EC3044 Economics of Education 2023-2024 Semester 2

Assessment Type:           Individual Assessment

Weighting:                         100%

Deadline:                           24/4/2024 at 15:00 via Turnitin on Blackboard

Academic Year:                    2023-2024 Semester 2

Assignment Brief

1. This written assignment makes up 100% of the module mark.

2. Due date: April 24, 2024, at 3pm UK time to be submitted in Blackboard

3. Release date: April 18, 2024, at 3pm UK time in Blackboard

4. Eight questions, three of which with multiple parts; the mark for each subpart is stated in the question.  Answer all questions.

5. All questions should be either straight from, or at least closely related to, materials in lecture notes, seminar questions, suggested readings mentioned in Blackboard.

6. No calculations question.

7. No word limits: see my answers to seminar questions for details expected. Background discussions should be limited to just suffice for a clear answer.

1. Consider the Benabou model.

(a) There are two districts in the city.  Suppose that district C1 has 30% and district C2 70% of the city’s housing stock. Also, 30% of households in the city are type A high income (human capital) households and 70% are type B low income (human capital). Let hA and hB  denote the respective human capital of the parents of types A and B households, ρ1 and ρ2  the respective rents in districts 1 and 2, x1  and x2  the respective fractions of type A households in districts 1 and 2 and V the indirect utility function.

(i) (5 points) Suppose that C1  is the high-income district in a segregated equilibrium; i.e., x1  > x2. Can the equilibrium rents be such that that V(hB, ρ1, x1) > V(hB, ρ2, x2)?  Why or why not?

(ii) (5 points) Suppose that C2  is the high-income district in a segregated equilibrium; i.e., x2  > x1. Can the equilibrium rents be such that that V(hA, ρ1, x1) > V(hA, ρ2, x2)?  Why or why not?

(b) (12 points) The UK shows low levels of social mobility, meaning that there is a high correlation between parent and children’s income or other socio-economic indicators. What are the conditions in the Benabou model that may cause the high correlation? Explain.  What policy interventions may counteract the effects of each of those conditions that cause the high correlation?

2. (8 points) There is an inherent efficiency-equality tradeoff in the Lazear model of optimal class size; i.e., efficiency may only be attained at the expense of sacrificing the equality of educational opportunity.  Explain what that tradeoff is about.

3. (7 points) There are two types of workers whose productivities are equal to a H  and aL, respectively, where aH  > aL. It costs a type H worker cH  to acquire a given educational qualification and a type L worker cL  to do so, where cL  > cH. Among the population of workers, a fraction h is type H and the rest are type L.  Consider the statement: Type L workers would choose to acquire the educational qualification if cL  < aH  - aL since the increase in wage earning suffices to cover the cost of acquiring the qualifications. True or false?  Explain.

4. Consider the model by Epple and Romano (1998) in the lecture, “Private Schools and School Vouchers” .

(a) (8 points) There are two private schools i = 1,2 and a public-school sector indexed by i = 0. The school qualities of these schools are, respectively, θ0  = 20, θ1  = 23 and θ2  = 40.  Suppose a student is offered admission by both schools 1 and 2 and the student is indifferent between the two schools. Is this student paying a tuition above or just equal to school 1’s EMC (effective marginal cost) to admit the student? Is this student paying a tuition above or just to school  2’s EMC to admit the student?  Explain.

(b) (7 points) Who should benefit the most in terms of income level and ability from the introduction of universal school vouchers?  Explain.

5. (8 points) In empirical studies of students’ educational performance, the usual finding is that parental inputs, but not school inputs, matter.  Suppose the truth is that both inputs do matter, but it is just that the usual OLS estimation somehow misses the impacts of school inputs on students’ educational performance but manages to capture the impacts of parental inputs.  Use the Ballentine diagram to illustrate how this might happen.  Explain why the sizes of the various circles and the extent to which they overlap in your diagram are reasonable depiction of reality.

6.  There are four schools (s1, s2, s3, s4), each with only one seat, and four students (i1, i2, i3, i4). Student preferences and school priorities are as follows:

(a) (6 points) Find the matching under the Boston Mechanism (BM), assuming that students truthfully reveal their preferences. Show your steps. Is the resulting matching strategy proof?  Explain.

(b) (6 points) Find the matching under the Deferred Acceptance Mechanism (DA). Show your steps.

(c) (6 points) Find the matching under the Top-Trading Cycle Mechanism (TTC). Show your steps.

(d) (6 points) Is the matching under DA Pareto Optimal?  Is the matching under TTC stable? Explain.

7. (8 points) Consider the cognitive and non-cognitive skill equations in Cunha et al. For s = 1,2,

θC,t+1  = [ys,C, 1θt(C),S   + ys,C,2θN(φ),t(C),S   + ys,C,3It(C),S   + ys,C,4θP(C),S   + ys,C, 5θN(φ),P(C),S ]1/φ C,S      θN,t+1  = [ys,N, 1θt(N),S   + ys,N,2θN(φ),t(N),S   + ys,N,3IN(φ),t(N),S   + ys,N,4θP(N),S   + ys,N, 5θN(φ),P(N),S ]1/φN,S

where the variables and parameters are as defined in slides 36-38 and 72-73 of the lecture, “Early Childhood Education - the formation of cognitive and noncognitive skills” .  The estimates are as follows:

Should remedial investment in s = 2 mainly be used for cognitive or non-cognitive skills?  Explain.

8. (8 points) In the lecture “Returns to Education”, we explain how we may use a student’s physical distance to an educational institution as an instrument for schooling to help eliminate the bias in OLS estimation. A possible alternative instrument for schooling is the education level of the student’s parents. Write down the two-stage least squares estimation equations in this case. Do you think this would also eliminate the bias in OLS estimation? Explain.