I propose a hypothesis test that is robust to the presence of weak instruments in binary outcome panel data. The test relies on a conditional maximum likelihood procedure, the conditional logit, to consistently estimate reduced-form parameters. Based on a distance function that relates reduced- and structural-form parameters, the test has the correct size regardless of instrument strength while standard Wald tests over-reject by up to 100% when instruments are weak. I investigate the findings of Nunn and Qian (2014) with the proposed test and find that claimed statistical significance vanishes at the 1% and 5% significance levels. Next, I show that quasi-maximum likelihood estimation (QMLE) ignoring second-stage heteroskedasticity yields inconsistent parameter and average marginal effect (AME) estimators in panel data. This is significant because QMLE is often employed in studies estimating heteroskedasticity or cluster robust standard errors. When instruments are weak, AME percentage bias can reach 650% in panels. Moreover, AME percentage bias in panels generally increases by a factor of 2-20 when heteroskedastic errors are assumed homoskedastic.