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R/tool_vcovG.R
In plm: Linear Models for Panel Data
Defines functions
dhat
vcovHC.pgmm
vcovDC.pggls
vcovBK.pggls
vcovSCC.pggls
vcovNW.pggls
vcovHC.pggls
vcovG.pggls
vcovDC.pcce
vcovBK.pcce
vcovBK.plm
vcovBK
vcovSCC.plm
vcovDC.plm
vcovNW.plm
vcovHC.plm
vcovG.plm
vcovG
vcovDC
vcovNW
vcovSCC
Documented in
vcovBK
vcovBK.plm
vcovDC
vcovDC.plm
vcovG
vcovG.plm
vcovHC.pgmm
vcovHC.plm
vcovNW
vcovNW.plm
vcovSCC
vcovSCC.plm
#' Driscoll and Kraay (1998) Robust Covariance Matrix Estimator
#'
#' Nonparametric robust covariance matrix estimators *a la
#' Driscoll and Kraay* for panel models with cross-sectional
#' *and* serial correlation.
#'
#' `vcovSCC` is a function for estimating a robust covariance matrix
#' of parameters for a panel model according to the
#' \insertCite{DRIS:KRAA:98;textual}{plm} method, which is consistent
#' with cross--sectional and serial correlation in a T-asymptotic
#' setting and irrespective of the N dimension. The use with random
#' effects models is undocumented.
#'
#' Weighting schemes specified by `type` are analogous to those in
#' [sandwich::vcovHC()] in package \CRANpkg{sandwich} and are
#' justified theoretically (although in the context of the standard
#' linear model) by \insertCite{MACK:WHIT:85;textual}{plm} and
#' \insertCite{CRIB:04;textual}{plm} \insertCite{@see @ZEIL:04}{plm}).
#'
#' The main use of `vcovSCC` (and the other variance-covariance estimators
#' provided in the package `vcovHC`, `vcovBK`, `vcovNW`, `vcovDC`) is to pass
#' it to plm's own functions like `summary`, `pwaldtest`, and `phtest` or
#' together with testing functions from the `lmtest` and `car` packages. All of
#' these typically allow passing the `vcov` or `vcov.` parameter either as a
#' matrix or as a function, e.g., for Wald--type testing: argument `vcov.` to
#' `coeftest()`, argument `vcov` to `waldtest()` and other methods in the
#' \CRANpkg{lmtest} package; and argument `vcov.` to
#' `linearHypothesis()` in the \CRANpkg{car} package (see the
#' examples), \insertCite{@see also @ZEIL:04}{plm}, 4.1-2, and examples below.
#'
#' @aliases vcovSCC
#' @param x an object of class `"plm"` or `"pcce"`
#' @param type the weighting scheme used, one of `"HC0"`, `"sss"`,
#' `"HC1"`, `"HC2"`, `"HC3"`, `"HC4"`, see Details,
#' @param cluster switch for vcovG; set at `"time"` here,
#' @param maxlag either `NULL` or a positive integer specifying the
#' maximum lag order before truncation
#' @param inner the function to be applied to the residuals inside the
#' sandwich: `"cluster"` for SCC, `"white"` for Newey-West,
#' (`"diagavg"` for compatibility reasons)
#' @param wj weighting function to be applied to lagged terms,
#' @param \dots further arguments
#' @return An object of class `"matrix"` containing the estimate of
#' the covariance matrix of coefficients.
#' @export
#' @author Giovanni Millo, partially ported from Daniel Hoechle's
#' (2007) Stata code
#' @seealso [sandwich::vcovHC()] from the \CRANpkg{sandwich}
#' package for weighting schemes (`type` argument).
#' @references
#'
#' \insertRef{CRIB:04}{plm}
#'
#' \insertRef{DRIS:KRAA:98}{plm}
#'
#' \insertRef{HOEC:07}{plm}
#'
#' \insertRef{MACK:WHIT:85}{plm}
#'
#' \insertRef{ZEIL:04}{plm}
#'
#' @keywords regression
#' @examples
#'
#' data("Produc", package="plm")
#' zz <- plm(log(gsp)~log(pcap)+log(pc)+log(emp)+unemp, data=Produc, model="pooling")
#' ## as function input to plm's summary method (with and without additional arguments):
#' summary(zz, vcov = vcovSCC)
#' summary(zz, vcov = function(x) vcovSCC(x, method="arellano", type="HC1"))
#' ## standard coefficient significance test
#' library(lmtest)
#' coeftest(zz)
#' ## SCC robust significance test, default
#' coeftest(zz, vcov.=vcovSCC)
#' ## idem with parameters, pass vcov as a function argument
#' coeftest(zz, vcov.=function(x) vcovSCC(x, type="HC1", maxlag=4))
#' ## joint restriction test
#' waldtest(zz, update(zz, .~.-log(emp)-unemp), vcov=vcovSCC)
#' \dontrun{
#' ## test of hyp.: 2*log(pc)=log(emp)
#' library(car)
#' linearHypothesis(zz, "2*log(pc)=log(emp)", vcov.=vcovSCC)
#' }
vcovSCC <- function(x, ...){
UseMethod("vcovSCC")
}
#' Newey and West (1987) Robust Covariance Matrix Estimator
#'
#' Nonparametric robust covariance matrix estimators *a la Newey
#' and West* for panel models with serial correlation.
#'
#' `vcovNW` is a function for estimating a robust covariance matrix of
#' parameters for a panel model according to the
#' \insertCite{NEWE:WEST:87;textual}{plm} method. The function works
#' as a restriction of the \insertCite{DRIS:KRAA:98;textual}{plm} covariance (see
#' [vcovSCC()]) to no cross--sectional correlation.
#'
#' Weighting schemes specified by `type` are analogous to those in
#' [sandwich::vcovHC()] in package \CRANpkg{sandwich} and are
#' justified theoretically (although in the context of the standard
#' linear model) by \insertCite{MACK:WHIT:85;textual}{plm} and
#' \insertCite{CRIB:04;textual}{plm} \insertCite{@see @ZEIL:04}{plm}.
#'
#' The main use of `vcovNW` (and the other variance-covariance estimators
#' provided in the package `vcovHC`, `vcovBK`, `vcovDC`, `vcovSCC`) is to pass
#' it to plm's own functions like `summary`, `pwaldtest`, and `phtest` or
#' together with testing functions from the `lmtest` and `car` packages. All of
#' these typically allow passing the `vcov` or `vcov.` parameter either as a
#' matrix or as a function, e.g., for Wald--type testing: argument `vcov.` to
#' `coeftest()`, argument `vcov` to `waldtest()` and other methods in the
#' \CRANpkg{lmtest} package; and argument `vcov.` to
#' `linearHypothesis()` in the \CRANpkg{car} package (see the
#' examples), see \insertCite{@see also @ZEIL:04}{plm}, 4.1-2, and examples below.
#'
#' @aliases vcovNW
#' @param x an object of class `"plm"` or `"pcce"`
#' @param type the weighting scheme used, one of `"HC0"`, `"sss"`,
#' `"HC1"`, `"HC2"`, `"HC3"`, `"HC4"`, see Details,
#' @param maxlag either `NULL` or a positive integer specifying the
#' maximum lag order before truncation
#' @param wj weighting function to be applied to lagged terms,
#' @param \dots further arguments
#' @return An object of class `"matrix"` containing the estimate of
#' the covariance matrix of coefficients.
#' @export
#' @author Giovanni Millo
#' @seealso [sandwich::vcovHC()] from the \CRANpkg{sandwich} package
#' for weighting schemes (`type` argument).
#' @references
#'
#' \insertRef{CRIB:04}{plm}
#'
#' \insertRef{DRIS:KRAA:98}{plm}
#'
#' \insertRef{MACK:WHIT:85}{plm}
#'
#' \insertRef{NEWE:WEST:87}{plm}
#'
#' \insertRef{ZEIL:04}{plm}
#'
#' @keywords regression
#' @examples
#'
#' data("Produc", package="plm")
#' zz <- plm(log(gsp)~log(pcap)+log(pc)+log(emp)+unemp, data=Produc, model="pooling")
#' ## as function input to plm's summary method (with and without additional arguments):
#' summary(zz, vcov = vcovNW)
#' summary(zz, vcov = function(x) vcovNW(x, method="arellano", type="HC1"))
#' ## standard coefficient significance test
#' library(lmtest)
#' coeftest(zz)
#' ## NW robust significance test, default
#' coeftest(zz, vcov.=vcovNW)
#' ## idem with parameters, pass vcov as a function argument
#' coeftest(zz, vcov.=function(x) vcovNW(x, type="HC1", maxlag=4))
#' ## joint restriction test
#' waldtest(zz, update(zz, .~.-log(emp)-unemp), vcov=vcovNW)
#' \dontrun{
#' ## test of hyp.: 2*log(pc)=log(emp)
#' library(car)
#' linearHypothesis(zz, "2*log(pc)=log(emp)", vcov.=vcovNW)
#' }
vcovNW <- function(x, ...){
UseMethod("vcovNW")
}
#' Double-Clustering Robust Covariance Matrix Estimator
#'
#' High-level convenience wrapper for double-clustering robust
#' covariance matrix estimators *a la*
#' \insertCite{THOM:11;textual}{plm} and
#' \insertCite{CAME:GELB:MILL:11;textual}{plm} for panel models.
#'
#' `vcovDC` is a function for estimating a robust covariance matrix of
#' parameters for a panel model with errors clustering along both dimensions.
#' The function is a convenience wrapper simply summing a group- and a
#' time-clustered covariance matrix and subtracting a diagonal one *a la*
#' White.
#'
#' Weighting schemes specified by `type` are analogous to those in
#' [sandwich::vcovHC()] in package \CRANpkg{sandwich} and are
#' justified theoretically (although in the context of the standard
#' linear model) by \insertCite{MACK:WHIT:85;textual}{plm} and
#' \insertCite{CRIB:04;textual}{plm} \insertCite{@see @ZEIL:04}{plm}.
#'
#' The main use of `vcovDC` (and the other variance-covariance estimators
#' provided in the package `vcovHC`, `vcovBK`, `vcovNW`, `vcovSCC`) is to pass
#' it to plm's own functions like `summary`, `pwaldtest`, and `phtest` or
#' together with testing functions from the `lmtest` and `car` packages. All of
#' these typically allow passing the `vcov` or `vcov.` parameter either as a
#' matrix or as a function, e.g., for Wald--type testing: argument `vcov.` to
#' `coeftest()`, argument `vcov` to `waldtest()` and other methods in the
#' \CRANpkg{lmtest} package; and argument `vcov.` to
#' `linearHypothesis()` in the \CRANpkg{car} package (see the
#' examples), see \insertCite{@see also @ZEIL:04}{plm}, 4.1-2, and examples below.
#'
#' @aliases vcovDC
#' @param x an object of class `"plm"` or `"pcce"`
#' @param type the weighting scheme used, one of `"HC0"`, `"sss"`,
#' `"HC1"`, `"HC2"`, `"HC3"`, `"HC4"`, see Details,
#' @param \dots further arguments
#' @return An object of class `"matrix"` containing the estimate of
#' the covariance matrix of coefficients.
#' @export
#' @author Giovanni Millo
#' @seealso [sandwich::vcovHC()] from the \CRANpkg{sandwich}
#' package for weighting schemes (`type` argument).
#' @references
#'
#' \insertRef{CAME:GELB:MILL:11}{plm}
#'
#' \insertRef{CRIB:04}{plm}
#'
#' \insertRef{MACK:WHIT:85}{plm}
#'
#' \insertRef{THOM:11}{plm}
#'
#' \insertRef{ZEIL:04}{plm}
#'
#' @keywords regression
#' @examples
#'
#' data("Produc", package="plm")
#' zz <- plm(log(gsp)~log(pcap)+log(pc)+log(emp)+unemp, data=Produc, model="pooling")
#' ## as function input to plm's summary method (with and without additional arguments):
#' summary(zz, vcov = vcovDC)
#' summary(zz, vcov = function(x) vcovDC(x, type="HC1", maxlag=4))
#' ## standard coefficient significance test
#' library(lmtest)
#' coeftest(zz)
#' ## DC robust significance test, default
#' coeftest(zz, vcov.=vcovDC)
#' ## idem with parameters, pass vcov as a function argument
#' coeftest(zz, vcov.=function(x) vcovDC(x, type="HC1", maxlag=4))
#' ## joint restriction test
#' waldtest(zz, update(zz, .~.-log(emp)-unemp), vcov=vcovDC)
#' \dontrun{
#' ## test of hyp.: 2*log(pc)=log(emp)
#' library(car)
#' linearHypothesis(zz, "2*log(pc)=log(emp)", vcov.=vcovDC)
#' }
vcovDC <- function(x, ...){
UseMethod("vcovDC")
}
#' Generic Lego building block for Robust Covariance Matrix Estimators
#'
#' Generic Lego building block for robust covariance matrix estimators
#' of the vcovXX kind for panel models.
