# GENDER DIFFERENCES IN THE VALUATION OF EMPLOYER-PROVIDED HEALTH INSURANCE

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5 804 ECONOMIC INQUIRY H i, as well as a vector of other factors, X i, such that: ð1þ ln E i 5 b 0 þ b 1 H i þ X i d þ e i ; where b 1 estimates the earnings/health insurance trade-off, d is a vector of other estimated coefficients, and e i is the unobserved variation. Compensating wage differential theory implies that under a perfectly specified model b 1, 0. Given the wage offer distribution and thus the budget constraint, a worker considers his/her marginal utility of health insurance and makes a choice about earning and health insurance combinations. This implies endogeneity between health insurance coverage and earning decisions. Thus, H i and e i in Equation (1) are correlated, and OLS estimates of b 1 will produce biased results. 5 Empirical validation of the compensating wage differential theory requires that the estimated equation is free from omitted-variable and endogeneity biases. In the case of health insurance, a worker s preference and thus marginal utility of health insurance determine the trade-off and hence the welfare and health of the entire family. The preferences are influenced by whether alternative sources of health insurance are available and the marginal utility of additional coverage. For married individuals, the best alternative is the availability of insurance through the spouse s job. This implies that in the case of married people, the probability of accepting a job that provides health insurance, H i in Equation (1), depends on the probability that the spouse has health insurance through his/her job. 6 That is, ð2þ H i 5 a 0 þ a 1 H s þ X i c þ m i ; where H s is equal to 1 if the spouse has health insurance through his/her employment, 0 otherwise, a 1 is the associated coefficient, expected to be negative, and m i represents unobserved variation. There are two potential problems with estimating Equation (2). First, there is an endogeneity/simultaneity problem in the sense that 5. Our discussion of the empirical model and the endogeneity issues that follow draws significantly on the discussion developed by Olson (2002). 6. Due to the lack of an alternative insurance source variable for singles, this paper concentrates on married men and women. acceptance of health insurance by one spouse, H i, may cause the other spouse, H s, to accept a job without health insurance. Thus, H s and m i in Equation (2) are correlated, and the OLS estimates of Equation (2) produce biased results. That is, the estimated coefficient will overstate the negative effect of the spouse s health insurance on the probability that the other spouse has health insurance, a 1, through his/her job. 7 The second problem is associated with assortive mating. 8 If the estimated equation suffers from unobserved variables that affect compensation packages of both spouses, then assortive mating will cause a positive correlation between H s and the error terms in Equation (2), m i, and Equation (1), e i. Thus, a 1 understates a negative causal relationship between the two spouses demand for health insurance and will produce biased estimates of the trade-off by understating the negative effect of b 1. 9 To overcome the problem, our strategy is to identify and include one or more instruments in Equation (2). The instruments must correlate with the spousal health insurance variable but not correlate with the own health insurance variable. We use two variables as such instruments the spouse s firm size (an indicator for firms with fewer than 100 employees) and whether the spouse s insurance plan provides family coverage. The former instruments H s and thus H i ; the latter directly instruments H i. As in Currie and Madrian (1999), small firms are less likely than larger firms to provide health insurance. Again, firm size, the same as spousal health insurance, may produce biased results due to assortive mating. In this case, if couples with low unobserved productivity factors take low-paying jobs with small firms that do not offer health insurance, then there will 7. According to Gruber and Madrian (2002), and based on empirical studies of job turnover, the joint determination of the health insurance decision by husbands and wives can perhaps be treated as exogenous. Empirical studies of the wage/health insurance trade-off, however, suggest the possibility of endogeneity. We examine this issue in the empirical section below. 8. Assuming the existence of a matching process by which men and women sort themselves out and marry alike person, a positive correlation with respect to ability, skill, and education between married couples is expected. This would cause dual or overlapping coverage and no coverage for high-income and low-income couples, respectively. 9. In fact, Olson (2002) found that husbands health insurance as an instrument produces a lower bound estimate of the trade-off for the wives wage equation.

