Testing for positive association in contingency tables with fixed margins

An exact conditional approach is developed to test for certain forms of positive association between two ordinal variables (e.g. positive quadrant dependence, total positivity of order 2). The approach is based on the use of a test statistic measuring the goodness-of-(t of the model formulated according to the type of positive association of interest. The nuisance parameters, corresponding to the marginal distributions of the two variables, are eliminated by conditioning the inference on the observed margins. This, in turn, allows to remove the uncertainty on the conclusion of the test, which typically arises in the unconditional context where the null distribution of the test statistic depends on such parameters. Since the multivariate generalized hypergeometric distribution, which results from conditioning, is normally intractable, Markov chain Monte Carlo methods are used to obtain maximum likelihood estimates of the parameters of the constrained model. The Pearson\u2019s chi-squared statistics is used as a test statistic; a p-value forthis statistic is computed through simulation, when the data are sparse, or exploiting the asymptotic theory based on the chi-bar squared distribution. The extension of the present approach to deal with bivariate contingency tables, strati(ed according to one or more explanatory discrete variables, is also outlined. Finally, three applications based on real data are presented

Essays on the economics of child labour and child education

This thesis focuses on the economics of child labour and child education within developing and developed countries. The first part of the thesis examines child labour and child education in developing countries. It investigates the motivations of parents to send their children to work and analyses the so-called commitment problem of child labour in a dynamic, overlapping generations game theoretical model. As a novelty, this model relaxes the requirement of an observable history of play and models the decision problem as an overlapping generations cyclic game. We show that first-best contracts may me implemented, implying optimal child education and low child labour, if a bequest sanction can be imposed by grandparents. We also discuss the special role that grandparents have within this model. The second part of the thesis analyses the economics of child education within a developed country context: the transmission of education across generations and the impact of a schooling reform on educational choice and later outcomes. In a first chapter of this second part, we examine specifically the influence of grandparents, as postulated by the model in part one, on the education of grandchildren. A unique dataset on three generations, the National Child Development Survey of the UK, is used. As a special feature, we apply recent econometric techniques to deal with censoring in a semi-parametric setting. The results indicate that it is not education but rather unobservable factors on the parent and grandparent level that affect the educational choice of grandchildren. These unobservable factors may be interpreted as innate ability or parenting skills. In a second chapter within this part, a schooling reform, the introduction of comprehensive schools in the UK and its impact on educational and labour market outcomes is evaluated. We find, using data from the National Child Development Survey and applying a new, quasi-differenced matching estimator, that bias corrected estimates of the reform suggest no effect on the means, but a sizeable effect on the variance of outcomes. We interpret this finding as indicative of a higher risk inherent to the selective education system. In summary the thesis sheds some new light on the economics of education and child labour, both in a theoretical and an empirical context, and provides a valuable reference and starting point for future research in this area