Premium Copayments and the Trade-off between Wages and Employer-Provided Health Insurance. February 2011

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1 PRELIMINARY DRAFT DO NOT CITE OR CIRCULATE COMMENTS WELCOMED Premium Copayments and the Trade-off between Wages and Employer-Provided Health Insurance February 2011 By Darren Lubotsky School of Labor & Employment Relations Department of Economics Institute of Government & Public Affairs University of Illinois-Urbana/Champaign Craig A. Olson School of Labor & Employment Relations Department of Economics University of Illinois-Urbana/Champaign Keywords: Health insurance, compensation, salary, copayments JEL Classification Codes: J32, J33, J41, J5

2 Abstract Compensating wage theory (Rosen 1984) predicts the wages paid to workers of equal productivity will adjust to reflect the expenditures employers spend on employer paid benefits and the value of these benefits to employees. When this theoretical predictions has been tested using employer provided health benefits very few studies (Gruber 1994, Olson 2002) have found the predicted negative relationship between wages and either coverage from own employer health insurance or the insurance premiums or benefit levels. It is widely believed the lack of support for the theoretical prediction is due to inadequate controls for worker productivity. We use a new dataset that reports the salary and premium costs for a family health insurance policy from over 600 school districts for four years that covers a 15 year period interval ( ). These data have three features lacking in the data used in most previous research. For each district and year we have the 9 month salary for a teacher with a master s degree and 10 years of teaching experience, the cost of a family health insurance policy and the premium copayment made by the covered teacher. We reject both simple OLS estimates that ignore constant unobserved heterogeneity and fixed effects panel estimates that account for constant unobserved heterogeneity using tests by Chamberlain (1984) and Angrist & Newey (1991) in favor of a 2SLS model estimated using first-differenced data Our 2SLS estimates that treat salary and premium copayment as predetermined suggest that teachers pay the entire cost of health family health insurance through lower after tax cash compensation due to lower wages and higher premium copayments. These results provide both compelling support for compensating wage theory and suggest that when health care costs are rising in the long-run (5 years) employers adjust cash compensation and shift the cost of health benefits to employees. Premium Copayments and the Trade-off between Wages and Employer-Provided Health Insurance 1. Introduction Employer-provided health insurance premiums and total employment costs have been rising steadily over the last thirty years. At the same time, employees monetary compensation has remained relatively flat. Economists traditionally interpret the disparity in these trends as reflecting an implicit (and sometimes explicit) trade-off that employees make between salary, other forms of compensation, and job attributes more generally. A long line of empirical research, however, has failed to find clear evidence that health insurance costs are borne by employees, which calls into question the long-standing views most economists hold about the 2

3 incidence of rising health insurance costs and, more generally, whether the labor market operates as a sorting mechanism. This paper estimates the trade-off between salary and health insurance costs using a unique data source on salary and benefits provided to public school teachers in over 600 schools districts in Illinois. Compensating wage theory offers a clear prediction about the relationship between wages, health insurance costs, and total compensation: In a competitive spot labor market where the total compensation received by a worker equals his or her marginal revenue product, employees pay for the health insurance provided by their employer through a reduced wage rate or a reduction in other benefits relative to what they would receive from an employer that does not offer health insurance (Rosen 1984). If the costs or benefits of providing health insurance varies across firms and workers differ in their preferences for health insurance versus monetary compensation, workers and firms will sort themselves based on employers cost to provide health insurance and employees preferences for insurance relative to monetary compensation: Workers with strong preferences for health insurance will work for employers that find it profitable to offer a compensation package that provides generous health insurance and workers with a strong preference for cash will work for firms with modest or no health insurance benefits. In equilibrium this matching process will reveal a negative relationship between wages and health insurance benefits that describe the marginal trade-off employees and employers make between these two components of compensation at different levels of cash compensation and health insurance expenditures. In this view, trends in salary and benefits partially reflect employees willingness to pay for additional health insurance expenditures. Data problems, as opposed to poor theory, have been the primary reasons offered to explain why it has been difficult to empirically confirm the prediction from Rosen s theory 3

4 applied to employer provided health insurance (Currie & Madrian 1999). One frequently cited reason for the lack of empirical support for the prediction is that data on individuals typically have incomplete measures of ability and skills that are positively correlated with wages and the presence or level of health benefits because of the tax treatment of benefits or the correlation between human capital and the demand for health care. This means an OLS wage regression often finds workers with health insurance have a higher wage rate compared to workers without health benefits. Failure to account for employee premium copayments may also explain why it has been difficult to find a negative relationship between wages and health insurance benefits. Over the last decade there has been a substantial growth in employee premium copayments that matches the increase in total premiums. The Kaiser Foundation surveys of private employers found that between 1999 and 2010 the average total premium for family coverage had increased 140 percent (compared to a 61 percent change in the CPI) and the increase in employer premium copayments had increased by almost as much (130 percent). These data suggests net take home wages were adjusting to higher insurance costs through increases in employee premium copayments. Since data on employee premium copayments is not part of many datasets used to study the wage-health insurance trade-off, the estimated relationship between cash compensation (before accounting for premium copayments) and the level of health insurance benefits will be biased toward zero if the adjustment in cash compensation come from variation in the employee premium copayment. This paper uses a new dataset on teacher salaries, premiums for employer provided family coverage and teacher premium copayments for family coverage for over 600 Illinois school districts for three academic years ( , and ). These data are 4

