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Update 08-STAR.Rmd #149

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How to best allocate spending on schooling is an important question. What's the impact of spending money to finance smaller classrooms on student performance and outcomes, both in the short and in the long run? A vast literature in economics is concerned with this question, and for a long time there was no consensus.

The big underlying problem in answering this question is that we do not really know how student outcomes are *produced*. In other words, what makes a successful student? Is it the quality of their teacher? Surely matters. is it quality of the school building? Could be. Is it that the other pupils are of high quality and this somehow *rubs off* to weaker pupils? Also possible. What about parental background? Sure. You see that there are many potential channels that could determine student outcomes. What is more, there could be several interdependencies amongst those factors. Here's a DAG!
The big underlying problem in answering this question is that we do not really know how student outcomes are *produced*. In other words, what makes a successful student? Is it the quality of their teacher? Surely matters. Is it quality of the school building? Could be. Is it that the other pupils are of high quality and this somehow *rubs off* to weaker pupils? Also possible. What about parental background? Sure.

You see that there are many potential channels that could determine student outcomes. What is more, there could be several interdependencies amongst those factors. Here's a DAG!

```{r star1,echo = FALSE,warning = FALSE,message = FALSE,fig.align = "center",fig.cap = "Possible Channels determining student outcomes. Dashed arrows represent potentially unobserved links."}
library(ggdag)
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2. regular classes with 22-25 students
3. regular classes with 22-25 students but with an additional full-time teaching aide.

The experiment involved about 6000 students per year, for a total of 11,600 students from 80 schools. Each school was required to have at least on class of each size-type above, and random assignment happened *at the school level*. At the end of each school grade (kindergarden and grades 1 thru 3) the pupils were given a standardized test. Now, looking back at figure \@ref(fig:star1), what are the complications when we'd like to assess the impact of *class size* on student outcome? Put differently, why can't we just look at observational data of all schools (absent any experiment!), group classes by their size, and compute the mean outcomes for each group? Here is a short list:
The experiment involved about 6000 students per year, for a total of 11,600 students from 80 schools. Each school was required to have at least one class of each size-type above, and random assignment happened *at the school level*. At the end of each school grade (kindergarden and grades 1 thru 3) the pupils were given a standardized test. Now, looking back at figure \@ref(fig:star1), what are the complications when we'd like to assess the impact of *class size* on student outcome? Put differently, why can't we just look at observational data of all schools (absent any experiment!), group classes by their size, and compute the mean outcomes for each group? Here is a short list:

1. There is selection into schools with different sized classes. Suppose parents have a prior that smaller classes are better - they will try to get their kids into those schools.
1. Relatedly, who ends up being in the classroom with a child could matter (peer effects). So, if high quality kids are sorting into schools with small classes, and if peer effects are strong, we could concluded that small classes improved student outcomes when in reality this was due to the high quality of peers in class.
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