Reflections on Modern Macroeconomics: Can We Travel Along a Safer Road?

In this paper we sketch some reflections on the pitfalls and inconsistencies of the research program - currently dominant among the profession - aimed at providing microfoundations to macroeconomics along a Walrasian perspective. We argue that such a methodological approach constitutes an unsatisfactory answer to a well-posed research question, and that alternative promising routes have been long mapped out but only recently explored. In particular, we discuss a recent agent-based, truly non-Walrasian macroeconomic model, and we use it to envisage new challenges for future research.Comment: Latex2e v1.6; 17 pages with 4 figures; for inclusion in the APFA5 Proceeding

The Genuine Savings Criterion and the Value of Population

Arrow, Dasgupta and Maler demonstrate thatin any dynamic model of the economy with changing population, population should properly be one of the state variables of the system. It enters both in the maxim and, at least under total utilitarianism, and into the production function in one way or another. If population growth is exponential and there are constant returns to scale, then a simple transformation to per capita variables can be used to eliminate one state variable. However, this simple transformation cannot be made if growth is not exponential, as it obviously is not and cannot be. If the growth of population is exogenous, then introducing it into the system does not affect the optimal policy. However, if one asks whether the system is sustainable, in the sense of at least maintaining total welfare (integral of discounted utilities), then the criterion is that the value of the rates of change of the state variables is non-negative, so that the shadow price of population becomes relevant. In this paper, we derive explicit formulas in a simple model, showing that the rate of growth of per capita capital is not the correct formula but must have other terms added to it. We also study the question under an alternative criterion of long-run average utilitarianism.

Evaluation of the “Three Steps in Screening for Dyslexia” Assessment Protocol Designed for New Zealand Teachers

Traditionally, the New Zealand Ministry of Education opposed the recognition of dyslexia. However, since 2007, the Ministry of Education’s position has started to change, evidenced by the development of a working definition. In 2021 the Ministry of Education released Three Steps in Screening for Dyslexia (TSSD), an assessment protocol designed to support teachers to screen for dyslexia. The current research evaluated the TSSD with a sample of 209 children in Years 4 to 6 (8–10 years-of-age) from New Zealand. The research investigated whether children could be accurately classified using tests from the TSSD, whether the three-step protocol described in the TSSD was a valid assessment approach, and what effect operationalising the term average at different cut-off points had on dyslexia screening. Children were classified using two cluster analyses. The first analysis was based on tests from the Woodcock Johnson IV and the second analysis was based on tests from the TSSD. Subsequent analyses investigated specific aspects of the TSSD protocol, including its sequential design and the placement of cut-off points. Results revealed a number of limitations to the TSSD approach. The authors discuss three changes that could be made to improve the validity and reliability of the TSSD, including a broader assessment of the decoding and language comprehension constructs; directing teachers to assess both decoding and language comprehension, irrespective of a child’s language comprehension ability; and placing a greater emphasis on discrepancy bands over cut-off points.Publishe

The identification and classification of struggling readers based on the simple view of reading.

The simple view of reading (SVR) predicts that reading difficulties can result from decoding difficulties, language comprehension difficulties, or a combination of these difficulties. However, classification studies have identified a fourth group of children whose reading difficulties are unexplained by the model. This may be due to the type of classification model used. The current research included 209 children in Grades 3-5 (8-10 years of age) from New Zealand. Children were classified using the traditional approach and a cluster analysis. In contrast to the traditional classification model, the cluster analysis approach eliminated the unexplained reading difficulties group, suggesting that poor readers can be accurately assigned to one of three groups, which are consistent with those predicted by the SVR. The second set of analyses compared the three poor reader groups across 14 measures of reading comprehension, decoding, language comprehension, phonological awareness, and rapid naming. All three groups demonstrated reading comprehension difficulties, but the dyslexia group showed particular weaknesses in word processing and phonological areas, the SCD group showed problems deriving meaning from oral language, and the mixed group showed general deficits in most measures. The findings suggest that the SVR does have the potential to determine reading profiles and differential intervention methods.Publishe

