4. Steps in Estimating a High School Graduation Shadow Price for the United States
In this article, we draw upon both WSIPP work and Boardman et al.
) to derive a current estimate of the total social value of a high school graduation. Boardman et al.
) updated the earlier WSIPP graduation shadow price by incorporating more recent earnings data. They also presented shadow prices for several different social discount rates. Here we reprise, review, and update the steps needed to derive a high school graduation shadow price and show how these kinds of shadow prices can be derived using information from a number of diverse sources.
Developing a shadow price for high school graduation involves nine steps. Performing all of them produces an estimate of the present value of net benefits that accrue directly to those graduating and indirectly to the rest of society. Step (1) is to predict earning increments for people with increasing levels of educational attainment over their working lives. Step (2) is to add an estimate of the value of fringe benefits to earnings in order to estimate the full economic value of compensation (“full compensation”) to individuals, as this is the appropriate measure of employee benefits from employment over employees’ working career. Step (3) is to adjust the expected value of full compensation for the effect of predicted real economic growth over a life cycle. Step (4) is to adjust the estimates to take account of mortality risk during the working lives of individuals. Step (5) is to net out the effects of educational attainment on earnings from those deriving from individuals’ initial cognitive and other endowments, as we are interested in the causal impact of the former. Step (6) is to discount earning gains to 2019 dollars in order to obtain current estimates of the present values of both costs and benefits, and of net benefits. Step (7) is to specify some alternative paths to further higher levels of education that are contingent on high school graduation and that thus only become available with achievement of graduation. Step (8) is to adjust estimates to take into account the costs of education. The final and ninth (9) step is to consider the potential external impacts (positive or negative externalities) that flow from changed productivity (which are expected to be an increase) over time; these are the benefits and costs that accrue to other members of society. In order to structure the discussion that follows, Table 1
summarizes the nine steps as well as the major sources for deriving each step (columns one and two respectively). In the third column, the table comments on some weaknesses of the currently available data and methods at each step. As well, it summarizes some “wish list” items for further research that would confirm, improve, or augment the estimates we provide here (which are italicized in the table).
We now explain the basis for each of the nine steps and the major sources for each of them. These data are not perfect (as is normally the case!). So, in the spirit of fostering the dissemination of shadow prices that might be usable in other CBA studies, we discuss both the weaknesses and potential improvements or augments to the value of the high school graduation shadow price.
(1) Life-Cycle Earnings by Educational Level
Conceptually, the social valuation of all increments to education begins with its effect on the productivity of individuals: better-educated workers are generally more productive, so that their labor produces greater value to the economy. Most of the value of that increased productivity accrues to employed individuals themselves, but some accrues to other members of society. The starting point for assessing productivity, therefore, is earnings, which depend on wages set by the marginal contribution of the worker to the value of output. Incremental earnings for higher levels of education reflect greater productivity.
WSIPP used data from the Community Population Survey (CPS) for the years 2002–2010 to estimate average earnings by age cohorts for people with four distinct levels of education: less than high school diploma, high school diploma, some college (including associates degrees), and four-year college or more advanced degree. In this analysis, we are primarily interested in high school graduation, but briefly discuss other levels of attainment because the various sequential levels are inextricably linked. As explanatory variables, the WSIPP model included both age and the square of age (a quadratic function), as well as indicators for years. Boardman et al.
) added data for years 2011–2014 and also re-estimated the model. Following WSIPP, they used the total value of personal earnings (PEARNVAL) as the dependent variable. It was derived from the March Supplement updated to 2016 dollars, using the U.S. Bureau of Labor Statistics (BLS) implicit price deflator. These earnings were weighted using basic standard socio-demographic probability factors (the variable MARSUPWT). The CPS data included individuals with no earnings and, therefore, the estimates took account of expected labor force participation (LFP) over individuals’ normal working years. Boardman et al.
) ignored part-time earnings, assumed on-time college graduation, and assumed zero earnings for both those aged 18 and 19 (for those with some college) and for those aged 18 to 21 (for those with a college degree). For age groups, Boardman et al.
) set the age 24 earnings at the real value estimated from the 2014 CPS; in other words, they used 24 as the reference point age in their model. They then predicted earnings for ages over 24 using the estimated equations. Earnings for those younger than 24 years were also taken for each group from the 2014 CPS.
