Bayesian analysis is given of an instrumental variable model that allows for t‐distributed errors in both the structural equation and the instrument equation. Specifically, the approach for dealing with t‐distributed errors is extended to the Bayesian instrumental variable estimator by modelling the variance for each error using a Gamma distributed hierarchical prior. The computation is carried out by using a Markov chain Monte Carlo sampling algorithm for the heteroskedastic case. An example using data illustrates the approach and shows that ignoring the presence of error terms with heavy tails in the instrument equation when it exists may lead to biased estimates.