Insurance Coverage and the Healthcare Utilization of Children
Lindsey Jeanne Leininger
Harris School of Public Policy Studies
Support from the AHRQ/NRSA T-32 training grant is gratefully acknowledged.
1. Introduction and background
Insurance coverage of poor and near-poor children has received a great deal of
research and popular attention in the past several decades. Approximately 19.8% of poor
children were uninsured for at least part of 2004. There is widespread concern that these
children are not receiving necessary medical care.1 Both altruistic motivations and a
desire to correct potential negative externalities (such as vaccine-preventable
communicable diseases) have led researchers and policymakers to explore options for
providing appropriate care to uninsured children. Direct provision of health insurance to
these children is the option that has received the greatest amount of discourse and dollars.
Beginning in the late 1980s, Congress drastically increased income eligibility cut-offs for
public insurance to include many children in families with incomes above the federal
poverty level. In 1984 the rate of public coverage of near-poor children was 9% and by
2002 this number had increased to 47%.2 The number of uninsured children has not
decreased in parallel with the increased public coverage rates, as private insurance
coverage has fallen for low-income children during this time period. The uninsurance rate
for near-poor children in 1984 was 27% and the comparable 2002 figure is 33%.
Whether these increases in eligibility have been associated with improvements in
child health is a major concern of both researchers and policymakers. Specifically, it is
important to know whether differences in utilization are attributable causally to
1 Source: Cohen RA, Martinez ME, Hao C. “Health Insurance Coverage: Estimates from the
National Health Interview Survey, January-September 2004.” Available:
http://www.cdc.gov/nchs/nhis.htm. Accessed: 4/04/05.
2 Source: CDC, “Health, United States 2004.” Available:
http://www.cdc.gov/nchs/data/hus/hus04trend.pdf#topic. Accessed: 4/04/05. Note that “near-
poor” is defined in this paragraph as having family income between 100-150% of FPL.
differences in insurance, or merely a reflection of adverse selection or other unobservable
It is also instructive to know the differences in utilization patterns among children
who are privately versus those who are publicly insured. Understanding the utilization
differences between uninsured, privately insured, and publicly insured low-income
children will help inform policymakers regarding the relative benefits of insurance status.
If privately insured children are receiving the most appropriate care, then incentivizing
private insurance coverage should receive more attention as a potentially successful
policy lever than increasing public coverage. If, by contrast, no differences in utilization
are found among children in various insurance categories, then the policy focus should
shift to different mechanisms. The relative benefits of private insurance compared with
public insurance need to be considered with their relative costs. Public insurance is free
or very low-cost for low-income families while private insurance can comprise a sizable
portion of their budget. It is important to acknowledge that the decision regarding optimal
insurance schemes for low-income children is not only about the direct provision of
healthcare but also about family income.
Many studies whose goal is to identify causal effects of health insurance on
various health outcomes have employed instrumental variables techniques (IV). This type
of study has been particularly prevalent in the literature on the health effects of the
Medicaid expansions. If results from IV models are to be given more weight in the search
for causal effects than their ordinary least squares (OLS) counterparts, it is imperative to
scrutinize whether the assumptions underlying their usage are being met and if their
results are robust to various changes in estimation procedure and divisions of the
instruments employed. There is no definitive test for the crucial assumption that the
instrument is uncorrelated with error term; however it is still possible to construct
convincing evidence that the instrument does indeed meet this requirement.3
The major goal of this paper is to provide new evidence on the robustness of
instrumental variables results in the identification of the effect of different types of health
insurance on child healthcare utilization. I use a fuller set of instruments than what
currently exists in the literature as well as examine results from linear and non-linear
estimation techniques to determine the sensitivity of incremental effect estimates from IV
Medicaid, the public health insurance program for low-income individuals, was
created along with Medicare in 1965 in Title XIX of the Social Security Act.4 It is jointly
funded by the state and federal governments, with the federal matching rate determined
by state per capita income. It is an entitlement program, thus all persons deemed eligible
are guaranteed access if sought. Medicaid is the largest funding source for healthcare of
low-income people. In fiscal year 2002, $214.9 billion was spent on Medicaid, with $34.4
billion being spent on children.
Medicaid covers several populations in addition to low-income children and their
parents. In fact, while low-income women and children comprise two-thirds of program
3 See, for example McClellan, Mark, Barbara McNeil, and Joseph Newhouse, “Does More
Intensive Treatment of Acute Myocardial Infarction in the Elderly Reduce Mortality? Analysis
Using Instrumental Variables,” Journal of the American Medical Association, CCLXXII (1994),
859-866. They provide compelling evidence on the validity of their instrument by demonstrating
that it is not correlated with observed variables in the data.
4 Centers for Medicare and Medicaid Services, “Medicaid: A Brief Summary.” Available:
enrollees, they only account for approximately 27% of total expenditures.5 The low-
income disabled, the low-income elderly and the institutionalized elderly, and medically-
needy populations account for three-quarters of Medicaid program dollars.
Each state exercises some discretion over provider payment rates and covered
services, with federal guidelines mandating the coverage of certain services. For children,
all states must provide inpatient and outpatient hospital services, vaccines, pediatric and
family nurse practitioner services, and early and periodic screening, diagnostic, and
treatment services (EPSDT) for children under age 21. Other services such as optometrist
services and eyeglasses and prescription drugs are optional and coverage varies by state.
Pregnant women and children are exempt from any cost-sharing by law. During the
Clinton and Bush II administrations, CMS and its predecessor HCFA have granted
waivers to basic Medicaid requirements for innovative programs.
Medicaid traditionally covered women and children who were receiving AFDC.
During the 1980s, Congress began to expand eligibility to low-income child populations
who met the income requirements for AFDC but were ineligible due to other
characteristics such as family structure. A timeline of the changes in Medicaid is outlined
in Appendix Table A. The Omnibus Reconciliation Act of 1987 ushered in a new era of
far-reaching Medicaid expansions that decoupled Medicaid from welfare receipt.
Legislation in 1987, 1988, 1989, and 1990 first allowed for and then mandated eligibility
for all low-income (up to 100% of the federal poverty level) women, infants, and children
through age 18. States differed in both the timing and extent of their expansions.
5 Gruber, Jonathan, “Medicaid,” NBER working paper #7829, August 2000. Available:
http://www.nber.org/papers/w7829. Accessed: 4/04/05.
Congress created the State Children’s Health Insurance Plan (SCHIP) in the
Balanced Budget Act of 1997. SCHIP was designed to provide insurance coverage for
children who exceed the income threshold for Medicaid. Specifically, children in
families with incomes up to 200% of the federal poverty level or 50% higher than their
state’s Medicaid cutoff are considered the “target children” for the SCHIP program.6
Federal funds for SCHIP are in the form of block grants to states, with $4.3 billion
appropriated in 1998, the first year of the program, and $5 billion scheduled to be
appropriated for 2007. States were allowed to design their SCHIP programs as stand-
alone programs, extensions of Medicaid, or a combination of both. Nineteen states chose
to expand their Medicaid programs while 15 states created a stand-alone program and 17
states chose to implement a hybrid program.7 States are allowed to implement cost-
sharing requirements in stand-alone SCHIP programs, however they are not allowed to
do so for preventive services nor for immunizations. And while states have some
flexibility in benefit packages offered, they must cover EPSDT services for children and
vaccines. States were required to implement outreach programs to reach eligible
children. And states were also required to protect against “crowd-out”—people dropping
private coverage to enroll in public coverage. The most common strategy employed to
prevent this phenomenon has been to limit coverage to children who had been uninsured
for a specific amount of time.
6 Centers for Medicare and Medicaid Services, “Welcome to the State Children’s Health
Insurance Program.” Available: http://www.cms.hhs.gov/schip/about-SCHIP.asp. Accessed:
7 For a detailed listing see LoSasso, Anthony, and Thomas Buchmueller, “The Effect of the State
Children’s Health Insurance Program on Health Insurance Coverage,” Journal of Health
Economics, XXIII (2004), 1059-1082.