This approach assumes that the estimates of the effects of age and education on earnings in recent years provide good predictions of these effects in the future. Demographic trends, such as the ageing of the population, and economic trends, such as increasing use of artificial intelligence and robots, may eventually change the underlying relationships between education and earnings. Accurately predicting such trends and their impacts is beyond the capabilities of social science. Fortunately, the discounting process we discuss in step 6 places greater weight on nearer term impacts less affected by trends. Nonetheless, the possibility of major shifts in the structure of the economy introduces uncertainty beyond that accounted for the sort of evidence-based analysis we present here.
Note that it would be possible to develop the relationships of earnings to age conditional on demographic characteristics as well as education attainment. For example, it could be that, specifically, in the U.S. context, the earnings of African Americans and other minorities depend more on high school graduation than do the earnings of whites. As most competent CBAs seek to measure benefits as the aggregation of the benefits and costs borne by individuals with standing, the higher earnings would be relevant for assessing the efficiency of a policy that differentially increases the graduation rate of African Americans. Most analysts would regard this finding as worth reporting. However, the corollary is that the effect of education on earnings is not as large as for whites. Would the politico-bureaucratic environment allow analysts to value other groups’ high school graduations less than for African Americans? These valuation questions are not purely hypothetical as is shown by the proposal of the Environmental Protection Agency to value mortality risk reductions more for younger than older people (Aldy and Viscusi 2007
(2) Adding Fringe Benefits to Estimate the Value of Total Compensation
Earnings do not fully capture the cost of labor to firms and therefore differences in earnings alone underestimate the value of gains in productivity to society. Additionally, firms not only pay wages, but also usually provide additional employment benefits, such as health insurance and retirement contributions. Estimates of the value of productivity gains from educational increments to the employed should be based on total compensation; that is, on dollar earnings plus the estimated dollar value of all fringe benefits. There is a significant difference in the value of earnings and total compensation to individuals. The WSIPP derived an average ratio of total compensation to wages of 1.441, using BLS data on the percent of total compensation paid to civilian workers as wages. Boardman et al.
), however, estimated the ratio of total earning to wages to be somewhat higher at 1.462. They then multiplied wages for an education level and projected age category by this ratio (United States Bureau of Labor Statistics 2017
Using contemporary estimates of the value of fringe benefits to predict future total compensation may introduce error in out-year predictions if the structure of the economy changes. For example, many so-called gig jobs, such as Uber and Lyft driving, do not provide the sort of fringe benefit packages commonly offered by conventional firms. If the proportion of the workforce in the gig economy grows, then the contemporary estimates of fringe benefits are likely to lead to overestimates of full compensation in future years.
(3) Adjusting for Predicted Real Growth in Total Compensation over Time
Both earnings and fringe benefits can be expected to grow in real terms over time as technological improvements increase the productivity of workers to some extent, either immediately or eventually. However, there is considerable evidence that technological change has differential effects on the value of labor for workers at different levels of education (Moretti 2004
). For example, technological change that induces plant automation almost certainly reduces the relative value of the labor of less-educated workers compared to that of more-educated workers (Doms et al. 1997
; Riddell and Song 2017
). Predictions of future earnings and total compensation, therefore, should try to take account of secular changes in productivity related to technological change and other related factors.
In terms of making plausible predictions about future productivity, the devil is in the implementation details. The most straightforward approach to predicting changes in future (real) earnings is to assume that the rate of change will continue to follow recent trends. WSIPP analysts estimated growth rates in real earnings and the ratio of total compensation to earnings based on time series analyses of annual data over the last six U.S. business cycles (a relatively long time period). Boardman et al.
) used the WSIPP estimates for the real annual growth rate in earnings. Most relevantly to this analysis, they estimated the change to be negative at −0.0062 for those without a high school diploma as against positive 0.0053 for those with a high school diploma. They also used the WSIPP estimate of 0.00041 for the annual growth rate in the total compensation to earnings ratio. Using these assumptions, they projected average real total compensation by age. Their estimates are averages at particular ages and, therefore, took into account an estimated LFP rate at particular ages; that is, they accounted for the zero earnings of those who are not employed. Workforce participation is predicted to decrease at older ages for all educational levels, so average earnings eventually decrease even for more highly educated groups that are predicted to enjoy positive real growth in wages. As with earnings and total compensation, predicting real wage growth assumes historical continuity.
