The Frisch–Waugh–Lovell theorem for the lasso and the ridge regression

The Frisch–Waugh–Lovell (FWL) (partitioned regression) theorem is essential in regression analysis. This is partly because it is quite useful to derive theoretical results. The lasso regression and the ridge regression, both of which are penalized least-squares regressions, have become popular statistical techniques. This article describes that the FWL theorem remains valid for these penalized least-squares regressions. More precisely, we demonstrate that the covariates corresponding to unpenalized regression parameters in these penalized least-squares regression can be projected out. Some other results related to the FWL theorem in such penalized least-squares regressions are also presented.     

The challenge of pension reform in Georgia: Non‐contributory pensions and elderly poverty

Georgia's national social security system offers almost universal non‐contributory basic pension coverage. The basic pension has, to date, proved effective in dealing with old‐age poverty. But Georgia's fiscal constraints and ageing population also highlight the importance of improving the pension system, in order to ensure its sustainability. This article presents policy reform choices, which suggest that, in Georgia, pension reform might include increasing the statutory retirement ages and reducing the generosity of benefits through means testing. The case of the Georgian non‐contributory basic pension might hold value for some low‐ and middle‐income countries that are considering the implementation of, or expanding coverage under, a non‐contributory pension programme.     

Electronic payment mechanisms in social security: Extending the reach of benefit and contribution transactions

More often than not, the existing modes of contribution collection and benefit payment of social security organizations are adapted to the collective arrangements that characterize employer‐employee relationships. Extending coverage to individuals in difficult‐to‐reach groups, however, may require new modalities of service that can cope with many separate, secure transactions rather than a few bulk data transfers between organizations. Recent developments in electronic payment show its wide applicability in enabling huge volumes of such individual transactions. It is in this light that the article explores the potentials of this technology and identifies possible arrangements through which electronic payments could surmount barriers that stand in the way of covering difficult‐to‐reach groups. The high level of mobile phone penetration on a global scale augurs well for using e‐payment mechanisms to collect social security contributions and to deliver social security benefits and services. A generic model is used to describe the requisite elements to implement electronic payments in social protection programmes. Based on empirical evidence of current social protection practices from around the world, five scenarios are presented to describe possible configurations for electronic payment, from the simplest to the most sophisticated. The broader objective is to contribute in a practical manner to the international commitment to extend social protection to all, as defined by the 2030 Sustainable Development Goals.     

The gender gap in pensions in Latin America

Lower female lifetime labour market participation rates, greater interruptions during their working lives, and wage gaps contribute to create gender gaps in pensions at the time of retirement. The design of social security systems may reinforce or attenuate these gaps. This article provides new evidence on gender gaps in access to pensions and in pension income in four Southern Cone countries in Latin America and analyses their evolution between 2000 and 2013, showing significant improvements in both gaps, with differential patterns by countries. The decrease in the gender gap in pension income has been particularly significant in Argentina and Brazil. In both cases, the largest increases in pension values during the period correspond to the lowest income percentiles, where women are overrepresented. The application of redistributive policies in these countries, aimed at reducing poverty and inequality but not necessarily focused on gender equity, has had positive and probably unintended consequences in terms of reduction in gender gaps in pensions.     

Pension reforms in EU11 countries: An evaluation of post‐socialist pension policies

This article evaluates the pension policy pathways of the 11 former state socialist nations that have joined the European Union since 2004. Focusing primarily on the post‐2004 period, the analysis discusses the most important measurable outcomes of these countries’ pension reforms, in terms of poverty alleviation, pension adequacy and fiscal sustainability. Going beyond the quantifiable concepts, we also investigate the quality of the 11 countries’ pension systems in terms of equity as well as efficiency, emphasizing the less conspicuous design errors present in these systems. Although these errors have received little attention to date, they may harm pension schemes along several dimensions, including their fiscal sustainability.     

The social security number: A small device underpinning big systems

The possession and use of a personal social security number helps to structure people's daily lives. However, despite its fundamental normative importance, the social security number remains a little‐known entity. Increasingly universal and yet diverse in form, it is a legal and technical norm which is as much a mechanism for surveillance and monitoring as it is a necessary instrument for giving effect to social rights. Analysis of this constituent element of social security systems permits as assessment of some of the technical difficulties presented by the ever‐increasing movement of people and data. Overcoming these technical difficulties should permit to envisage a first technical step towards realizing a universal and global social security system.     

Minimum variance unbiased estimation of stress–strength reliability under bivariate normal and its comparisons

In many industrial and natural phenomena, we need the probability that a component is smaller than the other component. Under a stress–strength model, this is reliability of an item. Under independent setup, there are different approaches for the estimation of such reliability. Here, estimation is considered under the dependent case. Under bi-variate setup uniformly minimum variance unbiased estimator is obtained. Also comparison with available estimator based on Maximum Likelihood Estimate (MLE) is done through Mean Square Error (MSE) and bias. Also these are compared by computing L₁ distance between their distribution functions. From this idea and numerical computations, UMVUE appears to be good.     

Une jeunesse stigmatisée: l'influence du chômage précoce sur le chômage ultérieur

Le chômage rencontré au début du parcours professionnel favorise‐t‐il le chômage ultérieur? Pour le savoir, les auteurs suivent la trajectoire de quelque 700 000 actifs allemands sur une période de vingt‐quatre ans en utilisant des données administratives appariées employeurs‐salariés. Grâce à la méthode des variables instrumentales (l'instrument étant ici la fermeture de l'entreprise), ils font apparaître des séquelles durables du chômage précoce, chaque nouvelle journée chômée pendant les huit premières années de vie active augmentant d'une demi‐journée en moyenne le chômage des seize années suivantes. Selon des régressions quantiles, le caractère prolongé et répété des épisodes de chômage initial renforce sensiblement cet «effet cicatrice».     

Sécurité sociale et résultats des entreprises: l'exemple des PME au Viet Nam

Les auteurs examinent les effets de la sécurité sociale – critère du caractère formel de l'activité – sur les résultats des PME vietnamiennes. À partir de données sur les entreprises déclarées (2006–2011), ils constatent qu'une élévation de 10 pour cent de la couverture du personnel est associée à une augmentation du chiffre d'affaires et des profits allant respectivement de 1,4 à 2 pour cent et jusqu'à 1,8 pour cent par travailleur. Toutefois, étant donné le décalage entre l'«investissement» (versement des cotisations) et son rendement (performances supérieures), des politiques d'accompagnement sont nécessaires pour encourager les petites entreprises à s'annoncer aux régimes obligatoires.