j-1 or j number of IMR after mlogit

[E. HABTE AWANO]

Hello!
I am trying to estimate treatment effect (endogenous switching regression) using multinomial selection equation with three treatment categories . I have in fact tried to browse regarding the IMR after mlogit. But I still have two confusions from the materials I read: 1) is it three or two IMR that I need to calculate 2) should I include all the IMR in each of the three outcome equation (one for each category), or I need to include only IMR of each categories in their respective outcome regime? When the selection equation is binary I normally have two IMR and I include for example IMR1 in regime 1 and IMR2 in regime 2. But somehow become peplexed when selection eqn becomes multinomial. THANK YOU for your help.

[E. HABTE AWANO]

I observed estimation of the outcome (second step) eqn with the inclusion of all the inverse mills ratios in each regime on http://www.stata.com/statalist/archi.../msg00191.html

[E. HABTE AWANO]

Another which I could not be sure about (even after reading Lee (1982) ; Dubin & McFaden (1984) as well as Bourguignon et.al. (2007) is related to the multiplier to be used while calculating the inverse mills for each outcome. Here is what I copied from what has been displayed on http://www.stata.com/statalist/archi.../msg00191.html.

It exactly poses same question as I do (Please, refer to the part copied and made bold, blue and underlined, below): Having four alternative outcomes, when only three mills are calculated, the multiplier is three; but what if I wanted to compute four mills, should the multiplier change to four? Does that mean that the multiplier should be a number that indicate the number of mills to be computed?

Copied from http://www.stata.com/statalist/archi.../msg00191.html

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Also, I would like to implement the model by myself:
1. Run a Multinomial logit model (type_HH is my dependent variable)
2. Calculate the inverse Mills ratio
3. Run a OLS regression where the dependent variable is expenditure in good i and include the mills ratios.
Because I have 4 outcomes, after running the mlogit I have to create the predict probabilities for each outcome:

predict p1, outcome(1)
predict p2, outcome(2)
predict p3, outcome(3)
predict p4, outcome(4)

Following the advice given by Mushfiq Mobarak (http://www.stata.com/statalist/archi.../msg00465.html)

The way to calculate the mills’ ratios and apply the Dubin and McFadden (1984) is the following
gen trnsp1=(p1*ln(p1))/(1-p1)
gen trnsp2=(p2*ln(p2))/(1-p2)
gen trnsp3=(p3*ln(p3))/(1-p3)
gen trnsp4=(p4*ln(p3))/(1-p4)

gen mills2= 3* ln(p2)+ trnsp1 + trnsp3 + trnsp4

gen mills3= 3* ln(p3)+ trnsp1 + trnsp2 + trnsp4

gen mills4= 3* ln(p4)+ trnsp1 + trnsp2 + trnsp3

2) What happen when I decide to apply the more flexible version of the Durbin and McFadden model? I should calculate 4 Mills ratios. Is it correct the following way?

gen mills1= 4* ln(p1)+ trnsp2 + trnsp3 + trnsp4

gen mills2= 4* ln(p2)+ trnsp1 + trnsp3 + trnsp4

gen mills3= 4* ln(p3)+ trnsp1 + trnsp2 + trnsp4

gen mills4= 4* ln(p4)+ trnsp1 + trnsp2 + trnsp3

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Please, bear with my ignorance and THANK YOU, FOR HELPING.