Pricing @ HealthCare.gov

There is an open pile of data points and superfine print on the HealthCare.gov and H&HS’ Assistant Secretary for Planning and Evaluation websites.  Many plans are available in each of the 36 states, which are currently operating as the main part of the federal marketplace.  Using an advanced statistical approach with data applications in a number of diverse industries, this note examines the key factors that are most associated with the premium pricing differentials within state plan levels.  Again we are not analyzing the actual price per plan, but the ranking in state premium rate differentials.  We find it peculiar to see that the important determinants to this pricing differential (beyond that for the catastrophic plan) are less likely to be related to actual actuarial risk for the youth consumer base.  While there is a tax subsidy available for many Americans, this analysis appears to be a headwind in enrolling a key group most likely to be helpful in the U.S. health insurance plan marketplace being successful.

For each state, we looked at the average premium rate of a 27 year-old individual, for each of the following plan levels: bronze, silver, gold, and catastrophic.  A linear principal component decomposition was performed to understand the most important drivers of these standardized premium rate differentials.  It should be noted that even as a former government executive quant used to analyzing data from numerous types of source entities globally, these websites above were considerably difficult to function through and extract data for offline analysis.  Leaving these problems aside, once one eventually retrieves the data, interesting statistical analysis can be performed.

Of the 36 states, 11 were eliminated from the analysis.  Of these 11 states, 2 had incomplete catastrophic plan data, 1 had incomplete enrollment data, and the other 8 showed numerous outliers in their pricing relationship relative to the eigenvector data.  If the data was not of high quality or noted as missing from the website tables above, then it was removed as not being a quality data point.  The eigenvector data shows nonsingular combinations of variables that can most efficiently factor our covariance matrix of pricing data, among most of the states we are analyzing.

Say that we are looking at the correlation matrix (A), where the correlation (ρ) is equal to the covariance among states, divided by the standard deviation of each state’s plan pricing rank.  Our solution would be equal to:

Aυ = λυ

Where υ are the eigenvector factors for our 25 (36-11) state health insurance premium data.  The λ are the eigenvalues that serve as scalar operators when the υ are taken one at a time.  Else a diagonal matrix of such values (i.e., a matrix with a 1 along the diagonal from the upper-left to lower-right and 0 elsewhere), if the characteristic vectors are assembled into a nonsingular square matrix.  Note that the υ data are already unit scaled so that the squares of each term in the vector sums to one.   This unit scaling jointly allows for easier interpretation of the eigenvalues on a per state basis, and collectively.  See the two possible algebraic frameworks, below.

[square matrix]|vector| = scalar|vector|
or
[square matrix][vector square] = [diagonal matrix][vector square]

For our work here there were two eigenvectors associated the state premium pricing data: υ₁ (explains about 25% of the variance) and υ₂ (explains about 50% of the variance).  There were seven state factors that were examined that could be good matches to understand their characteristic vectors: the portion of youth eligibility, the unemployment rate, the cost of living index, the requests for insurance rate increases relative to the population, the political party most represented, the gross product per capita, and the obesity rate.

For this group of 27 year-olds nationwide, representing the typical population subset termed the “Young Invincibles”, the portion of youth eligibility factor fit υ₂.  And a measure of liberal party representation was a factor that fit υ_1.  While other factors could be tested, we are here simply showing the mathematical results from the factors that were looked at to explain the characteristics most unique to explain the national plan rate differentials.  These two factors could explain nearly 75% (55%+25%) of the insurance plan premium differentials, while the remaining 25% of the variance was absorbed in the imperfect realities in empirical modeling.  Some of this is simply the factor of low cost of living regions are picking up slightly greater premium rate differentials as well.

The removal of eight states did not have any significant pattern in terms of their representation with these factors.  It is shown on the illustration below that the general bias between the two linearly independent (ρ=0) and distinct factors, higher enrollment was associated with generally high youth eligibility (~½ explanation), while lower enrollment was generally associated with more liberally represented states (~¼ explanation).

This bias if also, of course, only general as the eigenvectors we noted are minimally ranked independent vectors.  We can see how these factors are technically still of zero correlation as states with more enrollment progress (those on the left of the illustration above) are the larger sized data on the upper left of the representation below.  The elliptical pattern represents the joint internal scaling of the eigenvectors, as they orbit around the origin, even as we noted unity from each one's sum of the squares.

In summary, this note shows that the types of factors that mathematically match the differentials in state premium rates, among plan levels, have less to do with matching up against the unique underlying risks for the age group studied.  One should question why obesity, for example, ultimately didn't show to play a greater role given its concordance with serious health issues and higher service burdens.  With two eigenvectors selected between a group of seven possible factors, and 25 states, we have a strong basis for the conclusions here that we noted statistically covers ¾ of the explanation.  It is also clear that we could be more transparent in the factors associated with the tax subsidy, else be more creative in the pricing and design offerings in the more premium insurance product plans.  This would allow us to better understand and attract a broader set of the national constituents who have barely enrolled thusfar in the federal marketplace system.