Macroeconomic consequences of alternative reforms to the health insurance system in the United States

2.1 Demographics

The benchmark model considers an open economy with overlapping generations of agents who live a maximum of three periods as young, middle-aged, and old. Let denote the age. In the first period, the measure of newly born agents is normalized to 1. Individuals alive in period survive to the next period with a certain probability. For old people this probability is always 0. For young and middle-aged people, the survival probability is given by , which depends on the health status at the end of age as described below. The population of young individuals grows at a constant rate , implying that the population of young in period is . I denote the relative size of age to the population as , which is determined in the equilibrium.

2.2 Agent types

All individuals enter the economy with the same level of health , an idiosyncratic endowment , and an idiosyncratic health risk types . Health risk type determines the probability of drawing a certain health shock . The probability distribution of the shock is assumed to be age-type-dependent. Specifically, the probability of drawing by type agent at age is denoted by , with for all .1 A typical history of shocks up to time is denoted by , with . Agents are endowed with a fixed amount of time per period that can be allocated to leisure or labor. Agents participate in the labor market during the first two periods and receive a wage income . Here measures the effect of health on labor productivity.2 Health is an important form of human capital. It can enhance workers' productivity by increasing their physical capacities, such as strength and endurance, as well as their mental capacities. I postulate a positive relationship between health and labor productivity.

During their work stage agents supply labor and receive wage income from the firm. They can also save units of the consumption good by investing in physical capital with gross rate of return , where is the world real interest rate. Retired agents have income through previous saving, and consume all of their income at their last period of life.

The type of an agent is a triple , where is age; presents health risk type; and denotes their disposable resources at the beginning of each period defined as follows:

()

2.3 Preferences

Preferences over stochastic sequences of consumption, leisure, and health are given by

()

where denotes the discount factor, the survival probability, consumption, leisure, and health status. denotes the conditional expectation with the information available when the agent is born.

2.4 The evolution of health

I use the idea of health capital introduced by Grossman (1972). In the model, each agent chooses an optimal amount of medical consumption to offset the negative effect of health shock on health and builds up health capital . The accumulation process of health is given by:

()

where represents the natural deprecation rate of health and measures the medical technology.3 I assume that technological progress in the production of medical service is exogenously given. The price of medical care is exogenously given so that each unit of consumption good can be transformed into units of medical care.

In previous literature that explores the macroeconomic effects of health-related policies (e.g., Jeske & Kitao, 2009), the health expenditure is treated as an exogenous random shock. Individuals must pay the full amount for necessary health care after the health expenditure shock is revealed, independent of their income level and current health stock. In the current study, medical expenditures are endogenously chosen by agents to build up their health stocks. Since health expenditure is an endogenous choice, richer agents will spend more on health care to build up better health stock than the poor who has the same health status and faces the same health shocks. This can be explained by the fact that rich individuals have higher levels of consumption and lower marginal utility from consumption goods, therefore they will substitute some health for consumption goods.4

Conditional on being alive at the current age with end of period health stock , agent will survive to the next period with probability . Death is certain when health falls below zero ( if ). I assume that . Deceased agents leave their savings as an accidental bequest that is collected by the government as revenues.

2.5 Medical expenses and health insurance

Nonelderly can choose one out of three possible insurance states labeled as . To purchase private health insurance is denotes that the agent has Medicaid, and indicates that the agent is uninsured. The out of pocket health expenditure will be if the agent chooses to buy insurance and when he/she is covered by the government program. It will cost the entire expenditure if the agent does not have insurance (). Here is function that represents the coinsurance rate and varies with the health insurance state as we discuss in the following section. Agents take coinsurance rate as given and it is calibrated from the data. Retired agents are insured under Medicare.

2.6 Aggregate production function

The consumption goods are produced by a neoclassical production function. The aggregate production function takes a nested Cobb–Douglas specification in the following form.

()

()

where is a total factor productivity, denotes the total capital stock, and is an aggregate efficiency labor input, which depends on individual worker's health status. The distribution of households is defined over their state as discussed in the next section, and idiosyncratic health shock . The firm takes factor prices as given and demand capital stock and labor to maximize the profit. It also subtracts the cost of providing health insurance . The adjusted wage is given by , where and .

