Sources of heterogeneity in
health effects of Medicaid
J.G. Strikwerda
Master thesis Economics (EBM877A20)
Supervised by Dr D. Howdon, PhD
Faculty of Economics and Business, University of Groningen
Abstract Existing literature estimates the effect insurance has on health outcomes conditional on certain personal characteristics such as age, income or gender. This paper examines the possibility that these characteristics affect this treatment effect itself. Using data from the Oregon Health Experiment, a randomized expansion of Medicaid, three conclusions can be made: Insurance is associated with better physical and mental health, the treatment effect varies between subgroups and the health benefits differ per health domain for a given subgroup.
JEL classification H51, I13, I18
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I. INTRODUCTION
The number of uninsured individuals in the United States has dropped since the implementation of the Affordable Care Act (otherwise known as “Obamacare”) as well as due to expansions in Medicaid eligibility. (Barnett & Berchick, 2017). The implementation, however, has not changed the ongoing discussion about the importance and societal value of insurance in the US.
On an individual level, the value of insurance is expected to be reflected in people’s willingness to pay. A recent working paper by Finkelstein et al. (2015) examines how low-income individuals value Medicaid. They find that, given the health benefits provided under insurance, individuals value the insurance less than its costs. This implies that if people were to be given the money for insurance lump sum, they would not be willing to forgo consumption to buy the same insurance package. Taking this result without any other social welfare benefits, the Medicaid program could be seen as inefficient and potentially be reducing welfare. From a societal perspective, however, the justification for publicly-provided insurance is often not based on individual willingness to pay. A more relevant objective and motivation for a program like Medicaid might be to maximize health rather than maximizing some explicit conception of social welfare based on individual utility.
Ostensibly, the value of health insurance could stem from several theoretical mechanisms: a pure welfare effect from a reduction of uncertainty, an income effect from receiving insurance payouts, and a health effect.
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market. Health insurance allows these risks to be pooled and reduce overall uncertainty, creating more stable conditions for a functioning health care market. As such, the availability of insurance is welfare-improving by reducing uncertainty for risk-averse individuals.
Nyman (1999) describes the income effect of health insurance. For an individual, medical procedures can be prohibitively expensive as their costs can easily exceed a family’s net worth. Because insurance is essentially an income transfer from the healthy to the ill (either via premiums or taxes), it allows an individuals to “purchase” the procedures they couldn’t afford without insurance, effectively increasing their available resources at such a time that they suffer from ill-health.
A third way in which health insurance might create value is by improving health itself. Since health insurance enables the purchase of health goods, individuals would be expected to be in better health when having insurance. A side effect of this would be that insurance could cause people to seek treatment earlier and thus be in better health sooner, affecting their productivity. The health effects of insurance, however, are less well established in literature. Levy & Meltzer (2004) give an overview of existing literature covering the effect of insurance on health and supplement this overview in Levy & Meltzer (2008). While there does seem to be convincing evidence that insurance improves health in certain vulnerable subpopulations, such as children or individuals with AIDS, they remark that existing literature has yet to show a true causal relation between insurance and health. They conclude that the general effects of medical insurance on health can only be observed with future large scale social experiments.
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these characteristics affect the treatment effect of insurance itself, i.e. that the assumption that the treatment effect is constant across such subgroups is incorrect. It seems plausible that characteristics which affect health also affect the health impact of insurance.
This intuition is supported by the health capital model developed by Grossman (1972), which models a health production function (HPF) that increases with investment but at a decreasing rate. Therefore, individuals in poorer health are modeled to have higher marginal gains from investments in health. Subgroups with characteristics that would predict lower health would then implicitly be predicted to have higher marginal gains from investments in health. The potential health effects of insurance would then also be bigger in these groups. This, however, is under the assumption that all individuals have the same HPF and that differences in health are not caused by vertical shifts in the HPF, which could imply homogeneous marginal gains.
Courtemanche & Zapata (2014) suggest that a heterogeneous treatment effect may exist. Using a 2006 health care reform in the state of Massachusetts, which tried to achieve near-universal coverage, they compare overall health before and after the reform. They show that the reform led to better self-assessed overall health, and that improvements in several determinants of health can be observed. They find that the effect is significantly stronger for low-income individuals, nonwhites, near-elderly adults, and women, implying the relation between insurance and health to be heterogeneous. A limitation of this finding unacknowledged by the authors, however, is the fact that the self-selection into insurance before the reform is nonrandom. It is possible that self-selection played a larger role in the subgroups measured to benefit more from the reform, which would imply that Courtemanche & Zapata (2014) may have measured a general health effect of insurance and no direct differential effects.
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be sensitive to the composition of the pool of people it covers. Therefore, such heterogeneity in treatment effect would have to be taken into account when evaluating an insurance program. Moreover, the heterogeneity could be relevant and important for policymakers that model new policy based on programs from different states or countries, as the original population might differ from their own. More controversially, heterogenic health effects of insurance could even shape policy such as selection procedures. When the health effect of insurance is remarkably stronger in a certain subgroup, that group could be favored in the selection into state programs to increase the overall effectiveness of such programs.
This paper seeks to add to the existing literature surrounding the relation between insurance and health in two ways. First, it further explores the existence of a heterogeneous treatment effect of insurance on health. Second, it aims to give a better insight in the magnitude of the treatment effect by using more comprehensive measures of health. This is done using data from the Oregon Health Experiment (OHE), which was an expansion of the Medicaid program distributed according to a lottery draw. The next section will introduce the OHE and cover some of its findings. Section II will cover the data and methodology used, in section III the estimation results are presented. The results are discussed in section IV.
