Dropout in secondary education: an application of a multilevel discrete-time hazard model accounting for school changes

For several decades, researchers have focused on dropout in search for an explanation and prevention of this phenomenon. However, past research is characterized by methodological shortcomings. Most of this research was conducted without considering the hierarchical structure of educational data and ignored the longitudinal path towards dropout. Moreover, research that did take into account these shortcomings, did not correct for student mobility between schools, despite the strong correlation with dropout (South et al. 2007). In this study, we attempt to address these shortcoming by implementing a multilevel discrete-time hazard model and exploring the effect of different school classifications on the school effects. Partially analogous to Grady and Beretvas (2010) we compare models with estimated school effects based on the first and on the last school attended and compare these models with multiple membership models and cross-classified models. The results of this comparison indicate that ignoring student mobility can have strong implications on the predictors of dropout. Not only do models which take into account this mobility yield better model fits, models ignoring this mobility tend to miss the effect of school level variables. With respect to the conclusions on dropout research, our models provide evidence for the often cited student characteristics predicting dropout and indicate stronger school effects than generally assumed.     

Optimal insurance under maxmin expected utility

We examine a problem of demand for insurance indemnification, when the insured is sensitive to ambiguity and behaves according to the maxmin expected utility model of Gilboa and Schmeidler (J. Math. Econ. 18:141–153, 1989), whereas the insurer is a (risk-averse or risk-neutral) expected-utility maximiser. We characterise optimal indemnity functions both with and without the customary ex ante no-sabotage requirement on feasible indemnities, and for both concave and linear utility functions for the two agents. This allows us to provide a unifying framework in which we examine the effects of the no-sabotage condition, of marginal utility of wealth, of belief heterogeneity, as well as of ambiguity (multiplicity of priors) on the structure of optimal indemnity functions. In particular, we show how a singularity in beliefs leads to an optimal indemnity function that involves full insurance on an event to which the insurer assigns zero probability, while the decision maker assigns a positive probability. We examine several illustrative examples, and we provide numerical studies for the case of a Wasserstein and a Rényi ambiguity set.