Axiomatic Characterization of the Mean Function on Trees

A mean of a sequence π = (x1, x2, . . . , xk) of elements of a finite metric space (X, d) is an element x for which is minimum. The function Mean whose domain is the set of all finite sequences on X and is defined by Mean(π) = { x | x is a mean of π } is called the mean function on X. In this paper the mean function on finite trees is characterized axiomatically

Adaptive Investment Strategies For Periodic Environments

In this paper, we present an adaptive investment strategy for environments with periodic returns on investment. In our approach, we consider an investment model where the agent decides at every time step the proportion of wealth to invest in a risky asset, keeping the rest of the budget in a risk-free asset. Every investment is evaluated in the market via a stylized return on investment function (RoI), which is modeled by a stochastic process with unknown periodicities and levels of noise. For comparison reasons, we present two reference strategies which represent the case of agents with zero-knowledge and complete-knowledge of the dynamics of the returns. We consider also an investment strategy based on technical analysis to forecast the next return by fitting a trend line to previous received returns. To account for the performance of the different strategies, we perform some computer experiments to calculate the average budget that can be obtained with them over a certain number of time steps. To assure for fair comparisons, we first tune the parameters of each strategy. Afterwards, we compare the performance of these strategies for RoIs with different periodicities and levels of noise.Comment: Paper submitted to Advances in Complex Systems (November, 2007) 22 pages, 9 figure

Modularity and Optimality in Social Choice

Marengo and the second author have developed in the last years a geometric model of social choice when this takes place among bundles of interdependent elements, showing that by bundling and unbundling the same set of constituent elements an authority has the power of determining the social outcome. In this paper we will tie the model above to tournament theory, solving some of the mathematical problems arising in their work and opening new questions which are interesting not only from a mathematical and a social choice point of view, but also from an economic and a genetic one. In particular, we will introduce the notion of u-local optima and we will study it from both a theoretical and a numerical/probabilistic point of view; we will also describe an algorithm that computes the universal basin of attraction of a social outcome in O(M^3 logM) time (where M is the number of social outcomes).Comment: 42 pages, 4 figures, 8 tables, 1 algorithm

Exploiting Polyhedral Symmetries in Social Choice

A large amount of literature in social choice theory deals with quantifying the probability of certain election outcomes. One way of computing the probability of a specific voting situation under the Impartial Anonymous Culture assumption is via counting integral points in polyhedra. Here, Ehrhart theory can help, but unfortunately the dimension and complexity of the involved polyhedra grows rapidly with the number of candidates. However, if we exploit available polyhedral symmetries, some computations become possible that previously were infeasible. We show this in three well known examples: Condorcet's paradox, Condorcet efficiency of plurality voting and in Plurality voting vs Plurality Runoff.Comment: 14 pages; with minor improvements; to be published in Social Choice and Welfar

Utilitarian Collective Choice and Voting

In his seminal Social Choice and Individual Values, Kenneth Arrow stated that his theory applies to voting. Many voting theorists have been convinced that, on account of Arrow’s theorem, all voting methods must be seriously flawed. Arrow’s theory is strictly ordinal, the cardinal aggregation of preferences being explicitly rejected. In this paper I point out that all voting methods are cardinal and therefore outside the reach of Arrow’s result. Parallel to Arrow’s ordinal approach, there evolved a consistent cardinal theory of collective choice. This theory, most prominently associated with the work of Harsanyi, continued the older utilitarian tradition in a more formal style. The purpose of this paper is to show that various derivations of utilitarian SWFs can also be used to derive utilitarian voting (UV). By this I mean a voting rule that allows the voter to score each alternative in accordance with a given scale. UV-k indicates a scale with k distinct values. The general theory leaves k to be determined on pragmatic grounds. A (1,0) scale gives approval voting. I prefer the scale (1,0,-1) and refer to the resulting voting rule as evaluative voting. A conclusion of the paper is that the defects of conventional voting methods result not from Arrow’s theorem, but rather from restrictions imposed on voters’ expression of their preferences. The analysis is extended to strategic voting, utilizing a novel set of assumptions regarding voter behavior