The Determinants of Rising Inequality in
Health Insurance and Wages
Rong Hai∗
July 13, 2015
Abstract
Over the last 30 years in the U.S., less educated workers have experienced a sharp decline in health
insurance coverage rate and stagnant wage growth. In contrast, more educated workers’ health insurance
coverage rate has stayed relatively stable and their wages have rapidly grown. This paper investigates
the determinants of the increase in inequality in health insurance coverage and wages by estimating an
overlapping generations equilibrium model of labor and health insurance markets’ demand and supply.
The estimated model is used to quantify the effects of changes in aggregate factors (including rising cost
of medical care services, Medicaid eligibility expansion, skill-biased technological changes in the labor
market, and changes in the labor force composition) on the inequality of health insurance coverage and
wages. I find that the interaction between the rising cost of medical services and labor market technological change is the most important determinant of the widening gap of health insurance coverage.
JEL I11, J31, J32
∗ University of Chicago, 1155E 60th Street, Chicago, IL 60637 (email: ronghai@uchicago.edu). I am grateful to Hanming Fang,
James J. Heckman, Petra Todd, and Kenneth Wolpin for their guidance and support. For helpful discussions and suggestions, I thank
Daniel Aaronson, Gadi Barlevy, Marco Bassetto, Gary Becker, David Blau, Jeffrey Campbell, Indraneel Chakraborty, Mariacristina
De Nardi, Eric French, Donna Gilleskie, Naijia Guo, Matthew Harris, Luojia Hu, Dirk Krueger, Audrey Light, Lance Lochner,
Casey Mulligan, Svetlana Pashchenko, Gabriel Picone, Andrew Postlewaite, John Rust, Andrew Shephard, Christopher Taber,
Alessandra Voena, and all seminar participants at Federal Reserve Bank of Chicago, Ohio State University, Syracuse University,
University of Chicago, University of South Florida, University of Pennsylvania, the 2013 North American Summer Meeting, the
2013 Southern Economics Association Annual Meeting, the 2014 Federal Reserve Bank of Chicago Conference on the Affordable
Care Act and the Labor Market, 2015 Royal Economic Society Conference. First Draft: November 15, 2012.
1
Introduction
A majority of Americans obtain their health insurance coverage from their employers.1 However, over the
last 30 years the employer-provided health insurance coverage rate has been declining, especially among
the less-educated workers. As seen in Figure 1(a), the employer-provided health insurance coverage among
employed male workers with at most a high school degree fell from 87% in 1981 to only 63% in 2009,
while coverage among those with a 4-year college degree or more was relatively stable. As a result, the
health insurance coverage rate gap between 4-year college workers and high school workers rose from 7
percentage points in 1981 to 25 percentage points in 2009.2
Accompanying such a widening gap of health insurance coverage is the growth of wage inequality (see
Figure 1(b)), which has received an immense amount of attention exclusively in the earnings inequality
literature.3 The majority of this literature shows that much of the rise in wage inequality since the 1980s can
be explained by changes in relative demand and supplies for skilled workers in the labor market. Only a few
studies examine the changes in health insurance and other fringe benefits and find a larger total compensation
inequality (see Pierce (2001), Levy (2006)). In these studies, the relationship between fringe benefits and
wages is almost exclusively examined based on employers’ monetary cost of employee compensation. No
attention has been given to specific causes of the changing inequality in nonwage benefits (other than causes
examined in the wage inequality literature) or how these changes relate to wage changes over time.
In this paper, I focus on employer-provided health insurance coverage and investigate its joint determination with wages by education and cohort over time. Health expenditure accounts for 17% of the U.S. GDP in
2009.4 Employer-provided health insurance coverage is an important consideration for individuals’ employment decisions and research on health insurance has important public policy implications. Furthermore, an
important distinction between health insurance and other perquisites – such as pension or paid leave, which
are outside the scope of this paper – is that health insurance is also an investment in one’s health which is a
form of human capital. Lastly, the trade-off between health insurance and wages for an employee is based
on not only the pooling health insurance premium (i.e. the employer’s cost of health insurance) but also the
employee’s willingness to pay for health insurance, which depends on his own health, medical expenditure,
1 The reliance on employer-provided health insurance stems from wage controls during World War II (Stabilization Act of 1942)
and tax-exempt treatment for employer-provided health benefits since 1954 (Internal Revenue Code of 1954).
2 A similar pattern holds also for females (see Figure B.1 in the appendix.)
3 See, for example, Bound and Johnson (1992), Katz and Murphy (1992), Katz and Autor (1999), Juhn et al. (1993), Heckman
et al. (1998), Autor et al. (2008), Lee and Wolpin (2010).
4 Source: World Health Organization Global Health Expenditure database, 2009.
1
Hourly Wage (Employed Male)
30
15
20
25
Wage
.8
.7
.6
EHI Coverage Rate
.9
35
Employer-Provided HI (Employed Male)
1981
1986
1991
1996
2001
2006
2011
1981
Year
High School or Less
4-Year College or More
1986
1991
1996
2001
2006
2011
Year
Some College
High School or Less
4-Year College or More
(a) Health Insurance Coverage Inequality
Some College
(b) Wage Inequality
Figure 1: Employer-Provided Health Insurance Coverage Inequality
Source: Author’s calculation from March Current Population Survey (CPS) 1982-2010. A worker is considered employed if the
worker works no less than 800 hours annually. Here I do not distinguish between high school dropouts and high school graduates
because CPS does not differentiate between high school degree and GED starting from 1992.
risk aversion, income, and eligibility of public insurance program (e.g. Medicaid).
The objective of this paper is to develop and estimate an overlapping generations equilibrium model of
labor and health insurance markets to analyze the determinants of health insurance coverage, wages, and
labor supply over last thirty years. My work builds upon the works by Heckman, Lochner and Taber (1998)
and Lee and Wolpin (2006, 2010), which emphasize the supply of and demand for labor of heterogeneous
skills in a dynamic general equilibrium model with a competitive labor market. I extend their models in the
following four ways. First, I allow health to improve human capital production and allow the productivity
of health in producing human capital to be different across different skills. Second, I introduce the demand
for health insurance by allowing health insurance to affect health capital production and by reducing the
medical expenditure risk the individual faces. Third, my model allows both aggregate changes in medical
expenditure and Medicaid eligibility expansion to affect individuals’ choices and equilibrium outcomes over
time. Hence my model incorporates the models of health capital and health insurance into a neoclassical
dynamic overlapping generations equilibrium framework with aggregate trends and fluctuations. Lastly, my
model introduces unobserved heterogeneity in: (i) initial human capital levels across different skills, (ii)
tastes for leisure, (iii) risk aversion, and (iv) initial ability that affects health capital production.
My model explicitly considers exogenous changes in labor market factors (labor demand and supply)
and health insurance market factors (rising cost of medical care services and Medicaid eligibility expansion). The labor market demand changes, which are attributable to skill-biased technological changes, and
2
the supply changes, i.e., changes in the labor force composition (mainly the increasing supply of college
workers), have been shown as important determinants for earning inequality (see Autor, Katz and Kearney
(2008) for a review). My model shows that changes in these two factors can not only explain the overall
compensation changes, but can also create composition changes in terms of health insurance and wages for
a given total value of compensation. Furthermore, the model considers rising medical care cost and Medicaid eligibility expansion as possible explanations for the rising inequality in health insurance and wages.
Specifically, changes in these four factors can affect an individual’s choices in the following four channels.
First, skill-biased technological change increases the relative demand for high skilled (more educated)
workers, which tends to increase inequality in health insurance coverage and wages. In particular, by increasing the human capital productivity in the labor market among more educated workers, it raises the
demand for heath insurance as health insurance promotes better health which is a form of human capital.
Furthermore, in the presence of progressive labor income tax, the increase in income among more educated
workers leads to a higher demand for health insurance because health insurance premium is tax-exempt. On
the other hand, changes in the labor force composition, especially the increasing supply of college workers in the labor force, affects the inequality in health insurance and wages in the opposite direction as the
skilled-biased technological changes.
Second, the rising medical care cost (per unit of medical care consumption) directly affects individuals’
demand for health insurance because workers with lower and less risky medical expenditure value health
insurance less, ceteris paribus, and are more likely to opt out of employer-provided health insurance market
in a pooling equilibrium (“adverse selection”). In the presence of adverse selection, the rising medical care
cost, by raising a much higher equilibrium health insurance premium, reduces the coverage among the workers with less and safer medical care consumption and also reduces wage components of total compensation
among workers with coverage.5
Third, the Medicaid eligibility expansion can also affect the demand for employer-provided health insurance as well as employment due to its means-tested nature. In particular, over this time period, the Mediciad
program has been expanded and its coverage soared.6 The expansion of the Medicaid program can potentially crowd out the demand for private health insurance among low-educated workers given its means-tested
5 As
seen in Figure 2, the average cost of employer-provided health insurance premium has increased drastically, from about
$740 in 1981 to $6600 in 2009 per covered employee.
6 Medicaid is the largest public funded health insurance program for non-elderly adults in the U.S., and the fraction of the
population covered by Medicaid has almost doubled over the last thirty years. It has increased from 8.4% in 1987 to 15.7% in 2009
(Income, Poverty, and Health Insurance Coverage in the United States: 2010 the U.S. Census Bureau. Issued September 2011).
3
nature and even reduce their incentive to work.7
Finally, through labor and health insurance markets equilibrium, all these changes affect individuals’
employment and health insurance decisions by affecting the equilibrium prices of health insurance and
labor market skills.
The model is estimated using simulated method of moments (SMM); this approach overcomes an important hurdle in terms of data availability. A single comprehensive dataset that provides all relevant information for the analysis over the last 30 years does not exist.8 However, the SMM estimation method based
on the structure model enables me to combine data moments from four different sources: the 1982-2010
March Current Population Survey, the 1996 Survey of Income and Program Participation, the 2005 Medical
Expenditure Panel Survey, and the 1981-2009 Employment Cost Index from the Bureau of Labor Statistics.
The model is solved with an iterative algorithm by adopting a forecasting rule for equilibrium labor market
skill prices and for the equilibrium insurance premium that is consistent with agents’ optimization behavior
within the model.
Using the estimated model, I conduct counterfactual simulations to decompose the quantitative impact
of each individual factor and their interactions on the observed inequality trend. The model allows me
to isolate the individual effect of these factors as well as the effects of their interactions. I find that the
interaction between the rising cost of medical services and labor market technological change is the most
important determinant of the widening gap of health insurance coverage by education.
The rest of the paper is organized as follows. Section 2 discusses related literature. Section 3 presents
the model. Section 4 describes the empirical strategy including data, estimation method, identification, and
parameterization. Section 5 reports parameter estimates and model fit. Section 6 conducts an inequality
decomposition under different counterfactual scenarios, and Section 7 concludes.
2
Related Literature
This paper relates to the literature on wage inequality and compensation inequality. A large number of studies document a substantial rise in wage differentials by education, age, experience and occupation in the
7 Research has found crowding-out effects of Medicaid expansion on private health insurance among pregnant women and
children (see Cutler and Gruber (1996), Blumberg, Dubay and Norton (2000), Card and Shore-Sheppard (2004), Gruber and Simon
(2008)).
8 Specifically, such a comprehensive data set requires not only individual level panel information on labor market activity, health
insurance, medical expenditure, and health, representative of the U.S. economy over the last 30 years, but also aggregate information
regarding equilibrium prices on the labor market and the health insurance market.
4
U.S. since the 1980s.9 Many studies conclude that much of the U.S. wage inequality since 1980s can be
explained by the relative demand increase for more-skilled labor brought about by skill-biased technological
change in the labor market (e.g., Bound and Johnson (1992), Katz and Murphy (1992), Juhn, Murphy and
Pierce (1993), Autor, Katz and Krueger (1998), Autor, Katz and Kearney (2008)).10 Heckman, Lochner and
Taber (1998) and Lee and Wolpin (2006, 2010) develop and estimate an overlapping generations general
equilibrium model of competitive labor market and show that skill-biased technological change was especially important in accounting for the increase in college wage premium. As mentioned in the introduction,
only a few studies investigate the changes in nonwage benefits over time. In particular, Hamermesh (1999)
finds an increase in the inequality of nonwage compensation measured by the quantities of the workplace
amenities. Pierce (2001) documents an increasing inequality in employer-provided fringe benefits, measured
by employers’ monetary costs of health insurance and pensions. Building upon the existing inequality literature, this paper provides a uniform framework with labor and employment-based health insurance markets.
It quantitatively analyzes the determinants of both wage and health insurance inequality and their welfare
implications.
This study also relates to the literature linking health, health insurance, and labor market outcomes.
Most of the empirical analysis on health and labor market outcomes follows the theoretical work of Becker
(1964) and Grossman (1972a, 1972b), where health is modeled as a form of human capital stock. As reviewed by Currie and Madrian (1999), this stream of empirical literature finds that poor health reduces the
capacity to work and has substantive effects on wages, work-time, and job choice. The literature also investigates the effects of health insurance on wage/employment determination and job mobility (see Currie
and Madrian (1999) and Gruber (2000) for a review).11 Olson (2002) and Kolstad and Kowalski (2012)
show that workers receiving employer-provided health insurance are paid a lower wage, consistent with the
prediction of compensation differential theory. Many studies show that health insurance is a central determinant of retirement decisions.12 Cutler and Madrian (1998) show that rising health insurance costs during
the 1980s increased the hours worked by those with health insurance. Dey and Flinn (2005) develops and
estimates a model of employer-provided health insurance and wage determination under a search, matching,
9 See Katz and Murphy (1992), Katz and Autor (1999), Goldin and Katz (2001), Acemoglu (2002), Autor, Katz and Kearney
(2008), Kambourov and Manovskii (2009).
10 The literature also investigates other causes such as expansion of trade (Wood (1994, 1998), Acemoglu (2003)) or the erosion
of labor market institutions (Card and DiNardo (2002), DiNardo, Fortin and Lemieux (1996), Lemieux (2008)).
11 Also see Madrian (1994), Manovskii and Bruegemann (2010), Pashchenko and Porapakkarm (2013), Cole, Kim and Krueger
(2012), Garthwaite et al. (2013), Aizawa and Fang (2013).
12 See Gruber and Madrian (1995), Gruber and Madrian (2002), Blau and Gilleskie (2001, 2006, 2008), French and Jones (2011).
5
and bargaining framework. They find that the employer-provided health insurance system does not lead
to any serious inefficiencies in mobility decisions. This paper combines the above mentioned insights in a
structural framework to investigate the determinants of rising health insurance coverage gap over time.
Finally, this paper relates to the literature that evaluates the effects of Medicaid expansion on private
health insurance demand and labor supply. Aizer and Grogger (2003) evaluate the effects of Medicaid
eligibility expansion to low-income parents during the 1990s and find only small crowding out effects on
private coverage. Other studies find different magnitudes of crowding out effects by examining the Medicaid
eligibility expansion targeted towards different demographic groups, such as pregnant women (Cutler and
Gruber (1996), Blumberg, Dubay and Norton (2000), Card and Shore-Sheppard (2004), Gruber and Simon
(2008)) and old age population (Brown, Coe and Finkelstein (2007), Brown and Finkelstein (2008)). In
this paper, I explore the time-series variation of Medicaid eligibility changes towards non-elderly working
age population (mostly poor parents); the effects of Medicaid eligibility expansion are estimated in an
equilibrium model with individuals’ endogenous decisions on employment and private health insurance.
3
3.1
The Model
The Setup
The population of the economy at each calendar year t consists of individuals aged a = a0 to A. Every
individual is endowed with an education level j and an unobserved heterogeneity indexed by a discrete type
k ∈ {1, . . . , K}.13 Individuals also differ in their demographic characteristics, summarized by a vector Za ,
at age a. From now onwards, I use subscript a to denote an individuals age and use subscript t to denote a
specific calendar year.
An individuals’ preferences are defined over consumption (ca ), health status (ha ), employment status
(dae ), and are subject to an age-varying preference shock to employment (εal ). Specifically, an individual’s
flow utility function can be written as follows,
u(ca , dae , ha ; a,t, Za , εal ) = 1 − exp(−γ(k, Za ) · ca ) + φ (Za ) · ha + Γ(ha , j, k, Za , a,t; εal ) · (1 − dae )
(1)
13 The individual heterogeneity (i.e., type) includes not only the individual’s cognitive abilities that affect the individual’s productivity in the market and home sectors, but also socio-emotional skills or personality traits that shape individuals preferences over
risk and leisure.
6
where γ(k, Za ) is the risk aversion coefficient that depends on the individual’s unobserved type k and demographic characteristics Za , φ (Za ) is the flow utility of health which depends on the individual’s characteristics
Za , and Γ(ha , j, k, a,t, Za ; εal ) characterizes the value of leisure and home time which depends on the individual’s health, education, unobserved type, age, calendar time, and individual demographic characteristics.
At the beginning of each time period t, which corresponds to one year, an age-a individual decides
whether to work or not dae ∈ {0, 1}. If the individual decides to work (dae = 1), the individual can further
choose from two employee compensation packages: one consists of wages plus health insurance and the
other consists of just wages. Both compensation packages satisfy the employer’s zero profit condition,
which will be discussed later in Section 3.2.
The rest of the section is as follows. Sections 3.2 and 3.3 discuss the market value of employee compensation equation and budget constraint respectively. Section 3.4 presents the human capital accumulation in
terms of health and labor market experiences. Section 3.5 presents individual’s optimization problem. Sections 3.6 and 3.7 describe aggregate price sequences and market equilibrium. Finally, Section 3.8 presents
the model solution.
3.2
Employee Compensation: Wages and Health Insurance
The labor market skills are education specific. An age-a individual’s education-specific efficiency skill
units, saj , depends on the individual’s health status (ha ), work experience (expra ), unobserved type (k), and
exogenous demographic characteristics Za :
saj = s j (ha , expra , k, Za , εaj )
(2)
where εaj is an age-varying education-specific productivity shock.
Let rtj be the competitively determined skill rental price at time t associated with education level j, then
an individual’s market marginal productivity is the product of rtj and saj . Therefore, the individual’s wages
(wa ) and health insurance compensation (Iae ∈ {0, 1}) at age a and year t must satisfy the following equation:
wa + λ pt · Iae = rtj · s j (ha , expra , k, Za , εaj ),
j ∈ {HS, SC,CG}
(3)
where λ ∈ (0, 1) is the share of the health insurance premium paid by the employer if the individual is
7
covered by employer-provided health insurance (Iae = 1), and pt > 0 is the equilibrium group health insurance
premium at time t.
Equation (3) characterizes the compensation differentials between wage benefits and health insurance
benefits in a competitive labor market.14 Equation (3) is also the zero profit condition for employers: employers are indifferent between offering a compensation package that consists of just wages and a compensation package comprised of wages plus health insurance. In order to focus on the changes in the labor and
insurance markets over the last 30 years, here we abstract away from labor market search frictions.15
Health is a form of human capital, implying ∂ s j (ha , expra , k, Za , εaj )/∂ ha > 0. Under equation (3), by
affecting the equilibrium price of labor market skills, an increase in labor market demand leads to an increase
in the marginal productivity of health capital in the labor market.
