Measuring the Economic Output of the Education Sector in the National Accounts

Transcription

1 Catalogue no. 11F0027M No. 080 ISSN ISBN Research Paper Economic Analysis (EA) Research Paper Series Measuring the Economic Output of the Education Sector in the National Accounts by Wulong Gu and Ambrose Wong Economic Analysis Division 18-F, R.H. Coats Building, 100 Tunney s Pasture Driveway Telephone:

2 Measuring the Economic Output of the Education Sector in the National Accounts by Wulong Gu and Ambrose Wong 11F0027M No. 080 ISSN ISBN Statistics Canada Analysis Branch Economic Analysis Division 18-F, R.H. Coats Building, 100 Tunney s Pasture Driveway Ottawa K1A 0T6 How to obtain more information: National inquiries line: inquiries: infostats@statcan.gc.ca October 2012 Authors names are listed alphabetically. Published by authority of the Minister responsible for Statistics Canada Minister of Industry, 2012 All rights reserved. Use of this publication is governed by the Statistics Canada Open Licence Agreement ( La version française de cette publication est disponible (n o 11F0027M au catalogue, n o 080). Note of appreciation Canada owes the success of its statistical system to a long-standing partnership between Statistics Canada, the citizens of Canada, and Canada s businesses, governments, and other institutions. Accurate and timely statistical information could not be produced without the continued cooperation and goodwill of these partners. Standards of service to the public Statistics Canada is committed to serving its clients in a prompt, reliable, and courteous manner. To this end, the Agency has developed standards of service which its employees observe in serving its clients. To obtain a copy of these service standards, please contact Statistics Canada, toll-free, at The service standards are also published on Under "Our agency": click on "About us > The agency" and select "Providing services to Canadians."

3 Economic Analysis Research Paper Series The Economic Analysis Research Paper Series provides for the circulation of research conducted by the staff of National Accounts and Analytical Studies, visiting fellows, and academic associates. The Economic Analysis Research Paper Series is meant to stimulate discussion on a range of topics, including the impact of the New Economy, productivity issues, firm profitability, technology usage, the effect of financing on firm growth, depreciation functions, the use of satellite accounts, savings rates, leasing, firm dynamics, hedonic estimations, diversification patterns, investment patterns, differences in the performance of small and large firms and of domestic and multinational firms, and purchasing power parity estimates. Readers of the series are encouraged to contact the authors with comments and suggestions. The primary distribution medium for the research papers is the Internet. These papers can be accessed for free at All papers in the Economic Analysis Research Paper Series go through institutional and peer review, in order to ensure that they conform to Statistics Canada's mandate as a government statistical agency and adhere to generally accepted standards of good professional practice. The papers in the series often include results derived from multivariate analysis or other statistical techniques. It should be recognized that the results of these analyses are subject to uncertainty in the reported estimates. The level of uncertainty will depend on several factors: the nature of the functional form used in the multivariate analysis; the type of econometric technique employed; the appropriateness of the statistical assumptions embedded in the model or technique; the comprehensiveness of the variables included in the analysis; and the accuracy of the data that are utilized. The peer group review process is meant to ensure that the papers in the series have followed accepted standards, in order to minimize problems in each of these areas. Publications Review Committee Analysis Branch, Statistics Canada 18th Floor, R.H. Coats Building Ottawa, Ontario K1A 0T6 Symbols The following standard symbols are used in Statistics Canada publications:. not available for any reference period.. not available for a specific reference period not applicable 0 true zero or a value rounded to zero 0 s value rounded to 0 (zero) where there is a meaningful distinction between true zero and the value that was rounded p preliminary r revised x suppressed to meet the confidentiality requirements of the Statistics Act E use with caution F too unreliable to be published * significantly different from reference category (p < 0.05)

4 Acknowledgement The authors thank Isabelle Amano, Dan Boothby, John Baldwin, Winnie Chan, Gang Liu, Fabiola Riccardini, and Paul Schreyer for their helpful comments. The authors are grateful to the members of the National Accounts Advisory Committee of Statistics Canada as well as to the participants in the 2010 Canadian Economics Association annual meeting and the participants in the 2010 International Association for Research in Income and Wealth conference for their feedback. They would also like to thank Karim Moussaly for putting together data on the number of publications from the Canadian Bibliometric Database that is used a measure of research output of the Canadian universities.