#'
#' `vcovG` is the generic building block for use by higher--level
#' wrappers [vcovHC()], [vcovSCC()], [vcovDC()], and [vcovNW()]. The
#' main use of `vcovG` is to be used internally by the former, but it
#' is made available in the user space for use in non--standard
#' combinations. For more documentation, see see wrapper functions
#' mentioned.
#'
#' @aliases vcovG
#' @param x an object of class `"plm"` or `"pcce"`
#' @param type the weighting scheme used, one of `"HC0"`,
#' `"sss"`, `"HC1"`, `"HC2"`, `"HC3"`,
#' `"HC4"`,
#' @param cluster one of `"group"`, `"time"`,
#' @param l lagging order, defaulting to zero
#' @param inner the function to be applied to the residuals inside the
#' sandwich: one of `"cluster"` or `"white"` or
#' `"diagavg"`,
#' @param \dots further arguments
#' @return An object of class `"matrix"` containing the estimate
#' of the covariance matrix of coefficients.
#' @export
#' @author Giovanni Millo
#' @seealso [vcovHC()], [vcovSCC()],
#' [vcovDC()], [vcovNW()], and
#' [vcovBK()] albeit the latter does not make use of
#' vcovG.
#' @references
#'
#' \insertRef{mil17b}{plm}
#'
#' @keywords regression
#' @examples
#'
#' data("Produc", package="plm")
#' zz <- plm(log(gsp)~log(pcap)+log(pc)+log(emp)+unemp, data=Produc,
#' model="pooling")
#' ## reproduce Arellano's covariance matrix
#' vcovG(zz, cluster="group", inner="cluster", l=0)
#' ## define custom covariance function
#' ## (in this example, same as vcovHC)
#' myvcov <- function(x) vcovG(x, cluster="group", inner="cluster", l=0)
#' summary(zz, vcov = myvcov)
#' ## use in coefficient significance test
#' library(lmtest)
#' ## robust significance test
#' coeftest(zz, vcov. = myvcov)
#'
vcovG <- function(x, ...) {
UseMethod("vcovG")
}
#' @rdname vcovG
#' @export
vcovG.plm <- function(x, type = c("HC0", "sss", "HC1", "HC2", "HC3", "HC4"),
cluster = c("group", "time"),
l = 0,
inner = c("cluster", "white", "diagavg"),
...) {
## general building block for vcov
## for panel models (pooling, random, within or fd type plm obj.)
##
## * (7/11/2016): compliant with IV models
# stopping control for weighted regressions
if (!is.null(x$weights)) stop("vcovXX functions not implemented for weighted panel regressions")
type <- match.arg(type)
model <- describe(x, "model")
if (!model %in% c("random", "within", "pooling", "fd")) {
stop("Model has to be either \"random\", \"within\", \"pooling\", or \"fd\" model")
}
## extract demeaned data
demX <- model.matrix(x, model = model, rhs = 1, cstcovar.rm = "all")
## drop any linear dependent columns (corresponding to aliased coefficients)
## from model matrix X
## na.rm = TRUE because currently, RE tw unbalanced models set aliased simply to NA
if (!is.null(x$aliased) && any(x$aliased, na.rm = TRUE)) demX <- demX[ , !x$aliased, drop = FALSE]
## control: IV or not (two- or one-part formula)
if(length(formula(x))[2L] > 1L) {
demZ <- model.matrix(x, model = model, rhs = 2, cstcovar.rm = "all")
## substitute (transformed) X with projection of X on Z
## any linear dependence in Z (demZ) is appropriately taken care of by lm.fit()
nms <- colnames(demX)
demX <- lm.fit(demZ, demX)$fitted.values
# catches case with only one regressor -> need to convert numeric
# returned from lm.fit()$fitted.values to matrix:
if(!is.matrix(demX)) demX <- matrix(demX, dimnames = list(NULL, nms[1L]))
}
pdim <- pdim(x)
nT <- pdim$nT$N
Ti <- pdim$Tint$Ti
k <- dim(demX)[[2L]]
n0 <- pdim$nT$n
t0 <- pdim$nT$T
## extract residuals
uhat <- x$residuals
## define residuals weighting function omega(res)
## (code taken from meatHC and modified)
## (the weighting is defined "in sqrt" relative to the literature)
##
## (see the theoretical comments in pvcovHC)
## this is computationally heavy, do only if needed
diaghat <- switch(type, "HC0" = NULL,
"sss" = NULL,
"HC1" = NULL,
"HC2" = try(dhat(demX), silent = TRUE),
"HC3" = try(dhat(demX), silent = TRUE),
"HC4" = try(dhat(demX), silent = TRUE))
df <- nT - k
switch(type,
"HC0" = {
omega <- function(residuals, diaghat, df, g) residuals
}, "sss" = {
omega <- function(residuals, diaghat, df, g) residuals *
sqrt(g/(g-1)*((nT-1)/(nT-k)))
}, "HC1" = {
omega <- function(residuals, diaghat, df, g) residuals *
sqrt(length(residuals)/df)
}, "HC2" = {
omega <- function(residuals, diaghat, df, g) residuals /
sqrt(1 - diaghat)
}, "HC3" = {
omega <- function(residuals, diaghat, df, g) residuals /
(1 - diaghat)
}, "HC4" = {
omega <- function(residuals, diaghat, df, g) {
residuals/sqrt(1 - diaghat)^
pmin(4, length(residuals) *
diaghat/as.integer(round(sum(diaghat),
digits = 0)))
}
})
## Definition module for E(u,v)
if(is.function(inner)) {
E <- inner
} else {
## outer for clustering/arellano, diag(diag(inner)) for white
switch(match.arg(inner),
"cluster" = {
E <- function(u, v) outer(u, v)
},
"white" = {
E <- function(u, v) { # was simply: diag(diag(outer(u,v)))
# but unfortunately we have to manage unbalanced panels
# in the case l!=0 (the residual vectors are different)
# by producing a "pseudo-diagonal" with all those obs.
# common to both vectors
if(isTRUE(all.equal(names(u), names(v)))) {
## ..then keep it simple! (halves time on EmplUK ex.)
n <- length(u)
euv <- diag(u*v, n)
} else {
## calculate outer product
efull <- outer(u, v)
## make matrix of zeros with same dims and names
eres <- array(0, dim = dim(efull))
dimnames(eres) <- dimnames(efull)
## populate "pseudo-diagonal" with values from efull
for(i in seq_along(names(u))) {
for(j in seq_along(names(v))) {
if(names(u)[i] == names(v)[j]) {
eres[i, j] <- efull[i, j]
}
}
}
euv <- eres
}
return(euv)
}
},
"diagavg" = {
E <- function(u,v) {
## this is the averaged version for 'white2'
if(isTRUE(all.equal(names(u), names(v)))) {
## ..then keep it simple
n <- length(u)
euv <- diag(x = sum(u*v)/n, n)
} else {
## do just as for 'white' and then average nonzeros:
## calculate outer product
efull <- outer(u,v)
## make matrix of zeros with same dims and names
eres <- array(0, dim = dim(efull))
dimnames(eres) <- dimnames(efull)
## populate "pseudo-diagonal" with values from efull
for(i in seq_along(names(u))) {
for(j in seq_along(names(v))) {
if(names(u)[i] == names(v)[j]) {
eres[i, j] <- efull[i, j]
}
}
}
euv <- eres
## substitute nonzeros with average thereof
euv[euv != 0] <- mean(euv[euv != 0])
}
return(euv)
}
})
} ## END: Definition module for E(u,v)
## try passing: function (a or b) or matrix (unconditional) to vcovG
## robustifying against either serial or xs intragroup dependence:
## if 'group' then keep current indexing, if 'time' then swap i<->t
## so that residuals get 'clustered' by time period instead of by
## group (i.e., the vcov estimator is robust vs. xsectional dependence)
## extract indices
xindex <- unclass(attr(x$model, "index")) # unclass for speed
groupind <- as.numeric(xindex[[1L]])
timeind <- as.numeric(xindex[[2L]])
## adjust for 'fd' model (losing first time period)
if(model == "fd") {
groupi <- as.numeric(groupind)
## make vector =1 on first obs in each group, 0 elsewhere
selector <- groupi - c(0, groupi[-length(groupi)])
selector[1L] <- 1 # the first must always be 1
## eliminate first obs in time for each group
groupind <- groupind[!selector]
timeind <- timeind[!selector]
nT <- nT - n0
Ti <- Ti - 1
t0 <- t0 - 1
}
## set grouping indexes
cluster <- match.arg(cluster)
switch(cluster,
"group" = {
n <- n0
t <- t0
relevant.ind <- groupind
lab <- timeind},
"time" = {
n <- t0
t <- n0
relevant.ind <- timeind
lab <- groupind})
relevant.ind.GRP <- collapse::GRP(relevant.ind)
tind <- collapse::gsplit(seq_along(relevant.ind), relevant.ind.GRP)
tlab <- collapse::gsplit(lab, relevant.ind.GRP)
## lab were the 'labels' (a numeric, actually) for the relevant index;
## in use again from the need to make pseudo-diagonals for
## calc. the lagged White terms on unbalanced panels
## transform residuals by weights (here because type='sss' needs to
## know who the grouping index 'g' is
## set number of clusters for Stata-like small sample correction
## (if clustering, i.e., inner="cluster", then G is the cardinality of
## the grouping index; if inner="white" it is simply the sample size)
## find some more elegant solution for this!
## (perhaps if white then sss -> HC1 but check...)
G <- if(match.arg(inner) == "cluster") n else nT
uhat <- omega(uhat, diaghat, df, G)
## compute basic block: X'_t u_t u'_(t-l) X_(t-l) foreach t,
## then calculate Sl_t and sum over t (here i in place of t)
## here the benchmark case is time-clustering, but beware
## that group-clustering is the default
## preallocate k x k x (T-l) array for 'pile' of kxk matrices
## holding the X' E(u,ul) X elements
Sl <- array(dim = c(k, k, n-l))
## (l=0 gives the special contemporaneous case where Xi=Xil, ui=uil
## for computing W, CX, CT)
for(i in (1+l):n) {
X <- demX[tind[[i]], , drop = FALSE]
Xl <- demX[tind[[i-l]], , drop = FALSE]
u <- uhat[tind[[i]]]
ul <- uhat[tind[[(i-l)]]]
names(u) <- tlab[[i]]
names(ul) <- tlab[[(i-l)]]
## calculate V_yy
Sl[ , , i-l] <- crossprod(X, E(u, ul)) %*% Xl
}
## in order to sum on available observations two things can be done:
## a) apply sum(..., na.rm=TRUE) over the third dim
## b) apply mean(..., na.rm=TRUE) idem and multiply by n-l
## In case a) averaging is then done dividing each covariance point
## by (n-l), regardless of whether there are NAs in the "vertical"
## vector Sl[p,q, ]
## In case b) each mean is calculated correctly on the right number
## of observations, excluding missing data. 'salame' has to be
## multiplied by (n-l)
## But notice, here there should be none left! Each Sl_i is k x k.
## Hence use sum().
## meat
## salame <- apply(Sl, 1:2, mean, na.rm=TRUE) * (n-l)
salame <- rowSums(Sl, dims = 2L) # == apply(Sl, 1:2, sum) but faster
## bread by standard method
pane <- solve(crossprod(demX))
## sandwich
mycov <- tcrossprod(crossprod(t(pane), salame), t(pane)) # == pane %*% salame %*% pane
# save information about cluster variable in matrix (needed for e.g.,
# robust F test)
attr(mycov, which = "cluster") <- match.arg(cluster)
return(mycov)
}
#' Robust Covariance Matrix Estimators
#'
#' Robust covariance matrix estimators *a la White* for panel
#' models.
#'
#' `vcovHC` is a function for estimating a robust covariance matrix of
#' parameters for a fixed effects or random effects panel model
#' according to the White method
#' \insertCite{WHIT:80,WHIT:84b,AREL:87}{plm}. Observations may be
#' clustered by `"group"` (`"time"`) to account for serial
#' (cross-sectional) correlation.
#'
#' All types assume no intragroup (serial) correlation between errors
#' and allow for heteroskedasticity across groups (time periods). As
#' for the error covariance matrix of every single group of
#' observations, `"white1"` allows for general heteroskedasticity but
#' no serial (cross--sectional) correlation; `"white2"` is `"white1"`
#' restricted to a common variance inside every group (time period)
#' \insertCite{@see @GREE:03, Sec. 13.7.1-2, @GREE:12, Sec. 11.6.1-2
#' and @WOOL:02, Sec. 10.7.2}{plm}; `"arellano"` \insertCite{@see
#' ibid. and the original ref. @AREL:87}{plm} allows a fully general
#' structure w.r.t. heteroskedasticity and serial (cross--sectional)
#' correlation.
#'
#' Weighting schemes specified by `type` are analogous to those in
#' [sandwich::vcovHC()] in package \CRANpkg{sandwich} and are
#' justified theoretically (although in the context of the standard
#' linear model) by \insertCite{MACK:WHIT:85;textual}{plm} and
#' \insertCite{CRIB:04;textual}{plm}
#' \insertCite{ZEIL:04}{plm}. `type = "sss"` employs the small sample
#' correction as used by Stata.