3.3
Budget Constraint: Medicaid, Taxes, Transfers, and Risky Medical Expenditure
c ∈ {0, 1} be an indicator variable of Medicaid coverage, which is a probabilistic function of the indiLet Ia,t
vidual’s income, demographic characteristics, as well as calendar time. The time dependence of Medicaid
eligibility reflects the expansion of Medicaid eligibility over time. The details of Medicaid eligibility rule
specification is presented in Appendix C.4. An insured individual (either through employer-provided health
c ) does not pay his medical expenses (pm m ).16
insurance Iae or Medicaid Ia,t
a
t
The individual’s wage income, wa , is subject to a progressive income tax schedule, whereas the employerf(w) be the after tax income function (see appendix
provided health insurance benefit is tax exempt. Let T
C.1 for details of how to approximate this function), then the individual’s budget constraint is given as
follows:
f(wa − (1 − λ ) · pt · I e ) · d e − pm ma · 1(I e = 0 & I c = 0) + transfera,t
ca = T
a
a
t
a
a,t
(4)
where 1 − λ is the fraction of group health insurance premium (pt ) paid by the individual if the individual
is covered by employer-provided health insurance, and transfera,t is government transfers that guarantee a
minimum consumption floor (ctmin ). The existence of a consumption floor captures social safety net programs
other than Medicaid, such as Supplemental Security Income, Unemployment Insurance, Food Stamps, and
14 Kolstad and Kowalski (2012) finds that jobs with employer-based health insurance (EHI) pay lower wages, and that the compensating differential for EHI is about the same magnitude as the average cost of EHI to employers.
15 Dey and Flinn (2005) estimate a steady state equilibrium model on employment and health insurance with search and matching,
and they find the search friction is not quantitatively important for inefficient mobility decisions.
16 Here I only consider full coverage and no coverage, but the model can be extended to include partial insurance.
8
uncompensated care.17
Equation (4) has two implications. First, the Medicaid program coverage can potentially crowd out
employer-provided health insurance because private health insurance needs to pay the health insurance premium cost while Medicaid is free. Second, because employer-provided health insurance premium is exempt
from the progressive tax schedule, individuals with higher wages face a lower after-tax price of health insurance.
As noted, an individual’s medical service expenditure, ptm ma , is the product of the cost of medical service
at time t (pt ) and the amount of medical service consumption the individual purchases at age a (ma ). An
individual’s medical service consumption ma is assumed to be exogenous and is a stochastically function of
the individual’s health insurance coverage status, health, age, education, and demographics:18
c
m
m
, ha , a, j, Za ) + σm (ha , a, j, Za ) · (εa,0
+ εa,1
)
log(ma ) = µm (Iae , Ia,t
(5)
c , h , a, j, Z ) is an exogenous function that characterizes the average levels of medical exwhere µm (Iae , Ia,t
a
a
penditure, and σm (ha , a, j, Za ) controls the volatility controls the volatility of medical consumption risk. The
m + ε m ) is decomposed into a predictable component (ε m ), that is known to
medical expenditure risk (εa,0
a,1
a,0
the individual (but not to the econometrician) when making employment-coverage decisions, and an unprem ), that is realized after the decisions have been made.19
dictable component (εa,1
3.4
Individual State Transition: Health Dynamics and Human Capital Accumulation
Health status is assumed to be either good (ha = 1) or bad (ha = 0).20 The probability of being in good
c ), current health
health at the beginning of age a + 1 is a function of health insurance coverage status (Iae , Ia,t
17 Uncompensated
care is an overall measure of hospital care provided for which no payment was received from the patient or
insurer. In 2004, 85% of uncompensated care was paid by the government (Kaiser Family Foundation, 2004).
18 See Blau and Gilleskie (2001) and French and Jones (2011) for similar specifications.
19 French and Jones (2004) find that medical expenditure shocks are very volatile and persistent, even after controlling for observed individual characteristics such as health status. I decompose the medical expenditure shocks and allow individuals to make
m which is unobserved by econotheir employment and health insurance coverage decisions based on the predictable component εa,0
metricians.
20 Many studies have used a binary indicator for self-reported health status as a measure of health status. See Rust and Phelan
(1997), Blau and Gilleskie (2001), and French and Jones (2011) among others.
9
(ha ), age (a), education ( j), unobserved heterogeneity (k), and demographics (Za ):21
c
Pr(ha+1 = 1) = H(Iae , Ia,t
, ha , a, j, k, Za )
(6)
c , h , a, j, k, Z )/∂ I e > 0, employer-provided health insurance is an investment to the indiIf ∂ H(Iae , Ia,t
a
a
a
vidual’s health capital.22 An increase in the labor market productivity of health, which is caused by labor
market demand changes, will raise the net gain of having health insurance under such a condition. By allowing the health production function to depend on the unobserved type, the model can generate heterogeneous
health dynamics among individuals with the same observed characteristics such as education and current
health status. Furthermore, all the individual level variables that affect medical services consumption enter
health production function directly; therefore the estimated coefficients combine both their direct effects on
health production and also indirect effects from medical expenditure.
Given an individual’s current employment decision (dae ∈ {0, 1}), the individual’s labor market experience at age a + 1 is given by
expra+1 = expra + dae .
3.5
(7)
Individual Optimization
Denote Ωa,t an age-a individual’s state space at time t, including all individual level state variables as well
as all the relevant aggregate state variables. Thus
Ωa,t = { j, k, ha , expra , Za , a,t, εal , ψ t , Itc }
(8)
where ψ t is the entire sequence of realized equilibrium prices and shocks in the aggregate economy and the
eligibility rule of Medicaid is given by the time-varying function Itc .
An individual’s objective is to maximize the expected present discounted value of remaining lifetime
utility, subject to the employee compensation equation (including both wages and employer-provided health
insurance), budget constraint (including medical services expenditure), the transition of individual level
21 Among
others, Rust and Phelan (1997) estimate a health transition probability function that depends on age, previous health
status, and the lowest and highest average wage classes.
22 Many studies find positive impact of health insurance coverage on various measures of health. Card et al. (2009) and Doyle
(2005) find that health insurance coverage reduces mortality rate. Currie and Gruber (1996b) and Currie and Gruber (1996a)
find that Medicaid coverage improves birth outcome and improves children’s health. Finkelstein et al. (2012) find that Medicaid
coverage leads to better self-reported physical and mental health using data from the Oregon Health insurance experiment.
10
state variables (including human capital accumulation and health dynamics), the transition of aggregate
state variables, and equilibrium conditions.
Let δ ∈ (0, 1) be the subjective discount factor and denote the terminal value function at age A + 1 to be
VA+1 (ΩA+1 ); we can write an individual’s optimization problem using Bellman equation as follows
Va (Ωa,t ) = max {u(ca , dae , ha ; a,t, Za , εal ) + δ E[Va+1 (Ωa+1,t+1 )|Ωa,t , dae , Iae , ]}.
{dae ,Iae }
(9)
Proposition 1 below summarizes the optimal decision rule on employer-provided health insurance for
an individual who is not covered by Medicaid.
c = 0, then an employed individual’s health insurance choice is characterized by the
Proposition 1. If Ia,t
following threshold behavior
Iae
=


 1
∗
if ξa,t ≤ ξa,t

 0
otherwise
where ξa,t is the certainty equivalent consumption value for the individual in the presence of risky medical
∗ is the threshold value for health insurance coverage
expenditure and ξa,t
∗
ξa,t
=−
1
f(rtj s j − pt )) − δ π s ∆CVa+1 (Ωa,t )
log exp(−γ(k, Za ) · T
a
a+1
γ(k, Za )
∗ is increasing in the individual’s marginal productivity (r j s j ) and the net continuation value
Note that ξa,t
t a
of having health insurance ∆CVa+1 (Ωa,t ) = E[Va+1 |Ωa,t , Iae = 1, Iac = 0, dae = 1] − E[Va+1 |Ωa,t , Iae = 0, Iac =
0, dae = 1], but is decreasing in health insurance premium pt .23
3.6
Aggregate Trends and Fluctuations in Labor and Medical Service Markets
The cost for each unit of medical services consumption ptm is modeled as an exogenous process that evolves
over time:
m
m
log pt+1
− log ptm = gm + ϑt+1
.
(10)
As will be discussed later in the estimation section, I use the structure model to predict the underlying cost
sequence {ptm }t that is consistent with the observed medical services expenditure pattern and equilibrium
health insurance premium. I do not use the CPI on medical services from BLS to measure ptm , because
23 Proof
of Proposition 1 is provided in Appendix A.1.
11
there is large heterogeneity in the demand for medical services across different education and age groups.
The consumption bundle underlying the medical services CPI may not be the typical medical consumption
goods bundle for employed workers aged 25 to 64 over our sample period.
There are three education levels: high school or less (HS), some college (SC), and 4-year college or more
(CG). To introduce the aggregate demand changes in the labor market, I introduce an aggregate production
function of constant elasticity of substitution (CES) form:24
CG ν 1/ν
Ct ≡ ζt ztHS (StHS )ν + ztSC (StSC )ν + zCG
t (St )
(11)
where ζt represents the Hicks-neutral technical change, zt is the education-specific skill-augmenting technological change, and St is the aggregate quantity of education-specific skills. Skill-biased technology changes
HS
(SBTC) involve relative increases in the technologies that favor high skilled labor, i.e., ztSC /ztHS and zCG
t /zt .
The aggregate elasticity of substitution between different skills is 1/(1 − ν).
Aggregate neutral technical change, ζt , is assumed to evolve according to:
ζ
log ζt+1 − log ζt = gζ + ϑt+1 .
(12)
SBTC is assumed to follow a deterministic quadratic time trend as follows (see e.g. Autor et al. (2008)):
j
j
j 2
log(ztj /ztHS ) = gz0
+ gz1
t + gz2
t ,
j = SC,CG.
(13)
Without loss of generality, I normalize ztHS = 1 for all t.25
24 A
canonical wage structure model assumes a CES production function with only two skill groups (e.g. Katz and Murphy
(1992) and Autor et al. (2008)). I introduce three skill groups into a CES production function, assuming constant elasticity of
substitution. Alternatively, one could allow for different elasticity of substitution between different skill groups. Ex ante it is
difficult to determine which specification is better, except that the current specification under Equation 11 is more parsimonious.
However, as shown later by the goodness of model fit (Section 5.2), the current specification provides a good description of the
aggregate economy as it replicates the aggregate time trends well.
25 Under such normalization, the estimated log ζ also absorbs the effect of zHS over time.
t
t
12
3.7
Model Equilibrium
The equilibrium health insurance premium is given by the average medical services expenditure of those
who are covered by health insurance, that is,
La,t
pt =
e
∑Aa=a0 ∑i=1 ptm · mi,a,t · Ii,a,t
La,t
e
∑Aa=a0 ∑i=1 Ii,a,t
.
(14)
j
j
where La,t
is the population size of age-a individuals with education level j in the economy at time t. La,t
is
treated as exogenous and is directly obtained from the data.
In a competitive labor market, the equilibrium price, rtj , is given by the marginal product of aggregate
education-specific skills Stj :
rtj =
L
∂Ct
∂ Stj
CG ν
= ζt ztHS (StHS )ν + ztSC (StSC )ν + zCG
t (St )
1/ν−1
ztj (Stj )ν−1
(15)
j
a,t j
e . The distinction between the equilibrium skill price and the wage rate is
where Stj = ∑Aa=a0 ∑i=1
si,a,t di,a,t
important: only the equilibrium skill price provides a complete description of the individual’s labor market
opportunity and compensation.
Definition (Equilibrium Definition). The equilibrium of the economy consists of (i) value functions: Va (Ωa,t )
and associated policy functions, taking equilibrium prices (rtj , pt ) and their forecasting rules as given; (ii)
equilibrium health insurance premium: pt is given by the average medical expenditure of those who are
covered (Equation (14)); (iii) equilibrium skill prices: rtj that are determined by the marginal productivity
of aggregate skill units (Equation (15)); (iv) forecasting rules on equilibrium prices (rtj , pt ) are consistent
with agents’ policy functions and aggregate dynamics of ζt , ztj and ptm .
3.8
Model Solution
To solve the model, I need to specify individuals’ forecasting rules and the initial condition for each cohort
when entering the economy. In particular, I assume that individuals’ forecasting rules for the changes in the
logarithm of equilibrium prices (including skill prices and health insurance premium) can be approximated
by a linear function of changes in the previous period’s prices and changes in current exogenous aggregate
13
variables, specifically:
j
j
l
log rt+1
− log rtj = ρ0j + ∑ ρ1,l
(log rtl − log rt−1
) + ρ2j (log pt − log pt−1 )
l
m
+ρ3j (log ζt+1 − log ζt ) + ρ4j (log pt+1
− log ptm )
(16)
p
l
(log rtl − log rt−1
log pt+1 − log pt = ρ0p + ∑ ρ1,l
) + ρ2p (log pt − log pt−1 )
l
m
+ρ3p (log ζt+1 − log ζt ) + ρ4p (log pt+1
− log ptm )
(17)
where ρ’s are reduced form parameters that are consistent with the model. Parameters represented by ρ’s
are reduced form parameters that characterize the forecasting rule of equilibrium variables. Under the above
forecasting rule, the aggregate-level state variable vector that is relevant for an individual’s optimization
problem only includes aggregate variables in the current period and in the previous time period, i.e., ψ t =
j
{log pt , log pt−1 , {log rtj , log rt−1
} j=HS,SC,CG , log ζt , log ptm }.
Regarding the initial condition, each cohort enters the economy at age a0 = 25 with a distribution of
individual state vector (k, j, ha , expr25 , Z25 ). In order to allow for flexible correlation between observed
individual state variables at age 25 and the unobserved type, I assume that the conditional probability of
being a particular type k = {1, . . . , K} is a function of all these observed individual state variables at the initial
age, i.e., Pr(type = k| j, ha , expr25 , Z25 ) = Pk ( j, ha , expr25 , Z25 ) (see Appendix D for details). The underlying
assumption is that conditional on the unobserved type, the observed initial individual level state variables
( j, ha , expr25 , Z25 ) are exogenous. Although the conditional probability function of type k, Pk (·), is timeinvariant, the unconditional probability of each type may change over time due to changes in distribution of
( j, ha , expr25 , Z25 ) across different cohorts over time.
Under both the assumptions regarding the equilibrium forecasting rules and individual level initial conditions, the model can only be solved numerically. By introducing health insurance market equilibrium
together with labor market equilibrium over time, I extend the iterative solution method developed by Lee
and Wolpin (2006) to solve the model. The details of the solution algorithm are described in Appendix A.2.
14
4
Data and Estimation
To estimate the model, I need both longitudinal macro data and micro data on individual characteristics and
choices over time. However, such a comprehensive data set that provides information on all these aspects
does not exist. Therefore, I combine data from the following four sources: the 1982-2010 March Current
Population Survey (CPS), the 1996 Survey of Income and Program Participation (SIPP), the 1981-2009
Employment Cost Index (ECI), and the 2005 Medical Expenditure Panel Survey (MEPS).
The demographic characteristics Za includes an individual’s gender and an age-varying indicator variable
of whether having dependent children. The initial conditions for each cohort, such as the population size by
gender and education, health status, and presence of dependent children at age 25, come from CPS data; the
age-25 experience distribution is obtained from NLSY 1979-1994 for each education group and gender.
The model is estimated using the simulated method of moments (SMM). The SMM estimation method
allows me to combine data moments from the above mentioned four data sources on employer-provided
health insurance coverage, wages, employment, health dynamics, Medicaid coverage, health insurance premium, medical expenditure patterns, by education and age groups, and over different calendar years. The
SMM method also allows me to match different time frame, through simulations, as the sample frames of
our data sets may cover different time frames. For example, SIPP 1996 panel covers the reference period
1995 to 1999, while CPS covers from 1981 to 2009. Section 4.1 describe the data, Section 4.2 describes the
estimation method, and Section 4.3 discusses the identification.26
4.1
Data
March Current Population Survey (March CPS)
I use the March Current Population Survey (March CPS) data from 1982 to 2010, which covers earnings
from 1981 to 2009, to measure the aggregate distribution of employer-provided health insurance coverage,
wages, employment, and Medicaid coverage by year, education, age, and gender. The sample only includes
individuals aged 25 to 64. Individuals who are in the military, institutionalized, self-employed or working
for non-paid jobs are excluded. Details on variable description are provided in Appendix B.
Table 1 provides summary statistics in CPS for selected year. All nominal terms are in 2005 dollars
and statistics are weighted by CPS sampling weights. Among the employed workers, the average hourly
26 Details
on model parameterization are provided in Appendix D.
15
wage increased from 16.44 in 1981 to 21.11 in 2009, while the average coverage rate of employer-provided
health insurance (EHI) declined from 88% in 1981 to 77% in 2009. Among the non-employed population,
the average rate of Medicaid coverage increased from 13% in 1981 to 19% in 2009. The supply of college
workers grew steadily: 4-year college graduates comprised about 18% of total population in 1981 and 31%
by 2009. Individuals’ self-reported health status is available starting from survey year 1995. The fraction of
individuals that reports good health slightly declined over time (see appendix Figure B.3).
Table 1: Summary Statistics (CPS 1982-2010)
Employed
Hourly Wage (Employed)
EHI (Employed)
Medicaid
Medicaid (Not Employed)
Some college
4-year college or more
Age
Female
1981
0.66
16.44
0.88
0.05
0.13
0.19
0.18
41.87
0.54
1991
0.71
17.35
0.82
0.06
0.17
0.24
0.22
41.25
0.53
2001
0.74
20.82
0.82
0.05
0.17
0.27
0.28
42.65
0.53
2009
0.69
21.11
0.77
0.08
0.19
0.27
0.31
43.76
0.52
Employer′s Costs of Health Insurance Benefits (1981−2009)
Annualized Compensation (Employed Male)
Compensation
4000
45000
5000
65000
6000
25000
3000
2000
1985
1990
1995
Year
2000
1986
1991
1996
High School or Less
4-Year College or More
2005
Figure 2: Employers’ Cost of HI Benefits
1981
2001
2006
2011
Year
Per employee
Per covered employee
1000
Some College
Figure 3: Employee Compensation Inequality
(Employed Males)
Employment Cost Index (ECI)
I construct the average health insurance benefits per covered employee paid by an employer over the time
period 1981 to 2009 using the Employment Cost Index (ECI) and the Employer Costs for Employee Compensation Survey (ECEC). Detailed calculation and data description is presented in Appendix B. As seen in
16
Figure 2, employers’ cost of health insurance has increased drastically from 1981 to 2009. Combining CPS
data on wages, health insurance coverage status, and employment, I can calculate the average market value
of employee compensation as a sum of wages and employers’ cost of health insurance benefits, for each
education group and over time. As we can see in Figure 3, the educational differential in terms of employee
compensation has grown much wider than wages alone over the sample period.