It is important to know what effects these expansions in eligibility had on
healthcare utilization in the target populations. Specifically, it is vital that policymakers
know if insurance status is causally linked with increases in the level of healthcare
utilized. There are reasons to believe that this is indeed the case. If health insurance
lowers the cost of receiving care, then basic economic theory suggests that more care will
be demanded. Therefore we should see more provider visits among the insured than the
uninsured. It is also plausible that health insurance status does not greatly affect
utilization. If demand for healthcare is perfectly price inelastic, then we would not expect
insurance to have any effect on utilization. And even if the demand for healthcare has a
non-zero or negative price elasticity, previous work suggests that other factors are as
important or more important in influencing utilization patterns of low-income children.8
Geographic concentration of providers and Medicaid provider reimbursement rates are
two such factors that have been posited as important factors driving the utilization of low-
Identifying the causal effects of insurance coverage on access and utilization is
difficult due to the likely presence of confounding influences of unobservable
characteristics that are correlated with both insurance coverage and healthcare utilization.
Several studies that address and attempt to correct for these confounders adopt
instrumental variables techniques to parse out causal effects from confounding ones. A
wide variety of instruments have been used in the literature on the effects of health
insurance on health outcomes. However, there is little evidence with respect to the
robustness of the results arising from IV estimation in this context. IV studies enjoy
8 For a discussion of various factors influencing access see Currie, Janet, “Appendix D: What Can
We Learn about Child Care Policy from Public Investments in Children’s Health?” Available:
http://aspe.hhs.gov/hsp/cc-rationale02/appendixD.htm. Accessed: 4/04/05.
greater clout in the discussion of causal effects of health insurance than observational
studies with covariate adjustment even though the potential for violating the former’s
underlying assumptions is great and the robustness of IV estimates has not been well-
explored in the health insurance/health utilization literature.9 The goal of this study is to
shed new light on a technique that is commonly invoked upon to produce causal
estimates of the effects of public (and private) insurance on child health outcomes.
2. Previous literature
There is a substantial and growing research literature that aims to identify the
effects of health insurance on child health utilization and outcome measures. Much of the
work in this area is of a descriptive nature.10 As mentioned above, the relationship
between health insurance status and health outcome measures in observational studies is
likely to be confounded by unobservable characteristics.
There has been one randomized trial of the effects of health insurance on
healthcare utilization. The RAND Health Insurance Experiment (HIE) conducted from
1974-1982 was designed to overcome internal validity concerns through the use of an
experimental design. The HIE randomized 2,000 non-elderly families into insurance
9 For example, Levy and Meltzer in their 2004 review chapter state: “We do not believe that it is
generally possible to make any causal inference about the effect of health insurance on health
from observational studies. Therefore we devote most of our attention to reviewing the findings
of experimental and quasi-experimental studies, since we believe these studies do provide
evidence on the nature of the causal relationship between health insurance and health.” Included
in their set of quasi-experimental studies are several instrumental variable studies. Reference:
Levy, Helen, and David Meltzer, “What Do We Really Know about whether Health Insurance
Affects Health?” Health Policy and the Uninsured, Catherine G. McLaughlin, ed. (Washington,
D.C.: Urban Institute Press: 2004).
10 An example: Newacheck, P., et al., “Health Insurance and Access to Primary Care for
Children,” New England Journal of Medicine, CCCXXXVIII (1998), 513-519.
plans that varied the prices of healthcare services.11 Roughly 70 percent of the sample
was enrolled in the experiment for three years while the remaining sample members were
enrolled for five. Dependent variables studied included health utilization, costs, and
health status and functioning outcomes. The predicted annual use of medical services for
children in the study varied by coverage generosity, with more generous coverage being
associated with higher probabilities of the likelihood of any medical care use.12 For
example, the predicted probability of any medical care use for children on the free plan
(no copayment) was 84.0% compared to 63.5% for children whose families paid a 95%
While the HIE provides direct evidence of a causal link between insurance
generosity and utilization in children, its results cannot be used to answer the underlying
policy question of this paper. Specifically, the HIE did not have a publicly insured group,
nor did it have an uninsured group. Furthermore, its results are now almost thirty years
old. Changes in the structure of medical care and insurance coverage in the intervening
years may have altered the relationship between insurance and utilization.
Researchers interested in obtaining consistent effects of public and private
insurance on utilization and comparing these to the effects of being uninsured have
therefore been limited to the use of quasi-experimental techniques. Instrumental
variables, difference-in-difference, and fixed effects approaches have all been employed
to account and correct for selection into insurance. This paper is an inquiry into the use
of instrumental variables estimation, therefore this review focuses on results from papers
11 Newhouse, Joseph P. Free for All? Lessons from the RAND Health Insurance Experiment
(Cambridge, MA: Harvard University Press, 1993, p.9.
12 Manning, Willard, et al., “Health Insurance and the Demand for Medical Care: Evidence from a
Randomized Experiment,” American Economic Review, LVII (1987), 251-277. p.263.
utilizing this technique in estimating the insurance/utilization link for children. A brief
discussion of results from work using difference-in-differences and fixed effects methods
will also be included in order to provide a larger context in which to evaluate existing
knowledge on the insurance/utilization link for children.
Currie and Gruber (1996) examine the effect of public insurance eligibility on
healthcare utilization for children through age 15. Their instrument is the share of a
randomly-drawn national sample of the relevant age group that is eligible for Medicaid
under the eligibility regime for the state and year of the observation. This “natural
experiment” approach utilizes state-level variation in both the timing and extent of
Medicaid eligibility increases of the 1990s as its identification strategy and has been used
in several subsequent studies.13 This “simulated eligibility” variable is arguably
uncorrelated with child- or family- specific unobservables that are related to eligibility
and utilization. Additionally, by using a nationally-derived sample they also rid the
instrument of correlations with a given state’s economic or demographic characteristics
in any particular year.
Using the National Health Interview Survey (NHIS) for the years 1984-1992, they
estimate that making a child eligible for Medicaid lowers the probability of going without
a visit by 6.9 percentage points, which is almost one-half of the baseline probability of
going without a visit in their sample. They also find that Medicaid eligibility is associated
with a 4 percentage point increase in the probability of a hospitalization in the past year,
implying a doubling of the (baseline) probability of being hospitalized. A limitation of
their study is that their models do not include private insurance status, making a
13 Examples: crowd-out (Cutler, David, and Jonathan Gruber, “Does Public Insurance Crowd Out
Private Insurance?” Quarterly Journal of Economics, CXI(1996), 391-430.) and take-up of
SCHIP (LoSasso and Buchmueller (2004))
comparison between the effects of private insurance and public insurance on outcomes
impossible. Another limitation of their study is that they employ two-stage least squares
in a linear probability model framework (2SLS-LPM) for estimating models with
dichotomous dependent variables. As will be discussed later, this may be an inappropriate
estimation method for these types of outcome measures. Because the model is exactly
identified, an overidentification test of the exogeneity assumption cannot be performed.
Kaestner, Joyce, and Racine (1999) examine the effect of Medicaid participation
on a variety of child health measures using an IV approach. Using the 1989 and 1992
NHIS, they estimate the relationship between insurance status and the number of
physician visits in the past year for children ages 2-9. They stratify their sample by race
and estimate models for white children and black/Hispanic children separately. They use
state-year-income interactions and child age-year interactions to instrument for insurance
status. Their OLS results differ from their IV results for both white children and non-
white children. Their OLS estimates suggest that Medicaid participation is associated
with 1.7 more visits annually (significant) compared with being uninsured for white
children, while the 2SLS estimate is 0.3 more visits (not significant). For black and
Hispanic children these numbers are 0.9 visits and 2.4 visits, respectively, with the
former being significant and the latter being insignificant. In the OLS model for white
children, private insurance is associated with an increase of 0.5 visits per year
(significant) compared with being uninsured while the IV estimate shows a decrease of
1.3 visits per year (not significant). For black and Hispanic children the comparable
estimates are 0.09 visits for OLS (not significant) and 1.8 visits for IV (not significant).