5 used to estimate the relationships between the cost of family coverage, teacher premium copayments and teacher salaries. The multiple years of data, information on salaries for a precise level of education and experience and information on the total premium costs of family coverage and the teacher premium copayment allows us to improve on previous research. The estimates show teacher salary reductions associated with higher health insurance premiums occurs largely through teacher premium copayments and not through adjustments in the teacher salary schedule. Our preferred estimate shows a dollar decline in a teacher's salary through a dollar increase in the teacher premium copayment leads to an expected $.86 increase in expenditures on family health insurance coverage. This value is estimated very precisely and is significantly different from both zero and one. The point estimates also suggest greater employer expenditures on health insurance lead to a decline in the expected salary for a teacher with a master's degree and 10 years of experience. However, this latter effect is not precisely estimated. 2. How are benefits, copayments, and wages related? To understand the observed relationship between total compensation, take-home salary, health benefits, and premium copayments, we begin with a model of employer and employee behavior that makes clear the various sources of heterogeneity. Employees have preferences for take-home salary, s it, and health benefits, h it, and maximize utility U it = U(s it, h it ), where takehome salary is the difference between the employee s nominal salary, w it, and the health insurance premium copayment or contribution, c it. Heterogeneity across workers arises because of differences in productivity and differences in preferences for salary versus health insurance. Employers maximize profits by minimizing compensation costs, which is the sum of take-home 5

6 salary and the cost of health insurance. Heterogeneity across employers arises from two sources. First, the cost of health insurance varies by firm size and across geographic areas. (The cost of health insurance is also influenced by the expected medical expenditures by employees, though this source of heterogeneity is endogenous in so far as medical expenditures are correlated with preferences and productivity.) Employers may also differ in their willingness to offer a more generous compensation package in general, and a more generous health insurance plan in particular, if health benefits aid in attracting more productive employees or improve worker productivity in other ways (Dey & Flinn 2005, Lazear & Oyer 2009 ). Market equilibrium involves a matching of workers to firms. Workers who have stronger preferences for salary relative to health insurance will tend to work at firms that find it less costeffective to offer health insurance; workers who place a higher demand on health insurance will tend to work at first that can buy health insurance at a lower rate or those that tend to use health insurance as a selection mechanism. The locus of equilibrium salaries and health insurance combinations traces out a hedonic wage function a level of take-home salary for each observed level of health insurance. The equilibrium implies a marginal condition that ): the employees marginal rate of substitution between health insurance and salary is equal to the marginal change in salary that results from a marginal change in health insurance. Our aim is to control for the effects of other forms of heterogeneity so we can get an unbiased estimate the trade-off embodied in that results from differences in employees preference for health insurance and firm differences in the costs and benefits of health insurance. We begin with a simple specification that incorporates differences in employee productivity. We assume the marginal revenue product, π it, for worker i in period t is equal to total compensation: 6

7 (1) π it = w it + h it - c it The right hand side of equation 1 is total compensation provided by the employer; difference (h i,t - c it ) is the employer s contribution toward the health insurance premium. Employee s nominal salary, w it, is below their productivity by exactly the amount that the employer contributes towards the health insurance premium. The trade-off workers face between wages and health benefits can be described by noting that the gap between a worker's productivity and their takehome salary is equal to the portion of the health insurance premium directly paid for by the employer; the health benefits the employer pays for causes workers to accept lower cash compensation compared to what they could earn elsewhere (without health insurance). A standard hedonic wage function expresses an individuals take-home salary as a function of health insurance provision (and possibly other job attributes): (2) where is a constant that measures average productivity, X it are individual characteristics that are potentially correlated with health insurance and productivity, and is an error term that reflects the unobserved individual productivity. The parameter captures the trade-off between health insurance and wages. If, then a dollar increase in health insurance costs translates directly into a dollar less of take-home pay. There are three important difficulties in obtaining an unbiased estimate of equation 2. First, most data sources lack information on premium copayments, c it. To the extent that adjustments in take-home pay result from changes in copayments, the relationship between 7

8 health insurance and nominal wages will understate the true trade-off between take-home salary and health benefits. Second, most data sources lack information on the cost of employee health insurance plans and thus researchers are limited to measuring the relationship between wages and a simple indicator that the employee is covered by health insurance. Finally, employee productivity,, is likely to be correlated with other job attributes and the generosity of health insurance. We prefer to work with an alternative version of equation 2 formed by rearranging terms to express the cost of health insurance as a function of the components of compensation: (3) where and This specification allows us to more easily measure the tradeoff between nominal wages and health benefits, which is given by the parameter, and the trade-off between premium co-payments and health benefits, which is given by the parameter The test that employees pay for their full health insurance premium in the form of reduced takehome pay ( ) above is equivalent to testing, which implies that a dollar decrease in nominal salary translates into a dollar increase in health benefits. Alternatively, which implies employees pay the full cost of health benefits through adjustments in their premium copayment. Equation 3 is useful because it does not impose π 1 = - π 2. This means we can test whether, in practice, health insurance premiums are more strongly associated with premium copayments or with nominal salary. More generally, (1-z)(-π 1 ) +z(π 2 ), gives the change in health 8

