Computes the variance/covariance of a fixest object

This function extracts the variance-covariance of estimated parameters from a model estimated with femlm, feols or feglm.

# S3 method for fixest
vcov(
  object,
  vcov = NULL,
  se = NULL,
  cluster,
  ssc = NULL,
  attr = FALSE,
  forceCovariance = FALSE,
  keepBounded = FALSE,
  nthreads = getFixest_nthreads(),
  ...
)

Arguments

object	A `fixest` object. Obtained using the functions `femlm`, `feols` or `feglm`.
vcov	Versatile argument to specify the VCOV. In general, it is either a character scalar equal to a VCOV type, either a formula of the form: `vcov_type ~ variables`. The VCOV types implemented are: "iid", "hetero" (or "HC1"), "cluster", "twoway", "NW" (or "newey_west"), "DK" (or "driscoll_kraay"), and "conley". It also accepts object from `vcov_cluster`, `vcov_NW`, `NW`, `vcov_DK`, `DK`, `vcov_conley` and `conley`. It also accepts covariance matrices computed externally. Finally it accepts functions to compute the covariances. See the `vcov` documentation in the vignette.
se	Character scalar. Which kind of standard error should be computed: “standard”, “hetero”, “cluster”, “twoway”, “threeway” or “fourway”? By default if there are clusters in the estimation: `se = "cluster"`, otherwise `se = "iid"`. Note that this argument is deprecated, you should use `vcov` instead.
cluster	Tells how to cluster the standard-errors (if clustering is requested). Can be either a list of vectors, a character vector of variable names, a formula or an integer vector. Assume we want to perform 2-way clustering over `var1` and `var2` contained in the data.frame `base` used for the estimation. All the following `cluster` arguments are valid and do the same thing: `cluster = base[, c("var1", "var2")]`, `cluster = c("var1", "var2")`, `cluster = ~var1+var2`. If the two variables were used as fixed-effects in the estimation, you can leave it blank with `vcov = "twoway"` (assuming `var1` [resp. `var2`] was the 1st [res. 2nd] fixed-effect). You can interact two variables using `^` with the following syntax: `cluster = ~var1^var2` or `cluster = "var1^var2"`.
ssc	An object of class `ssc.type` obtained with the function `ssc`. Represents how the degree of freedom correction should be done.You must use the function `ssc` for this argument. The arguments and defaults of the function `ssc` are: `adj = TRUE`, `fixef.K="nested"`, `cluster.adj = TRUE`, `cluster.df = "conventional"`, `t.df = "conventional"`, `fixef.force_exact=FALSE)`. See the help of the function `ssc` for details.
attr	Logical, defaults to `FALSE`. Whether to include the attributes describing how the VCOV was computed.
forceCovariance	(Advanced users.) Logical, default is `FALSE`. In the peculiar case where the obtained Hessian is not invertible (usually because of collinearity of some variables), use this option to force the covariance matrix, by using a generalized inverse of the Hessian. This can be useful to spot where possible problems come from.
keepBounded	(Advanced users -- `feNmlm` with non-linear part and bounded coefficients only.) Logical, default is `FALSE`. If `TRUE`, then the bounded coefficients (if any) are treated as unrestricted coefficients and their S.E. is computed (otherwise it is not).
nthreads	The number of threads. Can be: a) an integer lower than, or equal to, the maximum number of threads; b) 0: meaning all available threads will be used; c) a number strictly between 0 and 1 which represents the fraction of all threads to use. The default is to use 50% of all threads. You can set permanently the number of threads used within this package using the function `setFixest_nthreads`.
...	Other arguments to be passed to `summary.fixest`. The computation of the VCOV matrix is first done in `summary.fixest`.

Value

It returns a \(K\times K\) square matrix where \(K\) is the number of variables of the fitted model. If attr = TRUE, this matrix has an attribute “type” specifying how this variance/covariance matrix has been computed.

Details

For an explanation on how the standard-errors are computed and what is the exact meaning of the arguments, please have a look at the dedicated vignette: On standard-errors.

Author

Laurent Berge

Examples


# Load panel data
data(base_did)

# Simple estimation on a panel
est = feols(y ~ x1, base_did)

# ======== #
# IID VCOV #
# ======== #

# By default the VCOV assumes iid errors:
se(vcov(est))
#> (Intercept)          x1 
#>   0.1491554   0.0501191 

# You can make the call for an iid VCOV explicitly:
se(vcov(est, "iid"))
#> (Intercept)          x1 
#>   0.1491554   0.0501191 

#
# Heteroskedasticity-robust VCOV
#

# By default the VCOV assumes iid errors:
se(vcov(est, "hetero"))
#> (Intercept)          x1 
#>  0.14902573  0.05101605 

# => note that it also accepts vcov = "White" and vcov = "HC1" as aliases.

# =============== #
# Clustered VCOVs #
# =============== #

# To cluster the VCOV, you can use a formula of the form cluster ~ var1 + var2 etc
# Let's cluster by the panel ID:
se(vcov(est, cluster ~ id))
#> (Intercept)          x1 
#>   0.1943525   0.0467892 

