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Abstract This paper proposes and tests new definitions of convergence and common trends for per capita output. We define convergence for a group of countries to mean that each country has identical long‐run trends, either stochastic or deterministic, while common trends allow for proportionality of the stochastic elements. These definitions lead naturally to the use of cointegration techniques in testing. Using century‐long time series for 15 OECD economies, we reject convergence but find substantial evidence for common trends. Smaller samples of European countries also reject convergence but are driven by a lower number of common stochastic trends.