#'
# % TODO: give formula for "sss";
# elaborate why different result for FE models (intercept)
#'
#' The main use of `vcovHC` (and the other variance-covariance estimators
#' provided in the package `vcovBK`, `vcovNW`, `vcovDC`, `vcovSCC`) is to pass
#' it to plm's own functions like `summary`, `pwaldtest`, and `phtest` or
#' together with testing functions from the `lmtest` and `car` packages. All of
#' these typically allow passing the `vcov` or `vcov.` parameter either as a
#' matrix or as a function, e.g., for Wald--type testing: argument `vcov.` to
#' `coeftest()`, argument `vcov` to `waldtest()` and other methods in the
#' \CRANpkg{lmtest} package; and argument `vcov.` to
#' `linearHypothesis()` in the \CRANpkg{car} package (see the
#' examples), see \insertCite{@see also @ZEIL:04}{plm}, 4.1-2, and examples below.
#'
#' A special procedure for `pgmm` objects, proposed by
#' \insertCite{WIND:05;textual}{plm}, is also provided.
#'
#' @name vcovHC.plm
#' @aliases vcovHC
#' @importFrom sandwich vcovHC
#' @export vcovHC
#' @param x an object of class `"plm"` which should be the result of a
#' random effects or a within model or a model of class `"pgmm"`
#' or an object of class `"pcce"`,
#' @param method one of `"arellano"`, `"white1"`, `"white2"`,
#' @param type the weighting scheme used, one of `"HC0"`, `"sss"`,
#' `"HC1"`, `"HC2"`, `"HC3"`, `"HC4"`, see Details,
#' @param cluster one of `"group"`, `"time"`,
#' @param \dots further arguments.
#' @return An object of class `"matrix"` containing the estimate of
#' the asymptotic covariance matrix of coefficients.
#' @note The function `pvcovHC` is deprecated. Use `vcovHC` for the
#' same functionality.
#' @author Giovanni Millo & Yves Croissant
#' @seealso [sandwich::vcovHC()] from the \CRANpkg{sandwich}
#' package for weighting schemes (`type` argument).
#' @references
#'
#' \insertRef{AREL:87}{plm}
#'
#' \insertRef{CRIB:04}{plm}
#'
#' \insertRef{GREE:03}{plm}
#'
#' \insertRef{GREE:12}{plm}
#'
#' \insertRef{MACK:WHIT:85}{plm}
#'
#' \insertRef{WIND:05}{plm}
#'
#' \insertRef{WHIT:84b}{plm}
#' chap. 6
#'
#' \insertRef{WHIT:80}{plm}
#'
#' \insertRef{WOOL:02}{plm}
#'
#' \insertRef{ZEIL:04}{plm}
#'
#' @keywords regression
#' @examples
#'
#' data("Produc", package = "plm")
#' zz <- plm(log(gsp) ~ log(pcap) + log(pc) + log(emp) + unemp,
#' data = Produc, model = "random")
#' ## as function input to plm's summary method (with and without additional arguments):
#' summary(zz, vcov = vcovHC)
#' summary(zz, vcov = function(x) vcovHC(x, method="arellano", type="HC1"))
#'
#' ## standard coefficient significance test
#' library(lmtest)
#' coeftest(zz)
#' ## robust significance test, cluster by group
#' ## (robust vs. serial correlation)
#' coeftest(zz, vcov.=vcovHC)
#' ## idem with parameters, pass vcov as a function argument
#' coeftest(zz, vcov.=function(x) vcovHC(x, method="arellano", type="HC1"))
#' ## idem, cluster by time period
#' ## (robust vs. cross-sectional correlation)
#' coeftest(zz, vcov.=function(x) vcovHC(x, method="arellano",
#' type="HC1", cluster="group"))
#' ## idem with parameters, pass vcov as a matrix argument
#' coeftest(zz, vcov.=vcovHC(zz, method="arellano", type="HC1"))
#' ## joint restriction test
#' waldtest(zz, update(zz, .~.-log(emp)-unemp), vcov=vcovHC)
#' \dontrun{
#' ## test of hyp.: 2*log(pc)=log(emp)
#' library(car)
#' linearHypothesis(zz, "2*log(pc)=log(emp)", vcov.=vcovHC)
#' }
#' ## Robust inference for CCE models
#' data("Produc", package = "plm")
#' ccepmod <- pcce(log(gsp) ~ log(pcap) + log(pc) + log(emp) + unemp, data = Produc, model="p")
#' summary(ccepmod, vcov = vcovHC)
#'
#' ## Robust inference for GMM models
#' data("EmplUK", package="plm")
#' ar <- pgmm(log(emp) ~ lag(log(emp), 1:2) + lag(log(wage), 0:1)
#' + log(capital) + lag(log(capital), 2) + log(output)
#' + lag(log(output),2) | lag(log(emp), 2:99),
#' data = EmplUK, effect = "twoways", model = "twosteps")
#' rv <- vcovHC(ar)
#' mtest(ar, order = 2, vcov = rv)
NULL
#' @rdname vcovHC.plm
#' @export
vcovHC.plm <- function(x, method=c("arellano", "white1", "white2"),
type=c("HC0", "sss", "HC1", "HC2", "HC3", "HC4"),
cluster=c("group", "time"), ...) {
## user-level wrapper for White-Arellano covariances
## translate arguments
inner <- switch(match.arg(method),
"arellano" = "cluster",
"white1" = "white",
"white2" = "diagavg")
return(vcovG(x, type=type, cluster=cluster,
l=0, inner=inner, ...))
}
#' @rdname vcovNW
#' @export
vcovNW.plm <- function(x, type=c("HC0", "sss", "HC1", "HC2", "HC3", "HC4"),
maxlag=NULL,
wj=function(j, maxlag) 1-j/(maxlag+1),
...) {
## user-level wrapper for panel Newey-West estimator
## set default lag order
if(is.null(maxlag)) maxlag <- floor((max(pdim(x)$Tint$Ti))^(1/4))
return(vcovSCC(x, type=type, maxlag=maxlag, inner="white", wj=wj, ...))
}
#' @rdname vcovDC
#' @export
vcovDC.plm <- function(x, type=c("HC0", "sss", "HC1", "HC2", "HC3", "HC4"),
...) {
## user-level wrapper for double-clustering (no persistence)
Vcx <- vcovG(x, type=type, cluster="group",
l=0, inner="cluster", ...)
Vct <- vcovG(x, type=type, cluster="time",
l=0, inner="cluster", ...)
Vw <- vcovG(x, type=type, l=0, inner="white", ...)
res <- Vcx + Vct - Vw
# save information about cluster variable in matrix (needed for e.g.,
# robust F test)
attr(res, which = "cluster") <- "group-time"
return(res)
}
#' @rdname vcovSCC
#' @export
vcovSCC.plm <- function(x, type=c("HC0", "sss", "HC1", "HC2", "HC3", "HC4"),
cluster="time",
maxlag=NULL,
inner=c("cluster", "white", "diagavg"),
wj=function(j, maxlag) 1-j/(maxlag+1),
...) {
## replicates vcovSCC
## set default lag order
if(is.null(maxlag)) maxlag <- floor((max(pdim(x)$Tint$Ti))^(1/4))
## def. Bartlett kernel
## wj <- function(j, maxlag) 1-j/(maxlag+1)
## has been passed as argument
S0 <- vcovG(x, type=type, cluster=cluster, l=0, inner=inner)
if(maxlag > 0) {
for(i in seq_len(maxlag)) {
Vctl <- vcovG(x, type=type, cluster=cluster,
l=i, inner=inner)
S0 <- S0 + wj(i, maxlag) * (Vctl + t(Vctl))
}
}
return(S0)
}
##############################################################
## separate function for BK (PCSE) covariance
#' Beck and Katz Robust Covariance Matrix Estimators
#'
#' Unconditional Robust covariance matrix estimators *a la Beck
#' and Katz* for panel models (a.k.a. Panel Corrected Standard Errors
#' (PCSE)).
#'
#' `vcovBK` is a function for estimating a robust covariance matrix of
#' parameters for a panel model according to the
#' \insertCite{BECK:KATZ:95;textual}{plm} method, a.k.a. Panel
#' Corrected Standard Errors (PCSE), which uses an unconditional
#' estimate of the error covariance across time periods (groups)
#' inside the standard formula for coefficient
#' covariance. Observations may be clustered either by `"group"` to
#' account for timewise heteroskedasticity and serial correlation or
#' by `"time"` to account for cross-sectional heteroskedasticity and
#' correlation. It must be borne in mind that the Beck and Katz
#' formula is based on N- (T-) asymptotics and will not be appropriate
#' elsewhere.
#'
#' The `diagonal` logical argument can be used, if set to
#' `TRUE`, to force to zero all non-diagonal elements in the
#' estimated error covariances; this is appropriate if both serial and
#' cross--sectional correlation are assumed out, and yields a
#' timewise- (groupwise-) heteroskedasticity--consistent estimator.
#'
#' Weighting schemes specified by `type` are analogous to those in
#' [sandwich::vcovHC()] in package \CRANpkg{sandwich} and are
#' justified theoretically (although in the context of the standard
#' linear model) by \insertCite{MACK:WHIT:85;textual}{plm} and
#' \insertCite{CRIB:04;textual}{plm} \insertCite{@see @ZEIL:04}{plm}.
#'
# % TODO: once "sss" has been added: `type = "sss"` employs the small
# % sample correction as used by Stata. give formula for "sss";
# % elaborate why different result for FE models (intercept)
#'
#' The main use of `vcovBK` (and the other variance-covariance estimators
#' provided in the package `vcovHC`, `vcovNW`, `vcovDC`, `vcovSCC`) is to pass
#' it to plm's own functions like `summary`, `pwaldtest`, and `phtest` or
#' together with testing functions from the `lmtest` and `car` packages. All of
#' these typically allow passing the `vcov` or `vcov.` parameter either as a
#' matrix or as a function, e.g., for Wald--type testing: argument `vcov.` to
#' `coeftest()`, argument `vcov` to `waldtest()` and other methods in the
#' \CRANpkg{lmtest} package; and argument `vcov.` to
#' `linearHypothesis()` in the \CRANpkg{car} package (see the
#' examples), see \insertCite{@see also @ZEIL:04}{plm}, 4.1-2, and examples below.
#'
#' @param x an object of class `"plm"`,
#' @param type the weighting scheme used, one of `"HC0"`, `"HC1"`,
#' `"HC2"`, `"HC3"`, `"HC4"`, see Details,
#' @param cluster one of `"group"`, `"time"`,
#' @param diagonal a logical value specifying whether to force
#' non-diagonal elements to zero,
#' @param \dots further arguments.
#' @export
#' @return An object of class `"matrix"` containing the estimate of
#' the covariance matrix of coefficients.
#' @author Giovanni Millo
#' @seealso [sandwich::vcovHC()] from the \CRANpkg{sandwich}
#' package for weighting schemes (`type` argument).
#' @references
#'
#'
#' \insertRef{BECK:KATZ:95}{plm}
#'
#' \insertRef{CRIB:04}{plm}
#'
#' \insertRef{GREE:03}{plm}
#'
#' \insertRef{MACK:WHIT:85}{plm}
#'
#' \insertRef{ZEIL:04}{plm}
#'
#' @keywords regression
#' @examples
#'
#' data("Produc", package="plm")
#' zz <- plm(log(gsp)~log(pcap)+log(pc)+log(emp)+unemp, data=Produc, model="random")
#' summary(zz, vcov = vcovBK)
#' summary(zz, vcov = function(x) vcovBK(x, type="HC1"))
#'
#' ## standard coefficient significance test
#' library(lmtest)
#' coeftest(zz)
#' ## robust significance test, cluster by group
#' ## (robust vs. serial correlation), default arguments
#' coeftest(zz, vcov.=vcovBK)
#' ## idem with parameters, pass vcov as a function argument
#' coeftest(zz, vcov.=function(x) vcovBK(x, type="HC1"))
#' ## idem, cluster by time period
#' ## (robust vs. cross-sectional correlation)
#' coeftest(zz, vcov.=function(x) vcovBK(x, type="HC1", cluster="time"))
#' ## idem with parameters, pass vcov as a matrix argument
#' coeftest(zz, vcov.=vcovBK(zz, type="HC1"))
#' ## joint restriction test
#' waldtest(zz, update(zz, .~.-log(emp)-unemp), vcov=vcovBK)
#' \dontrun{
#' ## test of hyp.: 2*log(pc)=log(emp)
#' library(car)
#' linearHypothesis(zz, "2*log(pc)=log(emp)", vcov.=vcovBK)
#' }
vcovBK <- function(x, ...) {
UseMethod("vcovBK")
