Malthus in state space: Macro economic-demographic relations in English history, 1540 to 1870

The history of preindustrial Europe provides an opportunity to examine the causes and consequences of population change at a macro level. However, serious statistical problems arise from the endogeneity of all observed variables in a Malthusian system (fertility, mortality, population size, and real wages), and from unobserved influences such as shifts in the demand for labor and variations in health. These problems have undermined both informal inference from the data and more complex econometric investigations. This paper takes a new statistical approach, finding the maximum likelihood estimate of a state space representation of the Malthusian system by repeated application of Kalman filter methods, using annual data from England, 1540 to 1870. The new estimates confirm some findings of the earlier literature and contradict others. Some variables are estimated for the first time. Implications are discussed for the interpretation of English economic-demographic history.