Instrumental Variables

We close the empirical analysis by using MA × During and MA × After as instruments to estimate the impact of having insurance coverage on health. This instrumental variables approach requires stricter assumptions than the reduced-form model, as the reform must only impact health along the extensive margin of insurance coverage, conditional on the controls. This assumption would be violated if the reform also influenced health through the intensive margin of coverage, for instance by causing some individuals to switch from high-deductible catastrophic coverage to more comprehensive coverage available through the Connector. This assumption would also be violated if the reform affected the health of those who did not switch insurance plans through system-wide changes to health care delivery or peer effects. Despite these caveats, the instrumental variables analysis is useful because it estimates the magnitude of the impact of insurance on health that would be necessary for the extensive margin to be the only channel through which the reform influenced health. If the magnitude is implausibly large, then other mechanisms must play a role as well.

The first stage predicts insurance coverage using the following linear probability model:

ist α 3 +ζ s +η t + u ist (15) where ins is a dummy variable equal to 1 if the person reported having any health

ins ′ ist =α 0 +α 1 s × During

2 s × After t

insurance coverage. Because of the nonlinearity of the second stage, we utilize a two-stage residual inclusion (2SRI) approach in which the residual from the first- stage regression is included as an additional regressor in the second stage. Terza, Basu, and Rathouz (2008) show that in nonlinear contexts 2SRI gives consistent coefficient estimates, while traditional two-stage least squares do not. The second

30 Specifically, the pretreatment trend lines are almost identical for the subsamples of women, men, ages 35 to 44, ages 45 to 54, ages 55 to 64, and those with low incomes. The pretreatment trend lines

look slightly different for the race groups and those with middle or high incomes, but the differences are small enough that they could be due merely to sampling error. 31

All appendices are available at the end of this article as it appears in JPAM online. Go to the publisher’s Web site and use the search engine to locate the article at http://www3.interscience .wiley.com/cgi-bin/jhome/34787.

32 In Massachusetts in the before period, the mean health status indices of nonwhites and whites were 2.559 and 2.898, respectively, for a difference of −0.339. The treatment effects imply changes in the

health status indices of nonwhites and whites of 0.054 and 0.036, for a difference of 0.018. We therefore estimate that the reform reduced racial health disparities by 5.3 percent.

Table 7. Heterogeneity in the effect on health by gender, age, race, and income.

Dependent variable: overall health

Income Published

White non-

< $25K $25K to $75K >$75K on

55 to 64 Hispanic

Other

0.024 0.015 behalf

MA×After

(0.007) *** (0.008) Statewide treatment effects of the reform

− 0.001 − 0.0002 of

Journal P(poor)

P(fair)

(0.001) *** (0.0005) ssociation P f P(good)

(0.001) *** (0.002) P(very good)

P(excellent)

0.022 0.014 P olicy Management

and Overall effect in

standard deviations

945,561 555,546 nalysis A

Notes: Standard errors, heteroskedasticity robust and clustered by state, are in parentheses. ***Statistically significant at the 0.1 percent level.

nd a DOI: **Statistically significant at the 1 percent level.

Health?

Management 10.1002/pam *Statistically significant at the 5 percent level. All regressions include MA × During, the individual-level control variables, state fixed effects, and fixed effects for each month in each year. The full control

group is used in all regressions. Observations are weighted using the BRFSS sampling weights.

60 / Does Universal Coverage Improve Health? stage is modeled as an ordered probit and the probabilities of being in each of the

five health states are given by

Pr (y

ist = λ 1 −π 1 ins ist − X ist π 2 −π 3 ˆu ist −σ s −ϕ t (16)

Pr (y ist =

λ j −π 1 ins ist − X ist π 2 −π 3 ˆu ist −σ s −ϕ t

j−1 −π 1 ins ist − X ist π 2 −π 3 ˆu ist −σ s −ϕ t , ∀ j ∈ (2, 3, 4) (17)

ist π 2 −π 3 ˆu ist −σ s −ϕ t ) (18) where ˆu ist is the first-stage residual. The effect of health insurance on the probability

Pr (y ′ ist = 4 −π 1 ins ist − X

of being in health state j is p j = Pr (y ist = j|ins ist =

1) − Pr (y ist = j|ins ist =

The asymptotic standard errors of these probabilities and the standard errors for the second stage estimates are calculated following Terza (2011). Equation (19) represents the local average treatment effect of insurance among those obtaining coverage as a result of the reform. This is not the same as the average effect of insurance across the entire population, as the coverage expansions are not evenly distributed across the population. We will show which subgroups experience the largest gains in coverage, and therefore contribute the most to the local average treatment effect, later in this subsection.

