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Optimal monetary policy maximizes the welfare of a representative agent, given frictions in the economic environment. Constructing a model with two sets of frictions-costly price adjustment by imperfectly competitive firms and costly exchange of wealth for goods-we find optimal monetary policy is governed by two familiar principles. First, the average level of the nominal interest rate should be sufficiently low, as suggested by Milton Friedman, that there should be deflation on average. Yet, the Keynesian frictions imply that the optimal nominal interest rate is positive. Second, as various shocks occur to the real and monetary sectors, the price level should be largely stabilized, as suggested by Irving Fisher, albeit around a deflationary trend path. Since expected inflation is roughly constant through time, the nominal interest rate must therefore vary with the Fisherian determinants of the real interest rate. Although the monetary authority has substantial leverage over real activity in our model economy, it chooses real allocations that closely resemble those which would occur if prices were flexible. In our benchmark model, there is some tendency for the monetary authority to smooth nominal and real interest rates.

The St. Louis model of the early 1970s, as described by Andersen and Carlson (1972), was a small-scale monetarist model of economic activity. Its structure was sharply at variance with the framework of the major, larger scale macroeconometric models used for policy analysis by the Federal Reserve, both at the time of the inception of the St. Louis model and today.The St. Louis model had four major features:• It was sufficiently small that one could actually understand how it worked by looking at the model' s behavioral equations and by conducting simulations of it.• It could be used for policy analysis, specifically for studying the effects of monetary and fiscal policy on inflation, output, and interest rates.• The monetarist background of its authors meant that the model (1) focused on the quantity of money as the key measure of the stance of monetary policy and (2) contained structural linkages from money to economic activity that are now widely accepted, including the central role of a long-run demand for money that is a relatively stable function of a small number of variables.• It combined short-run non-neutrality of changes in money with long-run neutrality, in line with the perspective of Friedman and Schwartz (1963a and b).With Lucas' (1976) critique of policy evaluation, the St. Louis model was largely abandoned by monetarists. The model fell victim to the critique in a particularly rapid and complete manner because its builders had stressed that it contained quantitatively important effects of expectations. 1In this article, we construct a smallscale modern macroeconomic model that can be used to study the effects of alternative monetary and fiscal policies in a manner consistent with Lucas' recommendations. That is, we build a rational expectations macroeconomic model in which the intertemporal optimization problems of households and firms are explicitly described. We call this a St. Louis model of the 21st century because we believe it is the type of small-scale macroeconomic model that will be systematically employed for the purpose of policy analysis by central banks in the coming years. The model is monetarist in five specific ways that it shares with the St. Louis model:• Our model contains a stable demand for money that is invariant to alternative monetary policies.• It incorporates short-run nonneutrality of money with long-run neutrality.• Frictions in the price-setting process yield a short-run non-neutrality of money that is quantitatively and economically important.

In a plain-vanilla New Keynesian model with two-period staggered price-setting, discretionary monetary policy leads to multiple equilibria. Complementarity between the pricing decisions of forward-looking firms underlies the multiplicity, which is intrinsically dynamic in nature. At each point in time, the discretionary monetary authority optimally accommodates the level of predetermined prices when setting the money supply because it is concerned solely about real activity. Hence, if other firms set a high price in the current period, an individual firm will optimally choose a high price because it knows that the monetary authority next period will accommodate with a high money supply. Under commitment, the mechanism generating complementarity is absent: the monetary authority commits not to respond to future predetermined prices. We compute a traditional inflation bias equilibrium, in which price-setters are optimistic, rationally expecting small adjustments by other firms. But there is another steady-state equilibrium in which price setters are pessimistic and inflation is much higher. Further, we find that there are multiple equilibria at a point in time, not just in steady states. In a stochastic setting with equilibrium selection each period determined by an i.i.d. sunspot, there is greater inflation bias on average than if price-setters were always optimistic. The sunspot realization also has real effects: periods of higher than average inflation are accompanied by low output. Thus, increased real volatility may be an additional cost of discretion in monetary policy.

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