Identifying Aggregate Demand and Aggregate Supply Components of Inflation Rate: A Structural Vector Autoregression Analysis for Japan

I estimate a bivariate output-price structural vector autoregression (VAR) model for Japan to decompose inflation rate time-series into two components explained by aggregate demand (AD) and aggregate supply (AS) shocks. For the modelfs identifying restriction, I assume that the long- run elasticity of output with respect to permanent changes in price due to AD shocks is zero; i.e., an AD shock has no long-run impact on the level of output. Dynamic properties of the estimated model are shown to be generally consistent with the predictions of the conventional AS-AD framework. The main features of the historical decomposition are the following: (1) the inflation rate explained by the AD shock shows a procyclical swing since 1970; (2) the inflation rate explained by the AS shock temporarily spikes during the two oil crises and experiences a large countercyclical swing in the 1990s; and (3) the coincidence of large and negative AS and AD shocks explains the combination of price stability and output stagnation during two recessions in the 1990s. These results are qualitatively robust to the sectoral shocks, alternative choices for the price variable, and assumptions for the lag length of VAR and the long-run elasticity of output with respect to permanent changes in price due to AD shocks. However, the bivariate approach does not allow the identification of more than three types of shocks with different dynaic effects on output and price. It might be necessary to expand the model to deal with this limitation.

The Phillips Curve and Underlying Inflation

This paper examines methods of controlling the supply shock in the estimation of the Phillips curve and discusses the relationship between the supply shock and inflation inertia. The empirical results clearly show that controlling the supply shock effect, not only for current inflation but also for lagged inflation using the asymmetry of the price change distribution, substantially outperforms the traditional method in terms of the robustness to alternative lag specifications, predictive power, and parameter stability for changes in the estimation period, which are the essential properties for the practical use of the Phillips curve. These results suggest that (1) because supply shocks hit broad sectors, it is not appropriate to restrict the proxy for the supply shock to the relative price changes of a fixed commodity basket; and (2) the inflation inertia corresponds to the underlying inflation from which the supply shock effect has been eliminated.

The quadratic form E_8 and exotic homology manifolds

An explicit (-1)^n-quadratic form over Z[Z^{2n}] representing the surgery problem E_8 x T^{2n} is obtained, for use in the Bryant-Ferry-Mio-Weinberger construction of 2n-dimensional exotic homology manifolds.Comment: This is the version published by Geometry & Topology Monographs on 22 April 200

On the Problem of Computing the Probability of Regular Sets of Trees

We consider the problem of computing the probability of regular languages of infinite trees with respect to the natural coin-flipping measure. We propose an algorithm which computes the probability of languages recognizable by \emph{game automata}. In particular this algorithm is applicable to all deterministic automata. We then use the algorithm to prove through examples three properties of measure: (1) there exist regular sets having irrational probability, (2) there exist comeager regular sets having probability $0$ and (3) the probability of \emph{game languages} $W_{i,k}$, from automata theory, is $0$ if $k$ is odd and is $1$ otherwise

Lukasiewicz mu-Calculus

We consider state-based systems modelled as coalgebras whose type incorporates branching, and show that by suitably adapting the definition of coalgebraic bisimulation, one obtains a general and uniform account of the linear-time behaviour of a state in such a coalgebra. By moving away from a boolean universe of truth values, our approach can measure the extent to which a state in a system with branching is able to exhibit a particular linear-time behaviour. This instantiates to measuring the probability of a specific behaviour occurring in a probabilistic system, or measuring the minimal cost of exhibiting a specific behaviour in the case of weighted computations