  We consider hypothesis testing in instrumental variable regression models
with few included exogenous covariates but many instruments -- possibly more
than the number of observations. We show that a ridge-regularised version of
the jackknifed Anderson Rubin (1949, henceforth AR) test controls asymptotic
size in the presence of heteroskedasticity, and when the instruments may be
arbitrarily weak. Asymptotic size control is established under weaker
assumptions than those imposed for recently proposed jackknifed AR tests in the
literature. Furthermore, ridge-regularisation extends the scope of jackknifed
AR tests to situations in which there are more instruments than observations.
Monte-Carlo simulations indicate that our method has favourable finite-sample
size and power properties compared to recently proposed alternative approaches
in the literature. An empirical application on the elasticity of substitution
between immigrants and natives in the US illustrates the usefulness of the
proposed method for practitioners.
