In this section I am presenting the statistical analyses aimed at answering my second research question. Now that I have established that there is indeed a private school advantage, it is important to identify what school factors explain this advantage, beyond the differences between types of students that I attempted to correct through propensity score matching.
I fitted several taxonomies of regression models, regressing student’s achievement in Mathematics on PRIVATE. I controlled for self-sorting into educational sector by including in the model the propensity score variable (pscore) created in the last section as a product of the propensity score matching estimation. I also included a set of peer group variables in the baseline model. Peer group effect is one of the most important factors explaining educational achievement. Although it is true that there has not been any previous educational policy in Mexico that attempted to alter this important educational input, it is not possible to properly identify the effect other school factors without
accounting for this effect. I then added systematically to the base-line model different set of predictors measuring the four main factors of school performance focus of this
dissertation: physical resources, school management, teacher quality, and teaching practices and classroom organization.
5.1 Analytical Methodology
In this dissertation, achievement is modeled following this specification14:
(3) A = f (I, B, SI, P)
where achievement A is a function of a vector of student’s ascribed characteristics I, such as and innate abilities (intelligence, for example); B is a vector of family background and socioeconomic status; SI is a vector of school inputs and management; and P is a vector of influences of peer group characteristics.
I am interested in analyzing the extent to what school inputs (SI) explain the private school advantage found in the previous section. Especially, I am interested in analyzing the school factors object of most of the educational policies implemented in Mexico. To do this, first I need to account for the effect of innate ability, family
background, and peer-group characteristics, and then isolate the effect that the inputs of interest have in student achievement in mathematics among poor students in Mexico: physical resources, school management, teacher quality, and teaching practices and school organization. My hypothesis is that if I consider school differences in these inputs (once I account for the effects of family background and peer-group characteristics), there is no really significant difference between both public and private schools, and that the private school advantage found in the previous section should fade away.
14 This explanation falls in the tradition of education production function. For an early discussion on the
To fully explain student achievement, therefore, it is necessary to use information about innate ability, family background and peer-group characteristics. However, it is very difficult to include student’s ascribed characteristics (I) in education production functions, unless information about cognitive skills is available. In my dissertation, however, I do not count with cognitive test resultsor information about previous
achievement, so achievement results can be affected by personal skills without having a way to identify it. Therefore, the only way to really estimate the effects of the main school inputs object of policy makers in Mexico in the context of the data at hand is to remove the effect of family background. It would also be necessary to account for peer- group effects, one of the factors with a recurrent effect in the literature.
Family socioeconomic background has been part of educational production function since the earlier studies appeared after the Coleman Report (Hanushek, 1986) and it has been almost unequivocally associated to achievement differences and variations in other well-being outcomes (Bradley & Corwyn, 2002). If family and environment has important weight in student achievement, it is likely that students from more educated families self-select themselves into private school, which would bias the estimates of mathematics achievement upwards. On the other hand, peer group
composition is at the same time one of the dimensions included in education production functions since the late 60’s and one of the most difficult to identify in statistical models (Hanushek, 1979; Murnane, 1975, 1984). Attending a school in which most students come from homes that they themselves provide strong support for academic achievement may also have a positive effect on the achievement of the individual student.
5.1.2 Identification Strategy
I am fitting a taxonomy of regression models, regressing student’s achievement in Mathematics (MATH) on my question predictor, PRIVATE, and main baseline variables. The objective is to form a baseline control model that removes the effect of family
background and peer-group composition in the school. The base-line model has the following form:
(4)
MATHij=β0+β1Privatej+β2Propensity+ β3
i=1
∑
PEij+εijWhere Private is a variable indicating whether the student belongs to a private school or not, Propensity is a variable containing the propensity scores for each student I obtained from fitting model (2) from the previous section, and β3
i=1