The contribution of rising school quality to U.S. economic growth

doi:10.1016/j.jmoneco.2014.01.006

Journal of Monetary Economics

Volume 63, April 2014, Pages 95-106

https://doi.org/10.1016/j.jmoneco.2014.01.006 Get rights and content

Highlights

•
This paper explores how much U.S. labor quality grew due to rising school quality.
•
A schooling model and cohort-variations in earnings are used for identification.
•
U.S. labor quality increased by 0.4% per year between 1967 and 2000.
•
One-fifth of the labor quality growth is attributable to the rise in school spending.
•
Labor quality growth explains one-quarter of the growth in U.S. labor productivity.

Abstract

U.S. public school expenditures per pupil increased by a factor of 9 during the 20th century. This paper quantifies how much U.S. labor quality has grown due to the rise in educational spending. A schooling model and cross-sectional earnings variations across cohorts are exploited to identify the effect of the increased school expenditures on labor quality growth. The findings are that (i) U.S. labor quality increased by 0.4% per year between 1967 and 2000, one-fifth of which is attributable to the rise in educational spending; and (ii) labor quality growth explains one-quarter of the rise in labor productivity.

Introduction

During the 20th century, the real spending per pupil in U.S. public elementary and secondary schools increased by a factor of 9. This paper explores how much U.S. labor quality has grown due to the rise in school expenditures. The Bureau of Labor Statistics (BLS) currently measures labor quality growth mainly based on increases in the mean years of schooling but fails to capture the impact of changes in the quality of education. If the increased educational expenditures improved school quality, then the BLS underestimates the growth in U.S. labor quality.

This paper proposes a new way of quantifying the rise in the quality of education with a schooling model in which human capital production depends not only on time in school but also on educational spending. This model as well as cross-sectional earnings variations across cohorts is exploited to identify the growth in school quality. Consider cross-sectional earnings differences between younger and older cohorts with the same years of schooling. The earnings variations reflect three components: (i) the impact of changing selection into different years of schooling; (ii) return to experience; and (iii) the growth in the quality of education. Without a model, these three components cannot be identified simultaneously.

To assess the effect of the changing selection in schooling choice, assume that ability distribution stays constant across cohorts. If years of schooling vary only by ability within cohorts, the cohort-invariant ability distribution can be estimated by the schooling distribution of any single cohort. The impact of the changing selection on the cohort-variations in earnings is then measured by accounting for changes in empirical schooling distribution across cohorts.

Once the selection effect is controlled for, a structural restriction derived from the model is used to disentangle the remaining two components, assuming the same return to experience across cohorts. In the model, optimizing agents choose both time in school and educational expenditures so that their relative marginal product in increasing human capital equals their relative costs. Given the data on individual earnings and educational expenditures, foregone earnings due to delayed experience are the key element in the relative cost of time spent in school. If earnings rise with work experience very rapidly, increasing time in school is relatively more costly than raising educational expenditures. Thus, agents substitute expenditure for time in school until the relative marginal product of expenditure equals its low relative cost. According to the model, the relative marginal product of expenditure for the last year in school equals the expenditure elasticity of human capital. Thus, the low relative marginal product of expenditure represents a low value for the elasticity. This implies little increase in the quality of education, given the rise in school expenditures. By the same mechanism, very flat experience-earnings profiles suggest a substantial rise in education quality, given the same increase in educational spending. This model implication on how the return to experience relates to the rise in school quality provides an additional condition, which identifies the growth in quality of education from the observed earnings variations across cohorts.

The main finding is that U.S. labor quality increased by 0.4% per year between 1967 and 2000, with one-fifth of this explained by the growth in school quality. Given the increased school expenditures per pupil, their contribution to U.S. labor quality growth has been fairly modest. The total labor quality growth explains one-quarter of the growth in U.S. labor productivity for the same period. The estimated rise in labor quality reduces the growth rate of total factor productivity (TFP) measured as a residual. The contribution of growth in TFP to U.S. labor productivity growth is about a quarter, whereas the BLS estimates it to be 40% by ignoring the growth in the quality of education. The estimated impact of the rise in school expenditures on labor quality growth is larger among men, while the baseline estimate changes little with a sample of full-time, full-year (FTFY) workers. I also find that the growth in school quality explains only 10% of the increases in empirical returns to schooling and that a rising skill premium explains the rest.

