# My standard errors are smaller when I use Newey-West? HELP!

I am looking at some time series regressions,

When I use OLS, my standard errors on one of the coefficients is 0.002777409.

When I use the Newey-West correction the standard errors are smaller:

       OLS: 0.002777409.
1 Lag:  0.001995232
3 Lags: 0.001902868
5 Lags: 0.001859962
7 Lags: 0.001834708
9 Lags: 0.001777297


Why is this possible and why do they decrease with lag length!

One possible explanation is that in the scores corresponding to your OLS estimates there are also some negative autocorrelations. These would cause the standard errors to be smaller than under independence.

Consider the following very basic artificial example in R using the sandwich package for Newey-West standard errors: Under independence the conventional standard error and the Newey-West standard error are very close.

set.seed(1)
y0 <- rnorm(250)
sqrt(diag(vcov(lm(y0 ~ 1))))
## (Intercept)
##  0.06087633
sqrt(diag(NeweyWest(lm(y0 ~ 1))))
## (Intercept)
##  0.05839612


However, if we create a time series with positive autocorrelation (here AR1 with 0.8) the conventional standard error is too small and the Newey-West standard error is much larger.

ypos <- filter(y0, 0.8, method = "recursive")
sqrt(diag(vcov(lm(ypos ~ 1))))
## (Intercept)
##  0.09946229
sqrt(diag(NeweyWest(lm(ypos ~ 1))))
## (Intercept)
##   0.2900413


Conversely, if we create a series with negative autocorrelation (here AR1 with -0.8), then the conventional standard error is too large and the Newey-West standard error much smaller.

yneg <- filter(y0, -0.8, method = "recursive")
sqrt(diag(vcov(lm(yneg ~ 1))))
## (Intercept)
##  0.09641663
sqrt(diag(NeweyWest(lm(yneg ~ 1))))
## (Intercept)
##  0.03262333


In a more complex regression model the situation may not be that simple and the effects might also not be the same for all regression coefficients. However, it is not completely unusual to get Newey-West standard errors that are smaller than the conventional standard errors.