Riddle: Estimate effect of x on y if you only have two noisy measures of x.

Web: https://www.r-bloggers.com/2022/01/riddle-estimate-effect-of-x-on-y-if-you-only-have-two-noisy-measures-of-x/

Consider the following data generating process:

set.seed(1)

n = 100000

x = rnorm(n)

eta1 = rnorm(n) # measurement error1

noisy1 = x + eta1

eta2 = rnorm(n) # measurement error2

noisy2 = x + eta2

u = rnorm(n)

beta0=0; beta1 = 1

y = beta0+beta1*x + u

...

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