Workers on the Margin: Who Drops Health Coverage when Prices Rise?

Edward N. Okeke Richard A. Hirth Kyle Grazier Workers on the Margin: Who Drops Health Coverage when Prices Rise? We revisit the question of price elasticity of employer-sponsored insurance (ESI) takeup by directly examining changes in the take-up of ESI at a large firm in response to exogenous changes in employee premium contributions. We find that, on average, a 10% increase in the employee s out-of-pocket premium increases the probability of dropping coverage by approximately 1%. More importantly, we find heterogeneous impacts: married workers are much more price-sensitive than single employees, and lower-paid workers are disproportionately more likely to drop coverage than higherpaid workers. Elasticity estimates for employees below the 25 th percentile of salary distribution in our sample are nearly twice the average. The vast majority of nonelderly Americans who have private health insurance get it through an employer. In 2005, this number amounted to 150 million people (DiJulio and Jacobs 2007). However, nearly 20% of those offered employer-sponsored insurance (ESI) do not accept it (Cooper and Schone 1997; Cunningham, Artiga, and Schwartz 2008) and this number has been growing (Farber and Levy 2000). Several studies have attributed this decline in take-up to expansions in Medicaid eligibility, slow growth in real incomes, and increases in health insurance costs (Kronick and Gilmer 1999; Chernew, Cutler, and Keenan 2005). Cutler (2003), for example, finds a strong negative correlation between employee out-of-pocket premiums and declining take-up. In this paper, we examine the effect of changes in employee out-of-pocket premium payments on the take-up of ESI. There is evidence that the amount of total premiums borne by employees has been rising. For workers electing single coverage, their share of premiums increased from about 11% in 1988 to 17% in 2009 (Gabel et al. 2002; Kaiser 2009); however, these numbers conceal the fact that percentage shares nearly doubled for workers electing single coverage between 1988 and 1996 (rising from 11% to 21%) before falling slightly and then stabilizing. More recently, the fraction of total premiums paid by employees has stayed relatively steady, but the cost of insurance in absolute terms has increased dramatically: the average dollar contribution for single coverage, for example, rose 145% between 1999 and 2009, while contributions for family coverage increased 128% over the same period (Kaiser 2009). Previous work has shown a correlation between rising health insurance costs and Edward N. Okeke, M.D., Ph.D., is a lecturer in health economics and policy in the Department of Public Health and Policy, London School of Hygiene and Tropical Medicine. Richard A. Hirth, Ph.D., and Kyle Grazier, Ph.D., are both professors in the Department of Health Management and Policy, University of Michigan School of Public Health. Address correspondence to Dr. Okeke at Department of Public Health and Policy, London School of Hygiene and Tropical Medicine, Keppel Street, London, U.K. WC1E 7HT. Email: edward.okeke@lshtm.ac.uk Inquiry 47: 33 47 (Spring 2010). 2010 Excellus Health Plan, Inc. ISSN 0046-9580 10.5034/inquiryjrnl_47.01.33 www.inquiryjournal.org 33

Inquiry/Volume 47, Spring 2010 increases in employee out-of-pocket contributions (Gruber and McKnight 2003). Dranove, Spier, and Baker (2000) proposed a model to explain this observed correlation. They argued that employers have an incentive to raise employee contribution levels to encourage employees with working spouses to take up insurance through their spouse s employer, and they went on to argue that this incentive is stronger as the cost of providing insurance goes up. Even though their model assumed only one coverage level family coverage the insights apply more broadly. For example, employers might raise the level of out-ofpocket contributions for single-party coverage not only because some married employees choose single coverage, 1 but also because there might be single employees who would be eligible for coverage under a public program like Medicaid. 2 Even though exposing employees to more of the true costs of health insurance might improve efficiency (especially for firms offering multiple plans), on the margin it may give employees an incentive to drop coverage. This has potential implications, depending on the type of person dropping coverage. It could undermine risk-pooling arrangements if younger, healthier people dropped out, or it might raise distributional and equity concerns if the burden of price increases fell disproportionately on low-income workers. In this paper, we revisit the question of price elasticity of ESI take-up by directly examining changes in the take-up of employeroffered insurance at a large employer the University of Michigan in response to exogenous changes in premium contributions. We show that when faced by out-of-pocket premium increases, some employees do indeed choose to drop coverage. We find that on average, a 10% increase in out-of-pocket premium costs increases the probability of dropping coverage by approximately 1%, but more importantly, we find that there are heterogeneous impacts. Married workers are much more price-sensitive than single employees; in fact, we find no statistically significant effect of price for unmarried employees. We also provide evidence that lower-paid workers are disproportionately more likely to drop coverage relative to higher-paid workers. Elasticity estimates for employees in our sample below the 25 th percentile of salary distribution are nearly twice the average. The remainder of this paper is organized as follows. In the next section, we develop a conceptual framework and review previous work in this area; in the third section, we describe our natural experiment. The fourth section presents the data and the fifth section describes our econometric model. We then discuss our results and in the last section offer conclusions. Conceptual Framework and Previous Literature Given the value that is generally placed on health insurance coverage, one might wonder why a rational employee would choose to waive coverage. When coverage is waived, the employee either has decided to take up insurance elsewhere (e.g., through a spouse or a public program), or has decided to remain uninsured. Consider an employee who is offered insurance costing P. An employee with income Y and without an alternative source of coverage will accept the offer if U(Uninsured,Y)ƒU(Insured,Y{P). U(Insured, Y{P) refers to the utility derived from accepting the health insurance offer and having $(Y{P) remaining for non-health insurance consumption; P represents the employee s out-of-pocket health insurance premium, and U(Uninsured,Y) refers to the utility derived from having no insurance, but $Y for all other consumption. We assume for simplicity that income when accepting vs. declining the health insurance offer differs by only the out-of-pocket contribution. This implies that additional compensating wage differentials are not applied on a personspecific basis as a function of the take-up decision. We also ignore the heterogeneity introduced by different marginal tax rates. If the employer raises employee contributions from P to Pze, then the employee who previously accepted coverage will continue to accept the insurance only if eƒ(1=l)v, where V~U(Insured, Y { P) { U (Uninsured, Y). That is, the employee will continue to accept 34

