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Purpose of experience rating
 relate an insured's premium to their loss experience (individual risk equity)
 actual losses are compared with expected loses to produce Mod
 Manual Premium * Mod = Modified Premium
 Modified Premium * Schedule Mod = Standard Premium

Characteristics of Worker's Compensation
 company management has a great deal of control over company safety practices
 experience rating help distinguish between risks for differences such as compensation, management, employee morale, relation to the community, etc.
 those aspects would typically not be rating variables but can be captured with experience rating

Credibility of WC Experience rating
 credibility of experience depends on size of insured (usually measured by payroll)
 credibility of individual risk experience also increases when there is greater between variance (variance of hypothetical means)
 when a classification plan is very strong, the experience rating will be less important

Goals of experience rating
 predictive accuracy: degree of charge based on past experience should be the degree in which it is predictive of future losses, ensuring equity (premium relates to the insured’s loss potential) and rates that aren't unfairly discriminatory
 safety incentive: financial incentive for loss control (safety programs, return to work programs, …)
 enhance market competition: more companies willing to sell insurance if profit is guaranteed on all risk after the application of the experience mod

Maximizing predictive accuracy
 minimize the error between the predicted losses and actual residual losses
 expected square error = best measure → leads to solvable equations and penalizes large errors
 to make the math simpler, experience mod is a linear function of losses

NoSplit Plan
 define A = actual historical losses, E = expected losses, Z = credibility = E / (E + K_{E})
 Mod = [ZA + (1  Z)E] / E = 1 + Z[(A  E)/E] = (A + K_{E}) / (E + K_{E})
 the term ZA + (1  Z)E is known as the Modified Expected Losses
 Surety Association Plans: Mod = (1  Z) + Z/[E/P] * A/P = premium mod + adj loss multiplier * adj LR

Credibility under NoSplit Plans
 K_{E} can be a constant, a function of E, or manually chosen to achieve the desired responsiveness
 3 conditions: 0 ≤ Z ≤ 1, ↑ as size ↑ (d/dE(Z) ≥ 0), % charge ↓ as size ↑ (d/dE(Z/E) < 0)
 note that condition 3 does not mean Z must increase at a decreasing rate
 all conditions are automatically satisfied if K_{E} is a constant

Split Plans
 actual and expected losses are split into primary and excess components; primary reflects frequency and receives the most weight, while excess reflects severity
 Mod = (1/E) * [Z_{p}A_{p} + (1  Z_{p})E_{p} + Z_{e}A_{e} + (1  Z_{e})E_{e}]
 Mod * E = Modified Expected Losses
 using Z_{p/e} = E / (E + K_{p/e}), Mod = 1 + (A_{p}  E_{p}) / (E + K_{p}) + (A_{e}  E_{e}) / (E + K_{e})

Perryman's First Formula
 Mod = [A_{p} + WA_{e} + (1  W)E_{e} + B] / [E + B]
 B = ballast = (1  W)K
 B limits the impact of any individual large claim on the Mod

Single and MultiSplit Plans
 under a single split plan, there is 1 split point below which losses are considered primary
 under a multisplit plan, a decreasing portion of loss increment is considered primary
 A_{p} = I + (1  d)I + (1  d)^{2}I + … + (1  d)^{N} (A  N * I), where I = $ increment, d = rate of discount
 maximum value of A_{p} = I/d, and A_{e} = A(capped)  A_{p}

WC Experience Rating  Pre1940
 used nosplit plan with Mod = (A + K_{E}) / (E + K_{E})
 Venter argues that it's problematic for highly skewed, heavytailed distributions such as WC claims, so by splitting the losses each component becomes less heavytailed and more predictable
 the flaw in the argument is that the distribution of excess losses is less heavy tailed but not necessarily more predictable (e.g. it's much easier to price a groundup policy than an excess policy)

