Methods for High-Dimensional Data in Econometrics

In the past decades, there has been an increasing demand for methodology that is suitable for data with a large number of parameters compared to the number of observations. In this thesis, methodology is proposed for three situations where such data is encountered.
First, this thesis discusses new methodology for a setting in which data comes from a linear model with parameters that add to one and are sparse in some sense. This has a variety of applications in Economics. In particular, an algorithm is proposed to fit such a model to data. Second, the thesis features a novel test for testing moment inequalities. The test is particularly well-suited against alternatives where multiple moment inequalities are violated. As a final part of this thesis, the proposed test for moment inequalities is generalized to testing against cones. This test is then contrasted to tests based on a quadratic statistic.