Elements of algebraic geometry and the positive theory of partially commutative groups

The first main result of the paper is a criterion for a partially commutative group G to be a domain. It allows us to reduce the study of algebraic sets over G to the study of irreducible algebraic sets, and reduce the elementary theory of G (of a coordinate group over G) to the elementary theories of the direct factors of G (to the elementary theory of coordinate groups of irreducible algebraic sets). Then we establish normal forms for quantifier-free formulas over a non-abelian directly indecomposable partially commutative group H. Analogously to the case of free groups, we introduce the notion of a generalised equation and prove that the positive theory of H has quantifier elimination and that arbitrary first-order formulas lift from H to H * F, where F is a free group of finite rank. As a consequence, the positive theory of an arbitrary partially commutative group is decidable.

A general construction of internal sheaves in algebraic set theory

We present a solution to the problem of defining a counterpart in Algebraic Set Theory of the construction of internal sheaves in Topos Theory. Our approach is general in that we consider sheaves as determined by Lawvere-Tierney coverages, rather than by Grothen-dieck coverages, and assume only a weakening of the axioms for small maps originally introduced by Joyal and Moerdijk, thus subsuming the existing topos-theoretic results.

Rational first integrals in the Darboux theory of integrability in Cn

"Vegeu el resum a l'inici del document del fitxer adjunt."

Weighted limits in simplicial homotopy theory

We extend the theory of Quillen adjunctions by combining ideas of homotopical algebra and of enriched category theory. Our results describe how the formulas for homotopy colimits of Bousfield and Kan arise from general formulas describing the derived functor of the weighted colimit functor.

Political economics and normative analysis

The approaches and opinions of economists often dominate public policy discussion. Economists have gained this privileged position partly (or perhaps mainly) because of the obvious relevance of their subject matter, but also because of the unified methodology (neo-classical economics) that the vast majority of modern economists bring to their analysis of policy problems and proposed solutions. The idea of Pareto efficiency and its potential trade-off with equity is a central idea that is understood by all economists and this common language provides the economics profession with a powerful voice in public affairs. The purpose of this paper is to review and reflect upon the way in which economists find themselves analysing and providing suggestions for social improvements and how this role has changed over roughly the last 60 years. We focus on the fundamental split in the public economics tradition between those that adhere to public finance and those that adhere to public choice. A pure public finance perspective views failures in society as failures of the market. The solutions are technical, as might be enacted by a benevolent dictator. The pure public choice view accepts (sometimes grudgingly) that markets may fail, but so, it insists, does politics. This signals institutional reforms to constrain the potential for political failure. Certain policy recommendations may be viewed as compatible with both traditions, but other policy proposals will be the opposite of that proposed within the other tradition. In recent years a political economics synthesis emerged. This accepts that institutions are very important and governments require constraints, but that some degree of benevolence on the part of policy makers should not be assumed non-existent. The implications for public policy from this approach are, however, much less clear and perhaps more piecemeal. We also discuss analyses of systematic failure, not so much on the part of markets or politicians, but by voters. Most clearly this could lead to populism and relaxing the idea that voters necessarily choose their interests. The implications for public policy are addressed. Throughout the paper we will relate the discussion to the experience of UK government policy-making.

The added value from adopting a CGE approach to analyse changes in environmental trade balances

The application of multi-region environmental input-output (IO) analysis to the problem of accounting for emissions generation (and/or resource use) under different accounting principles has become increasingly common in the ecological and environmental economics literature in particular, with applications at the international and interregional subnational level. However, while environmental IO analysis is invaluable in accounting for pollution flows in the single time period that the accounts relate to, it is limited when the focus is on modelling the impacts of any marginal change in activity. This is because a conventional demand-driven IO model assumes an entirely passive supply-side in the economy (i.e. all supply is infinitely elastic) and is further restricted by the assumption of universal Leontief (fixed proportions) technology implied by the use of the A and multiplier matrices. Where analysis of marginal changes in activity is required, extension from an IO accounting framework to a more flexible interregional computable general equilibrium (CGE) approach, where behavioural relationships can be modelled in a more realistic and theory-consistent manner, is appropriate. Our argument is illustrated by comparing the results of introducing a positive demand stimulus in the UK economy using IO and CGE interregional models of Scotland and the rest of the UK. In the case of the latter, we demonstrate how more theory consistent modelling of both demand and supply side behaviour at the regional and national levels effect model results, including the impact on the interregional CO2 ‘trade balance’.

Solovian and New Growth Theory from the Perspective of Allyn Young on Macroeconomic Increasing Returns

This paper evaluates, from an Allyn Youngian perspective, the neoclassical Solow model of growth and the associated empirical estimates of the sources of growth based on it. It attempts to clarify Young’s particular concept of generalised or macroeconomic “increasing returns” to show the limitations of a model of growth based on an assumption that the aggregate production function is characterised by constant returns to scale but “augmented” by exogenous technical progress. Young’s concept of endogenous, self-sustaining growth is also shown to differ in important respects (including in its policy implications) from modern endogenous growth theory.

