GDP is affected when you destroy it, because now all the people that rely on that city become much less productive (or die).

>If you destroy a city, GDP is not affected

Of course it is. Cities are engines for producing GDP. New construction, rolling infrastructure upgrades, the wages of all the people employed in it, the profits of corporations based in it, all add to GDP. Take away the city and all that GDP disappears off the books with it.

My example is a bit contrived, but it's a well-studied phenomenon that natural disasters tend to cause a net boost to GDP because of all the extra work needed to repair/rebuild/replace stuff.

We can write this kind of thing off as a statistical quirk, but if we actually attempt to increase GDP via policy changes, then there are definitely some perverse incentives that arise.

The immediate effect may be lots of economic activity, presumably paid for by borrowing, but consider the longer terms effects. Disruption of infrastructure reducing (or increasing the costs of) economic activity, disruption of businesses reducing profits and costing jobs which reduces wages. Death and injury of workers again reducing wage receipts by making more people non-contributing. These affects could last decades. Obviously I’ve not performed any studies on this, but it seems to me there would be significant impact on GDP. I’d be interested to see the results if a full case study.

I would find it hard to believe that the GDP of Puerto Rico, including reconstruction, has increased overall. It may depend on the scale though. A storm that knocks down a few trees and damages some buildings might generate a net gain if it’s not too disruptive but that gain must come from somewhere. Maybe increased future insurance costs, borrowing, increased taxation etc which would be difficult to quantify.

That still measures something meaningful doesn’t it? An alternative is that the city is destroyed and there are not enough resources to rebuild it.