pulls together these three initial steps in order to summarize the ratios of earnings for high school graduates, those with some college, and college graduates relative to the earnings of those who have not graduated from high school. These further levels of education are relevant to this analysis because almost all further education requires high school completion. Table 2
further disaggregates these ratios to the ages 30, 40, 50 and 60. As one would expect, given our discussion and the evidence, those ratios are consistently larger for a higher level of educational attainment at any age. Also as one would expect, the ratios increase in size with age. For example, on average at age 30 years those who graduate from high school—but obtain no further education—earn 1.54 times more than those who do not graduate from high school. This ratio grows to 2.25 by age 60. In sum, high school graduation pays off for employees. Furthermore, the individual gains from high school graduation (perhaps surprisingly) are somewhat equally spread over a working life, even though one might expect them to decline more quickly than they would at any higher level of education.
(4) Adjusting Estimated Earnings to Account for Predicted Early Mortality
demonstrates that productivity gains accrue over the whole working lives of individuals. As a starting point, it is reasonable to assume that people continue to work to the assumed standard age of retirement. However, some people die before they reach retirement age, unfortunately terminating the productivity gains that derive from education or anything else. To take account of the risk of premature mortality, each year of earnings is weighted by the probability of surviving to the next year. As these probabilities are solely based on age, they do not take account of important demographic differences, such as gender (Arias 2014
). Further, and most relevant to this analysis, using undifferentiated survival probabilities assumes that mortality risk is not causally related to education level. There is certainly a positive association between better health and higher levels of education (Goldman and Smith 2011
; Deaton 2015
). However, the causal
relationship of education on health—including mortality—is much more complex. Nonetheless, a higher education level almost certainly contributes to greater longevity and other positive behaviors and outcomes (the “health gradient”) though there is likely some reciprocal causality with better health contributing to educational attainment (Haas 2006
). Ignoring this, almost certainly results in a bias that underestimates the productivity gains deriving from education (Cutler and Lleras-Muney 2010
). However, the impact of these mortality differences is likely to be less important for young age cohorts. Furthermore, the impacts of the mortality difference on the present value of productivity gains are likely to be relatively small because of discounting.
(5) Netting out the (Non-Educational) Causal Effects
Superior cognitive, non-cognitive, health, and other endowments may make some individuals more productive than others at any level of education. Fortunate individuals with better cognitive and health endowments may very well have had earnings like others at their education level, even if they had not attained that level. Consequently, the difference in total compensation between high school non-completion versus completion risks overestimating the causal effect of moving from a lower to a higher level of educational attainment. Based on earlier analysis by Heckman et al.
), WSIPP provided an estimate of the causal effect of cognitive and other endowments versus those that can be reasonably be attributed to educational attainment. More recently, Boardman et al.
) employed the same causal factors as employed by WSIPP and applied them to high school graduates relative to those that did not graduate. They applied a causal effect of 50 percent to the present value of total compensation gains for those graduating from high school relative to the gains of those who drop out. In other words, half of the compensation gains were attributed to cognitive and other endowments rather than to educational attainments. Along the same lines, they imputed causal effects of 56 and 42 percent to the gains from some college relative to high school graduation and college degree or higher relative to some college, respectively.
Estimating the causal effect of educational attainment from observational data is challenging, requiring a number of modeling assumptions and the application of sophisticated econometrics. Additional efforts employing different data and methods would be welcome to increase the robustness of estimates of the causal effects of educational attainment.
(6) Discounting the Predicted Compensation Streams
When policies have costs and benefits that vary over time, CBA values them in terms of their present values, and ultimately in terms of the net present value (NPV). Present values of policies with long time horizons are quite sensitive to the selected social discount rate level. Estimates based on people’s willingness to trade current for future consumption (the marginal rate of pure time preference) tend to be lower than estimates based on the opportunity cost of public investment (the marginal rate of return on private investment), although the gap has been narrowing; estimates can also be modified based on optimal growth models (Moore et al. 2013
The present value of the benefits of high school graduation is found by discounting the benefits over the 18–65-age range. Note that, although this age range is conventionally used to define the working life, there is actually considerable variation. As long as there is no systematic relationship between educational attainment and length of working life, this variation will have only a small impact on the shadow price estimates. However, if there is a relationship, such as much later retirement by those with higher educational attainment, then there could be a more substantial effect on the shadow price. Specifically, if those with higher educational attainment tend to work longer, then the estimated shadow price will be too small.