Survey of Income and Program Participation (SIPP)
The longitudinal data on health, health insurance, employment transition, labor earnings, and individual
characteristics transition is obtained from the Census Bureau’s Survey of Income and Program Participation
(SIPP) 1996 panel. The SIPP panel is a nationally representative sample of the U.S. non-institutionalized
population. People in the SIPP 1996 panel are interviewed repeatedly over the time period 1996 to 2000. I
only include individuals aged 25 to 64 in the sample. Individuals who are in the military, institutionalized,
self-employed or working for non-paid jobs are excluded. As seen in Table 2, individuals’ choices are quite
persistent over time. On average, the rate of employment is higher for individuals who have good health
than those who do not (Table 3); similarly, conditional on being employed, the accepted hourly wage rate is
higher among workers with good health than workers without good health (Table 4).27
Table 2: Transition Matrix of Choices (Males)
Employed without EHI (t-1)
Employed with EHI (t-1)
Not Employed (t-1)
Employed without EHI
0.69
0.03
0.07
Employed with EHI
0.26
0.95
0.03
Not Employed
0.06
0.02
0.89
Table 3: Employment Rate by Health and Education (Males)
Unhealthy
Healthy
Total
High School or Less
0.69
0.93
0.81
Some College
0.80
0.95
0.89
4-Year College or More
0.90
0.97
0.96
27 Summary statistics for employed females are reported in Appendix Tables B.3 to B.5. Table B.2 in the appendix provides
additional summary statistics for the SIPP sample.
17
Table 4: Hourly Wage by Health and Education (Employed Males)
Unhealthy
Healthy
Total
High School or Less
14.75
15.84
15.39
Some College
17.43
19.64
18.96
4-Year College or More
27.27
30.12
29.53
Medical Expenditure Panel Survey (MEPS)
The Medical Expenditure Panel Survey (MEPS) data provide detailed information about the usage and
expenditure of health care. Medical expenditure is defined to include all health care services such as office
and hospital-based care, home health care, dental services, vision aids and prescribed medicines but not
over-the-counter drugs. The source of payment for medical expenditures can be households (out-of-pocket
expenditures), federal or state government (Medicaid, Medicare), private insurance firms and other sources.
But private insurance premiums are not included. The expenditure data was derived from both households
and the health care provider surveys, which makes the data set a reliable source for medical expenditure
data. I use MEPS 2005 to estimate individuals’ demand for medical services consumption. I only includes
individuals aged 25 to 64 in the sample. Individuals who are in the military, institutionalized, self-employed
or working for non-paid jobs are excluded. The average medical expenditure by education group is reported
in Table 5.28
Table 5: Total Medical Expenditure By Education
High School or Less
Some College
4-Year College or More
4.2
Mean
3358.91
3947.09
3362.34
SD
10763.65
10996.36
7822.32
Estimation Method and Moments
The model is estimated in two steps. In the first step, I estimate parameters that can be identified clearly
outside the structure model. In particular, these parameters includes: transition probability regarding the
presence of dependent children, progressive labor income tax, medical services consumption, and Medicaid
eligibility rules. The values for subjective discount factor δ and the fraction of health insurance premium
28 Table
B.6 in the appendix provides additional summary statistics for the MEPS sample.
18
paid by the employer λ are also calibrated before the structure estimation. These parameter values are
reported in Appendix C.
In the second step, I estimate the model structure parameters using Simulated Method of Moments
(SMM). These parameters include parameters on preferences (including risk aversion), probability of type
distribution, labor market skill production, health transition, and aggregate labor demand function.29 There
are 86 parameters to be estimated using SMM in total. I match 1530 moment conditions. Table E.11
lists all the targeted moments. For each education and gender group, I match the average employment
rate, employer-provided health insurance coverage rate, and wages over every calendar year and over every
age groups. I also match transition dynamics of individuals’ choices on employment and health insurance
coverage for each education and gender group. The weighting matrix is the inverse of the diagonal matrix
of the variance and covariance matrix of these moments. Appendix E reports standard error calculation.
Let θ be these structure parameters estimated using SMM and let ρ be the reduced form parameters
that characterize the forecasting rule of equilibrium variables. The objective of the SMM estimation is
to find the parameter vector θ and associated vector ρ, such that the weighted average distance between
sample moments and simulated moments from the model is minimized, and that the associated vector ρ is
consistent with the model system under parameter value θ . In particular, for any set of structure parameter
values of θ , I use an iterative algorithm to impose equilibrium conditions in order to match the moments
implied by model equilibrium. In step (i), I set an initial guess for reduced form parameters ρ’s that govern
the equilibrium forecasting rules of labor market rental prices and health insurance premium. In step (ii),
in every calendar year, I calculate equilibrium prices log rt ’s and unobserved medical services prices log ptm
that makes the model’s predicted aggregate compensation exactly equal to the data by solving a fixed point.
In step (iii), I update the value of ρ’s using the equilibrium labor market rental prices from step (ii) as well
as health insurance data. Then I repeat the above steps until the equilibrium price sequences and aggregate
shocks converge. In the model estimation procedure, the equilibrium health insurance premium is directly
observed from the data (see Section 4.1), and I use the model to calculate the underlying medical care cost
sequence for each time period that is consistent with observed data and model equilibrium.30
29 The Maximum Likelihood Estimation method is computationally infeasible here due to two reasons. First, there is no single
data set that includes all the variables. Second, there is no close-form solution for individual optimal behavior that can take into
account the equilibrium effects of time-varying aggregate variables.
30 In contrast, the model solution algorithm takes the exogenous medical service cost sequence as given and calculates the equilibrium prices, see Appendix A.2 for details.
19
4.3
Identification
To identify the preference parameters on leisure, I exploit variations of the presence of dependent children
and Medicaid eligibility, which enter into the individuals’ selection equation but not the outcome equation
(i.e. compensation equation in current context). The presence of dependent children, which changes exogenously and probabilistically over an individual’s lifecycle, does not enter compensation determination.
However, it affects an individual’s valuation of leisure and thus the individual’s labor supply decision.31
The Medicaid eligibility rule, that changes over time and depends on individuals’ age, income, employment
and other characteristics, is another source of variation that affects individuals’ incentive to work due to its
means-tested nature. But the Medicaid eligibility does not affect the individual’s labor market productivity. After identifying the preference parameter on leisure, we can directly control for the selection into labor
supply and separately identify the skill function parameters using data on observed employee compensation.
The risk aversion coefficient is identified by the average employer-provided health insurance coverage
rates. Conditional on an individual’s labor market productivity and medical expenditure, the choices of
health insurance coverage is a function of the risk aversion coefficient and the (observed) health insurance
premium. The utility of health is mainly identified by the life-cycle pattern of health insurance coverage.
As an individual ages, although the insurance value of health insurance increases due to rising medical
expenditure risk, the remaining lifetime utility of health declines, which offsets the individual’s demand
for health insurance and generates a relatively flat health insurance demand in the late part of the lifecycle.
Health transition parameters are identified by exploring the panel dimension of health status.
The distribution of unobserved types is identified by exploiting the panel structure of the data. Conditional on all observables, the persistence of individuals’ outcomes (and choices) over time helps separate
unobserved individual heterogeniety from transitory uncertainty. The parameters in the aggregate production function are mainly identified by the exogenous changes in cohort size over time, which allows for
exogenous variation in aggregate labor supply over time. The identification of the model also relies on the
model parameterization and distribution assumptions. All the contemporaneous shocks are assumed to be
independent and normally distributed. Details on model parameterization are provided in Appendix D.
31 The
presence of dependent children impacts an individuals’ decisions on private health insurance coverage by entering the
categorical eligibility of Medicaid.
20
Table 6: Estimates of Risk Aversion
γ: CARA Coef.
Male
Type 1
Type 2
Type 3
Female
Type 1
Type 2
Type 3
Implied CRRA Coef.a
Ave. Prob.b
2.24E-04
1.15E-04
2.95E-04
( 4.65E-06 )
( 4.07E-06 )
( 8.30E-06 )
8.025
4.106
10.582
( 0.1668 )
( 0.1460 )
( 0.2976 )
0.581
0.221
0.198
2.99E-04
1.53E-04
3.94E-04
( 4.82E-06 )
N.A.
N.A.
8.198
4.195
10.811
( 0.1323 )
N.A.
N.A.
0.496
0.186
0.318
Parameter restriction: γfemale,k = γfemale,1 · γmale,k /γmale,1 for k = 2, 3.
Standard errors in parentheses
a This column attempts to translate the absolute risk aversion estimates into relative risk aversion.
Following Cohen and Einav (2007), I do so by multiplying each absolute risk aversion estimate by the
average after-tax annual wage income.
b The average type probability is determined jointly by the parameter estimates of type probability
function (reported in appendix Table F.12) and the initial conditions over years 1981 to 2009.
5
5.1
Estimation Results
Key Parameter Estimates using SMM
Risk Aversion: As seen in Table 6, the estimated absolute risk aversion coefficients range from 1.15E-04
to 2.95E-04 for men and from 1.53E-04 to 3.94E-04 for women. These values are within the parameter
estimates value range [6.6E-05, 6.7E-03] from other existing studies on risk preferences.32 The implied
relative risk aversion coefficients range from 4.106 to 10.582 for men and from 4.195 to 10.811 for women.33
There is large heterogeneity in risk aversion coefficients based on unobserved types.34
Preferences over Health and Leisure: The parameter estimates of health and leisure are reported in appendix Table F.13. Here I only discuss the qualitative implications of these parameter estimates. The
consumption value of good health is slightly higher for men than for women. However women have a
higher valuation of good health at terminal age 65 than men, reflecting the longer life expectancy of women.
32 See, for example, Gertner (1993), Metrick (1995), Cohen and Einav (2007), Einav et al. (2011). However, the risk aversion
coefficient estimates in this paper should not be directly compared to the parameter estimates from other existing studies. This is
because this paper includes two features, (1) three types of risk (i.e., medical expenditure risk, health risk and earnings risk), and
(2) social insurance such as Medicaid and a minimum consumption floor, which have not been jointly incorporated in the previous
studies on risk preferences.
33 Following Cohen and Einav (2007), the relative risk aversion coefficient is calculated by multiplying the corresponding absolute
risk aversion estimate by the average after-tax annual wage income.
34 Type 3 individuals are most risk averse and type 2 individuals are least risk averse.
21
Both men and women value leisure more when in bad health status than when in good health status. In the
presence of dependent children, the value of leisure/home time increases for women but decreases for men.
There is large heterogeneity in the value of leisure among individuals by type and by gender.
Health Transition: As seen in appendix Table F.15, the estimated health transition process is very persistent: for a change in current health status from bad to good, the odds of being in good health next period
(versus bad health) increase by a factor of exp(1.668) = 5.3.35 Current health insurance coverage increases
the odds of being in good health next period by a factor of 1.2. Compared with individuals with high school
or less, ceteris paribus, the odds of good health increase by a factor of 1.3 and 2.1 for individuals with
some college and 4-year college respectively. Figures F.6 and F.7 in the appendix plot the health transition
function under estimated parameter values.
Skill Production: The parameter estimates for the production functions of logarithm of the educationspecific skills are reported in appendix Table F.16. Good health increases the education-specific skill level
by exp(0.083) − 1 = 8.7% for high-school skills, by 12.3% for some-college skills, and by 18.2% for 4year-college skills. Work experience increases the human capital level at a decreasing rate. There is also
large heterogeneity in the initial skill endowment.
Aggregate Production Technology: As seen in Table 7, the three education-specific skills are gross substitutes and the estimated elasticity of substitution is 1.723.36 Literature estimates the elasticity between low
skill and high skill to be below 2.0 and above 1.0 (see Heckman et al. (1998), Lee and Wolpin (2010), Goldin
and Katz (2007)). The estimated elasticity in this paper implies that, on average, a 10 percent increase in the
relative supply of college equivalents reduces the relative skill price by 10/1.723 = 5.8 percent. The estimated growth rate of the logarithm of SBTC is 0.027 for workers with 4-year college or more and 0.020 for
workers with some college, with both decreasing over time.37 Finally, the estimated value of the minimum
consumption floor is 3549.945, which is very stable over the years 1981 to 2009 (see appendix Table F.14).
Aggregate Price Sequences: Figure 4 plots the aggregate prices in the labor market and the health care
market. From 1981 to 2009, the equilibrium skill price sequences increased by about 0.3 log points for
4-year college skills, 0.07 log points for some college skills, and 0.03 for high school skills. The health
insurance premium increased by more than 2 log points over the last 30 years. The estimated values of the
35 The
transition probability of being in good health in the next period is assumed to follow a Logit model. The Logit model
implies that the odds of being in good health next period (ha+1 = 1) is given by ha+1 /(1 − ha+1 = exp(Xah β ).
36 The three skills are gross substitutes when 1/(1 − ν) > 1 and gross complements when 1/(1 − ν) < 1.
37 Autor et al. (2008) estimate the growth rate of skill-biased technological changes of college skills to be 0.028 using a quadratic
time trend, for the period 1963-2005.
22
Table 7: Elasticity of Substitution and Skill-Biased Technology Changes
Aggregate Production
0.420
SBTC
j
gz0
: Intercept
j
gz1
: Time Trend
j
gz2
· 100: Time Trend Squared
1
)
ES ( 1−ν
1.723
(0.0545)
ν
( 0.0184 )
j=SC
-0.531 ( 0.0134 )
0.020 ( 0.0010 )
-0.012 ( 0.0028 )
j=CG
-0.277 ( 0.0066 )
0.027 ( 0.0007 )
-0.011 ( 0.0009 )
Standard errors in parentheses
Changes in Log Prices in the Health Care Market
Changes in Log Prices in the Labor Market
0.3
High School or Less
Some College
4−Year College or More
0.25
2
HI Premium
Cost of Medical Servies
0.2
1.5
0.15
1
0.1
0.05
0.5
0
−0.05
0
−0.1
1981
1985
1990
1995
Year
2000
2005
2009
1981
1985
(a): Labor Market
1990
1995
Year
2000
2005
2009
(b): Health Care Market
Figure 4: Cumulative Log Changes in Prices
1
35
0.95
0.9
30
HS − data
SC − data
CG − data
HS − model
SC − model
CG − model
0.85
0.8
25
0.75
0.7
0.65
0.6
1980
20
HS − data
SC − data
CG − data
HS − model
SC − model
CG − model
1985
1990
1995
Year
2000
2005
2010
(a) EHI Coverage Rate
15
1980
1985
1990
1995
Year
2000
2005
(b) Hourly Wages
Figure 5: Model Fit: Time Trends in EHI and Wages by Eduction (Employed Males)
23
2010
reduced form forecasting rule parameters are reported in the appendix Table F.18.
5.2
Model Fit
Overall, the model fits the sample moments well. As mentioned in Section 4.2, I estimate 86 parameters by
matching 1530 sample moments (see appendix Table E.11 for all targeted moments). The model is overidentified.38 In particular, the model replicates the average wages, employer-provided insurance coverage
rates, and employment rates for each education and gender over the last thirty years. The model also does a
good job in replicating the employment rates and health insurance coverage rate across different age group.
Details are discussed in Appendix G.
As seen in Figure 5, the model successfully replicates the following time series patterns regarding
employer-provided health insurance coverage and wages: (i) a sharp decline in employer-provided health
insurance coverage among less educated workers and a relatively stable coverage rate among more educated
workers; and (ii) a relatively rapid wage growth among more educated workers and a stagnant and slightly
U-shaped wage growth among less educated male workers.39 Appendix G provides additional discussion
on the goodness of fit.
6
Inequality Decomposition Using Counterfactual Simulations
In the model, there are four sets of time-varying exogenous aggregate factors that have heterogeneous impact on individuals’ choices by education and cohort and can potentially account for the rising educational
inequality in health insurance coverage and wages:40 (i) increasing medical care cost (ptm ); (ii) Medicaid
c ); (iii) labor market technologieligibility expansion (income threshold ytcat and categorical standard da,t
cal changes, including labor market skill-biased technology ztSC , zCG
and Hicks-neutral technology ζt ; (iv)
t
changes in labor forces composition across cohorts for each gender-education category, especially the increasing supply of high educated cohort at later years.
Using our estimated model, I ask what is the quantitative impact of each of these factors on changes
in health insurance coverage, wages, and equilibrium skill and insurance prices over the 1981 to 2009.
38 As discussed in Appendix E, I use a diagonal weighting matrix due to large number of sample moments. The J-statistics may
not converge to a chi-square distribution.
39 The model also successfully replicates the time series patterns of the employee compensation for employed women (see appendix figure G.8).
40 The other two exogenously changing factors in the model are: the minimum consumption floor and value of home time. I did
not conduct experiments with respect to these two factors because the estimated time trend parameters are quantitatively small.
24
Specifically, in order to evaluate the effect of increasing medical care cost, I conduct the following thought
experiment. I consider a world where the medical care cost changes according to {ptm }t , obtained from
the model estimation, let all other factors remain at their 1981 levels, and compare individuals’ choices
and market equilibrium over time compared to their 1981 levels. Similarly, I conduct the same thought
experiment with respect to other factors (ii) to (iv). The solution algorithm of computing the equilibrium of
our model, the forecasting rules, and the implied transition path is given in Appendix A.2.
6.1
Human Capital Prices and Employment Rate
In this section, we discuss the changes in equilibrium prices (including labor market skill prices and health
insurance premium) and aggregate employment patterns in each of the counterfactual thought experiments.
Figures H.14 to H.17 in the appendix plot the time trends of average employment, health insurance coverage
rate, and equilibrium prices in labor and health insurance markets under each counterfactual simulation
scenario.
The increasing cost of medical care services reduces labor market employment rate, especially for
women without a college degree (Figures H.14(a) and H.14(b)). This is because, as the health care cost
grows in private market, the “insurance” value of nonemployment from government social insurance programs (captured by the existence of Medicaid and minimum consumption floor) becomes relatively more
attractive for those with a high valuation of leisure and low labor market skills (especially women with
less than high school degree). The average health insurance coverage rates (including both Medicaid and
employer-provided health insurance) also declines for all education groups (Figures H.14(c) and H.14(d)).
Such a decline in the overall health insurance coverage rate is due to both the reduction in employment and
the decline in employer-provided health insurance among those who are employed (which will be discussed
in detail in Section 6.2.1). In equilibrium, the price of high school labor market skills slightly increases and
the price of college workers slightly declines; the equilibrium health insurance premium increases sharply
over time (Figures H.14(e) and H.14(f)).
The individual impact of Medicaid eligibility expansion on aggregate labor market outcomes over the
time period 1981 to 2009 is quantitatively negligible (Figure H.15). In this counterfactual experiment, both
the labor market factors and private health care market factors are fixed to their 1981 levels respectively.
