The structure of the optimal income tax in the quasi-linear model

Existing numerical characterizations of the optimal income tax have been based on a limited number of model specifications. As a result, they do not reveal which properties are general. We determine the optimal tax in the quasi-linear model under weaker assumptions than have previously been used; in particular, we remove the assumption of a lower bound on the utility of zero consumption and the need to permit negative labor incomes. A Monte Carlo analysis is then conducted in which economies are selected at random and the optimal tax function constructed. The results show that in a significant proportion of economies the marginal tax rate rises at low skills and falls at high. The average tax rate is equally likely to rise or fall with skill at low skill levels, rises in the majority of cases in the centre of the skill range, and falls at high skills. These results are consistent across all the specifications we test. We then extend the analysis to show that these results also hold for Cobb-Douglas utility.

Radical Conservatism

In 1938, Yugoslav sculptor Oscar Nemon arrived in Britain, having fled the Nazi invasion of Brussels, where he was living with Magritte. He was part of the European avant-garde that came to the UK as a refugee. Shortly thereafter, Nemon proposed a bold architectural plan to construct a temple of universal ethics in London and was in correspondence over this with central figures in Britain. After the war, he became know for his portrayal of figures like Churchil, culminating in a bust of Margaret Thatcher that is currently at the Tory HQ. Shown at Castlefield Gallery in 2013-2014, Radical Conservatism was an exhibition that explored the space between these two moments and asked whether these two terms are really antithetical. In the British context in particular, where the European avant-garde never really took hold, a kind of reactionary modernism has always defined a culture wary of revolution. But today more than ever, with the left increasingly holding on to the past of the welfare state as an ideal, and the right quietly revolutionising our world through neoliberal reforms, the paradigms of radicalism and conservatism need to be redefined. Can conservatism be seen as a radical position in itself? If art is defined by a movement towards the new - could 'holding on to the past' stubbornly be seen as a critical position, now that neo-liberalism has forced a far more radical shift in politics than the left has managed in a long time? Curated by Pil and Galia Kollectiv, featuring work by Chris Evans, IRWIN, Pil and Galia Kollectiv, Joseph Lewis, Patrick Moran, Oscar Nemon and Public Movement and a symposium with contributions from Professor Alun Rowlands and Robert Garnett.

The MaPS project: mapping teacher conceptions of musical development

The chapter starts from the premise that an historically- and institutionally-formed orientation to music education at primary level in European countries privileges a nineteenth century Western European music aesthetic, with its focus on formal characteristics such as melody and rhythm. While there is a move towards a multi-faceted understanding of musical ability, a discrete intelligence and willingness to accept musical styles or 'open-earedness', there remains a paucity of documented evidence of this in research at primary school level. To date there has been no study undertaken which has the potential to provide policy makers and practitioners with insights into the degree of homogeneity or universality in conceptions of musical ability within this educational sector. Against this background, a study was set up to explore the following research questions: 1. What conceptions of musical ability do primary teachers hold a) of themselves and; b) of their pupils? 2. To what extent are these conceptions informed by Western classical practices? A mixed methods approach was used which included survey questionnaire and semi-structured interview. Questionnaires have been sent to all classroom teachers in a random sample of primary schools in the South East of England. This was followed up with a series of semi-structured interviews with a sub-sample of respondents. The main ideas are concerned with the attitudes, beliefs and working theories held by teachers in contemporary primary school settings. By mapping the extent to which a knowledge base for teaching can be resistant to change in schools, we can problematise primary schools as sites for diversity and migration of cultural ideas. Alongside this, we can use the findings from the study undertaken in an English context as a starting point for further investigation into conceptions of music, musical ability and assessment held by practitioners in a variety of primary school contexts elsewhere in Europe; our emphasis here will be on the development of shared understanding in terms of policies and practices in music education. Within this broader framework, our study can have a significant impact internationally, with potential to inform future policy making, curriculum planning and practice.

