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Measuring the Dynamics of the Achievement Gap Between Public and Private School Students During Early Life in India

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Abstract

It is well documented that private school students outperform their public school counterparts in India. However, researchers have only focused on the achievement gap in levels without considering the underlying dynamics of how students move through the distribution of achievement over time. We bridge this gap here by exploring the dynamics of the public-private school achievement gap in India by applying nonparametric measures of distributional mobility to panel data on math and Peabody Picture Vocabulary test scores from the Indian state of Andhra Pradesh. We find that public school students are at least as mobile as private school students during early childhood. During preadolescence, however, public school students, relative to private school students, are significantly less upwardly mobile while at the same time more downwardly mobile through the distribution of test scores. These mobility patterns, taken together with the level gap in test scores, suggests one would expect to see very little convergence in achievement between private and public school students during the middle and high school years of schooling.

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Fig. 1

Notes: Y-axis shows estimated staying probabilities. The dashed lines represent the 95% confidence interval for the estimated difference between public and private staying probabilities

Fig. 2

Notes: Y-axis shows estimated transition probabilities and X-axis shows movement from the first quartile in the initial period to some higher quartile in the final period. The dashed lines represent the 95% confidence interval for the estimated difference between public and private transition probabilities

Fig. 3

Notes: Y-axis shows estimated transition probabilities and X-axis shows movement from fourth quartile in the initial period to some lower quartile in the final period. The dashed lines represent the 95% confidence interval for the estimated difference between public and private transition probabilities

Fig. 4

Notes: Y-axis shows estimated upward rank mobilities. The dashed lines represent the 95% confidence interval for the estimated difference between public and private rank mobilities

Fig. 5

Notes: Y-axis shows estimated upward rank mobilities. The dashed lines represent the 95% confidence interval for the estimated difference between public and private rank mobilities

Fig. 6

Notes: Y-axis shows estimated upward rank mobilities. The dashed lines represent the 95% confidence interval for the estimated difference between public and private rank mobilities

Fig. 7

Notes: Y-axis shows estimated upward rank mobilities. The dashed lines represent the 95% confidence interval for the estimated difference between public and private rank mobilities

Fig. 8

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Notes

  1. We note upfront that our study is essentially descriptive in nature and may be considered as a “first pass” analysis of the dynamics of public-private achievement gap in India. Such “first pass” analysis is routinely carried out to examine the racial gaps in income mobility or gaps in academic achievement mobility in context of the US (see for e.g. Bhattacharya and Mazumder2011; Chetty et al., 2014; Mazumder 2011; McDonough 2015). While systematic investigation into the mechanisms underlying the evolution patterns documented here is important, it is outside the scope of current research, and perhaps is the next step in this research line.

  2. Similar arguments have been made by Kopczuk et al. (2010) and Glewwe (2012) in the literature on economic inequality to highlight the importance of studying income mobility.

  3. Bond and Lang (2013), in context of the black-white achievement gap in the US, rigorously show that by selectively choosing the scale, the initial black-white gap for reading could range from one-ninth of a standard deviation all the way up to roughly half a standard deviation. Jacob and Rothstein (2016) illustrates this issue by using a simple example and notes that elaborate examples could even produce reversals of the sign of the gap depending on the transformation and assessment used. Further, Jacob and Rothstein (2016, p. 89) note, “this problem worsens if one considers changes over time.”

  4. It is worth emphasizing that although our findings are based on data from Andhra Pradesh, they are likely to have relevance beyond Andhra Pradesh and even beyond the Indian context. As noted by Singh (2015), the share of students enrolling in low-fee private schools has increased in several developing countries and in many of these countries (in Latin America, Asia, and Africa) these students at low-fee private schools outperform their government school counterparts. As such, findings presented here may also be of importance for these other developing countries.

  5. For more details see Galab et al. (2003) and/or visit www.younglives.org.uk.

  6. In June 2014, Andhra Pradesh was bifurcated into two states named as Andhra Pradesh and Telangana. Since then the YLS continued in both the states.

  7. For more details on survey methodology see http://doc.ukdataservice.ac.uk/doc/5307/mrdoc/pdf/5307sampling_india.pdf; last accessed 21 August 2019.

  8. In addition to this, school surveys for a randomly selected sub-sample taken from the younger cohort were conducted in 2010 and late 2016/early 2017. Note, data for the latest round (2016-17) was not available in the public domain when we carried out this study.

  9. Notable attrition occurred between the first and the second round. See Outes-Leon and Dercon (2008) for more on attrition in the YLS.

  10. In the second round, Cognitive Development Assessment (CDA) is conducted where quantity based questions are asked from the children. A sample question of CDA is “Look at the plates of cupcakes. Point to the plate that has a few cupcakes… Point to the plate that has a few cupcakes”. We consider this test also as a form of Mathematics test as knowledge of numbers is required to answer to the questions in CDA.

  11. The PPVT was initiated in 1959 to analyze the verbal intelligence of a child. It also helps in evaluating the scholastic aptitude for the children in school going age.

