The Output of the Education Sector as Determined by Education’s Effect on Lifetime Income 1
Barbara M. Fraumeni Bureau of Economic Analysis
[email protected]
Brookings Program on Output and Productivity Measurement in the Service Sector WORKSHOP ON MEASURING THE OUTPUT OF THE EDUCATION SECTOR April 7, 2000 BROOKINGS INSTITUTION WASHINGTON, DC
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This paper represents views of the author and is not an official position of the Bureau of Economic Analysis or the Department of Commerce.
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I. Introduction
The importance of the education sector is unquestioned, yet measures of the output of this sector remain fairly basic and fail to capture the essence of what differentiates this sector from most other sectors in the economy: its role in human capital formation. The approach of Jorgenson and Fraumeni to measuring the output of the education sector clearly recognizes this difference. It is an approach that is firmly rooted in an underlying nonmarket production account and in the principle that the output of the education sector is an investment good--whose value is determined from estimates of lifetime income.2
Jorgenson and Fraumeni include only formal education activities in the education sector because of data constraints. Individuals are considered students if they are included in enrollment statistics collected by the statistical agencies; individuals self-report number of years of school completed. Enrollments in some courses are probably not captured in the data, e.g. courses not leading to a degree such as hobby and training courses, including on-the-job training courses. Self-education is not covered. Time spent in educational activities as measured by JorgensonFraumeni (J-F) include time at school and study time, but not uncompensated time spent by others to help students.
The primary purpose of this paper is to stimulate a debate about the conceptual and methodological features of the Jorgenson-Fraumeni approach. Aside from the discussants Michael Rothschild and Frank Wykoff, the profession has been largely silent.3 The secondary purpose is to summarize certain elements of this approach and to describe some methodological details not covered elsewhere.4 The critical first step in the debate is to discuss whether the 2
Jorgenson and Fraumeni assume all of the output of the education sector is investment although arguably there is a consumption component to education, e.g., students enjoying being with their fellow students. The investment-only assumption reduces the complexity of the measurement problem and has little impact on the magnitude of the estimates as the consumption component is arguably very small relative to the investment component. Accordingly the terms “investment in education” and “output of the education sector” are used interchangeably. 3
See Rothschild (1992) and Wykoff (1998).
4
This paper is a companion piece to J-F (1992b), not a stand-alone paper.
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output of the education sector should be treated as an investment good. If the general conclusion of this discussion is in the affirmative, then there are a number of other issues to debate. II. Magnitudes and the Investment or Consumption Decision
Although published J-F estimates of the output of the education sector have been available for over a decade, concepts and methodology underlying these estimates have not yet been widely accepted.5 The hesitancy to accept the concepts and methodology is likely largely due to the size of the estimates. Accordingly, this issue is raised up-front even though the conceptual and methodological issues are of primary importance. The appendix tables highlight the magnitude of the J-F estimates by comparing the size of estimates for household or nonmarket satellite accounts. This comparison is relevant as investment in education by individuals is a nonmarket activity which is one component of the J-F nonmarket accounts. The J-F estimates appear to be an outlier at 312.7% of GDP. However, as is demonstrated in the appendix, once adjustments are made for differences in coverage, the differences between the estimates come down to whether some uses of time are treated as investment or consumption.
Accordingly, the critical question for this paper is whether the output of the education sector should be treated as investment, not the magnitude of the estimates. An investment good differs from a consumption good in that there is a future flow of services arising from the investment good, whereas consumption yields only current services. As a result, under the theory of investment, the amount that someone is willing to pay for an investment good, therefore its value, is determined by the present discounted value of the future stream of services, which can be measured by the income from that good. Implicitly others who are estimating the value of nonmarket time spent in education are assuming that the output produced by this time (and other inputs such as teachers, books, buildings, etcetera) is a consumption good. This is apparent from the fact that the others use the same wage rate to value time spent in education and other
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Estimates first appeared in J-F (1989a) "The Accumulation of Human and Non-Human Capital, 1948-1984," and "Investment in Education," (1989b). Estimates using the J-F methodology have been constructed for Sweden by Sofia Ahlroth (1997) and for the Australian Capital Territory (ACT) by the Australian Bureau of Statistics.
