# st: Inverse Hyperbolic Transformation with 3SLS

 From "Song" <[email protected]> To <[email protected]> Subject st: Inverse Hyperbolic Transformation with 3SLS Date Fri, 11 Apr 2008 22:15:56 -0500

```Dear Stata users,

inverse hyperbolic sine transformation. I plan to estimate the following
model by 3SLS  (reg3).

IHS(Revenue in each country) = a0 + a1*Time window + controls
IHS(Time window) = b0 + b1*(expected) Revenue in each country + controls

Time window is difference in launching time (in days) of a product between
the US and international markets. Both revenue and time window are skewed,
so I want to use some transformation. Because time window includes a lot of
zeros and some negative values, I want to use inverse hyperbolic sine
transformation. My questions are:

1. Will the model I described above work in the context of system of
equations? Since most papers about IHS transformation are described in a

2. Estimation of scaling parameter

Burbidge, Magee, and Robb (1998) use a (concentrated) log-likelihood to
estimate the scaling parameter. If I use this method separately for each
equation and use the two estimated parameters to transform Revenue and Time
window each, and then estimate 3SLS, will it work?

I have read the following papers and related Q&A in Statalist archive, but
these things are not clear to me. I would appreciate any comment.

Burbidge, John B., Lonnie Magee, and A. Leslie Robb (1988), "Alternative
Transformations Handle Extreme Values of the Dependent Variable," Journal of
the American Statistical Association

Pence, Karen M. (2002), "401(k)s and Household Saving: New Evidence from the
Survey of Consumer Finances"

Pence, Karen M. (2006), "The role of wealth transformation: an application
to estimating the effect of tax incentives on saving"

Best,
Reo.

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```