Attenuation Bias and Power

* There is some debate as to if attenuation bias which biases coefficient estimates toward zero as a result of measurement error reduces the likelihood of rejecting the null.

* It seems to me that it must, but I may be wrong.

* Using the code from the previous post on classical measurement error we can easy simulate this.

cap program drop simME4
program define simME4
* First argument is number of observations
* Second argument is measurement error in the dependent variable

  clear
  set obs `1' // The first argument defines how many draws

  gen weight = rnormal()^2*2

  gen v = rnormal()*`2'
  gen oweight = weight + v
  gen u = rnormal()*10
  gen price = 3*weight + u

  reg price oweight

  test oweight=0

end

simulate p=r(p) b=_b[oweight], rep(2000): simME4 100 0
gen rej = 0
replace rej = 1 if p < .1
sum
* Rejection rate is 100%

simulate p=r(p) b=_b[oweight], rep(2000): simME4 100 20
gen rej = 0
replace rej = 1 if p < .1
sum
* Now are rejection rate is only 24%

* Thus measurement error could place a critical role in failing to reject the null.

Formatted By Econometrics by Simulation