As such, the public health insurance expansion has little impact on the employment rate in the labor market
outcomes. The means-tested Medicaid eligibility expansion, however, does increase the overall average
25
health insurance coverage rate by 6 percentage points among women with at most a high school degree and
by 4 percentage points among women with some college degrees. Such an expansion in health insurance
coverage mainly occurs among the nonemployed population who would not choose to work even in the
absence of Medicaid expansion. As a result, there is little change in both the equilibrium prices of skills in
the labor market and the equilibrium premium in the group health insurance market.
The labor market technological change, that favors the high skilled workers, tends to increases the
productivity of high-educated workers. In response, the employment of high-educated workers increases
while the employment of low-educated workers decreases (Figures H.16(a) and H.16(b)). In equilibrium, the
skill prices of high-educated workers increase and the skill price of low-educated workers decreases (Figure
H.16(e)). Among high-educated workers, their increase in employment is accompanied with an increase
in their health insurance coverage rate; on the other hand, there is a decrease in both the employment
and coverage for low-educated workers (Figures H.16(c) and H.16(d)). On average, the health insurance
coverage rate in the private health insurance market increases by a small fraction, the adverse selection
problem is slightly reduced, and thus the equilibrium premium declines slightly over time (Figure H.16(f)).
The changes in labor force composition, especially the increasing supply of college-educated workers in the labor market over time, have the opposite effects compared to the labor market technological
changes (Figure H.17). The increasing supply of high-educated labor pushes down the equilibrium skill
prices of high-educated workers and pushes up the skill price of low-educated workers. In equilibrium,
high-educated individuals experience both a decline in employment rate as well as in skill prices, while
low-educated workers experience increases in both employment rate and the skill price. The average health
insurance coverage rate decreases among individuals with more than a high school degree and increases
among individuals with at most a high school degree.
6.2
6.2.1
Inequality Decomposition among Employed Workers
Employer-Provided Health Insurance Coverage
In this section, we focus on quantifying the effects of the aforementioned four factors on the widening gap in
employer-provided health insurance coverage rate among those who are employed. Table 8 reports the relative changes of employer-provided health insurance coverage rates and inequality gap among the employed
male workers over time under each counterfactual simulation scenario, for illustration purpose. Figure 6
26
Table 8: Employer-Provided HI Coverage Rate under Counterfactual Simulations (Employed Males)
1981 to 2009
only Cost
only Medicaid
only Tech
only LF
Tech + LF
Tech + Cost
Tech + LF + Cost
Data
∆(EHICG )
-0.189
0.000
0.029
-0.014
0.026
-0.045
-0.065
-0.054
∆(EHI SC )
-0.128
0.000
0.021
0.005
0.027
-0.067
-0.056
-0.111
∆(EHI HS )
-0.169
0.001
-0.038
0.042
0.009
-0.223
-0.153
-0.237
∆(EHICG −EHI HS )
-0.020
-0.001
0.067
-0.055
0.017
0.178
0.088
0.183
∆(EHI SC − EHI HS )
0.041
-0.001
0.059
-0.036
0.018
0.156
0.097
0.126
summarizes the decomposition results by plotting the entire transition path of the employer-provided health
insurance coverage gap for employed men.41
The rising cost of medical care services alone reduces employer-provided health insurance coverage rate
among employed workers (first row in Table 8, “only Cost”). Moreover, such a reduction is heterogenous
across education and gender groups because of the underlying differences in risk aversion, health, and
medical expenditure risk. Specifically, when I allow the medical care cost to grow according to its estimated
trend while fixing all other factors to their 1981 level, the employer-provided health insurance coverage
rate among employed males declines by 19 percentage points for those with a 4-year college degree and
by 17 percentage points for those with at most a high school degree. Such declines occur because, as the
private health insurance premium rises, workers with low willingness to pay for health insurance (those with
low risk aversion and/or low medical expenditure risk) choose a wage-only compensation package and thus
effectively drop out of private health insurance market. This is the “selection effect”. The model estimates
suggest that high school male workers are on average more risk averse than 4-year college male workers.
From 1981 to 2009, the coverage rate gap between 4-year college males and high school males reduces by
2 percentage points. The entire path of the changes in the coverage rate gap can also be seen in Figure 6.
The effects of Medicaid eligibility expansion on the employer-provided health insurance coverage rate
and gap among employed workers are quantitatively negligible (second row in Table 8, “only Medicaid”).
As described in Section 6.1, Medicaid eligibility expansion has little impact on labor market aggregate
employment and skill prices. Employed workers are hardly eligible for the Medicaid even after the eligibility
expansion, because both income and categorical eligibility are still strict even after expansion from 1981
to 2009. The estimated aggregate crowding-out effect of Medicaid expansion on private health insurance
among the employed workers is quantitatively negligible.
41 The
employer-provided health insurance coverage gap by education for employed female is plotted in the appendix Figure
H.18.
27
Labor market technological change increases the employer-provided health insurance coverage rate
among high-educated employees and reduces the coverage rate among low-educated employees (third row
in Table 8, “only Tech”). As described in Section 6.1, the labor market technological changes raise the
skill price of high-educated workers and reduce the skill price of low-educated workers. Among the higheducated employees, the increase in skill prices raises the market returns of health capital and thus leads to a
higher demand for health insurance because health insurance is an investment to future health; it also moves
the employee to a higher income tax bracket, thus increasing the demand for health insurance indirectly
because the health insurance premium is tax-exempt. The reverse is true for low-educated workers. As a
result, the coverage rate gap between the 4-year college employed males and high school employed males
increases by 6.7 percentage points from 1981 to 2009.
The changes in the labor force composition, especially the increase in college workers in the labor force
across cohorts over time, act in the opposite direction to the labor market technological changes. As seen in
the 4th row of Table 8 (“only LF”), changes in the labor force composition decrease the employer-provided
health insurance coverage rate among high-educated employees and increase the coverage rate among the
low-educated employees. The converge rate gap between the employed workers with at most a high school
degree and those with at least a 4-year college degree reduces by 5.5 percentage points among employed
male workers.
The fifth row of Table 8 reports the overall net effects of changes in the labor market factors, including
both skill-biased technological changes and the increases in college workers in the labor force (“Tech +
LF”). The coverage rate of employed workers without a college degree slightly increases by 1 percentage
points and the coverage rate among 4-year college employees increases by 3 percentage points. As a result,
the coverage rate gap increases by about 2 percentage points over 1981 to 2009.
So far, we notice that only the changes in medical care cost can generate a rapid sizable decline in the
health insurance coverage rate.42 On the other hand, the changes in skill-biased technological changes in
the labor market can generate an increase in the health insurance coverage rate among college workers.
Therefore, I further investigate the interactions between changes in labor market factors and changes in
medical care cost. As seen in the sixth row of Table 8 (“Tech+Cost”), the interaction between changes in
medical care cost and labor market technology drastically reduces the health insurance coverage rate among
low-educated workers, while leaving the coverage rate of more educated workers relatively stable. As a
42 However
it also predicts a large reduction in coverage rate among college workers which is in contradiction with the data.
28
Table 9: Logarithm of Hourly Wages under Counterfactual Simulations (Employed Males)
1981 to 2009
only Cost
only Medicaid
only Tech
only LF
Tech + LF
Tech + Cost
Tech + LF + Cost
Data
∆(log(wCG ))
∆(log(wSC ))
∆(log(wHS ))
-0.084
-0.000
0.411
-0.175
0.287
0.337
0.216
0.290
-0.077
0.001
0.192
-0.100
0.145
0.112
0.075
0.075
-0.047
-0.000
-0.233
0.214
0.024
-0.261
-0.025
-0.032
∆(log(wCG ) −
log(wHS ))
-0.036
0.000
0.644
-0.390
0.264
0.597
0.242
0.321
∆(log(wSC ) −
log(wHS ))
-0.030
0.001
0.425
-0.314
0.121
0.373
0.101
0.106
result, the coverage rate gap between the 4-year college and high school employed males rises by 17.8
percentage points. Once we further introduce the changes in labor force composition, the model predicted
insurance coverage gap becomes smaller (the seventh row in Table 8, (“Tech+LF+Cost”)).
Figures 6 plots the entire time series paths of the health insurance coverage gap for employed men.43 As
we can see, the interaction between medical care services cost growth and labor mark technological changes
contributes to the widening gap of health insurance coverage rate over time. The intuition is as follows.
The rising cost of medical services drives up the insurance premium in the health insurance market and, in
the presence of government social insurance programs, exacerbates the selection in the insurance market
where workers with low expected medicare care expenditure or low risk aversion drop out of private health
insurance (“selection effect”). In contrast, labor market technological change increases the demand for
health insurance especially among the high skilled individuals as it raises a high skilled worker’s marginal
productivity of health as well as income (“productivity/income effect”). Among more educated workers,
the productivity/income effect offsets selection effect, leaving a relative stable health insurance coverage.
In contrast, among less educated workers, the selection effect dominates the productivity/income effect and
leads to a sharp decline in health insurance coverage.
6.2.2
Wages
Table 9 reports relative changes in wages between 1981 and 2009 under different counterfactual simulations.
The rising cost of medical services reduces accepted wages for all education groups and also reduces the log
wage ratio between high-educated and low-educated workers (the first row in Table 9, “only Cost”). Changes
in medical care cost can affect accepted wages in two ways. First, an increase in the cost of medical services
43 The employer-provided health insurance coverage gap decomposition for employed women is reported in appendix Figure
H.18.
29
Inequality Decomposition: Employer−Provided HI Gap among Employed Males (CG/HS)
0.3
0.25
Coverage Gap
0.2
only Cost
only Medicaid
only Tech
only LF
Cost + Tech
Cost + Tech + LF
Fitted Model
0.15
0.1
0.05
0
−0.05
1980
1985
1990
1995
Year
2000
2005
2010
(a) CG/HS
Inequality Decomposition: Employer−Provided HI Gap among Employed Males (SC/HS)
0.2
Coverage Gap
0.15
0.1
only Cost
only Medicaid
only Tech
only LF
Cost + Tech
Cost + Tech + LF
Fitted Model
0.05
0
−0.05
1980
1985
1990
1995
Year
2000
2005
2010
(b) SC/HS
Figure 6: Employer-Provided HI Inequality Decomposition among Employed Males
30
leads to a reduction in wage component among workers with employer-provided health insurance coverage
because it raises the equilibrium health insurance premium. Second, however, it can also lead to an increase
the wage component among workers who switch from being covered to not covered. On average, the rising
cost of medical services alone reduces the wages by 0.084 log points for 4-year college male workers, by
0.077 log points for some college male workers, and by 0.047 log points for high school male workers.
Notice that the magnitude of such reduction is especially larger for high-educated workers. As a result, the
log wage ratio between 4-year college male workers and high school male workers is reduced by 0.036 log
points. The second row in Table 9 (“only Medicaid”) indicates that the expansion in Medicaid eligibility has
little impact on the wage growth and educational wage gap between the period 1981 and 2009. This result
is consistent with our previous analysis on its small impact on equilibrium prices and employer-provided
health insurance coverage rate.
The labor market technological changes increase the wage for high skilled workers and reduce the wage
of low educated workers, which consequently lead to the large increase in log wage ratio between college
workers and high school workers. The changes of labor force composition have the opposite effect: it
decreases wages of college workers and increases wages of high school workers, thus shrinking the college
wage premium. Introducing both the changes in labor market technology and medical services cost, the
relative change of the log wage ratio between 4-year college male workers and high school male workers
becomes 0.597 (sixth row of Table 9, “Tech+Cost”), compared to 0.644 with labor market technological
changes alone. Combining all these three factors, the relative change in log wage ratio among 4-year college
male workers and high school male workers is 0.242 log points (seventh row of Table 9, “Tech+LF+Cost”),
compared to the 0.321 log points in the data.44
To summarize, Figure 7 plots the entire time series of log wage ratio between college workers and
high school workers for employed males and females, respectively.45 As we can see, the labor market
technological change increases the log wage ratio and labor force composition change decreases the log
wage ratio; the increase in the cost of medical services also has a small but negative impact on the log wage
ratio growth.
44 The effects of these aggregate factors on wage growth and relative changes in log wage ratio work in the similar direction for
female workers, compared to male workers.
45 Figure H.19 in the appendix plots the entire time series of log wage ratio between college workers and high school workers for
employed females.
31
Inequality Decomposition: Log Wage Ratio among Employed Males (CG/HS)
1.4
1.2
Log Wage Ratio
1
only Cost
only Medicaid
only Tech
only LF
Cost + Tech
Cost + Tech + LF
Fitted Model
0.8
0.6
0.4
0.2
0
1980
1985
1990
1995
Year
2000
2005
2010
(a) CG/HS
Inequality Decomposition: Log Wage Ratio among Employed Males (SC/HS)
0.7
0.6
0.5
Log Wage Ratio
0.4
only Cost
only Medicaid
only Tech
only LF
Cost + Tech
Cost + Tech + LF
Fitted Model
0.3
0.2
0.1
0
−0.1
−0.2
1980
1985
1990
1995
Year
2000
2005
(b) SC/HS
Figure 7: Wage Inequality Decomposition among Employed Males
32
2010
6.3
Welfare Analysis
In this section, we use the estimated model to assess the value of changes in the labor market factors, including skill-biased technological changes and changes in labor force composition. Labor market technological
changes and the changes in labor force composition have heterogenous impact on employee compensation
across different education and gender. Furthermore, with the overlapping generations framework, we can
conduct welfare analysis for different cohorts.
We begin by comparing each individual’s lifetime utility in the 1981 baseline world, where all exogenous
factors stay at their 1981 levels, with the lifetime utility in the counterfactual regime, where labor market
factors change according to their actual trends. First, we compute the lifetime utility in the counterfactual
regime where all the exogenous factors stop changing and remain at their 1981 level. Denote Va (Ωa,t ; ψ1981 )
to be the lifetime utility for an age-a individual at time t with information set Ωa,t under such regime. Then
we compute the lifetime value, Va (Ωa,t ; ψ̂t ), of the same individual in the counterfactual regime where labor
market factors evolve according their estimated trends (ψ̂t ). This counterfactual simulation is the same as
the sixth counterfactual (Tech + LF) conducted in Section 6. Throughout this section, the value of labor
market technological changes is measured as the percentage changes in lifetime utility, i.e., (Va (Ωa,t ; ψ̂t ) −
Va (Ωa,t ; ψ1981 ))/Va (Ωa,t ; ψ1981 ) · 100.
As seen in the first row of Table 10, changes in the labor market factors increase welfare by 0.27% for
high school males, by 0.355% for some college males, and by 1.18% for 4-year college males. We also
conduct welfare analysis for different cohorts. In particular, we focus on the cohort that has entered in the
model when the labor market technological changes start in 1981, and a cohort which has already entered
the labor market 10 years before such changes took place. The older cohorts which enter the labor markets
before the technological changes occur benefit less than the younger cohorts. Among high school males, the
value of labor market technological changes is 0.165% for the cohort aged 25 in 1981 and is only 0.125% for
the cohort aged 35 in 1981. Among 4-year college males, the value of labor market technological changes
is 1.057% for the cohort aged 25 in 1981 and is 0.746% for the cohort aged 35 in 1981. The similar cohorts
pattern holds among females as well.
33
Table 10: Welfare Analysis (%)
HS
0.271
0.165
0.125
Male
Male Aged 25 in 1981
Male Aged 35 in 1981
7
SC
0.355
0.155
0.210
CG
1.183
1.057
0.746
Conclusion
This paper provides the first step towards understanding the causes of inequality trends in employee health
insurance coverage in addition to wages by education in the U.S. over the last 30 years. It introduces both
the health care market factor (medical care cost) and the role of government (such as Medicaid) into a
neoclassical equilibrium model of labor demand and supply. The model allows for preference heterogeneity
in risk aversion and leisure and introduces human capital accumulation both in health capital dynamics and
labor market skills. The empirical results of this paper show that there is substantial heterogeneity both
preferences (including risk aversion and leisure) and human capital formation (including both labor market
skills and health capital dynamics) and heterogeneity plays important role when responding to aggregate
changes in the economy.
In the model, the rising cost of medical services raises the equilibrium health insurance premium and
reduces the coverage rate, which consequently exaggerates the selection in the insurance market as workers
with lower risk aversion and lower medical expenditure risk choose to opt out of insurance market. It also
has a negative impact on accepted wage component of the employee compensation for those with employerprovided health insurance coverage. Counterfactual simulation shows that the interaction between cost
growth of medical services and labor market technological changes can explain most of the increase in
the employer-provided health insurance coverage gap between college workers and high school workers.
Changes in the aggregate factors, such as the labor market technological changes, have a heterogenous
impact on individuals’ choices and welfare for different cohorts and education groups. Workers with higher
education benefit more, later cohorts benefit more than early cohorts, and males benefit more than females.
This paper’s framework can be extended to study the equilibrium interactions among labor market,
private health insurance market, government’s tax system, and public social insurance programs (such as
Medicaid and Medicare). In particular, one can introduce Medicare and extend the model to study the
retirement decisions over time and quantify the relative importance of Medicare, taxation, and social security
34
system, in the presence of changing labor market technology. Another important direction of future research
could be to introduce the changes in the marriage market and study the households’ joint decisions on labor
supply and health insurance. Marriage provides a natural insurance value between spouses. It could be
interesting to study how marriage market conditions interact with labor and health insurance markets in
equilibrium.
References
Acemoglu, Daron, “Technical Change, Inequality, and the Labor Market,” Journal of Economic Literature,
2002, 40 (1), pp. 7–72.
, “Patterns of Skill Premia,” The Review of Economic Studies, 2003, 70 (2), pp. 199–230.
Aizawa, Naoki and Hanming Fang, “Equilibrium Labor Market Search and Health Insurance Reform,”
Working Paper 18698, National Bureau of Economic Research January 2013.
Aizer, Anna and Jeffrey Grogger, “Parental Medicaid Expansions and Health Insurance Coverage,” NBER
Working Papers 9907, National Bureau of Economic Research, Inc 2003.
Autor, David H., Lawrence F. Katz, and Alan B. Krueger, “Computing Inequality: Have Computers
Changed the Labor Market?,” The Quarterly Journal of Economics, 1998, 113 (4), 1169–1213.
,
, and Melissa S. Kearney, “Trends in U.S. Wage Inequality: Revising the Revisionists,” The Review
of Economics and Statistics, May 2008, 90 (2), 300–323.
Becker, G.S., Human capital: a theoretical and empirical analysis, with special reference to education National bureau of economic research publications: General series, National Bureau of Economic Research;
distributed by Columbia University Press, 1964.
Blau, David M. and Donna B. Gilleskie, “Retiree Health Insurance and the Labor Force Behavior of Older
Men in the 1990s,” The Review of Economics and Statistics, February 2001, 83 (1), 64–80.
and
, “The Role of Retiree Health Insurance in the Employment Behavior of Older Men,” International
Economic Review, 2008, 49 (2), 475–514.
35
Blumberg, Linda J, Lisa Dubay, and Stephen A Norton, “Did the Medicaid expansions for children
displace private insurance? An analysis using the {SIPP},” Journal of Health Economics, 2000, 19 (1),
33 – 60.
