<p>You don't need to log transform these variables. Consider the following model</p>

<blockquote>
  <p>$\log y = \beta x.$</p>
</blockquote>

<p>Then, you can interpret $\beta$ as a <strong>semi-elasticity</strong>, i.e., the percentage change in $y$ when $x$ increases by 1 unit. </p>

<p>To see this you can transform the previous equation as: 
$y = \exp(\beta x),$ in which case $dy/dx = \beta \exp(\beta x)$. Thus, the percentage change in $y$ when $x$ changes is $\frac{dy/dx}{y} = \frac{\beta\exp(\beta x)}{\exp(\beta x)} = \beta$.</p>

<p>Note also that </p>

<blockquote>
  <p>$\Delta \log y = \beta \Delta x$ so $100.\Delta \log y = (100.\beta) \Delta x$</p>
</blockquote>

<p>It follows that </p>

<blockquote>
  <p>$\% \Delta y \approx (100.\beta) \Delta x$</p>
</blockquote>

CC BY-SA 3.0
2018-04-15T20:22:54.300Z
2018-04-15T20:22:54.300Z
emeryville
<p>Before regression (like fixed-effects, random-effects), for these two kinds of variables:</p>

<p>1) Price levels (e.g. price level of capital formation)
They are usually ratios like 0.987, 1.022..., based on USA 2010=1</p>

<p>2) % of GDP (e.g. broad money as % of GDP)
They are also ratios (%) like 80.5, 99.7 (or in decimal form 0.805, 0.997)</p>

<p>Do I need to log transform them, and how can I log transform them?</p>

<applied-econometrics><paneldata>
Do I need to log transform these two kinds of variables?
Yu Wang Dolby
# Do I need to log transform these two kinds of variables?

(Asked by: username_0 on 2018-04-15)

Before regression (like fixed-effects, random-effects), for these two kinds of variables:

1) Price levels (e.g. price level of capital formation)
They are usually ratios like 0.987, 1.022..., based on USA 2010=1

2) % of GDP (e.g. broad money as % of GDP)
They are also ratios (%) like 80.5, 99.7 (or in decimal form 0.805, 0.997)

Do I need to log transform them, and how can I log transform them?

**Tags:** applied-econometrics, paneldata


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## 1 answers

### Answer by username_1 on 2018-04-15. Score: 0 | Accepted answer

You don't need to log transform these variables. Consider the following model

> $\log y = \beta x.$

Then, you can interpret $\beta$ as a **semi-elasticity**, i.e., the percentage change in $y$ when $x$ increases by 1 unit.

To see this you can transform the previous equation as:
$y = \exp(\beta x),$ in which case $dy/dx = \beta \exp(\beta x)$. Thus, the percentage change in $y$ when $x$ changes is $\frac{dy/dx}{y} = \frac{\beta\exp(\beta x)}{\exp(\beta x)} = \beta$.

Note also that

> $\Delta \log y = \beta \Delta x$ so $100.\Delta \log y = (100.\beta) \Delta x$

It follows that

> $\% \Delta y \approx (100.\beta) \Delta x$


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