# demonstrate the effect of E(u|X) not equal to 0
set verbose off

# create an artificial dataset with 200 observations
nulldata 200

# uniform() generates a uniformly distributed r.v.
series x = 20 * uniform()

K = 5000
matrix slope = zeros(K,1)

loop i=1..K --quiet
  # the error term, u, is "purely random"
  series u = normal()
  series y = 10 + 1.5*x + u
  ols y 0 x --quiet
  slope[i] = $coeff[2]
endloop

# meanc() gives the column mean(s) for a matrix
printf "unbiased: mean slope = %g\n", meanc(slope)

loop i=1..K --quiet
  # the error term will be correlated with x
  series u = 0.2*x + normal()
  series y = 10 + 1.5*x + u
  ols y 0 x --quiet
  slope[i] = $coeff[2]
endloop

printf "biased: mean slope = %g\n", meanc(slope)