2.7 The representative agent's problem

A representative agent of generation enters the economy with characteristics , where is the risk type of the agent, is the net wealth, is the health status at the beginning of the period, and is the indicator function that signals the availability of the Medicaid benefit in the current period. Since all old agents are automatically enrolled in the Medicare program and leave the labor market, their characteristics simply are .

Agents observe at the beginning of the period. They take prices and taxes as given and make the insurance decision and choose a set of state-contingent decision rules, which can be denoted by , to solve the following problem.

()

subject to the budget constraint and a no-borrowing constraint

()

()

when young;

()

()

when middle-aged; and

()

when old, where

()

()

()

()

()

()

()

The timeline for the generation who was born in period is shown in Figure 1. Each agent born at is endowed with . Consumptions, out-of-pocket medical expenditures, payments of insurance premium and savings are financed by gross return from assets, labor incomes if applicable, net of incomes, and payroll taxes.

Equation (12) presents the individual's after-Medicare-tax adjusted wage income. The firm needs to share the Medicare tax with the agent. Hence, in equilibrium a fraction of tax is subtracted from the wage. The price of medical service , marginal cost of the insurance premium and coinsurance rate depend on the insurance states as given in Equations (13), (14), and (15). The individual is responsible to Medicare tax and a progressive income tax which is imposed on the labor income paid to a worker plus accrued interest on savings and profit from the firm as in (16). Equation (17) represents the income tax base, which depends on the agent's age. Health plays three important roles in the economy: good health promotes labor productivity at a factor of , agents derive utility from health and survive to the next period with probability . Equation (18) explains the evolution of health.

2.8 The government

I impose a government-balanced budget constraint period by period. The government has three different types of outlays: general public consumption, Medicaid, and Medicare expenses. The government collects revenues from various sources: income taxation according to a progressive tax function , consumption taxation at rate , Medicare taxation at rate , Medicare premium , Medicaid premium , and accidental bequests collected from deceased agents.

()

where is the taxable income for age agent.

2.9 Health insurance company

The health insurance company is competitive. Hence, in equilibrium the premium is charged such that expected expenditures on the insured are precisely covered.

()

Notice the coverage ratio function is taken as exogenously given.

2.10 Stationary competitive equilibrium

Let . The state space for age year old agents is , and the state space for the old is .

3.1 Data sources

The data used for estimating the process of health insurance decisions and health production come from the Household Component of the Medical Expenditure Panel Survey (MEPS), which is based on a series of national surveys conducted by the US Agency for Health Care Research and Quality (AHRQ). The MEPS consists of eight 2-year panels from 1996/1997 up to 2003/2004 and includes data on demographics, income, and most importantly health status and health insurance.

3.2 Demographics

In the model, one period is defined as 20 years. Agents enter the economy at the age of 25 () and survive up to the maximum age of 85 (). In line with Suen (2006), I assume that the survival probability function takes the form of the cumulative Weibull distribution function:

()

with and . The endogenous survival probability rules out the case that agents survive to the next period with negative health stock.

I consider a yearly population growth of 1.25%. Together with the survival probability , the ratio of retired people to active population (the dependency ratio) is equal to 30% (24.3% according to the 2000 Population Census for the United States).6 The initial level of health when agent enter the economy, , is assumed to be constant and is normalized to be 100.

3.3 Preferences and technology

Agents have period utility over consumption, leisure, and health:

()

The parameter is age-dependent and I choose parameter values such that the average fraction of the time endowment allocated to market work is 0.33, which implies , and . Notice old agents retire from the labor market and they spend all time on leisure. For simplicity, I set  . , which is age-dependent as is , measures the importance of health, and denotes the coefficient of relative risk aversion of health.

The annual subjective discount factor is taken to be 0.97, so . The average annual interest rate in the United States is 4%, so .

3.4 Production of health and health shocks

The health measure used in this paper is the Physical Component Summary scores formed from the answers to the Short-Form 12 questions. For people aged between 25 and 85, the lowest health level is 4.56 and the highest level is 72.17 in the MEPS data.7 This paper assumes that human beings can live up to 85 years without any accident or illness. I choose such that , where refers to annual health depreciation rate. I also assume that the depreciation rate increases with age. Therefore I choose depreciation rate of .

