This study investigates the differences in academic performances between primary school students in Nigeria's public, low-cost, and high-cost private schools. Unfortunately, reliable evidence on the causal differences in performance between different school types is unavailable in Nigeria. This is because it is difficult to derive causal estimates of the effect of school type on academic achievement when students are not randomly allocated to each school type.

Instead, students self-select into school types based on expected (in this case, their academic achievement) or are predisposed to attend particular school types due to certain demographic characteristics. This non-random selection of students into each school type introduces systematic bias between students in the different school types (Tooley & Yngstrom, 2014). Therefore, selection into a school type (high-cost private schools, for example) and academic achievement of students in that school type are confounded by pre-existing differences between students attending high-cost private schools and those not. 

The earliest studies that attempted to estimate the private school effect used simple regression models treating the school type variable as exogenous. This means that researchers treat the school type a student attends as an independent causal factor of any observed differences in academic achievement between public and private school students (Lipcan et al., 2019). However, the main challenge in using regression models is the issue of selection bias which occurs because selection into private schools is endogenous. Therefore, treating private schools as exogenous will likely lead to computational differences because the school type a child attends is influenced by some child and household factors. For example, children from higher socio-economic households are more likely to attend private schools because of the costs associated with private schooling. These children are also more likely to afford after-school tuition (extra lessons), have parents who are highly educated and have higher ambition, and have access to other forms of social capital that can impact academic achievement. Therefore, households that select one school type (private schools, for instance) might differ in key observable and unobservable demographic factors from households that select public schools. This means that estimates OLS estimates will be biased and would not be the true causal effect of attending a private school. 

In this study, I use the three advanced statistical techniques from a comparative perspective to assess the extent of selection bias, and control for it: Instrumental Variables, Heckman Correction, and Propensity Score Matching to evaluate the extent of selection bias and control for it (see Heckman, 1979; Rosenbaum & Rubin, 1983). 

Finally, most studies of the impact of school type on academic achievement divide schools into categories, public and private schools. However, this categorization is misleading for Nigeria (and most countries in SSA). Private schools differ in terms of tuition and other fees associated with them. To illustrate this, public schools are not completely free in Nigeria. While they are tuition-free, there are other direct costs associated with attending public schools, such as uniforms, exam fees, and books. In some instances, the tuition fees and costs associated with some private schools are cheaper than those associated with public schooling. Therefore, students attending lower-cost private schools will likely differ from those in higher-cost private schools along many dimensions. As a result, in this study, I intend to adopt a method of comparison that accounts for four school types: public schools, extremely low-cost private schools, low-cost private schools, and high-cost private schools. 

As I am concerned about the potential selection of unobserved variables, I use a Heckman and 2SLS approach. The Heckman and 2SLS are known to reduce bias in treatment effect estimates; however, from an analytical perspective, the main challenge is finding a valid instrument to implement both approaches. The Heckman and IV approaches take advantage of variables strongly correlated with the endogenous variable of interest and are conditionally independent of the error term. Therefore, for my purpose, a satisfactory instrument must influence school type (relevance restriction) but not influence academic performance except through school type (exclusion restriction). In line with the existing evidence on the determinants of school choice in Nigeria, I identified a set of potential instrumental variables in the data. Ultimately, measuring the household's proximity to the nearest government school proved to be a suitable instrument. In addition to the estimates of the school type effect obtained using Heckman and IVs, I estimate the effect of attendance in school type using the propensity score matching (PSM) framework. This uses a large collection of observed pre-treatment differences can be used to estimate a single score, the propensity score. The propensity score is the probability of assignment to a treatment condition, given a set of pre-treatment variables. This approach only addresses Selection based on observables and does not distinguish between factors that predict school selection and the factors that predict academic achievement. Data and Variables The data are from the Nigerian Education Data Survey (NEDS) 2015. NEDS is a nationally representative survey of 84 324 students from pre-primary to Junior Secondary School (JSS). The key dependent variable is student performance in literacy and numeracy outcomes. The survey implementers assessed two domains, literacy and numeracy. Data on basic education achievement in reading literacy and numeracy are from the assessment of eligible children ages five to sixteen. Literacy and numeracy skills were tested on children who had ever attended or dropped out of school. I use a set of student covariates informed by the existing research on the determinants of school choice, including student, caregiver, and household characteristics.

In this paper, I try to quantify the relative contribution of private schools on the academic achievement of primary school students in Nigeria. I use rich household survey data that enables me to use several estimation techniques to account for endogeneity. Furthermore, analyzing the effectiveness of private schools in Nigeria is challenging because private schools are heterogeneous, comprising low-cost and highly fragmented nonformal and higher-cost formal private schools. Fortunately, my data contains information on household education expenditure, which allows me to categorize schools by cost, thereby accounting for the heterogeneity in terms of cost. The consistent finding across all estimates in the binary school type analysis (public versus private schools) is that students in private schools outperform those in public schools. However, when the school type is broken into polychotomous categories (public schools versus three categories of private schools), only mid and high-cost private schools outperform public school students. Students in public schools outperformed low-cost private school students. Comparing the result from the OLS and the propensity score method suggest that a large section of the differences in school type are attributable to differences in the types of students attending the different school types. Further comparison of results from those obtained in the propensity score to those obtained using Heckman and IV models suggest that unobserved variables account for a large variation in student achievement beyond the effect of observed characteristics and differences between school types. These findings that private schools that not all private schools outperform public schools have clear implications for policymakers. Expanding access to public schools and improving the quality of education in public schools provides an opportunity to deal with the challenge of the declining quality of education in Nigeria.

Lipcan, A., Crawfurd, L., & Law, B. (2019). Learning in Lagos: Comparing Student Achievement in Bridge, Public, and Private Schools. Department for International Development. Oxford Policy Management. https://www.opml.co.uk/files/Publications/8022-education-data-research-evaluation-nigeria-edoren/learning-in-lagos.pdf?noredirect=1 Heckman, J. J. (1979). Sample selection bias as a specification error. Econometrica: Journal of the Econometric Society, 153-161 Rosenbaum, P. R., & Rubin, D. B. (1983). Assessing sensitivity to an unobserved binary covariate in an observational study with binary outcome. Journal of the Royal Statistical Society: Series B (Methodological), 45(2), 212-218. Tooley, J., & Yngstrom, I. (2014). School choice in Lagos State: Summary of extended research conducted on school choice in Lagos. Newcastle University.