RE: st: RE: Oxaca decomposition with heckman

["Rubil Ivica" <irubil@eizg.hr>]

Fabrizio,

I think there is an elegant solution to your situation which avoids multinomial or ordered probit. You basically want to correct for two types of selection:

1) participation vs. non-participation
2) full-time vs. part-time, CONDITIONAL ON PARTICIPATION

So, you can do it by estimating two different Mills ratios, one for each type of selection. However, this assumes the two types of choice are independent of each other. If, on the other hand, you think the two decisions are not independent from one another, then you can estimate one Mills ratio using binomial probit. Everything is nicely explained in this paper: Axel Heitmueller, 2004, "Public-Private Sector Wage Differentials in Scotland: An Endogenous Switching Model", IZA DP No. 992

I think this will work.

ivica





  

-----Original Message-----
From: owner-statalist@hsphsun2.harvard.edu [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Fabrizio Colella - 1348010
Sent: Wednesday, November 20, 2013 4:25 PM
To: statalist@hsphsun2.harvard.edu
Subject: Re: st: RE: Oxaca decomposition with heckman

Yes Ivica,

your explanation is good and it is perfect if I would have only 2 states (part-time and full time) with a probit at the first stage.
But at the first stage I would like to perform a multinomial probit (also an ordered probit could fit) among 3 states: part-time, full-time and non-employed, calculate lambdas and add them in the oaxaca with only two stages (part-time and full time).

So, how can I modify your code to assess this fact?

I am really grateful for your help.

Thanks

Fabrizio   

----- Original Message -----
From: "Rubil Ivica" <irubil@eizg.hr>
To: statalist@hsphsun2.harvard.edu
Sent: Wednesday, November 20, 2013 3:39:41 PM
Subject: RE: st: RE: Oxaca decomposition with heckman

Fabrizio,

as you know, according to the Heckman's paper on "sample selection as a specification error", one only needs to estimate the Mills ratio ("lambda") and include it in the set of covariates used in a wage regression. So, when you want to do an Oaxaca-Blinder decomposition, the mills ratio is just a covariate like any other, whose contribution to the raw wage difference can be estimated and then used to see how much of the raw gap comes from nonrandom selection into the two groups you are considering. That's why you want to include mills in the set of covariates in -oaxaca-. 

Concerning the code, I would use the following:


*** estimating mills ratio ***
probit full_time age ... clerk
predict Xb, xb
gen mills = .
replace mills =  normalden(Xb) / normal(Xb)  if full_time==1 replace mills = -normalden(Xb) / normal(-Xb) if part_time==1

(one should preferably add an additional variable in probit, which is excluded from the wage regression and affects the choice b/w part-time and full-time work; otherwise identification will come from nonlinearity only)

*** OB decomposition ***
oaxaca ln_hourly_wage age ... mills ... clerk, by(full_time) noisily detail

Hope it helps.

Ivica










-----Original Message-----
From: owner-statalist@hsphsun2.harvard.edu [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Fabrizio Colella - 1348010
Sent: Wednesday, November 20, 2013 3:18 PM
To: statalist@hsphsun2.harvard.edu
Subject: Re: st: RE: Oxaca decomposition with heckman

Well Ivica,

I didn't, now it works!

Anyway I am not sure that this is the correct form: I mean, is it fair to insert "mills" as regressor? 
And, if so, ajdust also using mills? Or it is better tho change the variables to be stored after -ohekman- (like storing directly lambda) ?

Can you please tell me which code would you implement in my place? 

Thanks again for your time,

Fabrizio

----- Original Message -----
From: "Rubil Ivica" <irubil@eizg.hr>
To: statalist@hsphsun2.harvard.edu
Sent: Wednesday, November 20, 2013 2:53:57 PM
Subject: RE: st: RE: Oxaca decomposition with heckman

Fabrizio,

did you include the variable "mills" in your set of covariates (age, ..., clerk)?

The command for decomposition should look as follows: 

oaxaca ln_hourly_wage age ... mills ... clerk, by(stat2) noisily detail adjust(mills)

And I would recommend you not to use adjust(), but rather let the contribution of mills be estimated and reported along with other covariates' contributions.

Hope it helps.

ivica






-----Original Message-----
From: owner-statalist@hsphsun2.harvard.edu [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Fabrizio Colella - 1348010
Sent: Wednesday, November 20, 2013 2:23 PM
To: statalist@hsphsun2.harvard.edu
Subject: Re: st: RE: Oxaca decomposition with heckman

Dear Rubil,

first of all thanks for your help!

I am not sure I understood what you mean. I do have tried to estimate the Heckman model separately, using the following code:

oheckman ln_hourly_wage age ... clerk , select(status = age age2 education couple benefits children) twostep predict xb generate mills = normalden(-xb) / (1 - normal(-xb)) oaxaca ln_hourly_wage age ... clerk, by(stat2) noisily detail adjust(mills)

where "status" assumes values 0,1, or 2 for non-employment, part-time, full-time and "stat2" assumes values .,1, or 2 for non-employment, part-time, full-time

and the result on the oaxaca estimation is:

mills not found
r(111);

Maybe you can suggest another way to adjust the -oaxaca-

Thank you again,

Fabrizio




----- Original Message -----
From: "Rubil Ivica" <irubil@eizg.hr>
To: statalist@hsphsun2.harvard.edu
Sent: Wednesday, November 20, 2013 1:53:15 PM
Subject: st: RE: Oxaca decomposition with heckman

Fabrizio,

why don't you first estimate the lambda separately and just use it as an additional covariate in -oaxaca-?

ir

-----Original Message-----
From: owner-statalist@hsphsun2.harvard.edu [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Fabrizio Colella - 1348010
Sent: Wednesday, November 20, 2013 1:43 PM
To: statalist@hsphsun2.harvard.edu
Subject: st: Oxaca decomposition with heckman

Dear Statalist,

I would like to perform an Oaxaca-Blinder Wage Decomposition comparing hourly wage of part-time and full-time employees. 

Moreover, I want to perform an Heckman model with a selection regarding the choices of workers among part-time, full-time and non-employment at the first step.

It seems it is impossible to achieve my goal using directly the command "Oaxaca" because the dependent variable at the first stage of the Heckman model is the same I have entered in the section "by(...)" of the Oaxaca structure. 
Any suggestions?

Any help will be highly appreciated.

Thanks
Fabrizio


------------------------------------------

Fabrizio Colella
Bocconi University and
Fondazione Rodolfo DeBenedetti
Milan, Italy
fabrizio.colella@studbocconi.it
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