## Tuesday, August 17, 2010

### A Little More on Disaster Loss Statistics

A little more on yesterday's discussion.  First, as I suspected, there does seem to be a statistically significant trend to this graph:

A simple linear regression is inappropriate here, since the numbers are obviously not normally distributed. We are getting up to 350 in a small sample, but we can't go below 0 (and the average is 100 by design), so clearly the tails of the distribution cannot be symmetric, at a minimum.  Further, we expect in general that disaster losses are dominated by very large disasters (eg in 2005 when the losses are heavily influenced by the Gulf hurricanes, so we would suspect a-priori a heavy-tailed distribution).

However, another quick and easy test is appropriate - the Wilcoxon rank sum test which doesn't depend on making any assumptions about the distribution of damage levels.  The idea here is that we divide the years up into 1975-1990, and 1991-2006 (I threw out 2007 for the sake of having equal sample sizes).  Then we test to see if it's the case that too many of the low values for damage/gdp fall into the first half.  It turns out that this is so - I get a significance level of p=0.003 (using the normal approximation for the test statistic on a one-sided test - my test statistic is 2.75 sigmas below the mean).

However, to me there is an obvious confound here - economic losses in natural disasters will be heavily influenced by property damage, since destroyed property is the most obvious and easily measured impact of a disaster (and is of definite sign - it's always bad).  And it's not reasonable to assume that the value of real estate has a fixed ratio to GDP.  Just to take the case of the US, we know that price/income ratios have varied substantially during the last 35 years, and it's not clear if you could control for this, whether the trend above would survive.

#### 1 comment:

Greg said...

Household income is not the right thing to compare to, since it's been falling as a proportion of GDP. You need the total value of property (not just houses) compared to GDP.

I still maintain that in a rational world with a constant probability distribution of disasters, the reported loss should fall as a proportion of GDP as the capital stock grows. Greater risk should mean more prevention measures are put in place. (And there's learning from experience...) Without a change in disaster size and occurrence, there *should* be a declining trend in reported loss as a proportion of GDP. But there isn't. No wonder that Munich Re is worried about global warming....