9 benefits that comes from a dollar change in total compensation, where z is the fraction of the adjustment that comes through the copayment. 2 The dollar for dollar trade-off between wages and health benefits is subject to several important assumptions. First, it assumes the value to workers of an additional dollar of health benefits provided by their employer's health plan is equal to the value of an additional dollar of cash compensation (Summers 1989). If an employer provides a costly new benefit,such as a smoking cessation program or a wellness (diet and weight loss) program, some employees (nonsmokers and those who are not overweight) may place very little value on these benefits and may be reluctant to give up additional cash compensation for these benefits while others may highly value the benefits. Because of this heterogeneity in worker preferences, in a competitive labor market several outcomes are possible: (a) firms choose not to offer some benefits because employees are free to buy these services on their own (join a gym or Weight Watchers TM ) based on their preferences, (b ) firms are able to adjust the cash compensation of individual workers based on each worker's willingness to pay for the benefits the firm provides, or (c) different firms offer different health benefit packages (including no benefits) and workers find the firm that offers the overall package of benefits they want, or (d) workers are willing to pay for some benefits they don't highly value because the entire package of benefits provided by the firm cannot be bought by the worker in the individual insurance market. There is some evidence to support each of these adjustments heterogeneity in worker preferences. Some benefits such as smoking cessation and wellness plans are offered by very few employers. The 2010 Kaiser Foundation (2010, p. 32 & 194) report on employer provided health benefits finds that among employers that offer health benefits (69 percent), only 30 2 Levy and Feldman (2001) estimate a model based on Eq. 3 using panel data from the Consumer Expenditure Panel Survey and the Medical Expenditure Panel Survey and fail to find a trade-off between wages and health insurance directly through wage adjustments or indirectly through employee premium copayments. 9

10 percent of those employers also offer gym membership discounts or on-site exercise facilities and 24 percent offer smoking cessation programs. Adjusting worker pay based on each individual worker's demand for health benefits is problematic because its difficulty for the firm to identify employee willingness to pay for different benefits, the administrative costs are likely to be substantial and it creates wage inequities that may have implications for employee morale. While wage adjustments at the individual level are unlikely, adjustments based on employee subgroups is possible. Levy (1998) argues that within firm adjustments to worker preferences can be partially accommodated for by offering different health plans that differ in their generosity and then set employee premium copayments so that workers that demand more protection pay for the additional coverage with higher employee premium copayments. There is some evidence that firms may adjust pay for certain demographic subgroups based on their demand for health care. Sheiner (1999) finds the wage-earnings profile is flatter in local labor markets where health insurance costs are higher. Gruber (1994) finds evidence of a wage offset among women when states mandated that health insurance policies include maternity benefits and the magnitude of the wage reduction was related to expected maternity benefit claims. Both the Sheiner and Gruber studies use CPS data so it's not possible to determine how much of the wage adjustment is a within firm or between firm adjustment to group demographic differences in expected health insurance claims. The Rosen model predicts that differences in worker preferences are reflected in how workers sort across firms. The substantial heterogeneity in the health benefit plans offered by employers (Kaiser Foundation, 2010), including employers that offer no health benefits is consistent with substantial worker heterogeneity in preferences for health benefits that leads to sorting across firms. The probability that some health benefits were offered to employees was 10

11 .73 for firms where more than 35 percent of the workforce was at least 26 years old and.31 for firms where more than 35 percent were 26 or less (Section 2, p. 2). The variation in family premiums across employers is also substantial. In percent of the employers offering family coverage had annual premium cost more than 120 percent of the $13,770 average and 19 percent had plans costing less than 80 percent of the average. Despite this variation, sorting across firms is unlikely to produce firm workforces with identical preferences for health insurance. For example, high and low skilled workers or young and older workers may be complementary inputs in the production process and differ in their demand for health insurance. Workers may be willing to give up a dollar in cash compensation for additional health benefits that they value at less than a dollar because the alternative of quitting their job is often unattractive. The evidence on job lock due to health insurance coverage suggests many workers find it costly and/or risky to quit and search for a job that provides benefits that might better matches their preferences. 3 Also, working for a firm without health benefits and using the additional cash compensation to buy an individual health insurance in the private insurance market that exactly matches their preferences is an unlikely choice because of the tax treatment of fringe benefits and features of the individual private insurance market. Economies of scale associated with administering a large group health plan makes the employer sponsored plan significantly less expensive than what would be paid to obtain comparable individual coverage and employees may not have access to private insurance or access at only very high price because of their health status or the health status of their dependents (pre-existing conditions in underwriting). Thus, a young worker expecting to work for a firm for a number of years may be willing to "overpay" for employer coverage and forego more in cash compensation than their current health care expenditures because as they age and face higher expected medical costs and 3 See Gruber (2000) for a review of the job lock literature. 11

