Unbounded asymmetry of stretch factors

A result of Handel-Mosher guarantees that the ratio of logarithms of stretch factors of any fully irreducible automorphism of the free group $F_N$ and its inverse is bounded by a constant $C_N$. In this short note we show that this constant $C_N$ cannot be chosen independent of $N$.Comment: 2 page

How forward-looking is the Fed? Direct estimates from a ‘Calvo-type’ rule

We estimate an alternative type of monetary policy rule, termed Calvo rule, according to which the central bank is assumed to target a discounted infinite sum of future expected inflation. Compared to conventional inflation forecast-based rules, which are typically of the Taylor-type with discrete forward looking horizons, this class of rule is less prone to the problem of indeterminacy. Parameter estimates obtained from GMM estimation provide support for Calvo-type rules, suggesting that the Federal Reserve targeted a mean forward horizon of between 4 and 8 quarters.Calvo-type interest rules, Inflation Forecast Based rules, GMM, indeterminacy.

VALUING WATER QUALITY MONITORING: A CONTINGENT VALUATION EXPERIMENT INVOLVING HYPOTHETICAL AND REAL PAYMENTS

This paper studies the preferences and willingness-to-pay for individuals for volunteer water quality monitoring programs. The study involves supporting water quality monitoring at two ponds in the state of Rhode Island. The paper uses both a hypothetical and a real-payment contingent valuation survey to directly measure individual preferences and willingness-to-pay (WTP) for volunteer water quality monitoring at the two ponds. The overall results of the study suggest that hypothetical WTP is not statistically greater than real WTP, and that the average survey respondent is willing to support water quality monitoring on one of the two ponds. The study also finds that the specified purpose of water quality monitoring and certain socioeconomic characteristics of a respondent significantly affect the respondent's decision to support volunteer water quality monitoring.Environmental Economics and Policy,

Strongly Peraluminous Granites across the Archean–Proterozoic Transition

Strongly peraluminous granites (SPGs) form through the partial melting of metasedimentary rocks and therefore represent archives of the influence of assimilation of sedimentary rocks on the petrology and chemistry of igneous rocks. With the aim of understanding how variations in sedimentary rock characteristics across the Archean–Proterozoic transition might have influenced the igneous rock record, we compiled and compared whole-rock chemistry, mineral chemistry, and isotope data from Archean and Paleo- to Mesoproterozoic SPGs. This time period was chosen as the Archean–Proterozoic transition broadly coincides with the stabilization of continents, the rise of subaerial weathering, and the Great Oxidation Event (GOE), all of which left an imprint on the sedimentary rock record. Our compilation of SPGs is founded on a detailed literature review of the regional geology, geochronology, and inferred origins of the SPGs, which suggest derivation from metasedimentary source material. Although Archean and Proterozoic SPGs are similar in terms of mineralogy or major-element composition owing to their compositions as near-minimum melts in the peraluminous haplogranite system, we discuss several features of their mineral and whole-rock chemistry. First, we review a previous analysis of Archean and Proterozoic SPGs biotite and whole-rock compositions indicating that Archean SPGs, on average, are more reduced than Proterozoic SPGs. This observation suggests that Proterozoic SPGs were derived from metasedimentary sources that on average had more oxidized bulk redox states relative to their Archean counterparts, which could reflect an increase in atmospheric O₂ levels and more oxidized sedimentary source rocks after the GOE. Second, based on an analysis of Al₂O₃/TiO₂ whole-rock ratios and zircon saturation temperatures, we conclude that Archean and Proterozoic SPGs formed through partial melting of metasedimentary rocks over a similar range of melting temperatures, with both ‘high-’ and ‘low-’temperature SPGs being observed across all ages. This observation suggests that the thermo-tectonic processes resulting in the heating and melting of metasedimentary rocks (e.g. crustal thickening or underplating of mafic magmas) occurred during generation of both the Archean and Proterozoic SPGs. Third, bulk-rock CaO/Na₂O, Rb/Sr, and Rb/Ba ratios indicate that Archean and Proterozoic SPGs were derived from partial melting of both clay-rich (i.e. pelites) and clay-poor (i.e. greywackes) source regions that are locality specific, but not defined by age. This observation, although based on a relatively limited dataset, indicates that the source regions of Archean and Proterozoic SPGs were similar in terms of sediment maturity (i.e. clay component). Last, existing oxygen isotope data for quartz, zircon, and whole-rocks from Proterozoic SPGs show higher values than those of Archean SPGs, suggesting that bulk sedimentary ¹⁸O/¹⁶O ratios increased across the Archean–Proterozoic boundary. The existing geochemical datasets for Archean and Proterozoic SPGs, however, are limited in size and further work on these rocks is required. Future work must include detailed field studies, petrology, geochronology, and constraints on sedimentary source ages to fully interpret the chemistry of this uniquely useful suite of granites

Large igneous provinces track fluctuations in subaerial exposure of continents across the Archean–Proterozoic transition

Geological observations and numerical models imply that Archean continents were mostly submarine. In contrast, approximately one third of modern earth's surface area consists of subaerial continental crust. To temporally constrain changes in the subaerial exposure of continents, we evaluate the eruptive environment (submarine vs subaerial) of 3.4–2.0 Ga continental large igneous provinces (LIPs). Our results indicate that up until 2.4 Ga LIPs predominantly erupted onto submerged continents. This period of low freeboard was punctuated by local subaerial eruptions at 2.8–2.7 Ga and 2.5 Ga. From 2.4 Ga–2.2 Ga, extensive subaerial continental volcanism is recorded in six different cratons, supporting widespread subaerial continents at this time. An increase in exposed continental crust significantly impacts atmospheric and oceanic geochemical cycles and the supply of nutrients for marine bioproductivity. Thus, the 2.4–2.2 Ga high-freeboard conditions may have triggered the earliest global glaciation event and the first significant rise of atmospheric oxygen