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activities. When an hour spent in washing dishes and going to school are evaluated at the same wage rate, it implies that the consumption value of the output produced by washing dishes is the same as the present discounted value of the output produced by educational activities. This is a reasonable assumption only if there is no future income from the education good, that all income is current, in other words a consumption good is being produced. III. Other Conceptual or Methodological Decisions
Once the proposition that the output of education is investment is accepted, the next question becomes how one implements this concept. J-F have made several conceptual or methodological decisions that other researchers might debate after they have made the “output-is-an-investmentgood” decision. Three of these are briefly discussed in this paper. The first, the most prominent of these decisions, is to value investment in education by the impact of completing another year of school on an individual’s lifetime income. Two individuals are compared.6 Both are of the same sex and age, and have completed the same number of years of education. However, one is enrolled in school and the other is not. The current and expected lifetime income of these two individuals is compared, the additional lifetime income earned by the individual enrolled in school is assumed to arise from the additional year of school about to be completed and is set equal to investment in education.7 A possible concern is the extent to which factors other than completing additional years of school impact on lifetime income. Notable among these is ability. Griliches (1970) and Griliches and Mason (1972) pursued this question of ability, income, and schooling. Their conclusion is that ability has little effect on income, but that schooling has a significant effect on
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In implementation, each cell of the data set which is cross-classified by sex, single year of age, and single year of education contains some number of individuals, so comparisons are across two groups of individuals. 7
It is assumed that enrolled individuals complete the year of school in which they are enrolled. Although theoretically one should be able to link enrollment with years of school completed to form a flow/stock relationship, the two sets of data do not tell a consistent story. A symptom of the apparent problems linking the two data sets is the “rose-colored glasses” effect. As individuals get older some significant portion of them report they have completed more years of education, even though they have not enrolled in school over the relevant time period.
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income. Another factor is work experience. It would be ideal to hold the number of years of work experience constant when making the investment in education calculation, as well as sex, age, and years of school completed, but again data constraints limit the possibilities. Other possible factors are summarized in a Journal of Economic Literature article by Hanushek (1986) and considered by Griliches (1970) and his discussants: Conlisk and Nelson.
The second of the J-F decisions discussed in this paper is the decision to include both market and nonmarket income. The rationale for including the increment to nonmarket lifetime income as part of investment in education is to recognize that education contributes to both spheres: market and nonmarket. In addition, as investment in education is produced as a result of a nonmarket activity, e.g., going to school and studying, there is an inconsistency in proposing that the value of this activity not depend on nonmarket activities. However, the techniques used to value other nonmarket activities and the associated outputs are in many cases experimental. Some might argue that the uncertainty surrounding the estimates of the output of education should be reduced by considering only the market impact of education. This is not a view shared by J-F.
The third of the J-F decisions discussed in this paper is the decision to use the market wage opportunity cost approach to directly value the consumption and indirectly the investment output of nonmarket time.8 The opportunity cost approach is at the core of the over-arching lifetime income approach to estimating investment in education.9 The objections to the opportunity cost approach center around five considerations: 1) In practice, average market wages, not marginal wages, are employed, 2) The estimates tend to be higher than the estimates produced under the housekeeper approach, 3) Doubts about whether activities, particularly leisure activities, undertaken by a high-wage person should be valued at a higher rate than the same activity by a low-wage person, 4) Labor market conditions driving wage rates, therefore estimates of investment in education, and 5) The value of activities by individuals over the age of 74 are assumed to be zero. With average wages, arguably the value of nonmarket activities are 8
Investment in human capital is a function of nonmarket lifetime income and therefore indirectly depends on opportunity cost valuation. 9
See Fraumeni (1998) pp. 5-8 for an expanded discussion of various valuation approaches, including the opportunity cost and lifetime income approach.
