Interest in the estimation of production functions and the measurement of productivity has a long history in economics. The concept of productivity is a measure of the e°ciency of an economy, an industry, or a ˝rm. In this paper we will focus the discussion on ˝rm-level productivity, but many of the ideas presented apply to more aggregate notions as well. The easiest way of understanding ˝rm-level productivity is to consider two ˝rms with the same level of input usage. If ˝rm 1 produces more output than ˝rm 2, it is considered to be more productive. This simple notion was notoriously di°cult to formalize. The ˝rst notions of productivity were focused on single-input measures such as the amount of output per worker produced by a ˝rm, as these measures could be computed from readily available data.