On Wed, 20 Apr 2016, Youba Ndiaye wrote:
Dear all,
I'm a Ph.D student and I'm working on spatial econometrics approach.
I want to implement a static spatial durbin model in R with "splm"
function. But the particular case of my model is that my durbin model is
partial such as:
y = rho.Wy + X.beta + WZ.theta + epsilon
X and Z are vectors of explanatory variables with respectively (N,k) and
(N, m) dimensions. k>m. In orders words, the Z is a spatially lagged subset
of X.
My aim is to calculate properly impact measures of this model in R.
All of the impacts methods expect k=m. A sketch of a possible approach is:
library(spdep)
example(columbus)
lw <- nb2listw(col.gal.nb)
f <- CRIME ~ INC + HOVAL + I(lag(lw, HOVAL))
mod <- lagsarlm(f, data=columbus, lw)
summary(mod)
by constructing the (dense) S(W)_r matrices differently for the non-Durbin
and Durbin variables:
iIrW <- invIrW(lw, mod$rho)
S_INC <- iIrW %*% (mod$coefficients[2]*diag(nrow(columbus)))
S_HOVAL <- iIrW %*% ((mod$coefficients[3]*diag(nrow(columbus))) -
(mod$coefficients[4]*listw2mat(lw)))
Then you can get the direct and total impacts in the usual way:
dir_INC <- sum(diag(S_INC))/nrow(columbus)
dir_HOVAL <- sum(diag(S_HOVAL))/nrow(columbus)
tot_INC <- sum(c(S_INC))/nrow(columbus)
tot_HOVAL <- sum(c(S_HOVAL))/nrow(columbus)
with indir_* = tot_* - dir_*.
No inference tools are available, though.
It might be possible to inject zero WZ coefficient values and covariances
for non-included WX variables in order to use the standard impacts
methods, but you need strong reasons apriori to assume that they are zero;
going with regular Durbin will be likely to be more robust, and will give
a clear test of the insignificance of the indirect impacts.
Hope this helps,
Roger
Thank You in advance.
Best regards.
Youba.
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Roger Bivand
Department of Economics, Norwegian School of Economics,
Helleveien 30, N-5045 Bergen, Norway.
voice: +47 55 95 93 55; fax +47 55 95 91 00
e-mail: [email protected]
http://orcid.org/0000-0003-2392-6140
https://scholar.google.no/citations?user=AWeghB0AAAAJ&hl=en
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