Bound, John and George Johnson, “Changes in the Structure of Wages in the 1980’s: An Evaluation of
Alternative Explanations,” American Economic Review, June 1992, 82 (3), 371–92.
Brown, Jeffrey R. and Amy Finkelstein, “The Interaction of Public and Private Insurance: Medicaid and
the Long-Term Care Insurance Market,” American Economic Review, 2008, 98 (3), 1083–1102.
, Norma B. Coe, and Amy Finkelstein, “Medicaid Crowd-Out of Private Long-Term Care Insurance
Demand: Evidence from the Health and Retirement Survey,” in “Tax Policy and the Economy, Volume
21” NBER Chapters, National Bureau of Economic Research, Inc, October 2007, pp. 1–34.
Card, David and John E. DiNardo, “Skill-Biased Technological Change and Rising Wage Inequality:
Some Problems and Puzzles,” Journal of Labor Economics, October 2002, 20 (4), 733–783.
and Lara D. Shore-Sheppard, “Using Discontinuous Eligibility Rules to Identify the Effects of the
Federal Medicaid Expansions on Low-Income Children,” The Review of Economics and Statistics, August
2004, 86 (3), 752–766.
, Carlos Dobkin, and Nicole Maestas, “Does Medicare Save Lives?,” The Quarterly Journal of Economics, 2009, 124 (2), 597–636.
Cohen, Alma and Liran Einav, “Estimating Risk Preferences from Deductible Choice,” American Economic Review, 2007, 97 (3), 745–788.
Cole, Harold L., Soojin Kim, and Dirk Krueger, “Analyzing the Effects of Insuring Health Risks: On the
Trade-off between Short Run Insurance Benefits vs. Long Run Incentive Costs,” Working Paper 18572,
National Bureau of Economic Research November 2012.
Currie, Janet and Brigitte C. Madrian, “Health, health insurance and the labor market,” in O. Ashenfelter
and D. Card, eds., Handbook of Labor Economics, Vol. 3 of Handbook of Labor Economics, Elsevier,
1999, chapter 50, pp. 3309–3416.
36
and Jonathan Gruber, “Health Insurance Eligibility, Utilization of Medical Care, and Child Health,”
The Quarterly Journal of Economics, May 1996, 111 (2), 431–66.
and
, “Saving Babies: The Efficacy and Cost of Recent Changes in the Medicaid Eligibility of Pregnant
Women,” Journal of Political Economy, December 1996, 104 (6), 1263–96.
Cutler, David M. and Brigitte C. Madrian, “Labor Market Responses to Rising Health Insurance Costs:
Evidence on Hours Worked,” The RAND Journal of Economics, 1998, 29 (3), pp. 509–530.
and Jonathan Gruber, “Does Public Insurance Crowd out Private Insurance?,” The Quarterly Journal
of Economics, 1996, 111 (2), 391–430.
Dey, Matthew S. and Christopher J. Flinn, “An Equilibrium Model of Health Insurance Provision and
Wage Determination,” Econometrica, 03 2005, 73 (2), 571–627.
DiNardo, John, Nicole M Fortin, and Thomas Lemieux, “Labor Market Institutions and the Distribution
of Wages, 1973-1992: A Semiparametric Approach,” Econometrica, September 1996, 64 (5), 1001–44.
Doyle, Joseph J., “Health Insurance, Treatment and Outcomes: Using Auto Accidents as Health Shocks,”
The Review of Economics and Statistics, May 2005, 87 (2), 256–270.
Einav, Liran, Amy Finkelstein, Stephen P. Ryan, Paul Schrimpf, and Mark R. Cullen, “Selection on
Moral Hazard in Health Insurance,” Working Paper 16969, National Bureau of Economic Research April
2011.
Finkelstein, Amy, “The Aggregate Effects of Health Insurance: Evidence from the Introduction of Medicare,” The Quarterly Journal of Economics, 2007, 122 (1), 1–37.
, Sarah Taubman, Bill Wright, Mira Bernstein, Jonathan Gruber, Joseph P. Newhouse, Heidi Allen,
Katherine Baicker, and Oregon Health Study Group, “The Oregon Health Insurance Experiment:
Evidence from the First Year,” The Quarterly Journal of Economics, 2012, 127 (3), pp. 1057–1106.
French, Eric and John Bailey Jones, “The Effects of Health Insurance and Self-Insurance on Retirement
Behavior,” Econometrica, 2011, 79 (3), 693–732.
French, Eric Baird and John Bailey Jones, “On the distribution and dynamics of health care costs,”
Journal of Applied Econometrics, 2004, 19 (6), 705–721.
37
Garthwaite, Craig, Tal Gross, and Matthew J. Notowidigdo, “Public Health Insurance, Labor Supply,
and Employment Lock,” Working Paper 19220, National Bureau of Economic Research July 2013.
Gertner, Robert, “Game Shows and Economic Behavior: Risk-Taking on ”Card Sharks”,” The Quarterly
Journal of Economics, 1993, 108 (2), pp. 507–521.
Gilleskie, Donna B. and David M. Blau, “Health insurance and retirement of married couples,” Journal of
Applied Econometrics, 2006, 21 (7), 935–953.
Goldin, Claudia and Lawrence F. Katz, “Decreasing (and then Increasing) Inequality in America: A Tale
of Two Half-Centuries,” in F. Welch, ed., The Causes and Consequences of Increasing Income Inequality,
Bush School Series in the Economics of P, University of Chicago Press, 2001, pp. 37–82.
and
, “The Race between Education and Technology: The Evolution of U.S. Educational Wage Dif-
ferentials, 1890 to 2005,” Working Paper 12984, National Bureau of Economic Research March 2007.
Grossman, Michael, The Demand for Health: A Theoretical and Empirical Investigation, National Bureau
of Economic Research, Inc, September 1972.
, “On the Concept of Health Capital and the Demand for Health,” Journal of Political Economy, 1972, 80
(2), pp. 223–255.
Gruber, Jonathan, “Health insurance and the labor market,” in Anthony J. Culyer and Joseph P. Newhouse,
eds., Handbook of Health Economics, Vol. 1, Part A of Handbook of Health Economics, Elsevier, 2000,
pp. 645 – 706.
and Brigitte C Madrian, “Health-Insurance Availability and the Retirement Decision,” American Economic Review, September 1995, 85 (4), 938–48.
and Brigitte C. Madrian, “Health Insurance, Labor Supply, and Job Mobility: A Critical Review of the
Literature,” NBER Working Papers 8817, National Bureau of Economic Research, Inc 2002.
and Kosali Simon, “Crowd-out 10 years later: Have recent public insurance expansions crowded out
private health insurance?,” Journal of Health Economics, 2008, 27 (2), 201 – 217.
Guvenen, Fatih, Burhanettin Kuruscu, and Serdar Ozkan, “Taxation of human capital and wage inequality: A cross-country analysis,” The Review of Economic Studies, 2013, p. rdt042.
38
Hamermesh, Daniel S., “Changing Inequality In Markets For Workplace Amenities,” The Quarterly Journal of Economics, November 1999, 114 (4), 1085–1123.
Heckman, James J, Lance Lochner, and Christopher Taber, “Explaining rising wage inequality: Explorations with a dynamic general equilibrium model of labor earnings with heterogeneous agents,” Review
of economic dynamics, 1998, 1 (1), 1–58.
Juhn, Chinhui, Kevin M. Murphy, and Brooks Pierce, “Wage Inequality and the Rise in Returns to Skill,”
Journal of Political Economy, 1993, 101 (3), pp. 410–442.
Kambourov, Gueorgui and Iourii Manovskii, “Occupational Mobility and Wage Inequality,” The Review
of Economic Studies, 2009, 76 (2), pp. 731–759.
Kaplan, Greg, “Inequality and the life cycle,” Quantitative Economics, 2012, 3 (3), 471–525.
Katz, Lawrence F. and David H. Autor, “Changes in the wage structure and earnings inequality,” in
O. Ashenfelter and D. Card, eds., Handbook of Labor Economics, Vol. 3 of Handbook of Labor Economics, Elsevier, 1999, chapter 26, pp. 1463–1555.
Katz, Lawrence F and Kevin M Murphy, “Changes in Relative Wages, 1963-1987: Supply and Demand
Factors,” The Quarterly Journal of Economics, February 1992, 107 (1), 35–78.
Kolstad, Jonathan T. and Amanda E. Kowalski, “Mandate-Based Health Reform and the Labor Market: Evidence from the Massachusetts Reform,” Working Paper 17933, National Bureau of Economic
Research March 2012.
Lee, Donghoon and Kenneth I. Wolpin, “Intersectoral Labor Mobility and the Growth of the Service
Sector,” Econometrica, 2006, 74 (1), 1–46.
and
, “Accounting for wage and employment changes in the US from 1968-2000: A dynamic model
of labor market equilibrium,” Journal of Econometrics, May 2010, 156 (1), 68–85.
Lemieux, Thomas, “The changing nature of wage inequality,” Journal of Population Economics, January
2008, 21 (1), 21–48.
Levy, Helen, “Health Insurance and the Wage Gap,” Working Paper 11975, National Bureau of Economic
Research January 2006.
39
Madrian, Brigitte C., “Employment-Based Health Insurance and Job Mobility: Is There Evidence of JobLock?,” The Quarterly Journal of Economics, 1994, 109 (1), pp. 27–54.
Manovskii, Iourii and Bjoern Bruegemann, “Fragility: A Quantitative Analysis of the US Health Insurance System,” 2010 Meeting Papers 787, Society for Economic Dynamics 2010.
Metrick, Andrew, “A Natural Experiment in “Jeopardy!”,” The American Economic Review, 1995, 85 (1),
pp. 240–253.
Olson, Craig A., “Do Workers Accept Lower Wages in Exchange for Health Benefits?,” Journal of Labor
Economics, 2002, 20 (S2), pp. S91–S114.
Pashchenko, Svetlana and Ponpoje Porapakkarm, “Quantitative analysis of health insurance reform:
Separating regulation from redistribution,” Review of Economic Dynamics, 2013, 16 (3), 383 – 404.
Pierce, Brooks, “Compensation Inequality,” The Quarterly Journal of Economics, 2001, 116 (4), 1493–
1525.
Rust, John and Christopher Phelan, “How Social Security and Medicare Affect Retirement Behavior In
a World of Incomplete Markets,” Econometrica, 1997, 65 (4), pp. 781–831.
Storesletten, Kjetil, Gianluca Violante, and Jonathan Heathcote, “Redistributive Taxation in a Partial
Insurance Economy,” Technical Report 2012.
Wood, Adrian, North-South Trade, Employment and Inequality: Changing Fortunes in a Skill-Driven
World, Oxford: Clarendon Press, 1994.
, “Globalisation and the Rise in Labour Market Inequalities,” The Economic Journal, 1998, 108 (450),
1463–1482.
40
For Online Publication:
The Determinants of Rising Inequality in
Health Insurance and Wages
A
The Model
A.1
Proof of Proposition 1
Here I sketch the proof of Proposition 1. Recall that an individual’s direct utility on consumption (ca ), health
status (ha ), employment status (dae ) is as follows (Equation 1). Therefore, based on the direct utility function,
we can define an individual’s indirect utility based on the individual’s choices as well as Medicaid coverage
status: (1) u1,0,a : employed at a job with no health insurance and not covered by Medicaid either; (2) u1,1,a :
employed at a job without health insurance but covered by Medicaid; (3) u2,a : employed at a job with health
insurance; (4) u3,a : not employed.
u1,0,a = 1 − exp(−γ(k, Za ) · ξa,t ) + φ (Za )ha
(18)
f(rtj s j )) + φ (Za )ha
u1,1,a = 1 − exp(−γ(k, Za ) · T
a
(19)
f(rtj s j − pt )) + φ (Za )ha
u2,a = 1 − exp(−γ(k, Za ) · T
a
(20)
u3,a = 1 − exp(−γ(k, Za ) · ctmin ) + φ (Za )ha + Γa,t
(21)
where ξa,t is the certainty equivalent consumption value for the individual in the presence of risky medical
f(rtj saj ) > cmin , the
expenditure and Γa,t ≡ Γ(ha , j, k, Za , a,t; εal ). For an individual with earning capacity T
certainty equivalent consumption under uninsured medical expenditure risk is implicitly defined as below
f(rtj s j ) − pt ma · σm (ha , a, j, Za ) · ε m ), cmin })],
m [exp(−γ(k, Za ) · max{T
exp(−γ(k, Za ) · ξa,t ) = Eεa,1
a
a,1
t
(22)
c , h , a, j, Z ) + σ (h , a, j, Z ) · ε m
where pt ma = ptm exp µm (Iae , Ia,t
a
a
m a
a
a,0 is the realized medical expenditure
component. Notice that when there is no consumption floor, or when the earnings are far away from con-
41
sumption floor, an individual’s consumption equivalent is given by
f(rtj s j ) −
ξa,t = T
a
1
m
m exp γ(k, Za ) · pt ma · exp(σm (ha , a, j, Za ) · ε
log Eεa,1
)
.
a,1
γ(k, Za )
(23)
Therefore an individual’s alternative-specific value functions are given by:
e
e
e
s
e
c
e
c
c
c
f
f
V1,a (Ωa,t ) =(1 − If
a,t (da = 1, Ωa,t ))u1,0,a + Ia,t (da = 1, Ωa,t )u1,1,a + δ πa+1 E[Va+1 |Ωa,t , Ia = 0, Ia = Ia,t (da = 1, Ωa,t ), da = 1]
s
V2,a (Ωa,t ) =u2,a + δ πa+1
E[Va+1 |Ωa,t , Iae = 1, Iac = 0, dae = 1]
s
e
e
c
V3,a (Ωa,t ) =u3,a + δ πa+1
E[Va+1 |Ωa,t , Iae = 0, Iac = If
a,t (da = 0, Ωa,t ), da = 0]
e
c
and If
a,t (da , Ωa,t ) is an indicator function of Medicaid coverage that depends on individual’s employment
status as well as other individual state variables summarized by Ωa,t . As we can see, if the individual is
covered by the employer-provided health insurance, then the individual can not be covered by Medicaid.
Consider an individual who chooses to work and is not eligible for Medicaid coverage once employed,
e
c
i.e., If
a,t (da = 1, Ωa,t ) = 0. Then such an individual prefers a job with employer-provided health insurance
coverage to a job without employer-provided health insurance coverage if and only if V2,a (Ωa,t ) ≥ V1,a (Ωa,t ),
that is
f(rtj s j − pt )) + exp(−γ(k, Za ) · ξa,t ) + δ π s ∆CVa+1 (Ωa,t ) ≥ 0
− exp(−γ(k, Za ) · T
a
a+1
where ∆CVa+1 (Ωa,t ) = E[Va+1 |Ωa,t , Iae = 1, Iac = 0, dae = 1] − E[Va+1 |Ωa,t , Iae = 0, Iac = 0, dae = 1].
∗ , then
Denote the threshold value for health insurance as ξa,t
∗
ξa,t
=−
1
f(rtj s j − pt )) − δ π s ∆CVa+1 (Ωa,t )
log exp(−γ(k, Za ) · T
a
a+1
γ(k, Za )
(24)
f(rtj saj − pt ))−δ π s ∆CVa+1 (Ωa,t ) > 0 and ξ ∗ = ∞ otherwise. Individuals choose to work
if exp(−γ(k, Za )T
a,t
a+1
for a job with health insurance when their consumption equivalent value ξa,t is lower than the threshold value
∗ .
ξa,t
A.2
Model Solution Algorithm
For any set of parameter values, I simulate a large sample of individuals for each cohort at each calendar
year, starting from the cohort that turned age 25 in 1941, and thus was age 64 in 1981, and ending with the
42
cohort that turned age 25 in 2009. The model is solved iterating the following steps:
Step 1: Choose a set of parameters that characterizes individuals’ forecasting of the equilibrium prices
HS , log r SC , log rCG , log p
process (log rt+1
t+1 ) and for the aggregate shock process log ζt .
t+1
t+1
Step 2: Solve the optimization problem at each age a and information set Ωa,t from t = 1 through t = T .
Individuals’ value function, Va (Ωa,t ), can be solved using Bellman Equation 9 through backward recursion
beginning with age a = A, for calendar year t = 1 to T .
Step 3: Guess an initial set of values for equilibrium prices (r1j )0 and (p1 )0 . Given the initial age distribution
and distribution of state variables for all cohorts alive at that time, simulate a sample of agents and their labor
market activities and outcomes, and calculate the aggregate quantity of supply in each intermediate goods
production. Solve the value of aggregate shock at that time using data on output.
Step 4: Update the initial guess for rental prices to be equal to the marginal products of aggregate quantity,
say (r1j )1 and (p1 )1 . Repeat steps 3, use (r1j )1 and (p1 )1 as initial guess in step 3, until the sequence of
equilibrium prices and aggregate shocks converge, say to (r1j )∗ and (p1 )∗ .
Specifically, log rtj , log pt , log ζt are updated using the five equations
j
j
log rtj = logCt − log(D(StHS , StSC , SCG
t )) + log(zt ) + (ν − 1) log(St ),
log pt = log ptm + log
j ∈ {HS, SC,CG}
!
La,t
e , h , a , j ) + σ (h , a , j ) · ε m ) · I e
∑a ∑i=1 exp(µm (Ii,a
i,a i i
m i,a i i
i,a
i,a
La,t
e
∑a ∑i=1 Ii,a
log ζt = logCt − (1/ν)log(D(StHS , StSC , SCG
t ))
HS HS ν
SC SC ν
CG CG ν
where D(StHS , StSC , SCG
t ) = zt (St ) + zt (St ) + zt (St ) , Ct is the total value of workers’ compen-
sation at time t paid by the employer. The gender index in medical expenditure function is suppressed
here.
Step 5: Guess an initial set of values for period two equilibrium prices. Repeat step 3 for t = 2 to obtain
equilibrium prices (r2j )∗ and (p2 )∗ .
Step 6: Repeat step 5 for t = 3, . . . , T .
Step 7: Using the calculated series of equilibrium prices and aggregate shocks, estimate the parameters
that govern the process of equilibrium prices and the process of aggregate shocks.
Step 8: Use these estimates, repeat steps 2-7 until the series of equilibrium prices and aggregate shocks
converge.
43
The above solution algorithm guarantees that individuals’ expectations regarding equilibrium prices are
consistent with the aggregation implications of their individual optimization behaviors. It is an extension of
the iterative method developed in Lee and Wolpin (2006).
B
Data
B.1
March Current Population Survey (March CPS)
The March CPS provides nationally representative data concerning health insurance coverage, labor market
activity, income, Medicaid coverage, educational attainment, and family characteristics. A worker is considered employed if the worker works no less than 800 hours annually. Hourly wages are equal to the annual
earnings divided by hours worked.46 An individual is covered under employer-provided health insurance
if the individual is covered by a group plan provided by an employer (including the spouse’s employer).
Table B.1 reports summary statistics for CPS sample across all the years. Calculations are weighted by CPS
sampling weights and are deflated using 2005 GDP deflator.
