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Let's assume to have a panel including observations for 88 individuals over 18 years (1584 observations). The panel is now populated with a broad set of 50 possible regressors that I would like to now reduce by applying a variable selection algorithm. Among the regressors, I also included the spatial and temporal lags. One of the possible options would be represented by the application of the general-to-specific (GETS) modeling procedure.

As I understand from the literature (for instance Sucarrat and Escribano 2011), GETS starts from a large unrestricted model (GUM) and then removes the features by means of a step-wise regression. So basically, it removes a regressor and then performs a misspecification and a backtest (BaT) against the GUM. In this way, it verifies whether the removal added autocorrelation and/or heteroscedasticity or the performance increased respect to the GUM. It stops when no insignificant regressors are identified.

As reported Pretis et al 2018,"It should be underlined, however, that gets is not limited to time series models: Static models (e.g., cross-sectional or panel) can be estimated by specifying the regression without dynamics."

What does this "without dynamics" mean? Should I get the average values of the variables of each of the 88 individuals over the 18 years? How would this eventually deal with time trends and spatial correlation? is there any other procedure that is more suitable for this case?

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"Without dynamics" in this context means that there are no lags of the dependent variable. Note that panel models commonly have fixed or random effects, which lead to bias in the coefficient estimates caused by mechanical correlated with error term induced by the fact that the individual effect will necessarily be correlated with past values of the outcome.

This can be overcome with the Arellano Bond GMM estimator (google it), which constructs instrumental variables for the lags using lags even farther back. Applying GETS to an Arellano-Bond GMM model might be possible, but it certainly isn't packaged conveniently and I'm not sure that it's been formally analyzed.

Your other option would be to leave out the fixed/random effects. You'd still however have residual autocorrelation because of the panel structure of the data, and it isn't obvious to me how or whether GETS can or could account for this out of the box. I know that the gets in R allows you to use White or Newey-West standard errors, but I don't know if it allows you to specify a cluster-robust covariance matrix estimator. That means that tests for significance -- upon which GETS's elimination algorithm is based -- would be wrong.

So in sum, it seems like this should be possible, but there are added difficulties in the panel context.

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