Test
Q1) Hanushek and co-authors (2008) examine the determinants of economic growth for 50 countries over 40 years.
a) What are the two main measures of education attained by the population that the authors use to compare to countries' economic growth? Which of these two measures is more strongly related to economic growth?
b) What are the two reasons the authors give for why one of their measures of human capital can explain economic growth better than their other measure?
2) For this question we will assume that workers choose education with the goal of maximizing the present discounted value (PDV) of net earnings. Workers live two periods. Assume that the discount rate = 0 throughout this question. Also, for all parts of this question, there are two options for years of schooling: ED = 0 or ED = 1. In the first case workers work both periods of their lives (ages 1 and 2). In the second case, with ED = 1, workers attend school at age 1 and do not work, and then work at age 2.
a) Assume that net earnings for workers at ages 1 and 2 are as listed below, for the two possible levels of education ED = 0 and ED = 1. In this country, the government does not subsidize education.
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Level of education
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Net Earnings, Age 1
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Net Earnings, Age 2
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ED = 0
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$2
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$2
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ED = 1
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-$3
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$8
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Note that if the worker goes to school in period 1, net earnings = -$3, which reflects the costs of tuition. Workers can borrow freely at an interest rate of 0.
Calculate the PDV of lifetime net earnings for ED = 0 and ED = 1. What is the optimal choice of education?
b) Now assume that there are liquidity constraints, such that workers cannot borrow when aged 1 against their future human capital. So the minimum possible net earnings per period is 0. (This is an example of a "credit market failure": banks won't loan to young people for their education if they are uncertain they will be repaid later.) Is it possible for workers to choose ED = 0? How about ED = 1? Calculate the PDV of lifetime net earnings for any of the two choices, ED=0 and ED=1, that are feasible. What is the optimal choice of education?
c) Now, continue to assume as in b) that workers cannot borrow at age 1. However, the government pays for schooling at age 1 for all workers who want education. It pays the $3 per person cost of education by instituting a progressive income tax, in which those with ED=1 who are age 2 pay a tax of $3. Therefore, net earnings for the two education levels are now as shown below.
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Level of education
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Net Earnings, Age 1
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Net Earnings, Age 2
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ED = 0
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$2
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$2
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ED = 1
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-$3 + $3 subsidy = $0
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$8-$3 tax = $5
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Calculate the PDV of lifetime net earnings for ED=0 and ED=1. What is the optimal choice of education?
d) Which government policy, the "no subsidy" policy in b) and the subsidy policy in c), leads to the higher PDV of net earnings for workers?
e) Above you demonstrated that one of the reasons for government to subsidize education is liquidity constraints due to a credit market failure. Explain in a sentence or two the two other reasons we outlined in class for government subsidies of education.
Q3. In the economy we are considering, there are two types of workers, Low Ability and High Ability, but firms cannot tell the ability of any individual worker before they hire them. Firms highly value high-ability employees, and they decide to use the level of education acquired by workers as a signal of ability.
a) What assumption would have to be true for High Ability workers to be able to use education as a signal?
b) Assume that workers' utility function is wages minus the cost of education. On the graph on the next page, workers receive Wage = 1 if firms believe that they are Low Ability, and Wage = 2 if firms believe they are High Ability. These two wage possibilities are drawn into the graph. Also shown are the costs of education for High Ability and Low Ability workers. Give an example of how firms could set wages as a function of education in a way that would create a separating equilibrium. Show on the graph the wages firms actually offer for each level of education with a solid line. Indicate the optimal level of education that each type of worker would acquire. Label this level of education as ED*-HIGH and ED*-LOW for high and low ability workers on the horizontal axis. Explain the optimal choices of the two types of workers in a few sentences.
c) Now, on the copy of the earlier diagram shown below, indicate the minimum and maximum levels of education that firms could require that would lead to a separating equilibrium. Write these two values on the x-axis as EDMIN and EDMAX. Explain your reasoning in a few sentences.
d) One of the papers we examined which attempts to test whether education provides a signal rather than human capital is by Wolpin (1977). Wolpin looked at the education level obtained by workers who are employees compared to that obtained by workers who are self-employed.
i) What was his insight, and what did he find when he looked at the data? Do his results suggest that the signaling theory is true or false?
ii) What were the two potential weaknesses in Wolpin's logic, which I discussed in class?