Employer-Provided Health Insurance in a Model with Labor Market Frictions Hubert Janicki∗

Abstract In this paper, I perform a quantitative analysis of the effect of frictions in the market for employer-based health insurance on coverage and labor market outcomes. I incorporate frictions in the form of 1) enrollment restrictions due to waiting periods or preexisting conditions, and 2) limits in duration of continuation coverage into a model of indivisible labor supply with idiosyncratic productivity and medical expenditure shocks. I find that the model is able to account for key features of the distribution of employer-based health insurance coverage. Frictions in the health insurance market have important implications for health insurance coverage and the distribution of employment across productivity levels, but matter less for aggregate labor force outcomes.

1

Introduction

The majority of working-age individuals are covered by employment-based health insurance, either through their current employer, a former employer, or a spouse’s employer through dependent coverage. The link between employment and health insurance opportunities has led to a rich empirical literature on measurement of “job lock,” the reduction in mobility in the labor market due to health insurance enrollment restrictions.1 These restrictions usually take the form of waiting periods or exclusions due to pre-existing conditions. There are also limits to the duration of continuation coverage, or health insurance Social, Economic & Housing Statistics Division, U.S. Census Bureau, Washington, DC 20233. Email: [email protected]. Any views expressed herein are those of the author and not necessarily those of the U.S. Census Bureau. I am grateful to Alex Bick, Matthew Day, Mark Klee, Brett O’Hara, and seminar participants of the U.S. Census Bureau, Bureau of Labor Statistics, University of West Virginia, and the 2012 ASU CASEE Reunion Conference for helpful comments and encouragement. First revision October, 2012. This revision June, 2013. 1 See Madrian (1994) and Palumbo (2011) for an example. Also see Gruber and Madrian (2004) for a thorough survey of this literature. ∗

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coverage obtained through a former employer, that reduce insurance opportunities outside the workplace. Several policy proposals have been introduced over the last thirty years to weaken the link between employment and health insurance opportunities. Most notably, the 1985 Consolidated Omnibus Budget Reconciliation Act (COBRA) required employers to offer continuation coverage for 18 to 36 months after job separation depending on eligibility. The Health Insurance Portability and Accountability Act of 1996 (HIPAA) limited health insurance enrollment exclusions to a maximum of 12 months following start of employment. The more recent 2010 Patient Protection and Affordable Care Act (ACA) is designed to expand health insurance opportunities for those not eligible for employment-based health insurance. Nevertheless, despite much policy interest and empirical work, there does not exist a quantitative framework for evaluating the effects of reduction in health insurance enrollment restrictions on coverage and labor supply. The purpose of this paper is to provide a quantitative model to study the interaction of employer-based health insurance coverage decisions and labor market turnover in the determination of employment. The root of the potential changes in labor mobility is the trade-off between improved risk-sharing provided through employment health insurance benefits and the decreased work incentives from the cost of insurance that is incurred by all employees. Improvements to risk-sharing reduce the out-of-pocket medical expenditures and allow agents to smooth consumption over time. The provision of health insurance through employment reduces the return to labor for agents by paying for insurance contracts that are not actuarially fair. To better understand this trade-off, I provide answers to the following questions. First, to what extent do enrollment restrictions in the market for health insurance impact health insurance enrollment and labor supply? Second, how does the presence and duration of continuation coverage change incentives to insure and participate in the labor force? Third, to what extent do these restrictions in the health insurance market affect labor market transitions and the mobility of workers? To formally study this trade-off, I construct an incomplete markets model with idiosyncratic shocks to labor productivity and medical expenditures. Agents face a discrete choice of labor supply and health insurance participation. Agent choices are subject to trading frictions. That is, there are frictions in the form of arrival of job offers and separations commonly used in the search-theoretic literature. Labor market frictions are key to capturing the reduction in health insurance coverage following the transition from employment to unemployment and exit from the labor force. In addition, I model restrictions to health insurance enrollment and continuation coverage as a trading friction defined by

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two parameters. Exogenous variation of these parameters allows for measurement of the net effect of these frictions on health insurance coverage rates and labor force outcomes. The model is calibrated to longitudinal data from the Survey of Income and Program Participation. The degree of frictions in the labor market and the market for health insurance generate the levels of insurance participation by labor force status as well as transitions between health insurance categories consistent with those observed in the data. The calibrated model is then used to establish the role of frictions in equilibrium labor force outcomes and health insurance participation. I find that frictions in the health insurance market have important implications for health insurance coverage. Restrictions to health insurance enrollment opportunities mitigate selection of agents by severity of medical expenditure shocks through changes in equilibrium health insurance premiums. In particular, I find that health insurance enrollment opportunities that arrive approximately once a year maximizes the aggregate level of health insurance coverage in equilibrium. Increases in frequency of enrollment opportunities from this level result in a reduction in aggregate levels of coverage. However, I find relatively small effects of duration of continuation coverage on aggregate insurance enrollment. Both health insurance enrollment and continuation coverage restrictions have important implications for labor force outcomes. While coverage restrictions have little effect on aggregate employment, access to employment-based health insurance increases employment among agents with high medical expenditures. Among this group, a reduction in enrollment restrictions does reduce the likelihood of employment among agents with low labor productivity. However, enrollment restrictions have little effect on employment among those with high labor productivity. The presence of continuation coverage benefits reduces employment among agents with low labor productivity and high medical expense shocks. Put another way, access to continuation coverage reduces incentives to use employment as a mechanism to smooth consumption in times of low labor productivity and high medical expenditures. This paper is related to several papers that introduce indivisible labor, frictions, and idiosyncratic labor shocks to capture flows of workers across employment, unemployment, and not in the labor force categories. Krusell et al. (2010) and Krusell et al. (2011) match labor flows across the three labor market states where workers face idiosyncratic wage shocks, but do not consider health expenditure shocks or employer-provision of insurance against these shocks. Several studies have developed models to analyze the role of household health insurance choice in an incomplete markets framework with idiosyncratic productivity and

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medical expenditure shocks. This literature includes Jeske and Kitao (2009), Huang and Huffman (2010), Pashchenko and Porapakkarm (2010), and Janicki (2012a). The majority of the models in this literature abstract from labor market frictions that limit access to employment-based health insurance. One exception is Huang and Huffman (2010). They consider a richer general equilibrium model with endogenous health accumulation. However, their model is not consistent with higher frequency labor market or health insurance participation transitions. Finally, other research explores the implications of the interactions between workers and employers for employment-based health insurance offer and participation rates (Dey and Flinn (2005), Br¨ ugemann and Manovskii (2010)). Dey and Flinn (2005) construct a search-theoretic model of health insurance provision and wage determination, but rely on bargaining between individual workers and firms over health insurance benefits. In contrast to this paper, Br¨ ugemann and Manovskii (2010) focus on the effects of the health insurance system on the firm size distribution. The remainder of the paper is organized as follows. Section 2 describes some key summary statistics of the distribution of the population with and without employmentbased health insurance coverage. Section 3 details the model. Section 4 outlines the calibration procedure. Section 5 presents an analysis of the role of health insurance frictions on health insurance enrollment and labor force participation. Section 6 offers a sensitivity analysis and Section 7 concludes.

