Hi all.

I have a panel dataset containing 5 dependent variables (X) and a single independent variable (y). The dataset is based on repeated observations on a spatial grid (T = 78, n = 686, N = 53508, where T is the number of months, and n is the number of grid cells).

I believe that y can be expressed as a function of X, but I don't know if the coefficients of such a model are static or if they too vary with T and n (in theory, the coefficients are likely to vary with n and potentially T, but I don't know if my dataset has enough observations to support either possibility).

To start with I have tried constructing a fixed-effects model using the plm R library, where n is the fixed effect. I get a reasonable R2 and all the variables are statistically significant. As well as this, the Hausman test suggests that the fixed effects model is better than a random effects one.

However, I have run a Breusch-Godfrey and Pesaran CD test, which say that my model suffers from serial correlation and cross-sectional dependence. As this is my first attempt at regression modelling I am not sure how to remedy this. What should I do to make my model more robust, and is there a way to test whether the fit coefficients vary with at least n? Is there a better way to fit a spatio-temporal model in R? Thanks in advance!