Inference under Covariate-Adaptive Randomization with Multiple Treatments

This paper studies inference in randomized controlled trials with covariate-adaptive randomization when there are multiple treatments. More specifically, we study inference about the average effect of one or more treatments relative to other treatments or a control. As in Bugni et al. (2018), covariate-adaptive randomization refers to randomization schemes that first stratify according to baseline covariates and then assign treatment status so as to achieve balance within each stratum. In contrast to Bugni et al. (2018), we not only allow for multiple treatments, but further allow for the proportion of units being assigned to each of the treatments to vary across strata. We first study the properties of estimators derived from a fully saturated linear regression, i.e., a linear regression of the outcome on all interactions between indicators for each of the treatments and indicators for each of the strata. We show that tests based on these estimators using the usual heteroskedasticity-consistent estimator of the asymptotic variance are invalid; on the other hand, tests based on these estimators and suitable estimators of the asymptotic variance that we provide are exact. For the special case in which the target proportion of units being assigned to each of the treatments does not vary across strata, we additionally consider tests based on estimators derived from a linear regression with strata fixed effects, i.e., a linear regression of the outcome on indicators for each of the treatments and indicators for each of the strata. We show that tests based on these estimators using the usual heteroskedasticity-consistent estimator of the asymptotic variance are conservative, but tests based on these estimators and suitable estimators of the asymptotic variance that we provide are exact. A simulation study illustrates the practical relevance of our theoretical results.Comment: 33 pages, 8 table

Prevalence and correlates of self-rated hunger in class seven and eight students in Kenya

No Abstrac

Electrochemistry of Dihalogenated Nicotonic Acids in Aqueous and Aprotic Media

The electrochemical reduction of several 2,5- and 5,6- dihalonicotinic acids have been studied in dimethyl sulfoxide as well as in aqueous buffers of different pH. The polarographic half-wave potentials for the reduction of these compounds in both media are reported here. The compounds appear to reduce at the carboxyl group. The presence of halogen atoms on the pyridine ring facilitates reduction

Market opportunities for African agriculture: A General Equilibrium examination of demand-side constraints on agricultural growth in East and Southern Africa

"This report focuses on demand-side constraints on agricultural growth and their implications for three broad alternative agricultural development strategies: promoting traditional exports, developing nontraditional exports, and increasing food staple growth. We address three major questions. First, how constraining will demand be for future agricultural growth in East and Southern Africa and, in particular, is there sufficient demand to permit agriculture to grow at a rate that can significantly reduce poverty and hunger? Second, if technological change and increase in supply are achieved, which agricultural subsectors offer the greatest potential and can become the most powerful vehicles for raising real incomes and increasing food consumption? Finally, what are the implications of reductions in marketing costs and growth linkages with nonagricultural sectors for achieving increased market demand for agricultural products? The report applies a general equilibrium framework for the analysis, focusing on seven East and Southern African countries—Madagascar, Malawi, Mozambique, Tanzania, Uganda, Zambia, and Zimbabwe—and finds that an export-led agricultural growth strategy is unlikely to generate substantial overall income growth in these countries." from Authors' SummaryAgricultural growth, exports, Poverty reduction, General equilibrium model, food consumption, Markets, income growth,