How Substitutable are Fixed Factors in Production? Evidence from Pre-industrial England

The extent to which fixed factors of production such as land constrain per-capita income growth has been a widely discussed topic in economics since at least Malthus (1798). Whether fixed factors limit growth depends crucially on two variables: the substitutability of fixed factors in production, and the extent to which innovation will be biased towards land-saving technologies. However, there are few estimates of either variable, and most models assume this elasticity of substitution is unity out of con- venience. This paper attempts to fill that gap in the literature. Using the timing of plague epidemics as an instrument for labor supply, this paper estimates the elasticity of substitution between fixed and non-fixed factors in pre-industrial England. I find that the elasticity of substitution between land and other factors during this period was signicantly less than one, which implies that the Malthusian effects of population on income were stronger than current models predict. In addition, I am able to esti- mate the direction and magnitude of induced innovation. I find evidence that denser populations -- and hence higher land scarcity -- induced innovation towards land-saving technologies. Specically, I find that a doubling of population density in England from its year 1500 level raises the difference in the growth rates of land- and labor-enhancing productivity by 0.22% per year.