We consider the estimation of Cobb-Douglas production functions using panel data covering a large sample of companies observed for a small number of time periods. Standard GMM estimators, which eliminate unobserved firm-specific e¤ects by taking first differences, have been found to produce unsatisfactory results in this context (Mairesse and Hall, 1996). We attribute this to weak instruments: the series on rm sales, capital and employment are highly persistent, so that lagged levels are only weakly correlated with subsequent first differences. As shown in Blundell and Bond (1998), this can result in large finite-sample biases when using the standard first-differenced GMM estimator. Blundell and Bond (1998) also show that these biases can be dramatically reduced by exploiting reasonable stationarity restrictions on the initial conditions process. This yields an extended GMM estimator in which lagged first-differences of the series are also used as instruments for the levels equations (cf. Arellano and Bover, 1995). Using data for a panel of R&D-performing US manufacturing companies, similar to that in Mairesse and Hall (1996), we show that the instruments available for the production function in first differences are indeed weak. We find that the additional instruments used in our extended GMM estimator appear to be both valid and informative in this context; this estimator yields much more reasonable parameter estimates. We also stress the importance of allowing for an autoregressive component in the productivity shocks.