The Friedman rule is a monetary policy rule proposed by Milton Friedman. Essentially, Friedman advocated setting the nominal interest rate at zero. According to the logic of the Friedman rule, the opportunity cost of holding money faced by private agents should equal the social cost of creating additional fiat money. It is assumed that the marginal cost of creating additional money is zero (or approximated by zero). Therefore, nominal rates of interest should be zero. In practice, this means that the central bank should seek a rate of deflation equal to the real interest rate on government bonds and other safe assets, to make the nominal interest rate zero.
The result of this policy is that those who hold money don't suffer any loss in the value of that money due to inflation. The rule is motivated by long-run efficiency considerations.
This is not to be confused with Friedman's k-percent rule which advocates a constant yearly expansion of the monetary base.
The Friedman rule has been shown to be the welfare maximizing monetary policy in many economic models of money. It has been shown to be optimal in monetary economies with monopolistic competition (Ireland, 1996) and, under certain circumstances, in a variety of monetary economies where the government levies other distorting taxes. However, there do exist several notable cases where deviation from the Friedman Rule becomes optimal. These include economies with decreasing returns to scale; economies with imperfect competition where the government does not either fully tax monopoly profits or set the tax equal to the labor income tax; economies with tax evasion; economies with sticky prices; and economies with downward nominal wage rigidity. While normally deviations from the Friedman Rule are typically small, if there is a significant foreign demand for a nation's currency, such as in the United States, the optimal rate of inflation is found to deviate significantly from what is called for by Friedman Rule in order to extract seigniorage revenue from foreign residents. In the case of the United States, where over half of all U.S. dollars are held overseas, the optimal rate of inflation is found to be anywhere from 2 to 10%, whereas the Friedman Rule would call for deflation of almost 4%.