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A type of the coefficient variance-covariance matrix estimator used to compute robust standard errors in time series context. Please consider using the more general *robust-standard-error* tag instead of this.

Newey-West standard errors are a version of standard errors that corrects for serial correlations of regression residuals. If a regression model is run as

$$ y_t = x_t' \beta + \epsilon_t $$

(where $x_t$ may contain lagged values of $y_t$ as needed), then Newey-West covariance matrix estimator has a form

$$ v[\hat\beta_{\rm OLS}] = (X'X)^{-1} \frac{n}{n-p} \sum_{l=0}^m K(l,m) e_t e_{t-l} (x_t' x_{t-l} + x_{t-l}' x_t) (X'X)^{-1} $$

where the leftmost summation is over possible lags that the regression errors are suspect of being correlated; $n$ is the sample size, $p$ is the number of regressors; $K(l,m)$ is a kernel of the estimator, $K(l,m)=1-l/(m+1), l>0; K(0,m)=1/2$ in the original Newey and West paper.

Technical coverage in Stata manuals:

Main reference:

Newey, W. K., and K. D. West. 1987. A simple, positive semi-definite, heteroskedasticity and autocorrelation consistent covariance matrix. Econometrica 55: 703–708.

Related tags:

  • -- generic set of questions and answers on the corrections to the standard errors when i.i.d. assumptions are violated
  • -- questions and answers on corrections to the standard errors that have the "sandwich" form (like $(X'X)^{-1}$ for the bread part and the lagged cross-product for the meat part in Newey-West estimator)
  • -- questions and answers on corrections to the standard errors that account for cross-sectional correlations of observations within clusters (e.g. due to complex sampling design)