Medicaid and the Oregon Health Experiment
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implementations of the program and has made that the program varies by state. This leeway allowed the state of Oregon to perform a large-scale insurance experiment when the Medicaid program was expanded in 2008. The Medicaid expansion in Oregon was allocated using a lottery, drawing names from a waiting list of low-income, uninsured adults, which provided a randomized setting to estimate the effects of Medicaid on a range of outcomes.
Individuals that were selected in the lottery were enrolled into the Oregon Health Program (OHP; Medicaid) as long as they submitted the appropriate paperwork in time and met the eligibility requirements. Because of people failing to submit the paperwork or not being eligible (mostly due to too high income), several lottery drawings were held until all 10,000 available OHP spots were filled. Of the 89,824 individuals that were placed on the waiting list, 35,169 individuals were selected in the lottery.
Finkelstein et al. (2012) give a more detailed view of the OHE and provide an overview of the first year’s results. They show that the treatment group (those selected in the lottery) had higher healthcare utilization, lower out-of-pocket medical expenditures and had better self-reported physical and mental health than the control group. Baicker et al (2013), who follow up with participants two years after the experiment, find no significant improvements in physical health outcomes, but do find lower rates of depression, reduction in financial strain and increased use of health care services. Subsequent literature, notably Taubman et al (2014), Finkelstein et al (2016) and Baicker (2017), has focused on the effects of Medicaid on use of emergency department services and medication use. After the lottery, the treatment group is observed to use both more intensively relative to the control group.
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a unique insight into the treatment effects of health expenditure coverage on health. Keeping such limitations in mind, this paper tries to investigate the existence of a heterogeneous treatment effect.
II. METHODS
DataBecause the OHE was funded by the state, its data is publicly available. The public dataset consists of three mailing surveys – one at the start of the program and two follow up surveys after six and twelve months – as well as data from emergency departments and data from the state programs included in the OHP during that timeframe. Additionally, Baicker et al. (2013) conducted a series of in-person interviews among selected OHE participants. This interview data will primarily form the basis for this paper.
The interviews were conducted from August 2009 to October 2011: on average 25 months after the lottery. They approached 20,745 individuals, of which 10,405 were selected in the lottery and 10,340 for the control group. Response rates were higher in the treatment group, being 63.4% compared to the 56.5% of the control group. In total they collected data on 12,229 individuals. Due to logistical constraints, all individuals were selected in the Portland metropolitan area.
8 Table 1. Descriptive statistics
Used sample Original set Selected Control Insured (.500) .518 (.486) .382 (.492) .413 PCS-8 score (10.4) 46.0 (10.5) 45.3 (10.4) 45.7 MCS-8 score (11.2) 45.4 (11.3) 44.2 (11.3) 44.8 female (.490) .601 (.489) .606 (.491) .595 Mean age (11.7) 42.4 (11.7) 42.2 (11.7) 40.8 Income 1 78.1 (71.5) (73.7) 76.8 76.9 + (69.1) Nonwhite (.440) .262 (.427) .240 (.382) .178 Living alone (.374) .168 (.386) .182 .168 (.374) + Finished high school (.460) .401 (.488) .390 (.474) .341 Smokes (.489) .394 (.488) .393 (4.95) .430
BMI (7.69) 29.7 (7.98) 30.1 (7.62) 29.9
Observations 2 2,689 2,395 23,386
The table reports variable averages with the corresponding standard deviation in brackets.
1 Income as a percentage of the federal poverty level.
2 The number of observations varies based by source and response rates. The
numbers indicated with a “+” are taken from the 12-month survey.
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attributed to the fact that the in-person interviews were conducted in the city of Portland, where the general population is more ethnically diverse compared to the state on the whole (US Census bureau, 2010a,b). The different ethnical composition of the sample compared to the whole state doesn’t affect the results of this paper directly, as it aims to investigate whether there is heterogeneity in the treatment effect. However, it leaves heterogeneity between several non-white population groups unobserved. Additionally, the sample differences do limit the extent to which the specific coefficients can be generalized to the OHE as a whole, let alone the United States.
The treatment effect of insurance on health will be measured in two health domains: physical and mental health. Both measures originate from the 8-item Short Form Health Survey (SF-8). The physical health score (PCS-8) and mental health score (MCS-8) both range from 0 to 100, where a higher score indicates better health. The scores are standardized for the US population to have an average of 50 and a standard deviation of 10. The PCS-8 and MCS-8 scores have been derived by Baicker et al (2013) based on questions in the in-person interview.
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Two dummy variables are used to capture the treatment effect of health insurance, being variables indicating having health insurance (either privately or through the OHP) and being selected in the OHE lottery.
The variables indicating personal characteristics are gender, age, income race, living alone, having finished high school, smoking and Body Mass Index (BMI). The selection of variables is based on literature around the OHE, such as Finkelstein (2012) and Baicker (2013), but has likewise been well established in literature around the RAND experiment (for example Brook, 1984).
In the dataset, income is denoted as a percentage of the federal poverty level, which differs depending on household composition1 and act as equivalence
scales. This income variable will be used to split the sample in three income groups (high, middle, low). Besides being a more conventional income indicator, creating three income groups alleviates issues that come with the precision of self-reported income and make the findings less sensitive to reporting errors. Because the OHE and Medicaid program only concerns low-income individuals, the division is limited to three groups. The lowest of the three income groups has an income of 7% of the federal poverty line on average, with nearly three quarters of these individuals reported having no income. Because Medicaid is aimed to cover the working-age population, the oldest person in the sample is 68 years old.
