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#' Angrist and Newey's version of Chamberlain test for fixed effects
#'
#' Angrist and Newey's version of the Chamberlain test
#'
#' Angrist and Newey's test is based on the results of the artifactual
#' regression of the within residuals on the covariates for all the
#' periods.
#'
#' @aliases aneweytest
#' @param formula a symbolic description for the model to be estimated,
#' @param data a `data.frame`,
#' @param subset see [lm()],
#' @param na.action see [lm()],
#' @param index the indexes,
#' @param \dots further arguments.
#' @return An object of class `"htest"`.
#' @export
#' @author Yves Croissant
#' @references
#' \insertRef{ANGR:NEWE:91}{plm}
#'
#' @seealso [piest()] for Chamberlain's test
#' @keywords htest
#' @examples
#'
#' data("RiceFarms", package = "plm")
#' aneweytest(log(goutput) ~ log(seed) + log(totlabor) + log(size), RiceFarms, index = "id")
#'
aneweytest <- function(formula, data, subset, na.action, index = NULL, ...){
# NB: code fails for unbalanced data -> is Angrist and Newey's test only for balanced data?
# unbalanced case is currently caught and a message is printed
mf <- match.call()
# compute the model.frame using plm with model = NA
mf[[1L]] <- as.name("plm")
mf$model <- NA
data <- eval(mf, parent.frame())
# estimate the within model without instrument and extract the fixed
# effects
formula <- as.Formula(formula)
mf$formula <- formula(formula, rhs = 1)
index <- index(data)
id <- index[[1L]]
time <- index[[2L]]
periods <- unique(time)
pdim <- pdim(data)
T <- pdim$nT$T
n <- pdim$nT$n
N <- pdim$nT$N
Ti <- pdim$Tint$Ti
balanced <- pdim$balanced
if(!balanced) stop("'aneweytest' not implemented for unbalanced data")
ht <- match.call(expand.dots = FALSE)
m <- match(c("formula", "data", "subset", "na.action",
"effect", "model", "inst.method", "restict.matrix",
"restrict.rhs", "index"), names(ht), 0)
ht <- ht[c(1L, m)]
ht[[1L]] <- as.name("plm")
ht$model <- "within"
ht$effect <- "individual"
ht <- eval(ht, parent.frame())
.resid <- split(resid(ht), time)
# extract the covariates (no intercept), and isolate time-invariant covariates
X <- model.matrix(data, model = "pooling", rhs = 1, lhs = 1)[ , -1, drop = FALSE]
cst <- attr(model.matrix(data, model = "within", rhs = 1, lhs = 1), "constant")
# get constant columns and remove the intercept
if (length(cst) > 0L) cst <- cst[- match("(Intercept)", cst)]
if (length(cst) > 0L){
vr <- colnames(X)[!(colnames(X) %in% cst)]
Z <- X[ , cst, drop = FALSE]
X <- X[ , vr, drop = FALSE]
Kz <- ncol(Z)
namesZ <- colnames(Z)
} else {
Z <- NULL
Kz <- 0
namesZ <- NULL
}
Kx <- ncol(X)
# time-demean and split by period:
attr(X, "index") <- index
X <- Within(X, effect ="time")
X.ncol <- NCOL(X)
namesX <- colnames(X)
X <- split(X, time)
X <- lapply(X, function(m) matrix(m, ncol = X.ncol))
# put column names for split matrices in X:
for (i in seq_along(periods)){
colnames(X[[i]]) <- paste(namesX, periods[i], sep = ".")
}
if (!is.null(Z)){
Z <- Z[time == periods[1], , drop = FALSE]
Z <- t(t(Z) - .colMeans(Z, nrow(Z), ncol(Z))) # TODO: could use Within() framework
}
XX <- cbind(Reduce("cbind", X), Z)
# compute the unconstrained estimates
# NA-freeness guaranteed by model frame construction, so can use lm.fit
# (non-collinearity is not catered for but code errors anywayif collinearity
# is present a bit later)
# was: LMS <- lapply(.resid, function(x) lm(x ~ XX - 1))
LMS <- lapply(.resid, function(x) lm.fit(XX, x))
YTOT <- vapply(.resid, function(x) crossprod(x), FUN.VALUE = 0.0, USE.NAMES = FALSE)
DEV <- vapply(LMS, function(x) crossprod(x$residuals), FUN.VALUE = 0.0, USE.NAMES = FALSE)
stat <- c("chisq" = sum(1 - DEV / YTOT) * (n - ncol(XX)))
df <- c("df" = (T ^ 2 - T - 1) * Kx)
aneweytest <- structure(list(statistic = stat,
parameter = df,
method = "Angrist and Newey's test of within model",
p.value = pchisq(stat, df = df, lower.tail = FALSE),
alternative = "within specification does not apply",
data.name = paste(deparse(formula))),
class = "htest")
aneweytest
}
#' Chamberlain estimator and test for fixed effects
#'
#' General estimator useful for testing the within specification
#'
#' The Chamberlain method consists in using the covariates of all the
#' periods as regressors. It allows to test the within specification.