These estimates suggest that the effects of insurance vary by race and that OLS and IV
yield different results.
Yacizi (1997) uses the NHIS to examine the effects of insurance status on various
child health outcomes, including the number of doctor visits received in the past year.
Using the 1988 and 1992 NHIS data, 2SLS is used to estimate the effects of private and
public insurance coverage on the number of doctor visits in the past year. State-year,
state-age, and year-age interactions are employed as instruments for insurance status. The
sample is restricted to include only those children ages 2-12 whose mother is unmarried
and has a high school degree or less. Age groups and races are pooled in the analysis. The
IV estimate suggests that having Medicaid is associated with 1.7 more visits per year
(significant) compared to being uninsured and is associated with -0.5 less visits per year
(insignificant) compared to being privately insured. The comparable OLS estimates are
0.5 visits (significant) and 0.4 visits (insignificant).
Both the Yacizi study and the Kaestner, Joyce, and Racine study perform
overidentification tests on their instruments and both sets of instruments “pass” these
tests. Precision is of potential concern with both of these studies; the sample sizes used
(ranging from roughly 3,600 to 6,600) were much smaller than the sample size employed
in this study (roughly 43,000). Their general lack of significant findings in the IV models
may be a result of a lack of power.
Long, Coughlin, and King (2005) examine the effects of private and public
insurance status on healthcare utilization in low-income adult women using the 1997 and
1999 waves of the National Survey of America’s Families. Their instruments for
insurance include: whether or not the respondent or her spouse work for a firm with more
than 50 employees, a simulated eligibility measure similar to the Currie and Gruber
variable, the percent of the respondent’s county that is on public assistance, and a dummy
variable capturing the respondent’s attitudes toward welfare receipt. The instrument set
“passes” an overidentification test. Their findings suggest that public insurance is
positively associated with a variety of utilization measures compared to uninsurance, and
that the IV results of these effects are stronger than OLS results. For example, their OLS
results show that being uninsured is associated with a 23 percentage point decrease in the
probability of having any doctor visit in the past year compared to being on Medicaid.
The corresponding IV result is roughly 43 percentage points. Both their OLS and IV
results suggest that there exists no difference in utilization between publicly and privately
insured low-income women. Although their study focuses on low-income adult women, it
is still highly relevant to this paper. Results from the HIE suggest that the link between
insurance generosity and utilization for outpatient utilization measures are similar for
adults and children.14 Therefore it is reasonable to hypothesize that the associations of
interest in this study may also be similar for adults and children. Additionally, this paper
uses the same dataset that I use in addition to many of the same instruments. A potential
limitation of this study is its use of linear probability models for estimating the
dichotomous dependent variables in the second stage.
Two difference-in-differences papers examine the effects of increases in Medicaid
eligibility on healthcare utilization in children. Using the 1989 and 1995 waves of the
NHIS, Racine et al. (2001) examine the effects of eligibility expansions on the
probability of seeing a doctor and the number of doctor visits received in the past year.
They find no significant effect for either outcome. Their treatment group is children in
14 Manning et al. (1997), p.263.
families with incomes less than 200% of the federal poverty level and their control group
is children in families with incomes between 300-400% of the federal poverty level.
Banthin and Selden (2003) also use a difference-in-differences approach to identify the
effects of eligibility by age. Unlike Racine et al., they do find a significant effect of
eligibility on the probability of having a doctor visit: 9.3 percentage points for the
treatment group of children made eligible for Medicaid between 1987 and 1996
compared to a control group of children ineligible for Medicaid during the time period of
the study but meeting SCHIP eligibility criterion. Their regression-adjusted effects of
eligibility on having a usual source of care, having at least one visit to a dentist, and
having at least one emergency room visit are all insignificant.
There are two studies that use the NLSY for fixed effects estimation of the
insurance/utilization relationship. Currie and Thomas (1995) find mixed evidence on the
nature of this relationship using the 1986 and 1988 child supplement waves of the NLSY.
Results from their fixed effects models suggest that privately insured children of all races
are no more likely to have had a routine check-up than uninsured children. They also find
that publicly insured white children are more likely to have a routine check-up than their
uninsured counterparts while publicly insured black children are not. Yacizi (1997) uses
the 1986, 1988, 1990, and 1992 child supplement waves. In this fixed effects model,
becoming covered by Medicaid is associated with a large (23 percentage point) increase
in the likelihood of having a check-up compared to being uninsured, while becoming
privately insured is associated with a significant increase of 19 percentage points
compared to being insured. It is striking that the results of these two studies using the
same sample differ so strongly.
We cannot draw definitive conclusions about the effect of insurance status on
children’s healthcare utilization from the current literature. The results from instrumental
variables studies differ from each other and from studies utilizing other methods to
control for selection into insurance status. This study seeks to provide evidence on
potential mechanisms that are driving the sensitivity of the results seen in this literature.
3. Theoretical approach
This paper adopts a variant of a neoclassical choice model for health insurance ex
ante and of medical care ex post the resolution of uncertainty, an extension of the
theoretical approach discussed in Manning and Marquis (1996). Individuals’ utility is
defined as a function of healthcare and all other goods. Choices about insurance status
must be made in anticipation of needed healthcare utilization before the patient knows
what his or her state of health will be. Thus, individuals choose the health insurance
status that yields them the highest expected indirect utility function, given the insurance
premium, generosity of coverage in terms of both scope of service, and levels of cost-
Parents make choices for their children regarding insurance status. This does not
change the theoretical model in any qualitatively important way. The arguments in the
utility function under this scenario become child’s health and all other goods and
One can also model utility as a function of health status and all other goods, with
healthcare providing no direct utility but rather affecting health status through a health
production function. Behaviorally, the family acts as if it received utility from medical
care, although technically it is intermediate in the production of health status changes.
Again, this would not change the implications derived from theory, except that there
would be a demand for healthcare observed ex post, rather then for health status.
Thus, the individual’s utility function can effectively be represented in equation (1):
U f M AOG
Utility is a function of health care (Mc) and all other goods (AOG).
The budget constraint an individual faces under private insurance with a premium
and a co-pay is:
I d p M
representing the premium paid by the family for health insurance with a
coinsurance rate d, 01
The budget constraint under public insurance is:
I e p M
p AOG θ+−
representing the premium paid, and 01
< < representing the
coinsurance rate for publicly provided insurance. The “premium” faced by individuals
on this budget constraint may include a cash premium (common for many states’ SCHIP
programs), or a non-cash premium. Such non-cash costs may include waiting times,
onerous application processes, and stigma associated with welfare program participation.
Similarly, e may represent an actual cash copay or non-cash costs of per-unit medical
care utilization. An example of such non-cash components of e are long waiting times to
see a doctor or difficulty in finding a provider.
The budget constraint under no insurance is:
I p Mp AOG
The individual maximizes expected utility over types of coverage (uninsured,
privately insured, and publicly insured) and chooses the coverage that gives the highest
expected utility. This is equivalent to selecting the type of coverage with the highest
expected indirect utility.
Let z be a vector of health status variables that serve as utility function shifters.
For example, if an individual has suffered a health shock in the past year, his marginal
rate of substitution of all other goods for medical care will be higher than an individual
with good health.
The indirect utility functions of the various states of the world become:
For private insurance: ()(,, ; )
E IU f p d p I
For public insurance: ()(,, ; )
E IUf pe p I
For no insurance: ()(, , ; )
E IU f pp I z
Once the ex ante decision about insurance coverage is made, the individual
chooses the amount of healthcare to utilize ex post. Using Roy’s identity on the indirect
utility function of the chosen insurance state, the ex ante demand for healthcare and all
other goods can be computed.
