What Do Longitudinal Data on
Millions of Hospital Visits
Tell us About the Value of
Public Health Insurance as a Safety Net
for the Young and Privately Insured?
Amanda E. Kowalski
Yale University and NBER
February 2015
What Do Longitudinal Data on Millions of Hospital Visits
Tell us About the Value of Public Health Insurance as a Safety Net
for the Young and Privately Insured?
• Young, privately insured individuals with
hospital visits for diagnoses that require more
hospital visits in future years are more likely to
transition to public health insurance in future
years
• If we ignore the longitudinal transitions in the
data, we miss over 80% of the value of public
health insurance as a safety net
What Do Longitudinal Data on Millions of Hospital Visits
Tell us About the Value of Public Health Insurance as a Safety Net
for the Young and Privately Insured?
• What the prior literature does not tell us
• What my data can tell us – stylized facts
• How I incorporate my data into a framework for
valuing public health insurance
• What we learn from the framework, along with
robustness
The longitudinal value of health insurance is much
greater than the sum of its cross-sectional parts
The current private health insurance system does not
offer long-term protection against financial risk
• I consider the value of public health insurance as a
“safety net” that fills gaps in the current private system
– Previous literature focuses on design and regulation of
private health insurance contracts to mitigate this risk
• Cochrane (1995), Pauly (1995)
• I use longitudinal data and a longitudinal framework
– Previous literature focuses on the value of public heath
insurance for those who have already been caught by it,
using cross-sectional data and a cross-sectional framework
• Medicare: Finkelstein and McKnight (2008), Khwaja (2010),
Barcellos and Jacobson (2014)
• Medicare Part D: Engelhardt and Gruber (2011)
• Medicaid: Finkelstein, Hendren, Luttmer (2014)
What Do Longitudinal Data on Millions of Hospital Visits
Tell us About the Value of Public Health Insurance as a Safety Net
for the Young and Privately Insured?
• What the prior literature does not tell us
• What my data can tell us – stylized facts
• How I incorporate my data into a framework for
valuing public health insurance
• What we learn from the framework, along with
robustness
The longitudinal value of health insurance is much
greater than the sum of its cross-sectional parts
I use longitudinal data on almost all
hospital visits in New York from 1995-2011
• Using my SPARCS data and population data, I
create a balanced panel to represent New York
State population
• I focus on individuals who are young and
privately insured in 1995 to isolate the value
of the safety net
Just for the stylized facts, I focus on individuals with
“persistent diagnoses,” likely to drive the value of private
health insurance as a safety net
ICD-9 Diagnosis
Code
403
282
277
707
710
340
250
414
595
345
295
555
Description
Chronic Kidney Disease (hypertensive renal disease)
Hereditary Anemia
Cystic Fibrosis
Ulcers
Lupus
Multiple Sclerosis
Diabetes
Heart Disease (Coronary Atherosclerosis)
Urinary Tract Infection
Epilepsy
Schizophrenic Disorders
Inflammation of Intestinal Tract
Average Subsequent
Years with Hospital Visits
through 2011
4.9
4.7
3.6
3.4
3.4
3.2
3.1
3.1
3.1
3.0
2.9
2.9
Young, privately insured individuals with persistent
diagnoses have higher costs in future years, and they
are more likely to transition to public insurance in
future years
Even after imposing an annual upper bound of 17.9% of individuals with persistent diagnoses
$30K, cumulative costs are $58K by 2011 for
have public coverage in 2011, in contrast to 3.7%
persistent diagnoses vs. 13K for other diagnoses with other diagnoses
What Do Longitudinal Data on Millions of Hospital Visits
Tell us About the Value of Public Health Insurance as a Safety Net
for the Young and Privately Insured?
