This thesis is comprised of three chapters which focus on inequality, and more closely, on the trends in inequality over time. Firstly, the second chapter addresses the issue of non-random selection into employment in the intergenerational mobility literature, by applying bounds to the distribution of wages conditional on parent income. We use the labour market attachment of the mother as a novel instrumental variable to tighten the bounds to the distribution of earnings. We find that there are substantial differences between parent income groups and changes over time by son's and daughter's. We find college to be important for all groups, but particularly for daughters. In addition, there is evidence of converging wages between sons and da...