# In Gelman’s 8 school example, why is the standard error of the individual estimate assumed known?

Context:

In Gelman’s 8-school example (Bayesian Data Analysis, 3rd edition, Ch 5.5) there are eight parallel experiments in 8 schools testing the effect of coaching. Each experiment yields an estimate for the effectiveness of coaching and the associated standard error.

The authors then build a hierarchical model for the 8 data points of coaching effect as follows:

$$yi∼N(θi,sei)θi∼N(μ,τ) y_i \sim N(\theta_i, se_i) \\ \theta_i \sim N(\mu, \tau)$$

Question
In this model, they assume that $$seise_i$$ is known. I do not understand this assumption — if we feel that we have to model $$θi\theta_i$$, why don’t we do the same for $$seise_i$$?

I’ve checked the Rubin’s original paper introducing the 8 school example, and there too the author says that (p 382):

the assumption of normality and known standard error is made routinely
when we summarize a study by an estimated effect and its standard
error, and we will not question its use here.

To summarize, why don’t we model $$seise_i$$? Why do we treat it as known?

In the school example, they rely on large sample size to assume that the variances are known “for all practical purposes” (p119), and I expect they estimate them using $$1n−1∑(xi−¯x)2\frac{1}{n-1} \sum (x_i - \overline{x})^2$$ and then pretend those are the exact known values.