Separating the dynamical effects of climate change and ozone depletion. Part I: Southern Hemisphere stratosphere

A version of the Canadian Middle Atmosphere Model that is coupled to an ocean is used to investigate the separate effects of climate change and ozone depletion on the dynamics of the Southern Hemisphere (SH) stratosphere. This is achieved by performing three sets of simulations extending from 1960 to 2099: 1) greenhouse gases (GHGs) fixed at 1960 levels and ozone depleting substances (ODSs) varying in time, 2) ODSs fixed at 1960 levels and GHGs varying in time, and 3) both GHGs and ODSs varying in time. The response of various dynamical quantities to theGHGand ODS forcings is shown to be additive; that is, trends computed from the sum of the first two simulations are equal to trends from the third. Additivity is shown to hold for the zonal mean zonal wind and temperature, the mass flux into and out of the stratosphere, and the latitudinally averaged wave drag in SH spring and summer, as well as for final warming dates. Ozone depletion and recovery causes seasonal changes in lower-stratosphere mass flux, with reduced polar downwelling in the past followed by increased downwelling in the future in SH spring, and the reverse in SH summer. These seasonal changes are attributed to changes in wave drag caused by ozone-induced changes in the zonal mean zonal winds. Climate change, on the other hand, causes a steady decrease in wave drag during SH spring, which delays the breakdown of the vortex, resulting in increased wave drag in summer

Four-dimensional data assimilation and balanced dynamics

The problem of spurious excitation of gravity waves in the context of four-dimensional data assimilation is investigated using a simple model of balanced dynamics. The model admits a chaotic vortical mode coupled to a comparatively fast gravity wave mode, and can be initialized such that the model evolves on a so-called slow manifold, where the fast motion is suppressed. Identical twin assimilation experiments are performed, comparing the extended and ensemble Kalman filters (EKF and EnKF, respectively). The EKF uses a tangent linear model (TLM) to estimate the evolution of forecast error statistics in time, whereas the EnKF uses the statistics of an ensemble of nonlinear model integrations. Specifically, the case is examined where the true state is balanced, but observation errors project onto all degrees of freedom, including the fast modes. It is shown that the EKF and EnKF will assimilate observations in a balanced way only if certain assumptions hold, and that, outside of ideal cases (i.e., with very frequent observations), dynamical balance can easily be lost in the assimilation. For the EKF, the repeated adjustment of the covariances by the assimilation of observations can easily unbalance the TLM, and destroy the assumptions on which balanced assimilation rests. It is shown that an important factor is the choice of initial forecast error covariance matrix. A balance-constrained EKF is described and compared to the standard EKF, and shown to offer significant improvement for observation frequencies where balance in the standard EKF is lost. The EnKF is advantageous in that balance in the error covariances relies only on a balanced forecast ensemble, and that the analysis step is an ensemble-mean operation. Numerical experiments show that the EnKF may be preferable to the EKF in terms of balance, though its validity is limited by ensemble size. It is also found that overobserving can lead to a more unbalanced forecast ensemble and thus to an unbalanced analysis.

Asymptotic behavior at infinity of solutions of multidimensional second kind integral equations

We consider second kind integral equations of the form x(s) - (abbreviated x - K x = y ), in which Ω is some unbounded subset of Rn. Let Xp denote the weighted space of functions x continuous on Ω and satisfying x (s) = O(|s|-p ),s → ∞We show that if the kernel k(s,t) decays like |s — t|-q as |s — t| → ∞ for some sufficiently large q (and some other mild conditions on k are satisfied), then K ∈ B(XP) (the set of bounded linear operators on Xp), for 0 ≤ p ≤ q. If also (I - K)-1 ∈ B(X0) then (I - K)-1 ∈ B(XP) for 0 < p < q, and (I- K)-1∈ B(Xq) if further conditions on k hold. Thus, if k(s, t) = O(|s — t|-q). |s — t| → ∞, and y(s)=O(|s|-p), s → ∞, the asymptotic behaviour of the solution x may be estimated as x (s) = O(|s|-r), |s| → ∞, r := min(p, q). The case when k(s,t) = к(s — t), so that the equation is of Wiener-Hopf type, receives especial attention. Conditions, in terms of the symbol of I — K, for I — K to be invertible or Fredholm on Xp are established for certain cases (Ω a half-space or cone). A boundary integral equation, which models three-dimensional acoustic propaga-tion above flat ground, absorbing apart from an infinite rigid strip, illustrates the practical application and sharpness of the above results. This integral equation mod-els, in particular, road traffic noise propagation along an infinite road surface sur-rounded by absorbing ground. We prove that the sound propagating along the rigid road surface eventually decays with distance at the same rate as sound propagating above the absorbing ground.

Rigorous bounds on the nonlinear saturation of instabilities to parallel shear flows

A novel method is presented for obtaining rigorous upper bounds on the finite-amplitude growth of instabilities to parallel shear flows on the beta-plane. The method relies on the existence of finite-amplitude Liapunov (normed) stability theorems, due to Arnol'd, which are nonlinear generalizations of the classical stability theorems of Rayleigh and Fjørtoft. Briefly, the idea is to use the finite-amplitude stability theorems to constrain the evolution of unstable flows in terms of their proximity to a stable flow. Two classes of general bounds are derived, and various examples are considered. It is also shown that, for a certain kind of forced-dissipative problem with dissipation proportional to vorticity, the finite-amplitude stability theorems (which were originally derived for inviscid, unforced flow) remain valid (though they are no longer strictly Liapunov); the saturation bounds therefore continue to hold under these conditions.

