I am trying to model the effect that proximity to transportation infrastructure has on home prices. It is common (and reasonable) to use some type of spatial dependence model, such as the Spatial Durbin Model, $$y = \rho W y + X\beta + XW\lambda + \varepsilon $$ In this model, the outcome is a result of
- autocorrelation $\rho W y$ (neighbor's home prices)
- individual effects $X\beta$ (own home characteristics)
- and neighbor effects $XW\lambda$ (neighbor's characteristics)
My question: in the case of a spatially-dependent explanatory variable (such as how far each observation is from a transit station), does this model introduce collinearity between the $X\beta$ and $XW\lambda$ terms? After all, if I live two miles away from the nearest train station, my neighbors by definition also live about two miles from the same train station.
If there is multicollinearity, how will this effect the $\beta$ and $\lambda$ estimates? Will they be consistent/unbiased? If so, how might I correct for this?