2

Data

Moments describing employment-based health insurance coverage and labor force participation come from the 2004 panel of the Survey of Income and Program Participation (SIPP). The SIPP is a longitudinal survey representing the civilian non-institutionalized population of the United States sponsored by the U.S. Census Bureau. The SIPP collects detailed information on demographic characteristics, labor force participation, and government program participation. The 2004 SIPP panel was fielded from February 2004 to September 2008. The SIPP panel is divided into four “rotation” groups, which are interviewed cyclically, one group per month, in a series of collections called “waves.” The estimates presented in this paper are based on data taken from the entire longitudinal panel composed of waves 1 through 12.2 2

For a complete discussion of the SIPP sample selection, weighting procedures, and the source and accuracy of the estimates, see the technical documentation at:

4

The data for this analysis are restricted to male respondents with ages between 25-54. I exclude respondents that reported themselves to be self-employed at any time during the reference period, since such respondents are not usually eligible for group health insurance coverage. I also exclude respondents that are union members, as union membership often includes non-employment-based health insurance provisions. Women are excluded from my analysis since spells of nonemployment due to fertility or childcare decision are outside the scope of the paper. In addition, I restrict my sample to prime-aged workers to minimize the effects of school attendance and retirement. Table 1: Health Insurance Coverage by Definition Source of coverage Employer-based (self) Employer-based (spouse) Public Direct-purchase Other

Entire year 57.2

Point-in-time 61.3

Anytime 66.4

(2.0)

(2.0)

(2.0)

6.4

8.5

11.4

(1.0)

(1.1)

(1.3)

8.3

10.2

11.3

(1.1)

(1.2)

(1.3)

1.3

2.4

4.1

(0.4)

(0.6)

(0.82)

2.3

4.2

4.6

(0.5)

(0.7)

(1.0)

18.2

21.9

25.0

(1.6) Source: 2004 SIPP, U.S. Census Bureau

(1.6)

(1.7)

No health insurance

To begin the analysis, I divide the population by source of health insurance coverage for alternative definitions of duration of coverage. The purpose of this exercise is to demonstrate that 1) employment-based insurance is the dominant provider of health insurance among the population regardless of duration of coverage, and 2) there is substantial turnover among sources of insurance coverage over the course of a year. The participation rates for 2007 are presented in Table 1.3 While the majority of coverage is provided through employment-based sources regardless of the definition of coverage used, Table 1 illustrates that there are significant flows between these insurance categories throughhttp://www.census.gov/apsd/techdoc/sipp/sipp.html 3 The estimates in this paper (which may be shown in the text or in the tables) are based on responses from a sample of the population and may differ from actual values because of sampling variability or other factors. As a result, apparent differences between estimates for two or more groups may not be statistically significant. All comparative statements have undergone statistical testing , and, unless otherwise noted, are statistically significant at the 90-percent confidence level.

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out the year. The strongest measure restricts the definition of coverage for the entire 12 month period. The two weaker measures, that give progressively larger estimates at a “point-in-time” and “any time” during the year allowing for substitution between sources of coverage.4 1 0.9 0.8 0.7

cdf

0.6 0.5 0.4 0.3 0.2

All spells Spell began before wave 1

0.1 0

0

20 30 40 10 Duration of Insurance Spell (Months) Source: 2004 SIPP, U.S. Census Bureau

50

Figure 1: Duration of Employer-based Coverage Spells Differences in coverage rates by degree of coverage over the year in Table 1 suggest that 1) the majority of the population has employment-based health insurance coverage and 2) spells of health insurance coverage by any source can be either transitory or persistent. Since employment-based insurance is the dominant provider of health insurance, this paper is focused on this type of coverage. Nevertheless, it is worth mentioning that between 8.6 percent and 18.2 percent of the population has a non-employment-based source of health coverage, depending on the definition of coverage used. Coverage can be obtained from public sources, direct-purchase, or through a spouse from a variety of sources. While these sources of coverage undoubtedly merit much further study, I focus on employment-based coverage since this is the dominant source of coverage in the U.S. and to draw the starkest contrast between spells of employment-based coverage and all 4

Estimates of Public coverage and Other coverage for point-in-time and anytime are not statistically different from each other at the 90 percent confidence level. Estimates of no health insurance for the entire year and point-in-time are not statistically different from each other at the 90 percent confidence level.

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1 0.9 0.8 0.7

cdf

0.6 0.5 0.4 0.3 0.2

All spells Spell began after wave 1

0.1 0

0

10 30 40 20 Duration of No-coverage Spell (Months) Source: 2004 SIPP, U.S. Census Bureau

50

Figure 2: Duration of No-coverage Spells others sources of insurance against medical expenditure risk. Therefore, I divide health insurance by employer-based participation. That is, respondents with no coverage can be either uninsured or insured through a source other than employment. Figure 1 plots the empirical cumulative distribution function of employer-based health insurance coverage spells by duration. The figures illustrate that more than half of spells are quite long, usually 32 months or more. However, about 27 percent of spells are 4 months or less. In contrast, Figure 2 details the time distribution of no-coverage spells. From the figure, it is clear that approximately half of these spells end within 20 months. Almost 60% end within 28 months. While about 60% of no-coverage spells last one year or more, the limited length of the panel fails to capture the length of spells that began before the first interview. To limit the effect of left censoring, Figure 2 also details the time distribution of no-coverage spells conditional on a respondent starting the no-coverage spell after the initial interview. Among these respondents, the vast majority (60%) have no-coverage that last 23 months or less. Almost 28 percent last four months or less. To get a better sense of the effect of labor market participation on employer-based health insurance coverage, I detail monthly employer-based coverage as a function of labor market status for the period 2004-2007 in Table 2.5 Focusing on monthly coverage 5

I define a respondent as employed if they claim to have a job and worked at least one week. Weeks

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Table 2: Employer-based Coverage by Labor Force Status Aggregate

Employer-based Coverage 60.6 (0.9)

69.5

Employed

(0.9)

21.2

Unemployed

(1.2)

8.7

Not-in-labor-force

(1.0) Source: 2004 SIPP, U.S. Census Bureau

rates limits the effect of labor market transitions within a year. Broadly speaking, the likelihood of employer-based coverage is correlated with labor market attachment. Employed individuals are most likely to be insured at any month (69.5 percent), followed by the unemployed (21.2 percent), and those not participating the the labor force (8.7 percent). While the levels of employer-based health insurance coverage vary by labor force status, it is worthwhile to document transitions across health insurance status by labor force status. Table 3 illustrates that health insurance flows exhibit a large degree of persistence. To see how these transitions vary by labor force transitions, I create transition matrices for respondents that change their labor force status between any period t and t + 1 and those respondents that do not see a change in their labor force status. It is important to note that the likelihood of transition from a coverage state to a no coverage state is significantly more likely when accompanied by a change in the labor force status. Since these labor transitions are due to both exogenous shocks (such as firing) and choice (such as quits and search), it is important that a model of employment-based health insurance transitions incorporate both endogenous and exogenous changes in labor supply.

3

Model

Consider an economy populated by a continuum of infinitely-lived agents with unit mass. Agents face idiosyncratic uncertainty in labor productivity and medical expenditures. not worked were not due to layoffs. Unemployed respondents included those with a job but on layoff or those without a job and looking for work. Those not in the labor force are defined by no job for the entire month and no time looking for work.

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Table 3: Employment-Based Health Insurance Transitions by Labor Force Status

From (t): Coverage No Coverage

Aggregate To (t+1): Coverage No Coverage 99.1 0.9 (0.1)

(0.1)

4.9

95.1

(0.2)

(0.2)

With Labor Force Transition To (t+1): From (t): Coverage No Coverage 90.7 9.3 Coverage No Coverage

(0.9)

(0.9)

3.1

96.9

(0.4)

(0.4)

No Labor Force Transition To (t+1): From (t): Coverage No Coverage 99.2 0.8 Coverage No Coverage

(0.1)

(0.1)

1.3

98.7

(0.1)

(0.1)

Statistics in percent. Source: 2004 SIPP, U.S. Census Bureau

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Agents make a choice of employment and health insurance coverage that are subject to trading frictions. Conditional on eligibility, there exists a competitive health insurance market against household medical expenditure risk. The government guarantees a minimum consumption level.

