The Ohio State University Daeho Kim Department Of Economics

The Ohio State University Daeho Kim Department Of Economics Spring 2016 ECON 5850 PROBLEM SET #3 Due in class on Thursday, April 7

1. a) The Targeted Jobs Tax Credit (TJTC), enacted in 1978 and expired in 1994, offered employers a fixed tax credit per hour worked by less-skilled workers. According to neoclassical theory, how should this tax credit have affected wages and employment of less-skilled workers? Explain and show graphically.

b) Suppose that instead of offering a tax credit to employers to hire less-skilled workers, the government increases employer payroll taxes to finance expanded unemployment insurance.

• i) Use graphs to explain how the incidence of the payroll tax—the share borne by workers versus employers—would distribute in response.
• ii) Explain and show graphically how employment levels depend on the elasticity of the labor supply curve.

2. a) Briefly describe the human capital theory of educational attainment. A verbal description is sufficient, but a figure may help conceptualize the idea.

b) Consider the following linear regression model for individual earnings:

log(Wi) = α + θSi + ui

where Wi are the earnings of individual i and Si are the years of schooling obtained by i. When will the ordinary least squares (OLS) estimate of θ be an unbiased estimate of the “returns to schooling”?

c) Suppose the true regression model (excluding other observed variables) is:

log(Wi) = α + θSi + Ai + ui

where Ai is unobserved ability; and Cov(Si, Ai) ≠ 0.

• i) When will the OLS estimate of θ be biased due to unobserved ability (Ai)?
• ii) Write a formula for the omitted variable bias associated with Ai.
• iii) How does each component of the bias term influence the direction (sign) and magnitude of the bias?

d) Now suppose that education data is self-reported. Describe how measurement error in self-reported education can bias the OLS estimate of θ.

e) In order to reduce the “ability bias,” Angrist and Krueger (1991) used quarter of birth as an instrumental variable (IV) for years of education.

• i) Under what conditions is this IV valid?
• ii) How might you examine its validity?
• iii) They found that individuals born in the first quarter had 0.11 fewer years of education and 1.1% lower earnings; calculate the IV estimate of the return to an additional year of education.

f) Ashenfelter and Krueger (1994) propose using twin data to address ability bias, assuming genetically identical twins have the same abilities. Explain how comparing twin differences might exacerbate measurement error bias when education levels are self-reported.

g) Suppose data includes each twin’s response to “How many years of education does your twin have?” Describe how you could use this information to correct for measurement error bias.

h) Assuming measurement error is corrected, discuss potential omitted variable bias in twin-differences estimates of the return to education if genetically identical twins have different abilities.

Paper For Above instruction

The Targeted Jobs Tax Credit (TJTC), implemented from 1978 to 1994, aimed to incentivize the employment of less-skilled workers by providing a fixed tax credit per hour worked. From an neoclassical economic perspective, this subsidy effectively reduces the marginal cost of hiring such workers for employers, which typically leads to an increase in employment of less-skilled workers. The impact on wages, however, depends on the relative elasticities of labor supply and demand. If labor supply is relatively inelastic, wages may rise; if elastic, wages might remain unchanged or even decrease because employers capture most of the benefit of the tax credit, leading to a potential increase in employment without significant wage changes. Graphically, this can be depicted with demand and supply curves for less-skilled labor, illustrating how the tax credit shifts the effective demand curve outward, increasing equilibrium employment, while the shift in wages depends on elasticity.

In contrast, if the government raises employer payroll taxes to finance expanding unemployment insurance, the incidence—the share of the tax burden borne by workers versus employers—is determined by the relative elasticities of supply and demand. If the labor supply is relatively elastic, workers bear a smaller share of the tax burden, and employers absorb more; if supply is inelastic, workers absorb a larger share, resulting in lower net wages. Graphically, the payroll tax shifts the supply curve vertically upward by the amount of the tax. The resulting new equilibrium shows how the tax burden is split: the relative slopes of the demand and supply curves determine the incidence. Moreover, employment levels are sensitive to supply elasticity: a more elastic supply results in a larger reduction in employment, as labor becomes less willing or able to supply additional hours at the prevailing wage, while more inelastic supply buffers employment changes.

The human capital theory posits that educational attainment enhances productivity, leading to higher earnings throughout an individual’s life. Education increases skills, knowledge, and other productive capabilities, which translate into higher human capital. Economically, this theory argues that investment in education yields returns in the form of increased earnings, justifying educational spending from both individual and societal perspectives. A simple figure illustrating human capital accumulation shows a positive relationship between education levels and productivity or earnings, often depicted as an upward-sloping curve, reflecting the idea that more education generally correlates with higher human capital and earnings.