}
# TODO: add type "sss" for vcovBK
#' @rdname vcovBK
#' @export
vcovBK.plm <- function(x, type = c("HC0", "HC1", "HC2", "HC3", "HC4"),
cluster = c("group", "time"),
diagonal = FALSE, ...) {
## Robust vcov a la Beck and Katz (1995; AKA 'pcse')
## for panel models (pooling, random, within or fd type plm obj.)
##
## This version: October 20th, 2009; allows choosing the clustering dimension
## so as to have serial- or x-sectional-correlation robustness;
##
## This function takes the demeaned data from the
## plm object, then estimates an *unconditional* error covariance by
## averaging the empirical covariance blocks by group (time period);
## this average block (say, OmegaM in EViews notation) is then put into
## White's formula instead of each Omega_i.
##
## The clustering defaults to "group" for consistency with vcovHC;
## nevertheless the most likely usage is cluster="time" for robustness vs.
## cross-sectional dependence, as in the original Beck and Katz paper (where
## it is applied to "pooling" models).
##
## This version: compliant with plm 1.2-0; lmtest.
## Code is identical to vcovHC until mark.
##
## Usage:
## myplm <- plm(<model>,<data>, ...)
## # default (cluster by group = robust vs. serial correlation):
## coeftest(myplm, vcov=vcovBK)
## # cluster by time period (robust vs. XS correlation):
## coeftest(myplm, vcov=function(x) vcovBK(x, cluster="time"))
## # idem, HC3 weighting:
## coeftest(myplm, vcov=function(x) vcovBK(x,cluster="time",type="HC3"))
## waldtest(myplm,update(myplm,<new formula>),vcov=vcovBK)
##
## This weighted version implements a system of weights as
## in vcovHC/meatHC. Sure this makes sense for white1, but it
## is open to question for white2 and arellano. We'll see.
##
## Results OK vs. EViews, vcov=PCSE. Unbal. case not exactly the
## same (but then, who knows what EViews does!)
# stopping control for weighted regressions
if (!is.null(x$weights)) stop("vcovXX functions not implemented for weighted panel regressions")
type <- match.arg(type)
model <- describe(x, "model")
if (!model %in% c("random", "within", "pooling", "fd")) {
stop("Model has to be either \"random\", \"within\", \"pooling\", or \"fd\" model")
}
## extract demeaned data
demX <- model.matrix(x, model = model, rhs = 1, cstcovar.rm = "all")
## drop any linear dependent columns (corresponding to aliased coefficients)
## from model matrix X
## na.rm = TRUE because currently, RE tw unbalanced models set aliased simply to NA
if (!is.null(x$aliased) && any(x$aliased, na.rm = TRUE)) demX <- demX[ , !x$aliased, drop = FALSE]
## control: IV or not (two- or one-part formula)
if(length(formula(x))[2L] > 1L) {
demZ <- model.matrix(x, model = model, rhs = 2, cstcovar.rm = "all")
## substitute (transformed) X with projection of X on Z
## any linear dependence in Z (demZ) is appropriately taken care of by lm.fit()
nms <- colnames(demX)
demX <- lm.fit(demZ, demX)$fitted.values
# catches case with only one regressor -> need to convert numeric
# returned from lm.fit()fitted.values to matrix:
if(!is.matrix(demX)) demX <- matrix(demX, dimnames = list(NULL, nms[1L]))
}
pdim <- pdim(x)
nT <- pdim$nT$N
Ti <- pdim$Tint$Ti
k <- dim(demX)[[2L]]
n0 <- pdim$nT$n
t0 <- pdim$nT$T
## extract residuals
uhat <- x$residuals
## robustifying against either serial or xs intragroup dependence:
## if 'group' then keep current indexing, if 'time' then swap i<->t
## so that residuals get 'clustered' by time period instead of by
## group (i.e., the vcov estimator is robust vs. xsectional dependence)
## extract indices
xindex <- unclass(attr(x$model, "index")) # unclass for speed
groupind <- as.numeric(xindex[[1L]])
timeind <- as.numeric(xindex[[2L]])
## Achim's fix for 'fd' model (losing first time period)
if(model == "fd") {
groupind <- groupind[timeind > 1]
timeind <- timeind[ timeind > 1]
nT <- nT - n0
Ti <- Ti - 1
t0 <- t0 - 1
}
## set grouping indexes
cluster <- match.arg(cluster)
switch(cluster,
"group" = {
n <- n0 # this is needed only for 'pcse'
t <- t0 # this is needed only for 'pcse'
relevant.ind <- groupind
lab <- timeind },
"time" = {
n <- t0 # this is needed only for 'pcse'
t <- n0 # this is needed only for 'pcse'
relevant.ind <- timeind
lab <- groupind
})
relevant.ind.GRP <- collapse::GRP(relevant.ind)
tind <- collapse::gsplit(seq_along(relevant.ind), relevant.ind.GRP)
tlab <- collapse::gsplit(lab, relevant.ind.GRP)
## define residuals weighting function omega(res)
## (code taken from meatHC and modified)
## (the weighting is defined "in sqrt" relative to the literature)
##
## (see the theoretical comments in pvcovHC)
## this is computationally heavy, do only if needed
diaghat <- switch(type, "HC0" = NULL,
"HC1" = NULL,
"HC2" = try(dhat(demX), silent = TRUE),
"HC3" = try(dhat(demX), silent = TRUE),
"HC4" = try(dhat(demX), silent = TRUE))
df <- nT - k
switch(type,
"HC0" = {
omega <- function(residuals, diaghat, df) residuals
}, "HC1" = {
omega <- function(residuals, diaghat, df) residuals *
sqrt(length(residuals)/df)
}, "HC2" = {
omega <- function(residuals, diaghat, df) residuals /
sqrt(1 - diaghat)
}, "HC3" = {
omega <- function(residuals, diaghat, df) residuals /
(1 - diaghat)
}, "HC4" = {
omega <- function(residuals, diaghat, df) residuals/sqrt(1 -
diaghat)^pmin(4, length(residuals) * diaghat/as.integer(round(sum(diaghat),
digits = 0)))
})
## transform residuals by weights
uhat <- omega(uhat, diaghat, df)
## CODE TAKEN FROM pvcovHC() UNTIL HERE except for ind/time labeling ##
## the PCSE covariance estimator is based on the unconditional estimate
## of the intragroup (intraperiod) covariance of errors, OmegaT or OmegaM
## in the EViews help.
## we calculate this based on code from pggls().
## the Omegai function is then:
## - constant if the panel is balanced
## - depending only on the intragroup (intraperiod) position index
## if the panel is unbalanced.
## (code for estimating OmegaM/OmegaT partly taken from pggls)
## est. omega submatrix
## "pre-allocate" an empty array
tres <- array(dim = c(t, t, n))
## array of n "empirical omega-blocks"
## with outer product of t(i) residuals
## for each group 1..n
## (use subscripting from condition 'label in labels' set',
## the rest stays NA if any)
unlabs <- unique(lab) # fetch (all, unique) values of the relevant labels
seq.len.t <- seq_len(t)
for(i in seq_len(n)) {
ut <- uhat[tind[[i]]]
tpos <- seq.len.t[unlabs %in% tlab[[i]]]
## put non-diag elements to 0 if diagonal=TRUE
tres[tpos, tpos, i] <- if(diagonal) diag(diag(ut %o% ut)) else ut %o% ut
}
## average over all omega blocks, removing NAs (apply preserving
## *two* dimensions, i.e., over the third) to get the unconditional
## covariance matrix of errors for a group (viz. time period):
OmegaT <- rowMeans(tres, dims = 2L, na.rm = TRUE) # == apply(tres, 1:2, mean, na.rm = TRUE) but faster
## end of PCSE covariance calculation.
salame <- array(dim = c(k, k, n))
for(i in seq_len(n)) {
groupinds <- tind[[i]]
grouplabs <- tlab[[i]]
xi <- demX[groupinds, , drop = FALSE]
## for every group, take relevant positions
tpos <- unlabs %in% grouplabs
OmegaTi <- OmegaT[tpos, tpos, drop = FALSE]
salame[ , , i] <- crossprod(xi, OmegaTi) %*% xi
}
## meat
salame <- rowSums(salame, dims = 2L) # == apply(salame, 1:2, sum) but faster
## bread
pane <- solve(crossprod(demX))
## sandwich
mycov <- tcrossprod(crossprod(t(pane), salame), t(pane)) # == pane %*% salame %*% pane
# save information about cluster variable in matrix (needed for e.g.,
# robust F test)
attr(mycov, which = "cluster") <- match.arg(cluster)
return(mycov)
}
#######################################################
#####################################
## vcovXX methods for pcce objects ##
#####################################
## pcce is compliant with plm so vcovXX.pcce <- vcovXX.plm
## for any vcov that makes sense computed on the transformed
## data from model.matrix.pcce and pmodel.response.pcce
## TODO: vcovBK.pcce, vcovDC.pcce missing? Or not valid?
## Have a stopping break for now w/ informative error
#' @export
vcovBK.pcce <- function(x, ...) stop("plm::vcovBK not implemented for 'pcce' models")
#' @export
vcovDC.pcce <- function(x, ...) stop("plm::vcovDC not implemented for 'pcce' models")
#' @rdname vcovG
#' @export
vcovG.pcce <- vcovG.plm
#' @rdname vcovHC.plm
#' @export
vcovHC.pcce <- vcovHC.plm
#' @rdname vcovNW
#' @export
vcovNW.pcce <- vcovNW.plm
#' @rdname vcovSCC
#' @export
vcovSCC.pcce <- vcovSCC.plm
########################################################
## vcovXX methods for pggls objects as stopping break ##
########################################################
vcovXX.pggls.error <- "not implemented as not sensible for 'pggls' models"
#' @export
vcovG.pggls <- function(x, ...) stop(paste0("plm::vcovG ", vcovXX.pggls.error))
#' @export
vcovHC.pggls <- function(x, ...) stop(paste0("plm::vcovHC ", vcovXX.pggls.error))
#' @export
vcovNW.pggls <- function(x, ...) stop(paste0("plm::vcovNW ", vcovXX.pggls.error))
#' @export
vcovSCC.pggls <- function(x, ...) stop(paste0("plm::vcovSCC ", vcovXX.pggls.error))
#' @export
vcovBK.pggls <- function(x, ...) stop(paste0("plm::vcovBK ", vcovXX.pggls.error))
#' @export
vcovDC.pggls <- function(x, ...) stop(paste0("plm::vcovDC ", vcovXX.pggls.error))
####################################
## vcovHC method for pgmm objects ##
####################################
#' @rdname vcovHC.plm
#' @importFrom MASS ginv
#' @export
vcovHC.pgmm <- function(x, ...) {
model <- describe(x, "model")
transformation <- describe(x, "transformation")
A1 <- x$A1
A2 <- x$A2
if(transformation == "ld") {
## yX <- lapply(x$model,function(x) rbind(diff(x),x))
## residuals <-lapply(x$residuals,function(x) c(diff(x),x))
yX <- x$model
residuals <- x$residuals
}
else {
yX <- x$model
residuals <- x$residuals
}
minevA2 <- min(abs(Re(eigen(A2)$values)))
eps <- 1E-9
SA2 <- if(minevA2 < eps){
warning("a general inverse is used")
ginv(A2)
} else solve(A2)
if(model == "twosteps") {
coef1s <- x$coefficients[[1L]]
res1s <- lapply(yX, function(x) x[ , 1L] - crossprod(t(x[ , -1L, drop = FALSE]), coef1s))
K <- ncol(yX[[1L]])
D <- c()
WX <- Reduce("+",
mapply(function(x, y) crossprod(x, y[ , -1L, drop = FALSE]), x$W, yX, SIMPLIFY = FALSE))
We <- Reduce("+", mapply(function(x, y) crossprod(x, y), x$W, residuals, SIMPLIFY = FALSE))
B1 <- solve(t(WX) %*% A1 %*% WX)
B2 <- vcov(x)
vcov1s <- B1 %*% (t(WX) %*% A1 %*% SA2 %*% A1 %*% WX) %*% B1
for (k in 2:K) {
exk <- mapply(
function(x, y){
z <- crossprod(t(x[ , k, drop = FALSE]), t(y))
- z - t(z)
},
yX, res1s, SIMPLIFY = FALSE)
wexkw <- Reduce("+",
mapply(
function(x, y)
crossprod(x, crossprod(y, x)),
x$W, exk, SIMPLIFY = FALSE))
Dk <- -B2 %*% t(WX) %*% A2 %*% wexkw %*% A2 %*% We
D <- cbind(D, Dk)
}
vcovr <- B2 + crossprod(t(D), B2) + t(crossprod(t(D), B2)) + D %*% vcov1s %*% t(D)
}
else {
# model = "onestep"
res1s <- lapply(yX, function(z) z[ , 1L] - crossprod(t(z[ , -1L, drop = FALSE]), x$coefficients))
K <- ncol(yX[[1L]])
WX <- Reduce("+", mapply(function(z, y) crossprod(z[ , -1L, drop = FALSE], y), yX, x$W, SIMPLIFY = FALSE))
B1 <- vcov(x)
vcovr <- B1 %*% (WX %*% A1 %*% SA2 %*% A1 %*% t(WX)) %*% B1
}
vcovr
}
## dhat: diaghat function for matrices
dhat <- function(x) {
rowSums(crossprod(t(x), solve(crossprod(x))) * x) # == (old) diag(crossprod(t(x), solve(crossprod(x), t(x)))
}
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Defines functions dhat vcovHC.pgmm vcovDC.pggls vcovBK.pggls vcovSCC.pggls vcovNW.pggls vcovHC.pggls vcovG.pggls vcovDC.pcce vcovBK.pcce vcovBK.plm vcovBK vcovSCC.plm vcovDC.plm vcovNW.plm vcovHC.plm vcovG.plm vcovG vcovDC vcovNW vcovSCC
Documented in vcovBK vcovBK.plm vcovDC vcovDC.plm vcovG vcovG.plm vcovHC.pgmm vcovHC.plm vcovNW vcovNW.plm vcovSCC vcovSCC.plm
#' Driscoll and Kraay (1998) Robust Covariance Matrix Estimator
#'
#' Nonparametric robust covariance matrix estimators *a la
#' Driscoll and Kraay* for panel models with cross-sectional
#' *and* serial correlation.