The transition of agent's health is described by Equation (3). Agents can offset the negative effect of a health shock by purchasing medical care. The productivity of medical care is captured by , and the price of medical care is . Both are exogenously given.

Brown (2006) found that uninsured people in California pay 65% more for common prescription drugs than the federal government does for the same medications. Anderson (2007) found that the uninsured patients pay up to 2.5 times for hospital service than health insurers. I assume that uninsured consumers pay a 60% higher price for medical services than the insured, so that . This is similar to Jung and Tran (2008). I assume that the relative price of medical service is the weighted average price paid by the insured and the uninsured, that is, , where is the fraction of uninsured in the population. According to Kaiser Family Foundataion (2007), the value of was 17% in 2006. Therefore, I pick , and .

I differentiate agents into two groups, which are high-risk and low-risk, by using the estimation procedure of Bundorf et al. (2005). The health shocks take two possible values . For the same age cohort high-risk people are different from low-risk people in terms of the probabilities of getting the same shock . The health shocks and the probability distribution of the shock are chosen so that the health insurance take-up rate (percentage of workers buying private insurance per age-type group) and the share of health expenditure in GDP are approximated.

3.5 Health insurance

3.5.1 Private health insurance

Data suggests that the coverage rate increases in the health expenditures incurred by the patients. Therefore I assume that the coverage ratio is a function of total health expenditure and takes the following form similar to Jeske and Kitao (2009).

()

First, I estimate the set of parameters using the MEPS data. I sort the health expenditure into quantiles and use five uniform-sized bins for health expenditure data. Then I plug in the health expenditure data to attain the average coverage ratio for each bin.

The coverage ratios of Medicaid and Medicare are estimated by the same procedure. I report the parameter values and coverage ratios for each expenditure grid in Tables A3 and A4. In Table A4, the standard errors in brackets and all coefficient estimates are significant at the 1% level. The insurance premium is determined in the equilibrium to ensure zero profits for the insurance company.

3.6 Firms

I choose a standard capital share in production of from NIPA. Without loss of generality, total factor productivity is normalized to such that the average labor income equals 10 in the benchmark. In line with Bloom and Canning (2005), I assume that individual worker's health status affects the efficiency of labor input by a factor of . Therefore, labor income is given by , where is the average wage rate. I estimate the parameter that fits the following equation using the MEPS data.

()

where is the Physical Component Summary scores that measure the individual's health status ranging from 0 to 100. I normalize the average labor income observed in the data to be 10.0 and I calculate in the benchmark.

3.7 Government

The value for is exogenously given and is fixed across all policy experiments. I calibrate it to 18.0% to match the share of government consumption, social security, and gross investment excluding transfers, at federal, state, and local levels. The consumption tax rate is 5.67%, as in Mendoza et al. (1994).

The income tax function follows the functional form studied by Gouveia and Strauss (1994), which is given as

()

Parameter is the limit of marginal taxes in the progressive part as income goes to infinity, denotes the curvature of marginal taxes and is a scaling parameter. I use the parameters estimated by Gouveia and Strauss (1994), which are . When they calibrate the tax function, the income has been normalized to the range of . In my model, I divide taxable income of every agent by the maximum income observed in the simulated economy to get the normalized income. Then I use this normalized income directly in Equation (32) to get the tax rate. The parameter in the proportional term of the income tax equals 4.46% in the benchmark.

4.1 Benchmark model

Table A5 reports the main features of the benchmark simulation. Under the baseline parameterizations the model is able to match the health insurance demand and aggregate health expenditure in the United States. The fraction of insured agents among all young and middle-aged agents is 82.9%, which is almost the same as 83.0% in the data. Among nonelderly, 10.3% are covered by the Medicaid program (12.9% in the data). The model slightly understates total health expenditure as a ratio of GDP, which is about 16.3% according to the Department of Health and Human Services. The model reports 16.1%.

My model does not match the wealth distribution accurately even though I introduce idiosyncratic health shock. This can be explained by the fact that agents do not have bequest motive and the profits generated from production have been uniformly distributed back as a lump sum payment in the model economy. Nevertheless, the accuracy of approximation of the entire wealth distribution won't impose strong effect on the prediction of health insurance demand, which will be determined by the fraction of the population whose wealth is below certain threshold. As described in the previous paragraph, the health insurance take-up profile and aggregate health expenditure match with the data fairly well. Therefore, I leave the current setting as it is.

