Education

Question 1

What are some of the reasons that parents may decide to send their children to school?

Answer 1

a. Education can increase future earnings potential
b. Education can lead to better health outcomes
c. Education provides a better overall understanding of the world

Question 2

Which of the following is meant by the “sheepskin” effect in the context of education?

Answer 2

“Sheepskin” refers to the pure signaling effect of education, where aside from any knowledge or skills learned, having completed a certain level of education enables someone to earn a higher wage.

Question 3

In which ways might additional education benefit girls?

Answer 3

• Improving how much they can earn in the labor market
• Improving standing in the marriage market
• Increasing future bargaining power within the household
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Question 4

What are some possible spillovers or externalities from education?

Answer 4

• Positive: Having more educated people in an area might lead to better labor market opportunities
• Positive: Having more educated people in an area might lead to more political activism and pressure on the government to develop more effective institutions
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Question 5

True or false: Many people in the developing world earn income from agriculture. For these people, the benefits of a traditional classroom education are almost surely near zero.

Answer 5

False.

Question 6

The graph above shows years of schooling on the x-axis and log income on the y-axis. Call the slope of this line β. How do we interpret the slope of this log-linear relationship?

Answer 6

The slope at any given point represents the proportional increase in income associated with a 1-year increase in schooling.

The graph above is of the form ln(y)=Bx + ε (where ε represents the error term). The mathematical interpretation of the slope is it represents the proportional change in income associated with a one-year increase in schooling attainment. To see this, differentiate the equation with respect to x (1/y)(dy/dx) = B

Discretizing the derivatives, you can see that when dx=1, B = (delta y)/y

Question 7

As shown in the same graph above, each additional year of schooling:

Answer 7

Is correlated with higher income in the future. The graph shows a clear positive association between years of schooling and future earnings. However, we cannot say that this relationship is causal, as in A, since there could be any number of other factors that would explain why children who are more likely to stay in school longer are also more likely to have higher income in the future. In other words, when we compare outcomes for someone who has 4 years of schooling to someone who has 10 years of schooling, we could be looking at very different people. Since there is a clear relationship between the two, the most we can say just from observing this relationship is that years of schooling are positively correlated with greater future income, as in B.

Question 8

What other factors could be driving the observed relationship between additional years of schooling and earning potential?

Answer 8

• Children who are more motivated or driven stay in school longer, and these same children are the ones that would earn more in the future anyways.
• Children with rich parents can afford to stay in school longer, and these are the same children that would earn more in the future anyways
• Smart children stay in school longer, and these are the same children that would earn more in the future anyways

Question 9

Using the table provided above, how does the probability of ever enrolling in senior high school differ between boys in the treatment group (assigned to scholarship) and boys in the control group (not assigned to scholarship)?

Answer 9

57% of the control group enrolls, 93% of the treatment group enrolls, and the difference is statistically significant.

Question 10

Let Yi denote cognitive test scores, Ai denote years of schooling, and Zi denote assignment to the scholarship. Use the following expressions to answer the next questions.

Answer 10

The effect of assignment to the scholarship on school participation, which can be interpreted as a causal relationship.

Question 11

Equation (2) describes which of the following?

Answer 11

The effect of assignment to the scholarship on cognitive test scores, which can be interpreted as a causal relationship.

Question 12

Equation (3) describes which of the following?

Answer 12

The instrumental variables estimate of the effect of years of schooling on cognitive test scores. Equation (3) describes the instrumental variables estimate of the effect of years of schooling on cognitive test scores, as in B. This is what is known as the “Wald Estimate,” which is the ratio of the effect of the scholarship program on cognitive test scores to the effect of the scholarship program on school attendance (or the reduced form estimate divided by the first stage estimate).

Question 13

Which of the following assumptions is needed for beta to be a valid estimate of the effect of years of schooling on cognitive test scores?

Answer 13

• Random assignment to the scholarship program is correlated with school attendance decisions
• Random assignment to the scholarship program impacts cognitive test scores ONLY through its impact on years of schooling

Question 14

Which of the following would make assignment to the scholarship an invalid instrument?

Answer 14

• The scholarship was not randomly assigned
• The scholarship came along with a study guide only available to scholarship winners, and this study guide gave them an advantage in the test compared to non-scholarship winning classmates

Question 15

According to the results presented in class, what is the causal effect of assignment to the scholarship group on ever enrolled in secondary high school for males?

Answer 15

36 percentage points.

Question 16

According to the results presented in class, what is the causal effect of assignment to the scholarship group on cognitive test scores for males in the 2008 cohort?

Answer 16

0.13 standard deviations. The causal effect of assignment to the scholarship group on cognitive test scores for males is 0.13 standard deviations. This can be calculated by taking the difference in means in cognitive test scores between the treatment and control groups, or 0.31-0.18=0.13. This represents the reduced form.

Question 17

According to the results presented in class, what is the effect additional years of schooling on cognitive test scores for males in the 2008 cohort?

