This paper examines the estimation of Cobb-Douglas production functions using panel data from a large sample of US manufacturing firms. Standard GMM estimators, which eliminate unobserved firm-specific effects by taking first differences, have been found to produce unsatisfactory results in this context. The authors attribute this to weak instruments: the series on firm sales, capital, and employment are highly persistent, so that lagged levels are only weakly correlated with subsequent first differences. This can result in large finite-sample biases when using the standard first-differenced GMM estimator. Blundell and Bond (1998) 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. Using data for a panel of R&D-performing US manufacturing firms, similar to that in Mairesse and Hall (1996), the authors show that the instruments available for the production function in first differences are indeed weak. They find that the additional instruments used in their extended GMM estimator appear to be both valid and informative in this context, yielding much more reasonable parameter estimates. The authors also stress the importance of allowing for an autoregressive component in the productivity shocks. They find that the first-differenced GMM estimator yields a low and statistically insignificant capital coefficient, and suggests sharply decreasing returns to scale. Using the extended GMM estimator, they find much more reasonable results: a higher and strongly significant capital coefficient, and they do not reject constant returns to scale. The additional instruments used in the extended GMM estimator are not rejected in this application, and the lagged first-differences are informative instruments for the endogenous variables in levels. The authors conclude that the system GMM estimator performs well in this application, yielding more reasonable parameter estimates and reducing finite-sample biases associated with first-differenced GMM. They also find that imposing constant returns to scale reduces weak instruments biases in the differenced GMM estimates, possibly because the capital-labour ratio is less persistent than the levels of either series. These results suggest that weak instruments biases are a potential problem when relying on first-differenced GMM estimators using these persistent series. However, the authors note that lagged combinations of the three series may be more informative than the lagged levels of any one series alone.This paper examines the estimation of Cobb-Douglas production functions using panel data from a large sample of US manufacturing firms. Standard GMM estimators, which eliminate unobserved firm-specific effects by taking first differences, have been found to produce unsatisfactory results in this context. The authors attribute this to weak instruments: the series on firm sales, capital, and employment are highly persistent, so that lagged levels are only weakly correlated with subsequent first differences. This can result in large finite-sample biases when using the standard first-differenced GMM estimator. Blundell and Bond (1998) 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. Using data for a panel of R&D-performing US manufacturing firms, similar to that in Mairesse and Hall (1996), the authors show that the instruments available for the production function in first differences are indeed weak. They find that the additional instruments used in their extended GMM estimator appear to be both valid and informative in this context, yielding much more reasonable parameter estimates. The authors also stress the importance of allowing for an autoregressive component in the productivity shocks. They find that the first-differenced GMM estimator yields a low and statistically insignificant capital coefficient, and suggests sharply decreasing returns to scale. Using the extended GMM estimator, they find much more reasonable results: a higher and strongly significant capital coefficient, and they do not reject constant returns to scale. The additional instruments used in the extended GMM estimator are not rejected in this application, and the lagged first-differences are informative instruments for the endogenous variables in levels. The authors conclude that the system GMM estimator performs well in this application, yielding more reasonable parameter estimates and reducing finite-sample biases associated with first-differenced GMM. They also find that imposing constant returns to scale reduces weak instruments biases in the differenced GMM estimates, possibly because the capital-labour ratio is less persistent than the levels of either series. These results suggest that weak instruments biases are a potential problem when relying on first-differenced GMM estimators using these persistent series. However, the authors note that lagged combinations of the three series may be more informative than the lagged levels of any one series alone.