Deriving the Taylor Principle when the Central Bank Supplies Money

The paper presents a human-capital-based endogenous growth, cash- in-advance economy with endogenous velocity where exchange credit is produced in a decentralized banking sector, and money is supplied stochastically by the central bank. From this it derives an exact functional form for a general equilibrium 'Taylor rule'. The inflation coefficient is always greater than one when the velocity of money exceeds one; velocity growth enters the equilibrium condition as a separate variable. The paper then successfully estimates the magnitude of the coefficient on inflation from 1000 samples of Monte Carlo simulated data. This shows that it would be spurious to conclude that the central bank has a reaction function with a strong response to inflation in a 'Taylor principle' sense, since it is only meeting fiscal needs through the inflation tax. The paper also estimates several deliberately misspecified models to show how an inflation coefficient of less than one can result from model misspecification. An inflation coefficient greater than one holds theoretically along the balanced growth path equilibrium, making it a sharply robust principle based on the economy's underlying structural parameters.