Dear all,

Suppose we have a lot of observations.
Suppose the following model : y = b*x + e , where e is distributed as N(0,epsilon).
Can a consistent estimator (OLS for example) for 'b' become inconsistent if 'epsilon' becomes very large? Or does it stays consistent but because relative to the huge value of epsilon, it remains close to the true value?

Thank you in advance for an answer,
Jordi