eligibility criterion is met if this ratio is smaller than a threshold, which depends upon the age of the child, state of residence, and year. The implementation of SCHIP plans
lead to dramatic increases in the eligibility thresholds across states.
A. Design Implementations
Does public insurance alter the incidence of insurance and the incidence and treatment of disease? Suppose I attempt to measure the effect of public medical insurance on
healthcare demand using the equation below: 1 c
i
= L
i
γ
c
+ X
i
β
c
+ ε
c,i
where c
i
is adult i’s insurance or healthcare outcome under study; L
i
is equal to one if the child in adult i’s household is eligible for public insurance; X
i
is a set of other relevant information, such as race, ethnicity, age, and state of residence;
3
and ε
c,i
is the usual residual. What does γ
c
measure? First, since this is a measurement of eligibility and not of takeup, there is no takeup endogeneity bias. In part, γ
c
measures the causal effect of public insurance eligibility on the healthcare outcome. However, because
eligibility is determined by family income and the child’s age, it also picks up the outstanding correlation between income and demand for healthcare. For example, if
health is a normal good, without controls for income, γ
c
would be biased down.
3. The AHRQ made available a coded variable that allows observations to be grouped by state but does not disclose the identity of the states.
.2 .4
.6 .8
1
P erc
ent
1996 1998
2000 2002
2004 2006
Year Any Insurance
Private Insurance Public Insurance
Figure 3 Insurance rates for non- elderly adults.
In order to overcome this, I employ a regression discontinuity design, similar to Card and Shore- Sheppard 2004 in their study of Medicaid expansion. Now, the fol-
lowing equation is estimated: 2 c
i
= L
i
γ
c
+ X
i
β
c
+ Gdistance
i
, Family Income
i
+ ε
c,i
, where Gdistance
i
, Family Income
i
is a nonlinear function of family income and “distance” from the eligibility threshold that is, family income as a fraction of the
poverty guideline less the governing threshold. This distance measure is the forcing, or running variable, as it determines eligibility. The effects picked up by G need not
be causal—it just needs to pick up all of the covariation between the outcome variable and the variables that determine eligibility, beyond the causal effects of eligibility
itself. Adding these controls leaves γ
c
to measure the effect of public insurance itself. Concerns about the many eligibility thresholds exploited here are addressed when γ
c
is estimated by eligibility thresholds. For the preferred specifi cations, Gdistance
i
, Family Income
i
is linear in distance from the eligibility guideline and the family income as a fraction of the poverty guide-
line. This last term is added because the relevant guidelines vary dramatically over the period of study.
4
Family income includes all nonself- employed wage income within the CPS- type family, and poverty guidelines are calculated accordingly. The public
insurance variable, L
i
, is equal to one if eligible for Medicaid or SCHIP, zero other- wise. Because the MEPS is collected using a complex survey design, all estimates and
standard errors are calculated using appropriate weights, strata, and PSU. Because the measures that determine eligibility are close to continuous income is measured in dol-
lars and cents, there is no need to cluster according to a discrete forcing variable, as in Lee and Card 2008. Similarly, the variation being exploited here is in the income
distribution in the cross- section and not across time and state as would be the case for simulated eligibility; thus, there is not the usual reason to cluster by the determinants
of eligibility threshold: state and year. The estimates provided below are pooled across the short twice- observed panel. Given the panel nature of the data, clustering by
individual may be appropriate. In the online appendix, I demonstrate that using only the fi rst of two observations per individual has the expected and modest impact on
statistical inference.
Because family income- to- poverty guideline ratios vary greatly within the popula- tion, Equation 2 is estimated using a restricted subsample, where the household has
to be within one and a half Federal poverty guidelines from the child’s eligibility threshold. The main specifi cation of Equation 2 requires only a control function G.
However, I can also add other control variables, such as a polynomial in adult age in months, and dummy variables for race, Hispanic ethnicity, and whether the parent
is a single mother. Year- and state- fi xed effects are also included. The sample and subsample means are reported in Table 1. The subsample represents a group of adults
well distributed over age groups. The age groups presented were constructed to be of similar size. The subsample is 78 percent white and 16 percent black.
Most of the specifi cations below employ a linear- probability model, save for the few spending and utilization outcomes considered. Because some of the specifi cations
4. In the online appendix, I check how robust the estimates of γ
c
are for various expansions of the polyno- mial G.
K oc
h 967
Table 1 Means of the sample
Mean Mean
Variable Full Sample
Subsample Variable
Full Sample Subsample
Subsample N Demographics
Spending and Self- Reported Health Age: 18 years-
0.1844 0.2187
Total 1,967.13
1,898.30 37,121
27 years, 1 month- 0.1949
0.231 Offi ce- based
442.77 408.54
37,121 33 years, 11 months-
0.2068 0.205
Out- of- pocket 360.76
320.74 37,121
39 years, 6 months- 0.2206
0.1846 46 years, 1 month-
0.1934 0.1607
Excellent or very good 0.624
0.597 37,121
1 = Male 0.465
0.450 1 = White
0.800 0.774
Preventive Care—All 1 = Black
0.136 0.164
Flu shot 0.172
0.155 25,784
1 = Hispanic 0.165
0.221 BP check
0.762 0.736
25,478 Cholesterol check
0.432 0.386
24,664 Insurance by Source
Annual exam 0.527
0.492 25,528
Private 0.684
0.642 Any
0.786 0.763
Preventive Care—Women Public
0.125 0.148
Pap smear 0.640
0.618 14,256
Breast exam 0.643
0.617 14,264
N = 79,253
37,121 Mammogram
0.361 0.315
9,293
Notes: Restricted sample is observations with measured income within 1.5 Federal poverty guidelines of the eligibility threshold. Age groups thresholds are set- up to match quintiles. The sample sizes for the preventive care variables vary due to changes in MEPS survey design over time.
involve a robust set of state- and year- fi xed effects, OLS is preferred; those fi xed ef- fects are useful in distinguishing whether or not the mean shifts at the discontinuity.
For censored outcomes, the use of traditional estimators with a global polynomial has been advised by Imbens and Wooldridge 2009. The tables report a fi rst- order
approximation of the marginal effects of the Tobit equation—⌽X
i
, the latent equa- tion estimate times the average fi tted probability that the observation is not censored.
Due to the nonlinear nature of these estimates, the t- statistics for the underlying pa- rameter estimates are reported for consistency, as they are for the linear probability
models.
I also provide graphical evidence of the discontinuities. In general, graphical anal- ysis can be carried out with the average value in “bins” according to the forcing vari-
able, as advised by Imbens and Lemieux 2008. Here, the forcing variable is the difference or distance in the graphs between the ratio of family income to Federal
poverty guideline and the relevant cutoff. The bins used here are as wide as 1 percent of the Federal poverty guideline. This corresponds to a 156- wide 1 percent bin for
a family of four in 1996. A fl exible fi tting of the bin averages is also provided in the form of a local linear smoother. The weighting function of the local linear smoother
uses a rectangular kernel, as advised by Lee and Lemieux 2010. The bandwidth of kernel is based upon the rule of thumb provided by Fan and Gijbels 1996, Sec-
tion 4.2.
5
B. Validity of the Design