Next, I examine the model's predictions on the life-cycle patterns of medical spending and consumption. Panel 1 of Figure 2 displays medical spending over various age groups with the same statistics from the MEPS. Both in the data and model, the average health expenditure is roughly constant between ages 25 and 64 and climbs afterward. The benchmark model is able to replicate the increasing pattern. However, the size of the health expenditure of nonelderly agents as a ratio of GDP is bigger than the one observed in the data. The main reason is that the agent enters the economy with same amount of health stock in the model. The labor productivity effect of health may overstate the investment in medical service among young agents. This can be resolved by introducing heterogeneity in initial health but with some extra computational cost. In the model, a representative agent age between 25 and 44 spends $4676 or about 11.9% of per capita GDP (7.5% in the data). Agents between ages 45 and 64 years old on average spend $4667, or about 11.8% of per capita GDP (11.0% in the data). Agents over 65 spend $12,848, or about 32.7% of per capita GDP (32.6% in the data).

Panel 2 of Figure 2 shows the consumption over various age groups. Fernandez-Villaverde and Krueger (2002) estimated the life-cycle consumption profiles using data from the Consumer Expenditure Survey. They found that nondurable consumption peaked at age 52 and was about 29% higher than at age 25. The current model is able to generate a similar hump-shaped pattern. However, there is a gap between the benchmark prediction and data. This can be attributed to the fact that there is no capital in the model for the sake of simplification. The direct consequence of this strategy is that the demand for saving is inelastic and therefore part of the government income taxation is distortion free as discussed in the section explaining the firm's problem.

4.2 Policy experiments

I now conduct experiments to determine the effect of reforming the health insurance system. All potential reforms start from the same initial steady state of the benchmark economy. In period 1, an unanticipated change of the policy is announced and implemented and the economy starts to make a transition to the new steady state. I first compare moments of associated invariant distributions and then discuss the welfare analysis associated with each of the reforms considered.

I am interested in changes in health expenditure as a ratio of GDP, changes in taxes that balances the government budget, aggregate labor supply, aggregate health status, savings rate, the output as well as welfare implications. I treat changes in government revenue as follows: expenditures , consumption tax rate , and the income tax remaining unchanged from the benchmark. The government adjusts the medicare tax to balance the budget.

In each experiment, I compute a steady state outcome under the stationary equilibrium. In line with the methodology as explained by Conesa and Krueger (1999), this paper measures the welfare effect of a reform by computing the consumption equivalent variation . I quantify the welfare change of a given policy reform for an individual type by asking how much (in percent) this individual's consumption has to be increased in all future periods and contingencies (keeping health expenditure, leisure and health insurance status constant) in the old steady state so that his expected life-time utility equals that under a specific policy reform. I denote it with . For example, a of −1.0% indicates that if the given policy reform is put into place, an individual type will experience a welfare loss which is equivalent to sacrificing 1.0% of her consumption in the initial steady state with leisure, health insurance and health expenditure constant at the initial choices.

To isolate the distortion effect of the labor taxation, I also conduct companion experiments in which the government funds the reform through a lump-sum transfer.

4.2.1 Policy experiment A: Expansion of Medicare/EHI

In this experiment, the private health insurance and Medicaid program are abolished. The government extends Medicare to the entire population. Since the paper is about the aspects of the reform which aim at reallocating existing resources more efficiently by reducing the market imperfection in the provision of health insurance, I keep the average price level for medical service and medical technology the same as the benchmark. It is also important to understand how individuals will respond to the changes in cost-sharing. Therefore, I consider two cases in which the government extends Medicare with different coinsurance rate to the nonelderly population. It is worth noting that Medicaid has the lowest cost-sharing in terms of coinsurance rate and Medicare has the highest according to MEPS data.

