The notion of “convergence” of economic variables across countries is a useful concept and in the case of income per capita, a well studied area. If there is empirical evidence of convergence of some economic variables across countries, then our ability to predict the future (or at least differences between countries in the future) is enhanced. It is common in long run projections of climate change to base these projections on some notion of full or partial convergence whether in incomes per capita, technologies, energy intensities, emissions intensities of energy or per capita carbon emissions. But what is the empirical basis of these assumptions? This paper explores the historical experience of a range of variables related to climate change projections with the goal of examining if there is any evidence historically of convergence. The focus of the paper is on per capita carbon emissions from fossil fuel use because this is the basis of many projections as well as a variety of policy proposals. We also present evidence on GDP per capita, energy intensity of output and the emissions intensity of energy supply. We find strong evidence that the wide variety of assumptions about “convergence” commonly used in emissions projections are not based on empirically observed phenomena.