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We consider inference about coefficients on a small number of variables ofinterest in a linear panel data model with additive unobserved individual andtime specific effects and a large number of additional time-varying confoundingvariables. We allow the number of these additional confounding variables to belarger than the sample size, and suppose that, in addition to unrestricted timeand individual specific effects, these confounding variables are generated by asmall number of common factors and high-dimensional weakly-dependentdisturbances. We allow that both the factors and the disturbances are relatedto the outcome variable and other variables of interest. To make informativeinference feasible, we impose that the contribution of the part of theconfounding variables not captured by time specific effects, individualspecific effects, or the common factors can be captured by a relatively smallnumber of terms whose identities are unknown. Within this framework, we providea convenient computational algorithm based on factor extraction followed bylasso regression for inference about parameters of interest and show that theresulting procedure has good asymptotic properties. We also provide a simplek-step bootstrap procedure that may be used to construct inferential statementsabout parameters of interest and prove its asymptotic validity. The proposedbootstrap may be of substantive independent interest outside of the presentcontext as the proposed bootstrap may readily be adapted to other contextsinvolving inference after lasso variable selection and the proof of itsvalidity requires some new technical arguments. We also provide simulationevidence about performance of our procedure and illustrate its use in twoempirical applications.

The Factor-Lasso and K-Step Bootstrap Approach for Inference in High-Dimensional Economic Applications