#'
#' `vcovSCC` is a function for estimating a robust covariance matrix
#' of parameters for a panel model according to the
#' \insertCite{DRIS:KRAA:98;textual}{plm} method, which is consistent
#' with cross--sectional and serial correlation in a T-asymptotic
#' setting and irrespective of the N dimension. The use with random
#' effects models is undocumented.
#'
#' Weighting schemes specified by `type` are analogous to those in
#' [sandwich::vcovHC()] in package \CRANpkg{sandwich} and are
#' justified theoretically (although in the context of the standard
#' linear model) by \insertCite{MACK:WHIT:85;textual}{plm} and
#' \insertCite{CRIB:04;textual}{plm} \insertCite{@see @ZEIL:04}{plm}).
#'
#' The main use of `vcovSCC` (and the other variance-covariance estimators
#' provided in the package `vcovHC`, `vcovBK`, `vcovNW`, `vcovDC`) is to pass
#' it to plm's own functions like `summary`, `pwaldtest`, and `phtest` or
#' together with testing functions from the `lmtest` and `car` packages. All of
#' these typically allow passing the `vcov` or `vcov.` parameter either as a
#' matrix or as a function, e.g., for Wald--type testing: argument `vcov.` to
#' `coeftest()`, argument `vcov` to `waldtest()` and other methods in the
#' \CRANpkg{lmtest} package; and argument `vcov.` to
#' `linearHypothesis()` in the \CRANpkg{car} package (see the
#' examples), \insertCite{@see also @ZEIL:04}{plm}, 4.1-2, and examples below.
#'
#' @aliases vcovSCC
#' @param x an object of class `"plm"` or `"pcce"`
#' @param type the weighting scheme used, one of `"HC0"`, `"sss"`,
#' `"HC1"`, `"HC2"`, `"HC3"`, `"HC4"`, see Details,
#' @param cluster switch for vcovG; set at `"time"` here,
#' @param maxlag either `NULL` or a positive integer specifying the
#' maximum lag order before truncation
#' @param inner the function to be applied to the residuals inside the
#' sandwich: `"cluster"` for SCC, `"white"` for Newey-West,
#' (`"diagavg"` for compatibility reasons)
#' @param wj weighting function to be applied to lagged terms,
#' @param \dots further arguments
#' @return An object of class `"matrix"` containing the estimate of
#' the covariance matrix of coefficients.
#' @export
#' @author Giovanni Millo, partially ported from Daniel Hoechle's
#' (2007) Stata code
#' @seealso [sandwich::vcovHC()] from the \CRANpkg{sandwich}
#' package for weighting schemes (`type` argument).
#' @references
#'
#' \insertRef{CRIB:04}{plm}
#'
#' \insertRef{DRIS:KRAA:98}{plm}
#'
#' \insertRef{HOEC:07}{plm}
#'
#' \insertRef{MACK:WHIT:85}{plm}
#'
#' \insertRef{ZEIL:04}{plm}
#'
#' @keywords regression
#' @examples
#'
#' data("Produc", package="plm")
#' zz <- plm(log(gsp)~log(pcap)+log(pc)+log(emp)+unemp, data=Produc, model="pooling")
#' ## as function input to plm's summary method (with and without additional arguments):
#' summary(zz, vcov = vcovSCC)
#' summary(zz, vcov = function(x) vcovSCC(x, method="arellano", type="HC1"))
#' ## standard coefficient significance test
#' library(lmtest)
#' coeftest(zz)
#' ## SCC robust significance test, default
#' coeftest(zz, vcov.=vcovSCC)
#' ## idem with parameters, pass vcov as a function argument
#' coeftest(zz, vcov.=function(x) vcovSCC(x, type="HC1", maxlag=4))
#' ## joint restriction test
#' waldtest(zz, update(zz, .~.-log(emp)-unemp), vcov=vcovSCC)
#' \dontrun{
#' ## test of hyp.: 2*log(pc)=log(emp)
#' library(car)
#' linearHypothesis(zz, "2*log(pc)=log(emp)", vcov.=vcovSCC)
#' }
vcovSCC <- function(x, ...){
UseMethod("vcovSCC")
}
#' Newey and West (1987) Robust Covariance Matrix Estimator
#'
#' Nonparametric robust covariance matrix estimators *a la Newey
#' and West* for panel models with serial correlation.
#'
#' `vcovNW` is a function for estimating a robust covariance matrix of
#' parameters for a panel model according to the
#' \insertCite{NEWE:WEST:87;textual}{plm} method. The function works
#' as a restriction of the \insertCite{DRIS:KRAA:98;textual}{plm} covariance (see
#' [vcovSCC()]) to no cross--sectional correlation.
#'
#' Weighting schemes specified by `type` are analogous to those in
#' [sandwich::vcovHC()] in package \CRANpkg{sandwich} and are
#' justified theoretically (although in the context of the standard
#' linear model) by \insertCite{MACK:WHIT:85;textual}{plm} and
#' \insertCite{CRIB:04;textual}{plm} \insertCite{@see @ZEIL:04}{plm}.
#'
#' The main use of `vcovNW` (and the other variance-covariance estimators
#' provided in the package `vcovHC`, `vcovBK`, `vcovDC`, `vcovSCC`) is to pass
#' it to plm's own functions like `summary`, `pwaldtest`, and `phtest` or
#' together with testing functions from the `lmtest` and `car` packages. All of
#' these typically allow passing the `vcov` or `vcov.` parameter either as a
#' matrix or as a function, e.g., for Wald--type testing: argument `vcov.` to
#' `coeftest()`, argument `vcov` to `waldtest()` and other methods in the
#' \CRANpkg{lmtest} package; and argument `vcov.` to
#' `linearHypothesis()` in the \CRANpkg{car} package (see the
#' examples), see \insertCite{@see also @ZEIL:04}{plm}, 4.1-2, and examples below.
#'
#' @aliases vcovNW
#' @param x an object of class `"plm"` or `"pcce"`
#' @param type the weighting scheme used, one of `"HC0"`, `"sss"`,
#' `"HC1"`, `"HC2"`, `"HC3"`, `"HC4"`, see Details,
#' @param maxlag either `NULL` or a positive integer specifying the
#' maximum lag order before truncation
#' @param wj weighting function to be applied to lagged terms,
#' @param \dots further arguments
#' @return An object of class `"matrix"` containing the estimate of
#' the covariance matrix of coefficients.
#' @export
#' @author Giovanni Millo
#' @seealso [sandwich::vcovHC()] from the \CRANpkg{sandwich} package
#' for weighting schemes (`type` argument).
#' @references
#'
#' \insertRef{CRIB:04}{plm}
#'
#' \insertRef{DRIS:KRAA:98}{plm}
#'
#' \insertRef{MACK:WHIT:85}{plm}
#'
#' \insertRef{NEWE:WEST:87}{plm}
#'
#' \insertRef{ZEIL:04}{plm}
#'
#' @keywords regression
#' @examples
#'
#' data("Produc", package="plm")
#' zz <- plm(log(gsp)~log(pcap)+log(pc)+log(emp)+unemp, data=Produc, model="pooling")
#' ## as function input to plm's summary method (with and without additional arguments):
#' summary(zz, vcov = vcovNW)
#' summary(zz, vcov = function(x) vcovNW(x, method="arellano", type="HC1"))
#' ## standard coefficient significance test
#' library(lmtest)
#' coeftest(zz)
#' ## NW robust significance test, default
#' coeftest(zz, vcov.=vcovNW)
#' ## idem with parameters, pass vcov as a function argument
#' coeftest(zz, vcov.=function(x) vcovNW(x, type="HC1", maxlag=4))
#' ## joint restriction test
#' waldtest(zz, update(zz, .~.-log(emp)-unemp), vcov=vcovNW)
#' \dontrun{
#' ## test of hyp.: 2*log(pc)=log(emp)
#' library(car)
#' linearHypothesis(zz, "2*log(pc)=log(emp)", vcov.=vcovNW)
#' }
vcovNW <- function(x, ...){
UseMethod("vcovNW")
}
#' Double-Clustering Robust Covariance Matrix Estimator
#'
#' High-level convenience wrapper for double-clustering robust
#' covariance matrix estimators *a la*
#' \insertCite{THOM:11;textual}{plm} and
#' \insertCite{CAME:GELB:MILL:11;textual}{plm} for panel models.
#'
#' `vcovDC` is a function for estimating a robust covariance matrix of
#' parameters for a panel model with errors clustering along both dimensions.
#' The function is a convenience wrapper simply summing a group- and a
#' time-clustered covariance matrix and subtracting a diagonal one *a la*
#' White.
#'
#' Weighting schemes specified by `type` are analogous to those in
#' [sandwich::vcovHC()] in package \CRANpkg{sandwich} and are
#' justified theoretically (although in the context of the standard
#' linear model) by \insertCite{MACK:WHIT:85;textual}{plm} and
#' \insertCite{CRIB:04;textual}{plm} \insertCite{@see @ZEIL:04}{plm}.
#'
#' The main use of `vcovDC` (and the other variance-covariance estimators
#' provided in the package `vcovHC`, `vcovBK`, `vcovNW`, `vcovSCC`) is to pass
#' it to plm's own functions like `summary`, `pwaldtest`, and `phtest` or
#' together with testing functions from the `lmtest` and `car` packages. All of
#' these typically allow passing the `vcov` or `vcov.` parameter either as a
#' matrix or as a function, e.g., for Wald--type testing: argument `vcov.` to
#' `coeftest()`, argument `vcov` to `waldtest()` and other methods in the
#' \CRANpkg{lmtest} package; and argument `vcov.` to
#' `linearHypothesis()` in the \CRANpkg{car} package (see the
#' examples), see \insertCite{@see also @ZEIL:04}{plm}, 4.1-2, and examples below.
#'
#' @aliases vcovDC
#' @param x an object of class `"plm"` or `"pcce"`
#' @param type the weighting scheme used, one of `"HC0"`, `"sss"`,
#' `"HC1"`, `"HC2"`, `"HC3"`, `"HC4"`, see Details,
#' @param \dots further arguments
#' @return An object of class `"matrix"` containing the estimate of
#' the covariance matrix of coefficients.
#' @export
#' @author Giovanni Millo
#' @seealso [sandwich::vcovHC()] from the \CRANpkg{sandwich}
#' package for weighting schemes (`type` argument).
#' @references
#'
#' \insertRef{CAME:GELB:MILL:11}{plm}
#'
#' \insertRef{CRIB:04}{plm}
#'
#' \insertRef{MACK:WHIT:85}{plm}
#'
#' \insertRef{THOM:11}{plm}
#'
#' \insertRef{ZEIL:04}{plm}
#'
#' @keywords regression
#' @examples
#'
#' data("Produc", package="plm")
#' zz <- plm(log(gsp)~log(pcap)+log(pc)+log(emp)+unemp, data=Produc, model="pooling")
#' ## as function input to plm's summary method (with and without additional arguments):
#' summary(zz, vcov = vcovDC)
#' summary(zz, vcov = function(x) vcovDC(x, type="HC1", maxlag=4))
#' ## standard coefficient significance test
#' library(lmtest)
#' coeftest(zz)
#' ## DC robust significance test, default
#' coeftest(zz, vcov.=vcovDC)
#' ## idem with parameters, pass vcov as a function argument
#' coeftest(zz, vcov.=function(x) vcovDC(x, type="HC1", maxlag=4))
#' ## joint restriction test
#' waldtest(zz, update(zz, .~.-log(emp)-unemp), vcov=vcovDC)
#' \dontrun{
#' ## test of hyp.: 2*log(pc)=log(emp)
#' library(car)
#' linearHypothesis(zz, "2*log(pc)=log(emp)", vcov.=vcovDC)
#' }
vcovDC <- function(x, ...){
UseMethod("vcovDC")
}
#' Generic Lego building block for Robust Covariance Matrix Estimators
#'
#' Generic Lego building block for robust covariance matrix estimators
#' of the vcovXX kind for panel models.
#'
#' `vcovG` is the generic building block for use by higher--level
#' wrappers [vcovHC()], [vcovSCC()], [vcovDC()], and [vcovNW()]. The
#' main use of `vcovG` is to be used internally by the former, but it
#' is made available in the user space for use in non--standard
#' combinations. For more documentation, see see wrapper functions
#' mentioned.