We do so initially separating the individual (private) benefits from the external (public) benefits as this facilitates replication or further adjustments. Table 2
which we discuss below in detail shows calculations including 3 percent and 7 percent, the dual discount rates recommended by the Office of Management and Budget (OMB) for use in regulatory CBAs (United States Office of Management and Budget 2003
(7) Specifying Pathways across Different Educational Levels
In a world where high school graduation was the only sheepskin effect, the difference in the present value of lifetime productivity of those who have—as against those who have not—graduated from high school would appropriately measure the total productivity gains from education. However, the completion of high school is a required gateway for most of the options for further levels of education and, therefore, for additional gains in productivity that are essentially contingent on achieving high school graduation.
WSIPP used percentage estimates of expected value of these mostly sequential options that were specific to Washington State. Their percentages were 26, 38, and 36, respectively, for the three levels of educational attainment. To develop a U.S. national estimate, Boardman et al.
) used data from the CPS. Using it, they estimated that, conditional on earning a high school diploma, 34 percent of those who graduated obtained no further formal education, 31 percent went on to obtain some college, and 35 percent continued on to earn a bachelor’s degree or higher. In sum, they estimated that nationally 66 percent of graduating high school students pursued some additional higher education, which is, not surprisingly, somewhat lower than the 74 percent found in Washington State.
As will be clear from the differences in probabilities between the Washington state and national educational pathways, the national shadow price can differ from that estimated for particular states. The pathways may also differ among local jurisdictions. Ideally, analysts should use the particular pathway probabilities relevant to the affected population of the policy being assessed. As these probabilities can be readily altered, this is one adjustment that most analysts would be able to make provided they have local data on educational paths available.
A more fundamental adjustment would be to relax the assumption that all post-secondary education occurs immediately after high school graduation. In practice, some adults will go on to obtain higher education after some period of employment. Estimates of the frequency of later attainment, as well as the assumption that later attainment has the same effect on productivity as earlier attainment, would allow these less traditional paths to be built into the shadow price estimate.
(8) Adjusting Estimates to Account for Educational Costs
Education involves both an opportunity cost for the student and imposes real resource costs on society. The WISPP analysis assumed that the marginal cost of completing high school is zero––that is, there would be negligible real resource savings by schools from each additional drop out. However, Boardman et al.
) estimated the opportunity cost to students from undertaking incremental study by assuming zero earnings for ages 18 and 19 for those who obtained some college and for ages 18 through 21 for those who obtained a college degree or higher. They calculated that the present value of the resource cost of education by discounting an average annual cost of college of $
19,281 for two-year colleges for those with some college and $
28,043 for four-year colleges over these age ranges (Ginder et al. 2016
). As with educational path probabilities, these costs can be readily updated by calculating the present value of annual incremental changes and subtracting their present value from shadow price.
(9) Adjusting Estimates to Account for Externalities
The higher earnings resulting from greater productivity can also create important external benefits (we assume there are no external costs or that they are already netted out). High school graduation raises what would otherwise be relatively low wages. As a consequence, it can reduce participation in crime, improve consumption and fertility choices, and enhance intra-family productivity. The evidence shows it normally does (Haveman and Wolfe 1984
; Wolfe and Haveman 2001
; McMahon 2018
). The WSIPP analysis drew upon a number of studies to specify a range of external benefits, expressed as a fraction of total compensation and estimate that range as being between 0.13 and 0.42 (Acemoglu and Angrist 2000
; Breton 2010
). WSIPP considered 0.37 to be the modal value of these external benefits (Belfield et al. 2011
Taking account of the externalities of educational attainment raises a number of shadow price estimation questions. First, is it reasonable to assume that externalities are proportional to total compensation across the income range? We think it is reasonable that external benefits, such as reductions in crime, would come disproportionately from increases in total compensation going to lower income individuals. Second, there might be non-market benefits, or “internalities,” that increase with education. For example, educational attainment almost certainly enables people to be more informed consumers. More speculatively, it is possible that educational attainment contribute to more effective participation in public affairs that increases the overall efficient use of resources. Evidence-based answers to these questions would have value in policy analysis beyond the estimation of the shadow price of high school graduation.