The Ohio State University Daeho Kim Department Of Eco 762205

1the Ohio State University Daeho Kim Department Of Economics

Suppose the marginal costs and benefits of getting more education are the same for all individuals (bi = b and ci = c for everyone). Also suppose that ability varies, but there are only two types of people (indexed by j and k) where the k-type has higher ability (ak) than the j-type (aj); and assume that ability has a constant effect on earnings – i.e., the difference in log-earnings between k- and j-types at each education level is ak − aj > 0.

Draw a figure (with log-earnings on the y-axis and education on the x-axis) to show the educational choice of the two-types of people. Will they choose different education levels?

Suppose that the two-types of people also have different marginal benefits (bj and bk) from an extra year of schooling; the k-type has a higher benefit than the j-type (bj aj). Use a figure to show the education choice made by the two-types, and what the OLS estimate of the return to education would be in this case? How does the OLS estimate compare to the “true” returns to education for the two-types?

Now suppose that everyone has the same abilities (ai = a) and marginal benefits to education (bi = b), but that marginal costs vary in the population; the j-type faces higher marginal costs than the k-type (cj > ck). Show graphically the education choices made by the two groups and illustrate the OLS estimate. How does it compare to the “true” return to education in the population?

Angrist and Krueger (1991) find that the instrumental variables estimate of the return to education is higher than the OLS estimate. Evidence from “twins’ studies (e.g., Ashenfelter and Krueger, 1994) suggests very little omitted variables bias in the conventional OLS estimate of the return to education.

i) Using a figure similar to those you made above, illustrate a situation that could explain these findings in a model that allows for heterogeneous marginal benefits and costs of schooling.

ii) Describe the relative importance of marginal benefits and costs in determining schooling choice in your figure.

iii) What do you conclude about the implications for the role of government in reducing education costs in order to increase the human capital of the U.S. population? Explain.

Paper For Above instruction

The educational investment decisions of individuals are profoundly influenced by the interplay between marginal costs and benefits, which in turn are affected by individual heterogeneity in ability and the valuation of education. This paper explores the theoretical underpinnings of these decisions, analyzing how different individual characteristics influence schooling choices and the implications for policy interventions aimed at enhancing human capital.

Introduction

Understanding the determinants of educational attainment requires examining how marginal costs and benefits shape individual choices. Variations in ability, perceived returns, and costs lead to differential schooling levels across the population. Developing a comprehensive model necessitates considering heterogeneity in these parameters and their effects on educational investment decisions.

Heterogeneity in Ability and Education Choice

In the simplest scenario where marginal costs and benefits are constant across individuals (bi = b and ci = c), individuals decide their optimal schooling level by equating marginal benefits to marginal costs. When ability varies between two types—high-ability (k) and lower-ability (j)—with abilities ak > aj, the higher ability individual experiences higher earnings at any given education level, shifting their earnings profile upward. If the marginal benefits and costs are identical for both types, their education choice depends on where their respective earnings profiles intersect the net benefits derived from schooling.

Graphically, the log-earnings profiles for both types increase with education, but the k-type’s curve lies consistently above the j-type’s. Both types will choose their optimal education level where the marginal benefit equals the marginal cost, typically resulting in higher schooling levels for the higher ability group. Consequently, different ability groups tend to choose different education levels, with high-ability individuals investing more in education.

This divergence in choices leads to heterogeneity in educational attainment and earnings. Importantly, the Ordinary Least Squares (OLS) estimate of the return to education in this context typically reflects an average of the true returns across the population. Given that higher ability individuals tend to attain more education and earn higher wages, the OLS estimate may be biased upward, overestimating the true return for the average individual.

Heterogeneity in Marginal Benefits with Constant Costs

Introducing variability in marginal benefits (bj and bk), with the higher benefit group (k-type) valuing additional schooling more than the lower benefit group (j-type), alters the decision framework. Both types face the same marginal costs, but their valuation of additional education differs. The k-type’s higher perceived benefits lead them to invest in more education, shifting their optimal education choice upward relative to the j-type.

Graphically, the earnings profiles remain identical, but the points where individuals equate benefits and costs differ, resulting in different education levels chosen across types. In estimating the return to education using OLS, the estimate tends to reflect an average benefit across groups, which may differ from the “true” returns experienced by each type. If the higher-benefit group invests more in education, the OLS estimate may be biased upward, overestimating the true average return, especially if a significant portion of the population has comparatively low marginal benefits from schooling.