#'
#' @aliases vcovG
#' @param x an object of class `"plm"` or `"pcce"`
#' @param type the weighting scheme used, one of `"HC0"`,
#' `"sss"`, `"HC1"`, `"HC2"`, `"HC3"`,
#' `"HC4"`,
#' @param cluster one of `"group"`, `"time"`,
#' @param l lagging order, defaulting to zero
#' @param inner the function to be applied to the residuals inside the
#' sandwich: one of `"cluster"` or `"white"` or
#' `"diagavg"`,
#' @param \dots further arguments
#' @return An object of class `"matrix"` containing the estimate
#' of the covariance matrix of coefficients.
#' @export
#' @author Giovanni Millo
#' @seealso [vcovHC()], [vcovSCC()],
#' [vcovDC()], [vcovNW()], and
#' [vcovBK()] albeit the latter does not make use of
#' vcovG.
#' @references
#'
#' \insertRef{mil17b}{plm}
#'
#' @keywords regression
#' @examples
#'
#' data("Produc", package="plm")
#' zz <- plm(log(gsp)~log(pcap)+log(pc)+log(emp)+unemp, data=Produc,
#' model="pooling")
#' ## reproduce Arellano's covariance matrix
#' vcovG(zz, cluster="group", inner="cluster", l=0)
#' ## define custom covariance function
#' ## (in this example, same as vcovHC)
#' myvcov <- function(x) vcovG(x, cluster="group", inner="cluster", l=0)
#' summary(zz, vcov = myvcov)
#' ## use in coefficient significance test
#' library(lmtest)
#' ## robust significance test
#' coeftest(zz, vcov. = myvcov)
#'
vcovG <- function(x, ...) {
UseMethod("vcovG")
}
#' @rdname vcovG
#' @export
vcovG.plm <- function(x, type = c("HC0", "sss", "HC1", "HC2", "HC3", "HC4"),
cluster = c("group", "time"),
l = 0,
inner = c("cluster", "white", "diagavg"),
...) {
## general building block for vcov
## for panel models (pooling, random, within or fd type plm obj.)
##
## * (7/11/2016): compliant with IV models
# stopping control for weighted regressions
if (!is.null(x$weights)) stop("vcovXX functions not implemented for weighted panel regressions")
type <- match.arg(type)
model <- describe(x, "model")
if (!model %in% c("random", "within", "pooling", "fd")) {
stop("Model has to be either \"random\", \"within\", \"pooling\", or \"fd\" model")
}
## extract demeaned data
demX <- model.matrix(x, model = model, rhs = 1, cstcovar.rm = "all")
## drop any linear dependent columns (corresponding to aliased coefficients)
## from model matrix X
## na.rm = TRUE because currently, RE tw unbalanced models set aliased simply to NA
if (!is.null(x$aliased) && any(x$aliased, na.rm = TRUE)) demX <- demX[ , !x$aliased, drop = FALSE]
## control: IV or not (two- or one-part formula)
if(length(formula(x))[2L] > 1L) {
demZ <- model.matrix(x, model = model, rhs = 2, cstcovar.rm = "all")
## substitute (transformed) X with projection of X on Z
## any linear dependence in Z (demZ) is appropriately taken care of by lm.fit()
nms <- colnames(demX)
demX <- lm.fit(demZ, demX)$fitted.values
# catches case with only one regressor -> need to convert numeric
# returned from lm.fit()$fitted.values to matrix:
if(!is.matrix(demX)) demX <- matrix(demX, dimnames = list(NULL, nms[1L]))
}
pdim <- pdim(x)
nT <- pdim$nT$N
Ti <- pdim$Tint$Ti
k <- dim(demX)[[2L]]
n0 <- pdim$nT$n
t0 <- pdim$nT$T
## extract residuals
uhat <- x$residuals
## define residuals weighting function omega(res)
## (code taken from meatHC and modified)
## (the weighting is defined "in sqrt" relative to the literature)
##
## (see the theoretical comments in pvcovHC)
## this is computationally heavy, do only if needed
diaghat <- switch(type, "HC0" = NULL,
"sss" = NULL,
"HC1" = NULL,
"HC2" = try(dhat(demX), silent = TRUE),
"HC3" = try(dhat(demX), silent = TRUE),
"HC4" = try(dhat(demX), silent = TRUE))
df <- nT - k
switch(type,
"HC0" = {
omega <- function(residuals, diaghat, df, g) residuals
}, "sss" = {
omega <- function(residuals, diaghat, df, g) residuals *
sqrt(g/(g-1)*((nT-1)/(nT-k)))
}, "HC1" = {
omega <- function(residuals, diaghat, df, g) residuals *
sqrt(length(residuals)/df)
}, "HC2" = {
omega <- function(residuals, diaghat, df, g) residuals /
sqrt(1 - diaghat)
}, "HC3" = {
omega <- function(residuals, diaghat, df, g) residuals /
(1 - diaghat)
}, "HC4" = {
omega <- function(residuals, diaghat, df, g) {
residuals/sqrt(1 - diaghat)^
pmin(4, length(residuals) *
diaghat/as.integer(round(sum(diaghat),
digits = 0)))
}
})
## Definition module for E(u,v)
if(is.function(inner)) {
E <- inner
} else {
## outer for clustering/arellano, diag(diag(inner)) for white
switch(match.arg(inner),
"cluster" = {
E <- function(u, v) outer(u, v)
},
"white" = {
E <- function(u, v) { # was simply: diag(diag(outer(u,v)))
# but unfortunately we have to manage unbalanced panels
# in the case l!=0 (the residual vectors are different)
# by producing a "pseudo-diagonal" with all those obs.
# common to both vectors
if(isTRUE(all.equal(names(u), names(v)))) {
## ..then keep it simple! (halves time on EmplUK ex.)
n <- length(u)
euv <- diag(u*v, n)
} else {
## calculate outer product
efull <- outer(u, v)
## make matrix of zeros with same dims and names
eres <- array(0, dim = dim(efull))
dimnames(eres) <- dimnames(efull)
## populate "pseudo-diagonal" with values from efull
for(i in seq_along(names(u))) {
for(j in seq_along(names(v))) {
if(names(u)[i] == names(v)[j]) {
eres[i, j] <- efull[i, j]
}
}
}
euv <- eres
}
return(euv)
}
},
"diagavg" = {
E <- function(u,v) {
## this is the averaged version for 'white2'
if(isTRUE(all.equal(names(u), names(v)))) {
## ..then keep it simple
n <- length(u)
euv <- diag(x = sum(u*v)/n, n)
} else {
## do just as for 'white' and then average nonzeros:
## calculate outer product
efull <- outer(u,v)
## make matrix of zeros with same dims and names
eres <- array(0, dim = dim(efull))
dimnames(eres) <- dimnames(efull)
## populate "pseudo-diagonal" with values from efull
for(i in seq_along(names(u))) {
for(j in seq_along(names(v))) {
if(names(u)[i] == names(v)[j]) {
eres[i, j] <- efull[i, j]
}
}
}
euv <- eres
## substitute nonzeros with average thereof
euv[euv != 0] <- mean(euv[euv != 0])
}
return(euv)
}
})
} ## END: Definition module for E(u,v)
## try passing: function (a or b) or matrix (unconditional) to vcovG
## robustifying against either serial or xs intragroup dependence:
## if 'group' then keep current indexing, if 'time' then swap i<->t
## so that residuals get 'clustered' by time period instead of by
## group (i.e., the vcov estimator is robust vs. xsectional dependence)
## extract indices
xindex <- unclass(attr(x$model, "index")) # unclass for speed
groupind <- as.numeric(xindex[[1L]])
timeind <- as.numeric(xindex[[2L]])
## adjust for 'fd' model (losing first time period)
if(model == "fd") {
groupi <- as.numeric(groupind)
## make vector =1 on first obs in each group, 0 elsewhere
selector <- groupi - c(0, groupi[-length(groupi)])
selector[1L] <- 1 # the first must always be 1
## eliminate first obs in time for each group
groupind <- groupind[!selector]
timeind <- timeind[!selector]
nT <- nT - n0
Ti <- Ti - 1
t0 <- t0 - 1
}
## set grouping indexes
cluster <- match.arg(cluster)
switch(cluster,
"group" = {
n <- n0
t <- t0
relevant.ind <- groupind
lab <- timeind},
"time" = {
n <- t0
t <- n0
relevant.ind <- timeind
lab <- groupind})
relevant.ind.GRP <- collapse::GRP(relevant.ind)
tind <- collapse::gsplit(seq_along(relevant.ind), relevant.ind.GRP)
tlab <- collapse::gsplit(lab, relevant.ind.GRP)
## lab were the 'labels' (a numeric, actually) for the relevant index;
## in use again from the need to make pseudo-diagonals for
## calc. the lagged White terms on unbalanced panels
## transform residuals by weights (here because type='sss' needs to
## know who the grouping index 'g' is
## set number of clusters for Stata-like small sample correction
## (if clustering, i.e., inner="cluster", then G is the cardinality of
## the grouping index; if inner="white" it is simply the sample size)
## find some more elegant solution for this!
## (perhaps if white then sss -> HC1 but check...)
G <- if(match.arg(inner) == "cluster") n else nT
uhat <- omega(uhat, diaghat, df, G)
## compute basic block: X'_t u_t u'_(t-l) X_(t-l) foreach t,
## then calculate Sl_t and sum over t (here i in place of t)
## here the benchmark case is time-clustering, but beware
## that group-clustering is the default
## preallocate k x k x (T-l) array for 'pile' of kxk matrices
## holding the X' E(u,ul) X elements
Sl <- array(dim = c(k, k, n-l))
## (l=0 gives the special contemporaneous case where Xi=Xil, ui=uil
## for computing W, CX, CT)
for(i in (1+l):n) {
X <- demX[tind[[i]], , drop = FALSE]
Xl <- demX[tind[[i-l]], , drop = FALSE]
u <- uhat[tind[[i]]]
ul <- uhat[tind[[(i-l)]]]
names(u) <- tlab[[i]]
names(ul) <- tlab[[(i-l)]]
## calculate V_yy
Sl[ , , i-l] <- crossprod(X, E(u, ul)) %*% Xl
}
## in order to sum on available observations two things can be done:
## a) apply sum(..., na.rm=TRUE) over the third dim
## b) apply mean(..., na.rm=TRUE) idem and multiply by n-l
## In case a) averaging is then done dividing each covariance point
## by (n-l), regardless of whether there are NAs in the "vertical"
## vector Sl[p,q, ]
## In case b) each mean is calculated correctly on the right number
## of observations, excluding missing data. 'salame' has to be
## multiplied by (n-l)
## But notice, here there should be none left! Each Sl_i is k x k.
## Hence use sum().
## meat
## salame <- apply(Sl, 1:2, mean, na.rm=TRUE) * (n-l)
salame <- rowSums(Sl, dims = 2L) # == apply(Sl, 1:2, sum) but faster
## bread by standard method
pane <- solve(crossprod(demX))
## sandwich
mycov <- tcrossprod(crossprod(t(pane), salame), t(pane)) # == pane %*% salame %*% pane
# save information about cluster variable in matrix (needed for e.g.,
# robust F test)
attr(mycov, which = "cluster") <- match.arg(cluster)
return(mycov)
}
#' Robust Covariance Matrix Estimators
#'
#' Robust covariance matrix estimators *a la White* for panel
#' models.
#'
#' `vcovHC` is a function for estimating a robust covariance matrix of
#' parameters for a fixed effects or random effects panel model
#' according to the White method
#' \insertCite{WHIT:80,WHIT:84b,AREL:87}{plm}. Observations may be
#' clustered by `"group"` (`"time"`) to account for serial
#' (cross-sectional) correlation.
#'
#' All types assume no intragroup (serial) correlation between errors
#' and allow for heteroskedasticity across groups (time periods). As
#' for the error covariance matrix of every single group of
#' observations, `"white1"` allows for general heteroskedasticity but
#' no serial (cross--sectional) correlation; `"white2"` is `"white1"`
#' restricted to a common variance inside every group (time period)
#' \insertCite{@see @GREE:03, Sec. 13.7.1-2, @GREE:12, Sec. 11.6.1-2
#' and @WOOL:02, Sec. 10.7.2}{plm}; `"arellano"` \insertCite{@see
#' ibid. and the original ref. @AREL:87}{plm} allows a fully general
#' structure w.r.t. heteroskedasticity and serial (cross--sectional)
#' correlation.
#'
#' Weighting schemes specified by `type` are analogous to those in
#' [sandwich::vcovHC()] in package \CRANpkg{sandwich} and are
#' justified theoretically (although in the context of the standard
#' linear model) by \insertCite{MACK:WHIT:85;textual}{plm} and
#' \insertCite{CRIB:04;textual}{plm}
#' \insertCite{ZEIL:04}{plm}. `type = "sss"` employs the small sample
#' correction as used by Stata.