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overstated. The difficulty of estimating marginal wages for all cells in the J-F data set necessitated the use of an average wage. Whether the opportunity cost approach results in estimates that are higher or lower than the housekeeper approach or the specialist approach is a moot question. The determinant of methodology chosen should be conceptual unless feasibility considerations over-ride conceptual considerations. In addition, there are problems with the housekeeper approach, the specialist approach, and the output-value approach. Opportunity cost is a basic foundation of economics commonly taught at the beginning of a principles class. The concept of opportunity cost maintains that a factor should be valued at the value of its bestforgone opportunity, which is a high-wage for a high-wage individual. Arguably, if a high-wage individual does not engage in leisure he will not be able to function as efficiently. The saying is: “All work and no play make Jack a dull fellow.” With regard to labor market conditions driving wage rates, the value of market goods in economic accounts are determined by supply and demand, therefore investment in education would follow the norm under the J-F methodology. Finally, the value of activities undertaken by individuals over the age of 74 are assumed to be zero as wage information historically has not been reported for this group. This is of little concern because the impact of this assumption on the estimates of investment in education are close, if not equal to zero. Any probably small amount of income earned by these elders would be even smaller when discounted back to the time when they attended school.
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IV. Thumbnail sketch of the estimation of lifetime income10
Lifetime income is estimated backwards from the oldest to the youngest individuals. In a given year, say 1980, lifetime income is estimated for those 74, then 73, then 72,..., then 0 (newborns). There are only certain broad categories of activities that J-F allow individuals of different ages to engage in. These are dictated by data constraints. The five life stages recognized and the activities allowed during them are: LIFE STAGES STAGE
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AGE
Stage 1: No work, no school
0-4
Stage 2: School, but no work
5-13(14)1
Stage 3: School and work
14(15)-341
Stage 4: Work
35-74
Stage 5: No school, no work
75 and over
In the most recent work on the J-F accounts, stage 2 ends at age 14 and stage 3 begins at age 15.
For those 74, who are in stage 4, there is only current income, so lifetime income is set equal to market and nonmarket labor income in a certain year, say 1980.11 For those 73, lifetime income is set equal to current income plus expected future income. Expected future income depends upon the probability of survival to the next age (74) and the current income of those one year older (74), in 1980. Expected future income is discounted and adjusted for the future growth in real income. In J-F (1992b) for all years the discount rate is 4.8% and the real income growth rate, which is applied to the wage rates, is 1.32%. Actual and future expected wage rates, hours worked, hours excluding work, school and maintenance time, and employment rates all enter in to the calculations. Similarly, for those 72, lifetime income is set equal to current income plus expected future income. Expected future income depends upon the probability of survival to the 10
The appendix to J-F (1992b) shows the specific equations used in the estimation of lifetime income. 11
Only labor income is counted in the calculation of market income.
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next age (73) and the expected lifetime income of the survivor who is one year older (73) in 1980. By working backwards in this way, the lifetime income of an individual depends upon the current income of that individual plus the expected lifetime income of an individual one year older. The calculations embed information about all older individuals in the given year. As a result, expected lifetime income depends on what is happening to older individuals in the year for which the calculation is being made, 1980 in this example. If the current situation does not well predict the future situation, e.g., survival rates or hours worked in the market change, then the lifetime income estimates will be inaccurate.
Once the calculation begins for those in stage 3, actual and expected school enrollment rates enter in to the calculations as well as the information entering into the stage 4 calculations. Significantly the separate equations used to calculate market and nonmarket lifetime income each have three parts: Part 1 for current income, Part 2 for those who are enrolled in school, and Part 3 for those who are not enrolled in school.12 The equations for stage 3 are the most complicated as both school and work are possible activities.
Since stage 2 individuals are assumed not to work, employment rates, hours worked, and wage rates no longer enter directly into the calculation.
In stage 1 and 2, although no current income is being generated, lifetime income is well-defined as the present discounted value of expected future lifetime income. Each year as individuals in this stage get older (if they survive), they are closer to stage 3, in which income, both market and nonmarket, is being generated. However, in stage 2 future income is being generated through investment in education. Consequently, lifetime income must be calculated for all individuals over the age of 4 to estimate investment in education as this investment is calculated as the impact on lifetime income of completing another year of school, as was previously described. 12
In the lifetime income equations in the appendix to J-F (1992b), the variables for part 1 are ymi and ynmi (yearly market and nonmarket income, respectively). The expression for part 2 begins with senr, the school enrollment rate, the probability that an individual is enrolled in school, and the expression for part 3 begins with (1-senr), one minus the school enrollment rate, the probability that an individual is not enrolled in school. As a final step, market lifetime income and nonmarket lifetime income are added together to determine total lifetime income.
