Directed technical change and the British Industrial Revolution

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 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 eventual dominance by the coal-using
sector, is the model's main 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.