12 higher medical cost risk they know they will continue to have insurance coverage at a price that is not fully experience rated based on their health. If they forego working for an employer with health benefits early in their career, they may find it difficult to find a job with health benefits or buy private insurance later in their career when their demand for health insurance changes. This intergenerational transfer means workers may be willing to pay more for health benefits compared to the current value of the benefits they receive early in their careers in exchange for paying less for the benefits (compared to their value) later in their careers when health risks are greater and the financial consequences of a major health expenditure is more consequential. A final point to note is that some firms may find it profitable to offer employee health insurance and this may affect the trade-off between wages and health insurance. Some firms may benefit more than other firms from having long-tenured workers because of their products or production technology. Offering health insurance may be more profitable than not offering health insurance because the benefit allows it to attract and retain a workforce less likely to turnover for the reasons discussed in the preceding paragraph. Offering health insurance may be profitable for the firm and create job lock just like firm specific human capital. Other benefits, like smoking cessation programs, may produce savings to the firm in the form of lower future health insurance expenditures or lower absenteeism that might make offering the benefit profitable even if many employees place little value on the benefit and are not willing to pay the full cost of the benefit through lower cash compensation (or non-health benefits). If the savings are sufficient a firm may offer this benefit even if none of the cost can be shifted to employees. The preceding discussion leads to several conclusions. While it is theoretically clear that health insurance costs are shifted to employees through lower wages or higher worker premium 12

13 copayments, it is unclear how close (π 2 - π 1 ) is to 1. If on average employees value benefits at less than their cost and the primary reason firms offer benefits is because of their favorable tax treatment, then (π 2 - π 1 ) could be less than 1; workers are willing to give up a dollar in compensation in exchange for benefits they value at only $.80 because the after tax cost reduction in cash compensation is, say, $.70. On the other hand, one could imagine that because of employee risk aversion and insurance underwriting practices in the individual health insurance market, some workers are willing to give up more than a dollar in cash compensation to gain an additional dollar of protection. 13

14 3. Estimating the value of health insurance using data on Illinois public school teachers We use data from Illinois public school teacher contacts to overcome many of the empirical obstacles detailed above. The Illinois State Board of Education has conducted a teacher salary and benefit survey for over 20 years in which they collect data from school districts on salaries paid to teachers at different points of the salary schedule, the cost of an individual and family health insurance policies (if these policies are offered to teachers), and teacher premium copayments for each of these policies. We use data from primary and secondary school districts in the state that participated in the survey during academic years , , and The balanced sample includes 618 school districts. 4 Virtually all public school teachers are represented by an affiliate of the Illinois Federation of Teachers (IFT) or the Illinois Education Association (IEA). In percent of the districts in the state had agreements with a teachers union. An IEA affiliate represented teachers in 75.9 percent of the districts and an IFT affiliate represented teachers in 22.6 percent of districts and the remaining districts had an unaffiliated local union. In virtually all primary and secondary school districts in Illinois, a teacher's nine-month salary is exactly determined by where their education level and years of teaching experience place them on a two dimensional salary grid. The salary survey data that we have includes information for seven points on this grid: BA minimum, BA maximum, MA minimum, MA maximum, MA and 10 years of experience, MA plus credits-minimum, and MA plus credits-maximum. The "minimum" salary points specify the compensation for a teacher beginning their teaching career and the salary maximum describes pay for someone whose experience equals the salary schedule maximum. There is variation across districts in the years 4 The sample does not include the largest school district in the state, Chicago Public Schools, because the district did not respond to the survey in all four years. 14

15 of experience required to reach the salary maximum (conditional on education). In this study we focus on the salary for a teacher with an MA degree and 10 years of experience. 5 These data have several strengths that allow us to address the difficulties described above. We implicitly control for two important dimensions of human capital that affect worker productivity by estimating the model using the salary paid to teachers with a specific level of credentials, namely a masters degree and ten years of teaching experience. This is an improvement over other datasets where experience is often measured imprecisely and years of education fail to capture specific kinds of college education. The data we use describes the pay for a college graduate certified to teach in Illinois with ten years of industry/occupation experience. Of course there is substantial variation across districts in this salary point and these differences may capture other important average differences in teacher quality that is not captured by education and experience. Since the analysis is based on data from a single occupation, the wage data do not include unmeasured selection effects related to occupational choice that could be correlated with health insurance premiums or salary. Most importantly, the data give us access to precise information that is not typically available in other nationally-representative data sources. Separate questions are asked about the costs of insurance covering hospitalization, prescription drugs, vision and dental coverage for both individual and family coverage. The cost of health insurance and the premium copayment measures that we use refer to the hospitalization and drug coverage for a family policy. We do not have data on the number or particular types of plans offered to teachers, benefit levels offered under each plan, the take-up rate of health insurance by teachers, nor demographic characteristics about the teachers. Thus, we use the data to construct measures of the real salary (w it ), the total cost of health insurance (h it ), and the teacher premium copayment (c it ). The real 5 We will be exploring the sensitivity of our results using other points on the salary grid. 15