5 Table of contents Abstract... 6 Executive summary Introduction Measuring the output of the education sector Income-based approach to the measurement of education services Cost-based approach to the measurement of education services Data Estimates of the output of the education sector Comparison with the System of National Accounts Accounting for quality changes in education services Education quality, test scores Hedonic regression Quality-adjusted price and volume indices of education output Conclusion References Economic Analysis Research Paper Series Statistics Canada Catalogue no.11f0027m, no. 080

6 Abstract This research paper constructs two experimental measures of the economic output of the education sector for Canada: an income-based measure and a cost-based measure. The measures differ from the existing measure currently used in the National Accounts, which is based on the volume of total input, and can be used to examine the productivity performance of the education sector. Both approaches are predicated on the notion that the output of the education sector represents investment in human capital. The income-based approach measures investment in education as increments in the future stream of earnings arising from education. The cost-based approach measures investment as total expenditures related to education. The paper finds that the two approaches yield similar estimates of the growth in real education output, but produce very different estimates of the level of education output. The paper also proposes and implements a hedonic approach in order to capture the quality of the output of the education sector. More studies related to National Economic Accounts and macro-economy and productivity are available in Update on Economic analysis. Economic Analysis Research Paper Series Statistics Canada Catalogue no.11f0027m, no. 080

7 Executive summary Education is an important economic activity in Canada. However, little is known about the productivity performance of the education sector, as the output of the education sector has been measured largely by inputs in Canada. In the System of National Accounts of Canada and those of most other countries, the volume of output of the education sector has been measured in the past by the volume of inputs, where total inputs include labour costs for teachers and administrative staff, capital input, and intermediate inputs. Since the volume of output is measured by the volume of inputs, the ratio of output to inputs does not measure productivity performance for that sector. The objective of this paper is to develop experimental measures of the output of the education sector for Canada that can be used to examine the productivity performance of this sector, based on the ongoing development of output-based measure in other Organization for Economic Cooperation and Development (OECD) countries (Schreyer 2009b, Fraumeni et al. 2008). This research paper focuses on four questions. 1. What are the approaches used by national statistical agencies to measure the economic output of the education sector? The approaches used by national statistical agencies to measure the economic output of the education sector can be classified into two groups. The first is the income-based approach, or human capital approach, developed in a series of papers by Jorgenson and Fraumeni (1989, 1992, 1996). The second approach is the cost-based approach, which can be traced back to the estimates of investment in education based on expenditures that was developed by Kendrick (1976). Both approaches start with the number of student enrolments or the number of graduates, disaggregated by education level, type of education program, age, and gender, as the quantity measure of education output. The two approaches differ in the weights assigned to, or the unit prices used to weigh, the different types of enrolments or graduates in order to derive a volume index of education output. For the income-based approach, the volume index of education output is calculated as a weighted sum of student enrolments using weights based on the value of education. The other is measured by its effect on students lifetime labour incomes. The value of education, measured in terms of its effect on lifetime income, is calculated as the difference between the lifetime income of an individual enrolled in that education level and the lifetime income of an individual with a lower education level. For the cost-based approach, the volume index of education output is calculated as a weighted sum of student enrolments using weights based on total expenditures per student as the unit price of education. Total expenditures include teacher salaries, intermediate inputs, and a capital consumption allowance. 2. What are the estimated growth rates of the output of the Canadian education sector that are derived from the two approaches? The income-based approach and the cost-based approach are used to estimate the output of the education sector, which includes primary and secondary education, colleges, and universities. The income-based measure of education output is estimated to have increased by 0.8% per year over the period from 1976 to 2005, while the cost-based estimate increased by 0.6% during the same period. The difference in the rate of growth between the two estimates can be attributed to the differences in the level of aggregation for enrolments and the weights used to Economic Analysis Research Paper Series Statistics Canada Catalogue no.11f0027m, no. 080