If we ignore the issue of corner solutions, the demands for healthcare under the
various types of insurance coverage are:
For those who have chosen private insurance:
*(,, ; )
Mp d p I
For those with public insurance:
*(,, ; )
Mp e p I
For those with no insurance:
*(, , ; )
Mp p I z
The theoretical model motivates the idea that the choice of insurance depends on
the nature of choices available. Different families face different premia, copays, dollar,
and non-dollar costs. Once an insurance plan (including no plan) has been chosen for a
child, the medical care choices for the child reflect the plan selected, not the plans not
taken. The properties of the plan not taken are good instruments for the plan chosen
because they influence insurance choice ex ante but do not influence medical care
utilization ex post.
4. Estimation strategy
The primary goal of this paper is to examine the robustness of estimates of the
insurance/utilization relationship derived from IV methods. This study uses a linear and a
non-linear technique and a variety of instruments—both new and previously used—to
assess the sensitivity of effect estimates arising from IV models.
4.1 Possible instruments
Ideal instruments would be those that measure arguments in the indirect utility
functions represented by equations (8)-(10). As mentioned above, the choice of insurance
depends on parameters such as premiums, co-pays, and non-cash costs. Once the choice
of insurance is made, the characteristics of the plan not chosen serve as instruments for
the type of insurance chosen. These characteristics influence insurance choice but not
medical care used once the choice has been made.
While the data do not have direct measures of many of the parameters of interest,
there are several proxies that I will use as instruments. For example, I do not observe
whether or not a parent has an insurance offer through their job nor do I observe the
generosity of the available coverage. I will proxy for these measures by employing a
commonly used instrument for insurance: the firm size of the worker. Larger firms have
lower loading fees than smaller firms, implying a lower per-employee insurance premium
and more generous coverage than their smaller counterparts.15 Thus workers in large
firms are more likely to receive offers of private insurance and to be privately insured
than those who are unemployed or employed by smaller firms. In this analysis, I use the
number of parents working in firms with 50 or more employees as an instrument for
insurance status (subsequently referred to as the “firm size variable”). The value of this
variable ranges from zero to two, with a zero value indicating that the child has no
parents working in a large firm, a value of one indicating that the child has one parent
working at a large firm, and a value of two indicating that the child has two parents
working at a large firm. Part-time employees are coded identically to full-time workers
while unemployed parents and those out of the labor force are coded as zeros.
Some firms impose a waiting period on new employees before they are eligible
for insurance benefits. Therefore, all else constant, workers with longer tenure are more
likely to be privately insured than those with shorter tenure. To capture this effect, I use
the number of parents who have worked at their current employer longer than one year as
another instrument for insurance status (subsequently referred to as the “tenure
15 Generosity of coverage encompasses the range of services covered and the level of cost-
sharing. More narrowly-defined measures of firm size will be explored in future work because the
dichotomous variable currently utilized does not approximate the relationship between firm size
and insurance provision and generosity as well as a more detailed measure.
variable”). This instrument takes on values of zero to two and is constructed in the same
way as the firm size variable described above. The assumption underlying the use of
these two family-level variables as instruments is that there is no independent correlation
between these employment characteristics and the healthcare utilization of the child.
In addition to the family-level variables, I use state-level variables as instruments
for insurance status. Currie and Gruber’s “simulated eligibility” instrument discussed
above has become the standard in the Medicaid literature. Identification is driven solely
by a measure that varies at the state level, thus its use as an instrument assumes that
people do not select state of residence based on Medicaid eligibility generosity. To
construct this instrument, I use the entire national sample of children in a given age-year
category from the Current Population Survey (CPS) and calculate the percentage of the
national sample that is eligible under each state’s income criterion. Because income
eligibility also differs by age in many states, the simulated eligibility measure varies at
the state-year-age level.
I also use the variation in state-level Medicaid enrollment procedures as an
instrument for insurance status. States vary with respect to the administrative burden
required to enroll in Medicaid. For example, some states require an asset test for
enrollment while others do not. Additionally, some states require a face-to-face interview
during the application process while other states allow parents to mail in the application.
On the whole, states reduced the administrative burden of Medicaid enrollment during
the late 1990s and early 2000s. These “barriers to enrollment” influence the decision to
enroll in public insurance, but presumably do not influence the decision to receive care,
making them a candidate instrument for insurance status. These non-cash costs are
represented in the above theoretical model as θ .
The measure used is an index of the various enrollment requirements states had in
place during the year of the survey round. The specific components of this index are:
presence of an asset test, joint Medicaid/SCHIP application form at initial enrollment,
joint Medicaid/SCHIP application form at redetermination, requirement of a face-to-face
interview at initial enrollment, requirement of a face-to-face interview at redetermination,
presumptive eligibility, being continuously eligible for at least 12 months after approval,
and acceptance of self-reported income as an income measure. The index varies at the
state-year level and takes on values from 2 to 8 in the sample. The index is increasing in
“ease” of Medicaid enrollment, therefore a higher value denotes a lower burden of
It is of note that in recent years states have begun to resurrect these administrative
requirements in response to budgetary concerns. Anecdotal evidence suggests that these
enrollment policies have an impact on the number of people signing up for Medicaid but
there is little quantitative evidence examining this claim.16 My first stage equation
showing the effect of these barriers on insurance status will provide new evidence on how
these changes in policy affect the number of people enrolled in Medicaid and private
State-level characteristics of private sector firms are also used as instruments in
the analysis. Specifically, I utilize a vector of state-level characteristics that reflect the
16 I am grateful to Mary Fredericks for providing feedback on these policies from a social
17 There is one recent study on this issue: Wolfe, Barbara, and Scott Scrivner, “The Devil May Be
in the Details: How the Characteristics of SCHIP Programs Affect Take-Up,” Journal of Policy
Analysis and Management, XXIV (2005), 499-522.
opportunity to enroll in employer-based insurance for employees in a given state for a
given year. I use three such variables: the percent of all firms in the state that offer
insurance to their employees, the percent of all firms that offer insurance that offer family
plans with no employee contribution, and the percent of all firms that require a waiting
period for insurance eligibility. Again, these instruments are proxying for the generosity
and availability of private coverage faced by the parent. It is worthwhile to restate the
assumption that underlies the use of these state-level instruments: that workers do not sort
across state based on employer insurance generosity.
4.2 Estimation procedure
After running OLS and probit models of the effect of insurance on utilization
measures, I employ two IV techniques. Models are run using two-stage least squares
(2SLS) with linear probability models (LPM). Although both the independent and the
dependent variables of interest are dichotomous in nature, the 2SLS-LPM approach is the
most commonly employed approach in the literature.
To account for the dichotomous nature of the dependent variables, I use a method
developed in Smith and Blundell (1986) and Terza (1999). The first step of this two-step
approach involves estimating a multinomial logit for insurance status using instruments
and covariates. The predicted values for public insurance and private insurance status are
obtained from the multinomial logit results. Residuals for public and private insurance
are then calculated as the actual values for these two indicator variables minus the
predicted values. The second step of the procedure is estimating a probit model for the
dichotomous dependent variable of interest, including the covariates (but not the
instruments), public and private insurance dummies, and the two residuals from the first
stage. Assuming that the instruments are valid, the inclusion of the residuals from the first
stage yields consistent coefficients on the public and private insurance variables.
All estimates from probit specifications (both instrumented and non-instrumented)
have been calculated such that their interpretation is one of average incremental effects of
insurance over uninsurance. For example, to obtain the average incremental effect of
public insurance over uninsurance I first perform the two-stage process and predict the
values of the dependent variable of interest when all sample members are uninsured
(coding uninsured=1 for all observations). An average of the predicted values of the
dependent variable is calculated. Then I calculate the predicted values of the dependent
variable when all sample members are publicly insured (coding public insurance=1 for all
observations) and the resulting average. The difference in these two averages is the
average incremental effect of public insurance over uninsurance. This calculation
facilitates the comparison of results from LPM models and non-linear methods.