In experiment A-1, the government extends the Medicare coverage to the entire population which implies that the reform provides an incentive for the nonelderly to be more cautious about their medical spending due to higher cost-sharing. While in experiment A-2, the nonelderly will be covered by a uniform health insurance program with premium and coinsurance rate . Specifically, they pay for a premium that equals 2.1% of the per capita GDP which is cheaper than the counterpart in the benchmark.8 A fraction of their health expenditure will be paid by the government. This reform leaves the majority of the nonelderly, namely those who have insurance coverage through their employers in the benchmark, unchanged in terms of cost-sharing. However, those low-income agents who rely on Medicaid will be responsible for a bigger share of their health expenditure.

The experiment results are summarized in columns A-1 and A-2 of Table 1. The top section displays some statistics of aggregate variables: fraction of insured nonelderly, Medicare tax rate, average effective income tax rate, average hours worked, and health expenditure as a ratio of GDP. The mortality rate for each age group is also presented as a proxy of health status. The lower section displays the welfare effects of each reform. % w/consumption equivalent variation (CEV)  0 indicates the fraction of agents in the benchmark that would experience a welfare gain (positive CEV) if an alternative reform is taken place.

Table 1. Medicare/EHI expansion: via labor tax.

	Bench.	A-1	A-2
Insured nonelderly (in %)	82.9	100.0	100.0
Medicare tax (in %)	2.2	6.0	14.7
Ave. income tax (in %)	20.4	20.6	20.1
Ave. working hours	32.4	30.2	27.3
Health exp. (in % of GDP)	16.1	14.8	16.4
(in % of per capita GDP)	8.7	2.1	2.1
Output	100.0	97.8	94.5
Aggregate saving rate (in %)	26.9	27.5	27.9
Average consumption	100.0	99.2	94.0
Mortality rate (age 25–44)	0.0322	0.0324	0.0322
Mortality rate (age 45–64)	0.1343	0.1343	0.1323
Lifetime CEV after transition
All (in %)	–	0.1	−2.6
Income (in %)	–	1.9	−0.03
Income (in %)	–	−5.7	−10.9
% w/CEV	–	77.6	37.3

• Note: A-1, Medicare expansion to the entire population. A-2, EHI expansion to all working age population.

Universal coverage is achieved by expanding Medicare to the entire population or extending Employer Health Insurance (EHI) to all individuals of working age, as evidenced by the increased proportion of insured nonelderly individuals. However, the aggregate health expenditure does not necessarily grow as the number of uninsured drops. In experiment A-1, the share of total spending in health care as a ratio of GDP shrinks to 14.8%, while the share expands by 0.3% in A-2. This can be attributed to the difference in changing cost-sharing which affects the agent's incentive. Higher cost sharing will contain spendings in health care by providing an incentive for the consumer to use the resource more cautiously as in experiment A-1. Consequently, the aggregate level of health status will deteriorate and the mortality rate will rise. While lower cost-sharing in experiment A-2 will encourage the nonelderly to spend more on medical service which results in improved health. A natural question is whether this deterioration/improvement in health can be justified by the cost saving/growth. The answer seems positive if we ignore the effect of tax distortion and reduced adverse selection which are the subject of welfare analysis. In experiment A-1, the government will save approximately $150 billion at a cost of higher mortality rate which will be around $136 billion if we assume that the value of statistical life is $6.8 million (c.f. Bellavance et al., 2009). Similarly, the value of life saved will amount to $406 billion after experiment A-2 is implemented, while the extra health cost is merely $34.6 billion.

The expansion of public health insurance requires the government to raise tax revenue to cover 17.1% of the nonelderly who would be uninsured in the benchmark. The government also needs to pay for part of the expenditure of the previously insured who pay about 20.0% of the premium before the reform. Meanwhile, the reform also saves some tax revenues through changes in the arrangement in the health care sector. In the benchmark, the government provides Medicaid to low incomes, which costs 1.2% of total GDP. It also subsidizes the purchase of group insurance, and the total subsidy amounts to 0.8% of total GDP. Once the reform is implemented, the government can save these spendings, since both Medicaid and private insurance are abolished. Considering both of them, the government raises the Medicare tax rate to 6.0% in experiment A-1 and 14.7% in A-2 which will discourage labor supply and the average hours worked decrease by 6.8% and 15.7% accordingly. Total output shrinks by 2.2% in A-1 and 5.5% in A-2 as labor supply drops.