8 aggregate enrolments between the two approaches. For the income-based approach, enrolments are disaggregated by gender, education level (one of five levels), and age (age 6 to 74). The five education levels are defined as: 0 8 years of schooling; some or completed high school; some or completed postsecondary school below bachelor s degree; bachelor s degree; and master s degree or above. For the cost-based approach, enrolments are disaggregated by three education levels (primary and secondary, college, and university). This disaggregation is determined by the availability of data on education expenditures. 3. What are the estimates of the nominal value of the output of the Canadian education sector from the two approaches? The nominal value of education output from the income-based approach is set equal to the value of education as measured by its effect on students lifetime income. The nominal value of education output from the cost-based approach is derived from total education expenditures, which include the labour costs of teachers and administrative staff, capital costs, and intermediate inputs. The income-based estimate of the nominal value of education services is found to be much higher than the cost-based estimate. In 2005, the income-based measure was estimated at about 6.8 times as large as the cost-based estimate. There are a number of potential explanations for this difference. First, the coverage of the education sector differs between the two approaches. The education services sector in the income-based approach includes the inputs of non-market activities (the opportunity cost of students time), while the cost-based approach does not. Second, the income-based approach attributes the earnings differentials among individuals to the effect of investment in formal education (Rosen 1989). To the extent that the earning differential also captures the effect of on-the-job training, gender discrimination, and individuals ability, the income-based approach overestimates the level of education output. Despite these differences, the two estimates generate quite similar rates of growth of real or volume measures. 4. What are the main challenges for measuring the output and the productivity performance of the education sector? The measures of the output of the education sector developed in this paper represent an important first step towards understanding the productivity performance of the education sector. However, significant challenges remain. Chief among them are the changes in education quality that must be taken into account in order to accurately estimate the productivity performance of the education sector. While the hedonic method can be applied in order to take into account the quality changes in education output as shown in the paper, the data for implementing quality adjustments are often not available or incomplete. The challenge facing statistical agencies is to collect time-consistent data on the various indicators of education quality (such as class size, test scores, and teacher quality) and to conduct surveys that can be used to estimate hedonic regressions that link the indicators of education quality to the unit price of education output in terms of the value of education or expenditures of education. Economic Analysis Research Paper Series Statistics Canada Catalogue no.11f0027m, no. 080

9 1 Introduction Education is an important economic activity in Canada. Education, at 15% of consolidated government expenditures, was the third-largest item, following health (19%) and social services (30%), in 2009 (Statistics Canada, CANSIM table ). However, little is known about the productivity performance of the education sector, as the output of the education sector has been measured largely by inputs in Canada. In the National Accounts of Canada and those of most other countries, the volume of output of the education sector has been measured in the past by the volume of inputs in the education sector, where total inputs include labour costs for teachers and administrative staff, capital input, and intermediate inputs. Since the volume of output is measured by the volume of inputs in the education sector, the ratio of output to inputs does not accurately measure productivity performance for that sector. The objective of this paper is to develop experimental measures of the output of the education sector for Canada that can be used to examine productivity performance in the education sector. In the last decade, several statistical agencies of countries belonging to the Organization for Economic Cooperation and Development (OECD) have carried out research to develop outputbased measures of education services and of other non-market service sectors, such as health services. The research has led to the development of improved methods for the measurement of education services. By 2006, nine OECD countries had implemented output-based measures of education services: Australia, Finland, France, Germany, Italy, the Netherlands, New Zealand, Spain, and the United Kingdom. A number of other OECD countries are expected to implement the output-based measures for education output (Schreyer 2009b). More recently, the U.S. Bureau of Economic Analysis has developed experimental output-based measures for the U.S. primary- and secondary-education sectors (Fraumeni et al. 2008). Schreyer (2009b) and Fraumeni et al. (2008) define the output of the education sector as the effect of education on the level of knowledge, skills, and competencies of students. This is also referred to as investment in human capital (OECD 2010). This characterization of educational output as investment in human capital dates back to Becker (1964), Mincer (1974), and Schultz (1961), and is further developed and implemented in a series of papers by Jorgenson and Fraumeni (1989, 1992, 1996). According to this definition of education output, the task of measuring education services is essentially one of measuring investment in human capital. The empirical literature has developed two competing approaches to measuring the value of investments in human capital. The first is the income-based approach, or human capital approach, developed in a series of papers by Jorgenson and Fraumeni (1989, 1992, 1996). The second approach is the costbased approach, which can be traced back to the estimates of investment in education based on expenditures (Kendrick 1976). Both approaches start with the number of student enrolments or the number of graduates, disaggregated by education level, type of education program, age, and gender. These are used to measure the quantity of education output. The two approaches differ in the weights assigned to, or the unit prices used to weigh, the different types of enrolments or graduates in order to derive a volume index of education output. For the income-based approach, the volume index of education output is calculated as a weighted sum of student enrolments. Weights are based on the value of education which is measured in terms of its effect on students lifetime labour incomes. The value of education in terms of its effect on lifetime income is calculated as the difference between the lifetime income of an individual enrolled in that education level and the lifetime income of an individual with a lower education level. For the cost-based approach, the volume index of education output is Economic Analysis Research Paper Series Statistics Canada Catalogue no.11f0027m, no. 080