The global distribution of phytoplankton size spectrum and size classes from their light-absorption spectra derived from satellite data

The absorption spectra of phytoplankton in the visible domain hold implicit information on the phytoplankton community structure. Here we use this information to retrieve quantitative information on phytoplankton size structure by developing a novel method to compute the exponent of an assumed power-law for their particle-size spectrum. This quantity, in combination with total chlorophyll-a concentration, can be used to estimate the fractional concentration of chlorophyll in any arbitrarily-defined size class of phytoplankton. We further define and derive expressions for two distinct measures of cell size of mixed populations, namely, the average spherical diameter of a bio-optically equivalent homogeneous population of cells of equal size, and the average equivalent spherical diameter of a population of cells that follow a power-law particle-size distribution. The method relies on measurements of two quantities of a phytoplankton sample: the concentration of chlorophyll-a, which is an operational index of phytoplankton biomass, and the total absorption coefficient of phytoplankton in the red peak of visible spectrum at 676 nm. A sensitivity analysis confirms that the relative errors in the estimates of the exponent of particle size spectra are reasonably low. The exponents of phytoplankton size spectra, estimated for a large set of in situ data from a variety of oceanic environments (~ 2400 samples), are within a reasonable range; and the estimated fractions of chlorophyll in pico-, nano- and micro-phytoplankton are generally consistent with those obtained by an independent, indirect method based on diagnostic pigments determined using high-performance liquid chromatography. The estimates of cell size for in situ samples dominated by different phytoplankton types (diatoms, prymnesiophytes, Prochlorococcus, other cyanobacteria and green algae) yield nominal sizes consistent with the taxonomic classification. To estimate the same quantities from satellite-derived ocean-colour data, we combine our method with algorithms for obtaining inherent optical properties from remote sensing. The spatial distribution of the size-spectrum exponent and the chlorophyll fractions of pico-, nano- and micro-phytoplankton estimated from satellite remote sensing are in agreement with the current understanding of the biogeography of phytoplankton functional types in the global oceans. This study contributes to our understanding of the distribution and time evolution of phytoplankton size structure in the global oceans.

"Where am I?" Impact of display and content variables on spatial presence and comprehension in virtual environments

Forgetting immediate physical reality and having awareness of one�s location in the simulated world is critical to enjoyment and performance in virtual environments be it an interactive 3D game such as Quake or an online virtual 3d community space such as Second Life. Answer to the question "where am I?" at two levels, whether the locus is in the immediate real world as opposed to the virtual world and whether one is aware of the spatial co-ordinates of that locus, hold the key to any virtual 3D experience. While 3D environments, especially virtual environments and their impact on spatial comprehension has been studied in disciplines such as architecture, it is difficult to determine the relative contributions of specific attributes such as screen size or stereoscopy towards spatial comprehension since most of them treat the technology as monolith (box-centered). Using a variable-centered approach put forth by Nass and Mason (1990) which breaks down the technology into its component variables and their corresponding values as its theoretical basis, this paper looks at the contributions of five variables (Stereoscopy, screen size, field of view, level of realism and level of detail) common to most virtual environments on spatial comprehension and presence. The variable centered approach can be daunting as the increase in the number of variables can exponentially increase the number of conditions and resources required. We overcome this drawback posed by adoption of such a theoretical approach by the use of a fractional factorial design for the experiment. This study has completed the first wave of data collection and starting the next phase in January 2007 and expected to complete by February 2007. Theoretical and practical implications of the study are discussed.

Beyond arousal and valence: the importance of the biological versus social relevance of emotional stimuli

The present study addressed the hypothesis that emotional stimuli relevant to survival or reproduction (biologically emotional stimuli) automatically affect cognitive processing (e.g., attention, memory), while those relevant to social life (socially emotional stimuli) require elaborative processing to modulate attention and memory. Results of our behavioral studies showed that (1) biologically emotional images hold attention more strongly than do socially emotional images, (2) memory for biologically emotional images was enhanced even with limited cognitive resources, but (3) memory for socially emotional images was enhanced only when people had sufficient cognitive resources at encoding. Neither images’ subjective arousal nor their valence modulated these patterns. A subsequent functional magnetic resonance imaging study revealed that biologically emotional images induced stronger activity in the visual cortex and greater functional connectivity between the amygdala and visual cortex than did socially emotional images. These results suggest that the interconnection between the amygdala and visual cortex supports enhanced attention allocation to biological stimuli. In contrast, socially emotional images evoked greater activity in the medial prefrontal cortex (MPFC) and yielded stronger functional connectivity between the amygdala and MPFC than did biological images. Thus, it appears that emotional processing of social stimuli involves elaborative processing requiring frontal lobe activity.