Workers on the Margin coverage only if the increase in out-of-pocket contributions is no more than the monetary value attached to the net value of insurance, V (l is a parameter denoting the monetary value of utility). This suggests that an employee facing an increase of e in out-ofpocket premiums will choose to waive coverage if ew1=l(v) even in the absence of alternative coverage. If the employee had access to an outside option for obtaining coverage but chose to take up coverage through his/her employer, then it must be that U(I A ) U(I B ) where U(I A ) is the utility attached to insurance from the own-employer net of out-of-pocket premiums and U(I B ) is the utility attached to the outside option net of out-of-pocket premiums for that option. If the price of ownemployer insurance, I A, increased from P to Pze, then the employee would choose to switch coverage from his/her own employer to the alternative source (i.e., waive own-employer coverage) if the price increase, e, exceeded the monetary value of the difference in utility between the two options. In other words, the money saved by switching to the previously less preferred outside option would have to exceed the utility losses incurred by switching. Clearly, one would expect that, on average, the threshold for waiving coverage would be lower for employees with an outside option relative to employees without access to an alternative. Several papers have investigated the effects of plan premiums on the take-up of ESI. Chernew, Frick, and McLaughlin (1997), in one of the earlier papers, used data from a sample of small businesses in seven metropolitan areas (single, low-income workers only). They found a modest negative effect of outof-pocket premiums on the probability of take-up and estimated elasticities of between 2.03 and 2.1. Blumberg, Nichols, and Banthin (2001) followed a similar approach using a more nationally representative sample and calculated elasticities of around 2.04 for married employees. As both studies acknowledge, there is a significant problem with exploiting cross-sectional differences between firms: workers are likely to sort themselves into firms based on unobserved tastes for insurance. Workers who place a higher value on insurance coverage may opt into firms with lower employee premium shares inducing a correlation between demand for insurance and out-of-pocket costs and biasing upward estimates of the absolute value of the elasticity of take-up. 3 On the other hand, as Gruber and Washington (2005) have argued, it is possible that elasticity estimates may be biased downward if firms cover a larger share of insurance premiums when employees have low valuation for health insurance (perhaps to meet insurer requirements on take-up). Cutler (2003) avoided the endogeneity problem by instrumenting for the employee share of premiums using state tax rates. His independent variables (IV) estimates, about 2.12, were at the upper end of previous estimates. The validity of his instrument rested on the assumption that state tax rates affect take-up of ESI only through employee premiums (he showed that states with higher tax rates have smaller premiums). But this assumption fails in practice because state tax rates are correlated with a firm s decision to offer any health insurance (Gruber and Lettau 2004). 4 Gruber and Washington (2005) took an approach very similar to ours, in that they exploited a natural experiment. They derived an exogenous measure of price by exploiting a change in how insurance premiums were deducted for federal government workers. Premium payments by federal postal workers were made post-tax prior to 1994, but pre-tax thereafter. They estimated elasticities of takeup for family coverage of 2.022, which is smaller than previous estimates, and (wrongsigned) elasticities of.028 for singles. While their paper avoided some of the problems of previous work, there was still the question of whether workers were fully aware of the impact of the tax change on their out-ofpocket premiums. A lack of knowledge could explain the very small price effect they found. As Royalty and Hagens (2005) point out, other ways of changing price subsidies may be more transparent than the move from posttax to pre-tax deductions and could have a larger effect than was observed in the study by Gruber and Washington. Royalty and Hagens (2005) took a completely different approach from the rest of the literature by carrying out a field experiment. They constructed an artificial menu of plan 35