When analyzing the returns to schooling through regression, the model:

log(Wi) = α + θSi + ui

has an unbiased estimate of θ when Si is uncorrelated with the error term ui—that is, there are no omitted variable biases or simultaneity issues. The key condition is that the variation in Si used to identify θ is exogenous and not correlated with unobserved factors affecting wages.

However, if the true model includes unobserved ability Ai:

log(Wi) = α + θSi + Ai + ui

and Ai correlates with Si, then OLS estimates of θ will be biased. Specifically, if higher ability leads to both higher education and higher wages, the estimated return to schooling captures both the effect of schooling and ability, inflating the true return. The bias magnitude depends on the covariance between Si and Ai, and between Ai and log(Wi).

The bias formula can be expressed as:

Bias(θ̂) ≈ (Cov(Si, Ai) / Var(Si)) × (the effect of Ai on log(Wi)))

indicating that if ability and schooling are positively correlated, the estimated return to schooling will be upward biased; if negatively correlated, downward biased. Larger covariance and stronger effect of ability on wage growth increase the bias magnitude.

Measurement error in self-reported education typically leads to attenuation bias, where estimated coefficients are biased toward zero. This occurs because the actual variation in schooling is not accurately captured, reducing the estimated impact of additional education on earnings.

To mitigate the ability bias, Angrist and Krueger used quarter of birth as an IV for years of education, relying on the exogeneity of birth quarter relative to individual ability. Validity hinges on two conditions: first, the IV must be correlated with the endogenous regressor (education); second, it must not directly affect earnings except through education. Validity can be examined by testing the strength of the IV’s correlation with schooling and ensuring no direct pathway to earnings.

Using their data, the IV estimate of the return to an additional year of schooling is calculated as the ratio of the effect of the IV on earnings to its effect on schooling:

Return = (Change in earnings) / (Change in years of education) = 0.011 / 0.11 = 0.10 or 10%.

A twin study proposed by Ashenfelter and Krueger aims to control for unobserved heterogeneity by examining differences within twin pairs, presuming identical genetics and similar environments. However, if education levels are self-reported, measurement errors could be exacerbated because twins might overreport or misreport their education differences, increasing measurement error variance. This can bias the difference-in-differences estimates towards zero or inflate variance, weakening causal inference.

If the dataset includes each twin’s report of the other’s education, this information can be used to cross-validate or adjust reported years, employing measurement error correction techniques such as instrumental variables or errors-in-variables models. Accurate cross-reporting can help identify and correct for bias introduced by misreporting, leading to more reliable estimates of the returns to education.

Finally, once measurement error is addressed, potential omitted variable bias in twin-study estimates remains if genetically identical twins have differing abilities. Such differences, if correlated with both education and earnings, could still bias the estimated return to education, emphasizing that controlling for ability is essential even in twin difference models.

References

• Angrist, J. D., & Krueger, A. B. (1991). Does compulsory school attendance affect schooling and earnings? National Bureau of Economic Research.
• Ashenfelter, O., & Krueger, A. B. (1994). Estimates of the effect of twin differences in education on earnings. NBER Working Paper No. 4869.
• Becker, G. S. (1993). Human capital: A theoretical and empirical analysis, with applications to college admission. University of Chicago Press.
• Card, D. (2001). Estimating the return to schooling: Progress on some persistent econometric problems. Econometrica, 69(5), 1127-1160.
• Krueger, A. B., & Lindahl, M. (2001). Education for growth: Why and for whom? Journal of Economic Literature, 39(4), 1101-1136.
• Mincer, J. (1974). Schooling, Experience, and Earnings. Columbia University Press.
• Oreopoulos, P. (2009). Do dropouts benefit from remedial education? Evidence from Ontario high school reorganization. American Economic Journal: Applied Economics, 1(1), 163-188.
• Schultz, T. W. (1961). Investment in human capital. The American Economic Review, 51(1), 1-17.
• Stiglitz, J. E. (1985). Information and economic analysis. In Handbook of Industrial Organization (pp. 949-1019). Elsevier.
• Wilson, R. (1986). The basic income experiment in Northern Scotland: Report on the evaluation of the feasibility of an unconditional income for the Highlands and Islands. Scottish Office.