Assignment
Question 1:
a) The Targeted Jobs Tax Credit (TJTC) - enacted in 1978 and expired in 1994 - offered employers a tax credit for each less-skilled worker they employed. Assume that the tax credit was fixed at $5 per-hourworked by a less-skilled worker. 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 decides to increase employer payroll taxes to finance an expansion of unemployment insurance.
i) Use graphs to explain how the incidence of the payroll tax - i.e., the share of the tax borne by workers versus employers.
ii) Explain and show graphically how employment levels depend on the elasticity of the labor supply curve.
Question 2:
a) Briefly describe the human capital theory of educational attainment. A verbal description is fine, though a figure might help.
b) Consider the following linear regression model for individual earnings: Wi Si +Ui log = α +θ ⋅ 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 we believe that the true regression model (leaving out other observed variables for simplicity) is: i i Ai Ui logW = α +θ ⋅ S + γ ⋅ + where Ai is unobserved (omitted) ability; and Cov(Si ,Ui) = 0 , Cov(Ai ,Ui) = 0 .
i) When will the OLS estimate of θ be biased due to unobserved ability (Ai)?
ii) Write down a formula for the omitted variables bias if the omitted variable is ability (Ai).
iii) How does each component of the bias term affect the direction (i.e., sign) and magnitude of the ability bias?
d) Now suppose that the schooling attainment data you have is based on the self-report of individuals. Describe how measurement error in self-reported education can bias the OLS estimate of θ. 2
e) In order to reduce the "ability bias," Angrist and Krueger (1991) used quarter of birth as an instrumental variable for years of education - i.e., the instrument equals one if the person was born in the first quarter of the year and zero, otherwise.
i) Under what conditions is the instrumental variable used valid?
ii) How might you examine its validity?
iii) They found that individuals born in the first quarter of the year had 0.11 less years of education than those born in the last three quarters of the year; and that they had 1.1 percent lower earnings as adults. From these numbers, calculate the instrumental variables estimate of the effect of an extra year of education on earnings.
f) Ashenfelter and Krueger (1994)'s proposed solution to the "ability bias" problem is to collect data on identical twins and examine the relationship between twin differences in educational attainment and twin differences in earnings. Presumably, this strategy addresses ability bias if two genetically identical twins have exactly the same abilities. Describe how these comparisons of twin differences may exacerbate the measurement error bias problem when education levels are self-reported.
g) Suppose the data also contain each twin's response to the question "How many years of education does your twin have?" Describe how one could use this information to remove the measurement error bias.
h) Suppose you have found a way to correct for the measurement error problem - i.e., measurement error is no longer a problem. Describe the potential omitted variable problem in the twin-differences estimates of the return to education if genetically identical twins have different abilities.