10 calculated as a weighted sum of student enrolments using weights based on total expenditures per student. Total expenditures include teacher salaries, intermediate inputs, and a capital consumption allowance. The two approaches also produce estimates of the nominal value of education output. The nominal value of education output that is associated with the income-based approach is set equal to the value of education measured in terms of its effect on students lifetime income. The nominal value of education output used in the cost-based approach is set equal to total education expenditures, which include labour costs for teachers and administrative staff, capital costs, and intermediate inputs. The income-based estimate of the nominal value of education services is higher than the cost-based estimate. The difference in the nominal value of education output reflects the difference in the coverage of the education sector in the two approaches. The education services sector in the income-based approach includes the inputs of non-market activities (the opportunity cost of students time), while the cost-based approach does not. The difference in the two estimates may be also due to the fact that the income-based approach attributes all earning differentials to the effect of formal education. Abraham (2010) provides a comprehensive discussion of the sources of the differences in the estimates of human capital investment and education output found in the two approaches. A major challenge with respect to the measurement of education services is to capture changes in the quality of the education that students receive. There have been numerous attempts to take into account quality changes in the measure of education output (see Schreyer 2009a and Abraham 2010 for a review). A contribution of this paper is to recognize that quality adjustment for education services is similar to the quality adjustment that has been made for the output of computer technology and other information and communications technologies (ICT) products, which have benefited from improvements in their quality over time. This paper then proceeds to present and apply the hedonic technique that has been used elsewhere (i.e., for quality adjustment to ICT products) in order to adjust the output of the education sector for changes in quality. The paper will focus on the education function of the education sector, which includes primary and secondary education, colleges, and universities. The research output of universities is estimated by the number of publications. It is then aggregated with university enrolments using the relative cost shares of teaching vs. research to form the cost-based estimate of university output. Education also yields benefits beyond increased future streams of earnings for students, such as making students better citizens and better parents. However, those benefits are excluded from the measure of education output in this paper, which focuses on the economic output. The rest of the paper is organized as follows. Section 2 presents the cost-based and incomebased estimates of education services for Canada. Section 3 presents estimates of qualityadjusted education output. Section 4 concludes the paper. 2 Measuring the output of the education sector This section presents two approaches for measuring the economic output of the education sector. One, the income-based approach, is based on the future stream of earnings that education can be expected to provide; the other, the cost-based approach, is based on the costs of education. The two approaches are described below, in subsections 2.1 and 2.2, and are used to produce estimates of the output of the Canadian education sector, in subsection 2.4. Economic Analysis Research Paper Series Statistics Canada Catalogue no.11f0027m, no. 080

11 2.1 Income-based approach to the measurement of education services The income-based approach, or human capital approach, to the measurement of education services is developed in a series of papers by Jorgenson and Fraumeni (1989, 1992, 1996). The approach measures the value of education services as the effect of education on an individual s lifetime income. As the value of education depends on the student s age, sex, and education level, the approach disaggregates students by their age, sex, and education level. Gu and Wong (2010) estimated the present discounted value of market lifetime labour income (or the value of human capital) for all individuals aged 15 to 74 in Canada, following the methodology developed by Jorgenson and Fraumeni (1989, 1992, 1996). 1 In the study, the estimate is derived by using cross-sectional data. It is assumed that expected incomes in future periods are equal to the incomes of individuals of the same gender and education, according to the age that the individuals will have in the future time period, adjusted for increases in real income. The lifetime incomes can be calculated by a backward recursion, starting with age 74, which is assumed to be the oldest age before retirement. The expected income for a person of a given age is that person s current labour income plus his or her expected lifetime income in the next period multiplied by survival probabilities. For example, the present value of lifetime income of 74-year-olds is their current labour income. The lifetime income of 73-year-olds is equal to their current labour income plus the present value of lifetime income of 74-year-olds, adjusted for increases in real income. t Let h s,, e a denote the discounted lifetime income (or human capital stock) of individuals of sex s, t educational attainment e, and age a in year t, and N s, e, a denote the number of students of sex s, and age a who are enrolled in education level e. It is assumed that individuals enroll in school in order to attain a higher education level that is, the individuals who are enrolled in education level e have already achieved education level e-1. The nominal value of education services (V) is estimated as increments in lifetime incomes arising from increases in education summed over all students:, 1, (1 ) / (1 ) s e a m a, a m s, e, a s, e, a s, e, a s, e, a. (1) V h g r sr h N I N t t m m t t t t s, e, a s, e, a It is assumed that individuals with education level e-1 who are enrolled in school need to spend an average of m additional years in school in order to achieve higher education level e. g is the expected growth rate in real income, and r is the discount rate used to calculate the present value of future lifetime labour income. sra, a m is the probability that an individual aged a will t t survive for m more years. I s,, e a is the investment in human capital for a student, and N s,, e a is the number of students. The nominal value of education output in Equation (1) can be divided into volume and price components (Diewert 1976). The volume index of education output (denoted by Q) is an index number derived through a Tornqvist aggregation of school enrolments. It is calculated as a weighted sum of student enrolments across different types of students by using as weights the increment in lifetime labour incomes due to education: 1. Liu (2011) estimated the stock of human capital as the present discounted value of market lifetime income for selected OECD countries. Economic Analysis Research Paper Series Statistics Canada Catalogue no.11f0027m, no. 080

