1 Estimation of Union-Nonunion Compensation Differentials For State and Local Government Workers William Even Raymond E. Glos Professor of Economics Miami University Oxford, OH David Macpherson E.M. Stevens Professor of Economics Trinity University San Antonio, TX July 2013
2 This paper describes the data sources and methods used to compute compensation differentials between union and nonunion employees of state and local government. It also describes the regression methods used to estimate the compensation difference between union and nonunion state/local government employees for each of the 50 states and D.C. Hourly wages. Data sources. Hourly wages are drawn from the monthly Current Population Survey Outgoing Rotation Group (CPS-ORG). Hourly wages are calculated as usual weekly earnings divided by usual weekly hours unless the person reports that work hours vary. In this case, hourly wages are defined as usual weekly earnings divided by hours worked last week. Usual weekly earnings in the public use CPS-ORG files are top coded or capped at a maximum value, $2,885 ($150,000 annually). The analysis addresses the problem of top codes by estimating mean earnings above the cap, which the enables us to calculate more accurate measures of mean hourly earnings. The mean of the open-ended category of weekly earnings is estimated by assuming that its upper tail follows a Pareto distribution. The parameters of the Pareto distribution are estimated separately by gender and year, based on workers above the median. The sample is restricted to full-time workers who are 18 or over and employed in the state or local government sector. Excluded from the sample are employees of the federal government, self-employed workers, anyone who has earnings imputed, and workers who report hourly earnings that imply an hourly wage below the state minimum wage. All earnings are converted into 2012 dollars using the Consumer Price Index for all urban consumers. Fringe Benefits We use data from several sources to estimate the employer s contributions for health insurance, pensions, retiree health insurance, and legally required contributions for fringe benefits. Since reported weekly earnings in the CPS-ORG are likely to include compensation for sick, vacation, and supplemental pay, we do not adjust earnings for those fringe benefits. The methods for estimating each of these fringe benefits are discussed below. An important data source for estimating the value of fringe benefits is the 2010 Employer Cost of Employee Compensation (ECEC). 1 Using unpublished data provided by the Bureau of Labor Statistics, we obtained estimates of the average hourly cost of fringe benefits for each of the 9 census divisions for state and local workers. There are 8 job cells based on occupation for each census division resulting in a total of 72 job cells. 2 1 A description of this data can be found at 2 In some cases, the BLS data do not provide estimates for detailed occupations and occupations had to be aggregated to higher levels to obtain an estimate. For example, if there wasn t an estimate provided
3 Health Insurance. The CPS-ORG data does not contain information on health insurance coverage. To estimate coverage for workers in the CPS-ORG, we draw data from the Current Population Survey Annual Social and Economic Supplement (CPS-ASE). The CPS-ASE survey, conducted annually in March, provides information on health insurance coverage for all workers. Unfortunately, the CPS-ASE has information on union status for only the outgoing rotation groups which make up one-fourth of the sample. To improve sample sizes, we merge the March data to the June through April data to obtain union status for the other three quarters of the sample. To make the CPS-ASE and CPS-ORG as consistent as possible, we restrict both samples to full-time workers who are 18 or over and employed in the state or local government sector. 3 We use the CPS-ASE to estimate a probit model of the determinants of health insurance coverage. The probit model is estimated separately for union and non-union workers and includes controls for a cubic in age, education (8 categories), sex, occupation (22), race (3), Hispanic status, marital (7), hours worked (4), metropolitan population (7), state (51 since District of Columbia is included), and year (5). The probit estimates from the CPS-ASE are then applied to data in the CPS- ORG to estimate the predicted probability of health insurance coverage for each state and local worker in the CPS-ORG. To compute the hourly cost of health insurance for a given worker, we take the following steps. First, we compute the coverage rate for the relevant job cell using data from the CPS-ASE. An hourly cost of health insurance coverage conditional on coverage is then calculated as the hourly cost estimate for the relevant job cell derived from the ECEC divided by the estimated coverage rate for that job cell. 4 To compute the predicted cost of health insurance coverage for a given worker in the CPS-ORG, we multiply the predicted probability of coverage by the hourly cost of health insurance conditional on coverage for their relevant job cell. 5 Retiree Health Insurance for SOC code 49 (installation, maintenance and repair), we used the estimate for the broader category of (natural resources, construction, and maintenance). 3 Since the CPS-ASE questions on health insurance refer to the job last year, we also restrict that sample to full-year workers. To improve the chances that the job held in March (when union status is reported) is the same as the longest job last year (for which health insurance and pension coverage are reported), we also restrict the sample to workers who had only one employer in the prior year. 4 For example, if the hourly cost for pension coverage is $2 per hour but only one-half of workers are covered by a pension, the hourly cost conditional on coverage would be $4=$2/.5. 5 Keefe (2010) Biggs and Richwine (2011), Munnell et al (2011) also use ECEC data to estimate the value of health insurance.
