We measure the efficiency of regional innovation systems (RIS) in Germany by means of a knowledge production function. This function relates private sector Research and Development (R&D) in a region to the number of inventions that have been registered by residents of that region. Two approaches are followed. First, it is assumed that differences in the productivity of private sector R&D between regions affect the slope of the KPF, which represents the marginal productivity of R&D input. The second approach assesses regional differences within the framework of a stochastic frontier knowledge production function. This approach mainly reveals differences with regard to the intercept of the knowledge production function and, therefore, with regard to the average productivity. We compare the results of both approaches and discuss a number of critical issues such as the properties of the distribution of efficiencies, the appropriate size of RIS, and how to deal with the issue of spatial autocorrelation.