This project explores some of the possibilities presented by geographically weighted fixed effects regression, a natural combination of weighted regression and panel regression that has gone almost entirely unused in the field of econometrics. I show that by relying on temporal heterogeneity to estimate effects, spatial heterogeneity can be used to account for spatial nonstationarity in regression effects. This treats spatial nonstationarity as a facet of relationships to be explored rather than a problem with the model as it is often seen. I also show that local spatial autocorrelation of estimated coefficients can be used to identify whether artificial boundaries influence effects.
3 thoughts on “Nonstationarity in Geographically Weighted Fixed Effects Regression”
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Hi August, this is a valuable first intervention in this literature, it appears. I wonder why the N-S banding of coefficients in the plains states and western coastal states? I can’t help but wonder if it has to do with your conceptualization of spatial relationships around K nearest neighbors, rather than IDW or contiguity, for example. Be that as it may, if the banding is real (rather than an artifact of the neighborhood parameter), what do you think accounts for it? If that pattern is robust to various neighborhood parameters, it would beg explication in that sense. Will be interesting to see where you take this and how it is received in economics.
The banding was one of the first things that struck me in the results as well, and I was also curious about if it was robust. If I had had more space than a poster, I would have elaborated, but I also ran analyses using IDW, second order contiguity, and distance bands methods and found similar results. I think the banding is actually something that comes from the structure of state boundaries and functionings of state governance in both regions. This phenomenon was actually one of the things that inspired me to look at the relationship between distance to state boundary and spatial autocorrelation. My theory is that it is ideological similarities in state governing bodies within each band accounts for the observed pattern, as we can see that the autocorrelation trails of as we move away from state boundaries. I do wish I had put in some other maps that accentuated state boundaries more though, as I think this would have clarified the point substantially.
This is an interesting tool to learn about, especially when you want to consider “time.” However, depending on what you are studying, if you can fix the time point, you can just use a GWR instead. Did you look at different time points and see how they affect the coefficient? It wasn’t clear to me why you need to use GWFER. Also, for the coefficients you showed, are they statistically significant or not? Do you have the residual values of your model, and what’s the R-Squared of your model? Without this important information, it’s hard to jump into the conclusion. I also believe Local Moran’s I give you a hot spots for your GWEFR coefficients studying the effect of “time”, but that’s different from considering “space” in your model. You need to run a GWR if you really want to know the spatial relationship between the variables because a “simple least-squares regression” used in this study is a global model and doesn’t capture the element of space. Also, we you determined this aspatial model, what does it look like across space? What are the residual values and t-values across space? I believe it would be helpful to include that critical information.