Beyond Piketty: A new perspective on poverty and inequality in India

The socio-economic literature has focused much on how overall inequality in income distribution (frequently measured by the Gini coefficient) undermines the “trickle down” effect. In other words, the higher the inequality in the income distribution, the lower is the growth elasticity of poverty. However, with the publication of Piketty’s magnum opus (2014), and a subsequent study by Chancel and Piketty (2017) of evolution of income inequality in India since 1922, the focus has shifted to the income disparity between the richest 1% (or 0.01%) and the bottom 50%. Their central argument is that the rapid growth of income at the top end of millionaires and billionaires is a by-product of growth. The present study extends this argument by linking it to poverty indices in India. Based on the India Human Development Survey 2005–12 – a nationwide panel survey-we examine the links between poverty and income inequality, especially in the upper tail relative to the bottom 50%, state affluence (measured in per capita income) and their interaction or their joint effect. Another feature of our research is that we analyse their effects on the FGT class of poverty indices. The results are similar in as much as direction of association is concerned but the elasticities vary with the poverty index. The growth elasticities are negative and significant for all poverty indices. In all three cases, the disparity between the income share of the top 1% and share of the bottom 50% is associated with greater poverty. These elasticities are much higher than the (absolute) income elasticities except in the case of the poverty gap. The largest increase occurs in the poverty gap squared – a 1% greater income disparity is associated with a 1.24% higher value of this index. Thus the consequences of even a small increase in the income disparity are alarming for the poorest.     

Sample size calculations for noninferiority trials for time-to-event data using the concept of proportional time

Noninferiority trials intend to show that a new treatment is ‘not worse'' than a standard-of-care active control and can be used as an alternative when it is likely to cause fewer side effects compared to the active control. In the case of time-to-event endpoints, existing methods of sample size calculation are done either assuming proportional hazards between the two study arms, or assuming exponentially distributed lifetimes. In scenarios where these assumptions are not true, there are few reliable methods for calculating the sample sizes for a time-to-event noninferiority trial. Additionally, the choice of the non-inferiority margin is obtained either from a meta-analysis of prior studies, or strongly justifiable ‘expert opinion'', or from a ‘well conducted'' definitive large-sample study. Thus, when historical data do not support the traditional assumptions, it would not be appropriate to use these methods to design a noninferiority trial. For such scenarios, an alternate method of sample size calculation based on the assumption of Proportional Time is proposed. This method utilizes the generalized gamma ratio distribution to perform the sample size calculations. A practical example is discussed, followed by insights on choice of the non-inferiority margin, and the indirect testing of superiority of treatment compared to placebo.KEYWORDS: Generalized gamma, noninferiority, non-proportional hazards, proportional time, relative time, sample size     

Changing educational inequalities in india in the context of affirmative action

Indian society suffers from substantial inequalities in education, employment, and income based on caste and ethnicity. Compensatory or positive discrimination policies reserve 15% of the seats in institutions of higher education and state and central government jobs for people of the lowest caste, the Scheduled Caste; 7.5% of the seats are reserved for the Scheduled Tribe. These programs have been strengthened by improved enforcement and increased funding in the 1990s. This positive discrimination has also generated popular backlash and on-the-ground sabotage of the programs. This paper examines the changes in educational attainment between various social groups for a period of nearly 20 years to see whether educational inequalities have declined over time. We use data from a large national sample survey of over 100,000 households for each of the four survey years--1983, 1987-1988, 1993-1994, and 1999-2000--and focus on the educational attainment of children and young adults aged 6-29. Our results show a declining gap between dalits, adivasis, and others in the odds of completing primary school. Such improvement is not seen for Muslims, a minority group that does not benefit from affirmative action. We find little improvement in inequality at the college level. Further, we do not find evidence that upper-income groups, the so-called creamy layer of dalits and adivasis, disproportionately benefit from the affirmative action programs at the expense of their lower-income counterparts.     

ON THE OPTIMAL ASYMPTOTIC TESTS FOR THE EFFECTS OF CLOUD SEEDING ON RAINFALL (1) THE CASE OF FIXED EFFECTS

In this paper we consider a sequence of experimental units {u_n} which are t o be treated according to some random scheme. A general randomized design is suggested for the purpose. Asymptotic tests, optimal in some sense, are derived for testing the absence of the effects of the treatment. These tests are applicable in various situations, for example, when the treatment effects are additive or when they are multiplicative. Based on the asymptotic power of the tests obtained, optimality of various designs is discussed. The randomized designs discussed here have a wide range of applicability, e.g. in weather modification experiments and bio-assay.     