Inquiry/Volume 47, Spring 2010 choices and offered it to employees of one firm. The advantage of their approach is that they were able to manipulate the prices that employees faced while keeping the plan quality constant. The disadvantage is that the choices were hypothetical. They did not observe actual employee behavior and therefore had no way of knowing whether the choices made under these artificial conditions reflect the choices that would have been made if the plans (and prices) were real. In addition, the sample they studied consisted of fewer than 500 workers, raising the question of its representativeness and generalizability. Overall, they found relatively small elasticities of around 2.01. Our study builds on earlier work in several significant ways. We provide direct evidence that workers drop coverage in response to out-of-pocket premium increases. Because we were able to follow the same set of workers over time and see how they responded to an exogenous price shock, this allowed us to avoid problems of correlation of price with time-invariant and unobserved components of workers demand for health insurance. In addition, the choice set of plans offered by the employer was common to all employees, and plan offerings and quality remained constant over the time period so that our measure of price was not correlated with plan quality. We extend Royalty and Hagens (2005) by studying actual choices of employees in response to exogenous increases in employee cost of insurance and are able to provide estimates of price responsiveness for different groups of workers: married vs. single and low income vs. high income. The Policy Change The University of Michigan (UM) is a large employer in southeast Michigan that provides health insurance to more than 30,000 employees as part of its benefit package. Every year during open enrollment, employees select from a menu of six options: two traditional fee-for-service (FFS) plans with different generosity of coverage, 5 three health maintenance organizations (HMOs) with different provider networks, and one point-of-service (POS) plan. Regular faculty or staff members with a half-time or greater appointment expected to last four continuous months or longer are eligible for health insurance. Dependent spouses or same sex domestic partners, and unmarried dependent children under age 25 are also eligible. 6 The university offers identical coverage on all three of its campuses, Ann Arbor, Dearborn, and Flint with Ann Arbor being the largest. In response to concerns about escalating costs and the potential impact of employee plan choice incentives on cost growth, the University of Michigan decided to change how health plans were priced to employees. Prior to 2004, the pricing formula imposed no cost to the active employees for single coverage under any health benefit plan: the university paid 100% of the premium. For two-person and three-or-more-person contracts, the university paid 85% of the threeor-more rate weighted by enrollment in the plans, with the balance of the premium charged to the employee. For enrollment year 2004, the contribution formula was changed so that active employees now paid a copremium corresponding to 5% of the total premium for the plan/tier combination or the amount determined using the formula applied to 2004, whichever was greater. For nearly two-thirds of the employees (all of those choosing single coverage and more than 83% of those covering a spouse or domestic partner), all of the price change was directly attributable to the new formula. For the remaining third, the price change induced by the current formula was almost arbitrary up in some cases and down in others. Magnitude of the 2004 Out-of-Pocket Premium Increases The price changes between 2003 and 2004 are shown in Table 1. Each value represents the change in employee share of premiums between 2003 and 2004 (in dollars). On average, out-of-pocket premiums rose more than 50% between 2003 and 2004. This conceals a great deal of variation because percentage changes ranged from a low of 228% for employees selecting family coverage in Plan 2, to a high of +195% for employees selecting two-party coverage in Plan 3. Employees selecting single coverage in any of the plans had no out-of-pocket premiums 36

Workers on the Margin Table 1. Price changes in employee s share of premiums for each plan/tier combination between 2003 and 2004 Price changes between 2003 and 2004 ($) Plan 1 Plan 2 Plan 3 Plan 4 Plan 5 Mean Tier 1 25.24 16.10 16.42 16.02 17.86 17.70 Tier 2 24.84 21.19 16.43 30.62.41 21.36 Tier 3 44.00 235.12 21.15 24.90 15.51 16.31 Note: All prices are in U.S. dollars. in 2003 so one cannot calculate percentage changes between 2003 and 2004. However, for employees who decided to waive coverage, the university offered a cash-back option amounting to approximately $67 per month. Assuming that employees who took up coverage realized they were forgoing the opt-out payment, the real out-of-pocket expenditure for workers was $67 plus whatever the nominal amount was. We can leverage this assumption and use it to calculate a percentage change for employees choosing single coverage. For this group of employees, the percentage increase ranged from 24% to 38% ($16/$67 and $25/$67). The price changes were sufficiently large that if the decision to waive coverage was fairly responsive to price, then we should expect to detect an effect. Data Data for this study were obtained from the University of Michigan Benefits and Human Resources information system. Complete data on health plan choices, premiums, and employee characteristics including age, sex, annual salary, job type, and zip code of residence are available for all benefits-eligible employees for each enrollment year between 2002 and 2004. Approximately 21,000 workers were continuously eligible for benefits between 2002 and 2004. Table 2 shows summary statistics for these employees. There are two things to note with regards to specific variables. First, the salaries are annualized values. Second, data on marital status were compiled for us by the benefits office from a number of different sources, including health insurance information, data from vision and dental benefits, and data on tax withholdings. We validated the data by comparing them to a sample for which marital status was known and the resulting correlation was about.9. For employees who were continuously eligible between 2002 and 2004, the respective percentages of those waiving coverage were 9.5%, 9.4%, and 10.5%. In comparison, ESI turndown rates at other large firms were slightly higher at around 15% over the same period (Kaiser 2006). Figure 1 shows the fraction of benefits-eligible employees who waived coverage in each year (left vertical axis), plotted along with the average out-ofpocket premium for the cheapest plan in each year (right vertical axis). Notice the sharp increase in out-of-pocket costs between 2003 and 2004. Notice also the increase in the fraction of employees who chose to waive coverage in 2004 relative to earlier years. Econometric Model The econometric problem is to identify the effect of the 2004 price shocks on the propensity to waive coverage. We do that in two stages. First, we estimate a panel probit model to ascertain whether there was an increased propensity to waive coverage in 2004 relative to previous years, after controlling for employee characteristics. The rationale for this specification is that estimating a panel probit including time dummies allows us to compare the coefficient on the 2004 dummy to coefficients from previous years. If our hypothesis is correct, then the coefficient on the 2004 dummy will be positive and significant. The model we estimate is of the following form: WAIVE it ~b 0 zb 1 X it z X t ðt~1, 2, 3Þ b t YEAR t ze it 37

