Panel FE and Clustering #

pdslasso and ivlasso can also be applied to fixed effect panel models using the methodology of Belloni et al., 2014. Since the appropriate level of regularization depends on the error structure, we need to accommodate cluster dependence that is likely to be present in panel data. Ignoring cluster dependence would lead to a regularization level that is too low.

For demonstation, we consider the nlswork example data set:

. webuse nlswork, clear
. xtset idcode year
. global controls age-south  

To estimate the effect of union membership on wages, we consider a large set of controls, including age, race, education, regional controls as well as industry and occupational codes. The total number of controls is 79.

We also include individual fixed effect using the fe option. (Note that the data is xtset by idcode.) Lastly, we cluster by individual to account for dependence over time.

. pdslasso ln_w union ( c.($controls)##c.($controls) i.ind_code i.occ_code ), ///
             cluster(idcode) fe

OLS using CHS lasso-orthogonalized vars
(Std. Err. adjusted for 4132 clusters in idcode)
------------------------------------------------------------------------------
             |               Robust
     ln_wage |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
       union |   .0978002   .0096037    10.18   0.000     .0789773    .1166231
------------------------------------------------------------------------------

OLS using CHS post-lasso-orthogonalized vars
(Std. Err. adjusted for 4132 clusters in idcode)
------------------------------------------------------------------------------
             |               Robust
     ln_wage |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
       union |   .0881405   .0092774     9.50   0.000     .0699571    .1063239
------------------------------------------------------------------------------

OLS with PDS-selected variables and full regressor set
(Std. Err. adjusted for 4132 clusters in idcode)
------------------------------------------------------------------------------
             |               Robust
     ln_wage |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
       union |   .0883666   .0092876     9.51   0.000     .0701633    .1065699
------------------------------------------------------------------------------

Note that the output above is abbreviated. In total, 16 controls are selected.