Implications of family risk pooling for individual health insurance markets

Abstract

While family purchase of health insurance may benefit insurance markets by pooling individual risk into family groups, the correlation across illness types in families could exacerbate adverse selection. We analyze the impact of family pooling on risk for health insurers to inform policy about family-level insurance plans. Using data on 8,927,918 enrollees in fee-for-service commercial health plans in the 2013 Truven MarketScan database, we compare the distribution of annual individual health spending across four pooling scenarios: (1) “Individual” where there is no pooling into families; (2) “real families” where costs are pooled within families; (3) “random groups” where costs are pooled within randomly generated small groups that mimic families in group size; and (4) “the Sims” where costs are pooled within random small groups which match families in demographics and size. These four simulations allow us to identify the separate contributions of group size, group composition, and family affinity in family risk pooling. Variation in individual spending under family pooling is very similar to that within “simulated families” and to that within random groups, and substantially lower than when there is no family pooling and individuals choose independently (standard deviation $12,526 vs. $11,919, $12,521 and $17,890 respectively). Within-family correlations in health status and utilization do not “undo” the gains from family pooling of risks. Family pooling can mitigate selection and improve the functioning of health insurance markets.

Appendix: Implications of family risk pooling for individual health insurance markets

This appendix provides additional detail describing the methods and results of sensitivity analyses conducted in the paper “Implications of family risk pooling for individual health insurance markets.”

1.1 Construction of measure of individual annual health spending

To construct our primary measure of annual health spending that is purged of the impact of health plan benefit design we first estimate a linear regression:

$$X_{n, actual} = \alpha_{0} + \delta_{p} + \varepsilon_{n}$$

where $X_{n, actual}$ represents an individual’s actual annual spending, and δ _p is a series of indicator variables for each health plan.

Using estimated coefficients from this regression we calculate predicted annual spending for each individual, $\hat{X}_{n}$, that accounts for the portion of spending attributed to health plan effects.

We then subtract this component of spending from the individual’s actual annual spending:

$$X_{n, actual} - \hat{X}_{n} = X_{n}$$

to arrive at X _n , purged of plan effects and our measure of individual spending, which we call “individual total spending.”

1.2 Analyses of within-family correlation in health spending

1.2.1 Analyses of variation in spending by types of pooling

We first calculate the SD of individual total spending, X _n , which represents the setting where individuals choose plans independently and there is no pooling of individual-level spending across individuals. Next, we calculate the SD of individual-level spending for the setting where individuals pool as real families to purchase insurance. To capture the effect of pooling we assign each individual within a given family the averaged spending among all members of that family. Thus, for all n = 1, 2…N individuals in a real family f:

$$X_{n,f} = \frac{{\mathop \sum \nolimits_{n = 1}^{N} X_{n} }}{N}$$

We assign all individuals n = 1, 2, …, N within the real family $X_{n,f }$, called “Family-averaged individual spending” and then estimate the SD in the distribution of $X_{n,f }$. Note that summing $X_{n,f }$ across individuals in the family results in the same total health spending for the family, but reflects the fact that the heterogeneous risks across individuals within the family are pooled through their family-level insurance contract.

1.3 Meet the Sims

We also study the distribution of spending under two alternative scenarios: (1) where individuals pool in “random groups,” and (2) where individuals pool in simulated families we refer to as the “Sims.” Random groups consist of randomly associated individuals and, to identify the contribution of small group pooling on spending, are the same size as real families. To capture the effects of demographic composition within a family (e.g., age and gender) but not the endogenous sorting from assortative mating and childbirth that generates real families, the Sims have both the same number of individuals and the same age and gender distributions as the real families.

We describe construction of these last two groups more formally. For every real family in the data we construct a corresponding group that matches the real family in number of individuals and is generated through random draw from among all individuals in the study sample with replacement. We call these groups “random groups.” For each individual n = 1, 2, …, N in a random group rg, we define “random group-averaged individual spending” as

$$X_{n,rg} = \frac{{\mathop \sum \nolimits_{n = 1}^{N} X_{n} }}{N}$$

and assign each individual n this value, X _n,rg , to replace their actual (e.g., non-averaged) individual total spending. We then estimate the SD in the distribution of X _n,rg . This process is repeated 5000 times through simulation.

For every real family in our sample we also construct a Sim family that matches the real family not only in the number of people in the family but also in the age and gender distribution of family members. We used stratified random sampling from our study sample with replacement. For example, to construct a Sim family to match a real family that includes a female age 32, male age 30, male age 6 and female age 4, we randomly selected a 32-year old female from among all 32-year old females in our sample, a 30-year old male from among all 30-year old males in our sample, etc. For each individual n = 1, 2, …, N in a simulated family Sim, we define “simulated family-averaged individual spending” as:

$$X_{n,Sim} = \frac{{\mathop \sum \nolimits_{n = 1}^{N} X_{n} }}{N}$$

and assign each individual in the Sim family $X_{n,Sim}$ to replace their own actual (e.g., non-averaged) individual total spending. We estimate the SD in the distribution of X _n,Sim and repeat this process 5000 times through simulation.

Comparing the SD in individual spending, family-averaged individual spending, random group-averaged individual spending, and simulated family-averaged individual spending measures how real family pooling affects the distribution of health spending relative to no pooling and to purely random associations.

