vcovCL {sandwich} | R Documentation |
Estimation of one-way and multi-way clustered covariance matrices using an object-oriented approach.
vcovCL(x, cluster = NULL, type = NULL, sandwich = TRUE, fix = FALSE, ...) meatCL(x, cluster = NULL, type = NULL, cadjust = TRUE, multi0 = FALSE, ...)
x |
a fitted model object. |
cluster |
a variable indicating the clustering of observations
or a |
type |
a character string specifying the estimation type (HC0–HC3).
The default is to use |
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? |
cadjust |
logical. Should a cluster adjustment be applied? |
multi0 |
logical. Should the HC0 estimate be used for the final adjustment in multi-way clustered covariances? |
... |
arguments passed to |
Clustered sandwich estimators are used to adjust inference when errors
are correlated within (but not between) clusters. vcovCL
allows
for clustering in arbitrary many cluster dimensions (e.g., firm, time, industry), given all
dimensions have enough clusters (for more details, see Cameron et al. 2011).
If each observation is its own cluster, the clustered sandwich
collapses to the basic sandwich covariance.
The function meatCL
is the work horse for estimating
the meat of clustered sandwich estimators. vcovCL
is a wrapper calling
sandwich
and bread
(Zeileis 2006). vcovCL
is applicable beyond lm
or glm
class objects.
bread
and meat
matrices are multiplied to
construct clustered sandwich estimators.
The meat of a clustered sandwich estimator is the cross product of
the clusterwise summed estimating functions. Instead of summing over
all individuals, first sum over cluster.
A two-way clustered sandwich estimator M (e.g., for cluster dimensions "firm" and "industry") is a linear combination of one-way clustered sandwich estimators for both dimensions (M_{firm}, M_{time}) minus the clustered sandwich estimator, with clusters formed out of the intersection of both dimensions (M_{id \cap time}):
M = M_{id} + M_{time} - M_{id \cap time}
Instead of substracting M_{id \cap time} as the last
substacted matrix, Ma (2014) suggests to substract the basic HC0
covariance matrix when only a single observation is in each
intersection of id and time.
Set multi0 = TRUE
to substract the basic HC0 covariance matrix as
the last substracted matrix in multi-way clustering. For details,
see also Petersen (2009) and Thompson (2011).
With the type
argument, HC0 to HC3 types of
bias adjustment can be employed.
HC2 and HC3 types of bias adjustment are geared towards the linear
model, but they are also applicable for GLMs (see Mc Caffrey and Bell
(2002) and Kauermann and Carroll (2001) for details).
A precondition for HC2 and HC3 types of bias adjustment is the existence
of a hat matrix or a weighted version of the hat matrix for GLMs,
respectively.
The cadjust
argument allows to
switch the cluster bias adjustment factor G/(G-1) on and
off (where G is the number of clusters in a cluster dimension g)
See Cameron et al. (2008) and Cameron et al. (2011) for more details about
small-sample modifications.
Cameron et al. (2011) observe that sometimes the covariance matrix is
not positive-semidefinite. To force the covariance matrix to be
positive-semidefinite, set
fix = TRUE
. Following Cameron et al. (2011), the eigendecomposition of the estimated
covariance matrix is used and any negative eigenvalue(s) are converted to zero.
A matrix containing the covariance matrix estimate.
Cameron AC & Gelbach JB & Miller DL (2008). “Bootstrap-Based Improvements for Inference with Clustered Errors”, The Review of Economics and Statistics, 90(3), 414–427. doi: 10.3386/t0344
Cameron AC & Gelbach JB & Miller DL (2011). “Robust Inference With Multiway Clustering”, Journal of Business & Ecomomic Statistics, 29(2), 238–249. doi: 10.1198/jbes.2010.07136
Kauermann G & Carroll RJ (2001). “A Note on the Efficiency of Sandwich Covariance Matrix Estimation”, Journal of the American Statistical Association, 96(456), 1387–1396. doi: 10.1198/016214501753382309
Ma MS (2014). “Are We Really Doing What We Think We Are Doing? A Note on Finite-Sample Estimates of Two-Way Cluster-Robust Standard Errors”, Mimeo, Availlable at SSRN: URL http://ssrn.com/abstract=2420421.
McCaffrey DF & Bell RM (2002). “Bias Reduction in Standard Errors for Linear Regression with Multi-Stage Samples”, Survey Methodology, 28(2), 169–181.
Petersen MA (2009). “Estimating Standard Errors in Finance Panel Data Sets: Comparing Approaches”, The Review of Financial Studies, 22(1), 435–480. doi: 10.1093/rfs/hhn053
Thompson SB (2011). “Simple Formulas for Standard Errors That Cluster by Both Firm and Time”, Journal of Financial Economics, 99(1), 1–10. doi: 10.1016/j.jfineco.2010.08.016
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
## Petersen's data data("PetersenCL", package = "sandwich") m <- lm(y ~ x, data = PetersenCL) ## clustered covariances ## one-way vcovCL(m, cluster = PetersenCL$firm) ## one-way with HC2 vcovCL(m, cluster = PetersenCL$firm, type = "HC2") ## two-way vcovCL(m, cluster = PetersenCL[, c("firm", "year")]) ## comparison with cross-section sandwiches ## HC0 all.equal(sandwich(m), vcovCL(m, type = "HC0", cadjust = FALSE)) ## HC2 all.equal(vcovHC(m, type = "HC2"), vcovCL(m, type = "HC2")) ## HC3 all.equal(vcovHC(m, type = "HC3"), vcovCL(m, type = "HC3")) ## Innovation data data("InstInnovation", package = "sandwich") ## replication of one-way clustered standard errors for model 3, Table I ## and model 1, Table II in Berger et al. (2016) ## count regression formula f1 <- cites ~ institutions + log(capital/employment) + log(sales) + industry + year ## model 3, Table I: Poisson model ## one-way clustered standard errors tab_I_3_pois <- glm(f1, data = InstInnovation, family = poisson) vcov_pois <- vcovCL(tab_I_3_pois, InstInnovation$company) sqrt(diag(vcov_pois))[2:4] ## coefficient tables if(require("lmtest")) { coeftest(tab_I_3_pois, vcov = vcov_pois)[2:4, ] } ## Not run: ## model 1, Table II: negative binomial hurdle model ## (requires "pscl" or alternatively "countreg" from R-Forge) library("pscl") library("lmtest") tab_II_3_hurdle <- hurdle(f1, data = InstInnovation, dist = "negbin") # dist = "negbin", zero.dist = "negbin", separate = FALSE) vcov_hurdle <- vcovCL(tab_II_3_hurdle, InstInnovation$company) sqrt(diag(vcov_hurdle))[c(2:4, 149:151)] coeftest(tab_II_3_hurdle, vcov = vcov_hurdle)[c(2:4, 149:151), ] ## End(Not run)