Monetary discretion, pricing complementarity and dynamic multiple equilibria

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. Multiple equilibria also arise in other similar contexts where (i) a policymaker cannot commit, and (ii) forward-looking agents determine a state variable to which future policy respond. JEL Klassifikation: E5, E61, D7

Monetary Discretion, Pricing Complementarity and Dynamic Multiple Equilibria

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.

Inflation targeting in a St. Louis model of the 21st century

Federal Reserve Bank of St. Louis ; Inflation (Finance)

Monetary discretion, pricing complementarity and dynamic multiple equilibria

In a plain-vanilla New Keynesian model with two-period staggered price-setting, discretionary monetary policy leads to multiple equilibria. Complementarity between 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. Multiple equilibria also arise in other similar contexts where (i) a policymaker cannot commit, and (ii) forward-looking agents determine a state variable to which future policy responds. JEL Classification: E5, E61, D78complementarity, discretion, monetary policy, Multiple Equilibria, time-consistency

Monetary Discretion, Pricing Complementarity and Dynamic Multiple Equilibria

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. Multiple equilibria also arise in other similar contexts where (i) a policymaker cannot commit, and (ii) forward-looking agents determine a state variable to which future policy responds.Monetary Policy, Discretion, Time-Consistency, Multiple Equilibria, Complementarity

Smooth bumps, a Borel theorem and partitions of smooth functions on p.c.f. fractals

We provide two methods for constructing smooth bump functions and for smoothly cutting off smooth functions on fractals, one using a probabilistic approach and sub-Gaussian estimates for the heat operator, and the other using the analytic theory for p.c.f. fractals and a fixed point argument. The heat semigroup (probabilistic) method is applicable to a more general class of metric measure spaces with Laplacian, including certain infinitely ramified fractals, however the cut off technique involves some loss in smoothness. From the analytic approach we establish a Borel theorem for p.c.f. fractals, showing that to any prescribed jet at a junction point there is a smooth function with that jet. As a consequence we prove that on p.c.f. fractals smooth functions may be cut off with no loss of smoothness, and thus can be smoothly decomposed subordinate to an open cover. The latter result provides a replacement for classical partition of unity arguments in the p.c.f. fractal setting.Comment: 26 pages. May differ slightly from published (refereed) versio

Optimal Monetary Policy

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 pitfalls of discretionary monetary policy.

In a canonical staggered pricing model, monetary discretion leads to multiple private sector equilibria. The basis for multiplicity is a form of policy complementarity. Specifically, prices set in the current period embed expectations about future policy, and actual future policy responds to these same prices. For a range of values of the fundamental state variable — a ratio of predetermined prices — there is complementarity between actual and expected policy, and multiple equilibria occur. Moreover, this multiplicity is not associated with reputational considerations: it occurs in a two-period model.Monetary policy