st: A cautionary tale re scaling

[Kit Baum <baum@bc.edu>]

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We normally do not think about the scale of variables entering a linear regression. As recent exchanges on Statalist have pointed out, that may be a problem when it comes to computing marginal effects of models including squared terms, where the variable being squared is quite large (say, 1991 rather than 91).

I ran into a similar problem when a student asked why one of the linear constraints he was trying to impose on a linear 3SLS regression (via reg3) was being rejected as 'inconsistent or redundant', when five other constraints were accepted. The constraint did not involve any variable from the other five, and even if it was the only constraint, it was rejected.

The problem arose because the constraint was on the coefficient of a variable, gdp, that appeared in two equations. The variable was measured in units yielding a range between 10^7 and 10^8, which is not unusual for economic data retrieved from, say, World Development Indicators; it is not scaled into millions, billions, trillions etc.  When I scaled the variable to 10^-6, the constraint worked fine.

The moral of the story, then, is that although the constrained least squares estimator (cnsreg) or any linear regression command accepting constraints (e.g., sureg, reg3) is indeed an exercise in linear algebra, it may not work properly if the scale of the variables is extreme. If problems are encountered, check for such scaling issues, as earlier exchanges have suggested you should when computing marginal effects.

Kit Baum   |   Boston College Economics & DIW Berlin   |   http://ideas.repec.org/e/pba1.html
                              An Introduction to Stata Programming  |   http://www.stata-press.com/books/isp.html
   An Introduction to Modern Econometrics Using Stata  |   http://www.stata-press.com/books/imeus.html


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