3.1

Environment

Preferences. All agents have identical preferences over streams of consumption and leisure represented by: E

(∞ X

)

β t [ln(ct ) − αht ]

t=0

where β denotes the discount factor and α is the disutility from labor. The variables ct and ht are consumption and employment participation at time t. Employment is a choice denoted by ht ∈ {0, 1}. Endowments. Agents are subject to idiosyncratic shocks to productivity that are modeled as shocks to the return to working. Labor productivity of agent i at time t is denoted zit where zit ∈ Z is a persistent shock that follows a Markov chain represented by the transition matrix Π(z, z ′ ). Agents are subject to idiosyncratic medical expenditure shocks. I follow Hubbard et al. (1995) in modeling medical expenditures as an exogenous stochastic process. Medical expenditures are defined as mit = exp(µ + sit ), where sit ∈ S and µ is a scaling parameter. Let sit be a persistent shock that follows a Markov chain ˜ s′ ). Realization of shocks are independently and identically distributed represented by Π(s, across agents. I assume realizations of productivity and medical expense shocks are not correlated.6 To capture frictions in the labor market and the market for health insurance, I restrict agent access to both markets. I focus on two frictions in the labor market commonly used in search and marching models (for example Pissarides (2000)) to capture equilibrium labor market outcomes. The first friction is a probability of a job offer for nonemployed agents and the second friction is a probability of job separation for employed agents. I include labor market frictions since levels of employer-based health insurance coverage are significantly different by labor market outcomes. As such, it is important for the model 6 There is some evidence to support this assumption. According to 1996-2008 MEPS-HC dataset, medical expenditures are not correlated with labor earnings among prime-age male heads of households when controlled for age and family size. However, there is much work exploring the correlation between health and earnings. See for example, Capatina (2012) and Ozkan (2012).

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to capture the incentives that motivate health insurance purchases across labor market categories. The market for employment-based health insurance is characterized by limited enrollment opportunities, waiting periods due to pre-existing conditions, and restrictions on duration of coverage following termination of employment. The model captures these limits in a minimalist fashion by modeling two frictions that limit opportunities for purchase of health insurance. The first friction is a probability of an enrollment opportunity for employer-based health insurance.7 This opportunity allows employed agents to enroll or if currently insured, to drop health insurance coverage. The second friction is the probability that a continuation coverage ends for currently insured for agents that terminate their employment or separate from their employer. I incorporate these four frictions into my model within the island framework similar to Lucas and Prescott (1974) and more recently, Krusell et al. (2011). Consider four islands characterized by employment opportunities (“production” and “leisure” islands) and employment-based health insurance opportunities (“insurance” or “no insurance”). Agents cannot move freely between islands. Each period a worker loses his employment offer with probability σ (job separation rate) regardless of health insurance status. Conversely, nonemployed agents receive employment opportunities with probability λ (job arrival rate). Workers receive an opportunity to purchase or terminate health insurance coverage with probability γ. Meanwhile, non-employed and insured workers lose health insurance coverage with probability θ. Non-employed uninsured workers cannot purchase coverage without receiving both employment and a health insurance enrollment opportunity.

3.2

Assets

Following Aiyagari (1994) and Huggett (1993), agents can accumulate assets to insure against idiosyncratic risk. These assets provide one-period risk-free claims to consumption at interest rate r. Let kit denote the asset holdings of household i at period t with kit ≥ 0, i.e. households face a no-borrowing constraint. 7

In reality, workers with pre-existing conditions might be eligible for health insurance through their employer, but treatment of the pre-existing condition is not covered under the health insurance policy. The model captures restrictions to health insurance rather than restrictions in the quality of health insurance.

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3.3

Health Insurance

While agents can use assets to insure consumption against both labor productivity and medical expenditure shocks, I model an explicit health insurance market against medical expenditures provided through employment. Let nit ∈ {0, 1} denote health insurance enrollment of household i in period t. First, I focus on employer-based health insurance coverage. This is a key assumption as most non-elderly households currently obtain health insurance through their employer contingent on full-time employment (Janicki, 2012b). In addition to the provision of health insurance benefits through the current employer, I model extensions of employer coverage outside employment. This feature of the model represents a variety of state-specific continuation coverage mandates and federally mandated extensions of health insurance coverage provided through 1985 Consolidated Omnibus Budget Reconciliation Act (COBRA). Specifically, insured agents that transition from employment to nonemployment are eligible to continue enrollment in the employer-based plan. Second, I assume that not all individuals face the same price for health insurance contracts. Currently, employment-based health insurance premiums are usually divided between an “employer contribution” and the “employee contribution”. The contribution depends on the individuals employment status, denoted ψh . For working agents, I model the employee contribution as a constant fraction (ψ1 ) of the total health insurance premium (π), denoted ψ1 π. For non-employed insured agents, the employee contribution is equal to ψ0 π. This feature reflects the fact that COBRA continuation coverage makes no provision for employer contribution toward health insurance benefits of former employees, but some employers nevertheless choose to subsidize premiums.8 The employer contribution is modeled as a proportional tax (ξ) on efficiency labor hours units imposed on all workers by the firm similar to Jeske and Kitao (2009). For an individual with gross labor earnings wzh, ξzh are collected by the firm to pay for the employer contribution. Finally, in reality premiums vary across firms of different sizes due to composition of medical expenditures by workers and employer contributions. I abstract from this dimension since I do not focus on the firm decision to offer health insurance benefits. See Dey and Flinn (2005) and Br¨ ugemann and Manovskii (2010) for recent work that explores this decision in more detail. Third, I assume working agents have access to a single pooling health insurance con8 See Bovbjerg et al. (2010). It is worth pointing out that the American Recovery and Reinvestment Act of 2009 mandated employer contributions to 65 percent of the total premium for employees upon involuntary termination of employment. Since the SIPP panel used in the calibration procedure ends in 2008, I disregard these recent changes to continuation coverage laws.

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tract. Currently, health insurers and employers are limited in their ability to “risk adjust” employer group health insurance plans by federal regulations such as 29 CFR Part 2590.702, IRS Section 125, and the 1996 Health Insurance Portability and Accountability Act. Furthermore, this assumption is consistent with evidence that suggests that households choose from a small set of health insurance contracts (Cardon and Hendel, 2001). I assume the contract takes the following form: households pay a premium and are reimbursed a fraction (1 − φ) of medical expenses. Employee health insurance benefits are not subject to payroll taxes. This feature is key as it provides an incentive for households to purchase insurance instead of self-insuring by saving. In equilibrium, π is chosen so as to cover all medical payments out of the health insurance pool. For ease of exposition, I summarize the net out-of-pocket medical expenditures by Ωit , where: ( exp(µ + sit ) if nit = 0 Ωit = φ exp(µ + sit ) + ψh · π · (1 − τ ) if nit = 1

3.4

Tax and Transfer Programs

In a model with exogenous medical expenditure shocks and borrowing constraints, even insured households may not be able to finance their out-of-pocket medical expenses. Therefore, I introduce government-provided transfers that guarantee a minimum consumption level c. Through this transfer program, the government also funds all medical expenditures net of household resources to mimic Medicaid transfers and “uncompensated care” benefits such as emergency-room treatment.9 There is a tax on labor earnings denoted by τ that is set exogenously. Government revenues that are not spent on the minimum consumption floor detailed above are renumerated lump-sum to all agents. I denote total government transfers to the household by Tit in the budget constraint. 9

By the 1986 Federal Emergency Medical Treatment and Labor Act (EMTALA) hospitals are required give emergency care regardless of insurance status, ability to pay, or citizenship. Furthermore, hospitals cannot discharge patients until they are stabilized or transferred to another facility. Hospitals and physicians are reimbursed for these services in part though Medicaid disproportional share hospital (DSH) payments. Note that “uncompensated care” in my model is not reflected in employer health insurance premiums due to hospital cost shifting. This is in line with evidence from Hadley et al. (2008) who calculate the majority (75 percent) of “uncompensated care” is paid for by the government.