12 ln Q ln Q v (ln N ln N ), (2) t t 1 t t 1 s, e, a s, e, a s, e, a s, e, a where v I N I N 1/ 2, P Q P Q t t t 1 t 1 s, e, a s, e, a s, e, a s, e, a s, e, a t t t 1 t 1 v is the share of individuals with s, e, a in the total value of investment in education, averaged over year t-1 and year t. The price index of education services (P) is estimated by dividing the nominal value of education services by the volume index of education services: P V / Q (3) t t t. The estimates of education output and prices in equations (1), (2), and (3) are based on the number of pupils enrolled at different levels of education. Alternatively, the estimates of education output can be based on the number of graduates who obtain a particular educational qualification in a given year and leave the school system. 2 The output of the education sector based on the number of graduates is estimated as the sum of lifetime incomes embodied in those graduates. It can be shown that the estimates of education output based on the number of enrolments are identical to those based on the number of graduates. In practice, data on enrolments are readily available. In addition, estimates of the education output for institutions of different levels of education, such as primary education, secondary education, and postsecondary education, can be derived based on school enrolments. The estimate based on graduates attaining a particular qualification reflects the sum of the contribution of all education institutions leading to the qualification. For these reasons, data on student enrolments are used to estimate education output. A key assumption of the income-based approach is that the earning differentials among individuals reflect the effect of investment in formal education (Rosen 1989). To the extent that the earning differentials also capture the effect of on-the-job training, gender discrimination, and individuals ability, the income-based approach overestimates the level of education output. In some studies, the output of the education sector arrived at by means of the income-based approach includes the effect of education on market income and on non-market income (Jorgenson and Fraumeni 1992). This paper will focus on the output of the education sector as measured by its effect only on market income. The methodologies for the measurement of nonmarket income are less established, and data for such measurement are limited. 2.2 Cost-based approach to the measurement of education services In contrast to the income-based approach, the cost-based approach measures the output of education services by using the cost of inputs to education. The approach typically disaggregates students by education level (elementary, secondary, or postsecondary), since students enrolled in the various education levels require different amounts of those inputs. In addition, as discussed by Fraumeni et al. (2008), it may be important to differentiate along the lines of other student characteristics, such as regular education versus special education or native English speakers versus non-native English speakers. 2. Fraumeni et al. (2008) provided a brief survey of methodologies used in a number of countries that are based on either student enrolments or the number of graduates. Economic Analysis Research Paper Series Statistics Canada Catalogue no.11f0027m, no. 080

13 The nominal value of education services V arrived at by using the cost-based approach is the following: V C N, (4) t t t i i i t where: N i is the number of students enrolled in a specific education level (primary, secondary, or postsecondary) or in a specific education program (regular education versus special education); and C is the costs of inputs per student. t i Once again, the nominal value of education services can be divided into price and volume components. The volume index of education services is a weighted sum of student enrolments across different education levels using the share of the education levels in total input costs as weights. The price index of education services is the ratio of the nominal value of education services to the volume index. A number of OECD countries have implemented this cost-based approach to the measurement of education services. 3 Schreyer (2009b) recommended the use of the cost-based approach over the income-based approach, since the cost-based approach is more consistent with the existing national accounts framework. It maintains the existing boundary of the national accounts while the income-based approach extends the boundary of national accounts to cover household activities. Diewert (2008) showed that valuing output at average costs in measuring output and productivity growth is a second-best option while the best option would be to use final-demand prices to value output. The use of final-demand prices corresponds to the incomebased approach for the measurement of education output. The nominal value of education services arrived at by using the income-based approach is found to be much larger than the nominal value estimated by means of the cost-based approach (Jorgenson and Fraumeni 1992). Abraham (2010) provided a number of possible explanations for this difference. The discount rate used to calculate the present value of future lifetime income may be too low. The costs of time spent by students in studying are not included in the cost estimates. The earning differences between more educated and less educated individuals may reflect a host of other factors, such as student ability, family background, and differences in on-the-job training. 2.3 Data The data required for estimating education output start with information on enrolment. In addition, the income-based approach requires data on the impact of education on lifetime labour income or data on investment in education, and the cost-based approach requires data on education expenditures at different levels of education. Data on student enrolments The data on enrolment are taken from various surveys on student enrolments. From those surveys, time series data are constructed on the number of pupils enrolled in school, crossclassified by gender, education level (one of five levels), and age (age 6 to 74). The five education levels are defined as follows: 0 8 years of schooling; some or completed high school; some or completed postsecondary school below bachelor s degree; bachelor s degree; and master s degree or above. The data cover the period from 1972 to There appears to be a break in enrolment data for education level 3 (some or completed postsecondary education 3. Fraumeni et al. (2008) and Schreyer (2009b) provided an extensive review of the approaches that a number of countries have adopted for measuring education services. Economic Analysis Research Paper Series Statistics Canada Catalogue no.11f0027m, no. 080

