Friedman rule is a monetary policy that was proposed by renowned economist Milton Friedman in 1969. The Friedman rule encourages setting the nominal interest rate to zero. As per the rule, a positive nominal interest rate generates inefficiency losses for society as there stands a gap between the private marginal cost of holding money, which is nominal interest rate, and the social marginal cost of producing money, which is practically zero. Thus, it implies that the central bank should seek a rate of deflation equal to the real interest rate.
Arguments in the favor of Friedman rule
Friedman argued that if any consumer saves on cash balances, an economy cannot be economically efficient. Consumers shouldn’t be constrained by immediate shortages of cash, but rather by their average flow of income. Wasteful saving of cash would be avoided if money earned a real rate of interest equal to consumers’ rate of time preference. The quantity of money which would be held by society in this situation is called the optimum quantity of money. 
Friedman established his main argument in the context of “a hypothetical simple society” wherein money is the only asset with no bonds and no physical capital. In this case, the optimal real rate of return on money (which is approximately equal to the deflation rate) is the subjective interest rate. Friedman then introduced default-free bonds and riskless physical capital, and argued that the policy maker can achieve his objective by choosing a rate of deflation that will make the nominal interest rate equal to zero. He made his arguments in terms of first order conditions that must hold in steady state equilibrium, but did not specify the agents’ problems. 
The theoretical optimality of the Friedman rule isn’t that compatible with real life results. In practice, economies that function with nominal interest rates of zero or near zero have been found to be performing poorly instead of performing well. In fact, typical experiences with low nominal interest rates such as those of Japan and the US in the recent past have indicated that low nominal interest rates are associated with severe and long-lasting recessions.
The Friedman rule has received acceptance and praise from economists around the world. Peter N. Ireland has demonstrated its optimality in monetary economies with monopolistic competition. Wilson, and Cole & Kocherlakota assessed Friedman’s proposals using fully-specified, general equilibrium models in which money is introduced through the imposition of a cash-in-advance constraint, and they confirmed the relevancy of the Friedman rule by demonstrating that equilibrium allocations are efficient only when the nominal interest rates are zero. However, they also discovered that the Friedman rule could be implemented through an array of monetary policies. Some of these policies call for the money supply to expand over an arbitrarily long, but finite horizon while others call for the money supply to contract at a rate slower than the representative household’s rate of time preference.
Chari, Christiano, and Kehoe showed the optimality of the Friedman rule in three distinct monetary models with distorting tax rates, and showed that there is no connection between the optimality of the Friedman rule and interest elasticity of money demand.
- The Optimum Quantity of Money: And Other Essays by Milton Friedman – Aldine Transaction – December 1969
- Costly Intermediation and the Friedman Rule by Benjamin Eden, Vanderbilt University – March 2012
- The sub-optimality of the Friedman rule and the Optimum Quantity of Money by Beatrix Paal, Stanford University – October 2000
- An Infinite Horizon Model with Money by Charles Wilson. In Jerry R. Green and Jose Alexandre Scheinkman, eds. General Equilibrium, Growth, and Trade: Essays in Honor of Lionel McKenzie. New York: Academic Press – 1979.
- Zero Nominal Interest Rates: Why They’re Good and How to Get Them by Harold L. Cole and Narayana Kocherlakota – Federal Reserve Bank of Minneapolis Quarterly Review 22 (Spring 1998)
- Implementing the Friedman Rule by Peter N. Ireland – National Bureau of Economic Research, Working Paper 8821 – March 2002
- Optimality of the Friedman Rule in Economies with Distorting Taxes by V. V. Chari, Lawrence J. Christiano, and Patrick J. Kehoe – Federal Reserve Bank of Minneapolis, Research Department Staff Report #158 – July 1993