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3.5

Household Problem

I define the household problem recursively. Each period, agent decisions depend on the location l that defines employment and health insurance opportunities, capital stock k, and realizations of labor shocks z and medical expenditure shocks s. The household problem is written in two stages. In the first stage, the period employment and health insurance opportunity shocks are realized as well as the period productivity shock z. In this stage, the household makes an employment and health insurance decision if applicable. At the beginning of the second stage the period medical expense shock s is realized. The household then makes a consumption and savings decision. Note that income and employment decisions are made before the current period meducal expense shock is realized. For compactness of notation, I summarize the state space (k, s, z, l) by x. The household problem is summarized by four value functions that represent the second-stage value of employment with and without insurance, and non-employment with and without insurance, defined by I(x), W (x), N(x), and U(x). The first stage values are denoted ˜ ˜ (x), N ˜ (x), and U˜ (x). Please see the timeline in Appendix A for an with a tilde, I(x), W illustration of the timing of the household problem. Let the value of employment with health insurance be defined as, (

log(c) − αh + β I(x) = max ′ c,k

X

′

Π(z, z )

z ′ ∈Z

h

˜ ′ ), W ˜ (x′ ), N(x ˜ ′ ), U(x ˜ ′ )} + (1 − γ) max{I(x ˜ ′ ), N ˜ (x′ ), U(x ˜ ′ )}]+ (1 − σ + λσ)[γ max{I(x ) i ˜ (x′ ), U˜ (x′ )}] σ(1 − λ)[θU˜ (x′ ) + (1 − θ) max{N subject to the following budget constraint: c + k ′ + Ω(x) =(1 − τ )(w − ξ)zh + (1 + r)k + T (x) c≥0

(1)

k′ ≥ 0

14

Let W (x) denotes the value of employment without health insurance: (

log(c) − αh + β W (x) = max ′ c,k

X

Π(z, z ′ )

z ′ ∈Z

h

˜ ′ ), W ˜ (x′ ), U(x ˜ ′ )} + (1 − γ) max{W ˜ (x′ ), U˜ (x′ )}]+ (1 − σ + λσ)[γ max{I(x ) i σ(1 − λ)U˜ (x′ ) subject to (1). The value of non-employment with health insurance from a former employer is defined, (

N(x) = max log(c) + β ′ c,k

X

Π(z, z ′ )

z ′ ∈Z

h

˜ ′ ), W ˜ (x′ ), U(x ˜ ′ )} + (1 − γ) max{W ˜ (x′ ), U(x ˜ ′ )}] + (1 − λ)U˜ (x′ )]+ θ[λ[γ max{I(x ˜ ′ ), W ˜ (x′ ), N(x ˜ ′ ), U˜ (x′ )} + (1 − γ) max{W ˜ (x′ ), N(x ˜ ′ ), U(x ˜ ′ )}]+ (1 − θ)[λ[γ max{I(x ) i ˜ ′ ), U(x ˜ ′ )}] (1 − λ) max{N(x subject to (1). The value of non-employment with no health insurance is defined, (

log(c) + β U(x) = max ′ c,k

X

z ′ ∈Z

′

Π(z, z )

h

˜ ′ ), W ˜ (x′ ), U(x ˜ ′ )} + (1 − γ) max{W ˜ (x′ ), U˜ (x′ )}] + (1 − λ)U(x ˜ ′) λ[γ max{I(x

) i

subject to (1). To obtain the first-stage value functions, I take an expectation over this period’s

15

medical expense shock: ˜ = I(x)

X

˜ s′ )I(x) Π(s,

s′ ∈S

˜ (x) = W

X

˜ s′ )W (x) Π(s,

s′ ∈S

˜ N(x) =

X

˜ s′ )N(x) Π(s,

s′ ∈S

˜ U(x) =

X

˜ s′ )U(x) Π(s,

s′ ∈S

Finally, let h(x) denote the optimal labor choice and n(x) denote the optimal health insurance decision rule. Nonemployed agents can be either unemployed or not in the labor force. The model distinguishes between the two categories by evaluating which nonemployed agents would optimally choose to work if presented with a job opportunity. Since health insurance opportunities arrive with probability γ conditional on a job offer, the value of employment should reflect this opportunity. In other words, if ˜ ˜ (x)} + (1 − γ)W ˜ (x) > N(x) ˜ γ max{I(x), W then a currently-insured nonemployed agent ˜ ˜ (x)} + (1 − γ)W ˜ (x) > U˜ (x) for agents with no is unemployed. Likewise, if γ max{I(x), W health insurance, then they are identified as unemployed.10

3.6

Equilibrium Definition

A stationary recursive competitive equilibrium is a list of functions I(x), W (x), N(x), U(x), and, h(x), n(x), c(x), k ′ (x), scalars π, b, and ξ, and a distribution of agents Ψ(x) such that: 1. Agents decision rules solve the household problem 2. Employer health insurance firms earn zero profits in equilibrium: Z

Z

πI[n = 1]dΨ = φexp(µ + s)I[n = 1]dΨ Z Z Z Z ξzh(x)dΨ + ψ πI[n = 1, h = 1]dΨ + πI[n = 1, h = 0]dΨ = πI[n = 1]dΨ 10 Note that this definition of unemployment is consistent with a job search decision where the cost of search is sufficiently small. See Krusell et al. (2011) for a more detailed discussion.

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3. Government budget is balanced: Z

τ [(w − ξ)zh(x) − n(x)π]dΨ =

Z

T (x)dΨ

4. Distribution of households Ψ is consistent with individual behavior 5. Markets clear: Z where M =

4

R

c(x)dΨ +

exp(µ + s)dΨ and Y =

Z R

k ′ (x)dΨ + M = Y rk ′ (x)dΨ +

R

zh(x)dΨ.

Calibration

Each model period corresponds to one month. Final calibration parameters are presented in Table 4 for reference. The discount rate β is set to 0.9967 following Krusell et al. (2011). Capital return to investment (r) is set at 4 percent annual rate and wage rate is normalized to one. The remaining utility parameter, friction parameters, value of the consumption floor, and premium contributions are chosen jointly using a simplex method to minimize the sum of squared error between the model and data. While the parameters are jointly identified, I choose targets that most intuitively related to the model parameters. I calibrate the labor disutility parameter α to match the employmentto-population rate of 84.5% among prime-age males from the SIPP dataset described earlier. I pick σ and λ to match targets outlined in Krusell et al. (2011). That is, the job separation rate σ is set to match the flow of workers from employment to unemployment in equilibrium (1.1%). The job finding rate λ is set to match the unemployment rate in the economy (4.7%). Next, consider the health insurance friction parameters. The parameter γ determines the frequency with which an agent has an opportunity to purchase or terminate employment-based health insurance conditional on working. I choose γ to match the equilibrium insurance participation rate among the employed population (69.5 percent). Likewise, θ determines the frequency with which an agent loses continuation coverage following entrance into the nonemployment pool. I set θ to match the participation rate among the unemployed population (21.2 percent) since continuation coverage is primarily aimed at the population transitioning between jobs.

17

Table 4: Calibration Parameters Name Disutility from labor Discount rate Interest rate (annual) Wage rate Job separation rate Job finding rate HI offer rate HI loss rate Labor productivity Medical expenditure Copayment Employee contribution (employed) Employee contribution (non-employed) Employer contribution Tax rate Consumption floor (relative to baseline Y )

4.1

Symbol α β r w σ λ γ θ ρ, σǫ ρ˜, σ ˜ǫ φ ψ1 ψ0 ξ τ c

Value 0.33 0.9967 0.04 1.0 0.005 0.117 0.125 0.001 0.9931,0.1017 0.9353,0.8630 0.3 0.2 0.94 0.063 0.3 0.21

Labor Productivity

There is a large literature that estimates the structure of the process for idiosyncratic shocks to labor earnings and wages. Notable examples include Floden and Lind´e (2001), Chang and Kim (2006), and Heathcote et al. (2010). I use estimates of ρ = 0.92 and σǫ = 0.21 for the autoregressive productivity process log(zi,t+1 ) = ρ log(zi,t ) + ǫi,t+1 where ǫij ∼ N(0, σǫ2 ) from Floden and Lind´e (2001). These parameters are then converted to monthly frequencies. The transition matrix Π(z, z ′ ) is created using the Tauchen (1986) method.

