Lasso with Instrumental Variables - tests of weak instruments

[Lois Miller]

I am using lasso on Stata 16 to make inference from a model with two endogenous variables (college quality and college quality squared - where college quality is measured as continuous index). I have many possible instruments, but most of them are weak (as indicated by Kleinbergen-Paap wald rk F statistic reported from variations of models estimated using ivreg2). From reading the Stata Lasso manual (and learning a bit about lasso), it seems like lasso might be a good option for me to select instruments. However, I would still like to know generally "how strong" the selected instruments are. poivregress and xpoivregress do not return the same weak identification tests as ivreg2. Can anyone help me understand how to assess instrument strength using lasso? Thank you!

[Achim Ahrens]

Hi Lois, you could try ivlasso (part of the pdslasso package) which returns weak-identification robust confidence sets (based on Section 4.2 in the Belloni et al. paper from 2012, Econometrica).

Note: if you think that you have many weak instruments (i.e. many first-stage coefficients that are non-zero but small), the lasso might not be your best choice. The lasso relies on the assumption of sparsity (i.e. small number of non-zero coefficients). The ridge might be better suited (see Hansen & Kozbur 2014).

References:

Belloni, A., Chen, D., Chernozhukov, V., & Hansen, C. (2012). Sparse Models and Methods for Optimal Instruments With an Application to Eminent Domain. Econometrica, 80(6), 2369–2429. https://doi.org/10.3982/ECTA9626

Hansen, C., & Kozbur, D. (2014). Instrumental variables estimation with many weak instruments using regularized JIVE. Journal of Econometrics, 182(2), 290–308. https://doi.org/http://dx.doi.org/10...om.2014.04.022

[Lois Miller]

Thank you very much!