This is Weird: Revisited

The other day, Hank posted on the difficulty he was having reconciling why a given person's group health insurance rate changed depending on whether they were the employee or the employee's spouse. That post, and some back-and-forth in the comments, sparked my curiosity. 

Hank said

"up until about age 40, the male spouse rate is actually lower than the male employee rate. And at age 35,female employees are actually more expensive than their(presumably) stay-at-home counterparts."

So I graphed the data based on the original post.

1.  Male employee vs male spouse
2.  Female employee vs female spouse

Graph #1 addresses the first reference above (click to enlarge):

The premium rates differ in specific amounts, but the differences are not material below age 50.  After age 50 the spouse rate rises above the employee rate.  This insurance company apparently has data that support the higher cost for older male spouses vs older male employees.  I’m guessing that older male spouses tend to have more health conditions that prevent them from working.  That would show up in the experience of the pool, and its effect would likely grow as the individuals age.

Graph #2 addresses the second reference:

The main difference in this graph vs. Graph #1, is seen in ages under 35.  My guess is that the female spouse rate is higher than the female employee rate through these younger ages because of marginally higher maternity liability.  That difference then closes rapidly.   After age 54 the female spouse again appears to be more costly.  Again, I don't dispute that the insurer’s cost data support the differences.  After taking maternity into account, the result observed in Graph #2 is consistent with the result observed in Graph #1.   It may well have the same origin i.e., that older female spouses tend to have more health conditions than older female employees, that prevent them from working.

Another possibility is that this insurance company’s pool includes marginally more male spouses who are employed (under age 50, anyway), and therefore represent a lesser liability to the female employee's plan because of COB (Coordination of Benefits).

Whatever, and aside from the actual dollars-and-cents differences in rates, the shapes of the lines on the graphs seem to me consistent.

I think the actuarial correspondent is correct about the beneficial effect of selection for employees vs spouses.  It’s visible in the premium rate relativities in all the other premium rate graphs I created.   I'm surprised he did not mention (or maybe he did?) the cost of maternity for younger females, regardless whether working or not.  That’s visible in the graphs, too.

In each of the questions you’ve raised, I’m not claiming I have a full explanation.  While I think my guesses may be a good part of the explanation, we’re still left with questions.

"We started with one question, and ended up with many questions."  One of my profs in college (philosophy, not mathematics) often made that remark at the end of his lectures - and then always concluded by saying "What a marvelous bargain!"    I still think that insight was worth the whole semester's tuition.  At least for his class.  (In 1965, the undergraduate tuition at my school for a 3-hour class was only about $150).

Which means - - this exercise was a bargain!