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Despite the scientific consensus that humans have dramatically altered the global environment, we have a limited knowledge of the specific forces driving those impacts. One key limitation to a precise understanding of anthropogenic impacts is the absence of a set of refined analytic tools. Here we assess the analytic utility of the well-known IPAT identity, the newly developed ImPACT identity, and their stochastic cousin, the STIRPAT model. We discuss the relationship between these three formulations, their similar conceptual underpinnings and their divergent uses. We then refine the STIRPAT model by developing the concept of ecological elasticity (EE). To illustrate the application of STIRPAT and EE, we compute the ecological elasticities of population, affluence and other factors for cross-national emissions of carbon dioxide (CO₂) from fossil fuel combustion and for the energy footprint, a composite measure …