Although agents are subject to a higher labor tax after the reform is implemented, the agents will benefit from the policy A-1 with guaranteed access to insurance coverage. The health insurance market is free of adverse selection problems after the reform is implemented. As shown in % w/CEV  0, 77.6% of agents would experience a welfare gain from this reform and the average welfare effect is in the order of 0.1% in terms of consumption in all states. However, low-income agents, especially those covered by Medicaid before the reform, will suffer from this policy because the new insurance program from such a reform is less generous than Medicaid. On average, low-income individuals would experience a welfare loss equivalent to 5.7% of consumption, compared with a welfare gain equivalent to 1.9% of consumption for agents who have incomes above the poverty line. In contrast to A-1, A-2 makes most of the individuals worse off because the after-reform labor tax is so high that the benefit cannot compensate for the cost.

4.2.2 Policy experiment B: Expansion of public health insurance

Reform B entails the expansion of public health insurance, encompassing programs such as Medicaid and S-CHIP, as per Gruber (2006) study. Strategies following this model typically enhance existing public programs by increasing income thresholds, thus extending coverage to a larger number of individuals in need. They eliminate all eligibility criteria except income. The outcomes of this experimental approach are summarized in columns B-1 and B-2 of Table 2. In experiment B-1, the government increases the Medicaid offer rate to , compared to a probability of 0.7 in the benchmark, that is, the new Medicaid program covers all the low income but not just eligible low-income parents and children as required in the current system. While in experiment B-2, the government keeps the categorical requirement of Medicaid unchanged and increases the maximum income requirement to 200% of the poverty line.

Table 2. Public health insurance expansion: via labor tax.

	Bench.	B-1	B-2
Insured nonelderly (in %)	82.9	85.0	93.4
Medicare tax (in %)	2.2	5.1	5.7
Ave. income tax (in %)	20.4	20.3	20.3
Ave. Working hours	32.4	31.4	31.1
Health exp. (in % of GDP)	16.1	16.6	16.6
(in % of per capita GDP)	8.7	8.5	8.5
Output	100.0	99.5	99.0
Aggregate saving rate (in %)	26.9	27.1	27.2
Average consumption	100.0	99.1	98.6
Mortality rate (age 25–44)	0.0322	0.0321	0.0321
Mortality rate (age 45–64)	0.1343	0.1335	0.1328
Lifetime CEV after transition
All (in %)	–	0.2	−1.1
Income (in %)	–	−1.1	−0.6
Income (in %)	–	0.8	−1.3
% w/CEV	–	7.5	4.3

• Note: B-1, Public health insurance expansion 1. B-2, Public health insurance expansion 2.

The spending in Medicaid as a ratio of GDP increases from 1.2% to 2.5% when the government extends Medicaid to include more low-income agents. These newly insured consume more medical services because Medicaid provides them with better insurance coverage. Aggregate health expenditure increases by 0.5% and the Medicare tax rate has been more than doubled to match this spending. Average hours worked decreases by 4.0% even though the labor productivity has been improved due to improved health. Medicaid expansion alone cannot achieve “universal insurance coverage” and this reform will still leave 15.0% of the nonelderly without insurance coverage. Those are agents in better health condition who think insurance is not critical important to them.

When the government increases the maximum income requirement in experiment B-2, some previously insured agents will choose to apply for Medicaid because Medicaid is the best insurance money can buy, even though they will face the risk of being uninsured because of categorical requirements of Medicaid. Overall, the insured as a fraction of nonelderly increases to 93.4%. Similar to the preceding experiment, the aggregate health expenditure increases. While average health outcome is better than after experiment B-1 is taken place due to the higher insurance coverage. Consequently, the aggregate hours worked decreases by 3.1% as Medicare tax jumps to 5.7%.

Compared to the benchmark, policy B-1 is intended to be beneficial for agents with income below the poverty line. These agents are qualified for Medicaid with a certain probability determined by categorical requirements of this program in the benchmark. Now they benefit from this reform with a guaranteed public insurance coverage and pay a cost in terms of a higher labor tax. Given the small size of the program, the benefit is enough to compensate for the loss due to the tax increment. They experience a welfare gain in the order of 0.8% in terms of consumption in all states. For high-income agents, their health benefits are intact after the reform since they are not qualify for Medicaid, but they subject to a higher income tax to support the expanded Medicaid program. Their welfare loss is equivalent to 1.1% in terms of consumption in all states.