4 The CPS-ASE does not provide information on retiree health coverage. We use information provided by Munnell et al (2011) to value Retiree Health Insurance. It is assumed that state and local workers who are eligible for health insurance coverage are also eligible for retiree health insurance. The average normal cost for retiree health in 2009 was 7.6 percent of payroll. After reducing the value by 50 percent because of the uncertainty of eventual receipt of retiree health and increasing the figure by 25 percent to reflect the value of having access to group instead of individual rates, the adjusted normal cost of retiree health in the public sector is value at 3.9 percent of earnings. Legally required benefits. The ECEC provides estimates of the hourly cost of legally required benefits for each job cell. The legally required benefits include Social Security, Medicare, federal unemployment insurance, state unemployment insurance, and workers' compensation. This is converted into a percentage of pay for each job cell by dividing by the average hourly wages in the ECEC. Using data on public pension plans (described below), we adjust legally required benefits to account for workers that are not covered. 6 For example, if only one-half of state and local workers are covered by Social Security, we reduce the employer s legally required contribution rate for Social Security by one-half of wages and salaries. Pensions. As with health insurance, the CPS-ORG does not contain information on pensions. As a result, we repeat the same process described above for health insurance to use data from the CPS-ASE to estimate the probability that each worker in the CPS-ORG has pension coverage. The same controls are used in estimating the probit models for health insurance and pension coverage. To estimate the value of employer contributions to pensions given coverage, we use data from the Public Plans Database (PPD) provided by the Center for Retirement Research at Boston College. 7 The PPD contains data on 126 state and local defined benefit (DB) plans and represents more than 85 percent of total state and local government pension assets and members. 8 The PPD also includes data for 20 state-administered defined contribution (DC) plans. 6 The percentage of state and local government workers with Social Security covered employment is available in Nuschler et al (2011) for each of the 50 states. 7 The Public Plans Database is available at We exclude 2010 data but it was incomplete and less representative of pensions than the other years. 8 The PPD covers 90 percent of all state government pension assets and members, but only about 20 percent for local governments.
5 For DC plans, for each state we estimate the average employer contribution rate to DC plans. For DB plans, we start with the reported normal cost in the PPD representing an actuarial estimate of the percentage of payroll that must be contributed to fund the benefit that is promised at retirement. The normal cost for a given DB plan is sensitive to the assumed rate of return, mortality rates for retirees, retirement age, and a host of other factors. Since employees frequently contribute to public sector DB plans, the employee contribution rate is subtracted from the normal cost to estimate the employer s share of normal cost. Most state and local pension plans assume an annual return of 8.0 percent when calculating normal cost. Several studies point out that this rate of return assumption is overly optimistic and should be adjusted to reflect the market risk inherent in the liabilities. 9 Thus, for example, if there is no chance that the state or local government would default on the pension payments, a risk free discount rate (e.g. the return on U.S. Treasury bonds) should be used. As noted by Novy-Marx and Rauh (2009), if there is some chance of default on pension promises, the appropriate discount rate for valuing liabilities should match the rate of return on a portfolio of bonds that would generate the same stream of payments with the same chance of default in different states of the world. 10 If the state cannot default on its pension promises, the return on a portfolio of risk-free treasury bonds would be an appropriate discount rate. If the probability of default on pension promises is similar to that for state debt obligations, the taxable yield on a portfolio of state municipal bonds would be appropriate. 11 Recent studies of the public sector wage differential correct for the overly optimistic discount rate assumption by adjusting the normal cost to reflect a risk free interest rate. 12 The size of these adjustments can be quite large. For example, Biggs and Richwine (2011) estimate changing the assumed rate of return from 8 to 4 percent would cause the normal cost to more than triple. To adjust for overly optimistic rates of return, we calculate a markup for reported normal cost to reflect a 4 percent rate of return which is slightly above the historical average for the risk free rate of return on treasury bonds. The calculation for a given plan is made for a worker with the plan s average age for active workers retiring at the plan s average age of retirement with mortality matching that for the U.S. population. 13 To describe how the calculation is performed, suppose that a worker of age A 9 See, for example, Novy-Marx and Rauh (2009, 2011), and Brown (2009). 10 The choice of an appropriate discount rate for pension plans is also discussed in Brown (2009), Petersen (1996) and Biggs and Richwine (2012). 11 Since state municipal bonds are tax exempt, the equivalent taxable yield can be calculated by dividing the tax exempt rate by (1-t) where t is the relevant tax rate. 12 See, for example, Biggs and Richwine (2011) and Munnell et al (2011). 13 See McGill (2005, p. 628) for a description of how normal cost is calculated and how the assumed rate of return enters the calculation.
