I am trying to use LASSO for variable selection, on a balanced panel. I have a total of 14 predictors, and would like to reduce this variable space.

The panel is comprised of n dependent variables, each having t observations. I am planning to run LASSO on the cross-section for each time t, then average the t models obtained.

The only problem is that the predictors are common across the panel. In other words, each predictor - independent variable - observes the same value at each time t for all the dependent variables n. In other words, the predictors are common factors - shocks - for the cross-section.

Having common factors (e.g Inflation, Oil Prices, ..), how can I then run LASSO on the cross-section? Should I first estimate the sensitivity of each dependent variable to the predictors (using univariate time-series regressions), and then use those estimates as the *independent variables, or x vector - in LASSO?

This is a very high priority/urgent issue for me, and I would appreciate any help I could get!

Thanks,