4.2

Medical Expenditures and Insurance Reimbursement

I use longitudinal data from the Medical Expenditure Panel Survey (MEPS) to estimate the process of medical expenditure shocks and insurance reimbursement. The MEPS contains detailed individual level data on medical expenditures, insurance reimbursements, and out-of-pocket expenditures. Each individual is interviewed for two years. I use data from 1996-2008 (Panels 1-12) of the MEPS Household Component (HC) files. To ensure data correspond to the model, I restrict my sample to males with ages between 25-54

18

with positive family medical expenditures.11 For respondents living in families, I divide family medical expenses by the number of family members to obtain per person expenses. I include expenditures of family members since employer-based plans often provide coverage for spouses and dependents. By omitting individuals (single person families) and families with zero medical expenses, I overestimate the risk of large medical expense shocks and the role of risk-sharing provided by health insurance. In other words, my estimates provide an upper bound of the effects of frictions in the market for health insurance. Similar to Janicki (2012a), I consider an autoregressive process for medical expenditures relative to average income: si,t+1 = ρ˜si,t + ǫ˜i,t+1 , where the log of medical expenditures regresses to the mean in the sample. I set µ so that the aggregate medical expenditure to output ratio is 12 percent.12 Estimates vary by year, as seen in Table 5. I explore the extent to which my results vary with these estimates in the sensitivity analysis section. I use the mean of the annual estimates provided, ρ = 0.448 and σ ˜ǫ = 1.417. ˜ s′ ) These estimates are then converted to monthly frequencies. The transition matrix Π(s, is created using the Tauchen (1986) process. I estimate the reimbursement share by aggregating annual household expenditures in the data and taking the average over all households with employer-based coverage yielding φ = 0.3. The employee contribution parameters depend on employment status. Using data from the MEPS-IC, I set ψ1 = 0.2.13 No reliable estimates exist for ψ0 . Therefore, I set ψ0 to match the employment health insurance rate among those not in the labor force. This yields ψ = 0.89. This is consistent with evidence that some employers contribute to their employees health insurance premium following separation (Bovbjerg et al. (2010)).

4.3

Government

I model transfers that guarantee consumption floor c following Hubbard et al. (1995). Transfers are made net of labor income, wealth, medical expenditures, and lump-sum 11

I use the definition of a family that includes related subfamilies in the construction of my estimates. I define unrelated individuals living together as separate economic agents since these individuals are usually not eligible for family coverage through employer health insurance contracts. 12 I define aggregate medical expenditures net of Medicare expenditures in 2008 as a fraction of GDP from National Health Expenditure data maintained by the Center for Medicare and Medicaid Services. This data is available from http://www.cms.gov. 13 The MEPS-IC tables are available from http://meps.ahrq.gov/. Private sector employee contributions range from 17.2 percent to 20.1 percent (over the period 1996-2008), when averaged across firms and plan types. For federal employees, employee contributions are between 25-27 percent (Mach (2013)).

19

Table 5: Calibration Parameters Panel Persistence square root of MSE 1 (1996-1997) 0.390 1.486 (0.04)

2 (1997-1998)

0.235

3 (1998-1999)

0.534

4 (1999-2000)

0.333

1.412

(0.06)

1.329

(0.06)

1.326

(0.04)

5 (2000-2001)

0.486

1.366

(0.06)

6 (2001-2002)

0.475

1.473

(0.07

7 (2002-2003)

0.396

8 (2003-2004)

0.409

9 (2004-2005)

0.597

1.445

(0.04)

1.268

(0.05)

1.554

(0.06)

10 (2005-2006)

0.607

1.432

(0.05)

11 (2006-2007)

0.368

12 (2007-2008)

0.547

1.513

(0.06)

1.407

(0.05) Data Source: 1996-2004 MEPS-HC

20

transfers b: T (x) = b + max{0, c − [(w − ξ)zh(x)(1 − τ ) + (1 + r)k − Ω(x) + b]} Estimates of the consumption floor vary, depending on the types of transfers included and the individual and family characteristics of agents (See for example Hubbard et al. (1995) and De Nardi et al. (2010)). The level of the consumption floor in a model with frictions has a significant impact on the likelihood that agents with a job offer accept employment. I therefore set c to match the flow of workers from unemployment to employment (9.7 percent). This yields c = 0.16.

4.4

Baseline Fit

The purpose of this section is to evaluate the ability of the model to match key features of the labor market and the market for employment-based health insurance. I begin by showing the labor force status distribution in Table 6. Recall that the labor disutility parameter is set to match the aggregate employment level. The model comes close to replicating the employment-to-population rate of 84.5 percent at 83.3. Likewise, the aggregate levels of unemployment and those not-in-the-labor-force are similar to those found in the data at 4.2 percent vs. 6.1 percent for the unemployed, and 11.3 percent and 10.6 percent for those not in the labor force, respectively. Table 6: Labor Force Status: Data and Model Data 84.5

Employed

Model 83.3

(0.6)

4.2

Unemployed

6.1

(0.2)

Not-in-labor-force

11.3

10.6

(0.5) Data Source: 2004 SIPP, U.S. Census Bureau

Table 7 demonstrates the ability of the model to match aggregate employment-based health insurance participation rate as well as health insurance coverage by labor force status. While aggregate health insurance coverage was not directly targeted in the calibration procedure, it is worth noting that the model manages to approximate it fairly well at 60.6 percent in the model and data. The model also replicates health insurance 21

coverage by labor force status. Among employed population, 70.1 percent have employerbased health insurance in the model compared to 69.5 percent in the data. Among the non-employed population the pattern is similar. For the unemployed, 19.9 percent are insured through a former-employer in the model compared with 9.7 percent in the data. For those not in the labor force, 7.8 percent in the model have health insurance versus 8.7 percent in the data. The fact that the model does well along these dimensions should not be surprising, since these moments are targeted in the calibration. Table 7: Health Insurance by Labor Force Status: Data and Model Data 60.6

Aggregate

Model 60.6

(0.9)

69.5

Employed

70.1

(0.9)

21.2

Unemployed

19.9

(1.2)

8.7

Not-in-labor-force

9.7

(1.0) Data Source: 2004 SIPP, U.S. Census Bureau

Recall that labor market friction parameter σ was chosen to best match flows between employment and unemployment (1.1 percent). Note that the respective flow in the model is 0.5 percent, which is below the target. The remaining transitions in the model and data are presented in Table 8. The calibrated baseline model does well at replicating the diagonal elements of the transition matrix. Specifically, duration of employment, unemployment, and not-in-labor-force are similar to those found in the data. The model does a reasonable job of matching flows in and out of the not-in-labor-force category. The model also captures the magnitude of flows between unemployment and employment at 11.2 percent versus 9.7 percent in the data. Recall that these flows were targeted in the calibration procedure through the consumption floor parameter that determines the set of job offers that the agent will accept. Table 9 shows transition probabilities between employer-based health insurance coverage in the data and those generated by the model. The spells of coverage and no coverage in the model exhibit a large degree of persistence that are consistent with the data. Nevertheless, the model underestimates the degree of persistence of coverage. A covered individual has a 99.1 percent chance of coverage in the following period according to the data. In the model, that probability declines to 97.7 percent. 22

Table 8: Labor Force Transitions: Data and Model Data To (t+1): From (t): E U E 98.7 1.1 U

(0.1)

(0.1)

N 0.2 (0.1)

9.7

87.5

2.8

(0.6)

(0.7)

(0.3)

1.5

3.7

94.8

(0.1)

(0.3)

(0.3)

Model To (t+1): From (t): E U E 99.1 0.5 U 11.2 85.3 N 0.6 4.5

N 0.4 3.5 94.8

N

Data Source: 2004 SIPP, U.S. Census Bureau

Table 9: Health Insurance Transitions: Data and Model Data To (t+1): From (t): Coverage No Coverage 99.1 0.9 Coverage No Coverage

From (t): Coverage No Coverage

(0.1)

(0.1)

4.9

95.1

(0.2)

(0.2)

Model To (t+1): Coverage No Coverage 97.7 2.3 3.5 96.5

Data Source: 2004 SIPP, U.S. Census Bureau

23

5

Results

In this section, I report the effect of frictions in the health insurance market on agent allocations. I first focus on health insurance coverage and disaggregate the effects of frictions by labor force status and magnitude of medical expenditure shocks s. Second, I detail the effect of health insurance frictions on labor supply outcomes.

