From Wood to Coal: Directed Technical Change and the British Industrial Revolution

Abstract

We build a directed technical change model where one intermediate goods sector uses a fixed quantity of biomass energy (“wood”) and another uses coal at a fixed price, matching stylized facts for the British Industrial Revolution. Unlike previous research, we do not assume that the level or growth rate of productivity is inherently higher in the coal-using sector. Analytically, greater initial wood scarcity, initial relative knowledge of coal-using technologies, and/or population growth will boost an industrial revolution, while the converse may prevent one forever. An industrial revolution, with accelerating growth in the coal-using sector, is the dominant dynamic outcome, but not inevitable if inter-good substitutability is high enough. Empirical calibration for 1560-1900 produces historically plausible results for changes in energy-related variables during British industrialization, and through counterfactual simulations confirms that it was the growing relative scarcity of wood caused by population growth that resulted in innovation to develop coal-using machines.