  12. Note, survey weights are unavailable in the public-use YLS data.

  13. There are 1132 students who were not in school in second round but were in school by the next round. Out of these 1132 students, 573 were in private and 559 in public school in third round.

  14. Note, in our analysis, while public schools refer to pure public schools, private school students refer to children going to pure private schools, community schools (run by NGOs, charitable organizations, religious organizations, etc.) and public aided private schools. However, in all the rounds, among the students classified as private school students, the majority are indeed students of pure private schools. Specifically, in the 2006/07 wave, 87% of children classified as private school students, attend pure private schools, in 2009/10 wave, 98% of students classified as private school students attend pure private schools, and in 2013/14 wave, 82% of students classified as private school students attend pure private schools.

  15. If we were to simply include all students, including those who switched from public to private schools, and vice versa, then our mobility estimates may be in part due to measurement error. Having said this we realize that if switching is based on test performance, then we may additionally have a selection problem. To get some sense of whether this is a problem, we compare test scores between switchers and non-switchers in previous rounds of the data. In doing so we do not find statistically significant differences in test scores (2006/07) between switchers (children who switched their school from 2006/07 to 2009/10) and non-switchers (children who stayed in the same type of school from 2006/07 to 2009/10). Similarly, we do not find statistically significant difference in test scores (2009/10) between switchers (children who switched their school from 2009/10 to 2013/14) and non-switchers (children who stayed in the same type of school from 2009/10 to 2013/14). Additionally, the population distributions, not just the averages, are remarkably similar between these switcher and non-switcher groups. While selection into switching on the basis of performance is understandably a concern, we do not think that it is a major issue here.

  16. We also include the coefficient estimates on the public school indicator without any controls to provide a sense of how these estimates change as additional covariates are added to the model.

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Authors and Affiliations

  1. Department of Economics, University of Nevada, Las Vegas, NV, USA

    Ian K. McDonough

  2. Nottingham University Business School, University of Nottingham, Nottingham, UK

    Punarjit Roychowdhury

  3. Department of Liberal Arts, Indian Institute of Technology Hyderabad, Hyderabad, India

    Gaurav Dhamija

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  1. Ian K. McDonough
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  2. Punarjit Roychowdhury
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  3. Gaurav Dhamija
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Correspondence to Ian K. McDonough.

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The authors have no potential conflicts of interest to report. However, Prof. Punarjit Roychowdhury acknowledges funding under IIM Indore Seed Grant SM/08/2018-19. Further, the authors do not have direct involvement with human participants and/or animals and thus informed consent does not apply. This will also be noted in a separate section before the references as advised in the instructions for authors.

The authors have no potential conflicts of interest to report. However, one of the authors acknowledges funding under a seed grant from his/her institution. Further, the current research does not involve human participants and/or animals and thus informed consent does not apply.

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The authors are very grateful to seminar participants at CSSS Calcutta, IIM Indore, ISI Delhi, Nanjing Audit University and South Asian University for insightful comments.

Appendix

Appendix

Fig. 9
figure 9

Kernel Density Plots of Test Scores in Math and PPVT by School Type

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Fig. 10
figure 10

Notes: Y-Axis shows estimated transition probabilities and X-axis shows movement from the second and third quartiles to some higher quartile in the final period. The dashed lines represent the 95% confidence interval for the estimated difference between public and private transition probabilities

Upward Transition Probabilities – Math.

Full size image
Fig. 11
figure 11

Notes: Y-Axis shows estimated transition probabilities and X-axis shows movement from the second and third quartiles to some higher quartile in the final period. The dashed lines represent the 95% confidence interval for the estimated difference between public and private transition probabilities

Upward Transition Probabilities – PPVT.

Full size image
Fig. 12
figure 12

Notes: Y-Axis shows estimated transition probabilities and X-axis shows movement from the third and second quartiles to some lower quartile in the final period. The dashed lines represent the 95% confidence interval for the estimated difference between public and private transition probabilities

Downward Transition Probabilities – Math.

Full size image
Fig. 13
figure 13

Notes: Y-Axis shows estimated transition probabilities and X-axis shows movement from the third and second quartiles to some lower quartile in the final period. The dashed lines represent the 95% confidence interval for the estimated difference between public and private transition probabilities

Downward Transition Probabilities – PPVT.

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Table 4 Transition probability estimates by school type, Math
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Table 5 Transition probability estimates by school type, PPVT
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Table 6 Upward rank mobility estimates by school type, Math
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Table 7 Upward rank mobility estimates by school type, PPVT
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Table 8 Downward rank mobility estimates by school type, Math
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Table 9 Downward rank mobility estimates by school type, PPVT
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McDonough, I.K., Roychowdhury, P. & Dhamija, G. Measuring the Dynamics of the Achievement Gap Between Public and Private School Students During Early Life in India. J Labor Res 42, 78–122 (2021). https://doi.org/10.1007/s12122-020-09307-2

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