“Naïve” model
To investigate the possible effect demographic factors have on the treatment effect of insurance, the experimental design of the OHE is initially ignored and the focus is on the effects of being insured at all. This will result in a biased model with a naïve estimated treatment effect, primarily due to the
1 The relevant poverty levels can be found in the 2008 HHS poverty guidelines (Department of Health and
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selection bias with people deciding to purchase private insurance, but allows for distinction of the treatment effect for each variable in the model. Additionally, comparing the “naïve” estimates to one using the randomization can offer some insight into the nature of self-selection. This first model is estimated using Ordinary Least Squares (OLS):
(1) Hij = β0 + β1×INSURANCEi + β2Xi + β3 Xi×INSURANCEi + εij
where i denotes the individual and j the health domain, which is either physical or mental health. INSURANCE is a dummy variable that indicates whether an individual is insured, either under the Medicaid program or under private insurance. Xi is a vector of personal characteristics listed in table 1. These
characteristics are also included as interaction between it and insurance. The interaction terms show the naïve health effect difference for insured individuals and are the main variables of interest. Since most variables are dummy indicators, their coefficients can be interpreted straightforwardly as the difference in the health scores. The coefficient for age will indicate the average marginal effect on health, that is the expected change in health when getting one year older.
IV Model
To include the effect of the lottery, an instrumental variable model is used similar to the models used in Finkelstein (2012) and Baicker et al (2013). The model is estimated by two stage least squares (2SLS) with the following first stage:
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where having insurance is estimated based on whether an individual was selected in the OHE (LOTTERY) and Xi, a vector of characteristics which
includes all the same variables as in equation (1). This estimated insurance indicator is then used in the second stage regression:
(3) Hij = β0 + β1×INSURANCE + β2Xi + µi
where all symbols have the same meaning as indicated before. Since INSURANCE is estimated based on the lottery, which is a randomized variable, this model won’t have the same bias as the naïve model. To answer the question of whether insurance has different effects for different demographic groups, the regression is run for several subgroups, being gender, income, race and age. In each the respective variables are omitted from that regression when it’s a dummy variable. The descriptive statistics by subgroup can be found in appendix A.
III. RESULTS
“Naïve” modelTable 2 shows the results of the naïve model described in equation (1), both with and without the interaction terms.
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(which is not surprising, since these are the same variables that are assumed to influence health itself). This idea is supported by the fact that nearly all interaction coefficients have a negative sign: for each characteristic, the individuals with insurance have lower expected health. The interacted variables, however, are not jointly significant (with a joint p-value of 0.217). Nonetheless, the notion that personal characteristics play a role in the process of self-selection would mean that they should be taken into account when examining natural experiments - such as the insurance reform in Massachusetts covered by Courtemanche & Zapata (2014) - where the researchers don’t have control over who is affected by increased insurance coverage.
The model for mental health differs from the physical health in several key parts, primarily the effect of insurance itself, which is negative but not statistically significant in both iteration of the model. By contrast, the interacted effect of insurance does show statistically significant effects for age, BMI and having finished high school in the mental health domain. A joint significance test of the interaction terms indicates statistical significance of the interaction terms (p-value of 0.016).
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Table 2. “Naïve” model regression results
Physical health
(PCS-8 score) Mental Health (MCS-8 score)
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It is interesting to note the variable of living alone. The interacted effect between it and health insurance has a relatively large coefficient in both domains. Individuals living alone might be more likely to purchase insurance, since they have less access to informal care in the form of a spouse or children. As such, they would rely more heavily on costly formal care. This rather straightforward variable might then indicate differences in self-selection and willingness to pay for health insurance between individuals.
Pooled IV model
The results from a pooled instrumented regression can be found in table 3. This version of the IV model can be compared with the naïve estimation without the interaction terms shown in columns 1 and 3 of table 2. The results show that, using the lottery as instrument, the coefficient for insurance becomes positive and has stronger relation for both physical and mental health compared to the naïve estimation. The contrast with the naïve estimates confirm that self-selection into insurance indeed affects the relationship between insurance and health.
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Table 3. Pooled IV model regression results
Physical health (PCS-8 score) Mental Health (MCS-8 score) insurance 4.060** (2.039) 7.784*** (2.363) Gender (female = 1 ) -1.489*** (0.294) -3.214*** (0.340) age -0.212*** (0.0126) -0.0469*** (0.0146) Income Poorest third -1.978*** (0.356) -1.673*** (0.413) Richest third 1.029*** (0.354) 1.031** (0.410) Nonwhite 1.264*** (0.345) 1.672*** (0.399) Living alone (0.396) -0.440 -2.495*** (0.459) Finished High School -0.0000500 (0.326) (0.378) -0.592 smoking -2.153*** (0.304) -2.737*** (0.352) BMI -0.300*** (0.0193) -0.0850*** (0.0223) Constant 63.60*** (1.045) 49.33*** (1.212)
Observations 5062 5062
R2 0.085 .
The coefficients of IV regressions, with standard errors reported in parentheses
The stars (*, **, ***) denote a statistical significant coefficient (at the 10, 5 and 1 percent level respectively)
To get an intuition about the magnitude of the coefficients, it is worth noting that the PCS-8 and MCS-8 scores are both standardized to have a standard deviation of ten for the US population. The coefficients then translate to 41% and 78% of this standard deviation.