Figure B.2 presents the educational distribution over years in the CPS sample. The proportion of the
ages 25-65 population who were college graduates grew steadily throughout the sample period. Four-year
college graduates comprised about 22% of males in 1981 and 30% by 2009. Fifteen percent of women have
4-year college degree in 1981, and this ratio grew to 32% in 2009.
Individuals’ self-reported health status is available starting from survey year 1995.47 I define an individual to be healthy (in good health) if the individual reported to be in excellent or very good health status.
Figure B.3 plots the changes in health status by gender and education categories. The ratio of individuals
who report to be in good health is steadily declining over time. Moreover, this decline follows a similar
trend across different education groups.
B.2
Employment Cost Index (ECI)
I use 1981Q4-2009Q4 Employment Cost Index (ECI) on health insurance benefits and 2005Q4 Employer
Costs for Employee Compensation Survey (ECEC) to generate the average health insurance benefits per
covered employee paid by an employer. Both series are from the Bureau of Labor Statistic’s (BLS). I first
46 Hourly earner of below $1/hour in 1982 dollars using personal consumption expenditures (PCE) deflator ($1.86/hour in 2005
dollars under PCE deflator) are dropped. Top-coded earnings observations are multiplied by 1.5.
47 March CPS does not collect individuals’ health status information in the earning year.
44
Table B.1: Summary Statistics (CPS 1982-2010)
Age
Female
Some college
4-year college or more
Employed
Hourly Wage (Employed)
EHI (Employed)
EHI (Employed)
Medicaid
Medicaid (Not Employed)
Healthy
mean
42.18
0.53
0.25
0.25
0.71
18.97
0.82
0.18
0.06
0.17
0.62
Hourly Wage (Employed Female)
20
15
Wage
.8
10
.7
.6
EHI Coverage Rate
.9
25
Employer-Provided HI (Employed Female)
N
2,166,231
2,166,231
2,166,231
2,166,231
2,166,231
1,550,523
1,550,523
1,550,523
2,166,231
615,708
1,284,022
1981
1986
1991
1996
2001
2006
2011
1981
1986
1991
Year
1996
2001
2006
2011
Year
High School or Less
4-Year College or More
Some College
High School or Less
4-Year College or More
(a) Health Insurance Coverage Inequality (Female)
Some College
(b) Wage Inequality (Female)
Figure B.1: Wage & Employer-Provided Health Insurance Coverage Inequality (Female)
Source: Author’s calculation from March Current Population Survey 1982-2010. A worker is considered employed if the worker
works no less than 800 hours annually.
.5
Ratio
.3
.1
.1
.3
Ratio
.5
.7
Education Distribution (Female)
.7
Education Distribution (Male)
1981
1986
1991
1996
2001
2006
2011
1981
1986
1991
Year
High School or Less
4-Year College or More
1996
2001
2006
Year
Some College
High School or Less
4-Year College or More
(a) Male
(b) Female
Figure B.2: Education Distribution Over Time (CPS)
45
Some College
2011
Health Distribution (Female)
.6
Ratio of Being Healthy
.4
.6
.4
Ratio of Being Healthy
.8
.8
Health Distribution (Male)
1995
2000
2005
2010
1995
Survey Year
High School or Less
4-Year College or More
2000
2005
2010
Survey Year
Some College
High School or Less
4-Year College or More
(a) Male
Some College
(b) Female
Figure B.3: Health Distribution Over Time (CPS)
convert ECI series - which provides changes over time - into dollars using the information from the ECEC
survey 2005Q4.48 I then calculate the cost of providing health insurance per covered employee over time as
the ratio of average costs of providing health insurance benefits and average coverage rate from CPS data.
B.3
Survey of Income and Program Participation (SIPP)
The SIPP panel is a nationally representative sample of the U.S. non-institutionalized population. People in
the SIPP 1996 panel are interviewed once every 4 months from 1996 to 2000. SIPP has detailed information
on individuals’ labor market activity, health insurance coverage, Medicaid coverage, and number of children
in the family. In addition, the 1996 SIPP collects information on individuals’ health and medical usage once
a year, and on their work history. Table B.2 reports sample size and mean value of key variables in the SIPP
sample.
B.4
Medical Expenditure Panel Survey (MEPS)
The Medical Expenditure Panel Survey (MEPS) data provide detailed information about the usage and
expenditure of health care. Table B.6 reports summary statistics for the MEPS sample.
48 The ECEC survey is based on the average employer cost presented in a dollar and cents, per employee, per hour worked format.
Therefore, each employee’s annualized cost is calculated as the per hour cost multiplied by 2080 hours, consist with the annualized
income calculation in CPS data.
46
Table B.2: Summary Statistics (SIPP 1996-2000)
Age
Female
Some college
4-year college or more
Employed without EHI
Employed with EHI
Not employed
Hourly Wage
Medicaid
Healthy
Experience
mean
43.78
0.53
0.28
0.22
0.12
0.65
0.23
17.88
0.05
0.59
7.76
N
29,554
29,554
29,554
29,554
29,554
29,554
29,554
22,499
29,554
29,554
29,554
Table B.3: Transition Matrix of Choices (Females)
Employed without EHI (t-1)
Employed with EHI (t-1)
Not Employed (t-1)
Employed without EHI
0.64
0.04
0.05
Employed with EHI
0.25
0.93
0.04
Not Employed
0.10
0.04
0.91
Table B.4: Employment Rate by Health and Education (Females)
Unhealthy
Healthy
Total
High School or Less
0.50
0.69
0.59
Some College
0.67
0.79
0.74
4-Year College or More
0.74
0.80
0.78
Table B.5: Hourly Wage by Health and Education (Employed Females)
Unhealthy
Healthy
Total
High School or Less
11.28
12.11
11.74
Some College
14.08
15.76
15.15
4-Year College or More
20.10
22.68
22.12
Table B.6: Summary Statistics (MEPS 2005)
Age
Female
Some college
4-year college or more
Covered by HI
Healthy
Log total medical expenditure
47
mean
43.45
0.53
0.23
0.30
0.78
0.41
7.20
N
13,887
13,887
13,887
13,887
13,887
13,887
11,228
C
Exogenous Parameter Estimates
I set the subjective discount factor (δ ), which has proven difficult to pin down in the dynamic discrete choice
literature, to be 0.95, a 5 percent discount rate. The share of health insurance premium paid by the firm is in
the range of 75-85% (Kaiser Family foundation), so I set the fraction of health insurance premium paid by
the employer to be λ = 0.8.49
C.1
Approximating Progressive Labor Income Taxes
I assume the following functional form for labor income taxes,
T (y) = τ0 + y − τ1
yτ2 +1
τ2 + 1
(25)
This specification is the same as the one in Storesletten et al. (2012) and Kaplan (2012), and is similar
to the one used by Guvenen et al. (2013). Under this specification, the logarithm of one minus the marginal
tax rate is linear in log labor earnings,
log(1 − τ 0 (y)) = log(τ1 ) + τ2 log y
Both Storesletten et al. (2012) and Guvenen et al. (2013) provide evidence that one minus the marginal tax
rate is approximately log-linear in earnings for the US.
To estimate (τ1 , τ2 ), I regress the logarithm of one minus marginal tax rates for each individual in the
sample on annualized labor wage income. Marginal tax rates are calculated using the NBER’s TAXSIM
program. The estimated parameter values are log(τ1 ) = 1.0355 and log(τ2 ) = −0.1266 with an R2 of 0.38.
I set τ0 to the value that equates the actual average tax rate in the sample (as computed by TAXSIM) to that
implied by Equation 25.50 A regression of the actual tax liability on the predicted tax liability yields an R2
of 0.93. Figure C.4 plots the approximated labor income taxes along individuals’ wage income.
49 My
model could potentially be extended to the case where the share of health insurance premium paid by employers varies
over time; however, due to limited data, I assume that this fraction is constant.
50 The actual average tax rate in the sample equals 0.1437, and thus τ = 322.5875.
0
48
Figure C.4: Approximated Labor Income Tax Schedule
C.2
Medical Services Consumption
Recall from Equation 5, I allow health insurance coverage status, health status, age, education, and demographic variables to affect the logarithm of medical services consumption through the mean shifter µm (·);
health status, age, education, and gender impact the medical services consumption through the variance
shifter σm (·). Specifically, I assume that µm (·) and σm (·) are linear functions of the following forms:
c
c
µm (Iae , Ia,t
, ha , a, j, Za ) = α0,m + α1,m 1(Iae + Ia,t
> 0) + α2,m ha + α3,m a + α4,m 1( j = SC)
+ α5,m 1( j = CG) + α6,m 1(female = 1) + α7,m a · 1(female = 1)
σm (ha , a, j, Za ) = ς0,m + ς1,m ha + ς2,m a + ς3,m 1( j = SC)
+ ς4,m 1( j = CG) + ς5,m 1(female = 1) + ς6,m a · 1(female = 1).
m + ε m ) ∼ N(0, 1) in order to separately identifying σ (h , a, j, Z )
Furthermore, I assume that εam ≡ (εa,0
m a
a
a,1
function.
To estimate the medical services consumption model, I use 2005 MEPS data. In the data, we observe individuals’ total medical services expenses (ptm ma ) instead of medical services consumption (ma ). Therefore,
m
the cost of medical services at 2005 (pt=2005
) and the constant term of the medical services consumption
function (α0,m ) can not be separately identified. In fact the level of the cost of medical services is directly related to how we define the medical consumption unit. Thus, without loss of generality, I normalize α0,m = 0
and estimate the logarithm of medical services expenses (ptm ma ) for t = 2005 by maximum likelihood using
49
the following model:
log(ptm ma ) = log ptm + µm (Ia , ha , a, j, female) + σm (ha , a, j, female) · εam .
(26)
Table C.7: Medical Services Consumption Function
µm (Ia , ha , a, j, female)
Covered by HI
Healthy
Age
Some college
4-year college or more
Female
Age × female
0.680∗∗
-0.667∗∗
0.045∗∗
0.211∗∗
0.262∗∗
0.965∗∗
-0.013∗∗
(0.036)
(0.030)
(0.002)
(0.036)
(0.035)
(0.122)
(0.003)
σm (ha , a, j, female)
Healthy
Age
Some college
4-year college or more
Female
Age × female
Constant
Observations
-0.158∗∗
-0.004∗∗
-0.121∗∗
-0.158∗∗
0.173∗∗
-0.004∗∗
1.812∗∗
11228
(0.021)
(0.001)
(0.025)
(0.024)
(0.087)
(0.002)
(0.070)
Standard errors in parentheses
∗
p < 0.10, ∗∗ p < 0.05
Table C.7 presents the estimation results for individuals’ medical consumption expenses (Equation (26)).
The positive and significant coefficient for health insurance coverage implies that an individual’s medical
care consumption is higher when covered by health insurance. As expected, good health reduces medical
expenditure. Medical care services consumption also increases as the individual ages. Finally, the positive
and significant coefficients for some college dummy and the 4-year college dummy are consistent with
many empirical findings that higher educated individuals tend to utilize medical services more, other things
being equal. The volatility of log medical care consumption is decreasing in health, age, and education. I
m and ε m are independent, ε m ∼ N(0, σ 2 ), and ε m ∼ N(0, σ 2 ). Following French and
assume that εa,0
m,0
m,0
a,1
a,0
a,1
2 = 0.6668.
Jones (2004), I set the variance of the transitory component of medical consumption to be σm,1
2 = 1 − σ 2 = 0.3332.
Therefore, σm,0
m,1
50
C.3
Transition Probability Regarding the Presence of Dependent Children
The transition function of the presence of dependent children is estimated using a Logit regression model
that depends on the presence of dependent children, education, age, age squared, and sex,
ch
ch
−1
Proba (zch
a = 1|za−1 , a, j) = (1 + exp(−Z a α ch ))
2
where Z ch α ch = α0,ch + α1,ch zch
a−1 + α2,1,ch 1(J = SC) + α2,2,ch 1(J = CG) + α3,ch a + α4,ch a + α5,ch · female.
Table C.8 reports the estimation result for the transition function regrading the presence of dependent children.
Table C.8: Transition Function of Having Children under 18
Kids < 18 yrs
Kids < 18 yrs, previous year
Some college
4-year college or more
Age
Age squared/100
Female
Constant
Observations
6.442∗∗
0.121∗
0.403∗∗
-0.222∗∗
0.133∗∗
-0.026
3.209∗∗
(0.075)
(0.073)
(0.074)
(0.030)
(0.034)
(0.060)
(0.631)
29554
Standard errors in parentheses
∗
C.4
p < 0.10, ∗∗ p < 0.05
Approximating Medicaid Coverage Eligibility Rules
Medicaid is the biggest public health insurance program for non-elderly adults in the U.S. It is a means-tested
program, and being poor is not the only standard for coverage. To be eligible for Medicaid, low income
individuals need to belong to certain eligibility groups based on factors such as presence of dependent
children, employment status, and age (i.e., “categorical standard”). Historically, Medicaid eligibility for
non-elderly adults was closely tied to Aid to Families with Dependent Children (AFDC) cash assistance
since its enactment in 1965. Starting in 1984, the link between Medicaid and welfare was gradually severed.
The 1996 welfare reform, Personal Responsibility and Work Opportunity Act of 1996, which ended the
linkage between eligibility for cash assistance and eligibility for Medicaid and allowed higher Medicaid
eligibility thresholds, caused the largest change in Medicaid eligibility since its enactment and before the
51
2010 Affordable Care Act.
c ∈ {0, 1}) is specified as a function of a time-varying
In the model, Medicaid coverage eligibility (Ia,t
c ∈ {0, 1}) as follows
income threshold (ytcat ) and categorical standard (da,t
c
c
Ia,t
= Itc ( j, Xa ) = da,t
· (ya ≤ ytcat ) · 1(Iae = 0)
(27)
where the last term 1(Iae = 0) ensures that individuals with private health insurance coverage are not eligible
c are allowed to change over
for Medicaid. Both the income threshold ytcat and the categorical standard da,t
time. Individuals form rational expectation regarding their changes. The Medicaid eligibility is externally
estimated outside the structure model.
The income threshold at time t, ytcat , is obtained as a fraction of Federal Poverty Level (FPL) that is
changing over time. Individuals form an expectation on changes in the income threshold ytcat according to
the following process,
cat
cat
log yt+1
− log ytcat = gcat + εt+1
(28)
Historically, Medicaid eligibility for adults is very limited in most states. In the median states, the
income eligibility threshold for adults is 63% of the poverty level.51 Denote by FPL the federal poverty level
for a one person family, the mean and standard deviation of log(FPLt ) − log(FPLt−1 ) from 1982 to 2009 are
0.0058 and 0.0118 respectively (deflated using 2005 GDP deflator). Therefore, I set the mean and standard
deviation of the logarithm of income threshold evolution process to be gcat = 0.0058 and σ cat = 0.0118.
On average, FPL increases by 34% for one additional person. For example, in 2005, FPL for a one person
family was $9,570, with $3,260 for each additional person. Thus, the annual income threshold adjusted by
the presence of dependent children is ycat = 0.63 · (9570 + 3260 · Z ch ).
The categorical standard of Medicaid eligibility is complex and it is difficult to incorporate all the factors
c ,
that may impact the eligibility into the model.52 I therefore approximate the categorical standard, da,t
as a function of model state variables, including age, education, employment status, and the presence of
dependent children, separately for men and women, and separately for different time periods.
To approximate the changes in categorical standard in Medicaid eligibility, I split the whole time period
into the following 7 sub-periods: (1) prior 1965 (no Medicaid), (2) 1965 to 1985, (3) 1986 to 1989, (4) 1990
51 The Kaiser Commission on Medicaid and the Uninsured, 5 Key Questions and Answers About Medicaid, Chartpack, May 2012
52 For example, marital status impacts medicaid coverage eligibility, however CPS does not collect individuals’ marital information for the reference year in which Medicaid coverage information is asked.
52
to 1995, (5) 1996 to 1999, (6) 2000 to 2006, and (7) 2007 to 2009. For each sub-period t¯, I estimate a Probit
model separately for men and women whose income is below the Medicaid income threshold and have no
private health insurance:
c
da,
t¯ =α0,t¯,gender + ∑ α1,i,t¯,gender 1(a0 + i · 5 ≤ a < a0 + (i + 1) · 5) +
i=1
+ α3,t¯,gender dae + α4,t¯,gender Zach + σt¯c,gender εtc
∑
α2, j,t¯,gender
j=SC,CG
(29)
where α1,i,t¯,gender captures the effect of being in age group i on Medicaid categorical eligibility, α2, j,t¯,gender
and α3,t¯,gender allows difference in eligibility by education groups and employment status, and α4,t¯,gender
reflects the eligibility standard based on having dependent children. The probabilistic feature of Medicaid
coverage captures the factors that impact Medicaid coverage but are not included in the model, such as
take-up cost as well as state-level differences.
Equation 29 is meant to be a first-order approximation of Medicaid categorical eligibility for workingage population who are making decisions on employment, mainly low income parents. The estimated parameter values could reflect the effects of other related variables that are not directly included in the specification. For example, we do not explicitly model disability status because adding another state variable
exaggerates an already heavy computational burden, as well as because disabled individuals only account
for a small fraction of the labor force and are not our primary population of interest. However, to the extent
that disability status is highly correlated with age, the estimated age group specific coefficients for different
time periods could partially pick up the effects of disability on eligibility.
c , I estimate the following Probit model for males and females
To estimate the categorical eligibility, da,t
separately, excluding those whose earnings exceed the calculated Medicaid income threshold or those with
private health insurance:
c
da,t
=



α0,1 + ∑i α1,i,1 1(a ∈ age groupi ) + ∑ j∈SC,CG α2, j,1 + α3,1 dae + α4,1 Zach + σ1c εtc , 1981 ≤ t ≤ 1985







α0,2 + ∑i α1,i,2 1(a ∈ age groupi ) + ∑ j∈SC,CG α2, j,2 + α3,2 dae + α4,2 Zach + σ2c εtc , 1986 ≤ t ≤ 1989





e
ch
c c
 α0,3 + ∑ α1,i,3 1(a ∈ age group ) + ∑
i
j∈SC,CG α2, j,3 + α3,3 da + α4,3 Za + σ3 εt , 1990 ≤ t ≤ 1995
i


α0,4 + ∑i α1,i,4 1(a ∈ age groupi ) + ∑ j∈SC,CG α2, j,4 + α3,4 dae + α4,4 Zach + σ4c εtc , 1996 ≤ t ≤ 1999







α0,5 + ∑i α1,i,5 1(a ∈ age groupi ) + ∑ j∈SC,CG α2, j,5 + α3,5 dae + α4,5 Zach + σ5c εtc , 2000 ≤ t ≤ 2006





e
ch
c c
 α0,6 + ∑ α1,i,6 1(a ∈ age group ) + ∑
i
j∈SC,CG α2, j,6 + α3,6 da + α4,6 Za + σ6 εt , 2007 ≤ t ≤ 2009
i
53
.
