Workers Compensation Classification

Study guides: Exam 8, Exam GI-302

Workers Compensation Classification assigns each employer to one or more payroll classifications describing its business, and charges a manual rate per \$100 of payroll for each class. In the United States the classes are maintained by rating bureaus such as NCCI. With hundreds of thinly populated levels, the class is the textbook high-dimensional rating variable.

\text{Manual Premium} = \sum_{c} \frac{\text{Payroll}_c}{100} \times \text{Rate}_c

\widehat{\text{LC}}_c = Z_c\,\text{LC}_c + (1 - Z_c)\,\text{LC}_{\text{group}}

• \text{LC}_c is class c's indicated loss cost per \$100 of payroll, \text{LC}_{\text{group}} that of the broader group it belongs to, and Z_c the class's credibility.
• How employers are classified. By the employer's business — the governing classification — rather than each worker's occupation. A short list of standard exceptions, such as clerical office employees and outside salespersons, is rated separately. Payroll is the exposure base: it tracks the exposure, moves with wage inflation, and is verified by premium audit. Classifying by business also stops payroll from being shifted into cheaper classes.
• Why it is high-dimensional. Robertson (2009) put the count at about 800 classes in NCCI states, many of them small. Their loss costs are dominated by rare, severe injuries (fatal, permanent total, major permanent partial), so raw class estimates are volatile. There are four ways to deal with that:
  • Credibility-weight each class toward its group, as in the formula above.
  • Use multi-dimensional credibility across injury types, estimating a class's rare serious-injury frequencies from its correlated, more common types (Couret and Venter).
  • Treat class as a random effect in a GLMM, whose shrinkage is the Bühlmann–Straub blend (Random Effects).
  • Cluster classes with similar loss characteristics into a few groups, as NCCI's hazard groups do.
• Hazard groups. NCCI moved to seven hazard groups in 2007, assigning classes by weighted k-means on credibility-weighted vectors of excess ratios at five loss limits, from \$100K to \$5M (Robertson). Classes in a hazard group share the same excess loss factors, which NCCI uses in class ratemaking and in pricing loss limits on retrospectively rated policies. The class sets the manual rate, and experience rating captures the differences between employers within a class.
• In Canada, workers compensation is run by provincial boards that assess employers by industry rate group. See Workers Compensation Insurance.

Manual Premium Across Two Classes A framing contractor has \$2{,}000{,}000 of carpentry payroll at a (hypothetical) rate of \$9.50 per \$100 and \$300{,}000 of clerical office payroll at \$0.25. Compute the manual premium, and explain why the carpentry crew's supervisor cannot be reported as clerical.

Answer

\begin{align*}
\text{Carpentry} &= \frac{2{,}000{,}000}{100} \times 9.50 \\
&= \$190{,}000 \\[4pt]
\text{Clerical} &= \frac{300{,}000}{100} \times 0.25 \\
&= \$750 \\[4pt]
\text{Manual premium} &= \$190{,}750
\end{align*}

The clerical exception covers only employees confined to clerical office work. A supervisor who is exposed to the job site belongs to the governing class. Otherwise any employer could cut its premium by 97\% per dollar of payroll (0.25 against 9.50) by relabelling staff. The audit exists to enforce this.

Estimating a Thin Class's Loss Cost A small class shows an indicated loss cost of \$3.20 per \$100 of payroll, based on \$400{,}000 of expected losses. Its industry group's loss cost is \$2.40. Credibility is Z = E/(E + K) with K = \$600{,}000. Estimate the class loss cost.

Answer

\begin{align*}
Z &= \frac{400{,}000}{400{,}000 + 600{,}000} \\
&= 0.40 \\[4pt]
\widehat{\text{LC}} &= 0.40(3.20) + 0.60(2.40) \\
&= \$2.72
\end{align*}

The class keeps 40\% of its apparent excess over the group. A large class with the same indication would keep most of it, and a GLMM with class as a random effect would shrink it by the same logic. If this class's excess ratios also differed from its group's, the hazard group assignment would be revisited too, because excess loss potential and loss cost per payroll are separate questions.