WC Experience Rating  1940 to 1961
 new NCCI splitplan has Mod = [A_{p} + WA_{e} + (1  W) E_{e} + B] / [E + B]
 split used to be with I = 500, d = 2/3 (primary portion = [2/3]x), with max(A_{p}) = I / d
 selecting B and W: prevent large swings in the mod for small insureds; provide 100% credibility for large insureds; as a result B and K decreased as risk size increased

WC Experience Rating  1961 to 1991
 simplified the formula with A_{p} = A if A ≤ 2,000, 10000A / (A + 8,000) if A > 2,000
 as a result the maximum value of A_{p} is 10,000

WC Experience Rating  Post 1991
 NCCI simplified the split to a singlesplit plan at 5,000
 values of B and K began to increase nonlinearly with premiums; in theory constant B and K means large risks are more stable, but empirical data showed a slower decrease in variance

Resulting impact on credibility
 small risks received larger primary credibility
 large risks received smaller primary credibility, with maximum now 91%
 small risks received larger excess credibility, with all risks having nonzero credibility
 large risks received much smaller excess credibility, with maximum now 57%
 quintile test: small and large performed better, medium performed equally well

Calculating a Medical Claim
 reduce the primary medicalonly portion by 70%
 e.g. for a $7,000 loss, A_{p} = 5,000 * 0.3 = 1,500 and A_{e} = 2,000 * 0.3 = 600

Dorweiler's 2 conditions for correct credibility
 necessary: credit and debit risks show equal standard loss ratios in prospective period
 sufficient: no way to select a subgroup of credit/debit risks on any experience basis that would produce a different loss ratio in the prospective period (more a goal than a requirement)

Testing the predictive accuracy of the plan
 conduct tests separately for each size group
 if premium is not available for manual loss ratio, use actual losses / expected losses
 if premium is not available for standard loss ratio, use actual losses / modified expected losses

Dorweiler's Test
 sort risk in increasing order, group in subdivisions, calculate manual and standard loss ratio for each
 maximal loss ratio dispersion → plan correctly identifies risk differences
 more importantly, equal standard loss ratios → plan corrects for risk differences (+ want no trend)

Quintile's Test
 essentially a quantified version of Dorweiler’s test
 sort risks by their mods in increasing order, group in 5 quintiles, calculate manual/standard LR
 test statistic = variance in standard loss ratios / variance in manual loss ratios
 lower test statistics indicates better plan performance

Efficiency test
 calculate manual and standard loss ratios for all risks
 test statistic = variance of standard loss ratios / variance of manual loss ratios
 lower test statistic indicates better plan performance

Data used for Experience Rating
 data comes from the Workers Compensation Statistical Plan (the Unit Plan)
 insurers report losses by injury type, payroll, and class codes for every risk up to 5th report
 NCCI uses this information in both experience rating and class ratemaking
 experience mod uses 3 prior years of actual loss experience

NCCI modifications to the data
 add contract medical losses to MedicalOnly losses
 separate Permanent Partial claims into Major PP and Minor PP based on $ threshold (critical value)
 NCCI does not develop or trend actual losses, or change them to the latest benefit levels, instead they detrend and dedevelop expected losses to make them comparable to the historical actual

NCCI loss groups
 serious: includes Fatal, Permanent Total, and Major Permanent Partial indemnity
 nonserious: includes Temporary Total and Minor Permanent Partial indemnity
 medical: includes medical amounts from all claims

Experience Rating Plan Parameters
 state reference point (SRP): index of benefits used to calculate G and SAL (by state)
 weighting value (W): used to limit weight of actual XS losses (varies by state and insurer size)
 ballast (B): used to provide stability by limiting impact of single loss (varies by state and size)
 expected loss rates (ELRs): expected loss / $100 payroll (varies by state and class)
 discount ratios (Dratios): expected primary % of expected loss (varies by state and class)

