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

from running regressions on a sample of weak and healthy insurers should be statistically
different than running separate regressions on weak insurers and healthy insurers. Thus,
we conduct a Chow test to determine if it is appropriate to include both weak and healthy
insurers in the same sample (Chow, 1960). The Chow test results reject the validity of

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pooling weak and healthy insurers in the same regression sample. Therefore, emphasis in
the results is given to regressions in which weak and healthy insurers are separated. 38

5.2 Descriptive Statistics
Descriptive statistics are presented in Table 3. Panel A shows the means and standard
deviations for the full sample of insurers and the PSM sample. The table indicates that the
mean reserve error (scaled by total admitted assets) is very small and positive for the full
sample, i.e., 0.014. It is 0.013 for the PSM sample.

The results in Table 3, Panel B contain the means for the full and PSM samples of
weak firms and healthy firms. The mean loss reserve errors for weak firms are less than
zero in the full and PSM samples, while they are positive for healthy firms in the full and
PSM samples. Weak and healthy firms are more likely to be mutual or publicly-traded

stock insurers rather than privately-held insurers.
Panel C of Table 3 contains average annual values for the loss reserve error for the
sample period. On average, the loss reserve error is negative for weak firms in the full and
PSM samples, signifying that weak firms are under-reserved for the entire time period

whether one considers the full or PSM sample. Conversely, healthy firms are consistently
over-reserved for the entire period, which are signified by their positive values in the full
and PSM samples. The weak and healthy firms’ loss reserve errors are statistically different
from each other at the 1% statistical level or better.

5.3 Regression Results and Discussion
Table 4 contains regression results in which the scaled loss reserve error is used as

37 The chi-squared statistic for the full (PSM) sample is 4,262.96 (5,402.06); therefore, the null
hypothesis that the weak and healthy insurer samples can be pooled is rejected at better than the 1%
level.
38 Pooled sample results in which weak and healthy insurer observations are combined are reported also
for comparison purposes.

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