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The concept of poverty has evolved over time and has now become a generalized notion covering material well-being, social well-being, physical well-being, security, freedom of action and lack of political power. Each dimension is generally not captured adequately by a single indicator and hence the number of variables measuring the level of development tends to proliferate. The first part of the thesis examines whether some subset of these factors are driving all others using conventional linear data reduction techniques and also using methods borrowed from the study of ~actals which capture some of the non-Iinearities in the relationships. The focus in the rest of the thesis moves to the particular relationship between health and income. While the traditional view was that economic growth improved health, recent research argues for the reverse direction of causation. In agreement with other literature, income is found to be a unit root process using a panel dataset. However, this thesis is unique as far as the author is aware in testing for unit roots in life expectancy and finding non-stationarity. This result was found to be robust to null hypotheses of stationarity or non-stationarity. Another significant contribution to the literature is that cointegration is found between health and income using the panel test given by Kao {1999}. The long-run relationship between the variables was then estimated using panel dynamic OLS which adjusts for possible endogeneity and serial correlation. The existence of cointegration implies causation and the direction of causality was explored in the final section. Life expectancy was found to be responding endogenously to changes in income while evidence of the reverse direction of causation was more ambiguous.

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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 isestimated using a pseudo-panel of cluster centers. Chapters 2 and 3 extend univariate kernel methods to the estimation of time-varyingdistributions and densities subject to moment constraints. Chapter 2 proposes a weighted kernel density estimator for a time-varying probabilitydensity 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 cumulativedistribution 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 uniformweights 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.

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