All models include a correction for design effects and differential sampling
probabilities. Linear models include a cluster correction at the state level. Estimates for
non-linear models are based on 1,000 replications of a weighted bootstrap with
observations clustered by state. Normal theory approximation was used to construct test
statistics to perform inferences. No bias corrections were made to the bootstrap results of
the estimates because they are quite close to the coefficients obtained running the various
non-linear procedures on the entire original sample.18 All analyses were performed using
18 Original sample estimates and the mean of the bootstraps differed by less than a third of the standard
deviation obtained by the bootstrap.
The main source of data is the merged file of the 1999 and 2002 waves of the
Urban Institute’s National Survey of America’s Families (NSAF).19 The NSAF is a
nationally representative survey of non-institutionalized people under the age of 65. The
NSAF contains state identifiers and is also representative within-state for 13 states. The
child sample used for this analysis contains measures on demographics, health insurance,
health utilization, and other measures of child well-being for children ages 0-17.20 The
two pooled cross-sections contain complete data on roughly 45,000 children.
I am able to link the child data with data on their parents. Specifically, I utilize
information on parental education as an independent variable in the analyses and, as
mentioned above, the number of parents working in firms greater than 50 employees and
the number of parents working at their current firm for longer than one year as
instruments. Because I do not have information on non-resident parental employment
variables, I assign the mean value calculated from the non-missing values of these
variables to children living in single-parent households.21
Appendix Table B contains information on basic demographic variables available
in the NSAF. These variables are used as controls in the regression models. The sample
contains children ages 0-17, with a mean age of 8.36 years. Nineteen percent of the
children in the sample live in families with incomes at or below the federal poverty level
19 The 1997 wave of the survey was not used since information on many of the instrumental
variables was not available for this year.
20 The NSAF was designed to track changes in family well-being during a time of major welfare
reform. Its focus is on low-income families. Other examples of well-being indicators measured
for children include child care arrangements, psychological well-being, and program
21 Although mean replacement leads to bias in non-linear models, the results are robust to the
usage of this technique. All models have been run with and without these observations and the
results are quite similar. Non-resident parents are coded as being high school graduates. Again,
the results are robust to this assumption.
and 24% of children in the sample live in families with incomes between 100% and
200% of the federal poverty line. Approximately 17% of the sample is black and 18% of
the sample is Hispanic. Of the low-income children in the sample, 26% of them are black
and 30% of them are Hispanic. Five percent of all sample children are in fair or poor
health. Health status exhibits a strong income gradient with 9% of low-income children
having fair or poor health compared with 3% of higher-income children. Ten percent of
the entire sample has a chronic health condition that limits activity. Approximately 13%
of low-income children have a limiting health condition while 8% of non-poor children
have such a condition. Immigrants comprise roughly 4% of the entire sample and 6% of
the low-income subsample. Approximately 35% of children in the sample live in single-
parent households, with 52% and 23% of low-income and higher-income children,
respectively, in such households.
Information on state Medicaid eligibility criteria is taken from the National
Governor’s Association annual Maternal and Child Health Updates.22 These updates also
serve as the source for Medicaid enrollment procedures.23
The simulated eligibility variable is constructed with data from the 1999 and 2002
Current Population Survey (CPS). State-level data on private firm characteristics are
drawn from the Insurance Component (IC) of the Medicaid Expenditure Panel Survey
(MEPS). The IC tracks trends in employer-provided health insurance by measuring
national- and state-level characteristics of private firms and their employees.
The main independent variables of interest are whether a child is privately
insured, publicly insured, or uninsured at the time of survey. The dependent variables are
22 Available: http://www.nga.org/center/topics/1,1188,D_8069,00.html. Accessed: 4/01/05.
23 Data are available beginning in 2000. The state-level enrollment procedures in 2000 are
assigned to the children in the 1999 wave of data.
three access and utilization measures: whether or not a child visited any medical provider
in the past 12 months, whether or not a child has a regular source of care outside of an
emergency room, and whether or not a child had a well-child visit to a medical provider
in the past 12 months. Future work will examine the effects of insurance on the number
of provider visits received in the past 12 months.
Table 1 contains sample means for the dependent and independent variables used
in the analysis. These means are also calculated separately by income level.
Approximately 23% of the sample is publicly insured while 66% and 11% are privately
insured and uninsured, respectively. These percentages vary greatly by income, with a
higher percent of low-income children having public insurance (37%) and no insurance
(19%) than their higher-income counterparts. The percentage of children in the sample
with private insurance coverage also exhibits a strong income gradient, varying from
37% for poor children to 88% for non-poor children. The percentage of children with
public insurance exhibits a correspondingly negative gradient, with 45% of low-income
children being covered by public insurance compared to 6% of higher-income children.
Approximately 19% of low-income children in the sample are uninsured. In contrast,
only 5% of higher-income children have no insurance.
The proportion of the sample that had any provider visit in the past year is 86%,
and 68% of the sample had a well-child visit. An overwhelming majority (92%) of
children in the sample have a usual source of care that is not an ER. An income gradient
exists for the utilization measures but it is much smaller than that seen for insurance
status. For example, the percentage of children having had any provider visit is 82% for
poor children and 90% for less-poor children.
Simple cross-tabs of utilization by insurance status are shown in Table 2. Again,
these calculations are performed for the entire sample as well as for different income sub-
Table 2 shows a strong association between having health insurance and utilizing
health care.24 Uninsured children in the sample are less likely to have had any provider
visit in the past year, are less likely to have had any well-child visit, and are less likely to
have a usual source of care outside of the ER. Sixty-four percent of uninsured children
had a provider visit in the past year, compared to 90% of privately insured children and
90% of publicly insured children. Less than half (47%) of the uninsured children in the
sample received a well-child visit in the past year, while 68% of privately insured and
76% of publicly insured children received such a visit. Insured children in the sample had
extremely high rates of having a usual source of care (96% for privately insured children
and 92% for publicly insured children). A large majority (73%) of uninsured children
also had a usual source of care, although this percentage is smaller than that of the
insured children in the sample.
Interestingly, the positive association between having insurance and utilizing care
exists for children in both low-income and higher-income families. The differences in
utilization between publicly insured and privately insured children are on the whole not
as pronounced as those between children with any insurance compared with those
children without insurance. Publicly insured low-income children are slightly more likely
24 All pairwise comparisons in Table 2 have been calculated using a correction for multiple
comparisons. A regression without a constant was run for each dependent variable of interest on a
public insurance dummy, a private insurance dummy, and an uninsured dummy. Pairwise
comparisons were made by testing whether or not the coefficients on these dummies were equal
to each other. See Stata, “How Can I Form Various Tests Comparing the Different Levels of a
Categorical Variable after ANOVA or Regress?” Available:
www.stata.com/support/faqs/stat/test1.html. Accessed: 8/18/05.
to have had any provider visit in the past year than their privately insured peers (89% vs.
85%, statistically significant at the 10% level). In contrast, there is no significant
difference in having seen a provider between privately and publicly insured children in
higher-income families. Public insurance is significantly associated with higher rates of
well-child care than private insurance. This is likely due to the fact that public insurance
plans must provide free preventive visits while private insurance plans vary in their
coverage of preventive visits.25 Sixty-eight percent of privately insured children in the
sample have received a well-child visit in the past year compared to 76% of publicly
insured children. This difference by insurance status is seen for both higher-income and
low-income children. In contrast to the probability of having had a well-child visit, the
probability of having a non-ER usual source of care is higher for privately insured
children than for publicly insured children. Ninety-six percent of privately insured
children have a usual source of care, while 92% of publicly-insured children have a usual
source of care. While this difference is statistically significant, it is appropriate to note
that a high level (over 90%) of children with either public or private insurance have usual
places where they receive care.
