Time series of production capital and total factor productivity (or "technology," as we call the latter here) are fundamental to understanding the processes of output and productivity growth. Unfortunately, capital and technology are unobserved except at the most disaggregated levels of production units and capital components and must be estimated prior to being used in empirical analysis. Standard methods for estimating capital and technology were developed decades ago (Jorgenson, 1963; Solow, 1957) and are based on analytical and computational methods of that era. We develop and apply a new method for estimating production capital and technology, based on advances in economics, dynamic optimization, statistics, and computing over the intervening years.