Interpreting results: 1-standard-deviation increase in an explanatory variable

[Olivia Johns]

This table provides results of the analysis of the role of tax avoidance on returns. The dependent variables are Cumulative abnormal returns.

The authors state: "Economically, a 1-standard-deviation increase in tax avoidance is associated with a 0.75% (=26.2%*2.859%) more negative firm value response in Column 1".

My question is where is "26.2%" coming from? The figures in parentheses are t -statistics, and they do not report standard deviation but I assume -2.859 corresponds to one standard deviation in tax avoidance ("Tax variable"). Then why do the authors multiply the coefficient -2.859 by "26.2%"???

I'd really appreciate any help in interpreting this result.



Paper: The Value of Offshore Secrets: Evidence from the Panama Papers

[Clyde Schechter]

My question is where is "26.2%" coming from? The figures in parentheses are t -statistics, and they do not report standard deviation but I assume -2.859 corresponds to one standard deviation in tax avoidance ("Tax variable"). Then why do the authors multiply the coefficient -2.859 by "26.2%"???

Well, this is a really good example of why it is a bad idea to report "standardized" effects denominated in standard deviation units. Particularly since the author has kept the actual standard deviation secret, he/she could say anything at all and you would have to take it on faith (or leave it!).

We do see that the regression coefficient for tax variable is -2.859. Nothing in what you show, though it might be explained elsewhere in the reference, says what the units for the "tax variable" is. But if we assume that the unit in which the tax variable is measured is 1 percentage point, and if the standard deviation of that variable is 26.2 (percentage points), then 26.2*-2.859 would, indeed, be the marginal effect of a1 standard deviation difference in the tax variable.

Moral of the story: the units of measurement of all key variables should be made explicit when reporting results, and reporting results in terms of standard deviation changes is tolerable only if the standard deviation is disclosed, and even then isn't a good idea unless the measurement units of the variable are arbitrary, meaningless, or will be unfamiliar to the intended audience anyway. I classify the reporting of standardized results as what Paul Romer calls "mathiness," the use of mathematical tricks to simultaneously look impressive while obscuring the facts of the matter.

[Olivia Johns]

Thank you!!!!!! After carefully searching for SDs, I did realize they do report summary statistics. But this was very helpful, thank you!!