6.1 First stage estimates
Parameters of special interest from the first stage equations using linear
probability models are shown in Table 3; qualitatively similar results occur with
multinomial methods. The full set of results is displayed in Appendix Table C. Both the
barriers to enrollment index and the simulated eligibility instrument are positively and
25 General Accounting Office, Health Insurance: Coverage Leads to Increased Health Care
Access for Children GAO/HEHS-98-14 (Washington, D.C.: GAO, 1997).
significantly associated with being publicly insured. The firm size variable and the tenure
variable are negatively correlated with having public insurance and are strongly
statistically significant. The percent of firms offering insurance in a state is negatively
and significantly associated with being publicly insured. Neither the percent of firms that
offer a family plan with no employee contribution nor the percent of firms with a waiting
period have statistically significant (at the 5% level) associations with public insurance.
Using an F-test on the exclusion of these two variables, one cannot reject the null that
they have no explanatory power.26
The F-statistic for excluding the simulated eligibility and enrollment variables is
9.34, with an associated p-value of less than .0004. Performing an exclusion test on the
state-level firm variables yields a F-statistic of 3.25 with a p-value of 0.029. The family-
level instruments exhibit the strongest association with public insurance status. Testing
their exclusion yields an F-statistic of 56.20 and a p-value of less than 0.0000.
From these results it is fair to conclude that employment characteristics of parents
have an incredibly strong relationship to being publicly insured and that simulated
eligibility and the enrollment index have a weaker but still reasonably significant
association with public insurance. If we employ the Staiger and Stock (1997) rule-of-
thumb of an F-statistic of 10 being the threshold for the strength of an instrument, it is
reasonable to conclude that the family-level variables are strong instruments, that the
enrollment index and simulated eligibility variables are marginally strong instruments,
and that the state-level firm characteristics taken from the MEPS are weak instruments
for public insurance status.
26 P-value < 0.219.
The enrollment index variable is negatively and significantly associated with
being privately insured. The simulated eligibility instrument is also negatively associated
with private insurance status, however this association is not significant. The number of
parents working in a large firm and the number of parents working at their current firm
for over a year are both very strong predictors of private insurance status. The percent of
firms that offer insurance is positively and significantly correlated with private insurance
status. Similar to the public insurance results, neither the percent of firms that offer a plan
with no employee contribution nor the percent of firms with a waiting period are
independently predictive of insurance status.27
Consistent with the results for public insurance, the family-level instruments
exhibit the strongest correlation with private insurance. Excluding the firm size and the
tenure instruments yields an F-statistic of 155.23 (p < 0.000). The test of the exclusion
restriction for the state-level MEPS variables is significant (F = 3.91, p < 0.01) though
much smaller than the test statistics of the family-level variables, in keeping with the
results seen for public insurance. In contrast to their relatively strong predictive power for
public insurance status, the combination of the enrollment index variable and the
simulated eligibility variable is not predictive of private insurance status. The F-statistic
for excluding the simulated eligibility measure and the enrollment index measure is 2.91
(p < 0.06) in the model for private insurance status, which is much lower than the 9.34
value seen in the public insurance status. For private insurance status the family-level
instruments are the only ones that “pass” the rule-of-thumb test for appropriate
correlation between the instrument and the endogenous regressor.
27 As with the public insurance case, one cannot reject the null that they have no effect using an
F-test. The p-value of this test is p < 0.747.
6.2 Comparison of ordinary least squares (OLS), probit, two-stage least squares (2SLS-
LPM) & two-stage non-linear residual included (2SNLRI) results
Table 4 displays the results from several models estimating the effect of insurance
status on the probability of having had any provider visit in the past year. The complete
set of coefficients from the linear models is displayed in Appendix Table D.
OLS and probit models for the effects of insurance on having any visit (without
controls) yield similar results. Public insurance is associated with roughly a 25
percentage point increase in the probability of having any provider in the past year in
both the LPM and probit models. Private insurance is also associated with a roughly 25
percentage point increase in the probability of having any provider visit in both the OLS
and probit specifications. All of these estimates are significant at the p < 0.01 level.
The coefficients on public and private insurance in the OLS and probit models
with control variables are lower than those in the models without controls and exhibit
greater differences from each other than the models with controls. The coefficient on
public insurance in the OLS model is 0.211 and is 0.176 in the probit model. The
estimates for private insurance are 0.174 and 0.149 for the OLS and probit
specifications, respectively. Again, all of these estimates are significant at the p < 0.01
Unlike the non-instrumented models, the linear and non-linear instrumental
variables specifications yield vastly different results from each other. The coefficient on
public insurance in the 2SLS-LPM specification is 1.071, an estimated effect size that is
out of the [0,1] range. The 2SLS-LPM coefficient on private insurance is 0.924, which
is within range but is a highly implausible effect size. Although standard errors increase
in a 2SLS-LPM set-up, both the effect of public insurance and the effect private
insurance remain significant at the 0.01 level in the 2SLS results.
In addition to producing out of range coefficient estimates, 2SLS-LPM estimation
yields predicted probabilities above 1 and below 0 for many observations in the sample.
Roughly 30% of all observations in the sample are predicted to be less than 0 or above 1
in 2SLS-LPM models for each of the three dependent variables.28 The large percent of
out-of-range predicted probabilities in the 2SLS-LPM coupled with the presence of an
out-of-range point estimate provides compelling evidence that this model is inappropriate
for the dependent variables of interest in this study and that the use of a non-linear
estimation technique is necessary.
Utilizing the 2SNLRI technique outlined in Section IV yields point estimates that
are more than double those in the probit specification but half of those seen using 2SLS-
LPM. The average incremental effect of being publicly insured versus having no
insurance on the probability of having received a provider visit is about 45 percentage
points. The comparable figure for private insurance compared to no insurance is roughly
42 percentage points. Both coefficients are statistically significant at the 0.01 level, but as
we would expect both of the corresponding confidence intervals are larger than their
A formal paired test of the differences between the coefficients of the 2SNLRI
model and the probit model showed that the average incremental effects of insurance
(both public and private separately) are statistically different at the seven percent level in
the two estimation procedures. Additionally, the hypothesis of equality of the average
28 Any visit: 35%, Any well-child visit: 33%, Has a usual source of care: 28%. 2SLS-LPM results
for the any well-child visit and the has a usual source of care models are not shown in the text of
the paper but are provided in Appendix Tables E and F, respectively.
incremental effects of insurance from the 2SLS-LPM and the 2SNLRI models was
rejected at the five percent level. All comparisons were made on bootstrapped average
incremental effects obtained from 1,000 replicates corrected for clustering at the state
level. A Bonferroni correction was made to account for multiple comparisons.29 Normal
theory approximation was used to construct test statistics; confidence intervals based on
percentiles of the results from the bootstrap yield similar inferences.
6.3 Comparison of models with various subsets of instruments
We see in the above section that the effect estimates are quite sensitive to the
estimation procedure utilized. We now turn to the question of whether the estimated
effect sizes are sensitive to the choice of instrument set employed. Table 5 displays the
results from models using different sets of instruments.
The estimates from the different specifications are quite different from each other
and from the non-instrumented results. Taken as a whole they suggest that the estimates
are quite sensitive to the instrument set employed. However, for the any visit models and
the any well-child visit models a consistent pattern emerges for all specifications except
for the one that includes only the family-level variables as instruments. The other four
specifications all produce estimates that are higher than the non-instrumented estimates.
All of these IV results are significant at the 10% level or better. The estimated average
incremental effects of public insurance over uninsurance for having any visit range from
0.363 to 0.532 for these specifications. The corresponding range for private insurance is
0.321 to 0.502. Similar magnitudes are seen in the well-child models, with the estimates
29 The Bonferroni procedure is an overcorrection in this case because there exists a strong positive
correlation between the differences-in-differences between estimation procedures for the private
and public coefficients. The Bonferroni procedure assumes zero correlation.
for public insurance ranging from 0.377 to 0.519 and from 0.233 to 0.524 for private
The results for having any usual source of care do not display the same consistent
pattern as those for any visit and any well-child visit. The specification using only the
enrollment and simulated eligibility instruments produces insignificant results and the
specification using only the family-level instruments produces an insignificant result for
public insurance. The other three specifications yield estimates that are higher than the
non-instrumented estimates, as seen for any visit and any well-child visit. These
specifications yield estimated average incremental effects ranging from 0.187 to 0.282
for public insurance and 0.186 to 0.287 for private insurance.