Inquiry/Volume 47, Spring 2010 Table 2. Summary statistics for employees eligible for coverage in 2003 and 2004 Variable N Mean Standard deviation Age 21,347 44.1 9.97 Sex (15male) 21,347.37.48 Length of service (years) 21,345 11.9 8.7 Annual salary/1,000s ($) 21,336 60.0 48.4 Marital status (15single) 21,347.3.46 Out-of-pocket premium in 2003 19,302 38.8 60.3 N Percent Cumulative Coverage Single 6,585 34.1 34.1 Two-party 5,903 30.6 64.7 Three or more people 6,814 35.3 100.0 Plan choice in 2003 Plan 1 978 4.6 4.6 Plan 2 2,491 11.7 16.3 Plan 3 670 3.1 19.4 Plan 4 10,941 51.3 70.6 Plan 5 4,222 19.8 90.4 Waives coverage 2,045 9.6 100.0 Job category Academic 3,489 16.3 16.3 Non-academic 12,806 60.0 76.3 Other 5,052 23.7 100.0 Work location Ann Arbor campus 12,955 60.7 60.7 Dearborn campus 539 2.5 63.2 Flint campus 361 1.7 64.9 UM Health System 7,491 35.1 100.0 Location of residence Ann Arbor 8,733 40.9 41.0 Washtenaw 4,917 23.0 63.9 Other Michigan 7,542 35.3 99.3 Out of state a 145.7 100.0 a Majority of those classified as out of state live in Toledo, Ohio, which is about an hour away from Ann Arbor. where WAIVE it is employee i s probability of waiving coverage in year t and X is a vector of controls including marital status, annual salary and the number of years the employee has been with the university, age, sex, zip code of residence, and location of the employee s work site. YEAR t represents the year dummies for 2003 and 2004, each relative to 2002, and we are interested primarily in the coefficient of the 2004 dummy. Results are in Table 3. We also present results for an alternative specification a linear probability model (LPM) with individual fixed effects. This latter specification gives us robust estimates of the year effects while controlling for time-invariant unobserved employee characteristics. 7 Even though the previous model allows us to say something about the propensity to waive coverage in 2004 relative to other years, it is important to realize that it says nothing about why the increased propensity occurred. Any effect we find may be due to: a) the increase in out-of-pocket costs, or b) some other shock that coincided in timing with the premium increases. We tackle the second possibility by constructing a measure of the price shocks to see whether it significantly predicts coverage-waiving behavior in 2004. To do this, we restrict our attention to employees who chose a plan in 2003 (i.e., did not waive coverage) and we estimate the following probit model: 38

Workers on the Margin Figure 1. Percentage of employees waiving coverage, 2002 2004 PrðWAIVE~1jX i, Z i Þ~c 0 zc 1 X i zc 2 Z i zn i The dependent variable is an indicator variable equal to 1 if an employee who chose a plan in 2003 waived coverage in 2004 8,Zis a price variable defined as the change in outof-pocket contributions for each employee within each plan/tier cell between 2003 and 2004 (see Table 1), and X is the same vector of control variables. Results are reported in Table 5. Results In all models, we restrict our attention to continuously eligible employees to mitigate the concern that our results might be driven by changes in the composition of employees over that time period. 9 The results from the year dummy models are in Table 3. Reported coefficients for the panel probit model are marginal effects. 10 Standard errors are clustered to account for within-person correlation. There are two results worth highlighting here. First, the coefficient on the 2004 time dummy is positive and significant relative to the reference year (2002), and also relative to 2003. The point estimate implies an increase in the probability of waiving coverage in 2004 of approximately one percentage point. This is a substantive increase given that the baseline probability of waiving coverage in 2003 in our sample was about 10%. Secondly, the results are robust to inclusion of control variables and are also robust to specification. We obtain nearly identical coefficients with the LPM as with the panel probit specification. Note that Table 3. Estimates of the decision to waive coverage: results from year dummy models (1) (2) (3) (4) Panel probit Panel probit LPM LPM 2003 dummy.00042 (.0010) 2.0017 (.0015).00042 (.00099) 2.00034 (.0012) 2004 dummy.011*** (.0015).0078*** (.0020).011*** (.0014).0063*** (.0016) Includes controls No Yes No Yes N 64,041 64,032 64,041 64,032 Notes: Reported coefficients are marginal effects. Standard errors are in parentheses. Omitted year is 2002. * p,.10; ** p,.05; *** p,.01. 39