17 Subgroup regressions
To investigate how the treatment effect of insurance differs by certain characteristics, the IV regression is run for several subgroups. The results for the physical and mental domain are shown in table 4 and 5 respectively (The first stage result is presented in Appendix C). Similar to the pooled estimation, insurance is positively related to both physical and mental health in each subgroup regression.
Comparing the coefficients for insurance between the different subgroups shows quite some variance in estimators, ranging from 2 to 11 in the physical domain. The coefficient for insurance is statistically significant at the ten percent level for only two subgroups, the white individuals and the middle income group. Given that the pooled estimation finds a statistically significant treatment effect, the coefficients for insurance are likely to be underpowered in the subgroup regressions due to having fewer observations in each regression. Nonetheless, the results are suggestive of a heterogeneous treatment effect. A larger, more powered sample would likely find statistically significant relations for more subgroups.
Table 4. IV Model results, Physical health
Dependent variable: PCS-8 score
Gender age Race Income
Male Female ≤ 35 36 – 50 > 50 White Other Poorest third Middle third Richest third
insurance (2.423) 2.665 (3.304)5.426 (5.841) 5.893 (3.182) 2.015 (2.751) 4.431 (2.128)4.122* (6.201)3.510 (1.665)2.082 (6.072)11.24* (28.98)2.140 Gender (female = 1 ) - - -1.265** (0.621) -1.447*** (0.475) -1.716*** (0.581) -1.207*** (0.349) -2.346*** (0.549) -1.308** (0.512) -2.392*** (0.666) (0.990)-1.198 age -0.194*** (0.0209) -0.219*** (0.0174) -0.183*** (0.0559) -0.319*** (0.0571) (0.0748) 0.0190 -0.207*** (0.0149) -0.230*** (0.0277) -0.241*** (0.0225) -0.199*** (0.0251) -0.193*** (0.0629) Income Poorest third -2.289*** (0.551) -1.743*** (0.472) -1.046* (0.590) -2.116*** (0.570) -2.355*** (0.722) -1.855*** (0.426) -2.107*** (0.635) - - Richest third (0.583) 0.558 1.366*** (0.455) (0.726) 0.617 1.339** (0.582) (0.693) 1.042 1.131*** (0.413) (0.674)0.555 - - -Nonwhite 1.851*** (0.510) (0.482)0.919* 1.323** (0.671) 2.052*** (0.573) -0.170 (0.721) (0.563)1.024* 1.789*** (0.683) (2.465)1.042 Living alone 0.0260 (0.597) -0.800 (0.553) (0.892) -0.167 (0.659) -0.773 (0.634) -0.331 (0.452)0.142 -2.912*** (0.834) (0.703)-0.350 -1.672* (0.982) (0.807)-0.141 Finished High School (0.494) 0.350 (0.448)-0.253 0.240 (0.691) -0.390 (0.580) (0.580) 0.456 (0.365)0.119 -0.299 (0.779) (0.572)0.354 (0.642)-0.826 (1.852)0.486 smoking -2.623*** (0.460) -1.845*** (0.408) -1.065** (0.536) -2.103*** (0.503) -3.132*** (0.600) -2.109*** (0.368) -2.005** (0.781) -2.808*** (0.523) -2.065*** (0.591) (2.311)-1.535 BMI -0.307*** (0.0347) -0.298*** (0.0240) -0.252*** (0.0345) -0.285*** (0.0306) -0.395*** (0.0400) -0.312*** (0.0219) -0.250*** (0.0407) -0.329*** (0.0350) -0.265*** (0.0384) -0.324*** (0.0340) Constant 63.80*** (1.425) 61.66*** (1.714) 59.77*** (2.522) 68.65*** (2.577) 53.92*** (4.564) 63.29*** (1.242) 65.38*** (1.810) 64.80*** (1.464) 59.82*** (2.332) 64.84*** (16.77) Observations 2009 3053 1678 1926 1458 3790 1272 1705 1672 1685 R2 0.096 0.056 . 0.082 0.033 0.079 0.109 0.110 - 0.132
Table 5. IV Model results, Mental health
Dependent variable: MCS-8 Score
Gender age Race Income
Male Female ≤ 35 36 – 50 > 50 White Other Poorest third Middle third Richest third
insurance 7.852*** (2.786) 7.839** (3.812) (6.995) 7.066 10.50*** (3.834) (2.999) 5.369* 7.474*** (2.430) (7.684) 9.207 4.457** (1.903) (6.854) 12.87* (73.09) 43.54 Gender (female = 1 ) - - -2.833*** (0.744) -3.080*** (0.573) -3.828*** (0.633) -3.055*** (0.398) -3.830*** (0.681) -3.033*** (0.585) -4.278*** (0.752) (2.496) -1.442 Age (0.024) -0.039 -0.0513** (0.020) -0.127* (0.067) -0.157** (0.069) (0.0815) 0.179** -0.0281* (0.017) -0.109*** (0.034) -0.095*** (0.0258) (0.028) -0.033 (0.159) 0.065 Income Poorest third -2.370*** (0.634) -1.203** (0.545) (0.707) -0.591 -2.067*** (0.686) -1.820** (0.788) -1.556*** (0.487) -1.774** (0.787) - - - Richest third (0.671) 0.374 1.434*** (0.525) (0.870) 0.944 (0.701) 1.066 (0.756) 1.000 0.903* (0.472) (0.835) 1.431* - - - Nonwhite 2.074*** (0.586) 1.322** (0.556) 1.789** (0.803) 3.262*** (0.690) (0.786) -0.710 (0.643) 1.200* 1.634** (0.771) (6.217) 5.481 Living alone -2.558*** (0.69) -2.429*** (0.638) (1.069) -0.261 -3.639*** (0.794) -2.552*** (0.691) -2.355*** (0.516) -2.994*** (1.034) -2.012** (0.803) -3.581*** (1.109) (2.036) -1.650 Finished High School -0.975* (0.568) (0.517) -0.381 -0.998 (0.828) (0.699) -1.056 (0.632) 0.471 (0.417) -0.191 -1.594* (0.965) (0.654) 0.452 -1.428** (0.724) (4.672) -2.722 smoking -1.497*** (0.528) -3.658*** (0.471) -2.637*** (0.642) -2.188*** (0.606) -2.810*** (0.654) -2.292*** (0.420) -4.195*** (0.967) -2.815*** (0.598) -3.118*** (0.668) (5.827) 0.623 BMI -0.104*** (0.040) -0.074*** (0.028) -0.082** (0.0413) -0.100*** (0.037) -0.0621 (0.044) -0.084*** (0.025) (0.051) -0.076 -0.139*** (0.040) (0.0433) -0.036 (0.0858) -0.106 Constant 49.44*** (1.638) 45.96*** (1.978) 51.29*** (3.021) 52.97*** (3.105) 37.60*** (4.976) 48.15*** (1.419) 53.71*** (2.243) 52.50*** (1.673) 46.36*** (2.632) (42.30) 27.28 Observations 2009 3053 1678 1926 1458 3790 1272 1705 1672 1685 R2 . . . . . - - 0.010 . .
