Spatial Lag

[John Friend]

Hello, I have a question regarding the application of a spatial lag. I would like to create the spatial lag of a dependent variable. I can use a Shapefile that contains the municipality data of my study area for this purpose. However, I am examining pairs of municipalities, which means I have two different X and Y coordinates for one observation. Additionally, I am using a panel dataset. Is there a way to create the lag even for pairs of municipalities?

Many Thanks!

[Daniel Schaefer]

When you say you are dealing with pairs of coordinates, does that mean each pair of coordinates is a single closely related observation, or does this data structure represent adjacent (or near) coordinates along which you might expect a diffusion-like process to propagate? If it is the former, then this makes sense only insofar as it makes theoretical sense to imagine spatial lag between any two pairs of municipalities, but not within a single pair of municipalities. If its the latter, than the answer is yes, probably, but as far as I am aware you will need to convert your edgelist-like data structure to an adjacency-matrix like data structure to use the Stata built in system.

Ultimately, the answer to your question depends on what you mean by "examining pairs of municipalities". At the end of the day, you need a theoretically coherent spatial weighting matrix for the model to work. If you can construct such a matrix, you can do the analysis.

[John Friend]

Thank you for the response. To provide more detail: I am investigating how commuting flows between bilateral pairs of municipalities change over time. This is intended to be explained by rent price differentials between the municipalities, which is why I've created a rent differential for each pair of municipalities. The goal is to analyze how changes in the rent differentials within municipality pairs impact the bilateral commuting flow within municipality pairs over several years. Therefore, I am using a Fixed-Effects model. In cross-section, Moran's I has indicated spatial autocorrelation at the municipal level regarding rent prices (also concerning the total number of commuters). Consequently, I have considered whether incorporating the spatial lag of rent differentials makes sense. However, I am not certain if this is necessary, as I am employing Fixed-Effects at the municipal level and clustering at the same level.

[Daniel Schaefer]

You may still need a spatial lag, especially if you think a diffusion-like process is at work here. Check out this paper for a bit more.