Inquiry/Volume 47, Spring 2010 Table 4. Estimates of the decision to waive coverage: probit model Waive coverage estimates (1) (2) (3) (4) Price.00039*** (.000095).00030*** (.000084).00030*** (.00010) Deltagap.00033*** (.00012) Age 2.00024* (.00012) 2.00029** (.00012) 2.00030** (.00012) Sex (male51) 2.0073** (.0034) 2.0096* (.0051) 2.0091* (.0048) Two-party 2.021*** (.0055) 2.013*** (.0060) coverage a Family 2.040*** (.0036) 2.036*** (.0035) coverage a Years of tenure 2.00081*** (.00017) 2.00078*** (.00016) 2.00078*** (.00016) Dearborn 2.012 (.0097) 2.020 (.014) 2.019 (.013) campus b Flint campus.016 (.017).023 (.024).020 (.023) Health System 2.013*** (.0028) 2.018*** (.0044) 2.017*** (.0042) Annual salary/ 2.00025*** (.000057) 2.00022*** (.000058) 2.00023*** (.000058) 1,000s ($) Non-academic 2.0037 (.0060) 2.0063 (.0088) 2.0049 (.0084) job c Other job 2.014** (.0055) 2.021** (.0083) 2.019** (.0079) Marital status 2.020*** (.0023) 2.042*** (.0032) 2.040*** (.0030) (15single) Includes No Yes Yes Yes controls Includes tier No No Yes Yes controls N 19,302 19,290 19,290 19,290 Pseudo R 2.005.050.064.064 Notes: Price is the change in out-of-pocket price for each employee within each plan/tier cell between 2003 and 2004. Deltagap is the change in relative pricing between the plan chosen in 2003, and an average of all the cheaper plans available (holding coverage level constant). Reported coefficients are marginal effects. Standard errors are in parentheses. a Comparison group is single coverage. b Comparison group is Ann Arbor campus. c Comparison group is the academic job category. * p,.10; ** p,.05; *** p,.01. since both coefficients are marginal effects, they can be compared directly. For the coefficients on the control variables (not shown), the signs were consistent with our priors. Overall, we find a significant increase in the propensity to waive coverage in 2004 relative to earlier years. This result is robust to the inclusion of a rich set of control variables. While the increased waiver of coverage suggests a response to the pricing changes of 2004, this is not conclusive evidence of causality. We therefore directly examine the effect of the price shocks in Table 4. Note that our analysis attempts to estimate the marginal propensity to waive coverage. That is, we focus on those who previously chose a plan, but decided to waive coverage after the price changes in other words, new waivers. Table 4 again reports marginal effects. In column 1, we regress WAIVE on the price variable alone and show that the price change is strongly correlated with the propensity to waive coverage in 2004. In column 2, we include a rich set of employee characteristics and show that the price effect declines only slightly. Based on the estimate in column 2, an increase of $10 in the out-ofpocket price increases the probability of waiving coverage by.3 percentage points. There are several concerns one might raise with this approach. First of all, the relevant price is specified as the increase in out-ofpocket premiums for the plan/coverage level chosen in 2003. But clearly, waiving coverage is not the only possible response to an increase in 40

Workers on the Margin premiums. The employee could choose to switch to a cheaper plan (and maintain the same level of coverage), or could choose to stay in the same plan but change coverage level for example, move from two-party to single coverage. We address each of these in turn. Changing Coverage Level To address the issue of changing coverage level, in column 3 of Table 4, we include dummies for the type of contract chosen in 2003. The rationale for this is simple: we expect that all else equal, employees choosing two-party or family coverage will be less likely to waive coverage than employees with single coverage. One reason is that unlike employees choosing single coverage, employees with twoparty or family coverage have the option of changing coverage level which acts as a substitute for dropping coverage entirely. Extending this logic, employees selecting family coverage should be more likely to switch contracts (and therefore less likely to waive coverage) than employees with twoperson contracts because the expected returns of switching down to a different contract type are greater than for employees with two-party coverage. As can be seen from Table 8, on average, the potential savings are greater when going from family coverage to two-party coverage (or single coverage) than going from a two-party to a single contract. As can be seen from Table 4, column 3, employees selecting family coverage are about half as likely to waive coverage as employees with a two-person contract. This finding is consistent with our previous explanation. Notice that including dummies for contract type, as a proxy to account for the possibility of switching coverage levels, does not affect the magnitude of the price coefficient. This is reassuring. Plan Switching To understand the rationale for the approach we take, we propose the following thought experiment. Imagine an employer offering only two health plans, A and B, where A costs $50 more than B in out-of-pocket premiums. If an employee chooses A over B, it means that the employee values the additional benefits offered by Plan A at more than $50. Let us assume that Plan A has two enrollees, one who values the additional benefits at $60 and the other who values them at $80. If in the next period, the employer increases out-of-pocket premiums for both plans such that A now costs $75 more than B (holding plan benefits constant), then clearly one would expect the first enrollee to switch from Plan A to B. In other words, plan switching is going to be affected by changes in relative pricing. Building on this intuition, we therefore construct a new price variable, DELTAGAP, defined as the change in relative pricing between the plan chosen in 2003 and an average of all the cheaper plans available (holding coverage level constant). Note that this price variable explicitly accounts for the possibility of plan switching as a substitute for waiving coverage, especially if the employer offers more than a single plan (as is the case here). Results are in Table 4, column 4. Probability of Waiving Coverage Overall, we see that our conclusions are robust to how we define the relevant price change. Based on the estimate in column 4, which is our preferred specification, a $10 increase in out-of-pocket premiums increases the probability of waiving coverage by.33 percentage points. The signs on the other coefficients are broadly consistent with our expectations. Higher-paid employees are less likely to waive coverage, as are employees who have been with the university longer. The point estimate for income implies that a $10,000 increase in salary, which is less than one standard deviation in our data, decreases the probability of waiving coverage by.23 percentage points. Unlike Royalty and Hagens (2005), we find that older workers are significantly less likely to waive coverage, which seems intuitively plausible given that older workers are more likely to use medical services. A slightly surprising finding is that workers employed in the health system are significantly less likely to waive coverage, even after controlling for income and other characteristics. We can think of at least two explanations for this finding. First, individuals who 41

