In this paper, we develop a new estimation method that is suitable for censored models with two high dimensional fixed effects and that is based on a sequence of least squares regressions, yielding significant savings in computing time and hence making it applicable to frameworks in which standard estimation techniques become unfeasible. We propose to apply this estimation method to investigate the role of firms in individual wage variation. Using a longitudinal match employer‐employee dataset from Spain, we show that the analysis of wage determination can be misleading when wages are censored. In particular, the role of firm wage policies in wage dispersion is overestimated by more than ten percentage points, while the role of time‐invariant individual characteristics is underestimated by fifteen percentage points. Hence, controlling for censored wages appears to reinforce the idea that when explaining individual wage dispersion, what workers ‘are’ is more important than what workers ‘do’.