International income poverty measurement: which way now?

We critically review conceptual and empirical issues surrounding the derivation of the international poverty line, expressed in PPP-adjusted dollars and linked to various rounds of the International Comparison Program (ICP). We find that there are some limitations in the current estimation of these lines, but show that statistically superior methods lead to lines that are relatively robust and confirm the $1.25 using 2005 PPPs and suggest $1.67–1.71 using 2011 PPPs (or close to the $1.90 proposed by the World Bank if we follow the World Bank’s approach of adjusting inflation rates in some countries); they also roughly confirm the current shape of the proposed ‘weakly relative’ poverty line. Using the new absolute line based on 2011 PPPs would lead to substantially lower poverty in our estimation. The extent of the decline depends on whether and how one treats China, India, and Indonesia differently from other countries in the 2005 and 2011 PPPs. More seriously, we note that the dependence on successive ICP rounds creates conceptual and empirical problems that have become worse over time so that we suggest that it would be best to consider alternatives to the current reliance on ICP rounds and the resulting PPPs. As a short-term solution we propose to fix the international poverty line in national currencies using either the 2005 or 2011 level; in the medium term, we argue for global poverty measurement based on internationally coordinated national poverty measurement.     

Second-Order Approximations to Two Classes of Sequential Estimation Procedures

For the model considered by Chaturvedi, Pandey and Gupta (1991), two classes of sequential procedures are developed to construct confidence regions (which may be interval, ellipsoidal or spherical) of ‘pre-assigned width and coverage probability’ for the parameters of interest and for the minimum risk point estimation (taking loss to be quadratic plus linear cost of sampling) of the nuisance parameter. Second-Order approximations are derived for the expected sample size, coverage probability and ‘regret’ associated with the two classes of sequential procedures. A simple and direct method of obtaining the asymptotic distribution of the stopping time is provided. By means of examples, it is illustrated that several estimation problems can be tackled with the help of proposed classes of sequential procedures.     

Construction of orthogonal factorial designs controlling interaction efficiencies

This paper employs some variants of the usual Kronecker product to construct orthogonal factorial designs controlling the interaction efficiencies. The methods suggested have a fairly wide coverage and the resulting designs involve a small number of replicates.     

Rejoinder to 'Ahmed, M.S. (1998). A note on regression-type estimators using multiple auxiliary information.'

In the estimators t ₃ , t ₄ , t ₅ of Mukerjee, Rao & Vijayan (1987), b _{y x} and b _{y z} are partial regression coefficients of y on x and z , respectively, based on the smaller sample. With the above interpretation of b _{y x} and b _{y z} in t ₃ , t ₄ , t ₅ , all the calculations in Mukerjee at al. (1987) are correct. In this connection, we also wish to make it explicit that b _{x z} in t ₅ is an ordinary and not a partial regression coefficient. The 'corrected' MSEs of t ₃ , t ₄ , t ₅ , as given in Ahmed (1998 Section 3) are computed assuming that our b _{y x} and b _{y z} are ordinary and not partial regression coefficients. Indeed, we had no intention of giving estimators using the corresponding ordinary regression coefficients which would lead to estimators inferior to those given by Kiregyera (1984). We accept responsibility for any notational confusion created by us and express regret to readers who have been confused by our notation. Finally, in consideration of the above, it may be noted that Tripathi & Ahmed's (1995) estimator t ₀ , quoted also in Ahmed (1998), is no better than t ₅ of Mukerjee at al. (1987).     

A note on the universal optimality criterion for full rank models

The aim of this note is to suggest a revised formulation of the universal optimality criterion for full rank models as stated in Kiefer (1975). We have presented the relevant results with indications of some possible applications.     

Two-level minimum aberration designs in N =2 (mod 4) runs

For two-level factorials, we consider designs in N=2 (mod 4) runs as obtained by adding two runs, with a certain coincidence pattern, to an orthogonal array of strength two. These designs are known to be optimal main effect plans in a very broad sense in the absence of interactions. Among them, we explore the ones having minimum aberration, with a view to ensuring maximum model robustness even when interactions are possibly present. This is done by sequentially minimizing a measure of the bias caused by interactions of successively higher orders.     

Framing the corporate responsibility-reputation linkage: The case of Tata Motors in India

This study, focusing on the emerging economy context of one of India's largest automotive companies, Tata Motors, analyzes the thematic framing of corporate social responsibility (CSR) and corporate reputation. Five CSR frames are shown: institutionalization, community development, modernization, mainstreaming, and nation-building. Reputation is framed via: heritage, nationbuilding, technological advancement, global footprint, and responsibility. The findings suggest how firms may better align their CSR efforts with regular business, and their larger public relations campaigns with wider social perceptions of their responsibilities.     

Hard‐to‐Solve Bimatrix Games

The Lemke–Howson algorithm is the classical method for finding one Nash equilibrium of a bimatrix game. This paper presents a class of square bimatrix games for which this algorithm takes, even in the best case, an exponential number of steps in the dimension d of the game. Using polytope theory, the games are constructed using pairs of dual cyclic polytopes with 2d suitably labeled facets in d‐space. The construction is extended to nonsquare games where, in addition to exponentially long Lemke–Howson computations, finding an equilibrium by support enumeration takes on average exponential time.     

Fuzzy choice functions

The R-greatest and maximal sets of standard choice theory are extended to fuzzy R-greatest and fuzzy maximal sets. Unlike the precise counterparts of these concepts, these two sets do not in general coincide when preferences are reflexive and connected. A stronger than usual version of connectedness under which the two sets are equal is provided. The concept of a fuzzy choice function is introduced and conditions under which a fuzzy choice function may be rationalized as a fuzzy R-greatest or a fuzzy maximal set are discussed. Rationalizability with transitive and weakly transitive fuzzy preference relations is also considered.We are indebted to Professor P. K. Pattanaik for his comments on an earlier version of this paper. We also wish to acknowledge comments made by an anonymous referee from which this paper has benefited greatly. The usual caveat about errors applies.     

The Voices Project

The purpose of the Voices Project was to give children and adolescents a greater voice in the local and global dialogues about the precursors and solutions to all forms of school violence. This exploratory project incorporates input from youngsters, educators, community partners, and university researchers into the development of a model for non-violent schools and communities. In this article, the Voices Project is described and implications for practice forwarded.