper age if female==0
. margins
. qui:probit married educ exper age if female==1
. margins

Thank you very much for the reply Fernando- it worked perfectly.

However, I realised- to reconcile results from #5 (i.e to compare WLD and ND) I have to do separate for male and female such that :

 keep if FEMALE == 1
  oaxaca emp ETH AGES1 URESMC1 HDPCH191 IND1 MARSTA1 HIQUAL81 REGWKR1 SKSBN911 FTPTWK1, probit by(WLD)
  qui: probit emp ETH AGES1 URESMC1 HDPCH191 IND1 MARSTA1 HIQUAL81 REGWKR1 SKSBN911 FTPTWK1 if WLD == 0
  margins
  qui: probit emp ETH AGES1 URESMC1 HDPCH191 IND1 MARSTA1 HIQUAL81 REGWKR1 SKSBN911 FTPTWK1 if WLD == 1
 margins

This may be a stupid question (and apologies if so, as I may have misunderstood #7) but I'd have to do this for WLD and ND for both male and female. Is there any way I can do the decomposition (and directly compare) for WLD = 1 and ND = 1 when still using only females?

I tried to do

 oaxaca emp ETH AGES1 URESMC1 HDPCH191 IND1 MARSTA1 HIQUAL81 REGWKR1 SKSBN911 FTPTWK1, probit by(WLD=1|ND=1)

but it didn't work?

Many thanks.

[FernandoRios]

Well, the option "by" only allows a single variable. ( in fact, for future reference, if you look in to oaxaca help file, you will see what other options you have, and what type of information it allows).
That being said.
Oaxaca does a decomposition between two groups, but defined by a single variable.
So, you need to create a variable , say wld_nd, that has the value of 1 if wld==1 and value of , say, 2 it nd==1
then you would type something like

oaxaca emp ETH AGES1 URESMC1 HDPCH191 IND1 MARSTA1 HIQUAL81 REGWKR1 SKSBN911 FTPTWK1 if female==1, probit by(WLD_ND)

[Will Murphy]

Well, the option "by" only allows a single variable. ( in fact, for future reference, if you look in to oaxaca help file, you will see what other options you have, and what type of information it allows).
That being said.
Oaxaca does a decomposition between two groups, but defined by a single variable.
So, you need to create a variable , say wld_nd, that has the value of 1 if wld==1 and value of , say, 2 it nd==1
then you would type something like

oaxaca emp ETH AGES1 URESMC1 HDPCH191 IND1 MARSTA1 HIQUAL81 REGWKR1 SKSBN911 FTPTWK1 if female==1, probit by(WLD_ND)

Thank you so much. Can I just clarify that, as WLD and ND were products of DISTYPE:

  gen WLD = 0
replace WLD = 1 if DISTYPE == 1
gen ND = 0
replace ND = 1 if DISTYPE == 4

and because DISTYPE can take 1 if work-limited disabled, 2 if daily activity-limiting disabled and 4 if non-disabled, then to create wld_nd I would definitely have to

 drop if DISTYPE == 2

? Thank you.

[FernandoRios]

 
 oaxaca emp ETH AGES1 URESMC1 HDPCH191 IND1 MARSTA1 HIQUAL81 REGWKR1 SKSBN911 FTPTWK1 if female==1 & inlist(DISTYPE,1,4), probit by(DISTYPE)

[Will Murphy]

Thank you very much for the help Fernando it has been greatly appreciated, all the best.

[Will Murphy]

oaxaca emp ETH AGES1 URESMC1 HDPCH191 IND1 MARSTA1 HIQUAL81 REGWKR1 SKSBN911 FTPTWK1 if female==1 & inlist(DISTYPE,1,4), probit by(DISTYPE)

Sorry Fernando, could I just check that interpreting the following:

 oaxaca emp ETH AGES1 URESMC1 HDPCH191 IND1 MARSTA1 HIQUAL81 REGWKR1 SKSBN911 FTPTWK1 if FEMALE==1 & inlist(DISTYPE,1,2), probit by(DISTYPE)

Blinder-Oaxaca decomposition                    Number of obs     =      2,278
                                                  Model           =     probit
Group 1: DISTYPE = 1                              N of obs 1      =       1879
Group 2: DISTYPE = 2                              N of obs 2      =        399

------------------------------------------------------------------------------
         emp |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
overall      |
     group_1 |   .5069096   .0086662    58.49   0.000     .4899243     .523895
     group_2 |   .3294188   .0190523    17.29   0.000      .292077    .3667606
  difference |   .1774909   .0209306     8.48   0.000     .1364675    .2185142
  endowments |   .1351331   .0184088     7.34   0.000     .0990526    .1712137
coefficients |   .0372206   .0156348     2.38   0.017      .006577    .0678642
 interaction |   .0051371   .0115974     0.44   0.658    -.0175934    .0278676
-------------+----------------------------------------------------------------

means that the explained (via differences in observed characteristics) = endowment = .1351331 and the unexplained (via parameter difference) = coefficients + interaction would be correct ? Apologies once again and thank you.

[Will Murphy]

Please disregard my last message, as I believe using 'pooled' on the end of each oaxaca input solves this. Many thanks.