Actuarial Notes

Risk Classification Restrictions

Study guide: Exam 6C

Risk Classification Restrictions are regulatory prohibitions on rating variables an insurer may otherwise find predictive. In Canadian auto insurance the restricted list typically includes age, sex, marital status (in some provinces), credit score, and limits on territory — restrictions imposed on social grounds even where the variable is statistically valid.

  • The regulator's test is not "does it predict?" but "is it acceptable to price on this?" — a distinction candidates must be able to hold. A prohibited variable can be highly correlated with loss and still be prohibited.
  • Standard criteria for whether a classification variable is acceptable: actuarial (statistically significant, homogeneous, credible), operational (objective, cheap to verify, not manipulable), social (privacy, causality, affordability, controllability) and legal (permitted in the jurisdiction). Restrictions are the social and legal criteria overriding the actuarial one.
  • Consequences of a restriction are predictable and appear on every exam: the removed variable's signal migrates into correlated proxy variables; cross-subsidy flows from the previously low-rated group to the previously high-rated one; adverse selection increases as the accurately-priced group's better risks leave; and residual market volumes grow if the restriction makes some segments unwritable at approved rates.
  • Proxy effects cut both ways. Banning a variable does not remove its influence if a permitted variable stands in for it, which is why territory restrictions and postal-code debates recur — see Bias in Actuarial Practice.
  • Restrictions differ by province, so a national insurer maintains different classification plans by jurisdiction and cannot simply port a model across the country.

What Happens When a Variable Is Banned A province bans the use of age in private passenger auto rating, effective immediately, with no change to the overall rate level. Currently, drivers under 25 have a pure premium of \$1{,}200 and drivers 25 and over \$600; the under-25 group is 12\% of exposures.

Describe the effects.

Answer The class-free average pure premium:

\begin{align*}
\bar{P} &= 0.12(\$1{,}200) + 0.88(\$600) \\
&= \$144 + \$528 \\
&= \$672
\end{align*}

Effects, in order of appearance:

  1. Cross-subsidy. Under-25 drivers pay \$672 instead of \$1{,}200 — a 44\% decrease; over-25 drivers pay \$672 instead of \$600 — a 12\% increase. Roughly \$63 million per million exposures moves from young drivers to everyone else.
  2. Proxy substitution. Insurers reweight toward variables correlated with age — years licensed, vehicle type, marital status where permitted — recovering part of the signal. The ban is therefore partly undone in practice, which is why regulators often ban a cluster of variables rather than one.
  3. Adverse Selection. Over-25 drivers are now overcharged; the best of them are the most likely to shop, and any insurer that finds a legal proxy can skim them. The insurer that moves last is left with the young drivers.
  4. Availability. Insurers restrict underwriting of segments they can no longer price, so young-driver risks migrate to the Facility Association — where they pay more than \$1{,}200, defeating the affordability purpose of the ban.

The honest summary is that a classification ban redistributes cost and degrades market efficiency; whether that trade is worth making is a policy judgement, not an actuarial one. The actuary's role is to quantify it, clearly, before it is made.