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I am doing a diff-in-diff analysis, looking at whether a regulation had an impact on British pollution-intensive exports. Initially I used 'total exports of pollution-intensive goods' as my dependent variable but to get my treatment effect as a percentage, I was thinking of making this dependent variable as the 'natural log of total exports of pollution-intensive goods'. Apart from giving a straightforward percentage change interpretation, what other justification would there be to use the natural log for exports? Is it appropriate to use the natural log for exports in the first place?

Mathew Chandy
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  • You can use a gravity model of trade flows to justify it. Have a look at this https://www.unescap.org/resources/gravity-model-international-trade-user-guide-r-version. This is an easy read. – Jesper for President May 03 '20 at 11:10
  • To ensure positive predictions from a model for exports. To model nonlinear relationships. To dampen adverse side-effects of skewness and outliers. – Nick Cox May 03 '20 at 11:14
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    And a reason not to use log is to allow for 0 export, since in reality many countries have zero export to some countries. – Jesper for President May 03 '20 at 11:18
  • There are many, many threads here on why logarithmic scale is a good idea (or whether ...). Although it's not quite evident from the thread title, the thread just cited contains good broad discussions of the point -- with a bonus for the OP that the examples are mostly from economics. – Nick Cox May 03 '20 at 11:18
  • @JesperforPresident Zero values for the response are not a real problem. Poisson regression implementations (more generally, generally generalized linear model implementations) should allow zero values for the response (if not, they are incompetent). The idea is to fit mean functions that are positive given the predictors. A positive mean doesn't rule out zeros (or even negative values). But the big deal is using a logarithmic link function, not just transforming the response – Nick Cox May 03 '20 at 11:21
  • I couldn't agree more, what I was hinting at was exactly that a better approach could be to use poisson regression rather than transform the observed export $z$ to $\log(z)$. – Jesper for President May 03 '20 at 11:26

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