<p>The max operator normally just returns the largest value from the set. So using function given by;</p>
<p><span class="math-container">$$\max\{0, \ln(x)\}$$</span></p>
<p>you will get output <span class="math-container">$\ln(x)$</span> whenever <span class="math-container">$x &gt; 1$</span> and zero otherwise since for <span class="math-container">$x&lt;1$</span> the <span class="math-container">$\ln(x)&lt;0$</span>. Basically output should be zero always when <span class="math-container">$x$</span> is less than, or actually also equal to, 1.</p>
<p>When <span class="math-container">$\ln(0)$</span> occurs result is not defined so maximum value in set is zero, so you avoid the issue altogether. Of course, one might debate whether this is particularly rigorous or elegant solution but it is a solution.</p>

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2023-08-18T13:11:06.650Z
2023-08-18T13:11:06.650Z
1muflon1
<p>in Acemoglu et. al. 2002b, which is about European Growth and Atlantic Trade, they do a log transformation of the atlantic trade variable. Since there are many observations where trade is 0, they say in the appendix the following:</p>
<blockquote>
<p>More formally, we use PATj · max {0, lnATjt} where ATjt is our estimate of Atlantic trade undertaken by country j at time t. The max operator avoids the “log of 0” problem.</p>
</blockquote>
<p>I understand why the log of zero is a problem, but I dont exactly understand how the max operator exactly works here, how it solves the problem and they dont mention it again. If the ATjt variable is zero, then isnt there still the &quot;log of 0&quot; problem?</p>
<p>Thanks!</p>

<macroeconomics><econometrics><economic-growth><applied-econometrics>
Log of 0 Probelm in Acemoglu et al. 2002b
Pajul
# Log of 0 Probelm in Acemoglu et al. 2002b

(Asked by: username_0 on 2023-08-18)

in Acemoglu et. al. 2002b, which is about European Growth and Atlantic Trade, they do a log transformation of the atlantic trade variable. Since there are many observations where trade is 0, they say in the appendix the following:

> More formally, we use PATj · max {0, lnATjt} where ATjt is our estimate of Atlantic trade undertaken by country j at time t. The max operator avoids the “log of 0” problem.

I understand why the log of zero is a problem, but I dont exactly understand how the max operator exactly works here, how it solves the problem and they dont mention it again. If the ATjt variable is zero, then isnt there still the "log of 0" problem?

Thanks!

**Tags:** macroeconomics, econometrics, economic-growth, applied-econometrics

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## 1 answers

### Answer by username_1 on 2023-08-18. Score: 1

The max operator normally just returns the largest value from the set. So using function given by;

$$\max\{0, \ln(x)\}$$

you will get output $\ln(x)$ whenever $x > 1$ and zero otherwise since for $x<1$ the $\ln(x)<0$. Basically output should be zero always when $x$ is less than, or actually also equal to, 1.

When $\ln(0)$ occurs result is not defined so maximum value in set is zero, so you avoid the issue altogether. Of course, one might debate whether this is particularly rigorous or elegant solution but it is a solution.


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