Open Market Operations and Money Supply at Zero Nominal Interest Rates Roberto Robatto∗ University of Chicago October 21, 2012 (first draft: February 2012) Abstract What are the paths of money supply that are consistent with zero nominal interest rates and that can be implemented through open market operations? To answer this question, I present an Irrelevance Proposition for some open market operations that exchange money and one-period bonds at the zero lower bound. The result has implications for the conduct of monetary policy (non-irrelevant open market operations modify the equilibrium) and for the implementation of the Friedman rule (any growth rate of money supply above the negative of the rate of time preferences can implement zero nominal interest rate forever, even a positive growth rate, provided that the government collects \large enough" surpluses). The result holds under several specifications, including models with heterogeneity, non- separable utility, borrowing constraints, incomplete and segmented markets and sticky prices; and generalizes to any situation in which the cost of holding money vs. bonds is zero, such as the payment of interest on money. ∗Email:
[email protected]. I am extremely greatful to Fernando Alvarez for his suggestions and guidance. I would like to thank also John Cochrane, Thorsten Drautzburg, Tom Sargent, Harald Uhlig and participants to the AMT, Capital Theory and Economic Dynamics Working Groups at the University of Chicago for their comments. 1 1 Introduction At zero nominal interest rates, money is perfect substitutes for bonds from the point of view of the private sector. Money demand is thus not uniquely determined, therefore the equilibrium in the money market depends on the supply of money.