How to use LASSO with common shocks

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!



No cake for spunky
We don't have many, if any, posters who do econometric modeling here. As I can tell you from painful experience time series related questions do not get addressed very often.


No cake for spunky
I don't know if this forum or applied statistics is better - we don't really have a time series forum. The real issue is not the forum, it is that we don't have very many (really any on a regular basis) posters who do time series a lot. Or at least that answer questions on them regularly if there are any time series experts here. :p

I am slowly learning time series, but I know nothing at all about the method you asked about.