Main article

View the most recent version.

Archived Content

Information identified as archived is provided for reference, research or recordkeeping purposes. It is not subject to the Government of Canada Web Standards and has not been altered or updated since it was archived. Please "contact us" to request a format other than those available.

Archived

This page has been archived on the Web.

1. Introduction
2. Measuring the output of the education sector
3. Accounting for quality changes in education services
4. Conclusion

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 385-0001). 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 output-based 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 cost-based 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 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 income-based estimates of education services for Canada. Section 3 presents estimates of quality-adjusted 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.

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.

Let Description: h subscript s, e, a and superscript t denote the discounted lifetime income (or human capital stock) of individuals of sex s, educational attainment e, and age a in year t, and Description: N subscript s, e, a and superscript t 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:

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. is the probability that an individual aged a will survive for m more years. is the investment in human capital for a student, and 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:

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:

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 non-market 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.

The nominal value of education services V arrived at by using the cost-based approach is the following:

where: 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 is the costs of inputs per student.

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 income-based 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, cross-classified 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 2005. There appears to be a break in enrolment data for education level 3 (some or completed postsecondary education below bachelor's degree) in 1976. 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 1997. 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.

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:

where: 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:

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 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:

In general, investment in education for students enrolled in education level 1 who are of age a can be estimated as the following:

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 1997. 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 1997.

2.4  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 2005. 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.

Chart 2 plots school enrolments by gender over the period from 1976 to 2005. 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.

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 2005. 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 2 presents the income-based estimates of investment in education in current dollars for the period from 1976 to 2005. 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.

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.

The price index of education output rose by an average of 2.4% per year for the period from 1976 to 2005. 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 2005. 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 2005. 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 2005. 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.

Investment in education per student in constant prices rose steadily over time for both men and women (Chart 3). This reflects rising enrolment in secondary and postsecondary education. The value of investment in education per student in constant dollars was greater for men than for women. The difference between women and men decreased slowly in the period before 1990. After 1990, the difference was broadly stable. In 2005, investment in education per student for women was about three-quarters that for men.

The real value of investment in education per student in colleges and universities also increased over time (Chart 4). In 2005, the real value of investment in education for a student enrolled in college or university was more than two times that for a student enrolled in primary education.

The cost-based estimate of education output

Table 8 and Chart 5 present the cost-based estimate of the value of education services in Canada. For comparison, they also present the income-based estimate of the value of education services.

The cost-based and income-based approaches yield similar estimates of the growth rates of the real education output, particularly after the mid-1980s. The cost-based estimate increased by 0.6% per year over the period from 1976 to 2005, while the income-based estimate rose by 0.8% per year over the period. The income-based approach yields a slightly higher growth rate of education output. 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 weights used to 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 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. For the cost-based approach, enrolments are disaggregated into three education levels (primary and secondary, college, and university) as a result of the availability of data on education expenditures. ⁶ 

While the two approaches yield similar estimates of the growth in real education output, they produce very different estimates of the level of education output (Chart 6). The income-based estimate of the nominal value of education services was about 6.8 times as large as the cost-based estimate in 2005.

The relative levels of the two estimates of education output in Chart 6 can be interpreted as the ratio of the economic benefits of education to the costs of education. That ratio declined from 1976 to the mid-1980s. It remained virtually unchanged from the mid-1980s to 2000, and declined again after 2000. This suggests that the return to education declined from 1976 to the mid-1980s; it declined again post 2000, following a period of little change from the mid-1980s to 2000. This is consistent with the findings on the trends in the rate of return to education in Canada (Emery 2004). Emery examined the rate of return to undergraduate university education for the period from 1960 to 2000 and observed reductions in returns to university education in the late 1970s and early 1980s; by 1985, the returns to education had resumed the levels of the 1960s and early 1970s.

The cost-based estimate in Table 8 can be extended to include the research component of the university sector output. The research output is estimated by the number of publications that can be obtained from the Canadian Bibliometric Database (Gingras et al., 2008). The estimated number of publications from that database increased by 3.3% per year over the period 1996 to 2005, while university enrolment increased by 2.6% per year for the same period. The cost-based estimate of the university output that aggregates research and teaching components using the relative cost shares of teaching and research is estimated to have increased by 2.8% per year for the 1996 to 2005 period, which was slightly higher than the 2.6% annual growth of university output estimate that only includes school enrolment. ⁷  The cost-based estimate of the output of the total education sector increased by 1.0% per year over the period 1996 to 2005 when university research is included, compared with 0.9% annual growth when university is not included.

