Applying Wooldridge 1995 Estimator

[Johann Abrahams]

Dear community members,

I am trying to apply the fixed effects estimator that accounts for a possible sample selection bias proposed by wooldridge (1995). I am wondering if anyone could tell me wheather the following is the right approach:

---

(A short Introduction to the model)
In the model the equation of primary interest is defined as:
y_it = x_itβ + α_i + ε_it
and the selection equation as:
d*_it = z_itγ + µ_i + u_it
d_it = 1 if d*_it>0, 0 otherwise

where y_it is only observed, if d_it=1 and α_i and µ_i are the individual-specific time-invariant unobserved effects.

Wooldridge (1995) then derives the following estimator:

Step 1: For each t, run a a cross-sectional probit model for participation and for d_it=1, compute the Inverse Mills Ratio (lambda_hat)
Step 2: Define: w_hat_it=(1,x_i1,x_i2,...x_iT,x_it,0,...,0,lambda_hat_it,0,...0)
Step 3: Run a pooled OLS regression on: y_it=w_hat_itθ+eit if d_it=1

---

What i have done so far is:

to obtain the x_i1,x_i2,...x_iT:
For each dependent variable I ran:

        forvalues i = 1991 1992 to 2012 {
        by personID: gen x1_i`i' = x1[`i'-1990]
        }

to obtain 0,...,0,lambda_hat_it,0,...0:

        forvalues i = 1991 1992 to 2012 {
        quietly probit d z1-z7 if year==`i'
        quietly predict xb_hat_`i', xb
        quietly gen lambda_hat_`i' = normalden(xb_hat_`i')/normal(xb_hat_`i') if d==1
        quietly gen lambda_hat_d_`i' = lambda_hat_`i'
        quietly replace lambda_hat_d_`i' = 0 if year!=`i'
        quietly drop xb_hat_`i' lambda_hat_`i'
        }

then I ran the following regression:

y= x1_i1991-2012 x2_i1991-2012 ... x5_i1991-2012 x1-x5 lambda_hat_d_1991-2012 if d_it=1

Thank you so much in advance

Johann

Wooldridge, J. M. (1995), ‘‘Selection Corrections for Panel Data Models under Conditional Mean IndependenceAssumptions,’’ Journal of Econometrics 68, 115-132.

[Nick Cox]

Please note our referencing policy: http://www.statalist.org/forums/help#references

Please give precise literature references. The literature familiar to you will be not be familiar to all members of Statalist. Do not refer to publications with just author and date, as in Sue, Grabbit, and Runne (1989).
References should be in a form that you would expect in an academic publication or technical document. Good practice is to give a web link accessible to all or alternatively full author name(s), date, paper title, journal title, and volume and page numbers in the case of a journal article.

Please cross-reference http://www.statalist.org/forums/foru...ooldridge-1995

[Johann Abrahams]

Thank you Nick! However, I was able to obtain the Standard Errors of the Regression via bootstrap. This question is only related to underlying estimation of the parameters, which I already figured that was wrong in my earlier attempt (http://www.statalist.org/forums/foru...ooldridge-1995).

[Dirk Enzmann]

Nick Cox : I very much appreciate your patient persistence of reminding (new) members of the Statalist Forum to follow the policy rules (here: to give precise literature references). But in this respect I can't see anything wrong here -- the reference is given in exactly the way I would consider it to be correct. Is it that you simply overlooked the reference or is there a problem that I am not aware of? [Of course, not to mention cross-reference was really something to object.]

ADDED: Sorry, Nick -- I just recognized that Johann did edit his post about 20 minutes after his answer to your objection (and about 30 minutes after the creation of the original post). Thus, it may be that he added the reference afterwards.

BTW: I wonder that it is possible to make changes to posts after such a long time, I thought the time window was only 10 minutes.

[Bashir Muhammad]

Dear community members,
First i obtain 0,...,0,lambda_hat_it,0,...0: from the following commands.

forvalues i = 2002 2003 to 2012 {
quietly probit dummy variable and all independent and control variable if year==`i'
quietly predict xb_hat_`i', xb
quietly gen lambda_hat_`i' = normalden(xb_hat_`i')/normal(xb_hat_`i') if dummy==1
quietly gen lambda_hat_d_`i' = lambda_hat_`i'
quietly replace lambda_hat_d_`i' = 0 if year!=`i'
quietly drop xb_hat_`i' lambda_hat_`i'
}

After this all i run the gravity model. but the lambda lambda_hat_2002 to 2012 is significant.
regression:

lambda__2002_2012	0.190**	-0.0372	-0.0967	-0.230***	-0.668***	-0.413***	-0.258***	-0.301***	-0.0856
	(0.0868)	(0.0834)	(0.0838)	(0.0850)	(0.0893)	(0.0857)	(0.0852)	(0.0889)	(0.0864)

Fixed effect

lambda__2002_2012	-0.138**	-0.155***	-0.150***	-0.151***	-0.162***	-0.155***	-0.152***	-0.131**	-0.145***
	(0.0566)	(0.0556)	(0.0557)	(0.0556)	(0.0561)	(0.0557)	(0.0557)	(0.0560)	(0.0557)

Its mean that there is problem so what i will apply next that remove this problem?
Thanks so much