Answer 17

0.36 standard deviations. According to the instrumental variables analysis presented in class, the effect of additional years of schooling on cognitive test scores for males in the 2008 cohort is 0.36 standard deviations. This is calculated by taking the reduced form estimate (0.13 standard deviations) and dividing by the first stage estimate (36% or 0.36). 0.13 standard deviations divided by 36% equals 0.36 standard deviations. This is known as the Wald estimate.

Question 18

True or false. Suppose schools are randomly assigned to receive or not receive deworming medication. (Randomization is done at the school, rather than the classroom or individual level.) Suppose a researcher would like to get the effect of actually receiving the deworming medication, but that not all children assigned to the treatment actually received deworming medication. True or false: being in a treatment school is a valid instrument for actually receiving deworming medication.

Answer 18

False, assignment to a treatment school is NOT a valid instrument for actually taking the deworming medication, in this case. This is because there could be (indeed there very likely are) positive spillovers from those who take deworming medication and those who do not, but are surrounded by others in their school who take deworming medication. If you used assignment to a treatment school as an instrument, and calculated the Wald estimate by dividing the impact of treatment on a certain outcome by the impact of assignment to treatment on taking deworming medication, you would end up with a biased overestimate of the impact of deworming on that outcome.

Question 19

In the schooling decisions model presented in class, what are some of the limitations of the parent’s utility function expressed as a function of their child’s income?

Answer 19

• Does not include benefits of education, aside from increases in future income
• Does not factor in the child’s utility and preferences related to education and future income
• Returns to education are assumed to be linear in log for all years of education, which may not be accurate

Question 20

What is one hypothesis for the belief that early years of education have higher returns than later years of education?

Answer 20

What children learn in the first years of education (for example, how to read) is more helpful than what children learn in later years. As discussed in class, one hypothesis for the belief that returns to education are high for low levels of education and flatten out for high levels of education is that the basic concepts learned early on are the most useful in terms of enable children to earn a higher future income. In contrast, what children learn in later years tends to provide a smaller marginal benefit to future income. Note that this is just a hypothesis discussed, as there seems to be evidence that returns to education are relatively constant over years of education.

Question 21

True or false: Parents tend to believe that returns to education are low for early years of education and high only for later years of education as a child earns a degree.

Answer 21

True. Many parents tend to believe that the first years of education are not useful on their own, but that returns to education are only realized when children complete many years of education, ultimately leading to a degree. One consequence of this belief is that parents may not invest in just a few years of a child’s education if they do not think that child will be able to continue on to many years of education and/or complete a degree.

Question 22

In the Indonesian school construction experiment Professor Duflo describes in class, what can we learn from using primary school construction as an instrument for school enrollment?

Answer 22

The weighted average of the returns to each year of education in primary school only. In the Indonesian school construction example presented in class, the instrumental variable estimates provide a weighted average of the returns to education for a year in primary school, weighted for each year by the fraction of children moved from that year to the next. This is because the instrument, construction of primary schools, only directly affects primary school enrollment decisions. Conceptually, in order to estimate the returns to education at each specific year of education, we would need a separate instrument that affects only that year of education. In this case, the instrument affected primary schooling decisions only, through the widespread construction of primary schools in Indonesia.

Question 23

Which of the following is consistent with how we would expect the costs of education h(S) and marginal cost of education h’(S) to look over years if costs of education are convex?

Answer 23

D. If the costs of education are convex over years of education, this means that the costs of education increase with more years of education. h(S) would slope upwards at an increasing rate, and marginal costs (the derivative of total costs) would be positive and slope upwards.

Question 24

Which of the following describes the process for deriving the model solution for the parent’s utility maximization problem, according to the model discussed in class?

Answer 24

Set the first derivative of parents’ benefits obtained from future income equal to the first derivative of cost of schooling, solve for optimal schooling S*. To find the optimal level of schooling within our model, we must solve the parent’s utility maximization problem with respect to schooling.

Question 25

What would we expect to happen to the optimal level of schooling chosen for children if how much parents value children’s future income (m) increases?

Question 26

How does the quality of education factor in to the optimal level of schooling chosen?

Question 27

Assume the following:

Parents believe that the returns to education are linear

Parents are credit-constrained, that is they cannot spend more than Ĥ per child on education

The cost associated with optimal schooling (S*) is less than Ĥ per child.

What will happen to the amount of schooling they choose to invest in for their children compared to the case without credit-constraints?

Question 28

Now assume the following:

Parents believe that the returns to education are linear

Parents are credit-constrained, that is, they cannot spend more than Ĥ per child on education

The cost associated with optimal schooling (S*) is more than Ĥ per child.

What will happen to the amount of schooling they choose to invest in for their children compared to the case without credit-constraints?

Answer 28

In the presence of a binding credit constraint, parents will not be able to educate their children for as many years as they would like. Assuming that returns to education are linear, parents would still invest in each child equally, but would invest less and be able to afford fewer years than would be optimal according to their utility maximization problem. This is because the cost of educations are convex, so if they did anything different, they could get more “bang for the buck” by reallocating some of the money from the child they are educating the most to a child they are educating less (and therefore has a lower marginal cost).