Our evidence suggests that the research component has little effect on the overall growth of education output, though there are some uncertainties in the consistency in the estimated number of publications over time. The rest of the paper will therefore focus on the estimate that excludes university research.

2.5  Comparison with the System of National Accounts

In contrast to the two experimental estimates presented above, the System of National Accounts also produces an estimate of the education sector output that is based mostly on inputs. The nominal value of education output is the sum of labour compensation, intermediate inputs, and capital consumption allowance. The volume of education output is equal to the volume of total inputs used for primary and secondary education and for college education. For university education, the volume of education output was measured in the past by the volume of total inputs; it is measured by student enrolments for more recent years.

The existing national accounts input-based estimate of education output is compared with the income-based estimate and the cost-based estimate of education output in Chart 7. The results show that the two new estimates of the volume of education output increased at a slower rate than the current national accounts estimate of education output. The national accounts estimate of education output increased by 1.2% per year over the period from 1976 to 2005, while the income-based estimate and the cost-based estimate rose by 0.8% and 0.6%, respectively. The nominal value of education output estimated from the cost-based approach and the nominal value of education output estimated from the existing national accounts are both equal to the sum of labour costs, capital consumption allowance, and intermediate inputs in the education sector. The growth in the nominal value of education output from the cost-based approach and from the existing national accounts is much faster than the growth from the income-based approach (5.8% per year versus 3.2% per year).

Chart 8 presents the underlying data on the cost of education per student that are used to produce cost-based estimates of education output. The unit cost was the highest for university education, the lowest for primary and secondary education, and in between for college education. The unit cost increased for university education and for primary and secondary education from 1997 to 2005, while it changed little for college education during this period.

Some of the differences in expenditures per student between university education and other types of education are due to the presence of a research function in universities. As the exact split in total expenditures between teaching and research is not available, all expenditures are included in the cost-based measure of education output used here. ⁸ 

Chart 9 plots trends in labour productivity of the Canadian education sector based on the three alternative measures of education output (two output-based measures of education services and one input-based measure of education services). All three measures of labour productivity show that labour productivity declined in the Canadian education sector before 1990 and increased after 1990. Labour productivity based on income-based estimates of education output declined at an average annual rate of 1.6% in the education sector for the period from 1976 to 1990. During the period from 1990 to 2005, labour productivity increased by 0.4% per year.

The decline in labour productivity before 1990 reflects the high growth in the number of teachers in that period. Total hours worked in the education sector increased by 2.5% per year before 1990 while the number of students barely increased during that period. After 1990, the growth in total hours worked in the education sector was slow, while the number of students increased at a faster pace. For that period, labour productivity growth increased by half of one percentage point per year.

3   Accounting for quality changes in education services

A significant challenge for measuring the output of the education sector arises when it comes to adjusting for changes in the quality of education services over time. To the extent that the income and cost estimates of the volume of education output do not capture quality improvements, the changes in real education output will be underestimated and price changes will be overestimated.

The weighted sum of student enrolments across different categories (classified by education level, gender, and age) is a correct measure of the volume of education output when students within each category are homogeneous and comparable over time. When students within each group are heterogeneous and their characteristics change over time, the weighted sum of student enrolments is no longer a correct measure of education output. Students taught in smaller classes by more experienced teachers require an upward adjustment of the volume of education services and a downward adjustment of their price. Similar adjustments must be made for students with higher scores who graduate rather than drop out.

The human capital approach, or income-based approach, for the measurement of education output has been suggested as being an approach to quality-adjusting education output. As discussed above, the human capital approach is best viewed as an alternative to the cost-based approach for measuring education output. The two approaches differ in the prices used to value education services. The cost-based approach values education services by using expenditures per student, while the income-based approach values education services by using increments in lifetime labour income from increases in education.