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The model split by age groups shows differences in the estimated treatment, but none of the three coefficients for insurance reach strong significance (however, the coefficient of the oldest age group has a p-value of 0.11). Taking the coefficients as is, the model shows a non-linear relation in age between insurance and physical health: The youngest and oldest age groups have a larger estimated treatment effect than the group aged 36 to 50. In the context of the Grossman model of health the lower estimated constants in these two groups can help to explain this difference: individuals in lower health states will have higher marginal gains. The non-linearity of health and age, however, is in contrast with the notion that health generally decreases with age. A possible reason why that pattern doesn’t show up in this dataset is that the OHE only concerns low-income individuals. The relation between being in poor health and having no or low income makes it more likely to observe individuals in poor health in the younger age group compared to the general population.
When comparing the results by race groups the difference in the treatment effect of insurance is relatively small, with coefficients of 4.1 for whites and 3.5 for non-whites. The coefficient is statistically significant for white individuals. The difference in estimation, however, further confirms the expectations from the Grossman model. The difference in estimated treatment effect in line with the general health difference between whites and non-white seen in the pooled IV model in table 3, where non-whites have a positive estimated coefficient, indicating better health on average.
Other differences worth noting between the two race groups is the coefficient of gender, which is nearly twice as large among non-white individuals and the coefficient for living alone, which has a significant negative effect among non-whites.
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that there is a substantial relation between having no income and being in poor health, a relation which could run both ways.
Table 5 for shows the results for the estimations in the mental health domain. Just as for the physical health, the estimated treatment effect of insurance is positive for mental health. For each subgroup regression, the magnitude of the insurance coefficient exceed those in the physical health domain. This is in line with the findings of the pooled IV regression. The estimated treatment effect of insurance for mental health differs from the physical health estimation for several subgroups, which means that the treatment effect might not be uniform across health domains.
In the regression for gender, the insurance coefficients are nearly identical, indicating a similar treatment effect despite women reporting lower MCS-8 scores on average. This result contradicts the notion of higher marginal gains for individuals in poorer health and as such doesn’t support the Grossman model as previously assumed. Rather than dismissing the model altogether, a more reasonable explanation is that the Grossman model of health simply doesn’t apply to mental health. For instance, mental health doesn’t deteriorate with age the way physical health tends to.
Whereas the age group 36-50 has the lowest estimated coefficient of insurance in the physical health domain, they report the highest coefficient in the mental health domain. A similar results is observable in the regression split by race, where the coefficient of non-whites is larger only in the mental health domain. Depending on the relative weights of mental and physical health in determining a measure of overall health, the differences in the effect for mental and physical health might balance out, such that insurance in each group can be seen as equally effective.
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IV. Discussion
Several conclusions can be drawn from the results described above. Firstly, the estimated treatment effect of insurance is positive for both physical and mental health. In magnitude, the treatment effect is the largest in the mental health domain. Secondly, the coefficient of insurance varies between different subgroups in both domains of health, giving an indication of a heterogeneous treatment effect. Thirdly, the treatment effect of insurance is not uniform between the physical and mental health domain for several subgroups.
An estimation of the relation between health and insurance using the OHE lottery as instruments finds a positive and significant relation between insurance and both physical and mental health, with coefficients of 4.1 and 7.8 respectively for a pooled regression. The results fit within previous literature using the OHE to study the impact of insurance on health. The findings are in consistent with the findings of Finkelstein et al. (2012), but differ from Baicker et al. (2013). This different outcome, however, is most likely caused by the type of health indicator used: The PCS-8 and MCS-8 scores used in the estimations of this paper might be more sensitive to changes in health than the self-reported measures of health used by the previous studies of the OHE.
The use of these interval variables also allows for a better insight into the magnitude of the treatment effect. Both coefficients can be compared against the designed standard deviation of ten in both scores. The estimated treatment effect translates to 41% of this standard deviation for physical health and as 78% for mental health. The availability of such numbers allows for a more nuanced debate around health insurance, beyond the binary debate where insurance either is or isn’t effective.