#'
#' @aliases piest
#' @param formula a symbolic description for the model to be estimated,
#' @param object,x an object of class `"piest"` and of class `"summary.piest"`
#' for the print method of summary for piest objects,
#' @param data a `data.frame`,
#' @param subset see [lm()],
#' @param na.action see [lm()],
#' @param index the indexes,
#' @param robust logical, if `FALSE`, the error is assumed to be spherical,
#' if `TRUE`, a robust estimation of the covariance matrix is computed,
#' @param \dots further arguments.
#' @return An object of class `"piest"`.
#' @export
#' @author Yves Croissant
#' @references
#'
#' \insertRef{CHAM:82}{plm}
#'
#' @seealso [aneweytest()]
#' @keywords htest
#' @examples
#'
#' data("RiceFarms", package = "plm")
#' pirice <- piest(log(goutput) ~ log(seed) + log(totlabor) + log(size), RiceFarms, index = "id")
#' summary(pirice)
#'
piest <- function(formula, data, subset, na.action, index = NULL, robust = TRUE, ...){
# NB: code fails for unbalanced data -> is Chamberlain's test only for balanced data?
# unbalanced case is currently caught and a message is printed
cl <- match.call(expand.dots = TRUE)
mf <- match.call()
# compute the model.frame using plm with model = NA
mf[[1L]] <- as.name("plm")
mf$model <- NA
data <- eval(mf, parent.frame())
# estimate the within model without instrument and extract the fixed
# effects
formula <- as.Formula(formula)
mf$formula <- formula(formula, rhs = 1)
index <- index(data)
id <- index[[1L]]
time <- index[[2L]]
pdim <- pdim(data)
balanced <- pdim$balanced
T <- pdim$nT$T
n <- pdim$nT$n
N <- pdim$nT$N
Ti <- pdim$Tint$Ti
if(!balanced) stop("'piest' not implemented for unbalanced data")
# extract the response, time-demean and split by period
y <- pmodel.response(data, model = "pooling", effect = "individual")
Y <- Within(y, "time")
Y <- split(Y, time)
# extract the covariates, and isolate time-invariant covariates
X <- model.matrix(data, model = "pooling", rhs = 1, lhs = 1)[ , -1, drop = FALSE]
cst <- attr(model.matrix(data, model = "within", rhs = 1, lhs = 1), "constant")
# get constant columns and remove the intercept
if (length(cst) > 0L) cst <- cst[- match("(Intercept)", cst)]
if (length(cst) > 0L){
vr <- colnames(X)[!(colnames(X) %in% cst)]
Z <- X[ , cst, drop = FALSE]
X <- X[ , vr, drop = FALSE]
Kz <- ncol(Z)
namesZ <- colnames(Z)
} else {
Z <- NULL
Kz <- 0
namesZ <- NULL
}
Kx <- ncol(X)
namesX <- colnames(X)
# time-demean X and split by period:
attr(X, "index") <- index
X <- Within(X, effect ="time")
periods <- unique(time)
X.ncol <- NCOL(X)
X <- split(X, time)
X <- lapply(X, function(m) matrix(m, ncol = X.ncol))
# put column names for split matrices in X:
for (i in seq_along(periods)){
colnames(X[[i]]) <- paste(namesX, periods[i], sep = ".")