The effects of both private and public insurance are consistently lower across all
specifications for having a usual source of care than for having any visit and having any
well-child visit. For example, the estimated average incremental effects of public
insurance over uninsurance and private insurance over uninsurance for having a usual
source of care in the specification with all of the instruments are 0.282 and 0.287,
respectively. The corresponding estimates for having any visit are 0.449 and 0.418 and
for having any well-child visit are 0.456 and 0.357. These results provide suggestive
evidence that insurance has a stronger effect on having contact with a healthcare provider
than on having a usual source of care.
There are several limitations of this study that merit careful discussion. First, the
independent variable of interest—insurance status—is measured at a point in time.
Research shows that insurance status is a dynamic phenomenon, with many children
churning between different insurance categories throughout the year.30 It is possible that
capturing the effects of duration of insurance coverage (or lack of) may be a more
relevant independent variable of interest.
Second, employing instrumental variables techniques decreases the precision of
the estimates of interest. Because of this decrease in precision, I am unable to perform
sub-group analyses. For example, existing literature suggests that insurance may have
differing effects on utilization for different race groups. Additionally, insurance’s
influence on utilization may differ for children from families of differing income levels
or for children of different ages. Due to insufficient precision, I am unable to examine
any of these potentially interesting sub-group differences.
Third, a serious limitation of all instrumental variables studies is that the
assumption that the instrument/s is/are uncorrelated with the error term is untestable.
While overidentification tests and other informal checks can be used to provide
suggestive evidence regarding this assumption, it is impossible to know with certainty
whether the instruments are valid. However, as mentioned earlier, it is possible to provide
suggestive evidence about the validity of the instruments.31
Fourth, there is a particular cause for concern with the family-level instruments.
Although the firm size variable has commonly been used as an instrument in the health
insurance literature and has “passed” an overidentification test in a recent study of a
similar nature to this one, it is plausible that there are observable and unobservable
30 See Mathematica’s “Children’s Health Insurance Patterns: A Review of the Literature.”
Available: http://aspe.hhs.gov/health/uninchil/front.htm. Accessed: 7/26/05.
31 Future work will examine the validity of the instruments via an examination of the criteria set
forth in Angrist, Joshua, Guido Imbens, and Donald Rubin, “Identification of Causal Effects
Using Instrumental Variables,” Journal of the American Statistical Association,
XCI (1996), 444-455.
characteristics that are related to both a parent’s choice of firm and their choice of
healthcare utilization for their children.32 For example, a parent whose child has a chronic
condition may be more likely to seek employment at a large firm, knowing that the health
insurance benefits are more generous at large firms than at small firms. If this parent has
a higher propensity to seek healthcare for the sick child than a parent of a child without a
chronic condition, then the firm size instrument is not a valid instrument for insurance
status and the resulting coefficient will be biased in an upwards direction. The validity of
the tenure variable is similarly tenuous. It is possible that workers with longer tenure are
more responsible and attentive workers than those with shorter tenure. These traits may
also influence healthcare decisions that they make on their children’s behalf. If such
unobserved traits drive both job tenure and healthcare utilization, the tenure variable is an
inappropriate instrument and again the resulting coefficient will be biased. While
plausible conjectures may be made about the bias, it is impossible to unambiguously sign
it. Appendix Tables G and H show the mean values of the independent variables across
different values of the firm size and tenure instruments. That the means of observable
characteristics differ across values of the instruments causes concern that unobservable
characteristics may also differ across values of the instruments.
The family-level variables are the strongest predictors of insurance status in the
first stage models. It is important to note that if these instruments are excluded from the
analysis due to their potential correlation with the error term, there are no other
instruments that strongly predict private insurance status. Omitting these variables from
the analysis may lead to weak instruments bias as discussed in Staiger and Stock (1997).
Potential ways to deal with this issue are discussed below in the future directions section.
32 Long, Coughlin, and King (2005) perform an overidentification test on their instruments.
Because of the limited number of cross-sections available in the data, I am unable
to include state fixed effects in the models. It is possible that the state-level instruments
are picking up unobserved characteristics that may be correlated with child healthcare
utilization. It is worthwhile to restate the assumption that validates the use of the state-
level variables under consideration as instruments: that these variables are uncorrelated
with unmeasured variables that influence the healthcare utilization decision.
VIII. Future directions
I am interested in extending and improving upon this work in the near future. The
first priority in continuing with this research is to identify and perform an
overidentification test in a non-linear context on weighted data.33 Results from
overidentification tests will help guide the selection of appropriate instruments to include
in the analyses. The most interesting comparisons will be between results derived from
different sets of instruments that both “pass” an overidentification test and display
appropriate power in first-stage estimation.
To complement the overidentification tests, I also hope to provide suggestive
evidence on the validity of the instruments. LoSasso and Buchmueller (2004) test their
version of the “simulated eligibility” variable by running models on single men—a group
ineligible for public insurance. This “test” serves as a reassurance that their instrument is
not picking up state-specific characteristics that are correlated with public insurance
eligibility and may also be correlated with the dependent variables of interest. I can
33 As a first step, I ran overidentification tests for each of the models in this paper in a linear
(2SLS-LPM) specification without weights. Each model “passes” this test. However, we know
that the 2SLS-LPM results are inconsistent. Thus the overidentification results are of dubious
implement this test for both the simulated eligibility instrument and the enrollment index
instrument with data from the NSAF childless adult sample.
I am also interested in including other instruments in future analyses. For
example, I would like to construct a simulated eligibility variable capturing state-level
generosity of public insurance with respect to parental coverage. Research suggests that
increasing public insurance eligibility thresholds for parents has spillover effects on the
enrollment of children.34 I also plan to include more instruments from existing literature
in the robustness tests of future drafts of this work. For example, Long, Coughlin, and
King (2005) use parental attitudes toward welfare receipt as an instrument for insurance
status. I will conduct a more extensive literature review of instruments used for health
insurance status studies outside of my target population (children) to see if there are other
plausible instruments to test.
As mentioned earlier, there are few instruments that strongly predict private
insurance status and those that do may violate the assumption of having no independent
influence on the dependent variables of interest. If I am unable to find other instruments
that both predict private insurance status and have no direct influence on utilization
measures, it may be appropriate to perform the robustness tests for models that
dichotomize insurance status into insured and uninsured as opposed to those that compare
public insurance to private insurance to uninsurance. Grouping the publicly and privately
insured may be an acceptable compromise if both insurance types tend to confer similar
benefits with respect to access to care. Results from this paper suggest that this may
34 See Institute of Medicine, Health Insurance is a Family Matter (Washington, D.C.: National
Academy Press: 2002).
indeed be the case for having a usual source of care and the probability of having any
provider visit in the past year.
As discussed above in the limitations section, there is a concern that the state-
level instruments may be picking up effects that are correlated to the outcome variables
of interest. Including state fixed effects would control for all time-invariant state
characteristics and would help lessen this possibility. This paper utilizes pooled cross-
sections from 1999 and 2002, a period over which there was little within-state variation
in Medicaid eligibility. The inclusion of state fixed effects would likely greatly reduce the
variation in my state-level instruments. There is an additional cross-section available for
the NSAF that was collected in 1997. Between the years 1997 and 1999 there was a great
deal of within-state expansion in Medicaid eligibility, which suggests that the recovery of
these observations may allow for the inclusion of state fixed effects. I did not use the
1997 wave of the NSAF in this paper because data on the “barriers to enrollment” are not
(to my knowledge) publicly available for this year. I would like to spend some time in the
near future pursuing whether or not this data exists and how I might obtain it.