#'
# % TODO: give formula for "sss";
# elaborate why different result for FE models (intercept)
#'
#' The main use of `vcovHC` (and the other variance-covariance estimators
#' provided in the package `vcovBK`, `vcovNW`, `vcovDC`, `vcovSCC`) is to pass
#' it to plm's own functions like `summary`, `pwaldtest`, and `phtest` or
#' together with testing functions from the `lmtest` and `car` packages. All of
#' these typically allow passing the `vcov` or `vcov.` parameter either as a
#' matrix or as a function, e.g., for Wald--type testing: argument `vcov.` to
#' `coeftest()`, argument `vcov` to `waldtest()` and other methods in the
#' \CRANpkg{lmtest} package; and argument `vcov.` to
#' `linearHypothesis()` in the \CRANpkg{car} package (see the
#' examples), see \insertCite{@see also @ZEIL:04}{plm}, 4.1-2, and examples below.
#'
#' A special procedure for `pgmm` objects, proposed by
#' \insertCite{WIND:05;textual}{plm}, is also provided.
#'
#' @name vcovHC.plm
#' @aliases vcovHC
#' @importFrom sandwich vcovHC
#' @export vcovHC
#' @param x an object of class `"plm"` which should be the result of a
#' random effects or a within model or a model of class `"pgmm"`
#' or an object of class `"pcce"`,
#' @param method one of `"arellano"`, `"white1"`, `"white2"`,
#' @param type the weighting scheme used, one of `"HC0"`, `"sss"`,
#' `"HC1"`, `"HC2"`, `"HC3"`, `"HC4"`, see Details,
#' @param cluster one of `"group"`, `"time"`,
#' @param \dots further arguments.
#' @return An object of class `"matrix"` containing the estimate of
#' the asymptotic covariance matrix of coefficients.
#' @note The function `pvcovHC` is deprecated. Use `vcovHC` for the
#' same functionality.
#' @author Giovanni Millo & Yves Croissant
#' @seealso [sandwich::vcovHC()] from the \CRANpkg{sandwich}
#' package for weighting schemes (`type` argument).
#' @references
#'
#' \insertRef{AREL:87}{plm}
#'
#' \insertRef{CRIB:04}{plm}
#'
#' \insertRef{GREE:03}{plm}
#'
#' \insertRef{GREE:12}{plm}
#'
#' \insertRef{MACK:WHIT:85}{plm}
#'
#' \insertRef{WIND:05}{plm}
#'
#' \insertRef{WHIT:84b}{plm}
#' chap. 6
#'
#' \insertRef{WHIT:80}{plm}
#'
#' \insertRef{WOOL:02}{plm}
#'
#' \insertRef{ZEIL:04}{plm}
#'
#' @keywords regression
#' @examples
#'
#' data("Produc", package = "plm")
#' zz <- plm(log(gsp) ~ log(pcap) + log(pc) + log(emp) + unemp,
#' data = Produc, model = "random")
#' ## as function input to plm's summary method (with and without additional arguments):
#' summary(zz, vcov = vcovHC)
#' summary(zz, vcov = function(x) vcovHC(x, method="arellano", type="HC1"))
#'
#' ## standard coefficient significance test
#' library(lmtest)
#' coeftest(zz)
#' ## robust significance test, cluster by group
#' ## (robust vs. serial correlation)
#' coeftest(zz, vcov.=vcovHC)
#' ## idem with parameters, pass vcov as a function argument
#' coeftest(zz, vcov.=function(x) vcovHC(x, method="arellano", type="HC1"))
#' ## idem, cluster by time period
#' ## (robust vs. cross-sectional correlation)
#' coeftest(zz, vcov.=function(x) vcovHC(x, method="arellano",
#' type="HC1", cluster="group"))
#' ## idem with parameters, pass vcov as a matrix argument
#' coeftest(zz, vcov.=vcovHC(zz, method="arellano", type="HC1"))
#' ## joint restriction test
#' waldtest(zz, update(zz, .~.-log(emp)-unemp), vcov=vcovHC)
#' \dontrun{
#' ## test of hyp.: 2*log(pc)=log(emp)
#' library(car)
#' linearHypothesis(zz, "2*log(pc)=log(emp)", vcov.=vcovHC)
#' }
#' ## Robust inference for CCE models
#' data("Produc", package = "plm")
#' ccepmod <- pcce(log(gsp) ~ log(pcap) + log(pc) + log(emp) + unemp, data = Produc, model="p")
#' summary(ccepmod, vcov = vcovHC)
#'
#' ## Robust inference for GMM models
#' data("EmplUK", package="plm")
#' ar <- pgmm(log(emp) ~ lag(log(emp), 1:2) + lag(log(wage), 0:1)
#' + log(capital) + lag(log(capital), 2) + log(output)
#' + lag(log(output),2) | lag(log(emp), 2:99),
#' data = EmplUK, effect = "twoways", model = "twosteps")
#' rv <- vcovHC(ar)
#' mtest(ar, order = 2, vcov = rv)
NULL
#' @rdname vcovHC.plm
#' @export
vcovHC.plm <- function(x, method=c("arellano", "white1", "white2"),
type=c("HC0", "sss", "HC1", "HC2", "HC3", "HC4"),
cluster=c("group", "time"), ...) {
## user-level wrapper for White-Arellano covariances
## translate arguments
inner <- switch(match.arg(method),
"arellano" = "cluster",
"white1" = "white",
"white2" = "diagavg")
return(vcovG(x, type=type, cluster=cluster,
l=0, inner=inner, ...))
}
#' @rdname vcovNW
#' @export
vcovNW.plm <- function(x, type=c("HC0", "sss", "HC1", "HC2", "HC3", "HC4"),
maxlag=NULL,
wj=function(j, maxlag) 1-j/(maxlag+1),
...) {
## user-level wrapper for panel Newey-West estimator
## set default lag order
if(is.null(maxlag)) maxlag <- floor((max(pdim(x)$Tint$Ti))^(1/4))
return(vcovSCC(x, type=type, maxlag=maxlag, inner="white", wj=wj, ...))
}
#' @rdname vcovDC
#' @export
vcovDC.plm <- function(x, type=c("HC0", "sss", "HC1", "HC2", "HC3", "HC4"),
...) {
## user-level wrapper for double-clustering (no persistence)
Vcx <- vcovG(x, type=type, cluster="group",
l=0, inner="cluster", ...)
Vct <- vcovG(x, type=type, cluster="time",
l=0, inner="cluster", ...)
Vw <- vcovG(x, type=type, l=0, inner="white", ...)
res <- Vcx + Vct - Vw
# save information about cluster variable in matrix (needed for e.g.,
# robust F test)
attr(res, which = "cluster") <- "group-time"
return(res)
}
#' @rdname vcovSCC
#' @export
vcovSCC.plm <- function(x, type=c("HC0", "sss", "HC1", "HC2", "HC3", "HC4"),
cluster="time",
maxlag=NULL,
inner=c("cluster", "white", "diagavg"),
wj=function(j, maxlag) 1-j/(maxlag+1),
...) {
## replicates vcovSCC
## set default lag order
if(is.null(maxlag)) maxlag <- floor((max(pdim(x)$Tint$Ti))^(1/4))
## def. Bartlett kernel
## wj <- function(j, maxlag) 1-j/(maxlag+1)
## has been passed as argument
S0 <- vcovG(x, type=type, cluster=cluster, l=0, inner=inner)
if(maxlag > 0) {
for(i in seq_len(maxlag)) {
Vctl <- vcovG(x, type=type, cluster=cluster,
l=i, inner=inner)
S0 <- S0 + wj(i, maxlag) * (Vctl + t(Vctl))
}
}
return(S0)
}
##############################################################
## separate function for BK (PCSE) covariance
#' Beck and Katz Robust Covariance Matrix Estimators
#'
#' Unconditional Robust covariance matrix estimators *a la Beck
#' and Katz* for panel models (a.k.a. Panel Corrected Standard Errors
#' (PCSE)).
#'
#' `vcovBK` is a function for estimating a robust covariance matrix of
#' parameters for a panel model according to the
#' \insertCite{BECK:KATZ:95;textual}{plm} method, a.k.a. Panel
#' Corrected Standard Errors (PCSE), which uses an unconditional
#' estimate of the error covariance across time periods (groups)
#' inside the standard formula for coefficient
#' covariance. Observations may be clustered either by `"group"` to
#' account for timewise heteroskedasticity and serial correlation or
#' by `"time"` to account for cross-sectional heteroskedasticity and
#' correlation. It must be borne in mind that the Beck and Katz
#' formula is based on N- (T-) asymptotics and will not be appropriate
#' elsewhere.
#'
#' The `diagonal` logical argument can be used, if set to
#' `TRUE`, to force to zero all non-diagonal elements in the
#' estimated error covariances; this is appropriate if both serial and
#' cross--sectional correlation are assumed out, and yields a
#' timewise- (groupwise-) heteroskedasticity--consistent estimator.
#'
#' Weighting schemes specified by `type` are analogous to those in
#' [sandwich::vcovHC()] in package \CRANpkg{sandwich} and are
#' justified theoretically (although in the context of the standard
#' linear model) by \insertCite{MACK:WHIT:85;textual}{plm} and
#' \insertCite{CRIB:04;textual}{plm} \insertCite{@see @ZEIL:04}{plm}.
#'
# % TODO: once "sss" has been added: `type = "sss"` employs the small
# % sample correction as used by Stata. give formula for "sss";
# % elaborate why different result for FE models (intercept)
#'
#' The main use of `vcovBK` (and the other variance-covariance estimators
#' provided in the package `vcovHC`, `vcovNW`, `vcovDC`, `vcovSCC`) is to pass
#' it to plm's own functions like `summary`, `pwaldtest`, and `phtest` or
#' together with testing functions from the `lmtest` and `car` packages. All of
#' these typically allow passing the `vcov` or `vcov.` parameter either as a
#' matrix or as a function, e.g., for Wald--type testing: argument `vcov.` to
#' `coeftest()`, argument `vcov` to `waldtest()` and other methods in the
#' \CRANpkg{lmtest} package; and argument `vcov.` to
#' `linearHypothesis()` in the \CRANpkg{car} package (see the
#' examples), see \insertCite{@see also @ZEIL:04}{plm}, 4.1-2, and examples below.
#'
#' @param x an object of class `"plm"`,
#' @param type the weighting scheme used, one of `"HC0"`, `"HC1"`,
#' `"HC2"`, `"HC3"`, `"HC4"`, see Details,
#' @param cluster one of `"group"`, `"time"`,
#' @param diagonal a logical value specifying whether to force
#' non-diagonal elements to zero,
#' @param \dots further arguments.
#' @export
#' @return An object of class `"matrix"` containing the estimate of
#' the covariance matrix of coefficients.
#' @author Giovanni Millo
#' @seealso [sandwich::vcovHC()] from the \CRANpkg{sandwich}
#' package for weighting schemes (`type` argument).
#' @references
#'
#'
#' \insertRef{BECK:KATZ:95}{plm}
#'
#' \insertRef{CRIB:04}{plm}
#'
#' \insertRef{GREE:03}{plm}
#'
#' \insertRef{MACK:WHIT:85}{plm}
#'
#' \insertRef{ZEIL:04}{plm}
#'
#' @keywords regression
#' @examples
#'
#' data("Produc", package="plm")
#' zz <- plm(log(gsp)~log(pcap)+log(pc)+log(emp)+unemp, data=Produc, model="random")
#' summary(zz, vcov = vcovBK)
#' summary(zz, vcov = function(x) vcovBK(x, type="HC1"))
#'
#' ## standard coefficient significance test
#' library(lmtest)
#' coeftest(zz)
#' ## robust significance test, cluster by group
#' ## (robust vs. serial correlation), default arguments
#' coeftest(zz, vcov.=vcovBK)
#' ## idem with parameters, pass vcov as a function argument
#' coeftest(zz, vcov.=function(x) vcovBK(x, type="HC1"))
#' ## idem, cluster by time period
#' ## (robust vs. cross-sectional correlation)
#' coeftest(zz, vcov.=function(x) vcovBK(x, type="HC1", cluster="time"))
#' ## idem with parameters, pass vcov as a matrix argument
#' coeftest(zz, vcov.=vcovBK(zz, type="HC1"))
#' ## joint restriction test
#' waldtest(zz, update(zz, .~.-log(emp)-unemp), vcov=vcovBK)
#' \dontrun{
#' ## test of hyp.: 2*log(pc)=log(emp)
#' library(car)
#' linearHypothesis(zz, "2*log(pc)=log(emp)", vcov.=vcovBK)
#' }
vcovBK <- function(x, ...) {
UseMethod("vcovBK")