Analysing the impact of public capital stock using the NEG wage equation: a panel data approach

This paper examines the relationship between the level of public infrastructure and the level of productivity using panel data for the Spanish provinces over the period 1984-2004, a period which is particularly relevant due to the substantial changes occurring in the Spanish economy at that time. The underlying model used for the data analysis is based on the wage equation, which is one of a handful of simultaneous equations which when satisfied correspond to the short-run equilibrium of New Economic Geography theory. This is estimated using a spatial panel model with fixed time and province effects, so that unmodelled space and time constant sources of heterogeneity are eliminated. The model assumes that productivity depends on the level of educational attainment and the public capital stock endowment of each province. The results show that although changes in productivity are positively associated with changes in public investment within the same province, there is a negative relationship between productivity changes and changes in public investment in other regions.

A Soft Edge Target Zone Model: Theory And Application To Hong Kong

Hong Kong’s currency is pegged to the US dollar in a currency board arrangement. In autumn 2003, the Hong Kong dollar appreciated from close to 7.80 per US dollar to 7.70, as investors feared that the currency board would be abandoned. In the wake of this appreciation, the monetary authorities revamped the one-sided currency board mechanism into a symmetric two-sided system with a narrow exchange rate band. This paper reviews the characteristics of the new currency board arrangement and embeds a theoretical soft edge target zone model typifying many intermediate regimes, to explain the notable achievement of speculative peace and credibility since May 2005.

Industrial Structure, Trade and Regional Economics : Market Segmentation

We consider a general equilibrium model a la Bhaskar (Review of Economic Studies 2002): there are complementarities across sectors, each of which comprise (many) heterogenous monopolistically competitive firms. Bhaskar's model is extended in two directions: production requires capital, and labour markets are segmented. Labour market segmentation models the difficulties of labour migrating across international barriers (in a trade context) or from a poor region to a richer one (in a regional context), whilst the assumption of a single capital market means that capital flows freely between countries or regions. The model is solved analytically and a closed form solution is provided. Adding labour market segmentation to Bhaskar's two-tier industrial structure allows us to study, inter alia, the impact of competition regulations on wages and - financial flows both in the regional and international context, and the output, welfare and financial implications of relaxing immigration laws. The analytical approach adopted allows us, not only to sign the effect of policies, but also to quantify their effects. Introducing capital as a factor of production improves the realism of the model and refi nes its empirically testable implications.

A Salience Theory of Choice Errors

We study a psychologically based foundation for choice errors. The decision maker applies a preference ranking after forming a 'consideration set' prior to choosing an alternative. Membership of the consideration set is determined both by the alternative specific salience and by the rationality of the agent (his general propensity to consider all alternatives). The model turns out to include a logit formulation as a special case. In general, it has a rich set of implications both for exogenous parameters and for a situation in which alternatives can a¤ect their own salience (salience games). Such implications are relevant to assess the link between 'revealed' preferences and 'true' preferences: for example, less rational agents may paradoxically express their preference through choice more truthfully than more rational agents.

Off-the-Record Target Zones: Theory with an Application to Hong Kongs Currency Board

This paper provides a modelling framework for evaluating the exchange rate dynamics of a target zone regime with undisclosed bands. We generalize the literature to allow for asymmetric one-sided regimes. Market participants' beliefs concerning an undisclosed band change as they learn more about central bank intervention policy. We apply the model to Hong Kong's one-sided currency board mechanism. In autumn 2003, the Hong Kong dollar appreciated from close to 7.80 per US dollar to 7.70, as investors feared that the currency board would be abandoned. In the wake of this appreciation, the monetary authorities finally revamped the regime as a symmetric two-sided system with a narrow exchange rate band.

Corruption and the Military in Politics: Theory and Evidence from around the World

Recent theoretical developments and case study evidence suggests a relationship between the military in politics and corruption. This study contributes to this literature by analyzing theoretically and empirically the role of the military in politics and corruption for the first time. By drawing on a cross sectional and panel data set covering a large number of countries, over the period 1984-2007, and using a variety of econometric methods substantial empirical support is found for a positive relationship between the military in politics and corruption. In sum, our results reveal that a one standard deviation increase in the military in politics leads to a 0.22 unit increase in corruption index. This relationship is shown to be robust to a variety of specification changes, different econometric techniques, different sample sizes, alternative corruption indices and the exclusion of outliers. This study suggests that the explanatory power of the military in politics is at least as important as the conventionally accepted causes of corruption, such as economic development.

Optimism and commitment: An elementary theory of bargaining and war

We propose an elementary theory of wars fought by fully rational contenders. Two parties play a Markov game that combines stages of bargaining with stages where one side has the ability to impose surrender on the other. Under uncertainty and incomplete information, in the unique equilibrium of the game, long confrontations occur: war arises when reality disappoints initial (rational) optimism, and it persist longer when both agents are optimists but reality proves both wrong. Bargaining proposals that are rejected initially might eventually be accepted after several periods of confrontation. We provide an explicit computation of the equilibrium, evaluating the probability of war, and its expected losses as a function of i) the costs of confrontation, ii) the asymmetry of the split imposed under surrender, and iii) the strengths of contenders at attack and defense. Changes in these parameters display non-monotonic effects.