Is the long-term association between symbolic numerical magnitude processing and arithmetic bi-directional?

By analyzing longitudinal data from the start to the end of primary education, we aimed to investigate whether symbolic numerical magnitude processing at the start of primary education predicted arithmetic at the end, and whether arithmetic at the start of primary education predicted later symbolic numerical magnitude processing skills at the end. In the first grade (start) and sixth grade (end) of primary education, the same group of children’s symbolic numerical magnitude processing skills and arithmetic competence were assessed. We were particularly interested in exploring the direction of the association between symbolic numerical magnitude processing and arithmetic and observed that this association was bi-directional across primary education. Symbolic numerical magnitude processing skills in first grade predicted arithmetic in sixth grade; but also the reversed direction turned out significant: Early arithmetic predicted later symbolic numerical magnitude processing skills. Both directions remained significant after controlling for motor speed and nonverbal reasoning. Critically, when controlling for auto-regressive effects of prior abilities, the symbolic comparison-arithmetic association was no longer significant, the reversed direction became marginally significant. This suggests that children’s arithmetic development across primary education to some extent strengthens their ability to process the numerical meaning of Arabic digits.

Optimal Taxation and the Tradeoff Between Efficiency and Redistribution

This paper studies the aggregate and distributional implications of introducing consumption taxes into an otherwise deterministic version of the standard neoclassical growth model with income taxes only and heterogeneity across agents. In particular, the economic agents differ among each other with respect to whether they are allowed to save (in physical capital) or not. Policy is optimally chosen by a benevolent Ramsey government. The main theoretical finding comes to confirm the widespread belief that the introduction of consumption taxes into a model with income taxes only, creates substantial efficiency gains for the economy as whole, but at the cost of higher income inequality. In other words, consumption taxes reduce the progressivity of the tax system, and maybe, from a normative point of view, this result justifies the design of a set of subsidies policies which will aim to outweigh the regressive effects of the otherwise more efficient consumption taxes.