}
# TODO: add type "sss" for vcovBK
#' @rdname vcovBK
#' @export
vcovBK.plm <- function(x, type = c("HC0", "HC1", "HC2", "HC3", "HC4"),
cluster = c("group", "time"),
diagonal = FALSE, ...) {
## Robust vcov a la Beck and Katz (1995; AKA 'pcse')
## for panel models (pooling, random, within or fd type plm obj.)
##
## This version: October 20th, 2009; allows choosing the clustering dimension
## so as to have serial- or x-sectional-correlation robustness;
##
## This function takes the demeaned data from the
## plm object, then estimates an *unconditional* error covariance by
## averaging the empirical covariance blocks by group (time period);
## this average block (say, OmegaM in EViews notation) is then put into
## White's formula instead of each Omega_i.
##
## The clustering defaults to "group" for consistency with vcovHC;
## nevertheless the most likely usage is cluster="time" for robustness vs.
## cross-sectional dependence, as in the original Beck and Katz paper (where
## it is applied to "pooling" models).
##
## This version: compliant with plm 1.2-0; lmtest.
## Code is identical to vcovHC until mark.
##
## Usage:
## myplm <- plm(<model>,<data>, ...)
## # default (cluster by group = robust vs. serial correlation):
## coeftest(myplm, vcov=vcovBK)
## # cluster by time period (robust vs. XS correlation):
## coeftest(myplm, vcov=function(x) vcovBK(x, cluster="time"))
## # idem, HC3 weighting:
## coeftest(myplm, vcov=function(x) vcovBK(x,cluster="time",type="HC3"))
## waldtest(myplm,update(myplm,<new formula>),vcov=vcovBK)
##
## This weighted version implements a system of weights as
## in vcovHC/meatHC. Sure this makes sense for white1, but it
## is open to question for white2 and arellano. We'll see.
##
## Results OK vs. EViews, vcov=PCSE. Unbal. case not exactly the
## same (but then, who knows what EViews does!)
# stopping control for weighted regressions
if (!is.null(x$weights)) stop("vcovXX functions not implemented for weighted panel regressions")
type <- match.arg(type)
model <- describe(x, "model")
if (!model %in% c("random", "within", "pooling", "fd")) {
stop("Model has to be either \"random\", \"within\", \"pooling\", or \"fd\" model")
}
## extract demeaned data
demX <- model.matrix(x, model = model, rhs = 1, cstcovar.rm = "all")
## drop any linear dependent columns (corresponding to aliased coefficients)
## from model matrix X
## na.rm = TRUE because currently, RE tw unbalanced models set aliased simply to NA
if (!is.null(x$aliased) && any(x$aliased, na.rm = TRUE)) demX <- demX[ , !x$aliased, drop = FALSE]
## control: IV or not (two- or one-part formula)
if(length(formula(x))[2L] > 1L) {
demZ <- model.matrix(x, model = model, rhs = 2, cstcovar.rm = "all")
## substitute (transformed) X with projection of X on Z
## any linear dependence in Z (demZ) is appropriately taken care of by lm.fit()
nms <- colnames(demX)
demX <- lm.fit(demZ, demX)$fitted.values
# catches case with only one regressor -> need to convert numeric
# returned from lm.fit()fitted.values to matrix:
if(!is.matrix(demX)) demX <- matrix(demX, dimnames = list(NULL, nms[1L]))
}
pdim <- pdim(x)
nT <- pdim$nT$N
Ti <- pdim$Tint$Ti
k <- dim(demX)[[2L]]
n0 <- pdim$nT$n
t0 <- pdim$nT$T
## extract residuals
uhat <- x$residuals
## robustifying against either serial or xs intragroup dependence:
## if 'group' then keep current indexing, if 'time' then swap i<->t
## so that residuals get 'clustered' by time period instead of by
## group (i.e., the vcov estimator is robust vs. xsectional dependence)
## extract indices
xindex <- unclass(attr(x$model, "index")) # unclass for speed
groupind <- as.numeric(xindex[[1L]])
timeind <- as.numeric(xindex[[2L]])
## Achim's fix for 'fd' model (losing first time period)
if(model == "fd") {
groupind <- groupind[timeind > 1]
timeind <- timeind[ timeind > 1]
nT <- nT - n0
Ti <- Ti - 1
t0 <- t0 - 1
}
## set grouping indexes
cluster <- match.arg(cluster)
switch(cluster,
"group" = {
n <- n0 # this is needed only for 'pcse'
t <- t0 # this is needed only for 'pcse'
relevant.ind <- groupind
lab <- timeind },
"time" = {
n <- t0 # this is needed only for 'pcse'
t <- n0 # this is needed only for 'pcse'
relevant.ind <- timeind
lab <- groupind
})
relevant.ind.GRP <- collapse::GRP(relevant.ind)
tind <- collapse::gsplit(seq_along(relevant.ind), relevant.ind.GRP)
tlab <- collapse::gsplit(lab, relevant.ind.GRP)
## define residuals weighting function omega(res)
## (code taken from meatHC and modified)
## (the weighting is defined "in sqrt" relative to the literature)
##
## (see the theoretical comments in pvcovHC)
## this is computationally heavy, do only if needed
diaghat <- switch(type, "HC0" = NULL,
"HC1" = NULL,
"HC2" = try(dhat(demX), silent = TRUE),
"HC3" = try(dhat(demX), silent = TRUE),
"HC4" = try(dhat(demX), silent = TRUE))
df <- nT - k
switch(type,
"HC0" = {
omega <- function(residuals, diaghat, df) residuals
}, "HC1" = {
omega <- function(residuals, diaghat, df) residuals *
sqrt(length(residuals)/df)
}, "HC2" = {
omega <- function(residuals, diaghat, df) residuals /
sqrt(1 - diaghat)
}, "HC3" = {
omega <- function(residuals, diaghat, df) residuals /
(1 - diaghat)
}, "HC4" = {
omega <- function(residuals, diaghat, df) residuals/sqrt(1 -
diaghat)^pmin(4, length(residuals) * diaghat/as.integer(round(sum(diaghat),
digits = 0)))
})
## transform residuals by weights
uhat <- omega(uhat, diaghat, df)
## CODE TAKEN FROM pvcovHC() UNTIL HERE except for ind/time labeling ##
## the PCSE covariance estimator is based on the unconditional estimate
## of the intragroup (intraperiod) covariance of errors, OmegaT or OmegaM
## in the EViews help.
## we calculate this based on code from pggls().
## the Omegai function is then:
## - constant if the panel is balanced
## - depending only on the intragroup (intraperiod) position index
## if the panel is unbalanced.
## (code for estimating OmegaM/OmegaT partly taken from pggls)
## est. omega submatrix
## "pre-allocate" an empty array
tres <- array(dim = c(t, t, n))
## array of n "empirical omega-blocks"
## with outer product of t(i) residuals
## for each group 1..n
## (use subscripting from condition 'label in labels' set',
## the rest stays NA if any)
unlabs <- unique(lab) # fetch (all, unique) values of the relevant labels
seq.len.t <- seq_len(t)
for(i in seq_len(n)) {
ut <- uhat[tind[[i]]]
tpos <- seq.len.t[unlabs %in% tlab[[i]]]
## put non-diag elements to 0 if diagonal=TRUE
tres[tpos, tpos, i] <- if(diagonal) diag(diag(ut %o% ut)) else ut %o% ut
}
## average over all omega blocks, removing NAs (apply preserving
## *two* dimensions, i.e., over the third) to get the unconditional
## covariance matrix of errors for a group (viz. time period):
OmegaT <- rowMeans(tres, dims = 2L, na.rm = TRUE) # == apply(tres, 1:2, mean, na.rm = TRUE) but faster
## end of PCSE covariance calculation.
salame <- array(dim = c(k, k, n))
for(i in seq_len(n)) {
groupinds <- tind[[i]]
grouplabs <- tlab[[i]]
xi <- demX[groupinds, , drop = FALSE]
## for every group, take relevant positions
tpos <- unlabs %in% grouplabs
OmegaTi <- OmegaT[tpos, tpos, drop = FALSE]
salame[ , , i] <- crossprod(xi, OmegaTi) %*% xi
}
## meat
salame <- rowSums(salame, dims = 2L) # == apply(salame, 1:2, sum) but faster
## bread
pane <- solve(crossprod(demX))
## sandwich
mycov <- tcrossprod(crossprod(t(pane), salame), t(pane)) # == pane %*% salame %*% pane
# save information about cluster variable in matrix (needed for e.g.,
# robust F test)
attr(mycov, which = "cluster") <- match.arg(cluster)
return(mycov)
}
#######################################################
#####################################
## vcovXX methods for pcce objects ##
#####################################
## pcce is compliant with plm so vcovXX.pcce <- vcovXX.plm
## for any vcov that makes sense computed on the transformed
## data from model.matrix.pcce and pmodel.response.pcce
## TODO: vcovBK.pcce, vcovDC.pcce missing? Or not valid?
## Have a stopping break for now w/ informative error
#' @export
vcovBK.pcce <- function(x, ...) stop("plm::vcovBK not implemented for 'pcce' models")
#' @export
vcovDC.pcce <- function(x, ...) stop("plm::vcovDC not implemented for 'pcce' models")
#' @rdname vcovG
#' @export
vcovG.pcce <- vcovG.plm
#' @rdname vcovHC.plm
#' @export
vcovHC.pcce <- vcovHC.plm
#' @rdname vcovNW
#' @export
vcovNW.pcce <- vcovNW.plm
#' @rdname vcovSCC
#' @export
vcovSCC.pcce <- vcovSCC.plm
########################################################
## vcovXX methods for pggls objects as stopping break ##
########################################################
vcovXX.pggls.error <- "not implemented as not sensible for 'pggls' models"
#' @export
vcovG.pggls <- function(x, ...) stop(paste0("plm::vcovG ", vcovXX.pggls.error))
#' @export
vcovHC.pggls <- function(x, ...) stop(paste0("plm::vcovHC ", vcovXX.pggls.error))
#' @export
vcovNW.pggls <- function(x, ...) stop(paste0("plm::vcovNW ", vcovXX.pggls.error))
#' @export
vcovSCC.pggls <- function(x, ...) stop(paste0("plm::vcovSCC ", vcovXX.pggls.error))
#' @export
vcovBK.pggls <- function(x, ...) stop(paste0("plm::vcovBK ", vcovXX.pggls.error))
#' @export
vcovDC.pggls <- function(x, ...) stop(paste0("plm::vcovDC ", vcovXX.pggls.error))
####################################
## vcovHC method for pgmm objects ##
####################################
#' @rdname vcovHC.plm
#' @importFrom MASS ginv
#' @export
vcovHC.pgmm <- function(x, ...) {
model <- describe(x, "model")
transformation <- describe(x, "transformation")
A1 <- x$A1
A2 <- x$A2
if(transformation == "ld") {
## yX <- lapply(x$model,function(x) rbind(diff(x),x))
## residuals <-lapply(x$residuals,function(x) c(diff(x),x))
yX <- x$model
residuals <- x$residuals
}
else {
yX <- x$model
residuals <- x$residuals
}
minevA2 <- min(abs(Re(eigen(A2)$values)))
eps <- 1E-9
SA2 <- if(minevA2 < eps){
warning("a general inverse is used")
ginv(A2)
} else solve(A2)
if(model == "twosteps") {
coef1s <- x$coefficients[[1L]]
res1s <- lapply(yX, function(x) x[ , 1L] - crossprod(t(x[ , -1L, drop = FALSE]), coef1s))
K <- ncol(yX[[1L]])
D <- c()
WX <- Reduce("+",
mapply(function(x, y) crossprod(x, y[ , -1L, drop = FALSE]), x$W, yX, SIMPLIFY = FALSE))
We <- Reduce("+", mapply(function(x, y) crossprod(x, y), x$W, residuals, SIMPLIFY = FALSE))
B1 <- solve(t(WX) %*% A1 %*% WX)
B2 <- vcov(x)
vcov1s <- B1 %*% (t(WX) %*% A1 %*% SA2 %*% A1 %*% WX) %*% B1
for (k in 2:K) {
exk <- mapply(
function(x, y){
z <- crossprod(t(x[ , k, drop = FALSE]), t(y))
- z - t(z)
},
yX, res1s, SIMPLIFY = FALSE)
wexkw <- Reduce("+",
mapply(
function(x, y)
crossprod(x, crossprod(y, x)),
x$W, exk, SIMPLIFY = FALSE))
Dk <- -B2 %*% t(WX) %*% A2 %*% wexkw %*% A2 %*% We
D <- cbind(D, Dk)
}
vcovr <- B2 + crossprod(t(D), B2) + t(crossprod(t(D), B2)) + D %*% vcov1s %*% t(D)
}
else {
# model = "onestep"
res1s <- lapply(yX, function(z) z[ , 1L] - crossprod(t(z[ , -1L, drop = FALSE]), x$coefficients))
K <- ncol(yX[[1L]])
WX <- Reduce("+", mapply(function(z, y) crossprod(z[ , -1L, drop = FALSE], y), yX, x$W, SIMPLIFY = FALSE))
B1 <- vcov(x)
vcovr <- B1 %*% (WX %*% A1 %*% SA2 %*% A1 %*% t(WX)) %*% B1
}
vcovr
}
## dhat: diaghat function for matrices
dhat <- function(x) {
rowSums(crossprod(t(x), solve(crossprod(x))) * x) # == (old) diag(crossprod(t(x), solve(crossprod(x), t(x)))
}
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