7 806 ECONOMIC INQUIRY The job characteristics vector includes indicators for industry and occupation, categorical variables for federal and state/local government employment, union membership, and firm size (firms with less than 100 employees are the omitted category). Hours worked per week and a categorical variable for whether worked part time or full time are also included. 14 To capture the quality of jobs, two additional indicators for whether the job provides paid sick leave and provides paid vacation leave are included. As discussed earlier, the notion of good versus bad jobs, with good jobs having higher benefits and higher wages, implies a positive sign for these variables. Inclusion of these variables reduces the possibility of confounding the effect of health insurance on wages with the effects of other job characteristics. 15 These measures together will also reduce the possible correlation between health insurance and the error term in the wage equation. The human capital vector includes potential labor market experience and its square, tenure with current firm, and education. Previous studies of wages have found differences in the valuation of prior potential experiences and tenure (experience) with current employer. We divide the total potential labor market experiences to experience prior to working for current employer and tenure with current employer. Then, given the shape of the earning/labor market experience profile, we include prior work experience and its square, tenure and its square, and interaction between prior experience and tenure in the estimated models. One interpretation of the interaction term is that the effect of tenure on wages depends on prior experience. 14. In general, the likelihood of part-time workers not having health insurance is higher than that for full-time workers. Omitting such workers from the sample, however, will most likely cause selectivity biases similar to the studies of discouraged workers and labor force participation. Part-time work is a decision that individuals might make based on the availability of health insurance through a job or through a spouse s job. The inclusion of such individuals in the sample provides a more complete picture of the wage/health insurance trade-offs. 15. It is plausible that paid vacation and sick leave, as the provision of health insurance, are endogenous in Equation (1). We performed chi-squared tests for endogeneity. The null hypothesis of exogeneity could not be rejected for either the paid vacation or the sick leave variables. On the other hand, the exogeneity of the insurance variable was rejected at p values below.01. These results were robust across all specifications that are reported in the empirical section. Finally, based on the past literature, several control variables are included in the model. These include the number of children under age 6, number of children of ages 6 18, and dichotomous variables for black workers, Hispanic workers, workers residing in four regions of the United States, and workers residing in metropolitan areas. Other control variables include spouse s education and wage income. Inclusion of these variables controls for variation in the own health insurance variable that might otherwise correlate with the error term in the spouse s wage equation. They control for assortive-mating effects and reduce the possibility/size of the bias in the coefficient of health insurance. IV. EMPIRICAL RESULTS A. Data The data used in this study come from the Agency for Healthcare Research and Quality (AHRQ). Since 1996, AHRQ has been conducting the MEPS. MEPS files include three survey components. The core survey is the household component (HC), which forms the basis for the medical provider component and the insurance component. The MEPS-HC uses an overlapping panel of six rounds over a period of 2.5 years. It also produces annual end-of-the-year information. The 2001 MEPS-HC contains approximately 12,700 civilian noninstitutionalized families and 33,553 individuals. Though the HC was released earlier, the supplementary file that contains information about persons with private insurance, including the health insurance premiums paid by the policyholder, entitled 2001 Person Round Plan Public Use File, was released to the public for the first time during the summer of Previous years files do not provide the premium information. Evans, Levy, and Simon (2000) provide an excellent survey and description of available data sets, including MEPS, that can be used in health economics Private insurance means that the insurance is purchased versus free provision of health care by the public sector. Private insurance may be obtained from an employer, a union, an insurance agent, an insurance company, or a professional association. 17. MEPS and its predecessor, the National Medical Expenditure Survey, files have been used by a few researchers to investigate issues such as employer-provided insurance and job lock and health-care use. See Evans, Levy, and Simon (2000) for details.

