Clustered Covariance Matrix Estimation for Panel Data
Estimation of sandwich covariances a la Newey-West (1987) and Driscoll and Kraay (1998) for panel data.
vcovPL(x, cluster = NULL, order.by = NULL, kernel = "Bartlett", sandwich = TRUE, fix = FALSE, ...) meatPL(x, cluster = NULL, order.by = NULL, kernel = "Bartlett", lag = "NW1987", bw = NULL, adjust = TRUE, ...)
x |
a fitted model object. |
cluster |
a variable indicating the clustering of observations,
a |
order.by |
a variable, list/data.frame, or formula indicating the
aggregation within time periods. By default |
kernel |
a character specifying the kernel used. All kernels
described in Andrews (1991) are supported, see |
lag |
character or numeric, indicating the lag length used.
Three rules of thumb ( |
bw |
numeric. The bandwidth of the kernel which by default corresponds
to |
sandwich |
logical. Should the sandwich estimator be computed?
If set to |
fix |
logical. Should the covariance matrix be fixed to be positive semi-definite in case it is not? |
adjust |
logical. Should a finite sample adjustment be made? This amounts to multiplication with n/(n - k) where n is the number of observations and k is the number of estimated parameters. |
... |
arguments passed to the |
vcovPL is a function for estimating the Newey-West (1987) and
Driscoll and Kraay (1998) covariance matrix.
Driscoll and Kraay (1998) apply a Newey-West type correction to the
sequence of cross-sectional averages of the moment conditions (see
Hoechle (2007)). For large T (and regardless of the length of the
cross-sectional dimension), the Driscoll and Kraay (1998)
standard errors are robust to general forms of cross-sectional and
serial correlation (Hoechle (2007)).
The Newey-West (1978) covariance matrix restricts the Driscoll and
Kraay (1998) covariance matrix to no cross-sectional correlation.
Default lag length is the "NW1987".
For lag = "NW1987", the lag length is chosen from the heuristic
floor[T^{(1/4)}]. More details on lag length selection in Hoechle (2007).
For lag = "NW1994", the lag length is taken from the first step
of Newey and West's (1994) plug-in procedure.
The cluster/order.by specification can be made in a number of ways:
Either both can be a single variable or cluster can be a
list/data.frame of two variables.
If expand.model.frame works for the model object x,
the cluster (and potentially additionally order.by) can also be
a formula. By default (cluster = NULL, order.by = NULL),
attr(x, "cluster") and attr(x, "order.by") are checked and
used if available. If not, every observation is assumed to be its own cluster,
and observations within clusters are assumed to be ordered accordingly.
If the number of observations in the model x is smaller than in the
original data due to NA processing, then the same NA processing
can be applied to cluster if necessary (and x$na.action being
available).
A matrix containing the covariance matrix estimate.
Andrews DWK (1991). “Heteroscedasticity and Autocorrelation Consistent Covariance Matrix Estimation”, Econometrica, 817–858.
Driscoll JC & Kraay AC (1998). “Consistent Covariance Matrix Estimation with Spatially Dependent Panel Data”, The Review of Economics and Statistics, 80(4), 549–560.
Hoechle D (2007). “Robust Standard Errors for Panel Regressions with Cross-Sectional Dependence”, Stata Journal, 7(3), 281–312.
Newey WK & West KD (1987). “Hypothesis Testing with Efficient Method of Moments Estimation”, International Economic Review, 777-787.
Newey WK & West KD (1994). “Automatic Lag Selection in Covariance Matrix Estimation”, The Review of Economic Studies, 61(4), 631–653.
White H (1980). “A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity”, Econometrica, 817–838. doi: 10.2307/1912934
Zeileis A (2004). “Econometric Computing with HC and HAC Covariance Matrix Estimator”, Journal of Statistical Software, 11(10), 1–17. doi: 10.18637/jss.v011.i10
Zeileis A (2006). “Object-Oriented Computation of Sandwich Estimators”, Journal of Statistical Software, 16(9), 1–16. doi: 10.18637/jss.v016.i09
Zeileis A, Köll S, Graham N (2020). “Various Versatile Variances: An Object-Oriented Implementation of Clustered Covariances in R.” Journal of Statistical Software, 95(1), 1–36. doi: 10.18637/jss.v095.i01
## Petersen's data
data("PetersenCL", package = "sandwich")
m <- lm(y ~ x, data = PetersenCL)
## Driscoll and Kraay standard errors
## lag length set to: T - 1 (maximum lag length)
## as proposed by Petersen (2009)
sqrt(diag(vcovPL(m, cluster = ~ firm + year, lag = "max", adjust = FALSE)))
## lag length set to: floor(4 * (T / 100)^(2/9))
## rule of thumb proposed by Hoechle (2007) based on Newey & West (1994)
sqrt(diag(vcovPL(m, cluster = ~ firm + year, lag = "NW1994")))
## lag length set to: floor(T^(1/4))
## rule of thumb based on Newey & West (1987)
sqrt(diag(vcovPL(m, cluster = ~ firm + year, lag = "NW1987")))
## the following specifications of cluster/order.by are equivalent
vcovPL(m, cluster = ~ firm + year)
vcovPL(m, cluster = PetersenCL[, c("firm", "year")])
vcovPL(m, cluster = ~ firm, order.by = ~ year)
vcovPL(m, cluster = PetersenCL$firm, order.by = PetersenCL$year)
## these are also the same when observations within each
## cluster are already ordered
vcovPL(m, cluster = ~ firm)
vcovPL(m, cluster = PetersenCL$firm)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.