Grouping strategies and thresholding for high dimensional linear models

The estimation problem in a high regression model with structured sparsity is investigated. An algorithm using a two-step block thresholding procedure called GR-LOL is provided. Convergence rates are produced: they depend on simple coherence-type indices of the Gram matrix – easily checkable on the data – as well as sparsity assumptions of the model parameters measured by a combination of l₁ within-blocks with _lq$l_q$, q<1$q<1$ between-blocks norms. The simplicity of the coherence indicator suggests ways to optimize the rates of convergence when the group structure is not naturally given by the problem or is unknown. In such a case, an auto-driven procedure is provided to determine the regressor groups (number and contents). An intensive practical study compares our grouping methods with the standard LOL algorithm. We prove that the grouping rarely deteriorates the results but can improve them very significantly. GR-LOL is also compared with group-Lasso procedures and exhibits a very encouraging behavior. The results are quite impressive, especially when GR-LOL algorithm is combined with a grouping pre-processing.     

A Time-Series Study of the Formation and Predictive Performance of EEC Production Survey Expectations

Generalized method of moments (GMM) has been an important innovation in econometrics. Its usefulness has motivated a search for good inference procedures based on GMM. This article presents a novel method of bootstrapping for GMM based on resampling from the empirical likelihood distribution that imposes the moment restrictions. We show that this approach yields a large-sample improvement and is efficient, and give examples. We also discuss the development of GMM and other recent work on improved inference.     

Characterizations of egalitarian binary relations as transitive closures with a special reference to Lorenz dominance and to single-crossing conditions

This article considers, in the context of the fixed-population constant-sum comparison of income distributions, a number of intransitive binary relations smaller than Lorenz dominance. We determine their transitive closure, and we study how they relate to each other and to other relations that have appeared in the literature. Among other results, we provide alternative characterizations of Lorenz dominance.     

Gender inequalities in pensions: different components similar levels of dispersion

While the average gender gap in pensions is quite well documented, gender differences in the distribution of pensions have rarely been explored. We show in this paper that pension dispersion is very similar for men and women within the French pension system of a given sector (public or private). Gender differences are less marked among retired civil servants than among former private sector employees. However, the determinants of these inequalities are not the same for men and women. Using a regression-based decomposition of the Gini coefficient, we find that pension dispersion is mostly due to dispersion of the reference wage for all retirees but gender differences exist. For women, in particular, pension dispersion is also due to the dispersion in contribution periods. We also decompose the Gini coefficient by source of pension to measure the impact of institutional rules (minimum pensions, survivor’s pension) on the extent of pension inequality. Unexpectedly, we find that the impact of minimum pensions is limited, although slightly larger for civil servants than for private-sector employees. Survivor’s pension schemes, on the other hand, contribute positively to pension dispersion among retired women.     

Mixed Unemployment and Differentiated Policies

ABSTRACT: The works related to the disequilibrium theory often show that situations of classical unemployment and of Keynesian unemployment coexist on a long-term basis. The following study deals with a theoretical model of mixed unemployment reflecting this coexistence. In this model, prices are assumed to be flexible upward, but not downward. Hence, classical unemployment leads to inflation, without quantitative rationing on demand, which is closer to reality. The study analyses the asymmetric relations between the classical and the Keynesian sectors as well as the resulting implications for economic policy. What comes out is that differentiated policies always have a stronger impact than aggregate policies. The highest level of efficiency is obtained by stimulating the supply of firms set in the classical situation, provided that one acts on the non-wage determinants of supply in order not to further depress the outlets for firms set in the Keynesian situation.     

Condorcet efficiencies under the maximal culture condition

The Condorcet winner in an election is a candidate that could defeat each other candidate in a series of pairwise majority rule elections. The Condorcet efficiency of a voting rule is the conditional probability that the voting rule will elect the Condorcet winner, given that such a winner exists. The study considers the Condorcet efficiency of basic voting rules under various assumptions about how voter preference rankings are obtained. Particular attention is given to situations in which the maximal culture condition is used as a basis for obtaining voter preferences. Received: 4 February 1998/Accepted: 13 April 1998     

Beyond composition: What the study of diversity in K12 schools can learn from research in higher education

Several decades of interdisciplinary research have demonstrated the benefits of racially and ethnically integrated K12 schools. However, there is still much we do not know about what happens inside diverse schools that lead to these outcomes. In this article, we argue that the study of diversity in higher education, with its greater focus on internal institutional dynamics and a broader range of outcomes, can help K12 researchers fill in these gaps. However, the framework for studying diversity in higher education cannot be applied to K12 schools without first accounting for developmental and structural differences across students and sectors. To that end, this article summarizes the main components of the framework for studying diversity in the higher education literature—compositional, interactional, and organizational diversity—as well as the broad range of outcomes including not only academic achievement but also skills for lifelong learning and dispositions for citizenship in a multiracial democracy, and suggests how they can be adapted for K12 research. We argue that with this comprehensive but adapted framework, research on K12 education can inform practice and policy by providing more insight into the underlying mechanisms of school diversity and its consequences.