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Re: st: Standard error for correlation coefficient in "biprobit"

From   kubo kensuke <>
Subject   Re: st: Standard error for correlation coefficient in "biprobit"
Date   Mon, 18 Oct 2010 20:17:37 +0900

Dear Scott,
Thank you very much for the formula!  I see that the standard error is
indeed calculated by the delta method.  When I was trying to apply the
method earlier, I must have been using an erroneous analytical
Thanks again for your time,

On Mon, Oct 18, 2010 at 18:41, Scott Merryman <> wrote:
> . local est = (exp([athrho]_cons)-exp(-[athrho]_cons))/(exp([athrho]_cons)+exp(-[athrho]_cons))
> . local se = (1 - (`est')^2)*[athrho]_se[_cons]
> Scott
> On Sun, Oct 17, 2010 at 9:03 PM, kubo kensuke <> wrote:
>> I am using the "biprobit" command for bivariate probit regression, and
>> would like to know how Stata computes the standard error for the
>> correlation coefficient ("rho") between the two error terms.
>> I have read the manual and understand that Stata indirectly estimates
>> "rho", by estimating its arc-hyperbolic tangent ("\athrho"), and
>> transforming it back to the original parameter using the inverse
>> function.  I also understand how the confidence interval of "rho" is
>> calculated from the confidence interval of "\athrho".  However,
>> nowhere can I find any explanation on how the reported standard error
>> of "rho" is calculated.  I tried a delta-method calculation to obtain
>> the standard error of "rho" from the standard error of "\athrho" and
>> the analytical derivative of the hyperbolic tangent function, but the
>> result was clearly different from what was reported by Stata.
>> Hoping for an explanation, I purchased Professor Cox's Stata Journal
>> article ("Speaking Stata: Correlation with confidence, or Fisher’s z
>> revisited", 2008), but could not find a direct answer to this specific
>> question.
>> All I need is the formula that Stata uses to obtain the standard error
>> of "rho", based on its direct estimation of the arc-hyperbolic
>> tangent.   Any suggestions on this topic would be greatly appreciated.
>> With thanks,
>> Ken Kubo
>> Institute of Developing Economies, Japan
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