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From |
Andrew <abrudevo@gmu.edu> |

To |
statalist@hsphsun2.harvard.edu |

Subject |
st: two-stage mvprobit and ghk vs. sem algorithm questions |

Date |
Mon, 16 Jul 2012 14:35:28 -0400 |

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 * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

**Follow-Ups**:**st: RE: two-stage mvprobit and ghk vs. sem algorithm questions***From:*"Lachenbruch, Peter" <Peter.Lachenbruch@oregonstate.edu>

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