Essays in econometrics
This dissertation contributes to the theoretical understanding and practical application of non- and semi-parametric methods in econometrics. It consists of three chapters. The first chapter advocates the use of unsupervised statistical learning (clustering) techniques to group observations from a series of repeated cross-sections to create a pseudo-panel of group averages. This clustering method is based on features of the data space and does not require external grouping variables unlike many other methods. Using a model of enterprise training as an example, fixed eff ects panel data model is estimated using a pseudo-panel of cluster centers. Chapters 2 and 3 extend univariate kernel methods to the estimation of time-varying distributions and densities subject to moment constraints. Chapter 2 proposes a weighted kernel density estimator for a time-varying probability density function and the corresponding cumulative distribution function. Time-varying quantiles are estimated by inverting an estimate of the cumulative distribution function. Weighting schemes are derived from those used in time series modelling. Parameters, including the bandwidth, may be estimated by maximum likelihood or cross-validation. Diagnostic checks are constructed based on residuals given by the predictive cumulative distribution function. Chapter 3 considers a set-up where additional information concerning the distribution of random variables is available in the form of moment conditions. A weighted kernel density estimate reflecting the extra information is constructed by replacing the uniform weights associated with standard kernel density estimator by generalised empirical likelihood implied probabilities. This chapter shows that the resulting density estimator provides an improved approximation to the moment conditions. Moreover, a reduction in variance is achieved due to the systematic use of the extra moment information.