This paper proposes a measure of the intensity of competition in labor markets on the basis of limited data. Large-scale socioeconomic surveys often lack detailed information on competitive behavior. It is particularly difficult to determine whether a worker moves between the different segments of the labor market. Here, the Maximum Entropy principle is used to make inferences about the unobserved mobility decisions of workers in US household data. A class of models is proposed that reflects a parsimonious conception of competition in the Smithian tradition, as well as being consistent with a range of detailed behavioral models. The Quantal Response Statistical Equilibrium (QRSE) class of models can be seen to give robust microfoundations to the persistent patterns of wage inequality among equivalent workers. Furthermore, the QRSE effectively endogenizes the definition of labor market segments, allowing us to interpret the estimated competition intensities as partial measures of labor market segmentation. Models of this class generate predictions that capture between 97.5 and 99.5 percent of the informational content of the sample wage distributions. In addition to providing a very good fit to the wage data, the predictions are also consistent with bounded rationality of workers.