The purpose of quality adjustment is to isolate pure price changes from price changes due to changes in characteristics of students (Schreyer 2009a). To the extent that education expenditures and the increments in lifetime income due to education reflect improvements in education quality, they should be counted as increases in the volume of education output rather than as increases in the price of education output.

Quality adjustment is not new in the National Accounts. Quality adjustment has been made for the output of computers and telecommunication equipment in Canada, and other countries. To construct a quality-constant price index for computers, semiconductors, and telecommunications equipment, previous studies have used hedonic methods. Triplet (2006) has provided an extensive survey of the research on the construction of hedonic price indices for computers and other information and communication products.

The two components of data used to estimate the volume and price indices of education output are the price and quantity data associated with student enrolments, disaggregated by education level, gender, and age. The quantity component is the number of students or the number of student hours. The corresponding price component is increments in lifetime income due to education, per student, for the income-based approach; it is unit expenditures for the cost-based approach.

Diewert (2011) and Schreyer (2009a) discussed the hedonic method that can be used to take into account quality changes in the output of the education sector. The hedonic method has two steps. First, data are collected on various factors that may affect the quality of the education that students receive. These factors can include the quality and quantity of inputs to student education (class size or the number of experienced teachers) and the outcomes of education (test scores).

The next step is to estimate a hedonic function that relates the indicators of education quality to the price component of education output, which is investment in education per student for the income-based approach and education expenditures per student for the cost-based approach. The coefficients on the indicators of education quality are also known as the implicit prices of the indicators of education quality (Triplet 2006). This second step is often ignored in previous empirical studies. Rather, the coefficients that relate the indicators of education quality to education output are assumed in those studies.

Once the indicators of education quality are collected and implicit prices associated with those indicators are estimated from hedonic regressions, changes in the price index of education output that can be attributed to the changes in education quality can be estimated. The imputed changes in the price index of education output resulting from changes in education quality are then included in the change in the quality-adjusted volume index of education output.

The rest of the paper will focus on hedonic quality adjustment for the volume and price indices of education output from the income-based approach. Nevertheless, the same approach can be used for quality adjustment with respect to the measures of education output from the cost-based approach.

3.1  Education quality, test scores

For this paper, test scores are used as an indicator of education quality. Specifically, time-series data on test scores in literacy and related cognitive skills for the individuals that obtained a specific qualification in different years are used as an indicator of education quality. The time series data on test scores are constructed from the Canadian data from the 2003 International Adult Literacy and Skills Survey (2003 IALSS), a seven-country initiative conducted in 2003 that measured prose and document literacy as well as numeracy and problem-solving skills (Statistics Canada and OECD 2005). ⁹ 

The 2003 IALSS includes standard questions on demographics, labour force status, and earnings, but it also attempts to measure literacy and related cognitive skills in four broad areas: prose literacy, document literacy, numeracy, and problem solving. Test scores in those four broad areas of literacy and cognitive skills will be used to capture the quality of education. Hanushek and Zhang (2006) also used the literacy scores from the 2003 IALSS to measure the quality of education.

The "prose literacy" questions in the surveys assess skills ranging from identifying recommended dosages of aspirin from the instructions on an aspirin bottle to using an announcement from a personnel department in order to answer a question set out in phrasing different from that used in the text. The "document literacy" questions, which are intended to assess capabilities to locate and use information in various forms, range from identifying percentages in categories in a pictorial graph to assessing an average price by combining several pieces of information. The "numeracy" component ranges from simple addition of pieces of information on an order form to calculating the percentage of calories from fat in a Big Mac from figures provided in a table. The "problem-solving" component assesses goal-directed thinking and action in situations for which no routine solutions exist.

The 2003 IALSS asks respondents about their age at the time of the survey (2003) and the age at which they completed their highest level of education. The information is then used to infer the year when respondents completed the highest level of education. The average test scores for individuals who completed an education level in a given year is used as indicators of education quality at the education level in that year.

Individuals may lose and gain skills as a result of the aging process and on-the-job training, respectively. On the one hand, if individuals tend to lose skills over time as a result of aging, exam scores for early cohorts of graduates will underestimate the quality of education for those cohorts. On the other hand, if individuals tend to gain skills over time as a result of on-the-job training, exam scores for early cohorts will overestimate the quality of education for those cohorts. The effect of aging and on-the-job training on the text scores for various cohorts of graduates is controlled for in regression analysis in order to provide an unbiased estimate of changes in education quality.

