The probability of informed trading (PIN) is used widely as a measure of information asymmetry. Relatively little work has appeared on how well PIN models fit empirical trade data. We reveal structural limitations in PIN models by examining their marginal distributions and dependence structures represented by copulas. We develop a distribution‐free test of the goodness‐of‐fit of PIN models. Our results indicate that estimated PIN models have generally poor fit to actual trade data. These results suggest that researchers should be cautious when PIN estimates are plugged into empirical models as explanatory variables.