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!
Re: How to use LASSO with common shocks
Can you use whatever software/data-environment you have and select the subset of data you are interested in and analyze this particular subset? (In other words treat it as a conditional distribution).
If you are doing a conditional analyses, you will need to think about how the degrees of freedom will change as a result (i.e. do you have enough data to be able to fit a particular model?).
If you are using something like R or SAS, getting the subset data should be straight-forward (for SAS use the DATA command and R you can use any of a tonne of procedures like data.frame()).