I have a panel dataset with three dimensions: firms (i), regions (j), and years (t). For the moment, ignore the time dimension. I want to run the following spatial regression: y_ij = W*y_ij + M*y_ij. Note that I plan to use two spatially lagged dependent variables with different weight matrices. In reading through the Stata spatial autoregressive models reference manual (found here: https://www.stata.com/manuals/sp.pdf), I notice that I can't use spxtregress (the command for spatial panel data) while also specifying two spatially lagged dependent variables. However, this is possible in a cross-sectional context. See this on page 141:
"Add a higher-order spatial lag of y specified by another weighting matrix M
spregress y x1 x2, gs2sls dvarlag(W) errorlag(W) ivarlag(W: x1 x2) /// dvarlag(M)"
I'm wondering if I can treat my panel data as cross-sectional, and thus be able to use spregress. Doing so would require me to create my own fixed effects (no problem here). It would also mean that my spatial weight matrices would need to change from being (i x j) by (i x j) to (i x j x t) by (i x j x t). I am thinking about constructing this new matrix such that different years are always non-neighbors (i.e., they take a value of 0). Can I do this? Will it bias my results in some way?
Please let me your thoughts. Thanks!
"Add a higher-order spatial lag of y specified by another weighting matrix M
spregress y x1 x2, gs2sls dvarlag(W) errorlag(W) ivarlag(W: x1 x2) /// dvarlag(M)"
I'm wondering if I can treat my panel data as cross-sectional, and thus be able to use spregress. Doing so would require me to create my own fixed effects (no problem here). It would also mean that my spatial weight matrices would need to change from being (i x j) by (i x j) to (i x j x t) by (i x j x t). I am thinking about constructing this new matrix such that different years are always non-neighbors (i.e., they take a value of 0). Can I do this? Will it bias my results in some way?
Please let me your thoughts. Thanks!