5.1

Health Insurance Frictions and Coverage

What impact do health insurance frictions (γ, θ) have on employment-based health insurance coverage? This question is important since limits on enrollment have been the subject of numerous health policies with contradictory goals. The Employee Retirement Income Security Act of 1974 removed state regulatory authority to exclude coverage of pre-existing conditions by large firms. In contrast, the 1996 HIPAA legislation imposed maximum time limits of exclusion from group health insurance. Finally, the 2010 Affordable Care Act imposes fines on firms with 50 full-time workers or larger that do not offer health insurance benefits to workers. I begin by exploring the impact of exogenous changes in the arrival rate of a health insurance insurance coverage opportunity, γ. The focus of this experiment is to compare the equilibrium health insurance participation rates by agent characteristics relative to exogenous changes in the parameter γ. Each exogenous change in γ implies a new equilibrium with a possibly distinct set of decision rules, prices, and transfers. All remaining utility and friction parameters are held at their calibrated values in the benchmark economy. Figure 3 illustrates the effect of γ on health insurance participation. As γ increases, agents make health insurance coverage decisions with greater frequency. A key result is that changes in γ have large effects on insurance participation. In the figure, the solid line represents the aggregate health insurance participation rate. As γ increases, the aggregate participation rate increases and then falls. As γ increases, more agents are eligible to participate and aggregate coverage increases. However, once γ surpasses some critical value, aggregate coverage begins to fall. This observed fall is due to selection of agents with lower medical expenditures out of health insurance that results in higher equilibrium premiums. Higher equilibrium premiums along with a greater frequency of coverage opportunities allows agents to drop coverage if their expected expenses are not sufficiently large. To illustrate this more clearly, the figure also plots insurance participation rates for agents with high and low realizations of s that reflect the magnitude of medical expenditure shocks. As the frequency of insurance enrollment 24

1 0.9 0.8 Coverage Rate

0.7

Low s only Aggregate High s only

0.6 0.5 0.4 0.3 0.2 0.1 0

0

0.2

0.4

0.6

0.8

1

γ

Figure 3: Health Insurance Offer Probability and Coverage opportunities increases, agents with high values of s will choose to enroll at higher rates than those with low realizations of s. A key implication of this experiment is that abstracting from enrollment frictions, i.e. γ = 1, results in decreased incentives to purchase health insurance, especially among agents with low realizations of medical expense shocks s. Conversely, in the presence of enrollment frictions, low-s agents find it optimal to purchase health insurance only if frictions are “sufficiently” severe. To get a better sense of the magnitude of health insurance frictions introduced by γ, I express the average length of the waiting period by 1/γ. The baseline calibration implies average waiting periods of 11.6 months. Figure 3 illustrates that an increase in enrollment opportunities from the current baseline of γ = 0.12 will reduce aggregate health insurance coverage by selection of low-s agents out of the health insurance pool. Nevertheless, the majority of agents with high-s realizations choose to purchase insurance coverage for any value of γ > 0. Another central friction introduced in this model is the health insurance separation rate of employer-based coverage provided by a former employer. As discussed earlier, this separation rate θ is a reduced-form representation of a variety of factors that might induce a termination of health insurance coverage such as limits to COBRA coverage, an employer decision to cancel provision of health insurance benefits to employees, or employer bankruptcy. Again, each value of θ implies a new set of equilibrium allocations 25

1

Low s only Aggregate High s only

0.9 0.8 Coverage Rate

0.7 0.6 0.5 0.4 0.3 0.2 0.1 0

0

0.2

0.6

0.4

0.8

1

θ

Figure 4: Health Insurance Loss Probability and Coverage and prices. I set γ at its baseline value for each equilibrium. As θ increases, the likelihood that an insured agent faces a loss of health insurance coverage from a former employer also increases. Figure 4 illustrates health insurance coverage by θ. From the figure, it is clear that changes in θ result in relatively small changes in aggregate health insurance enrollment. The effect of the separation friction is larger for high-s agents than low-s agents. One implication of this finding is that state and federal laws that mandate continued access to employer-provided health insurance have little effect on all but those agents with high expense shocks. Furthermore, the complete elimination of continuation coverage limits (θ = 0) increases coverage for those with high expense shocks by less than 2 percentage points from the baseline value. Figures 5 and 6 repeat the exercise, but disaggregate the response of changes in the frictions by shocks to medical expenses and labor productivity. I note that restrictions to health insurance enrollment among employed agents have differential effects on incentives to purchase health insurance among the unemployed and those not in the labor force. Since the composition of these groups varies by (γ, θ), I examine coverage along characteristics that remain constant across economies. In Figure 5, I illustrate that the impact of complete elimination of enrollment frictions among employed agents on health insurance coverage depends critically on the size of medical expense shocks. As the size of medical expense shocks increases, agents are less likely to purchase health insurance than 26

1 0.9

γ = γb γ=1

Coverage Probability

0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 -3 -2 -1 0 1 2 3 Standard Deviation from Mean (Log) Medical Expenses

Figure 5: Effect of Enrollment Restrictions on Health Insurance Coverage by Medical Expense Shock

1 0.9

Coverage Probability

0.8 0.7 0.6 0.5 0.4 0.3 0.2

θ = θb θ=0 θ=1

0.1 0 -3 -2 -1 1 2 3 0 Standard Deviation from Mean (Log) Medical Expenses

Figure 6: Effect of Continuation Coverage Restrictions on Health Insurance Coverage by Medical Expense Shock

27

1 0.9

Coverage Probability

0.8 0.7 0.6 0.5 0.4 0.3 0.2

γ = γb γ=1

0.1 0 -3

-2 -1 0 1 2 3 Standard Deviation from Mean (Log) Productivity

Figure 7: Effect of Enrollment Restrictions on Health Insurance Coverage by Productivity

1 0.9

Coverage Probability

0.8 0.7 0.6 0.5 0.4 0.3 0.2

θ = θb θ=0 θ=1

0.1 0 -3

-2 -1 0 1 2 3 Standard Deviation from Mean (Log) Productivity

Figure 8: Effect of Continuation Coverage Restrictions on Health Insurance Coverage by Productivity

28

in the baseline economy as shown previously. Furthermore, agents with above-average expense shocks are more likely to purchase health insurance coverage than in the baseline economy. A striking finding is that agents with the largest medical expense shocks are less likely to purchase coverage despite the absence of frictions. How do these agents insure consumption in the face of large medical expense shocks? These agents choose to forgo health insurance coverage and are more likely to rely on social insurance transfers in the form of the consumption floor. Social insurance transfers in the the economy with no enrollment frictions increase relative to the baseline economy by 30 percent from 1.2 percent of output to 1.6 percent of output. Note that removal of continuation coverage restrictions in Figure 6 has little effect on coverage, even among those with the largest medical expense shocks. To illustrate the effect of enrollment frictions on coverage by labor productivity, I plot health insurance participation by magnitude of the labor productivity shock in Figure 7. The least productive agents in the economy are unlikely to participate in employmentbased coverage regardless of the presence of enrollment frictions. As productivity increases, agents are less likely to rely on health insurance to insure consumption against medical expense shocks and rely instead on savings. In Figure 8, I repeat the analysis by eliminating frictions to duration of continuation coverage. The effect of these frictions on health insurance enrollment is small across all productivity levels.