Inquiry/Volume 47, Spring 2010 choose a health-related occupation place greater value on health insurance, and secondly, working in the health system may cause people to develop a greater appreciation of the importance of having insurance. Alternative Models Next, we address two more issues. First, it would seem that given the nature of this policy experiment, a more obvious specification would have been a difference-in-differences specification, where the relevant coefficient of interest would be the interaction between the price variable and a dummy for 2004. Secondly, it is not at all obvious that the price change we have chosen to use is necessarily the best price measure. Other alternatives could be the change in price of the cheapest plan (conditional on tier) or the change in the average price of all the plans. 11 We address these concerns jointly. We estimate a different model where we specify price as the increase in the cost of the cheapest plan (conditional on coverage level). This price specification obviates the need to control for plan switching, but still does not address the issue of switching the level of coverage. To address this, the price variable we use is the change in relative price between the cost of the cheapest plan and the cost of choosing a lower coverage level (specified as the price of single coverage for employees choosing two-person contracts, and as the average of the price of single and two-person contracts for employees choosing family coverage). The basic point is that what factors into the employee s decision is not the change in the price of the cheapest plan alone, but the change in the price of the cheapest plan relative to the alternative of switching to a less expensive coverage level. We estimate a linear probability model with individual fixed effects, using three years of data on employee plan choices (2002 2004). Unfortunately, there is not enough price variation to separately identify a mean 2004 effect from a price effect (results not shown). Nearly all of the price variation in the data occurs between 2003 and 2004; between 2002 and 2003, the average change in price is only $2. In Table 7, we report results from a LPM model without year dummies as a robustness check and as a comparison with the results from our previous model in which we focus on years 2003 and 2004. We find that the results are quantitatively and qualitatively similar. The coefficients in Table 7, column 2, imply that a $10 increase in price raises the probability of waiving coverage by approximately.2 percentage points. A strength of our study is that we observe both marital status and the type of contract chosen. This distinction is important because even though marital status is correlated with coverage level, the two are not perfectly correlated. In our data, 14% of married workers elected single coverage and 28% of workers in the single tier actually were married. Similarly, some single employees covered dependents. We find that married employees were much more likely than single ones to waive coverage. The point estimate implies a difference of about two percentage points. As we have argued earlier, this is intuitively plausible given that single employees have fewer alternatives for coverage than workers with spouses. Heterogeneous Effects Even though, on average, the estimated price elasticity is small, it may vary across groups. We are particularly interested in whether the effects of the price shocks differ by income and by marital status. Income We hypothesize that the responsiveness to price will be larger for lower-paid employees. To investigate this, we estimate the same regression as in Table 4 (columns 3 and 4), but do it separately for three groups of workers: workers earning a salary below the 25 th percentile of salary distribution in our data (approximately $34,000), workers earning between the 25 th and 75 th percentile, and workers earning at or above the 75 th percentile (approximately $68,000). Results are in Table 5 for each price measure. Overall, we find evidence that price responsiveness differs by income. The coefficient for workers at or below the 25 th percentile of income is more than twice as large as the average for the entire sample. 42

Workers on the Margin Table 5. Estimates of the decision to waive coverage: heterogeneous effects by income Price.00063*** (.00023) Deltagap.00068*** (.00028),25 th percentile 25 th 75 th percentile.75 th percentile (1) (2) (1) (2) (1) (2).00036** (.00016).00034** (.00017).000032 (.00014).000057 (.00017) N 4,713 4,713 9,393 9,393 4,893 4,893 Pseudo R 2.103.103.071.071.068.068 Percent waiving coverage 11.5 10.0 6.9 Notes: Price is the change in out-of-pocket price for each employee within each plan/tier cell between 2003 and 2004. Deltagap is the change in relative pricing between the plan chosen in 2003, and an average of all the cheaper plans available (holding coverage level constant). Standard errors are in parentheses. All models include controls for age, sex, marital status, zip code of residence, job type, annual salary, length of employment at the university, and work location. * p,.10; ** p,.05; *** p,.01. Marital Status Next we model the decision to waive coverage separately for single and married workers. Overall, 12% of married employees waived coverage in 2003 compared with just 4.5% of single employees. In 2004, the percentage of married employees who waived coverage increased by one percentage point to 13%. The first thing we notice from the results in Table 6 is that the coefficient on price for single workers is imprecisely estimated and is statistically indistinguishable from zero. Our results suggest that married workers are much more responsive to price. In addition, we find that married female employees are significantly more likely to waive coverage than married male employees. The coefficient implies a difference of approximately.2 percentage points in the probability of waiving coverage relative to married male workers. This is reasonable if we believe that working women are more likely to have a working spouse than working men. Overall, our results are consistent with the Dranove, Spier, and Baker (2000) model. We find that married workers are significantly more likely to drop their own employer s ESI, and that married female workers in particular are more likely to waive coverage than their male counterparts. These results allow us to draw some inferences about those who waive coverage. As mentioned earlier, an important policy question Table 6. Estimates of the decision to waive coverage: heterogeneous effects by marital status (1) (2) (3) (4) Married Married Single Single Price.00040*** (.00013) Deltagap.00045*** (.00015) 2.000012 (.00016) 2.000043 (.00022) N 13,129 13,129 5,968 5,968 Pseudo R 2.077.077.042.042 Percent waiving coverage 11.8 4.5 Notes: Price is the change in out-of-pocket price for each employee within each plan/tier cell between 2003 and 2004. Deltagap is the change in relative pricing between the plan chosen in 2003, and an average of all the cheaper plans available (holding coverage level constant). Standard errors are in parentheses. All models include controls for age, sex, marital status, zip code of residence, job type, annual salary, length of employment at the university, and work location. * p,.10; ** p,.05; *** p,.01. 43

