| pedroni99m {pco} | R Documentation |
panel cointegration tests - multivatiate case
Description
Computation of the Pedroni (1999) panel cointegration test statistics. All statistics are asymptotically normal. Reported are their empirical values and their standardized values (as suggested in Pedroni, 1999).
Usage
pedroni99m(X, kk = 0, type.stat = 1, ka = 2)
Arguments
X |
The data to be tested for cointegration. Must be a 'cube', an array (TxNxM) with multiple 'sheets', the first 'sheet' is the 'dependent' variable, 'independent' variables are the rest. The first dimension is 'time', the second is 'individuals' and the third is 'variables'. No missing values are allowed. |
kk |
Parameter for the Newey-West (1994) long term variance estimation (number of lags). Can be a vector, with a different value for each individual series, or a scalar. By default it is set to 'round(4 * (T/100)^(2/9))'. |
type.stat |
Type of the main regresion: 1 - 'none', 2 - 'intercept', 3 - 'intercept and time trend'. |
ka |
Number of lags for the ADF type regression on residuals, for the parametric statistics. |
Details
The function closely follows the instructions in Pedroni (1999). Calculated and reported are the 7 statistics on page 660 in Pedroni (1999) for the multivariate case. Also reported are their standardized values, as described on page 665 and by use of the adjustment terms in Table 2, page 666, op.cit. H0 is 'no cointegration'.
Value
CALL |
The result of 'match.call()'. |
METHOD |
Title of the test. |
STATISTIC |
The 7 test statistics in Pedroni (1999), in two columns - for the empirical and the standardized values. |
Note
Under H0 ('no cointegration') the autoregressive coefficients, gamma_i = 1 for all i, versus H1: gamma_i < 1 for all i.
The standardized values of the test statistics are asymptotically normal (0,1) under H0.
Author(s)
Georgi Marinov
References
Newey, Whitney K.; West, Kenneth D. (1994). "Automatic lag selection in covariance matrix estimation". Review of Economic Studies 61 (4): 631-654.
Pedroni, Peter, 1999. "Critical Values for Cointegration Tests in Heterogeneous Panels with Multiple Regressors," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 61(0), pages 653-70, Special I.
See Also
Examples
xx<-array(cumsum(rnorm(10000)),dim=c(100,20,5))
pedroni99m(xx)
## The function is currently defined as
function (X, kk = 0, type.stat = 1, ka = 2)
{
ffm <- function(Y2, X2) {
NN = ncol(X2)
sapply(1:NN, function(l) {
lm(Y2[, l] ~ X2[, l, ] - 1)$residuals
})
}
ff1m <- function(Y2, X2) {
NN = ncol(X2)
sapply(1:NN, function(l) {
lm(Y2[, l] ~ X2[, l, ])$residuals
})
}
ff2m <- function(Y2, X2) {
NN = ncol(X2)
trend = 1:nrow(X2)
sapply(1:NN, function(l) {
lm(Y2[, l] ~ X2[, l, ] + trend)$residuals
})
}
ffmm <- function(Y1, X1) {
NN = ncol(X1)
sapply(1:NN, function(l) {
lm(Y1[, l] ~ X1[, l] - 1)$residuals
})
}
nwm <- function(xx, ki) {
tt = length(xx)
(1/tt) * sum(sapply(1:ki, function(s) {
(1 - s/(ki + 1)) * sum(xx[(s + 1):tt] * xx[1:(tt -
s)])
}))
}
adflm<-function (ee, lags) {
nn<-length(ee)
z<-ee[(lags+1):nn]
zl<-ee[lags:(nn-1)]
zd<-matrix(cbind(rep(z,lags)),ncol=lags)
ii<-embed(1:nn,lags)
ii<-ii[-(nrow(ii)),]
zd<-zd-ee[ii]
zd<-zd[,-1]
z<-ee[(lags+1):nn]
zl<-ee[lags:(nn-1)]
return(lm(z ~ zl + zd -1)$residuals)
}
na.fail(X)
Y <- as.matrix(X[, , 1])
XX <- X[, , (2:dim(X)[3])]
TD <- dim(X)[1]
N <- dim(X)[2]
M <- dim(X)[3]
if (is.vector(kk) && length(kk) == N) {
k = kk
}
else if (kk > 0) {
k = rep(round(kk), N)
}
else {
i = round(4 * (TD/100)^(2/9))
k = rep(i, N)
}
if (ka < 2) {
ka = 2
warning("Parameter 'ka' was changed to 2.")