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which predict a SF-6D score based on PCS-8 and MCS-8 scores. The SF-6D score is a preference-based “health utility” score, similar to the EQ-5D score. The SF-6D ranges from zero (death) to one (full health) which means that its value can be interpreted as a quality adjusted life year (QALY). The weights calculated by Hanmer (2009) are based SF-6D scores by Brazier & Roberts (2004), who use a standard gamble technique on a sample of 611 members of the UK general population. For the purpose of this calculation the SF-6D valuation is assumed to be consistent between the US and UK population - A US valuation of the SF-6D is available in Craig et al. (2013), but these have not yet been linked to the PCS-8 and MCS-8 health scores. Given the weights calculated by Hanmer (2009), the estimated treatment effects for the PCS-8 and MCS-8 scales can be combined and converted to 0.105 QALY, with a 95% confidence interval ranging from 0.052 to 0.159 (calculations are described in appendix D).
The use of QALYs is well established in health economics, notably in the area of cost-effectiveness analysis of medical procedures, so that the QALY value can put the treatment effect of insurance in a wider perspective. Finkelstein et al. (2015) estimate the average annual medical spending to be $3,600 in the treatment group, $900 higher than the average annual medical spending of the control group. With the calculated health benefit of 0.105 QALY, the Medicaid program in Oregon would be cost effective when health is valued above $34,300 per QALY. When individual and state spending on medical care would be seen as equal, the incremental costs of $900 would imply the program to be cost effective a value of just $8,600 per QALY. This type of calculation for insurance, however, is far from established in literature. Nonetheless, it offers the prospect of potential cost-effectiveness analyses of insurance itself in future research.
24
treatment effect. For example, the treatment effect on physical health is estimated to be larger for women, people under 35 years and white individuals. This means that there is a relatively stronger positive relation between insurance and health in these groups. Given the composition of the dataset, this result fits within the Grossman model of health: on average, physical health is lower in the subgroups that have a higher estimated treatment effect. In the context of the Grossman model this means these subgroups have higher expected marginal gains in health. The potential effect of insurance on health then also is expected to be higher.
The possible heterogeneity of the treatment effect could be of relevance and importance to literature: It makes that the a homogeneous treatment effect can’t be assumed implicitly. Ideally, the heterogeneity would be accounted for in future research, or at least be part of a sensitivity analysis: the heterogeneity suggest that the health outcomes of insurance could be affected by the composition of the dataset studied.
Additionally these findings have some implications the research and literature surrounding the OHE. Foremost, they affect how the outcomes of the OHE can be generalized to the Medicaid program in other states and to the United States as a whole. Especially differences in population composition in terms of age and race might be important, as both vary significantly between US states.
25
In several subgroup regressions, the estimated treatment effect is not uniform between the two health domains. In the estimation by age groups, for example, the group aged 36-50 shows the smallest estimated treatment effect of insurance on physical health, but reports the largest treatment effect in the mental health domain. The notion that insurance is more strongly associated different parts of overall health in different subgroups could be of value in the larger debate on the effect of insurance. For instance, this type variance in the treatment effect can’t directly be measured when using a wider oriented health measure, which gives one score that implicitly includes several measures of health.
Limitations
The different estimated treatment effects in several subgroup regressions shows that the health effect of insurance is positive likely to be heterogeneous. However, the analysis of this paper is limited by several factors and as such can only be taken as an indication that such heterogeneity exist, but can’t be taken as a true indication of such heterogeneity.
26
Another limitation originates from the design of the OHE, which causes that research using its data is limited to using instrumented regressions: The lottery only increased the chance of an individual having insurance by 25% (Finkelstein, 2012). An experiment in which insurance itself is the treatment (such as in the RAND experiment) would have allowed for much stronger conclusions. The estimated treatment effect in this paper can only be argued to be causal on the basis of the randomization in the OHE.
Despite these limitations the findings of this paper are still relevant to the wider discussion about the relation between insurance and health. It tests the assumption of a constant treatment effect across subgroups and gives an indication that this is assumption is likely to be false. Additionally, it gives a more detailed look into the magnitude of the treatment effect.
27
References
Arrow, K. (1963). Uncertainty and the Welfare Economics of Medical Care. The
American Economic Review, 53(5), 941-973.
Baicker, K., Taubman, S. L., Allen, H. L., Bernstein, M., Gruber, J. H., Newhouse, J. P., & Finkelstein, A. N. (2013). The Oregon experiment—effects of Medicaid on clinical outcomes. New England Journal of Medicine, 368(18), 1713-1722.
Baicker, K., Allen, H. L., Wright, B. J., & Finkelstein, A. N. (2017). The Effect Of Medicaid On Medication Use Among Poor Adults: Evidence From Oregon. Health
Affairs, 36(12), 2110-2114.
Barnett, J. C., & Berchick, E. R. (2017). Health Insurance Coverage in the United States: 2016. United States Census Bureau.
Brazier, J. E., & Roberts, J. (2004). The estimation of a preference-based measure of health from the SF-12. Medical care, 42(9), 851-859.
Brook, R. H., Ware, J. E., Rogers, W. H., Keeler, E. B., Davies, A. R., Sherbourne, C. D., & Newhouse, J. P. (1984). The effect of coinsurance on the health of adults.
