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

Locally accurate MPS approximations for ground states of one-dimensional gapped local Hamiltonians

A key feature of ground states of gapped local 1D Hamiltonians is their relatively low entanglement --- they are well approximated by matrix product states (MPS) with bond dimension scaling polynomially in the length $N$ of the chain, while general states require a bond dimension scaling exponentially. We show that the bond dimension of these MPS approximations can be improved to a constant, independent of the chain length, if we relax our notion of approximation to be more local: for all length-$k$ segments of the chain, the reduced density matrices of our approximations are $\epsilon$-close to those of the exact state. If the state is a ground state of a gapped local Hamiltonian, the bond dimension of the approximation scales like $(k/\epsilon)^{1+o(1)}$, and at the expense of worse but still $\text{poly}(k,1/\epsilon)$ scaling of the bond dimension, we give an alternate construction with the additional features that it can be generated by a constant-depth quantum circuit with nearest-neighbor gates, and that it applies generally for any state with exponentially decaying correlations. For a completely general state, we give an approximation with bond dimension $\exp(O(k/\epsilon))$, which is exponentially worse, but still independent of $N$. Then, we consider the prospect of designing an algorithm to find a local approximation for ground states of gapped local 1D Hamiltonians. When the Hamiltonian is translationally invariant, we show that the ability to find $O(1)$-accurate local approximations to the ground state in $T(N)$ time implies the ability to estimate the ground state energy to $O(1)$ precision in $O(T(N)\log(N))$ time.Comment: 24 pages, 3 figures. v2: Theorem 1 extended to include construction for general states; Lemma 7 & Theorem 2 slightly improved; figures added; lemmas rearranged for clarity; typos fixed. v3: Reformatted & additional references inserte

PrAGMATiC: a Probabilistic and Generative Model of Areas Tiling the Cortex

Much of the human cortex seems to be organized into topographic cortical maps. Yet few quantitative methods exist for characterizing these maps. To address this issue we developed a modeling framework that can reveal group-level cortical maps based on neuroimaging data. PrAGMATiC, a probabilistic and generative model of areas tiling the cortex, is a hierarchical Bayesian generative model of cortical maps. This model assumes that the cortical map in each individual subject is a sample from a single underlying probability distribution. Learning the parameters of this distribution reveals the properties of a cortical map that are common across a group of subjects while avoiding the potentially lossy step of co-registering each subject into a group anatomical space. In this report we give a mathematical description of PrAGMATiC, describe approximations that make it practical to use, show preliminary results from its application to a real dataset, and describe a number of possible future extensions

Motion of a vortex line near the boundary of a semi-infinite uniform condensate

We consider the motion of a vortex in an asymptotically homogeneous condensate bounded by a solid wall where the wave function of the condensate vanishes. For a vortex parallel to the wall, the motion is essentially equivalent to that generated by an image vortex, but the depleted surface layer induces an effective shift in the position of the image compared to the case of a vortex pair in an otherwise uniform flow. Specifically, the velocity of the vortex can be approximated by $U \approx (\hbar/2m)(y_0-\sqrt 2 \xi)^{-1}$, where $y_0$ is the distance from the center of the vortex to the wall, $\xi$ is the healing length of the condensate and $m$ is the mass of the boson.Comment: submitted to Phys Rev

Non-Volatile Magnonic Logic Circuits Engineering

We propose a concept of magnetic logic circuits engineering, which takes an advantage of magnetization as a computational state variable and exploits spin waves for information transmission. The circuits consist of magneto-electric cells connected via spin wave buses. We present the result of numerical modeling showing the magneto-electric cell switching as a function of the amplitude as well as the phase of the spin wave. The phase-dependent switching makes it possible to engineer logic gates by exploiting spin wave buses as passive logic elements providing a certain phase-shift to the propagating spin waves. We present a library of logic gates consisting of magneto-electric cells and spin wave buses providing 0 or p phase shifts. The utilization of phases in addition to amplitudes is a powerful tool which let us construct logic circuits with a fewer number of elements than required for CMOS technology. As an example, we present the design of the magnonic Full Adder Circuit comprising only 5 magneto-electric cells. The proposed concept may provide a route to more functional wave-based logic circuitry with capabilities far beyond the limits of the traditional transistor-based approach