Inquiry/Volume 47, Spring 2010 Table 7. Estimates of the decision to waive coverage: linear probability model (1) (2) Waives coverage Waives coverage Price.00025*** (.00005).00020*** (.00005) Includes controls No Yes N 57,463 57,457 Notes: Standard errors are in parentheses. Models include controls for age, sex, marital status, zip code of residence, job type, annual salary, length of employment at the university, and work location. * p,.10; ** p,.05; *** p,.01. is whether those who drop coverage become uninsured or whether they substitute with coverage elsewhere. Our results suggest that the marginal waivers are probably taking up coverage elsewhere and not becoming uninsured. If we make the assumption that married workers are much more likely to have other sources of coverage, such as through their spouses, then finding a price response of essentially zero for single employees, with all the price responsiveness coming from married employees, suggests that those dropping coverage are probably substituting one type of coverage for another. Obviously, this is not conclusive evidence, but it is certainly suggestive. Alternative Explanations The Unmeasured Shock Explanation Another objection to our findings could be that something unmeasured, other than the price shocks, happened in 2004, and this could have increased the propensity to waive coverage. It is possible, for example, that a larger than usual number of employees married working partners in 2003 (just prior to the enrollment period for 2004 benefits) and therefore had access to another source of coverage. Or possibly more employee spouses entered the workforce in 2003, again increasing access to other coverage. Even though it is unclear why this would suddenly occur in 2003, either potentially could be an underlying explanation for an increased propensity to waive coverage in 2004. One way to address this would have been to include year dummies to capture mean year trends, but as we discussed in an earlier section, we did not have enough variation in price to separately identify mean year effects as well as price effects. Overall, however, the pattern of results we found makes this an unlikely explanation. Omitted Variables Important variables that affect the demand for ESI may not all have been included as controls. However, we do not believe that omitted variables are likely to account for our findings. Many of these potentially important variables are time-invariant (e.g., race/ethnicity and education), and thus are not a problem for this study because they do not change between 2003 and 2004. But what about variables that do change over time? A key variable we would have liked to include, Table 8. Out-of-pocket premiums in 2003 and 2004 Out-of-pocket premiums ($) Plan 1 Plan 2 Plan 3 Plan 4 Plan 5 2003 Single 0 0 0 0 0 Two-party 313.36 31.95 14.93 0 55.81 Family 455.82 127.28 107.41 63.74 155.11 2004 Single 25.24 16.10 16.42 16.02 17.86 Two-party 338.20 30.76 31.36 30.62 56.22 Family 499.82 92.16 106.26 88.64 170.62 44

