Re: st: RE: two-stage mvprobit and ghk vs. sem algorithm questions

[Andrew <abrudevo@gmu.edu>]

Peter,

Please excuse me, I thought it would come through from the email system.

Thank you for any help you can provide.
Regards,
Andrew Brudevold

On Mon, Jul 16, 2012 at 8:28 PM, Lachenbruch, Peter
<Peter.Lachenbruch@oregonstate.edu> wrote:
> With all the fuss about names recently, you owe us a first AND A LAST NAME!
>
> ________________________________________
> From: owner-statalist@hsphsun2.harvard.edu [owner-statalist@hsphsun2.harvard.edu] On Behalf Of Andrew [abrudevo@gmu.edu]
> Sent: Monday, July 16, 2012 11:35 AM
> To: statalist@hsphsun2.harvard.edu
> Subject: st: two-stage mvprobit and ghk vs. sem algorithm questions
>
> Hi Statalist,
>
> I have two questions:
>
> Question 1:
> I have been trying to confirm if the following two-stage mvprobit
> analysis is valid and would appreciate any thoughts/comments.  I have
> a 3 equations of interest that I believe have correlated errors:
>
> W1 = aA + dW2 + e1
> X1 = bB + eX2 + e2
> Y1  = cC + fY2 + e3
>
> where
> W, X, Y are dichotomous variables
> A,B,C are exogenous variables
> a,b,c are exogenous variable coefficients
> W', X', Y'  are endogenous dichotomous variables
> d, e, f are endogenous variable coefficients
> e1, e2, e3 are errors that are jointly normally distributed
>
> Each of these equations is itself part of a two equation system of the
> type described by Mallar (1977) and Maddala (1983, pg 246)  such that:
> W1 = aA + dW2 + e1
> W2 = a'A' + d'W1 + u1
> with analogous equations defined for X and X', and Y and Y'.
>
> Mallar and Maddala solve this smaller system by estimating the reduced
> form equations for each of these two, obtaining fitted values, and
> then running further ml probits to obtain estimates of d/sigma1 and
> a/sigma1.
>
> My hope is that I can estimate the reduced form for the endogenous
> variables (W2, X2, Y2):
>        W2 = a'A' + aA + v1
>  obtain their predicted estimates (W2*, X2*, Y2*) and then use those
> in the original system to allow for the correlated errors among the
> W1,X1,Y1 equations using the mvprobit command.
>
>  mvprobit (W1 = A W2*) (X1 = B X2*) (Y1 = C Y2*)
>
> This is based on the idea that the you could estimate the coefficients
> in each of the smaller systems by performing the 2 stage least squares
> to obtain consistent results but that then performing the mvprobit we
> are obtaining more efficient estimates that take into account the
> error correlations. This is analogous to estimating OLS equations one
> by one or by SUR.
>
> Question 2:
> The mvprobit command uses the GHK simulator.  My understanding is that
> the GHK simulator is computationally efficient for systems of 4 or 5
> equations but that for larger systems a stochastic EM algorithm is
> likely to be a better option.  Is this correct?
>
> Thank you all in advance.
> Regards,
> Andrew
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