st: endogeneity in mixed process models

[Jordana Rodrigues Cunha <jordana.rodrigues@unibo.it>]

Hi, anyone can help me how to allow for endogeneity in a mixed model with 4 equations each one with different functional distribution: an OLS regression, 2 probits and one ordered probit and where there is endogeneity?
I'm using stata 10. Thanks a lot.


Jordana Rodrigues Cunha
PhD. Candidate
University of Bologna
Department of Management
Via Capo di Lucca, 34, 1st floor
40126 – Bologna, ITALY
Fixed line:  0039 (051) 20 98 073
Fax: 0039 (051) 20 98 074
jordana.rodrigues@unibo.it
www.sa.unibo.it

Oggetto: st: -cmp for mixed and nonrecursive process?

Dear statalisters, I really need your help, seems that this is an impossible mission. I have consulted all the precedent faq's to arrive until here, but without success.

I am estimating the effects of X, Z  and W over Y, where they are (in sequence): a dummy, an ordinal, a dummy and a continuous variable. The three independent variables are linked by a nonrecursive looping, meaning that they are linked by reciprocal feedbacks: X determines Z and W, as well as Z determines X and W and W determines Z and Y.

X = a1+ bZ + cW + λ1Controls + e1; (binary dummy that varies from 0 to 1)
Z = a2 + dX + eW + λ2Controls + e2;(ordinal variable that varies form 1 to 5)
W = a3 + fX + gZ + λ3Controls + e3 ; (binary dummy that varies from 0 to 1)

the full model would be:

Y = a4 + hX + iZ + jW + λ4Controls + e4 (continuous variable)


I have made simple probits and ordered probits to check the relationship among the independent variables and I executed -cmp models to check the correlations among their error terms (in pairs of variables), confirming that they were really non-independent of each other. The problem is that as -cmp doesn't allow for reciprocal interaction among the variables and I included the second variable in the first equation and omitted the first variable in the second equation and so on. I have run, a naive OLS where the coefficients of X and Z were significant but not the coefficient of  W. I think that the best would run a SEM to use the 3 equations of X, Z and W with the fourth Y in the full model structured to allow for endogeneity but I have two main problems:

1- I cannot execute a Hausmann test ( to check for endogeneity in the full model) because when I ask for the residuals prediction after running oprobit (for estimate the variable Z) this option is not allowed and so I cannot regress the full model with the residual of Y and check the significance of its coefficient.

2- I have four different functional distributions and so if I would like to do 2sls or 3sls in different stages I wouldn't know  how to indicate the nature of the distribution for each variable and 3sls assumes that all the variables are continuous, right?

3 - I am using the same controls in all the equations, this could be a problem?


Please, somebody could give me an advice? I hope I had been clear in explaining, thank you all in advance,

jordana
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