Quantum gravity in three dimensions, Witten spinors and the quantisation of length

In this paper, I investigate the quantisation of length in euclidean quantum gravity in three dimensions. The starting point is the classical hamiltonian formalism in a cylinder of finite radius. At this finite boundary, a counter term is introduced that couples the gravitational field in the interior to a two-dimensional conformal field theory for an SU(2) boundary spinor, whose norm determines the conformal factor between the fiducial boundary metric and the physical metric in the bulk. The equations of motion for this boundary spinor are derived from the boundary action and turn out to be the two-dimensional analogue of the Witten equations appearing in Witten's proof of the positive mass theorem. The paper concludes with some comments on the resulting quantum theory. It is shown, in particular, that the length of a one-dimensional cross section of the boundary turns into a number operator on the Fock space of the theory. The spectrum of this operator is discrete and matches the results from loop quantum gravity in the spin network representation.Comment: 22 pages, one figur

Learning, endogenous indexation and disinflation in the New-Keynesian Model

This paper introduces adaptive learning and endogenous indexation in the New-Keynesian Phillips curve and studies disinflation under inflation targeting policies. The analysis is motivated by the disinflation performance of many inflation-targeting countries, in particular the gradual Chilean disinflation with temporary annual targets. At the start of the disinflation episode price-setting firms’ expect inflation to be highly persistent and opt for backward-looking indexation. As the central bank acts to bring inflation under control, price-setting firms revise their estimates of the degree of persistence. Such adaptive learning lowers the cost of disinflation. This reduction can be exploited by a gradual approach to disinflation. Firms that choose the rate for indexation also re-assess the likelihood that announced inflation targets determine steady-state inflation and adjust indexation of contracts accordingly. A strategy of announcing and pursuing short-term targets for inflation is found to influence the likelihood that firms switch from backward-looking indexation to the central bank’s targets. As firms abandon backward-looking indexation the costs of disinflation decline further. We show that an inflation targeting strategy that employs temporary targets can benefit from lower disinflation costs due to the reduction in backward-looking indexation

Quantitative easing: a rationale and some evidence from Japan

This paper reviews the rationale for quantitative easing when central bank policy rates reach near zero levels in light of recent announcements regarding direct asset purchases by the Bank of England, the Bank of Japan, the U.S. Federal Reserve and the European Central Bank. Empirical evidence from the previous period of quantitative easing in Japan between 2001 and 2006 is presented. During this earlier period the Bank of Japan was able to expand the monetary base very quickly and significantly. Quantitative easing translated into a greater and more lasting expansion of M1 relative to nominal GDP. Deflation subsided by 2005. As soon as inflation appeared to stabilize near a rate of zero, the Bank of Japan rapidly reduced the monetary base as a share of nominal income as it had announced in 2001. The Bank was able to exit from extensive quantitative easing within less than a year. Some implications for the current situation in Europe and the United States are discussed

Fiscal stimulus and the promise of future spending cuts: a comment

Recent evaluations of the fiscal stimulus packages recently enacted in the United States and Europe such as Cogan, Cwik, Taylor and Wieland (2009) and Cwik and Wieland (2009) suggest that the GDP effects will be modest due to crowding-out of private consumption and investment. Corsetti, Meier and Mueller (2009a,b) argue that spending shocks are typically followed by consolidations with substantive spending cuts, which enhance the short-run stimulus effect. This note investigates the implications of this argument for the estimated impact of recent stimulus packages and the case for discretionary fiscal policy