8 DANESHVARY & CLAURETIE: GENDER DIFFERENCES IN THE VALUATION The MEPS questionnaire also asked participants whether or not they were offered health insurance through their current job. Due to a skip pattern of the question and inconsistencies in responses, a significant portion of the data set includes missing values for the offer variable, making it unreliable, if not impossible, to use. Limiting the sample to observations with reliable values for the offer variable reduces its size significantly. The 2001 MEPS-HC includes information on an individual s age, race, employment status, marital status, wages, family size, healthcare total and out-of-pocket expenditures, and other demographic data. 18 There are 20,092 civilian noninstitutionalized men and women of ages The private insurance supplementary file contains 11,260 policyholders, covering 22,069 individuals, for which outof-pocket premiums, including zero dollar amounts, and type of policy (single versus family) were reported. When the two files are merged by person identifiers, 19,971 individuals have records in both files. Restricting the merged sample to ages reduced the sample size to 13,143 individuals and 8,595 policyholders. The data set provides annual total medical expenditures, total out-of-pocket expenditures paid by the user or user s family, and thus, the total medical benefit, and the premium paid by the policyholder. Appendix 1 shows, by age group and by gender, the average amount of expenditures (Panel A), the percentage of the sample with nonzero expenditures (Panel B), the average amount of medical benefits received (Panel C), and the medical benefit as a percentage of expenses (Panel D). Information on these four panels is based on the sample of 20,092 individuals in MEPS-HC. Appendix 1 also shows insurance premiums paid by policyholders by the type of coverage (single/family) and by gender, based on the 8,595 policyholders (Panel E). Information from Appendix 1 suggests that women, in general, experience higher health-care expenses, receive higher benefit payments from insurance, exhibit a higher probability of utilizing health-care services, and exhibit a higher probability of receiving insurance benefits. These results raise questions regarding relative costs of employerprovided health insurance, effects on wages of men and women, and effects on genderwage differentials. To estimate the model outlined earlier using spouse s variables as instruments, we concentrate on two separate samples of married men and married women. We use family identifiers to obtain spousal variables. We restrict samples to ages of working men and women, excluding self-employed individuals, individuals attending college, noncivilian labor-force workers, and farm workers. Further, deleting records with missing values for needed variables produced samples of 3,723 working married men and 3,042 working married women. We report sample means and standard deviations in Appendix 2. The personal and job characteristics variables seem reasonable and consistent with other nationally representative data sets. The means of the health-related variables, such as personal annual health expenditure and number of days missed work, are lower for men than for women. A slightly larger percentage of men, relative to women, hold jobs that provide vacation leave. As expected, a larger portion of the men sample has employer-provided health insurance and a family plan policy than the women s sample. Thus, men pay a higher premium and have larger total health-care benefits for the entire family. B. Estimation of Earning Equations To disentangle the effects of heterogeneity of jobs, the insurance cost sharing, and healthrelated variables and to check for the severity of potential endogeneity of the employer-provided health insurance variable, the earnings model outlined above was first estimated for married men and married women, separately, using the OLS. The OLS results do not account for endogeneity of the health insurance variable. They provide a baseline for comparison and allow us to investigate the endogeneity issue. Table 1 reports the results. Table 1 also reports the results of four specifications applied to each of the two samples. Column 1, for each sample, reports results from a baseline model that includes the human capital and other control variables as well as the variable representing employer-provided health insurance. They exclude job characteristics and other health- and health insurance related variables. Column 2 adds variables related to jobs. Column 3 includes other health and health insurance variables but not job variables. Finally, Column 4 reports results of a complete model and includes all variables.

9 808 ECONOMIC INQUIRY TABLE 1 Heteroskedasticity-Corrected OLS Estimates of Natural Logarithm of Annual Earnings: Married Men and Married Women Married Men Alternative Specifications Married Women Alternative Specifications Variables (1) (2) (3) (4) (1) (2) (3) (4) Own employer-provided.103* * * *.026 health insurance Job characteristics quality Job has paid.056*.052*.101*.100* sick leave Job has paid.145*.149*.140*.139* vacation leave Health status and health insurance variables Annual health expenditure (self,.000) Work-limiting disability.179**.175** No. of half-days.002*.002* missed work (self) No. of half-days missed work (others) Contribution to premium (.000) Total annual health-care benefits (.000) Plan is a HMO Notes: In addition to the variables shown in the table, each model includes own experience, tenure, and their squares and interaction; own education, spouse s education and wage income, as well as indicator variables for race, occupation, industry, other job characteristics, union membership, firm size, Metropolitan Statistical Area residency, region of residency, number of children under age 6, and number of children of ages See the text and Appendix 1 for details. * and **Significant at.01 and.05 levels, respectively. Estimated coefficients of human capital and other control variables, not reported in Table 1 but available upon request, are reasonable and have the correct signs. These coefficients are robust across all specifications for both samples. In addition, the coefficients of variables that are reported in Table 1 are stable across specifications. Coefficients of the health insurance variable are positive in all specifications, contrary to the prediction of the compensating wage differential theory but consistent with the findings of most previous research. Coefficients are statistically significant in the baseline models and in models that exclude job characteristics but include other health- and health insurance related variables. When the job characteristic variables are included, Columns 2 and 4, the positive coefficients for the health insurance variable fall and prove insignificant. These results provide evidence of the job heterogeneity s confounding effect on the estimation of the trade-off between wages and health insurance. In addition, the results in Table 1 strongly suggest biased estimates resulting from the use of OLS. To obtain an accurate estimate of the tradeoff requires that the measured insurance variable does not correlate with the error term in the earnings equation. This can be accomplished by identifying IVs for H i in Equation (1). To be potentially valid, each IV must correlate with the likelihood of having own health insurance, H s in Equation (2), which, in turn, affects the likelihood of the spouse receiving his/her health insurance, H i in Equation (2) and, thus, affecting earnings in Equation (1). For the reasons discussed earlier, we consider spouse s firm size and whether spouse s insurance plan includes family coverage as potential instruments. Table 2, Panel A, shows the first-stage heteroskedasticity-robust conditional linear probability estimates of Equation (2), where

