There exists an extensive literature estimating idiosyncratic labor income processes. While a wide variety of models are estimated, GMM estimators are almost always used. We examine the validity of using likelihood based estimation in this context by comparing the small sample properties of a Bayesian estimator to those of GMM. Our baseline studies estimators of a commonly used simple earnings process. We extend our analysis to more complex environments, allowing for real world phenomena such as time varying and heterogeneous parameters, missing data, unbalanced panels, and non-normal errors. The Bayesian estimators are demonstrated to have favorable bias and efficiency properties.