Calculating State Reference Point
 first calculate trended State Average Cost per Claim (SACC)
 trended SACC = (∑ Incurred Losses_{y} / ∑ Claim Count_{y}) * e^{rt} over the 3 years
 Incurred for Employer’s Liability capped at $100K
 SRP = 250 * trended SACC, rounded to the nearest $5K
 G & SRP not allowed to decrease from last year unless there is a significant reduction in benefits
 any change over 20% to the SRP will be further investigated

Uses of SRP
 state accident limit (SAL): per claim limit for losses in experience mod calculation = 10% * SRP
 scale factor G: used in calculating values for B and W; G = SRP / 250,000, rounded to nearest .05
 B = max[7500, E* (0.1E + 2500G) / (E + 700G)]
 C = K_{E} = max[150000, E * (0.75E + 200000G) / (E + 5100G)]
 W = (E + B) / (E + C) rounded to the nearest 0.01
 W also can not increase when E decreases, and 0 < W < 1, B > 0 so no insured has 100% credibility

Calculating class ELR  data prep
 should be proportional to the loss cost underlying manual rate
 multiply class rate by PLR to remove profit, taxes, expenses
 adjust for time frame differences (benefit level, loss development, trend)
 adjust for the fact that claims covered by the policy have no limits, unlike claims used in rating

Steps to calculating ELR
 calculate a factor to reduce manual rates to pure premium at 2nd report
 calculate class Hazard Group ELR and ELR; correcting for loss limitation includes:
 calculate ratio of SAL to average loss (entry ratio by Hazard Group and Injury Type)
 weight 3 excess ratios for each HG by injury type to get single excess ratio by HG
 calculate HG adjustment factor = 1  HG excess ratio
 multiply ELR level factor by HG adjustment factor to get HG ELR factors
 apply for HG ELR to rates and check ELRs for reasonableness

Calculating Dratios
 use the 3 most recent single history year of statistical plan available
 because of policy years extending over 2 calendar years, plus reporting, verification and processing, a rate filing effective Jan 1, X would generally contain Dratios based on X3 policy year
 use Dratio by class = weighted average of Dratio Factors (partial Dratios) by type of injury
 Application of NCCI Experience Rating Plan
 apply mod factor to the manual premium → differentiates loss potential within not between classes
 having a debit ≠ stigma, it may not reflect poor safety habits; any accident is a matter of chance

Offbalance factor
 offbalance: ratio of standard premium to manual premium = weighted average of mods
 when ELRs and Dratios are adequate, the offbalance will be near 1 or a slight credit since risks large enough to be experience rated tend to have better loss experience
 offbalance is not used to try and change overall premium adequacy
 in states where rate adequacy deteriorates, problem is that rate indication is based on standard loss ratios, but changes are applied to manual rates

Offbalance vs rate inadequacy
 expected loss will be too low
 mods will increase, increasing offbalance
 this will increase the overall premium
 rate indications are based on premium including mods, so it'll partially lower indication as a result of the higher offbalance
 note that premium level contemplates no changes in offbalance factor in the prospective period

Offbalance factor vs rate increase
 assuming the rate increase is to correct inadequate rates
 as the rates come up, the offbalance will decrease
 this will lower the premium which increases the rate indication
 rates will still be slightly inadequate

Using the NCCI Manual
 Rule 1.C.8 lists some reasons why a risk high have a mod of 1.0
 Rule 2.A.2 shows premium eligibility for exp rating by state (only need to satisfy 1)
 Rule 2.A.5 specifies interstate experience rating requirements
 Rule 2.B.2 talks about rating effective dates
 Rule 2.C describes all items in the experience mod formula
 Rule 2.C.13 talks about rules to apply when different loss limits apply
 Rule 2.D.2 gives the maximum debit mod (cap varying by risk)
 Rule 3 explains how a change in ownership or combination of entities impact experience used
 Rule 4.B.1/2/3 describe the correction to payroll, losses or classifications resulting in revised mods

