Rigorous Confidence Intervals on Critical Thresholds in 3 Dimensions

We extend the method of Balister, Bollob\'as and Walters for determining rigorous confidence intervals for the critical threshold of two dimensional lattices to three (and higher) dimensional lattices. We describe a method for determining a full confidence interval and apply it to show that the critical threshold for bond percolation on the simple cubic lattice is between 0.2485 and 0.2490 with 99.9999% confidence, and the critical threshold for site percolation on the same lattice is between 0.3110 and 0.3118 with 99.9999% confidence

Unital hyperarchimedean vector lattices

We prove that the category of unital hyperarchimedean vector lattices is equivalent to the category of Boolean algebras. The key result needed to establish the equivalence is that, via the Yosida representation, such a vector lattice is naturally isomorphic to the vector lattice of all locally constant real-valued continuous functions on a Boolean (=compact Hausdorff totally disconnected) space. We give two applications of our main result.Comment: 15 pages. Submitted pape

Agricultural influences on carbon emissions and sequestration

This report was presented at the UK Organic Research 2002 Conference. Agricultural systems contribute to carbon emissions through several mechanisms: the direct use of fossil fuels in farm operations, the indirect use of embodied energy in inputs that are energy intensive to manufacture (e.g. fertilizers), and the cultivation of soils resulting in the loss of soil organic matter. However agriculture can also sequester carbon when organic matter accumulates in the soil or above-ground woody biomass acts as a permanent sink or is used as an energy source that substitutes for fossil fuels. The latest empirical data on agricultural carbon emissions and carbon sequestration opportunities in agricultural systems are reviewed and the necessary land use and management practices that will need to be employed to optimise carbon sequestration are considered

What Do Budget Deficits Do?

This paper discusses the effects of budget deficits on the economy in four steps. First, it reviews standard theory about how budget deficits influence saving, investment, the trade balance, interest rates, exchange rates, and long-term growth. Second, it offers a rough estimate of the magnitude of some of the effects. Third, it discusses how budget deficits affect economic welfare. Finally, it considers the possibility that continuing budget deficits in a country could lead to a 'hard landing' in which the demand for the country's assets suddenly collapses.

A Sticky-Price Manifesto

Macroeconomists are divided on the best way to explain short-run economic fluctuations. This paper presents the case for traditional theories based on short-run price stickiness. It discusses the fundamental basis for believing in this class of macreconomic models. It also discusses recent research on the microeconomic foundations of sticky prices.

The NAIRU in Theory and Practice

This paper discusses the NAIRU -- the non-accelerating inflation rate of unemployment. It first considers the role of the NAIRU concept in business cycle theory, arguing that this concept is implicit in any model in which monetary policy influences both inflation and unemployment. The exact value of the NAIRU is hard to measure, however, in part because it changes over time. The paper then discusses why the NAIRU changes and, in particular, why it fell in the United States during the 1990s. The most promising hypothesis is that the decline in the NAIRU is attributable to the acceleration in productivity growth.

Intergenerational Risk Sharing in the Spirit of Arrow, Debreu, and Rawls, with Applications to Social Security Design

This paper examines the optimal allocation of risk in an overlapping-generations economy. It compares the allocation of risk the economy reaches naturally to the allocation that would be reached if generations behind a Rawlsian 'veil of ignorance' could share risk with one another through complete Arrow-Debreu contingent-claims markets. The paper then examines how the government might implement optimal intergenerational risk sharing with a social security system. One conclusion is that the system must either hold equity claims to capital or negatively index benefits to equity returns.

The NAIRU in Theory and Practice

This paper discusses the NAIRU - the non-accelerating inflation rate unemployment. It first considers the role of the NAIRU concept in business cycle theory, arguing that this concept is implicit in any model in which monetary policy influences both inflation and unemployment. The exact value of the NAIRU is hard to measure, however, in part because it changes over time. The paper then discusses why the NAIRU changes and, in particular, why it fell in the United States during the 1990s. The most promising hypothesis is that the decline in the NAIRU is attributable to the acceleration in productivity growth.