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Can someone explain to me how the estimation of the spatial Durbin model is made in Stata ? The documentation of XSMLE command (for spatial panels) says that for dynamic cases the estimator are based upon the article of Yu et. al. (2008). But I have not found references in the article to the estimation process of the Spatial Durbin model.

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Here is a detailed worked example of how to use the xsmle command, including an example of the Spatial Durbin model. As the document says, it is estimated using Maximum Likelihood. The model can be of Random Effects or Fixed Effects.

Key screenshots below:

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You need to use model(sdm) in the options to get the spatial Durbin model. To get the dynamic version of the model, add dlag to the options.

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I'm assuming you know how to do spatial weights matrices and such, so I will just skip that and throw out a disclaimer that I use R as my primary statistical programming language, not STATA, so let's first observe a generic spatial model:

spatreg $ylist $xlist, weights(W) eigenvalues(E) model(lag)

The lag in that function can be replaced with an error option if you want the SEM. To do a spatial durbin model (SDM) in R I find that using mixed or a durbin option does the job. Try and see if that works in place of lag in model(), for future reference. Sometimes the option is there but not many people use it because they don't usually care about estimating the model.

Next, try out the spmlreg function which appears to have the spatial durbin option:

spmlreg $ylist $xlist, weights(W) wfrom(Stata) eigenvar(E) model(durbin)

For a better understanding of the function, check out P. Wilner Jeanty's documentation of spmlreg.

Maybe both of them work fine, and that'd be cool. The more options the better.

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