Weighting observations in a spdep::lagsarlm Model?

I would like to estimate a spdep::lagsarlm Model (Spatially 
Autoregressive Regression) in R. My observations (n=447) are polygons, 
each representing an administrative region of Berlin and my attributes 
are aggregated on this regional level (e.g. unemployment rate, median 
house prices etc.).
?However, the problem is that the regions have a highly varying number 
of inhabitants (between 500 and 32000).
?Therefore, I would like to weight each observation with its number of 
inhabitants. With lm this is easypeasy, because it accepts the optional 
argument weights=... How can I do something similar with 
spdep::lagsarlm? Is there a workaround? Or does weighting not make any 
sense at all in the case of SAR Models?

Good question!

Weighting is potentially important in spatial regression, and is often 
used in epidemiology and criminology, but hasn't been asked for in 
econometrics.

So you can use spautolm() with weights, and as the SAR error model is the 
same thing as errorsarlm(), you can fit weighted SLX (lm), weighted SEM 
and SDEM (spautolm), but not the models with lagged y. Before this can be 
considered, someone has to do the math to work out its consequences for 
estimation and impact methods; I'm not aware of any relevant literature 
for ML estimation. Treated additively, you could look at Bayesian methods, 
either in Matlab where LeSage & Pace fit a heteroskedasticity effect (not 
weights) or maybe using the "slm" model in INLA, but neither of these 
ideas have been thought through. You could also look at GM HAC methods, 
but again, they do not take given weights.

If you can find such literature, or develop the missing reasoning, I'd be 
willing to implement it in ML, as it is an obviously relevant robustness 
check.

Roger

?

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