14 below bachelor s degree) in The data for the period from 1976 to 2005 are used in this paper. The enrolment data for elementary and secondary education are obtained from the Elementary- Secondary Education Statistics Project (ESESP) for the years after For 1997 and prior years, the enrollment data are obtained from the Elementary/Secondary School Enrolment (ESSE) survey. The ESESP is an annual survey that collects aggregate data from each provincial/territorial Ministry or Department of Education. Specifically, the information on enrolments pertains to the following two streams: regular education; and minority- and second-language education. Information on regular-education programs is collected by type of program (regular, upgrading, or professional), education sector (youth or adult), grade, and sex. Information on minority- and second-language programs is collected by type of program (immersion, as language of instruction, as a subject taught) and grade. For 1997 and prior years, the data on enrolment are obtained from the ESSE survey. This survey collects data on enrolments by type of school (public, private, schools for the visually or hearing impaired, federal schools, and Department of National Defence schools). The data are broken down by age and gender and by grade and gender. Data on public schools are provided to Statistics Canada by the provinces and territories. For private schools, survey methods vary. Some provinces supply both private and public schools, while, for other provinces, Statistics Canada surveys institutions directly. The enrolment statistics for primary and secondary education from the ESESP provide information on the grades in which students are enrolled (grade 1 to grade 13), but the ESESP does not have information on the ages of the pupils. The age of pupils is inferred from the fact that pupils generally start grade 1 at age 6 in Canada. The pupils enrolled in grade 1 are assumed to be 6 years old; those enrolled in grade 2 are set to be 7 years old; and so forth. The enrolment data for postsecondary education are obtained from the Postsecondary Student Information System (PSIS) for 1992 and subsequent years. For the years before 1992, the data are obtained from three separate surveys: the University Student Information System (USIS); the Community College Student Information System (CCSIS); and the Trade/Vocational Enrolment Survey (TVOC). The PSIS is a national survey that provides detailed information on enrolments and graduates of Canadian postsecondary education institutions. The PSIS collects information pertaining to the programs and courses offered at an institution, as well as information regarding the students themselves and the program(s) and courses in which they were registered or from which they have graduated. In the year 2001, the PSIS began to replace the USIS, the CCSIS, and the TVOC with a single survey offering common variables for all levels of postsecondary education. Historical enrolment and graduate data from previous surveys have been converted by using PSIS variable definitions and code sets in order to maintain the historical continuity of the statistical series. Data on investment in human capital Data on investment in human capital arising from the education of each student, cross-classified by gender, education, and age are obtained from Gu and Wong (2010). The human capital estimate from Gu and Wong (2010) includes all individuals in the Canadian working-age population aged 15 to 74. For the purpose of this paper, the human capital estimates from Gu and Wong (2010) are extended to include individuals aged 6 to 14. Economic Analysis Research Paper Series Statistics Canada Catalogue no.11f0027m, no. 080