Workers on the Margin for example, would have been a health status measure. In a related paper, where we examined the demand for dependent coverage using the same data (Okeke, Hirth, and Grazier 2008), we included a proxy for health risk by including drug cost per capita quartiles; in this case, that approach was impossible because we only had drug cost information for 2004 (i.e., for employees who chose a plan in 2004). As a consequence, we did not have drug cost information for employees who waived coverage in 2004. There is some evidence that people in worse health are less likely to drop coverage all else equal, but this does not hold true across all studies. Monheit and Vistnes (2005), for example, showed mixed results. Assuming we believe that health status is an important determinant of take-up, is health status an important omitted variable in this study? If health status primarily reflects the presence or absence of chronic health conditions an approach often taken in the literature it is reasonable to think of health status as being sticky from year to year, in which case health status in 2003 would be a good predictor for health status in 2004. Since this paper focuses on marginal waivers that is, those who chose a plan in 2003 and then waived coverage in 2004 employees would have to expect suddenly to be in better health in 2004, an expectation that was unique to 2004, for health status to explain our results. Keep in mind that the distribution of expectation also would have to follow the same pattern as our price shocks. Conclusion Overall, we find evidence that the decision to take up ESI is responsive to price. Our point estimates imply elasticities of about 2.12. In other words, a 10% increase in premiums paid by workers would lead to an approximate 1.2% decrease in the take-up of employer-sponsored insurance. To relate our findings to previous work, this estimate is at the upper end of elasticities reported in the literature. At the upper end lie the 2.12 IV estimates of Cutler (2003), while at the lower end there is the 2.013 value obtained by Royalty and Hagens (2005). As in most of the previous literature, we do not observe whether people waiving coverage are taking up insurance elsewhere or not; thus our estimates are probably best thought of as elasticities of ESI take-up and not as elasticities of health insurance demand broadly defined. In that sense, our estimates are probably least comparable to those of Chernew, Frick, and McLaughlin (1997), who restricted their attention to single low-income employees and therefore can speak more definitively about whether the workers have alternative sources of coverage. The elasticity estimates imply that within the range of premiums that we observe, doubling the out-of-pocket premiums will result in about a 12% decline in the take-up of ESI. This is a substantively important effect. We also show that there are heterogeneous effects across groups. Specifically, we find that low-income workers, on average, are more likely to waive coverage in response to price increases, and this effect is statistically significant. We also find that married employees are much more responsive to price than single employees. In addition, we have provided some evidence suggesting that employees dropping coverage are probably taking up coverage elsewhere and not becoming uninsured. Future work might explore what fraction of employees waiving coverage is taking up insurance elsewhere versus choosing to remain uninsured. Each of these results could be useful inputs to policy and managerial simulations of the insurance take-up decision. A potential limitation of our work is the extent to which one can generalize these findings. First of all, we use data from a single employer. However, this study is not unique in that regard since other studies have used single employers (e.g., Buchmueller and Feldstein 1997; Royalty and Solomon 1999; Strombom, Buchmueller, and Feldstein 2002), and Royalty and Hagens (2005) conducted their experiment with a sample of fewer than 500 employees drawn from a single firm. It is important to note that the firm we study is not a small idiosyncratic firm; the University of Michigan is a large public employer providing insurance to more than 30,000 employees and their dependents. Secondly, the parameter we estimate may not 45

Inquiry/Volume 47, Spring 2010 generalize to all employees because we do not include in our analysis people who previously waived coverage (i.e., we select based on prior insurance choice). Another limitation is that we are not able to address the issue of worker sorting. It is unlikely that this constitutes a significant problem. Blumberg, Nichols, and Banthin (2001), for example, found no evidence that worker sorting greatly affects demand elasticities. However, to the extent that workers who place more value on insurance coverage choose to work for a large employer that offers benefits, then our estimates should be interpreted as lower bounds on the true effect. Our study has several policy implications. It provides evidence that at least part of the recent increase in the percentage of workers declining ESI is a result of price increases, thus complementing previous work. It also provides suggestive evidence that the marginal worker one who had coverage and then drops it at least in a large employer like the one we study here, is probably taking it up somewhere else. Finally, we show that lower-paid workers are the most sensitive to increases in out-of-pocket premium contributions suggesting that particular attention be paid to this group of employees when changes in premium contributions are being contemplated. Future research could focus on the likelihood that lower-paid workers within a large, diverse firm are more likely to drop coverage rather than obtain it from another source. Notes The authors are grateful to the University of Michigan Office of Human Resources and Affirmative Action for providing the data used in this study. 1 As we show later, this is a nontrivial fraction of married employees. 2 We thank one of the reviewers for pointing this out. 3 Blumberg, Nichols, and Banthin (2001) attempt to correct for worker sorting by using a bivariate selection model. 4 See Gruber and Washington (2005) for a fuller discussion. 5 One of the two FFS plans has much higher cost-sharing and coinsurance rates and is much less generous than the other FFS plan. It consistently has only a tiny fraction of total enrollment; thus, in our analyses, we restrict our attention to the other five plans. 6 Children by birth, adoption, or legal guardianship of university employees who have never been married are eligible for coverage as dependents from birth until age 19. They can maintain their eligibility through the month they turn 25, as long as they meet the following criteria: 1) they live primarily with the UM employee (but may be temporarily away from home attending school), 2) the UM employee provides over 50% of their total support, and 3) they are not eligible for coverage through the university as an employee and are not already covered as dependents under another university employee s coverage. 7 We thank an anonymous reviewer for reminding us of this. 8 By definition, those who waived coverage in 2003 were not exposed to the price shocks in 2004. 9 Our results are robust to the inclusion of all employees in the sample. This is not surprising given the relative stability of the employee pool at the university. 10 These are the partial derivatives of the outcome variable with respect to each explanatory variable evaluated at their mean values. 11 We are grateful to an anonymous reviewer for pointing this out. References Abraham, J., W. B. Vogt, and M. S. Gaynor. 2006. How Do Households Choose their Employer- Based Health Insurance? Inquiry 43(3):315 332. Blumberg, L. J., L. M. Nichols, and J. S. Banthin. 2001. Worker Decisions to Purchase Health Insurance. International Journal of Health Care Finance and Economics 1(3/4):305 325. Branscome, J., P. Cooper, J. Sommers, et al. 2000. Private Employer-Sponsored Health Insurance: New Estimates by State. Health Affairs 15:139 147. Buchmueller, T. C., and P. J. Feldstein. 1997. The Effect of Price on Switching Among Health Plans. Journal of Health Economics 16(2):231 247. 46

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