This paper investigates the effect of the label bias problem of maximum entropy Markov models for part-of-speech tagging, a typical sequence prediction task in natural language processing. This problem has been underexploited and underappreciated. The investigation reveals useful information about the entropy of local transition probability distributions of the tagging model which enables us to exploit and quantify the label bias effect of part-of-speech tagging. Experiments on a Vietnamese treebank and on a French treebank show a significant effect of the label bias problem in both of the languages.