# Newey-West standard errors with cross-sectional OLS?

Consider the cross sectional:

$Y_i = a + b X_i + e_i$

where I have reason to believe that $E[e_j e_k] \not= 0$ for a concerning number of $j\not= k$.

What happens if I use a serial correlation robust standard error here (such as Newey West)? Is it okay to do so even though, of course, I have no serial correlation in my data, yet I have dependence? Will Newey West correct for the fact that I have non-zero non-diagonal elements of my variance-covariance matrix?

## 1 Answer

Newey-West standard errors are asymptotically consistent, meaning that the estimated variance-covariance matrix should converge to the true one.

Why do you suspect that you have non-zero off-diagonal elements of your true variance covariance matrix? Newey-West usually assumes that the rows of your model matrix are ordered from earliest to latest observations and the size of the correlation is inversely related to the number of rows apart the observations are. Is this consistent with the correlation structure that you envision for your data?

• Hi charlie, I think you've misunderstood my model to be time-series. It's a cross-sectional model. There's no "correlation structure" and no "latest observation". – user14281 Oct 31 '12 at 15:11
• Yes, I understand that, but a standard Newey-West estimator doesn't. It assumes that you have a time series model. Proximity in time, which is proxied by proximity in location in the model matrix, is how it models the correlation structure. If there is no correlation structure, then there should be no non-zero off-diagonal terms in the variance covariance matrix. The Newey-West estimator will converge to this result. – Charlie Oct 31 '12 at 15:13