What we would like to discuss in this thesis is how the existence and composition of private school affects the educational output when the main issue is about peer effects. In order to do so we need to show what aspects educational economists have been focusing on according to the past research related to peer effects. Peer effects have been an indispensable element to take into consideration in most of the preceding works on the production of education. Some consider the issue in a framework with public schools only, and some even include both public and private schools in their model.
When dealing with peer effects that affect the quality of educational output in classrooms, Arnott and Rowse (1987) discussed how educational expenditures should be allocated over classrooms when peer group effect is present with the use of a model where there is an education planner who wants to maximize social welfare subject to the budget constraint and the ability of students. Numerical tests were taken to see what the conditions are for streaming and mixing to occur as the best way to distribute students. The result is that the optimal allocation depends on the production function. Different production functions may provide different results. Similarly, Lazear (2001) analyzed peer effects by focusing on the problem of sorting of students and the quality of teachers by using a disruption model of educational production. The model takes the interruption of students’ asking questions into consideration, with the result that the optimal class size rises when the teacher’s age increases, when the probability of students behaving well increases, and when the value of a unit of education falls. Also, when the optimal class size is decided with certain assumptions, educational output is higher in classes that are larger in size with students that relatively behave well, vice versa. When dealing with peer effects that affect the
quality of educational output in “communities”, de Bartolome (1995) showed different composition of families by using a community model. First the model was used to see how families are allocated through migrating. Then the problem was dealt with as a central planner problem. The result shows that in order for a heterogeneous equilibrium to exist, the peer effect should neither be too strong nor too weak.
Some research treats schools as firms that attempt to maximize profit subject to their budget constraint. Rothchild and White (1995) concerned the problem of pricing of higher education in which the customers are also inputs. In this paper, students themselves which are simultaneously customers and the input of producing human capital may bring externality since the existence of better students are considered as a component of educational output for those who are less able. This externality is claimed to be internalized by charging different tuition in the paper. The result is that competitive firms are able to find a zero-profit price that efficiently allocates peer effects.
Education can be viewed as public goods. Tiebout (1956) intended to show that the Musgrave-Samuelson analysis need not apply to local expenditures. The paper showed that given several local governments with different economic structures and provision of public goods and assuming that the consumers are fully mobile, which means they choose where to live by their feet, then the optimal level of expenditure on public goods are actually decided by the consumers themselves. This is because the choice they make fits their preferences the best so that the governments do not have to play as a central planner and decide different expenditure levels on public goods according to different types of customers. That is to say, the customers distinguish themselves. Sandler and Tschrhart (1980) did a survey on the past research of club theory. Methods such as the Buchanan’s model, the general model and the game theory model were discussed. Miscellaneous issues were discussed in the theory of
club goods. For example, the membership heterogeneity, discrimination, and crowding effects, etc. The conclusion is that the theories of club goods can be applied to numerous issues, such as education. One of the extensions of club goods model they mentioned is the intergenerational clubs, which stands for clubs with multiple over-lapping generations of members. They claim it can be used to examine the principles of school district design.
Epple and Romano (1998) discussed the effect of vouchers and peer effects on social welfare when using both a theoretical and computational model with tax-financed, tuition free public schools and competitive, tuition financed private schools. In the model, achievement depends on the students own ability and ability of their peers. Private schools can discriminate in their tuition policies. The paper also included the effects of vouchers. The result is that the equilibrium has a strict hierarchy of school qualities and two-dimensional student sorting with stratification by ability and income. Also it showed that voucher programs could have significant distributional consequences. Winston (1999) tried to find out how well our knowledge of microeconomic theories can help us on understanding the economics of higher education. A review of literature regarding non-profit enterprises subsides and peer effects were cited and discussed. The paper also mentioned that colleges can buy important inputs to their production only from the customers who buy their products, which is similar to Rothchild and White (1995). The paper also discussed the hierarchy of colleges and universities, which is different from Epple and Romano (1998) where the focus was on high-school education, also the issue was discussed empirically. The conclusion is that standard economic intuition and analogies based on the knowledge of profit making firms are likely to be a poor guide to understanding higher education.
There has been controversy on how school voucher programs influence education. Ladd (2002) tried to provide evidence that large-scale vouchers will not derive significant gains in students’ achievement and might even be detrimental to disadvantaged students. By making a discussion on the past research, the conclusion is that widespread use of school vouchers is not likely to generate substantial gains in the productivity of the U.S. education system. Despite the fact that many claim that school vouchers play a small role in the education system, Neal (2002) argued that we cannot confidently predict the outcomes that would result from various voucher schemes. By describing both theoretical and empirical work that has been done on this topic, the conclusion is that vouchers cannot prove to be efficiently used, or might even create significant social costs.
The peer effect in this thesis affects the allocation of families among communities. We will not only borrow the community model of de Bartolome (1990), but will also make some revisions on the model itself, where the revisions are close to the assumptions made on the standard by which we discriminate the types of schools, types of students in Epple and Romano (1998), except that in our thesis, public schools are not exempted from charging tuition. The level of educational input of public schools is chosen the same way as in Tiebout (1956), which is by means of majority voting, while the level of input of private school is chosen similar to Rothschild and White (1995), where private school is treated as a kind of firm trying to solve its maximization problem subject to some constraints. In the following section, we will introduce the work of de Bartolome (1990) briefly and display the model. To confirm the conclusions in Ladd (2002) and Neal (2002), we try to find out how the voucher program promotes private school and its influence on educational output.