}
ka <- as.vector(ka)
if (length(ka) != N) {
ka <- rep(ka[1], N)
}
stamm <- array(dim = c(7, 3, 6))
stamm[, , 1] <- cbind(c(6.982, -6.388, -1.662, -1.662, -9.889,
-1.992, -1.992), c(11.754, -9.495, -2.177, -2.177, -12.938,
-2.453, -2.453), c(21.162, -14.011, -2.648, -2.648, -17.359,
-2.872, -2.872))
stamm[, , 2] <- cbind(c(10.402, -10.191, -2.156, -2.156,
-13.865, -2.44, -2.44), c(15.197, -13.256, -2.567, -2.567,
-16.888, -2.827, -2.827), c(24.556, -17.6, -2.967, -2.967,
-21.116, -3.179, -3.179))
stamm[, , 3] <- cbind(c(14.254, -14.136, -2.571, -2.571,
-17.834, -2.819, -2.819), c(18.91, -17.163, -2.93, -2.93,
-20.841, -3.157, -3.157), c(28.046, -21.287, -3.262,
-3.262, -24.93, -3.464, -3.464))
stamm[, , 4] <- cbind(c(18.198, -18.042, -2.926, -2.926,
-21.805, -3.151, -3.151), c(22.715, -21.013, -3.241,
-3.241, -24.775, -3.452, -3.452), c(31.738, -25.13, -3.545,
-3.545, -28.849, -3.737, -3.737))
stamm[, , 5] <- cbind(c(22.169, -21.985, -3.244, -3.244,
-25.75, -3.45, -3.45), c(26.603, -24.944, -3.531, -3.531,
-28.72, -3.726, -3.726), c(35.537, -28.981, -3.806, -3.806,
-32.716, -3.986, -3.986))
stamm[, , 6] <- cbind(c(26.12, -25.889, -3.533, -3.533, -29.627,
-3.723, -3.723), c(30.457, -28.795, -3.795, -3.795, -32.538,
-3.976, -3.976), c(39.231, -32.756, -4.047, -4.047, -36.494,
-4.217, -4.217))
rownames(stamm) <- c("nipanel", "rhopanel", "tpanelnonpar",
"tpanelpar", "rhogroup", "tgroupnonpar", "tgrouppar")
colnames(stamm) <- c("none", "intercept", "trend")
stavv <- array(dim = c(7, 3, 6))
stavv[, , 1] <- cbind(c(81.145, 64.288, 1.559, 1.559, 41.943,
0.649, 0.649), c(104.546, 57.61, 0.964, 0.964, 51.49,
0.618, 0.618), c(160.249, 64.219, 0.69, 0.69, 66.387,
0.555, 0.555))
stavv[, , 2] <- cbind(c(140.804, 89.962, 1.286, 1.286, 57.801,
0.6, 0.6), c(151.094, 81.772, 0.923, 0.923, 67.123, 0.585,
0.585), c(198.167, 83.815, 0.686, 0.686, 81.832, 0.548,
0.548))
stavv[, , 3] <- cbind(c(182.45, 103.176, 1.028, 1.028, 72.097,
0.567, 0.567), c(190.661, 99.331, 0.843, 0.843, 81.835,
0.56, 0.56), c(239.425, 103.905, 0.688, 0.688, 97.362,
0.543, 0.543))
stavv[, , 4] <- cbind(c(217.784, 120.787, 0.928, 0.928, 88.611,
0.559, 0.559), c(231.864, 119.546, 0.8, 0.8, 98.278,
0.553, 0.553), c(276.997, 124.613, 0.686, 0.686, 113.145,
0.538, 0.538))
stavv[, , 5] <- cbind(c(256.53, 132.499, 0.82, 0.82, 103.371,
0.544, 0.544), c(270.451, 134.341, 0.75, 0.75, 113.131,
0.542, 0.542), c(310.982, 138.227, 0.654, 0.654, 127.989,
0.53, 0.53))
stavv[, , 6] <- cbind(c(277.429, 143.561, 0.75, 0.75, 117.059,
0.53, 0.53), c(293.431, 144.615, 0.685, 0.685, 126.059,
0.525, 0.525), c(348.217, 154.378, 0.638, 0.638, 140.756,
0.518, 0.518))
rownames(stavv) <- c("nipanel", "rhopanel", "tpanelnonpar",
"tpanelpar", "rhogroup", "tgroupnonpar", "tgrouppar")
colnames(stavv) <- c("none", "intercept", "trend")
statsm <- matrix(nrow = 7, ncol = 2)
