Essay 2: Testing for Adverse Selection and Moral Hazard in Reinsurance Markets
4.1 Testing for Adverse Selection
4.1.2 Results on Adverse Selection
Table 3A, 3B and 3C contain the summary statistics for the variables used in the empirical
regression models for each line of business. As previously discussed, variables winsorized
at the 1
stand 99
thpercentiles are line-specific net amount of reinsurance, loss ratio volatil-
ity, loss reserve error, experience rating, retention limit, line-specific premiums growth rate,
9STATA commandxttobitis used here to exploit the panel data feature of our data samples. Since uncon- ditional fixed-effects Tobit estimates are biased, we employ random-effects Tobit model here. Please refer to STATA manual for further discussion (http://www.stata.com/help.cgi?xttobit).
firm premiums growth rate, leverage, tax rate, product Herfindahl, geographic Herfindahl,
proportion of premiums written in long tail lines, and return on assets.
Table 4A, 4B and 4C report the random-effects Tobit regression results for the follow-
ing three lines of reinsurance, respectively: private passenger auto liability reinsurance,
homeowners reinsurance, and product liability reinsurance. Since there is a number of
observations containing missing values of SUSTAIN and RHERF, we run our regressions
with and without these two variables.
10Table 4A reports the regression results for the private passenger auto liability reinsur-
ance. The coefficient on our risk measure,
loss reserve error, is positive and statistically
significant at the 1 percent level whenSUSTAINandRHERFare included, and statistically
significant at the 10 percent level whenSUSTAIN
andRHERFare excluded. The positive
correlation between our risk measure and the amount of reinsurance purchased conforms
to our hypothesis that high risk insurers tend to purchase a larger amount of reinsurance.
Therefore, we conclude that adverse selection is present in the private passenger auto lia-
bility reinsurance market.
The coefficient on
experience rating
is positive as hypothesized, but insignificant at
conventional significance levels. The coefficient onretention limitis always negative and
significant at the 1 percent level, suggesting that an insurer retaining a higher proportion
of direct business premiums purchases a smaller amount of reinsurance. This may imply
that reinsurers use retention limit to mitigate the adverse selection problem.
firm premiums
growth rate
is positive and significant at the 1 percent level in every econometric spec-
ification, suggesting that rapidly growing primary insurers utilize reinsurance to resolve
their growth-related problems, such as surplus drain and volatile profitability. However,
auto premiums growth rateis never significant, suggesting that reinsurance purchase deci-
sion is made at the firm level. The coefficient on
auto concentrationis positive but only
statistically significant at the 10 percent level whenSUSTAINandRHERFare included, in-
10BecauseSUSTAIN is defined as the percentage of premiums ceded over a three-year period to external reinsurers which are present in all three years, the construction of this variable will reduce our sample size by
dicating that an insurer tends to purchase more private passenger auto liability reinsurance
if the insurer’s business is highly concentrated in this line of business.
The coefficient on
leverage
is negative and significant at the 1 percent level in both
econometric specifications. Since
leverage
proxies for the probability of bankruptcy, a
negative and statistically significant coefficient on it implies that the higher the probability
of bankruptcy, the smaller amount of reinsurance purchased. This may be because rein-
surers are reluctant to provide reinsurance coverage to those financially weak insurers or
because higher reinsurance price charged by reinsurers to those financially weak insurers
dampens these insurers’ desire to purchase reinsurance coverage. The coefficient onfirm
size
is always negative and statistically significant at the 1 percent level, suggesting that
larger primary insurers tend to purchase less private passenger auto liability reinsurance.
The two proxies for long-term contracting relationship,
SUSTAIN
and
RHERF, are never
significant.
The coefficient on
geographic Herfindahlis always negative, and statistically signifi-
cant at the 1 percent level whenSUSTAINandRHERFare included, suggesting that a more
geographically diversified primary insurer tends to purchase a larger amount of reinsurance.
This finding is consistent with the real service hypothesis
11of Mayers and Smith (1990).
The coefficient on
lead company
is always negative, and statistically significant at the 1
percent level when
SUSTAIN
and
RHERF
are included, indicating that those financially
strong lead companies within an insurance group tend to purchase less private passenger
auto liability reinsurance. Other variables such astax rate,long tail lines,product Herfind-
ahl,
ROA, and
year dummies
are not statistically significant at conventional significance
levels.
Table 4B contains the regression results for homeowners reinsurance. The coefficient
on
loss reserve error
is positive and statistically significant at the 5 percent level when
SUSTAIN
and
RHERF
are included, and statistically significant at the 10 percent level
11This hypothesis states that those small insurance companies that geographically diversified or that offer insurance across many lines put a greater value on the set of services provided by reinsurance companies and thus tend to purchase more reinsurance.
when
SUSTAIN
and
RHERF
are excluded. Again, this positive correlation between our
risk measure and the net amount of reinsurance purchased suggests that adverse selection
exists in homeowners reinsurance markets.
The coefficient onexperience ratingis always positive and significant at the 5 percent
level, suggesting that a favorable loss experience in previous year helps a primary insurer to
secure better homeowners reinsurance coverage.
12As in the line of private passenger auto
liability reinsurance, the coefficient onretention limitis always negative and significant at
the 1 percent level, suggesting that an insurer retaining a higher proportion of direct busi-
ness premiums purchases a smaller amount of reinsurance. The two proxies for long-term
contracting relationship,SUSTAINandRHERF, are not statistically significant. Therefore,
we conclude that adverse selection is present in the homeowners reinsurance market, and
reinsurers useexperience ratingandretention limitto mitigate the adverse selection prob-
lem.
Table 4C reports the regression results for product liability reinsurance. In both econo-
metric specifications, the risk measure,
loss reserve error, is not statistically significant at
conventional significance levels, indicating that the adverse selection problem does not ex-
ist in product liability reinsurance market.
retention limitis again negative and significant
at the 1 percent level in both econometric specifications. However, the coefficients onexpe-
rience ratingare not significant, though positive as hypothesized. Also, bothSUSTAINand
RHERF
are not statistically significant at the conventional 5 percent level. Therefore, we
claim that we find no evidence for the existence of adverse selection in the product liability
reinsurance market.
In sum, we find evidence for the existence of adverse selection in private passenger
auto liability and homeowners reinsurance markets, but not in product liability reinsurance
market. In addition,retention limit
is widely used in every reinsurance market to mitigate
the adverse selection problem, while
experience rating
is found to be important in con-
12Experience ratingis defined as the ratio of lagged total premiums earned to lagged total losses incurred. Thus, a larger number ofExperience ratingimplies a better loss experience in the previous year.