• What the prior literature does not tell us
• What my data can tell us – stylized facts
• How I incorporate my data into a framework for
valuing public health insurance
• What we learn from the framework, along with
robustness
The longitudinal value of health insurance is much
greater than the sum of its cross-sectional parts
Simple indifference condition for valuing
public health insurance
• Rooted in frameworks used in the literature
With public insurance
Without public insurance
• Closed form solution for ρ under CARA
Goal: calculate how much we miss by using
cross-sectional in lieu of longitudinal data
• Special Cases of the Value of Insurance
• Ratio of interest
Contrast to other frameworks that produce
the same value with cross-sectional or
longitudinal data
• Kowalski (2015)
• Handel, Hendel, and Whinston (2013)
The cross-sectional value of insurance from our framework φ is
almost the same as the alternative cross-sectional value of
insurance μ
Implement the indifference condition
empirically
• Costs in actual world with public insurance:
where:
• Costs in counterfactual world without public insurance:
where:
• Uses all paths observed in the data, people with public
coverage either gain private coverage or go uninsured
• Examine robustness to wide range of parameters
What Do Longitudinal Data on Millions of Hospital Visits
Tell us About the Value of Public Health Insurance as a Safety Net
for the Young and Privately Insured?
• What the prior literature does not tell us
• What my data can tell us – stylized facts
• How I incorporate my data into a framework for
valuing public health insurance
• What we learn from the framework, along with
robustness
The longitudinal value of health insurance is much
greater than the sum of its cross-sectional parts
Longitudinal value of insurance much
larger than cross-sectional value for a large
range of risk aversion parameters
Red dashed line shows traditional framework that gives the same answer for longitudinal
And cross-sectional data
Robustness to Parameters: α
Across a broad range, lose over 90% of value
Even though the levels vary a lot with α, the ratio stabilizes
Rather than calibrating one value,
consider robustness to a large range
• All necessary parameters
– α, coefficient of absolute risk aversion
– M, upper bound for annual individual costs
– T, number of years of data in sample
– N, percentage of population in sample
• Private Information on Persistent Diagnoses
• Robustness to Including Uninsured
Robustness to Parameters: M
Across broad range, lose over 90% of value
At very small values of M, there is not much risk, so all three values are close.
We choose 30K as our baseline value because that is where the ratio stabilizes.
As M gets really large, variability within a period increases while mean changes little,
so cross-sectional value increases relative to risk-neutral value
Both are small relative to longitudinal value – frequent visits dominate expensive visits
Robustness to Parameters: T
Across broad range, lose over 90% of value
Use all years as our baseline value.
Ratio stabilizes after about 8 years. MEPS only has 2.5 – not long enough for values to diverge.
Robustness to Parameters: N
Across broad range, lose over 90% of value
Full sample contains 1.69 million individuals.
MEPS is approximately 0.3% of our sample. Results at that size are highly variable.
Results from 100 draws of the size of the MEPS range from 8.2% of 95.7% - too small for tails!
Furthermore, this calculation assumes MEPS has 17 years of data, but it only has 2.5!
Robustness to Private Information on
Persistent Diagnoses
Even with extreme private info, results persist
Robustness to Including Uninsured
These are baseline, somewhat less intuitive
What Do Longitudinal Data on Millions of Hospital Visits
Tell us About the Value of Public Health Insurance as a Safety Net
for the Young and Privately Insured?
• What the prior literature does not tell us
• What my data can tell us – stylized facts
• How I incorporate my data into a framework for
valuing public health insurance
• What we learn from the framework, along with
robustness
The longitudinal value of health insurance is much
greater than the sum of its cross-sectional parts
Appendix Slides
Hospital Count – SPARCS vs. AHA
Inpatient Cost – SPARCS vs. MEPS
Insurance Coverage – SPARCS vs. CPS
• Indifference condition with private
information:
• Closed form solution for λ:
Robustness to Including Uninsured (cont.)
• Theoretically possible for the longitudinal value of
insurance ρ to be equal to zero, even if the risk neutral
value of insurance λ is positive