Literacy scores of cohorts of graduates may also reflect the effect of student ability and family background in addition to the effect of education.To control for the effect of student ability,the following three dummy variables from the 2003 IALSS are included in the regression for literacy scores (Green and Riddell 2007). A dummy variable equals 1 if the respondent agreed or strongly agreed with the statement that he or she got good grades in math while in school; a dummy variable equals 1 if the respondent agreed or strongly agreed with the statement that teachers often went too fast and he or she often got lost; and a dummy variable equals 1 if the respondent answered that he or she received remedial help or attended special classes to assist him or her with reading at school. To control for the effect of family background on test scores, variables on parental education and immigrant status are added.

Since the objective of this study is to examine the education sector in Canada, anyone born outside of Canada or educated outside of Canada is excluded from the sample. The over-sampled First Nations observations from the 2003 IALSS are also dropped. The survey covers individuals over age 16, but individuals who list their main activity as student are excluded, in order to highlight the effect of completed schooling and what happens to literacy and skills once individuals have completed their schooling. Those individuals who completed the highest level of education before 1976 are excluded, since the focus of the paper is on the changes in the education quality for the period after 1976 in this paper.

The method that is used to obtain time series data on test scores for various cohorts of graduates from IALSS 2003 is similar to the one used by Coulombe et al. (2004) in their study on the long-term relationship between human capital and economic growth.

In summary, to estimate the test scores for the cohorts of graduates at each education level, the following regression on literacy scores is estimated using the Canadian data in the 2003 IALSS:

The dependent variable is the literacy scores of the individual i who achieved the highest level of education in year t, where the literacy score is an average score in four broad areas of literacy and related cognitive skills: prose literacy, document literacy, numeracy, and problem solving. The variables E1 to E5 are the dummy variables indicating the highest level of education that the individual achieved. For example, E1 is set equal to 1 if the highest level of education for that individual is level 1 (0-8 years of schooling). t is the year in which the individual completed the highest level of education, and is set equal to 1 for the year 1976, 2 for the year 1977, and so forth. The vector Z is the set of control variables, including gender, age, age squared, proxies for student abilities, and variables for family background.

The estimated coefficients to measure the percent change in the literacy scores of graduates at each education level over time and will be used to capture the change in the quality of education services at each education level.

The equation (9) is estimated using the weighted least square approach that uses population size as weights. The regression results are presented in Table 9: for instance, the coefficient on the variable time x 0 to 8 years of schooling shows the change in the literacy scores for the individuals who obtained 0 to 8 years of schooling. The results show that test scores increased over time for graduates at education levels 1 (primary education) and 2 (secondary education). However, no statistically significant changes in test scores are observed for graduates at the postsecondary education (education levels 3 to 5). Literacy scores increased by 1% per year at the primary education level and increased by 0.2% per year at the secondary-education level.

The results for the effects of the student-ability and family-background variables on literacy scores are consistent with those in Green and Riddell (2007). Student ability and parental education levels both have positive effects on literacy scores. The immigration status of parents does not appear to have a significant effect on literacy scores. Controlling for the effect of student ability and of family background does not lead to a significant difference in the estimated changes in education quality.

3.2  Hedonic regression

Canadian data from the 2003 IALSS are used to estimate the hedonic function for education output that relates test scores to increments in lifetime incomes. Ideally, it would be prefereable to construct increments in lifetime incomes for all individuals in the sample and to estimate a hedonic function that relates test scores to gains in lifetime income. In this paper, marginal gains in current labour income from education (or returns to education) are used as a proxy for gains in lifetime labour incomes.

The hedonic regression for the output of education services is estimated as a standard Mincer-type human capital earnings function:

The earnings are annual earnings. The dummy variables A2 to A5 are the dummy variables that represent the levels of education achieved. It is assumed that the individuals who achieved a higher education level also received the lower level. For an individual whose highest level of education is level 5, dummy variables A2 to A5 are all set equal to 1. For an individual whose highest level of education is level 4, dummy variables A2 to A4 are all set equal to 1, and dummy variable A5 is set equal to 0. The vector Z is the set of control variables including gender, age, age squared, and proxies for student abilities. The variables for family background are excluded in the estimation, since the variables are found to have no effect on individuals' earnings.