In addition to testing new instruments, I would like to test different non-linear IV
estimation techniques. Several other non-linear techniques have been proposed as
alternatives to 2SLS-LPM and knowing the robustness of estimates resulting from these
different estimation techniques will be instructive.35 If possible I would also like to
perform some simulation work on the performance of these various techniques with
respect to consistency and precision when estimating dichotomous dependent variables
that are in ranges in which the LPM is inappropriate. Many dichotomous dependent
35 For example, Stata has included an ivprobit command in its newest version. Another potential
method is the trivariate probit model.
variables of interest in health services research fall in these ranges and it is important to
understand which techniques are appropriate for these types of analyses.
IX. Discussion and Conclusions
The results in this paper suggest that IV estimates of the effect of insurance status
on children’s healthcare utilization are sensitive to changes in both instruments used and
estimator employed. My results show that non-linear techniques may be more appropriate
for estimating IV models of dichotomous dependent variables with values close to one.
The point estimates of models using various instrument sets vary greatly and have wide
and often overlapping confidence intervals. Thus, putting too much focus on the point
estimates themselves may be inappropriate and it is not possible to make definitive
statements about the direction of the bias in the insurance/utilization relationship based
on these results.
Setting this caveat aside, it is interesting that in all but one of the specifications
the IV result was larger than the OLS result. It is difficult to understand on a priori
grounds why the bias would work in this direction for children. Enrolling a child in
Medicaid is costly with respect to time and effort and it is reasonable to hypothesize that
parents bearing these costs do so because their children are in need of care. Additionally,
hospitals and doctors may enroll uninsured children onto Medicaid when they arrive at
the ER or the office to receive care, causing Medicaid children to “look sicker” than
uninsured children. Both of these cases would result in an upwards bias on the public
Unlike public insurance, enrollment in private insurance has dollar costs
associated with it. Again theory suggests that these costs would be borne only if the
potential benefit exceeds them, which is more likely for a sick child than a healthy one.
This adverse selection argument has been of concern to researchers for decades and was
one of the motivations for the RAND HIE.
The results in this paper are inconsistent with these two selection processes. Some
researchers have found that those who end up with insurance demand less healthcare than
one would expect based on their observable characteristics.36 In the context of children,
this “favorable selection” implies that children with insurance are less likely to utilize
care than their uninsured peers, possibly because they are healthier or otherwise less
inclined to need care. Long, Coughlin, and King (2005) posit that individuals with strong
attachments to safety net providers serve as one potential example of favorable selection.
It is possible that children who frequently use these providers are less likely to have
Medicaid but they may be more likely to use healthcare.
Another potential source of favorable selection is that employers screen potential
employees and hire the healthiest people in their candidate pool. If this screening does
happen then employed adults are healthier than their unemployed peers. Employed
people face lower premiums and more generous coverage than the unemployed which
suggests that they have higher rates of insurance. If this screening process happens along
dimensions that are unobserved in the data and employed people indeed are healthier and
using less medical care than their unemployed counterparts, the resulting bias on the
effect of insurance would be downward. This argument could be extended to children if
health status is correlated across generations and the children of the employed are
healthier than the children of the unemployed.
36 An example: Pauly, Mark, “Effects of Insurance Coverage on Use of Care and Health
Outcomes for Non-poor Young Women,” mimeo, University of Pennsylvania, 2004.
Another explanation posited in previous work for the potential of a downward
bias in OLS is measurement error in the insurance status variables.37 If there is classical
measurement error in the insurance status variables then we would expect the estimates
arising from OLS to be attenuated towards zero. However, it is unclear that any
measurement error of insurance status would be classical in nature. It is likely that
measurement error of insurance status is correlated with income, with people at high
incomes unlikely to misreport Medicaid status since their incomes put them above the
eligibility criteria.38 Another potential source of measurement error may arise from states
designing their SCHIP programs to look and operate like private insurance plans. For
example, families often receive SCHIP insurance cards that look similar to cards for
private insurance. Recent work shows that these policies lead to a misreporting of
insurance status among SCHIP-enrolled families.39 This measurement error is of concern
only for the part of the income distribution eligible for SCHIP. It is possible that this non-
random measurement error of insurance status is biasing the effect of insurance on
utilization, but it may not be biasing it towards zero as the random measurement error
case would imply. Furthermore, the SCHIP example motivates the possibility that
individuals are more likely to misreport whether they are publicly or privately insured
than whether they are insured versus uninsured. These various examples of potential
measurement error sources raise doubt about the assumption that measurement error of
insurance status is classical in nature and that its effects are unambiguously attenuating
the effect estimates.
37 I am grateful to Tom Selden for pointing this out.
38 Yacizi, Ezel, “Does Medicaid Improve Infant and Child Health?” Ph.D. dissertation, City
University of New York, 1997.
39 LoSasso and Buchmueller (2004)
Neither theory nor existing empirical results can definitively sign the bias of the
effects of interest. This does not mean that we know nothing about the effect of insurance
on children’s healthcare utilization. While the results from this study show that the exact
magnitude of the effect may be unclear, they suggest that there is indeed a positive effect
of both private and public insurance on access to care measures for children. All of the
models show a positive relationship between both private insurance and public insurance
and utilization and many of them find a statistically significant association. Taken as a
whole, the results from this paper support the conclusion that insurance is efficacious in
facilitating healthcare utilization for children.
Table 1-Descriptive statistics from the National Survey of America's Families, 1999 and 2002
Variable namesAll children
Any well-child care
Any usual source of care
Standard errors are in parentheses and account for clustering and differential sampling probabilities. Low-income refers to
children in families with incomes at or below 200% of the federal poverty level. Higher-income refers to children in families with
incomes above 200% of the federal poverty level.
Table 2-Utilization by insurance status
% with any
% with any well
% with usual
source of care
Low income (n=18,577)
Higher income (n=26,796)
All pairwise comparisons between public vs. uninsured and private vs. uninsured are significant at the p < .01 level
*Denotes that the difference between public and private is significantly different at the p < .10 level
**Denotes that the difference between public and private is signficantly different at the p < 0.05 level
All comparisons have been calculated using a correction for multiple comparisons.
Standard errors are in parentheses and account for clustering and differential sampling probabilities. Low-
income refers to children in families with incomes at or below 200% of the federal poverty level. Higher-
income refers to children in families with incomes above 200% of the federal poverty level.
Table 3-First stage regressions
% offer insurance
% offer plan with no employee
% with wtg. period
Tests of joint sig.
State-level public = enrollment index & simulated eligibility
State-level firm = % offer insurance, % offer plan with no employee contribution
Family-level = number of parents working in a large firm, number of parents at current job > 1 yr
Publicly insured Privately insured
Linear probability results. Probit and multinomial logit estimation yields similar qualitative results. All models
include controls for immigrant status, single parent household, race, sex, age, poor health, presence of a limiting
condition, mother education, father education, and a year 2002 dummy. All models account for clustering and
differential sampling probabilities.
Table 4-Two-stage least squares and two-stage nonlinear residual included estimation
Dependent variable: Having any provider visit in the past year
n = 43,373 for all models
All models significant at the p < 0.01 level
2SNLRI = two-stage non-linear residual included model
All models with controls include the following covariates: immigrant status, single parent household, race, sex, age, poor health, presence of a limiting
condition, mother education, father education, and a year 2002 dummy. All models account for clustering and differential sampling probabilities.
Standard errors are in parentheses. Standard errors for all non-linear models have been bootstrapped.
Table 5-Average incremental effects of insurance status over uninsured
Results from 2SNLRI estimation
Publicly insured0.176 ***
Any well-child visit
Publicly insured 0.214 ***
Has usual source of care
Publicly insured 0.136 ***
n = 43,373 for all models
significant at the 1% level: *** significant at the 5% level: ** significant at the 10% level: *
All models include controls for immigrant status, single parent household, race, sex, age, poor health, presence of a limiting condition, mother education, father education, and a year
2002 dummy. All models account for clustering and differential sampling probabilities. Standard errors are in parentheses and have been bootstrapped.
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