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High-dimensional models that include many covariates which might potentially affect an outcome are increasingly common. This paper begins by introducing a lasso-based approach and a stepwise-based approach to valid inference for a high-dimensional model. It then discusses several essential extensions to the literature that make the estimators more usable in practice. Finally, it presents Monte Carlo evidence to help applied researchers choose which of several available estimators should be used in practice. The Monte Carlo evidence shows that our extensions to the literature perform well. It also shows that a BIC-stepwise approach performs well for a data-generating process for which the lasso-based approaches and a testing-stepwise approach fail. The Monte Carlo evidence also indicates the BIC-based lasso and plugin-based lasso can produce better inferential results than the ubiquitous CV-based lasso. Easy-to-use Stata commands are available for all the methods that we discuss.

Finite-sample results for lasso and stepwise Neyman-orthogonal Poisson estimators