Are money demand equations still alive and kicking? Historical evidence of cointegration for the UK, using nonlinear techniques

Since the influential works of Friedman and Schwartz (1963, 1982) and Hendry and Ericsson (1991), on the monetary history of the United States of America and the United Kingdom from 1876 to 1975, there has been a great concern in the literature about the instability of money demand functions. This concern together with the results of the New Keynesian´s models (Woodford, 2003), produced the abandon of money as an instrument of monetary policy. Recently, using M1 as the measure of money, Benati, Lucas, Nicolini and Weber (2021) have shown, for a shorter and recent period of time, that there is a stable long-run money demand for a long list of countries. However, to date there are no studies showing that stable long-run and short-run money demand equations exist since the XIX century and how it can be used to inform monetary policy based on the quantitative theory of money. By means of nonlinear cointegration and nonlinear error-correction models, this paper presents evidence of UK stable long-run and short-run money demands of real broad monetary balances from 1874 to 2023. These equations provide with key elements to identify periods of excess money demand generating periods of 6.5% excess inflation, over the historical 2.2% average. Stable Money demand estimates provide useful policy rules and additional cross-check instruments for monetary policy to reach inflation targets. Furthermore, they help identifying spurious transmission channels of monetary policy, when theoretical models impose invalid common factor restrictions.