To increase the maximum income requirement makes more agents worse off. Agents whose income is below the existing maximum income requirement have the same public insurance coverage as in the benchmark. However, they are required to pay for a higher tax rate to fund the expanded Medicaid. Therefore, they experience a welfare loss in the order of 1.3% in consumption equivalence. High-income agents benefit from the reform with a chance of being covered by Medicaid depending on their income level. While the cost of higher income tax cannot be offset by this benefit. Consequently, they experience a welfare loss of the order of 0.6% in terms of consumption, which is in a smaller magnitude compared with low-income agents who do not benefit from this reform.

4.2.3 Policy experiment C: Individual mandate

In this experiment, those agents who are uninsured in the benchmark are required to purchase private insurance. Their entry into the insurance market makes the risk pool more inclusive and the price of the group insurance falls to $3340 from the benchmark price of $3418. The aggregate health expenditure as a ratio of GDP rises to 16.7% as the insurance coverage increases, see column C of Table 3. The aggregate health status has been improved and the average hours worked decrease by 2.2% as the reform requires a higher Medicare tax since the tax deductibility has been extended to the previously uninsured. In terms of welfare, an individual mandate makes everybody worse off. Such a reform imposes a higher tax rate since more individuals will deduct premiums from income taxes. This welfare loss cannot be compensated by the cheaper insurance resulting from a more inclusive risk pool. On average, agents experience welfare loss in the order of 0.6% of consumption in all states. Among low-income agents, only a small fraction holds private insurance since most of them are covered by Medicaid. Consequently, they benefit less from the cheaper insurance and they experience a welfare loss at the magnitude of 3.8% in consumption equivalence, compared with a loss in the order of 1.1% for high-income agents.

Table 3. Reforms on private insurance: labor tax.

	Bench.	C	D
Insured nonelderly (in %)	82.9	100	79.2
Medicare tax (in %)	2.2	4.8	1.8
Ave. income tax (in %)	20.4	20.2	20.5
Ave. Working hours	32.4	31.7	32.5
Health exp. (in % of GDP)	16.1	16.8	15.9
(in % of per capita GDP)	8.7	8.3	9.0
Output	100.0	99.3	100.1
Aggregate saving rate (in %)	26.9	27.0	26.8
Average consumption	100.0	98.2	100.5
Mortality rate (age 25–44)	0.0322	0.0321	0.0322
Mortality rate (age 45–64)	0.1343	0.1317	0.1349
Lifetime CEV after transition
All (in %)	–	−1.7	−2.1
Income (in %)	–	−1.1	−2.8
Income (in %)	–	−3.8	−0.1
% w/CEV	–	0.0	16.4

• Note: C, Individual mandate on private insurance purchase. D, Abolish private insurance deductibility from income tax base.

4.2.4 Policy experiment D: Abolishing tax-deductibility of EHI premiums

To understand the economic effects of endogenizing medical spending and labor-leisure choice, I conduct policy experiment A considered by Jeske and Kitao (2009). Under this experiment, the deductibility of the insurance premium for income tax is removed. The taxable income does not depend on the insurance status and it is given as follows:

()

Experiment results are summarized in column D of Table 3. Removing the subsidy in D leads to a drop in insurance take-up as found by Jeske and Kitao (2009). Since I don't differentiate between group insurance and insurance purchased in the private market, the magnitude of drop is much smaller. The fraction of nonelderly who purchase private insurance falls from 72.6% to 68.9%. There are only about 4% of the nonelderly opt out of the private insurance market and choose to be self-insured. Those are healthy agents who face a lower probability of suffering a bad health shock. The exit of these agents out of the insurance market deteriorates the risk pool and the price of the private insurance jumps by 3.5% to $3536. The aggregate health expenditure as a ratio of GDP falls by 1.2% because taking away the tax deductibility discourages investment in health.

The Medicare tax on labor income that balances the government budget falls from 2.2% to 1.8%, since the income tax base is expanded by eliminating the deductibility of the EHI premium. Consequently, the average hours worked increase by 0.5%. Although the tax rate is lower than in the benchmark, it is not enough to compensate for the welfare loss due to the lower insurance coverage, increased exposure to health shocks, and deteriorated health. Most agents will face a welfare loss except those low-income individuals who relies on Medicaid will benefit from the policy with their insurance coverage intact.