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V. Inputs and Outputs Inputs to education include intermediate inputs such as books and supplies, capital inputs such as school buildings, desks, chairs, and computers, and labor inputs such as teachers and the time of students. On the input side the value of student time inputs dominates, amounting to 97.6% of the current value of all inputs in 1982 as reported in J-F (1992a).13 To determine the input value of student time, the value of all other inputs is subtracted from the value of the output of the education sector.
To calculate productivity as was done in J-F (1992a), an index of real output and input is needed. Real output is calculated as a translog index of student time weighted by the corresponding investment in education. Structures, equipment, labor inputs other than student labor input, student labor input, and intermediate inputs are deflated separately. Student labor input is student time, so the deflator used for this input component is identical to the output deflator. The index of real input is constructed as a translog index of intermediate, capital and labor inputs.
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See Table 2, pp. S56-57.
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VI. Conclusion There are a number of sectors in the economy, including education, whose output is difficult to measure. Unlike most of the other hard-to-measure sectors, estimating the output of the education sector requires thinking about nonmarket activities. There is always a reluctance to expand the boundary of the national accounts or to bring in to the core accounts estimates from satellite accounts, such as nonmarket or household production satellite accounts. However, student time, a nonmarket activity, is the crucial input to the educational process and it is the outcome of this process that determines the output of the education sector. In many ways measuring the output of the education sector is among the most difficult challenges as it requires this leap beyond the traditional set of national accounts.
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Appendix The calculations in this appendix support the conclusion that once adjustments are made for differences in coverage, the difference between the estimates comes down to whether some uses of time are treated as investment or consumption. Currently the J-F accounts assume that having a child and time in school and school work represent investment in human capital. Other investment in human capital could include child-rearing, non-maintenance time spent in healthimproving activities, on-the-job and off-the-job training, and informal education. The chart below relates estimates for household or nonmarket accounts to the size of GDP.14 Many, if not most of the components included in these accounts, are not part of GDP or a typical set of input-output accounts. These accounts expand the borders of traditional economic accounts with various imputations for nonmarket activities. Accordingly, there is no expectation that these estimates, in combination with omitted estimates which are in national accounts, sum up to GDP. The estimates are related to GDP to provide an approximate yardstick by which estimates covering different time periods can be compared. SIZE ESTIMATES FOR HOUSEHOLD OR NONMARKET ACCOUNTS AS A % OF CURRENT$ GDP Landefeld and Howell (1997) 41.6-51.2% Eisner (1989)
54.8%
Ironmonger (1996, 1997)
74.6%
Jorgenson and Fraumeni
312.7%
A further decomposition of the J-F estimates in the following table shows how the conceptual innovations account for the significant differences between the estimates, as well as isolating investment in education.
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As a general the accounts which define the range of activities included more narrowly are called household accounts, those which include a wider range of activities are called nonmarket accounts.
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FURTHER DECOMPOSITION OF THE JORGENSON AND FRAUMENI ESTIMATES AS A % OF CURRENT$ GDP Investment in Human Capital: Formal Education
87.4%
+ Investment in Human Capital: Births
80.1%
+ Time in Household Production & Leisure
145.2% = TOTAL
312.7%
Excluding Nonmarket from Investment in Education
-36.7%
Excluding Leisure
-73.8% = REVISED TOTAL
Excluding the Rest of Investment in Human Capital = FINAL REVISED TOTAL
202.2% -130.8% 71.4%
These two tables illustrate that if investment in human capital and the consumption good leisure are eliminated from the J-F nonmarket accounts, the magnitude of their estimates (71.4% of GDP) is very similar to the magnitude of the Ironmonger estimates (74.6% of GDP). If the value of time spent in education is eliminated from the Ironmonger estimates to be strictly comparable with J-F estimates excluding investment in education, the Ironmonger estimate is 70.5% of GDP, clearly not significantly different from the revised J-F estimates. In this decomposition of the original 312.7% figure, if the value of the output of the education sector depends upon both market and nonmarket activities, then the output of the education sector is 87.4% of GDP. If it only depends on market activities, then it is 50.7% of GDP (87.4%-36.7%). As noted in the body of the paper, there is an inconsistency in proposing that the value of this activity not depend on nonmarket activities as investment in education is produced as a result of a nonmarket activity, e.g., going to school and studying. Finally, although the other adjustments shown come directly from J-F, Ironmonger’s estimates of leisure hours are used to estimate the leisure exclusion, -73.8%. Differences between the adjusted Ironmonger and J-F estimates and the Landefeld and Howell and the Eisner estimates are due to additional coverage differences which are difficult to demonstrate in a table.15
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See Fraumeni (1998) for more details of the comparison summarized above.
