Set of functions to compute the VCOVs robust to different forms correlation in panel or time series settings.

vcov_DK(x, time = NULL, lag = NULL, ssc = NULL)

vcov_NW(x, unit = NULL, time = NULL, lag = NULL, ssc = NULL)

NW(lag = NULL)

newey_west(lag = NULL)

DK(lag = NULL)

driscoll_kraay(lag = NULL)

## Arguments

x

A fixest object.

time

A character scalar or a one sided formula giving the name of the variable representing the time.

lag

An integer scalar, default is NULL. If NULL, then the default lag is equal to n_t^0.25 with n_t the number of time periods (as of Newey and West 1987) for panel Newey-West and Driscoll-Kraay. The default for the time series Newey-West is computed via bwNeweyWest which implements the Newey and West 1994 method.

ssc

An object returned by the function ssc. It specifies how to perform the small sample correction.

unit

A character scalar or a one sided formula giving the name of the variable representing the units of the panel.

## Value

If the first argument is a fixest object, then a VCOV is returned (i.e. a symmetric matrix). If the first argument is not a fixest object, then a) implicitly the arguments are shifted to the left (i.e. vcov_DK(~year) is equivalent to vcov_DK(time = ~year)) and b) a VCOV-request is returned and NOT a VCOV. That VCOV-request can then be used in the argument vcov of various fixest functions (e.g. vcov.fixest or even in the estimation calls).

## Details

There are currently three VCOV types: Newey-West applied to time series, Newey-West applied to a panel setting (when the argument 'unit' is not missing), and Driscoll-Kraay.

The functions on this page without the prefix "vcov_" do not compute VCOVs directly but are meant to be used in the argument vcov of fixest functions (e.g. in vcov.fixest or even in the estimation calls).

Note that for Driscoll-Kraay VCOVs, to ensure its properties the number of periods should be long enough (a minimum of 20 periods or so).

## Lag selection

The default lag selection depends on whether the VCOV applies to a panel or a time series.

For panels, i.e. panel Newey-West or Driscoll-Kraay VCOV, the default lag is n_t^0.25 with n_t the number of time periods. This is based on Newey and West 1987.

For time series Newey-West, the default lag is found thanks to the bwNeweyWest function from the sandwich package. It is based on Newey and West 1994.

## References

Newey WK, West KD (1987). "A Simple, Positive Semi-Definite, Heteroskedasticity and Autocorrelation Consistent Covariance Matrix." Econometrica, 55(3), 703-708. doi:10.2307/1913610.

Driscoll JC, Kraay AC (1998). "Consistent Covariance Matrix Estimation with Spatially Dependent Panel Data." The Review of Economics and Statistics, 80(4), 549-560. doi:10.1162/003465398557825.

Millo G (2017). "Robust Standard Error Estimators for Panel Models: A Unifying Approach" Journal of Statistical Software, 82(3). doi:10.18637/jss.v082.i03.

## Examples


data(base_did)

#
# During the estimation
#

# Panel Newey-West, lag = 2
feols(y ~ x1, base_did, NW(2) ~ id + period)
#> OLS estimation, Dep. Var.: y
#> Observations: 1,080
#> Standard-errors: Newey-West (L=2)
#>             Estimate Std. Error t value   Pr(>|t|)
#> (Intercept) 1.988753   0.186061 10.6887 2.0500e-06 ***
#> x1          0.983110   0.051618 19.0457 1.3968e-08 ***
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#> RMSE: 4.89686   Adj. R2: 0.262357

# Driscoll-Kraay
feols(y ~ x1, base_did, DK ~ period)
#> OLS estimation, Dep. Var.: y
#> Observations: 1,080
#> Standard-errors: Driscoll-Kraay (L=1)
#>             Estimate Std. Error  t value   Pr(>|t|)
#> (Intercept) 1.988753   0.789538  2.51888 3.2829e-02 *
#> x1          0.983110   0.036115 27.22141 5.9051e-10 ***
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#> RMSE: 4.89686   Adj. R2: 0.262357

# If the estimation is made with a panel.id, the dimensions are
# automatically deduced:
est = feols(y ~ x1, base_did, "NW", panel.id = ~id + period)
est
#> OLS estimation, Dep. Var.: y
#> Observations: 1,080
#> Standard-errors: Newey-West (L=1)
#>             Estimate Std. Error t value   Pr(>|t|)
#> (Intercept) 1.988753   0.174111 11.4223 1.1709e-06 ***
#> x1          0.983110   0.052699 18.6551 1.6762e-08 ***
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#> RMSE: 4.89686   Adj. R2: 0.262357

#
# Post estimation
#

# If missing, the unit and time are automatically deduced from
# the panel.id used in the estimation
vcov_NW(est, lag = 2)
#>             (Intercept)          x1
#> (Intercept) 0.034618659 0.000265638
#> x1          0.000265638 0.002664456