Compared with the findings in Jeske and Kitao (2009), the welfare implications are qualitatively identical. While my numerical simulations complement theirs by suggesting that output will expand as labor supply increases and medical spending drops as agents are more aware of the cost of insurance. Furthermore, the agents will spend more on consumption goods instead of less as found in their paper.

4.3 To fund reforms by a lump-sum transfer

The analysis so far indicates that the change in taxes may play a dominant role in how health care reforms affect the welfare. To isolate the effect of tax distortion, I also conducted companion exercises in which the government funds the reform through a lump sum transfer. In the companion experiments, the tax rates are kept intact as in the benchmark. The government returns a lump sum transfer to each individual. The transfer is determined so that the government's budget is balanced.

Numerical results in Table 4 indicate that the labor supply effect of health care reforms is rather small. The greatest change in hours worked is observed in experiment A-1 in which the hours worked decreases by 2.2%, compared to an average 5.3% change when the reforms are funded through the Medicare tax. Nevertheless, reforms to the health insurance system have quite sizable effects on the welfare. Medicare expansion increases welfare by improving health status and reducing adverse selection in the health insurance market. While expansion of Medicaid and individual mandate decreases welfare by distorting health insurance purchase and health expenditure decision, even thought average health status has been improved after reforms are carried out.

Table 4. Fund the reforms by lump-sum transfer.

	Bench.	A-1	A-2	B-1	B-2	C	D
Insured nonelderly (in %)	82.9	100.0	100.0	87.3	93.6	100	80.5
Medicare tax (in %)	2.2	2.2	2.2	2.2	2.2	2.2	2.2
Ave. income tax (in %)	20.4	20.8	20.9	20.4	20.5	20.3	20.4
Ave. Working hours	32.4	31.7	32.6	32.5	32.4	32.7	32.3
Health exp. (in % of GDP)	16.1	14.7	16.1	16.5	16.7	16.7	16.0
(in % of per capita GDP)	8.7	2.1	2.1	8.7	8.5	8.3	9.0
Output	100.0	99.5	100.7	100.3	100.4	100.4	99.9
Aggregate saving rate (in %)	26.9	27.4	27.6	26.9	27.1	26.9	26.8
Average consumption	100.0	100.9	99.3	99.8	100.6	99.2	100.3
Mortality rate (age 25–44)	0.0322	0.0324	0.0322	0.0320	0.0320	0.0321	0.0322
Mortality rate (age 45–64)	0.1343	0.1341	0.1318	0.1337	0.1328	0.1316	0.1347
Lifetime CEV after transition
All (in %)	–	0.9	−1.1	0.9	0.5	−1.7	−2.2
Income (in %)	–	2.5	0.6	0.2	0.6	−1.2	−2.8
Income (in %)	–	−3.9	−6.7	1.8	0.4	−3.3	−0.3
% w/CEV	–	80.6	71.6	19.4	10.3	0.0	16.4

• Note: A-1, Medicare expansion to the entire population. A-2, EHI expansion to all working age population. B-1, Public health insurance expansion 1. B-2, Public health insurance expansion 2. C, Individual mandate. on private insurance purchase. D, Abolish private insurance deductibility from income tax base.

Overall, reforms that can decrease the number of uninsured (as in A-2, B-1, B-2, and C) while do not alter agents incentives in medical spending will improve the aggregate health status. As the newly insured can invest more in health, the aggregate health spending rises as well. Improved health encourages labor supply as labor productivity is positively correlated with health. As shown in experiment C, average hours worked increases by 0.9%. Among the reforms considered, only experiment D fails to decrease the number of the uninsured. Aggregate health expenditure decreases as fewer people have insurance coverage in experiment D. The average health stock falls as well.

The comparison between policy A-1 and A-2 highlights the importance of cost-sharing in containing the health care growth. Both policies expand the insurance coverage to the entire population. While policy A-1 can actually save more than $150 billion per year if we assume that the delivery of health care maintains at the current state. This cost-saving mainly comes from providing incentive for consumers so that they are more aware of their spending.