Say Katrina comes along and knocks down some hotels, which are then rebuilt.
We all know the "broken window fallacy" — this sequence of events is not good for the economy. But under what conditions will it increase measured gdp?
Under one view, the money spent rebuilding the hotels would otherwise have been spent buying shoes or something else. Measured gdp should not go up. See Alex’s comments below for more along these lines. (But note that Alex’s fifth paragraph makes a mistake. I am not just "buying a new CD," but rather a new CD is being produced, generating income, in the analogous example he sets out, just as a new hotel is being produced to replace the old one destroyed by the storm. He doesn’t come squarely to terms with how new output ever increases measured gdp. A second factual but not theoretical point is that most Katrina refugees are now earning more elsewhere.)
An alternative approach invokes the assumption of "gross substitutability," or more prosaically that new production attracts a greater expenditure than the relevant alternative. (Addendum: We also can speak of the velocity of money rising.) New production in general raises measured gdp. If a new hotel is built, why should the "gdp consequences" of that production depend on whether the lot had always been vacant, or a previous hotel on that lot was destroyed by a storm?
A further complication is that the hurricane destroys wealth. The loss of hotels induces negative income effects, which probably will lower measured gdp in other sectors of the economy. Natural disasters are not a good way to build up gdp in the longer run.
Many factors are at play. Will we consider Keynesian effects through a possible employment increase for rebuilding, or intertemporal substitution effects through a temporary boost in labor supply in repair industries? If the repairs dig into future productive capacities, short-run gdp is more likely to rise than long-run gdp.
Will natural disasters increase measured gdp in the short run, once we consider expenditure switching effects?