Given the method used to obtain the sample, probabilities of selection are not available. However, it is possible to derive survey weights by appropriately representing each filing’s relative size from the 2011 NAIC (number of member-months by carrier), 2010 MEPS-IC (estimated enrollment distribution by state by product for the small group market), and, in some cases, carrier filings (number of reported members). We combined the individual and conversion markets for weight calculation and refer to them in this discussion as the “individual market”. The final weights represent the contribution to the estimates for each filing.
A multi-step process was used to calculate weights. The first six steps implemented at the “state-marketyear” level – (that is, each observation with a specific combination of those three variables gets its own weight). The last three steps are calculations at the level of “market-year”. The list below, as well as Tables 4 and 5, summarize each step used for weighting.
- Initial carrier weights were generated (to reflect the carrier’s relative contribution to the estimates);
- Applied within-carrier filing adjustments to the initial carrier weight (to adjust for multiple filings by a carrier);
- Applied state-level product adjustments to the initial carrier weights (small group market only) (to adjust for product enrollment distributions);
- Applied within-carrier enrollment adjustments to the initial carrier weights (to adjust for the relative size of each filing);
- Applied weight control adjustments to the initial carrier weights (to control the weights to sum to one within a state-year);
- Calculated final state-level weights (for use in deriving state-level estimates);
- Applied national-level adjustments (to adjust for the relative size of each state);
- Applied national-level single-filer adjustments (to control the influence of single-filers within a state);
- Calculated final national-level weights (for use in deriving state-level estimates).
Initial Carrier Weights: The source for the initial carrier weights is the 2011 NAIC supplemental data file. We used information on member-months from NAIC to assign initial carrier weights to reflect the relative contribution to the estimates by carrier within strata defined by market (individual, small group), year, and state. Initial carrier weights are defined as:
MTYSi = number of member-months reported from the 2011 NAIC for sample carrier i reporting in year Y from market type T in state S
Within-Carrier Filing Adjustments: As each carrier may have multiple filings within a market type/year/state, the initial carrier weight must be adjusted to reflect the number of filings within each carrier so as not to over-represent carriers with multiple filings.29 The within-carrier filing adjustment is defined as:
nTYSi = number of filings for carrier i from market type T for year Y in state S
State-Level Product Adjustments (small group market only): For the small group market, an adjustment to the survey weights is made so that distributions of the resulting survey weights reflect estimated enrollment distributions from MEPS-IC by state and product. (This information is not available for the individual market.) The sum of the within-carrier filing adjusted weights by product type is adjusted to reflect the MEPS-IC distributions. The product adjustment is defined as:
where the sum in the first term of the denominator is across all filings for product type P for which small group filings G30 were obtained for year Y from state S, and the sum in the second term is across all filings for which small group filings were obtained for year Y from state S. This latter term is used to scale the first term to sum to 1.0.
estimated enrollment distribution of the small group market for product type P (relative to product types for which filings were obtained in year Y) within state S from the 2010 MEPS-IC data; f refers to a filing obtained from sample carrier i reporting in year Y from market type G (see footnote 28, infra) in state S
For example, from Table 4 ID=234, the numerator=0.258, the first part of the denominator is the sum of filing adjusted weights for P=HMO (0.803314), and the second part of the denominator is the sum of all filing adjusted weights (1.0). The formula then is 0.258 / (0.803314 / 1) = 0.320880, which is Column I in Table 4.
Not all small group filings had their product type identified. As a result, no adjustment is applied to those specific filings.
Within-Carrier Enrollment Adjustments: The survey weights are further adjusted to reflect the relative size (if known) of each filing for a carrier. Each filing contained information on either the number of covered members, the number of contracts, both, or neither. Using filings with both the number of covered members and the number of contracts, an estimate of the number of covered members was imputed for those filings with only the number of contracts. The within-carrier product adjustment is defined as:
ETYSPi = number of members reported on filing f from individual carrier i for product P from market type T for year Y in state S
nTYSPi = number of filings for carrier i for product P from market type T for year Y in state S
State-Level Weight Adjustments
As the sum of the preliminary survey weights are not constrained to equal 1.0, the weights must by adjusted so as to control the sum of the survey weights to be equal to 1.0.
For the individual market, the state-level weight adjustment is defined as:
For the small group market, the state-level weight adjustment is defined as:
Final State-Level Weights
The final state-level survey weight for the individual market can thus be defined as the product of the initial carrier weight and the adjustments made for the individual market:
SWIYSPif = IWIYSi * CFAIYSi * CEAIYSPif * SWAIYSPif
The final state-level survey weight for the small group market can thus be defined as the product of the initial carrier weight and the adjustments made for the individual market:
SWGYSPif = IWGYSi * CFAGYSP * SPAGYSP * CEAGYSPif * SWAGYSPif
These final state-level survey weights sum to one with a state/market/year.
We applied a national adjustment to the final state-level survey weights to reflect the relative sizes across states within a market type (Table 5). The national adjustment is defined as:
S’ = set of sample states for which more than one filing was obtained for year Y
MTS' = number of member-months reported from the 2011 NAIC for all carriers from market type T in state S’
National-Level Single-Filer Adjustments
Given the uncertainty associated with estimates from states with only one filer a final adjustment is applied so as to have those single filers included in the estimates but representing only themselves. This is accomplished through separate adjustments being applied to the single filers and all other filers. Note that this adjustment factor applies to only four filings in the individual market in 2011 and two in the individual market in 2012.
The national-level single filer adjustment is defined as:
S” = set of sample states for which only one filing was obtained for year Y
MTSY = number of member-months reported from the 2011 NAIC for all carriers from market type T in state S (the set of sample states for which filings were obtained for year Y)
MTS'Yi = number of member-months reported from the 2011 NAIC for sample carrier i reporting in year Y from market type T in state S”
Final National-Level Weights
The final national-level survey weight is then defined as:
NWTYSPif = SWTYSPif * NATSY * NSATSYi
Table 4: State-Level Weight Calculation for 2012 Connecticut Small Group Market
Table 5: National-Level Weight Calculation for 2012 Connecticut Small Group Market
29 While we aggregate conversion filings with those from the individual market for the purposes of analysis, we do not expect these conversion filings to measurably impact the findings as they are few in number (approximately 11% of the individual market sample by count) and they tend to have low enrollments.
30 In this case, G is a constant – the market type T is either small group (G) or individual (I), but the product adjustment is only possible for the small group (G) market type.