<p>You can use summary statistics to compare the one unit change to the standard deviation and could say that it represents a 1, 1.2 2 etc. standard deviation change. For example, if in the regular form:
<span class="math-container">$$y_i=\beta_{0}+\beta_{1}x_i+u_i$$</span>
say <span class="math-container">$\beta_{1}=6$</span> and from your summary statistics, the standard deviation of <span class="math-container">$y$</span> is 3, you could in turn explain the coefficient as: "A one unit change in <span class="math-container">$x$</span> is associated with a 2 standard deviation change in <span class="math-container">$y$</span>, ceteris paribus".</p>

<p>To interpret the unit change as a 1% change, you can convert the coefficient to read it in terms of percents relative to the levels of <span class="math-container">$x$</span> and <span class="math-container">$y$</span> or, to much more convenience, you can run the model in log-log form:
<span class="math-container">$$\log(y)_i=\beta_{0}+\beta_{1}\log(x)_{i}+u_i$$</span>
In this form, <span class="math-container">$\beta_{1}$</span> is the <strong>percentage</strong> change in <span class="math-container">$y$</span> from a 1% change in <span class="math-container">$x$</span>. Exactly what you are looking for!
<span class="math-container">$$\beta_{1}=\frac{\%\Delta y}{\%\Delta x}$$</span>
where the denominator is usually a 1% change.</p>

CC BY-SA 4.0
2019-08-29T08:43:32.657Z
Thanks Brennan. Just need clarifcation on the matter - much appreciated.
EB3112
CC BY-SA 4.0
2019-08-29T23:20:17.263Z
No problem! If you are satisfied with the answer please accept it as it helps get the site off of beta!
Brennan
CC BY-SA 4.0
2019-08-28T16:11:43.900Z
2019-08-28T16:11:43.900Z
Brennan
<p>I have a conceptual question in terms of econometrics. </p>

<p>I understand for example that the primary goal of econometrics is to use estimated parameters to calculate the average change in the dependent variable conditional upon a unit change in the independent/explanatory variable(s). </p>

<p>However, may I ask if this 'unit change' is represented by the standard deviation, or in fact is representative of a 1% change?</p>

<p>Any feedback/discussion on this would be appreciated, </p>

<p>Best,</p>

<econometrics>
'One Unit Change in the Explanatory Variable'
EB3112
# 'One Unit Change in the Explanatory Variable'

(Asked by: username_0 on 2019-08-28)

I have a conceptual question in terms of econometrics.

I understand for example that the primary goal of econometrics is to use estimated parameters to calculate the average change in the dependent variable conditional upon a unit change in the independent/explanatory variable(s).

However, may I ask if this 'unit change' is represented by the standard deviation, or in fact is representative of a 1% change?

Any feedback/discussion on this would be appreciated,

Best,

**Tags:** econometrics

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## 1 answers

### Answer by username_1 on 2019-08-28. Score: 3

You can use summary statistics to compare the one unit change to the standard deviation and could say that it represents a 1, 1.2 2 etc. standard deviation change. For example, if in the regular form:
$$y\_i=\beta\_{0}+\beta\_{1}x\_i+u\_i$$
say $\beta\_{1}=6$ and from your summary statistics, the standard deviation of $y$ is 3, you could in turn explain the coefficient as: "A one unit change in $x$ is associated with a 2 standard deviation change in $y$, ceteris paribus".

To interpret the unit change as a 1% change, you can convert the coefficient to read it in terms of percents relative to the levels of $x$ and $y$ or, to much more convenience, you can run the model in log-log form:
$$\log(y)\_i=\beta\_{0}+\beta\_{1}\log(x)\_{i}+u\_i$$
In this form, $\beta\_{1}$ is the **percentage** change in $y$ from a 1% change in $x$. Exactly what you are looking for!
$$\beta\_{1}=\frac{\%\Delta y}{\%\Delta x}$$
where the denominator is usually a 1% change.

> **Comments:**
> **username_0**: Thanks Brennan. Just need clarifcation on the matter - much appreciated.  
> **username_1**: No problem! If you are satisfied with the answer please accept it as it helps get the site off of beta!  

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