Courtemanche, C. J., & Zapata, D. (2014). Does universal coverage improve health? The Massachusetts experience. Journal of Policy Analysis and Management, 33(1), 36-69. Craig, B. M., Pickard, A. S., Stolk, E., & Brazier, J. E. (2013). US valuation of the SF-6D. Medical Decision Making, 33(6), 793-803.
Crossley, T. F., & Kennedy, S. (2002). The reliability of self-assessed health status.
Journal of health economics, 21(4), 643-658.
Department of Health and Human Services, Leavitt, M.O. (2008). The 2008 HHS poverty guidelines. Secretary of Health and Human Services. Federal Register Doc. 08-256
Finkelstein, A., Taubman, S., Wright, B., Bernstein, M., Gruber, J., Newhouse, J. P., & Oregon Health Study Group. (2012). The Oregon health insurance experiment: evidence from the first year. The Quarterly journal of economics, 127(3), 1057-1106.
Finkelstein, A., Taubman, S. L., Allen, H. L., Wright, B. J., & Baicker, K. (2016). Effect of Medicaid coverage on ED use—further evidence from Oregon’s experiment. New
28
Finkelstein, A., Hendren, N., & Luttmer, E. F. (2015). The value of medicaid: Interpreting results from the oregon health insurance experiment (No. w21308).
National Bureau of Economic Research.
Grossman, M. (1972). On the concept of health capital and the demand for health.
Journal of Political economy, 80(2), 223-255.
Hanmer, J. (2009). Predicting an SF-6D Preference-Based Score Using MCS and PCS Scores from the SF-12 or SF-36. Value in Health : The Journal of the International Society for Pharmacoeconomics and Outcomes Research, 12(6), 958–966.
Joseph P. Newhouse, & Rand Corporation. Insurance Experiment Group. (1993). Free for all?: lessons from the RAND health insurance experiment. Harvard University Press. Jylhä, M. (2009). What is self-rated health and why does it predict mortality? Towards a unified conceptual model. Social science & medicine, 69(3), 307-316.
Kawachi, I., Daniels, N., & Robinson, D. E. (2005). Health disparities by race and class: why both matter. Health Affairs, 24(2), 343-352.
Levy, H., & Meltzer, D. (2004). What do we really know about whether health insurance affects health. Health policy and the uninsured, 179-204.
Levy, H., & Meltzer, D. (2008). The impact of health insurance on health. Annu. Rev.
Public Health, 29, 399-409.
Nyman, J. A. (1999). The value of health insurance: the access motive. Journal of health
economics, 18(2), 141-152.
Taubman, S. L., Allen, H. L., Wright, B. J., Baicker, K., & Finkelstein, A. N. (2014). Medicaid increases emergency-department use: evidence from Oregon's Health Insurance Experiment. Science, 343(6168), 263-268.
U.S. Census Bureau (2010a). QuickFacts: Portland city, Oregon. Retrieved from [https://www.census.gov/quickfacts/fact/table/portlandcityoregon/POP010210] U.S. Census Bureau (2010b). QuickFacts: Oregon. Retrieved from
[https://www.census.gov/quickfacts/fact/table/OR/POP010210]
Zajacova, A., & Dowd, J. B. (2011). Reliability of self-rated health in US adults. American
Appendix
A. Descriptive Statistics by subgroup
B. First stage results pooled IV estimation
C First stage results per subgroup
App
endi
x A
D escri p tive st atis tic s b y su bg rou pGender Age Race Income
Male Female < 36 36-50 > 50 White Nonwhite Low Mid High
Insured 0.44 (0.50) (0.50) 0.47 (0.50) 0.45 (0.50) 0.45 (0.50) 0.46 (0.50) 0.47 (0.49) 0.42 (0.50) 0.46 (0.50) 0.43 (0.50) 0.47 PCS-8 score 46.48 (10.27) (10.55) 45.16 (8.85) 49.10 (10.60) 45.25 (10.78) 42.31 (10.68) 45.25 (9.68) 46.96 (10.87) 43.94 (10.11) 45.98 (10.12) 47.14 MCS-8 score 46.55 (10.61) (11.52) 43.74 (10.69) 45.97 (11.46) 44.64 (11.48) 43.84 (11.33) 44.36 (10.87) 46.30 (11.78) 43.43 (11.32) 44.97 (10.43) 46.17 female - - 0.65 (0.48) (0.49) 0.58 (0.49) 0.59 (0.49) 0.61 (0.49) 0.59 (0.49) 0.57 (0.48) 0.62 (0.49) 0.61 Mean age 42.99 (11.42) (11.84) 41.88 28.72 (4.01) 43.42 (4.36) 56.53 (3.79) (11.85) 42.77 (11.09) 41.00 (11.52) 42.54 (11.77) 41.95 (11.77) 42.47 Income 1 74.94 (73.39) (71.91) 79.16 (71.18) 79.38 (70.95) 75.06 (75.98) 78.50 (74.70) 81.36 (64.27) 65.93 (9.43) 7.95 (18.73) 65.30 (59.38) 159.93 Nonwhite - - Living alone 0.18 (0.38) (0.38) 0.17 (0.25) 0.07 (0.36) 0.15 (0.47) 0.33 (0.39) 0.19 (0.33) 0.12 (0.37) 0.16 (0.35) 0.14 (0.41) 0.22 Finished high school (0.47) 0.33 (0.50) 0.44 (0.49) 0.40 (0.48) 0.38 (0.49) 0.41 (0.50) 0.43 (0.45) 0.29 (0.46) 0.29 (0.49) 0.40 (0.50) 0.50 Smokes 0.45 (0.50) (0.48) 0.36 (0.47) 0.34 (0.50) 0.43 (0.49) 0.41 (0.50) 0.44 (0.44) 0.27 (0.50) 0.49 (0.49) 0.38 (0.46) 0.31 BMI 28.96 (6.64) (8.46) 30.51 (7.66) 28.72 30.46 (7.94) 30.49 (7.72) (8.08) 29.97 29.66 (7.02) (7.60) 29.75 30.01 (8.11) 29.92 (7.76) Observations 2009 3053 1678 1926 1458 3790 1272 1705 1672 1685
The table reports variable averages with the corresponding standard deviation in brackets.