Note here I suppress the gender subscript associated with the above parameters for abbreviation.
Table C.9: Medicaid Categorical Eligibility Regression (Male)
(1)
1981 to 1985
0.065
(0.041)
(2)
1986 to 1989
0.064∗
(0.037)
(3)
1990 to 1995
0.137∗∗
(0.038)
(4)
1996 to 1999
0.217∗∗
(0.057)
(5)
2000 to 2006
0.095∗∗
(0.036)
(6)
2007 to 2009
0.115∗∗
(0.049)
Age ∈ [35, 39]
0.057
(0.043)
0.077∗
(0.040)
0.109∗∗
(0.040)
0.351∗∗
(0.055)
0.168∗∗
(0.035)
0.178∗∗
(0.048)
Age ∈ [40, 44]
0.119∗∗
(0.047)
0.087∗∗
(0.043)
0.099∗∗
(0.040)
0.352∗∗
(0.055)
0.187∗∗
(0.034)
0.267∗∗
(0.046)
Age ∈ [45, 49]
-0.139∗∗
(0.048)
-0.115∗∗
(0.044)
-0.042
(0.043)
0.158∗∗
(0.056)
0.200∗∗
(0.033)
0.207∗∗
(0.043)
Age ∈ [50, 54]
-0.205∗∗
(0.044)
-0.194∗∗
(0.040)
-0.017
(0.041)
0.080
(0.056)
0.011
(0.033)
0.131∗∗
(0.044)
Age ∈ [55, 59]
-0.350∗∗
(0.041)
-0.345∗∗
(0.038)
-0.257∗∗
(0.041)
-0.130∗∗
(0.054)
-0.205∗∗
(0.033)
0.013
(0.043)
Age ∈ [60, 64]
-0.506∗∗
(0.038)
-0.529∗∗
(0.035)
-0.636∗∗
(0.037)
-0.480∗∗
(0.052)
-0.527∗∗
(0.032)
-0.330∗∗
(0.042)
Some College
-0.417∗∗
(0.034)
-0.407∗∗
(0.031)
-0.457∗∗
(0.027)
-0.424∗∗
(0.034)
-0.350∗∗
(0.020)
-0.323∗∗
(0.026)
4-Year College
-0.697∗∗
(0.049)
-0.712∗∗
(0.045)
-0.727∗∗
(0.037)
-0.647∗∗
(0.045)
-0.717∗∗
(0.027)
-0.606∗∗
(0.035)
Employed
-0.598∗∗
(0.057)
-0.609∗∗
(0.052)
-0.587∗∗
(0.049)
-0.527∗∗
(0.064)
-0.443∗∗
(0.040)
-0.463∗∗
(0.050)
Having Dependent Children
0.222∗∗
(0.025)
0.218∗∗
(0.023)
0.217∗∗
(0.022)
-0.058∗
(0.030)
-0.093∗∗
(0.019)
0.043∗
(0.025)
Constant
-0.775∗∗
(0.030)
27204
-0.767∗∗
(0.028)
32306
-0.675∗∗
(0.029)
32979
-0.721∗∗
(0.044)
18731
-0.595∗∗
(0.027)
49590
-0.748∗∗
(0.034)
25729
Age ∈ [30, 34]
Observations
Standard errors in parentheses
∗ p < 0.10, ∗∗ p < 0.05
54
Table C.10: Medicaid Categorical Eligibility Regression (Female)
(1)
1981 to 1985
-0.147∗∗
(0.021)
(2)
1986 to 1989
-0.145∗∗
(0.019)
(3)
1990 to 1995
-0.175∗∗
(0.020)
(4)
1996 to 1999
-0.043
(0.029)
(5)
2000 to 2006
-0.100∗∗
(0.019)
(6)
2007 to 2009
-0.081∗∗
(0.028)
Age ∈ [35, 39]
-0.217∗∗
(0.022)
-0.217∗∗
(0.020)
-0.317∗∗
(0.021)
-0.138∗∗
(0.029)
-0.150∗∗
(0.019)
-0.168∗∗
(0.029)
Age ∈ [40, 44]
-0.293∗∗
(0.024)
-0.298∗∗
(0.022)
-0.393∗∗
(0.022)
-0.178∗∗
(0.030)
-0.130∗∗
(0.020)
-0.187∗∗
(0.029)
Age ∈ [45, 49]
-0.325∗∗
(0.026)
-0.343∗∗
(0.024)
-0.484∗∗
(0.025)
-0.197∗∗
(0.033)
-0.216∗∗
(0.021)
-0.155∗∗
(0.029)
Age ∈ [50, 54]
-0.389∗∗
(0.027)
-0.409∗∗
(0.024)
-0.555∗∗
(0.026)
-0.295∗∗
(0.034)
-0.238∗∗
(0.022)
-0.161∗∗
(0.031)
Age ∈ [55, 59]
-0.360∗∗
(0.026)
-0.385∗∗
(0.024)
-0.580∗∗
(0.026)
-0.372∗∗
(0.035)
-0.342∗∗
(0.023)
-0.309∗∗
(0.032)
Age ∈ [60, 64]
-0.404∗∗
(0.026)
-0.434∗∗
(0.024)
-0.722∗∗
(0.025)
-0.481∗∗
(0.034)
-0.482∗∗
(0.022)
-0.434∗∗
(0.032)
Some College
-0.420∗∗
(0.019)
-0.425∗∗
(0.017)
-0.454∗∗
(0.015)
-0.391∗∗
(0.020)
-0.336∗∗
(0.012)
-0.288∗∗
(0.017)
4-Year College
-0.953∗∗
(0.030)
-0.960∗∗
(0.028)
-1.113∗∗
(0.027)
-0.997∗∗
(0.031)
-0.941∗∗
(0.018)
-0.869∗∗
(0.024)
Employed
-0.452∗∗
(0.033)
-0.463∗∗
(0.030)
-0.348∗∗
(0.026)
-0.154∗∗
(0.032)
-0.084∗∗
(0.022)
-0.160∗∗
(0.033)
Having Dependent Children
0.173∗∗
(0.018)
0.170∗∗
(0.016)
0.162∗∗
(0.016)
-0.003
(0.021)
-0.104∗∗
(0.013)
-0.014
(0.018)
Constant
-0.863∗∗
(0.021)
91929
-0.839∗∗
(0.019)
108778
-0.451∗∗
(0.019)
88534
-0.580∗∗
(0.027)
48872
-0.531∗∗
(0.017)
125492
-0.505∗∗
(0.025)
56209
Age ∈ [30, 34]
Observations
Standard errors in parentheses
∗ p < 0.10, ∗∗ p < 0.05
55
D
Parameterization of the Structural Model
An individual’s utility function is given as follows,
u(ca , dae , ha ; a,t, Za , εal ) = 1 − exp(−γ(k, Za ) · ca ) + φ (Za ) · ha + Γ(ha , j, k, Za , a,t; εal ) · (1 − dae )
where γ(k, Za ) is the risk aversion coefficient that depends on unobserved type and demographic characteristics, φ (Za ) is the flow utility of health which depends on the individual’s characteristics Za , and finally
Γ(ha , j, k, a,t, Za ; εal ) characterizes the value of leisure and home time which depends on the individual’s
health, education, unobserved type, age, calendar time, and individual demographic characteristics.
I allow the risk aversion coefficients to be gender-type specific; I also allow the flow utility of good
health to be gender specific.
γ(k, Za ) = γgender,k
φ (Za ) = φh,gender
An individual’s preference towards leisure/work, Γ(ha , j, k, Za , a,t; εal ), is also gender-specific and depends
on the individual’s unobserved type, presence of dependent children, age, health, education, and calendar
time, specifically:
Γ(ha , j, k, Za , a,t; εal ) = ∑ φ0,gender,k 1(type = k) + φ1,gender (1 − ha ) + φ2,gender zch
a + φ3,gender 1(a ≥ 45)(a − 45)
k
+ φ4,gender 1( j = SC) + φ5,gender 1( j = CG) + φ6,gendert + φ7,gendert 2 + σl,gender · εal
l
where zch
a ∈ {0, 1} is an indicator variable for the presence of dependent children and and εa ∼ N(0, 1)
is an age-varying preference shock to home time. The evolution of zch
a is modeled as an exogenous and
probabilistic function that depends on zch
a−1 and other individual characteristics such as age, gender, and
education.53 Motivated by the observed patterns between employment and age (see Figure G.12), I allow
an individual’s valuation of home time to vary proportionally with age after age 45. Finally, the linear and
quadratic time trends are introduced to capture the productivity progress in the home sector over time.
The efficient skill units of an individual with education j, saj , depends on the individual’s initial skill en53 Please
see Appendix C.3 for details of parameterization and estimation.
56
j
dowment (κ0,gender,k
), health status that is determined at the end of the previous period (ha ), work experience
(expra ), and a productivity shock (εaj ):
j
saj = exp(∑ κ0,k
· 1(type = k) + κ1j ha + κ2j expra + κ3j expr2a + εaj )
k
j
where εaj ∼ N(0, σ 2j ). Note κ0,gender,k
is the gender-type specific parameter that introduces permanent het-
erogeneity among individuals of the same education category even after controlling for all the observables.
The probability of making a transition from health status ha at age a to good health status at age a + 1 is
assumed to follow a Logit model:
c
Pr(ha+1 = 1) = H(Iae , Ia,t
, ha , a, j, k, Za ) =
exp(Xah β )
1 + exp(Xah β )
(30)
j
where Xah β = ∑k β0,gender,k
· 1(type = k) + β1j ha + β2 Ia + β3 a + β4 1( j = SC) + β5 1( j = CG) + β6 a2 and Ia ≡
c > 0) is an indicator variable for health insurance coverage status.
1(Iae + Ia,t
Due to the unavailability of reliable data linking medical cost and health dynamics over the entire sample
period, I exclude the cost of medical services consumption (ptm ) from entering the health transition dynamics. In particular, to estimate the health effect of the unit cost of medical services, ptm , we need a nationally
representative micro-level panel data set, that includes information on medical expenditure, health insurance, and health from 1980 to 2009; however, such data is not available.54 This assumption is appropriate if
changes in ptm are not primarily driven by quality changes of medical care services for the working-age population. Reasons for such a cost increase include growing aging population and expansion of public health
insurance for the elderly population (i.e. Medicare).55 However, if the sharp increase in ptm is mainly driven
by the quality improvement in medical services, the welfare benefit of the increase in ptm will be underestimated in this model; in such a case, we expect to see the health status to be improving over time (especially
for 4-year college workers who experience little reduction in health insurance coverage). However, this is
not supported by data; as seen from the time-series sequence of health status from CPS data (Figure B.3),
the fraction of individuals aged 25 to 64 who report good health is uniformly declining over time.
Another restriction regarding the health transition dynamics is that I do not distinguish between employer54 Medical
Expenditure Panel Survey (MEPS) is available since 1996.
example, Finkelstein (2007) shows that the introduction of Medicare in 1965 has a large impact on hospital spending and
that the overall spread of health insurance between 1950 and 1990 can explain about half of the increase in real per capita health
spending over this time period.
55 For
57
provided insurance versus public health insurance in their effects on health. If Medicaid has lower health
effects than employer-provided health insurance, this will likely introduce an upward bias of the crowding
out effect of Medicaid on private health insurance among those who are eligible. However as we see in Section 6.2, the estimated effect of Medicaid is small on average, so the quantitative impact of this assumption
is small as well.
I model the conditional probability of being a particular type k = {1, . . . , K} using a Multinomial Logistic
model as follows:
ch
Pr(type = k|female, j, h25 , expr25 , Z25
)=
exp(Πk )
,
1 + exp(Π1 ) + exp(Π2 )
k>1
where Πk = π0k +π1k 1(female = 1)+π2k 1( j = SC)+π3k 1( j = CG)+π4k 1(female = 1)1( j = SC)+π5k 1(female =
ch . In the estimation, I use three discrete types to approximate un1)v1( j = CG) + π6k h25 + π7k expr25 + π8k Z25
observed individual heterogeneity, corresponding to three education levels. As seen from the discussion on
model fit (Section 5.2), the model with three unobserved types is sufficient to capture salient features in the
data.56
E
SMM Moment Conditions and the Asymptotic Distribution of Parameter
Estimates
I estimate a vector of parameters on preference, human capital accumulation, health transition, aggregate production function, and skill-biased technology change, θ , using the simulated method of moments
(SMM). There are 86 parameters to be estimated in total. The estimate, θ̂ , is the value of θ that minimizes
the weighted distance between the estimated life cycle profiles for labor participation, health insurance coverage, wage, and health for different cohorts over the time period 1981 to 2009. Specifically, I match 1,530
moment conditions. Table E.11 lists all the moment conditions used in the estimation.
Let G(θ ) denote the vector of moment conditions that is described above and let Ĝ(θ ) denote its sample
analog. Denote Ŵ as the weighting matrix, then the SMM estimator θ is given by (see, also French and
Jones (2011)),
arg min
θ
56 Three
I
ĜI (θ )0Ŵ ĜI (θ )
1 + ñ
is also the minimum number of discrete points in order to approximate a normal distribution.
58
(31)
where I is the number of independent individuals in the sample and ñ is the ratio of the number of observations to the number of simulated observations.
The asymptotical distribution of SMM estimator θ̂ is given by
√
d
I(θ̂ − θ0 ) → N(0, Σ)
(32)
with the variance-covariance matrix Σ given by
Σ = (1 + ñ)(D0W D)−1 D0W SW D(D0W D)−1
where S is the variance-covariance matrix of the data moments,
D=
∂ G(θ )
∂θ0
θ =θ0
I use a “diagonal” weighting matrix, as suggested by French and Jones (2011). The diagonal weighting
scheme uses the inverse of the matrix that is the same as S along the diagonal and has zeros off the diagonal
of the matrix. I estimate D with its sample analogs. Specifically, I calculate D as the Jacobian matrix of
sample moments at the estimated parameter values: D̂ =
∂ Ĝ(θ )
∂ θ 0 θ =θ̂ .
Furthermore, I employed the Savitzky-
Golay filter to calculate the numerical first-order derivative of Ĝ(θ ) to deal with the issue of potential
non-smoothness in numerical derivation calculation.
59
Table E.11: Targeted Moments
Targeted Moments from CPS
# of Moments
Employed% by age, education and sex
EHI% by age, education and sex
Wage rate by age, education and sex
Employed% by year, education and sex
EHI% by year, education and sex
Wage rate by year, education and sex
Employed% by presence of dependent children and sex
Wage rate square by education and sex
Healthy% by age and sexa
Healthy% by education and sex
Targeted Moments from SIPPb
40 × 3 × 2
40 × 3 × 2
40 × 3 × 2
29 × 3 × 2
29 × 3 × 2
29 × 3 × 2
2×2
3×2
40 × 2
3×2
# of Moments
Healthy% by prev. health and sex
Healthy% by prev. health insurance coverage and sex
Healthy% by 4 age groups and sexc
Healthy% by education and sex
Employed% by 4 age groups , health and sex
EHI% by 4 age groups , health and sex
Employed% by education, health and sex
EHI% by education, health and sex
Wage rate by education, health, and sex
Wage rate by education, 4 experience groups, and sex
Prob. distribution of 4 experience groups by education and sex
Diagonal matrix of one-period choice transition prob by education and sex
Diagonal matrix of one-period choice transition prob by 4 age groups and sex
Diagonal matrix of one-period choice transition prob by health and sex
Product of current wage rate and prev. wage rate by education and sex
2×2
2×2
4×2
3×2
4×2×2
4×2×2
3×2×2
3×2×2
3×2×2
3×4×2
3×3×2
3×3×2
3×4×2
3×2×2
3×2
Note: All the moments are unconditional moments; wage rate is assigned to be zero for individuals who were not employed. EHI
refers to employer-provided health insurance.
a CPS
collects information on health status from survey year 1995 onwards.
data covers the 1996-2000 period, thus when matching moments from SIPP, I also restrict the model generated moments
to the same time period.
c Due to the concern of small sample size, I calculate health distribution over 4 age groups for each gender: 25-34, 35-44, 45-54,
55-64.
b SIPP
60
F
Additional Parameter Estimates
Figure F.5 graphs the estimated type distribution conditional on education level among men and women. As
we can see there is a relatively large fraction of type 2 individuals in high school or less category and 4-year
college category.
Table F.12: Type Probability Function (Multinomial Logit Model)
Type 2 (k = 2)
π0k :
π1k :
π2k :
π3k :
π4k :
π5k :
π6k :
π7k :
π8k :
constant
female
some college
4-year college or more
female × some college
female × 4-year college
health at age 25
work experience at age 25
presence of children at age 25
-1.023
-0.167
-0.973
-0.624
-0.048
-0.325
0.495
-0.110
1.684
( 0.1404 )
( 0.0648 )
( 0.0695 )
( 0.1010 )
( 0.0875 )
( 0.1279 )
( 0.0712 )
( 0.0301 )
( 0.1302 )
Type 3 (k = 3)
0.323
0.181
-0.890
-1.749
-0.041
0.132
0.049
-0.355
1.745
( 0.0324 )
( 0.0393 )
( 0.0542 )
( 0.0967 )
( 0.0364 )
( 0.0732 )
( 0.0567 )
( 0.0101 )
( 0.0223 )
Standard errors in parentheses
Preferences over Leisure: Table F.17 presents the estimated parameter on preference towards leisure. There
is large heterogeneity in the value of leisure (φ0 ) among individuals by type and by gender: type 3 individuals
value leisure the most and type 2 the least; women value leisure more than men on average. Women value
home production much more when there are dependent children (φ1 = 0.091) while the opposite is true for
men (φ1 = −0.155). The valuation of leisure (φ2 ) increases with age both for men and women at a similar
rate. More importantly, both men and women value leisure more when in bad health status than when in
good health status (φ3 is positive and significant). Lastly, the value of home time decreases over time at a
much higher rate for women than for men (φ6 is much more negative for women than for men), reflecting
the relatively large impact of technical improvement on women’s productivity in the home sector.
The probability of being in good health deteriorates with age at an increasing rate. Individuals also
differ in terms of the efficiency of their health production: type 1 individuals are most efficient in health
production and type 3 the least. To illustrate the health transition dynamics under estimated parameter
values, we plot the health transition probability for 4-year college and high school males in Figure F.6
and F.7.57 The probability of maintaining good health decreases over age, increases with education, and
differs across types; health insurance coverage improves the probability of maintaining good health but the
57 Here
we assume that realized health production shocks are zeros.