rownames(statsm) <- c("nipanel", "rhopanel", "tpanelnonpar",
"tpanelpar", "rhogroup", "tgroupnonpar", "tgrouppar")
colnames(statsm) <- c("empirical", "standardized")
e <- matrix(ncol = N, nrow = TD)
if (type.stat == 2) {
e <- ff1m(Y, XX)
}
else if (type.stat == 3) {
e <- ff2m(Y, XX)
}
else {
e <- ffm(Y, XX)
type.stat = 1
}
De <- diff(e)
estar <- e
Destar <- diff(estar)
DXX <- array(dim = c((dim(XX)[1] - 1), dim(XX)[2], dim(XX)[3]))
DXX[, , 1:dim(XX)[3]] <- sapply(1:dim(XX)[3], function(i) {
DXX[, , i] <- diff(XX[, , i])
})
DY <- diff(Y)
eta <- ffm(DY, DXX)
L11hat2 <- sapply(1:N, function(i) {
(1/nrow(eta)) * sum(eta[, i]^2) + 2 * nwm(eta[, i], k[i])
})
mu <- matrix(ncol = ncol(DY), nrow = nrow(DY))
mu <- ffmm(e[2:TD, ], e[1:(TD - 1), ])
lambdahat <- sapply(1:N, function(i) {
nwm(mu[, i], k[i])
})
mustar <- matrix(ncol = ncol(DY), nrow = nrow(DY))
mustar <- sapply(1:N, function(i) {
adflm(e[, i], ka[i])
})
shatstar2 <- sapply(1:N, function(i) {
(1/nrow(mustar)) * sum(mustar[, i]^2)
})
stildestar2 <- (1/N) * sum(shatstar2)
shat2 <- sapply(1:N, function(i) {
(1/nrow(mu)) * sum(mu[, i]^2)
})
sigmahat2 <- shat2 + 2 * lambdahat
sigmatilde2 <- (1/N) * sum(L11hat2^(-2) * sigmahat2)
nipa <- sum(sapply(1:N, function(i) {
sum((L11hat2[i]^(-2)) * (e[1:(TD - 1), i]^2))
}))
lel <- sum(sapply(1:N, function(i) {
(L11hat2[i]^(-2)) * sum(sapply(2:(nrow(De)), function(ttt) {
(e[(ttt - 1), i] * De[ttt, i] - lambdahat[i])
}))
}))
nipanel <- (TD^2) * (N^(3/2)) * nipa^(-1)
statsm[1, 1] <- nipanel
rhopanel <- TD * (N^(1/2)) * (nipa^(-1)) * lel
statsm[2, 1] <- rhopanel
tpanelnonpar <- ((sigmatilde2 * nipa)^(-1/2)) * lel
statsm[3, 1] <- tpanelnonpar
tpanelpar <- ((stildestar2 * sum(sapply(1:N, function(i) {
sum((L11hat2[i]^(-2)) * estar[1:(nrow(estar) - 1), i]^2)
})))^(-1/2)) * sum(sapply(1:N, function(i) {
sum(sapply(2:(nrow(Destar)), function(ttt) {
(L11hat2[i]^(-2)) * (estar[(ttt - 1), i] * Destar[ttt,
i])
}))
}))
statsm[4, 1] <- tpanelpar
rhogroup <- TD * (N^(-1/2)) * sum(sapply(1:N, function(i) {
((sum(e[1:(nrow(e) - 1), i]^2))^(-1)) * sum(sapply(2:(nrow(De)),
function(ttt) {
(e[(ttt - 1), i] * De[ttt, i] - lambdahat[i])
}))
}))
statsm[5, 1] <- rhogroup
tgroupnonpar <- (N^(-1/2)) * sum(sapply(1:N, function(i) {
((sigmahat2[i] * sum(e[1:(nrow(e) - 1), i]^2))^(-1/2)) *
sum(sapply(2:(nrow(De)), function(ttt) {
(e[(ttt - 1), i] * De[ttt, i] - lambdahat[i])
}))
}))
statsm[6, 1] <- tgroupnonpar
tgrouppar <- (N^(-1/2)) * sum(sapply(1:N, function(i) {
(sum(shat2[i] * estar[1:(nrow(estar) - 1), i]^2))^(-1/2) *
sum(sapply(2:nrow(Destar), function(tt1) {
estar[(tt1 - 1), i] * Destar[tt1, i]
}))
}))
statsm[7, 1] <- tgrouppar
statsm[, 2] <- sapply(1:7, function(i) {
(statsm[i, 1] - stamm[i, type.stat, M] * sqrt(N))/sqrt(stavv[i,
type.stat, M])
})
list(CALL = match.call(), METHOD = "Pedroni(1999) panel tests for cointegration",
STATISTIC = statsm)
}