40 Years of Empirical Evidence of Cointegration and Nonlinear Equilibrium Correction in UK Money Demand since the XIX Century

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 models, produced the abandonment 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 alternative stable longrun and short-run money demand equations exist since the XIX century. By means of nonlinear cointegration and nonlinear equilibrium corrections (NEC), we present empirical evidence of stable nonlinear UK money demands models of real broad money balances from 1877 to 2023. The properties of these NEC models are assessed via Monte Carlo simulations. Rational polynomials error-correction models are used to generate a simple nonlinear Granger´s representation theorem together with a two-step estimation procedure, which satisfies well-stablished asymptotic conditions. As a byproduct, with four different but stable money demand specifications, we empirically identify key abrupt historical periods, corresponding to World Wars I and II, regulatory changes and the COVID period, generating a common 6.5% excess inflation effect, over the historical 2.2% constant average inflation rate since 1877.