5.2

Health Insurance Frictions and the Labor Market

What role do frictions in the health insurance market (γ, θ) have on employment? To answer this question, I plot in Figures 9 and 10 the aggregate employment level across exogenous changes in parameters γ and θ (solid line). While elimination of employer-based health insurance frictions (γ = 1) would have little effect on the aggregate employment rate, elimination of employment-based health insurance (γ = 0) would reduce aggregate employment slightly to from 83.3 to 82.4 percent. Meanwhile, changes in duration of continuation coverage (θ = 0) would likewise have small effects on aggregate employment. The aggregate changes in employment level mask more substantial effects when decomposing the effects by magnitude of the expense shock s. In particular, the effect of changes in both γ and θ on the employment rate are larger for agents with high realizations of s than low realizations of s. In Figure 9, the elimination of employment-based insurance (a decrease in γ from the baseline value to zero) decreases employment among agents with high s from 84.0 percent to 73.8 percent. In comparison, agents with low-s values see an increase in employment from 84.0 percent to 86.0 percent. The elimination 29

1 0.9

Employment Rate

0.8 0.7 0.6 0.5 0.4 0.3

Low s only Aggregate High s only

0.2 0.1 0

0

0.2

0.4

0.6

0.8

1

γ

Figure 9: Health Insurance Offer Probability and Employment

1 0.9

Employment Rate

0.8 0.7 0.6 0.5 0.4 0.3

Low s only Aggregate High s

0.2 0.1 0

0

0.2

0.4

0.6

0.8

θ

Figure 10: Health Insurance Loss Probability and Employment

30

1

of employer-based health insurance is associated with a dramatic decline in employment among agents with the highest realizations of medical expense shocks. Why do agents with the highest medical expense shocks choose not to work in the absence of employerbased health insurance? Holding the level of assets fixed, a large medical expense shock can easily eliminate the majority of labor earnings for all but the most productive agents. This results in both employed and non-employed agents choosing to consume c. Agents choose to substitute consumption for leisure by foregoing employment. Note that in the presence of employment-based insurance, the magnitude of health insurance frictions has a substantially smaller effect on employment by medical expense shock s that the complete removal of the employment-based insurance market (γ = 0) To what extent do frictions in the market for health insurance affect agents of different productivity levels? In Figure 11 and 12, I show the distribution of employment across different productivity levels z for select values of γ for agents with low and high realizations of medical expense shocks s. From Alonso-Ortiz and Rogerson (2010), we know that an incomplete markets model with indivisible labor choice generates too much employment among low productivity agents relative to a complete markets model. That is, the inability of agents to move consumption from periods of high productivity to low productivity leads agents to smooth consumption using employment despite the high value of leisure in low productivity periods. The introduction of idiosyncratic medical expenditures that are insurable though employment substantially strengthens this motive. In Figure 12, the introduction of a employment-based health insurance market increases employment among low-z agents. This is seen in comparing employment rates when γ = 0 versus γ = γ b or γ = 1. This is not the case among agents with low medical expense shocks as seen in Figure 11. Figure 11 shows that employment incentives for low-z agents remain approximately unchanged when accompanied by small realizations of medical expense shocks. I repeat the exercise above but for θ rather than γ. The results are similar and are presented in Figure 13 and 14. For low values of s, continuation coverage has little effect on employment by productivity level. For higher values of s, the effect of continuation coverage is larger. Agents with low productivity are more likely to work when no continuation coverage is available (θ = 1). The figure shows that as the duration of continuation coverage is expanded from the baseline value, the employment rate among the most unproductive agent does not change, but declines for those between grid 4 and grid 8. Therefore expansion of continuation coverage will reduce employment among agents with high-s shocks that have productivity below the median.

31

1

Employment Probability

0.9 0.8 0.7 0.6 0.5 0.4 0.3

γ = γb γ=0 γ=1

0.2 0.1 0 -3

-2 -1 0 2 3 1 Standard Deviation from Mean (Log) Productivity

Figure 11: Employment By Productivity and γ, Low Medical Expense Shock

1

Employment Probability

0.9

γ = γb γ=0 γ=1

0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 -3

-2 -1 0 1 2 3 Standard Deviation from Mean (Log) Productivity

Figure 12: Employment By Productivity and γ, High Medical Expense Shock

32

1

Employment Probability

0.9 0.8 0.7

θ = θb θ=0 θ=1

0.6 0.5 0.4 0.3 0.2 0.1 0 -3

1 2 3 -2 -1 0 Standard Deviation from Mean (Log) Productivity

Figure 13: Employment By Productivity and θ, Low Medical Expense Shock

1

Employment Probability

0.9 0.8 0.7

θ = θb θ=0 θ=1

0.6 0.5 0.4 0.3 0.2 0.1 0 -3

-2 -1 0 1 2 3 Standard Deviation from Mean (Log) Productivity

Figure 14: Employment By Productivity and θ, High Medical Expense Shock

33

Table 10: Labor Force Transitions by γ E-E U-U N-N

γ = 0 γ = γb 99.0 99.1 85.7 85.3 94.7 94.8

γ=1 99.1 85.4 94.8

Lastly, I return to the effect of health insurance frictions on job mobility, known as “job lock.” Specifically, this model is able to quantify the extent to which health insurance frictions alter the duration of employment spells and the movement through the labor force categories. I perform the following experiment. I solve for the equilibrium implied by three values of γ and calculate the diagonal elements of the labor supply transition matrix calculated earlier. I chose γ = 0 (no health insurance system), γ = γ b (baseline), and γ = 1 (no enrollment restrictions). The results are found in Table 10 and illustrate that the effect of frictions or waiting periods in the market for health insurance has little effect on aggregate measures of job mobility. The likelihood of transition from employment at month t to employment at month t + 1 (E-E) is approximately constant. The same is true for transitions across spells of unemployment (U-U) and non-participation (N-N). This result suggests that, within this model framework, employment-provision of health insurance has little effect on the duration of average employment, unemployment spells, and flows between labor force categories.

6 6.1

Sensitivity Analysis Persistence of Medical Expense Shocks

One of the central findings of this paper is that a reduction in enrollment frictions for current employees reduces aggregate enrollment. This finding is driven by selection of agents with low expected medical expenses out of the insurance pool as enrollment opportunities arrive more frequently. Agent selection is determined by the persistence of the medical expenditure process. Estimates of persistence (˜ ρ) vary from 0.24 to 0.65. The purpose of this section is to determine the degree to which changes in the persistence parameter alter this result. To do so, I recalibrate the model for several different values of ρ˜, specifically 0.01, 0.1, and 0.7. In each economy, parameters (α, σ, λ, γ, θ, c, ψ0 ) are chosen to match to match their respective targets and the remaining parameters are held fixed at the baseline equilibrium values. The baseline values of γ for these three economies are 34

0.086, 0.024, and 0.016.14 Table 11: Employment-Based Enrollment by γ and ρ˜ γ = γb ρ˜ = 0.01 63.0 ρ˜ = 0.1 61.9 ρ˜ = 0.448 60.6 ρ˜ = 0.7 61.8

γ = 0.5 γ = 0.75 γ = 1 76.3 62.2 50.0 60.9 50.1 34.5 33.8 20.0 19.9 12.1 12.1 12.2

I detail aggregate enrollment as a function of ρm for several values of γ in Table 11. Note that differences in aggregate enrollment at the baseline level of frictions for each ρ˜ reflect the differences in calibration results obtained by the simplex method. The tables shows that the decline in aggregate coverage that is accompanied by a reduction in enrollment frictions depends on the degree of persistence in the medical expenditure process. Relative to the baseline equilibrium (˜ ρ = 0.448), the economy with a higher persistence of expense shocks experiences a faster decrease in enrollment as γ increases. Likewise, economies with less persistent expense shocks see slower declines in enrollment. An increase in γ from its benchmark value to 0.5 results in little decline in aggregate coverage when ρ˜ = 0.1 and an increase in coverage when ρ˜ = 0.01. A key result of this section is that persistence of medical expense shocks matters in a quantitative analysis of the health insurance frictions. The results suggest that a modest amount of persistence is needed to generate a decline in aggregate coverage when accompanied by a reduction in enrollment eligibility restrictions. The degree to which persistence matters depends largely on the size of the potential policy that alters γ. For small increases in γ, the degree of persistence is important for estimates of aggregate enrollment. However, for a large increase in γ, for example in the case where γ = 1, the degree of persistence matters less.