The national dialogue on behaviour change in UK climate policy: some observations on responsibility, agency and political dimensions

This chapter explores the politics around the role of agency in the UK climate change debate. Government interventions on the demand side of consumption have increasingly involved attempts to obtain greater traction with the values, attitudes and beliefs of citizens in relation to climate change and also in terms of influencing consumer behaviour at an individual level. With figures showing that approximately 40% of the UK’s carbon emissions are attributable to household and transport behaviour, policy initiatives have progressively focused on the facilitation of “sustainable behaviours”. Evidence suggests however, that mobilisation of pro-environmental attitudes in addressing the perceived “value-action gap” has so far had limited success. Research in this field suggests that there is a more significant and nuanced “gap” between context and behaviour; a relationship that perhaps provides a more adroit reflection of reasons why people do not necessarily react in the way that policy-makers anticipate. Tracing the development of the UK Government’s behaviour change agenda over the last decade, we posit that a core reason for the limitations of this programme relates to an excessively narrow focus on the individual. This has served to obscure some of the wider political and economic aspects of the debate in favour of a more simplified discussion. The second part of the chapter reports findings from a series of focus groups exploring some of the wider political views that people hold around household energy habits, purchase and use of domestic appliances, and transport behaviour-and discusses these insights in relation to the literature on the agenda’s apparent limitations. The chapter concludes by considering whether the aims of the Big Society approach (recently established by the UK’s Coalition Government) hold the potential to engage more directly with some of these issues or whether they merely constitute a “repackaging” of the individualism agenda.

Critical slip and time dependence in sea ice friction

Recent research into sea ice friction has focussed on ways to provide a model which maintains much of the clarity and simplicity of Amonton's law, yet also accounts for memory effects. One promising avenue of research has been to adapt the rate- and state- dependent models which are prevalent in rock friction. In such models it is assumed that there is some fixed critical slip displacement, which is effectively a measure of the displacement over which memory effects might be considered important. Here we show experimentally that a fixed critical slip displacement is not a valid assumption in ice friction, whereas a constant critical slip time appears to hold across a range of parameters and scales. As a simple rule of thumb, memory effects persist to a significant level for 10 s. We then discuss the implications of this finding for modelling sea ice friction and for our understanding of friction in general.

Responding to the EU Emissions Trading Scheme: an empirical analysis of corporate carbon disclosure strategy

The purpose of this paper is to explore how companies that hold carbon trading accounts under European Union Emissions Trading Scheme (EU ETS) respond to the climate change by using disclosures on carbon emissions as a means to generate legitimacy compared to others. The study is based on disclosures made in annual reports and stand-alone sustainability reports of UK listed companies from 2001- 2012. The study uses content analysis to capture both the quality and volume of the carbon disclosures. The results show that there is a significant increase in both the quality and volume of the carbon disclosures after the launch of EU ETS. Companies with carbon trading accounts provide greater detailed disclosures as compared to the others without an account. We also find that company size is positively correlated with the disclosures while the association with the industry produces an inconclusive result.

International terrorism, domestic political instability, and the escalation effect

What are the main causes of international terrorism? Despite the meticulous examination of various candidate explanations, existing estimates still diverge in sign, size, and significance. This article puts forward a novel explanation and supporting evidence. We argue that domestic political instability provides the learning environment needed to successfully execute international terror attacks. Using a yearly panel of 123 countries over 1973–2003, we find that the occurrence of civil wars increases fatalities and the number of international terrorist acts by 45%. These results hold for alternative indicators of political instability, estimators, subsamples, subperiods, and accounting for competing explanations.

Combining probability forecasts

We consider different methods for combining probability forecasts. In empirical exercises, the data generating process of the forecasts and the event being forecast is not known, and therefore the optimal form of combination will also be unknown. We consider the properties of various combination schemes for a number of plausible data generating processes, and indicate which types of combinations are likely to be useful. We also show that whether forecast encompassing is found to hold between two rival sets of forecasts or not may depend on the type of combination adopted. The relative performances of the different combination methods are illustrated, with an application to predicting recession probabilities using leading indicators.