Marginal Revolution has a point / counterpoint regarding whether measured real GDP increases or decreases in response to natural disasters.
My summary answer: with high confidence, we know that real measured GDP decreases in the disaster area in the immediate quarter. With less confidence, huge government borrowing to aid victims in the next several quarters does increase local and national measured real GDP, but disruptions in local markets cause increases in national prices that will have a negative impact more than offsetting the short-term gains from borrowing; llocal gains in the quarters following a disaster are paid at large national expense. Even the gains are transitory, since they are spent largely on non-investment goods, and repayment will lower measured GDP. GDP growth will be low in the disaster area for several years. National growth will be largely unaffected.
