One of the most remarkable aspects of our species is that while we show surprisingly little genetic diversity, we demonstrate astonishing amounts of cultural diversity. Perhaps most impressive is the diversity of our technologies, broadly defined as all the physical objects we produce and the skills we use to produce them. Despite considerable focus on the evolution of technology by social scientists and philosophers, there have been few attempts to systematically quantify technological diversity, and therefore the dynamics of technological change remain poorly understood. Here we show a novel Bayesian model for examining technological diversification adopted from palaeontological analysis of occurrence data. We use this framework to estimate the tempo of diversification in American car and truck models produced between 1896 and 2014, and to test the relative importance of competition and extrinsic factors in shaping changes in macro-evolutionary rates. Our results identify a four-fold decrease in the origination and extinction rates of car models, and a negative net diversification rate over the last 30 years. We also demonstrate that competition played a more significant role in car model diversification than either changes in oil prices or gross domestic product. Together our analyses provide a set of tools that can enhance current research on technological and cultural evolution by providing a flexible and quantitative framework for exploring the dynamics of diversification.