Elasticity-Negative dependent variable

[Angeliki Skoura]

Hello statalisters,

I am a bit confused about my project and I need your help. I would like to examine the relationship between taxable income and flactuations of tax rates through elasticities (Stata 17.0 MP) but my dependent variable contains negative values.
How could I overcome this problem?

Any help in this regard will be extremely helpful to me.

Many thanks in advance.

Angeliki

[Nick Cox]

So, the idea of elasticity is moot here: what do you think is the right answer for elasiticity as income passes through zero? Or (weaker) the ideal [NB] of constant elasticity you can report is moot too.

A generalized linear model with logarithmic link can tolerate some negative outcomes. The point is that the main model assumption is that the mean outcome is positive given covariates, which is consistent with some zero or negative values in the outcome. Note that poisson won't accept negative outcomes, but glm, link(log) will accept them.

[Angeliki Skoura]

Of course, I understand and for these reasons I am ambiguous . So in the case of glm link(log) the idea of elasticity is moot?
Maybe a transformation based on the literature would be more reliable.

Many thanks for help!


Best regards,
Angeliki

[Nick Cox]

All depends on exactly what you mean by elasticity, which is not a debating point, as people seem to jump between (a) a general calculus-based definition, whereby elasticity is in general a variable if it is defined at all, and (b) specific elasticity-constant models, making it inevitable that each elasticity is produced as a parameter estimate.

link(log) is just a specification of how to handle the outcome. What can or should be done otherwise would seem to depends on e..g whether your predictors are logged.

I should have underlined that I am not an economist, so you should look to your community for more guidance here.

[Angeliki Skoura]

Thanks for your advice, I really appreciate your reply.

Best regards,
Angeliki