Large sample estimation and prediction for explosive growth curve models

Asymptotic distributions of maximum likelihood estimators for the parameters in explosive growth curve models are derived. Limit distributions of prediction errors when the parameters are estimated are also obtained. The growth curve models are viewed as multivariate time-series models, and the usual time-series methods are used for prediction. Estimation constrained by a hypothesis of homogeneity of growth rates is also considered.     

To adjust or not to adjust for baseline when analyzing repeated binary responses? The case of complete data when treatment comparison at study end is of interest

The benefits of adjusting for baseline covariates are not as straightforward with repeated binary responses as with continuous response variables. Therefore, in this study, we compared different methods for analyzing repeated binary data through simulations when the outcome at the study endpoint is of interest. Methods compared included chi‐square, Fisher's exact test, covariate adjusted/unadjusted logistic regression (Adj.logit/Unadj.logit), covariate adjusted/unadjusted generalized estimating equations (Adj.GEE/Unadj.GEE), covariate adjusted/unadjusted generalized linear mixed model (Adj.GLMM/Unadj.GLMM). All these methods preserved the type I error close to the nominal level. Covariate adjusted methods improved power compared with the unadjusted methods because of the increased treatment effect estimates, especially when the correlation between the baseline and outcome was strong, even though there was an apparent increase in standard errors. Results of the Chi‐squared test were identical to those for the unadjusted logistic regression. Fisher's exact test was the most conservative test regarding the type I error rate and also with the lowest power. Without missing data, there was no gain in using a repeated measures approach over a simple logistic regression at the final time point. Analysis of results from five phase III diabetes trials of the same compound was consistent with the simulation findings. Therefore, covariate adjusted analysis is recommended for repeated binary data when the study endpoint is of interest. Copyright © 2015 John Wiley & Sons, Ltd.     

A note on the strategic aspects of the transfer paradox

It is well known that an agent can be hurt by accepting a gift, the donor of which is made better off. Why then does the recipient accept this welfare reducing gift? This paper examines the strategic aspects of the paradox. It shows that if the recipient refuses the gift, it would suffer an even greater loss of welfare since there is a mutually advantageous reallocation between the donor and a third agent. It is shown that the recipient does have a viable alternative strategy: it could destroy some of its endowment, raising its welfare level and reducing that of the potential donor.     

Analysis of Revenue Maximization Under Two Movie‐Screening Policies

A few weeks before the start of a major season, movie distributors arrange a private screening of the movies to be released during that season for exhibitors and, subsequently, solicit bids for these movies (from exhibitors). Since the number of such solicitations far exceeds the number of movies that can be feasibly screened at a multiplex (i.e., a theater with multiple screens), the problem of interest for an exhibitor is that of choosing a subset of movies for which to submit bids to the distributors. We consider the problem of the selection and screening of movies for a multiplex to maximize the exhibitor's cumulative revenue over a fixed planning horizon. The release times of the movies that can potentially be selected during the planning horizon are known a priori. If selected for screening, a movie must be scheduled through its obligatory period, after which its run may or may not be extended. The problem involves two primary decisions: (i) the selection of a subset of movies for screening from those that can potentially be screened during the planning horizon and (ii) the determination of the duration of screening for the selected movies. We investigate two basic and popular screening policies: preempt‐resume and non‐preempt. In the preempt‐resume policy, the screening of a movie can be preempted and resumed in its post‐obligatory period. In the non‐preempt policy, a movie is screened continuously from its release time until the time it is permanently withdrawn from the multiplex. We show that optimizing under the preempt‐resume policy is strongly NP‐hard while the problem under the non‐preempt policy is polynomially solvable. We develop efficient algorithms for the problem under both screening policies and show that the revenue obtained from the preempt‐resume policy can be significantly higher as compared with that from the non‐preempt policy. Our work provides managers of multiplexes with valuable insights into the selection and screening of movies and offers an easy‐to‐use computational tool to compare the revenues obtainable from adopting these popular policies.     

An improved graphical procedure for multivariate-quality control

In an earlier article (Kulkarni and Paranjape 1984) we proposed a procedure based on Andrews' function plot technique for the quality control of multivariate process. It was shown that this procedure may lead to an erroneous conclusions regarding the status of the process. This article presents an improved method which avoids the above drawback. A heuristic justification is provided to show that the new method is free from the error. Simulation studies are carried out to support the claim. An example is included to illustrate the use of the new technique.