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In-House Provision of Corporate Services: The Case of Property-Casualty Insurers and In-House Actuarial
Loss Reserve Certification

to occur in long-tail lines so we use the proportion of business in long-tail commercial
business lines as a control variable (Beaver et al., 2003). And we use the fraction of
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business in personal lines as another control variable. Compared to commercial long-tail
lines, personal lines are simpler and have a shorter-tail (Mayers and Smith, 1988). (The

omitted variable is the proportion of business in commercial, short-tail lines.) We have no
priors on the expected signs for the coefficients of these variables.
We measure diversification by line of business and by geographic area using

Herfindahl indexes of premiums earned by line and state, respectively. Grace and Leverty
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(2012) find these variables to be positively related to the loss reserve error, implying that
over-reserving is positively related to higher concentration by line and by state of business.
We also include reinsurance usage and growth in the regression model. Reinsurance
usage is measured as the percentage of gross premiums written ceded to reinsurers, while

growth is measured as the percentage increase in net premiums written from the previous
to the current year. Grace and Leverty (2012) find that reinsurance usage and growth are
negatively related to the loss reserve error. Group affiliation is associated with intragroup

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reinsurance, which may increase the complexity of the insurer. Finally, we include an
indicator variable in the regressions that is set equal to one for privately-held stock insurers
and equal to zero otherwise. We include this variable and the indicator for publicly-traded
stock insurers in the regression models. The omitted organizational form is mutuals.

24 The term “long-tail” refers to lines of insurance for which there is a long lag between premiums and
claim payments. The fraction of net premiums written for commercial long-tail business lines is the
proportion of net premiums written in long-tail lines (workers’ compensation, other liability, and
commercial automobile liability) to total net premiums written. The fraction of net premiums written
from personal lines is the proportion of net premiums written in personal lines (farmowners multiple
peril, homeowners multiple peril, automobile private passenger physical damage and private passen-
ger automobile liability) to total net premiums written.
25 The product or business line Herfindahl index is measured as the sum of the squared percentage of di-
rect premiums earned in each of the lines written by the P-C insurer; the geographic Herfindahl index
is measured using the sum of the squared percentage of direct business written in each of the 50 states
and the District of Columbia by the insurer.
26 We have no priors on the sign and significance of the Herfindahl variables and the group affiliation
variable. These are merely control variables.

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