15 To estimate human capital stock for individuals aged 6 to 14, the paper makes the following assumptions. Individuals aged 6 are assumed to be enrolled in grade 1 and are expected to complete grade 8 when they are 14 years old. Those individuals are assigned the lifetime income of individuals aged 15 with education level 1 in 8 years. Individuals aged 7 are assumed to be enrolled in grade 2 and are expected to complete grade 8 when they are 14 years old. Those individuals will be assigned the lifetime income of individuals aged 15 with education level 1 in 7 years. The lifetime labour income of those individuals aged 8 to 14 is estimated in a similar fashion. The discounted lifetime labour income for individuals aged 6 to 14 can be estimated as the following: t t 15 a 15 a s, e, a s, e,15 s, a,15 h h (1 g) / (1 r) sr, for 6 a 14 and e = 1, (5) where: sr a,15 is the probability that an individual of sex s and age a will survive to age 15; g is real income growth; and r is the discount rate used to discount future income. Investment in education is measured as the increase in the discounted lifetime labour income resulting from spending an additional year in school. For students enrolled in education level 2 or above, the estimate of investment in education is based on the difference in human capital stock between individuals enrolled in that education level and individuals enrolled in a lower education level: t t m m t s, e, a s, e 1, a m a, a m s, e, a I h (1 g) / (1 r) sr h, for e 2, (6) where m in the equation denotes the number of years that an individual spends in order to complete the next education level. It is assumed that individuals with 0 8 years of schooling spend 3 years to complete the next education level (some or completed high school), that individuals with some or completed high school spend 2 years to obtain some or completed postsecondary education below bachelor s degree, that individuals with some or completed postsecondary education below bachelor s degree spend 2 years to obtain a bachelor s degree, and that individuals with a bachelor s degree spend at least 2 years to obtain a master s degree or above. 4 For students enrolled in education level 1 (0 8 years of schooling), investment in education is measured as the increase in their lifetime labour income compared with the lifetime labour income of those individuals who do not have education. But the human capital stock for those individuals with no education cannot be estimated directly using data from the Census of Population, as individuals are not coded as having no education in the household surveys or in the Census. To estimate investment in education for those pupils enrolled in education level 1 (0 8 years of schooling), the fact that individuals start grade 1 at age 6 and that primary-level education is mandatory in Canada is used. For individuals enrolled in grade 8 who are age 14, investment in human capital is calculated as the difference between the lifetime income of those individuals and the lifetime income of the individuals of the same age who are enrolled in a lower grade (grade 7). Since the individuals who are enrolled in grade 7 are all presumed to be 13 years old, the lifetime income of individuals who are enrolled in grade 7 who are 14 years of age is not observed. It is assumed that the individuals who are enrolled in grade 7 who are 14 years of 4. The number of years m that is required to obtain an education level depends on students ages. The year of education of younger students within the education level is calculated by inference. It is assumed that older students are equally distributed among the various years of education in the education level (for details, see Gu and Wong 2010). Economic Analysis Research Paper Series Statistics Canada Catalogue no.11f0027m, no. 080

16 age will achieve the lifetime income of individuals enrolled in grade 7 who are 13 years of age, with a one-year lag. Investment in human capital for 14-year-olds is estimated as the following: t t t s,1,14 s,1,14 s,1,13 s,13,14 I h h (1 g) / (1 r) sr. (7) In general, investment in education for students enrolled in education level 1 who are of age a (6 a 14 ) can be estimated as the following: t t t s,1, a s,1, a s,1, a 1 s, a 1, a I h h (1 g) / (1 r) sr. (8) Data on expenditures by education level Student enrolments are disaggregated by education level in order to construct the cost-based estimates of education services. The cost of education includes labour costs (salaries of teachers), capital costs, and intermediate inputs. 5 Data are obtained from the Canadian Input-Output Tables for three levels of education: primary and secondary education, college education, and university education. Data on the costs of education are not available at individual education levels before It is assumed that the relative differences in unit costs across three education levels did not change for the period before 1997 and are set to be equal to those in year Estimates of the output of the education sector This section first presents the income-based estimate and the cost-based estimate of the output of the education sector. It then compares the two estimates. The income-based estimate of education output Chart 1 plots trends in school enrolments by education level over the period from 1976 to Enrolment in primary and secondary education fell from 1976 to the mid-1980s as the baby boomers left the primary and secondary education sectors. Enrolment in grades 1 8 then gradually increased after the mid-1980s and fell again after the mid-1990s as the school-aged population declined. Enrolment in secondary school (grades 9 to 13) increased after the mid- 1980s and levelled off after the mid-1990s. 5. Capital cost in the education sector is restricted to capital consumption in the National Accounts and does not include a return to capital. Economic Analysis Research Paper Series Statistics Canada Catalogue no.11f0027m, no. 080

