Lessons from the Texas Homeowners Insurance Crisis Bob Puelz ...

of exposure relative to the peril. 28 Exponentiation of the empirical equation ln Prem = f(X)
yields Prem = e f(X) !
. Thus, for example, ∂Prem/∂Fire = " 1 ⋅ e f(X) . Rearranging e f(X) to the left-
!
hand side implies " 1 = ∂Prem/∂Fire ⋅ (1/Prem) and the elasticity is obtained by multiplying both
sides of the equation by the mean value of the Fire variable. Mean values from the overall
sample were used. In this instance, 0.00882 ⋅ 0.8466 = 0.007467 — which reveals the
percentage change in premium per $1,000 of exposure for a 1% change in the dollar amount of
current year fire losses per $1,000 of exposure — is 0.747%, on average, over the 1996 to 2001
period. The association between all the perils and the premium can be considered in a similar
fashion.
[Table 8 about here]
Evaluation of the relative magnitudes of the individual perils permits an exploration of
which perils were important during this crisis. To set a standard for comparison, the elasticity on
Fire is used as a benchmark to assess relative impact of the perils on homeowners premiums.
Table 8 lists the elasticities of the statistically significant property perils with respect to the
premium and the differences are contrasted with the fire peril, Fire. As can be seen from the
table, VMM and Liability categories provide less of an impact compared to the fire peril for the
sample period. Notable are wind and water. The estimated elasticity for the Wind peril is about
53% smaller than the Fire peril elasticity, while the Water peril is about 125% larger. The
elasticity of the Water peril is about 374% greater than the elasticity of the Wind peril. Thus,
28 See http://garnet.acns.fsu.edu/~dmacpher/teaching/ECO5421/Pdf/chap6b.pdf for a discussion of the
elasticity calculation.
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