6.2

Risk Aversion

Suppose preferences are now defined by a CRRA utility function for consumption, E

(∞ X t=0

14

βt



ct1−η − αht 1−η

)

The remaining parameter values are not detailed here, but are available from the author upon request.

35

where γ ≈ 1 is approximately the logarithmic utility function used in the baseline model. This value is consistent with the predictions of risk aversion in the neoclassical growth model given average return on capital and consumption growth observed in the United States (Lucas (2003)). However, larger values are often found (Cagetti (2003)). To examine the extent to which the main results of this paper depend on estimates of relative risk aversion, I recalibrate the model for parameters η = 2 and η = 4. The baseline equilibrium values of γ are 0.05 and 0.11. Table 12 details the aggregate coverage rates for these values of risk aversion for selected values of γ. When enrollment frictions are reduced from γ b to 0.5, aggregate coverage declines from 62.3 percent to 20.6 percent in the baseline economy. In the alternative calibrations with higher values of risk aversion, the decline in aggregate coverage is smaller. For example, there is a decline in coverage from 61.8 percent to 34.8 percent when η = 4 and γ is increased from its baseline value to 0.5. Table 12: Employment-Based Enrollment by γ and η γ = γb η≈1 60.6 η=2 60.6 η=4 61.8

γ = 0.5 33.8 32.5 34.8

γ = 0.75 γ = 1 20.0 19.9 20.0 20.0 24.4 22.4

It is worth pointing out, that in the case of larger risk aversion a larger value of ψ0 is needed to match the level of employment-based coverage among those not in the labor force observed in the data. In the baseline economy, ψ0 = 0.89. In comparison, when η = 4 the calibration procedure yields a much less plausible value of ψ0 = 1.34. This value is less plausible since COBRA coverage imposes only a 2 percent administrative fee on top of the health insurance premium.15

7

Conclusion

The purpose of this paper is to provide a quantitative model of employer-based health insurance coverage characterized by frictions in the market for health insurance. In particular, I construct an incomplete markets model with idiosyncratic shocks to labor productivity and medical expenditures. Agents face a discrete choice of labor supply and health insurance participation that are subject to frictions. The degree of frictions in the labor 15

See http://www.dol.gov/ebsa/publications/cobraemployer.html.

36

market and the market for health insurance generates the levels of insurance participation by labor force status as well as transitions between health insurance categories consistent those observed in the data. I find that frictions in the health insurance market have important implications for health insurance coverage. Restrictions to health insurance enrollment opportunities play an important role in mitigating selection of agents by expected medical expenditures. However, I find relatively small effects of generosity of continuation coverage on aggregate insurance enrollment. Both health insurance enrollment restrictions and continuation coverage have important implications for labor force outcomes. In particular, employmentbased health insurance with enrollment restrictions increases work incentives among those with high medical expenses. While limits in the duration of continuation coverage have little effect on aggregate employment, the presence of continuation coverage benefits reduces employment among agent with low labor productivity. There is considerable room for expansion of the model to answer related questions. For example, introduction of a “storage” technology for medical expense shocks could be used to address the role of delays in treatment on health insurance coverage. Spousal health insurance coverage is an important source of insurance coverage. How does dependency coverage alter the household labor supply decision when health insurance is modeled as a benefit to employment? Finally, introduction of a Medicaid program and a Medicaid enrollment decision into the model could be used to address the reasons why eligible workers do not enroll in Medicaid coverage and the implications of the program on labor supply.

37

A

Appendix: Timeline of Household Problem Time t

Time t+1

Shock z’

No-separation or separation with new offer (1- + )

No HI Opp. (1- )

Employment Decision

HI Opp. ( ) Employment and Insurance Coverage Decision

I(x) or W(x)

Shock s’

Consumption and Savings Decision

Shock s’

Consumption and Savings Decision

Insurance Coverage Decision if HI Coverage at t

Separation, No Job Offer *(1- ) COBRA Opp. (1- ) Shock z’

Shock z’

No COBRA Opp. ( )

No HI Opp. (1- )

No Decisions

Employment Decision

HI Opp. ( ) Employment and Insurance Coverage Decision

Job offer ( ) N(x) or U(x)

Insurance Coverage Decision if Coverage at t

No Job Offer (1- ) COBRA Opp. (1- ) Shock z’

No COBRA Opp. ( )

38

No Decisions

B

Appendix: Discretization of State Space

The process for labor productivity implied by the Tauchen discretization method yields the following transition matrix Π(z, z ′ ), 

0.9764   0.0122   0   0    0   0   0    0   0    0 0

0.0236 0.9658 0.0132 0 0 0 0 0 0 0 0

0 0.0220 0.9663 0.0142 0 0 0 0 0 0 0

0 0 0.0205 0.9667 0.0153 0 0 0 0 0 0

0 0 0 0.0191 0.9669 0.0165 0 0 0 0 0

0 0 0 0 0.0178 0.9670 0.0178 0 0 0 0

0 0 0 0 0 0.0165 0.9669 0.0191 0 0 0

0 0 0 0 0 0 0.0153 0.9667 0.0205 0 0

0 0 0 0 0 0 0 0.0142 0.9663 0.0220 0

0 0 0 0 0 0 0 0 0.0132 0.9658 0.0236

0 0 0 0 0 0 0 0 0 0.0122 0.9764



0 0 0 0 0.0003 0.0168 0.1989 0.5128 0.3003 0.0390 0.0010

0 0 0 0 0 0.0002 0.0134 0.1763 0.5039 0.3269 0.0472

0 0 0 0 0 0 0.0001 0.0106 0.1550 0.4916 0.3533

0 0 0 0 0 0 0 0.0001 0.0083 0.1418 0.5985



                    

with support vector Z:                      

0.1144 0.1765 0.2723 0.4201 0.6482 1.0000 1.5428 2.3803 3.6724 5.6658 8.7413

                     

˜ s′) is defined by, Likewise, the transition matrix Π(s, 

0.5985   0.1418   0.0083   0.0001    0   0   0    0   0    0 0

0.3533 0.4916 0.1550 0.0106 0.0001 0 0 0 0 0 0

0.0472 0.3269 0.5039 0.1763 0.0134 0.0002 0 0 0 0 0

0.0010 0.0390 0.3003 0.5128 0.1989 0.0168 0.0003 0 0 0 0

0 0.0008 0.0319 0.2739 0.5183 0.2229 0.0210 0.0004 0 0 0

0 0 0.0006 0.0260 0.2480 0.5201 0.2480 0.0260 0.0006 0 0

0 0 0 0.0004 0.0210 0.2229 0.5183 0.2739 0.0319 0.0008 0

with support vector S:                      

−6.0971 −4.8777 −3.6583 −2.4388 −1.2194 0 1.2194 2.4388 3.6583 4.8777 6.0971

39

                     

                    

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