The Linkage between School Autonomy and Inequality in Achievement in 69 Countries: Does Development Level Matter?

Abstract Whether schooling systems with greater autonomy offset or reinforce educational inequalities remains debateable. Yet school autonomy is often advocated by different actors including donors and international organisations in many countries. This study examines the association between school autonomy and the inequality in maths achievement of 15-year-olds by socioeconomic status (SES), and whether this correlation differs by countries’ level of development. We construct a country-level panel using six waves of the Programme for International Student Assessment (PISA) from 69 countries in 322 country waves. We first estimate the gradient of SES and maths achievement as a measure of achievement inequality at the country level and take the country mean of the relevant covariates including school autonomy. Results from weighted mixed-effects models suggest that the association between all autonomy variables and inequality in achievement is not significant. However, academic autonomy is linked to increasing achievement inequality in high- and upper-middle-income countries compared with low- and lower-middle-income countries. But the coefficients for budget and personnel autonomy do not differ by the development level. The results remain similar in several specification tests including country and year fixed effects, which leads us to suggest not to simplistically apply autonomy reforms regardless of context.


Introduction
Do decentralised and self-governing schooling systems close the learning achievement gaps between advantaged and disadvantaged children? This question has been consistently at the centre of education policymaking processes worldwide to understand which educational systems help equalise learning inequalities. Decentralised or autonomous educational systems share more responsibilities with local government and schools, especially at the pre-tertiary levels (Barrera-Osorio, Fasih, & Patrinos 2009;McGinn & Welsh, 1999). Greater school autonomy HICs and LMICs. Since PISA data is cross-sectional at the student level, we create a countrylevel panel dataset containing countries and territories that participated in at least two PISA waves.

School autonomy and learning inequality
To capture holistic policy areas in a school, we define school autonomy by three key elementsthe autonomy of a school in (1) determining academic courses and selecting textbooks, (2) making budget decisions, and (3) managing personnel. Hanushek et al. (2013) and van Hek, Buchmann, and Kraaykamp (2019) also employ these school autonomy indicators although their focus was not primarily to explore learning inequality by SES.
Existing research exploring the linkage between autonomy in educational systems and inequality in outcomes has mostly focused on HICs. Past research suggests that standardised educational systems, as opposed to de-standardised or autonomous systems, tend to generate more equitable learning outcomes by implementing uniform policies and providing homogeneous educational services to all schools ( Van de Werfhorst & Mijs, 2010). Bodovski, Byun, Chykina, and Chung (2017) observe that having government-prescribed textbooks in schools (indicating lower school autonomy) is associated with decreasing achievement gaps. Similarly, Gamoran (1996) also finds that greater standardisation in the national curriculum is associated with more equal learning outcomes. However, research also finds null (Montt, 2011) or mixed results, that is, higher standardisation (less autonomy) either has no connection or leads to a reduction in inequality in attainment (Bukodi et al., 2018).

Why focus on the development level?
There are several reasons to assume that the association between school autonomy and learning inequality may differ across LMICs and HICs. First, school autonomy in the developing world in recent decades has been a borrowed phenomenon, exported from the Global North (Steiner-Khamsi, 2012). Decreasing standardisation has gained prominence in the education sector of LMICs during the post-Washington Consensus era by development banks and donors throughout the 1990s and onward. School autonomy reforms have been quite similar around the world emphasising the 'importance' of autonomous governance to mobilise local resources and reduce dependence on the government (Hossain, 2021). For instance, the name 'school-based management' can be found across the globe with similar structures and guidelines (Barrera-Osorio et al., 2009).
School autonomy has also been promoted in HICs by the OECD (Beatriz et al., 2008). Nonetheless, the effectiveness of these remains debateable while the effects of some of these policy features remain inconclusive in HICs as we discussed. More importantly, since these reforms were exported from institutions in HICs, they may not fit the context of LMICs. Past research suggests that greater school autonomy to serve marginalised people may bring negative consequences. An embedded culture of informal governance in institutions of many LMICs may strengthen the 'patron-client' relationship between local politicians, teachers, and school administration. This may lead to keeping parents aloof from making any school decisions (Nishimura, 2017), resulting in more irregularities such as the recruitment of teachers by favouritism. For instance, Joshi (2014) finds that parents prefer sending their children to private schools in Nepal as excessive political interference in the school management committee (as a result of more autonomy) and negligence of teachers impede the learning environment in public schools. Essuman and Akyeampong (2011) argue that local political actors in Ghana influence school decisions due to more autonomy keeping little or no room for community participation.

School autonomy and inequality in achievement 1493
Second, proponents argue that devolving educational responsibilities would empower marginalised parents, which would then result in less learning inequality. This mechanism implicitly assumes that people from all walks of life will be empowered by having a voice and decisionmaking power 'who know more about the local education systems than do central policy makers' (Barrera-Osorio et al., 2009, p. 2). This mechanism disregards the socioeconomic background of individuals that may hinder the empowerment process. Evidence is, however, scarce supporting or opposing this second point.

Hypotheses
Aligning with previous studies (for example, Allmendinger, 1989;Park, 2008), we expect that autonomy in educational systems would be associated with increases in achievement gaps (Hypothesis 1). We assume that all three elements of autonomy would have a similar direction of association with the inequality in achievement.
Hypothesis 1: Increasing school autonomy in academic, budget and personnel management decisions is associated with widening the achievement gap by SES.
To elaborate, higher academic autonomy means schools have the freedom to choose different curricula and textbooks. By having better informational and knowledge capital, higher-SES parents would be able to identify schools that have better teaching methods and innovative curricula. They would also have more economic resources to send their children to better-quality schools (Park, 2008).
Moreover, granting greater autonomy, especially in budgetary responsibilities, is likely to result in disparities in resource mobilisation among schools. This means schools in affluent neighbourhoods may attract more resources by collecting taxes, fees, and donations, potentially leading to widening achievement gaps. This issue is particularly pronounced in LMICs, where significant disparities in resources between schools are already evident (Gruijters & Behrman, 2020).
Likewise, more autonomy regarding personnel management issues such as teacher recruitment and determining their salary may have an influence on teaching methods and therefore learning outcomes of children. When schools control the personnel management aspect, the quality of teachers may likely vary depending on the capacity of school leadership and how rich schools are (Gingrich & Ansell, 2014). This eventually may lead to widening learning inequality by SES.
However, we also expect that the coefficient for academic autonomy will likely be greater than that of budget and personnel autonomy (Hypothesis 1a). Academic autonomy involves decisions about textbooks, curricula, and course content that are more directly related to the learning of children. An existing body of literature finds that a more standardised academic curriculum is associated with closing the SES achievement gap (for example, Chmielewski & Reardon, 2016;Gamoran, 1996). In other words, academic autonomy has been consistently found to be associated with widening learning inequality. For budget and financial aspects, such evidence is limited. Bukodi et al. (2018) use budget decisions as one of the standardisation measures in their study but find that its effect is mixed or not conclusive. Besides, when using personnel management as a measure of school autonomy, Hanushek et al. (2013) do not observe any effect of this factor on overall learning achievement across countries.
For question 2, enquiring whether the inequality effect of school autonomy differs by the development level of countries, our hypothesis is the following: Hypothesis 2: While increasing school autonomy may likely lead to greater inequality in learning achievement among countries, it may be more pronounced in high-and uppermiddle-income countries than in the low-and lower-middle-income groups. This hypothesis is in line with past findings from advanced economies that autonomous governance leads to formulating education policies differently for different schools, which obstructs the smooth navigation of educational systems by lower-SES parents (Park, 2008;Van de Werfhorst & Mijs, 2010). The same logic would ideally apply to lower-income countries. But the effect size is likely to be smaller in these latter set of countries due to the presence of informal governance in the educational systems as explained in the previous section. Parents, regardless of their socioeconomic status, may not feel encouraged (or invited) to participate in school meetings since local political actors are likely to make them feel unwelcome. Just because school autonomy creates scope for participation does not mean that it will inevitably attract everyone to do so. For instance, Hossain (2021) finds no evidence of the linkage between involving the local community in school decision-making, or participatory decision-making, and increased face-to-face parent-teacher interaction in seven LMICs.

Data
We construct a country-level panel dataset on 69 countries/territories from six waves of PISA-2000PISA- , 2003PISA- , 2006PISA- , 2009PISA- , 2012PISA- , and 2015 students. 1 PISA measures the ability of 15-year-old pupils in maths, reading, and science across OECD member and non-member countries every three years. Fifteen-year-olds are roughly at the lower-secondary level, which is the focus of this study. PISA data is cross-sectional, that is, in every cycle, a different cohort from different schools participates in the assessment. We aggregate data to construct a country-level panel. The number of PISA-participating countries ranged from 43 in 2000 to 72 in 2015 (OECD, n.d.). We include countries that took part in at least two assessment waves making the final country-wave observations 322 (see the bottom of Table S1 in the Supplementary Material). We exclude PISA 2018 as it does not have the school autonomy measures used in this study. We calculate achievement gaps for each country from each year and aggregate all other variables by country mean.
Using PISA data gives the advantage of including countries from various income ranges. While it predominantly includes HICs, PISA also surveys LMICs. In our study, 33 countries are identified as high-income, 16 as upper-middle-income, 15 as lower-middle-income, and 5 as low-income, according to the categorisation of the World Bank in 2000 (the rationale for the choice of the year is described in the variable section). The selection of countries with a wide regional diversity gives the advantage of examining the linkage between school autonomy and inequality, which has not been investigated at this scale.

Variables
3.2.1. Maths achievement. To measure the inequality in achievement, we use achievement in mathematics as it is viewed to be more comparable across countries (Hanushek et al., 2013). Each subject area in PISA, including reading and science, is tested using a wide range of tasks with different difficulty levels to capture students' abilities in a comprehensive way. The maths achievement is scaled to have a mean of 500 test-score points and a standard deviation of 100 points across the OECD countries. 2 3.2.2. SES percentile position. In each wave, PISA has an index of the economic, social, and cultural status (ESCS) of parents. We use this to signify the family SES of students. The variable is a composite score of (1) the highest parental occupation (ISEI), (2) the highest education of either of the parents, and (3) home possessions including books at home (see Table S2 in the School autonomy and inequality in achievement 1495 Supplementary Material for the third item's description), estimated by using principal component analysis (PCA). PCA is frequently used to reduce the dimensionality of datasets and increase the interpretability of the measure while minimising information loss (Jolliffe & Cadima, 2016). As mentioned, this index has been used in the existing literature as a proxy for family SES (for example, Gruijters & Behrman, 2020).
The SES measure may arguably not be comparable across countries as someone's SES position with a certain level in one country may be different for others in another country. For instance, an SES value may situate a pupil at the 90th percentile while the same value may situate other students in a different country at the 80th percentile. To address the issue of comparability across countries and study waves, we convert the SES variable into percentile ranking through which each student is assigned an SES percentile. We assume that family SES is a positional good rather than an absolute one (Chmielewski, 2019). 3 Converting the index into percentile is particularly important in this study as it involves countries from different income levels; the composition of students by SES level is also likely to vary across countries. The mean SES percentile position is around 0.5 (as the pupils in each country are evenly assigned with percentile positions) (Table S1 in the Supplementary Material).

Development level.
The initial development level of countries is the only time-invariant country-level variable. All other variables are at the country-wave level. Among 69 countries, 20 countries were categorised as (1) lower-or lower-middle-income, 16 as (2) upper-middleincome, and 33 as (3) high-income countries as of 2000 (Table S3 in the Supplementary Material). This is according to World Bank (n.d.) categorisation at the outset of the PISA test in 2000. 4 The development level, instead of the measure of Gross Domestic Product (GDP) per capita, is utilised for the following reasons. As we argue, many LMICs have received reforms to provide schools with more autonomy. Receiving these reforms by international organisations (IOs) through aid depends on countries' development level, that is, whether they have surpassed certain income thresholds, not the continuum of their GDP per capita (see World Bank, n.d.). Hence, the development level is theoretically more suitable. But we run robustness checks to see whether controlling for GDP per capita's within-country variation changes the effect of the development level. Nonetheless, we do not account for how much aid LMICs have received since this will limit analysis to only aid receiving LMICs.
Additionally, we keep the development level variable time-invariant (from 2000) for two reasons. First, this is to align with the theoretical assumption that school autonomy-related reforms started increasingly taking place in LMICs in the late 1990s and continuing in the early 2000s (Ball & Youdell, 2009). Second, there have been limited changes in countries' development levels if we compare the status of 2000 with that of 2015. As shown in Table S3 in the Supplementary Material, 47 countries, out of 69, remained at the same development level one and a half decades apart. Most of the remaining countries have moved just one level, from the low/lower-middle to the upper-middle or the upper-middle to the high-income group. As said, to capture this change, we account for the GDP per capita as part of robustness checks. Additionally, the year fixed effects would further capture some unobserved time-related factors.
3.2.4. School autonomy. We use four continuous variables for school autonomy, broadly divided into three categories: academic autonomy, budget autonomy, and personnel autonomy. (1) Academic autonomy is measured by three indicatorsautonomy in deciding (a) course content, (b) courses offered, and (c) textbook materials. (2) Budget autonomy is measured by autonomy in (a) formulating and (b) allocating the budget. Finally, to measure personnel autonomy, we use two variables: autonomy in (3) hiring teachers, and (4) determining teachers' (a) starting salaries, and (b) salary increase. The questionnaire asks school principal(s) who is/are responsible for performing the academic, budget, and personnel responsibilities to choose from among five stakeholders (a) Principal; (b) Teachers; (c) School governing board; (d) Regional or local education authority; and (e) National educational authority (Table S4 in the Supplementary  Material). We code schools as autonomous when principals answer options a, b and/or c as principals, teachers and the school governing board are school stakeholders. When one or more of these three actors is/are responsible for these designated tasks, a school is coded 1, otherwise 0. Thus, 1 indicates a school is fully autonomous to perform a responsibility. A limitation of this approach is that we could not include schools where autonomy may be partly shared with the local or central government. Despite this, we make an important contribution by examining how changes in autonomy are associated with changes in achievement inequality, which remains understudied due to a lack of longitudinal data.
To aggregate variables at the country level, we follow two steps. First, we estimate the country-year mean of each of the eight indicators under four autonomy variables, weighted by PISA student weights. Second, since the indicators under each autonomy category are consistently highly correlated in most of the PISA waves 5 (see Table S5 in the Supplementary Material), we combine them by taking the arithmetic mean. Autonomy in selecting course content, textbooks and courses offered are highly correlated to each other (r ¼ 0.7 or higher) and, thus, combined into one variable. The scale of the resulting variables is a proportion ranging from 0 to 1. Similarly, budget formulation and allocation are highly correlated (r ¼ 0.64) and, thus, we combine them by taking the arithmetic mean. However, we estimate two separate variables for personnel autonomy as although determining teachers' salary and salary increase are highly correlated (r ¼ 0.91), hiring autonomy is less so, as demonstrated in Table S5 in the Supplementary Material. Thus, hiring and salary autonomy are kept separate.
Figures S1 and S2 in the Supplementary Material suggest that school autonomy scores vary across countries regardless of their development levels. On average, schools have more autonomy over the budget formulation and allocation and less so over salary autonomy while hiring teachers and academic autonomy being in the middle.
LMICs do not show much of a sharp decline in autonomy. These countries do not have schools with zero autonomy compared to some high-income countries such as Germany, Greece and Hong Kong in recent years and Singapore in all reported years. This could be because LMICs have received many decentralisation initiatives in the education sector during the past few decades aided by donors/IOs (for example, Bandur, 2012).
3.2.5. Proportion in private schooling. Data on the proportion of students enrolled in private schools come from PISA, which accounts for private schools' propensity to have more autonomy as they are independently run. Data on the proportion of private school students are not available for some countries in some waves. We use aggregated data from the UNESCO Institute for Statistics (UIS) for the missing cases (UIS, n.d.). To ensure that the results are not driven by the sources of private schooling data, we use a dummy in the analysis indicating whether data come from PISA or UIS. We find aggregated measures from PISA and UIS consistent.
3.2.6. Pupil-teacher ratio. The country average of the pupil-to-teacher ratio (PTR) in school data comes from PISA, which is a continuous variable. A lower PTR may facilitate running the school more autonomously as teachers will have more time to interact with parents. Similar to the private school variable, when PISA waves do not have this variable, we use the aggregated measure from UIS and indicate this with a dummy in the analytical models.
3.2.7. Gini coefficients. To account for country income inequality in the analysis, we use Gini coefficients data primarily from the World Bank, but also from the World Income Inequality Database (WIID) when data is unavailable (UNU, n.d.). 6 This time-varying continuous variable ranges from 0 to 1 where 0 means no inequality and 1 indicates absolute inequality.
School autonomy and inequality in achievement 1497 3.2.8. Rural school ratio. The rural school ratio variable is continuous and taken from UIS and also OECD for very few cases when data is missing in UIS. Similar to the above two variables, we adjust for the differences in sources using a dummy indicator. This variable intends to account for achievement inequality triggered by school location.

Methods
3.3.1. Estimating inequality in learning achievement. The outcome variable in this study is the inequality in maths achievement by SES at the country level. To address the issue of comparability across countries and study waves, we convert students' family SES into percentile, as explained in the variable section. We measure achievement inequality by Equation (1), which estimates the relationship between the SES percentile position C and maths achievement A of students i . d is the coefficient on SES position and e i is an error term. The gradient d becomes the dependent variable at the second stage of panel analysis in Equation (2). We run this regression on each country and PISA wave separately.
As PISA data has multiple plausible values for achievement scores created by multiple imputations, we incorporate these in the regressions, weighted by student and school survey weights using the 'repest' command in Stata (Avvisati & Keslair, 2020). The trend in inequality in achievement is presented in the findings section. After calculating the achievement inequality gradients for each country and year, we build a panel dataset by combining the country-year mean of all other covariates.

Regression models.
We employ mixed-effects regression models on unbalanced panel data of 322 country-waves at level 1 nested within 69 countries at level 2. To account for standard errors of the gradients from Equation (1), we run the regression analysis weighted by the estimated inverse squared standard error of the gradient, similar to the weighted least squares (WLS) method. Using mixed models allows for examining heterogeneity across countries in the association between autonomy and achievement inequality, and the extent to which this crossnational heterogeneity can be explained by the time-constant development level.
As shown in Equation (2),d is the true achievement gap in maths by SES estimated employing Equation (1) in year y (level 1) and country c (level 2). c is an intercept, k is a vector of coefficients on four variables of autonomy T yc , and h is the coefficient on countries' development level D c . w is the vector of coefficients on the cross-level interaction between the development level D c and four autonomy variables T yc . The interaction term examines whether the autonomy coefficients differ by the level of development. Without the interaction, the equation will answer research question (RQ) 1. a is a vector of coefficients on control variables L yc for level 1 and l is year fixed effects to account for any secular trends in achievement gaps across waves. u c is the country-level random intercept and e yc is a level 1 time-varying error. Before running this final model, we add variables step by step. All time-varying country covariates are meancentred within countries. Hence, the coefficients for these time-varying covariates indicate the relationship between changes in autonomy and changes in achievement gaps within countries over time after accounting for secular trends.

Inequality in achievement
We first present the inequality in achievement trend over time across countries estimated by Equation (1). We find the gradients statistically significant for all country-years (p < .05). Figure 1 Figure 1(B) shows initially LMICs. Both figures suggest that the trend in maths achievement inequality differs across countries. But in most cases, the trend remains steady over time. Additionally, the achievement gap is overall higher in upper-middle and high-income countries compared to lower-income countries (Table S1 in the Supplementary Material).

RQ 1: the association between school autonomy and achievement inequality
The country-pooled regression models in Table 1 demonstrate that the association between all school autonomy variables and inequality in achievement is not significant (p > .05). We also do not observe noticeable changes in the variance in achievement inequality between and within countries in all these models as shown in parameters Ru and Re, respectively, in Table 1.
The results in Table 1 do not correspond to our initial hypothesis (H1) that there might be an association between school autonomy and an increase in the achievement gap in mathematics by students' SES. To answer RQ 2, we estimate the interaction between the four measures of school autonomy and the development level using Equation (2). Table 2 demonstrates that only the coefficient for academic autonomy significantly differs by the level of development. Model 8 in the table suggests that when all four autonomy areas are added to the model, only the association between academic autonomy and achievement gap significantly differs by the countries' development level. Specifically, the slopes for high-income (109.5, p < .001) and upper-middleincome countries (70.6, p < .01) are significantly steeper than that of lower-middle and lowincome countries. The coefficient for upper-middle countries is larger than that of HICs.
However, the coefficients for budget and personnel (salary and hiring) autonomy do not significantly differ by the development level. These results remain similar in a number of alternative specifications including unweighted mixed effects, the inclusion of alternative controls, and fixed and random effects models. We explain these in the 'Robustness' section and Table S6 in the Supplementary Material. Additionally, as explained in the variable section (development level), we control for time-varying GDP per capita to examine whether accounting for it changes the coefficients for the time-constant development level. The results, however, remain largely unaffected (Table S7 in the Supplementary Material).
The academic autonomy slope varying by the development level is partially in line with our initial expectation (Hypothesis 2) that the effect of this autonomy would be higher for HICs. Although the HICs slope is higher than that of lower-income countries, the slope for uppermiddle-income countries is the steepest as illustrated in Figure 2 (using model 8 in Table 2). The slope for the lower-income countries is downward while the other two are upward. One limitation in this analysis is that we could not further disaggregate the low-and lower-income groups as the former has only five countries in our sample. In sum, in the high-and upper-middle-income groups, academic autonomy in schools is associated with a greater increase in inequality in achievement compared to the lower-income countries.
Additionally, when we check model 8 in Table 2, the interaction term explains around 10 per cent of the between-country variance in the inequality in achievement compared to the noninteraction model (4) in Table 1. This also suggests the significance of countries' development level and its interaction with autonomy to explain the inequality in achievement.
Although these findings only hold true for academic autonomy, it partially corresponds to our Hypothesis 1a that academic autonomy would matter more for achievement inequality as it is related to the core of the learning processes compared to other autonomy areas. This conforms to the evidence from past research that maintaining greater standards in academic aspects such as curriculum and assessment methods are associated with decreases in learning inequality (for example, Chmielewski & Reardon, 2016;Van de Werfhorst & Mijs, 2010). By contrast, budget and personnel management aspects may not hold similar significance to addressing disadvantages in learning processes. Related to this, earlier research does not find a strong effect of standardisation of educational systems (less autonomy) on achievement inequality when budget autonomy is considered as an indicator (Bukodi et al., 2018). Personnel autonomy is not found associated with overall learning achievement (Hanushek et al., 2013). Notes: (a) Control variables include the Gini coefficient, the proportion of students in private schools, pupil-to-teacher ratio, rural school ratio, and the dummy indicators for the sources of the latter three variables. Source: Author's calculations based on PISA data. Robust standard errors are in parentheses. Ã p < .05; ÃÃÃ p < .001.

Discussion and conclusion
We find a null association between school autonomy variables and inequality in maths achievement in pooled analyses. However, the association differs by the countries' development level only for academic autonomy, the slope for upper-middle-income countries being the steepest and statistically significant followed by that of HICs compared to lower-income countries. Our results align with findings from previous studies (for example, Gamoran, 1996;Van de Werfhorst & Mijs, 2010) that school autonomy in deciding academic course content, and selecting courses and textbooks is associated with widening the achievement gap by SES. We observe the null association of school autonomy in formulating and allocating the budget and in personnel management, as well as their interaction with the development level, although these two elements often get highlighted in decentralisation and autonomy reforms in development projects (Torche, 2005). Regarding academic autonomy, we assume that this could be because academic aspects play a more influential role in deciding how the learning environment should be and how teachers can design courses and deliver teaching. In a more autonomous system, the standards of teaching quality and curriculum would widely vary across schools, which may induce greater inequality (Van de Werfhorst & Mijs, 2010). Nevertheless, our measure of budget autonomy is limited in the study. Budget autonomy is defined in the PISA questionnaire by whether schools have the capacity to formulate and allocate budgets. But we do not know whether the financing of the budget comes from the central or local government. To address this limitation, we estimate models by alternative measures of budget autonomy as explained in the 'Robustness' section in the Supplementary Material. The results, however, remain unchanged or null (see Table S8 in the Supplementary Material).
As discussed, academic autonomy is associated with a higher level of achievement inequality in upper-middle-income countries, compared to other income groups. This is a notable point as many of these upper-middle-income countries are the first to experience an influx of School autonomy and inequality in achievement 1503 decentralisation reforms by development actors, for instance, Argentina, Brazil, Chile, and Mexico in Latin America. Evidence suggests that educational decentralisation and autonomyrelated reforms may have widened the achievement gaps in the region (for example, Galiani, Gertler, & Schargrodsky, 2008;Prawda, 1993).
Opposite to the claims often made by IOs in support of school autonomy in LMICs, we find limited evidence of its association with minimising learning inequality. These results raise the question of whether school autonomy reforms in both LMICs and HICs should be encouraged irrespective of context. Policy practitioners and advocates for decentralisation and autonomy should carefully evaluate educational management reforms.
IOs such as the World Bank have implemented school autonomy reforms across LMICs over the past four decades involving a considerable amount of resources (Hossain, 2022). While its goal is to improve overall learning achievement and decrease disparities, our paper suggests contrasting results for the upper-middle-income group in academic autonomy. Despite school autonomy reforms being primarily exported from the Global North, it does not seem to yield positive outcomes in those countries (HICs) either. The validity of these reforms to implement in LMICs by IOs, thus, remains questionable. We argue that equitable resource distribution across schools should require primary attention from policymakers as research shows that disparities in school quality explains considerable achievement inequality between advantaged and disadvantaged pupils in many LMICs (for example, Gruijters & Behrman, 2020).
In addition to this, more attention should be given to contextual aspects when considering autonomy reforms. It may work in some contexts, but not in others. Currently, we have a limited understanding of those micro-mechanisms, which requires evidence with finer context-specific data. Indeed, school autonomy and decentralisation reforms are often prescribed to LMICs based on theory rather than sufficient evidence, let alone the consideration of the context.

Limitations
We highlight some major limitations in the paper. First, while our results remain unaffected or robust to several specification tests, the findings cannot be considered causal. There can still be endogeneity bias in predicting inequality in achievement by autonomy. Future research can address this issue by using causal designs with new data. Second, we could not take into account all context-specific variables. Different socio-cultural settings may induce school autonomy differently, which may also shape parents' attitudes towards participating in decision-making processes. Since we have limited country-year observations, we could not incorporate many variables which would otherwise overfit the models. We, however, run models using country and year fixed effects as robustness checks to account for the time-varying and invariant factors, which gives us quite similar results as discussed. Third, we use three major aspects of school autonomy. But one can argue that they are not comprehensive enough. There might be other aspects of school autonomy such as implementing school development plans, school inspection and supervision, which may also affect inequality in achievement. Fourth, our study is limited to analysing country-level autonomy and learning inequality. This is partly due to the scarcity of individual-level comparative longitudinal data. Since our main objective was to examine the changes in school autonomy and inequality, we required a panel dataset, which we could achieve by aggregating measures at the country level. By doing so, we could not further estimate the variance in achievement between and within schools. We will focus on this aspect in future endeavours by analysing a country case as there are some longitudinal datasets in some LMICs, such as in Indonesia. Fifth, as mentioned in the variable section, our school autonomy measures do not include whether autonomy is shared between schools and local governments or the central government, which we aim to address in the future. Sixth, hiring autonomy in PISA means a school can select teachers for hiring and the measure in our study signifies full school autonomy for hiring. Despite this, it is not clear if schools' ability to hire could be limited because of the mandatory involvement of local or central government officials in the hiring committee, for instance, for monitoring purposes. Notes 1. Some variables have missing observations for both student and school-level variables but less than 10 per cent.
We exclude all the missing values in the paper. Since the proportion of missing cases is small it is not likely to bias the results as also argued by Sun, Bradley, and Akers (2012) when using PISA data. A similar approach is observed in van Hek et al. (2019) with PISA data. 2. Since we combine data from six PISA waves, a few non-OECD countries moved to the OECD in the later waves, which may have affected the overall standard deviation in the high-income group as presented in Table S1 in the Supplementary Material. 3. We do not use the rescaled indices of ESCS provided by OECD along with PISA 2015 for comparable trend analysis as doing so leads to losing a significant number of observations, especially for earlier waves. Besides, it does not address the comparability issue regarding the SES position across countries. 4. In 2000, the World Bank classified countries with GDP per capita lower than 755$USD in the low-income group, between 756 and 2995$USD in the lower-middle-income group, and between 2996 and 9265$USD and higher than 9265$USD in the upper-middle-and high-income groups, respectively (World Bank, n.d.). All these low and lower-middle-income countries were on the Development Assistance Committee (DAC) list and therefore eligible to receive Official Development Assistance (ODA) or Official Aid in 2000 (OECD, 2000). 5. The correlation matrix for all autonomy indicators and aggregated measures was checked for each year and is available upon request. 6. World Bank and WIID data on the Gini coefficient are not perfectly comparable. However, as we are interested in comparing time-varying independent variables over time within countries, we use one source for each country. Thus, the validity of the results depends on that each unit change in the Gini coefficient is approximately equivalent, but the level of each measure is not fully comparable. We would like to also note that the Gini coefficient measure is not available for Liechtenstein from either of the two sources. Hence, we use national sources for the country where available.