EQUITY, ECONOMIC SCALE, AND THE ROLE OF EXCHANGE IN A SUSTAINABLE ECONOMY

This paper explores these theoretical and practical issues, considering the question of the environmental and ecological impacts of economic activity from the viewpoint of the scale at which this activity takes place and the exchanges across time and space which affect its sustainability. Following a consideration of the dynamics of economic change in the next section, the paper discusses the meaning of trade/exchange, economic scale, and political/ecological/economic boundaries before returning in the final section to the two equity-related issues outlined above.This research was supported by the International Development Research Centr

Children Capabilities and Family Characteristics in Italy

This paper explores the possibilities of using structural equation modelling to measure capabilities of Italian children. In particular the paper focuses on two capabilities: “Senses, Imagination and Thought” and “Leisure and Play Activities ”. The indicators used to measure the capability of ‘Senses, imagination and thought’ for 6-13 years old children are attitude towards education, attendance to arts classes and other type of extra curriculum classes like computing and languages. The variables used as indicators of the capability of “Leisure and play activities” include how often children play in playground, various types of games, attendance to sports classes. We use both descriptive statistics, an ordered probit model, and a structural equation model in order to investigate the relation among the above mentioned indicators, the latent construct for capabilities and a set of covariates. Moreover we use a new data set in order to include family income among the covariates. The data result from the matching (through a propensity score method) of two data sets: Bank of Italy Survey on Income and Wealth for year 2000 and Istat Families, social subjects and childhood condition for year 1998.Education, Capabilities, Child Well Being, Structural Equation Modelling

Minimum Rates of Approximate Sufficient Statistics

Given a sufficient statistic for a parametric family of distributions, one can estimate the parameter without access to the data. However, the memory or code size for storing the sufficient statistic may nonetheless still be prohibitive. Indeed, for $n$ independent samples drawn from a $k$-nomial distribution with $d=k-1$ degrees of freedom, the length of the code scales as $d\log n+O(1)$. In many applications, we may not have a useful notion of sufficient statistics (e.g., when the parametric family is not an exponential family) and we also may not need to reconstruct the generating distribution exactly. By adopting a Shannon-theoretic approach in which we allow a small error in estimating the generating distribution, we construct various {\em approximate sufficient statistics} and show that the code length can be reduced to $\frac{d}{2}\log n+O(1)$. We consider errors measured according to the relative entropy and variational distance criteria. For the code constructions, we leverage Rissanen's minimum description length principle, which yields a non-vanishing error measured according to the relative entropy. For the converse parts, we use Clarke and Barron's formula for the relative entropy of a parametrized distribution and the corresponding mixture distribution. However, this method only yields a weak converse for the variational distance. We develop new techniques to achieve vanishing errors and we also prove strong converses. The latter means that even if the code is allowed to have a non-vanishing error, its length must still be at least $\frac{d}{2}\log n$.Comment: To appear in the IEEE Transactions on Information Theor

Backwards is the way forward: feedback in the cortical hierarchy predicts the expected future

Clark offers a powerful description of the brain as a prediction machine, which offers progress on two distinct levels. First, on an abstract conceptual level, it provides a unifying framework for perception, action, and cognition (including subdivisions such as attention, expectation, and imagination). Second, hierarchical prediction offers progress on a concrete descriptive level for testing and constraining conceptual elements and mechanisms of predictive coding models (estimation of predictions, prediction errors, and internal models)