Table 8 reports the coefficient estimates of interest from the first and second stage regressions for the full sample, along with the estimated impacts of insurance on the health state probabilities. The first stage estimates an increase in the coverage rate of 2.1 percentage points in the during period and 5.6 percentage points in the after period. The F-statistic from a test of the joint significance of MA × During and MA × After is large, suggesting the instruments are sufficiently strong. Turning to the second stage, obtaining insurance leads to a positive and statistically significant improvement in health. The first-stage residual is significant and negatively associ- ated with health, providing evidence that downward bias would result if instruments were not used. Insurance is estimated to reduce the probabilities of being in poor, fair, and good health by 5.8, 9.2, and 8.5 percentage points, while increasing the probabilities of being in very good and excellent health by 8.1 and 15.3 percentage points. The overall effect of insurance on the health status index, encompassing changes in all five probabilities, is 0.594 of the sample standard deviation.

These effects are strikingly large, but assessing their plausibility requires a com- parison to other estimates from the literature. Finkelstein et al. (2012) employ the cleanest research design to date among studies of the impact of insurance on self- assessed health: a randomized intervention in Oregon granting Medicaid eligibility to a subset of the uninsured. They estimate that Medicaid enrollment increases the probability of being in good, very good, or excellent health by 13.3 percentage points. The sum of our estimated effects on the probabilities of being in those three health states is a similar 14.9 percentage points. The results from the two papers are not directly comparable given the differences in interventions and populations, but this

Does Universal Coverage Improve Health? / 61 Table 8. Instrumental variables.

First stage: any insurance coverage Coefficient estimates MA × During

0.021 (0.002) * MA × After

0.056 (0.003) * First-stage F-statistic

179.41 Second stage: overall health

Coefficient estimates Insurance

0.655 (0.154) * First-stage residual

− 0.634 (0.124) * Treatment effects of insurance P(poor)

− 0.058 (0.012) * P(fair)

− 0.092 (0.016) * P(good)

− 0.085 (0.015) * P(very good)

0.081 (0.014) * P(excellent)

0.153 (0.029) * Overall effect in standard deviations

0.594 Observations

1,976,564 Notes: A linear probability model is estimated in the first stage so the coefficient estimate equals the

treatment effect. Standard errors, heteroskedasticity robust and clustered by state, are in parentheses. *Statistically significant at the 0.1 percent level. All regressions include the individual-level control variables, state fixed effects, and fixed effects for each

month in each year. The full control group is used. Observations are weighted using the BRFSS sampling weights.

similarity suggests that it is at least conceivable that the reform’s entire effect on the self-assessed health of the nonelderly could have occurred through the extensive margin of coverage. Future research should more directly investigate the roles of other potential channels, in particular the intensive margin of coverage.

We also conduct instrumental variables analyses for the gender, race, age, and income subgroups, allowing us to assess whether the heterogeneity in the reform’s effect on health observed previously comes from heterogeneity in the effect on coverage or the effect of coverage. Table 9 reports the results. The coverage expansions are larger for men than women, but women have greater health gains from coverage, explaining the greater net effect of the reform for women. Specifically, the increase in the insurance rate is 6.8 percentage points for men, while 14 percent of newly insured men transition into one of the top two health categories. Multiplying these numbers leads to an approximate population-wide effect of the reform on the probabilities of men transitioning into very good or excellent health of 1 percentage point, which comes close to the 0.8 percentage point estimate from the correspond- ing reduced-form regression in the earlier Table 7. A similar calculation suggests a population-wide effect for women of 1.6 percentage points, which exactly matches the reduced-form results. Among the age subsamples, those under 35 years old have

Table 9. Instrumental variables: stratified by gender, age, race, and income. Published Journal

$25K to $75K > $75K on olicy P

behalf First-stage coefficient estimates: any insurance coverage

Universal

0.016 0.007 Analysis

MA × During

MA × After

321.62 26.61 ssociation A and

Second stage: overall health Management

Coefficient estimates Insurance

− 0.258 − for 1.010 residual

Treatment effects of insurance P

− 0.019 − 0.082 olicy 10.1002/pam

P(poor)

P(fair)

P(good)

(0.019) ** (0.010) *** P(very good)

nd a (0.014) ***

P(excellent)

(0.027) ** (0.166) Overall effect in

0.302 1.159 standard deviations

944,457 555,137 Notes: A linear probability model is estimated in the first stage so the coefficient estimate equals the treatment effect. Standard errors, heteroskedasticity robust and

clustered by state, are in parentheses. ***Statistically significant at the 0.1 percent level. **Statistically significant at the 1 percent level. *Statistically significant at the 5 percent level. All regressions include the individual-level control variables, state fixed effects, and fixed effects for each month in each year. The full control group is used. Observations

are weighted using the BRFSS sampling weights.

