Topics in nonparametric identification and estimation

This dissertation consists of three chapters in which nonparametric methods are developed to estimate econometric models in different contexts. Chapter one and two focus on the collective household consumption model, whereas Chapter three considers the estimation of a smooth transition conditional quantile model in a financial time series context. They all have in common that the distribution of the model's unobserved components as well as some or all of the model's primitives are identified nonparametrically.

Chapter one establishes conditions for nonparametric identification of structural components of the collective household model, as for example the conditional sharing rule. In particular it deals with the nonseparable nature of observed demands with respect to unobserved heterogeneity, which arises as a consequence of the bargaining structure of the model. As a result, this allows researches to answer welfare-related questions on an individual level for a heterogeneous population.

Chapter two deals with the Collective Axiom of Revealed Preference also in the context of unobserved heterogeneity and shows how one can exploit data from single households in a nonparametric setting to study the empirical validity of the collective axiom. This approach makes use of a finite-dimensional characterization of demands and shows how one can test the collective model or the assumption of preference stability with respect to household composition using a partial-identification approach.

Chapter three treats the estimation of Value at Risk in the context of financial time series. To be more precise, it is shown how one can directly estimate a smooth transition generalized conditional quantile model which allows for asymmetric responses to past innovations such as different dynamic behaviour succeeding negative and positive news. The model is generalized in a sense that it may depend on past conditional volatilities for which an auxiliary estimator is developed based on composite quantile regression.