This thesis addresses welfare measurement issues, with an emphasis on the measurement of happiness and inequality. It contributes to the economic literature in both methodological and empirical terms, with the empirical analysis employing the PACO/CHER, ECHP and GSS datasets. Although human welfare is a multidimensional concept, a classical approach is to simply investigate the distribution of wealth and/or income. Our first chapter analyses income distribution in Poland, using comprehensive data from the year 2000. We use the concept of stochastic dominance to investigate the extent to which the income of certain subgroups (based largely on combinations of gender, education, and region) unambiguously exceeds that of others, and examine and formally assess hypotheses of stochastic dominance using recently developed statistical tests. The results of this approach are contrasted with simple scalar measures of inequality that are conventionally used. We find that males, the higher educated and those living in the urban areas are better off while the regional dominance relationship are difficult to establish. However, to a large extent human welfare draws on subjective feelings of happiness or similar subjective well-being concepts. While self-assessments of well-being can be elicited, the relation of such expressions to the underlying concept is intrinsically problematic. Consequently, in our second and third chapters we present a semiparametric framework that allows for the modeling of latent variables. This item response theory methodology is first applied to assess the differences in \happiness"across selected European states. A more detailed analysis suggests that the genesis of happiness is affected by relative social status; income is more important to high status individuals for example. The third chapter concerns further challenges in happiness measurement in the presence of framing effects and/or differential item functioning (\DIF"). The impact of the ordering of questions on subjective well-being responses is studied under an extended item response theory model incorporating the DIF feature of the survey. Contrary to previous studies, the results indicate that individuals' happiness estimates are largely unbiased when the framing experiment is ignored. The methodology we develop allows for the assessment of framing and DIF effects and permits inter-subject comparison and analysis even when such effects are large.