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Bibliography Ahlroth, Sofia (1997) “The Output of the Swedish Education Sector,” Review of Income and Wealth, vol. 43, no. 1, March, pp. 89-104. Conlisk, John (1970) “Comments” in W. Lee Hansen, (ed.), Education, Income and Human Capital, Studies in Income and Wealth, vol. 35, New York, NBER, pp. 115-124. Eisner, Robert (1989) The Total Incomes System of Accounts, Chicago: The University of Chicago Press. Fraumeni, Barbara M. (forthcoming) in Lawrence J. Lau, (ed.),"The Jorgenson System of National Accounting," in Lawrence J. Lau, (ed.), Econometrics and the Cost of Capital, Essays in Honor of Dale W. Jorgenson, MIT Press, Cambridge, MA. Fraumeni, Barbara M. (1998) “Expanding Economic Accounts for Productivity Analysis: A Nonmarket and Human Capital Perspective,” paper presented at the Conference on New Developments in Productivity Analysis,” Conference on Research in Income and Wealth, National Bureau of Economic Research, Silver Spring, MD, March 21. Griliches, Zvi (1970) “Notes on the Role of Education and Production Functions and Growth Accounting,” in W. Lee Hansen, (ed.), Education, Income and Human Capital, Studies in Income and Wealth, vol. 35, New York, NBER, pp. 71-115. Griliches, Zvi and William Mason (1972) “Education, Income, and Ability,” Journal of Political Economy, May/June, 80(3), part 2, pp. S64-S103. Ironmonger, Duncan (1996) "Counting Outputs, Capital Inputs and Caring Labor: Estimating Gross Household Product,” Feminist Economics, Volume 2, Number 3, Fall, pp. 37-64. Ironmonger, Duncan (1997) "National Accounts of Household Production Activities," presentation at the Conference on Time-Use, Nonmarket Work, and Family Well-being, Bureau of Labor Statistics and MacArthur Network on the Family and the Economy Conference, November 20-21, Washington, D.C. Jorgenson, Dale W. and Barbara M. Fraumeni (1989a) "The Accumulation of Human and NonHuman Capital, 1948-1984," in R. Lipsey and H. Tice, (eds.), The Measurement of Saving, Investment and Wealth, Chicago, University of Chicago Press, NBER, pp. 227-282. Jorgenson, Dale W. and Barbara M. Fraumeni (1989b) "Investment in Education," Educational Researcher, Volume XVIII, No. 4, pp. 35-44, May.
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Jorgenson, Dale W. and Barbara M. Fraumeni (1992a) "Investment in Education and U.S. Economic Growth," Scandinavian Journal of Economics, Vol. 94, supplement, pp. S51-70. Jorgenson, Dale W. and Barbara M. Fraumeni (1992b) "The Output of the Education Sector," in Z. Griliches, T. Breshnahan, M. Manser, and E. Berndt (eds.), The Output of the Service Sector, Chicago, NBER, pp. 303-341. Landefeld, J. Steven and Stephanie L. Howell (1997) "Accounting for Nonmarketed Household Production within a National Accounts Framework", presentation at the Conference on TimeUse, Nonmarket Work, and Family Well-being, Bureau of Labor Statistics and MacArthur Network on the Family and the Economy Conference, November 20-21, Washington, D.C. Nelson, Richard R. (1970) “Comments” in W. Lee Hansen, (ed.), Education, Income and Human Capital, Studies in Income and Wealth, vol. 35, New York, NBER, pp.124-127. Rothschild, Michael (1992) "The Output of the Education Sector," in Z. Griliches, T. Breshnahan, M. Manser, and E. Berndt (eds.), The Output of the Service Sector, Chicago, NBER, pp. 339-341. Wykoff, Frank (1998) “Discussant Comments,” Conference on New Developments in Productivity Analysis,” Conference on Research in Income and Wealth, National Bureau of Economic Research, Silver Spring, MD, March 21, dated June.
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