Question 29

Now assume the following:

Parents believe that the returns to education are non-linear, specifically that returns to education are zero up until a certain point Ŝ, and then increasing with years of education thereafter

They have two children

“Parents are credit-constrained, that is, they cannot spend more than Ĥ*2 on education”

The cost associated with optimal schooling (S*) is more than Ĥ*2 per child

The cost associated with Ŝ is more than Ĥ and less than Ĥ*2

S* is greater than Ŝ

Assume that parents are maximizing the sum of their children’s net returns to schooling. What may happen to the amount of schooling they choose to invest in for their children compared to the case without credit-constraints?

Answer 29

This describes the situation where parents do not believe that just a handful of years would be valuable for their children, and that the only benefits to education occur when they can afford to send their child to school for many years, for example, to earn a degree. If they cannot afford to send both their children to school, they may select one to send to school for some number of years, and will not send the other to school at all.

Question 30

Now assume the following:

Parents believe that the returns to education are non-linear, specifically that returns to education are zero up until a certain point Ŝ, and then increasing with years of education thereafter

They have two children

“Parents are credit-constrained, that is, they cannot spend more than Ĥ*2 on education”

The cost associated with optimal schooling (S*) is more than Ĥ*2 per child

The cost associated with Ŝ is more than Ĥ*2

The cost associated with S* is more than Ĥ*2

What may happen to the amount of schooling they choose to invest in for their children compared to the case without credit-constraints?

Answer 30

If parents believe that the benefits of education are zero up until a certain threshold level Ŝ, and they cannot afford to send even one child to school at that cost they will not send any children to school and will not invest in any education for their children (even though they have a budget to send children to school for at least some small number of years). This describes the case where credit-constraints combined with distorted beliefs about the returns to education can lead to a poverty trap.

Question 31

Suppose that a set of parents have two children, Neel and Rajkumar. Suppose further, that the parents DO believe that returns to education are linear, but that the returns to education are higher for Neel than for Rajkumar at all levels of education, as shown in the graph above. True or false: If the parents cannot afford to educate both children fully, they should spend their entire education budget sending Neel to school and will not educate Rajkumar for any number of years.

Answer 31

This is false. Even if one child has higher returns to education than another, if parents believe that returns to education are linear, then they should educate both children for at least some number of years. As Professor Duflo discusses in class, under linear returns to education (and some available budget to spend on education), no child’s optimal level of schooling would be zero years. What would likely happen in this family is that Neel will be educated for more years than Rajkumar.

The key here is to realize that though returns are linear, costs of schooling is convex.

Question 32

Conditional cash transfers (conditioned on school attendance) are often designed to ________________________

Answer 32

Increase over time, to offset direct costs and opportunity costs that are higher for later years of education. As children become older, the opportunity cost of education increases, since the alternative to school attendance may be working in the labor force for a wage. Later years of education may also have higher direct costs. Combining these two, the total cost of education tends to increase over years of education. Conditional cash transfers are often designed so that they increase over time, as a way of offsetting these increasing costs and making it easier for families to continue to send their children to school.

Question 33

True or false: Providing information about the true returns to education has no impact on perceived returns to education.

Answer 33

False. Despite initial distorted beliefs about the returns to education, Tran Nguyen found that when parents in Madagascar were informed about the returns to education, they updated their beliefs about the returns to education. This suggests that parents are responsive to information about the returns to education and that distorted beliefs about the returns to education could be addressed using informational interventions.

Question 34

Which of the following describes social desirability bias?

Answer 34

If you ask parents about the education decisions they make for their children, they are likely to tell you what they think you want to hear. Social desirability bias refers to bias that can occur at the stage of data collection. The refers to the biases that could be introduced if interview or survey respondents answer questions so as to respond with what they think the interviewer or surveyor would like to hear, rather than what may be the truth or the most accurate answer.

Question 35

The graph above shows believed versus actual achievement. According to the graph, between __________ of parents overestimate their children’s achievement.

Answer 35

Somewhere between 75% and 90%. The graph above shows the gap between believed and actual achievement of children in the sample in Malawi. The graph shows that somewhere between 75% and 90% (corresponding to the distribution crossing believed-actual score=0 somewhere between the 10th and 25th percentile) of parents overestimate their children’s scores.

Question 36

Imagine that the marginal cost of school increases with the number of years you are in school. Which of the following sets of indifference curves represents this graphically, where the arrow indicates the direction of increasing utility?

Answer 36

A. Utility increases up and to the left – people prefer to earn more and prefer to spend less on education.

Question 37

Suppose that the returns to education are given by the equation:

y_i=a_i*S_i

Which of the following lines represents the returns to schooling, where returns are on the Y-axis and years of schooling are on the X-axis for any given ability ai?

Answer 37

A.