6 accumulates an additional $1 of pension benefits that will start at age R. cost of this additional $1 of benefit obligation is given by The normal ( ) ( ) where r is the interest rate and α(r,r) is the price of a $1 life annuity starting at age R. A higher assumed interest rate reduces normal cost by reducing the cost of a $1 annuity at retirement and by reducing the amount of money that must be invested today to cover the cost of any given annuity. The mark-up to normal cost is calculated by computing the ratio of normal cost with the 4 percent discount rate to that with the actual return assumed by the pension plan. The normal cost calculations are for a worker whose age matches the average age of active workers and whose retirement occurs at the average age of retirement reported by the pension plan. For each plan, we compute normal cost with and without markup for the 4 percent discount rate. We then compute a state-specific value for normal cost as the participant weighted average of normal cost across plans for that state. To compute the employer s share of normal cost for a given worker, we multiply the predicted probability of coverage times adjusted normal cost net of employee contributions. Paid leave and vacation. The earnings report in CPS-ORG includes usual weekly earnings from the employer. If, however, workers receive different amounts of paid or vacation time, an adjustment should be made to reflect the differences. For example, if two workers have identical earnings for the year and one receives no paid vacation and the other receives 4 weeks of paid vacation, the latter person is receiving a higher level of compensation. To adjust compensation to reflect differences in paid time off, we estimate how much a person would have earned if they had not taken any time off. To make this calculation, we use the ECEC to estimate the fraction x which is defined as the hourly cost of paid leave as a fraction of total earnings (wages + supplemental pay + paid leave). We then estimate the adjusted level of compensation by dividing total earnings by (1-x). For example, if a person reports $1,000 of total weekly earnings and 20% of earnings are for paid leave, the person s adjusted annual compensation is $1,000/(1-.2)=$1,250. That is a person who earns $1,000 per week for working 80% of the year would earn $1,250 per week if they worked 100% of the year. 14 Estimating the Union-Nonunion Differential in Compensation. 14 Podgursky and Tongrut (2006) adjust hours worked instead of annual pay to account for differences in paid leave across jobs using the ECEC estimates of the share of total earnings due to paid leave. Either approach implies the same hourly wage for work hours.
7 To estimate the public-private pay differential, we use a regression method to control for other factors that might result in pay differences. The regression model is where the subscript i indexes workers, is the natural log of annual compensation, is a dummy variable indicating that the worker is covered by a collective bargaining contract, is a vector of characteristics describing the worker, and is an error term that is assumed to be independently and identically distributed across workers. A separate regression is estimated for each state. The coefficient corresponding to the union coverage dummy variable ( ) is the estimate of the union premium or penalty in log points. To convert the estimate of the differential expressed in log-points to a percentage point differential, we calculate ( ) For example, if the estimate of is.1, union workers earn a.1 log point premium, which converts into a 10.5 percentage point advantage. The control variables included in our regression analysis match those used in several other studies of the union differential in compensation. The controls are as follows: (1) a quadratic in potential work experience (age years of schooling -6) (2) 8 different education categories; (3) sex; (4) 3 race categories (white, black, other); (5) controls for that earnings were measured in the CPS-ORG; (6) 22 occupation categories; (7) 7 marital status categories; (8) 7 categories for metropolitan population and rural residence; (9) 4 categories for hours worked (35-39, 40-44, 45-49, and 50 and over). Results The results for our analysis are summarized in an excel spreadsheet. Table 1 contains sample means for compensation and worker characteristics by state and for the U.S. Table 2 contains estimates of the union-nonunion premium for hourly earnings (wages without fringe benefits) and compensation measured in log-points and after conversion to percentage points. Estimates are provided by state and for the U.S. as a whole. Table 2 also contains t-statistics for the estimated differentials, 95 percent confidence intervals for the estimates, and sample sizes. Table 3 contains estimates of the differential by state for 3 education groups. Table 4 has estimates of the differential by state for 5 occupation groups. Appendix table 1 contains the coefficient estimates for all the control variables included in our estimates of the differential by state that are reported in table 1. It provides regression estimates for each state using either earnings or total compensation as the dependent variable.
8 References Biggs, Andrew and Jason Richwine. Public vs. Private Sector Compensation in Ohio. Report submitted to Ohio Business Roundtable. September Brown, Jeffrey R., and David W. Wilcox "Discounting State and Local Pension Liabilities." American Economic Review 99, no. 2: Keefe, Jeffrey Debunking the Myth of the Overcompensated Public Employee: The Evidence. Economic Policy Institute Briefing Paper #276. McGill, Dan M. Fundamentals of Private Pensions. Oxford: Oxford University Press, Munnell, Alicia; Jean-Pierre Aubry, Josh Hurwitz, and Laura Quinby. September Comparing Compensation: State-Local versus Private Sector Workers. Center for Retirement Research at Boston College, Report 20. Novy-Marx, Robert, and Joshua Rauh. The Liabilities and Risks of State-Sponsored Pension Plans. Journal of Economic Perspectives 22 (Fall 2009): Public Pension Promises: How Big Are They and What Are They Worth? Journal of Finance 66 (August 2011): Nuschler, Dawn, Alison Shelton, and JohnTopoleski. July Social Security: Mandatory Coverage of New State and Local Government Employees. Congressional Research Service Report Available at Podgursky, Michael, and Ruttaya Tongrut "(Mis-)measuring the Relative Pay of Public School Teachers." Education Finance And Policy 1, no. 4: