Large amounts of government resources and development aid are dedicated to education worldwide, yet educational attainment and learning remain low in many developing countries.

This raises the question if not only lack of resources for education, but also inefficient allocation of resources within education systems holds back education in these countries. In this paper, I study the allocation of a key resource in education systems, teachers. In particular, I examine how the distribution of the existing stock of teachers across public primary schools affects educational outcomes.

It is well known that pupil-teacher ratios (PTRs) are larger in poorer countries. I show, however, that high average PTRs in low-income countries mask large differences in PTRs between schools. In fact, within low-income countries, there exist both schools with PTRs as low as in many high-income countries and schools with much higher PTRs. For example, in the US PTRs in public primary schools vary between 10 and 25. In India, 30 per cent of public primary school pupils also attend schools with PTRs in this range, but at the same time 10 per cent attend schools with PTRs above 80. In other words, there is much more variation in PTRs across public primary schools in low-income countries.

It is well known that pupil teacher ratios (PTRs) are larger in poorer countries.

Given the importance of teachers for education, this is certainly worrisome from an equity point of view. What I seek to understand in this paper in addition is in how far this is also worrisome from an efficiency point of view. I ask whether aggregate educational attainment in developing countries could be larger if the stock of public primary school teachers were distributed differently across schools.

I address this question in two steps. First, I build a new global school-level data set from administrative micro-data from almost two million public primary schools in 86 countries and present new stylized facts about the distribution of teachers across schools supporting the idea that teacher reallocation could be beneficial. Second, I build a model of teacher allocation that allows me to simulate the effects of alternative teacher distributions on educational outcomes in multiple countries.

The primary data source for this paper are national school censuses as they are conducted at least annually by nearly every government. Reaching out to more than 250 education authorities and statistical agencies worldwide, I obtained information on the universe of public primary schools in 70 countries. In addition, I gathered data on subsamples of schools from state-level school censuses and representative school surveys from another 16 countries.

The final data contains nearly 2 million public primary schools with a total enrolment of 273 million pupils – about 22 per cent of the global population between the ages of 5 and 14 – and covers countries across all continents and income levels. It contains three key pieces of information. First, the PTR at each school, as given by the headcount of pupils over the headcount of teachers. Second, the location of each school, as given by the administrative unit in which the school is located and/or school coordinates. Third, a school-level measure of educational performance, grade progression, for each school in 19 of the 86 countries. I use this data to document three new stylized facts.

1. Variation in PTRs across public primary schools is negatively correlated with per capita income, both across countries and within countries over time.
2. PTR variation is negatively correlated with primary school completion across countries, and across districts within countries - even after controlling for differences in per capita income and aggregate PTR.
3. The spatial variation in PTRs within lowincome countries cannot be explained by school remoteness, as measured by population density around schools, nighttime luminosity around schools, or travel time to the closest city. Moreover, the majority of PTR variation is within second tier administrative units (eg, districts) rather than across these.

Taken together these facts suggest that more equal PTR distributions could be beneficial for education on aggregate and implementing these would not require large movement of teachers, neither across administrative units nor between urban and rural areas.

To quantify potential gains from alternative teacher allocations, I build a stylized model of teacher allocation in which a social planner aims to maximize total learning, as measured by the national grade progression rate, by allocating a given stock of teachers across existing schools, taking as given a simple education production function. Then I use this model to simulate different counterfactual teacher allocations. I find that even the implementation of a simple rule-based allocation scheme that aims to equalize PTRs across schools would lead to substantial gains in many low- and lower-middle-income countries: up to 6 per cent of the gap in educational attainment between many lowand lower-middle-income countries and the US could be closed. Gains from other alternative teacher allocations that are informed by the model would be larger still. In high- and uppermiddle- income countries, in contrast, there would be no gains from teacher reallocation.

Given that public primary school teachers are only one of many inputs into education systems, the projected gains are large. To highlight this, I conduct an additional simulation in which I ask: how many additional teachers would have to be hired in order to achieve equivalent gains in educational attainment if governments were to simply decrease aggregate PTRs holding fixed relative PTRs between schools? I find that this would require significant work force increases, ranging between 6 per cent and 40 per cent. Hence, the paper suggests that inefficient allocation of teachers is an important obstacle to education in low-income countries, and improving the efficiency of teacher allocation may be more cost-effective than hiring additional teachers.

The implications of this paper also go beyond the education sector. After all, the state is a key player in many other important domains, such as health or law enforcement for example, and the paper illustrates the potential importance of factor misallocation through the state.