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

Youba Ndiaye youba.ndiaye at dijon.inra.fr
Wed Apr 20 15:17:25 CEST 2016

```  Thanks a lot. That's very helpful

Best regards.
Youba.

Roger Bivand <Roger.Bivand at nhh.no> a écrit :

> 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
>
>> Best regards.
>> Youba.
>>
>>         [[alternative HTML version deleted]]
>>
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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
>