Appendix B
First stage results pooled IV estimation
Dependent variable: Insurance
Treatment 0.138*** (0.0138) Gender (female = 1 ) 0.0154 (0.0143) age (0.000620) -0.000117 Income Poorest third 0.0400** (0.0170) Richest third (0.0171) 0.0269 Nonwhite -0.0464*** (0.0164) Living alone 0.0426** (0.0191)
Finished High School 0.0622*** (0.0147)
smoking -0.0232 (0.0147)
BMI 0.00309*** (0.000898)
Constant (0.0405) 0.251***
Observations 5062
R2 -
The results of the first stage corresponding to table 3 in the main text. The standard errors are reported in parentheses.
Ap
pen
dix C
F irs t s tag e re su lt s p er su bg ro u pDependent variable: Insurance
Gender age Race Income
Male Female ≤ 35 36 – 50 > 50 White Other Poorest third Middle third Richest third
Treatment 0.181*** (0.0217) 0.113*** (0.0179) 0.0764*** (0.0241) 0.146*** (0.0224) 0.203*** (0.0256) 0.157*** (0.0160) 0.0831*** (0.0276) 0.299*** (0.0229) 0.0920*** (0.0241) (0.0243) 0.0159 Gender (female = 1 ) - - 0.0728*** (0.0256) -0.00339 (0.0229) (0.0264) -0.0328 (0.0166) 0.0182 (0.0287) 0.0196 (0.0234) 0.0147 0.0563** (0.0254) -0.0299 (0.0252) age (0.000985) 0.00271*** -0.00180** (0.000796) -0.000777 (0.00301) 0.00616** (0.00259) -0.000888 (0.00343) -0.000900 (0.000709) 0.00221* (0.00127) (0.00103) 0.00155 0.0000763 (0.00108) -0.00204* (0.00109) Income Poorest third 0.0634** (0.0266) (0.0222) 0.0289 (0.0299) 0.0346 (0.0273) 0.0160 0.0692** (0.0319) 0.0394** (0.0200) (0.0325) 0.0322 - - - Richest third 0.0801*** (0.0274) -0.00346 (0.0219) 0.0784*** (0.0294) 0.00792 (0.0279) 0.00552 (0.0318) (0.0195) 0.0285 (0.0355) 0.0186 - - - Nonwhite -0.0352 (0.0251) -0.0550** (0.0217) 0.0761*** -(0.0278) -0.0645** (0.0260) (0.0326) 0.0391 - - (0.0258) -0.0325 (0.0282) -0.0379 -0.0827*** (0.0311) Living alone (0.0296) 0.0152 0.0625** (0.0248) -0.00378 (0.0482) (0.0314) 0.0301 0.0784*** (0.0276) 0.0426** (0.0213) (0.0429) 0.0374 0.0649** (0.0317) 0.0898** (0.0365) (0.0309) -0.0182 Finished High School 0.0505** (0.0237) 0.0667*** (0.0187) 0.0822*** (0.0257) 0.0956*** (0.0240) -0.00270 (0.0266) 0.0450*** (0.0167) 0.0880*** (0.0309) 0.0723*** (0.0256) 0.0424* (0.0251) 0.0619** (0.0249) smoking (0.0226) -0.0258 (0.0195) -0.0190 (0.0265) -0.0384 (0.0237) -0.0289 0.000675 (0.0275) -0.0545*** (0.0167) 0.0779** (0.0322) (0.0240) 0.00911 -0.00550 (0.0255) -0.0779*** (0.0266) BMI 0.00381** (0.00166) 0.00288*** (0.00107) 0.00314** (0.00158) 0.00245* (0.00142) 0.00558*** (0.00173) 0.00291*** (0.00101) (0.00197) 0.00287 0.00604*** (0.00153) 0.00277* (0.00151) 0.000564 (0.00160) Constant (0.0689) 0.0670 0.365*** (0.0492) 0.262*** (0.0999) 0.00970 (0.124) (0.207) 0.198 0.299*** (0.0460) (0.0821) 0.115 (0.0669) 0.0225 0.243*** (0.0676) 0.567*** (0.0684) Observations 2009 3053 1678 1926 1458 3790 1272 1705 1672 1685 R2 - - - - - - - - - -
Appendix D.
Transformation coefficients to SF-6D/QALY
The transformation from the individual PCS-8 and MCS-8 scores to a combined SF-6D score is done using the relative weights estimated by Hanmer (2009). They estimate the following relation between the PCS-8 and MCS-8 scores and the SF-6d score:
(D1) SF-6D = -0.06449 – 0.00328 (female) + 0.00012 (age) + 0.00781 (PCS-8) + 0.00946 (MCS-8)
Since the pooled IV estimation assumes a constant treatment effect of insurance, the formula for the treatment effect on the SF-6D can be reduced to:
(D2) SF-6D = 0.00781 x PCS-8 + 0.00946 x MCS-8