Heterogeneity in Marginal Costs with Constant Ability and Benefits

When marginal costs vary among individuals, with the j-type facing higher costs (cj > ck) than the k-type, their schooling choices diverge accordingly. Both types perceive the same benefits and ability levels but differ in their cost burdens. The lower-cost group (k) is incentivized to attain higher education levels, as their net benefit from additional schooling is greater at each stage.

Graphically, the education choices can be depicted through the intersection points of identical benefit and ability profiles with different cost curves. The higher-cost individuals tend to choose lower education levels, resulting in a negative correlation between marginal costs and schooling attainment. The estimated return to education via OLS in this scenario reflects the average benefit relative to costs, but it may be biased downward if higher-cost individuals are underinvesting relative to their potential due to higher costs. Thus, the true return for the population may be underrepresented in the aggregate estimate.

Insights from Instrumental Variables and Twin Studies

Empirical findings by Angrist and Krueger (1991) suggest that instrumental variables (IV) estimates of the return to education are higher than the traditional OLS estimates. This discrepancy can be explained by heterogeneity in the marginal benefits and costs of schooling across individuals. A graphical representation illustrates how IV estimates isolate exogenous variation in educational attainment, often capturing the true causal effect when unobserved heterogeneity biases OLS estimates downward.

Similarly, twin studies by Ashenfelter and Krueger (1994) indicate that the OLS estimates are relatively unbiased, implying that omitted variable bias may not substantially distort the estimates in some contexts. However, the heterogeneity in marginal benefits and costs still plays a crucial role in understanding the decision-making process and the resulting evaluation of returns.

Implications for Policy and Government Intervention

Graphically representing these concepts reveals that policies aimed at reducing marginal costs—such as providing subsidies, scholarships, or lowering tuition—can significantly influence schooling choices, especially for high-cost individuals. As the models indicate, decreasing costs shifts the optimal education level upward, increasing the overall human capital in the economy. Additionally, policies that enhance perceived benefits—such as providing better information about future earnings or improving the quality of education—can further incentivize higher educational attainment.

Given the evidence that the true returns to education are often underestimated by OLS and that heterogeneity in costs and benefits influences schooling decisions, government intervention that reduces costs may be a particularly effective strategy. Such measures ensure that more individuals, especially those facing higher costs, can access the benefits of higher education, ultimately elevating the human capital and productivity of the entire population.

Furthermore, understanding the differential treatment of various groups through these models can help tailor policies to maximize their effectiveness, ensuring equitable access to education and optimizing social returns.

Conclusion

The decision to invest in education is multifaceted, impacted by individual heterogeneity in abilities, perceived benefits, and costs. Graphical analysis of these factors demonstrates how different groups choose different levels of schooling, and how estimation techniques like OLS and IV can yield different insights into the true return to education. Policy measures aimed at reducing costs and increasing benefits are vital in promoting higher educational attainment and improving the socio-economic landscape of the United States. Addressing heterogeneity through targeted interventions can lead to a more educated, productive, and equitable society.

References

• Angrist, J. D., & Krueger, A. B. (1991). Does compulsory schooling attendance affect schooling and earnings? Quarterly Journal of Economics, 106(2), 979–1014.
• Ashenfelter, O., & Krueger, A. (1994). Estimates of the economic return to schooling from sibling differences: Children of twins and twins itself. American Economic Review, 84(5), 1155–1174.
• Becker, G. S. (1993). Human capital: A theoretical and empirical analysis, with special reference to education. University of Chicago Press.
• Card, D. (1999). The causal effect of education on earnings. In O. C. Ashenfelter & D. Card (Eds.), Handbook of Labor Economics (Vol. 3, pp. 1801-1863). Elsevier.
• Heckman, J. J., Lochner, L., & Taber, C. (1998). General-equilibrium treatment effects: A study of tuition policy. handbook of Econometrics, 5, 4363–4464.
• Moretti, E. (2004). Estimating the social economic gains from education. The Journal of Economic Perspectives, 18(4), 22–43.
• Oreopoulos, P. (2007). Do dropouts drop out too soon? Wealth and the returns to education. Canadian Journal of Economics, 40(4), 1231-1264.
• Pischke, J. S., & Velling, J. (2008). Estimating the return to college cross-sectional versus long-run methods. Economics of Education Review, 27(4), 424-432.
• Schultz, T. W. (1961). Investment in human capital. The American Economic Review, 51(1), 1–17.
• Weil, D. N. (2014). Economic growth. Pearson.