The coefficients on the variables A2 to A5 represent the marginal wage gains of achieving that education level over the previous level of education. The estimated marginal gains are used as a proxy for investment in education at that level. In the regression, those marginal gains are allowed to change with test scores. The coefficient on the log of literacy scores represents the implicit prices associated with literacy scores. It is assumed that a 1% increase in test scores will have the same percentage-point contribution to the marginal gains of achieving an education level, since are no statistically significant differences are found in that coefficient between the five levels of education used for this paper. In general, coefficient will vary across education levels.

The sample used for estimating the hedonic regression is similar to the one used for estimating literacy scores, except that those individuals who are self-employed are eliminated for the hedonic regression. Those individuals whose annual earnings are less than $2,000 or over $1,000,000 are eliminated from the sample. The latter restriction eliminates retired individuals, the unemployed, and others who are not in the labour force. It also cuts out a small number of individuals with earnings that are substantial outliers relative to the rest of the sample. Self-employed workers are also dropped from the sample in order that the remuneration of skills in the labour market be examined, since self-employment earnings reflect both remuneration and returns to capital.

The parameter estimates from the hedonic regression are presented in Table 10. The estimated is 0.57 and is statistically significant. This suggests that a 1% increase in test scores is associated with a 0.57% increase in marginal gains from achieving a higher level of education.

3.3  Quality-adjusted price and volume indices of education output

The results from estimating the literary score and earnings regressions can be used to estimate the quality-adjusted price and volume indices of education output. The estimated literacy score equation provides an estimate of average literacy scores for individuals who achieved education level e in year t The earnings regression provides an estimate of the effect of literacy scores on returns to education The quality-adjusted price index for student enrolments disaggregated by sex, education level, and age is estimated as follows:

Those quality-adjusted price indices are then aggregated to obtain the quality-adjusted price index of education services by means of Tornqvist aggregation. The quality-adjusted quantity index of education services is calculated by dividing the nominal value of education output by the quality-adjusted price index.

Table 11 presents the quality-adjusted output of the education sector. The quality adjustment raised the growth of education output by 0.2 percentage points per year and lowered the growth of the corresponding price index by 0.2 percentage points per year. The 0.2-percentage-point quality-adjustment factor for Canada is similar to the 0.25% quality-adjustment factor per year that is utilized in the U.K. official estimates of the volume index of education services (see Fraumeni et al. 2008).

4   Conclusion

Several statistical agencies of OECD countries have carried out research to develop output-based measures of education services and of other non-market service sectors, such as health services, over the last decade. The various approaches can be classified into two broad 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 put forward by Kendrick (1976).

This paper uses both approaches to estimate the output of the Canadian education sector. It finds that the two approaches yield similar estimates of the growth in education output. Over the period from 1976 to 2005, the income-based measure of the real output of the education sector in Canada is estimated to have increased by 0.8% per year, while the cost-based estimate rose by an estimated 0.6% per year.

However, the two approaches produce very different estimates of the level of education output. In 2005, the income-based estimate of the nominal education output was about 6.8 times as large as the cost-based estimate of the education output. There are a number of potential explanations for this difference. First, the coverage of the education sector between the two approaches differs. 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 earning 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.

The paper also makes a methodological contribution to the measurement of education output. While previous studies have attempted to capture quality changes in education output, they have often lacked precise methodologies to do so. This paper points out that quality adjustment for education output is no different from quality adjustment for computer output. The hedonic methods that are used to construct a quality-constant price index for computers can also be used to capture quality improvement in education output.

The paper finds that the hedonic adjustment for quality changes in education services raised the growth of education output by 0.2 percentage points per year over the period from 1976 to 2005.

While the appropriate approach for this type of adjustment should be the hedonic methods that have been used by statistical agencies for quality adjustment with respect to products such as computer output, the data for implementing such methods are often not available or incomplete. Both time-consistent data on the various indicators of education quality (such as class size, test scores, and teacher qualities) and surveys that can be used to estimate hedonic regressions that link the indicators of education quality to the price of education output are needed for better hedonic estimates.