This paper is related to two strands of literature. One branch includes papers that estimate the effects of various measures of school quality, including school expenditures on student achievement and labor market outcomes at the micro-level. Although the estimates vary depending on the data and method used, most papers did not find strong effects of measured school quality.¹ My study differs from these studies in two ways: (i) it suggests an aggregate measure of labor quality growth due to increased school expenditures; and (ii) it focuses on cohort variations in the quality of education instead of cross-sectional or geographical variations. To this aim, the biggest challenge is to identify the growth in education quality from other earnings variations across cohorts such as return to experience and changing selection in schooling choice. This paper proposes a way of overcoming this difficulty using a schooling model and measures the average impact of increased school expenditures on growth in human capital for cohorts born from the early 20th century to the early 1980s. The estimated impact of school expenditures is modest in line with this micro-literature.

Another related strand of literature is on the role of human capital in economic growth and development. The most widely used method to measure country-level human capital stocks is to multiply the mean years of schooling of the population by the estimated Mincerian return to schooling.² However, this method does not allow for differences in the quality of education across countries. To correct this, Bils and Klenow (2000) add teachers׳ human capital to the standard Mincer-type human capital specification, yet they ignore the role of expenditure in human capital production. Manuelli and Seshadri (2007) and Erosa et al. (2010) explicitly incorporate expenditure as well as time as inputs for human capital production to account for cross-country income differences. The contribution of human capital growth to U.S. real income growth implied by Manuelli and Seshadri (2007) is more than twice my estimate, whereas that suggested by Erosa et al. (2010) is only slightly greater than mine. One explanation is that Manuelli and Seshadri (2007) view that earnings growth with work experience is solely due to human capital investments, excluding the effects of learning-by-doing or technological progress. This framework tends to amplify the differences in human capital accumulated after leaving school across cohorts, overstating the role of human capital in explaining real income growth. In addition, both Manuelli and Seshadri (2007) and Erosa et al. (2010) assume a common wage per unit of labor regardless of education, whereas my study considers different skill prices by education; failing to do so overestimates the impact of rising school spending on labor quality growth. This paper also relates to Rangazas (2002), who examines the impact of the quantity and quality of schooling on U.S. labor productivity growth. A key difference is that my paper proposes a new way of estimating the expenditure elasticity of human capital, instead of taking it from micro-study estimates that vary by the data and method used. Moreover, I control for the rise in skill premium and unobserved heterogeneity correlated with schooling choice to remove upward bias in the estimated growth in U.S. labor quality.

The remainder of this paper is organized as follows. Section 2 describes the growth accounting framework this paper suggests and discusses the BLS׳s measure of labor quality growth. In Section 3, a schooling model with a Ben-Porath-type human capital production function is introduced. The identification scheme and the estimation procedure are described in Section 4, and the main findings are reported in Section 5. Section 6 concludes the paper.

Section snippets

Measuring labor quality growth

This study suggests that the traditional growth accounting framework should be extended by incorporating labor quality growth. Consider a production function in which economic output Y depends on m types of physical capital inputs $k_{1}$ , $k_{2}$ , …, $k_{m}$ ; n types of labor inputs $h_{1} l_{1}$ , $h_{2} l_{2}$ , …, $h_{n} l_{n}$ ; and a time-specific factor t. $Y = f (k_{1}, \dots, k_{m}, h_{1} l_{1}, \dots, h_{n} l_{n}, t)$ In this formula, l_j is raw hours provided by type j workers and h_j is its quality per hour.

Assuming a constant returns to scale technology, perfectly

The model

This paper develops a schooling model with a Ben-Porath-type human capital production function.⁵ Individuals born in period T choose the optimal level of schooling and goods investment associated with each year in school to maximize the present value of their net lifetime income: $\max_{d (a), s} \int_{s}^{R} e^{- ra} w_{T + a} (s) H (s, a) da - \int_{0}^{s} e^{- ra} p_{T + a} d (a) da + ξ_{T} h (s) s . t . H (s, a) = h (s) ϕ (a - s) for a \geq s \overset{•}{h} (a) = γ_{0} h {(a)}^{γ_{1}} d {(a)}^{γ_{2}} for a < s 0 < γ_{1}, γ_{2} < 1 and h (0) = 1$ here r is the market interest rate; w_t(s) is the wage

Identification and estimation

In this section, how to identify the growth in school quality from other sources of earnings variations across cohorts is addressed. The estimation procedure then follows.

Results

This section starts with a discussion of the estimates for the human capital production function. It then presents the main growth accounting results, followed by a sensitivity analysis.

