Another possibility is the inverse hyperbolic since transformation. A
recent paper that uses this method is available at:
http://www.bepress.com/bejeap/contributions/vol5/iss1/art20/
The data and Stata code is also available to download.
Scott
AUTHOR:
Karen M. Pence, Federal Reserve Board of Governors
TITLE:
The Role of Wealth Transformations: An Application to Estimating the Effect
of Tax Incentives on Saving
SUGGESTED CITATION:
Karen M. Pence (2006) "The Role of Wealth Transformations: An Application to
Estimating the Effect of Tax Incentives on Saving", Contributions to
Economic Analysis & Policy: Vol. 5: No. 1, Article 20.
http://www.bepress.com/bejeap/contributions/vol5/iss1/art20
ABSTRACT:
Researchers may want to estimate the percentage change of a variable, such
as household wealth or corporate profits, that takes on economically
significant nonpositive values. Using the logarithmic transformation,
however, requires discarding observations with nonpositive values. This
paper describes a possible solution to this problem-the inverse hyperbolic
sine transformation-and shows how to implement this transformation optimally
in the case of median regression. As an illustration of the usefulness of
this transformation, I revisit a specification sometimes used to estimate
the effect of tax incentives on household saving.
> -----Original Message-----
> From: owner-statalist@hsphsun2.harvard.edu [mailto:owner-
> statalist@hsphsun2.harvard.edu] On Behalf Of paul d jacobs
> Sent: Wednesday, November 08, 2006 3:46 PM
> To: statalist@hsphsun2.harvard.edu
> Subject: st: Grid Search in a Log Plus Constant Model
>
> I am working with health data (MEPS) where
> out-of-pocket medical expenses (OOP) are a dependent
> variable in an OLS regression. Because of the
> positive skewness of such a variable, I would like to
> use a normalizing transformation, i.e. the log of OOP.
> However, because of the many zero observations for
> OOP, the options are to either add a constant to OOP,
> (some have used $1 arbitrarily), or to model the data
> separately for the zeroes and the positive values,
> which I'd rather not do. (I have also considered the
> square root transformation, etc., but would like to
> test out the results using a log-constant).
>
> My question is: do you know of a method for searching
> for the optimal constant to add to a variable so that
> a log-transformation produces the optimal result? Deb
> et al. (2005), suggest a 'grid search' for this value
> (see link below for document). I know that grid
> searches are used in the context of maximum
> likelihood; is this a similar process? Would running
> the model with different values and comparing R2s and
> standard errors be more appropriate?
>
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