Does Universal Coverage Improve Health? / 63 the largest gains in coverage, but also the smallest health improvements from ob-

taining coverage. Fifty-five to 64 year olds have the smallest effect of the reform on coverage but the largest effect of coverage on health. The implied population- wide percentage point increases in the probability of being in the top two health categories are 1.3, 0.7, 1.1, and 1.5 for 18 to 34, 35 to 44, 45 to 54, and 55 to 64 year olds. These numbers again come close to those from Table 7. Stratifying by race shows that coverage rates increase the most for nonwhites, but that the health effects of coverage are the largest for whites. The estimates imply population-wide effects on the probability of very good or excellent health of 1.3 percentage points for whites and 2.0 percentage points for nonwhites, compared to 1.4 and 1.9 in Table 7. Finally, the coverage expansions are by far the largest for the low-income group, second largest for the middle-income group, and relatively small for those with high incomes. However, the effect of coverage on health is the strongest for the high-income group. The implied population-wide increases in the probability of having at least very good health are 2.1, 0.9, and 0.6 for the low-, middle-, and high-income groups, again similar to the reduced-form results.

The results from Table 9 also shed light on the generalizability of the local average treatment effect for the whole sample from Table 8. Since the coverage gains are largest for men, young adults, minorities, and low-income individuals, these groups contribute disproportionately to the local average treatment effect. The second- stage estimated effects on health are smaller for each of these groups than for other gender, age, race, and income categories. If anything, then, this suggests that the whole-sample local average treatment effect understates the average effect of insurance across the whole population. Of course, this again assumes that the intensive margin of coverage is the only mechanism through which the reform impacts health.

Finally, Table 10 reports the results from instrumental variables analyses for the “other health outcomes” from Table 6. We estimate the second stages using 2SRI and utilize the same functional forms as the reduced-form models. Details on our derivations of the treatment effects of insurance are available upon request. Health insurance coverage leads to statistically significant reductions in days not in good physical health, days not in good mental health, days with health limitations, activity-limiting joint pain, and BMI. Among these five dimensions of health, the absolute values of the effects of insurance expressed in standard deviations of the dependent variable range from 0.485 to 0.781, compared to 0.594 for the overall health index in Table 8. Since these are roughly similar, it appears that the same comment from the overall index applies to these other outcomes as well: It is conceivable that the entire effects of the reform could occur via the extensive margin of coverage, but it is also possible (perhaps probable) that other dimensions such as the intensive margin of coverage play a role as well. 33

33 Of particular relevance to the BMI results is an initiative called Mass in Motion that aimed to reduce overweight and obesity among Massachusetts residents through a multipronged approach that included

a statewide public information campaign, workplace wellness initiatives, an interactive wellness Web site, and a public-private partnership to support healthy cities and towns. However, this program did not begin to take effect until 2009, and we observe the full improvement in BMI in Massachusetts relative to other states starting in 2008 (see online Appendix Figure A5). We therefore do not think this program plays a major role in explaining the effect on BMI. All appendices are available at the end of this article as it appears in JPAM online. Go to the publisher’s Web site and use the search engine to locate the article at http://www3.interscience.wiley.com/cgi-bin/jhome/34797.

Published Journal

64 Does /

f on o P olicy

Table 10. Instrumental variables: other health outcomes. behalf

Universal

Analysis

Days not in

Days with

Activity-

the

Cardinalized and

Minutes of

joint pain

overall health A

Coverage

ssociation Management

First-stage coefficient estimates: any insurance coverage MA × During

MA× After

Public DOI:

214.62 Second stage: overall health

P 10.1002/pam Coefficient estimates olicy

(0.067) * A nalysis

(0.068) * Treatment effects

nd * of insurance (0.768)

Effect in standard

0.968 deviations Observations

1,976,687 789,901 Notes: A linear probability model is estimated in the first stage so the coefficient estimate equals the treatment effect. Standard errors, heteroskedasticity robust

and clustered by state, are in parentheses. *Statistically significant at the 0.1 percent level. All regressions include the individual-level control variables, state fixed effects, and fixed effects for each month in each year. The full control group is used.

Observations are weighted using the BRFSS sampling weights. MA×During is not included for joint pain, exercise, and cardinalized health, since these variables are only available in odd-numbered years.

Does Universal Coverage Improve Health? / 65

Instrumental Variables