16 salary is the nine-month salary paid to a teacher with a master s degree and 10 years of teaching experience. Three additional control variables are included in the model; average daily attendance in the district, real assessed value of local property per student in the district, and real federal and state aid to the district per student. These data are collected separately by the Illinois State Board of Education. All of the monetary variables were converted to July 2009 dollars using the national CPI for all items. Table 1 reports descriptive statistics for the pooled sample and each of the four academic years. The first point to note is the substantial increase in health insurance costs over 15 years. After adjusting for changes in the overall price index, the mean cost of family coverage rose at a compounded annual rate of 4.3 percent per year, or by 89.4 percent overall. 6 Most of the cost increases occurred between 1998 and The second variable in the table is an indicator equal to one if the district offers a group family health insurance plan to teachers and is equal to zero if it does not offer family coverage. The fraction of districts offering coverage is somewhat variable from year to year, but centers around 79 percent. The relatively stable percentage of districts offering family coverage masks the fact that a large number of districts added or dropped group coverage over the 15 years. Twenty seven of the 618 districts (4.4 percent) in our sample did not offer family coverage in any of the four years and 331 (53.6 percent) districts offered it in all four years. Thus, 42.1 percent (260) of districts in the sample added or dropped family coverage over the 15 years. Among these insurance changers, 147 districts that offered family coverage in 1993 did not offer coverage in one of the later four years and 140 districts that did not offer coverage in 1993 provided coverage in at least one of the three later years. 7 6 This percentage change is based on changes in mean premiums for the sample in each year excluding districts that did not offer family coverage. 7 Since the total premium and the teacher copayment are zero when a district does not offer coverage, identification of parameters in the school fixed effect models below comes from both the change in premiums in districts that 16

17 The next rows in Table 1 show the evolution of teacher premium copayments and the salary for teachers with a masters degree and ten years of teaching experience. Over the fifteen years the mean increase in teacher premium copayments rose at a compounded annual rate of 4.5 percent, or by 93.9 percent overall, closely matching the increase in total premiums. On the other hand, the real salary paid to teachers increased by a total of 1.5 percent over the entire 15 year period, which is an average annual rate of 0.1 percent. These data imply that, after paying the teacher premium copayment out of their salary, the mean real take-home compensation decline by $3654 over the fifteen years. However, this overstates the actual decline in take-home compensation because the premium copayments paid with pre-tax dollars. Assuming a 30 percent combined federal and state marginal tax rate mean taxable income, real take-home compensation declined by $2364 over the 15 years. Our data show the familiar pattern that employers who pay higher salaries are also more likely to offer health insurance to employees. In Figure 1 we break up the sample of school districts into 100 groups based on the salary paid to teachers with a masters degree and ten years of experience, where each group has approximately the same number of districts. For each group, we plot the fraction of schools that offer health insurance on the horizontal axes and the average salary on the vertical axes. We also include an OLS regression line. The positive relationship between salary and the probability of offering health insurance is clear, with each additional percentage point increase in the insurance probability being associated with an additional $509 in salary. Thus, even with data where the sample is restricted to the pay for a homogenous group, the data fail to show the negative relationship predicted by the theory. In Figure 2 we compare the probability of offering health insurance to teachers takeoffered family coverage over the entire time period and the changes when districts add or drop family coverage. For this reason we will estimate some specifications that include an indicator for offering family coverage. These estimates can be compared to Levy and Feldman (2001) who also estimate wage changes for insurance changers. 17

18 home pay, the difference between their salary and the premium copayment. Adjusting the salary for the teacher premium copayments eliminates the strong positive relationship shown in Figure 1, but the resulting plot shows no significant relationship between the variables. The slope indicates a one percent change in the probability of being offered health insurance is associated with $59 in take-home salary, with a standard error of $71. Figures 3 and 4 illustrate the benefits of having a panel dataset. Figure 3 uses the same data as Figures 1 and 2 but shows a simple fixed-effects estimator constructed by calculating the mean and median changes in health insurance premiums, teacher premium copayments, and teacher take-home pay (i.e. the difference between salary and the copayment) from one period to the next for districts that add, drop, or continued with or without coverage from one period to the next. On the y-axis -1 denotes districts that dropped family coverage, 0 denotes districts that made no change in their offering and 1 denotes the group that added family coverage. The key comparison is between the districts that dropped and added coverage. For districts that dropped coverage, the average premium for family coverage prior to dropping the plan was $6546. Teachers in these districts saved an average of $4939 in premium copayments and their pre-tax take-home salary (after deducting premium copayments) increased by $5117. In districts that added family coverage, benefit costs increased an average of $8587. $5927 of this was paid for by the teacher in premium copayments and their total pre-tax take-home compensation after the premium copayments declined by $5817. In contrast to the conclusion implied by Figures 1 and 2, by focusing on changes within districts that added and dropped coverage we eliminate 18

