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We model the Industrial Revolution in Britain using a directed technological change model. The industrial sector of the economy has two sub-sectors, a wood-using and a coal-using sector, each of which has fuel-specific varieties of machines. Wood is supplied inelastically and coal elastically. In a departure from the existing endogenous technological change literature, we allow the elasticity of substitution between machines and energy to be less than unity. The outputs from these two sub-sectors combine into a composite final good through a constant elasticity of substitution production function with an elasticity of substitution of greater than unity. As the labor force grows exogenously, the amount of wood per worker declines and the price of wood rises. This fosters an increasing shift of innovative activity to the coal-using sector where the supply of energy can be increased without limit. New types of coal-using machines are developed, which were necessary to expand the use of coal to new applications.
The model produces behaviour that matches the stylised facts of the British Industrial Revolution. We evaluate the role of coal in driving growth by comparing our model results to the available historical data, carrying out counterfactual simulations, and carrying out a comprehensive Monte Carlo analysis of the effects of the model parameters on growth behaviour. We generate more realistic behaviour when we allow the elasticity of substitution between energy and machines to be less than unity.