Using a nonlinear panel data model, we examine the threshold effects in the productivity of the public capital stocks for a panel of 21 OECD countries observed over 1965-2001. Using the so-called "augmented production function" approach, we estimate various specifications of a Panel Smooth Threshold Regression (PSTR) model recently developed by Gonzalez, Teräsvirta and Van Dijk (2004). One of our main results is the existence of strong threshold effects in the relationship between output and private and public inputs: whatever the transition mechanism specified, tests strongly reject the linearity assumption. Moreover, this model allows cross-country heterogeneity and time instability of the productivity without specification of an ex-ante classification over individuals. Consequently, it is possible to give estimates of productivity coefficients for both private and public capital stocks at any time and for all the countries. Finally we proposed estimates of individual time varying elasticities that are much more reasonable than those previously published.