We propose that the formation of beliefs be treated as statistical hypothesis tests, and label such beliefs inferential expectations. If a belief is overturned due to sufficient contrarian evidence, we assume agents switch to the rational expectation. We build a state dependent Phillips curve, and show that adjustments to equilibria may be contaminated by signal censoring, where agents in possession of extreme information are the first to adjust to changed economic circumstances. This approach is able to replicate recent micro-level evidence on firms?pricing behavior and sheds light onto the dynamics of disaggregated prices.