[R-sig-Geo] Help: impact measures in spatial panel durbin model

[Roger Bivand]

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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>
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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: Roger.Bivand at nhh.no
http://orcid.org/0000-0003-2392-6140
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http://depsy.org/person/434412