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Help: impact measures in spatial panel durbin model

3 messages · Roger Bivand, Youba Ndiaye

Youba Ndiaye
# 
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.

Thank You?in advance.
Best regards.
Youba.
Roger Bivand
#
On Wed, 20 Apr 2016, Youba Ndiaye wrote:

            

      
      
      
    

        
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

            

      
      
      
    

        

      
      
    

        

  
    

      
      
    

  


  


      

    

    

      
      

        


  

        

      Youba Ndiaye
    

    

      
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Thanks a lot. That's very helpful

Best regards.
Youba.

Roger Bivand <Roger.Bivand at nhh.no> a ?crit?:

            

      
      
      
    

        
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is:

            

      
      
      
    

        

      
      
    

            

      
      
      
    

        
https://scholar.google.no/citations?user=AWeghB0AAAAJ&hl=enhttp://depsy.org/person/434412