A stochastic frontier production function is defined for panel data on firms, in which the non-negative technical inefficiency effects are assumed to be a function of firm-specific variables and time. The inefficiency effects are assumed to be independently distributed as truncations of normal distributions with constant variance, but with means which are a linear function of observable variables. This panel data model is an extension of recently proposed models for inefficiency effects in stochastic frontiers for cross-sectional data. An empirical application of the model is obtained using up to ten years of data on paddy farmers from an Indian village. The null hypotheses, that the inefficiency effects are not stochastic or do not depend on the farmer-specific variables and time of observation, are rejected for these data.