19 unobserved district heterogeneity and, as a result, the data indicate teachers paid for well over half of the cost health insurance through lower pay or higher premium copayments. 8 Figures 4a 4d use data only from districts that continued to offer coverage from one period to the next and plot a simple fixed-effects estimator of the change in health insurance premiums against the change in teacher premium copayment. Figure 4a plots the relationship for the pooled sample and the other figures show the relationship separately for changes between adjacent time period (i.e to 1998, 1998 to 2003, and 2003 to 2008). Each graph shows a strong positive relationship between changes in the cost of insurance and changes in teacher premium copayments. The pooled data imply that teachers pay $.76 in premium copayments for each additional dollar in premium costs and the estimates for each sub-period range from $.57 to $.81. For the pooled sample the $0.76 is significantly different from both zero and one (SE=.028). Figures 3 and 4 show that when simple FE estimates are used to control for constant unobserved district and workforce heterogeneity, the wage-health insurance relationship looks very different from the results in Figures 1 and 2 that don t take advantage of the panel data. The bivariate relationship for districts that continue coverage is consistent with the results for districts that add or drop coverage and suggest employees pay some but not all of the cost of insurance through lower cash compensation. The remainder of the paper builds on these simple bivariate results by testing the FE assumptions and controlling for other covariates. 8 When models for teacher take-home pay and health insurance premiums are jointly estimated, the hypothesis that teachers pay for all of the cost of health insurance through lower take-home compensation is rejected (p-value<.001) for districts that change coverage in both directions (add or drop coverage). 19

20 4. Fixed-Effects models of the value of health insurance Fixed-effects models compare the change in take-home salary, premium copayments, and health insurance costs within the same district over time. Eq 3 above, and the cross-sectional evidence in the previous section, indicate that unobserved factors could lead to a spurious, positive association between health insurance premiums and health insurance costs. In particular, more productive teachers could work in districts that provide higher salaries and better health insurance. If we assume these unobserved district-specific factors are constant over the study period, then u it in Equation 3 can be decomposed into a district fixed-effect,v i, and an timevarying component, e it. Equation 3 becomes (4) The difference in health insurance costs between two periods (e.g and 2008) removes the influence of the district-fixed effect and is given by: (5) Equation 5 assumes the changes over time in wages, health insurance costs, and other variables on the right-hand side are strictly exogenous; i.e. cov[( e i2008 -e i2003 ), (X i2008 -X i2003 )] = cov[( e i2008 -e i2003 ), (w i2008 -w i2003 )] = cov[( e i e i2003 ),(c i c i2003 )]= 0 for all i (Chamberlain 1982, 1984); or the random shocks that influence health insurance costs are uncorrelated with past and future values of the differences on the right-hand side of Equation 5. This rules out the possibility that unanticipated health care shocks that raise health insurance premiums in

21 also have an impact on salaries or teacher premium copayments in 2008 or later periods. We might especially worry that this assumption will be violated in our context because teachers wages and benefits are set through collective bargaining agreements. With multi-year agreements a health care price shock that affects a district s premiums costs in one year could lead to a permanent adjustment in wages and teacher premium copayments in the next negotiation period if wages or premium copayments cannot be adjusted during the term of the contract when premiums change. The preceding discussion suggests it is important to test the fixed effect assumptions to conclude OLS applied to Equation 5 will give unbiased estimates of π 1, π 2, and θ. Chamberlain shows that if the fixed effect assumptions are met and the right-hand side variables in Equation 4 are strictly exogenous, when h it from each period is regressed on the right-hand side variables in Equation 4, as well as on past and future values of these right-hand side variables, the coefficients will follow a well-defined pattern. Focusing on data for three academic years, , and , and ignoring the characteristics X it, the unobserved district fixed-effect can be described by a linear projection on the leads and lags of salary and the premium copayment, plus a residual that is independent of the various values of w it and c it (by construction): (6a) v i = λ 0 + λ 1 w i λ 2 w i λ 3 w i λ 4 c i λ 5 c i λ 6 c i τ i Each λ i in this equation captures the relationship between the unobserved district fixed effect and each observed variable in the model, conditional on the other variables. While v i cannot, by 21

22 definition, be observed and Equation 6a cannot be directly estimated, this equation is useful for showing and testing the underlying assumptions in a fixed effect model. The fixed effect specification described by Equation 4 (ignoring X it ) and Equation 6a allow the variation in health insurance premiums for the three years to be described by two first difference equations and one equation for the level of premiums: (6b) h i1998 = a + π 1 w i π 2 c i v i + e i1998 (6c) h i h i1998 = π 1 (w i w i1998 ) + π 2 (c, c i1998 ) + (e, e i1998 ) (6d) h i h i1998 = π 1 (w i w i1998 ) + π 2 (c i c i1998 ) + (e i e i1998 ) Substituting the expression for v i in Equation 6a into 6b, and substituting the resulting expression for h i1998 into Equations 6c and 6d, Equations 6b - 6d become: (6b') h i1998 = a + (π 1 + λ 1 )w i λ 2 w i λ 3 w i (π 2 + λ 4 )c i λ 5 c i λ 6 c i τ i + e i1998 (6c') h i2003 = λ 0 + λ 1 w i, (π 1 + λ 2 )w i λ 3 w i λ 4 c i (π 2 + λ 5 )c i λ 6 c i τ i + e i2003 (6d') h i2008 = λ 0 + λ 1 w i1998 +λ 2 w i (π 1 + λ 3 )w i λ 4 c i λ 5 c i (π 2 + λ 6 )c i τ i + e i2008 These equations describe the level of h it in each year as a function of the lags, leads, and contemporaneous values of w it and c it and are the reduced form equations that define the two 22