Conclusion

Building upon Denison (1962), the BLS incorporates labor quality growth as a source of U.S. labor productivity growth. Although the BLS measure of labor quality growth adjusts for the increases in mean years of schooling of the workforce, it fails to capture any impact of the rise in school quality. Public school spending per pupil in the U.S. increased drastically during the 20th century. If this contributed to the quality of U.S. education, then the BLS approach underestimates labor quality

Acknowledgments

I am deeply indebted to Mark Bils for his generous support and encouragement. For their valuable comments and helpful discussions, I thank Mark Aguiar, Yongsung Chang, Jay H. Hong, Byoung Hoon Seok, and seminar participants at the University of Rochester, the State University of New York at Buffalo, the Federal Reserve Bank of Richmond, Korea Development Institute, University of Western Ontario, Korea University, Far Eastern Meetings of the Econometric Society 2008, and Midwest Macro Meetings

References (18)

J.J. Heckman et al.
Explaining rising wage inequalityexplanations with a dynamic general equilibrium model of labor earnings with heterogeneous agents
Rev. Econ. Dyn.
(1998)
P. Rangazas
The quantity and quality of schooling and U.S. labor productivity growth (1870–2000)
Rev. Econ. Dyn.
(2002)
Y. Ben-Porath
The production of human capital and the life cycle of earnings
J. Polit. Econ.
(1967)
J.R. Betts
Does school quality matter? Evidence from the national longitudinal survey of youth
Rev. Econ. Stat.
(1995)
M. Bils et al.
Does schooling cause growth?
Am. Econ. Rev.
(2000)
L. Dearden et al.
The effect of school quality on educational attainment and wages
Rev. Econ. Stat.
(2002)
Denison, E.F., 1962. The Sources of Economic Growth in the United States and the Alternatives Before us. Committee for...
A. Erosa et al.
How important is human capital? A quantitative theory assessment of world income inequality
Rev. Econ. Stud.
(2010)
R.E. Hall et al.
Why do some countries produce so much more output per worker than others?
Q. J. Econ.
(1999)

There are more references available in the full text version of this article.

Cited by (5)

Labor supply and gender differences in occupational choice
2019, European Economic Review
This paper uses data on the task content of occupations to study the role of labor supply in occupational choice. In 1970, married women were less likely to choose occupations characterized by analytically intensive tasks than were men. By 2010, gender differences in occupational choice had narrowed significantly. I use the Dictionary of Occupational Titles to measure the value of skill in an occupation and find an increase in this value with the analytical intensity of occupational tasks. I argue that, as a significant part of skill is accumulated on the job, sources that encourage women to commit to market work contributed to the gender convergence in occupational choice. A quantitative exercise measures that labor-saving technical change in the household sector, occupation-biased technical change in final good production, declining gender gaps in wages and schooling account for 58% of the gender convergence in occupational choice, via the labor supply channel.
Early childhood education and economic growth
2019, Journal of Economic Dynamics and Control
Citation Excerpt :
This article extends and improves the previous literature in several directions. First, we relate to the literature that studies human capital accumulation in a dynamic macroeconomic framework (Castro and Coen-Pirani, 2016; Kong et al., 2018; Lee and Wolpin, 2010; Rangazas, 2000; 2002; Restuccia and Vandenbroucke, 2013a; 2013b; You, 2014). None of these articles studies early childhood education.
We study the effects of early childhood skill formation on productivity and schooling. We add early childhood human capital to a standard continuous time life cycle economy and assume complementarity between educational stages. Agents are homogenous and choose the intensity of preschool education, how long to stay in formal school, labor effort and consumption. The model is calibrated to the US from 1961 to 2008 and matches the data very well and closely reproduces the paths of schooling, hours worked, relative prices and GDP. We find that early childhood education can explain a large part of the observed increase of years of schooling in the U.S. since 1961, and it was as important as formal education for the increase of labor productivity in the period. Furthermore, we show that small reallocations of public expenditures from formal education to early childhood education would have sizable impacts on income per capita and productivity.
The Role of Human Capital in Explaining Labor Productivity Growth in Korea since 2001
2020, SSRN
Knowledge capital and aggregate income differences: Development accounting for US States
2017, American Economic Journal: Macroeconomics
Explaining the evolution of educational attainment in the United States
2016, American Economic Journal: Macroeconomics

View full text

The contribution of rising school quality to U.S. economic growth

Highlights

Abstract

Introduction

Section snippets

Measuring labor quality growth

The model

Identification and estimation

Results

Conclusion

Acknowledgments

Rev. Econ. Dyn.

Rev. Econ. Dyn.

The production of human capital and the life cycle of earnings

J. Polit. Econ.

Does school quality matter? Evidence from the national longitudinal survey of youth

Rev. Econ. Stat.

Does schooling cause growth?

Am. Econ. Rev.

The effect of school quality on educational attainment and wages

Rev. Econ. Stat.

How important is human capital? A quantitative theory assessment of world income inequality

Rev. Econ. Stud.

Why do some countries produce so much more output per worker than others?

Q. J. Econ.