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From |
"Alfredo Paloyo" <arpaloyo@up.edu.ph> |

To |
<statalist@hsphsun2.harvard.edu> |

Subject |
st: Clarification on biprobit |

Date |
Fri, 25 Feb 2005 10:58:01 +0800 |

Dear all, First, a public thanks to Gustavo Sanchez and Jonathan Beck (who replied in private) for answering my initial question. I hope you have some time to answer more questions regarding the biprobit model I am working on. I would be very grateful. I have the following model: p = a1X + b1s + c1Z s = a2X + b2p. The variables p and s are binary. The first thing I did is to run a biprobit model (all runs are with pweight) like this: p = a1X s = a2X, which I implemented in Stata as [1] . biprobit p s X and [2] . biprobit (p = X s) (s = X p), with the second one constained with [p]s = 0 and [s]p = 0. 1. They produce the same result in terms of the coefficients and everything else on that table. However, they differ in computing the (log-)likelihood functions. The first one produces a "Comparison: log pseudolikelihood" of -1576 while the second reports -1528. Why is this different and which one is the correct specification? Does it make a difference at all, considering that the coefficients are the same, anyway? 2. -mfx- is able to compute the marginal effects of the first specification (with standard errors, too). However, when I try it on the constrained -biprobit-, it responds with "warning: derivative missing; try rescaling variable p". How could this happen? Next, I ran [3] . biprobit (p = X s) (s = X p), with the constraint that [athrho]_cons = 0. 3. Would this be equivalent to running a two separate probits? I ran ". probit p X s" and did not get the same results. 4. -mfx- is able to compute the marginal effects but fails for the standard error, returning "warning: predict() expression unsuitable for standard error calculation". Can I still be confident in interpreting the marginal effects in this case? Since rho is effectively a test for exogeneity [Fabbri et al., 2004; also discussed in Statalist previously], what I want to do is to test whether p and s are exogenous. So, I run [4] . biprobit (p = X s Z) (s = X p) to test whether s is exogenous to the first equation, with the constraint that [s]p = 0. I include Z for identification purposes (should I have done this for [2], too?). If the output of [2] says that rho is significantly different from zero and the output of [4] says that it is not, then I can conclude that s is exogenous. Similarly, to examine whether p is exogenous, I must run [5] . biprobit (p = X s Z) (s = X p) with the constraint [p]s = 0. I get the essentially same result (the rho has become zero) so I can conclude that p is exogenous to the second equation. 5. Is this how the test for exogeneity should be implemented? 6. s is significant in [4] and p is significant in [5]. This means that the the reason why rho is significant in [2] is that p and s are the omitted variables that make the error terms correlated. Thus, I can run [6] . probit p = X s Z [7] . probit s = X p. 7. The thing is, s is a significant regressor and p is also a significant regressor. Does this not, in fact, tell us to estimate the two equations jointly? I am unsure of what to do next. Please let me know (kindly?) where I have committed the disastrous blunder. :) -- Paloys * * For searches and help try: * http://www.stata.com/support/faqs/res/findit.html * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

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