23 first-difference "structural" equations (i.e. subtracting 6b' from 6c' gives 6c and subtracting 6b' from 6d' gives 6d). If 6b'-6d' are stacked, the coefficient matrix for w it and c it is: (π 1 +λ 1 ) λ 2 λ 3 (π 2 +λ 4 ) λ 5 λ 6 λ 1 (π 1 +λ 2 ) λ 3 λ 4 (π 2 +λ 5 ) λ 6 λ 1 λ 2 (π 1 +λ 3 ) λ 4 λ 5 (π 2 +λ 6 ) The rows refer to an equation describing h it for a specific year and each column shows the coefficients on one of the variables from one of the time periods. This matrix shows the fixedeffect specification constrains the coefficients on the lags and leads for each variable to be the same across the three equations and the causal effect of c it on h it for period t is equal to the coefficient on c it in period t minus the coefficient on the variable in one of the lagged or leading periods. That is, the causal effect of c i2003 on h i2003 is (π 2 +λ 5 ) - λ 5 = π 2. Therefore, when Equations 6b' - 6d' are estimated as a system of seemingly unrelated regression equations (Zellner 1962, 1963), the fixed-effect model imposes 10 (2*T 2 - (2*T+2)) restrictions on the parameters in this 3SLS model (Angrist & Newey 1991). Let [h,t ]D w(s) equal the coefficient on w it for year s in the year t equation. The fixed-effect constraints on the leads and lags are: [h 2003 ] D w(1998) = [h i,2008 ] D w(1998) [h 1998 ] D w(2003) = [h i,2008 ] D w(2003) [h 1998 ] D w(2008) = [h i,2003 ] D w(2008) [h 2003 ] D c(1998) = [h i,2008 ] D c(1998) [h 1998 ] D c(2003) = [h i,2008 ] D c(2003) 23

24 [h 1998 ] D c(2008) = [h i,2003 ] D c(2008), and the constraints on the contemporaneous variables are: [h 1998 ] D w1998) - [h 2003 ] D c(1998) = [h i,2003 ] D w(2003) - [h i,2008 ] D c(2003) [h 1998 ] D w1998) - [h 2008 ] D c(1998) = [h i,2008 ] D w(2008) - [h i,2003 ] D w(2008) [h 1998 ] D c(1998) - [h i,2008 ] D c(1998) = [h 2003 ] D c(2003) - [h i,2008 ] D c(2003) [h 1998 ] D c(1998) - [h i,2003 ] D c(1998) = [h 2008 ] D c(2008) - [h i,2003 ] D c(2008) Angrist and Newey (1991) show two tests of the strict exogeneity assumption can be constructed from Chamberlain's results. If the fixed-effect model is estimated using the three years of data that have been demeaned to remove the effects of v i, and w it and c it are strictly exogenous, then the leads and lags of w it and c it can be treated as excluded instruments for each period of time period. For the three years of data the equation for each year is: (7a) (7b) (7c) h 1998 = π 1 w i π 2 c i e i1998 h 2003 = π 1 w i π 2 c i e i2003 h 1998 = π 1 h i π 2 c i e i2008 The fixed effect parameters can be estimated using OLS on the three years of stacked data. Strict exogeneity means w is and c is are excluded from the h it equation where s t. Angrist and Newey (1991) show a test statistic for the strict exogeneity of w it and c it can be constructed from a regression of the residuals from the fixed effect model for each year on the 24

25 leads and lags of w it and c it. For example, if e 1998 is the vector of fixed-effects residuals for 1998 ( e 1998 = h i w i1998 c i1998 ), the regression equation is (8) e i1998 = a 1,1998 w i a 2,1998 w i a 2,1998 c i a 3,1998 c i g i1998 The test statistic is constructed from the R 2 s from this regression and the comparable regressions explaining e i2003 and e i2008. Strict exogeneity implies the leads and lags of w it and c it should explain very little of the fixed-effects residual variation. A second test developed by Angrist & Newey (1991) is based on the SUR estimates of the three equations described by Equations 6b' - 6d'. As discussed above, if w it and c it are strictly exogenous then the ten constraints on the SUR equations explaining the level of h it each year that are listed above will not be rejected by the data. Thus, the second test of the assumptions of the fixed-effects model is simply the joint test obtained from imposing the ten constraints on equations 6b' - 6d'. 4.b. Models with Predetermined Variables If the two tests described above reject the strict exogeneity assumption required for the fixed effect model, strict exogeneity can be replaced by assuming all or some of the right-hand side variables in Equation 4 are predetermined. A variable X it is predetermined if Cov(e it, X is ) = 0 for s < t and Cov(e it, X is ) 0 for s > t. w it and c it are predetermined if a random shock to a school district's premium costs in 1998 (through e i1998 ) has an impact on w it or c it in later periods, but w it and c it in 1998 does not affect h it in later years through its correlation with e it in later years. If w it or c it are predetermined then OLS applied to the equation 25