61
Table F.13: Estimates of Preference Parameters on Health and Leisure
Male
φh : flow utility of good health
φRE : value of good health in VA+1 (·)
φ0 : constant term, leisure
type 1
type 2
type 3
φ1 : leisure × bad health
φ2 : leisure × dep. children
φ3 : leisure × (age-45) if age > 45
φ4 : leisure × some college
φ5 : leisure × 4-year college
φ6 : time trend linear
φ7 · 100: time trend square
σl : s.d of shocks to leisure
Female
0.200
0.113
( 0.0079 )
( 0.0966 )
0.175
0.199
( 0.0068 )
( 0.0904 )
0.176
0.042
0.399
0.057
-0.155
0.015
0.007
0.003
-0.002
0.001
0.029
( 0.0076 )
( 0.0023 )
( 0.0110 )
( 0.0029 )
( 0.0057 )
( 0.0005 )
( 0.0012 )
( 0.0006 )
( 0.0001 )
( 0.0001 )
( 0.0020 )
0.204
0.049
0.462
0.047
0.091
0.014
0.016
0.020
-0.010
0.011
0.025
( 0.0081 )
N.A.
N.A.
( 0.0033 )
( 0.0041 )
( 0.0005 )
( 0.0022 )
( 0.0029 )
( 0.0003 )
( 0.0004 )
( 0.0022 )
Parameter restriction: φ0,female,k = φ0,female,1 · φ0,male,k /φ0,male,1 for k = 2, 3.
Standard errors in parentheses
Table F.14: Minimum Consumption Floor Parameters
cmin
0 : initial value of consumption floor
gc : time trend
Standard errors in parentheses
62
3549.945
15.478
( 66.5834 )
( 1.1776 )
100
Type Distribution (Male)
13.2
20.5
80
23.0
22.8
25.6
40
Percent
60
13.9
65.5
64.0
Some College
4-year College or More
0
20
51.4
High School or Less
Type 1
Type 2
Type 3
100
Type Distribution (Female)
21.0
18.5
15.9
20.1
57.7
60.6
Some College
4-year College or More
40.3
0
20
40
Percent
60
80
26.4
39.6
High School or Less
Type 1
Type 2
Type 3
Figure F.5: Type Distribution Conditional on Education and Gender
63
Table F.15: Health Transition Function Parameters
β0,gender,k : constant
male, type 1
male, type 2
male, type 3
female, type 1
female, type 2
female, type 3
β1 : current health
β2 : health insurance coverage
β3 : some college
β4 : 4-year college or more
β5 : age
β6 · 100: age square
-0.214
-0.645
-0.676
-0.192
-0.622
-0.653
1.668
0.223
0.257
0.723
-0.024
-0.011
(
(
(
(
(
(
(
(
(
(
0.0142 )
0.0234 )
0.0442 )
0.0171 )
N.A.
N.A.
0.0254 )
0.0063 )
0.0278 )
0.0301 )
0.0006 )
0.0023 )
Parameter restrictions: β0,female,k = β0,female,1 + β0,male,k − β0,male,1 for k = 2, 3.
Standard errors in parentheses
Table F.16: Skill Production Function Parameters
j=HS
j
κ0,gender,k
: constant
male, type 1
male, type 2
male, type 3
female, type 1
female, type 2
female, type 3
j
κ1 : health
κ2j : experience
κ3j · 100: exper. square
s.d of shocks
j
0.000
-0.919
-1.534
-0.353
-1.272
-1.887
0.083
0.029
-0.052
0.401
j=SC
N.A.
( 0.0273 )
( 0.0625 )
( 0.0088 )
N.A.
N.A.
( 0.0067 )
( 0.0009 )
( 0.0019 )
( 0.0086 )
j
0.000
-1.263
0.760
-0.078
-1.341
0.681
0.116
0.033
-0.036
0.331
j
N.A.
( 0.0206 )
( 0.0421 )
( 0.0113 )
N.A.
N.A.
( 0.0027 )
( 0.0013 )
( 0.0029 )
( 0.0113 )
j=CG
0.000
0.409
0.618
-0.232
0.177
0.386
0.167
0.026
-0.057
0.576
N.A.
( 0.0185 )
( 0.0345 )
( 0.0101 )
N.A.
N.A.
( 0.0072 )
( 0.0010 )
( 0.0027 )
( 0.0080 )
j
Parameter restrictions: κ0,male,1 = 0 and κ0,female,k = κ0,female,1 + κ0,male,k for k = 2, 3.
Standard errors in parentheses
magnitude is small. The probability of recovering from bad health to good health also decreases with age
and differ by education and type; health instance coverage improves the recovery probability.
64
Table F.17: Estimates of Preference Parameters on Health and Leisure
Male
φ0 : constant term, leisure
type 1
type 2
type 3
φ1 : leisure × dep. children
φ2 : leisure × (age-45) if age > 45
φ3 : leisure × bad health
φ4 : leisure × some college
φ5 : leisure × 4-year college
φ6 : time trend linear
φ7 · 100: time trend square
σl : s.d of shocks to leisure
0.176
0.042
0.399
-0.155
0.015
0.057
0.007
0.003
-0.002
0.001
0.029
Female
( 0.0076 )
( 0.0023 )
( 0.0110 )
( 0.0057 )
( 0.0005 )
( 0.0029 )
( 0.0012 )
( 0.0006 )
( 0.0001 )
( 0.0001 )
( 0.0020 )
0.204
0.049
0.462
0.091
0.014
0.047
0.016
0.020
-0.010
0.011
0.025
( 0.0081 )
N.A.
N.A.
( 0.0041 )
( 0.0005 )
( 0.0033 )
( 0.0022 )
( 0.0029 )
( 0.0003 )
( 0.0004 )
( 0.0022 )
Parameter restriction: φ0,female,k = φ0,female,1 · φ0,male,k /φ0,male,1 for k = 2, 3.
Standard errors in parentheses
Table F.18: Equilibrium Forecasting Rules (ρ’s)
SC
∆ log rt+1
CG
∆ log rt+1
∆ log pt+1
0.027
0.123
-0.095
0.089
0.025
1.060
0.001
0.036
-0.073
0.088
-0.033
-0.118
1.154
0.065
0.038
0.020
0.037
-0.096
0.032
0.798
-0.039
0.008
-0.052
0.082
-0.154
0.012
-0.063
0.976
1
1
0.9
0.9
0.8
0.8
Probability
Probability
constant
∆ log rtHS
∆ log rtSC
∆ log rtCG
∆ log pt
∆ log ζt+1
m
∆ log pt+1
HS
∆ log rt+1
0.7
0.6
0.5
0.4
25
0.7
0.6
0.5
HS, Type 1
HS, Type 3
CG, Type 1
CG, Type 3
30
35
40
45
Age
50
55
60
0.4
25
65
(a) Covered by HI
HS, Type 1
HS, Type 3
CG, Type 1
CG, Type 3
30
35
40
45
Age
50
(b) Not Covered by HI
Figure F.6: Probability of Maintaining Good Health: Pr(ha = 1|ha = 1)
65
55
60
65
0.6
0.5
0.5
Probability
Probability
0.6
0.4
0.3
0.2
0.1
25
0.4
0.3
0.2
HS, Type 1
HS, Type 3
CG, Type 1
CG, Type 3
30
35
40
45
Age
50
55
60
0.1
25
65
(a) Covered by HI
HS, Type 1
HS, Type 3
CG, Type 1
CG, Type 3
30
35
40
45
Age
50
55
60
65
(b) Not Covered by HI
Figure F.7: Probability of Recovering from Bad Health: Pr(ha = 1|ha = 0)
G
Goodness of Fit
The model replicates a slight decline in employment rate among men across all education groups and a
rapid increase in women’s employment rate for the same time period (see appendix Figure G.9). The model
also replicates the important patterns on employment, health insurance coverage, and wage patterns across
different age groups (see Figures G.10 to G.12). In particular, the model replicates the large increase in
health insurance coverage in the earlier part of life and the hump-shaped health insurance coverage over the
later part of life very well for less educated workers. However, the model slightly overpredicts the health
insurance coverage after age 45 for workers with a 4-year college degree. This is mainly because currently
I restrict the utility of health to be a constant parameter across age and education groups.
As seen in Figure G.13, the model replicates the health distribution across insurance-employment groups:
the worst health distribution is among those not employed and the best is among those with employerprovided health insurance. This pattern is generated from three mechanisms of the model: (1) ex ante
selection based on risk aversion; (2) ex ante selection based on health: healthy individuals select into the
employment group, resulting in a better health distribution among the employed;58 (3) ex post productivity
of health insurance: health insurance coverage increases health stochastically.
58 Because
health is productive and healthy individuals value leisure less than unhealthy individuals.
66
1
26
0.95
24
0.9
22
0.85
20
0.8
18
0.75
16
0.7
14
HS − data
SC − data
CG − data
HS − model
SC − model
CG − model
0.65
0.6
1980
1985
HS − data
SC − data
CG − data
HS − model
SC − model
CG − model
12
1990
1995
Year
2000
2005
10
1980
2010
1985
1990
(a) EHI Coverage Rate
1995
Year
2000
2005
2010
(b) Hourly Wages
Figure G.8: Model Fit: EHI and Wages (Employed Females)
0.95
0.95
0.9
0.9
0.85
0.85
0.8
0.8
0.75
0.75
0.7
0.7
0.65
0.65
0.6
0.5
0.45
1980
0.6
HS − data
SC − data
CG − data
HS − model
SC − model
CG − model
0.55
1985
1990
1995
Year
2000
2005
HS − data
SC − data
CG − data
HS − model
SC − model
CG − model
0.55
0.5
2010
0.45
1980
(a) Male
1985
1990
1995
Year
(b) Female
Figure G.9: Model Fit: Employment Rate
67
2000
2005
2010
1
40
0.95
35
0.9
HS − data
SC − data
CG − data
HS − model
SC − model
CG − model
30
0.85
25
0.8
0.75
20
HS − data
SC − data
CG − data
HS − model
SC − model
CG − model
0.7
0.65
0.6
25
30
35
40
45
Age
15
10
50
55
60
65
25
30
35
(a) EHI Coverage Rate
40
45
Age
50
55
60
65
60
65
(b) Hourly Wages
Figure G.10: Model Fit Across Age Groups: EHI and Wages (Employed Males)
1
40
0.95
35
0.9
HS − data
SC − data
CG − data
HS − model
SC − model
CG − model
30
0.85
25
0.8
0.75
20
0.7
HS − data
SC − data
CG − data
HS − model
SC − model
CG − model
0.65
0.6
25
30
35
40
45
Age
15
10
50
55
60
65
(a) EHI Coverage Rate
25
30
35
40
45
Age
50
55
(b) Hourly Wages
Figure G.11: Model Fit Across Age Groups: EHI and Wages (Employed Females)
68
1
1
0.9
0.9
0.8
0.8
0.7
0.7
HS − data
SC − data
CG − data
HS − model
SC − model
CG − model
0.6
0.5
0.6
0.5
0.4
0.4
0.3
0.3
0.2
0.2
0.1
25
30
35
40
45
Age
50
55
60
65
0.1
25
HS − data
SC − data
CG − data
HS − model
SC − model
CG − model
30
(a) Male
35
40
45
Age
50
55
60
65
(b) Female
Figure G.12: Model Fit Across Age Groups: Employment Rate
Male
0.7
Data
Model
Healthy Ratio
0.6
0.5
0.4
0.3
0.2
0.1
0
Employed & Not Covered
Employed & Covered
Not Employed
Female
0.7
Data
Model
Healthy Ratio
0.6
0.5
0.4
0.3
0.2
0.1
0
Employed & Not Covered
Employed & Covered
Not Employed
Figure G.13: Model Fit: Heath Distribution By Previous Choices
Source: Data moments are from CPS 1995-2010. The calculation of model moments is restricted to the sample time period.
69
H
Additional Figures for Counterfactual Simulations
70
Employment Rate (Male)
Employment Rate (Female)
1
0.8
0.95
0.75
0.9
0.7
0.85
0.65
0.8
0.6
0.75
0.55
0.7
0.5
0.65
0.45
0.6
0.55
0.5
1981
High School or Less
Some College
4−Year College or More
0.4
High School or Less
Some College
4−Year College or More
1985
1990
0.35
1995
Year
2000
2005
0.3
1981
2009
1985
1990
1995
Year
(a)
Overall HI Coverage Rate (Male)
2009
2000
2005
2009
2000
2005
2009
Overall HI Coverage Rate (Female)
0.8
0.95
0.75
0.9
0.7
0.85
0.65
0.8
0.6
0.75
0.55
0.7
0.5
0.65
0.45
0.6
0.5
1981
2005
(b)
1
0.55
2000
High School or Less
Some College
4−Year College or More
0.4
High School or Less
Some College
4−Year College or More
1985
1990
0.35
1995
Year
2000
2005
0.3
1981
2009
1985
1990
(c)
1995
Year
(d)
Log HI Premium
Changes in Log Prices in the Labor Market
0.3
0.25
High School or Less
Some College
4−Year College or More
8.5
0.2
0.15
8
0.1
7.5
0.05
0
7
−0.05
−0.1
1981
1985
1990
1995
Year
2000
2005
1981
2009
(e)
1985
1990
1995
Year
(f)
Figure H.14: Labor and Health Insurance Markets Trends for Medical Care Cost Growth
71
Employment Rate (Male)
Employment Rate (Female)
1
0.8
0.95
0.75
0.9
0.7
0.85
0.65
0.8
0.6
0.75
0.55
0.7
0.5
0.65
0.45
0.6
0.55
0.5
1981
High School or Less
Some College
4−Year College or More
0.4
High School or Less
Some College
4−Year College or More
1985
1990
0.35
1995
Year
2000
2005
0.3
1981
2009
1985
1990
1995
Year
(a)
Overall HI Coverage Rate (Male)
2009
2000
2005
2009
2000
2005
2009
Overall HI Coverage Rate (Female)
0.8
0.95
0.75
0.9
0.7
0.85
0.65
0.8
0.6
0.75
0.55
0.7
0.5
0.65
0.45
0.6
0.5
1981
2005
(b)
1
0.55
2000
High School or Less
Some College
4−Year College or More
0.4
High School or Less
Some College
4−Year College or More
1985
1990
0.35
1995
Year
2000
2005
0.3
1981
2009
1985
1990
(c)
1995
Year
(d)
Log HI Premium
Changes in Log Prices in the Labor Market
0.3
0.25
High School or Less
Some College
4−Year College or More
7.1
0.2
7
0.15
6.9
0.1
0.05
6.8
0
6.7
−0.05
−0.1
1981
1985
1990
1995
Year
2000
2005
2009
6.6
1981
(e)
1985
1990
1995
Year
(f)
Figure H.15: Labor and Health Insurance Markets Trends for Medicaid Eligibility Expansion
72
Employment Rate (Male)
Employment Rate (Female)
1
0.8
0.95
0.75
0.9
0.7
0.85
0.65
0.8
0.6
0.75
0.55
0.7
0.5
0.65
0.45
0.6
High School or Less
Some College
4−Year College or More
0.4
High School or Less
Some College
4−Year College or More
0.55
0.5
1981
1985
1990
0.35
1995
Year
2000
2005
0.3
1981
2009
1985
1990
1995
Year
(a)
2000
2005
2009
2000
2005
2009
2000
2005
2009
(b)
Overall HI Coverage Rate (Male)
Overall HI Coverage Rate (Female)
1
0.8
0.95
0.75
0.9
0.7
0.85
0.65
0.8
0.6
0.75
0.55
0.7
0.5
0.65
0.45
0.6
High School or Less
Some College
4−Year College or More
0.4
High School or Less
Some College
4−Year College or More
0.55
0.5
1981
1985
1990
0.35
1995
Year
2000
2005
0.3
1981
2009
1985
1990
(c)
(d)
Log HI Premium
Changes in Log Prices in the Labor Market
0.4
1995
Year
High School or Less
Some College
4−Year College or More
7.1
0.3
0.2
7
0.1
6.9
0
6.8
−0.1
6.7
−0.2
1981
1985
1990
1995
Year
2000
2005
2009
6.6
1981
(e)
1985
1990
1995
Year
(f)
Figure H.16: Labor and Health Insurance Markets Trends for Labor Market Technological Changes
73
Employment Rate (Male)
Employment Rate (Female)
1
0.8
0.95
0.75
0.9
0.7
0.85
0.65
0.8
0.6
0.75
0.55
0.7
0.5
0.65
0.45
0.6
High School or Less
Some College
4−Year College or More
0.4
High School or Less
Some College
4−Year College or More
0.55
0.5
1981
1985
1990
0.35
1995
Year
2000
2005
0.3
1981
2009
1985
1990
1995
Year
(a)
2000
2005
2009
2000
2005
2009
2000
2005
2009
(b)
Overall HI Coverage Rate (Male)
Overall HI Coverage Rate (Female)
1
0.8
0.95
0.75
0.9
0.7
0.85
0.65
0.8
0.6
0.75
0.55
0.7
0.5
0.65
0.45
0.6
High School or Less
Some College
4−Year College or More
0.4
High School or Less
Some College
4−Year College or More
0.55
0.5
1981
1985
1990
0.35
1995
Year
2000
2005
0.3
1981
2009
1985
1990
(c)
1995
Year
(d)
Log HI Premium
Changes in Log Prices in the Labor Market
0.3
High School or Less
Some College
4−Year College or More
0.25
7.1
0.2
0.15
7
0.1
6.9
0.05
0
6.8
−0.05
6.7
−0.1
−0.15
1981
1985
1990
1995
Year
2000
2005
2009
6.6
1981
(e)
1985
1990
1995
Year
(f)
Figure H.17: Labor and Health Insurance Markets Trends for Labor Force Composition Changes
74
Inequality Decomposition: Employer−Provided HI Gap among Employed Females (CG/HS)
0.25
Coverage Gap
0.2
0.15
only Cost
only Medicaid
only Tech
only LF
Cost + Tech
Cost + Tech + LF
Fitted Model
0.1
0.05
0
1980
1985
1990
1995
Year
2000
2005
2010
(a) CG/HS
Inequality Decomposition: Employer−Provided HI Gap among Employed Females (SC/HS)
0.2
Coverage Gap
0.15
0.1
only Cost
only Medicaid
only Tech
only LF
Cost + Tech
Cost + Tech + LF
Fitted Model
0.05
0
−0.05
1980
1985
1990
1995
Year
2000
2005
2010
(b) SC/HS
Figure H.18: Employer-Provided HI Inequality Decomposition among Employed Females
75
Inequality Decomposition: Log Wage Ratio among Employed Females (CG/HS)
1.4
1.2
Log Wage Ratio
1
only Cost
only Medicaid
only Tech
only LF
Cost + Tech
Cost + Tech + LF
Fitted Model
0.8
0.6
0.4
0.2
0
1980
1985
1990
1995
Year
2000
2005
2010
(a) CG/HS
Inequality Decomposition: Log Wage Ratio among Employed Females (SC/HS)
0.7
0.6
0.5
Log Wage Ratio
0.4
only Cost
only Medicaid
only Tech
only LF
Cost + Tech
Cost + Tech + LF
Fitted Model
0.3
0.2
0.1
0
−0.1
1980
1985
1990
1995
Year
2000
2005
2010
(b) SC/HS
Figure H.19: Wage Inequality Decomposition among Employed Females
76