theorem ols_downward_bias {ρ covZε varZ : ℝ}
(hcov : covZε < 0) (hvar : 0 < varZ) :
olsPlim ρ covZε varZ < ρ := by
simp only [olsPlim, simultaneityBias]
linarith [div_neg_of_neg_of_pos hcov hvar]CES Estimation Theory: Connecting Theory to Data