  We propose and implement an approach to inference in linear instrumental
variables models which is simultaneously robust and computationally tractable.
Inference is based on self-normalization of sample moment conditions, and
allows for (but does not require) many (relative to the sample size), weak,
potentially invalid or potentially endogenous instruments, as well as for many
regressors and conditional heteroskedasticity. Our coverage results are uniform
and can deliver a small sample guarantee. We develop a new computational
approach based on semidefinite programming, which we show can equally be
applied to rapidly invert existing tests (e.g,. AR, LM, CLR, etc.).
