Studies of public-private and foreign-domestic wage differentials face difficulties distinguishing ownership effects from correlated characteristics of workers and firms. This paper estimates these ownership differentials using linked employer-employee data (LEED) from Hungary containing 1.35mln worker-year observations for 21,238 firms from 1986 to 2003. We find that ownership type is highly correlated with characteristics of both workers (education, experience, gender, and occupation) and firms (size, industry, and productivity), suggesting ownership type is systematically selected along these dimensions. The large unconditional wage gaps (0.24 for public-private and 0.40 for foreign-domestic) in the data are little affected by conditioning on worker characteristics, but controlling for industry reduces the public and foreign premia (to 0.16 and 0.34, respectively), and controlling for employment size further reduces them (to 0.07 and 0.28). We also exploit the presence of 3,700 switches of ownership type in the data to estimate firm fixed-effects and random trend models, accounting for unobserved firm characteristics affecting the average level and trend growth of wages. These controls have little effect on the conditional public-private gap, but they reduce the estimated foreign premium (to 0.07). The results imply that the substantial unconditional wage differentials are mostly, but not entirely, a function of differences in worker and firm characteristics, and that linked panel data are necessary to take these correlated factors into account.