<p>In practice, econometricians just interpret it as if the regressor had the natural log transformation. &quot;The approximate average change in the outcome that is associated with the regressor increasing 100%.&quot;</p>
<p>This interpretation is an approximation even with the log transformation. It's just more of an approximation with the inverse hyperbolic sine transformation.</p>
<p>EDIT:
If you care, a recent paper that does this is <a href="https://www.aeaweb.org/articles?id=10.1257/aer.20201015" rel="nofollow noreferrer">https://www.aeaweb.org/articles?id=10.1257/aer.20201015</a></p>
<p>The math is,
<a href="https://i.sstatic.net/gwLMV6kI.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/gwLMV6kI.png" alt="enter image description here" /></a></p>
<p><a href="https://i.sstatic.net/0bpie9FC.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/0bpie9FC.png" alt="enter image description here" /></a></p>

CC BY-SA 4.0
2024-06-10T09:23:49.833Z
that's interesting. thank you.
mark leeds
CC BY-SA 4.0
2024-06-13T18:04:14.037Z
Thanks so much! This helps a lot
jheelum sarkar
CC BY-SA 4.0
2024-06-08T15:39:48.317Z
2024-06-10T08:24:44.883Z
2024-06-10T08:24:44.883Z
Michael Gmeiner
<p>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.</p>

CC BY-SA 4.0
2024-06-08T15:46:08.543Z
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. https://en.wikipedia.org/wiki/Zero-inflated_model
mark leeds
<econometrics><labor-economics>
Inverse Hyperbolic Transformation of Dependent Variable
jheelum sarkar
# Inverse Hyperbolic Transformation of Dependent Variable

(Asked by: username_0 on 2024-06-07)

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.

**Tags:** econometrics, labor-economics

> **Comments:**
> **username_1**: 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. https://en.wikipedia.org/wiki/Zero-inflated_model  

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## 1 answers

### Answer by username_2 on 2024-06-08. Score: 0

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](https://i.sstatic.net/gwLMV6kI.png)](https://i.sstatic.net/gwLMV6kI.png)

[![enter image description here](https://i.sstatic.net/0bpie9FC.png)](https://i.sstatic.net/0bpie9FC.png)

> **Comments:**
> **username_1**: that's interesting. thank you.  
> **username_0**: Thanks so much! This helps a lot  

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