10 DANESHVARY & CLAURETIE: GENDER DIFFERENCES IN THE VALUATION 809 TABLE 2 Estimates of the Effects of Spousal Firm Size and Spousal Family Policy on the Probability of Having Own Employer-Provided Health Insurance and on the Natural Logarithm of Annual Earnings Married Men Married Women Variable (1) (2) (3) (1) (2) (3) Panel A: Probability of having own employer-provided health insurance Spouse works.099*.033*.100*.030** for a small firm Spouse s policy.346*.338*.330*.322* includes family plan Panel B: Natural logarithm of annual earnings Spouse works.052**.045** for a small firm Spouse s policy includes family plan.050**.041***.053*.049** Notes: Estimates in both panels are corrected for heteroskedasticity. Panel A estimates are conditional (first-stage) linear probabilities. In addition to the variables shown in the table, each model includes own experience, tenure, and their squares and interaction; own education, spouse s education and wage income, as well as indicator variables for race, occupation, industry, other job characteristics, union membership, firm size, Metropolitan Statistical Area residency, region of residency, number of children under age 6, and number of children of ages See the text and Appendix 1 for details. *, **, and ***Significant at.01,.05, and.10 levels, respectively. spousal health insurance is captured by one or two instruments. Panel B provides estimates of the relationship between the spousal instruments (firm size and family coverage) and own annual earnings. Estimates are provided for each instrument separately, Columns 1 and 2, and for the combination of the two instruments, Column 3. Each specification in Table 2 includes all the explanatory variables that are included in estimating the earnings equations. The results in Table 2, Panel A, indicate that even after accounting for the list of exogenous variables, individually and jointly, both instruments strongly relate to spouse receiving health insurance and exhibit the expected signs. The results are consistent and similar across gender. A spouse working for a small firm increases the likelihood of the other spouse having health insurance by 10 percentage points. A spouse having a family insurance policy reduces the probability of having own employer-provided insurance by about percentage points. As shown in Column 3 of both samples, when both instruments are included in the model, the coefficients have the expected sign and are significant at the 1% level. These results show that the two instruments, individually and jointly, are good predictors of the probability of spousal health insurance, H i in Equation (2). Panel B of Table 2 shows that coefficients of both instruments, separately or jointly, have the expected signs. Men married to women who work for small firms (whose wives have a family health insurance policy) earn about 4% 5% less (more). This perhaps indicates that men whose wives work for larger firms and have family insurance do not have a need for employer-provided health insurance and seek higher paying jobs without insurance. For the sample of women, the coefficients of husband working for a small firm have the expected sign but are insignificant. Women whose husbands have a family insurance policy earn about 5% more. Table 3 reports heteroskedasticity-robust IV/2SLS estimates of wage/health insurance coverage trade-offs for working married men and married women, separately. The results are presented according to the identification exclusion restrictions. Row A presents the estimated trade-offs when spousal firm size is the excluded variable (the instrument). Row B reports the trade-off results when spousal family coverage is the instrument. Row C includes both instruments. Coefficients of job- and health-related variables are also reported for the specification in Row C. Column arrangements are the same as in Table 1, each column representing a different model

11 810 ECONOMIC INQUIRY TABLE 3 IV/2SLS Estimates of the Effects of Health Insurance Coverage on the Natural Logarithm of Annual Earnings: Married Men and Married Women Married Men Alternative Specifications Married Women Alternative Specifications Variables (1) (2) (3) (4) (1) (2) (3) (4) Own employer-provided health insurance A. Instrument: **.515**.529** Spouse s firm size B. Instrument: ** ** *.122***.198** Spouse has family coverage C. Instrument: ** ** ** * Spouse s firm size and family coverage (2SLS) Job characteristics quality Job has paid sick leave.067**.066**.138*.128* Job has paid vacation leave.191*.199*.171*.177* Health status and health insurance variables Annual health expenditure (self, 10 3 ) Work-limiting disability.207*.199*.143***.132*** No. of half-days missed.002*.002* work (self) No. of half-days missed work (others) Contribution to premium **.022*.020***.020*** Total annual health-care benefits 10 3 Plan is a HMO.040** p-values chi-squared test of overidentification (orthogonality) of both instruments Notes: In addition to the variables shown in the table, each model includes own experience, tenure, and their squares and interaction; own education, spouse s education and wage income, as well as indicator variables for race, occupation, industry, other job characteristics, union membership, firm size, Metropolitan Statistical Area residency, region of residency, number of children under age 6, and number of children of ages See the text and Appendix 1 for details. *, **, and ***Significant at.01,.05, and.10 levels, respectively. specification. All specifications in Columns 1 4, for each gender, include human capital and other control variables discussed before. Estimated coefficients of these variables, not reported in Table 3 but available upon request, are reasonable and have the correct signs. These coefficients are robust across all specifications. In addition, all statistically significant variables in Columns 1 4 have their expected signs. The results of all three instrumental models, Rows A C and Columns 1 4, show that IV/ 2SLS estimates of the trade-off are negative, suggesting that accounting for the endogeneity of the health insurance variable corrects for OLS-biased estimates. The results of the models that use spousal firm size as the only instrument, Row A, are relatively large and significant only at the 10% level in the men sample and insignificant in the women sample. As predicted by our earlier discussion, these estimates probably overestimate the tradeoff resulting from assortive mating. When spousal family coverage, Row B, or spousal family coverage and spousal firm size, Row C, are included as instruments, the estimates of the trade-off are of the correct sign and are significant, except in Specification 2. The estimated trade-offs are similar between the two models that use family coverage alone or with firm size. For example, in Specification

