To illustrate, Browne and Frees (2007) examined c=4 health insurance choices, consisting of:
- y=1 – an individual covered by group insurance,
- y=2 – an individual covered by private, non-group insurance,
- y=3 – an individual covered by government, but not private insurance or
- y=4) – an individual not covered by health insurance.
Their data on health insurance coverage came from the March supplement of the Current Population Survey (CPS), conducted by the Bureau of Labor Statistics. Browne and Frees (2007) analyzed approximately 10,800 single person households per year, covering 1988-1995, yielding n=86,475 observations. They examined whether underwriting restrictions, laws passed to prohibit insurers from discrimination, facilitate or discourage consumption of health insurance. They focused on disability laws that prohibited insurers from using physical impairment (disability) as an underwriting criterion.
Table 11.4 suggests that disability laws have little effect on the average health insurance purchasing behavior. To illustrate, for individuals surveyed with disability laws in effect, 57.6% purchased group health compared to 59.3% of those where restrictions were not in effect. Similarly, 19.9% were uninsured when disability restrictions were in effect compared to 20.1% when they were not. In terms of odds, when disability restrictions were in effect, the odds of purchasing group health insurance compared to becoming uninsured are 57.6/19.9 = 2.895. When disability restrictions were not in effect, the odds are 2.946. The odds ratio, 2.895/2.946 = 0.983, indicates that there is little change in the odds when comparing whether or not disability restrictions were in effect.
begin{matrix}
begin{array}{c}
text{Table 11.4. Percentages of Health Coverage by Law Variable}
end{array}\scriptsize
begin{array}{crrrrrrr}
hline
text{} & & & & & & text{Odds -} & text{} \
text{Disability} & & & & & & text{comparing} & text{} \
text{Law} & & & Non & & & text{Group to} & text{Odds} \
text{in Effect} & text{Number} & text{Uninsured} & text{Group} & text{Government} & text{Group} & text{Uninsured} & text{Ratio} \hline
text{No} & 82,246 & 20 & 12.2 & 8.4 & 59.3 & 2.946 & \
text{Yes} & 4,229 & 20 & 10.1 & 12.5 & 57.6 & 2.895 & 0.983 \hline
text{Total} & 86,475 & 20.1 & 12.1 & 8.6 & 59.2 & & \
hline
end{array}
end{matrix}
In contrast, Table 11.5 suggests disability laws may have important effects on the average health insurance purchasing behavior of selected subgroups of the sample. Table 11.5 shows the percent uninsured and odds of purchasing group insurance (compared to being uninsured) for selected subgroups. To illustrate, for disabled individuals, the odds of purchasing group insurance are 1.329 times higher when disability restrictions are in effect. Table 11.4 suggests that disability restrictions have no effect; this may be true when looking at the entire sample. However, by examining subgroups, Table 11.5 shows that we may see important effects associated with legal underwriting restrictions that are not evident when looking at averages over the whole sample.
begin{matrix}
begin{array}{c}
text{Table 11.5. Odds of Health Coverage by Law and Physical Impairment}
end{array}\scriptsize
begin{array}{ccrrrrrrr}hline
& & & & & text{ Odds -} & \
text{} & text{Disability} & & & & text{comparing} & \
text{Selected} & text{Law} & & text{Percent} & text{Percent} & text{ Group to} & Odds \hline
text{Subgroups} & text{in Effect} & text{Number} & text{Group} & text{Uninsured} & text{Uninsured} & Ratio \
text{Nondisabled} & text{No} & 72,150 & 64.2 & 20.5 & 3.134 & \
text{Nondisabled} & text{Yes} & 3,649 & 63.4 & 21.2 & 2.985 & 0.952 \
text{Disabled} & text{No} & 10,096 & 24.5 & 17.6 & 1.391 & \
text{Disabled} & text{Yes} & 580 & 21 & 11.4 & 1.848 & 1.329 \hline
end{array}
end{matrix}
There are many ways of picking subgroups of interest. With a large dataset of n=86,475 observations, one could probably pick subgroups to confirm almost any hypothesis. Further, there is a concern that the CPS data may not provide a representative sample of state populations. Thus, it is customary to use regression techniques to “control” for explanatory variables, such as physical impairment.
Table 11.6 reports the main results from a multinomial logit model with many control variables included. A dummy variable for each of 50 states was included (the District of Columbia is a “state” in this data set, so we need 51-1=50 dummy variables). These variables were suggested in the literature and are further described in Browne and Frees (2007). They include an individual’s gender, marital status, race, education, whether or not self-employed and whether an individual worked full-time, part-time or not at all.
In Table 11.6, “Law” refers to the binary variable that is 1 if a legal restriction was in effect and “Disabled” is a binary variable that is 1 if an individual is physically impaired. Thus, the interaction “Law*Disabled” reports the effect of a legal restriction on a physically impaired individual. The interpretation is similar to Table 11.5. Specifically, we interpret the coefficient 1.419 to mean that disabled individuals are 41.9% more likely to purchase group health insurance compared to purchasing no insurance, when the disability underwriting restriction is in effect. Similarly, non-disabled individuals are 21.2% (=1/0.825 – 1) less likely to purchase group health insurance compared to purchasing no insurance, when the disability underwriting restriction is in effect. This result suggests that the non-disabled are more likely to be uninsured as a result of prohibitions on the use of disability status as an underwriting criteria. Overall, the results are statistically significant, confirming that this legal restriction does have an impact on the consumption of health insurance.
begin{matrix}
begin{array}{c}
text{Table 11.6. Odds Ratios from Multinomial Logit Regression Model}
end{array}\scriptsize
begin{array}{crrrrrrrr}
hline
text{Variable} & text{Group} & text{Non-Group} & text{Government} & text{Group} & text{Group} & text{Non-Group} \
& text{versus} & text{versus} & text{versus} & text{versus} & text{versus} & text{versus} \
&text{Uninsured} &text{Uninsured} &text{Uninsured} &text{Non-Group} &text{Government} & text{Government} \
hline
text{Law*Nondisabled} & 0.825 & 1.053 & 1.010 & 0.784 & 0.818 & 1.043 \
p-text{value} & 0.001 & 0.452 & 0.900 & 0.001 & 0.023 & 0.677 \
text{Law*Disabled} & 1.419 & 0.953 & 1.664 & 1.490 & 0.854 & 0.573 \
p-text{value} & 0.062 & 0.789 & 0.001 & 0.079 & 0.441 & 0.001 \
hline
end{array}\scriptsize
begin{array}{c}
text{Notes: The regression includes 150 }(= 50 times 3) text{state-specific effects, several continuous variables (age,}\
text{education and income, as well as higher order terms) and categorical variables (such as race and year).}
end{array}
end{matrix}