This paper presents a new approach to, simultaneously, provide an estimate of factor elasticities as well as time-varying technical change utilizing the Kalman filter. Using a simulation exercise we show that this approach performs well for different types of non-linear technical change. The method is subsequently applied on Danish macroeconomic data from 1966-2016 for the private sector and at the sectoral level. Using a nested CES production function we find that all inputs in production are gross complements. The estimates suggest that the relevant elasticity of substitution between capital and labor is around 0.5 for the private sector. Moreover, technological change in the private sector has been labor-augmenting in the long run, thus supporting an assumption of Harrod-neutral growth in the long run. However, we find important “medium run” fluctuations and periods where technical change has been capital-augmenting. This may be driven by periods of relatively slow labor productivity growth in the service sector in the early 1990’s and after the financial crisis.