رد نظریه سلطه تعادل پولی پاره تو

It is well known that under nominal money supply rules accomplished through lump sum transfers, non-uniqueness and non-optimality of the resource allocation often obtains in monetary models. We show that uniqueness and optimality of the resource allocation obtains if the monetary authority conducts Friedman's rule through open market operations. Our result necessitates and we provide a clarification of existing irrelevance theorems for open market operations. Our result also provides a partial resolution of the uniqueness-efficiency conflict of nominal money supply rules raised by Woodford (Economic Theory 4 (1994) 345–380).

Monetary policy determines the composition of the government's portfolio. This fact has been underemphasized in the study of nominal money supply rules. Early work on equilibrium monetary models, such as Brock 1974 and Brock 1975 and Lucas and Stokey 1983 and Lucas and Stokey 1987, studied monetary policies of the k-percent rule recommended by Milton Friedman. In these models, changes in the money stock are accomplished through nominal lump sum transfers. Subsequently, researchers, including Gray (1984), Matsuyama 1990 and Matsuyama 1991, Obstfeld and Rogoff 1983 and Obstfeld and Rogoff 1986, Obstfeld (1984), Woodford (1994), show, in both cash-in-advance and money-in-the-utility function models, that nominal money supply rules under lump sum taxes can imply multiple equilibria. Often, there are important differences in welfare across equilibria. If monetary policy determines the composition of the government's portfolio, then the emphasis given to lump sum injections may be misplaced.

Friedman's rule through open market operations ensures that any monetary equilibrium that obtains in the Lucas–Stokey model is pareto optimal. If additionally, agents do not hold excess cash (than is necessary to make purchases), then the equilibrium is globally unique in both real and nominal variables. Neither of these statements is generally true when Friedman's rule is accomplished through lump sum taxes. We explained how this result is consistent with existing irrelevance theorems for open market operations. In addition, we offered a partial solution to the ‘conflict between the aims of choosing a money supply growth rate that results in a high level of welfare in the steady state equilibrium and choosing a rate that makes this steady state the unique equilibrium (Woodford 1994, p. 345)’. By implementing Friedman's rule through open market operations, the monetary authority can ensure a unique, pareto optimal resource allocation. It is true, however, that in absence of our assumption (13), the nominal price sequence is not unique under OMO. If this is the case, why would anyone care about this result?