26 (9) h i h i2003 = (X i X i2003 ) β + π 1 (w i w i2003 ) + π 2 (c i c i2003 ) + (e i e i2003 ) will be biased because cov(e i2003, w i2008 ) and cov(e i2003, c i2008 ) are not equal to zero. Two-stage least squares can correct this bias using data from a third year. Specifically, (w i w i1998 ) and (c i c i1998 ), or w i2003, w i1998, c i,2003 and c i,1998, could be used as instruments. A third model with unmeasured school district heterogeneity, where the right hand side variables are not strictly exogenous, is a dynamic model where h it depends on lagged values of h. A new drug or treatment that becomes available may raise premiums this period as well as next period as use of the drug or treatment expands. A model with a one period lag is: (10) h i2008 = ρ h i X it β + π 1 w i π 2 c i v i + e it, where Cov(e it, X is ) 0 for all s and t, Cov(e it, w is ) = Cov(e it, c is ) = 0 for s < t, and Cov(e it, w is ) and Cov(u it, c is ) 0 for s > t. In this model e it is correlated with h it+1 through its impact on h it. The first difference equation that controls for v i is: (11) h i h i2003 = ρ (h i h i1998 ) + β (X i X i2003 ) + π 1 (w i w i2003 ) + π 2 (c i c i2003 ) + (e i2008 -e i2003 ) 26

27 In addition to instruments for (w i w i2003 ) and (c i c i2003 ), additional instruments are required because (e i e i2003 ) is correlated with (h i h i1998 ). One possibility is to use h i1998 as an instrument because (e i e i2003 ) is uncorrelated with h i1998 so long as cov(e it, e it+1 ) = 0. However, h i1998 may be a weak instrument because the correlation between h i1998 and (h i h i1998 ) may be modest. Another possibility is to use additional data from the school year and use (h i h i1993 ) or h i1998 and h i1993 as an instrument(s) for (h i h i1998 ). Data from will also include w i1993 and c i1993 and provide additional instruments for (w i w i2003 ) and (c i c i2003 ). Equation 11 is overidentified with the data and allows us to test additional alternative hypotheses. 5. Empirical Estimates 5.a. Estimates of the MA+10 Salary The first set of regression results we present are estimates based on Equation 2 which replicates specifications comparable to models used in previous research. Panel A of Table 2 reports coefficients on the family health insurance indicator variable in salary regressions. Other variables in the model include district size, property wealth and state and federal aid and a set of year dummies. Each cell in this panel reports estimates for a different specification using the pooled sample of 2472 observations. Columns (1) and (3) report estimates using real compensation and columns (2) and (4) report ln(real compensation). The estimates in the first row of columns(1) and (2) report OLS results that regress the salary on the insurance indicator. These estimates are comparable to a model that can be estimated using March CPS data. The estimates reported here show the conditional mean salary is no different between districts that do and do not offer health benefits. In contrast, comparable specifications using CPS data find a 27

28 large positive coefficient that is attributed to omitted variables, such as ability. We do not get this result in these data because our focus on a particular industry/occupation avoids the substantial omitted selection effects that are reflected in a nationally representative dataset. The second and third rows exploit the panel structure of the data and report random and fixed effect estimates. The coefficients on the insurance variable are negative, but statistically insignificant in both models. A Hausman test clearly rejects the random effects specification and shows there are important omitted variables correlated with the right-hand side covariates. The fixed-effects specification implies the MA+10 salary is 0.5 percent lower in districts that provide family health insurance. Columns (3) and (4) show results for models where the salary equals MA+10 minus the teacher premium copayment. Since the results in columns (1) and (2) show no conditional mean difference in salaries between districts that do and do not offer family coverage, the significantly different results in columns (3) and (4) show the conditional impact of coverage on cash compensation through changes in the premium copayment. The OLS results in row (a) of Column 3 show the conditional mean salary net of the premium copayment is $4900 dollars lower in districts that offer family coverage compared to those that do not offer family coverage. The column 4 estimates show this differential corresponds to a 12.6 percent decline in pre-tax cash compensation. The OLS estimates of the effect of coverage is identified from both the insurance changers and districts that always or never offered family coverage in the four years. The fixed-effects estimates arguably control for time-invariant unmeasured district characteristics that are correlated with net wages and coverage that the Hausman test shows to be important. The fixed-effects estimates based on only the insurance changers controls for this unobserved heterogeneity if the exogeneity assumptions of the fixed-effects model are met. The 28

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