Natural Disasters and GDP for National Income Accounting Nerds (UPDATED)

The broken windows falacy has been well addressed following our recent quakes, but there is an interesting technical issue with the measurement of GDP following a disaster, brought to my attention by a graduate of ours (and a former colleague of mine at the Bank of Canada), James Yetman.  

By way of background, consider how the contribution of a lottery to GDP should be measured. From total revenue, one needs to subtract off not only expenditure by the lottery seller on intermediate goods (such as the cost of the paper lottery tickets are printed on), but the payout on prizes. In effect, a lottery provides a valuable service (it would seem, from revealed preference) for transferring money from some ticket buyers to others. It is the commission earned on this transfer that constitutes the lottery seller’s revenue from which one subtracts expenditure on intermediate goods to calculate the contribution to GDP.

Now imagine that a country runs a really large lottery in which the prize jackpots if it is not won. And imagine that the probability of any particular lottery having a winner is so low that in most years the jackpot is never won. In this case, in most years, the lottery would be appear to be making a large contribution to GDP (high ticket revenue with no prize disbursement subtracted off), and then in years when the jackpot was won, would appear to be making a large negative contribution. The lottery market, however, is providing the same lottery services each year. In this example, the appropriate way to measure GDP would be subtract off the expected level of prize payment from revenue each year, not the realised payments.

Now consider the insurance market. Just as with a lottery, one should measure the revenue in the insurance industry as the difference between income received (premium payments plus interest on accumulated investments) and payouts in claims. But there is a lottery component to insurance. In the year of a really large natural disaster, payouts on claims will be unusually high, so in normal years, the difference between income received and claim payments will need to be higher to cover this contingency. Just as with the lottery example, the true contribution of insurance to GDP (the production of peace-of-mind), does not fluctuate in this way. Apparently after 9/11, the way the contribution of insurance services to GDP is measured was changed in the U.S. to subtract off expected claim payments rather than realised payments. I have no idea what the definition is in New Zealand. Can anyone with a background in official statistics enlighten me?

UPDATE: James Yetman has emailed me a reply he got from Statistics New Zealand about this. The upshot:

Premium income is used as the indicator for insurance in quarterly GDP, which affected directly by changes in insurance claims. Premium income may rise as prices rise in the longer term, but unless more people actually take out insurance it won't affect GDP in constant prices.

Annual GDP in current prices is a bit trickier. We get the output of this industry by deriving a service charge that represents the service the insurance industry offers policyholders. This starts with a service charge ratio, which measures the proportion of premiums that aren't used in paying claims (with a few other adjustments for supplementary income and reinsurance). The service charge ratio is averaged over five years to smooth out volatility and then multiplied by the premiums received for the year (again with extra adjustments I won't detail here), to give the service charge/output of the insurance industry.

A big rise in claims could potentially pull down the service charge ratio significantly, even with the five year average, though it would likely be offset by reinsurance claims by NZ insurers. So the final impact would depend on the difference between insurance claims and reinsurance claims. It's also possible that we would intervene here if we didn't think the service charge ratio was realistic, as the service charge is intended to be based on the 'normal losses' you mentioned (as the insurance industry calculates its premiums based on probabilities over the long term).