1.4 Analysis of variation in spending across clinical categories

Health care spending can be decomposed into types of care (inpatient, outpatient or pharmaceuticals 0 and into Major Diagnostic Categories (MDC)—clinical categories that divide all possible principal diagnoses into one of 25 mutually exclusive clinical areas. We combine these further to construct fifteen categories (Table 3). We assess how spending on each type of medical care, and across clinical categories, contributes to the variance in total spending for individuals versus real families.

Table 3 Crosswalk MDC categories to clinical categories analyzed here

More formally, for each type of medical care, let X _n  = X _ip  + X _op  + X _rx represent individual total spending which is the sum of inpatient (ip), outpatient (op), and prescription drug (rx) spending. The variance of X _n can be decomposed into the sum of variances and covariances. We estimate the following covariance matrix:

$$\left[ {\begin{array}{*{20}c} {Var\left( {X_{ip} } \right)} & {Cov\left( {X_{ip} ,X_{op} } \right)} & {Cov\left( {X_{ip} ,X_{rx} } \right)} \\ {Cov\left( {X_{ip} ,X_{op} } \right)} & {Var\left( {X_{op} } \right)} & {Cov\left( {X_{op} ,X_{rx} } \right)} \\ {Cov\left( {X_{ip} ,X_{op} } \right)} & {Cov\left( {X_{op} ,X_{rx} } \right)} & {Var\left( {X_{rx} } \right)} \\ \end{array} } \right]$$

We then calculate the contribution of each component of the variance to the total variance. For Var _ip this is:

$$\left( {\theta_{ip} } \right) = \frac{{Var \left( {X_{ip} } \right)}}{{Var(X_{n)} }}$$

The difference in variance in total spending under individual purchase of health insurance and under family pooling is

$$\Delta Var\left( {X_{n} } \right) = Var_{ind} \left( {X_{n} } \right) - Var_{fam} \left( {X_{n} } \right).$$

We identify the portion of $\Delta Var\left( {X_{n} } \right)$ that is due to the difference in the variance of each component under the different pooling regimes. For example, for inpatient spending we calculate the following:

$$\phi_{ip} = \frac{{Var_{ind} \left( {X_{ip} } \right) - Var_{fam} \left( {X_{ip} } \right)}}{{\Delta Var\left( {X_{n} } \right)}}$$

Similarly, to determine the portion of the difference due to the change in the covariance of inpatient and outpatient spending we would calculate the following:

$$\phi_{ip,op} = \frac{{Cov_{ind} \left( {X_{ip} ,X_{op} } \right) - Cov_{fam} \left( {X_{ip} ,X_{op} } \right)}}{{\Delta Var\left( {X_{n} } \right)}}$$

We then compare θ to ϕ for each type of medical spending (inpatient, outpatient, prescription drug) to assess whether the family pooling effect is disproportionately due to reduced variance in any particular type of spending.

We repeat the methods used for type of spending to assess whether the family pooling effect is disproportionately due reduced variance in any of our fifteen clinical category of spending.

1.5 Impact of family pooling: results from sensitivity analyses

In our main results presented in Fig. 2 in the paper, we find that family pooling reduces the variation of individual health spending for a population. In sensitivity analyses, we assess whether the results vary across family composition by repeating the analysis above only including two-adult families, and then only including two-adult, two-child families.

Figure 3 presents results for two-adult families in the top panel, and two-adult, two-child families on the bottom. While the magnitudes of the SD in health spending for two-adult families are much higher than those observed for the full-sample, a reflection of the fact that adults have significantly higher variance in health care spending than children, the result across pooling scenarios is the same. Spousal pooling results in a SD in real family-averaged individual spending that is $7328 smaller (equal to 0.29 SDs) than when all individuals purchase a health plan on their own, and is very similar to the SD in random group-averaged individual spending and Sim family-averaged individual spending.

Fig. 3

Source: Truven MarketScan 2013. Authors’ analysis of enrollees in two-adult insurance contracts (N = 1,142,718), and enrollees in two-adult, two-child contracts (N = 2,217,163)

SD of within group-averaged individual health spending by family type. Notes: The bar for individual contracts displays the SD in individual health spending treating study sample as enrolling in a separate health plan (e.g., no pooling). The bars for Real families, The Sims, and Random groups display the SD in the distribution of within group-averaged individual health spending. Difference between random groups and real families is statistically significant p < 0.01. Differences between the Sims and real families is statistically significant p < 0.01.

Among two-adult families with two children, the findings are again similar as those in the main analysis. The SD of Sim family-averaged individual spending is $7144 and of random group-averaged individual spending is $7183, which are slightly lower ($61 and $22 respectively) than that of real family-averaged individual spending, $7205. Although these differences are statistically significant (again, a reflection of our large sample), random group and Sim family pooling represents only a very small incremental reduction in risk from a scenario of no pooling (equal to 0.01 SDs) than that achieved through real family pooling.

1.5.1 Data supporting Figs. 2 and 3 in the paper

Figure 2. SD of within group-averaged individual health spending

	SD	Bootstrapped SE
Individual contracts	18,826	24
True families	13,166	9
The Sims	13,194	0.3
Random family-sized groups	12,564	0.9

Figure 3. SD of within group-averaged individual health spending by family type

	SD	Bootstrapped SE
Enrollees in two-adult insurance contracts
Individual contracts	25,568	45
True families	18,240	21
The Sims	18,099	0.6
Random family-sized groups	18,084	0.5
Enrollees in two-adult, two-child insurance contracts
Individual contracts	14,248	35
True families	7205	10
The Sims	7144	0.3
Random family-sized groups	7183	0.3