}
if (!is.null(Z)){
Z <- Z[time == periods[1L], , drop = FALSE]
Z <- t(t(Z) - .colMeans(Z, nrow(Z), ncol(Z))) # TODO: can use Within() framework
}
XX <- cbind(Reduce("cbind", X), Z)
# compute the unconstrained estimates
# NA-freeness guaranteed by model frame construction, so can use lm.fit
# (non-collinearity is not cared for but code error if collinearity is
# present anyway a bit later)
# was: LMS <- lapply(Y, function(x) lm(x ~ XX - 1))
LMS <- lapply(Y, function(x) lm.fit(XX, x))
# compute the empirical covariance of the covariates
Sxxm1 <- solve(crossprod(XX) / n)
# compute the residuals matrix
.resid <- sapply(LMS, resid)
# extract the pi vector of unconstrained estimates
pi <- unlist(lapply(LMS, coef), use.names = FALSE)
if(robust) {
Omega <- lapply(seq_len(n),
function(i)
tcrossprod(.resid[i, ]) %x%
(Sxxm1 %*% tcrossprod(XX[i, ]) %*% Sxxm1))
Omega <- Reduce("+", Omega) / n
} else {
Omega <- (crossprod(.resid) / n) %x% Sxxm1
}
# construct the matrix of linear restrictions R | R x theta = pi
R <- matrix(0, T * (T * Kx + Kz), (T + 1) * Kx + Kz)
for (i in seq_len(Kx)){
R[ ((1:T) - 1) * (Kx * T + Kz) + (Kx * (1:T - 1)) + i , i] <- 1
}
if (Kz > 0){
for (i in seq_len(Kz)){
R[ (Kx * T) + (1:T - 1) * (Kx * T + Kz) + i, Kx + i] <- 1
}
}
for (i in seq_len(Kx * T)){
R[((1:T) - 1) * (Kx * T + Kz) + i , Kx + Kz + i] <- 1
}
solve_Omega <- solve(Omega)
A <- solve(t(R) %*% solve_Omega %*% R)
.coef <- as.numeric(A %*% t(R) %*% solve_Omega %*% as.numeric(pi))
# .coef <- as.numeric(solve(t(R) %*% R) %*% t(R) %*% as.numeric(pi))
namescoef <- if(Kz > 0) c(namesX, namesZ, colnames(XX)[- c(ncol(XX) - 0:(Kz-1))])
else c(namesX, namesZ, colnames(XX))
names(.coef) <- rownames(A) <- colnames(A) <- namescoef
resb <- as.numeric(R %*% .coef) - as.numeric(pi)
piconst <- matrix(R %*% .coef, ncol = T)
OOmega <- Omega ## TODO: OOmega is never used
.resid <- matrix(unlist(Y, use.names = FALSE), ncol = length(Y)) - XX %*% piconst
if(TRUE){ ## TODO: this is always TRUE...!
if(robust) { ## and Omega is calc. again, with a
## new .resid input but with same lapply-construct
Omega <- lapply(seq_len(n),
function(i)
tcrossprod(.resid[i, ]) %x%
(Sxxm1 %*% tcrossprod(XX[i, ]) %*% Sxxm1))
Omega <- Reduce("+", Omega) / n
} else {
Omega <- (crossprod(.resid) / n) %x% Sxxm1
}
}
A <- solve(t(R) %*% solve(Omega) %*% R)
stat <- c("chisq" = n * resb %*% solve(Omega) %*% resb)
df <- c("df" = Kx * (T ^ 2 - T - 1)) ## TODO: df is overwritten in next line...?!
df <- c("df" = length(pi) - length(.coef))
pitest <- list(statistic = stat,
parameter = df,
method = "Chamberlain's pi test",
p.value = pchisq(stat, df = df, lower.tail = FALSE),
alternative = "within specification does not apply",
data.name = paste(deparse(formula))
)
structure(list(coefficients = .coef,
pi = pi,
daub = resb,
vcov = A / n,
formula = formula,
R = R,
model = data,
pitest = structure(pitest, class = "htest"),
Omega = Omega,
moments = resb,
call = cl),
class = c("piest", "panelmodel"))
}
#' @rdname piest
#' @export
print.piest <- function(x, ...) print(x$pitest, ...)
#' @rdname piest
#' @export
summary.piest <- function(object,...){
# construct the table of coefficients
std.err <- sqrt(diag(vcov(object)))
b <- coefficients(object)
z <- b / std.err
p <- 2 * pnorm(abs(z), lower.tail = FALSE)
object$coefficients <- cbind("Estimate" = b,
"Std. Error" = std.err,
"z-value" = z,
"Pr(>|z|)" = p)
class(object) <- c("summary.piest", "piest", "panelmodel")
object
}
#' @rdname piest
#' @param digits number of digits for printed output,
#' @param width the maximum length of the lines in the printed output,
#' @export
print.summary.piest <- function(x, digits = max(3, getOption("digits") - 2),
width = getOption("width"), subset = NULL, ...){
if(is.null(subset)) printCoefmat(coef(x), digits = digits, ...)
else printCoefmat(coef(x)[subset, , drop = FALSE], digits = digits, ...)
print(x$pitest, ...)
invisible(x)
}
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