Estimating the Inflation-Output Variability Frontier with Inflation Targeting: A VAR Approach

This paper (i) illustrates how a VAR model can be used to evaluate inflation targeting, (ii) derives the policy frontier available to the central bank using counterfactual experiments with real time data, and (iii) estimates how this frontier has changed over time in terms of the position and slope of the available tradeoff between output gap variability and inflation variability under inflation targeting. Various inflation targets are considered as are tolerance bands of varying width around these targets. The results indicate that over time (i) a given reduction in inflation variability is associated with a smaller rise in output variability and that (ii) a given inflation variability is achieved with smaller interest rate volatility. Consistent with the data, our results require federal funds rate persistence, though no instrument instability was observed.

Inflation Forecast Targeting: A VAR Approach

We show how to implement inflation forecast targeting using a VAR model and derive the implied inflation-output variability frontier. Our approach is based on dynamic, stochastic simulations of the average inflation rate over a two-year horizon using the moving average representation of the VAR model. Using real time data over two samples, we estimate the inflation-output variability frontier for the U.S. and show that it has shifted favorably over time. We consider the frequency and nature of the policy interventions required to achieve target inflation in both samples and compare these interventions over time.

Estimating the Inflation-Output Variability Frontier with Inflation Targeting: A VAR Approach

This paper (i) illustrates how a VAR model can be used to evaluate inflation targeting, (ii) derives the policy frontier available to the central bank using counterfactual experiments with real time data, and (iii) estimates how this frontier has changed over time in terms of the position and slope of the available tradeoff between output gap variability and inflation variability under inflation targeting. Various inflation targets are considered as are tolerance bands of varying width around these targets. The results indicate that over time (i) a given reduction in inflation variability is associated with a smaller rise in output variability and that (ii) a given inflation variability is achieved with smaller interest rate volatility. Consistent with the data, our results require federal funds rate persistence, though no instrument instability was observed. One interpretation of these results is that they reflect the growing credibility of the Federal Reserve.

Quantum imaging of spin states in optical lattices

We investigate imaging of the spatial spin distribution of atoms in optical lattices using non-resonant light scattering. We demonstrate how scattering spatially correlated light from the atoms can result in spin state images with enhanced spatial resolution. Furthermore, we show how using spatially correlated light can lead to direct measurement of the spatial correlations of the atomic spin distribution

Multi-latin squares

A multi-latin square of order $n$ and index $k$ is an $n\times n$ array of multisets, each of cardinality $k$, such that each symbol from a fixed set of size $n$ occurs $k$ times in each row and $k$ times in each column. A multi-latin square of index $k$ is also referred to as a $k$-latin square. A $1$-latin square is equivalent to a latin square, so a multi-latin square can be thought of as a generalization of a latin square. In this note we show that any partially filled-in $k$-latin square of order $m$ embeds in a $k$-latin square of order $n$, for each $n\geq 2m$, thus generalizing Evans' Theorem. Exploiting this result, we show that there exist non-separable $k$-latin squares of order $n$ for each $n\geq k+2$. We also show that for each $n\geq 1$, there exists some finite value $g(n)$ such that for all $k\geq g(n)$, every $k$-latin square of order $n$ is separable. We discuss the connection between $k$-latin squares and related combinatorial objects such as orthogonal arrays, latin parallelepipeds, semi-latin squares and $k$-latin trades. We also enumerate and classify $k$-latin squares of small orders.Comment: Final version as sent to journa