# #StackBounty: #least-squares #measurement-error Measurement error in one indep variable in OLS with multivariate regression

### Bounty: 50

Suppose I regress (with OLS) $$y$$ on $$x_1$$ and $$x_2$$. Suppose I have i.i.d. sample of size n, and that $$x_1$$ is observed with error but $$y$$ and $$x_2$$ are observed without error. What is the probability limit of the estimated coefficient on $$x_1$$?

Let us suppose for tractability that the measurement error of $$x_1$$ is "classical". That is the measurement error is normally distributed with mean 0 and is uncorrelated with $$x_2$$ or the error term.

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