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In this paper we explore a new approach to estimation for autoregressive panel data models, based on projecting the unobserved individual effects on the vector of observations on the lagged dependent variable. This approach yields estimators which coincide with known generalised method of moments (GMM) estimators for models where stationarity is not imposed on the initial conditions and for models which satisfy mean stationarity. Our approach allows us to obtain a simple linear estimator for models which satisfy covariance stationarity, which although not fully efficient performs very well in simulations.