This paper develops a long‐run output relation for a major oil‐exporting economy where the oil income‐to‐output ratio remains sufficiently high over a prolonged period. It extends the stochastic growth model developed in Binder and Pesaran (1999) by including oil exports as an additional factor in the capital accumulation process. The paper distinguishes between the two cases where the growth of oil income, go, is less than the natural growth rate (the sum of the population growth, n, and the growth of technical progress, g), and when go ≥ g + n. Under the former, the effects of oil income on the economy's steady growth rate will vanish eventually, while under the latter oil income enters the long‐run output equation with a coefficient which is equal to the share of capital if it is further assumed that the underlying production technology can be represented by a Cobb–Douglas production function. The long‐run theory is tested using quarterly data on nine major oil economies. Overall, the test results support the long‐run theory, with the existence of long‐run relations between real output, foreign output and real oil income established for six of the nine economies considered. Copyright © 2012 John Wiley & Sons, Ltd.