regression without intercept

Question

i just want to clarify if the estimator for a ordinary least square regression without a intercept consistent. I could prove that it is biased but im not how to prove whether it is or not consistent. Someone pls advise.

Answer 1

Consistency implies asymptotic unbiasedness. If your actual problem has an honest-to-goodness intercept, then omitting it from the regression model will prevent it from being consistent. Unless the bias dissappears as you collect more data, your model is inconsistent.