  I propose a new identification-robust test for the structural parameter in a
heteroskedastic linear instrumental variables model. The proposed test
statistic is similar in spirit to a jackknife version of the K-statistic and
the resulting test has exact asymptotic size so long as an auxiliary parameter
can be consistently estimated. This is possible under approximate sparsity even
when the number of instruments is much larger than the sample size. As the
number of instruments is allowed, but not required, to be large, the limiting
behavior of the test statistic is difficult to examine via existing central
limit theorems. Instead, I derive the asymptotic chi-squared distribution of
the test statistic using a direct Gaussian approximation technique. To improve
power against certain alternatives, I propose a simple combination with the
sup-score statistic of Belloni et al. (2012) based on a thresholding rule. I
demonstrate favorable size control and power properties in a simulation study
and apply the new methods to revisit the effect of social spillovers in movie
consumption.
