The impacts of transition to middle school on student cognitive, non-cognitive and perceptual developments: evidence from China

ABSTRACT

We examine the effect of the transition to a separate middle school after grade six on student cognitive, non-cognitive, and perceptual developments in China. We use an approach that combines inverse propensity score weighting and discrete factor approximation to address the endogeneity of the transition. We find that transitioning students report worse overall development in health, social adaptation and academic achievement and lower evaluation of the school than non-transitioning students. Transitioning students are also less likely to feel confident or popular among peers. The lower performance on the first exam in middle school only partly explains these observed transition effects.

KEYWORDS:

• Grade configuration
• cognition
• non-cognitive development
• propensity score
• discrete factor approximation

SUBJECT CLASSIFICATION CODES:

• I21
• I28
• H52

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1. Source: Administrative data from Ministry of Education, China. http://www.moe.gov.cn/jyb_sjzl/

2. In some regions, such as Shanghai and Shandong, there is another type of elementary school that serves grade one through five (G5). In our study, we focus on G6 schools in Beijing, which adopted G6 as the primary configuration for separate elementary schools.

3. Source: administrative data from the Ministry of Education, China. http://www.moe.gov.cn/jyb_sjzl/

4. Schwerdt and West (2013) and Dhuey (2013) find negative impacts of attending a middle school on student test scores in high school grades. To our knowledge there is no evidence on long-term impacts beyond high school grades.

5. This means six-year elementary school, three-year middle school, three-year high school, and four-year college.

6. Students can enter an elementary school out of the assigned school district but at significant pecuniary cost. Students who move are more likely to choose an elementary school that is famous for high quality.

7. Those assumptions include: 1) ${ϵ}_k^{l}i$ is independent from ${ϵ}_k^{l^{\mathrm{\prime }}}$and ${ϵ}_{k^{\mathrm{\prime }}}^{l^{\mathrm{\prime }}}$, where $l\ne l^{\mathrm{\prime }}$ and $k\ne k^{\mathrm{\prime }}$; 2) ${ϵ}_k^l$is independent from ${\theta }_k$, for $k=1,\dots ,K$; 3) $\mathrm{V}\mathrm{a}\mathrm{r}\left({\theta }_k\right)=1$, for $k=1,\dots ,K$; 4) $g_k^1$is positive, for $k=1,\dots ,K$.

8. Several features of the middle school assignment system in Beijing may help adjust for the endogeneity problem to some extent. Given their preferences, some students are randomly assigned to middle school within the same district, and this assignment may partially eliminate the self-choice of middle school. However, the assignment rule includes other merit-based criteria as well, and the students who satisfy those criteria are not assigned randomly. The overall assignment rule does not generate a random experiment, and the endogenous choice of elementary schools remains.

9. Compared with other propensity score methods, such as propensity score matching, our IPSW method with regression adjustment is more flexible and robust by allowing for potential misspecification in either the outcome or the transition (Hirano and Imbens 2001).

10. In the literature, discrete-factor approximation is also known as the finite mixture model or latent class analysis.

11. Ideally, the common terms should include school fixed effects to control for school-specific covariates such as school quality. However, since our model is so complicated with multiple (numerical) identification approaches combined, we are not able to obtain converged estimations after controlling for school fixed effects with more than 60 schools. As a suboptimal solution, in our models, in addition to controlling for a number of observed school characteristics, we allow the unobserved common terms to be freely correlated with the controlled school characteristics. As a robustness check we also allow the unobserved common terms to be correlated with school fixed effects and obtain similar results. The results of the robustness check are available upon request.

12. The discrete factor approximation is more flexible because a misspecified parametric distribution may lead to inconsistent estimates (Mroz 1999).

13. The indirect effect $c_{0k}$depends on the values of the regressors. We focus on the students at the mean.

14. The criterion using eigenvalues suggests that we choose all factors with eigenvalues greater than one (Kaiser 1960) or choose the number of factors where we observe an elbow in the scree plot (Cattel 1966). Both methods suggest a model with five factors from our data. Preacher et al. (2013) choose the smallest number of factors for which the lower bound of the root mean square error of approximation (RMSEA) 90% confidence interval drops below 0.05. This criterion using RMSEA suggests a model with four factors from our data. The difference between the Kaiser/Cattel and the Preacher et al. conclusions is whether the factor of overall evaluation of the school is a separate factor. We choose a model with five factors because the factor of overall evaluation of the school was defined to be a separate dimension when we designed the questionnaire. The relationship between each observed item and the five latent outcomes from our EFA is summarized in Appendix Table A1. The estimation results (factor loadings) from the measurement system (Equation (1)) are reported in Appendix Table A2.

15. School and Teacher are about perceptual development. Peer and Self mainly measure personal development from the perspective of non-cognition. Learning and Improvement are mixtures of cognitive and non-cognitive developments.

16. One concern about inverse propensity score weighting is whether there is sufficient overlap between the transitioning and non-transitioning groups. We can see that, while the distributions of the two groups are different, they overlap along most of the entire support (see Appendix Figure A1 for the distributions of the obtained propensity score by transition status).

17. Specifically, we conduct sequential comparisons of models with different numbers of student groups (1 group vs. 2 groups, 2 groups vs. 3 groups, and so forth). If the test indicates that the model with fewer points is preferred, we choose the simpler model without going to the next comparison. The results of the likelihood ratio chi-square test are shown in Appendix Table A4.

18. It is shown that a discrete factor approximation with a small number of points of support (2–5) is generally sufficient for approximating unobserved heterogeneity (Heckman and Singer 1984). In our case a simple model that does not control for discrete factors, which is the model with one point, leads to significantly biased results. Moreover, we are not able to get convergent results with the model with three points. See Appendix Table A4 for the comparison between models with different numbers of points of support.

19. Since we have six identified latent outcomes, theoretically it is possible for us to observe at least one significant effect by chance, even though the correlations between the outcomes are high with an average of 0.71. To address that issue regarding multiple hypotheses testing, we conduct a step-down correction procedure that is based on Holm–Bonferroni method but takes into account the correlations between tests (Sankoh, Huque, and Dubey 1997). After the correction the total effect on improvement is still statistically significant at 5% (adjusted p-value = 0.049) while the total effects on overall evaluation of school, popularity among peers and self-confidence, which were original statistically significant at the 10% significance level, become insignificant with the adjusted p-values ranging from 0.12 to 0.14.

20. One potential concern about indirect effect through exam performance, especially for the indirect effect on learning habits, is reverse causality, which means that in elementary school transitioning students had already developed bad learning habits that lead to both low performance on the first exam in middle school and bad learning habits later at grade eight. Such reverse causality, if any, has been incorporated into the unobserved heterogeneity controlled by discrete factor approximation: The positive correlation (0.488) between the unobserved heterogeneities in transition and student developments indicates that the reverse causality is not likely.