We consider fixed-effect estimation of a production function where inputs and outputs vary over time, space, and individual, and identify estimates of time-varying individual effects, without parametric assumptions on the effects. We discuss sufficient conditions for unbiasedness and for consistency and asymptotic normality along the spatial dimension. Results are applied to estimation of a harvest function for bottom trawler fishing vessels in the flatfish and groundfish fisheries of the Bering Sea. We conclude that vessel individual effects did not change between 2002 and 2004. Ranking and selection theory determines that individual effects are not statistically significant across vessels. Copyright 2010, Oxford University Press.