15 814 ECONOMIC INQUIRY adjust for heterogeneity of jobs, variations in health status, and variations among other health insurance related measures, such as family plan and cost sharing. We find results consistent with the prediction of the compensating differential theory. We identified and tested four different models. Our overall estimated average trade-offs equal 16.5 and 20.0 percentage points for married men and married women, respectively. Out-of-pocket premiums increase annual earnings by 2.2% and 2.0% for men and women, respectively. The estimated gender-trade-off differential is about 3.5 percentage points. Decomposition of the gender-pay gap shows that about 3% of the explained differentials can be attributed to employer-provided health insurance. Health insurance does not appear to contribute to the unexplained differentials or statistical discrimination. APPENDIX 1 Medical Expenditures and Benefits: Amounts and Proportions by Gender and Age Group, Ages Age group Male Female Difference Male Female A. Total expenditures (\$) No. of observations , * ,031 1,048* 4,562 5, ,914 2, * 2,254 2, ,453 3, ,683 1, ,571 4, ,890 2, * 9,532 10,560 B. Percentage of the nonzero medical expenses * * * * * * C. Total benefits (\$) , * , * ,544 1, * ,843 2, ,714 3, ,532 2, * D. Medical benefit as a percent of medical expenses * * * * * E. Insurance premium by type of coverage and gender of the policyholder (\$) No. of observations Single coverage \$30 1,949 2,108 Family coverage 1,673 1, * 2,776 1,762 Notes: Source: U.S. Department of Health and Human Resources, Agency for Healthcare Research and Quality, Household 2001 Full-Year Consolidated Data File, MEPS HC-060 and HC-057. *Signifies differences between male and female are significant at.05 or less.

16 DANESHVARY & CLAURETIE: GENDER DIFFERENCES IN THE VALUATION 815 APPENDIX 2 Sample Means and Standard Deviations: Married Men and Married Women Male Female Variables Mean Standard Deviation Mean Standard Deviation Annual wage income 41,797 31,105 32,807 24,162 Personal characteristics Prior experience Experience with current job Education Black 0.09 n/a 0.10 n/a Hispanic 0.17 n/a 0.15 n/a No. of children under No. of children Residence Metropolitan area 0.79 n/a 0.78 n/a Northeast 0.16 n/a 0.16 n/a Midwest 0.24 n/a 0.25 n/a South 0.35 n/a 0.36 n/a West 0.24 n/a 0.23 n/a Job characteristics Federal government 0.04 n/a 0.03 n/a State/local government 0.11 n/a 0.21 n/a Union member 0.16 n/a 0.11 n/a Small-size firm 0.57 n/a 0.60 n/a Medium- and large-size firm 0.43 n/a 0.40 n/a Part-time workers 0.02 n/a 0.10 n/a Hours worked per week Job characteristics ( quality of job) Paid sick leave 0.64 n/a 0.65 n/a Paid vacation leave 0.74 n/a 0.70 n/a Health status and health insurance variables Annual health expenditure 4,502 2,525 4,591 (self) 1,712 Work-limiting disability 0.02 n/a 0.03 n/a No. of half-days missed work (self) No. of 1/2-days missed work (others) Employer-provided 0.75 n/a 0.57 n/a health insurance Family plan 0.61 n/a 0.40 n/a HMO plan 0.47 n/a 0.48 n/a Contribution to health 971 1, ,238 insurance premiums Total health-care benefits 2,720 5,929 1,931 4,928 No. of observations 3,723 3,042 Notes: Industry and occupation variables are not shown. Source: U.S. Department of Health and Human Resources, Agency for Healthcare Research and Quality, Household 2001 Full-Year Consolidated Data File, MEPS HC-060 and HC-057. n/a, not applicable.

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