17 Chart 1 School enrolment in Canada, by education level thousands 3,500 3,000 2,500 2,000 1,500 1, Grades 0 to 8 High school College or above Chart 2 plots school enrolments by gender over the period from 1976 to Enrolments increased faster for women than for men, as a result of large increases in the former s participation in colleges and universities over the period. After the mid-1980s, enrolment by women exceeded enrolment by men. Women now account for more than half of all pupils enrolled in schools in Canada. Economic Analysis Research Paper Series Statistics Canada Catalogue no.11f0027m, no. 080

18 Chart 2 School enrolment in Canada, by gender thousands 3,200 2,900 2,600 2,300 2, Male Female Table 1 presents annual growth rates of student enrolments. The most notable increase was observed for enrolments in colleges and universities: 2.6% per year from 1976 to While some of this increase was due to the demographics of the baby boomers, most of the increase was attributable to increases in participation in college and university education among Canadians aged 18 to 26 (Emery 2004). Table 1 Annual growth in school enrolment in Canada, 1976 to 2005 Characteristic 1976 to to to to 2005 percent Total Male Female Grades 0 to High school College or above Table 2 presents the income-based estimates of investment in education in current dollars for the period from 1976 to The nominal value of education services in Canada, as measured by the impact of education on the lifetime labour income of students, is large. In 2005, investment in education was estimated at $469.9 billion, representing about 34% of gross domestic product (GDP) in Canada for that year. Economic Analysis Research Paper Series Statistics Canada Catalogue no.11f0027m, no. 080

19 Table 2 Nominal investment in education in Canada, by gender and education level, 1976 to 2005 Year Total Male Female Grades 0 to 8 High school College or above billions of current dollars The nominal value of education services is divided into price and quantity components in tables 3, 4, and 5. The quantity index of education output (weighted sum of enrolments) is estimated to have increased at an average rate of 0.8% per year for the period from 1976 to 2005, while unweighted enrolments increased at an average rate of 0.4% per year over the period. The difference between the weighted and unweighted measures reflects the rising enrolments in secondary and postsecondary education over the period. Economic Analysis Research Paper Series Statistics Canada Catalogue no.11f0027m, no. 080

20 Table 3 Real investment in education in Canada, by gender and education level, 1976 to 2005 Year Total Male Female Grades High school College or 0 to 8 above billions of 2002 dollars Table 4 Annual growth in the volume index of investment in education in Canada, 1976 to 2005 Characteristics 1976 to to to to 2005 percent Total Male Female Grades 0 to High school College or above Economic Analysis Research Paper Series Statistics Canada Catalogue no.11f0027m, no. 080

21 Table 5 Annual growth in the price index of investment in education in Canada, 1976 to to to to to 2005 percent Total Male Female Grades 0 to High school College or above The price index of education output rose by an average of 2.4% per year for the period from 1976 to It increased at a much slower rate after the mid-1990s. It grew at an average annual rate of 0.9% over the period from 1996 to The slower growth in the price index of education for that period reflects slower earnings growth in that period. The growth rates of the price and volume indices of education output are lower than the growth rates of the price and volume index of gross domestic product (GDP). Real GDP increased by 2.9% per year over the period from 1976 to The price index of GDP increased by 3.9% per year during the period. The rate of growth in the price of education output accounts for about two-thirds of the rate of growth of nominal education output. In contrast, the rate of growth of the GDP price index accounts for a lower portion (60%) of the rate of growth in nominal GDP. The level of investment in education for men has consistently exceeded that for women, as shown in Table 2. The difference between the two narrowed around the mid-1980s as a result of increased enrolments by women over that period. After the mid-1980s, the difference in investment in education between women and men was virtually unchanged. The growth rate of investment in education in constant prices was much higher for women than for men before the mid-1980s; the growth rates for women and for men were similar after the mid-1980s (as shown in Table 4). This difference in investment in education between men and women reflects the difference in their enrolment numbers as discussed above. For the period from 1976 to 1986, investment in education for women increased by 1.3% per year, while investment in education for men remained unchanged over the period. After the mid-1980s, investment in education for men grew at a rate similar to that for women. The real output of the postsecondary education sector (colleges and universities), as measured by investment in education, increased the most (as shown in Table 4), growing by 2.7% per year during the period from 1976 to The output of the primary and secondary education sector changed little over that period. Tables 6 and 7 present the underlying data on investment per student in current and constant dollars that are used to produce the income-based estimates of education output. Those estimates of real investment per student are also plotted in Charts 3 and 4. Economic Analysis Research Paper Series Statistics Canada Catalogue no.11f0027m, no. 080