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I am trying to transform a dependent variable which is a measure of time (minutes per day). To account for zero values of the dependent variable in the regression, I am taking its inverse hyperbolic transformation. Can anyone tell me how I can interpret the coefficient? My independent variable is a dummy.

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  • $\begingroup$ Hi: I've never used them ( and don't know much about them ) but another approach is zero-inflated models. These really depend on the underlying distribution assumed for the response. en.wikipedia.org/wiki/Zero-inflated_model $\endgroup$
    – mark leeds
    Commented Jun 8 at 15:46

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In practice, econometricians just interpret it as if the regressor had the natural log transformation. "The approximate average change in the outcome that is associated with the regressor increasing 100%."

This interpretation is an approximation even with the log transformation. It's just more of an approximation with the inverse hyperbolic sine transformation.

EDIT: If you care, a recent paper that does this is https://www.aeaweb.org/articles?id=10.1257/aer.20201015

The math is, enter image description here

enter image description here

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  • $\begingroup$ that's interesting. thank you. $\endgroup$
    – mark leeds
    Commented Jun 10 at 9:23
  • $\begingroup$ Thanks so much! This helps a lot $\endgroup$ Commented Jun 13 at 18:04

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