(Adaptive) Lasso with some invalid instruments

sivreg estimates a linear instrumental variables regression where some of the instruments fail the exclusion restriction and are thus invalid. The LARS algorithm (Efron et al., 2004) is applied as long as the Hansen statistic (OID test) rejects. The results report the instruments, which are identified as invalid, and report the Post-Lasso estimate from a 2SLS regression applying the (adaptive) Lasso selection. For general information about adaptive Lasso see Zou (2006).

sivreg uses the moremata package. If it is not already installed, type "ssc install moremata" in Stata.

Way 1: Use the Stata module github to install sivreg. Type the following code in Stata:

1. net install github, from("https://haghish.github.io/github/")
   

2. github install farbmacher/sivreg
   

Way 2: Copy the sivreg.ado and sivreg.sthlp files into your personal ado folder or the current working directory.

Let y be the outcome, d an endogenous regressor, x an exogenous control variable and z1 z2 z3 a set of potentially exogenous instruments, then the adaptive Lasso regression would be

1. sivreg y d x, endog(d) exog(x z1 z2 z3) adaptive
   

• Windmeijer F., Farbmacher H., Davies N., Davey Smith G. (2019): On the Use of the Lasso for Instrumental Variables Estimation with Some Invalid Instruments, Journal of the American Statistical Association, forthcoming.
• Zou H. (2006): The Adaptive Lasso and Its Oracle Properties, Journal of the American Statistical Association 101, 1418-1429.
• Efron B., Hastie T., Johnstone I., Tibshirani R. (2004): Least Angle Regression, Annals of Statistics 32, 407-499.