# Alternative ways:

# -> cluster is implicitly assumed when a one-sided formula is provided
se(vcov(est, ~ id))
#> (Intercept)          x1 
#>   0.1943525   0.0467892 

# -> using the argument cluster instead of vcov
se(vcov(est, cluster = ~ id))
#> (Intercept)          x1 
#>   0.1943525   0.0467892 

# For two-/three- way clustering, just add more variables:
se(vcov(est, ~ id + period))
#> (Intercept)          x1 
#>  0.61496508  0.04721779 

# -------------------|
# Implicit deduction |
# -------------------|
# When the estimation contains FEs, the dimension on which to cluster
# is directly inferred from the FEs used in the estimation, so you don't need
# to explicitly add them.

est_fe = feols(y ~ x1 | id + period, base_did)

# Clustered along "id"
se(vcov(est_fe, "cluster"))
#>         x1 
#> 0.04578726 

# Clustered along "id" and "period"
se(vcov(est_fe, "twoway"))
#>         x1 
#> 0.03417711 


# =========== #
# Panel VCOVs #
# =========== #

# ---------------------|
# Newey West (NW) VCOV |
# ---------------------|
# To obtain NW VCOVs, use a formula of the form NW ~ id + period
se(vcov(est, NW ~ id + period))
#> (Intercept)          x1 
#>  0.17411100  0.05269927 

# If you want to change the lag:
se(vcov(est, NW(3) ~ id + period))
#> (Intercept)          x1 
#>  0.19450009  0.05104156 

# Alternative way:

# -> using the vcov_NW function
se(vcov(est, vcov_NW(unit = "id", time = "period", lag = 3)))
#> (Intercept)          x1 
#>  0.19450009  0.05104156 

# -------------------------|
# Driscoll-Kraay (DK) VCOV |
# -------------------------|
# To obtain DK VCOVs, use a formula of the form DK ~ period

se(vcov(est, DK ~ period))
#> (Intercept)          x1 
#>  0.78953790  0.03611533 

# If you want to change the lag:
se(vcov(est, DK(3) ~ period))
#> (Intercept)          x1 
#>  0.97148590  0.02841491 

# Alternative way:

# -> using the vcov_DK function
se(vcov(est, vcov_DK(time = "period", lag = 3)))
#> (Intercept)          x1 
#>  0.97148590  0.02841491 

# -------------------|
# Implicit deduction |
# -------------------|
# When the estimation contains a panel identifier, you don't need
# to re-write them later on

est_panel = feols(y ~ x1, base_did, panel.id = ~id + period)

# Both methods, NM and DK, now work automatically
se(vcov(est_panel, "NW"))
#> (Intercept)          x1 
#>  0.17411100  0.05269927 
se(vcov(est_panel, "DK"))
#> (Intercept)          x1 
#>  0.78953790  0.03611533 


# =================================== #
# VCOVs robust to spatial correlation #
# =================================== #

data(quakes)
est_geo = feols(depth ~ mag, quakes)

# ------------|
# Conley VCOV |
# ------------|
# To obtain a Conley VCOV, use a formula of the form conley(cutoff) ~ lat + lon
# with lat/lon the latitude/longitude variable names in the data set
se(vcov(est_geo, conley(100) ~ lat + long))
#> (Intercept)         mag 
#>   108.90052    19.23233 

# Alternative way:

# -> using the vcov_DK function
se(vcov(est_geo, vcov_conley(lat = "lat", lon = "long", cutoff = 100)))
#> (Intercept)         mag 
#>   108.90052    19.23233 

# -------------------|
# Implicit deduction |
# -------------------|
# By default the latitude and longitude are directly fetched in the data based
# on pattern matching. So you don't have to specify them.
# Furhter, an automatic cutoff is deduced by default.

# The following works:
se(vcov(est_geo, "conley"))
#> (Intercept)         mag 
#>   110.67271    20.17456 


# ======================== #
# Small Sample Corrections #
# ======================== #

# You can change the way the small sample corrections are done with the argument ssc.
# The argument ssc must be created by the ssc function
se(vcov(est, ssc = ssc(adj = FALSE)))
#> (Intercept)          x1 
#>  0.14908629  0.05009587 

# You can add directly the call to ssc in the vcov formula.
# You need to add it like a variable:
se(vcov(est, iid ~ ssc(adj = FALSE)))
#> (Intercept)          x1 
#>  0.14908629  0.05009587 
se(vcov(est, DK ~ period + ssc(adj = FALSE)))
#> (Intercept)          x1 
#>  0.78917195  0.03609859

Computes the variance/covariance of a `fixest` object

Arguments

Value

Details

See also

Author

Examples